Properties

Label 349.2.e.a.123.15
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.15
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.15

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0377450 + 0.0217921i) q^{2} +(1.71622 - 2.97259i) q^{3} +(-0.999050 + 1.73041i) q^{4} +(1.73771 - 3.00980i) q^{5} +0.149601i q^{6} +(-2.79927 + 1.61616i) q^{7} -0.174254i q^{8} +(-4.39085 - 7.60517i) q^{9} +O(q^{10})\) \(q+(-0.0377450 + 0.0217921i) q^{2} +(1.71622 - 2.97259i) q^{3} +(-0.999050 + 1.73041i) q^{4} +(1.73771 - 3.00980i) q^{5} +0.149601i q^{6} +(-2.79927 + 1.61616i) q^{7} -0.174254i q^{8} +(-4.39085 - 7.60517i) q^{9} +0.151473i q^{10} +0.153470i q^{11} +(3.42919 + 5.93953i) q^{12} +(2.06169 - 1.19032i) q^{13} +(0.0704389 - 0.122004i) q^{14} +(-5.96459 - 10.3310i) q^{15} +(-1.99430 - 3.45423i) q^{16} +5.10067 q^{17} +(0.331465 + 0.191372i) q^{18} +(-2.56067 + 4.43522i) q^{19} +(3.47212 + 6.01388i) q^{20} +11.0947i q^{21} +(-0.00334444 - 0.00579273i) q^{22} +(2.19639 + 3.80426i) q^{23} +(-0.517985 - 0.299059i) q^{24} +(-3.53927 - 6.13019i) q^{25} +(-0.0518790 + 0.0898571i) q^{26} -19.8454 q^{27} -6.45849i q^{28} +(2.29456 - 3.97429i) q^{29} +(0.450268 + 0.259962i) q^{30} +5.19023 q^{31} +(0.452367 + 0.261174i) q^{32} +(0.456203 + 0.263389i) q^{33} +(-0.192525 + 0.111154i) q^{34} +11.2336i q^{35} +17.5467 q^{36} -1.35934 q^{37} -0.223210i q^{38} -8.17140i q^{39} +(-0.524470 - 0.302803i) q^{40} +7.68887 q^{41} +(-0.241778 - 0.418772i) q^{42} +(1.29737 + 0.749037i) q^{43} +(-0.265565 - 0.153324i) q^{44} -30.5201 q^{45} +(-0.165806 - 0.0957280i) q^{46} -2.44212i q^{47} -13.6907 q^{48} +(1.72393 - 2.98593i) q^{49} +(0.267179 + 0.154256i) q^{50} +(8.75388 - 15.1622i) q^{51} +4.75675i q^{52} +6.29968i q^{53} +(0.749063 - 0.432472i) q^{54} +(0.461914 + 0.266686i) q^{55} +(0.281622 + 0.487783i) q^{56} +(8.78937 + 15.2236i) q^{57} +0.200013i q^{58} +(-7.84880 - 4.53151i) q^{59} +23.8357 q^{60} +4.70242i q^{61} +(-0.195905 + 0.113106i) q^{62} +(24.5823 + 14.1926i) q^{63} +7.95445 q^{64} -8.27370i q^{65} -0.0229592 q^{66} +5.98833 q^{67} +(-5.09582 + 8.82622i) q^{68} +15.0780 q^{69} +(-0.244805 - 0.424014i) q^{70} +(8.67606 - 5.00912i) q^{71} +(-1.32523 + 0.765123i) q^{72} +(2.31215 - 4.00477i) q^{73} +(0.0513082 - 0.0296228i) q^{74} -24.2967 q^{75} +(-5.11648 - 8.86201i) q^{76} +(-0.248032 - 0.429604i) q^{77} +(0.178072 + 0.308430i) q^{78} +9.12273i q^{79} -13.8621 q^{80} +(-20.8865 + 36.1765i) q^{81} +(-0.290217 + 0.167557i) q^{82} +(2.69012 + 4.65943i) q^{83} +(-19.1984 - 11.0842i) q^{84} +(8.86347 - 15.3520i) q^{85} -0.0652924 q^{86} +(-7.87594 - 13.6415i) q^{87} +0.0267428 q^{88} +(-0.728326 - 0.420499i) q^{89} +(1.15198 - 0.665096i) q^{90} +(-3.84748 + 6.66403i) q^{91} -8.77722 q^{92} +(8.90759 - 15.4284i) q^{93} +(0.0532188 + 0.0921777i) q^{94} +(8.89941 + 15.4142i) q^{95} +(1.55273 - 0.896467i) q^{96} +(-13.5267 + 7.80965i) q^{97} +0.150272i q^{98} +(1.16717 - 0.673863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0377450 + 0.0217921i −0.0266898 + 0.0154093i −0.513286 0.858218i \(-0.671572\pi\)
0.486596 + 0.873627i \(0.338238\pi\)
\(3\) 1.71622 2.97259i 0.990862 1.71622i 0.378622 0.925551i \(-0.376398\pi\)
0.612240 0.790672i \(-0.290269\pi\)
\(4\) −0.999050 + 1.73041i −0.499525 + 0.865203i
\(5\) 1.73771 3.00980i 0.777127 1.34602i −0.156464 0.987684i \(-0.550010\pi\)
0.933591 0.358340i \(-0.116657\pi\)
\(6\) 0.149601i 0.0610741i
\(7\) −2.79927 + 1.61616i −1.05802 + 0.610850i −0.924885 0.380248i \(-0.875839\pi\)
−0.133138 + 0.991097i \(0.542505\pi\)
\(8\) 0.174254i 0.0616081i
\(9\) −4.39085 7.60517i −1.46362 2.53506i
\(10\) 0.151473i 0.0479001i
\(11\) 0.153470i 0.0462730i 0.999732 + 0.0231365i \(0.00736523\pi\)
−0.999732 + 0.0231365i \(0.992635\pi\)
\(12\) 3.42919 + 5.93953i 0.989921 + 1.71459i
\(13\) 2.06169 1.19032i 0.571810 0.330135i −0.186062 0.982538i \(-0.559573\pi\)
0.757872 + 0.652403i \(0.226239\pi\)
\(14\) 0.0704389 0.122004i 0.0188256 0.0326069i
\(15\) −5.96459 10.3310i −1.54005 2.66745i
\(16\) −1.99430 3.45423i −0.498576 0.863559i
\(17\) 5.10067 1.23709 0.618547 0.785748i \(-0.287722\pi\)
0.618547 + 0.785748i \(0.287722\pi\)
\(18\) 0.331465 + 0.191372i 0.0781271 + 0.0451067i
\(19\) −2.56067 + 4.43522i −0.587459 + 1.01751i 0.407105 + 0.913381i \(0.366538\pi\)
−0.994564 + 0.104127i \(0.966795\pi\)
\(20\) 3.47212 + 6.01388i 0.776389 + 1.34475i
\(21\) 11.0947i 2.42107i
\(22\) −0.00334444 0.00579273i −0.000713036 0.00123501i
\(23\) 2.19639 + 3.80426i 0.457979 + 0.793244i 0.998854 0.0478596i \(-0.0152400\pi\)
−0.540875 + 0.841103i \(0.681907\pi\)
\(24\) −0.517985 0.299059i −0.105733 0.0610451i
\(25\) −3.53927 6.13019i −0.707853 1.22604i
\(26\) −0.0518790 + 0.0898571i −0.0101743 + 0.0176224i
\(27\) −19.8454 −3.81924
\(28\) 6.45849i 1.22054i
\(29\) 2.29456 3.97429i 0.426089 0.738007i −0.570433 0.821344i \(-0.693225\pi\)
0.996521 + 0.0833373i \(0.0265579\pi\)
\(30\) 0.450268 + 0.259962i 0.0822073 + 0.0474624i
\(31\) 5.19023 0.932193 0.466096 0.884734i \(-0.345660\pi\)
0.466096 + 0.884734i \(0.345660\pi\)
\(32\) 0.452367 + 0.261174i 0.0799679 + 0.0461695i
\(33\) 0.456203 + 0.263389i 0.0794147 + 0.0458501i
\(34\) −0.192525 + 0.111154i −0.0330177 + 0.0190628i
\(35\) 11.2336i 1.89883i
\(36\) 17.5467 2.92445
\(37\) −1.35934 −0.223474 −0.111737 0.993738i \(-0.535641\pi\)
−0.111737 + 0.993738i \(0.535641\pi\)
\(38\) 0.223210i 0.0362094i
\(39\) 8.17140i 1.30847i
\(40\) −0.524470 0.302803i −0.0829260 0.0478773i
\(41\) 7.68887 1.20080 0.600400 0.799700i \(-0.295008\pi\)
0.600400 + 0.799700i \(0.295008\pi\)
\(42\) −0.241778 0.418772i −0.0373071 0.0646179i
\(43\) 1.29737 + 0.749037i 0.197847 + 0.114227i 0.595651 0.803243i \(-0.296894\pi\)
−0.397804 + 0.917471i \(0.630228\pi\)
\(44\) −0.265565 0.153324i −0.0400355 0.0231145i
\(45\) −30.5201 −4.54966
\(46\) −0.165806 0.0957280i −0.0244467 0.0141143i
\(47\) 2.44212i 0.356219i −0.984011 0.178110i \(-0.943002\pi\)
0.984011 0.178110i \(-0.0569982\pi\)
\(48\) −13.6907 −1.97608
\(49\) 1.72393 2.98593i 0.246275 0.426561i
\(50\) 0.267179 + 0.154256i 0.0377849 + 0.0218151i
\(51\) 8.75388 15.1622i 1.22579 2.12313i
\(52\) 4.75675i 0.659642i
\(53\) 6.29968i 0.865328i 0.901555 + 0.432664i \(0.142426\pi\)
−0.901555 + 0.432664i \(0.857574\pi\)
\(54\) 0.749063 0.432472i 0.101935 0.0588520i
\(55\) 0.461914 + 0.266686i 0.0622845 + 0.0359600i
\(56\) 0.281622 + 0.487783i 0.0376333 + 0.0651828i
\(57\) 8.78937 + 15.2236i 1.16418 + 2.01642i
\(58\) 0.200013i 0.0262630i
\(59\) −7.84880 4.53151i −1.02183 0.589952i −0.107195 0.994238i \(-0.534187\pi\)
−0.914633 + 0.404286i \(0.867520\pi\)
\(60\) 23.8357 3.07718
\(61\) 4.70242i 0.602083i 0.953611 + 0.301041i \(0.0973342\pi\)
−0.953611 + 0.301041i \(0.902666\pi\)
\(62\) −0.195905 + 0.113106i −0.0248800 + 0.0143645i
\(63\) 24.5823 + 14.1926i 3.09708 + 1.78810i
\(64\) 7.95445 0.994306
\(65\) 8.27370i 1.02623i
\(66\) −0.0229592 −0.00282608
\(67\) 5.98833 0.731590 0.365795 0.930695i \(-0.380797\pi\)
0.365795 + 0.930695i \(0.380797\pi\)
\(68\) −5.09582 + 8.82622i −0.617959 + 1.07034i
\(69\) 15.0780 1.81518
\(70\) −0.244805 0.424014i −0.0292598 0.0506794i
\(71\) 8.67606 5.00912i 1.02966 0.594474i 0.112772 0.993621i \(-0.464027\pi\)
0.916887 + 0.399147i \(0.130694\pi\)
\(72\) −1.32523 + 0.765123i −0.156180 + 0.0901706i
\(73\) 2.31215 4.00477i 0.270617 0.468723i −0.698403 0.715705i \(-0.746106\pi\)
0.969020 + 0.246982i \(0.0794389\pi\)
\(74\) 0.0513082 0.0296228i 0.00596446 0.00344358i
\(75\) −24.2967 −2.80554
\(76\) −5.11648 8.86201i −0.586901 1.01654i
\(77\) −0.248032 0.429604i −0.0282658 0.0489579i
\(78\) 0.178072 + 0.308430i 0.0201627 + 0.0349228i
\(79\) 9.12273i 1.02639i 0.858273 + 0.513194i \(0.171538\pi\)
−0.858273 + 0.513194i \(0.828462\pi\)
\(80\) −13.8621 −1.54983
\(81\) −20.8865 + 36.1765i −2.32072 + 4.01961i
\(82\) −0.290217 + 0.167557i −0.0320491 + 0.0185035i
\(83\) 2.69012 + 4.65943i 0.295279 + 0.511439i 0.975050 0.221986i \(-0.0712540\pi\)
−0.679770 + 0.733425i \(0.737921\pi\)
\(84\) −19.1984 11.0842i −2.09472 1.20939i
\(85\) 8.86347 15.3520i 0.961379 1.66516i
\(86\) −0.0652924 −0.00704066
\(87\) −7.87594 13.6415i −0.844390 1.46253i
\(88\) 0.0267428 0.00285079
\(89\) −0.728326 0.420499i −0.0772024 0.0445728i 0.460902 0.887451i \(-0.347526\pi\)
−0.538104 + 0.842878i \(0.680859\pi\)
\(90\) 1.15198 0.665096i 0.121429 0.0701073i
\(91\) −3.84748 + 6.66403i −0.403325 + 0.698580i
\(92\) −8.77722 −0.915089
\(93\) 8.90759 15.4284i 0.923674 1.59985i
\(94\) 0.0532188 + 0.0921777i 0.00548910 + 0.00950741i
\(95\) 8.89941 + 15.4142i 0.913060 + 1.58147i
\(96\) 1.55273 0.896467i 0.158474 0.0914952i
\(97\) −13.5267 + 7.80965i −1.37343 + 0.792950i −0.991358 0.131183i \(-0.958122\pi\)
−0.382071 + 0.924133i \(0.624789\pi\)
\(98\) 0.150272i 0.0151798i
\(99\) 1.16717 0.673863i 0.117305 0.0677258i
\(100\) 14.1436 1.41436
\(101\) 8.83219i 0.878836i −0.898283 0.439418i \(-0.855185\pi\)
0.898283 0.439418i \(-0.144815\pi\)
\(102\) 0.763062i 0.0755544i
\(103\) 13.9242i 1.37199i 0.727607 + 0.685994i \(0.240633\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(104\) −0.207418 0.359258i −0.0203390 0.0352281i
\(105\) 33.3930 + 19.2794i 3.25882 + 1.88148i
\(106\) −0.137283 0.237782i −0.0133341 0.0230954i
\(107\) −7.56872 + 4.36980i −0.731696 + 0.422445i −0.819042 0.573733i \(-0.805495\pi\)
0.0873463 + 0.996178i \(0.472161\pi\)
\(108\) 19.8265 34.3405i 1.90781 3.30442i
\(109\) −2.56617 + 4.44473i −0.245794 + 0.425728i −0.962355 0.271797i \(-0.912382\pi\)
0.716560 + 0.697525i \(0.245715\pi\)
\(110\) −0.0232466 −0.00221648
\(111\) −2.33293 + 4.04075i −0.221431 + 0.383531i
\(112\) 11.1652 + 6.44621i 1.05501 + 0.609110i
\(113\) −6.95228 + 4.01390i −0.654015 + 0.377596i −0.789993 0.613116i \(-0.789916\pi\)
0.135978 + 0.990712i \(0.456583\pi\)
\(114\) −0.663511 0.383078i −0.0621435 0.0358785i
\(115\) 15.2668 1.42363
\(116\) 4.58476 + 7.94103i 0.425684 + 0.737306i
\(117\) −18.1051 10.4530i −1.67382 0.966380i
\(118\) 0.395005 0.0363631
\(119\) −14.2781 + 8.24348i −1.30887 + 0.755678i
\(120\) −1.80022 + 1.03935i −0.164336 + 0.0948797i
\(121\) 10.9764 0.997859
\(122\) −0.102476 0.177493i −0.00927770 0.0160694i
\(123\) 13.1958 22.8558i 1.18983 2.06084i
\(124\) −5.18530 + 8.98120i −0.465654 + 0.806536i
\(125\) −7.22377 −0.646114
\(126\) −1.23715 −0.110214
\(127\) 7.06750i 0.627139i −0.949565 0.313569i \(-0.898475\pi\)
0.949565 0.313569i \(-0.101525\pi\)
\(128\) −1.20497 + 0.695693i −0.106506 + 0.0614911i
\(129\) 4.45316 2.57103i 0.392079 0.226367i
\(130\) 0.180301 + 0.312291i 0.0158135 + 0.0273897i
\(131\) 21.5664i 1.88427i 0.335234 + 0.942135i \(0.391184\pi\)
−0.335234 + 0.942135i \(0.608816\pi\)
\(132\) −0.911539 + 0.526278i −0.0793393 + 0.0458066i
\(133\) 16.5538i 1.43540i
\(134\) −0.226030 + 0.130498i −0.0195260 + 0.0112733i
\(135\) −34.4854 + 59.7305i −2.96803 + 5.14079i
\(136\) 0.888812i 0.0762150i
\(137\) −13.4902 7.78856i −1.15254 0.665422i −0.203039 0.979171i \(-0.565082\pi\)
−0.949506 + 0.313749i \(0.898415\pi\)
\(138\) −0.569120 + 0.328581i −0.0484467 + 0.0279707i
\(139\) 3.54489 0.300674 0.150337 0.988635i \(-0.451964\pi\)
0.150337 + 0.988635i \(0.451964\pi\)
\(140\) −19.4388 11.2230i −1.64288 0.948514i
\(141\) −7.25940 4.19122i −0.611352 0.352964i
\(142\) −0.218319 + 0.378139i −0.0183209 + 0.0317327i
\(143\) 0.182678 + 0.316408i 0.0152763 + 0.0264593i
\(144\) −17.5134 + 30.3340i −1.45945 + 2.52784i
\(145\) −7.97454 13.8123i −0.662250 1.14705i
\(146\) 0.201547i 0.0166801i
\(147\) −5.91729 10.2490i −0.488050 0.845327i
\(148\) 1.35805 2.35220i 0.111631 0.193350i
\(149\) −3.56236 + 2.05673i −0.291840 + 0.168494i −0.638771 0.769397i \(-0.720557\pi\)
0.346932 + 0.937890i \(0.387224\pi\)
\(150\) 0.917079 0.529476i 0.0748792 0.0432315i
\(151\) 10.3680 17.9579i 0.843737 1.46140i −0.0429765 0.999076i \(-0.513684\pi\)
0.886714 0.462319i \(-0.152983\pi\)
\(152\) 0.772854 + 0.446208i 0.0626868 + 0.0361922i
\(153\) −22.3962 38.7914i −1.81063 3.13610i
\(154\) 0.0187239 + 0.0108103i 0.00150882 + 0.000871116i
\(155\) 9.01911 15.6216i 0.724432 1.25475i
\(156\) 14.1398 + 8.16364i 1.13209 + 0.653614i
\(157\) 9.75898 16.9031i 0.778852 1.34901i −0.153753 0.988109i \(-0.549136\pi\)
0.932604 0.360901i \(-0.117531\pi\)
\(158\) −0.198804 0.344338i −0.0158160 0.0273941i
\(159\) 18.7264 + 10.8117i 1.48510 + 0.857421i
\(160\) 1.57216 0.907690i 0.124291 0.0717592i
\(161\) −12.2966 7.09943i −0.969106 0.559513i
\(162\) 1.82064i 0.143043i
\(163\) 8.83252i 0.691817i −0.938268 0.345908i \(-0.887571\pi\)
0.938268 0.345908i \(-0.112429\pi\)
\(164\) −7.68157 + 13.3049i −0.599830 + 1.03894i
\(165\) 1.58550 0.915387i 0.123431 0.0712628i
\(166\) −0.203078 0.117247i −0.0157619 0.00910012i
\(167\) 3.25894i 0.252184i −0.992019 0.126092i \(-0.959757\pi\)
0.992019 0.126092i \(-0.0402435\pi\)
\(168\) 1.93330 0.149158
\(169\) −3.66629 + 6.35020i −0.282022 + 0.488477i
\(170\) 0.772615i 0.0592569i
\(171\) 44.9741 3.43925
\(172\) −2.59228 + 1.49665i −0.197659 + 0.114119i
\(173\) −5.29351 + 3.05621i −0.402458 + 0.232359i −0.687544 0.726143i \(-0.741311\pi\)
0.285086 + 0.958502i \(0.407978\pi\)
\(174\) 0.594556 + 0.343267i 0.0450731 + 0.0260230i
\(175\) 19.8147 + 11.4400i 1.49785 + 0.864784i
\(176\) 0.530122 0.306066i 0.0399594 0.0230706i
\(177\) −26.9406 + 15.5542i −2.02498 + 1.16912i
\(178\) 0.0366542 0.00274735
\(179\) 1.55969i 0.116576i 0.998300 + 0.0582882i \(0.0185642\pi\)
−0.998300 + 0.0582882i \(0.981436\pi\)
\(180\) 30.4911 52.8121i 2.27267 3.93638i
\(181\) −4.33550 −0.322255 −0.161127 0.986934i \(-0.551513\pi\)
−0.161127 + 0.986934i \(0.551513\pi\)
\(182\) 0.335379i 0.0248599i
\(183\) 13.9783 + 8.07040i 1.03331 + 0.596581i
\(184\) 0.662908 0.382730i 0.0488702 0.0282152i
\(185\) −2.36213 + 4.09133i −0.173667 + 0.300801i
\(186\) 0.776461i 0.0569329i
\(187\) 0.782800i 0.0572440i
\(188\) 4.22585 + 2.43980i 0.308202 + 0.177940i
\(189\) 55.5524 32.0732i 4.04084 2.33298i
\(190\) −0.671817 0.387874i −0.0487387 0.0281393i
\(191\) −7.30153 12.6466i −0.528320 0.915078i −0.999455 0.0330162i \(-0.989489\pi\)
0.471135 0.882061i \(-0.343845\pi\)
\(192\) 13.6516 23.6453i 0.985220 1.70645i
\(193\) −1.45959 0.842697i −0.105064 0.0606587i 0.446547 0.894760i \(-0.352653\pi\)
−0.551611 + 0.834101i \(0.685987\pi\)
\(194\) 0.340377 0.589551i 0.0244377 0.0423273i
\(195\) −24.5943 14.1995i −1.76123 1.01685i
\(196\) 3.44458 + 5.96619i 0.246041 + 0.426156i
\(197\) −19.5668 11.2969i −1.39407 0.804869i −0.400310 0.916380i \(-0.631098\pi\)
−0.993763 + 0.111511i \(0.964431\pi\)
\(198\) −0.0293698 + 0.0508700i −0.00208722 + 0.00361517i
\(199\) −14.4447 + 8.33963i −1.02395 + 0.591181i −0.915247 0.402893i \(-0.868005\pi\)
−0.108708 + 0.994074i \(0.534671\pi\)
\(200\) −1.06821 + 0.616732i −0.0755339 + 0.0436095i
\(201\) 10.2773 17.8008i 0.724905 1.25557i
\(202\) 0.192472 + 0.333371i 0.0135423 + 0.0234559i
\(203\) 14.8335i 1.04110i
\(204\) 17.4911 + 30.2955i 1.22462 + 2.12111i
\(205\) 13.3610 23.1420i 0.933174 1.61630i
\(206\) −0.303437 0.525568i −0.0211414 0.0366181i
\(207\) 19.2880 33.4079i 1.34061 2.32201i
\(208\) −8.22327 4.74771i −0.570181 0.329194i
\(209\) −0.680673 0.392987i −0.0470831 0.0271835i
\(210\) −1.68056 −0.115970
\(211\) −20.3484 + 11.7481i −1.40084 + 0.808775i −0.994479 0.104938i \(-0.966536\pi\)
−0.406360 + 0.913713i \(0.633202\pi\)
\(212\) −10.9010 6.29370i −0.748684 0.432253i
\(213\) 34.3871i 2.35617i
\(214\) 0.190454 0.329877i 0.0130192 0.0225499i
\(215\) 4.50891 2.60322i 0.307505 0.177538i
\(216\) 3.45813i 0.235296i
\(217\) −14.5288 + 8.38822i −0.986281 + 0.569430i
\(218\) 0.223689i 0.0151501i
\(219\) −7.93634 13.7461i −0.536288 0.928879i
\(220\) −0.922951 + 0.532866i −0.0622254 + 0.0359258i
\(221\) 10.5160 6.07141i 0.707382 0.408407i
\(222\) 0.203357i 0.0136485i
\(223\) −12.2642 −0.821273 −0.410637 0.911799i \(-0.634694\pi\)
−0.410637 + 0.911799i \(0.634694\pi\)
\(224\) −1.68839 −0.112811
\(225\) −31.0807 + 53.8334i −2.07205 + 3.58890i
\(226\) 0.174943 0.303010i 0.0116370 0.0201559i
\(227\) −2.56741 4.44689i −0.170405 0.295150i 0.768156 0.640262i \(-0.221174\pi\)
−0.938562 + 0.345112i \(0.887841\pi\)
\(228\) −35.1241 −2.32615
\(229\) −9.63795 + 5.56447i −0.636894 + 0.367711i −0.783417 0.621496i \(-0.786525\pi\)
0.146523 + 0.989207i \(0.453192\pi\)
\(230\) −0.576245 + 0.332695i −0.0379964 + 0.0219373i
\(231\) −1.70271 −0.112030
\(232\) −0.692536 0.399836i −0.0454672 0.0262505i
\(233\) 8.54545 + 14.8012i 0.559831 + 0.969656i 0.997510 + 0.0705246i \(0.0224673\pi\)
−0.437679 + 0.899131i \(0.644199\pi\)
\(234\) 0.911171 0.0595651
\(235\) −7.35028 4.24369i −0.479479 0.276828i
\(236\) 15.6827 9.05441i 1.02086 0.589392i
\(237\) 27.1181 + 15.6566i 1.76151 + 1.01701i
\(238\) 0.359285 0.622301i 0.0232890 0.0403378i
\(239\) 0.513859 0.0332388 0.0166194 0.999862i \(-0.494710\pi\)
0.0166194 + 0.999862i \(0.494710\pi\)
\(240\) −23.7904 + 41.2062i −1.53566 + 2.65985i
\(241\) 1.70481 2.95282i 0.109817 0.190208i −0.805879 0.592080i \(-0.798307\pi\)
0.915696 + 0.401872i \(0.131640\pi\)
\(242\) −0.414306 + 0.239200i −0.0266326 + 0.0153764i
\(243\) 41.9238 + 72.6142i 2.68942 + 4.65820i
\(244\) −8.13709 4.69795i −0.520924 0.300755i
\(245\) −5.99137 10.3774i −0.382774 0.662985i
\(246\) 1.15026i 0.0733378i
\(247\) 12.1921i 0.775762i
\(248\) 0.904418i 0.0574306i
\(249\) 18.4674 1.17032
\(250\) 0.272661 0.157421i 0.0172446 0.00995619i
\(251\) 14.1782i 0.894919i 0.894304 + 0.447459i \(0.147671\pi\)
−0.894304 + 0.447459i \(0.852329\pi\)
\(252\) −49.1179 + 28.3582i −3.09414 + 1.78640i
\(253\) −0.583840 + 0.337080i −0.0367057 + 0.0211921i
\(254\) 0.154016 + 0.266763i 0.00966380 + 0.0167382i
\(255\) −30.4234 52.6949i −1.90519 3.29988i
\(256\) −7.92412 + 13.7250i −0.495258 + 0.857812i
\(257\) 1.16555 0.0727051 0.0363525 0.999339i \(-0.488426\pi\)
0.0363525 + 0.999339i \(0.488426\pi\)
\(258\) −0.112056 + 0.194087i −0.00697632 + 0.0120833i
\(259\) 3.80514 2.19690i 0.236440 0.136509i
\(260\) 14.3169 + 8.26584i 0.887894 + 0.512626i
\(261\) −40.3002 −2.49452
\(262\) −0.469978 0.814026i −0.0290354 0.0502907i
\(263\) 13.8050 0.851252 0.425626 0.904899i \(-0.360054\pi\)
0.425626 + 0.904899i \(0.360054\pi\)
\(264\) 0.0458966 0.0794952i 0.00282474 0.00489259i
\(265\) 18.9608 + 10.9470i 1.16475 + 0.672470i
\(266\) 0.360742 + 0.624824i 0.0221185 + 0.0383104i
\(267\) −2.49994 + 1.44334i −0.152994 + 0.0883310i
\(268\) −5.98264 + 10.3622i −0.365448 + 0.632974i
\(269\) 16.8251 1.02585 0.512923 0.858434i \(-0.328562\pi\)
0.512923 + 0.858434i \(0.328562\pi\)
\(270\) 3.00604i 0.182942i
\(271\) −7.24870 12.5551i −0.440327 0.762669i 0.557386 0.830253i \(-0.311804\pi\)
−0.997714 + 0.0675842i \(0.978471\pi\)
\(272\) −10.1723 17.6189i −0.616785 1.06830i
\(273\) 13.2063 + 22.8739i 0.799280 + 1.38439i
\(274\) 0.678917 0.0410149
\(275\) 0.940801 0.543171i 0.0567324 0.0327545i
\(276\) −15.0637 + 26.0911i −0.906727 + 1.57050i
\(277\) 16.6258 9.59892i 0.998949 0.576743i 0.0910115 0.995850i \(-0.470990\pi\)
0.907937 + 0.419107i \(0.137657\pi\)
\(278\) −0.133802 + 0.0772507i −0.00802492 + 0.00463319i
\(279\) −22.7895 39.4726i −1.36437 2.36316i
\(280\) 1.95751 0.116983
\(281\) −9.04315 + 15.6632i −0.539469 + 0.934388i 0.459464 + 0.888197i \(0.348042\pi\)
−0.998933 + 0.0461911i \(0.985292\pi\)
\(282\) 0.365342 0.0217558
\(283\) −19.8833 −1.18194 −0.590970 0.806693i \(-0.701255\pi\)
−0.590970 + 0.806693i \(0.701255\pi\)
\(284\) 20.0175i 1.18782i
\(285\) 61.0935 3.61887
\(286\) −0.0137904 0.00796188i −0.000815442 0.000470796i
\(287\) −21.5232 + 12.4264i −1.27047 + 0.733508i
\(288\) 4.58710i 0.270298i
\(289\) 9.01679 0.530399
\(290\) 0.601999 + 0.347564i 0.0353506 + 0.0204097i
\(291\) 53.6124i 3.14281i
\(292\) 4.61991 + 8.00193i 0.270360 + 0.468277i
\(293\) −4.54943 7.87984i −0.265780 0.460345i 0.701987 0.712189i \(-0.252296\pi\)
−0.967768 + 0.251844i \(0.918963\pi\)
\(294\) 0.446697 + 0.257900i 0.0260519 + 0.0150411i
\(295\) −27.2779 + 15.7489i −1.58818 + 0.916936i
\(296\) 0.236870i 0.0137678i
\(297\) 3.04567i 0.176728i
\(298\) 0.0896409 0.155263i 0.00519276 0.00899412i
\(299\) 9.05656 + 5.22881i 0.523754 + 0.302390i
\(300\) 24.2736 42.0431i 1.40144 2.42736i
\(301\) −4.84225 −0.279103
\(302\) 0.903764i 0.0520057i
\(303\) −26.2545 15.1580i −1.50828 0.870805i
\(304\) 20.4270 1.17157
\(305\) 14.1533 + 8.17143i 0.810418 + 0.467895i
\(306\) 1.69069 + 0.976122i 0.0966505 + 0.0558012i
\(307\) −7.56181 13.0974i −0.431575 0.747510i 0.565434 0.824794i \(-0.308709\pi\)
−0.997009 + 0.0772833i \(0.975375\pi\)
\(308\) 0.991185 0.0564780
\(309\) 41.3908 + 23.8970i 2.35464 + 1.35945i
\(310\) 0.786181i 0.0446521i
\(311\) 4.62828i 0.262446i −0.991353 0.131223i \(-0.958110\pi\)
0.991353 0.131223i \(-0.0418903\pi\)
\(312\) −1.42390 −0.0806125
\(313\) −24.2089 −1.36837 −0.684185 0.729309i \(-0.739842\pi\)
−0.684185 + 0.729309i \(0.739842\pi\)
\(314\) 0.850675i 0.0480064i
\(315\) 85.4337 49.3252i 4.81365 2.77916i
\(316\) −15.7860 9.11407i −0.888034 0.512706i
\(317\) 2.51279 + 1.45076i 0.141132 + 0.0814827i 0.568903 0.822404i \(-0.307368\pi\)
−0.427771 + 0.903887i \(0.640701\pi\)
\(318\) −0.942436 −0.0528492
\(319\) 0.609934 + 0.352146i 0.0341498 + 0.0197164i
\(320\) 13.8225 23.9413i 0.772702 1.33836i
\(321\) 29.9982i 1.67434i
\(322\) 0.618846 0.0344869
\(323\) −13.0611 + 22.6226i −0.726741 + 1.25875i
\(324\) −41.7334 72.2843i −2.31852 4.01579i
\(325\) −14.5937 8.42570i −0.809515 0.467374i
\(326\) 0.192479 + 0.333384i 0.0106604 + 0.0184644i
\(327\) 8.80824 + 15.2563i 0.487097 + 0.843676i
\(328\) 1.33982i 0.0739790i
\(329\) 3.94684 + 6.83613i 0.217596 + 0.376888i
\(330\) −0.0398964 + 0.0691026i −0.00219623 + 0.00380397i
\(331\) −7.88875 4.55457i −0.433605 0.250342i 0.267276 0.963620i \(-0.413876\pi\)
−0.700881 + 0.713278i \(0.747210\pi\)
\(332\) −10.7503 −0.589998
\(333\) 5.96864 + 10.3380i 0.327079 + 0.566518i
\(334\) 0.0710191 + 0.123009i 0.00388599 + 0.00673073i
\(335\) 10.4060 18.0237i 0.568539 0.984738i
\(336\) 38.3239 22.1263i 2.09074 1.20709i
\(337\) 6.47887 + 11.2217i 0.352927 + 0.611287i 0.986761 0.162182i \(-0.0518532\pi\)
−0.633834 + 0.773469i \(0.718520\pi\)
\(338\) 0.319585i 0.0173831i
\(339\) 27.5550i 1.49658i
\(340\) 17.7101 + 30.6748i 0.960466 + 1.66358i
\(341\) 0.796545i 0.0431353i
\(342\) −1.69755 + 0.980080i −0.0917929 + 0.0529967i
\(343\) 11.4817i 0.619951i
\(344\) 0.130523 0.226072i 0.00703732 0.0121890i
\(345\) 26.2012 45.3818i 1.41062 2.44327i
\(346\) 0.133203 0.230714i 0.00716101 0.0124032i
\(347\) 31.0899 17.9497i 1.66899 0.963592i 0.700807 0.713351i \(-0.252823\pi\)
0.968183 0.250242i \(-0.0805101\pi\)
\(348\) 31.4739 1.68718
\(349\) 13.4876 + 12.9261i 0.721975 + 0.691919i
\(350\) −0.997209 −0.0533030
\(351\) −40.9150 + 23.6223i −2.18388 + 1.26086i
\(352\) −0.0400824 + 0.0694248i −0.00213640 + 0.00370035i
\(353\) −12.1970 + 21.1259i −0.649183 + 1.12442i 0.334136 + 0.942525i \(0.391556\pi\)
−0.983318 + 0.181893i \(0.941778\pi\)
\(354\) 0.677916 1.17419i 0.0360308 0.0624072i
\(355\) 34.8176i 1.84793i
\(356\) 1.45527 0.840199i 0.0771290 0.0445305i
\(357\) 56.5906i 2.99509i
\(358\) −0.0339889 0.0588704i −0.00179637 0.00311140i
\(359\) 37.6526i 1.98723i 0.112826 + 0.993615i \(0.464010\pi\)
−0.112826 + 0.993615i \(0.535990\pi\)
\(360\) 5.31824i 0.280296i
\(361\) −3.61409 6.25980i −0.190216 0.329463i
\(362\) 0.163644 0.0944796i 0.00860091 0.00496574i
\(363\) 18.8380 32.6284i 0.988740 1.71255i
\(364\) −7.68765 13.3154i −0.402942 0.697917i
\(365\) −8.03570 13.9182i −0.420608 0.728514i
\(366\) −0.703484 −0.0367717
\(367\) 9.90695 + 5.71978i 0.517138 + 0.298570i 0.735763 0.677239i \(-0.236824\pi\)
−0.218625 + 0.975809i \(0.570157\pi\)
\(368\) 8.76054 15.1737i 0.456675 0.790984i
\(369\) −33.7606 58.4751i −1.75751 3.04409i
\(370\) 0.205903i 0.0107044i
\(371\) −10.1813 17.6345i −0.528586 0.915537i
\(372\) 17.7983 + 30.8275i 0.922797 + 1.59833i
\(373\) −1.76180 1.01718i −0.0912227 0.0526675i 0.453695 0.891157i \(-0.350106\pi\)
−0.544917 + 0.838490i \(0.683439\pi\)
\(374\) −0.0170589 0.0295468i −0.000882092 0.00152783i
\(375\) −12.3976 + 21.4733i −0.640210 + 1.10888i
\(376\) −0.425549 −0.0219460
\(377\) 10.9250i 0.562666i
\(378\) −1.39789 + 2.42121i −0.0718995 + 0.124534i
\(379\) −25.8662 14.9338i −1.32866 0.767100i −0.343564 0.939129i \(-0.611634\pi\)
−0.985092 + 0.172029i \(0.944968\pi\)
\(380\) −35.5638 −1.82439
\(381\) −21.0087 12.1294i −1.07631 0.621408i
\(382\) 0.551193 + 0.318231i 0.0282015 + 0.0162821i
\(383\) 1.70520 0.984500i 0.0871319 0.0503056i −0.455801 0.890082i \(-0.650647\pi\)
0.542933 + 0.839776i \(0.317314\pi\)
\(384\) 4.77586i 0.243717i
\(385\) −1.72403 −0.0878646
\(386\) 0.0734566 0.00373884
\(387\) 13.1556i 0.668738i
\(388\) 31.2089i 1.58439i
\(389\) −2.76192 1.59459i −0.140035 0.0808491i 0.428346 0.903615i \(-0.359097\pi\)
−0.568381 + 0.822766i \(0.692430\pi\)
\(390\) 1.23775 0.0626759
\(391\) 11.2031 + 19.4043i 0.566563 + 0.981316i
\(392\) −0.520310 0.300401i −0.0262796 0.0151726i
\(393\) 64.1081 + 37.0128i 3.23383 + 1.86705i
\(394\) 0.984730 0.0496100
\(395\) 27.4576 + 15.8527i 1.38154 + 0.797634i
\(396\) 2.69289i 0.135323i
\(397\) 11.8828 0.596383 0.298192 0.954506i \(-0.403617\pi\)
0.298192 + 0.954506i \(0.403617\pi\)
\(398\) 0.363476 0.629559i 0.0182194 0.0315569i
\(399\) −49.2076 28.4100i −2.46346 1.42228i
\(400\) −14.1167 + 24.4509i −0.705837 + 1.22255i
\(401\) 6.23113i 0.311168i 0.987823 + 0.155584i \(0.0497259\pi\)
−0.987823 + 0.155584i \(0.950274\pi\)
\(402\) 0.895857i 0.0446813i
\(403\) 10.7006 6.17802i 0.533037 0.307749i
\(404\) 15.2833 + 8.82380i 0.760371 + 0.439001i
\(405\) 72.5894 + 125.729i 3.60700 + 6.24750i
\(406\) −0.323252 0.559889i −0.0160427 0.0277868i
\(407\) 0.208617i 0.0103408i
\(408\) −2.64207 1.52540i −0.130802 0.0755185i
\(409\) 17.8181 0.881050 0.440525 0.897740i \(-0.354792\pi\)
0.440525 + 0.897740i \(0.354792\pi\)
\(410\) 1.16466i 0.0575184i
\(411\) −46.3044 + 26.7338i −2.28403 + 1.31868i
\(412\) −24.0945 13.9109i −1.18705 0.685343i
\(413\) 29.2945 1.44149
\(414\) 1.68131i 0.0826318i
\(415\) 18.6986 0.917878
\(416\) 1.24352 0.0609686
\(417\) 6.08383 10.5375i 0.297926 0.516024i
\(418\) 0.0342560 0.00167552
\(419\) −8.27828 14.3384i −0.404420 0.700477i 0.589833 0.807525i \(-0.299193\pi\)
−0.994254 + 0.107048i \(0.965860\pi\)
\(420\) −66.7225 + 38.5223i −3.25573 + 1.87969i
\(421\) 19.1881 11.0783i 0.935173 0.539923i 0.0467292 0.998908i \(-0.485120\pi\)
0.888444 + 0.458985i \(0.151787\pi\)
\(422\) 0.512033 0.886867i 0.0249254 0.0431720i
\(423\) −18.5727 + 10.7230i −0.903036 + 0.521368i
\(424\) 1.09775 0.0533112
\(425\) −18.0526 31.2680i −0.875680 1.51672i
\(426\) 0.749367 + 1.29794i 0.0363070 + 0.0628855i
\(427\) −7.59984 13.1633i −0.367782 0.637017i
\(428\) 17.4626i 0.844087i
\(429\) 1.25407 0.0605469
\(430\) −0.113459 + 0.196517i −0.00547149 + 0.00947690i
\(431\) 17.7796 10.2651i 0.856414 0.494451i −0.00639581 0.999980i \(-0.502036\pi\)
0.862810 + 0.505529i \(0.168703\pi\)
\(432\) 39.5776 + 68.5505i 1.90418 + 3.29814i
\(433\) 9.52497 + 5.49925i 0.457741 + 0.264277i 0.711094 0.703097i \(-0.248200\pi\)
−0.253353 + 0.967374i \(0.581533\pi\)
\(434\) 0.365594 0.633228i 0.0175491 0.0303959i
\(435\) −54.7444 −2.62479
\(436\) −5.12746 8.88102i −0.245561 0.425324i
\(437\) −22.4970 −1.07618
\(438\) 0.599115 + 0.345899i 0.0286268 + 0.0165277i
\(439\) −0.460783 + 0.266033i −0.0219920 + 0.0126971i −0.510956 0.859607i \(-0.670708\pi\)
0.488964 + 0.872304i \(0.337375\pi\)
\(440\) 0.0464712 0.0804904i 0.00221543 0.00383723i
\(441\) −30.2780 −1.44181
\(442\) −0.264618 + 0.458331i −0.0125866 + 0.0218006i
\(443\) −1.01879 1.76459i −0.0484041 0.0838383i 0.840808 0.541333i \(-0.182080\pi\)
−0.889212 + 0.457495i \(0.848747\pi\)
\(444\) −4.66142 8.07381i −0.221221 0.383166i
\(445\) −2.53124 + 1.46141i −0.119992 + 0.0692775i
\(446\) 0.462914 0.267263i 0.0219196 0.0126553i
\(447\) 14.1192i 0.667816i
\(448\) −22.2666 + 12.8556i −1.05200 + 0.607372i
\(449\) −7.90622 −0.373117 −0.186559 0.982444i \(-0.559733\pi\)
−0.186559 + 0.982444i \(0.559733\pi\)
\(450\) 2.70926i 0.127716i
\(451\) 1.18001i 0.0555646i
\(452\) 16.0404i 0.754475i
\(453\) −35.5877 61.6396i −1.67205 2.89608i
\(454\) 0.193814 + 0.111899i 0.00909615 + 0.00525167i
\(455\) 13.3716 + 23.1603i 0.626870 + 1.08577i
\(456\) 2.65278 1.53158i 0.124228 0.0717230i
\(457\) −6.59094 + 11.4158i −0.308311 + 0.534011i −0.977993 0.208637i \(-0.933097\pi\)
0.669682 + 0.742648i \(0.266430\pi\)
\(458\) 0.242523 0.420063i 0.0113324 0.0196282i
\(459\) −101.225 −4.72476
\(460\) −15.2523 + 26.4177i −0.711140 + 1.23173i
\(461\) 15.8446 + 9.14790i 0.737958 + 0.426060i 0.821326 0.570459i \(-0.193235\pi\)
−0.0833684 + 0.996519i \(0.526568\pi\)
\(462\) 0.0642689 0.0371057i 0.00299006 0.00172631i
\(463\) 27.0568 + 15.6213i 1.25744 + 0.725982i 0.972576 0.232586i \(-0.0747187\pi\)
0.284863 + 0.958568i \(0.408052\pi\)
\(464\) −18.3042 −0.849750
\(465\) −30.9576 53.6201i −1.43562 2.48657i
\(466\) −0.645097 0.372447i −0.0298835 0.0172533i
\(467\) 36.2994 1.67973 0.839867 0.542792i \(-0.182633\pi\)
0.839867 + 0.542792i \(0.182633\pi\)
\(468\) 36.1759 20.8861i 1.67223 0.965462i
\(469\) −16.7629 + 9.67807i −0.774040 + 0.446892i
\(470\) 0.369915 0.0170629
\(471\) −33.4972 58.0188i −1.54347 2.67337i
\(472\) −0.789634 + 1.36769i −0.0363458 + 0.0629529i
\(473\) −0.114955 + 0.199108i −0.00528563 + 0.00915498i
\(474\) −1.36477 −0.0626858
\(475\) 36.2516 1.66334
\(476\) 32.9426i 1.50992i
\(477\) 47.9102 27.6609i 2.19366 1.26651i
\(478\) −0.0193956 + 0.0111981i −0.000887135 + 0.000512188i
\(479\) 7.67071 + 13.2861i 0.350484 + 0.607056i 0.986334 0.164756i \(-0.0526838\pi\)
−0.635850 + 0.771812i \(0.719350\pi\)
\(480\) 6.23119i 0.284414i
\(481\) −2.80253 + 1.61804i −0.127784 + 0.0737764i
\(482\) 0.148606i 0.00676880i
\(483\) −42.2073 + 24.3684i −1.92050 + 1.10880i
\(484\) −10.9660 + 18.9937i −0.498456 + 0.863350i
\(485\) 54.2836i 2.46489i
\(486\) −3.16483 1.82722i −0.143560 0.0828843i
\(487\) 1.13023 0.652541i 0.0512158 0.0295695i −0.474173 0.880431i \(-0.657253\pi\)
0.525389 + 0.850862i \(0.323920\pi\)
\(488\) 0.819415 0.0370932
\(489\) −26.2554 15.1586i −1.18731 0.685495i
\(490\) 0.452289 + 0.261129i 0.0204323 + 0.0117966i
\(491\) −3.83732 + 6.64643i −0.173176 + 0.299949i −0.939528 0.342471i \(-0.888736\pi\)
0.766353 + 0.642420i \(0.222070\pi\)
\(492\) 26.3666 + 45.6682i 1.18870 + 2.05888i
\(493\) 11.7038 20.2715i 0.527111 0.912983i
\(494\) −0.265691 0.460190i −0.0119540 0.0207049i
\(495\) 4.68391i 0.210526i
\(496\) −10.3509 17.9283i −0.464769 0.805003i
\(497\) −16.1911 + 28.0437i −0.726268 + 1.25793i
\(498\) −0.697053 + 0.402444i −0.0312357 + 0.0180339i
\(499\) 37.6940 21.7626i 1.68742 0.974230i 0.730929 0.682454i \(-0.239087\pi\)
0.956487 0.291776i \(-0.0942462\pi\)
\(500\) 7.21691 12.5001i 0.322750 0.559019i
\(501\) −9.68747 5.59306i −0.432804 0.249880i
\(502\) −0.308972 0.535156i −0.0137901 0.0238852i
\(503\) −37.4705 21.6336i −1.67073 0.964596i −0.967231 0.253899i \(-0.918287\pi\)
−0.703498 0.710697i \(-0.748380\pi\)
\(504\) 2.47312 4.28356i 0.110161 0.190805i
\(505\) −26.5831 15.3478i −1.18293 0.682967i
\(506\) 0.0146914 0.0254462i 0.000653112 0.00113122i
\(507\) 12.5843 + 21.7967i 0.558890 + 0.968027i
\(508\) 12.2296 + 7.06078i 0.542602 + 0.313272i
\(509\) 18.2933 10.5617i 0.810838 0.468138i −0.0364086 0.999337i \(-0.511592\pi\)
0.847247 + 0.531199i \(0.178258\pi\)
\(510\) 2.29666 + 1.32598i 0.101698 + 0.0587154i
\(511\) 14.9472i 0.661226i
\(512\) 3.47350i 0.153509i
\(513\) 50.8175 88.0184i 2.24365 3.88611i
\(514\) −0.0439938 + 0.0253998i −0.00194048 + 0.00112034i
\(515\) 41.9090 + 24.1961i 1.84673 + 1.06621i
\(516\) 10.2744i 0.452303i
\(517\) 0.374792 0.0164833
\(518\) −0.0957502 + 0.165844i −0.00420702 + 0.00728678i
\(519\) 20.9806i 0.920944i
\(520\) −1.44173 −0.0632239
\(521\) 12.9141 7.45598i 0.565778 0.326652i −0.189683 0.981845i \(-0.560746\pi\)
0.755461 + 0.655193i \(0.227413\pi\)
\(522\) 1.52113 0.878226i 0.0665781 0.0384389i
\(523\) −24.8498 14.3471i −1.08661 0.627353i −0.153936 0.988081i \(-0.549195\pi\)
−0.932671 + 0.360728i \(0.882528\pi\)
\(524\) −37.3187 21.5460i −1.63028 0.941240i
\(525\) 68.0129 39.2673i 2.96833 1.71376i
\(526\) −0.521070 + 0.300840i −0.0227197 + 0.0131172i
\(527\) 26.4736 1.15321
\(528\) 2.10111i 0.0914390i
\(529\) 1.85172 3.20728i 0.0805097 0.139447i
\(530\) −0.954234 −0.0414493
\(531\) 79.5886i 3.45385i
\(532\) 28.6448 + 16.5381i 1.24191 + 0.717017i
\(533\) 15.8521 9.15219i 0.686629 0.396425i
\(534\) 0.0629069 0.108958i 0.00272225 0.00471507i
\(535\) 30.3738i 1.31317i
\(536\) 1.04349i 0.0450719i
\(537\) 4.63630 + 2.67677i 0.200071 + 0.115511i
\(538\) −0.635066 + 0.366655i −0.0273796 + 0.0158076i
\(539\) 0.458251 + 0.264571i 0.0197383 + 0.0113959i
\(540\) −68.9054 119.348i −2.96522 5.13590i
\(541\) 12.8923 22.3300i 0.554282 0.960044i −0.443677 0.896187i \(-0.646326\pi\)
0.997959 0.0638573i \(-0.0203402\pi\)
\(542\) 0.547205 + 0.315929i 0.0235045 + 0.0135703i
\(543\) −7.44068 + 12.8876i −0.319310 + 0.553062i
\(544\) 2.30737 + 1.33216i 0.0989278 + 0.0571160i
\(545\) 8.91851 + 15.4473i 0.382027 + 0.661690i
\(546\) −0.996942 0.575585i −0.0426652 0.0246328i
\(547\) −2.18920 + 3.79181i −0.0936035 + 0.162126i −0.909025 0.416742i \(-0.863172\pi\)
0.815421 + 0.578868i \(0.196505\pi\)
\(548\) 26.9548 15.5623i 1.15145 0.664790i
\(549\) 35.7627 20.6476i 1.52631 0.881217i
\(550\) −0.0236737 + 0.0410041i −0.00100945 + 0.00174842i
\(551\) 11.7512 + 20.3537i 0.500619 + 0.867097i
\(552\) 2.62740i 0.111830i
\(553\) −14.7438 25.5370i −0.626969 1.08594i
\(554\) −0.418361 + 0.724623i −0.0177745 + 0.0307863i
\(555\) 8.10789 + 14.0433i 0.344161 + 0.596104i
\(556\) −3.54153 + 6.13410i −0.150194 + 0.260144i
\(557\) −2.49880 1.44268i −0.105878 0.0611285i 0.446126 0.894970i \(-0.352803\pi\)
−0.552004 + 0.833842i \(0.686137\pi\)
\(558\) 1.72038 + 0.993262i 0.0728295 + 0.0420481i
\(559\) 3.56637 0.150841
\(560\) 38.8036 22.4033i 1.63975 0.946712i
\(561\) 2.32694 + 1.34346i 0.0982434 + 0.0567209i
\(562\) 0.788277i 0.0332515i
\(563\) 0.704029 1.21941i 0.0296713 0.0513922i −0.850808 0.525476i \(-0.823887\pi\)
0.880480 + 0.474084i \(0.157221\pi\)
\(564\) 14.5050 8.37447i 0.610771 0.352629i
\(565\) 27.9000i 1.17376i
\(566\) 0.750496 0.433299i 0.0315457 0.0182129i
\(567\) 135.024i 5.67046i
\(568\) −0.872860 1.51184i −0.0366244 0.0634353i
\(569\) 18.2195 10.5190i 0.763801 0.440981i −0.0668580 0.997763i \(-0.521297\pi\)
0.830659 + 0.556782i \(0.187964\pi\)
\(570\) −2.30598 + 1.33136i −0.0965867 + 0.0557644i
\(571\) 16.2009i 0.677986i 0.940789 + 0.338993i \(0.110086\pi\)
−0.940789 + 0.338993i \(0.889914\pi\)
\(572\) −0.730018 −0.0305236
\(573\) −50.1242 −2.09397
\(574\) 0.541596 0.938071i 0.0226058 0.0391543i
\(575\) 15.5472 26.9286i 0.648364 1.12300i
\(576\) −34.9267 60.4949i −1.45528 2.52062i
\(577\) −6.87072 −0.286032 −0.143016 0.989720i \(-0.545680\pi\)
−0.143016 + 0.989720i \(0.545680\pi\)
\(578\) −0.340339 + 0.196495i −0.0141562 + 0.00817311i
\(579\) −5.00998 + 2.89251i −0.208208 + 0.120209i
\(580\) 31.8679 1.32324
\(581\) −15.0607 8.69532i −0.624825 0.360743i
\(582\) −1.16833 2.02360i −0.0484287 0.0838810i
\(583\) −0.966813 −0.0400413
\(584\) −0.697847 0.402902i −0.0288771 0.0166722i
\(585\) −62.9229 + 36.3285i −2.60154 + 1.50200i
\(586\) 0.343437 + 0.198283i 0.0141872 + 0.00819100i
\(587\) −9.02221 + 15.6269i −0.372386 + 0.644992i −0.989932 0.141543i \(-0.954794\pi\)
0.617546 + 0.786535i \(0.288127\pi\)
\(588\) 23.6467 0.975172
\(589\) −13.2905 + 23.0198i −0.547625 + 0.948514i
\(590\) 0.686403 1.18888i 0.0282588 0.0489456i
\(591\) −67.1618 + 38.7759i −2.76267 + 1.59503i
\(592\) 2.71093 + 4.69547i 0.111418 + 0.192982i
\(593\) −16.4537 9.49956i −0.675674 0.390100i 0.122549 0.992462i \(-0.460893\pi\)
−0.798223 + 0.602362i \(0.794226\pi\)
\(594\) 0.0663715 + 0.114959i 0.00272326 + 0.00471682i
\(595\) 57.2991i 2.34903i
\(596\) 8.21910i 0.336667i
\(597\) 57.2507i 2.34311i
\(598\) −0.455787 −0.0186385
\(599\) 10.2888 5.94021i 0.420387 0.242711i −0.274856 0.961485i \(-0.588630\pi\)
0.695243 + 0.718775i \(0.255297\pi\)
\(600\) 4.23380i 0.172844i
\(601\) 38.1423 22.0215i 1.55586 0.898274i 0.558211 0.829699i \(-0.311488\pi\)
0.997646 0.0685752i \(-0.0218453\pi\)
\(602\) 0.182771 0.105523i 0.00744918 0.00430079i
\(603\) −26.2938 45.5422i −1.07077 1.85462i
\(604\) 20.7163 + 35.8817i 0.842936 + 1.46001i
\(605\) 19.0739 33.0369i 0.775463 1.34314i
\(606\) 1.32130 0.0536742
\(607\) −0.350397 + 0.606905i −0.0142222 + 0.0246335i −0.873049 0.487633i \(-0.837861\pi\)
0.858827 + 0.512266i \(0.171194\pi\)
\(608\) −2.31673 + 1.33756i −0.0939557 + 0.0542454i
\(609\) 44.0937 + 25.4575i 1.78677 + 1.03159i
\(610\) −0.712291 −0.0288398
\(611\) −2.90689 5.03488i −0.117600 0.203690i
\(612\) 89.4999 3.61782
\(613\) 15.2102 26.3449i 0.614336 1.06406i −0.376165 0.926553i \(-0.622757\pi\)
0.990501 0.137508i \(-0.0439092\pi\)
\(614\) 0.570842 + 0.329576i 0.0230373 + 0.0133006i
\(615\) −45.8610 79.4336i −1.84929 3.20307i
\(616\) −0.0748602 + 0.0432205i −0.00301620 + 0.00174141i
\(617\) −12.6704 + 21.9458i −0.510092 + 0.883506i 0.489839 + 0.871813i \(0.337055\pi\)
−0.999932 + 0.0116932i \(0.996278\pi\)
\(618\) −2.08306 −0.0837930
\(619\) 33.7826i 1.35784i 0.734214 + 0.678918i \(0.237551\pi\)
−0.734214 + 0.678918i \(0.762449\pi\)
\(620\) 18.0211 + 31.2134i 0.723744 + 1.25356i
\(621\) −43.5882 75.4969i −1.74913 3.02959i
\(622\) 0.100860 + 0.174695i 0.00404412 + 0.00700462i
\(623\) 2.71837 0.108909
\(624\) −28.2259 + 16.2963i −1.12994 + 0.652372i
\(625\) 5.14352 8.90884i 0.205741 0.356353i
\(626\) 0.913767 0.527564i 0.0365215 0.0210857i
\(627\) −2.33637 + 1.34891i −0.0933058 + 0.0538701i
\(628\) 19.4994 + 33.7740i 0.778112 + 1.34773i
\(629\) −6.93352 −0.276458
\(630\) −2.14980 + 3.72356i −0.0856501 + 0.148350i
\(631\) −22.4495 −0.893701 −0.446851 0.894609i \(-0.647454\pi\)
−0.446851 + 0.894609i \(0.647454\pi\)
\(632\) 1.58967 0.0632338
\(633\) 80.6497i 3.20554i
\(634\) −0.126460 −0.00502238
\(635\) −21.2718 12.2813i −0.844144 0.487367i
\(636\) −37.4171 + 21.6028i −1.48369 + 0.856606i
\(637\) 8.20808i 0.325216i
\(638\) −0.0306960 −0.00121527
\(639\) −76.1904 43.9886i −3.01405 1.74016i
\(640\) 4.83565i 0.191146i
\(641\) 15.2130 + 26.3497i 0.600878 + 1.04075i 0.992688 + 0.120705i \(0.0385156\pi\)
−0.391810 + 0.920046i \(0.628151\pi\)
\(642\) −0.653725 1.13228i −0.0258005 0.0446877i
\(643\) −6.05668 3.49683i −0.238852 0.137901i 0.375797 0.926702i \(-0.377369\pi\)
−0.614649 + 0.788801i \(0.710702\pi\)
\(644\) 24.5698 14.1854i 0.968185 0.558982i
\(645\) 17.8708i 0.703663i
\(646\) 1.13852i 0.0447944i
\(647\) 0.325177 0.563224i 0.0127840 0.0221426i −0.859563 0.511030i \(-0.829264\pi\)
0.872347 + 0.488888i \(0.162597\pi\)
\(648\) 6.30390 + 3.63956i 0.247641 + 0.142975i
\(649\) 0.695451 1.20456i 0.0272988 0.0472830i
\(650\) 0.734455 0.0288077
\(651\) 57.5843i 2.25691i
\(652\) 15.2839 + 8.82414i 0.598562 + 0.345580i
\(653\) −8.60111 −0.336587 −0.168294 0.985737i \(-0.553826\pi\)
−0.168294 + 0.985737i \(0.553826\pi\)
\(654\) −0.664934 0.383900i −0.0260010 0.0150117i
\(655\) 64.9107 + 37.4762i 2.53627 + 1.46432i
\(656\) −15.3339 26.5592i −0.598690 1.03696i
\(657\) −40.6092 −1.58432
\(658\) −0.297947 0.172020i −0.0116152 0.00670604i
\(659\) 1.04842i 0.0408406i −0.999791 0.0204203i \(-0.993500\pi\)
0.999791 0.0204203i \(-0.00650043\pi\)
\(660\) 3.65807i 0.142390i
\(661\) −6.85802 −0.266746 −0.133373 0.991066i \(-0.542581\pi\)
−0.133373 + 0.991066i \(0.542581\pi\)
\(662\) 0.397015 0.0154304
\(663\) 41.6796i 1.61870i
\(664\) 0.811925 0.468765i 0.0315088 0.0181916i
\(665\) −49.8236 28.7657i −1.93208 1.11549i
\(666\) −0.450573 0.260138i −0.0174593 0.0100802i
\(667\) 20.1590 0.780559
\(668\) 5.63928 + 3.25584i 0.218190 + 0.125972i
\(669\) −21.0482 + 36.4565i −0.813769 + 1.40949i
\(670\) 0.907072i 0.0350432i
\(671\) −0.721680 −0.0278602
\(672\) −2.89766 + 5.01890i −0.111780 + 0.193608i
\(673\) 1.38508 + 2.39903i 0.0533910 + 0.0924759i 0.891486 0.453049i \(-0.149664\pi\)
−0.838095 + 0.545525i \(0.816330\pi\)
\(674\) −0.489091 0.282377i −0.0188391 0.0108767i
\(675\) 70.2380 + 121.656i 2.70346 + 4.68253i
\(676\) −7.32562 12.6883i −0.281754 0.488013i
\(677\) 31.0863i 1.19474i 0.801965 + 0.597371i \(0.203788\pi\)
−0.801965 + 0.597371i \(0.796212\pi\)
\(678\) −0.600482 1.04006i −0.0230614 0.0399434i
\(679\) 25.2432 43.7226i 0.968746 1.67792i
\(680\) −2.67515 1.54450i −0.102587 0.0592287i
\(681\) −17.6250 −0.675392
\(682\) −0.0173584 0.0300656i −0.000664687 0.00115127i
\(683\) −10.7592 18.6355i −0.411691 0.713069i 0.583384 0.812196i \(-0.301728\pi\)
−0.995075 + 0.0991272i \(0.968395\pi\)
\(684\) −44.9314 + 77.8234i −1.71799 + 2.97565i
\(685\) −46.8841 + 27.0685i −1.79135 + 1.03423i
\(686\) 0.250209 + 0.433375i 0.00955304 + 0.0165463i
\(687\) 38.1995i 1.45740i
\(688\) 5.97523i 0.227804i
\(689\) 7.49862 + 12.9880i 0.285675 + 0.494803i
\(690\) 2.28392i 0.0869472i
\(691\) −12.7097 + 7.33796i −0.483501 + 0.279149i −0.721874 0.692024i \(-0.756719\pi\)
0.238374 + 0.971174i \(0.423386\pi\)
\(692\) 12.2132i 0.464277i
\(693\) −2.17814 + 3.77265i −0.0827406 + 0.143311i
\(694\) −0.782325 + 1.35503i −0.0296967 + 0.0514361i
\(695\) 6.15999 10.6694i 0.233662 0.404714i
\(696\) −2.37709 + 1.37242i −0.0901035 + 0.0520213i
\(697\) 39.2183 1.48550
\(698\) −0.790777 0.193974i −0.0299314 0.00734201i
\(699\) 58.6636 2.21886
\(700\) −39.5918 + 22.8583i −1.49643 + 0.863963i
\(701\) −6.99985 + 12.1241i −0.264381 + 0.457921i −0.967401 0.253249i \(-0.918501\pi\)
0.703020 + 0.711170i \(0.251834\pi\)
\(702\) 1.02956 1.78325i 0.0388582 0.0673043i
\(703\) 3.48082 6.02895i 0.131281 0.227386i
\(704\) 1.22077i 0.0460095i
\(705\) −25.2294 + 14.5662i −0.950196 + 0.548596i
\(706\) 1.06320i 0.0400139i
\(707\) 14.2742 + 24.7237i 0.536837 + 0.929829i
\(708\) 62.1576i 2.33602i
\(709\) 46.1829i 1.73444i −0.497929 0.867218i \(-0.665906\pi\)
0.497929 0.867218i \(-0.334094\pi\)
\(710\) 0.758749 + 1.31419i 0.0284753 + 0.0493207i
\(711\) 69.3799 40.0565i 2.60195 1.50224i
\(712\) −0.0732737 + 0.126914i −0.00274605 + 0.00475629i
\(713\) 11.3998 + 19.7450i 0.426925 + 0.739456i
\(714\) −1.23323 2.13601i −0.0461524 0.0799383i
\(715\) 1.26977 0.0474865
\(716\) −2.69889 1.55821i −0.100862 0.0582329i
\(717\) 0.881897 1.52749i 0.0329350 0.0570452i
\(718\) −0.820530 1.42120i −0.0306219 0.0530387i
\(719\) 6.76173i 0.252170i −0.992019 0.126085i \(-0.959759\pi\)
0.992019 0.126085i \(-0.0402412\pi\)
\(720\) 60.8662 + 105.423i 2.26835 + 3.92890i
\(721\) −22.5036 38.9774i −0.838079 1.45160i
\(722\) 0.272828 + 0.157517i 0.0101536 + 0.00586219i
\(723\) −5.85167 10.1354i −0.217626 0.376939i
\(724\) 4.33138 7.50217i 0.160974 0.278816i
\(725\) −32.4842 −1.20643
\(726\) 1.64208i 0.0609434i
\(727\) −19.8092 + 34.3106i −0.734684 + 1.27251i 0.220178 + 0.975460i \(0.429336\pi\)
−0.954862 + 0.297050i \(0.903997\pi\)
\(728\) 1.16123 + 0.670439i 0.0430382 + 0.0248481i
\(729\) 162.484 6.01791
\(730\) 0.606616 + 0.350230i 0.0224518 + 0.0129626i
\(731\) 6.61745 + 3.82059i 0.244755 + 0.141310i
\(732\) −27.9301 + 16.1255i −1.03233 + 0.596014i
\(733\) 28.2153i 1.04215i −0.853510 0.521077i \(-0.825530\pi\)
0.853510 0.521077i \(-0.174470\pi\)
\(734\) −0.498584 −0.0184031
\(735\) −41.1301 −1.51711
\(736\) 2.29456i 0.0845787i
\(737\) 0.919029i 0.0338529i
\(738\) 2.54859 + 1.47143i 0.0938150 + 0.0541641i
\(739\) 10.3735 0.381594 0.190797 0.981629i \(-0.438893\pi\)
0.190797 + 0.981629i \(0.438893\pi\)
\(740\) −4.71978 8.17489i −0.173502 0.300515i
\(741\) 36.2419 + 20.9243i 1.33138 + 0.768673i
\(742\) 0.768585 + 0.443743i 0.0282157 + 0.0162903i
\(743\) 17.1978 0.630926 0.315463 0.948938i \(-0.397840\pi\)
0.315463 + 0.948938i \(0.397840\pi\)
\(744\) −2.68846 1.55218i −0.0985638 0.0569058i
\(745\) 14.2960i 0.523764i
\(746\) 0.0886658 0.00324629
\(747\) 23.6238 40.9177i 0.864351 1.49710i
\(748\) −1.35456 0.782056i −0.0495276 0.0285948i
\(749\) 14.1246 24.4645i 0.516101 0.893913i
\(750\) 1.08068i 0.0394608i
\(751\) 20.9053i 0.762846i −0.924401 0.381423i \(-0.875434\pi\)
0.924401 0.381423i \(-0.124566\pi\)
\(752\) −8.43564 + 4.87032i −0.307616 + 0.177602i
\(753\) 42.1459 + 24.3329i 1.53588 + 0.886741i
\(754\) 0.238079 + 0.412365i 0.00867032 + 0.0150174i
\(755\) −36.0332 62.4113i −1.31138 2.27138i
\(756\) 128.171i 4.66153i
\(757\) −18.7721 10.8381i −0.682283 0.393916i 0.118432 0.992962i \(-0.462213\pi\)
−0.800715 + 0.599046i \(0.795547\pi\)
\(758\) 1.30176 0.0472820
\(759\) 2.31402i 0.0839937i
\(760\) 2.68599 1.55076i 0.0974312 0.0562519i
\(761\) 7.19378 + 4.15333i 0.260774 + 0.150558i 0.624688 0.780875i \(-0.285226\pi\)
−0.363913 + 0.931433i \(0.618560\pi\)
\(762\) 1.05730 0.0383020
\(763\) 16.5893i 0.600574i
\(764\) 29.1784 1.05564
\(765\) −155.673 −5.62835
\(766\) −0.0429087 + 0.0743200i