Properties

Label 1110.2.l.a.697.10
Level $1110$
Weight $2$
Character 1110.697
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.l (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 697.10
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.a.43.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.87641 - 1.21617i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.24767 - 2.24767i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.87641 - 1.21617i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.24767 - 2.24767i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-1.21617 - 1.87641i) q^{10} -5.65930i q^{11} +(-0.707107 - 0.707107i) q^{12} +4.81453i q^{13} +(-2.24767 + 2.24767i) q^{14} +(2.18679 + 0.466864i) q^{15} +1.00000 q^{16} -7.58373 q^{17} +1.00000 q^{18} +(-3.73408 - 3.73408i) q^{19} +(-1.87641 + 1.21617i) q^{20} -3.17868i q^{21} -5.65930 q^{22} -4.23021i q^{23} +(-0.707107 + 0.707107i) q^{24} +(2.04186 - 4.56408i) q^{25} +4.81453 q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.24767 + 2.24767i) q^{28} +(3.26498 - 3.26498i) q^{29} +(0.466864 - 2.18679i) q^{30} +(1.98809 + 1.98809i) q^{31} -1.00000i q^{32} +(4.00173 - 4.00173i) q^{33} +7.58373i q^{34} +(-6.95110 - 1.48401i) q^{35} -1.00000i q^{36} +(-4.17208 + 4.42648i) q^{37} +(-3.73408 + 3.73408i) q^{38} +(-3.40439 + 3.40439i) q^{39} +(1.21617 + 1.87641i) q^{40} +2.43043i q^{41} -3.17868 q^{42} +3.34656i q^{43} +5.65930i q^{44} +(1.21617 + 1.87641i) q^{45} -4.23021 q^{46} +(6.04560 + 6.04560i) q^{47} +(0.707107 + 0.707107i) q^{48} +3.10403i q^{49} +(-4.56408 - 2.04186i) q^{50} +(-5.36251 - 5.36251i) q^{51} -4.81453i q^{52} +(8.02058 - 8.02058i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-6.88266 - 10.6192i) q^{55} +(2.24767 - 2.24767i) q^{56} -5.28079i q^{57} +(-3.26498 - 3.26498i) q^{58} +(-9.84721 - 9.84721i) q^{59} +(-2.18679 - 0.466864i) q^{60} +(-1.11855 - 1.11855i) q^{61} +(1.98809 - 1.98809i) q^{62} +(2.24767 - 2.24767i) q^{63} -1.00000 q^{64} +(5.85528 + 9.03405i) q^{65} +(-4.00173 - 4.00173i) q^{66} +(6.91167 - 6.91167i) q^{67} +7.58373 q^{68} +(2.99121 - 2.99121i) q^{69} +(-1.48401 + 6.95110i) q^{70} -6.12087 q^{71} -1.00000 q^{72} +(-2.58794 - 2.58794i) q^{73} +(4.42648 + 4.17208i) q^{74} +(4.67110 - 1.78347i) q^{75} +(3.73408 + 3.73408i) q^{76} +(-12.7202 + 12.7202i) q^{77} +(3.40439 + 3.40439i) q^{78} +(-2.85317 - 2.85317i) q^{79} +(1.87641 - 1.21617i) q^{80} -1.00000 q^{81} +2.43043 q^{82} +(0.906248 - 0.906248i) q^{83} +3.17868i q^{84} +(-14.2302 + 9.22310i) q^{85} +3.34656 q^{86} +4.61737 q^{87} +5.65930 q^{88} +(10.1878 - 10.1878i) q^{89} +(1.87641 - 1.21617i) q^{90} +(10.8215 - 10.8215i) q^{91} +4.23021i q^{92} +2.81158i q^{93} +(6.04560 - 6.04560i) q^{94} +(-11.5480 - 2.46541i) q^{95} +(0.707107 - 0.707107i) q^{96} -2.87834 q^{97} +3.10403 q^{98} +5.65930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{4} + 4q^{7} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{7} - 4q^{10} + 4q^{14} + 36q^{16} - 32q^{17} + 36q^{18} + 4q^{19} + 8q^{22} - 4q^{25} + 8q^{26} - 4q^{28} + 36q^{29} - 4q^{31} + 4q^{33} - 12q^{35} - 4q^{37} + 4q^{38} + 4q^{39} + 4q^{40} - 16q^{42} + 4q^{45} + 16q^{47} - 16q^{50} - 8q^{53} + 16q^{55} - 4q^{56} - 36q^{58} - 4q^{59} - 4q^{61} - 4q^{62} - 4q^{63} - 36q^{64} + 52q^{65} - 4q^{66} + 16q^{67} + 32q^{68} - 8q^{69} - 28q^{70} - 8q^{71} - 36q^{72} - 4q^{73} + 28q^{74} + 16q^{75} - 4q^{76} + 8q^{77} - 4q^{78} - 12q^{79} - 36q^{81} - 8q^{82} + 8q^{83} + 8q^{85} + 32q^{86} - 8q^{87} - 8q^{88} - 24q^{89} + 56q^{91} + 16q^{94} - 20q^{95} + 40q^{97} - 12q^{98} - 8q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) 1.87641 1.21617i 0.839158 0.543888i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −2.24767 2.24767i −0.849539 0.849539i 0.140537 0.990075i \(-0.455117\pi\)
−0.990075 + 0.140537i \(0.955117\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −1.21617 1.87641i −0.384587 0.593374i
\(11\) 5.65930i 1.70634i −0.521632 0.853171i \(-0.674676\pi\)
0.521632 0.853171i \(-0.325324\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 4.81453i 1.33531i 0.744471 + 0.667655i \(0.232702\pi\)
−0.744471 + 0.667655i \(0.767298\pi\)
\(14\) −2.24767 + 2.24767i −0.600715 + 0.600715i
\(15\) 2.18679 + 0.466864i 0.564626 + 0.120544i
\(16\) 1.00000 0.250000
\(17\) −7.58373 −1.83932 −0.919662 0.392710i \(-0.871537\pi\)
−0.919662 + 0.392710i \(0.871537\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.73408 3.73408i −0.856657 0.856657i 0.134285 0.990943i \(-0.457126\pi\)
−0.990943 + 0.134285i \(0.957126\pi\)
\(20\) −1.87641 + 1.21617i −0.419579 + 0.271944i
\(21\) 3.17868i 0.693646i
\(22\) −5.65930 −1.20657
\(23\) 4.23021i 0.882059i −0.897493 0.441030i \(-0.854613\pi\)
0.897493 0.441030i \(-0.145387\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 2.04186 4.56408i 0.408373 0.912815i
\(26\) 4.81453 0.944207
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 2.24767 + 2.24767i 0.424769 + 0.424769i
\(29\) 3.26498 3.26498i 0.606291 0.606291i −0.335684 0.941975i \(-0.608967\pi\)
0.941975 + 0.335684i \(0.108967\pi\)
\(30\) 0.466864 2.18679i 0.0852373 0.399251i
\(31\) 1.98809 + 1.98809i 0.357071 + 0.357071i 0.862732 0.505661i \(-0.168751\pi\)
−0.505661 + 0.862732i \(0.668751\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.00173 4.00173i 0.696611 0.696611i
\(34\) 7.58373i 1.30060i
\(35\) −6.95110 1.48401i −1.17495 0.250844i
\(36\) 1.00000i 0.166667i
\(37\) −4.17208 + 4.42648i −0.685886 + 0.727709i
\(38\) −3.73408 + 3.73408i −0.605748 + 0.605748i
\(39\) −3.40439 + 3.40439i −0.545138 + 0.545138i
\(40\) 1.21617 + 1.87641i 0.192293 + 0.296687i
\(41\) 2.43043i 0.379570i 0.981826 + 0.189785i \(0.0607791\pi\)
−0.981826 + 0.189785i \(0.939221\pi\)
\(42\) −3.17868 −0.490482
\(43\) 3.34656i 0.510346i 0.966895 + 0.255173i \(0.0821324\pi\)
−0.966895 + 0.255173i \(0.917868\pi\)
\(44\) 5.65930i 0.853171i
\(45\) 1.21617 + 1.87641i 0.181296 + 0.279719i
\(46\) −4.23021 −0.623710
\(47\) 6.04560 + 6.04560i 0.881842 + 0.881842i 0.993722 0.111880i \(-0.0356873\pi\)
−0.111880 + 0.993722i \(0.535687\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 3.10403i 0.443433i
\(50\) −4.56408 2.04186i −0.645458 0.288763i
\(51\) −5.36251 5.36251i −0.750901 0.750901i
\(52\) 4.81453i 0.667655i
\(53\) 8.02058 8.02058i 1.10171 1.10171i 0.107507 0.994204i \(-0.465713\pi\)
0.994204 0.107507i \(-0.0342868\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −6.88266 10.6192i −0.928058 1.43189i
\(56\) 2.24767 2.24767i 0.300357 0.300357i
\(57\) 5.28079i 0.699458i
\(58\) −3.26498 3.26498i −0.428712 0.428712i
\(59\) −9.84721 9.84721i −1.28200 1.28200i −0.939530 0.342468i \(-0.888737\pi\)
−0.342468 0.939530i \(-0.611263\pi\)
\(60\) −2.18679 0.466864i −0.282313 0.0602718i
\(61\) −1.11855 1.11855i −0.143216 0.143216i 0.631864 0.775080i \(-0.282290\pi\)
−0.775080 + 0.631864i \(0.782290\pi\)
\(62\) 1.98809 1.98809i 0.252487 0.252487i
\(63\) 2.24767 2.24767i 0.283180 0.283180i
\(64\) −1.00000 −0.125000
\(65\) 5.85528 + 9.03405i 0.726259 + 1.12054i
\(66\) −4.00173 4.00173i −0.492578 0.492578i
\(67\) 6.91167 6.91167i 0.844395 0.844395i −0.145032 0.989427i \(-0.546328\pi\)
0.989427 + 0.145032i \(0.0463284\pi\)
\(68\) 7.58373 0.919662
\(69\) 2.99121 2.99121i 0.360099 0.360099i
\(70\) −1.48401 + 6.95110i −0.177373 + 0.830816i
\(71\) −6.12087 −0.726413 −0.363207 0.931709i \(-0.618318\pi\)
−0.363207 + 0.931709i \(0.618318\pi\)
\(72\) −1.00000 −0.117851
\(73\) −2.58794 2.58794i −0.302896 0.302896i 0.539250 0.842146i \(-0.318708\pi\)
−0.842146 + 0.539250i \(0.818708\pi\)
\(74\) 4.42648 + 4.17208i 0.514568 + 0.484995i
\(75\) 4.67110 1.78347i 0.539373 0.205938i
\(76\) 3.73408 + 3.73408i 0.428329 + 0.428329i
\(77\) −12.7202 + 12.7202i −1.44960 + 1.44960i
\(78\) 3.40439 + 3.40439i 0.385471 + 0.385471i
\(79\) −2.85317 2.85317i −0.321007 0.321007i 0.528146 0.849153i \(-0.322887\pi\)
−0.849153 + 0.528146i \(0.822887\pi\)
\(80\) 1.87641 1.21617i 0.209790 0.135972i
\(81\) −1.00000 −0.111111
\(82\) 2.43043 0.268396
\(83\) 0.906248 0.906248i 0.0994737 0.0994737i −0.655619 0.755092i \(-0.727592\pi\)
0.755092 + 0.655619i \(0.227592\pi\)
\(84\) 3.17868i 0.346823i
\(85\) −14.2302 + 9.22310i −1.54348 + 1.00039i
\(86\) 3.34656 0.360869
\(87\) 4.61737 0.495034
\(88\) 5.65930 0.603283
\(89\) 10.1878 10.1878i 1.07990 1.07990i 0.0833830 0.996518i \(-0.473428\pi\)
0.996518 0.0833830i \(-0.0265725\pi\)
\(90\) 1.87641 1.21617i 0.197791 0.128196i
\(91\) 10.8215 10.8215i 1.13440 1.13440i
\(92\) 4.23021i 0.441030i
\(93\) 2.81158i 0.291547i
\(94\) 6.04560 6.04560i 0.623556 0.623556i
\(95\) −11.5480 2.46541i −1.18480 0.252946i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) −2.87834 −0.292251 −0.146125 0.989266i \(-0.546680\pi\)
−0.146125 + 0.989266i \(0.546680\pi\)
\(98\) 3.10403 0.313554
\(99\) 5.65930 0.568781
\(100\) −2.04186 + 4.56408i −0.204186 + 0.456408i
\(101\) 16.0893i 1.60095i 0.599367 + 0.800474i \(0.295419\pi\)
−0.599367 + 0.800474i \(0.704581\pi\)
\(102\) −5.36251 + 5.36251i −0.530967 + 0.530967i
\(103\) 11.0997 1.09369 0.546845 0.837234i \(-0.315829\pi\)
0.546845 + 0.837234i \(0.315829\pi\)
\(104\) −4.81453 −0.472103
\(105\) −3.86582 5.96453i −0.377265 0.582078i
\(106\) −8.02058 8.02058i −0.779028 0.779028i
\(107\) 8.64549 + 8.64549i 0.835791 + 0.835791i 0.988302 0.152511i \(-0.0487359\pi\)
−0.152511 + 0.988302i \(0.548736\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −13.7592 13.7592i −1.31790 1.31790i −0.915438 0.402458i \(-0.868156\pi\)
−0.402458 0.915438i \(-0.631844\pi\)
\(110\) −10.6192 + 6.88266i −1.01250 + 0.656236i
\(111\) −6.08010 + 0.179886i −0.577098 + 0.0170740i
\(112\) −2.24767 2.24767i −0.212385 0.212385i
\(113\) 4.68689 0.440906 0.220453 0.975398i \(-0.429246\pi\)
0.220453 + 0.975398i \(0.429246\pi\)
\(114\) −5.28079 −0.494591
\(115\) −5.14465 7.93762i −0.479741 0.740187i
\(116\) −3.26498 + 3.26498i −0.303145 + 0.303145i
\(117\) −4.81453 −0.445103
\(118\) −9.84721 + 9.84721i −0.906509 + 0.906509i
\(119\) 17.0457 + 17.0457i 1.56258 + 1.56258i
\(120\) −0.466864 + 2.18679i −0.0426186 + 0.199625i
\(121\) −21.0276 −1.91160
\(122\) −1.11855 + 1.11855i −0.101269 + 0.101269i
\(123\) −1.71858 + 1.71858i −0.154959 + 0.154959i
\(124\) −1.98809 1.98809i −0.178535 0.178535i
\(125\) −1.71931 11.0474i −0.153780 0.988105i
\(126\) −2.24767 2.24767i −0.200238 0.200238i
\(127\) −14.6086 14.6086i −1.29630 1.29630i −0.930816 0.365488i \(-0.880902\pi\)
−0.365488 0.930816i \(-0.619098\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −2.36638 + 2.36638i −0.208348 + 0.208348i
\(130\) 9.03405 5.85528i 0.792339 0.513542i
\(131\) 9.26219 + 9.26219i 0.809241 + 0.809241i 0.984519 0.175278i \(-0.0560824\pi\)
−0.175278 + 0.984519i \(0.556082\pi\)
\(132\) −4.00173 + 4.00173i −0.348306 + 0.348306i
\(133\) 16.7860i 1.45553i
\(134\) −6.91167 6.91167i −0.597078 0.597078i
\(135\) −0.466864 + 2.18679i −0.0401812 + 0.188209i
\(136\) 7.58373i 0.650299i
\(137\) 1.63948 + 1.63948i 0.140071 + 0.140071i 0.773665 0.633595i \(-0.218421\pi\)
−0.633595 + 0.773665i \(0.718421\pi\)
\(138\) −2.99121 2.99121i −0.254629 0.254629i
\(139\) 17.9432 1.52192 0.760959 0.648800i \(-0.224729\pi\)
0.760959 + 0.648800i \(0.224729\pi\)
\(140\) 6.95110 + 1.48401i 0.587476 + 0.125422i
\(141\) 8.54977i 0.720021i
\(142\) 6.12087i 0.513652i
\(143\) 27.2468 2.27850
\(144\) 1.00000i 0.0833333i
\(145\) 2.15568 10.0972i 0.179020 0.838528i
\(146\) −2.58794 + 2.58794i −0.214180 + 0.214180i
\(147\) −2.19488 + 2.19488i −0.181031 + 0.181031i
\(148\) 4.17208 4.42648i 0.342943 0.363854i
\(149\) 9.20482i 0.754088i 0.926195 + 0.377044i \(0.123059\pi\)
−0.926195 + 0.377044i \(0.876941\pi\)
\(150\) −1.78347 4.67110i −0.145620 0.381394i
\(151\) 5.59713i 0.455488i −0.973721 0.227744i \(-0.926865\pi\)
0.973721 0.227744i \(-0.0731349\pi\)
\(152\) 3.73408 3.73408i 0.302874 0.302874i
\(153\) 7.58373i 0.613108i
\(154\) 12.7202 + 12.7202i 1.02502 + 1.02502i
\(155\) 6.14832 + 1.31262i 0.493845 + 0.105432i
\(156\) 3.40439 3.40439i 0.272569 0.272569i
\(157\) −0.998661 0.998661i −0.0797019 0.0797019i 0.666132 0.745834i \(-0.267949\pi\)
−0.745834 + 0.666132i \(0.767949\pi\)
\(158\) −2.85317 + 2.85317i −0.226986 + 0.226986i
\(159\) 11.3428 0.899543
\(160\) −1.21617 1.87641i −0.0961466 0.148344i
\(161\) −9.50811 + 9.50811i −0.749344 + 0.749344i
\(162\) 1.00000i 0.0785674i
\(163\) −7.74976 −0.607008 −0.303504 0.952830i \(-0.598157\pi\)
−0.303504 + 0.952830i \(0.598157\pi\)
\(164\) 2.43043i 0.189785i
\(165\) 2.64212 12.3757i 0.205689 0.963445i
\(166\) −0.906248 0.906248i −0.0703385 0.0703385i
\(167\) 19.2547 1.48997 0.744985 0.667081i \(-0.232457\pi\)
0.744985 + 0.667081i \(0.232457\pi\)
\(168\) 3.17868 0.245241
\(169\) −10.1797 −0.783053
\(170\) 9.22310 + 14.2302i 0.707379 + 1.09141i
\(171\) 3.73408 3.73408i 0.285552 0.285552i
\(172\) 3.34656i 0.255173i
\(173\) 8.58579 + 8.58579i 0.652765 + 0.652765i 0.953658 0.300893i \(-0.0972846\pi\)
−0.300893 + 0.953658i \(0.597285\pi\)
\(174\) 4.61737i 0.350042i
\(175\) −14.8480 + 5.66910i −1.12240 + 0.428544i
\(176\) 5.65930i 0.426585i
\(177\) 13.9261i 1.04675i
\(178\) −10.1878 10.1878i −0.763605 0.763605i
\(179\) −14.0961 + 14.0961i −1.05359 + 1.05359i −0.0551080 + 0.998480i \(0.517550\pi\)
−0.998480 + 0.0551080i \(0.982450\pi\)
\(180\) −1.21617 1.87641i −0.0906479 0.139860i
\(181\) 13.7831 1.02449 0.512245 0.858839i \(-0.328814\pi\)
0.512245 + 0.858839i \(0.328814\pi\)
\(182\) −10.8215 10.8215i −0.802140 0.802140i
\(183\) 1.58187i 0.116935i
\(184\) 4.23021 0.311855
\(185\) −2.44521 + 13.3799i −0.179775 + 0.983708i
\(186\) 2.81158 0.206155
\(187\) 42.9186i 3.13852i
\(188\) −6.04560 6.04560i −0.440921 0.440921i
\(189\) 3.17868 0.231215
\(190\) −2.46541 + 11.5480i −0.178860 + 0.837777i
\(191\) 18.4453 18.4453i 1.33466 1.33466i 0.433509 0.901149i \(-0.357275\pi\)
0.901149 0.433509i \(-0.142725\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 22.9897i 1.65484i 0.561585 + 0.827419i \(0.310192\pi\)
−0.561585 + 0.827419i \(0.689808\pi\)
\(194\) 2.87834i 0.206652i
\(195\) −2.24773 + 10.5284i −0.160963 + 0.753951i
\(196\) 3.10403i 0.221716i
\(197\) −1.69341 1.69341i −0.120650 0.120650i 0.644204 0.764854i \(-0.277189\pi\)
−0.764854 + 0.644204i \(0.777189\pi\)
\(198\) 5.65930i 0.402189i
\(199\) 7.33672 7.33672i 0.520087 0.520087i −0.397511 0.917597i \(-0.630126\pi\)
0.917597 + 0.397511i \(0.130126\pi\)
\(200\) 4.56408 + 2.04186i 0.322729 + 0.144382i
\(201\) 9.77458 0.689446
\(202\) 16.0893 1.13204
\(203\) −14.6772 −1.03014
\(204\) 5.36251 + 5.36251i 0.375451 + 0.375451i
\(205\) 2.95582 + 4.56050i 0.206443 + 0.318519i
\(206\) 11.0997i 0.773355i
\(207\) 4.23021 0.294020
\(208\) 4.81453i 0.333828i
\(209\) −21.1323 + 21.1323i −1.46175 + 1.46175i
\(210\) −5.96453 + 3.86582i −0.411592 + 0.266767i
\(211\) 11.9466 0.822435 0.411218 0.911537i \(-0.365104\pi\)
0.411218 + 0.911537i \(0.365104\pi\)
\(212\) −8.02058 + 8.02058i −0.550856 + 0.550856i
\(213\) −4.32811 4.32811i −0.296557 0.296557i
\(214\) 8.64549 8.64549i 0.590993 0.590993i
\(215\) 4.06999 + 6.27954i 0.277571 + 0.428261i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 8.93712i 0.606691i
\(218\) −13.7592 + 13.7592i −0.931894 + 0.931894i
\(219\) 3.65991i 0.247314i
\(220\) 6.88266 + 10.6192i 0.464029 + 0.715945i
\(221\) 36.5121i 2.45607i
\(222\) 0.179886 + 6.08010i 0.0120732 + 0.408070i
\(223\) 11.0520 11.0520i 0.740100 0.740100i −0.232497 0.972597i \(-0.574690\pi\)
0.972597 + 0.232497i \(0.0746896\pi\)
\(224\) −2.24767 + 2.24767i −0.150179 + 0.150179i
\(225\) 4.56408 + 2.04186i 0.304272 + 0.136124i
\(226\) 4.68689i 0.311768i
\(227\) −6.40168 −0.424894 −0.212447 0.977173i \(-0.568143\pi\)
−0.212447 + 0.977173i \(0.568143\pi\)
\(228\) 5.28079i 0.349729i
\(229\) 16.3225i 1.07862i 0.842107 + 0.539310i \(0.181315\pi\)
−0.842107 + 0.539310i \(0.818685\pi\)
\(230\) −7.93762 + 5.14465i −0.523391 + 0.339228i
\(231\) −17.9891 −1.18360
\(232\) 3.26498 + 3.26498i 0.214356 + 0.214356i
\(233\) 0.738837 + 0.738837i 0.0484028 + 0.0484028i 0.730894 0.682491i \(-0.239103\pi\)
−0.682491 + 0.730894i \(0.739103\pi\)
\(234\) 4.81453i 0.314736i
\(235\) 18.6965 + 3.99158i 1.21963 + 0.260382i
\(236\) 9.84721 + 9.84721i 0.640999 + 0.640999i
\(237\) 4.03499i 0.262101i
\(238\) 17.0457 17.0457i 1.10491 1.10491i
\(239\) 5.10981 + 5.10981i 0.330526 + 0.330526i 0.852786 0.522260i \(-0.174911\pi\)
−0.522260 + 0.852786i \(0.674911\pi\)
\(240\) 2.18679 + 0.466864i 0.141157 + 0.0301359i
\(241\) −8.22613 + 8.22613i −0.529892 + 0.529892i −0.920540 0.390648i \(-0.872251\pi\)
0.390648 + 0.920540i \(0.372251\pi\)
\(242\) 21.0276i 1.35171i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 1.11855 + 1.11855i 0.0716080 + 0.0716080i
\(245\) 3.77503 + 5.82445i 0.241178 + 0.372110i
\(246\) 1.71858 + 1.71858i 0.109572 + 0.109572i
\(247\) 17.9778 17.9778i 1.14390 1.14390i
\(248\) −1.98809 + 1.98809i −0.126244 + 0.126244i
\(249\) 1.28163 0.0812199
\(250\) −11.0474 + 1.71931i −0.698696 + 0.108739i
\(251\) −10.0396 10.0396i −0.633694 0.633694i 0.315299 0.948992i \(-0.397895\pi\)
−0.948992 + 0.315299i \(0.897895\pi\)
\(252\) −2.24767 + 2.24767i −0.141590 + 0.141590i
\(253\) −23.9400 −1.50509
\(254\) −14.6086 + 14.6086i −0.916626 + 0.916626i
\(255\) −16.5840 3.54057i −1.03853 0.221719i
\(256\) 1.00000 0.0625000
\(257\) 15.5767 0.971645 0.485823 0.874057i \(-0.338520\pi\)
0.485823 + 0.874057i \(0.338520\pi\)
\(258\) 2.36638 + 2.36638i 0.147324 + 0.147324i
\(259\) 19.3267 0.571801i 1.20090 0.0355300i
\(260\) −5.85528 9.03405i −0.363129 0.560268i
\(261\) 3.26498 + 3.26498i 0.202097 + 0.202097i
\(262\) 9.26219 9.26219i 0.572220 0.572220i
\(263\) 17.2063 + 17.2063i 1.06099 + 1.06099i 0.998015 + 0.0629697i \(0.0200571\pi\)
0.0629697 + 0.998015i \(0.479943\pi\)
\(264\) 4.00173 + 4.00173i 0.246289 + 0.246289i
\(265\) 5.29555 24.8043i 0.325303 1.52372i
\(266\) 16.7860 1.02921
\(267\) 14.4077 0.881735
\(268\) −6.91167 + 6.91167i −0.422198 + 0.422198i
\(269\) 16.7896i 1.02368i −0.859080 0.511841i \(-0.828964\pi\)
0.859080 0.511841i \(-0.171036\pi\)
\(270\) 2.18679 + 0.466864i 0.133084 + 0.0284124i
\(271\) −3.47058 −0.210823 −0.105411 0.994429i \(-0.533616\pi\)
−0.105411 + 0.994429i \(0.533616\pi\)
\(272\) −7.58373 −0.459831
\(273\) 15.3039 0.926232
\(274\) 1.63948 1.63948i 0.0990449 0.0990449i
\(275\) −25.8295 11.5555i −1.55757 0.696823i
\(276\) −2.99121 + 2.99121i −0.180050 + 0.180050i
\(277\) 5.08835i 0.305730i −0.988247 0.152865i \(-0.951150\pi\)
0.988247 0.152865i \(-0.0488499\pi\)
\(278\) 17.9432i 1.07616i
\(279\) −1.98809 + 1.98809i −0.119024 + 0.119024i
\(280\) 1.48401 6.95110i 0.0886867 0.415408i
\(281\) 22.3585 22.3585i 1.33380 1.33380i 0.431856 0.901943i \(-0.357859\pi\)
0.901943 0.431856i \(-0.142141\pi\)
\(282\) 8.54977 0.509131
\(283\) −4.97011 −0.295442 −0.147721 0.989029i \(-0.547194\pi\)
−0.147721 + 0.989029i \(0.547194\pi\)
\(284\) 6.12087 0.363207
\(285\) −6.42234 9.90895i −0.380426 0.586956i
\(286\) 27.2468i 1.61114i
\(287\) 5.46281 5.46281i 0.322459 0.322459i
\(288\) 1.00000 0.0589256
\(289\) 40.5129 2.38311
\(290\) −10.0972 2.15568i −0.592929 0.126586i
\(291\) −2.03529 2.03529i −0.119311 0.119311i
\(292\) 2.58794 + 2.58794i 0.151448 + 0.151448i
\(293\) −3.76385 + 3.76385i −0.219886 + 0.219886i −0.808450 0.588564i \(-0.799693\pi\)
0.588564 + 0.808450i \(0.299693\pi\)
\(294\) 2.19488 + 2.19488i 0.128008 + 0.128008i
\(295\) −30.4533 6.50157i −1.77306 0.378536i
\(296\) −4.42648 4.17208i −0.257284 0.242497i
\(297\) 4.00173 + 4.00173i 0.232204 + 0.232204i
\(298\) 9.20482 0.533221
\(299\) 20.3665 1.17782
\(300\) −4.67110 + 1.78347i −0.269686 + 0.102969i
\(301\) 7.52196 7.52196i 0.433559 0.433559i
\(302\) −5.59713 −0.322078
\(303\) −11.3769 + 11.3769i −0.653584 + 0.653584i
\(304\) −3.73408 3.73408i −0.214164 0.214164i
\(305\) −3.45922 0.738519i −0.198074 0.0422875i
\(306\) −7.58373 −0.433533
\(307\) −10.3413 + 10.3413i −0.590210 + 0.590210i −0.937688 0.347478i \(-0.887038\pi\)
0.347478 + 0.937688i \(0.387038\pi\)
\(308\) 12.7202 12.7202i 0.724802 0.724802i
\(309\) 7.84870 + 7.84870i 0.446497 + 0.446497i
\(310\) 1.31262 6.14832i 0.0745520 0.349201i
\(311\) 2.08224 + 2.08224i 0.118073 + 0.118073i 0.763675 0.645601i \(-0.223393\pi\)
−0.645601 + 0.763675i \(0.723393\pi\)
\(312\) −3.40439 3.40439i −0.192735 0.192735i
\(313\) 5.86237i 0.331361i 0.986179 + 0.165681i \(0.0529820\pi\)
−0.986179 + 0.165681i \(0.947018\pi\)
\(314\) −0.998661 + 0.998661i −0.0563577 + 0.0563577i
\(315\) 1.48401 6.95110i 0.0836146 0.391650i
\(316\) 2.85317 + 2.85317i 0.160503 + 0.160503i
\(317\) −3.30695 + 3.30695i −0.185737 + 0.185737i −0.793850 0.608113i \(-0.791927\pi\)
0.608113 + 0.793850i \(0.291927\pi\)
\(318\) 11.3428i 0.636073i
\(319\) −18.4775 18.4775i −1.03454 1.03454i
\(320\) −1.87641 + 1.21617i −0.104895 + 0.0679859i
\(321\) 12.2266i 0.682421i
\(322\) 9.50811 + 9.50811i 0.529866 + 0.529866i
\(323\) 28.3183 + 28.3183i 1.57567 + 1.57567i
\(324\) 1.00000 0.0555556
\(325\) 21.9739 + 9.83061i 1.21889 + 0.545304i
\(326\) 7.74976i 0.429220i
\(327\) 19.4585i 1.07606i
\(328\) −2.43043 −0.134198
\(329\) 27.1770i 1.49832i
\(330\) −12.3757 2.64212i −0.681258 0.145444i
\(331\) 2.03744 2.03744i 0.111988 0.111988i −0.648892 0.760880i \(-0.724768\pi\)
0.760880 + 0.648892i \(0.224768\pi\)
\(332\) −0.906248 + 0.906248i −0.0497368 + 0.0497368i
\(333\) −4.42648 4.17208i −0.242570 0.228629i
\(334\) 19.2547i 1.05357i
\(335\) 4.56340 21.3749i 0.249325 1.16784i
\(336\) 3.17868i 0.173411i
\(337\) 4.38679 4.38679i 0.238963 0.238963i −0.577457 0.816421i \(-0.695955\pi\)
0.816421 + 0.577457i \(0.195955\pi\)
\(338\) 10.1797i 0.553702i
\(339\) 3.31414 + 3.31414i 0.179999 + 0.179999i
\(340\) 14.2302 9.22310i 0.771742 0.500193i
\(341\) 11.2512 11.2512i 0.609285 0.609285i
\(342\) −3.73408 3.73408i −0.201916 0.201916i
\(343\) −8.75685 + 8.75685i −0.472826 + 0.472826i
\(344\) −3.34656 −0.180435
\(345\) 1.97493 9.25056i 0.106327 0.498034i
\(346\) 8.58579 8.58579i 0.461575 0.461575i
\(347\) 6.84918i 0.367683i 0.982956 + 0.183842i \(0.0588533\pi\)
−0.982956 + 0.183842i \(0.941147\pi\)
\(348\) −4.61737 −0.247517
\(349\) 11.3003i 0.604891i −0.953167 0.302445i \(-0.902197\pi\)
0.953167 0.302445i \(-0.0978030\pi\)
\(350\) 5.66910 + 14.8480i 0.303026 + 0.793657i
\(351\) −3.40439 3.40439i −0.181713 0.181713i
\(352\) −5.65930 −0.301641
\(353\) −21.3525 −1.13648 −0.568240 0.822863i \(-0.692375\pi\)
−0.568240 + 0.822863i \(0.692375\pi\)
\(354\) −13.9261 −0.740162
\(355\) −11.4853 + 7.44401i −0.609576 + 0.395087i
\(356\) −10.1878 + 10.1878i −0.539950 + 0.539950i
\(357\) 24.1063i 1.27584i
\(358\) 14.0961 + 14.0961i 0.745000 + 0.745000i
\(359\) 5.23042i 0.276051i 0.990429 + 0.138025i \(0.0440756\pi\)
−0.990429 + 0.138025i \(0.955924\pi\)
\(360\) −1.87641 + 1.21617i −0.0988957 + 0.0640978i
\(361\) 8.88674i 0.467723i
\(362\) 13.7831i 0.724424i
\(363\) −14.8688 14.8688i −0.780408 0.780408i
\(364\) −10.8215 + 10.8215i −0.567199 + 0.567199i
\(365\) −8.00344 1.70868i −0.418919 0.0894362i
\(366\) −1.58187 −0.0826858
\(367\) −0.560713 0.560713i −0.0292690 0.0292690i 0.692321 0.721590i \(-0.256588\pi\)
−0.721590 + 0.692321i \(0.756588\pi\)
\(368\) 4.23021i 0.220515i
\(369\) −2.43043 −0.126523
\(370\) 13.3799 + 2.44521i 0.695586 + 0.127120i
\(371\) −36.0552 −1.87189
\(372\) 2.81158i 0.145774i
\(373\) 3.16048 + 3.16048i 0.163643 + 0.163643i 0.784179 0.620535i \(-0.213085\pi\)
−0.620535 + 0.784179i \(0.713085\pi\)
\(374\) 42.9186 2.21927
\(375\) 6.59592 9.02739i 0.340612 0.466173i
\(376\) −6.04560 + 6.04560i −0.311778 + 0.311778i
\(377\) 15.7193 + 15.7193i 0.809586 + 0.809586i
\(378\) 3.17868i 0.163494i
\(379\) 1.59897i 0.0821335i 0.999156 + 0.0410667i \(0.0130756\pi\)
−0.999156 + 0.0410667i \(0.986924\pi\)
\(380\) 11.5480 + 2.46541i 0.592398 + 0.126473i
\(381\) 20.6597i 1.05843i
\(382\) −18.4453 18.4453i −0.943746 0.943746i
\(383\) 1.83857i 0.0939464i −0.998896 0.0469732i \(-0.985042\pi\)
0.998896 0.0469732i \(-0.0149575\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −8.39846 + 39.3384i −0.428025 + 2.00487i
\(386\) 22.9897 1.17015
\(387\) −3.34656 −0.170115
\(388\) 2.87834 0.146125
\(389\) −21.9756 21.9756i −1.11421 1.11421i −0.992575 0.121630i \(-0.961188\pi\)
−0.121630 0.992575i \(-0.538812\pi\)
\(390\) 10.5284 + 2.24773i 0.533124 + 0.113818i
\(391\) 32.0807i 1.62239i
\(392\) −3.10403 −0.156777
\(393\) 13.0987i 0.660743i
\(394\) −1.69341 + 1.69341i −0.0853126 + 0.0853126i
\(395\) −8.82367 1.88379i −0.443967 0.0947838i
\(396\) −5.65930 −0.284390
\(397\) −14.3901 + 14.3901i −0.722218 + 0.722218i −0.969057 0.246838i \(-0.920608\pi\)
0.246838 + 0.969057i \(0.420608\pi\)
\(398\) −7.33672 7.33672i −0.367757 0.367757i
\(399\) −11.8695 + 11.8695i −0.594217 + 0.594217i
\(400\) 2.04186 4.56408i 0.102093 0.228204i
\(401\) −1.56403 1.56403i −0.0781040 0.0781040i 0.666976 0.745080i \(-0.267589\pi\)
−0.745080 + 0.666976i \(0.767589\pi\)
\(402\) 9.77458i 0.487512i
\(403\) −9.57170 + 9.57170i −0.476800 + 0.476800i
\(404\) 16.0893i 0.800474i
\(405\) −1.87641 + 1.21617i −0.0932398 + 0.0604320i
\(406\) 14.6772i 0.728416i
\(407\) 25.0508 + 23.6110i 1.24172 + 1.17036i
\(408\) 5.36251 5.36251i 0.265484 0.265484i
\(409\) −6.64945 + 6.64945i −0.328794 + 0.328794i −0.852128 0.523334i \(-0.824688\pi\)
0.523334 + 0.852128i \(0.324688\pi\)
\(410\) 4.56050 2.95582i 0.225227 0.145978i
\(411\) 2.31858i 0.114367i
\(412\) −11.0997 −0.546845
\(413\) 44.2665i 2.17821i
\(414\) 4.23021i 0.207903i
\(415\) 0.598346 2.80265i 0.0293716 0.137577i
\(416\) 4.81453 0.236052
\(417\) 12.6877 + 12.6877i 0.621321 + 0.621321i
\(418\) 21.1323 + 21.1323i 1.03361 + 1.03361i
\(419\) 22.2951i 1.08919i −0.838701 0.544593i \(-0.816684\pi\)
0.838701 0.544593i \(-0.183316\pi\)
\(420\) 3.86582 + 5.96453i 0.188633 + 0.291039i
\(421\) −1.74485 1.74485i −0.0850387 0.0850387i 0.663308 0.748347i \(-0.269152\pi\)
−0.748347 + 0.663308i \(0.769152\pi\)
\(422\) 11.9466i 0.581549i
\(423\) −6.04560 + 6.04560i −0.293947 + 0.293947i
\(424\) 8.02058 + 8.02058i 0.389514 + 0.389514i
\(425\) −15.4849 + 34.6127i −0.751130 + 1.67896i
\(426\) −4.32811 + 4.32811i −0.209697 + 0.209697i
\(427\) 5.02827i 0.243335i
\(428\) −8.64549 8.64549i −0.417896 0.417896i
\(429\) 19.2664 + 19.2664i 0.930192 + 0.930192i
\(430\) 6.27954 4.06999i 0.302826 0.196272i
\(431\) −23.7856 23.7856i −1.14571 1.14571i −0.987387 0.158327i \(-0.949390\pi\)
−0.158327 0.987387i \(-0.550610\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −9.00285 + 9.00285i −0.432649 + 0.432649i −0.889529 0.456879i \(-0.848967\pi\)
0.456879 + 0.889529i \(0.348967\pi\)
\(434\) −8.93712 −0.428995
\(435\) 8.66411 5.61551i 0.415412 0.269243i
\(436\) 13.7592 + 13.7592i 0.658948 + 0.658948i
\(437\) −15.7959 + 15.7959i −0.755622 + 0.755622i
\(438\) −3.65991 −0.174877
\(439\) −4.79636 + 4.79636i −0.228918 + 0.228918i −0.812240 0.583323i \(-0.801752\pi\)
0.583323 + 0.812240i \(0.301752\pi\)
\(440\) 10.6192 6.88266i 0.506250 0.328118i
\(441\) −3.10403 −0.147811
\(442\) −36.5121 −1.73670
\(443\) 7.85980 + 7.85980i 0.373430 + 0.373430i 0.868725 0.495295i \(-0.164940\pi\)
−0.495295 + 0.868725i \(0.664940\pi\)
\(444\) 6.08010 0.179886i 0.288549 0.00853702i
\(445\) 6.72642 31.5065i 0.318863 1.49355i
\(446\) −11.0520 11.0520i −0.523330 0.523330i
\(447\) −6.50879 + 6.50879i −0.307855 + 0.307855i
\(448\) 2.24767 + 2.24767i 0.106192 + 0.106192i
\(449\) 16.4657 + 16.4657i 0.777066 + 0.777066i 0.979331 0.202265i \(-0.0648303\pi\)
−0.202265 + 0.979331i \(0.564830\pi\)
\(450\) 2.04186 4.56408i 0.0962543 0.215153i
\(451\) 13.7545 0.647676
\(452\) −4.68689 −0.220453
\(453\) 3.95777 3.95777i 0.185952 0.185952i
\(454\) 6.40168i 0.300446i
\(455\) 7.14482 33.4663i 0.334954 1.56892i
\(456\) 5.28079 0.247296
\(457\) −5.42876 −0.253947 −0.126973 0.991906i \(-0.540526\pi\)
−0.126973 + 0.991906i \(0.540526\pi\)
\(458\) 16.3225 0.762699
\(459\) 5.36251 5.36251i 0.250300 0.250300i
\(460\) 5.14465 + 7.93762i 0.239871 + 0.370094i
\(461\) 12.8604 12.8604i 0.598967 0.598967i −0.341071 0.940038i \(-0.610790\pi\)
0.940038 + 0.341071i \(0.110790\pi\)
\(462\) 17.9891i 0.836929i
\(463\) 36.1282i 1.67902i −0.543345 0.839509i \(-0.682843\pi\)
0.543345 0.839509i \(-0.317157\pi\)
\(464\) 3.26498 3.26498i 0.151573 0.151573i
\(465\) 3.41936 + 5.27569i 0.158569 + 0.244654i
\(466\) 0.738837 0.738837i 0.0342260 0.0342260i
\(467\) 4.96873 0.229925 0.114963 0.993370i \(-0.463325\pi\)
0.114963 + 0.993370i \(0.463325\pi\)
\(468\) 4.81453 0.222552
\(469\) −31.0703 −1.43469
\(470\) 3.99158 18.6965i 0.184118 0.862407i
\(471\) 1.41232i 0.0650763i
\(472\) 9.84721 9.84721i 0.453255 0.453255i
\(473\) 18.9392 0.870825
\(474\) −4.03499 −0.185333
\(475\) −24.6671 + 9.41815i −1.13181 + 0.432135i
\(476\) −17.0457 17.0457i −0.781289 0.781289i
\(477\) 8.02058 + 8.02058i 0.367237 + 0.367237i
\(478\) 5.10981 5.10981i 0.233717 0.233717i
\(479\) −21.0873 21.0873i −0.963504 0.963504i 0.0358527 0.999357i \(-0.488585\pi\)
−0.999357 + 0.0358527i \(0.988585\pi\)
\(480\) 0.466864 2.18679i 0.0213093 0.0998127i
\(481\) −21.3114 20.0866i −0.971717 0.915871i
\(482\) 8.22613 + 8.22613i 0.374690 + 0.374690i
\(483\) −13.4465 −0.611837
\(484\) 21.0276 0.955801
\(485\) −5.40095 + 3.50054i −0.245245 + 0.158952i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) −10.6041 −0.480519 −0.240259 0.970709i \(-0.577233\pi\)
−0.240259 + 0.970709i \(0.577233\pi\)
\(488\) 1.11855 1.11855i 0.0506345 0.0506345i
\(489\) −5.47991 5.47991i −0.247810 0.247810i
\(490\) 5.82445 3.77503i 0.263122 0.170538i
\(491\) 2.33716 0.105475 0.0527373 0.998608i \(-0.483205\pi\)
0.0527373 + 0.998608i \(0.483205\pi\)
\(492\) 1.71858 1.71858i 0.0774794 0.0774794i
\(493\) −24.7607 + 24.7607i −1.11517 + 1.11517i
\(494\) −17.9778 17.9778i −0.808862 0.808862i
\(495\) 10.6192 6.88266i 0.477297 0.309353i
\(496\) 1.98809 + 1.98809i 0.0892677 + 0.0892677i
\(497\) 13.7577 + 13.7577i 0.617116 + 0.617116i
\(498\) 1.28163i 0.0574312i
\(499\) 15.9396 15.9396i 0.713555 0.713555i −0.253723 0.967277i \(-0.581655\pi\)
0.967277 + 0.253723i \(0.0816550\pi\)
\(500\) 1.71931 + 11.0474i 0.0768899 + 0.494053i
\(501\) 13.6151 + 13.6151i 0.608278 + 0.608278i
\(502\) −10.0396 + 10.0396i −0.448089 + 0.448089i
\(503\) 18.1285i 0.808309i −0.914691 0.404155i \(-0.867566\pi\)
0.914691 0.404155i \(-0.132434\pi\)
\(504\) 2.24767 + 2.24767i 0.100119 + 0.100119i
\(505\) 19.5674 + 30.1903i 0.870736 + 1.34345i
\(506\) 23.9400i 1.06426i
\(507\) −7.19813 7.19813i −0.319680 0.319680i
\(508\) 14.6086 + 14.6086i 0.648152 + 0.648152i
\(509\) −14.6649 −0.650010 −0.325005 0.945712i \(-0.605366\pi\)
−0.325005 + 0.945712i \(0.605366\pi\)
\(510\) −3.54057 + 16.5840i −0.156779 + 0.734352i
\(511\) 11.6337i 0.514644i
\(512\) 1.00000i 0.0441942i
\(513\) 5.28079 0.233153
\(514\) 15.5767i 0.687057i
\(515\) 20.8277 13.4992i 0.917778 0.594844i
\(516\) 2.36638 2.36638i 0.104174 0.104174i
\(517\) 34.2138 34.2138i 1.50472 1.50472i
\(518\) −0.571801 19.3267i −0.0251235 0.849167i
\(519\) 12.1421i 0.532981i
\(520\) −9.03405 + 5.85528i −0.396169 + 0.256771i
\(521\) 13.9917i 0.612988i 0.951873 + 0.306494i \(0.0991560\pi\)
−0.951873 + 0.306494i \(0.900844\pi\)
\(522\) 3.26498 3.26498i 0.142904 0.142904i
\(523\) 16.6140i 0.726479i −0.931696 0.363239i \(-0.881671\pi\)
0.931696 0.363239i \(-0.118329\pi\)
\(524\) −9.26219 9.26219i −0.404621 0.404621i
\(525\) −14.5078 6.49044i −0.633170 0.283266i
\(526\) 17.2063 17.2063i 0.750230 0.750230i
\(527\) −15.0771 15.0771i −0.656769 0.656769i
\(528\) 4.00173 4.00173i 0.174153 0.174153i
\(529\) 5.10534 0.221971
\(530\) −24.8043 5.29555i −1.07743 0.230024i
\(531\) 9.84721 9.84721i 0.427332 0.427332i
\(532\) 16.7860i 0.727764i
\(533\) −11.7014 −0.506844
\(534\) 14.4077i 0.623481i
\(535\) 26.7369 + 5.70814i 1.15594 + 0.246784i
\(536\) 6.91167 + 6.91167i 0.298539 + 0.298539i
\(537\) −19.9348 −0.860251
\(538\) −16.7896 −0.723853
\(539\) 17.5666 0.756648
\(540\) 0.466864 2.18679i 0.0200906 0.0941043i
\(541\) −15.0297 + 15.0297i −0.646177 + 0.646177i −0.952067 0.305890i \(-0.901046\pi\)
0.305890 + 0.952067i \(0.401046\pi\)
\(542\) 3.47058i 0.149074i
\(543\) 9.74613 + 9.74613i 0.418246 + 0.418246i
\(544\) 7.58373i 0.325150i
\(545\) −42.5516 9.08447i −1.82271 0.389136i
\(546\) 15.3039i 0.654945i
\(547\) 1.60901i 0.0687964i −0.999408 0.0343982i \(-0.989049\pi\)
0.999408 0.0343982i \(-0.0109514\pi\)
\(548\) −1.63948 1.63948i −0.0700353 0.0700353i
\(549\) 1.11855 1.11855i 0.0477387 0.0477387i
\(550\) −11.5555 + 25.8295i −0.492728 + 1.10137i
\(551\) −24.3834 −1.03877
\(552\) 2.99121 + 2.99121i 0.127314 + 0.127314i
\(553\) 12.8260i 0.545416i
\(554\) −5.08835 −0.216183
\(555\) −11.1900 + 7.73198i −0.474990 + 0.328204i
\(556\) −17.9432 −0.760959
\(557\) 13.8846i 0.588309i −0.955758 0.294155i \(-0.904962\pi\)
0.955758 0.294155i \(-0.0950381\pi\)
\(558\) 1.98809 + 1.98809i 0.0841624 + 0.0841624i
\(559\) −16.1121 −0.681470
\(560\) −6.95110 1.48401i −0.293738 0.0627109i
\(561\) −30.3480 + 30.3480i −1.28129 + 1.28129i
\(562\) −22.3585 22.3585i −0.943138 0.943138i
\(563\) 36.2994i 1.52984i 0.644126 + 0.764919i \(0.277221\pi\)
−0.644126 + 0.764919i \(0.722779\pi\)
\(564\) 8.54977i 0.360010i
\(565\) 8.79456 5.70006i 0.369990 0.239803i
\(566\) 4.97011i 0.208909i
\(567\) 2.24767 + 2.24767i 0.0943932 + 0.0943932i
\(568\) 6.12087i 0.256826i
\(569\) −4.09043 + 4.09043i −0.171480 + 0.171480i −0.787629 0.616149i \(-0.788692\pi\)
0.616149 + 0.787629i \(0.288692\pi\)
\(570\) −9.90895 + 6.42234i −0.415040 + 0.269002i
\(571\) 9.17017 0.383760 0.191880 0.981418i \(-0.438542\pi\)
0.191880 + 0.981418i \(0.438542\pi\)
\(572\) −27.2468 −1.13925
\(573\) 26.0857 1.08974
\(574\) −5.46281 5.46281i −0.228013 0.228013i
\(575\) −19.3070 8.63750i −0.805157 0.360209i
\(576\) 1.00000i 0.0416667i
\(577\) −35.0406 −1.45876 −0.729381 0.684108i \(-0.760192\pi\)
−0.729381 + 0.684108i \(0.760192\pi\)
\(578\) 40.5129i 1.68512i
\(579\) −16.2562 + 16.2562i −0.675585 + 0.675585i
\(580\) −2.15568 + 10.0972i −0.0895099 + 0.419264i
\(581\) −4.07389 −0.169014
\(582\) −2.03529 + 2.03529i −0.0843655 + 0.0843655i
\(583\) −45.3908 45.3908i −1.87990 1.87990i
\(584\) 2.58794 2.58794i 0.107090 0.107090i
\(585\) −9.03405 + 5.85528i −0.373512 + 0.242086i
\(586\) 3.76385 + 3.76385i 0.155483 + 0.155483i
\(587\) 33.5312i 1.38398i 0.721907 + 0.691990i \(0.243266\pi\)
−0.721907 + 0.691990i \(0.756734\pi\)
\(588\) 2.19488 2.19488i 0.0905153 0.0905153i
\(589\) 14.8474i 0.611775i
\(590\) −6.50157 + 30.4533i −0.267665 + 1.25374i
\(591\) 2.39484i 0.0985106i
\(592\) −4.17208 + 4.42648i −0.171472 + 0.181927i
\(593\) 1.10793 1.10793i 0.0454971 0.0454971i −0.683992 0.729489i \(-0.739758\pi\)
0.729489 + 0.683992i \(0.239758\pi\)
\(594\) 4.00173 4.00173i 0.164193 0.164193i
\(595\) 52.7153 + 11.2543i 2.16112 + 0.461383i
\(596\) 9.20482i 0.377044i
\(597\) 10.3757 0.424649
\(598\) 20.3665i 0.832846i
\(599\) 0.823976i 0.0336668i −0.999858 0.0168334i \(-0.994642\pi\)
0.999858 0.0168334i \(-0.00535848\pi\)
\(600\) 1.78347 + 4.67110i 0.0728100 + 0.190697i
\(601\) 7.88760 0.321742 0.160871 0.986975i \(-0.448570\pi\)
0.160871 + 0.986975i \(0.448570\pi\)
\(602\) −7.52196 7.52196i −0.306572 0.306572i
\(603\) 6.91167 + 6.91167i 0.281465 + 0.281465i
\(604\) 5.59713i 0.227744i
\(605\) −39.4565 + 25.5732i −1.60414 + 1.03970i
\(606\) 11.3769 + 11.3769i 0.462154 + 0.462154i
\(607\) 1.34105i 0.0544316i 0.999630 + 0.0272158i \(0.00866413\pi\)
−0.999630 + 0.0272158i \(0.991336\pi\)
\(608\) −3.73408 + 3.73408i −0.151437 + 0.151437i
\(609\) −10.3783 10.3783i −0.420551 0.420551i
\(610\) −0.738519 + 3.45922i −0.0299018 + 0.140060i
\(611\) −29.1067 + 29.1067i −1.17753 + 1.17753i
\(612\) 7.58373i 0.306554i
\(613\) 3.50859 + 3.50859i 0.141711 + 0.141711i 0.774403 0.632693i \(-0.218050\pi\)
−0.632693 + 0.774403i \(0.718050\pi\)
\(614\) 10.3413 + 10.3413i 0.417342 + 0.417342i
\(615\) −1.13468 + 5.31484i −0.0457548 + 0.214315i
\(616\) −12.7202 12.7202i −0.512512 0.512512i
\(617\) 1.91217 1.91217i 0.0769810 0.0769810i −0.667568 0.744549i \(-0.732665\pi\)
0.744549 + 0.667568i \(0.232665\pi\)
\(618\) 7.84870 7.84870i 0.315721 0.315721i
\(619\) 19.7786 0.794968 0.397484 0.917609i \(-0.369883\pi\)
0.397484 + 0.917609i \(0.369883\pi\)
\(620\) −6.14832 1.31262i −0.246923 0.0527162i
\(621\) 2.99121 + 2.99121i 0.120033 + 0.120033i
\(622\) 2.08224 2.08224i 0.0834904 0.0834904i
\(623\) −45.7974 −1.83484
\(624\) −3.40439 + 3.40439i −0.136285 + 0.136285i
\(625\) −16.6616 18.6384i −0.666464 0.745538i
\(626\) 5.86237 0.234308
\(627\) −29.8855 −1.19351
\(628\) 0.998661 + 0.998661i 0.0398509 + 0.0398509i
\(629\) 31.6399 33.5692i 1.26157 1.33849i
\(630\) −6.95110 1.48401i −0.276939 0.0591244i
\(631\) −2.64808 2.64808i −0.105418 0.105418i 0.652430 0.757849i \(-0.273749\pi\)
−0.757849 + 0.652430i \(0.773749\pi\)
\(632\) 2.85317 2.85317i 0.113493 0.113493i
\(633\) 8.44749 + 8.44749i 0.335758 + 0.335758i
\(634\) 3.30695 + 3.30695i 0.131336 + 0.131336i
\(635\) −45.1783 9.64526i −1.79285 0.382760i
\(636\) −11.3428 −0.449772
\(637\) −14.9444 −0.592120
\(638\) −18.4775 + 18.4775i −0.731530 + 0.731530i
\(639\) 6.12087i 0.242138i
\(640\) 1.21617 + 1.87641i 0.0480733 + 0.0741718i
\(641\) −25.9245 −1.02395 −0.511977 0.858999i \(-0.671087\pi\)
−0.511977 + 0.858999i \(0.671087\pi\)
\(642\) 12.2266 0.482544
\(643\) −6.75346 −0.266331 −0.133165 0.991094i \(-0.542514\pi\)
−0.133165 + 0.991094i \(0.542514\pi\)
\(644\) 9.50811 9.50811i 0.374672 0.374672i
\(645\) −1.56239 + 7.31822i −0.0615190 + 0.288155i
\(646\) 28.3183 28.3183i 1.11417 1.11417i
\(647\) 17.0199i 0.669122i 0.942374 + 0.334561i \(0.108588\pi\)
−0.942374 + 0.334561i \(0.891412\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −55.7283 + 55.7283i −2.18753 + 2.18753i
\(650\) 9.83061 21.9739i 0.385588 0.861886i
\(651\) 6.31950 6.31950i 0.247681 0.247681i
\(652\) 7.74976 0.303504
\(653\) 2.21356 0.0866234 0.0433117 0.999062i \(-0.486209\pi\)
0.0433117 + 0.999062i \(0.486209\pi\)
\(654\) −19.4585 −0.760888
\(655\) 28.6441 + 6.11531i 1.11922 + 0.238945i
\(656\) 2.43043i 0.0948925i
\(657\) 2.58794 2.58794i 0.100965 0.100965i
\(658\) −27.1770 −1.05947
\(659\) −10.5454 −0.410790 −0.205395 0.978679i \(-0.565848\pi\)
−0.205395 + 0.978679i \(0.565848\pi\)
\(660\) −2.64212 + 12.3757i −0.102844 + 0.481722i
\(661\) 26.5280 + 26.5280i 1.03182 + 1.03182i 0.999477 + 0.0323414i \(0.0102964\pi\)
0.0323414 + 0.999477i \(0.489704\pi\)
\(662\) −2.03744 2.03744i −0.0791872 0.0791872i
\(663\) 25.8179 25.8179i 1.00269 1.00269i
\(664\) 0.906248 + 0.906248i 0.0351693 + 0.0351693i
\(665\) 20.4146 + 31.4974i 0.791643 + 1.22142i
\(666\) −4.17208 + 4.42648i −0.161665 + 0.171523i
\(667\) −13.8115 13.8115i −0.534784 0.534784i
\(668\) −19.2547 −0.744985
\(669\) 15.6300 0.604289
\(670\) −21.3749 4.56340i −0.825786 0.176299i
\(671\) −6.33022 + 6.33022i −0.244375 + 0.244375i
\(672\) −3.17868 −0.122620
\(673\) −18.5100 + 18.5100i −0.713507 + 0.713507i −0.967267 0.253760i \(-0.918333\pi\)
0.253760 + 0.967267i \(0.418333\pi\)
\(674\) −4.38679 4.38679i −0.168973 0.168973i
\(675\) 1.78347 + 4.67110i 0.0686460 + 0.179791i
\(676\) 10.1797 0.391527
\(677\) 19.4458 19.4458i 0.747364 0.747364i −0.226620 0.973983i \(-0.572767\pi\)
0.973983 + 0.226620i \(0.0727674\pi\)
\(678\) 3.31414 3.31414i 0.127279 0.127279i
\(679\) 6.46955 + 6.46955i 0.248278 + 0.248278i
\(680\) −9.22310 14.2302i −0.353690 0.545704i
\(681\) −4.52667 4.52667i −0.173462 0.173462i
\(682\) −11.2512 11.2512i −0.430830 0.430830i
\(683\) 45.5661i 1.74354i −0.489916 0.871770i \(-0.662972\pi\)
0.489916 0.871770i \(-0.337028\pi\)
\(684\) −3.73408 + 3.73408i −0.142776 + 0.142776i
\(685\) 5.07024 + 1.08246i 0.193724 + 0.0413587i
\(686\) 8.75685 + 8.75685i 0.334338 + 0.334338i
\(687\) −11.5417 + 11.5417i −0.440345 + 0.440345i
\(688\) 3.34656i 0.127587i
\(689\) 38.6153 + 38.6153i 1.47113 + 1.47113i
\(690\) −9.25056 1.97493i −0.352163 0.0751843i
\(691\) 14.6674i 0.557973i −0.960295 0.278986i \(-0.910002\pi\)
0.960295 0.278986i \(-0.0899984\pi\)
\(692\) −8.58579 8.58579i −0.326383 0.326383i
\(693\) −12.7202 12.7202i −0.483201 0.483201i
\(694\) 6.84918 0.259991
\(695\) 33.6688 21.8219i 1.27713 0.827753i
\(696\) 4.61737i 0.175021i
\(697\) 18.4317i 0.698152i
\(698\) −11.3003 −0.427722
\(699\) 1.04487i 0.0395207i
\(700\) 14.8480 5.66910i 0.561200 0.214272i
\(701\) −2.72887 + 2.72887i −0.103068 + 0.103068i −0.756760 0.653692i \(-0.773219\pi\)
0.653692 + 0.756760i \(0.273219\pi\)
\(702\) −3.40439 + 3.40439i −0.128490 + 0.128490i
\(703\) 32.1077 0.949941i 1.21097 0.0358277i
\(704\) 5.65930i 0.213293i
\(705\) 10.3980 + 16.0429i 0.391610 + 0.604211i
\(706\) 21.3525i 0.803612i
\(707\) 36.1635 36.1635i 1.36007 1.36007i
\(708\) 13.9261i 0.523373i
\(709\) −1.20334 1.20334i −0.0451926 0.0451926i 0.684149 0.729342i \(-0.260174\pi\)
−0.729342 + 0.684149i \(0.760174\pi\)
\(710\) 7.44401 + 11.4853i 0.279369 + 0.431035i
\(711\) 2.85317 2.85317i 0.107002 0.107002i
\(712\) 10.1878 + 10.1878i 0.381803 + 0.381803i
\(713\) 8.41002 8.41002i 0.314958 0.314958i
\(714\) 24.1063 0.902155
\(715\) 51.1264 33.1368i 1.91202 1.23925i
\(716\) 14.0961 14.0961i 0.526794 0.526794i
\(717\) 7.22636i 0.269873i
\(718\) 5.23042 0.195197
\(719\) 34.8068i 1.29807i 0.760757 + 0.649037i \(0.224828\pi\)
−0.760757 + 0.649037i \(0.775172\pi\)
\(720\) 1.21617 + 1.87641i 0.0453240 + 0.0699298i
\(721\) −24.9485 24.9485i −0.929131 0.929131i
\(722\) 8.88674 0.330730
\(723\) −11.6335 −0.432655
\(724\) −13.7831 −0.512245
\(725\) −8.23497 21.5682i −0.305839 0.801024i
\(726\) −14.8688 + 14.8688i −0.551832 + 0.551832i
\(727\) 29.0229i 1.07640i −0.842817 0.538200i \(-0.819105\pi\)
0.842817 0.538200i \(-0.180895\pi\)
\(728\) 10.8215 + 10.8215i 0.401070 + 0.401070i
\(729\) 1.00000i 0.0370370i
\(730\) −1.70868 + 8.00344i −0.0632410 + 0.296220i
\(731\) 25.3794i 0.938692i
\(732\) 1.58187i 0.0584677i
\(733\) −6.55654 6.55654i −0.242171 0.242171i 0.575577 0.817748i \(-0.304778\pi\)
−0.817748 + 0.575577i \(0.804778\pi\)
\(734\) −0.560713 + 0.560713i −0.0206963 + 0.0206963i
\(735\) −1.44916 + 6.78785i −0.0534530 + 0.250374i
\(736\) −4.23021 −0.155928
\(737\) −39.1152 39.1152i −1.44083 1.44083i
\(738\) 2.43043i 0.0894655i
\(739\) −3.57785 −0.131613 −0.0658067 0.997832i \(-0.520962\pi\)
−0.0658067 + 0.997832i \(0.520962\pi\)
\(740\) 2.44521 13.3799i 0.0898876 0.491854i
\(741\) 25.4245 0.933993
\(742\) 36.0552i 1.32363i
\(743\) −29.2655 29.2655i −1.07365 1.07365i −0.997063 0.0765832i \(-0.975599\pi\)
−0.0765832 0.997063i \(-0.524401\pi\)
\(744\) −2.81158 −0.103077
\(745\) 11.1946 + 17.2720i 0.410139 + 0.632799i
\(746\) 3.16048 3.16048i 0.115713 0.115713i
\(747\) 0.906248 + 0.906248i 0.0331579 + 0.0331579i
\(748\) 42.9186i 1.56926i
\(749\) 38.8644i 1.42007i
\(750\) −9.02739 6.59592i −0.329634 0.240849i
\(751\) 17.5101i 0.638951i 0.947595 + 0.319476i \(0.103507\pi\)
−0.947595 + 0.319476i \(0.896493\pi\)
\(752\) 6.04560 + 6.04560i 0.220460 + 0.220460i
\(753\) 14.1981i 0.517409i
\(754\) 15.7193 15.7193i 0.572464 0.572464i
\(755\) −6.80705 10.5025i −0.247734 0.382226i
\(756\) −3.17868 −0.115608
\(757\) −15.4393 −0.561153 −0.280576 0.959832i \(-0.590526\pi\)
−0.280576 + 0.959832i \(0.590526\pi\)
\(758\) 1.59897 0.0580771
\(759\) −16.9281 16.9281i −0.614452 0.614452i
\(760\) 2.46541 11.5480i 0.0894298 0.418889i
\(761\) 19.6274i 0.711492i 0.934583 + 0.355746i \(0.115773\pi\)
−0.934583 + 0.355746i \(0.884227\pi\)
\(762\) −20.6597 −0.748422
\(763\) 61.8524i 2.23921i
\(764\) −18.4453 + 18.4453i −0.667329 + 0.667329i
\(765\) −9.22310 14.2302i −0.333462 0.514495i
\(766\) −1.83857 −0.0664301
\(767\) 47.4097 47.4097i 1.71186 1.71186i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 38.3252 38.3252i 1.38204 1.38204i 0.541058 0.840985i \(-0.318024\pi\)
0.840985 0.541058i \(-0.181976\pi\)
\(770\) 39.3384 + 8.39846i 1.41766 + 0.302660i
\(771\) 11.0144 + 11.0144i 0.396672 + 0.396672i
\(772\) 22.9897i 0.827419i
\(773\) 13.6080 13.6080i 0.489445 0.489445i −0.418686 0.908131i \(-0.637509\pi\)
0.908131 + 0.418686i \(0.137509\pi\)
\(774\) 3.34656i 0.120290i
\(775\) 13.1332 5.01438i 0.471758 0.180122i
\(776\) 2.87834i 0.103326i
\(777\) 14.0704 + 13.2617i 0.504772 + 0.475762i
\(778\) −21.9756 + 21.9756i −0.787862 + 0.787862i
\(779\) 9.07544 9.07544i 0.325161 0.325161i
\(780\) 2.24773 10.5284i