Properties

Label 1110.2.o.a.253.9
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 253.9
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.9

$q$-expansion

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

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) 1.21617 1.87641i 0.543888 0.839158i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −2.24767 + 2.24767i −0.849539 + 0.849539i −0.990075 0.140537i \(-0.955117\pi\)
0.140537 + 0.990075i \(0.455117\pi\)
\(8\) −1.00000 −0.353553
\(9\) 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
\(13\) −4.81453 −1.33531 −0.667655 0.744471i \(-0.732702\pi\)
−0.667655 + 0.744471i \(0.732702\pi\)
\(14\) 2.24767 2.24767i 0.600715 0.600715i
\(15\) 0.466864 + 2.18679i 0.120544 + 0.564626i
\(16\) 1.00000 0.250000
\(17\) 7.58373i 1.83932i 0.392710 + 0.919662i \(0.371537\pi\)
−0.392710 + 0.919662i \(0.628463\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.73408 + 3.73408i 0.856657 + 0.856657i 0.990943 0.134285i \(-0.0428739\pi\)
−0.134285 + 0.990943i \(0.542874\pi\)
\(20\) 1.21617 1.87641i 0.271944 0.419579i
\(21\) 3.17868i 0.693646i
\(22\) 5.65930i 1.20657i
\(23\) 4.23021 0.882059 0.441030 0.897493i \(-0.354613\pi\)
0.441030 + 0.897493i \(0.354613\pi\)
\(24\) 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 −0.941975 0.335684i \(-0.891033\pi\)
0.335684 + 0.941975i \(0.391033\pi\)
\(30\) −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 \(0.668751\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.00173 + 4.00173i 0.696611 + 0.696611i
\(34\) 7.58373i 1.30060i
\(35\) 1.48401 + 6.95110i 0.250844 + 1.17495i
\(36\) 1.00000i 0.166667i
\(37\) 4.42648 + 4.17208i 0.727709 + 0.685886i
\(38\) −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 \(0.939221\pi\)
\(42\) 3.17868i 0.490482i
\(43\) −3.34656 −0.510346 −0.255173 0.966895i \(-0.582132\pi\)
−0.255173 + 0.966895i \(0.582132\pi\)
\(44\) 5.65930i 0.853171i
\(45\) −1.87641 1.21617i −0.279719 0.181296i
\(46\) −4.23021 −0.623710
\(47\) 6.04560 6.04560i 0.881842 0.881842i −0.111880 0.993722i \(-0.535687\pi\)
0.993722 + 0.111880i \(0.0356873\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 3.10403i 0.443433i
\(50\) 2.04186 + 4.56408i 0.288763 + 0.645458i
\(51\) −5.36251 5.36251i −0.750901 0.750901i
\(52\) −4.81453 −0.667655
\(53\) 8.02058 + 8.02058i 1.10171 + 1.10171i 0.994204 + 0.107507i \(0.0342868\pi\)
0.107507 + 0.994204i \(0.465713\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −10.6192 6.88266i −1.43189 0.928058i
\(56\) 2.24767 2.24767i 0.300357 0.300357i
\(57\) −5.28079 −0.699458
\(58\) 3.26498 3.26498i 0.428712 0.428712i
\(59\) 9.84721 + 9.84721i 1.28200 + 1.28200i 0.939530 + 0.342468i \(0.111263\pi\)
0.342468 + 0.939530i \(0.388737\pi\)
\(60\) 0.466864 + 2.18679i 0.0602718 + 0.282313i
\(61\) −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 \(-0.453672\pi\)
−0.989427 + 0.145032i \(0.953672\pi\)
\(68\) 7.58373i 0.919662i
\(69\) −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 \(0.618318\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 2.58794 2.58794i 0.302896 0.302896i −0.539250 0.842146i \(-0.681292\pi\)
0.842146 + 0.539250i \(0.181292\pi\)
\(74\) −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 0.849153 0.528146i \(-0.177113\pi\)
−0.528146 + 0.849153i \(0.677113\pi\)
\(80\) 1.21617 1.87641i 0.135972 0.209790i
\(81\) −1.00000 −0.111111
\(82\) 2.43043i 0.268396i
\(83\) 0.906248 + 0.906248i 0.0994737 + 0.0994737i 0.755092 0.655619i \(-0.227592\pi\)
−0.655619 + 0.755092i \(0.727592\pi\)
\(84\) 3.17868i 0.346823i
\(85\) 14.2302 + 9.22310i 1.54348 + 1.00039i
\(86\) 3.34656 0.360869
\(87\) 4.61737i 0.495034i
\(88\) 5.65930i 0.603283i
\(89\) −10.1878 + 10.1878i −1.07990 + 1.07990i −0.0833830 + 0.996518i \(0.526572\pi\)
−0.996518 + 0.0833830i \(0.973428\pi\)
\(90\) 1.87641 + 1.21617i 0.197791 + 0.128196i
\(91\) 10.8215 10.8215i 1.13440 1.13440i
\(92\) 4.23021 0.441030
\(93\) −2.81158 −0.291547
\(94\) −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
\(97\) 2.87834i 0.292251i 0.989266 + 0.146125i \(0.0466803\pi\)
−0.989266 + 0.146125i \(0.953320\pi\)
\(98\) 3.10403i 0.313554i
\(99\) −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
\(103\) 11.0997i 1.09369i 0.837234 + 0.546845i \(0.184171\pi\)
−0.837234 + 0.546845i \(0.815829\pi\)
\(104\) 4.81453 0.472103
\(105\) −5.96453 3.86582i −0.582078 0.377265i
\(106\) −8.02058 8.02058i −0.779028 0.779028i
\(107\) 8.64549 8.64549i 0.835791 0.835791i −0.152511 0.988302i \(-0.548736\pi\)
0.988302 + 0.152511i \(0.0487359\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 13.7592 + 13.7592i 1.31790 + 1.31790i 0.915438 + 0.402458i \(0.131844\pi\)
0.402458 + 0.915438i \(0.368156\pi\)
\(110\) 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
\(113\) 4.68689i 0.440906i 0.975398 + 0.220453i \(0.0707536\pi\)
−0.975398 + 0.220453i \(0.929246\pi\)
\(114\) 5.28079 0.494591
\(115\) 5.14465 7.93762i 0.479741 0.740187i
\(116\) −3.26498 + 3.26498i −0.303145 + 0.303145i
\(117\) 4.81453i 0.445103i
\(118\) −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
\(125\) −11.0474 1.71931i −0.988105 0.153780i
\(126\) −2.24767 2.24767i −0.200238 0.200238i
\(127\) −14.6086 + 14.6086i −1.29630 + 1.29630i −0.365488 + 0.930816i \(0.619098\pi\)
−0.930816 + 0.365488i \(0.880902\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.36638 2.36638i 0.208348 0.208348i
\(130\) 5.85528 9.03405i 0.513542 0.792339i
\(131\) 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
\(133\) −16.7860 −1.45553
\(134\) 6.91167 + 6.91167i 0.597078 + 0.597078i
\(135\) 2.18679 0.466864i 0.188209 0.0401812i
\(136\) 7.58373i 0.650299i
\(137\) 1.63948 1.63948i 0.140071 0.140071i −0.633595 0.773665i \(-0.718421\pi\)
0.773665 + 0.633595i \(0.218421\pi\)
\(138\) 2.99121 2.99121i 0.254629 0.254629i
\(139\) −17.9432 −1.52192 −0.760959 0.648800i \(-0.775271\pi\)
−0.760959 + 0.648800i \(0.775271\pi\)
\(140\) 1.48401 + 6.95110i 0.125422 + 0.587476i
\(141\) 8.54977i 0.720021i
\(142\) 6.12087 0.513652
\(143\) 27.2468i 2.27850i
\(144\) 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
\(148\) 4.42648 + 4.17208i 0.363854 + 0.342943i
\(149\) 9.20482i 0.754088i −0.926195 0.377044i \(-0.876941\pi\)
0.926195 0.377044i \(-0.123059\pi\)
\(150\) −4.67110 1.78347i −0.381394 0.145620i
\(151\) 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
\(153\) 7.58373 0.613108
\(154\) −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 −0.745834 0.666132i \(-0.767949\pi\)
0.666132 + 0.745834i \(0.267949\pi\)
\(158\) −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
\(162\) 1.00000 0.0785674
\(163\) 7.74976i 0.607008i −0.952830 0.303504i \(-0.901843\pi\)
0.952830 0.303504i \(-0.0981566\pi\)
\(164\) 2.43043i 0.189785i
\(165\) 12.3757 2.64212i 0.963445 0.205689i
\(166\) −0.906248 0.906248i −0.0703385 0.0703385i
\(167\) 19.2547i 1.48997i −0.667081 0.744985i \(-0.732457\pi\)
0.667081 0.744985i \(-0.267543\pi\)
\(168\) 3.17868i 0.245241i
\(169\) 10.1797 0.783053
\(170\) −14.2302 9.22310i −1.09141 0.707379i
\(171\) 3.73408 3.73408i 0.285552 0.285552i
\(172\) −3.34656 −0.255173
\(173\) −8.58579 + 8.58579i −0.652765 + 0.652765i −0.953658 0.300893i \(-0.902715\pi\)
0.300893 + 0.953658i \(0.402715\pi\)
\(174\) 4.61737i 0.350042i
\(175\) 14.8480 + 5.66910i 1.12240 + 0.428544i
\(176\) 5.65930i 0.426585i
\(177\) −13.9261 −1.04675
\(178\) 10.1878 10.1878i 0.763605 0.763605i
\(179\) 14.0961 14.0961i 1.05359 1.05359i 0.0551080 0.998480i \(-0.482450\pi\)
0.998480 0.0551080i \(-0.0175503\pi\)
\(180\) −1.87641 1.21617i −0.139860 0.0906479i
\(181\) 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
\(183\) 1.58187 0.116935
\(184\) −4.23021 −0.311855
\(185\) 13.2119 3.23195i 0.971359 0.237618i
\(186\) 2.81158 0.206155
\(187\) 42.9186 3.13852
\(188\) 6.04560 6.04560i 0.440921 0.440921i
\(189\) −3.17868 −0.231215
\(190\) −11.5480 + 2.46541i −0.837777 + 0.178860i
\(191\) 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
\(193\) −22.9897 −1.65484 −0.827419 0.561585i \(-0.810192\pi\)
−0.827419 + 0.561585i \(0.810192\pi\)
\(194\) 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 −0.764854 0.644204i \(-0.777189\pi\)
0.644204 + 0.764854i \(0.277189\pi\)
\(198\) 5.65930 0.402189
\(199\) −7.33672 + 7.33672i −0.520087 + 0.520087i −0.917597 0.397511i \(-0.869874\pi\)
0.397511 + 0.917597i \(0.369874\pi\)
\(200\) 2.04186 + 4.56408i 0.144382 + 0.322729i
\(201\) 9.77458 0.689446
\(202\) 16.0893i 1.13204i
\(203\) 14.6772i 1.03014i
\(204\) −5.36251 5.36251i −0.375451 0.375451i
\(205\) 4.56050 + 2.95582i 0.318519 + 0.206443i
\(206\) 11.0997i 0.773355i
\(207\) 4.23021i 0.294020i
\(208\) −4.81453 −0.333828
\(209\) 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
\(217\) −8.93712 −0.606691
\(218\) −13.7592 13.7592i −0.931894 0.931894i
\(219\) 3.65991i 0.247314i
\(220\) −10.6192 6.88266i −0.715945 0.464029i
\(221\) 36.5121i 2.45607i
\(222\) 6.08010 0.179886i 0.408070 0.0120732i
\(223\) 11.0520 + 11.0520i 0.740100 + 0.740100i 0.972597 0.232497i \(-0.0746896\pi\)
−0.232497 + 0.972597i \(0.574690\pi\)
\(224\) 2.24767 2.24767i 0.150179 0.150179i
\(225\) −4.56408 + 2.04186i −0.304272 + 0.136124i
\(226\) 4.68689i 0.311768i
\(227\) 6.40168i 0.424894i 0.977173 + 0.212447i \(0.0681433\pi\)
−0.977173 + 0.212447i \(0.931857\pi\)
\(228\) −5.28079 −0.349729
\(229\) 16.3225i 1.07862i −0.842107 0.539310i \(-0.818685\pi\)
0.842107 0.539310i \(-0.181315\pi\)
\(230\) −5.14465 + 7.93762i −0.339228 + 0.523391i
\(231\) −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 \(-0.760897\pi\)
0.682491 + 0.730894i \(0.260897\pi\)
\(234\) 4.81453i 0.314736i
\(235\) −3.99158 18.6965i −0.260382 1.21963i
\(236\) 9.84721 + 9.84721i 0.640999 + 0.640999i
\(237\) −4.03499 −0.262101
\(238\) 17.0457 + 17.0457i 1.10491 + 1.10491i
\(239\) −5.10981 5.10981i −0.330526 0.330526i 0.522260 0.852786i \(-0.325089\pi\)
−0.852786 + 0.522260i \(0.825089\pi\)
\(240\) 0.466864 + 2.18679i 0.0301359 + 0.141157i
\(241\) −8.22613 + 8.22613i −0.529892 + 0.529892i −0.920540 0.390648i \(-0.872251\pi\)
0.390648 + 0.920540i \(0.372251\pi\)
\(242\) 21.0276 1.35171
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −1.11855 1.11855i −0.0716080 0.0716080i
\(245\) −5.82445 3.77503i −0.372110 0.241178i
\(246\) 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
\(253\) 23.9400i 1.50509i
\(254\) 14.6086 14.6086i 0.916626 0.916626i
\(255\) −16.5840 + 3.54057i −1.03853 + 0.221719i
\(256\) 1.00000 0.0625000
\(257\) 15.5767i 0.971645i −0.874057 0.485823i \(-0.838520\pi\)
0.874057 0.485823i \(-0.161480\pi\)
\(258\) −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 −0.0629697 + 0.998015i \(0.520057\pi\)
−0.998015 + 0.0629697i \(0.979943\pi\)
\(264\) −4.00173 4.00173i −0.246289 0.246289i
\(265\) 24.8043 5.29555i 1.52372 0.325303i
\(266\) 16.7860 1.02921
\(267\) 14.4077i 0.881735i
\(268\) −6.91167 6.91167i −0.422198 0.422198i
\(269\) 16.7896i 1.02368i 0.859080 + 0.511841i \(0.171036\pi\)
−0.859080 + 0.511841i \(0.828964\pi\)
\(270\) −2.18679 + 0.466864i −0.133084 + 0.0284124i
\(271\) −3.47058 −0.210823 −0.105411 0.994429i \(-0.533616\pi\)
−0.105411 + 0.994429i \(0.533616\pi\)
\(272\) 7.58373i 0.459831i
\(273\) 15.3039i 0.926232i
\(274\) −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
\(277\) −5.08835 −0.305730 −0.152865 0.988247i \(-0.548850\pi\)
−0.152865 + 0.988247i \(0.548850\pi\)
\(278\) 17.9432 1.07616
\(279\) 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 \(-0.142141\pi\)
\(282\) 8.54977i 0.509131i
\(283\) 4.97011i 0.295442i −0.989029 0.147721i \(-0.952806\pi\)
0.989029 0.147721i \(-0.0471938\pi\)
\(284\) −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
\(288\) 1.00000i 0.0589256i
\(289\) −40.5129 −2.38311
\(290\) −2.15568 10.0972i −0.126586 0.592929i
\(291\) −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 0.588564 0.808450i \(-0.299693\pi\)
−0.808450 + 0.588564i \(0.799693\pi\)
\(294\) −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
\(298\) 9.20482i 0.533221i
\(299\) −20.3665 −1.17782
\(300\) 4.67110 + 1.78347i 0.269686 + 0.102969i
\(301\) 7.52196 7.52196i 0.433559 0.433559i
\(302\) 5.59713i 0.322078i
\(303\) −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 \(-0.112962\pi\)
−0.347478 + 0.937688i \(0.612962\pi\)
\(308\) 12.7202 + 12.7202i 0.724802 + 0.724802i
\(309\) −7.84870 7.84870i −0.446497 0.446497i
\(310\) −6.14832 + 1.31262i −0.349201 + 0.0745520i
\(311\) 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
\(313\) −5.86237 −0.331361 −0.165681 0.986179i \(-0.552982\pi\)
−0.165681 + 0.986179i \(0.552982\pi\)
\(314\) 0.998661 0.998661i 0.0563577 0.0563577i
\(315\) 6.95110 1.48401i 0.391650 0.0836146i
\(316\) 2.85317 + 2.85317i 0.160503 + 0.160503i
\(317\) 3.30695 + 3.30695i 0.185737 + 0.185737i 0.793850 0.608113i \(-0.208073\pi\)
−0.608113 + 0.793850i \(0.708073\pi\)
\(318\) 11.3428 0.636073
\(319\) 18.4775 + 18.4775i 1.03454 + 1.03454i
\(320\) 1.21617 1.87641i 0.0679859 0.104895i
\(321\) 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
\(325\) 9.83061 + 21.9739i 0.545304 + 1.21889i
\(326\) 7.74976i 0.429220i
\(327\) −19.4585 −1.07606
\(328\) 2.43043i 0.134198i
\(329\) 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
\(333\) 4.17208 4.42648i 0.228629 0.242570i
\(334\) 19.2547i 1.05357i
\(335\) −21.3749 + 4.56340i −1.16784 + 0.249325i
\(336\) 3.17868i 0.173411i
\(337\) −4.38679 4.38679i −0.238963 0.238963i 0.577457 0.816421i \(-0.304045\pi\)
−0.816421 + 0.577457i \(0.804045\pi\)
\(338\) −10.1797 −0.553702
\(339\) −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
\(347\) 6.84918 0.367683 0.183842 0.982956i \(-0.441147\pi\)
0.183842 + 0.982956i \(0.441147\pi\)
\(348\) 4.61737i 0.247517i
\(349\) 11.3003i 0.604891i 0.953167 + 0.302445i \(0.0978030\pi\)
−0.953167 + 0.302445i \(0.902197\pi\)
\(350\) −14.8480 5.66910i −0.793657 0.303026i
\(351\) −3.40439 3.40439i −0.181713 0.181713i
\(352\) 5.65930i 0.301641i
\(353\) 21.3525i 1.13648i −0.822863 0.568240i \(-0.807625\pi\)
0.822863 0.568240i \(-0.192375\pi\)
\(354\) 13.9261 0.740162
\(355\) −7.44401 + 11.4853i −0.395087 + 0.609576i
\(356\) −10.1878 + 10.1878i −0.539950 + 0.539950i
\(357\) 24.1063 1.27584
\(358\) −14.0961 + 14.0961i −0.745000 + 0.745000i
\(359\) 5.23042i 0.276051i −0.990429 0.138025i \(-0.955924\pi\)
0.990429 0.138025i \(-0.0440756\pi\)
\(360\) 1.87641 + 1.21617i 0.0988957 + 0.0640978i
\(361\) 8.88674i 0.467723i
\(362\) −13.7831 −0.724424
\(363\) 14.8688 14.8688i 0.780408 0.780408i
\(364\) 10.8215 10.8215i 0.567199 0.567199i
\(365\) −1.70868 8.00344i −0.0894362 0.418919i
\(366\) −1.58187 −0.0826858
\(367\) −0.560713 + 0.560713i −0.0292690 + 0.0292690i −0.721590 0.692321i \(-0.756588\pi\)
0.692321 + 0.721590i \(0.256588\pi\)
\(368\) 4.23021 0.220515
\(369\) 2.43043 0.126523
\(370\) −13.2119 + 3.23195i −0.686854 + 0.168021i
\(371\) −36.0552 −1.87189
\(372\) −2.81158 −0.145774
\(373\) −3.16048 + 3.16048i −0.163643 + 0.163643i −0.784179 0.620535i \(-0.786915\pi\)
0.620535 + 0.784179i \(0.286915\pi\)
\(374\) −42.9186 −2.21927
\(375\) 9.02739 6.59592i 0.466173 0.340612i
\(376\) −6.04560 + 6.04560i −0.311778 + 0.311778i
\(377\) 15.7193 15.7193i 0.809586 0.809586i
\(378\) 3.17868 0.163494
\(379\) 1.59897i 0.0821335i −0.999156 0.0410667i \(-0.986924\pi\)
0.999156 0.0410667i \(-0.0130756\pi\)
\(380\) 11.5480 2.46541i 0.592398 0.126473i
\(381\) 20.6597i 1.05843i
\(382\) −18.4453 + 18.4453i −0.943746 + 0.943746i
\(383\) 1.83857 0.0939464 0.0469732 0.998896i \(-0.485042\pi\)
0.0469732 + 0.998896i \(0.485042\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 39.3384 8.39846i 2.00487 0.428025i
\(386\) 22.9897 1.17015
\(387\) 3.34656i 0.170115i
\(388\) 2.87834i 0.146125i
\(389\) 21.9756 + 21.9756i 1.11421 + 1.11421i 0.992575 + 0.121630i \(0.0388122\pi\)
0.121630 + 0.992575i \(0.461188\pi\)
\(390\) 2.24773 + 10.5284i 0.113818 + 0.533124i
\(391\) 32.0807i 1.62239i
\(392\) 3.10403i 0.156777i
\(393\) −13.0987 −0.660743
\(394\) 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 \(-0.0793916\pi\)
−0.246838 + 0.969057i \(0.579392\pi\)
\(398\) 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 \(0.767589\pi\)
\(402\) −9.77458 −0.487512
\(403\) −9.57170 9.57170i −0.476800 0.476800i
\(404\) 16.0893i 0.800474i
\(405\) −1.21617 + 1.87641i −0.0604320 + 0.0932398i
\(406\) 14.6772i 0.728416i
\(407\) 23.6110 25.0508i 1.17036 1.24172i
\(408\) 5.36251 + 5.36251i 0.265484 + 0.265484i
\(409\) 6.64945 6.64945i 0.328794 0.328794i −0.523334 0.852128i \(-0.675312\pi\)
0.852128 + 0.523334i \(0.175312\pi\)
\(410\) −4.56050 2.95582i −0.225227 0.145978i
\(411\) 2.31858i 0.114367i
\(412\) 11.0997i 0.546845i
\(413\) −44.2665 −2.17821
\(414\) 4.23021i 0.207903i
\(415\) 2.80265 0.598346i 0.137577 0.0293716i
\(416\) 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 \(0.183316\pi\)
−0.838701 + 0.544593i \(0.816684\pi\)
\(420\) −5.96453 3.86582i −0.291039 0.188633i
\(421\) −1.74485 1.74485i −0.0850387 0.0850387i 0.663308 0.748347i \(-0.269152\pi\)
−0.748347 + 0.663308i \(0.769152\pi\)
\(422\) −11.9466 −0.581549
\(423\) −6.04560 6.04560i −0.293947 0.293947i
\(424\) −8.02058 8.02058i −0.389514 0.389514i
\(425\) 34.6127 15.4849i 1.67896 0.751130i
\(426\) −4.32811 + 4.32811i −0.209697 + 0.209697i
\(427\) 5.02827 0.243335
\(428\) 8.64549 8.64549i 0.417896 0.417896i
\(429\) −19.2664 19.2664i −0.930192 0.930192i
\(430\) 4.06999 6.27954i 0.196272 0.302826i
\(431\) −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 0.456879 0.889529i \(-0.348967\pi\)
−0.889529 + 0.456879i \(0.848967\pi\)
\(434\) 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
\(438\) 3.65991i 0.174877i
\(439\) 4.79636 4.79636i 0.228918 0.228918i −0.583323 0.812240i \(-0.698248\pi\)
0.812240 + 0.583323i \(0.198248\pi\)
\(440\) 10.6192 + 6.88266i 0.506250 + 0.328118i
\(441\) −3.10403 −0.147811
\(442\) 36.5121i 1.73670i
\(443\) −7.85980 + 7.85980i −0.373430 + 0.373430i −0.868725 0.495295i \(-0.835060\pi\)
0.495295 + 0.868725i \(0.335060\pi\)
\(444\) −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 0.202265 0.979331i \(-0.435170\pi\)
−0.979331 + 0.202265i \(0.935170\pi\)
\(450\) 4.56408 2.04186i 0.215153 0.0962543i
\(451\) 13.7545 0.647676
\(452\) 4.68689i 0.220453i
\(453\) 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
\(457\) 5.42876i 0.253947i 0.991906 + 0.126973i \(0.0405263\pi\)
−0.991906 + 0.126973i \(0.959474\pi\)
\(458\) 16.3225i 0.762699i
\(459\) −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 \(0.110790\pi\)
\(462\) 17.9891 0.836929
\(463\) 36.1282 1.67902 0.839509 0.543345i \(-0.182843\pi\)
0.839509 + 0.543345i \(0.182843\pi\)
\(464\) −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
\(467\) 4.96873i 0.229925i −0.993370 0.114963i \(-0.963325\pi\)
0.993370 0.114963i \(-0.0366748\pi\)
\(468\) 4.81453i 0.222552i
\(469\) 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
\(473\) 18.9392i 0.870825i
\(474\) 4.03499 0.185333
\(475\) 9.41815 24.6671i 0.432135 1.13181i
\(476\) −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 0.999357 0.0358527i \(-0.0114147\pi\)
−0.0358527 + 0.999357i \(0.511415\pi\)
\(480\) −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
\(483\) 13.4465i 0.611837i
\(484\) −21.0276 −0.955801
\(485\) 5.40095 + 3.50054i 0.245245 + 0.158952i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 10.6041i 0.480519i 0.970709 + 0.240259i \(0.0772325\pi\)
−0.970709 + 0.240259i \(0.922767\pi\)
\(488\) 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
\(495\) −6.88266 + 10.6192i −0.309353 + 0.477297i
\(496\) 1.98809 + 1.98809i 0.0892677 + 0.0892677i
\(497\) 13.7577 13.7577i 0.617116 0.617116i
\(498\) 1.28163 0.0574312
\(499\) −15.9396 + 15.9396i −0.713555 + 0.713555i −0.967277 0.253723i \(-0.918345\pi\)
0.253723 + 0.967277i \(0.418345\pi\)
\(500\) −11.0474 1.71931i −0.494053 0.0768899i
\(501\) 13.6151 + 13.6151i 0.608278 + 0.608278i
\(502\) 10.0396 + 10.0396i 0.448089 + 0.448089i
\(503\) 18.1285 0.808309 0.404155 0.914691i \(-0.367566\pi\)
0.404155 + 0.914691i \(0.367566\pi\)
\(504\) −2.24767 2.24767i −0.100119 0.100119i
\(505\) 30.1903 + 19.5674i 1.34345 + 0.870736i
\(506\) 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 \(-0.394634\pi\)
0.325005 + 0.945712i \(0.394634\pi\)
\(510\) 16.5840 3.54057i 0.734352 0.156779i
\(511\) 11.6337i 0.514644i
\(512\) −1.00000 −0.0441942
\(513\) 5.28079i 0.233153i
\(514\) 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
\(518\) 19.3267 0.571801i 0.849167 0.0251235i
\(519\) 12.1421i 0.532981i
\(520\) 5.85528 9.03405i 0.256771 0.396169i
\(521\) 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
\(523\) 16.6140 0.726479 0.363239 0.931696i \(-0.381671\pi\)
0.363239 + 0.931696i \(0.381671\pi\)
\(524\) 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
\(532\) −16.7860 −0.727764
\(533\) 11.7014i 0.506844i
\(534\) 14.4077i 0.623481i
\(535\) −5.70814 26.7369i −0.246784 1.15594i
\(536\) 6.91167 + 6.91167i 0.298539 + 0.298539i
\(537\) 19.9348i 0.860251i
\(538\) 16.7896i 0.723853i
\(539\) −17.5666 −0.756648
\(540\) 2.18679 0.466864i 0.0941043 0.0200906i
\(541\) −15.0297 + 15.0297i −0.646177 + 0.646177i −0.952067 0.305890i \(-0.901046\pi\)
0.305890 + 0.952067i \(0.401046\pi\)
\(542\) 3.47058 0.149074
\(543\) −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
\(547\) −1.60901 −0.0687964 −0.0343982 0.999408i \(-0.510951\pi\)
−0.0343982 + 0.999408i \(0.510951\pi\)
\(548\) 1.63948 1.63948i 0.0700353 0.0700353i
\(549\) −1.11855 + 1.11855i −0.0477387 + 0.0477387i
\(550\) 25.8295 11.5555i 1.10137 0.492728i
\(551\) −24.3834 −1.03877
\(552\) 2.99121 2.99121i 0.127314 0.127314i
\(553\) −12.8260 −0.545416
\(554\) 5.08835 0.216183
\(555\) −7.05689 + 11.6276i −0.299548 + 0.493563i
\(556\) −17.9432 −0.760959
\(557\) −13.8846 −0.588309 −0.294155 0.955758i \(-0.595038\pi\)
−0.294155 + 0.955758i \(0.595038\pi\)
\(558\) −1.98809 + 1.98809i −0.0841624 + 0.0841624i
\(559\) 16.1121 0.681470
\(560\) 1.48401 + 6.95110i 0.0627109 + 0.293738i
\(561\) −30.3480 + 30.3480i −1.28129 + 1.28129i
\(562\) −22.3585 + 22.3585i −0.943138 + 0.943138i
\(563\) −36.2994 −1.52984 −0.764919 0.644126i \(-0.777221\pi\)
−0.764919 + 0.644126i \(0.777221\pi\)
\(564\) 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
\(568\) 6.12087 0.256826
\(569\) 4.09043 4.09043i 0.171480 0.171480i −0.616149 0.787629i \(-0.711308\pi\)
0.787629 + 0.616149i \(0.211308\pi\)
\(570\) 6.42234 9.90895i 0.269002 0.415040i
\(571\) 9.17017 0.383760 0.191880 0.981418i \(-0.438542\pi\)
0.191880 + 0.981418i \(0.438542\pi\)
\(572\) 27.2468i 1.13925i
\(573\) 26.0857i 1.08974i
\(574\) 5.46281 + 5.46281i 0.228013 + 0.228013i
\(575\) −8.63750 19.3070i −0.360209 0.805157i
\(576\) 1.00000i 0.0416667i
\(577\) 35.0406i 1.45876i 0.684108 + 0.729381i \(0.260192\pi\)
−0.684108 + 0.729381i \(0.739808\pi\)
\(578\) 40.5129 1.68512
\(579\) 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
\(587\) 33.5312 1.38398 0.691990 0.721907i \(-0.256734\pi\)
0.691990 + 0.721907i \(0.256734\pi\)
\(588\) 2.19488 + 2.19488i 0.0905153 + 0.0905153i
\(589\) 14.8474i 0.611775i
\(590\) −30.4533 + 6.50157i −1.25374 + 0.267665i
\(591\) 2.39484i 0.0985106i
\(592\) 4.42648 + 4.17208i 0.181927 + 0.171472i
\(593\) 1.10793 + 1.10793i 0.0454971 + 0.0454971i 0.729489 0.683992i \(-0.239758\pi\)
−0.683992 + 0.729489i \(0.739758\pi\)
\(594\) −4.00173 + 4.00173i −0.164193 + 0.164193i
\(595\) −52.7153 + 11.2543i −2.16112 + 0.461383i
\(596\) 9.20482i 0.377044i
\(597\) 10.3757i 0.424649i
\(598\) 20.3665 0.832846
\(599\) 0.823976i 0.0336668i 0.999858 + 0.0168334i \(0.00535848\pi\)
−0.999858 + 0.0168334i \(0.994642\pi\)
\(600\) −4.67110 1.78347i −0.190697 0.0728100i
\(601\) 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
\(605\) −25.5732 + 39.4565i −1.03970 + 1.60414i
\(606\) 11.3769 + 11.3769i 0.462154 + 0.462154i
\(607\) 1.34105 0.0544316 0.0272158 0.999630i \(-0.491336\pi\)
0.0272158 + 0.999630i \(0.491336\pi\)
\(608\) −3.73408 3.73408i −0.151437 0.151437i
\(609\) 10.3783 + 10.3783i 0.420551 + 0.420551i
\(610\) 3.45922 0.738519i 0.140060 0.0299018i
\(611\) −29.1067 + 29.1067i −1.17753 + 1.17753i
\(612\) 7.58373 0.306554
\(613\) −3.50859 + 3.50859i −0.141711 + 0.141711i −0.774403 0.632693i \(-0.781950\pi\)
0.632693 + 0.774403i \(0.281950\pi\)
\(614\) −10.3413 10.3413i −0.417342 0.417342i
\(615\) −5.31484 + 1.13468i −0.214315 + 0.0457548i
\(616\) −12.7202 12.7202i −0.512512 0.512512i
\(617\) −1.91217 1.91217i −0.0769810 0.0769810i 0.667568 0.744549i \(-0.267335\pi\)
−0.744549 + 0.667568i \(0.767335\pi\)
\(618\) 7.84870 + 7.84870i 0.315721 + 0.315721i
\(619\) −19.7786 −0.794968 −0.397484 0.917609i \(-0.630117\pi\)
−0.397484 + 0.917609i \(0.630117\pi\)
\(620\) 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
\(623\) 45.7974i 1.83484i
\(624\) 3.40439 3.40439i 0.136285 0.136285i
\(625\) −16.6616 + 18.6384i −0.666464 + 0.745538i
\(626\) 5.86237 0.234308
\(627\) 29.8855i 1.19351i
\(628\) −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
\(635\) 9.64526 + 45.1783i 0.382760 + 1.79285i
\(636\) −11.3428 −0.449772
\(637\) 14.9444i 0.592120i
\(638\) −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 \(0.671087\pi\)
\(642\) 12.2266i 0.482544i
\(643\) 6.75346i 0.266331i −0.991094 0.133165i \(-0.957486\pi\)
0.991094 0.133165i \(-0.0425141\pi\)
\(644\) −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
\(647\) 17.0199 0.669122 0.334561 0.942374i \(-0.391412\pi\)
0.334561 + 0.942374i \(0.391412\pi\)
\(648\) 1.00000 0.0392837
\(649\) 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
\(652\) 7.74976i 0.303504i
\(653\) 2.21356i 0.0866234i 0.999062 + 0.0433117i \(0.0137909\pi\)
−0.999062 + 0.0433117i \(0.986209\pi\)
\(654\) 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
\(658\) 27.1770i 1.05947i
\(659\) 10.5454 0.410790 0.205395 0.978679i \(-0.434152\pi\)
0.205395 + 0.978679i \(0.434152\pi\)
\(660\) 12.3757 2.64212i 0.481722 0.102844i
\(661\) 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
\(668\) 19.2547i 0.744985i
\(669\) −15.6300 −0.604289
\(670\) 21.3749 4.56340i 0.825786 0.176299i
\(671\) −6.33022 + 6.33022i −0.244375 + 0.244375i
\(672\) 3.17868i 0.122620i
\(673\) −18.5100 18.5100i −0.713507 0.713507i 0.253760 0.967267i \(-0.418333\pi\)
−0.967267 + 0.253760i \(0.918333\pi\)
\(674\) 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 \(-0.427233\pi\)
−0.973983 + 0.226620i \(0.927233\pi\)
\(678\) 3.31414 + 3.31414i 0.127279 + 0.127279i
\(679\) −6.46955 6.46955i −0.248278 0.248278i
\(680\) −14.2302 9.22310i −0.545704 0.353690i
\(681\) −4.52667 4.52667i −0.173462 0.173462i
\(682\) −11.2512 + 11.2512i −0.430830 + 0.430830i
\(683\) 45.5661 1.74354 0.871770 0.489916i \(-0.162972\pi\)
0.871770 + 0.489916i \(0.162972\pi\)
\(684\) 3.73408 3.73408i 0.142776 0.142776i
\(685\) −1.08246 5.07024i −0.0413587 0.193724i
\(686\) 8.75685 + 8.75685i 0.334338 + 0.334338i
\(687\) 11.5417 + 11.5417i 0.440345 + 0.440345i
\(688\) −3.34656 −0.127587
\(689\) −38.6153 38.6153i −1.47113 1.47113i
\(690\) −1.97493 9.25056i −0.0751843 0.352163i
\(691\) 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
\(695\) −21.8219 + 33.6688i −0.827753 + 1.27713i
\(696\) 4.61737i 0.175021i
\(697\) −18.4317 −0.698152
\(698\) 11.3003i 0.427722i
\(699\) 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
\(703\) 0.949941 + 32.1077i 0.0358277 + 1.21097i
\(704\) 5.65930i 0.213293i
\(705\) 16.0429 + 10.3980i 0.604211 + 0.391610i
\(706\) 21.3525i 0.803612i
\(707\) −36.1635 36.1635i −1.36007 1.36007i
\(708\) −13.9261 −0.523373
\(709\) 1.20334 + 1.20334i 0.0451926 + 0.0451926i 0.729342 0.684149i \(-0.239826\pi\)
−0.684149 + 0.729342i \(0.739826\pi\)
\(710\) 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
\(717\) 7.22636 0.269873
\(718\) 5.23042i 0.195197i
\(719\) 34.8068i 1.29807i −0.760757 0.649037i \(-0.775172\pi\)
0.760757 0.649037i \(-0.224828\pi\)
\(720\) −1.87641 1.21617i −0.0699298 0.0453240i
\(721\) −24.9485 24.9485i −0.929131 0.929131i
\(722\) 8.88674i 0.330730i
\(723\) 11.6335i 0.432655i
\(724\) 13.7831 0.512245
\(725\) 21.5682 + 8.23497i 0.801024 + 0.305839i
\(726\) −14.8688 + 14.8688i −0.551832 + 0.551832i
\(727\) −29.0229 −1.07640 −0.538200 0.842817i \(-0.680895\pi\)
−0.538200 + 0.842817i \(0.680895\pi\)
\(728\) −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
\(732\) 1.58187 0.0584677
\(733\) 6.55654 6.55654i 0.242171 0.242171i −0.575577 0.817748i \(-0.695222\pi\)
0.817748 + 0.575577i \(0.195222\pi\)
\(734\) 0.560713 0.560713i 0.0206963 0.0206963i
\(735\) 6.78785 1.44916i 0.250374 0.0534530i
\(736\) −4.23021 −0.155928
\(737\) −39.1152 + 39.1152i −1.44083 + 1.44083i
\(738\) −2.43043 −0.0894655
\(739\) 3.57785 0.131613 0.0658067 0.997832i \(-0.479038\pi\)
0.0658067 + 0.997832i \(0.479038\pi\)
\(740\) 13.2119 3.23195i 0.485679 0.118809i
\(741\) 25.4245 0.933993
\(742\) 36.0552 1.32363
\(743\) 29.2655 29.2655i 1.07365 1.07365i 0.0765832 0.997063i \(-0.475599\pi\)
0.997063 0.0765832i \(-0.0244011\pi\)
\(744\) 2.81158 0.103077
\(745\) −17.2720 11.1946i −0.632799 0.410139i
\(746\) 3.16048 3.16048i 0.115713 0.115713i
\(747\) 0.906248 0.906248i 0.0331579 0.0331579i
\(748\) 42.9186 1.56926
\(749\) 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
\(753\) 14.1981 0.517409
\(754\) −15.7193 + 15.7193i −0.572464 + 0.572464i
\(755\) −10.5025 6.80705i −0.382226 0.247734i
\(756\) −3.17868 −0.115608
\(757\) 15.4393i 0.561153i 0.959832 + 0.280576i \(0.0905256\pi\)
−0.959832 + 0.280576i \(0.909474\pi\)
\(758\) 1.59897i 0.0580771i
\(759\) 16.9281 + 16.9281i 0.614452 + 0.614452i
\(760\) −11.5480 + 2.46541i −0.418889 + 0.0894298i
\(761\) 19.6274i 0.711492i 0.934583 + 0.355746i \(0.115773\pi\)
−0.934583 + 0.355746i \(0.884227\pi\)
\(762\) 20.6597i 0.748422i
\(763\) −61.8524 −2.23921
\(764\) 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 \(0.681976\pi\)
−0.840985 + 0.541058i \(0.818024\pi\)
\(770\) −39.3384 + 8.39846i −1.41766 + 0.302660i
\(771\) 11.0144 + 11.0144i 0.396672 + 0.396672i
\(772\) −22.9897 −0.827419
\(773\) 13.6080 + 13.6080i 0.489445 + 0.489445i 0.908131 0.418686i \(-0.137509\pi\)
−0.418686 + 0.908131i \(0.637509\pi\)
\(774\) 3.34656i 0.120290i
\(775\) 5.01438 13.1332i 0.180122 0.471758i
\(776\) 2.87834i 0.103326i
\(777\) 13.2617 14.0704i 0.475762 0.504772i
\(778\) −21.9756 21.9756i −0.787862 0.787862i
\(779\) −9.07544 + 9.07544i −0.325161 + 0.325161i
\(780\) −2.24773