Properties

Label 605.2.j.e.269.3
Level $605$
Weight $2$
Character 605.269
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: 16.0.6879707136000000000000.7
Defining polynomial: \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 269.3
Root \(0.304260 - 0.418778i\) of defining polynomial
Character \(\chi\) \(=\) 605.269
Dual form 605.2.j.e.9.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.492303 - 0.159959i) q^{2} +(1.13551 - 1.56290i) q^{3} +(-1.40126 + 1.01807i) q^{4} +(-0.809764 - 2.08429i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.96677 - 2.70702i) q^{7} +(-1.13551 + 1.56290i) q^{8} +(-0.226216 - 0.696222i) q^{9} +O(q^{10})\) \(q+(0.492303 - 0.159959i) q^{2} +(1.13551 - 1.56290i) q^{3} +(-1.40126 + 1.01807i) q^{4} +(-0.809764 - 2.08429i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.96677 - 2.70702i) q^{7} +(-1.13551 + 1.56290i) q^{8} +(-0.226216 - 0.696222i) q^{9} +(-0.732051 - 0.896575i) q^{10} +3.34607i q^{12} +(-4.03499 + 1.31105i) q^{13} +(-1.40126 - 1.01807i) q^{14} +(-4.17704 - 1.10116i) q^{15} +(0.761449 - 2.34350i) q^{16} +(-3.67460 - 1.19395i) q^{17} +(-0.222734 - 0.306567i) q^{18} +(3.39476 + 2.46644i) q^{19} +(3.25665 + 2.09624i) q^{20} -6.46410 q^{21} -3.48477i q^{23} +(1.15327 + 3.54939i) q^{24} +(-3.68856 + 3.37557i) q^{25} +(-1.77672 + 1.29087i) q^{26} +(4.16690 + 1.35391i) q^{27} +(5.51190 + 1.79092i) q^{28} +(-5.60503 + 4.07230i) q^{29} +(-2.23251 + 0.126049i) q^{30} +(-2.69835 - 8.30467i) q^{31} -5.13922i q^{32} -2.00000 q^{34} +(-4.04962 + 6.29137i) q^{35} +(1.02579 + 0.745282i) q^{36} +(-1.05399 - 1.45069i) q^{37} +(2.06578 + 0.671212i) q^{38} +(-2.53275 + 7.79500i) q^{39} +(4.17704 + 1.10116i) q^{40} +(1.40126 + 1.01807i) q^{41} +(-3.18230 + 1.03399i) q^{42} -6.45189i q^{43} +(-1.26795 + 1.03528i) q^{45} +(-0.557420 - 1.71556i) q^{46} +(6.73156 - 9.26519i) q^{47} +(-2.79802 - 3.85115i) q^{48} +(-1.29668 + 3.99078i) q^{49} +(-1.27594 + 2.25182i) q^{50} +(-6.03859 + 4.38729i) q^{51} +(4.31932 - 5.94504i) q^{52} +(2.06578 - 0.671212i) q^{53} +2.26795 q^{54} +6.46410 q^{56} +(7.70959 - 2.50500i) q^{57} +(-2.10798 + 2.90138i) q^{58} +(-1.02579 + 0.745282i) q^{59} +(6.97418 - 2.70952i) q^{60} +(3.62540 - 11.1578i) q^{61} +(-2.65681 - 3.65679i) q^{62} +(-1.43977 + 1.98168i) q^{63} +(0.700835 + 2.15695i) q^{64} +(6.00000 + 7.34847i) q^{65} +2.20925i q^{67} +(6.36459 - 2.06798i) q^{68} +(-5.44634 - 3.95700i) q^{69} +(-0.987277 + 3.74503i) q^{70} +(-2.53275 + 7.79500i) q^{71} +(1.34500 + 0.437016i) q^{72} +(2.87955 + 3.96336i) q^{73} +(-0.750932 - 0.545584i) q^{74} +(1.08727 + 9.59787i) q^{75} -7.26795 q^{76} +4.24264i q^{78} +(0.452432 + 1.39244i) q^{79} +(-5.50114 + 0.310597i) q^{80} +(8.62433 - 6.26594i) q^{81} +(0.852694 + 0.277057i) q^{82} +(-9.41498 - 3.05911i) q^{83} +(9.05788 - 6.58093i) q^{84} +(0.487015 + 8.62577i) q^{85} +(-1.03204 - 3.17629i) q^{86} +13.3843i q^{87} -0.464102 q^{89} +(-0.458614 + 0.712489i) q^{90} +(11.4849 + 8.34429i) q^{91} +(3.54775 + 4.88306i) q^{92} +(-16.0434 - 5.21282i) q^{93} +(1.83192 - 5.63806i) q^{94} +(2.39183 - 9.07291i) q^{95} +(-8.03209 - 5.83565i) q^{96} +(8.69420 - 2.82492i) q^{97} +2.17209i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{6} - 4 q^{9} + 16 q^{10} - 4 q^{15} + 4 q^{16} - 4 q^{19} - 12 q^{20} - 48 q^{21} - 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} - 12 q^{35} + 12 q^{36} + 12 q^{39} + 4 q^{40} - 48 q^{45} + 28 q^{46} - 4 q^{49} + 24 q^{50} - 16 q^{51} + 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} - 40 q^{61} - 16 q^{64} + 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} + 24 q^{74} - 24 q^{75} - 144 q^{76} + 8 q^{79} - 24 q^{80} + 8 q^{81} + 24 q^{84} + 8 q^{85} + 48 q^{86} + 48 q^{89} - 16 q^{90} + 36 q^{91} + 4 q^{94} + 36 q^{95} - 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.492303 0.159959i 0.348111 0.113108i −0.129742 0.991548i \(-0.541415\pi\)
0.477853 + 0.878440i \(0.341415\pi\)
\(3\) 1.13551 1.56290i 0.655589 0.902341i −0.343736 0.939066i \(-0.611693\pi\)
0.999325 + 0.0367251i \(0.0116926\pi\)
\(4\) −1.40126 + 1.01807i −0.700629 + 0.509037i
\(5\) −0.809764 2.08429i −0.362137 0.932125i
\(6\) 0.309017 0.951057i 0.126156 0.388267i
\(7\) −1.96677 2.70702i −0.743368 1.02316i −0.998418 0.0562307i \(-0.982092\pi\)
0.255049 0.966928i \(-0.417908\pi\)
\(8\) −1.13551 + 1.56290i −0.401465 + 0.552569i
\(9\) −0.226216 0.696222i −0.0754054 0.232074i
\(10\) −0.732051 0.896575i −0.231495 0.283522i
\(11\) 0 0
\(12\) 3.34607i 0.965926i
\(13\) −4.03499 + 1.31105i −1.11911 + 0.363619i −0.809426 0.587222i \(-0.800222\pi\)
−0.309679 + 0.950841i \(0.600222\pi\)
\(14\) −1.40126 1.01807i −0.374502 0.272092i
\(15\) −4.17704 1.10116i −1.07851 0.284319i
\(16\) 0.761449 2.34350i 0.190362 0.585875i
\(17\) −3.67460 1.19395i −0.891221 0.289575i −0.172613 0.984990i \(-0.555221\pi\)
−0.718609 + 0.695414i \(0.755221\pi\)
\(18\) −0.222734 0.306567i −0.0524989 0.0722585i
\(19\) 3.39476 + 2.46644i 0.778811 + 0.565839i 0.904622 0.426215i \(-0.140153\pi\)
−0.125811 + 0.992054i \(0.540153\pi\)
\(20\) 3.25665 + 2.09624i 0.728210 + 0.468733i
\(21\) −6.46410 −1.41058
\(22\) 0 0
\(23\) 3.48477i 0.726624i −0.931668 0.363312i \(-0.881646\pi\)
0.931668 0.363312i \(-0.118354\pi\)
\(24\) 1.15327 + 3.54939i 0.235410 + 0.724516i
\(25\) −3.68856 + 3.37557i −0.737713 + 0.675114i
\(26\) −1.77672 + 1.29087i −0.348444 + 0.253160i
\(27\) 4.16690 + 1.35391i 0.801921 + 0.260560i
\(28\) 5.51190 + 1.79092i 1.04165 + 0.338453i
\(29\) −5.60503 + 4.07230i −1.04083 + 0.756206i −0.970447 0.241314i \(-0.922422\pi\)
−0.0703816 + 0.997520i \(0.522422\pi\)
\(30\) −2.23251 + 0.126049i −0.407599 + 0.0230133i
\(31\) −2.69835 8.30467i −0.484638 1.49156i −0.832504 0.554019i \(-0.813093\pi\)
0.347866 0.937544i \(-0.386907\pi\)
\(32\) 5.13922i 0.908494i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −4.04962 + 6.29137i −0.684510 + 1.06344i
\(36\) 1.02579 + 0.745282i 0.170965 + 0.124214i
\(37\) −1.05399 1.45069i −0.173275 0.238492i 0.713543 0.700611i \(-0.247089\pi\)
−0.886818 + 0.462119i \(0.847089\pi\)
\(38\) 2.06578 + 0.671212i 0.335114 + 0.108885i
\(39\) −2.53275 + 7.79500i −0.405565 + 1.24820i
\(40\) 4.17704 + 1.10116i 0.660449 + 0.174109i
\(41\) 1.40126 + 1.01807i 0.218840 + 0.158996i 0.691804 0.722085i \(-0.256816\pi\)
−0.472964 + 0.881082i \(0.656816\pi\)
\(42\) −3.18230 + 1.03399i −0.491039 + 0.159548i
\(43\) 6.45189i 0.983905i −0.870622 0.491952i \(-0.836283\pi\)
0.870622 0.491952i \(-0.163717\pi\)
\(44\) 0 0
\(45\) −1.26795 + 1.03528i −0.189015 + 0.154330i
\(46\) −0.557420 1.71556i −0.0821870 0.252946i
\(47\) 6.73156 9.26519i 0.981899 1.35147i 0.0460982 0.998937i \(-0.485321\pi\)
0.935800 0.352530i \(-0.114679\pi\)
\(48\) −2.79802 3.85115i −0.403860 0.555865i
\(49\) −1.29668 + 3.99078i −0.185240 + 0.570111i
\(50\) −1.27594 + 2.25182i −0.180445 + 0.318456i
\(51\) −6.03859 + 4.38729i −0.845571 + 0.614343i
\(52\) 4.31932 5.94504i 0.598982 0.824428i
\(53\) 2.06578 0.671212i 0.283757 0.0921981i −0.163681 0.986513i \(-0.552337\pi\)
0.447437 + 0.894315i \(0.352337\pi\)
\(54\) 2.26795 0.308629
\(55\) 0 0
\(56\) 6.46410 0.863802
\(57\) 7.70959 2.50500i 1.02116 0.331795i
\(58\) −2.10798 + 2.90138i −0.276791 + 0.380970i
\(59\) −1.02579 + 0.745282i −0.133547 + 0.0970274i −0.652553 0.757743i \(-0.726302\pi\)
0.519006 + 0.854770i \(0.326302\pi\)
\(60\) 6.97418 2.70952i 0.900363 0.349798i
\(61\) 3.62540 11.1578i 0.464185 1.42862i −0.395819 0.918329i \(-0.629539\pi\)
0.860004 0.510287i \(-0.170461\pi\)
\(62\) −2.65681 3.65679i −0.337416 0.464413i
\(63\) −1.43977 + 1.98168i −0.181394 + 0.249668i
\(64\) 0.700835 + 2.15695i 0.0876044 + 0.269618i
\(65\) 6.00000 + 7.34847i 0.744208 + 0.911465i
\(66\) 0 0
\(67\) 2.20925i 0.269903i 0.990852 + 0.134952i \(0.0430879\pi\)
−0.990852 + 0.134952i \(0.956912\pi\)
\(68\) 6.36459 2.06798i 0.771820 0.250780i
\(69\) −5.44634 3.95700i −0.655663 0.476367i
\(70\) −0.987277 + 3.74503i −0.118002 + 0.447617i
\(71\) −2.53275 + 7.79500i −0.300582 + 0.925097i 0.680707 + 0.732556i \(0.261673\pi\)
−0.981289 + 0.192541i \(0.938327\pi\)
\(72\) 1.34500 + 0.437016i 0.158509 + 0.0515028i
\(73\) 2.87955 + 3.96336i 0.337026 + 0.463876i 0.943570 0.331174i \(-0.107445\pi\)
−0.606544 + 0.795050i \(0.707445\pi\)
\(74\) −0.750932 0.545584i −0.0872941 0.0634229i
\(75\) 1.08727 + 9.59787i 0.125547 + 1.10827i
\(76\) −7.26795 −0.833691
\(77\) 0 0
\(78\) 4.24264i 0.480384i
\(79\) 0.452432 + 1.39244i 0.0509026 + 0.156662i 0.973277 0.229636i \(-0.0737536\pi\)
−0.922374 + 0.386298i \(0.873754\pi\)
\(80\) −5.50114 + 0.310597i −0.615046 + 0.0347258i
\(81\) 8.62433 6.26594i 0.958259 0.696216i
\(82\) 0.852694 + 0.277057i 0.0941643 + 0.0305958i
\(83\) −9.41498 3.05911i −1.03343 0.335781i −0.257283 0.966336i \(-0.582827\pi\)
−0.776145 + 0.630555i \(0.782827\pi\)
\(84\) 9.05788 6.58093i 0.988295 0.718039i
\(85\) 0.487015 + 8.62577i 0.0528242 + 0.935596i
\(86\) −1.03204 3.17629i −0.111288 0.342508i
\(87\) 13.3843i 1.43494i
\(88\) 0 0
\(89\) −0.464102 −0.0491947 −0.0245973 0.999697i \(-0.507830\pi\)
−0.0245973 + 0.999697i \(0.507830\pi\)
\(90\) −0.458614 + 0.712489i −0.0483421 + 0.0751030i
\(91\) 11.4849 + 8.34429i 1.20395 + 0.874719i
\(92\) 3.54775 + 4.88306i 0.369878 + 0.509094i
\(93\) −16.0434 5.21282i −1.66362 0.540544i
\(94\) 1.83192 5.63806i 0.188948 0.581521i
\(95\) 2.39183 9.07291i 0.245396 0.930861i
\(96\) −8.03209 5.83565i −0.819771 0.595599i
\(97\) 8.69420 2.82492i 0.882762 0.286827i 0.167658 0.985845i \(-0.446379\pi\)
0.715104 + 0.699018i \(0.246379\pi\)
\(98\) 2.17209i 0.219414i
\(99\) 0 0
\(100\) 1.73205 8.48528i 0.173205 0.848528i
\(101\) −5.99255 18.4432i −0.596281 1.83516i −0.548243 0.836319i \(-0.684703\pi\)
−0.0480385 0.998845i \(-0.515297\pi\)
\(102\) −2.27103 + 3.12580i −0.224865 + 0.309500i
\(103\) 2.49376 + 3.43237i 0.245718 + 0.338201i 0.914006 0.405701i \(-0.132973\pi\)
−0.668288 + 0.743903i \(0.732973\pi\)
\(104\) 2.53275 7.79500i 0.248357 0.764363i
\(105\) 5.23440 + 13.4731i 0.510825 + 1.31484i
\(106\) 0.909623 0.660880i 0.0883504 0.0641903i
\(107\) −1.74403 + 2.40046i −0.168602 + 0.232061i −0.884954 0.465678i \(-0.845810\pi\)
0.716352 + 0.697739i \(0.245810\pi\)
\(108\) −7.21729 + 2.34504i −0.694484 + 0.225651i
\(109\) 9.19615 0.880832 0.440416 0.897794i \(-0.354831\pi\)
0.440416 + 0.897794i \(0.354831\pi\)
\(110\) 0 0
\(111\) −3.46410 −0.328798
\(112\) −7.84150 + 2.54786i −0.740952 + 0.240750i
\(113\) −1.66251 + 2.28825i −0.156396 + 0.215260i −0.880023 0.474930i \(-0.842473\pi\)
0.723628 + 0.690190i \(0.242473\pi\)
\(114\) 3.39476 2.46644i 0.317948 0.231003i
\(115\) −7.26328 + 2.82184i −0.677304 + 0.263138i
\(116\) 3.70820 11.4127i 0.344298 1.05964i
\(117\) 1.82556 + 2.51267i 0.168773 + 0.232296i
\(118\) −0.385786 + 0.530989i −0.0355145 + 0.0488815i
\(119\) 3.99503 + 12.2955i 0.366224 + 1.12712i
\(120\) 6.46410 5.27792i 0.590089 0.481806i
\(121\) 0 0
\(122\) 6.07296i 0.549820i
\(123\) 3.18230 1.03399i 0.286938 0.0932318i
\(124\) 12.2359 + 8.88987i 1.09881 + 0.798334i
\(125\) 10.0226 + 4.95464i 0.896444 + 0.443156i
\(126\) −0.391818 + 1.20589i −0.0349059 + 0.107429i
\(127\) 0.852694 + 0.277057i 0.0756644 + 0.0245848i 0.346605 0.938011i \(-0.387335\pi\)
−0.270940 + 0.962596i \(0.587335\pi\)
\(128\) 6.73156 + 9.26519i 0.594991 + 0.818935i
\(129\) −10.0837 7.32622i −0.887818 0.645037i
\(130\) 4.12927 + 2.65792i 0.362161 + 0.233115i
\(131\) 3.12436 0.272976 0.136488 0.990642i \(-0.456418\pi\)
0.136488 + 0.990642i \(0.456418\pi\)
\(132\) 0 0
\(133\) 14.0406i 1.21747i
\(134\) 0.353390 + 1.08762i 0.0305282 + 0.0939562i
\(135\) −0.552263 9.78140i −0.0475312 0.841849i
\(136\) 6.03859 4.38729i 0.517804 0.376207i
\(137\) −8.43037 2.73919i −0.720255 0.234025i −0.0741215 0.997249i \(-0.523615\pi\)
−0.646134 + 0.763224i \(0.723615\pi\)
\(138\) −3.31421 1.07685i −0.282124 0.0916677i
\(139\) 11.8023 8.57488i 1.00106 0.727312i 0.0387439 0.999249i \(-0.487664\pi\)
0.962315 + 0.271937i \(0.0876643\pi\)
\(140\) −0.730523 12.9386i −0.0617405 1.09352i
\(141\) −6.83680 21.0415i −0.575763 1.77202i
\(142\) 4.24264i 0.356034i
\(143\) 0 0
\(144\) −1.80385 −0.150321
\(145\) 13.0266 + 8.38494i 1.08180 + 0.696332i
\(146\) 2.05158 + 1.49056i 0.169790 + 0.123360i
\(147\) 4.76479 + 6.55817i 0.392993 + 0.540909i
\(148\) 2.95382 + 0.959754i 0.242802 + 0.0788913i
\(149\) −3.17297 + 9.76540i −0.259940 + 0.800013i 0.732876 + 0.680362i \(0.238177\pi\)
−0.992816 + 0.119651i \(0.961823\pi\)
\(150\) 2.07053 + 4.55114i 0.169058 + 0.371599i
\(151\) 3.39476 + 2.46644i 0.276262 + 0.200716i 0.717285 0.696780i \(-0.245384\pi\)
−0.441024 + 0.897495i \(0.645384\pi\)
\(152\) −7.70959 + 2.50500i −0.625330 + 0.203182i
\(153\) 2.82843i 0.228665i
\(154\) 0 0
\(155\) −15.1244 + 12.3490i −1.21482 + 0.991894i
\(156\) −4.38685 13.5013i −0.351229 1.08097i
\(157\) −12.8546 + 17.6928i −1.02591 + 1.41204i −0.117931 + 0.993022i \(0.537626\pi\)
−0.907977 + 0.419020i \(0.862374\pi\)
\(158\) 0.445468 + 0.613134i 0.0354395 + 0.0487783i
\(159\) 1.29668 3.99078i 0.102834 0.316489i
\(160\) −10.7116 + 4.16155i −0.846829 + 0.329000i
\(161\) −9.43334 + 6.85373i −0.743452 + 0.540149i
\(162\) 3.24349 4.46428i 0.254833 0.350747i
\(163\) −4.88769 + 1.58811i −0.382833 + 0.124390i −0.494110 0.869399i \(-0.664506\pi\)
0.111277 + 0.993789i \(0.464506\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) −5.12436 −0.397727
\(167\) 0.492303 0.159959i 0.0380956 0.0123780i −0.289907 0.957055i \(-0.593624\pi\)
0.328003 + 0.944677i \(0.393624\pi\)
\(168\) 7.34008 10.1027i 0.566299 0.779444i
\(169\) 4.04508 2.93893i 0.311160 0.226071i
\(170\) 1.61953 + 4.16859i 0.124212 + 0.319716i
\(171\) 0.949237 2.92145i 0.0725900 0.223409i
\(172\) 6.56850 + 9.04077i 0.500844 + 0.689352i
\(173\) 12.7949 17.6107i 0.972779 1.33892i 0.0321489 0.999483i \(-0.489765\pi\)
0.940630 0.339433i \(-0.110235\pi\)
\(174\) 2.14093 + 6.58911i 0.162304 + 0.499519i
\(175\) 16.3923 + 3.34607i 1.23914 + 0.252939i
\(176\) 0 0
\(177\) 2.44949i 0.184115i
\(178\) −0.228479 + 0.0742372i −0.0171252 + 0.00556431i
\(179\) −12.5107 9.08957i −0.935095 0.679386i 0.0121398 0.999926i \(-0.496136\pi\)
−0.947235 + 0.320540i \(0.896136\pi\)
\(180\) 0.722737 2.74156i 0.0538696 0.204343i
\(181\) −5.37452 + 16.5411i −0.399485 + 1.22949i 0.525929 + 0.850529i \(0.323718\pi\)
−0.925413 + 0.378959i \(0.876282\pi\)
\(182\) 6.98881 + 2.27080i 0.518045 + 0.168323i
\(183\) −13.3219 18.3360i −0.984784 1.35544i
\(184\) 5.44634 + 3.95700i 0.401510 + 0.291714i
\(185\) −2.17018 + 3.37154i −0.159555 + 0.247880i
\(186\) −8.73205 −0.640265
\(187\) 0 0
\(188\) 19.8362i 1.44670i
\(189\) −4.53027 13.9427i −0.329528 1.01418i
\(190\) −0.273789 4.84921i −0.0198628 0.351799i
\(191\) 5.87989 4.27199i 0.425454 0.309111i −0.354374 0.935104i \(-0.615306\pi\)
0.779829 + 0.625993i \(0.215306\pi\)
\(192\) 4.16690 + 1.35391i 0.300720 + 0.0977100i
\(193\) 14.4346 + 4.69008i 1.03902 + 0.337599i 0.778352 0.627828i \(-0.216056\pi\)
0.260672 + 0.965428i \(0.416056\pi\)
\(194\) 3.82831 2.78143i 0.274857 0.199695i
\(195\) 18.2980 1.03312i 1.31035 0.0739830i
\(196\) −2.24592 6.91223i −0.160423 0.493731i
\(197\) 17.2480i 1.22887i −0.788969 0.614433i \(-0.789385\pi\)
0.788969 0.614433i \(-0.210615\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) −1.08727 9.59787i −0.0768815 0.678672i
\(201\) 3.45284 + 2.50864i 0.243545 + 0.176946i
\(202\) −5.90030 8.12107i −0.415144 0.571397i
\(203\) 22.0476 + 7.16370i 1.54744 + 0.502793i
\(204\) 3.99503 12.2955i 0.279708 0.860854i
\(205\) 0.987277 3.74503i 0.0689544 0.261565i
\(206\) 1.77672 + 1.29087i 0.123790 + 0.0899389i
\(207\) −2.42617 + 0.788310i −0.168630 + 0.0547914i
\(208\) 10.4543i 0.724875i
\(209\) 0 0
\(210\) 4.73205 + 5.79555i 0.326543 + 0.399931i
\(211\) 4.05565 + 12.4820i 0.279202 + 0.859297i 0.988077 + 0.153962i \(0.0492033\pi\)
−0.708874 + 0.705335i \(0.750797\pi\)
\(212\) −2.21135 + 3.04366i −0.151876 + 0.209039i
\(213\) 9.30685 + 12.8098i 0.637695 + 0.877711i
\(214\) −0.474619 + 1.46073i −0.0324443 + 0.0998532i
\(215\) −13.4476 + 5.22451i −0.917122 + 0.356309i
\(216\) −6.84760 + 4.97507i −0.465920 + 0.338511i
\(217\) −17.1739 + 23.6379i −1.16584 + 1.60464i
\(218\) 4.52729 1.47101i 0.306627 0.0996292i
\(219\) 9.46410 0.639525
\(220\) 0 0
\(221\) 16.3923 1.10267
\(222\) −1.70539 + 0.554114i −0.114458 + 0.0371897i
\(223\) −0.912780 + 1.25633i −0.0611243 + 0.0841303i −0.838485 0.544925i \(-0.816558\pi\)
0.777361 + 0.629055i \(0.216558\pi\)
\(224\) −13.9120 + 10.1076i −0.929533 + 0.675345i
\(225\) 3.18456 + 1.80445i 0.212304 + 0.120297i
\(226\) −0.452432 + 1.39244i −0.0300953 + 0.0926240i
\(227\) 11.8225 + 16.2722i 0.784684 + 1.08002i 0.994750 + 0.102337i \(0.0326321\pi\)
−0.210066 + 0.977687i \(0.567368\pi\)
\(228\) −8.25286 + 11.3591i −0.546559 + 0.752274i
\(229\) 1.25825 + 3.87251i 0.0831478 + 0.255903i 0.983984 0.178256i \(-0.0570456\pi\)
−0.900836 + 0.434159i \(0.857046\pi\)
\(230\) −3.12436 + 2.55103i −0.206014 + 0.168210i
\(231\) 0 0
\(232\) 13.3843i 0.878720i
\(233\) −1.60882 + 0.522738i −0.105397 + 0.0342457i −0.361241 0.932473i \(-0.617647\pi\)
0.255844 + 0.966718i \(0.417647\pi\)
\(234\) 1.30065 + 0.944980i 0.0850263 + 0.0617752i
\(235\) −24.7624 6.52793i −1.61532 0.425835i
\(236\) 0.678648 2.08867i 0.0441762 0.135961i
\(237\) 2.68999 + 0.874032i 0.174734 + 0.0567745i
\(238\) 3.93354 + 5.41405i 0.254973 + 0.350941i
\(239\) −4.57924 3.32701i −0.296207 0.215207i 0.429749 0.902948i \(-0.358602\pi\)
−0.725955 + 0.687742i \(0.758602\pi\)
\(240\) −5.76119 + 8.95042i −0.371883 + 0.577747i
\(241\) −14.1244 −0.909830 −0.454915 0.890535i \(-0.650330\pi\)
−0.454915 + 0.890535i \(0.650330\pi\)
\(242\) 0 0
\(243\) 7.45001i 0.477918i
\(244\) 6.27938 + 19.3260i 0.401996 + 1.23722i
\(245\) 9.36796 0.528920i 0.598497 0.0337915i
\(246\) 1.40126 1.01807i 0.0893410 0.0649100i
\(247\) −16.9314 5.50136i −1.07732 0.350043i
\(248\) 16.0434 + 5.21282i 1.01876 + 0.331014i
\(249\) −15.4719 + 11.2410i −0.980494 + 0.712370i
\(250\) 5.72667 + 0.835986i 0.362187 + 0.0528724i
\(251\) −1.17545 3.61767i −0.0741940 0.228346i 0.907082 0.420955i \(-0.138305\pi\)
−0.981276 + 0.192609i \(0.938305\pi\)
\(252\) 4.24264i 0.267261i
\(253\) 0 0
\(254\) 0.464102 0.0291203
\(255\) 14.0342 + 9.03352i 0.878858 + 0.565701i
\(256\) 1.12640 + 0.818376i 0.0703999 + 0.0511485i
\(257\) −8.69833 11.9722i −0.542587 0.746806i 0.446396 0.894835i \(-0.352707\pi\)
−0.988983 + 0.148029i \(0.952707\pi\)
\(258\) −6.13612 1.99374i −0.382018 0.124125i
\(259\) −1.85410 + 5.70634i −0.115208 + 0.354575i
\(260\) −15.8888 4.18866i −0.985384 0.259770i
\(261\) 4.10317 + 2.98113i 0.253980 + 0.184527i
\(262\) 1.53813 0.499769i 0.0950260 0.0308758i
\(263\) 6.79367i 0.418915i −0.977818 0.209458i \(-0.932830\pi\)
0.977818 0.209458i \(-0.0671699\pi\)
\(264\) 0 0
\(265\) −3.07180 3.76217i −0.188699 0.231108i
\(266\) −2.24592 6.91223i −0.137706 0.423816i
\(267\) −0.526994 + 0.725345i −0.0322515 + 0.0443904i
\(268\) −2.24918 3.09573i −0.137391 0.189102i
\(269\) 5.02707 15.4717i 0.306506 0.943329i −0.672605 0.740002i \(-0.734825\pi\)
0.979111 0.203327i \(-0.0651754\pi\)
\(270\) −1.83650 4.72707i −0.111766 0.287681i
\(271\) 9.27465 6.73843i 0.563395 0.409330i −0.269305 0.963055i \(-0.586794\pi\)
0.832700 + 0.553725i \(0.186794\pi\)
\(272\) −5.59604 + 7.70229i −0.339310 + 0.467020i
\(273\) 26.0826 8.47475i 1.57859 0.512915i
\(274\) −4.58846 −0.277199
\(275\) 0 0
\(276\) 11.6603 0.701865
\(277\) −29.6606 + 9.63732i −1.78213 + 0.579051i −0.999079 0.0429019i \(-0.986340\pi\)
−0.783055 + 0.621952i \(0.786340\pi\)
\(278\) 4.43868 6.10933i 0.266215 0.366413i
\(279\) −5.17148 + 3.75730i −0.309609 + 0.224944i
\(280\) −5.23440 13.4731i −0.312815 0.805171i
\(281\) 5.35233 16.4728i 0.319293 0.982684i −0.654658 0.755925i \(-0.727187\pi\)
0.973951 0.226758i \(-0.0728128\pi\)
\(282\) −6.73156 9.26519i −0.400858 0.551734i
\(283\) −4.74294 + 6.52810i −0.281939 + 0.388055i −0.926375 0.376603i \(-0.877092\pi\)
0.644436 + 0.764658i \(0.277092\pi\)
\(284\) −4.38685 13.5013i −0.260312 0.801157i
\(285\) −11.4641 14.0406i −0.679075 0.831693i
\(286\) 0 0
\(287\) 5.79555i 0.342101i
\(288\) −3.57803 + 1.16257i −0.210838 + 0.0685053i
\(289\) −1.67612 1.21777i −0.0985952 0.0716336i
\(290\) 7.75429 + 2.04421i 0.455348 + 0.120040i
\(291\) 5.45732 16.7959i 0.319914 0.984593i
\(292\) −8.06998 2.62210i −0.472260 0.153447i
\(293\) −8.86138 12.1966i −0.517687 0.712535i 0.467505 0.883991i \(-0.345153\pi\)
−0.985192 + 0.171455i \(0.945153\pi\)
\(294\) 3.39476 + 2.46644i 0.197986 + 0.143845i
\(295\) 2.38404 + 1.53455i 0.138804 + 0.0893450i
\(296\) 3.46410 0.201347
\(297\) 0 0
\(298\) 5.31508i 0.307894i
\(299\) 4.56870 + 14.0610i 0.264214 + 0.813169i
\(300\) −11.2949 12.3422i −0.652111 0.712576i
\(301\) −17.4654 + 12.6894i −1.00669 + 0.731404i
\(302\) 2.06578 + 0.671212i 0.118872 + 0.0386239i
\(303\) −35.6295 11.5767i −2.04686 0.665065i
\(304\) 8.36503 6.07755i 0.479767 0.348571i
\(305\) −26.1919 + 1.47881i −1.49975 + 0.0846765i
\(306\) 0.452432 + 1.39244i 0.0258638 + 0.0796007i
\(307\) 7.82894i 0.446821i 0.974724 + 0.223411i \(0.0717191\pi\)
−0.974724 + 0.223411i \(0.928281\pi\)
\(308\) 0 0
\(309\) 8.19615 0.466263
\(310\) −5.47044 + 8.49872i −0.310700 + 0.482695i
\(311\) −8.13269 5.90875i −0.461163 0.335054i 0.332825 0.942989i \(-0.391998\pi\)
−0.793987 + 0.607935i \(0.791998\pi\)
\(312\) −9.30685 12.8098i −0.526896 0.725211i
\(313\) 16.3072 + 5.29854i 0.921739 + 0.299491i 0.731180 0.682185i \(-0.238970\pi\)
0.190559 + 0.981676i \(0.438970\pi\)
\(314\) −3.49823 + 10.7664i −0.197417 + 0.607586i
\(315\) 5.29628 + 1.39622i 0.298411 + 0.0786681i
\(316\) −2.05158 1.49056i −0.115411 0.0838508i
\(317\) 12.0084 3.90177i 0.674459 0.219145i 0.0482913 0.998833i \(-0.484622\pi\)
0.626168 + 0.779688i \(0.284622\pi\)
\(318\) 2.17209i 0.121805i
\(319\) 0 0
\(320\) 3.92820 3.20736i 0.219593 0.179297i
\(321\) 1.77130 + 5.45150i 0.0988644 + 0.304273i
\(322\) −3.54775 + 4.88306i −0.197708 + 0.272122i
\(323\) −9.52958 13.1163i −0.530240 0.729813i
\(324\) −5.70572 + 17.5604i −0.316985 + 0.975578i
\(325\) 10.4578 18.4563i 0.580094 1.02377i
\(326\) −2.15219 + 1.56366i −0.119199 + 0.0866030i
\(327\) 10.4424 14.3727i 0.577464 0.794811i
\(328\) −3.18230 + 1.03399i −0.175713 + 0.0570926i
\(329\) −38.3205 −2.11268
\(330\) 0 0
\(331\) −18.1962 −1.00015 −0.500075 0.865982i \(-0.666694\pi\)
−0.500075 + 0.865982i \(0.666694\pi\)
\(332\) 16.3072 5.29854i 0.894975 0.290795i
\(333\) −0.771573 + 1.06198i −0.0422819 + 0.0581961i
\(334\) 0.216775 0.157497i 0.0118614 0.00861783i
\(335\) 4.60473 1.78897i 0.251583 0.0977421i
\(336\) −4.92209 + 15.1486i −0.268522 + 0.826425i
\(337\) −10.3608 14.2605i −0.564391 0.776817i 0.427486 0.904022i \(-0.359399\pi\)
−0.991876 + 0.127205i \(0.959399\pi\)
\(338\) 1.52130 2.09389i 0.0827478 0.113893i
\(339\) 1.68850 + 5.19667i 0.0917067 + 0.282244i
\(340\) −9.46410 11.5911i −0.513263 0.628616i
\(341\) 0 0
\(342\) 1.59008i 0.0859816i
\(343\) −8.92268 + 2.89915i −0.481779 + 0.156540i
\(344\) 10.0837 + 7.32622i 0.543675 + 0.395003i
\(345\) −3.83730 + 14.5560i −0.206593 + 0.783670i
\(346\) 3.48199 10.7165i 0.187193 0.576120i
\(347\) 4.16690 + 1.35391i 0.223691 + 0.0726816i 0.418718 0.908116i \(-0.362479\pi\)
−0.195027 + 0.980798i \(0.562479\pi\)
\(348\) −13.6262 18.7548i −0.730439 1.00536i
\(349\) 5.92242 + 4.30289i 0.317020 + 0.230328i 0.734903 0.678173i \(-0.237228\pi\)
−0.417883 + 0.908501i \(0.637228\pi\)
\(350\) 8.60522 0.974818i 0.459968 0.0521062i
\(351\) −18.5885 −0.992178
\(352\) 0 0
\(353\) 13.0053i 0.692204i 0.938197 + 0.346102i \(0.112495\pi\)
−0.938197 + 0.346102i \(0.887505\pi\)
\(354\) 0.391818 + 1.20589i 0.0208249 + 0.0640924i
\(355\) 18.2980 1.03312i 0.971158 0.0548321i
\(356\) 0.650326 0.472490i 0.0344672 0.0250419i
\(357\) 23.7530 + 7.71781i 1.25714 + 0.408470i
\(358\) −7.61302 2.47362i −0.402361 0.130735i
\(359\) −28.8498 + 20.9606i −1.52263 + 1.10626i −0.562468 + 0.826819i \(0.690148\pi\)
−0.960164 + 0.279437i \(0.909852\pi\)
\(360\) −0.178260 3.15725i −0.00939513 0.166402i
\(361\) −0.430246 1.32416i −0.0226445 0.0696927i
\(362\) 9.00292i 0.473183i
\(363\) 0 0
\(364\) −24.5885 −1.28879
\(365\) 5.92905 9.21121i 0.310341 0.482137i
\(366\) −9.49143 6.89593i −0.496125 0.360456i
\(367\) 9.93721 + 13.6774i 0.518718 + 0.713954i 0.985359 0.170493i \(-0.0545359\pi\)
−0.466641 + 0.884447i \(0.654536\pi\)
\(368\) −8.16655 2.65347i −0.425711 0.138322i
\(369\) 0.391818 1.20589i 0.0203972 0.0627762i
\(370\) −0.529080 + 2.00696i −0.0275056 + 0.104337i
\(371\) −5.87989 4.27199i −0.305269 0.221791i
\(372\) 27.7880 9.02886i 1.44074 0.468125i
\(373\) 0.175865i 0.00910597i 0.999990 + 0.00455298i \(0.00144926\pi\)
−0.999990 + 0.00455298i \(0.998551\pi\)
\(374\) 0 0
\(375\) 19.1244 10.0382i 0.987577 0.518370i
\(376\) 6.83680 + 21.0415i 0.352581 + 1.08513i
\(377\) 17.2773 23.7801i 0.889826 1.22474i
\(378\) −4.46053 6.13939i −0.229425 0.315776i
\(379\) −0.452432 + 1.39244i −0.0232399 + 0.0715250i −0.962004 0.273036i \(-0.911972\pi\)
0.938764 + 0.344561i \(0.111972\pi\)
\(380\) 5.88532 + 15.1485i 0.301911 + 0.777104i
\(381\) 1.40126 1.01807i 0.0717886 0.0521575i
\(382\) 2.21135 3.04366i 0.113142 0.155727i
\(383\) −36.5787 + 11.8852i −1.86909 + 0.607303i −0.877209 + 0.480109i \(0.840597\pi\)
−0.991878 + 0.127194i \(0.959403\pi\)
\(384\) 22.1244 1.12903
\(385\) 0 0
\(386\) 7.85641 0.399881
\(387\) −4.49195 + 1.45952i −0.228339 + 0.0741917i
\(388\) −9.30685 + 12.8098i −0.472483 + 0.650318i
\(389\) 4.95471 3.59981i 0.251214 0.182517i −0.455051 0.890465i \(-0.650379\pi\)
0.706265 + 0.707948i \(0.250379\pi\)
\(390\) 8.84291 3.43554i 0.447778 0.173965i
\(391\) −4.16064 + 12.8051i −0.210412 + 0.647583i
\(392\) −4.76479 6.55817i −0.240658 0.331238i
\(393\) 3.54775 4.88306i 0.178960 0.246318i
\(394\) −2.75897 8.49123i −0.138995 0.427782i
\(395\) 2.53590 2.07055i 0.127595 0.104181i
\(396\) 0 0
\(397\) 32.9802i 1.65523i 0.561298 + 0.827614i \(0.310302\pi\)
−0.561298 + 0.827614i \(0.689698\pi\)
\(398\) 0.984606 0.319918i 0.0493538 0.0160360i
\(399\) −21.9441 15.9433i −1.09858 0.798163i
\(400\) 5.10200 + 11.2145i 0.255100 + 0.560724i
\(401\) 0.717076 2.20693i 0.0358091 0.110209i −0.931554 0.363602i \(-0.881547\pi\)
0.967363 + 0.253393i \(0.0815467\pi\)
\(402\) 2.10112 + 0.682697i 0.104795 + 0.0340498i
\(403\) 21.7757 + 29.9716i 1.08472 + 1.49299i
\(404\) 27.1736 + 19.7428i 1.35194 + 0.982241i
\(405\) −20.0437 12.9017i −0.995981 0.641091i
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 14.4195i 0.713873i
\(409\) −8.07287 24.8457i −0.399178 1.22854i −0.925660 0.378357i \(-0.876489\pi\)
0.526482 0.850186i \(-0.323511\pi\)
\(410\) −0.113012 2.00162i −0.00558128 0.0988528i
\(411\) −13.8539 + 10.0654i −0.683362 + 0.496492i
\(412\) −6.98881 2.27080i −0.344314 0.111874i
\(413\) 4.03499 + 1.31105i 0.198549 + 0.0645125i
\(414\) −1.06831 + 0.776175i −0.0525047 + 0.0381469i
\(415\) 1.24782 + 22.1007i 0.0612531 + 1.08488i
\(416\) 6.73776 + 20.7367i 0.330346 + 1.01670i
\(417\) 28.1827i 1.38011i
\(418\) 0 0
\(419\) 12.3397 0.602836 0.301418 0.953492i \(-0.402540\pi\)
0.301418 + 0.953492i \(0.402540\pi\)
\(420\) −21.0513 13.5503i −1.02720 0.661186i
\(421\) 13.7958 + 10.0232i 0.672367 + 0.488503i 0.870817 0.491608i \(-0.163591\pi\)
−0.198450 + 0.980111i \(0.563591\pi\)
\(422\) 3.99322 + 5.49619i 0.194387 + 0.267550i
\(423\) −7.97342 2.59072i −0.387681 0.125965i
\(424\) −1.29668 + 3.99078i −0.0629725 + 0.193809i
\(425\) 17.5843 7.99992i 0.852962 0.388053i
\(426\) 6.63083 + 4.81758i 0.321265 + 0.233412i
\(427\) −37.3349 + 12.1308i −1.80676 + 0.587052i
\(428\) 5.13922i 0.248413i
\(429\) 0 0
\(430\) −5.78461 + 4.72311i −0.278959 + 0.227769i
\(431\) 1.56727 + 4.82357i 0.0754928 + 0.232343i 0.981681 0.190531i \(-0.0610211\pi\)
−0.906188 + 0.422874i \(0.861021\pi\)
\(432\) 6.34577 8.73420i 0.305311 0.420225i
\(433\) −16.8915 23.2492i −0.811754 1.11728i −0.991050 0.133488i \(-0.957382\pi\)
0.179297 0.983795i \(-0.442618\pi\)
\(434\) −4.67368 + 14.3841i −0.224344 + 0.690460i
\(435\) 27.8967 10.8381i 1.33755 0.519647i
\(436\) −12.8862 + 9.36236i −0.617136 + 0.448376i
\(437\) 8.59495 11.8299i 0.411152 0.565903i
\(438\) 4.65921 1.51387i 0.222625 0.0723354i
\(439\) 28.2487 1.34824 0.674119 0.738623i \(-0.264524\pi\)
0.674119 + 0.738623i \(0.264524\pi\)
\(440\) 0 0
\(441\) 3.07180 0.146276
\(442\) 8.06998 2.62210i 0.383850 0.124720i
\(443\) −16.2015 + 22.2994i −0.769754 + 1.05948i 0.226585 + 0.973991i \(0.427244\pi\)
−0.996339 + 0.0854846i \(0.972756\pi\)
\(444\) 4.85410 3.52671i 0.230365 0.167370i
\(445\) 0.375813 + 0.967324i 0.0178152 + 0.0458556i
\(446\) −0.248403 + 0.764504i −0.0117622 + 0.0362003i
\(447\) 11.6594 + 16.0478i 0.551471 + 0.759034i
\(448\) 4.46053 6.13939i 0.210740 0.290059i
\(449\) −10.6662 32.8273i −0.503371 1.54922i −0.803492 0.595315i \(-0.797027\pi\)
0.300122 0.953901i \(-0.402973\pi\)
\(450\) 1.85641 + 0.378937i 0.0875118 + 0.0178633i
\(451\) 0 0
\(452\) 4.89898i 0.230429i
\(453\) 7.70959 2.50500i 0.362228 0.117695i
\(454\) 8.42312 + 6.11975i 0.395316 + 0.287214i
\(455\) 8.09187 30.6949i 0.379353 1.43900i
\(456\) −4.83928 + 14.8938i −0.226620 + 0.697465i
\(457\) 20.1750 + 6.55524i 0.943745 + 0.306641i 0.740171 0.672418i \(-0.234744\pi\)
0.203573 + 0.979060i \(0.434744\pi\)
\(458\) 1.23889 + 1.70518i 0.0578893 + 0.0796778i
\(459\) −13.6952 9.95015i −0.639237 0.464433i
\(460\) 7.30489 11.3487i 0.340592 0.529135i
\(461\) 33.0000 1.53696 0.768482 0.639872i \(-0.221013\pi\)
0.768482 + 0.639872i \(0.221013\pi\)
\(462\) 0 0
\(463\) 20.3166i 0.944194i 0.881547 + 0.472097i \(0.156503\pi\)
−0.881547 + 0.472097i \(0.843497\pi\)
\(464\) 5.27548 + 16.2362i 0.244908 + 0.753749i
\(465\) 2.12632 + 37.6603i 0.0986058 + 1.74646i
\(466\) −0.708411 + 0.514691i −0.0328165 + 0.0238426i
\(467\) −0.588870 0.191335i −0.0272496 0.00885394i 0.295360 0.955386i \(-0.404560\pi\)
−0.322610 + 0.946532i \(0.604560\pi\)
\(468\) −5.11616 1.66234i −0.236495 0.0768418i
\(469\) 5.98050 4.34509i 0.276154 0.200638i
\(470\) −13.2348 + 0.747243i −0.610475 + 0.0344678i
\(471\) 13.0556 + 40.1809i 0.601569 + 1.85144i
\(472\) 2.44949i 0.112747i
\(473\) 0 0
\(474\) 1.46410 0.0672484
\(475\) −20.8474 + 2.36164i −0.956545 + 0.108360i
\(476\) −18.1158 13.1619i −0.830334 0.603273i
\(477\) −0.934625 1.28640i −0.0427935 0.0589003i
\(478\) −2.78656 0.905408i −0.127454 0.0414124i
\(479\) 0.783636 2.41178i 0.0358052 0.110197i −0.931557 0.363597i \(-0.881549\pi\)
0.967362 + 0.253399i \(0.0815487\pi\)
\(480\) −5.65912 + 21.4667i −0.258302 + 0.979818i
\(481\) 6.15475 + 4.47169i 0.280633 + 0.203892i
\(482\) −6.95346 + 2.25932i −0.316722 + 0.102909i
\(483\) 22.5259i 1.02496i
\(484\) 0 0
\(485\) −12.9282 15.8338i −0.587039 0.718974i
\(486\) −1.19170 3.66766i −0.0540564 0.166368i
\(487\) 7.48128 10.2971i 0.339009 0.466606i −0.605142 0.796117i \(-0.706884\pi\)
0.944152 + 0.329511i \(0.106884\pi\)
\(488\) 13.3219 + 18.3360i 0.603054 + 0.830033i
\(489\) −3.06798 + 9.44228i −0.138739 + 0.426995i
\(490\) 4.52727 1.75888i 0.204521 0.0794580i
\(491\) 32.1283 23.3426i 1.44993 1.05344i 0.464084 0.885791i \(-0.346383\pi\)
0.985847 0.167646i \(-0.0536166\pi\)
\(492\) −3.40654 + 4.68870i −0.153579 + 0.211383i
\(493\) 25.4584 8.27193i 1.14659 0.372549i
\(494\) −9.21539 −0.414620
\(495\) 0 0
\(496\) −21.5167 −0.966127
\(497\) 26.0826 8.47475i 1.16996 0.380144i
\(498\) −5.81878 + 8.00886i −0.260746 + 0.358886i
\(499\) 14.2449 10.3495i 0.637690 0.463309i −0.221366 0.975191i \(-0.571051\pi\)
0.859056 + 0.511882i \(0.171051\pi\)
\(500\) −19.0884 + 3.26097i −0.853658 + 0.145835i
\(501\) 0.309017 0.951057i 0.0138059 0.0424901i
\(502\) −1.15736 1.59297i −0.0516555 0.0710976i
\(503\) −4.34117 + 5.97510i −0.193563 + 0.266417i −0.894756 0.446554i \(-0.852651\pi\)
0.701193 + 0.712971i \(0.252651\pi\)
\(504\) −1.46228 4.50045i −0.0651353 0.200466i
\(505\) −33.5885 + 27.4249i −1.49467 + 1.22039i
\(506\) 0 0
\(507\) 9.65926i 0.428983i
\(508\) −1.47691 + 0.479877i −0.0655273 + 0.0212911i
\(509\) −6.53022 4.74448i −0.289447 0.210296i 0.433580 0.901115i \(-0.357250\pi\)
−0.723027 + 0.690819i \(0.757250\pi\)
\(510\) 8.35409 + 2.20233i 0.369925 + 0.0975208i
\(511\) 5.06550 15.5900i 0.224085 0.689661i
\(512\) −21.0983 6.85527i −0.932424 0.302963i
\(513\) 10.8063 + 14.8736i 0.477110 + 0.656685i
\(514\) −6.19728 4.50258i −0.273350 0.198600i
\(515\) 5.13471 7.97714i 0.226262 0.351515i
\(516\) 21.5885 0.950379
\(517\) 0 0
\(518\) 3.10583i 0.136462i
\(519\) −12.9950 39.9944i −0.570415 1.75556i
\(520\) −18.2980 + 1.03312i −0.802421 + 0.0453051i
\(521\) 7.48236 5.43626i 0.327808 0.238167i −0.411692 0.911323i \(-0.635062\pi\)
0.739500 + 0.673156i \(0.235062\pi\)
\(522\) 2.49686 + 0.811279i 0.109285 + 0.0355087i
\(523\) 24.3772 + 7.92063i 1.06594 + 0.346345i 0.788905 0.614515i \(-0.210648\pi\)
0.277035 + 0.960860i \(0.410648\pi\)
\(524\) −4.37803 + 3.18083i −0.191255 + 0.138955i
\(525\) 23.8433 21.8200i 1.04061 0.952305i
\(526\) −1.08671 3.34454i −0.0473827 0.145829i
\(527\) 33.7381i 1.46965i
\(528\) 0 0
\(529\) 10.8564 0.472018
\(530\) −2.11405 1.36077i −0.0918284 0.0591079i
\(531\) 0.750932 + 0.545584i 0.0325877 + 0.0236763i
\(532\) 14.2944 + 19.6745i 0.619739 + 0.852998i
\(533\) −6.98881 2.27080i −0.302719 0.0983593i
\(534\) −0.143415 + 0.441387i −0.00620619 + 0.0191007i
\(535\) 6.41551 + 1.69128i 0.277367 + 0.0731203i
\(536\) −3.45284 2.50864i −0.149140 0.108357i
\(537\) −28.4122 + 9.23168i −1.22608 + 0.398376i
\(538\) 8.42091i 0.363051i
\(539\) 0 0
\(540\) 10.7321 + 13.1440i 0.461834 + 0.565629i
\(541\) 0.805822 + 2.48007i 0.0346450 + 0.106626i 0.966884 0.255218i \(-0.0821472\pi\)
−0.932239 + 0.361844i \(0.882147\pi\)
\(542\) 3.48807 4.80091i 0.149825 0.206217i
\(543\) 19.7492 + 27.1824i 0.847519 + 1.16651i
\(544\) −6.13597 + 18.8846i −0.263077 + 0.809669i
\(545\) −7.44671 19.1675i −0.318982 0.821045i
\(546\) 11.4849 8.34429i 0.491510 0.357103i
\(547\) 16.8915 23.2492i 0.722228 0.994062i −0.277218 0.960807i \(-0.589413\pi\)
0.999447 0.0332552i \(-0.0105874\pi\)
\(548\) 14.6018 4.74442i 0.623759 0.202672i
\(549\) −8.58846 −0.366546
\(550\) 0 0
\(551\) −29.0718 −1.23850
\(552\) 12.3688 4.01887i 0.526451 0.171054i
\(553\) 2.87955 3.96336i 0.122451 0.168539i
\(554\) −13.0604 + 9.48897i −0.554885 + 0.403148i
\(555\) 2.80510 + 7.22021i 0.119070 + 0.306481i
\(556\) −7.80823 + 24.0312i −0.331143 + 1.01915i
\(557\) −22.1018 30.4205i −0.936482 1.28896i −0.957277 0.289173i \(-0.906620\pi\)
0.0207955 0.999784i \(-0.493380\pi\)
\(558\) −1.94492 + 2.67696i −0.0823352 + 0.113325i
\(559\) 8.45874 + 26.0333i 0.357767 + 1.10109i
\(560\) 11.6603 + 14.2808i 0.492736 + 0.603475i
\(561\) 0 0
\(562\) 8.96575i 0.378198i
\(563\) −15.1907 + 4.93576i −0.640212 + 0.208017i −0.611093 0.791559i \(-0.709270\pi\)
−0.0291185 + 0.999576i \(0.509270\pi\)
\(564\) 31.0019 + 22.5242i 1.30542 + 0.948441i
\(565\) 6.11562 + 1.61222i 0.257286 + 0.0678265i
\(566\) −1.29074 + 3.97248i −0.0542537 + 0.166976i
\(567\) −33.9241 11.0226i −1.42468 0.462906i
\(568\) −9.30685 12.8098i −0.390507 0.537486i
\(569\) −24.3711 17.7067i −1.02169 0.742301i −0.0550616 0.998483i \(-0.517536\pi\)
−0.966629 + 0.256181i \(0.917536\pi\)
\(570\) −7.88973 5.07844i −0.330465 0.212713i
\(571\) 19.7128 0.824956 0.412478 0.910968i \(-0.364663\pi\)
0.412478 + 0.910968i \(0.364663\pi\)
\(572\) 0 0
\(573\) 14.0406i 0.586554i
\(574\) −0.927051 2.85317i −0.0386944 0.119089i
\(575\) 11.7631 + 12.8538i 0.490554 + 0.536040i
\(576\) 1.34317 0.975873i 0.0559656 0.0406614i
\(577\) −3.57803 1.16257i −0.148955 0.0483986i 0.233590 0.972335i \(-0.424953\pi\)
−0.382546 + 0.923937i \(0.624953\pi\)
\(578\) −1.01995 0.331402i −0.0424244 0.0137845i
\(579\) 23.7208 17.2342i 0.985802 0.716227i
\(580\) −26.7901 + 1.51259i −1.11240 + 0.0628067i
\(581\) 10.2360 + 31.5031i 0.424660 + 1.30697i
\(582\) 9.14162i 0.378932i
\(583\) 0 0
\(584\) −9.46410 −0.391627
\(585\) 3.75887 5.83967i 0.155410 0.241441i
\(586\) −6.31345 4.58699i −0.260806 0.189487i
\(587\) 11.9855 + 16.4966i 0.494695 + 0.680889i 0.981245 0.192764i \(-0.0617451\pi\)
−0.486551 + 0.873652i \(0.661745\pi\)
\(588\) −13.3534 4.33878i −0.550685 0.178928i
\(589\) 11.3227 34.8477i 0.466544 1.43587i
\(590\) 1.41913 + 0.374116i 0.0584248 + 0.0154021i
\(591\) −26.9569 19.5853i −1.10886 0.805632i
\(592\) −4.20225 + 1.36539i −0.172711 + 0.0561173i
\(593\) 0.859411i 0.0352918i 0.999844 + 0.0176459i \(0.00561715\pi\)
−0.999844 + 0.0176459i \(0.994383\pi\)
\(594\) 0 0
\(595\) 22.3923 18.2832i 0.917995 0.749540i
\(596\) −5.49575 16.9142i −0.225115 0.692831i
\(597\) 2.27103 3.12580i 0.0929470 0.127931i
\(598\) 4.49837 + 6.19147i 0.183952 + 0.253188i
\(599\) 11.8801 36.5632i 0.485408 1.49393i −0.345980 0.938242i \(-0.612454\pi\)
0.831389 0.555692i \(-0.187546\pi\)
\(600\) −16.2351 9.19922i −0.662796 0.375557i
\(601\) 16.1803 11.7557i 0.660010 0.479525i −0.206656 0.978414i \(-0.566258\pi\)
0.866666 + 0.498888i \(0.166258\pi\)
\(602\) −6.56850 + 9.04077i −0.267712 + 0.368474i
\(603\) 1.53813 0.499769i 0.0626375 0.0203522i
\(604\) −7.26795 −0.295729
\(605\) 0 0
\(606\) −19.3923 −0.787759
\(607\) 34.6095 11.2453i 1.40476 0.456433i 0.494031 0.869444i \(-0.335523\pi\)
0.910726 + 0.413011i \(0.135523\pi\)
\(608\) 12.6756 17.4464i 0.514061 0.707545i
\(609\) 36.2315 26.3237i 1.46817 1.06669i
\(610\) −12.6578 + 4.91766i −0.512500 + 0.199110i
\(611\) −15.0147 + 46.2104i −0.607428 + 1.86947i
\(612\) −2.87955 3.96336i −0.116399 0.160209i
\(613\) 1.05399 1.45069i 0.0425702 0.0585928i −0.787201 0.616696i \(-0.788471\pi\)
0.829771 + 0.558103i \(0.188471\pi\)
\(614\) 1.25231 + 3.85421i 0.0505391 + 0.155543i
\(615\) −4.73205 5.79555i −0.190815 0.233699i
\(616\) 0 0
\(617\) 13.0053i 0.523575i 0.965126 + 0.261787i \(0.0843119\pi\)
−0.965126 + 0.261787i \(0.915688\pi\)
\(618\) 4.03499 1.31105i 0.162311 0.0527381i
\(619\) 10.3430 + 7.51461i 0.415719 + 0.302037i 0.775913 0.630840i \(-0.217290\pi\)
−0.360194 + 0.932877i \(0.617290\pi\)
\(620\) 8.62095 32.7018i 0.346226 1.31334i
\(621\) 4.71806 14.5207i 0.189329 0.582695i
\(622\) −4.94891 1.60800i −0.198433 0.0644748i
\(623\) 0.912780 + 1.25633i 0.0365698 + 0.0503340i
\(624\) 16.3390 + 11.8710i 0.654085 + 0.475220i
\(625\) 2.21102 24.9020i 0.0884409 0.996081i
\(626\) 8.87564 0.354742
\(627\) 0 0
\(628\) 37.8792i 1.51154i
\(629\) 2.14093 + 6.58911i 0.0853646 + 0.262725i
\(630\) 2.83071 0.159824i 0.112778 0.00636752i
\(631\) 12.3946 9.00517i 0.493419 0.358490i −0.313078 0.949727i \(-0.601360\pi\)
0.806498 + 0.591237i \(0.201360\pi\)
\(632\) −2.68999 0.874032i −0.107002 0.0347671i
\(633\) 24.1134 + 7.83491i 0.958421 + 0.311410i
\(634\) 5.28765 3.84170i 0.210000 0.152574i
\(635\) −0.113012 2.00162i −0.00448476 0.0794317i
\(636\) 2.24592 + 6.91223i 0.0890565 + 0.274088i
\(637\) 17.8028i 0.705371i
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 13.8604 21.5332i 0.547881 0.851173i
\(641\) 6.35597 + 4.61788i 0.251046 + 0.182395i 0.706190 0.708022i \(-0.250412\pi\)
−0.455144 + 0.890418i \(0.650412\pi\)
\(642\) 1.74403 + 2.40046i 0.0688315 + 0.0947385i
\(643\) 10.0038 + 3.25045i 0.394513 + 0.128185i 0.499554 0.866283i \(-0.333497\pi\)
−0.105041 + 0.994468i \(0.533497\pi\)
\(644\) 6.24095 19.2077i 0.245928 0.756889i
\(645\) −7.10460 + 26.9498i −0.279743 + 1.06115i
\(646\) −6.78952 4.93287i −0.267130 0.194081i
\(647\) 35.5329 11.5453i 1.39694 0.453894i 0.488742 0.872428i \(-0.337456\pi\)
0.908201 + 0.418534i \(0.137456\pi\)
\(648\) 20.5940i 0.809010i
\(649\) 0 0
\(650\) 2.19615 10.7589i 0.0861402 0.421999i
\(651\) 17.4424 + 53.6823i 0.683622 + 2.10397i
\(652\) 5.23210 7.20137i 0.204905 0.282027i
\(653\) 7.13919 + 9.82625i 0.279378 + 0.384531i 0.925528 0.378680i \(-0.123622\pi\)
−0.646150 + 0.763211i \(0.723622\pi\)
\(654\) 2.84177 8.74606i 0.111122 0.341998i
\(655\) −2.52999 6.51208i −0.0988549 0.254448i
\(656\) 3.45284 2.50864i 0.134811 0.0979458i
\(657\) 2.10798 2.90138i 0.0822400 0.113194i
\(658\) −18.8653 + 6.12971i −0.735446 + 0.238961i
\(659\) −23.3205 −0.908438 −0.454219 0.890890i \(-0.650082\pi\)
−0.454219 + 0.890890i \(0.650082\pi\)
\(660\) 0 0
\(661\) 29.5885 1.15086 0.575429 0.817852i \(-0.304835\pi\)
0.575429 + 0.817852i \(0.304835\pi\)
\(662\) −8.95802 + 2.91064i −0.348163 + 0.113125i
\(663\) 18.6137 25.6195i 0.722896 0.994981i
\(664\) 15.4719 11.2410i 0.600427 0.436236i
\(665\) −29.2647 + 11.3696i −1.13484 + 0.440893i
\(666\) −0.209975 + 0.646235i −0.00813635 + 0.0250411i
\(667\) 14.1910 + 19.5322i 0.549478 + 0.756291i
\(668\) −0.526994 + 0.725345i −0.0203900 + 0.0280644i
\(669\) 0.927051 + 2.85317i 0.0358419 + 0.110310i
\(670\) 1.98076 1.61729i 0.0765235 0.0624812i
\(671\) 0 0
\(672\) 33.2204i 1.28151i
\(673\) 38.8118 12.6107i 1.49608 0.486107i 0.557211 0.830371i \(-0.311871\pi\)
0.938873 + 0.344264i \(0.111871\pi\)
\(674\) −7.38176 5.36316i −0.284335 0.206581i
\(675\) −19.9401 + 9.07170i −0.767495 + 0.349170i
\(676\) −2.67617 + 8.23639i −0.102929 + 0.316784i
\(677\) −19.3576 6.28967i −0.743973 0.241732i −0.0875873 0.996157i \(-0.527916\pi\)
−0.656386 + 0.754425i \(0.727916\pi\)
\(678\) 1.66251 + 2.28825i 0.0638482 + 0.0878795i
\(679\) −24.7466 17.9794i −0.949687 0.689988i
\(680\) −14.0342 9.03352i −0.538188 0.346420i
\(681\) 38.8564 1.48898
\(682\) 0 0
\(683\) 29.8372i 1.14169i −0.821058 0.570844i \(-0.806616\pi\)
0.821058 0.570844i \(-0.193384\pi\)
\(684\) 1.64413 + 5.06010i 0.0628648 + 0.193478i
\(685\) 1.11732 + 19.7895i 0.0426908 + 0.756117i
\(686\) −3.92892 + 2.85452i −0.150007 + 0.108986i
\(687\) 7.48111 + 2.43076i 0.285422 + 0.0927393i
\(688\) −15.1200 4.91279i −0.576445 0.187298i
\(689\) −7.45541 + 5.41667i −0.284028 + 0.206359i
\(690\) 0.439251 + 7.77978i 0.0167220 + 0.296171i
\(691\) 11.7145 + 36.0536i 0.445641 + 1.37154i 0.881779 + 0.471663i \(0.156346\pi\)
−0.436138 + 0.899880i \(0.643654\pi\)
\(692\) 37.7033i 1.43326i
\(693\) 0 0
\(694\) 2.26795 0.0860902
\(695\) −27.4297 17.6559i −1.04047 0.669725i
\(696\) −20.9183 15.1980i −0.792905 0.576079i
\(697\) −3.93354 5.41405i −0.148993 0.205072i
\(698\) 3.60391 + 1.17098i 0.136410 + 0.0443223i
\(699\) −1.00985 + 3.10800i −0.0381961 + 0.117556i
\(700\) −26.3764 + 11.9999i −0.996934 + 0.453553i
\(701\) 30.6265 + 22.2514i 1.15675 + 0.840425i 0.989363 0.145467i \(-0.0464684\pi\)
0.167383 + 0.985892i \(0.446468\pi\)
\(702\) −9.15115 + 2.97339i −0.345388 + 0.112223i
\(703\) 7.52433i 0.283786i
\(704\) 0 0
\(705\) −38.3205 + 31.2886i −1.44323 + 1.17840i
\(706\) 2.08032 + 6.40256i 0.0782938 + 0.240964i
\(707\) −38.1402 + 52.4954i −1.43441 + 1.97429i
\(708\) −2.49376 3.43237i −0.0937213 0.128996i
\(709\) −0.805822 + 2.48007i −0.0302633 + 0.0931408i −0.965047 0.262076i \(-0.915593\pi\)
0.934784 + 0.355217i \(0.115593\pi\)
\(710\) 8.84291 3.43554i 0.331869 0.128933i
\(711\) 0.867102 0.629986i 0.0325189 0.0236263i
\(712\) 0.526994 0.725345i 0.0197499 0.0271834i
\(713\) −28.9398 + 9.40313i −1.08381 + 0.352150i
\(714\) 12.9282 0.483826
\(715\) 0 0
\(716\) 26.7846 1.00099
\(717\) −10.3996 + 3.37903i −0.388380 + 0.126192i
\(718\) −10.8500 + 14.9337i −0.404918 + 0.557322i
\(719\) −40.6095 + 29.5046i −1.51448 + 1.10033i −0.550340 + 0.834941i \(0.685502\pi\)
−0.964140 + 0.265394i \(0.914498\pi\)
\(720\) 1.46069 + 3.75975i 0.0544367 + 0.140118i
\(721\) 4.38685 13.5013i 0.163375 0.502816i
\(722\) −0.423623 0.583067i −0.0157656 0.0216995i
\(723\) −16.0384 + 22.0750i −0.596475 + 0.820977i
\(724\) −9.30894 28.6500i −0.345964 1.06477i
\(725\) 6.92820 33.9411i 0.257307 1.26054i
\(726\) 0 0
\(727\) 8.24504i 0.305792i −0.988242 0.152896i \(-0.951140\pi\)
0.988242 0.152896i \(-0.0488599\pi\)
\(728\) −26.0826 + 8.47475i −0.966685 + 0.314095i
\(729\) 14.2294 + 10.3382i 0.527013 + 0.382898i
\(730\) 1.44547 5.48311i 0.0534994 0.202939i
\(731\) −7.70324 + 23.7081i −0.284915 + 0.876877i
\(732\) 37.3349 + 12.1308i 1.37994 + 0.448369i
\(733\) 5.47668 + 7.53800i 0.202286 + 0.278423i 0.898093 0.439807i \(-0.144953\pi\)
−0.695807 + 0.718229i \(0.744953\pi\)
\(734\) 7.07994 + 5.14388i 0.261325 + 0.189864i
\(735\) 9.81080 15.2418i 0.361877 0.562202i
\(736\) −17.9090 −0.660133
\(737\) 0 0
\(738\) 0.656339i 0.0241602i
\(739\) −12.0295 37.0229i −0.442511 1.36191i −0.885190 0.465230i \(-0.845972\pi\)
0.442679 0.896680i \(-0.354028\pi\)
\(740\) −0.391486 6.93380i −0.0143913 0.254892i
\(741\) −27.8240 + 20.2153i −1.02214 + 0.742627i
\(742\) −3.57803 1.16257i −0.131354 0.0426794i
\(743\) 41.2733 + 13.4105i 1.51417 + 0.491984i 0.944113 0.329621i \(-0.106921\pi\)
0.570057 + 0.821605i \(0.306921\pi\)
\(744\) 26.3646 19.1550i 0.966574 0.702257i
\(745\) 22.9233 1.29426i 0.839846 0.0474181i
\(746\) 0.0281313 + 0.0865791i 0.00102996 + 0.00316989i
\(747\) 7.24693i 0.265151i
\(748\) 0 0
\(749\) 9.92820 0.362769
\(750\) 7.80928 8.00095i 0.285155 0.292153i
\(751\) −39.3514 28.5905i −1.43595 1.04328i −0.988869 0.148789i \(-0.952462\pi\)
−0.447084 0.894492i \(-0.647538\pi\)
\(752\) −16.5872 22.8304i −0.604874 0.832538i
\(753\) −6.98881 2.27080i −0.254686 0.0827526i
\(754\) 4.70181 14.4707i 0.171230 0.526992i
\(755\) 2.39183 9.07291i 0.0870475 0.330197i
\(756\) 20.5428 + 14.9252i 0.747135 + 0.542825i
\(757\) 47.3387 15.3813i 1.72056 0.559042i 0.728522 0.685022i \(-0.240207\pi\)
0.992033 + 0.125980i \(0.0402075\pi\)
\(758\) 0.757875i 0.0275273i
\(759\) 0 0
\(760\) 11.4641 + 14.0406i 0.415847 + 0.509306i
\(761\) 6.13597 + 18.8846i 0.222429 + 0.684565i 0.998542 + 0.0539721i \(0.0171882\pi\)
−0.776114 + 0.630593i \(0.782812\pi\)
\(762\) 0.526994 0.725345i 0.0190910 0.0262765i
\(763\) −18.0867 24.8942i −0.654782 0.901231i
\(764\) −3.89005 + 11.9723i −0.140737 + 0.433144i
\(765\) 5.89527 2.29036i 0.213144 0.0828081i
\(766\) −16.1067 + 11.7022i −0.581958 + 0.422818i
\(767\) 3.16196 4.35207i 0.114172 0.157144i
\(768\) 2.55808 0.831171i 0.0923068 0.0299923i
\(769\) −9.85641 −0.355431 −0.177716 0.984082i \(-0.556871\pi\)
−0.177716 + 0.984082i \(0.556871\pi\)
\(770\) 0 0
\(771\) −28.5885 −1.02959
\(772\) −25.0014 + 8.12345i −0.899821 + 0.292369i
\(773\) 7.07951 9.74411i 0.254632 0.350471i −0.662495 0.749067i \(-0.730502\pi\)
0.917127 + 0.398596i \(0.130502\pi\)
\(774\) −1.97794 + 1.43705i −0.0710955 + 0.0516539i
\(775\) 37.9861 + 21.5238i 1.36450 + 0.77315