Properties

Label 91.2.q.a.36.1
Level $91$
Weight $2$
Character 91.36
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 36.1
Root \(-1.12906 - 0.851598i\) of defining polynomial
Character \(\chi\) \(=\) 91.36
Dual form 91.2.q.a.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.34104 + 1.35160i) q^{2} +(0.172975 + 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} -3.25812i q^{5} +(-0.809880 - 0.467584i) q^{6} +(0.866025 + 0.500000i) q^{7} +8.94020i q^{8} +(1.44016 - 2.49443i) q^{9} +O(q^{10})\) \(q+(-2.34104 + 1.35160i) q^{2} +(0.172975 + 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} -3.25812i q^{5} +(-0.809880 - 0.467584i) q^{6} +(0.866025 + 0.500000i) q^{7} +8.94020i q^{8} +(1.44016 - 2.49443i) q^{9} +(4.40367 + 7.62739i) q^{10} +(-1.59871 + 0.923014i) q^{11} +1.83605 q^{12} +(3.60550 + 0.0186461i) q^{13} -2.70320 q^{14} +(0.976136 - 0.563573i) q^{15} +(-6.77628 - 11.7369i) q^{16} +(1.07657 - 1.86467i) q^{17} +7.78607i q^{18} +(-2.07929 - 1.20048i) q^{19} +(-14.9751 - 8.64587i) q^{20} +0.345949i q^{21} +(2.49509 - 4.32162i) q^{22} +(0.906314 + 1.56978i) q^{23} +(-2.67849 + 1.54643i) q^{24} -5.61537 q^{25} +(-8.46582 + 4.82954i) q^{26} +2.03429 q^{27} +(4.59623 - 2.65363i) q^{28} +(1.36703 + 2.36777i) q^{29} +(-1.52345 + 2.63869i) q^{30} -1.74236i q^{31} +(16.2422 + 9.37743i) q^{32} +(-0.553071 - 0.319316i) q^{33} +5.82036i q^{34} +(1.62906 - 2.82162i) q^{35} +(-7.64331 - 13.2386i) q^{36} +(-5.14042 + 2.96783i) q^{37} +6.49025 q^{38} +(0.618074 + 1.08344i) q^{39} +29.1283 q^{40} +(3.65577 - 2.11066i) q^{41} +(-0.467584 - 0.809880i) q^{42} +(-4.34111 + 7.51903i) q^{43} +9.79737i q^{44} +(-8.12716 - 4.69222i) q^{45} +(-4.24343 - 2.44994i) q^{46} +5.87774i q^{47} +(2.34425 - 4.06036i) q^{48} +(0.500000 + 0.866025i) q^{49} +(13.1458 - 7.58972i) q^{50} +0.744877 q^{51} +(9.65339 - 16.5222i) q^{52} -9.30628 q^{53} +(-4.76235 + 2.74954i) q^{54} +(3.00729 + 5.20878i) q^{55} +(-4.47010 + 7.74244i) q^{56} -0.830609i q^{57} +(-6.40054 - 3.69535i) q^{58} +(9.31173 + 5.37613i) q^{59} -5.98206i q^{60} +(-5.05504 + 8.75558i) q^{61} +(2.35497 + 4.07893i) q^{62} +(2.49443 - 1.44016i) q^{63} -23.5929 q^{64} +(0.0607514 - 11.7472i) q^{65} +1.72635 q^{66} +(0.716130 - 0.413458i) q^{67} +(-5.71365 - 9.89633i) q^{68} +(-0.313538 + 0.543065i) q^{69} +8.80735i q^{70} +(-2.03884 - 1.17712i) q^{71} +(22.3007 + 12.8753i) q^{72} +3.19482i q^{73} +(8.02261 - 13.8956i) q^{74} +(-0.971316 - 1.68237i) q^{75} +(-11.0353 + 6.37126i) q^{76} -1.84603 q^{77} +(-2.91130 - 1.70098i) q^{78} +0.801911 q^{79} +(-38.2402 + 22.0780i) q^{80} +(-3.96860 - 6.87381i) q^{81} +(-5.70552 + 9.88225i) q^{82} -9.97031i q^{83} +(1.59006 + 0.918023i) q^{84} +(-6.07534 - 3.50760i) q^{85} -23.4698i q^{86} +(-0.472923 + 0.819127i) q^{87} +(-8.25193 - 14.2928i) q^{88} +(13.0886 - 7.55674i) q^{89} +25.3680 q^{90} +(3.11313 + 1.81890i) q^{91} +9.62010 q^{92} +(0.522012 - 0.301384i) q^{93} +(-7.94435 - 13.7600i) q^{94} +(-3.91130 + 6.77458i) q^{95} +6.48823i q^{96} +(7.99489 + 4.61585i) q^{97} +(-2.34104 - 1.35160i) q^{98} +5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + O(q^{10}) \) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + 12q^{10} + 6q^{11} - 4q^{12} + 4q^{13} - 8q^{14} + 6q^{15} - 8q^{16} - 4q^{17} - 12q^{20} + 6q^{22} - 12q^{23} + 12q^{24} - 20q^{25} - 42q^{26} + 12q^{27} + 8q^{29} + 8q^{30} + 36q^{32} - 30q^{33} + 6q^{35} - 10q^{36} - 42q^{37} + 4q^{38} - 4q^{39} + 92q^{40} + 30q^{41} + 4q^{42} + 2q^{43} + 12q^{46} - 2q^{48} + 6q^{49} - 18q^{50} + 52q^{51} + 2q^{52} - 44q^{53} + 12q^{54} - 6q^{55} - 12q^{56} - 12q^{58} + 18q^{59} + 14q^{61} - 4q^{62} + 12q^{63} - 52q^{64} + 60q^{65} - 52q^{66} - 24q^{67} - 8q^{68} + 4q^{69} - 24q^{71} + 60q^{72} + 6q^{74} + 46q^{75} - 18q^{76} + 8q^{77} - 10q^{78} - 56q^{79} - 72q^{80} + 2q^{81} + 14q^{82} + 18q^{84} - 48q^{85} - 2q^{87} - 14q^{88} - 12q^{89} + 24q^{90} + 14q^{91} + 24q^{92} - 18q^{93} + 4q^{94} - 22q^{95} + 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34104 + 1.35160i −1.65536 + 0.955724i −0.680549 + 0.732702i \(0.738259\pi\)
−0.974813 + 0.223022i \(0.928408\pi\)
\(3\) 0.172975 + 0.299601i 0.0998669 + 0.172975i 0.911629 0.411013i \(-0.134825\pi\)
−0.811763 + 0.583988i \(0.801492\pi\)
\(4\) 2.65363 4.59623i 1.32682 2.29811i
\(5\) 3.25812i 1.45708i −0.685005 0.728539i \(-0.740200\pi\)
0.685005 0.728539i \(-0.259800\pi\)
\(6\) −0.809880 0.467584i −0.330632 0.190890i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 8.94020i 3.16084i
\(9\) 1.44016 2.49443i 0.480053 0.831477i
\(10\) 4.40367 + 7.62739i 1.39256 + 2.41199i
\(11\) −1.59871 + 0.923014i −0.482028 + 0.278299i −0.721261 0.692663i \(-0.756437\pi\)
0.239233 + 0.970962i \(0.423104\pi\)
\(12\) 1.83605 0.530021
\(13\) 3.60550 + 0.0186461i 0.999987 + 0.00517151i
\(14\) −2.70320 −0.722460
\(15\) 0.976136 0.563573i 0.252037 0.145514i
\(16\) −6.77628 11.7369i −1.69407 2.93422i
\(17\) 1.07657 1.86467i 0.261107 0.452250i −0.705430 0.708780i \(-0.749246\pi\)
0.966536 + 0.256530i \(0.0825793\pi\)
\(18\) 7.78607i 1.83519i
\(19\) −2.07929 1.20048i −0.477021 0.275408i 0.242153 0.970238i \(-0.422146\pi\)
−0.719174 + 0.694830i \(0.755480\pi\)
\(20\) −14.9751 8.64587i −3.34853 1.93328i
\(21\) 0.345949i 0.0754923i
\(22\) 2.49509 4.32162i 0.531954 0.921372i
\(23\) 0.906314 + 1.56978i 0.188979 + 0.327322i 0.944910 0.327329i \(-0.106149\pi\)
−0.755931 + 0.654652i \(0.772815\pi\)
\(24\) −2.67849 + 1.54643i −0.546744 + 0.315663i
\(25\) −5.61537 −1.12307
\(26\) −8.46582 + 4.82954i −1.66028 + 0.947151i
\(27\) 2.03429 0.391500
\(28\) 4.59623 2.65363i 0.868606 0.501490i
\(29\) 1.36703 + 2.36777i 0.253851 + 0.439683i 0.964583 0.263780i \(-0.0849693\pi\)
−0.710732 + 0.703463i \(0.751636\pi\)
\(30\) −1.52345 + 2.63869i −0.278142 + 0.481756i
\(31\) 1.74236i 0.312937i −0.987683 0.156468i \(-0.949989\pi\)
0.987683 0.156468i \(-0.0500110\pi\)
\(32\) 16.2422 + 9.37743i 2.87124 + 1.65771i
\(33\) −0.553071 0.319316i −0.0962774 0.0555858i
\(34\) 5.82036i 0.998183i
\(35\) 1.62906 2.82162i 0.275362 0.476940i
\(36\) −7.64331 13.2386i −1.27389 2.20643i
\(37\) −5.14042 + 2.96783i −0.845081 + 0.487908i −0.858988 0.511996i \(-0.828906\pi\)
0.0139073 + 0.999903i \(0.495573\pi\)
\(38\) 6.49025 1.05286
\(39\) 0.618074 + 1.08344i 0.0989710 + 0.173489i
\(40\) 29.1283 4.60558
\(41\) 3.65577 2.11066i 0.570935 0.329629i −0.186588 0.982438i \(-0.559743\pi\)
0.757523 + 0.652809i \(0.226410\pi\)
\(42\) −0.467584 0.809880i −0.0721498 0.124967i
\(43\) −4.34111 + 7.51903i −0.662014 + 1.14664i 0.318072 + 0.948067i \(0.396965\pi\)
−0.980086 + 0.198575i \(0.936369\pi\)
\(44\) 9.79737i 1.47701i
\(45\) −8.12716 4.69222i −1.21153 0.699475i
\(46\) −4.24343 2.44994i −0.625659 0.361224i
\(47\) 5.87774i 0.857357i 0.903457 + 0.428678i \(0.141021\pi\)
−0.903457 + 0.428678i \(0.858979\pi\)
\(48\) 2.34425 4.06036i 0.338363 0.586062i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 13.1458 7.58972i 1.85910 1.07335i
\(51\) 0.744877 0.104304
\(52\) 9.65339 16.5222i 1.33868 2.29122i
\(53\) −9.30628 −1.27832 −0.639158 0.769076i \(-0.720717\pi\)
−0.639158 + 0.769076i \(0.720717\pi\)
\(54\) −4.76235 + 2.74954i −0.648074 + 0.374166i
\(55\) 3.00729 + 5.20878i 0.405503 + 0.702352i
\(56\) −4.47010 + 7.74244i −0.597342 + 1.03463i
\(57\) 0.830609i 0.110017i
\(58\) −6.40054 3.69535i −0.840432 0.485224i
\(59\) 9.31173 + 5.37613i 1.21228 + 0.699912i 0.963256 0.268584i \(-0.0865557\pi\)
0.249028 + 0.968496i \(0.419889\pi\)
\(60\) 5.98206i 0.772281i
\(61\) −5.05504 + 8.75558i −0.647231 + 1.12104i 0.336550 + 0.941665i \(0.390740\pi\)
−0.983781 + 0.179371i \(0.942594\pi\)
\(62\) 2.35497 + 4.07893i 0.299081 + 0.518024i
\(63\) 2.49443 1.44016i 0.314269 0.181443i
\(64\) −23.5929 −2.94911
\(65\) 0.0607514 11.7472i 0.00753529 1.45706i
\(66\) 1.72635 0.212499
\(67\) 0.716130 0.413458i 0.0874892 0.0505119i −0.455617 0.890176i \(-0.650581\pi\)
0.543106 + 0.839664i \(0.317248\pi\)
\(68\) −5.71365 9.89633i −0.692881 1.20011i
\(69\) −0.313538 + 0.543065i −0.0377456 + 0.0653773i
\(70\) 8.80735i 1.05268i
\(71\) −2.03884 1.17712i −0.241965 0.139699i 0.374114 0.927383i \(-0.377947\pi\)
−0.616080 + 0.787684i \(0.711280\pi\)
\(72\) 22.3007 + 12.8753i 2.62816 + 1.51737i
\(73\) 3.19482i 0.373925i 0.982367 + 0.186963i \(0.0598644\pi\)
−0.982367 + 0.186963i \(0.940136\pi\)
\(74\) 8.02261 13.8956i 0.932610 1.61533i
\(75\) −0.971316 1.68237i −0.112158 0.194263i
\(76\) −11.0353 + 6.37126i −1.26584 + 0.730833i
\(77\) −1.84603 −0.210374
\(78\) −2.91130 1.70098i −0.329640 0.192598i
\(79\) 0.801911 0.0902220 0.0451110 0.998982i \(-0.485636\pi\)
0.0451110 + 0.998982i \(0.485636\pi\)
\(80\) −38.2402 + 22.0780i −4.27538 + 2.46839i
\(81\) −3.96860 6.87381i −0.440955 0.763757i
\(82\) −5.70552 + 9.88225i −0.630069 + 1.09131i
\(83\) 9.97031i 1.09438i −0.837007 0.547192i \(-0.815697\pi\)
0.837007 0.547192i \(-0.184303\pi\)
\(84\) 1.59006 + 0.918023i 0.173490 + 0.100164i
\(85\) −6.07534 3.50760i −0.658963 0.380452i
\(86\) 23.4698i 2.53081i
\(87\) −0.472923 + 0.819127i −0.0507027 + 0.0878196i
\(88\) −8.25193 14.2928i −0.879658 1.52361i
\(89\) 13.0886 7.55674i 1.38739 0.801012i 0.394373 0.918950i \(-0.370962\pi\)
0.993021 + 0.117938i \(0.0376284\pi\)
\(90\) 25.3680 2.67402
\(91\) 3.11313 + 1.81890i 0.326345 + 0.190672i
\(92\) 9.62010 1.00296
\(93\) 0.522012 0.301384i 0.0541301 0.0312520i
\(94\) −7.94435 13.7600i −0.819397 1.41924i
\(95\) −3.91130 + 6.77458i −0.401291 + 0.695057i
\(96\) 6.48823i 0.662202i
\(97\) 7.99489 + 4.61585i 0.811758 + 0.468669i 0.847566 0.530690i \(-0.178067\pi\)
−0.0358079 + 0.999359i \(0.511400\pi\)
\(98\) −2.34104 1.35160i −0.236480 0.136532i
\(99\) 5.31715i 0.534394i
\(100\) −14.9011 + 25.8095i −1.49011 + 2.58095i
\(101\) 7.41169 + 12.8374i 0.737491 + 1.27737i 0.953622 + 0.301007i \(0.0973228\pi\)
−0.216131 + 0.976364i \(0.569344\pi\)
\(102\) −1.74378 + 1.00677i −0.172660 + 0.0996855i
\(103\) 4.28286 0.422003 0.211001 0.977486i \(-0.432328\pi\)
0.211001 + 0.977486i \(0.432328\pi\)
\(104\) −0.166700 + 32.2339i −0.0163463 + 3.16079i
\(105\) 1.12715 0.109998
\(106\) 21.7863 12.5783i 2.11608 1.22172i
\(107\) 9.56289 + 16.5634i 0.924479 + 1.60124i 0.792397 + 0.610006i \(0.208833\pi\)
0.132082 + 0.991239i \(0.457834\pi\)
\(108\) 5.39827 9.35007i 0.519448 0.899711i
\(109\) 4.27153i 0.409139i −0.978852 0.204569i \(-0.934421\pi\)
0.978852 0.204569i \(-0.0655794\pi\)
\(110\) −14.0804 8.12930i −1.34251 0.775099i
\(111\) −1.77833 1.02672i −0.168791 0.0974516i
\(112\) 13.5526i 1.28060i
\(113\) −1.37488 + 2.38137i −0.129338 + 0.224020i −0.923420 0.383790i \(-0.874619\pi\)
0.794082 + 0.607810i \(0.207952\pi\)
\(114\) 1.12265 + 1.94448i 0.105146 + 0.182118i
\(115\) 5.11454 2.95288i 0.476934 0.275358i
\(116\) 14.5104 1.34726
\(117\) 5.23901 8.96682i 0.484347 0.828983i
\(118\) −29.0655 −2.67569
\(119\) 1.86467 1.07657i 0.170934 0.0986890i
\(120\) 5.03845 + 8.72685i 0.459945 + 0.796649i
\(121\) −3.79609 + 6.57502i −0.345099 + 0.597729i
\(122\) 27.3295i 2.47430i
\(123\) 1.26471 + 0.730180i 0.114035 + 0.0658381i
\(124\) −8.00828 4.62358i −0.719165 0.415210i
\(125\) 2.00495i 0.179329i
\(126\) −3.89303 + 6.74293i −0.346819 + 0.600708i
\(127\) −4.86719 8.43022i −0.431893 0.748061i 0.565143 0.824993i \(-0.308821\pi\)
−0.997036 + 0.0769320i \(0.975488\pi\)
\(128\) 22.7475 13.1333i 2.01061 1.16083i
\(129\) −3.00361 −0.264453
\(130\) 15.7352 + 27.5827i 1.38007 + 2.41916i
\(131\) −18.6615 −1.63046 −0.815230 0.579138i \(-0.803389\pi\)
−0.815230 + 0.579138i \(0.803389\pi\)
\(132\) −2.93530 + 1.69470i −0.255485 + 0.147504i
\(133\) −1.20048 2.07929i −0.104095 0.180297i
\(134\) −1.11766 + 1.93584i −0.0965509 + 0.167231i
\(135\) 6.62797i 0.570445i
\(136\) 16.6706 + 9.62475i 1.42949 + 0.825315i
\(137\) −7.29328 4.21078i −0.623107 0.359751i 0.154971 0.987919i \(-0.450472\pi\)
−0.778078 + 0.628168i \(0.783805\pi\)
\(138\) 1.69511i 0.144298i
\(139\) 8.81809 15.2734i 0.747941 1.29547i −0.200867 0.979619i \(-0.564376\pi\)
0.948808 0.315853i \(-0.102291\pi\)
\(140\) −8.64587 14.9751i −0.730709 1.26563i
\(141\) −1.76098 + 1.01670i −0.148301 + 0.0856216i
\(142\) 6.36399 0.534054
\(143\) −5.78135 + 3.29812i −0.483461 + 0.275803i
\(144\) −39.0357 −3.25298
\(145\) 7.71448 4.45396i 0.640653 0.369881i
\(146\) −4.31811 7.47919i −0.357370 0.618982i
\(147\) −0.172975 + 0.299601i −0.0142667 + 0.0247107i
\(148\) 31.5021i 2.58946i
\(149\) −3.48232 2.01052i −0.285283 0.164708i 0.350530 0.936552i \(-0.386002\pi\)
−0.635813 + 0.771843i \(0.719335\pi\)
\(150\) 4.54777 + 2.62566i 0.371324 + 0.214384i
\(151\) 18.9010i 1.53814i 0.639165 + 0.769069i \(0.279280\pi\)
−0.639165 + 0.769069i \(0.720720\pi\)
\(152\) 10.7325 18.5892i 0.870521 1.50779i
\(153\) −3.10086 5.37086i −0.250690 0.434208i
\(154\) 4.32162 2.49509i 0.348246 0.201060i
\(155\) −5.67682 −0.455973
\(156\) 6.61987 + 0.0342352i 0.530014 + 0.00274101i
\(157\) −11.5735 −0.923670 −0.461835 0.886966i \(-0.652809\pi\)
−0.461835 + 0.886966i \(0.652809\pi\)
\(158\) −1.87730 + 1.08386i −0.149350 + 0.0862273i
\(159\) −1.60975 2.78817i −0.127661 0.221116i
\(160\) 30.5528 52.9190i 2.41541 4.18362i
\(161\) 1.81263i 0.142855i
\(162\) 18.5813 + 10.7279i 1.45988 + 0.842863i
\(163\) −3.81520 2.20271i −0.298830 0.172529i 0.343087 0.939304i \(-0.388527\pi\)
−0.641917 + 0.766774i \(0.721861\pi\)
\(164\) 22.4037i 1.74943i
\(165\) −1.04037 + 1.80197i −0.0809927 + 0.140284i
\(166\) 13.4759 + 23.3409i 1.04593 + 1.81160i
\(167\) −7.81076 + 4.50954i −0.604415 + 0.348959i −0.770776 0.637106i \(-0.780131\pi\)
0.166362 + 0.986065i \(0.446798\pi\)
\(168\) −3.09285 −0.238619
\(169\) 12.9993 + 0.134457i 0.999947 + 0.0103429i
\(170\) 18.9635 1.45443
\(171\) −5.98901 + 3.45776i −0.457991 + 0.264421i
\(172\) 23.0395 + 39.9055i 1.75674 + 3.04277i
\(173\) 3.04600 5.27583i 0.231583 0.401114i −0.726691 0.686964i \(-0.758943\pi\)
0.958274 + 0.285851i \(0.0922761\pi\)
\(174\) 2.55681i 0.193831i
\(175\) −4.86305 2.80769i −0.367612 0.212241i
\(176\) 21.6666 + 12.5092i 1.63318 + 0.942917i
\(177\) 3.71974i 0.279592i
\(178\) −20.4273 + 35.3812i −1.53109 + 2.65193i
\(179\) 1.93982 + 3.35987i 0.144989 + 0.251128i 0.929369 0.369152i \(-0.120352\pi\)
−0.784380 + 0.620281i \(0.787019\pi\)
\(180\) −43.1330 + 24.9029i −3.21495 + 1.85615i
\(181\) −6.58392 −0.489379 −0.244690 0.969601i \(-0.578686\pi\)
−0.244690 + 0.969601i \(0.578686\pi\)
\(182\) −9.74638 0.0504042i −0.722450 0.00373621i
\(183\) −3.49757 −0.258548
\(184\) −14.0342 + 8.10262i −1.03461 + 0.597333i
\(185\) 9.66954 + 16.7481i 0.710919 + 1.23135i
\(186\) −0.814700 + 1.41110i −0.0597367 + 0.103467i
\(187\) 3.97476i 0.290663i
\(188\) 27.0155 + 15.5974i 1.97030 + 1.13756i
\(189\) 1.76175 + 1.01715i 0.128148 + 0.0739865i
\(190\) 21.1460i 1.53410i
\(191\) 6.87168 11.9021i 0.497218 0.861206i −0.502777 0.864416i \(-0.667688\pi\)
0.999995 + 0.00320983i \(0.00102172\pi\)
\(192\) −4.08097 7.06845i −0.294519 0.510122i
\(193\) 19.7047 11.3765i 1.41838 0.818899i 0.422219 0.906494i \(-0.361251\pi\)
0.996156 + 0.0875946i \(0.0279180\pi\)
\(194\) −24.9551 −1.79167
\(195\) 3.52997 2.01376i 0.252786 0.144208i
\(196\) 5.30727 0.379091
\(197\) −12.5809 + 7.26358i −0.896352 + 0.517509i −0.876015 0.482284i \(-0.839807\pi\)
−0.0203371 + 0.999793i \(0.506474\pi\)
\(198\) −7.18665 12.4476i −0.510733 0.884615i
\(199\) 11.9202 20.6464i 0.845001 1.46358i −0.0406192 0.999175i \(-0.512933\pi\)
0.885620 0.464410i \(-0.153734\pi\)
\(200\) 50.2025i 3.54985i
\(201\) 0.247745 + 0.143035i 0.0174746 + 0.0100889i
\(202\) −34.7021 20.0353i −2.44163 1.40968i
\(203\) 2.73406i 0.191894i
\(204\) 1.97663 3.42363i 0.138392 0.239702i
\(205\) −6.87678 11.9109i −0.480295 0.831896i
\(206\) −10.0263 + 5.78871i −0.698568 + 0.403318i
\(207\) 5.22095 0.362881
\(208\) −24.2131 42.4437i −1.67887 2.94294i
\(209\) 4.43223 0.306584
\(210\) −2.63869 + 1.52345i −0.182087 + 0.105128i
\(211\) −2.15764 3.73714i −0.148538 0.257275i 0.782149 0.623091i \(-0.214123\pi\)
−0.930687 + 0.365816i \(0.880790\pi\)
\(212\) −24.6955 + 42.7738i −1.69609 + 2.93772i
\(213\) 0.814450i 0.0558052i
\(214\) −44.7741 25.8504i −3.06070 1.76709i
\(215\) 24.4979 + 14.1439i 1.67075 + 0.964605i
\(216\) 18.1870i 1.23747i
\(217\) 0.871180 1.50893i 0.0591395 0.102433i
\(218\) 5.77339 + 9.99981i 0.391024 + 0.677273i
\(219\) −0.957171 + 0.552623i −0.0646796 + 0.0373428i
\(220\) 31.9210 2.15212
\(221\) 3.91635 6.70301i 0.263442 0.450893i
\(222\) 5.55083 0.372548
\(223\) −20.2604 + 11.6973i −1.35674 + 0.783312i −0.989182 0.146691i \(-0.953138\pi\)
−0.367553 + 0.930003i \(0.619804\pi\)
\(224\) 9.37743 + 16.2422i 0.626556 + 1.08523i
\(225\) −8.08703 + 14.0071i −0.539135 + 0.933810i
\(226\) 7.43315i 0.494446i
\(227\) −23.1427 13.3614i −1.53603 0.886829i −0.999065 0.0432270i \(-0.986236\pi\)
−0.536968 0.843602i \(-0.680431\pi\)
\(228\) −3.81767 2.20413i −0.252831 0.145972i
\(229\) 3.00670i 0.198688i −0.995053 0.0993442i \(-0.968326\pi\)
0.995053 0.0993442i \(-0.0316745\pi\)
\(230\) −7.98222 + 13.8256i −0.526332 + 0.911634i
\(231\) −0.319316 0.553071i −0.0210094 0.0363894i
\(232\) −21.1683 + 12.2215i −1.38977 + 0.802383i
\(233\) 11.7148 0.767462 0.383731 0.923445i \(-0.374639\pi\)
0.383731 + 0.923445i \(0.374639\pi\)
\(234\) −0.145180 + 28.0727i −0.00949072 + 1.83517i
\(235\) 19.1504 1.24924
\(236\) 49.4199 28.5326i 3.21696 1.85731i
\(237\) 0.138710 + 0.240253i 0.00901019 + 0.0156061i
\(238\) −2.91018 + 5.04058i −0.188639 + 0.326732i
\(239\) 1.42797i 0.0923677i 0.998933 + 0.0461838i \(0.0147060\pi\)
−0.998933 + 0.0461838i \(0.985294\pi\)
\(240\) −13.2292 7.63786i −0.853938 0.493021i
\(241\) −2.32068 1.33984i −0.149488 0.0863069i 0.423390 0.905947i \(-0.360840\pi\)
−0.572878 + 0.819640i \(0.694173\pi\)
\(242\) 20.5232i 1.31928i
\(243\) 4.42437 7.66323i 0.283824 0.491597i
\(244\) 26.8284 + 46.4682i 1.71751 + 2.97482i
\(245\) 2.82162 1.62906i 0.180267 0.104077i
\(246\) −3.94764 −0.251692
\(247\) −7.47450 4.36710i −0.475591 0.277872i
\(248\) 15.5770 0.989143
\(249\) 2.98711 1.72461i 0.189301 0.109293i
\(250\) −2.70989 4.69367i −0.171389 0.296854i
\(251\) 5.46696 9.46906i 0.345072 0.597681i −0.640295 0.768129i \(-0.721188\pi\)
0.985367 + 0.170447i \(0.0545213\pi\)
\(252\) 15.2866i 0.962967i
\(253\) −2.89786 1.67308i −0.182187 0.105186i
\(254\) 22.7885 + 13.1570i 1.42988 + 0.825541i
\(255\) 2.42690i 0.151978i
\(256\) −11.9089 + 20.6268i −0.744307 + 1.28918i
\(257\) 2.07569 + 3.59520i 0.129478 + 0.224262i 0.923474 0.383660i \(-0.125337\pi\)
−0.793996 + 0.607922i \(0.792003\pi\)
\(258\) 7.03156 4.05967i 0.437766 0.252744i
\(259\) −5.93565 −0.368823
\(260\) −53.8315 31.4519i −3.33849 1.95057i
\(261\) 7.87497 0.487448
\(262\) 43.6872 25.2228i 2.69900 1.55827i
\(263\) −2.02680 3.51052i −0.124978 0.216468i 0.796747 0.604314i \(-0.206553\pi\)
−0.921724 + 0.387846i \(0.873219\pi\)
\(264\) 2.85475 4.94457i 0.175698 0.304317i
\(265\) 30.3210i 1.86260i
\(266\) 5.62072 + 3.24513i 0.344629 + 0.198971i
\(267\) 4.52801 + 2.61425i 0.277110 + 0.159989i
\(268\) 4.38866i 0.268080i
\(269\) −2.00011 + 3.46430i −0.121949 + 0.211222i −0.920536 0.390657i \(-0.872248\pi\)
0.798587 + 0.601879i \(0.205581\pi\)
\(270\) 8.95836 + 15.5163i 0.545188 + 0.944294i
\(271\) −2.41189 + 1.39251i −0.146512 + 0.0845888i −0.571464 0.820627i \(-0.693624\pi\)
0.424952 + 0.905216i \(0.360291\pi\)
\(272\) −29.1806 −1.76933
\(273\) −0.00645062 + 1.24732i −0.000390409 + 0.0754913i
\(274\) 22.7651 1.37529
\(275\) 8.97733 5.18306i 0.541353 0.312551i
\(276\) 1.66403 + 2.88219i 0.100163 + 0.173487i
\(277\) 8.34618 14.4560i 0.501474 0.868578i −0.498525 0.866875i \(-0.666125\pi\)
0.999999 0.00170243i \(-0.000541901\pi\)
\(278\) 47.6741i 2.85930i
\(279\) −4.34619 2.50928i −0.260200 0.150226i
\(280\) 25.2258 + 14.5641i 1.50753 + 0.870373i
\(281\) 13.3731i 0.797774i 0.917000 + 0.398887i \(0.130603\pi\)
−0.917000 + 0.398887i \(0.869397\pi\)
\(282\) 2.74834 4.76026i 0.163661 0.283470i
\(283\) −9.44312 16.3560i −0.561335 0.972261i −0.997380 0.0723362i \(-0.976955\pi\)
0.436045 0.899925i \(-0.356379\pi\)
\(284\) −10.8207 + 6.24731i −0.642088 + 0.370710i
\(285\) −2.70623 −0.160303
\(286\) 9.07663 15.5351i 0.536712 0.918609i
\(287\) 4.22131 0.249176
\(288\) 46.7827 27.0100i 2.75669 1.59158i
\(289\) 6.18199 + 10.7075i 0.363647 + 0.629855i
\(290\) −12.0399 + 20.8537i −0.707008 + 1.22457i
\(291\) 3.19370i 0.187218i
\(292\) 14.6841 + 8.47789i 0.859324 + 0.496131i
\(293\) −2.95999 1.70895i −0.172925 0.0998380i 0.411040 0.911617i \(-0.365166\pi\)
−0.583964 + 0.811779i \(0.698499\pi\)
\(294\) 0.935168i 0.0545401i
\(295\) 17.5161 30.3388i 1.01983 1.76639i
\(296\) −26.5329 45.9564i −1.54220 2.67116i
\(297\) −3.25224 + 1.87768i −0.188714 + 0.108954i
\(298\) 10.8697 0.629663
\(299\) 3.23845 + 5.67675i 0.187284 + 0.328295i
\(300\) −10.3101 −0.595252
\(301\) −7.51903 + 4.34111i −0.433390 + 0.250218i
\(302\) −25.5465 44.2479i −1.47004 2.54618i
\(303\) −2.56407 + 4.44110i −0.147302 + 0.255134i
\(304\) 32.5391i 1.86625i
\(305\) 28.5268 + 16.4699i 1.63344 + 0.943066i
\(306\) 14.5185 + 8.38225i 0.829966 + 0.479181i
\(307\) 16.3679i 0.934165i −0.884214 0.467083i \(-0.845305\pi\)
0.884214 0.467083i \(-0.154695\pi\)
\(308\) −4.89868 + 8.48477i −0.279128 + 0.483464i
\(309\) 0.740826 + 1.28315i 0.0421441 + 0.0729958i
\(310\) 13.2896 7.67278i 0.754801 0.435785i
\(311\) −23.6979 −1.34378 −0.671891 0.740650i \(-0.734518\pi\)
−0.671891 + 0.740650i \(0.734518\pi\)
\(312\) −9.68614 + 5.52570i −0.548370 + 0.312831i
\(313\) −5.18025 −0.292805 −0.146403 0.989225i \(-0.546769\pi\)
−0.146403 + 0.989225i \(0.546769\pi\)
\(314\) 27.0941 15.6428i 1.52901 0.882774i
\(315\) −4.69222 8.12716i −0.264377 0.457914i
\(316\) 2.12798 3.68577i 0.119708 0.207341i
\(317\) 6.06537i 0.340665i −0.985387 0.170332i \(-0.945516\pi\)
0.985387 0.170332i \(-0.0544842\pi\)
\(318\) 7.53697 + 4.35147i 0.422652 + 0.244018i
\(319\) −4.37096 2.52358i −0.244727 0.141293i
\(320\) 76.8686i 4.29709i
\(321\) −3.30827 + 5.73010i −0.184650 + 0.319823i
\(322\) −2.44994 4.24343i −0.136530 0.236477i
\(323\) −4.47700 + 2.58480i −0.249107 + 0.143822i
\(324\) −42.1248 −2.34027
\(325\) −20.2462 0.104705i −1.12306 0.00580799i
\(326\) 11.9087 0.659562
\(327\) 1.27975 0.738866i 0.0707706 0.0408594i
\(328\) 18.8697 + 32.6833i 1.04190 + 1.80463i
\(329\) −2.93887 + 5.09027i −0.162025 + 0.280636i
\(330\) 5.62465i 0.309627i
\(331\) 14.9605 + 8.63743i 0.822301 + 0.474756i 0.851209 0.524826i \(-0.175870\pi\)
−0.0289082 + 0.999582i \(0.509203\pi\)
\(332\) −45.8258 26.4576i −2.51502 1.45205i
\(333\) 17.0966i 0.936886i
\(334\) 12.1902 21.1140i 0.667017 1.15531i
\(335\) −1.34710 2.33324i −0.0735998 0.127479i
\(336\) 4.06036 2.34425i 0.221511 0.127889i
\(337\) −8.35464 −0.455106 −0.227553 0.973766i \(-0.573073\pi\)
−0.227553 + 0.973766i \(0.573073\pi\)
\(338\) −30.6136 + 17.2551i −1.66516 + 0.938552i
\(339\) −0.951279 −0.0516664
\(340\) −32.2435 + 18.6158i −1.74865 + 1.00958i
\(341\) 1.60822 + 2.78552i 0.0870901 + 0.150844i
\(342\) 9.34700 16.1895i 0.505428 0.875427i
\(343\) 1.00000i 0.0539949i
\(344\) −67.2216 38.8104i −3.62435 2.09252i
\(345\) 1.76937 + 1.02155i 0.0952598 + 0.0549983i
\(346\) 16.4679i 0.885318i
\(347\) −14.4110 + 24.9606i −0.773623 + 1.33995i 0.161942 + 0.986800i \(0.448224\pi\)
−0.935565 + 0.353154i \(0.885109\pi\)
\(348\) 2.50993 + 4.34733i 0.134546 + 0.233041i
\(349\) −10.1516 + 5.86103i −0.543403 + 0.313734i −0.746457 0.665434i \(-0.768247\pi\)
0.203054 + 0.979167i \(0.434913\pi\)
\(350\) 15.1794 0.811376
\(351\) 7.33464 + 0.0379317i 0.391494 + 0.00202464i
\(352\) −34.6220 −1.84536
\(353\) 15.4466 8.91811i 0.822141 0.474663i −0.0290134 0.999579i \(-0.509237\pi\)
0.851154 + 0.524916i \(0.175903\pi\)
\(354\) −5.02759 8.70804i −0.267213 0.462827i
\(355\) −3.83521 + 6.64278i −0.203552 + 0.352562i
\(356\) 80.2113i 4.25119i
\(357\) 0.645082 + 0.372438i 0.0341414 + 0.0197115i
\(358\) −9.08239 5.24372i −0.480019 0.277139i
\(359\) 5.68162i 0.299864i −0.988696 0.149932i \(-0.952094\pi\)
0.988696 0.149932i \(-0.0479055\pi\)
\(360\) 41.9494 72.6584i 2.21093 3.82943i
\(361\) −6.61771 11.4622i −0.348300 0.603274i
\(362\) 15.4132 8.89882i 0.810100 0.467712i
\(363\) −2.62651 −0.137856
\(364\) 16.6212 9.48199i 0.871188 0.496991i
\(365\) 10.4091 0.544838
\(366\) 8.18794 4.72731i 0.427991 0.247100i
\(367\) 9.81580 + 17.0015i 0.512381 + 0.887469i 0.999897 + 0.0143554i \(0.00456964\pi\)
−0.487516 + 0.873114i \(0.662097\pi\)
\(368\) 12.2829 21.2746i 0.640289 1.10901i
\(369\) 12.1587i 0.632958i
\(370\) −45.2735 26.1387i −2.35366 1.35888i
\(371\) −8.05947 4.65314i −0.418427 0.241579i
\(372\) 3.19905i 0.165863i
\(373\) −16.0323 + 27.7687i −0.830119 + 1.43781i 0.0678240 + 0.997697i \(0.478394\pi\)
−0.897943 + 0.440111i \(0.854939\pi\)
\(374\) −5.37227 9.30505i −0.277794 0.481153i
\(375\) −0.600686 + 0.346806i −0.0310193 + 0.0179090i
\(376\) −52.5482 −2.70997
\(377\) 4.88468 + 8.56248i 0.251574 + 0.440990i
\(378\) −5.49909 −0.282843
\(379\) −16.4745 + 9.51154i −0.846237 + 0.488575i −0.859379 0.511339i \(-0.829150\pi\)
0.0131425 + 0.999914i \(0.495816\pi\)
\(380\) 20.7583 + 35.9545i 1.06488 + 1.84443i
\(381\) 1.68380 2.91643i 0.0862637 0.149413i
\(382\) 37.1510i 1.90081i
\(383\) 0.606070 + 0.349915i 0.0309687 + 0.0178798i 0.515404 0.856947i \(-0.327642\pi\)
−0.484436 + 0.874827i \(0.660975\pi\)
\(384\) 7.86948 + 4.54345i 0.401588 + 0.231857i
\(385\) 6.01459i 0.306532i
\(386\) −30.7529 + 53.2657i −1.56528 + 2.71115i
\(387\) 12.5038 + 21.6572i 0.635604 + 1.10090i
\(388\) 42.4310 24.4976i 2.15411 1.24368i
\(389\) 20.0547 1.01681 0.508407 0.861117i \(-0.330235\pi\)
0.508407 + 0.861117i \(0.330235\pi\)
\(390\) −5.54200 + 9.48539i −0.280630 + 0.480311i
\(391\) 3.90284 0.197375
\(392\) −7.74244 + 4.47010i −0.391052 + 0.225774i
\(393\) −3.22796 5.59099i −0.162829 0.282028i
\(394\) 19.6349 34.0086i 0.989192 1.71333i
\(395\) 2.61272i 0.131460i
\(396\) 24.4388 + 14.1098i 1.22810 + 0.709043i
\(397\) −19.2953 11.1401i −0.968403 0.559108i −0.0696541 0.997571i \(-0.522190\pi\)
−0.898749 + 0.438463i \(0.855523\pi\)
\(398\) 64.4453i 3.23035i
\(399\) 0.415304 0.719328i 0.0207912 0.0360114i
\(400\) 38.0513 + 65.9069i 1.90257 + 3.29534i
\(401\) −4.16341 + 2.40374i −0.207911 + 0.120037i −0.600340 0.799745i \(-0.704968\pi\)
0.392429 + 0.919782i \(0.371635\pi\)
\(402\) −0.773306 −0.0385690
\(403\) 0.0324883 6.28208i 0.00161836 0.312933i
\(404\) 78.6717 3.91406
\(405\) −22.3957 + 12.9302i −1.11285 + 0.642506i
\(406\) −3.69535 6.40054i −0.183397 0.317653i
\(407\) 5.47869 9.48937i 0.271568 0.470370i
\(408\) 6.65935i 0.329687i
\(409\) 31.8727 + 18.4017i 1.57601 + 0.909907i 0.995409 + 0.0957164i \(0.0305142\pi\)
0.580597 + 0.814191i \(0.302819\pi\)
\(410\) 32.1976 + 18.5893i 1.59013 + 0.918060i
\(411\) 2.91343i 0.143709i
\(412\) 11.3651 19.6850i 0.559921 0.969811i
\(413\) 5.37613 + 9.31173i 0.264542 + 0.458200i
\(414\) −12.2224 + 7.05662i −0.600699 + 0.346814i
\(415\) −32.4845 −1.59460
\(416\) 58.3864 + 34.1132i 2.86263 + 1.67254i
\(417\) 6.10122 0.298778
\(418\) −10.3760 + 5.99059i −0.507507 + 0.293009i
\(419\) −14.6334 25.3457i −0.714887 1.23822i −0.963003 0.269490i \(-0.913145\pi\)
0.248116 0.968730i \(-0.420188\pi\)
\(420\) 2.99103 5.18062i 0.145947 0.252788i
\(421\) 7.53862i 0.367410i −0.982981 0.183705i \(-0.941191\pi\)
0.982981 0.183705i \(-0.0588091\pi\)
\(422\) 10.1022 + 5.83251i 0.491768 + 0.283922i
\(423\) 14.6616 + 8.46489i 0.712872 + 0.411577i
\(424\) 83.2000i 4.04055i
\(425\) −6.04534 + 10.4708i −0.293242 + 0.507910i
\(426\) 1.10081 + 1.90666i 0.0533343 + 0.0923778i
\(427\) −8.75558 + 5.05504i −0.423712 + 0.244630i
\(428\) 101.506 4.90646
\(429\) −1.98815 1.16161i −0.0959886 0.0560829i
\(430\) −76.4674 −3.68759
\(431\) −27.0426 + 15.6131i −1.30260 + 0.752055i −0.980849 0.194771i \(-0.937604\pi\)
−0.321748 + 0.946825i \(0.604270\pi\)
\(432\) −13.7849 23.8762i −0.663228 1.14874i
\(433\) 2.94202 5.09573i 0.141384 0.244885i −0.786634 0.617420i \(-0.788178\pi\)
0.928018 + 0.372535i \(0.121511\pi\)
\(434\) 4.70994i 0.226084i
\(435\) 2.66882 + 1.54084i 0.127960 + 0.0738777i
\(436\) −19.6329 11.3351i −0.940247 0.542852i
\(437\) 4.35204i 0.208186i
\(438\) 1.49385 2.58742i 0.0713788 0.123632i
\(439\) −4.97821 8.62251i −0.237597 0.411530i 0.722427 0.691447i \(-0.243026\pi\)
−0.960024 + 0.279917i \(0.909693\pi\)
\(440\) −46.5676 + 26.8858i −2.22002 + 1.28173i
\(441\) 2.88032 0.137158
\(442\) −0.108527 + 20.9853i −0.00516212 + 0.998170i
\(443\) −35.8813 −1.70477 −0.852385 0.522915i \(-0.824845\pi\)
−0.852385 + 0.522915i \(0.824845\pi\)
\(444\) −9.43805 + 5.44906i −0.447910 + 0.258601i
\(445\) −24.6208 42.6444i −1.16714 2.02154i
\(446\) 31.6202 54.7678i 1.49726 2.59333i
\(447\) 1.39108i 0.0657956i
\(448\) −20.4321 11.7965i −0.965324 0.557330i
\(449\) 3.46001 + 1.99764i 0.163288 + 0.0942744i 0.579417 0.815031i \(-0.303280\pi\)
−0.416129 + 0.909306i \(0.636614\pi\)
\(450\) 43.7217i 2.06106i
\(451\) −3.89633 + 6.74864i −0.183471 + 0.317781i
\(452\) 7.29687 + 12.6386i 0.343216 + 0.594467i
\(453\) −5.66274 + 3.26939i −0.266059 + 0.153609i
\(454\) 72.2371 3.39026
\(455\) 5.92620 10.1430i 0.277825 0.475510i
\(456\) 7.42580 0.347745
\(457\) 35.6995 20.6111i 1.66995 0.964147i 0.702291 0.711890i \(-0.252160\pi\)
0.967660 0.252257i \(-0.0811729\pi\)
\(458\) 4.06385 + 7.03880i 0.189891 + 0.328901i
\(459\) 2.19006 3.79329i 0.102223 0.177056i
\(460\) 31.3435i 1.46140i
\(461\) 21.4139 + 12.3633i 0.997343 + 0.575816i 0.907461 0.420136i \(-0.138018\pi\)
0.0898818 + 0.995952i \(0.471351\pi\)
\(462\) 1.49506 + 0.863173i 0.0695565 + 0.0401585i
\(463\) 24.4057i 1.13423i −0.823639 0.567115i \(-0.808060\pi\)
0.823639 0.567115i \(-0.191940\pi\)
\(464\) 18.5268 32.0893i 0.860084 1.48971i
\(465\) −0.981946 1.70078i −0.0455366 0.0788718i
\(466\) −27.4248 + 15.8337i −1.27043 + 0.733482i
\(467\) 4.44860 0.205857 0.102928 0.994689i \(-0.467179\pi\)
0.102928 + 0.994689i \(0.467179\pi\)
\(468\) −27.3111 47.8744i −1.26246 2.21299i
\(469\) 0.826916 0.0381834
\(470\) −44.8318 + 25.8837i −2.06794 + 1.19392i
\(471\) −2.00193 3.46744i −0.0922441 0.159771i
\(472\) −48.0637 + 83.2487i −2.21231 + 3.83183i
\(473\) 16.0276i 0.736951i
\(474\) −0.649451 0.374961i −0.0298303 0.0172225i
\(475\) 11.6760 + 6.74113i 0.535730 + 0.309304i
\(476\) 11.4273i 0.523769i
\(477\) −13.4025 + 23.2139i −0.613660 + 1.06289i
\(478\) −1.93004 3.34293i −0.0882780 0.152902i
\(479\) −27.4328 + 15.8383i −1.25343 + 0.723671i −0.971790 0.235848i \(-0.924213\pi\)
−0.281645 + 0.959519i \(0.590880\pi\)
\(480\) 21.1394 0.964879
\(481\) −18.5892 + 10.6047i −0.847593 + 0.483531i
\(482\) 7.24372 0.329942
\(483\) −0.543065 + 0.313538i −0.0247103 + 0.0142665i
\(484\) 20.1469 + 34.8954i 0.915767 + 1.58616i
\(485\) 15.0390 26.0483i 0.682887 1.18279i
\(486\) 23.9199i 1.08503i
\(487\) 23.3096 + 13.4578i 1.05626 + 0.609832i 0.924395 0.381436i \(-0.124570\pi\)
0.131864 + 0.991268i \(0.457904\pi\)
\(488\) −78.2766 45.1930i −3.54341 2.04579i
\(489\) 1.52405i 0.0689200i
\(490\) −4.40367 + 7.62739i −0.198938 + 0.344570i
\(491\) 4.86358 + 8.42396i 0.219490 + 0.380168i 0.954652 0.297723i \(-0.0962273\pi\)
−0.735162 + 0.677891i \(0.762894\pi\)
\(492\) 6.71215 3.87526i 0.302607 0.174710i
\(493\) 5.88682 0.265129
\(494\) 23.4006 + 0.121018i 1.05284 + 0.00544487i
\(495\) 17.3239 0.778653
\(496\) −20.4498 + 11.8067i −0.918225 + 0.530137i
\(497\) −1.17712 2.03884i −0.0528012 0.0914543i
\(498\) −4.66196 + 8.07475i −0.208907 + 0.361838i
\(499\) 7.87525i 0.352545i 0.984341 + 0.176272i \(0.0564039\pi\)
−0.984341 + 0.176272i \(0.943596\pi\)
\(500\) 9.21523 + 5.32042i 0.412118 + 0.237936i
\(501\) −2.70213 1.56007i −0.120722 0.0696989i
\(502\) 29.5565i 1.31917i
\(503\) 4.87603 8.44553i 0.217411 0.376568i −0.736604 0.676324i \(-0.763572\pi\)
0.954016 + 0.299756i \(0.0969053\pi\)
\(504\) 12.8753 + 22.3007i 0.573512 + 0.993352i
\(505\) 41.8259 24.1482i 1.86123 1.07458i
\(506\) 9.04533 0.402114
\(507\) 2.20827 + 3.91786i 0.0980725 + 0.173998i
\(508\) −51.6630 −2.29217
\(509\) −19.9407 + 11.5128i −0.883857 + 0.510295i −0.871928 0.489634i \(-0.837130\pi\)
−0.0119288 + 0.999929i \(0.503797\pi\)
\(510\) 3.28019 + 5.68146i 0.145249 + 0.251579i
\(511\) −1.59741 + 2.76680i −0.0706653 + 0.122396i
\(512\) 11.8512i 0.523752i
\(513\) −4.22988 2.44212i −0.186754 0.107822i
\(514\) −9.71853 5.61100i −0.428666 0.247490i
\(515\) 13.9541i 0.614891i
\(516\) −7.97048 + 13.8053i −0.350881 + 0.607744i
\(517\) −5.42524 9.39679i −0.238602 0.413270i
\(518\) 13.8956 8.02261i 0.610537 0.352493i
\(519\) 2.10752 0.0925100
\(520\) 105.022 + 0.543130i 4.60552 + 0.0238178i
\(521\) 0.486481 0.0213131 0.0106566 0.999943i \(-0.496608\pi\)
0.0106566 + 0.999943i \(0.496608\pi\)
\(522\) −18.4356 + 10.6438i −0.806904 + 0.465866i
\(523\) 17.3135 + 29.9878i 0.757065 + 1.31128i 0.944341 + 0.328968i \(0.106701\pi\)
−0.187275 + 0.982307i \(0.559966\pi\)
\(524\) −49.5207 + 85.7724i −2.16332 + 3.74698i
\(525\) 1.94263i 0.0847834i
\(526\) 9.48962 + 5.47883i 0.413767 + 0.238888i
\(527\) −3.24893 1.87577i −0.141526 0.0817099i
\(528\) 8.65510i 0.376665i
\(529\) 9.85719 17.0732i 0.428574 0.742311i
\(530\) −40.9818 70.9826i −1.78014 3.08329i
\(531\) 26.8208 15.4850i 1.16392 0.671990i
\(532\) −12.7425 −0.552458
\(533\) 13.2202 7.54182i 0.572632 0.326672i
\(534\) −14.1336 −0.611622
\(535\) 53.9656 31.1571i 2.33314 1.34704i
\(536\) 3.69639 + 6.40234i 0.159660 + 0.276539i
\(537\) −0.671080 + 1.16234i −0.0289592 + 0.0501589i
\(538\) 10.8134i 0.466198i
\(539\) −1.59871 0.923014i −0.0688612 0.0397570i
\(540\) −30.4637 17.5882i −1.31095 0.756876i
\(541\) 22.5384i 0.969002i 0.874791 + 0.484501i \(0.160999\pi\)
−0.874791 + 0.484501i \(0.839001\pi\)
\(542\) 3.76422 6.51982i 0.161687 0.280050i
\(543\) −1.13885 1.97255i −0.0488728 0.0846502i
\(544\) 34.9717 20.1909i 1.49940 0.865678i
\(545\) −13.9172 −0.596146
\(546\) −1.67078 2.92874i −0.0715026 0.125339i
\(547\) 39.3716 1.68341 0.841704 0.539940i \(-0.181553\pi\)
0.841704 + 0.539940i \(0.181553\pi\)
\(548\) −38.7074 + 22.3477i −1.65350 + 0.954648i
\(549\) 14.5601 + 25.2189i 0.621411 + 1.07631i
\(550\) −14.0108 + 24.2675i −0.597424 + 1.03477i
\(551\) 6.56436i 0.279651i
\(552\) −4.85510 2.80310i −0.206647 0.119308i
\(553\) 0.694475 + 0.400955i 0.0295321 + 0.0170504i
\(554\) 45.1227i 1.91708i
\(555\) −3.34517 + 5.79401i −0.141995 + 0.245942i
\(556\) −46.8000 81.0600i −1.98476 3.43771i
\(557\) 0.629579 0.363487i 0.0266761 0.0154015i −0.486603 0.873623i \(-0.661764\pi\)
0.513279 + 0.858222i \(0.328431\pi\)
\(558\) 13.5661 0.574300
\(559\) −15.7921 + 27.0289i −0.667935 + 1.14320i
\(560\) −44.1559 −1.86593
\(561\) −1.19084 + 0.687532i −0.0502773 + 0.0290276i
\(562\) −18.0751 31.3070i −0.762452 1.32061i
\(563\) 20.8038 36.0333i 0.876777 1.51862i 0.0219200 0.999760i \(-0.493022\pi\)
0.854857 0.518863i \(-0.173645\pi\)
\(564\) 10.7918i 0.454417i
\(565\) 7.75879 + 4.47954i 0.326415 + 0.188456i
\(566\) 44.2134 + 25.5266i 1.85843 + 1.07296i
\(567\) 7.93720i 0.333331i
\(568\) 10.5237 18.2276i 0.441565 0.764813i
\(569\) −12.6944 21.9873i −0.532177 0.921757i −0.999294 0.0375618i \(-0.988041\pi\)
0.467118 0.884195i \(-0.345292\pi\)
\(570\) 6.33537 3.65773i 0.265360 0.153205i
\(571\) −16.9992 −0.711393 −0.355697 0.934602i \(-0.615756\pi\)
−0.355697 + 0.934602i \(0.615756\pi\)
\(572\) −0.182683 + 35.3244i −0.00763836 + 1.47699i
\(573\) 4.75451 0.198622
\(574\) −9.88225 + 5.70552i −0.412477 + 0.238144i
\(575\) −5.08929 8.81490i −0.212238 0.367607i
\(576\) −33.9776 + 58.8508i −1.41573 + 2.45212i
\(577\) 15.9759i 0.665084i −0.943088 0.332542i \(-0.892094\pi\)
0.943088 0.332542i \(-0.107906\pi\)
\(578\) −28.9445 16.7111i −1.20393 0.695092i
\(579\) 6.81682 + 3.93570i 0.283298 + 0.163562i
\(580\) 47.2767i 1.96306i
\(581\) 4.98516 8.63454i 0.206819 0.358221i
\(582\) −4.31660 7.47657i −0.178929 0.309914i
\(583\) 14.8780 8.58982i 0.616184 0.355754i
\(584\) −28.5623 −1.18192
\(585\) −29.2150 17.0693i −1.20789 0.705731i
\(586\) 9.23926 0.381670
\(587\) −13.8404 + 7.99075i −0.571254 + 0.329814i −0.757650 0.652661i \(-0.773653\pi\)
0.186396 + 0.982475i \(0.440319\pi\)
\(588\) 0.918023 + 1.59006i 0.0378586 + 0.0655730i
\(589\) −2.09166 + 3.62287i −0.0861855 + 0.149278i
\(590\) 94.6989i 3.89869i
\(591\) −4.35235 2.51283i −0.179032 0.103364i
\(592\) 69.6660 + 40.2217i 2.86325 + 1.65310i
\(593\) 29.0532i 1.19307i −0.802586 0.596536i \(-0.796543\pi\)
0.802586 0.596536i \(-0.203457\pi\)
\(594\) 5.07574 8.79143i 0.208260 0.360717i
\(595\) −3.50760 6.07534i −0.143797 0.249065i
\(596\) −18.4816 + 10.6704i −0.757037 + 0.437075i
\(597\) 8.24757 0.337551
\(598\) −15.2540 8.91240i −0.623783 0.364455i
\(599\) 3.45554 0.141190 0.0705948 0.997505i \(-0.477510\pi\)
0.0705948 + 0.997505i \(0.477510\pi\)
\(600\) 15.0407 8.68376i 0.614035 0.354513i
\(601\) −7.76518 13.4497i −0.316748 0.548624i 0.663059 0.748567i \(-0.269258\pi\)
−0.979808 + 0.199943i \(0.935924\pi\)
\(602\) 11.7349 20.3254i 0.478278 0.828402i
\(603\) 2.38178i 0.0969936i
\(604\) 86.8732 + 50.1563i 3.53482 + 2.04083i
\(605\) 21.4222 + 12.3681i 0.870938 + 0.502836i
\(606\) 13.8624i 0.563120i
\(607\) −7.73922 + 13.4047i −0.314125 + 0.544081i −0.979251 0.202650i \(-0.935044\pi\)
0.665126 + 0.746731i \(0.268378\pi\)
\(608\) −22.5148 38.9967i −0.913095 1.58153i
\(609\) −0.819127 + 0.472923i −0.0331927 + 0.0191638i
\(610\) −89.0429 −3.60524
\(611\) −0.109597 + 21.1922i −0.00443383 + 0.857345i
\(612\) −32.9142 −1.33048
\(613\) −6.17669 + 3.56611i −0.249474 + 0.144034i −0.619523 0.784978i \(-0.712674\pi\)
0.370049 + 0.929012i \(0.379341\pi\)
\(614\) 22.1228 + 38.3178i 0.892804 + 1.54638i
\(615\) 2.37902 4.12058i 0.0959312 0.166158i
\(616\) 16.5039i 0.664959i
\(617\) −4.30142 2.48342i −0.173168 0.0999789i 0.410911 0.911676i \(-0.365211\pi\)
−0.584079 + 0.811697i \(0.698544\pi\)
\(618\) −3.46860 2.00260i −0.139528 0.0805563i
\(619\) 42.3570i 1.70247i −0.524784 0.851235i \(-0.675854\pi\)
0.524784 0.851235i \(-0.324146\pi\)
\(620\) −15.0642 + 26.0920i −0.604993 + 1.04788i
\(621\) 1.84371 + 3.19339i 0.0739854 + 0.128146i
\(622\) 55.4776 32.0300i 2.22445 1.28429i
\(623\) 15.1135 0.605508
\(624\) 8.52791 14.5959i 0.341390 0.584305i
\(625\) −21.5445 −0.861779
\(626\) 12.1272 7.00162i 0.484699 0.279841i
\(627\) 0.766663 + 1.32790i 0.0306176 + 0.0530312i
\(628\) −30.7120 + 53.1947i −1.22554 + 2.12270i
\(629\) 12.7803i 0.509583i
\(630\) 21.9693 + 12.6840i 0.875278 + 0.505342i
\(631\) −5.42803 3.13387i −0.216086 0.124758i 0.388050 0.921638i \(-0.373149\pi\)
−0.604137 + 0.796881i \(0.706482\pi\)
\(632\) 7.16924i 0.285177i
\(633\) 0.746432 1.29286i 0.0296680 0.0513865i
\(634\) 8.19794 + 14.1992i 0.325582 + 0.563924i
\(635\) −27.4667 + 15.8579i −1.08998 + 0.629302i
\(636\) −17.0868 −0.677534
\(637\) 1.78660 + 3.13178i 0.0707878 + 0.124086i
\(638\) 13.6434 0.540149
\(639\) −5.87250 + 3.39049i −0.232313 + 0.134126i
\(640\) −42.7898 74.1142i −1.69142 2.92962i
\(641\) −15.7818 + 27.3350i −0.623345 + 1.07967i 0.365513 + 0.930806i \(0.380894\pi\)
−0.988858 + 0.148860i \(0.952440\pi\)
\(642\) 17.8858i 0.705897i
\(643\) 15.8053 + 9.12520i 0.623300 + 0.359863i 0.778153 0.628075i \(-0.216157\pi\)
−0.154852 + 0.987938i \(0.549490\pi\)
\(644\) 8.33125 + 4.81005i 0.328297 + 0.189543i
\(645\) 9.78613i 0.385329i
\(646\) 6.98721 12.1022i 0.274908 0.476155i
\(647\) 11.5137 + 19.9423i 0.452649 + 0.784011i 0.998550 0.0538387i \(-0.0171457\pi\)
−0.545901 + 0.837850i \(0.683812\pi\)
\(648\) 61.4532 35.4800i 2.41411 1.39379i
\(649\) −19.8490 −0.779140
\(650\) 47.5387 27.1197i 1.86462 1.06372i
\(651\) 0.602768 0.0236243
\(652\) −20.2483 + 11.6904i −0.792985 + 0.457830i
\(653\) −14.4062 24.9523i −0.563759 0.976459i −0.997164 0.0752597i \(-0.976021\pi\)
0.433405 0.901199i \(-0.357312\pi\)
\(654\) −1.99730 + 3.45943i −0.0781006 + 0.135274i
\(655\) 60.8014i 2.37571i
\(656\) −49.5450 28.6048i −1.93441 1.11683i
\(657\) 7.96926 + 4.60105i 0.310910 + 0.179504i
\(658\) 15.8887i 0.619406i
\(659\) 15.6114 27.0397i 0.608134 1.05332i −0.383414 0.923577i \(-0.625252\pi\)
0.991548 0.129742i \(-0.0414149\pi\)
\(660\) 5.52153 + 9.56356i 0.214925 + 0.372261i
\(661\) −23.0000 + 13.2791i −0.894598 + 0.516496i −0.875444 0.483320i \(-0.839431\pi\)
−0.0191541 + 0.999817i \(0.506097\pi\)
\(662\) −46.6973 −1.81494
\(663\) 2.68566 + 0.0138891i 0.104302 + 0.000539407i
\(664\) 89.1366 3.45917
\(665\) −6.77458 + 3.91130i −0.262707 + 0.151674i
\(666\) −23.1077 40.0237i −0.895405 1.55089i
\(667\) −2.47792 + 4.29188i −0.0959454 + 0.166182i
\(668\) 47.8667i 1.85202i
\(669\) −7.00906 4.04668i −0.270986 0.156454i
\(670\) 6.30721 + 3.64147i 0.243669 + 0.140682i
\(671\) 18.6635i 0.720495i
\(672\) −3.24411 + 5.61897i −0.125144 + 0.216756i
\(673\) −9.86930 17.0941i −0.380434 0.658930i 0.610691 0.791869i \(-0.290892\pi\)
−0.991124 + 0.132939i \(0.957559\pi\)
\(674\) 19.5585 11.2921i 0.753366 0.434956i
\(675\) −11.4233 −0.439683
\(676\) 35.1134 59.3910i 1.35052 2.28427i
\(677\) −13.1440 −0.505163 −0.252582 0.967576i \(-0.581280\pi\)
−0.252582 + 0.967576i \(0.581280\pi\)
\(678\) 2.22698 1.28575i 0.0855266 0.0493788i
\(679\) 4.61585 + 7.99489i 0.177140 + 0.306816i
\(680\) 31.3586 54.3147i 1.20255 2.08287i
\(681\) 9.24475i 0.354260i
\(682\) −7.52981 4.34734i −0.288331 0.166468i
\(683\) −5.85654 3.38128i −0.224094 0.129381i 0.383750 0.923437i \(-0.374632\pi\)
−0.607845 + 0.794056i \(0.707966\pi\)
\(684\) 36.7025i 1.40336i
\(685\) −13.7192 + 23.7624i −0.524185 + 0.907915i
\(686\) −1.35160 2.34104i −0.0516043 0.0893812i
\(687\) 0.900810 0.520083i 0.0343681 0.0198424i
\(688\) 117.666 4.48599
\(689\) −33.5538 0.173526i −1.27830 0.00661082i
\(690\) −5.52288 −0.210253
\(691\) 7.94223 4.58545i 0.302137 0.174439i −0.341266 0.939967i \(-0.610856\pi\)
0.643402 + 0.765528i \(0.277522\pi\)
\(692\) −16.1659 28.0002i −0.614537 1.06441i
\(693\) −2.65857 + 4.60479i −0.100991 + 0.174921i
\(694\) 77.9115i 2.95748i
\(695\) −49.7626 28.7304i −1.88760 1.08981i
\(696\) −7.32316 4.22803i −0.277584 0.160263i
\(697\) 9.08908i 0.344273i
\(698\) 15.8435 27.4418i 0.599686 1.03869i
\(699\) 2.02636 + 3.50976i 0.0766440 + 0.132751i
\(700\) −25.8095 + 14.9011i −0.975509 + 0.563210i
\(701\) 47.4700 1.79292 0.896459 0.443127i \(-0.146131\pi\)
0.896459 + 0.443127i \(0.146131\pi\)
\(702\) −17.2219 + 9.82469i −0.650000 + 0.370809i
\(703\) 14.2512 0.537495
\(704\) 37.7181 21.7766i 1.42156 0.820736i
\(705\) 3.31253 + 5.73748i 0.124757 + 0.216086i
\(706\) −24.1074 + 41.7552i −0.907294 + 1.57148i
\(707\) 14.8234i 0.557491i
\(708\) 17.0968 + 9.87082i 0.642535 + 0.370968i
\(709\) 30.2866 + 17.4860i 1.13744 + 0.656699i 0.945795 0.324766i \(-0.105285\pi\)
0.191642 + 0.981465i \(0.438619\pi\)
\(710\) 20.7347i 0.778158i
\(711\) 1.15488 2.00031i 0.0433114 0.0750175i
\(712\) 67.5587 + 117.015i 2.53187 + 4.38533i
\(713\) 2.73512 1.57912i 0.102431 0.0591387i
\(714\) −2.01355 −0.0753552
\(715\) 10.7457 + 18.8364i 0.401866 + 0.704440i
\(716\) 20.5903 0.769496
\(717\) −0.427821 + 0.247002i −0.0159773 + 0.00922448i
\(718\) 7.67926 + 13.3009i 0.286588 + 0.496384i
\(719\) −4.18051 + 7.24085i −0.155907 + 0.270038i −0.933389 0.358867i \(-0.883163\pi\)
0.777482 + 0.628905i \(0.216497\pi\)
\(720\) 127.183i 4.73984i
\(721\) 3.70907 + 2.14143i 0.138133 + 0.0797511i
\(722\) 30.9846 + 17.8890i 1.15313 + 0.665758i
\(723\) 0.927035i 0.0344768i
\(724\) −17.4713 + 30.2612i −0.649317 + 1.12465i
\(725\) −7.67639 13.2959i −0.285094 0.493797i
\(726\) 6.14875 3.54998i 0.228202 0.131752i
\(727\) −27.4014 −1.01626 −0.508131 0.861280i \(-0.669663\pi\)
−0.508131 + 0.861280i \(0.669663\pi\)
\(728\) −16.2613 + 27.8320i −0.602685 + 1.03152i
\(729\) −20.7504 −0.768532
\(730\) −24.3681 + 14.0689i −0.901905 + 0.520715i
\(731\) 9.34703 + 16.1895i 0.345712 + 0.598791i
\(732\) −9.28127 + 16.0756i −0.343046 + 0.594173i
\(733\) 12.1569i 0.449026i −0.974471 0.224513i \(-0.927921\pi\)
0.974471 0.224513i \(-0.0720792\pi\)
\(734\) −45.9583 26.5340i −1.69635 0.979389i
\(735\) 0.976136 + 0.563573i 0.0360053 + 0.0207877i
\(736\) 33.9956i 1.25309i
\(737\) −0.763255 + 1.32200i −0.0281148 + 0.0486963i
\(738\) 16.4337 + 28.4640i 0.604934 + 1.04778i
\(739\) −41.9537 + 24.2220i −1.54329 + 0.891019i −0.544662 + 0.838656i \(0.683342\pi\)
−0.998628 + 0.0523634i \(0.983325\pi\)
\(740\) 102.638 3.77304
\(741\) 0.0154876 2.99476i 0.000568953 0.110015i
\(742\) 25.1567 0.923531
\(743\) −14.7143 + 8.49532i −0.539816 + 0.311663i −0.745004 0.667060i \(-0.767553\pi\)
0.205188 + 0.978722i \(0.434219\pi\)
\(744\) 2.69443 + 4.66689i 0.0987826 + 0.171097i
\(745\) −6.55052 + 11.3458i −0.239993 + 0.415679i
\(746\) 86.6767i 3.17346i
\(747\) −24.8702 14.3588i −0.909955 0.525363i
\(748\) 18.2689 + 10.5475i 0.667977 + 0.385657i
\(749\) 19.1258i 0.698841i
\(750\) 0.937485 1.62377i 0.0342321 0.0592917i
\(751\) 21.5162 + 37.2671i 0.785136 + 1.35990i 0.928918 + 0.370287i \(0.120741\pi\)
−0.143781 + 0.989610i \(0.545926\pi\)
\(752\) 68.9863 39.8292i 2.51567 1.45242i
\(753\) 3.78258 0.137845
\(754\) −23.0083 13.4430i −0.837911 0.489563i
\(755\) 61.5817 2.24119
\(756\) 9.35007 5.39827i 0.340059 0.196333i
\(757\) −14.5892 25.2693i −0.530255 0.918428i −0.999377 0.0352949i \(-0.988763\pi\)
0.469122 0.883133i \(-0.344570\pi\)
\(758\) 25.7116 44.5337i 0.933886 1.61754i
\(759\) 1.15760i 0.0420183i
\(760\) −60.5661 34.9678i −2.19696 1.26842i
\(761\) −25.4829 14.7126i −0.923754 0.533330i −0.0389234 0.999242i \(-0.512393\pi\)
−0.884831 + 0.465912i \(0.845726\pi\)
\(762\) 9.10328i 0.329777i
\(763\) 2.13577 3.69925i 0.0773199 0.133922i
\(764\) −36.4699 63.1677i −1.31943 2.28533i
\(765\) −17.4989 + 10.1030i −0.632675 + 0.365275i
\(766\) −1.89178 −0.0683526
\(767\) 33.4732 + 19.5573i 1.20865 + 0.706172i
\(768\) −8.23976 −0.297327
\(769\) 14.8839 8.59322i 0.536727 0.309879i −0.207024 0.978336i \(-0.566378\pi\)
0.743751 + 0.668456i \(0.233045\pi\)
\(770\) −8.12930 14.0804i −0.292960 0.507421i
\(771\) −0.718083 + 1.24376i −0.0258611 + 0.0447928i
\(772\) 120.756i 4.34612i
\(773\) 19.0180 + 10.9801i 0.684031 + 0.394926i 0.801372 0.598166i \(-0.204104\pi\)
−0.117341 + 0.993092i \(0.537437\pi\)
\(774\) −58.5437 33.8002i −2.10431 1.21492i
\(775\) 9.78399i 0.351451i
\(776\) −41.2666 + 71.4759i