Properties

Label 95.2.p.a.9.8
Level $95$
Weight $2$
Character 95.9
Analytic conductor $0.759$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [95,2,Mod(4,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.4"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.p (of order \(18\), degree \(6\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 9.8
Character \(\chi\) \(=\) 95.9
Dual form 95.2.p.a.74.8

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.93197 - 0.340658i) q^{2} +(0.120656 + 0.143793i) q^{3} +(1.73706 - 0.632239i) q^{4} +(-2.15043 + 0.612911i) q^{5} +(0.282088 + 0.236700i) q^{6} +(0.586358 + 0.338534i) q^{7} +(-0.257316 + 0.148561i) q^{8} +(0.514826 - 2.91972i) q^{9} +(-3.94576 + 1.91668i) q^{10} +(-1.42035 - 2.46011i) q^{11} +(0.300499 + 0.173493i) q^{12} +(-3.06393 + 3.65145i) q^{13} +(1.24815 + 0.454289i) q^{14} +(-0.347595 - 0.235264i) q^{15} +(-3.27865 + 2.75111i) q^{16} +(5.10518 - 0.900181i) q^{17} -5.81619i q^{18} +(3.00824 + 3.15444i) q^{19} +(-3.34792 + 2.42425i) q^{20} +(0.0220691 + 0.125160i) q^{21} +(-3.58212 - 4.26900i) q^{22} +(-0.359434 - 0.987537i) q^{23} +(-0.0524089 - 0.0190753i) q^{24} +(4.24868 - 2.63604i) q^{25} +(-4.67552 + 8.09823i) q^{26} +(0.969633 - 0.559818i) q^{27} +(1.23257 + 0.217336i) q^{28} +(0.247630 - 1.40438i) q^{29} +(-0.751687 - 0.336112i) q^{30} +(-0.135532 + 0.234748i) q^{31} +(-5.01508 + 5.97674i) q^{32} +(0.182372 - 0.501064i) q^{33} +(9.55639 - 3.47824i) q^{34} +(-1.46841 - 0.368607i) q^{35} +(-0.951679 - 5.39724i) q^{36} -0.603754i q^{37} +(6.88641 + 5.06949i) q^{38} -0.894735 q^{39} +(0.462285 - 0.477182i) q^{40} +(5.15980 - 4.32958i) q^{41} +(0.0852737 + 0.234288i) q^{42} +(-1.92538 + 5.28994i) q^{43} +(-4.02261 - 3.37537i) q^{44} +(0.682434 + 6.59420i) q^{45} +(-1.03083 - 1.78544i) q^{46} +(-7.77543 - 1.37102i) q^{47} +(-0.791181 - 0.139507i) q^{48} +(-3.27079 - 5.66517i) q^{49} +(7.31032 - 6.54009i) q^{50} +(0.745413 + 0.625476i) q^{51} +(-3.01365 + 8.27993i) q^{52} +(-2.35594 - 6.47288i) q^{53} +(1.68259 - 1.41186i) q^{54} +(4.56218 + 4.41974i) q^{55} -0.201172 q^{56} +(-0.0906217 + 0.813167i) q^{57} -2.79757i q^{58} +(1.75779 + 9.96889i) q^{59} +(-0.752538 - 0.188906i) q^{60} +(7.02134 - 2.55556i) q^{61} +(-0.181874 + 0.499695i) q^{62} +(1.29030 - 1.53772i) q^{63} +(-3.37297 + 5.84216i) q^{64} +(4.35075 - 9.73010i) q^{65} +(0.181646 - 1.03016i) q^{66} +(-4.05478 - 0.714967i) q^{67} +(8.29889 - 4.79137i) q^{68} +(0.0986326 - 0.170837i) q^{69} +(-2.96249 - 0.211912i) q^{70} +(7.14680 + 2.60122i) q^{71} +(0.301285 + 0.827775i) q^{72} +(10.3665 + 12.3543i) q^{73} +(-0.205674 - 1.16643i) q^{74} +(0.891675 + 0.292874i) q^{75} +(7.21986 + 3.57753i) q^{76} -1.92334i q^{77} +(-1.72860 + 0.304799i) q^{78} +(-11.3733 + 9.54332i) q^{79} +(5.36431 - 7.92559i) q^{80} +(-8.16041 - 2.97015i) q^{81} +(8.49365 - 10.1223i) q^{82} +(-12.2815 - 7.09076i) q^{83} +(0.117467 + 0.203458i) q^{84} +(-10.4266 + 5.06480i) q^{85} +(-1.91771 + 10.8759i) q^{86} +(0.231818 - 0.133840i) q^{87} +(0.730955 + 0.422017i) q^{88} +(-6.31059 - 5.29521i) q^{89} +(3.56481 + 12.5073i) q^{90} +(-3.03270 + 1.10381i) q^{91} +(-1.24872 - 1.48817i) q^{92} +(-0.0501079 + 0.00883537i) q^{93} -15.4889 q^{94} +(-8.40240 - 4.93961i) q^{95} -1.46451 q^{96} +(-5.64144 + 0.994738i) q^{97} +(-8.24894 - 9.83071i) q^{98} +(-7.91407 + 2.88049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93197 0.340658i 1.36611 0.240881i 0.557963 0.829866i \(-0.311583\pi\)
0.808144 + 0.588985i \(0.200472\pi\)
\(3\) 0.120656 + 0.143793i 0.0696611 + 0.0830188i 0.799750 0.600334i \(-0.204966\pi\)
−0.730088 + 0.683353i \(0.760521\pi\)
\(4\) 1.73706 0.632239i 0.868531 0.316120i
\(5\) −2.15043 + 0.612911i −0.961701 + 0.274102i
\(6\) 0.282088 + 0.236700i 0.115162 + 0.0966325i
\(7\) 0.586358 + 0.338534i 0.221622 + 0.127954i 0.606701 0.794930i \(-0.292492\pi\)
−0.385079 + 0.922884i \(0.625826\pi\)
\(8\) −0.257316 + 0.148561i −0.0909749 + 0.0525244i
\(9\) 0.514826 2.91972i 0.171609 0.973241i
\(10\) −3.94576 + 1.91668i −1.24776 + 0.606109i
\(11\) −1.42035 2.46011i −0.428250 0.741751i 0.568468 0.822706i \(-0.307536\pi\)
−0.996718 + 0.0809546i \(0.974203\pi\)
\(12\) 0.300499 + 0.173493i 0.0867467 + 0.0500832i
\(13\) −3.06393 + 3.65145i −0.849781 + 1.01273i 0.149930 + 0.988697i \(0.452095\pi\)
−0.999711 + 0.0240334i \(0.992349\pi\)
\(14\) 1.24815 + 0.454289i 0.333581 + 0.121414i
\(15\) −0.347595 0.235264i −0.0897487 0.0607450i
\(16\) −3.27865 + 2.75111i −0.819663 + 0.687779i
\(17\) 5.10518 0.900181i 1.23819 0.218326i 0.484049 0.875041i \(-0.339166\pi\)
0.754139 + 0.656715i \(0.228054\pi\)
\(18\) 5.81619i 1.37089i
\(19\) 3.00824 + 3.15444i 0.690138 + 0.723678i
\(20\) −3.34792 + 2.42425i −0.748618 + 0.542079i
\(21\) 0.0220691 + 0.125160i 0.00481588 + 0.0273122i
\(22\) −3.58212 4.26900i −0.763710 0.910154i
\(23\) −0.359434 0.987537i −0.0749472 0.205916i 0.896562 0.442919i \(-0.146057\pi\)
−0.971509 + 0.237003i \(0.923835\pi\)
\(24\) −0.0524089 0.0190753i −0.0106979 0.00389373i
\(25\) 4.24868 2.63604i 0.849736 0.527208i
\(26\) −4.67552 + 8.09823i −0.916944 + 1.58819i
\(27\) 0.969633 0.559818i 0.186606 0.107737i
\(28\) 1.23257 + 0.217336i 0.232935 + 0.0410727i
\(29\) 0.247630 1.40438i 0.0459838 0.260787i −0.953145 0.302513i \(-0.902175\pi\)
0.999129 + 0.0417259i \(0.0132856\pi\)
\(30\) −0.751687 0.336112i −0.137239 0.0613654i
\(31\) −0.135532 + 0.234748i −0.0243422 + 0.0421620i −0.877940 0.478771i \(-0.841082\pi\)
0.853598 + 0.520933i \(0.174416\pi\)
\(32\) −5.01508 + 5.97674i −0.886549 + 1.05655i
\(33\) 0.182372 0.501064i 0.0317469 0.0872240i
\(34\) 9.55639 3.47824i 1.63891 0.596513i
\(35\) −1.46841 0.368607i −0.248207 0.0623060i
\(36\) −0.951679 5.39724i −0.158613 0.899540i
\(37\) 0.603754i 0.0992566i −0.998768 0.0496283i \(-0.984196\pi\)
0.998768 0.0496283i \(-0.0158037\pi\)
\(38\) 6.88641 + 5.06949i 1.11712 + 0.822380i
\(39\) −0.894735 −0.143272
\(40\) 0.462285 0.477182i 0.0730936 0.0754492i
\(41\) 5.15980 4.32958i 0.805825 0.676167i −0.143783 0.989609i \(-0.545927\pi\)
0.949607 + 0.313442i \(0.101482\pi\)
\(42\) 0.0852737 + 0.234288i 0.0131580 + 0.0361513i
\(43\) −1.92538 + 5.28994i −0.293618 + 0.806709i 0.701912 + 0.712264i \(0.252330\pi\)
−0.995530 + 0.0944453i \(0.969892\pi\)
\(44\) −4.02261 3.37537i −0.606431 0.508856i
\(45\) 0.682434 + 6.59420i 0.101731 + 0.983005i
\(46\) −1.03083 1.78544i −0.151987 0.263249i
\(47\) −7.77543 1.37102i −1.13416 0.199983i −0.425112 0.905141i \(-0.639765\pi\)
−0.709051 + 0.705157i \(0.750876\pi\)
\(48\) −0.791181 0.139507i −0.114197 0.0201360i
\(49\) −3.27079 5.66517i −0.467256 0.809311i
\(50\) 7.31032 6.54009i 1.03384 0.924908i
\(51\) 0.745413 + 0.625476i 0.104379 + 0.0875841i
\(52\) −3.01365 + 8.27993i −0.417918 + 1.14822i
\(53\) −2.35594 6.47288i −0.323613 0.889118i −0.989689 0.143235i \(-0.954250\pi\)
0.666076 0.745884i \(-0.267973\pi\)
\(54\) 1.68259 1.41186i 0.228972 0.192130i
\(55\) 4.56218 + 4.41974i 0.615164 + 0.595958i
\(56\) −0.201172 −0.0268828
\(57\) −0.0906217 + 0.813167i −0.0120031 + 0.107707i
\(58\) 2.79757i 0.367339i
\(59\) 1.75779 + 9.96889i 0.228844 + 1.29784i 0.855198 + 0.518301i \(0.173435\pi\)
−0.626354 + 0.779539i \(0.715454\pi\)
\(60\) −0.752538 0.188906i −0.0971522 0.0243876i
\(61\) 7.02134 2.55556i 0.898990 0.327206i 0.149142 0.988816i \(-0.452349\pi\)
0.749848 + 0.661610i \(0.230127\pi\)
\(62\) −0.181874 + 0.499695i −0.0230980 + 0.0634614i
\(63\) 1.29030 1.53772i 0.162562 0.193734i
\(64\) −3.37297 + 5.84216i −0.421622 + 0.730270i
\(65\) 4.35075 9.73010i 0.539644 1.20687i
\(66\) 0.181646 1.03016i 0.0223591 0.126805i
\(67\) −4.05478 0.714967i −0.495370 0.0873472i −0.0796188 0.996825i \(-0.525370\pi\)
−0.415752 + 0.909478i \(0.636481\pi\)
\(68\) 8.29889 4.79137i 1.00639 0.581039i
\(69\) 0.0986326 0.170837i 0.0118740 0.0205663i
\(70\) −2.96249 0.211912i −0.354085 0.0253283i
\(71\) 7.14680 + 2.60122i 0.848169 + 0.308708i 0.729294 0.684201i \(-0.239849\pi\)
0.118875 + 0.992909i \(0.462071\pi\)
\(72\) 0.301285 + 0.827775i 0.0355068 + 0.0975542i
\(73\) 10.3665 + 12.3543i 1.21330 + 1.44596i 0.859879 + 0.510497i \(0.170539\pi\)
0.353425 + 0.935463i \(0.385017\pi\)
\(74\) −0.205674 1.16643i −0.0239091 0.135595i
\(75\) 0.891675 + 0.292874i 0.102962 + 0.0338182i
\(76\) 7.21986 + 3.57753i 0.828175 + 0.410371i
\(77\) 1.92334i 0.219185i
\(78\) −1.72860 + 0.304799i −0.195725 + 0.0345117i
\(79\) −11.3733 + 9.54332i −1.27959 + 1.07371i −0.286294 + 0.958142i \(0.592423\pi\)
−0.993300 + 0.115565i \(0.963132\pi\)
\(80\) 5.36431 7.92559i 0.599748 0.886108i
\(81\) −8.16041 2.97015i −0.906713 0.330016i
\(82\) 8.49365 10.1223i 0.937966 1.11782i
\(83\) −12.2815 7.09076i −1.34808 0.778312i −0.360098 0.932914i \(-0.617257\pi\)
−0.987977 + 0.154603i \(0.950590\pi\)
\(84\) 0.117467 + 0.203458i 0.0128167 + 0.0221991i
\(85\) −10.4266 + 5.06480i −1.13092 + 0.549354i
\(86\) −1.91771 + 10.8759i −0.206792 + 1.17278i
\(87\) 0.231818 0.133840i 0.0248535 0.0143492i
\(88\) 0.730955 + 0.422017i 0.0779201 + 0.0449872i
\(89\) −6.31059 5.29521i −0.668921 0.561291i 0.243825 0.969819i \(-0.421598\pi\)
−0.912746 + 0.408528i \(0.866042\pi\)
\(90\) 3.56481 + 12.5073i 0.375763 + 1.31838i
\(91\) −3.03270 + 1.10381i −0.317913 + 0.115711i
\(92\) −1.24872 1.48817i −0.130188 0.155152i
\(93\) −0.0501079 + 0.00883537i −0.00519594 + 0.000916185i
\(94\) −15.4889 −1.59756
\(95\) −8.40240 4.93961i −0.862068 0.506793i
\(96\) −1.46451 −0.149471
\(97\) −5.64144 + 0.994738i −0.572801 + 0.101000i −0.452543 0.891742i \(-0.649483\pi\)
−0.120258 + 0.992743i \(0.538372\pi\)
\(98\) −8.24894 9.83071i −0.833269 0.993051i
\(99\) −7.91407 + 2.88049i −0.795394 + 0.289500i
\(100\) 5.71362 7.26515i 0.571362 0.726515i
\(101\) −1.54918 1.29992i −0.154149 0.129347i 0.562451 0.826831i \(-0.309858\pi\)
−0.716601 + 0.697484i \(0.754303\pi\)
\(102\) 1.65319 + 0.954467i 0.163690 + 0.0945064i
\(103\) −15.7927 + 9.11792i −1.55610 + 0.898415i −0.558477 + 0.829520i \(0.688614\pi\)
−0.997624 + 0.0688957i \(0.978052\pi\)
\(104\) 0.245934 1.39476i 0.0241158 0.136767i
\(105\) −0.124170 0.255622i −0.0121178 0.0249461i
\(106\) −6.75663 11.7028i −0.656262 1.13668i
\(107\) 5.38097 + 3.10671i 0.520198 + 0.300337i 0.737016 0.675876i \(-0.236234\pi\)
−0.216817 + 0.976212i \(0.569568\pi\)
\(108\) 1.33037 1.58548i 0.128015 0.152563i
\(109\) 15.0243 + 5.46840i 1.43907 + 0.523777i 0.939515 0.342507i \(-0.111276\pi\)
0.499551 + 0.866284i \(0.333498\pi\)
\(110\) 10.3196 + 6.98466i 0.983935 + 0.665961i
\(111\) 0.0868155 0.0728469i 0.00824017 0.00691432i
\(112\) −2.85381 + 0.503203i −0.269659 + 0.0475482i
\(113\) 7.88392i 0.741657i −0.928701 0.370828i \(-0.879074\pi\)
0.928701 0.370828i \(-0.120926\pi\)
\(114\) 0.101934 + 1.60188i 0.00954696 + 0.150030i
\(115\) 1.37821 + 1.90333i 0.128519 + 0.177486i
\(116\) −0.457755 2.59606i −0.0425015 0.241038i
\(117\) 9.08384 + 10.8257i 0.839801 + 1.00084i
\(118\) 6.79196 + 18.6608i 0.625251 + 1.71786i
\(119\) 3.29820 + 1.20045i 0.302346 + 0.110045i
\(120\) 0.124393 + 0.00889804i 0.0113555 + 0.000812276i
\(121\) 1.46524 2.53787i 0.133204 0.230715i
\(122\) 12.6944 7.32913i 1.14930 0.663548i
\(123\) 1.24513 + 0.219549i 0.112269 + 0.0197961i
\(124\) −0.0870104 + 0.493461i −0.00781376 + 0.0443141i
\(125\) −7.52082 + 8.27268i −0.672683 + 0.739931i
\(126\) 1.96898 3.41037i 0.175410 0.303820i
\(127\) 10.1395 12.0838i 0.899736 1.07226i −0.0972942 0.995256i \(-0.531019\pi\)
0.997030 0.0770082i \(-0.0245368\pi\)
\(128\) 0.810645 2.22723i 0.0716516 0.196861i
\(129\) −0.992966 + 0.361410i −0.0874258 + 0.0318204i
\(130\) 5.09087 20.2803i 0.446499 1.77870i
\(131\) −0.706095 4.00446i −0.0616918 0.349872i −0.999992 0.00404921i \(-0.998711\pi\)
0.938300 0.345822i \(-0.112400\pi\)
\(132\) 0.985682i 0.0857926i
\(133\) 0.696022 + 2.86802i 0.0603527 + 0.248689i
\(134\) −8.07726 −0.697769
\(135\) −1.74201 + 1.79815i −0.149928 + 0.154760i
\(136\) −1.17991 + 0.990064i −0.101177 + 0.0848973i
\(137\) −0.893360 2.45449i −0.0763249 0.209701i 0.895662 0.444735i \(-0.146702\pi\)
−0.971987 + 0.235034i \(0.924480\pi\)
\(138\) 0.132358 0.363651i 0.0112671 0.0309560i
\(139\) −6.87238 5.76661i −0.582908 0.489118i 0.302993 0.952993i \(-0.402014\pi\)
−0.885901 + 0.463875i \(0.846459\pi\)
\(140\) −2.78377 + 0.288092i −0.235271 + 0.0243483i
\(141\) −0.741013 1.28347i −0.0624046 0.108088i
\(142\) 14.6935 + 2.59086i 1.23305 + 0.217420i
\(143\) 13.3348 + 2.35129i 1.11511 + 0.196624i
\(144\) 6.34456 + 10.9891i 0.528713 + 0.915758i
\(145\) 0.328249 + 3.17179i 0.0272596 + 0.263403i
\(146\) 24.2363 + 20.3367i 2.00581 + 1.68307i
\(147\) 0.419969 1.15386i 0.0346385 0.0951684i
\(148\) −0.381717 1.04876i −0.0313770 0.0862075i
\(149\) 1.32378 1.11078i 0.108448 0.0909989i −0.586951 0.809622i \(-0.699672\pi\)
0.695399 + 0.718623i \(0.255227\pi\)
\(150\) 1.82246 + 0.262067i 0.148803 + 0.0213977i
\(151\) 11.0738 0.901177 0.450589 0.892732i \(-0.351214\pi\)
0.450589 + 0.892732i \(0.351214\pi\)
\(152\) −1.24270 0.364779i −0.100796 0.0295875i
\(153\) 15.3692i 1.24252i
\(154\) −0.655201 3.71583i −0.0527976 0.299430i
\(155\) 0.147572 0.587878i 0.0118533 0.0472195i
\(156\) −1.55421 + 0.565687i −0.124437 + 0.0452912i
\(157\) 0.671940 1.84614i 0.0536267 0.147338i −0.909987 0.414637i \(-0.863909\pi\)
0.963614 + 0.267298i \(0.0861310\pi\)
\(158\) −18.7218 + 22.3118i −1.48943 + 1.77503i
\(159\) 0.646495 1.11976i 0.0512704 0.0888029i
\(160\) 7.12136 15.9263i 0.562993 1.25909i
\(161\) 0.123558 0.700730i 0.00973771 0.0552253i
\(162\) −16.7775 2.95832i −1.31816 0.232427i
\(163\) 17.4341 10.0656i 1.36554 0.788395i 0.375186 0.926950i \(-0.377579\pi\)
0.990355 + 0.138555i \(0.0442457\pi\)
\(164\) 6.22556 10.7830i 0.486134 0.842009i
\(165\) −0.0850711 + 1.18928i −0.00662277 + 0.0925853i
\(166\) −26.1431 9.51530i −2.02910 0.738530i
\(167\) 6.10733 + 16.7798i 0.472600 + 1.29846i 0.915656 + 0.401963i \(0.131672\pi\)
−0.443056 + 0.896494i \(0.646106\pi\)
\(168\) −0.0242727 0.0289271i −0.00187268 0.00223178i
\(169\) −1.68799 9.57308i −0.129846 0.736391i
\(170\) −18.4185 + 13.3369i −1.41263 + 1.02289i
\(171\) 10.7588 7.15925i 0.822747 0.547481i
\(172\) 10.4063i 0.793470i
\(173\) 2.68082 0.472701i 0.203819 0.0359388i −0.0708064 0.997490i \(-0.522557\pi\)
0.274625 + 0.961551i \(0.411446\pi\)
\(174\) 0.402271 0.337545i 0.0304961 0.0255893i
\(175\) 3.38364 0.107341i 0.255779 0.00811421i
\(176\) 11.4249 + 4.15831i 0.861181 + 0.313444i
\(177\) −1.22137 + 1.45557i −0.0918036 + 0.109407i
\(178\) −13.9957 8.08042i −1.04902 0.605653i
\(179\) 3.85817 + 6.68254i 0.288373 + 0.499477i 0.973422 0.229021i \(-0.0735524\pi\)
−0.685049 + 0.728497i \(0.740219\pi\)
\(180\) 5.35454 + 11.0231i 0.399104 + 0.821612i
\(181\) −0.185874 + 1.05414i −0.0138159 + 0.0783537i −0.990936 0.134334i \(-0.957111\pi\)
0.977120 + 0.212688i \(0.0682217\pi\)
\(182\) −5.48305 + 3.16564i −0.406431 + 0.234653i
\(183\) 1.21464 + 0.701273i 0.0897888 + 0.0518396i
\(184\) 0.239198 + 0.200711i 0.0176339 + 0.0147966i
\(185\) 0.370048 + 1.29833i 0.0272064 + 0.0954551i
\(186\) −0.0937969 + 0.0341393i −0.00687752 + 0.00250321i
\(187\) −9.46566 11.2807i −0.692198 0.824929i
\(188\) −14.3732 + 2.53439i −1.04827 + 0.184839i
\(189\) 0.758069 0.0551414
\(190\) −17.9159 6.68082i −1.29975 0.484677i
\(191\) 5.38296 0.389497 0.194749 0.980853i \(-0.437611\pi\)
0.194749 + 0.980853i \(0.437611\pi\)
\(192\) −1.24703 + 0.219885i −0.0899967 + 0.0158689i
\(193\) 9.94387 + 11.8506i 0.715775 + 0.853028i 0.994213 0.107426i \(-0.0342610\pi\)
−0.278438 + 0.960454i \(0.589817\pi\)
\(194\) −10.5602 + 3.84360i −0.758179 + 0.275954i
\(195\) 1.92406 0.548393i 0.137785 0.0392712i
\(196\) −9.26331 7.77284i −0.661665 0.555203i
\(197\) −18.3882 10.6164i −1.31010 0.756388i −0.327989 0.944682i \(-0.606371\pi\)
−0.982113 + 0.188294i \(0.939704\pi\)
\(198\) −14.3085 + 8.26100i −1.01686 + 0.587083i
\(199\) −1.31646 + 7.46602i −0.0933214 + 0.529252i 0.901927 + 0.431888i \(0.142152\pi\)
−0.995249 + 0.0973643i \(0.968959\pi\)
\(200\) −0.701639 + 1.30949i −0.0496134 + 0.0925946i
\(201\) −0.386429 0.669314i −0.0272566 0.0472098i
\(202\) −3.43580 1.98366i −0.241742 0.139570i
\(203\) 0.620630 0.739638i 0.0435597 0.0519124i
\(204\) 1.69028 + 0.615211i 0.118343 + 0.0430734i
\(205\) −8.44212 + 12.4729i −0.589623 + 0.871149i
\(206\) −27.4049 + 22.9954i −1.90939 + 1.60217i
\(207\) −3.06838 + 0.541038i −0.213267 + 0.0376048i
\(208\) 20.4011i 1.41456i
\(209\) 3.48752 11.8810i 0.241237 0.821826i
\(210\) −0.326972 0.451553i −0.0225632 0.0311601i
\(211\) −2.30936 13.0971i −0.158983 0.901639i −0.955053 0.296434i \(-0.904202\pi\)
0.796070 0.605204i \(-0.206909\pi\)
\(212\) −8.18481 9.75428i −0.562135 0.669927i
\(213\) 0.488271 + 1.34151i 0.0334558 + 0.0919189i
\(214\) 11.4542 + 4.16898i 0.782992 + 0.284986i
\(215\) 0.898132 12.5557i 0.0612521 0.856294i
\(216\) −0.166335 + 0.288100i −0.0113176 + 0.0196027i
\(217\) −0.158940 + 0.0917642i −0.0107896 + 0.00622936i
\(218\) 30.8893 + 5.44661i 2.09209 + 0.368891i
\(219\) −0.525675 + 2.98125i −0.0355218 + 0.201454i
\(220\) 10.7191 + 4.79299i 0.722683 + 0.323143i
\(221\) −12.3550 + 21.3994i −0.831084 + 1.43948i
\(222\) 0.142909 0.170312i 0.00959142 0.0114306i
\(223\) 6.79915 18.6805i 0.455304 1.25094i −0.473640 0.880719i \(-0.657060\pi\)
0.928944 0.370220i \(-0.120718\pi\)
\(224\) −4.96396 + 1.80673i −0.331668 + 0.120717i
\(225\) −5.50918 13.7621i −0.367279 0.917472i
\(226\) −2.68572 15.2315i −0.178651 1.01318i
\(227\) 27.3022i 1.81211i 0.423163 + 0.906054i \(0.360920\pi\)
−0.423163 + 0.906054i \(0.639080\pi\)
\(228\) 0.356700 + 1.46982i 0.0236231 + 0.0973410i
\(229\) 14.6429 0.967633 0.483816 0.875170i \(-0.339250\pi\)
0.483816 + 0.875170i \(0.339250\pi\)
\(230\) 3.31104 + 3.20766i 0.218323 + 0.211507i
\(231\) 0.276562 0.232063i 0.0181965 0.0152686i
\(232\) 0.144918 + 0.398158i 0.00951431 + 0.0261403i
\(233\) 2.26737 6.22953i 0.148540 0.408110i −0.843000 0.537914i \(-0.819212\pi\)
0.991540 + 0.129804i \(0.0414347\pi\)
\(234\) 21.2375 + 17.8204i 1.38834 + 1.16496i
\(235\) 17.5608 1.81737i 1.14554 0.118552i
\(236\) 9.35611 + 16.2053i 0.609031 + 1.05487i
\(237\) −2.74452 0.483933i −0.178276 0.0314348i
\(238\) 6.78096 + 1.19567i 0.439544 + 0.0775036i
\(239\) −6.33959 10.9805i −0.410074 0.710269i 0.584823 0.811161i \(-0.301164\pi\)
−0.994897 + 0.100892i \(0.967830\pi\)
\(240\) 1.78688 0.184925i 0.115343 0.0119368i
\(241\) 10.8118 + 9.07218i 0.696450 + 0.584391i 0.920761 0.390127i \(-0.127569\pi\)
−0.224311 + 0.974518i \(0.572013\pi\)
\(242\) 1.96625 5.40222i 0.126395 0.347268i
\(243\) −1.70633 4.68812i −0.109461 0.300743i
\(244\) 10.5808 8.87833i 0.677365 0.568377i
\(245\) 10.5058 + 10.1778i 0.671194 + 0.650239i
\(246\) 2.48033 0.158140
\(247\) −20.7353 + 1.31946i −1.31936 + 0.0839555i
\(248\) 0.0805392i 0.00511425i
\(249\) −0.462249 2.62154i −0.0292938 0.166134i
\(250\) −11.7118 + 18.5446i −0.740721 + 1.17286i
\(251\) −6.55337 + 2.38523i −0.413645 + 0.150554i −0.540456 0.841372i \(-0.681748\pi\)
0.126811 + 0.991927i \(0.459526\pi\)
\(252\) 1.26912 3.48689i 0.0799472 0.219653i
\(253\) −1.91893 + 2.28689i −0.120642 + 0.143776i
\(254\) 15.4728 26.7996i 0.970847 1.68156i
\(255\) −1.98632 0.888169i −0.124388 0.0556193i
\(256\) 3.15026 17.8660i 0.196891 1.11663i
\(257\) 15.5410 + 2.74031i 0.969424 + 0.170936i 0.635871 0.771796i \(-0.280641\pi\)
0.333553 + 0.942731i \(0.391752\pi\)
\(258\) −1.79526 + 1.03649i −0.111768 + 0.0645293i
\(259\) 0.204391 0.354016i 0.0127003 0.0219975i
\(260\) 1.40578 19.6525i 0.0871825 1.21880i
\(261\) −3.97292 1.44602i −0.245917 0.0895066i
\(262\) −2.72830 7.49595i −0.168555 0.463102i
\(263\) 12.7872 + 15.2391i 0.788490 + 0.939686i 0.999284 0.0378448i \(-0.0120492\pi\)
−0.210794 + 0.977531i \(0.567605\pi\)
\(264\) 0.0275114 + 0.156025i 0.00169321 + 0.00960268i
\(265\) 9.03357 + 12.4755i 0.554928 + 0.766363i
\(266\) 2.32170 + 5.30381i 0.142353 + 0.325198i
\(267\) 1.54632i 0.0946331i
\(268\) −7.49544 + 1.32165i −0.457857 + 0.0807325i
\(269\) 8.70147 7.30140i 0.530538 0.445174i −0.337749 0.941236i \(-0.609666\pi\)
0.868287 + 0.496062i \(0.165221\pi\)
\(270\) −2.75295 + 4.06739i −0.167539 + 0.247533i
\(271\) −22.4471 8.17007i −1.36356 0.496296i −0.446409 0.894829i \(-0.647297\pi\)
−0.917154 + 0.398533i \(0.869519\pi\)
\(272\) −14.2616 + 16.9963i −0.864737 + 1.03055i
\(273\) −0.524635 0.302898i −0.0317523 0.0183322i
\(274\) −2.56208 4.43766i −0.154781 0.268089i
\(275\) −12.5195 6.70813i −0.754957 0.404516i
\(276\) 0.0633214 0.359114i 0.00381150 0.0216161i
\(277\) −4.06428 + 2.34652i −0.244199 + 0.140988i −0.617105 0.786881i \(-0.711695\pi\)
0.372906 + 0.927869i \(0.378361\pi\)
\(278\) −15.2417 8.79978i −0.914134 0.527776i
\(279\) 0.615624 + 0.516570i 0.0368564 + 0.0309262i
\(280\) 0.432606 0.123301i 0.0258532 0.00736862i
\(281\) −21.1014 + 7.68028i −1.25880 + 0.458167i −0.883367 0.468681i \(-0.844729\pi\)
−0.375436 + 0.926848i \(0.622507\pi\)
\(282\) −1.86884 2.22719i −0.111288 0.132628i
\(283\) −10.7176 + 1.88981i −0.637097 + 0.112337i −0.482862 0.875697i \(-0.660403\pi\)
−0.154236 + 0.988034i \(0.549291\pi\)
\(284\) 14.0590 0.834250
\(285\) −0.303523 1.80420i −0.0179792 0.106872i
\(286\) 26.5634 1.57073
\(287\) 4.49119 0.791919i 0.265107 0.0467455i
\(288\) 14.8685 + 17.7196i 0.876137 + 1.04414i
\(289\) 9.27778 3.37683i 0.545752 0.198637i
\(290\) 1.71466 + 6.01598i 0.100688 + 0.353271i
\(291\) −0.823712 0.691177i −0.0482869 0.0405175i
\(292\) 25.8181 + 14.9061i 1.51089 + 0.872312i
\(293\) −10.8004 + 6.23561i −0.630965 + 0.364288i −0.781126 0.624374i \(-0.785354\pi\)
0.150161 + 0.988662i \(0.452021\pi\)
\(294\) 0.418297 2.37228i 0.0243955 0.138354i
\(295\) −9.89003 20.3600i −0.575820 1.18541i
\(296\) 0.0896946 + 0.155356i 0.00521339 + 0.00902986i
\(297\) −2.75443 1.59027i −0.159828 0.0922767i
\(298\) 2.17910 2.59695i 0.126232 0.150437i
\(299\) 4.70722 + 1.71329i 0.272226 + 0.0990821i
\(300\) 1.73406 0.0550106i 0.100116 0.00317604i
\(301\) −2.91979 + 2.44999i −0.168294 + 0.141215i
\(302\) 21.3943 3.77239i 1.23110 0.217077i
\(303\) 0.379605i 0.0218077i
\(304\) −18.5412 2.06628i −1.06341 0.118510i
\(305\) −13.5326 + 9.79900i −0.774872 + 0.561089i
\(306\) −5.23562 29.6927i −0.299301 1.69742i
\(307\) 2.68594 + 3.20098i 0.153295 + 0.182689i 0.837226 0.546857i \(-0.184176\pi\)
−0.683932 + 0.729546i \(0.739731\pi\)
\(308\) −1.21601 3.34096i −0.0692886 0.190369i
\(309\) −3.21658 1.17074i −0.182985 0.0666011i
\(310\) 0.0848388 1.18603i 0.00481852 0.0673621i
\(311\) 6.04544 10.4710i 0.342806 0.593757i −0.642147 0.766582i \(-0.721956\pi\)
0.984953 + 0.172825i \(0.0552894\pi\)
\(312\) 0.230230 0.132923i 0.0130342 0.00752529i
\(313\) −9.43307 1.66330i −0.533188 0.0940155i −0.0994297 0.995045i \(-0.531702\pi\)
−0.433759 + 0.901029i \(0.642813\pi\)
\(314\) 0.669264 3.79558i 0.0377688 0.214197i
\(315\) −1.83221 + 4.09759i −0.103233 + 0.230873i
\(316\) −13.7224 + 23.7680i −0.771948 + 1.33705i
\(317\) 7.17941 8.55609i 0.403236 0.480558i −0.525768 0.850628i \(-0.676222\pi\)
0.929004 + 0.370070i \(0.120666\pi\)
\(318\) 0.867550 2.38358i 0.0486498 0.133664i
\(319\) −3.80665 + 1.38551i −0.213132 + 0.0775735i
\(320\) 3.67261 14.6305i 0.205305 0.817868i
\(321\) 0.202527 + 1.14859i 0.0113040 + 0.0641080i
\(322\) 1.39588i 0.0777893i
\(323\) 18.1972 + 13.3960i 1.01252 + 0.745374i
\(324\) −16.0530 −0.891833
\(325\) −3.39229 + 23.5905i −0.188170 + 1.30857i
\(326\) 30.2531 25.3854i 1.67556 1.40597i
\(327\) 1.02646 + 2.82018i 0.0567635 + 0.155956i
\(328\) −0.684489 + 1.88062i −0.0377946 + 0.103840i
\(329\) −4.09505 3.43615i −0.225767 0.189441i
\(330\) 0.240783 + 2.32663i 0.0132547 + 0.128077i
\(331\) 10.8439 + 18.7822i 0.596034 + 1.03236i 0.993400 + 0.114701i \(0.0365911\pi\)
−0.397366 + 0.917660i \(0.630076\pi\)
\(332\) −25.8169 4.55221i −1.41688 0.249835i
\(333\) −1.76280 0.310829i −0.0966006 0.0170333i
\(334\) 17.5153 + 30.3374i 0.958396 + 1.65999i
\(335\) 9.15773 0.947733i 0.500340 0.0517802i
\(336\) −0.416687 0.349642i −0.0227322 0.0190745i
\(337\) 0.0180757 0.0496626i 0.000984647 0.00270530i −0.939199 0.343372i \(-0.888431\pi\)
0.940184 + 0.340667i \(0.110653\pi\)
\(338\) −6.52229 17.9198i −0.354766 0.974711i
\(339\) 1.13365 0.951246i 0.0615715 0.0516646i
\(340\) −14.9095 + 15.3900i −0.808580 + 0.834638i
\(341\) 0.770008 0.0416983
\(342\) 18.3468 17.4965i 0.992082 0.946103i
\(343\) 9.16856i 0.495056i
\(344\) −0.290450 1.64722i −0.0156600 0.0888124i
\(345\) −0.107395 + 0.427825i −0.00578194 + 0.0230333i
\(346\) 5.01823 1.82649i 0.269782 0.0981925i
\(347\) 8.68262 23.8553i 0.466107 1.28062i −0.454715 0.890637i \(-0.650259\pi\)
0.920822 0.389982i \(-0.127519\pi\)
\(348\) 0.318063 0.379053i 0.0170500 0.0203194i
\(349\) −7.80995 + 13.5272i −0.418057 + 0.724096i −0.995744 0.0921622i \(-0.970622\pi\)
0.577687 + 0.816259i \(0.303956\pi\)
\(350\) 6.50050 1.36004i 0.347467 0.0726973i
\(351\) −0.926741 + 5.25581i −0.0494658 + 0.280534i
\(352\) 21.8266 + 3.84862i 1.16336 + 0.205132i
\(353\) −10.8004 + 6.23564i −0.574850 + 0.331890i −0.759084 0.650993i \(-0.774353\pi\)
0.184234 + 0.982882i \(0.441019\pi\)
\(354\) −1.86379 + 3.22818i −0.0990593 + 0.171576i
\(355\) −16.9630 1.21339i −0.900302 0.0644001i
\(356\) −14.3097 5.20831i −0.758414 0.276040i
\(357\) 0.225334 + 0.619100i 0.0119259 + 0.0327662i
\(358\) 9.73031 + 11.5961i 0.514263 + 0.612875i
\(359\) 5.84204 + 33.1318i 0.308331 + 1.74863i 0.607396 + 0.794399i \(0.292214\pi\)
−0.299065 + 0.954233i \(0.596675\pi\)
\(360\) −1.15524 1.59541i −0.0608868 0.0840855i
\(361\) −0.900964 + 18.9786i −0.0474191 + 0.998875i
\(362\) 2.09989i 0.110368i
\(363\) 0.541718 0.0955195i 0.0284328 0.00501347i
\(364\) −4.57011 + 3.83478i −0.239539 + 0.200997i
\(365\) −29.8644 20.2133i −1.56318 1.05801i
\(366\) 2.58554 + 0.941060i 0.135148 + 0.0491900i
\(367\) 16.4618 19.6184i 0.859299 1.02407i −0.140125 0.990134i \(-0.544750\pi\)
0.999424 0.0339392i \(-0.0108053\pi\)
\(368\) 3.89529 + 2.24894i 0.203056 + 0.117234i
\(369\) −9.98479 17.2942i −0.519787 0.900298i
\(370\) 1.15721 + 2.38227i 0.0601603 + 0.123848i
\(371\) 0.809867 4.59299i 0.0420462 0.238456i
\(372\) −0.0814544 + 0.0470277i −0.00422322 + 0.00243827i
\(373\) −18.8456 10.8805i −0.975788 0.563372i −0.0747923 0.997199i \(-0.523829\pi\)
−0.900996 + 0.433828i \(0.857163\pi\)
\(374\) −22.1302 18.5695i −1.14433 0.960204i
\(375\) −2.09699 0.0832880i −0.108288 0.00430098i
\(376\) 2.20442 0.802344i 0.113684 0.0413777i
\(377\) 4.36930 + 5.20713i 0.225031 + 0.268181i
\(378\) 1.46456 0.258242i 0.0753290 0.0132825i
\(379\) 6.63029 0.340575 0.170288 0.985394i \(-0.445530\pi\)
0.170288 + 0.985394i \(0.445530\pi\)
\(380\) −17.7185 3.26809i −0.908940 0.167649i
\(381\) 2.96096 0.151695
\(382\) 10.3997 1.83375i 0.532095 0.0938226i
\(383\) −17.3693 20.7000i −0.887532 1.05772i −0.997960 0.0638349i \(-0.979667\pi\)
0.110429 0.993884i \(-0.464778\pi\)
\(384\) 0.418069 0.152165i 0.0213345 0.00776512i
\(385\) 1.17884 + 4.13600i 0.0600790 + 0.210790i
\(386\) 23.2482 + 19.5076i 1.18330 + 0.992910i
\(387\) 14.4539 + 8.34499i 0.734735 + 0.424200i
\(388\) −9.17062 + 5.29466i −0.465568 + 0.268796i
\(389\) −4.51305 + 25.5948i −0.228821 + 1.29771i 0.626424 + 0.779483i \(0.284518\pi\)
−0.855245 + 0.518224i \(0.826593\pi\)
\(390\) 3.53041 1.71492i 0.178769 0.0868386i
\(391\) −2.72394 4.71800i −0.137755 0.238599i
\(392\) 1.68325 + 0.971827i 0.0850171 + 0.0490847i
\(393\) 0.490618 0.584696i 0.0247484 0.0294940i
\(394\) −39.1419 14.2465i −1.97194 0.717727i
\(395\) 18.6082 27.4930i 0.936281 1.38332i
\(396\) −11.9261 + 10.0072i −0.599308 + 0.502879i
\(397\) −21.0231 + 3.70695i −1.05512 + 0.186046i −0.674191 0.738557i \(-0.735507\pi\)
−0.380930 + 0.924604i \(0.624396\pi\)
\(398\) 14.8726i 0.745494i
\(399\) −0.328421 + 0.446128i −0.0164416 + 0.0223343i
\(400\) −6.67789 + 20.3313i −0.333894 + 1.01656i
\(401\) 4.52547 + 25.6652i 0.225991 + 1.28166i 0.860781 + 0.508975i \(0.169975\pi\)
−0.634790 + 0.772685i \(0.718913\pi\)
\(402\) −0.974574 1.16145i −0.0486073 0.0579280i
\(403\) −0.441911 1.21414i −0.0220131 0.0604806i
\(404\) −3.51289 1.27859i −0.174773 0.0636120i
\(405\) 19.3688 + 1.38548i 0.962444 + 0.0688452i
\(406\) 0.947073 1.64038i 0.0470024 0.0814106i
\(407\) −1.48530 + 0.857540i −0.0736237 + 0.0425067i
\(408\) −0.284728 0.0502053i −0.0140961 0.00248553i
\(409\) 4.05420 22.9925i 0.200467 1.13691i −0.703948 0.710252i \(-0.748581\pi\)
0.904415 0.426654i \(-0.140308\pi\)
\(410\) −12.0609 + 26.9732i −0.595645 + 1.33211i
\(411\) 0.245148 0.424608i 0.0120922 0.0209444i
\(412\) −21.6682 + 25.8232i −1.06752 + 1.27222i
\(413\) −2.34412 + 6.44041i −0.115346 + 0.316912i
\(414\) −5.74370 + 2.09054i −0.282288 + 0.102744i
\(415\) 30.7566 + 7.72067i 1.50978 + 0.378993i
\(416\) −6.45791 36.6246i −0.316625 1.79567i
\(417\) 1.68398i 0.0824648i
\(418\) 2.69043 24.1417i 0.131593 1.18081i
\(419\) −21.9951 −1.07453 −0.537265 0.843413i \(-0.680543\pi\)
−0.537265 + 0.843413i \(0.680543\pi\)
\(420\) −0.377305 0.365526i −0.0184106 0.0178358i
\(421\) 2.85822 2.39833i 0.139301 0.116888i −0.570475 0.821315i \(-0.693241\pi\)
0.709776 + 0.704428i \(0.248796\pi\)
\(422\) −8.92323 24.5164i −0.434376 1.19344i
\(423\) −8.00599 + 21.9963i −0.389264 + 1.06950i
\(424\) 1.56784 + 1.31557i 0.0761410 + 0.0638899i
\(425\) 19.3174 17.2820i 0.937030 0.838303i
\(426\) 1.40032 + 2.42542i 0.0678457 + 0.117512i
\(427\) 4.98216 + 0.878489i 0.241104 + 0.0425131i
\(428\) 11.3113 + 1.99448i 0.546751 + 0.0964069i
\(429\) 1.27083 + 2.20115i 0.0613564 + 0.106272i
\(430\) −2.54205 24.5632i −0.122588 1.18454i
\(431\) −19.0853 16.0145i −0.919307 0.771390i 0.0545594 0.998511i \(-0.482625\pi\)
−0.973867 + 0.227120i \(0.927069\pi\)
\(432\) −1.63896 + 4.50302i −0.0788547 + 0.216651i
\(433\) −3.75273 10.3105i −0.180345 0.495492i 0.816274 0.577666i \(-0.196036\pi\)
−0.996618 + 0.0821730i \(0.973814\pi\)
\(434\) −0.275807 + 0.231430i −0.0132392 + 0.0111090i
\(435\) −0.416476 + 0.429897i −0.0199685 + 0.0206120i
\(436\) 29.5555 1.41545
\(437\) 2.03386 4.10456i 0.0972927 0.196348i
\(438\) 5.93875i 0.283765i
\(439\) 1.47943 + 8.39029i 0.0706096 + 0.400447i 0.999544 + 0.0302020i \(0.00961507\pi\)
−0.928934 + 0.370245i \(0.879274\pi\)
\(440\) −1.83052 0.459507i −0.0872668 0.0219061i
\(441\) −18.2246 + 6.63322i −0.867840 + 0.315868i
\(442\) −16.5795 + 45.5518i −0.788606 + 2.16668i
\(443\) −6.05322 + 7.21394i −0.287597 + 0.342745i −0.890428 0.455124i \(-0.849595\pi\)
0.602831 + 0.797869i \(0.294039\pi\)
\(444\) 0.104747 0.181428i 0.00497109 0.00861018i
\(445\) 16.8160 + 7.51914i 0.797153 + 0.356441i
\(446\) 6.77206 38.4063i 0.320667 1.81859i
\(447\) 0.319445 + 0.0563268i 0.0151092 + 0.00266417i
\(448\) −3.95554 + 2.28373i −0.186881 + 0.107896i
\(449\) 4.86372 8.42421i 0.229533 0.397563i −0.728137 0.685432i \(-0.759613\pi\)
0.957670 + 0.287869i \(0.0929468\pi\)
\(450\) −15.3317 24.7111i −0.722744 1.16489i
\(451\) −17.9799 6.54416i −0.846642 0.308153i
\(452\) −4.98452 13.6949i −0.234452 0.644152i
\(453\) 1.33613 + 1.59234i 0.0627769 + 0.0748146i
\(454\) 9.30069 + 52.7468i 0.436503 + 2.47553i
\(455\) 5.84506 4.23244i 0.274021 0.198420i
\(456\) −0.0974869 0.222704i −0.00456524 0.0104291i
\(457\) 10.4686i 0.489700i −0.969561 0.244850i \(-0.921261\pi\)
0.969561 0.244850i \(-0.0787387\pi\)
\(458\) 28.2897 4.98823i 1.32189 0.233085i
\(459\) 4.44621 3.73082i 0.207531 0.174140i
\(460\) 3.59739 + 2.43484i 0.167729 + 0.113525i
\(461\) 21.3065 + 7.75492i 0.992342 + 0.361183i 0.786626 0.617429i \(-0.211826\pi\)
0.205715 + 0.978612i \(0.434048\pi\)
\(462\) 0.455255 0.542552i 0.0211804 0.0252418i
\(463\) 30.8631 + 17.8188i 1.43433 + 0.828110i 0.997447 0.0714094i \(-0.0227497\pi\)
0.436881 + 0.899519i \(0.356083\pi\)
\(464\) 3.05172 + 5.28573i 0.141672 + 0.245384i
\(465\) 0.102338 0.0497115i 0.00474581 0.00230531i
\(466\) 2.25833 12.8076i 0.104615 0.593303i
\(467\) −2.51286 + 1.45080i −0.116281 + 0.0671350i −0.557013 0.830504i \(-0.688052\pi\)
0.440731 + 0.897639i \(0.354719\pi\)
\(468\) 22.6236 + 13.0618i 1.04578 + 0.603780i
\(469\) −2.13551 1.79191i −0.0986088 0.0827426i
\(470\) 33.3078 9.49332i 1.53637 0.437894i
\(471\) 0.346536 0.126129i 0.0159675 0.00581170i
\(472\) −1.93330 2.30402i −0.0889873 0.106051i
\(473\) 15.7486 2.77689i 0.724119 0.127682i
\(474\) −5.46718 −0.251116
\(475\) 21.0963 + 5.47235i 0.967964 + 0.251089i
\(476\) 6.48816 0.297384
\(477\) −20.1119 + 3.54627i −0.920862 + 0.162373i
\(478\) −15.9885 19.0543i −0.731296 0.871524i
\(479\) 27.5809 10.0386i 1.26020 0.458676i 0.376365 0.926471i \(-0.377174\pi\)
0.883837 + 0.467795i \(0.154952\pi\)
\(480\) 3.14933 0.897617i 0.143747 0.0409704i
\(481\) 2.20458 + 1.84986i 0.100520 + 0.0843464i
\(482\) 23.9786 + 13.8440i 1.09219 + 0.630578i
\(483\) 0.115668 0.0667810i 0.00526308 0.00303864i
\(484\) 0.940673 5.33482i 0.0427578 0.242492i
\(485\) 11.5218 5.59681i 0.523179 0.254138i
\(486\) −4.89363 8.47601i −0.221979 0.384480i
\(487\) −2.95906 1.70841i −0.134088 0.0774157i 0.431456 0.902134i \(-0.358000\pi\)
−0.565543 + 0.824719i \(0.691334\pi\)
\(488\) −1.42705 + 1.70069i −0.0645993 + 0.0769865i
\(489\) 3.55089 + 1.29242i 0.160577 + 0.0584451i
\(490\) 23.7641 + 16.0844i 1.07355 + 0.726617i
\(491\) −19.2938 + 16.1894i −0.870717 + 0.730618i −0.964249 0.264998i \(-0.914629\pi\)
0.0935323 + 0.995616i \(0.470184\pi\)
\(492\) 2.30167 0.405846i 0.103767 0.0182970i
\(493\) 7.39253i 0.332943i
\(494\) −39.6105 + 9.61281i −1.78216 + 0.432501i
\(495\) 15.2532 11.0449i 0.685579 0.496431i
\(496\) −0.201457 1.14252i −0.00904569 0.0513007i
\(497\) 3.30998 + 3.94468i 0.148473 + 0.176943i
\(498\) −1.78610 4.90727i −0.0800370 0.219900i
\(499\) −32.6388 11.8795i −1.46111 0.531801i −0.515441 0.856925i \(-0.672372\pi\)
−0.945671 + 0.325124i \(0.894594\pi\)
\(500\) −7.83383 + 19.1251i −0.350340 + 0.855301i
\(501\) −1.67592 + 2.90278i −0.0748746 + 0.129687i
\(502\) −11.8483 + 6.84064i −0.528817 + 0.305313i
\(503\) −22.1171 3.89983i −0.986151 0.173885i −0.342760 0.939423i \(-0.611362\pi\)
−0.643391 + 0.765538i \(0.722473\pi\)
\(504\) −0.103569 + 0.587367i −0.00461332 + 0.0261634i
\(505\) 4.12814 + 1.84587i 0.183700 + 0.0821402i
\(506\) −2.92826 + 5.07189i −0.130177 + 0.225473i
\(507\) 1.17287 1.39778i 0.0520891 0.0620774i
\(508\) 9.97312 27.4009i 0.442486 1.21572i
\(509\) 2.20641 0.803067i 0.0977974 0.0355953i −0.292658 0.956217i \(-0.594540\pi\)
0.390455 + 0.920622i \(0.372318\pi\)
\(510\) −4.14006 1.03926i −0.183325 0.0460191i
\(511\) 1.89612 + 10.7534i 0.0838794 + 0.475704i
\(512\) 30.8493i 1.36336i
\(513\) 4.68280 + 1.37458i 0.206751 + 0.0606892i
\(514\) 30.9583 1.36551
\(515\) 28.3726 29.2869i 1.25025 1.29054i
\(516\) −1.49635 + 1.25558i −0.0658730 + 0.0552740i
\(517\) 7.67094 + 21.0757i 0.337367 + 0.926909i
\(518\) 0.274279 0.753575i 0.0120511 0.0331102i
\(519\) 0.391429 + 0.328448i 0.0171818 + 0.0144173i
\(520\) 0.326000 + 3.15006i 0.0142961 + 0.138139i
\(521\) −0.761964 1.31976i −0.0333822 0.0578197i 0.848852 0.528631i \(-0.177295\pi\)
−0.882234 + 0.470811i \(0.843961\pi\)
\(522\) −8.16814 1.44026i −0.357510 0.0630386i
\(523\) −13.2229 2.33156i −0.578198 0.101952i −0.123101 0.992394i \(-0.539284\pi\)
−0.455096 + 0.890442i \(0.650395\pi\)
\(524\) −3.75831 6.50958i −0.164183 0.284372i
\(525\) 0.423692 + 0.473591i 0.0184915 + 0.0206692i
\(526\) 29.8957 + 25.0855i 1.30351 + 1.09378i
\(527\) −0.480599 + 1.32043i −0.0209352 + 0.0575190i
\(528\) 0.780548 + 2.14454i 0.0339690 + 0.0933291i
\(529\) 16.7730 14.0742i 0.729260 0.611922i
\(530\) 21.7024 + 21.0249i 0.942693 + 0.913262i
\(531\) 30.0114 1.30238
\(532\) 3.02231 + 4.54188i 0.131034 + 0.196915i
\(533\) 32.1063i 1.39068i
\(534\) −0.526765 2.98744i −0.0227954 0.129279i
\(535\) −13.4755 3.38269i −0.582598 0.146247i
\(536\) 1.14958 0.418412i 0.0496541 0.0180726i
\(537\) −0.495389 + 1.36107i −0.0213776 + 0.0587345i
\(538\) 14.3237 17.0703i 0.617537 0.735952i
\(539\) −9.29130 + 16.0930i −0.400205 + 0.693175i
\(540\) −1.88912 + 4.22486i −0.0812946 + 0.181809i
\(541\) 2.81801 15.9817i 0.121156 0.687109i −0.862361 0.506294i \(-0.831015\pi\)
0.983517 0.180815i \(-0.0578737\pi\)
\(542\) −46.1502 8.13752i −1.98232 0.349537i
\(543\) −0.174005 + 0.100462i −0.00746726 + 0.00431123i
\(544\) −20.2227 + 35.0268i −0.867043 + 1.50176i
\(545\) −35.6603 2.55084i −1.52752 0.109266i
\(546\) −1.11676 0.406468i −0.0477930 0.0173952i
\(547\) −3.39107 9.31688i −0.144992 0.398361i 0.845845 0.533429i \(-0.179097\pi\)
−0.990836 + 0.135068i \(0.956875\pi\)
\(548\) −3.10364 3.69878i −0.132581 0.158004i
\(549\) −3.84676 21.8160i −0.164176 0.931086i
\(550\) −26.4725 8.69501i −1.12879 0.370757i
\(551\) 5.17496 3.44358i 0.220461 0.146702i
\(552\) 0.0586120i 0.00249469i
\(553\) −9.89954 + 1.74556i −0.420971 + 0.0742286i
\(554\) −7.05270 + 5.91792i −0.299641 + 0.251428i
\(555\) −0.142042 + 0.209862i −0.00602934 + 0.00890815i
\(556\) −15.5836 5.67198i −0.660894 0.240546i
\(557\) −14.7090 + 17.5295i −0.623240 + 0.742748i −0.981624 0.190826i \(-0.938883\pi\)
0.358384 + 0.933574i \(0.383328\pi\)
\(558\) 1.36534 + 0.788279i 0.0577994 + 0.0333705i
\(559\) −13.4167 23.2385i −0.567467 0.982882i
\(560\) 5.82849 2.83123i 0.246299 0.119641i
\(561\) 0.479995 2.72219i 0.0202654 0.114931i
\(562\) −38.1508 + 22.0264i −1.60930 + 0.929128i
\(563\) 10.8081 + 6.24004i 0.455505 + 0.262986i 0.710153 0.704048i \(-0.248626\pi\)
−0.254647 + 0.967034i \(0.581959\pi\)
\(564\) −2.09865 1.76097i −0.0883690 0.0741504i
\(565\) 4.83214 + 16.9538i 0.203290 + 0.713252i
\(566\) −20.0623 + 7.30209i −0.843283 + 0.306930i
\(567\) −3.77943 4.50414i −0.158721 0.189156i
\(568\) −2.22543 + 0.392403i −0.0933768 + 0.0164649i
\(569\) −1.90233 −0.0797500 −0.0398750 0.999205i \(-0.512696\pi\)
−0.0398750 + 0.999205i \(0.512696\pi\)
\(570\) −1.20101 3.38226i −0.0503049 0.141667i
\(571\) −12.2153 −0.511193 −0.255596 0.966784i \(-0.582272\pi\)
−0.255596 + 0.966784i \(0.582272\pi\)
\(572\) 24.6500 4.34646i 1.03067 0.181734i
\(573\) 0.649489 + 0.774030i 0.0271328 + 0.0323356i
\(574\) 8.40707 3.05992i 0.350904 0.127719i
\(575\) −4.13031 3.24825i −0.172246 0.135461i
\(576\) 15.3210 + 12.8558i 0.638375 + 0.535660i
\(577\) −21.9021 12.6452i −0.911796 0.526425i −0.0307872 0.999526i \(-0.509801\pi\)
−0.881008 + 0.473100i \(0.843135\pi\)
\(578\) 16.7740 9.68448i 0.697707 0.402821i
\(579\) −0.504245 + 2.85971i −0.0209557 + 0.118846i
\(580\) 2.57552 + 5.30207i 0.106943 + 0.220157i
\(581\) −4.80092 8.31544i −0.199176 0.344982i
\(582\) −1.82684 1.05473i −0.0757249 0.0437198i
\(583\) −12.5778 + 14.9896i −0.520917 + 0.620805i
\(584\) −4.50283 1.63890i −0.186328 0.0678180i
\(585\) −26.1693 17.7123i −1.08197 0.732313i
\(586\) −18.7418 + 15.7262i −0.774216 + 0.649644i
\(587\) −6.22574 + 1.09777i −0.256964 + 0.0453097i −0.300646 0.953736i \(-0.597202\pi\)
0.0436821 + 0.999045i \(0.486091\pi\)
\(588\) 2.26984i 0.0936067i
\(589\) −1.14821 + 0.278652i −0.0473112 + 0.0114817i
\(590\) −26.0430 35.9658i −1.07217 1.48069i
\(591\) −0.692087 3.92502i −0.0284687 0.161454i
\(592\) 1.66100 + 1.97950i 0.0682666 + 0.0813569i
\(593\) −0.199642 0.548512i −0.00819832 0.0225247i 0.935526 0.353258i \(-0.114926\pi\)
−0.943724 + 0.330733i \(0.892704\pi\)
\(594\) −5.86320 2.13403i −0.240570 0.0875603i
\(595\) −7.82832 0.559972i −0.320930 0.0229566i
\(596\) 1.59721 2.76645i 0.0654242 0.113318i
\(597\) −1.23240 + 0.711526i −0.0504387 + 0.0291208i
\(598\) 9.67784 + 1.70646i 0.395756 + 0.0697825i
\(599\) −7.38388 + 41.8761i −0.301697 + 1.71101i 0.336961 + 0.941519i \(0.390601\pi\)
−0.638658 + 0.769491i \(0.720510\pi\)
\(600\) −0.272952 + 0.0571072i −0.0111432 + 0.00233139i
\(601\) −8.13809 + 14.0956i −0.331960 + 0.574971i −0.982896 0.184161i \(-0.941043\pi\)
0.650936 + 0.759132i \(0.274377\pi\)
\(602\) −4.80632 + 5.72795i −0.195891 + 0.233454i
\(603\) −4.17501 + 11.4708i −0.170020 + 0.467125i
\(604\) 19.2360 7.00132i 0.782701 0.284880i
\(605\) −1.59540 + 6.35557i −0.0648624 + 0.258391i
\(606\) −0.129315 0.733384i −0.00525308 0.0297917i
\(607\) 6.86749i 0.278743i 0.990240 + 0.139371i \(0.0445082\pi\)
−0.990240 + 0.139371i \(0.955492\pi\)
\(608\) −33.9398 + 2.15972i −1.37644 + 0.0875881i
\(609\) 0.181238 0.00734412
\(610\) −22.8063 + 23.5413i −0.923402 + 0.953160i
\(611\) 28.8296 24.1909i 1.16632 0.978658i
\(612\) −9.71698 26.6972i −0.392786 1.07917i
\(613\) 1.99841 5.49059i 0.0807150 0.221763i −0.892770 0.450512i \(-0.851241\pi\)
0.973485 + 0.228749i \(0.0734636\pi\)
\(614\) 6.27958 + 5.26920i 0.253423 + 0.212647i
\(615\) −2.81212 + 0.291026i −0.113395 + 0.0117353i
\(616\) 0.285734 + 0.494906i 0.0115126 + 0.0199403i
\(617\) 37.9767 + 6.69631i 1.52888 + 0.269583i 0.873917 0.486075i \(-0.161572\pi\)
0.654966 + 0.755658i \(0.272683\pi\)
\(618\) −6.61315 1.16608i −0.266020 0.0469065i
\(619\) 5.46007 + 9.45712i 0.219459 + 0.380114i 0.954643 0.297754i \(-0.0962375\pi\)
−0.735184 + 0.677868i \(0.762904\pi\)
\(620\) −0.115338 1.11448i −0.00463207 0.0447586i
\(621\) −0.901359 0.756330i −0.0361703 0.0303505i
\(622\) 8.11256 22.2891i 0.325284 0.893711i
\(623\) −1.90765 5.24123i −0.0764285 0.209986i
\(624\) 2.93352 2.46152i 0.117435 0.0985396i
\(625\) 11.1026 22.3994i 0.444103 0.895976i
\(626\) −18.7910 −0.751039
\(627\) 2.12919 0.932038i 0.0850318 0.0372220i
\(628\) 3.63169i 0.144920i
\(629\) −0.543488 3.08228i −0.0216703 0.122898i
\(630\) −2.14389 + 8.54056i −0.0854147 + 0.340264i
\(631\) −7.62467 + 2.77515i −0.303533 + 0.110477i −0.489297 0.872117i \(-0.662746\pi\)
0.185763 + 0.982595i \(0.440524\pi\)
\(632\) 1.50876 4.14528i 0.0600152 0.164890i
\(633\) 1.60462 1.91231i 0.0637780 0.0760077i
\(634\) 10.9557 18.9758i 0.435106 0.753626i
\(635\) −14.3980 + 32.2000i −0.571367 + 1.27782i
\(636\) 0.415045 2.35383i 0.0164576 0.0933356i
\(637\) 30.7076 + 5.41457i 1.21668 + 0.214533i
\(638\) −6.88234 + 3.97352i −0.272474 + 0.157313i
\(639\) 11.2742 19.5275i 0.446001 0.772496i
\(640\) −0.378141 + 5.28635i −0.0149473 + 0.208961i
\(641\) −13.0690 4.75673i −0.516195 0.187880i 0.0707688 0.997493i \(-0.477455\pi\)
−0.586964 + 0.809613i \(0.699677\pi\)
\(642\) 0.782552 + 2.15004i 0.0308849 + 0.0848555i
\(643\) −24.4957 29.1929i −0.966017 1.15125i −0.988456 0.151506i \(-0.951588\pi\)
0.0224393 0.999748i \(-0.492857\pi\)
\(644\) −0.228402 1.29533i −0.00900029 0.0510432i
\(645\) 1.91379 1.38579i 0.0753554 0.0545653i
\(646\) 39.7198 + 19.6816i 1.56276 + 0.774364i
\(647\) 28.6072i 1.12466i 0.826912 + 0.562332i \(0.190096\pi\)
−0.826912 + 0.562332i \(0.809904\pi\)
\(648\) 2.54105 0.448056i 0.0998221 0.0176013i
\(649\) 22.0279 18.4836i 0.864671 0.725545i
\(650\) 1.48249 + 46.7317i 0.0581482 + 1.83297i
\(651\) −0.0323722 0.0117825i −0.00126877 0.000461793i
\(652\) 23.9202 28.5070i 0.936787 1.11642i
\(653\) 10.2937 + 5.94304i 0.402822 + 0.232569i 0.687701 0.725994i \(-0.258620\pi\)
−0.284879 + 0.958563i \(0.591953\pi\)
\(654\) 2.94381 + 5.09883i 0.115112 + 0.199380i
\(655\) 3.97278 + 8.17854i 0.155230 + 0.319562i
\(656\) −5.00599 + 28.3904i −0.195451 + 1.10846i
\(657\) 41.4080 23.9069i 1.61548 0.932699i
\(658\) −9.08204 5.24352i −0.354055 0.204414i
\(659\) 28.2769 + 23.7271i 1.10151 + 0.924278i 0.997526 0.0703009i \(-0.0223959\pi\)
0.103986 + 0.994579i \(0.466840\pi\)
\(660\) 0.604135 + 2.11964i 0.0235159 + 0.0825068i
\(661\) 8.49572 3.09219i 0.330445 0.120272i −0.171469 0.985189i \(-0.554851\pi\)
0.501914 + 0.864917i \(0.332629\pi\)
\(662\) 27.3483 + 32.5925i 1.06292 + 1.26674i
\(663\) −4.56779 + 0.805424i −0.177398 + 0.0312801i
\(664\) 4.21365 0.163521
\(665\) −3.25458 5.74087i −0.126207 0.222621i
\(666\) −3.51155 −0.136070
\(667\) −1.47588 + 0.260238i −0.0571465 + 0.0100765i
\(668\) 21.2176 + 25.2862i 0.820935 + 0.978353i
\(669\) 3.50648 1.27626i 0.135568 0.0493429i
\(670\) 17.3696 4.95064i 0.671045 0.191260i
\(671\) −16.2597 13.6435i −0.627698 0.526701i
\(672\) −0.858729 0.495787i −0.0331262 0.0191254i
\(673\) 34.4994 19.9182i 1.32985 0.767791i 0.344577 0.938758i \(-0.388022\pi\)
0.985277 + 0.170967i \(0.0546891\pi\)
\(674\) 0.0180037 0.102104i 0.000693478 0.00393291i
\(675\) 2.64396 4.93448i 0.101766 0.189928i
\(676\) −8.98462 15.5618i −0.345562 0.598532i
\(677\) −15.6221 9.01941i −0.600405 0.346644i 0.168796 0.985651i \(-0.446012\pi\)
−0.769201 + 0.639007i \(0.779345\pi\)
\(678\) 1.86613 2.22396i 0.0716682 0.0854108i
\(679\) −3.64465 1.32655i −0.139869 0.0509081i
\(680\) 1.93050 2.85224i 0.0740311 0.109379i
\(681\) −3.92585 + 3.29418i −0.150439 + 0.126233i
\(682\) 1.48763 0.262309i 0.0569643 0.0100443i
\(683\) 15.4271i 0.590301i 0.955451 + 0.295151i \(0.0953698\pi\)
−0.955451 + 0.295151i \(0.904630\pi\)
\(684\) 14.1624 19.2382i 0.541512 0.735591i
\(685\) 3.42549 + 4.73065i 0.130881 + 0.180749i
\(686\) −3.12334 17.7134i −0.119250 0.676299i
\(687\) 1.76677 + 2.10555i 0.0674063 + 0.0803317i
\(688\) −8.24059 22.6408i −0.314169 0.863173i
\(689\) 30.8538 + 11.2299i 1.17544 + 0.427824i
\(690\) −0.0617410 + 0.863129i −0.00235044 + 0.0328588i
\(691\) −1.51912 + 2.63119i −0.0577901 + 0.100095i −0.893473 0.449117i \(-0.851739\pi\)
0.835683 + 0.549212i \(0.185072\pi\)
\(692\) 4.35789 2.51603i 0.165662 0.0956452i
\(693\) −5.61562 0.990185i −0.213320 0.0376140i
\(694\) 8.64803 49.0454i 0.328275 1.86174i
\(695\) 18.3130 + 8.18853i 0.694651 + 0.310609i
\(696\) −0.0397670 + 0.0688784i −0.00150736 + 0.00261083i
\(697\) 22.4443 26.7481i 0.850138 1.01315i
\(698\) −10.4804 + 28.7947i −0.396689 + 1.08990i
\(699\) 1.16933 0.425603i 0.0442283 0.0160978i
\(700\) 5.80972 2.32572i 0.219587 0.0879041i
\(701\) −7.95179 45.0968i −0.300335 1.70328i −0.644690 0.764444i \(-0.723013\pi\)
0.344355 0.938840i \(-0.388098\pi\)
\(702\) 10.4697i 0.395155i
\(703\) 1.90451 1.81624i 0.0718298 0.0685008i
\(704\) 19.1631 0.722238
\(705\) 2.38015 + 2.30584i 0.0896416 + 0.0868430i
\(706\) −18.7419 + 15.7263i −0.705360 + 0.591867i
\(707\) −0.468309 1.28667i −0.0176126 0.0483901i
\(708\) −1.20132 + 3.30061i −0.0451485 + 0.124045i
\(709\) −16.8950 14.1766i −0.634506 0.532414i 0.267819 0.963469i \(-0.413697\pi\)
−0.902326 + 0.431055i \(0.858141\pi\)
\(710\) −33.1853 + 3.43435i −1.24542 + 0.128889i
\(711\) 22.0086 + 38.1200i 0.825386 + 1.42961i
\(712\) 2.41048 + 0.425032i 0.0903365 + 0.0159288i
\(713\) 0.280537 + 0.0494663i 0.0105062 + 0.00185253i
\(714\) 0.646239 + 1.11932i 0.0241849 + 0.0418894i
\(715\) −30.1167 + 3.11678i −1.12630 + 0.116561i
\(716\) 10.9268 + 9.16871i 0.408355 + 0.342651i
\(717\) 0.814003 2.23645i 0.0303995 0.0835219i
\(718\) 22.5732 + 62.0195i 0.842426 + 2.31455i
\(719\) 5.43476 4.56031i 0.202682 0.170071i −0.535797 0.844347i \(-0.679989\pi\)
0.738479 + 0.674276i \(0.235544\pi\)
\(720\) −20.3789 19.7426i −0.759475 0.735764i
\(721\) −12.3469 −0.459822
\(722\) 4.72459 + 36.9730i 0.175831 + 1.37599i
\(723\) 2.64928i 0.0985277i
\(724\) 0.343596 + 1.94863i 0.0127696 + 0.0724202i
\(725\) −2.64990 6.61953i −0.0984149 0.245843i
\(726\) 1.01404 0.369081i 0.0376346 0.0136979i
\(727\) 9.64932 26.5113i 0.357873 0.983249i −0.621893 0.783103i \(-0.713636\pi\)
0.979766 0.200147i \(-0.0641418\pi\)
\(728\) 0.616378 0.734570i 0.0228445 0.0272250i
\(729\) −12.5580 + 21.7510i −0.465110 + 0.805594i
\(730\) −64.5829 28.8778i −2.39032 1.06882i
\(731\) −5.06752 + 28.7393i −0.187429 + 1.06296i
\(732\) 2.55328 + 0.450212i 0.0943719 + 0.0166403i
\(733\) −0.897082 + 0.517931i −0.0331345 + 0.0191302i −0.516476 0.856302i \(-0.672756\pi\)
0.483341 + 0.875432i \(0.339423\pi\)
\(734\) 25.1205 43.5100i 0.927214 1.60598i
\(735\) −0.195903 + 2.73869i −0.00722598 + 0.101018i
\(736\) 7.70484 + 2.80433i 0.284004 + 0.103369i
\(737\) 4.00029 + 10.9907i 0.147353 + 0.404848i
\(738\) −25.1817 30.0103i −0.926950 1.10470i
\(739\) −3.37137 19.1200i −0.124018 0.703340i −0.981886 0.189471i \(-0.939323\pi\)
0.857868 0.513869i \(-0.171788\pi\)
\(740\) 1.46365 + 2.02132i 0.0538049 + 0.0743053i
\(741\) −2.69158 2.82239i −0.0988777 0.103683i
\(742\) 9.14938i 0.335884i
\(743\) −12.5098 + 2.20582i −0.458941 + 0.0809237i −0.398339 0.917238i \(-0.630413\pi\)
−0.0606022 + 0.998162i \(0.519302\pi\)
\(744\) 0.0115810 0.00971758i 0.000424579 0.000356264i
\(745\) −2.16588 + 3.20002i −0.0793518 + 0.117240i
\(746\) −40.1156 14.6009i −1.46874 0.534576i
\(747\) −27.0259 + 32.2082i −0.988826 + 1.17844i
\(748\) −23.5746 13.6108i −0.861972 0.497660i
\(749\) 2.10345 + 3.64328i 0.0768584 + 0.133123i
\(750\) −4.07968 + 0.553446i −0.148969 + 0.0202090i
\(751\) −0.801897 + 4.54778i −0.0292616 + 0.165951i −0.995937 0.0900552i \(-0.971296\pi\)
0.966675 + 0.256006i \(0.0824068\pi\)
\(752\) 29.2647 16.8960i 1.06717 0.616134i
\(753\) −1.13369 0.654534i −0.0413138 0.0238525i
\(754\) 10.2152 + 8.57157i 0.372016 + 0.312158i
\(755\) −23.8135 + 6.78728i −0.866663 + 0.247014i
\(756\) 1.31681 0.479281i 0.0478920 0.0174313i
\(757\) −4.37741 5.21680i −0.159100 0.189608i 0.680606 0.732650i \(-0.261717\pi\)
−0.839705 + 0.543042i \(0.817272\pi\)
\(758\) 12.8095 2.25866i 0.465262 0.0820382i
\(759\) −0.560370 −0.0203401
\(760\) 2.89591 + 0.0227681i 0.105046 + 0.000825885i
\(761\) 24.4864 0.887632 0.443816 0.896118i \(-0.353624\pi\)
0.443816 + 0.896118i \(0.353624\pi\)
\(762\) 5.72048 1.00867i 0.207231 0.0365404i
\(763\) 6.95837 + 8.29266i 0.251910 + 0.300215i
\(764\) 9.35053 3.40332i 0.338290 0.123128i
\(765\) 9.41992 + 33.0503i 0.340578 + 1.19493i
\(766\) −40.6086 34.0746i −1.46725 1.23117i
\(767\) −41.7867 24.1255i −1.50883 0.871123i
\(768\) 2.94910 1.70266i 0.106417 0.0614396i
\(769\) −0.519478 + 2.94611i −0.0187329 + 0.106239i −0.992741 0.120276i \(-0.961622\pi\)
0.974008 + 0.226515i \(0.0727333\pi\)
\(770\) 3.68643 + 7.58904i 0.132850 + 0.273490i
\(771\) 1.48109 + 2.56533i 0.0533402 + 0.0923880i
\(772\) 24.7656 + 14.2984i 0.891332 + 0.514611i
\(773\) 12.7042 15.1403i 0.456938 0.544557i −0.487554 0.873093i \(-0.662111\pi\)
0.944491 + 0.328536i \(0.106555\pi\)
\(774\) 30.7673 + 11.1984i 1.10591 + 0.402518i
\(775\) 0.0429739 + 1.35464i 0.00154367 + 0.0486600i
\(776\) 1.30385 1.09406i 0.0468056 0.0392745i
\(777\) 0.0755661 0.0133243i 0.00271092 0.000478008i
\(778\) 50.9857i 1.82792i
\(779\) 29.1793 + 3.25183i 1.04546 + 0.116509i
\(780\) 2.99550 2.16906i 0.107256 0.0776649i
\(781\) −3.75163 21.2765i −0.134244 0.761335i
\(782\) −6.86978 8.18709i −0.245663 0.292770i
\(783\) −0.546087 1.50036i −0.0195155 0.0536185i
\(784\) 26.3093 + 9.57581i 0.939618 + 0.341993i
\(785\) −0.313440 + 4.38183i −0.0111871 + 0.156394i
\(786\) 0.748677 1.29675i 0.0267044 0.0462534i
\(787\) 20.3920 11.7733i 0.726895 0.419673i −0.0903901 0.995906i \(-0.528811\pi\)
0.817285 + 0.576233i \(0.195478\pi\)
\(788\) −38.6535 6.81565i −1.37697 0.242798i
\(789\) −0.648425 + 3.67740i −0.0230846 + 0.130919i
\(790\) 26.5847 59.4546i 0.945843 2.11530i
\(791\) 2.66897 4.62280i 0.0948977 0.164368i
\(792\) 1.60849 1.91692i 0.0571551 0.0681148i
\(793\) −12.1814 + 33.4681i −0.432574 + 1.18849i
\(794\) −39.3532 + 14.3234i −1.39659 + 0.508318i
\(795\) −0.703926 + 2.80421i −0.0249657 + 0.0994551i
\(796\) 2.43353 + 13.8013i 0.0862543 + 0.489173i
\(797\) 5.96976i 0.211460i 0.994395 + 0.105730i \(0.0337179\pi\)
−0.994395 + 0.105730i \(0.966282\pi\)
\(798\) −0.482522 + 0.973784i −0.0170811 + 0.0344716i
\(799\) −40.9291 −1.44797
\(800\) −5.55254 + 38.6132i −0.196312 + 1.36518i
\(801\) −18.7094 + 15.6991i −0.661064 + 0.554699i
\(802\) 17.4861 + 48.0427i 0.617456 + 1.69645i
\(803\) 15.6689 43.0500i 0.552945 1.51920i
\(804\) −1.09442 0.918325i −0.0385971 0.0323868i
\(805\) 0.163783 + 1.58260i 0.00577260 + 0.0557793i
\(806\) −1.26736 2.19514i −0.0446409 0.0773204i
\(807\) 2.09978 + 0.370247i 0.0739157 + 0.0130333i
\(808\) 0.591747 + 0.104341i 0.0208176 + 0.00367070i
\(809\) −12.9533 22.4358i −0.455414 0.788801i 0.543297 0.839540i \(-0.317176\pi\)
−0.998712 + 0.0507393i \(0.983842\pi\)
\(810\) 37.8919 3.92143i 1.33139 0.137785i
\(811\) 21.1791 + 17.7713i 0.743698 + 0.624036i 0.933828 0.357723i \(-0.116447\pi\)
−0.190130 + 0.981759i \(0.560891\pi\)
\(812\) 0.610445 1.67718i 0.0214224 0.0588576i
\(813\) −1.53359 4.21350i −0.0537853 0.147774i
\(814\) −2.57743 + 2.16272i −0.0903388 + 0.0758032i
\(815\) −31.3214 + 32.3308i −1.09714 + 1.13250i
\(816\) −4.16470 −0.145794
\(817\) −22.4788 + 9.83993i −0.786434 + 0.344256i
\(818\) 45.8018i 1.60142i
\(819\) 1.66151 + 9.42291i 0.0580580 + 0.329263i
\(820\) −6.77861 + 27.0037i −0.236719 + 0.943011i
\(821\) 9.72970 3.54132i 0.339569 0.123593i −0.166607 0.986023i \(-0.553281\pi\)
0.506175 + 0.862431i \(0.331059\pi\)
\(822\) 0.328971 0.903841i 0.0114742 0.0315251i
\(823\) 27.2218 32.4417i 0.948893 1.13085i −0.0423901 0.999101i \(-0.513497\pi\)
0.991284 0.131746i \(-0.0420583\pi\)
\(824\) 2.70914 4.69237i 0.0943775 0.163467i
\(825\) −0.545983 2.60960i −0.0190087 0.0908546i
\(826\) −2.33478 + 13.2412i −0.0812374 + 0.460720i
\(827\) −22.2391 3.92136i −0.773330 0.136359i −0.226962 0.973904i \(-0.572879\pi\)
−0.546369 + 0.837545i \(0.683990\pi\)
\(828\) −4.98791 + 2.87977i −0.173342 + 0.100079i
\(829\) −6.32446 + 10.9543i −0.219657 + 0.380458i −0.954703 0.297560i \(-0.903827\pi\)
0.735046 + 0.678017i \(0.237161\pi\)
\(830\) 62.0508 + 4.43860i 2.15381 + 0.154066i
\(831\) −0.827794 0.301292i −0.0287159 0.0104517i
\(832\) −10.9978 30.2162i −0.381280 1.04756i
\(833\) −21.7977 25.9774i −0.755244 0.900065i
\(834\) −0.573661 3.25339i −0.0198642 0.112656i
\(835\) −23.4179 32.3404i −0.810409 1.11919i
\(836\) −1.45358 22.8430i −0.0502732 0.790041i
\(837\) 0.303492i 0.0104902i
\(838\) −42.4938 + 7.49280i −1.46792 + 0.258834i
\(839\) −35.3478 + 29.6603i −1.22034 + 1.02399i −0.221535 + 0.975152i \(0.571107\pi\)
−0.998807 + 0.0488360i \(0.984449\pi\)
\(840\) 0.0699265 + 0.0473287i 0.00241269 + 0.00163299i
\(841\) 25.3401 + 9.22305i 0.873797 + 0.318036i
\(842\) 4.70498 5.60717i 0.162144 0.193236i
\(843\) −3.65039 2.10755i −0.125726 0.0725880i
\(844\) −12.2920 21.2903i −0.423108 0.732844i
\(845\) 9.49735 + 19.5516i 0.326719 + 0.672596i
\(846\) −7.97410 + 45.2234i −0.274155 + 1.55481i
\(847\) 1.71831 0.992066i 0.0590418 0.0340878i
\(848\) 25.5319 + 14.7409i 0.876770 + 0.506203i
\(849\) −1.56489 1.31310i −0.0537070 0.0450655i
\(850\) 31.4333 39.9690i 1.07815 1.37092i
\(851\) −0.596230 + 0.217010i −0.0204385 + 0.00743900i
\(852\) 1.69631 + 2.02159i 0.0581147 + 0.0692585i
\(853\) 36.8941 6.50543i 1.26323 0.222742i 0.498386 0.866955i \(-0.333926\pi\)
0.764846 + 0.644214i \(0.222815\pi\)
\(854\) 9.92463 0.339614
\(855\) −18.7481 + 21.9896i −0.641170 + 0.752030i
\(856\) −1.84615 −0.0631000
\(857\) −33.3201 + 5.87524i −1.13819 + 0.200694i −0.710816 0.703378i \(-0.751674\pi\)
−0.427379 + 0.904073i \(0.640563\pi\)
\(858\) 3.20505 + 3.81962i 0.109418 + 0.130400i
\(859\) −19.9349 + 7.25572i −0.680171 + 0.247562i −0.658921 0.752212i \(-0.728987\pi\)
−0.0212498 + 0.999774i \(0.506765\pi\)
\(860\) −6.37811 22.3779i −0.217492 0.763081i
\(861\) 0.655764 + 0.550251i 0.0223484 + 0.0187525i
\(862\) −42.3277 24.4379i −1.44169 0.832358i
\(863\) 25.2353 14.5696i 0.859019 0.495955i −0.00466481 0.999989i \(-0.501485\pi\)
0.863684 + 0.504034i \(0.168152\pi\)
\(864\) −1.51690 + 8.60277i −0.0516060 + 0.292672i
\(865\) −5.47519 + 2.65961i −0.186162 + 0.0904296i
\(866\) −10.7625 18.6412i −0.365725 0.633454i
\(867\) 1.60499 + 0.926641i 0.0545083 + 0.0314704i
\(868\) −0.218072 + 0.259888i −0.00740185 + 0.00882119i
\(869\) 39.6316 + 14.4247i 1.34441 + 0.489325i
\(870\) −0.658169 + 0.972423i −0.0223140 + 0.0329682i
\(871\) 15.0342 12.6152i 0.509416 0.427450i
\(872\) −4.67838 + 0.824925i −0.158430 + 0.0279355i
\(873\) 16.9836i 0.574806i
\(874\) 2.53110 8.62273i 0.0856157 0.291668i
\(875\) −7.21047 + 2.30470i −0.243758 + 0.0779129i
\(876\) 0.971733 + 5.51097i 0.0328318 + 0.186198i
\(877\) 4.13842 + 4.93198i 0.139745 + 0.166541i 0.831377 0.555708i \(-0.187553\pi\)
−0.691633 + 0.722249i \(0.743108\pi\)
\(878\) 5.71644 + 15.7058i 0.192920 + 0.530045i
\(879\) −2.19977 0.800652i −0.0741965 0.0270053i
\(880\) −27.1170 1.93972i −0.914114 0.0653881i
\(881\) −7.19996 + 12.4707i −0.242573 + 0.420148i −0.961446 0.274993i \(-0.911325\pi\)
0.718874 + 0.695141i \(0.244658\pi\)
\(882\) −32.9497 + 19.0235i −1.10948 + 0.640556i
\(883\) 25.4096 + 4.48039i 0.855100 + 0.150777i 0.583980 0.811768i \(-0.301495\pi\)
0.271121 + 0.962545i \(0.412606\pi\)
\(884\) −7.93179 + 44.9834i −0.266775 + 1.51296i
\(885\) 1.73433 3.87868i 0.0582988 0.130381i
\(886\) −9.23713 + 15.9992i −0.310327 + 0.537503i
\(887\) 16.6762 19.8739i 0.559931 0.667300i −0.409601 0.912265i \(-0.634332\pi\)
0.969532 + 0.244965i \(0.0787764\pi\)
\(888\) −0.0115168 + 0.0316421i −0.000386478 + 0.00106184i
\(889\) 10.0362 3.65286i 0.336602 0.122513i
\(890\) 35.0493 + 8.79825i 1.17486 + 0.294918i
\(891\) 4.28371 + 24.2942i 0.143510 + 0.813885i
\(892\) 36.7479i 1.23041i
\(893\) −19.0656 28.6515i −0.638005 0.958785i
\(894\) 0.636346 0.0212826
\(895\) −12.3925 12.0056i −0.414236 0.401303i
\(896\) 1.22932 1.03152i 0.0410687 0.0344607i
\(897\) 0.321598 + 0.883584i 0.0107379 + 0.0295020i
\(898\) 6.52677 17.9321i 0.217801 0.598404i
\(899\) 0.296114 + 0.248469i 0.00987595 + 0.00828690i
\(900\) −18.2707 20.4225i −0.609024 0.680749i
\(901\) −17.8542 30.9245i −0.594811 1.03024i
\(902\) −36.9660 6.51810i −1.23083 0.217029i
\(903\) −0.704583 0.124237i −0.0234470 0.00413435i
\(904\) 1.17125 + 2.02866i 0.0389551 + 0.0674722i
\(905\) −0.246387 2.38078i −0.00819018 0.0791398i
\(906\) 3.12381 + 2.62118i 0.103781 + 0.0870830i
\(907\) −10.2352 + 28.1209i −0.339853 + 0.933740i 0.645582 + 0.763691i \(0.276615\pi\)
−0.985436 + 0.170049i \(0.945607\pi\)
\(908\) 17.2615 + 47.4255i 0.572843 + 1.57387i
\(909\) −4.59296 + 3.85395i −0.152339 + 0.127828i
\(910\) 9.85065 10.1681i 0.326546 0.337069i
\(911\) 3.36120 0.111362 0.0556808 0.998449i \(-0.482267\pi\)
0.0556808 + 0.998449i \(0.482267\pi\)
\(912\) −1.94000 2.91540i −0.0642398 0.0965386i
\(913\) 40.2853i 1.33325i
\(914\) −3.56621 20.2250i −0.117960 0.668982i
\(915\) −3.04182 0.763571i −0.100559 0.0252429i
\(916\) 25.4357 9.25784i 0.840419 0.305888i
\(917\) 0.941622 2.58708i 0.0310951 0.0854330i
\(918\) 7.31900 8.72245i 0.241563 0.287884i
\(919\) 3.46233 5.99694i 0.114212 0.197821i −0.803253 0.595639i \(-0.796899\pi\)
0.917464 + 0.397818i \(0.130232\pi\)
\(920\) −0.637396 0.285007i −0.0210143 0.00939642i
\(921\) −0.136202 + 0.772437i −0.00448799 + 0.0254527i
\(922\) 43.8052 + 7.72404i 1.44265 + 0.254378i
\(923\) −31.3955 + 18.1262i −1.03340 + 0.596632i
\(924\) 0.333687 0.577962i 0.0109775 0.0190136i
\(925\) −1.59152 2.56516i −0.0523289 0.0843419i
\(926\) 65.6965 + 23.9116i 2.15892 + 0.785783i
\(927\) 18.4913 + 50.8045i 0.607335 + 1.66864i
\(928\) 7.15173 + 8.52310i 0.234767 + 0.279785i
\(929\) −4.74769 26.9255i −0.155767 0.883396i −0.958082 0.286495i \(-0.907510\pi\)
0.802315 0.596901i \(-0.203601\pi\)
\(930\) 0.180779 0.130903i 0.00592798 0.00429248i
\(931\) 8.03112 27.3597i 0.263209 0.896679i
\(932\) 12.2546i 0.401413i
\(933\) 2.23508 0.394105i 0.0731732 0.0129024i
\(934\) −4.36053 + 3.65892i −0.142681 + 0.119724i
\(935\) 27.2693 + 18.4568i 0.891802 + 0.603602i
\(936\) −3.94570 1.43612i −0.128969 0.0469409i
\(937\) −23.8716 + 28.4491i −0.779851 + 0.929390i −0.998927 0.0463175i \(-0.985251\pi\)
0.219076 + 0.975708i \(0.429696\pi\)
\(938\) −4.73616 2.73443i −0.154641 0.0892822i
\(939\) −0.898989 1.55710i −0.0293374 0.0508139i
\(940\) 29.3552 14.2595i 0.957461 0.465094i
\(941\) 8.80177 49.9173i 0.286929 1.62726i −0.411382 0.911463i \(-0.634954\pi\)
0.698311 0.715794i \(-0.253935\pi\)
\(942\) 0.626529 0.361727i 0.0204134 0.0117857i
\(943\) −6.13023 3.53929i −0.199628 0.115255i
\(944\) −33.1887 27.8487i −1.08020 0.906396i
\(945\) −1.63017 + 0.464628i −0.0530295 + 0.0151144i
\(946\) 29.4797 10.7297i 0.958468 0.348854i
\(947\) −2.61402 3.11527i −0.0849442 0.101233i 0.721898 0.691999i \(-0.243270\pi\)
−0.806842 + 0.590767i \(0.798825\pi\)
\(948\) −5.07336 + 0.894571i −0.164775 + 0.0290543i
\(949\) −76.8732 −2.49541
\(950\) 42.6215 + 3.38579i 1.38282 + 0.109849i
\(951\) 2.09655 0.0679852
\(952\) −1.02702 + 0.181091i −0.0332859 + 0.00586921i
\(953\) −9.53460 11.3629i −0.308856 0.368080i 0.589180 0.808002i \(-0.299451\pi\)
−0.898036 + 0.439921i \(0.855006\pi\)
\(954\) −37.6475 + 13.7026i −1.21888 + 0.443637i
\(955\) −11.5757 + 3.29927i −0.374580 + 0.106762i
\(956\) −17.9546 15.0657i −0.580692 0.487258i
\(957\) −0.658523 0.380198i −0.0212870 0.0122901i
\(958\) 49.8656 28.7899i 1.61108 0.930160i
\(959\) 0.307098 1.74164i 0.00991671 0.0562405i
\(960\) 2.54688 1.23717i 0.0822002 0.0399294i
\(961\) 15.4633 + 26.7832i 0.498815 + 0.863973i
\(962\) 4.88934 + 2.82286i 0.157639 + 0.0910128i
\(963\) 11.8410 14.1115i 0.381571 0.454738i
\(964\) 24.5166 + 8.92330i 0.789626 + 0.287400i
\(965\) −28.6470 19.3893i −0.922178 0.624162i
\(966\) 0.200717 0.168422i 0.00645797 0.00541888i
\(967\) −55.8584 + 9.84935i −1.79629 + 0.316734i −0.969372 0.245595i \(-0.921017\pi\)
−0.826914 + 0.562329i \(0.809905\pi\)
\(968\) 0.870712i 0.0279858i
\(969\) 0.269358 + 4.23294i 0.00865301 + 0.135982i
\(970\) 20.3532 14.7379i 0.653501 0.473204i
\(971\) −2.18689 12.4025i −0.0701805 0.398014i −0.999581 0.0289410i \(-0.990786\pi\)
0.929401 0.369073i \(-0.120325\pi\)
\(972\) −5.92802 7.06474i −0.190141 0.226602i
\(973\) −2.07748 5.70783i −0.0666010 0.182985i
\(974\) −6.29879 2.29257i −0.201826 0.0734588i
\(975\) −3.80144 + 2.35856i −0.121744 + 0.0755343i
\(976\) −15.9899 + 27.6953i −0.511824 + 0.886505i
\(977\) −31.9540 + 18.4486i −1.02230 + 0.590224i −0.914769 0.403978i \(-0.867627\pi\)
−0.107529 + 0.994202i \(0.534294\pi\)
\(978\) 7.30047 + 1.28727i 0.233443 + 0.0411623i
\(979\) −4.06359 + 23.0458i −0.129873 + 0.736546i
\(980\) 24.6841 + 11.0374i 0.788506 + 0.352575i
\(981\) 23.7011 41.0515i 0.756718 1.31067i
\(982\) −31.7599 + 37.8500i −1.01350 + 1.20784i
\(983\) −3.26993 + 8.98405i −0.104295 + 0.286547i −0.980853 0.194748i \(-0.937611\pi\)
0.876559 + 0.481295i \(0.159833\pi\)
\(984\) −0.353007 + 0.128484i −0.0112535 + 0.00409592i
\(985\) 46.0493 + 11.5595i 1.46725 + 0.368317i
\(986\) −2.51832 14.2821i −0.0801997 0.454835i
\(987\) 1.00343i 0.0319396i
\(988\) −35.1843 + 15.4017i −1.11936 + 0.489992i
\(989\) 5.91606 0.188120
\(990\) 25.7061 26.5345i 0.816993 0.843321i
\(991\) −12.4584 + 10.4538i −0.395755 + 0.332077i −0.818850 0.574008i \(-0.805388\pi\)
0.423095 + 0.906085i \(0.360944\pi\)
\(992\) −0.723325 1.98732i −0.0229656 0.0630974i
\(993\) −1.39236 + 3.82546i −0.0441851 + 0.121397i
\(994\) 7.73855 + 6.49342i 0.245452 + 0.205959i
\(995\) −1.74505 16.8620i −0.0553218 0.534561i
\(996\) −2.46040 4.26153i −0.0779607 0.135032i
\(997\) 36.0838 + 6.36254i 1.14278 + 0.201504i 0.712823 0.701344i \(-0.247416\pi\)
0.429961 + 0.902848i \(0.358527\pi\)
\(998\) −67.1039 11.8322i −2.12414 0.374543i
\(999\) −0.337992 0.585420i −0.0106936 0.0185219i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 95.2.p.a.9.8 yes 48
3.2 odd 2 855.2.da.b.199.1 48
5.2 odd 4 475.2.l.f.351.8 48
5.3 odd 4 475.2.l.f.351.1 48
5.4 even 2 inner 95.2.p.a.9.1 48
15.14 odd 2 855.2.da.b.199.8 48
19.6 even 9 1805.2.b.k.1084.4 24
19.13 odd 18 1805.2.b.l.1084.21 24
19.17 even 9 inner 95.2.p.a.74.1 yes 48
57.17 odd 18 855.2.da.b.739.8 48
95.13 even 36 9025.2.a.ct.1.21 24
95.17 odd 36 475.2.l.f.226.8 48
95.32 even 36 9025.2.a.ct.1.4 24
95.44 even 18 1805.2.b.k.1084.21 24
95.63 odd 36 9025.2.a.cu.1.4 24
95.74 even 18 inner 95.2.p.a.74.8 yes 48
95.82 odd 36 9025.2.a.cu.1.21 24
95.89 odd 18 1805.2.b.l.1084.4 24
95.93 odd 36 475.2.l.f.226.1 48
285.74 odd 18 855.2.da.b.739.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.9.1 48 5.4 even 2 inner
95.2.p.a.9.8 yes 48 1.1 even 1 trivial
95.2.p.a.74.1 yes 48 19.17 even 9 inner
95.2.p.a.74.8 yes 48 95.74 even 18 inner
475.2.l.f.226.1 48 95.93 odd 36
475.2.l.f.226.8 48 95.17 odd 36
475.2.l.f.351.1 48 5.3 odd 4
475.2.l.f.351.8 48 5.2 odd 4
855.2.da.b.199.1 48 3.2 odd 2
855.2.da.b.199.8 48 15.14 odd 2
855.2.da.b.739.1 48 285.74 odd 18
855.2.da.b.739.8 48 57.17 odd 18
1805.2.b.k.1084.4 24 19.6 even 9
1805.2.b.k.1084.21 24 95.44 even 18
1805.2.b.l.1084.4 24 95.89 odd 18
1805.2.b.l.1084.21 24 19.13 odd 18
9025.2.a.ct.1.4 24 95.32 even 36
9025.2.a.ct.1.21 24 95.13 even 36
9025.2.a.cu.1.4 24 95.63 odd 36
9025.2.a.cu.1.21 24 95.82 odd 36