Properties

Label 105.2.j.a.92.11
Level $105$
Weight $2$
Character 105.92
Analytic conductor $0.838$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,2,Mod(8,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 92.11
Character \(\chi\) \(=\) 105.92
Dual form 105.2.j.a.8.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.54414 - 1.54414i) q^{2} +(-1.73204 + 0.00622252i) q^{3} -2.76875i q^{4} +(-0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.18705 - 1.18705i) q^{8} +(2.99992 - 0.0215553i) q^{9} +O(q^{10})\) \(q+(1.54414 - 1.54414i) q^{2} +(-1.73204 + 0.00622252i) q^{3} -2.76875i q^{4} +(-0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.18705 - 1.18705i) q^{8} +(2.99992 - 0.0215553i) q^{9} +(-3.82062 - 3.04083i) q^{10} +3.38507i q^{11} +(0.0172286 + 4.79558i) q^{12} +(-0.206632 + 0.206632i) q^{13} +2.18375 q^{14} +(0.451165 + 3.84662i) q^{15} +1.87154 q^{16} +(0.167409 - 0.167409i) q^{17} +(4.59902 - 4.66559i) q^{18} +5.31419i q^{19} +(-6.15151 + 0.699108i) q^{20} +(-1.22914 - 1.22034i) q^{21} +(5.22702 + 5.22702i) q^{22} +(-5.07773 - 5.07773i) q^{23} +(2.06341 + 2.04864i) q^{24} +(-4.87249 + 1.12199i) q^{25} +0.638138i q^{26} +(-5.19585 + 0.0560017i) q^{27} +(1.95780 - 1.95780i) q^{28} -2.84268 q^{29} +(6.63638 + 5.24306i) q^{30} +9.11776 q^{31} +(5.26402 - 5.26402i) q^{32} +(-0.0210636 - 5.86307i) q^{33} -0.517005i q^{34} +(1.39248 - 1.74957i) q^{35} +(-0.0596812 - 8.30602i) q^{36} +(-5.27013 - 5.27013i) q^{37} +(8.20586 + 8.20586i) q^{38} +(0.356609 - 0.359180i) q^{39} +(-2.33762 + 2.93708i) q^{40} +0.0314968i q^{41} +(-3.78233 + 0.0135884i) q^{42} +(-3.76875 + 3.76875i) q^{43} +9.37239 q^{44} +(-0.805371 - 6.65968i) q^{45} -15.6815 q^{46} +(-3.56639 + 3.56639i) q^{47} +(-3.24158 + 0.0116457i) q^{48} +1.00000i q^{49} +(-5.79130 + 9.25632i) q^{50} +(-0.288917 + 0.291000i) q^{51} +(0.572111 + 0.572111i) q^{52} +(3.55291 + 3.55291i) q^{53} +(-7.93665 + 8.10960i) q^{54} +(7.52082 - 0.854729i) q^{55} -1.67875i q^{56} +(-0.0330677 - 9.20439i) q^{57} +(-4.38949 + 4.38949i) q^{58} -10.3168 q^{59} +(10.6503 - 1.24916i) q^{60} -6.80634 q^{61} +(14.0791 - 14.0791i) q^{62} +(2.13651 + 2.10602i) q^{63} -12.5137i q^{64} +(0.511262 + 0.406913i) q^{65} +(-9.08593 - 9.02088i) q^{66} +(6.34806 + 6.34806i) q^{67} +(-0.463512 - 0.463512i) q^{68} +(8.82642 + 8.76323i) q^{69} +(-0.551396 - 4.85177i) q^{70} +3.95454i q^{71} +(-3.58665 - 3.53548i) q^{72} +(8.61099 - 8.61099i) q^{73} -16.2757 q^{74} +(8.43236 - 1.97365i) q^{75} +14.7136 q^{76} +(-2.39360 + 2.39360i) q^{77} +(-0.00397083 - 1.10528i) q^{78} -11.4449i q^{79} +(-0.472563 - 4.15812i) q^{80} +(8.99907 - 0.129328i) q^{81} +(0.0486356 + 0.0486356i) q^{82} +(3.88059 + 3.88059i) q^{83} +(-3.37880 + 3.40317i) q^{84} +(-0.414214 - 0.329672i) q^{85} +11.6390i q^{86} +(4.92363 - 0.0176886i) q^{87} +(4.01825 - 4.01825i) q^{88} +2.00190 q^{89} +(-11.5271 - 9.03989i) q^{90} -0.292222 q^{91} +(-14.0589 + 14.0589i) q^{92} +(-15.7923 + 0.0567354i) q^{93} +11.0140i q^{94} +(11.8069 - 1.34183i) q^{95} +(-9.08474 + 9.15025i) q^{96} +(2.26760 + 2.26760i) q^{97} +(1.54414 + 1.54414i) q^{98} +(0.0729661 + 10.1549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.54414 1.54414i 1.09187 1.09187i 0.0965442 0.995329i \(-0.469221\pi\)
0.995329 0.0965442i \(-0.0307789\pi\)
\(3\) −1.73204 + 0.00622252i −0.999994 + 0.00359257i
\(4\) 2.76875i 1.38437i
\(5\) −0.252500 2.22177i −0.112921 0.993604i
\(6\) −2.66491 + 2.68412i −1.08794 + 1.09579i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) −1.18705 1.18705i −0.419686 0.419686i
\(9\) 2.99992 0.0215553i 0.999974 0.00718510i
\(10\) −3.82062 3.04083i −1.20819 0.961593i
\(11\) 3.38507i 1.02064i 0.859986 + 0.510318i \(0.170472\pi\)
−0.859986 + 0.510318i \(0.829528\pi\)
\(12\) 0.0172286 + 4.79558i 0.00497346 + 1.38436i
\(13\) −0.206632 + 0.206632i −0.0573094 + 0.0573094i −0.735181 0.677871i \(-0.762903\pi\)
0.677871 + 0.735181i \(0.262903\pi\)
\(14\) 2.18375 0.583631
\(15\) 0.451165 + 3.84662i 0.116490 + 0.993192i
\(16\) 1.87154 0.467884
\(17\) 0.167409 0.167409i 0.0406026 0.0406026i −0.686514 0.727117i \(-0.740860\pi\)
0.727117 + 0.686514i \(0.240860\pi\)
\(18\) 4.59902 4.66559i 1.08400 1.09969i
\(19\) 5.31419i 1.21916i 0.792725 + 0.609579i \(0.208662\pi\)
−0.792725 + 0.609579i \(0.791338\pi\)
\(20\) −6.15151 + 0.699108i −1.37552 + 0.156325i
\(21\) −1.22914 1.22034i −0.268220 0.266299i
\(22\) 5.22702 + 5.22702i 1.11440 + 1.11440i
\(23\) −5.07773 5.07773i −1.05878 1.05878i −0.998161 0.0606179i \(-0.980693\pi\)
−0.0606179 0.998161i \(-0.519307\pi\)
\(24\) 2.06341 + 2.04864i 0.421191 + 0.418176i
\(25\) −4.87249 + 1.12199i −0.974497 + 0.224398i
\(26\) 0.638138i 0.125149i
\(27\) −5.19585 + 0.0560017i −0.999942 + 0.0107775i
\(28\) 1.95780 1.95780i 0.369989 0.369989i
\(29\) −2.84268 −0.527872 −0.263936 0.964540i \(-0.585021\pi\)
−0.263936 + 0.964540i \(0.585021\pi\)
\(30\) 6.63638 + 5.24306i 1.21163 + 0.957247i
\(31\) 9.11776 1.63760 0.818799 0.574081i \(-0.194640\pi\)
0.818799 + 0.574081i \(0.194640\pi\)
\(32\) 5.26402 5.26402i 0.930557 0.930557i
\(33\) −0.0210636 5.86307i −0.00366671 1.02063i
\(34\) 0.517005i 0.0886657i
\(35\) 1.39248 1.74957i 0.235372 0.295731i
\(36\) −0.0596812 8.30602i −0.00994686 1.38434i
\(37\) −5.27013 5.27013i −0.866404 0.866404i 0.125668 0.992072i \(-0.459893\pi\)
−0.992072 + 0.125668i \(0.959893\pi\)
\(38\) 8.20586 + 8.20586i 1.33117 + 1.33117i
\(39\) 0.356609 0.359180i 0.0571031 0.0575149i
\(40\) −2.33762 + 2.93708i −0.369611 + 0.464394i
\(41\) 0.0314968i 0.00491898i 0.999997 + 0.00245949i \(0.000782881\pi\)
−0.999997 + 0.00245949i \(0.999217\pi\)
\(42\) −3.78233 + 0.0135884i −0.583627 + 0.00209674i
\(43\) −3.76875 + 3.76875i −0.574728 + 0.574728i −0.933446 0.358718i \(-0.883214\pi\)
0.358718 + 0.933446i \(0.383214\pi\)
\(44\) 9.37239 1.41294
\(45\) −0.805371 6.65968i −0.120058 0.992767i
\(46\) −15.6815 −2.31210
\(47\) −3.56639 + 3.56639i −0.520211 + 0.520211i −0.917635 0.397424i \(-0.869904\pi\)
0.397424 + 0.917635i \(0.369904\pi\)
\(48\) −3.24158 + 0.0116457i −0.467881 + 0.00168091i
\(49\) 1.00000i 0.142857i
\(50\) −5.79130 + 9.25632i −0.819013 + 1.30904i
\(51\) −0.288917 + 0.291000i −0.0404564 + 0.0407482i
\(52\) 0.572111 + 0.572111i 0.0793376 + 0.0793376i
\(53\) 3.55291 + 3.55291i 0.488030 + 0.488030i 0.907684 0.419654i \(-0.137849\pi\)
−0.419654 + 0.907684i \(0.637849\pi\)
\(54\) −7.93665 + 8.10960i −1.08004 + 1.10358i
\(55\) 7.52082 0.854729i 1.01411 0.115252i
\(56\) 1.67875i 0.224332i
\(57\) −0.0330677 9.20439i −0.00437992 1.21915i
\(58\) −4.38949 + 4.38949i −0.576369 + 0.576369i
\(59\) −10.3168 −1.34313 −0.671565 0.740946i \(-0.734378\pi\)
−0.671565 + 0.740946i \(0.734378\pi\)
\(60\) 10.6503 1.24916i 1.37495 0.161266i
\(61\) −6.80634 −0.871462 −0.435731 0.900077i \(-0.643510\pi\)
−0.435731 + 0.900077i \(0.643510\pi\)
\(62\) 14.0791 14.0791i 1.78805 1.78805i
\(63\) 2.13651 + 2.10602i 0.269175 + 0.265334i
\(64\) 12.5137i 1.56422i
\(65\) 0.511262 + 0.406913i 0.0634143 + 0.0504714i
\(66\) −9.08593 9.02088i −1.11840 1.11039i
\(67\) 6.34806 + 6.34806i 0.775539 + 0.775539i 0.979069 0.203530i \(-0.0652413\pi\)
−0.203530 + 0.979069i \(0.565241\pi\)
\(68\) −0.463512 0.463512i −0.0562091 0.0562091i
\(69\) 8.82642 + 8.76323i 1.06258 + 1.05497i
\(70\) −0.551396 4.85177i −0.0659044 0.579898i
\(71\) 3.95454i 0.469318i 0.972078 + 0.234659i \(0.0753973\pi\)
−0.972078 + 0.234659i \(0.924603\pi\)
\(72\) −3.58665 3.53548i −0.422691 0.416660i
\(73\) 8.61099 8.61099i 1.00784 1.00784i 0.00787086 0.999969i \(-0.497495\pi\)
0.999969 0.00787086i \(-0.00250540\pi\)
\(74\) −16.2757 −1.89201
\(75\) 8.43236 1.97365i 0.973685 0.227898i
\(76\) 14.7136 1.68777
\(77\) −2.39360 + 2.39360i −0.272776 + 0.272776i
\(78\) −0.00397083 1.10528i −0.000449608 0.125148i
\(79\) 11.4449i 1.28766i −0.765170 0.643828i \(-0.777345\pi\)
0.765170 0.643828i \(-0.222655\pi\)
\(80\) −0.472563 4.15812i −0.0528342 0.464892i
\(81\) 8.99907 0.129328i 0.999897 0.0143698i
\(82\) 0.0486356 + 0.0486356i 0.00537090 + 0.00537090i
\(83\) 3.88059 + 3.88059i 0.425951 + 0.425951i 0.887246 0.461296i \(-0.152615\pi\)
−0.461296 + 0.887246i \(0.652615\pi\)
\(84\) −3.37880 + 3.40317i −0.368658 + 0.371316i
\(85\) −0.414214 0.329672i −0.0449278 0.0357580i
\(86\) 11.6390i 1.25506i
\(87\) 4.92363 0.0176886i 0.527868 0.00189642i
\(88\) 4.01825 4.01825i 0.428347 0.428347i
\(89\) 2.00190 0.212201 0.106100 0.994355i \(-0.466164\pi\)
0.106100 + 0.994355i \(0.466164\pi\)
\(90\) −11.5271 9.03989i −1.21506 0.952888i
\(91\) −0.292222 −0.0306332
\(92\) −14.0589 + 14.0589i −1.46574 + 1.46574i
\(93\) −15.7923 + 0.0567354i −1.63759 + 0.00588319i
\(94\) 11.0140i 1.13601i
\(95\) 11.8069 1.34183i 1.21136 0.137669i
\(96\) −9.08474 + 9.15025i −0.927208 + 0.933894i
\(97\) 2.26760 + 2.26760i 0.230240 + 0.230240i 0.812793 0.582553i \(-0.197946\pi\)
−0.582553 + 0.812793i \(0.697946\pi\)
\(98\) 1.54414 + 1.54414i 0.155982 + 0.155982i
\(99\) 0.0729661 + 10.1549i 0.00733337 + 1.02061i
\(100\) 3.10651 + 13.4907i 0.310651 + 1.34907i
\(101\) 8.63630i 0.859344i −0.902985 0.429672i \(-0.858629\pi\)
0.902985 0.429672i \(-0.141371\pi\)
\(102\) 0.00321708 + 0.895474i 0.000318538 + 0.0886651i
\(103\) 0.964332 0.964332i 0.0950185 0.0950185i −0.658000 0.753018i \(-0.728597\pi\)
0.753018 + 0.658000i \(0.228597\pi\)
\(104\) 0.490566 0.0481039
\(105\) −2.40095 + 3.03899i −0.234308 + 0.296575i
\(106\) 10.9724 1.06573
\(107\) −2.95847 + 2.95847i −0.286007 + 0.286007i −0.835499 0.549492i \(-0.814821\pi\)
0.549492 + 0.835499i \(0.314821\pi\)
\(108\) 0.155055 + 14.3860i 0.0149201 + 1.38429i
\(109\) 2.82182i 0.270281i −0.990826 0.135141i \(-0.956851\pi\)
0.990826 0.135141i \(-0.0431486\pi\)
\(110\) 10.2934 12.9330i 0.981436 1.23312i
\(111\) 9.16087 + 9.09528i 0.869511 + 0.863286i
\(112\) 1.32338 + 1.32338i 0.125047 + 0.125047i
\(113\) 2.01798 + 2.01798i 0.189835 + 0.189835i 0.795625 0.605790i \(-0.207143\pi\)
−0.605790 + 0.795625i \(0.707143\pi\)
\(114\) −14.2639 14.1618i −1.33594 1.32638i
\(115\) −9.99939 + 12.5636i −0.932448 + 1.17157i
\(116\) 7.87065i 0.730771i
\(117\) −0.615426 + 0.624334i −0.0568961 + 0.0577197i
\(118\) −15.9306 + 15.9306i −1.46653 + 1.46653i
\(119\) 0.236752 0.0217030
\(120\) 4.03058 5.10169i 0.367940 0.465719i
\(121\) −0.458667 −0.0416970
\(122\) −10.5099 + 10.5099i −0.951526 + 0.951526i
\(123\) −0.000195990 0.0545538i −1.76718e−5 0.00491895i
\(124\) 25.2448i 2.26705i
\(125\) 3.72311 + 10.5422i 0.333005 + 0.942925i
\(126\) 6.55107 0.0470713i 0.583616 0.00419345i
\(127\) −11.6271 11.6271i −1.03174 1.03174i −0.999480 0.0322583i \(-0.989730\pi\)
−0.0322583 0.999480i \(-0.510270\pi\)
\(128\) −8.79491 8.79491i −0.777367 0.777367i
\(129\) 6.50417 6.55107i 0.572660 0.576789i
\(130\) 1.41779 0.161130i 0.124349 0.0141320i
\(131\) 12.7013i 1.10972i −0.831943 0.554861i \(-0.812772\pi\)
0.831943 0.554861i \(-0.187228\pi\)
\(132\) −16.2333 + 0.0583199i −1.41293 + 0.00507609i
\(133\) −3.75770 + 3.75770i −0.325834 + 0.325834i
\(134\) 19.6046 1.69358
\(135\) 1.43638 + 11.5298i 0.123623 + 0.992329i
\(136\) −0.397446 −0.0340807
\(137\) −5.19451 + 5.19451i −0.443797 + 0.443797i −0.893286 0.449489i \(-0.851606\pi\)
0.449489 + 0.893286i \(0.351606\pi\)
\(138\) 27.1609 0.0975782i 2.31209 0.00830641i
\(139\) 12.3138i 1.04444i −0.852810 0.522221i \(-0.825103\pi\)
0.852810 0.522221i \(-0.174897\pi\)
\(140\) −4.84412 3.85543i −0.409402 0.325843i
\(141\) 6.15493 6.19932i 0.518339 0.522077i
\(142\) 6.10637 + 6.10637i 0.512435 + 0.512435i
\(143\) −0.699463 0.699463i −0.0584920 0.0584920i
\(144\) 5.61447 0.0403416i 0.467872 0.00336180i
\(145\) 0.717776 + 6.31576i 0.0596080 + 0.524495i
\(146\) 26.5932i 2.20087i
\(147\) −0.00622252 1.73204i −0.000513225 0.142856i
\(148\) −14.5917 + 14.5917i −1.19943 + 1.19943i
\(149\) 18.9350 1.55121 0.775607 0.631216i \(-0.217444\pi\)
0.775607 + 0.631216i \(0.217444\pi\)
\(150\) 9.97316 16.0684i 0.814305 1.31198i
\(151\) −1.90527 −0.155049 −0.0775243 0.996990i \(-0.524702\pi\)
−0.0775243 + 0.996990i \(0.524702\pi\)
\(152\) 6.30822 6.30822i 0.511665 0.511665i
\(153\) 0.498604 0.505822i 0.0403098 0.0408933i
\(154\) 7.39212i 0.595674i
\(155\) −2.30223 20.2575i −0.184920 1.62712i
\(156\) −0.994479 0.987359i −0.0796221 0.0790520i
\(157\) −4.31728 4.31728i −0.344557 0.344557i 0.513521 0.858077i \(-0.328341\pi\)
−0.858077 + 0.513521i \(0.828341\pi\)
\(158\) −17.6726 17.6726i −1.40596 1.40596i
\(159\) −6.17589 6.13167i −0.489780 0.486273i
\(160\) −13.0246 10.3663i −1.02968 0.819525i
\(161\) 7.18099i 0.565941i
\(162\) 13.6961 14.0955i 1.07607 1.10745i
\(163\) 3.57655 3.57655i 0.280137 0.280137i −0.553027 0.833164i \(-0.686527\pi\)
0.833164 + 0.553027i \(0.186527\pi\)
\(164\) 0.0872068 0.00680970
\(165\) −13.0210 + 1.52722i −1.01369 + 0.118894i
\(166\) 11.9844 0.930168
\(167\) −6.39241 + 6.39241i −0.494659 + 0.494659i −0.909771 0.415111i \(-0.863743\pi\)
0.415111 + 0.909771i \(0.363743\pi\)
\(168\) 0.0104460 + 2.90765i 0.000805929 + 0.224330i
\(169\) 12.9146i 0.993431i
\(170\) −1.14866 + 0.130544i −0.0880986 + 0.0100123i
\(171\) 0.114549 + 15.9422i 0.00875978 + 1.21913i
\(172\) 10.4347 + 10.4347i 0.795638 + 0.795638i
\(173\) 3.88791 + 3.88791i 0.295592 + 0.295592i 0.839285 0.543692i \(-0.182974\pi\)
−0.543692 + 0.839285i \(0.682974\pi\)
\(174\) 7.57546 7.63009i 0.574294 0.578436i
\(175\) −4.23874 2.65200i −0.320418 0.200472i
\(176\) 6.33528i 0.477540i
\(177\) 17.8691 0.0641964i 1.34312 0.00482529i
\(178\) 3.09121 3.09121i 0.231696 0.231696i
\(179\) −14.6322 −1.09366 −0.546832 0.837242i \(-0.684166\pi\)
−0.546832 + 0.837242i \(0.684166\pi\)
\(180\) −18.4390 + 2.22987i −1.37436 + 0.166205i
\(181\) −9.83718 −0.731192 −0.365596 0.930774i \(-0.619135\pi\)
−0.365596 + 0.930774i \(0.619135\pi\)
\(182\) −0.451232 + 0.451232i −0.0334475 + 0.0334475i
\(183\) 11.7888 0.0423526i 0.871456 0.00313079i
\(184\) 12.0551i 0.888710i
\(185\) −10.3783 + 13.0397i −0.763027 + 0.958698i
\(186\) −24.2980 + 24.4732i −1.78161 + 1.79446i
\(187\) 0.566689 + 0.566689i 0.0414404 + 0.0414404i
\(188\) 9.87442 + 9.87442i 0.720166 + 0.720166i
\(189\) −3.71362 3.63442i −0.270126 0.264365i
\(190\) 16.1595 20.3035i 1.17234 1.47297i
\(191\) 6.37886i 0.461558i −0.973006 0.230779i \(-0.925873\pi\)
0.973006 0.230779i \(-0.0741275\pi\)
\(192\) 0.0778669 + 21.6743i 0.00561956 + 1.56421i
\(193\) 7.56336 7.56336i 0.544422 0.544422i −0.380400 0.924822i \(-0.624214\pi\)
0.924822 + 0.380400i \(0.124214\pi\)
\(194\) 7.00299 0.502785
\(195\) −0.888059 0.701608i −0.0635952 0.0502432i
\(196\) 2.76875 0.197768
\(197\) −1.01490 + 1.01490i −0.0723090 + 0.0723090i −0.742336 0.670027i \(-0.766282\pi\)
0.670027 + 0.742336i \(0.266282\pi\)
\(198\) 15.7933 + 15.5680i 1.12238 + 1.10637i
\(199\) 9.40041i 0.666378i 0.942860 + 0.333189i \(0.108125\pi\)
−0.942860 + 0.333189i \(0.891875\pi\)
\(200\) 7.11576 + 4.45204i 0.503160 + 0.314806i
\(201\) −11.0346 10.9556i −0.778320 0.772748i
\(202\) −13.3357 13.3357i −0.938295 0.938295i
\(203\) −2.01007 2.01007i −0.141080 0.141080i
\(204\) 0.805705 + 0.799937i 0.0564107 + 0.0560068i
\(205\) 0.0699786 0.00795295i 0.00488752 0.000555458i
\(206\) 2.97813i 0.207496i
\(207\) −15.3422 15.1233i −1.06636 1.05114i
\(208\) −0.386719 + 0.386719i −0.0268142 + 0.0268142i
\(209\) −17.9889 −1.24432
\(210\) 0.985230 + 8.40003i 0.0679873 + 0.579657i
\(211\) −8.29157 −0.570815 −0.285407 0.958406i \(-0.592129\pi\)
−0.285407 + 0.958406i \(0.592129\pi\)
\(212\) 9.83710 9.83710i 0.675615 0.675615i
\(213\) −0.0246072 6.84942i −0.00168606 0.469315i
\(214\) 9.13661i 0.624566i
\(215\) 9.32488 + 7.42166i 0.635952 + 0.506153i
\(216\) 6.23422 + 6.10127i 0.424185 + 0.415139i
\(217\) 6.44723 + 6.44723i 0.437666 + 0.437666i
\(218\) −4.35729 4.35729i −0.295113 0.295113i
\(219\) −14.8610 + 14.9682i −1.00421 + 1.01145i
\(220\) −2.36653 20.8232i −0.159551 1.40390i
\(221\) 0.0691839i 0.00465382i
\(222\) 28.1901 0.101276i 1.89199 0.00679717i
\(223\) 3.86020 3.86020i 0.258498 0.258498i −0.565945 0.824443i \(-0.691489\pi\)
0.824443 + 0.565945i \(0.191489\pi\)
\(224\) 7.44445 0.497404
\(225\) −14.5929 + 3.47092i −0.972860 + 0.231394i
\(226\) 6.23208 0.414552
\(227\) 1.50739 1.50739i 0.100049 0.100049i −0.655310 0.755360i \(-0.727462\pi\)
0.755360 + 0.655310i \(0.227462\pi\)
\(228\) −25.4846 + 0.0915560i −1.68776 + 0.00606344i
\(229\) 6.26009i 0.413678i −0.978375 0.206839i \(-0.933682\pi\)
0.978375 0.206839i \(-0.0663177\pi\)
\(230\) 3.95957 + 34.8405i 0.261086 + 2.29732i
\(231\) 4.13092 4.16071i 0.271795 0.273755i
\(232\) 3.37440 + 3.37440i 0.221541 + 0.221541i
\(233\) −2.67422 2.67422i −0.175194 0.175194i 0.614063 0.789257i \(-0.289534\pi\)
−0.789257 + 0.614063i \(0.789534\pi\)
\(234\) 0.0137553 + 1.91436i 0.000899209 + 0.125146i
\(235\) 8.82419 + 7.02317i 0.575627 + 0.458141i
\(236\) 28.5645i 1.85939i
\(237\) 0.0712164 + 19.8231i 0.00462600 + 1.28765i
\(238\) 0.365578 0.365578i 0.0236969 0.0236969i
\(239\) 2.08521 0.134881 0.0674406 0.997723i \(-0.478517\pi\)
0.0674406 + 0.997723i \(0.478517\pi\)
\(240\) 0.844372 + 7.19909i 0.0545040 + 0.464699i
\(241\) −5.43686 −0.350219 −0.175110 0.984549i \(-0.556028\pi\)
−0.175110 + 0.984549i \(0.556028\pi\)
\(242\) −0.708247 + 0.708247i −0.0455279 + 0.0455279i
\(243\) −15.5859 + 0.279999i −0.999839 + 0.0179619i
\(244\) 18.8450i 1.20643i
\(245\) 2.22177 0.252500i 0.141943 0.0161316i
\(246\) −0.0845414 0.0839361i −0.00539016 0.00535157i
\(247\) −1.09808 1.09808i −0.0698692 0.0698692i
\(248\) −10.8233 10.8233i −0.687278 0.687278i
\(249\) −6.74549 6.69720i −0.427478 0.424418i
\(250\) 22.0277 + 10.5297i 1.39315 + 0.665956i
\(251\) 23.3428i 1.47339i −0.676227 0.736693i \(-0.736386\pi\)
0.676227 0.736693i \(-0.263614\pi\)
\(252\) 5.83104 5.91545i 0.367321 0.372638i
\(253\) 17.1884 17.1884i 1.08063 1.08063i
\(254\) −35.9078 −2.25305
\(255\) 0.719486 + 0.568428i 0.0450559 + 0.0355963i
\(256\) −2.13372 −0.133358
\(257\) 10.9273 10.9273i 0.681627 0.681627i −0.278740 0.960367i \(-0.589917\pi\)
0.960367 + 0.278740i \(0.0899167\pi\)
\(258\) −0.0724236 20.1591i −0.00450890 1.25505i
\(259\) 7.45309i 0.463112i
\(260\) 1.12664 1.41556i 0.0698712 0.0877890i
\(261\) −8.52781 + 0.0612747i −0.527858 + 0.00379281i
\(262\) −19.6127 19.6127i −1.21167 1.21167i
\(263\) 18.1808 + 18.1808i 1.12108 + 1.12108i 0.991580 + 0.129497i \(0.0413364\pi\)
0.129497 + 0.991580i \(0.458664\pi\)
\(264\) −6.93477 + 6.98477i −0.426805 + 0.429883i
\(265\) 6.99662 8.79084i 0.429799 0.540017i
\(266\) 11.6048i 0.711539i
\(267\) −3.46737 + 0.0124569i −0.212199 + 0.000762347i
\(268\) 17.5762 17.5762i 1.07364 1.07364i
\(269\) 28.5125 1.73844 0.869219 0.494428i \(-0.164622\pi\)
0.869219 + 0.494428i \(0.164622\pi\)
\(270\) 20.0216 + 15.5857i 1.21848 + 0.948516i
\(271\) 3.12214 0.189656 0.0948282 0.995494i \(-0.469770\pi\)
0.0948282 + 0.995494i \(0.469770\pi\)
\(272\) 0.313312 0.313312i 0.0189973 0.0189973i
\(273\) 0.506139 0.00181836i 0.0306330 0.000110052i
\(274\) 16.0421i 0.969139i
\(275\) −3.79802 16.4937i −0.229029 0.994607i
\(276\) 24.2631 24.4381i 1.46047 1.47100i
\(277\) 12.2472 + 12.2472i 0.735861 + 0.735861i 0.971774 0.235913i \(-0.0758081\pi\)
−0.235913 + 0.971774i \(0.575808\pi\)
\(278\) −19.0142 19.0142i −1.14040 1.14040i
\(279\) 27.3526 0.196536i 1.63756 0.0117663i
\(280\) −3.72978 + 0.423883i −0.222897 + 0.0253319i
\(281\) 12.7181i 0.758698i 0.925254 + 0.379349i \(0.123852\pi\)
−0.925254 + 0.379349i \(0.876148\pi\)
\(282\) −0.0685349 19.0767i −0.00408120 1.13600i
\(283\) −19.8271 + 19.8271i −1.17860 + 1.17860i −0.198495 + 0.980102i \(0.563605\pi\)
−0.980102 + 0.198495i \(0.936395\pi\)
\(284\) 10.9491 0.649711
\(285\) −20.4416 + 2.39758i −1.21086 + 0.142020i
\(286\) −2.16014 −0.127732
\(287\) −0.0222716 + 0.0222716i −0.00131465 + 0.00131465i
\(288\) 15.6782 15.9051i 0.923847 0.937219i
\(289\) 16.9439i 0.996703i
\(290\) 10.8608 + 8.64408i 0.637767 + 0.507598i
\(291\) −3.94168 3.91346i −0.231066 0.229411i
\(292\) −23.8416 23.8416i −1.39523 1.39523i
\(293\) −6.72836 6.72836i −0.393075 0.393075i 0.482707 0.875782i \(-0.339654\pi\)
−0.875782 + 0.482707i \(0.839654\pi\)
\(294\) −2.68412 2.66491i −0.156541 0.155420i
\(295\) 2.60499 + 22.9215i 0.151668 + 1.33454i
\(296\) 12.5118i 0.727236i
\(297\) −0.189570 17.5883i −0.0109999 1.02058i
\(298\) 29.2383 29.2383i 1.69373 1.69373i
\(299\) 2.09844 0.121356
\(300\) −5.46455 23.3471i −0.315496 1.34794i
\(301\) −5.32981 −0.307205
\(302\) −2.94201 + 2.94201i −0.169293 + 0.169293i
\(303\) 0.0537396 + 14.9584i 0.00308726 + 0.859339i
\(304\) 9.94571i 0.570426i
\(305\) 1.71860 + 15.1221i 0.0984068 + 0.865888i
\(306\) −0.0111442 1.55098i −0.000637072 0.0886634i
\(307\) 10.1105 + 10.1105i 0.577034 + 0.577034i 0.934085 0.357051i \(-0.116218\pi\)
−0.357051 + 0.934085i \(0.616218\pi\)
\(308\) 6.62728 + 6.62728i 0.377624 + 0.377624i
\(309\) −1.66426 + 1.67626i −0.0946765 + 0.0953592i
\(310\) −34.8355 27.7255i −1.97852 1.57470i
\(311\) 0.394155i 0.0223505i −0.999938 0.0111752i \(-0.996443\pi\)
0.999938 0.0111752i \(-0.00355726\pi\)
\(312\) −0.849680 + 0.00305256i −0.0481036 + 0.000172817i
\(313\) −10.3810 + 10.3810i −0.586767 + 0.586767i −0.936754 0.349987i \(-0.886186\pi\)
0.349987 + 0.936754i \(0.386186\pi\)
\(314\) −13.3330 −0.752424
\(315\) 4.13962 5.27859i 0.233241 0.297415i
\(316\) −31.6881 −1.78260
\(317\) −19.8075 + 19.8075i −1.11250 + 1.11250i −0.119688 + 0.992812i \(0.538190\pi\)
−0.992812 + 0.119688i \(0.961810\pi\)
\(318\) −19.0046 + 0.0682759i −1.06573 + 0.00382872i
\(319\) 9.62264i 0.538764i
\(320\) −27.8026 + 3.15971i −1.55421 + 0.176633i
\(321\) 5.10579 5.14260i 0.284977 0.287032i
\(322\) −11.0885 11.0885i −0.617936 0.617936i
\(323\) 0.889642 + 0.889642i 0.0495010 + 0.0495010i
\(324\) −0.358078 24.9161i −0.0198932 1.38423i
\(325\) 0.774972 1.23865i 0.0429877 0.0687080i
\(326\) 11.0454i 0.611748i
\(327\) 0.0175588 + 4.88750i 0.000971005 + 0.270279i
\(328\) 0.0373884 0.0373884i 0.00206443 0.00206443i
\(329\) −5.04363 −0.278065
\(330\) −17.7481 + 22.4646i −0.977000 + 1.23663i
\(331\) −24.7348 −1.35955 −0.679774 0.733422i \(-0.737922\pi\)
−0.679774 + 0.733422i \(0.737922\pi\)
\(332\) 10.7444 10.7444i 0.589674 0.589674i
\(333\) −15.9236 15.6964i −0.872607 0.860157i
\(334\) 19.7416i 1.08021i
\(335\) 12.5010 15.7068i 0.683004 0.858154i
\(336\) −2.30038 2.28391i −0.125496 0.124597i
\(337\) −3.40139 3.40139i −0.185286 0.185286i 0.608369 0.793655i \(-0.291824\pi\)
−0.793655 + 0.608369i \(0.791824\pi\)
\(338\) 19.9420 + 19.9420i 1.08470 + 1.08470i
\(339\) −3.50777 3.48266i −0.190516 0.189152i
\(340\) −0.912779 + 1.14685i −0.0495024 + 0.0621968i
\(341\) 30.8642i 1.67139i
\(342\) 24.7938 + 24.4401i 1.34070 + 1.32157i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 8.94740 0.482411
\(345\) 17.2412 21.8229i 0.928233 1.17491i
\(346\) 12.0070 0.645498
\(347\) 24.0324 24.0324i 1.29013 1.29013i 0.355421 0.934706i \(-0.384337\pi\)
0.934706 0.355421i \(-0.115663\pi\)
\(348\) −0.0489753 13.6323i −0.00262535 0.730766i
\(349\) 9.37078i 0.501607i 0.968038 + 0.250803i \(0.0806947\pi\)
−0.968038 + 0.250803i \(0.919305\pi\)
\(350\) −10.6403 + 2.45015i −0.568747 + 0.130966i
\(351\) 1.06206 1.08520i 0.0566884 0.0579237i
\(352\) 17.8191 + 17.8191i 0.949759 + 0.949759i
\(353\) 14.5888 + 14.5888i 0.776481 + 0.776481i 0.979231 0.202750i \(-0.0649878\pi\)
−0.202750 + 0.979231i \(0.564988\pi\)
\(354\) 27.4932 27.6915i 1.46125 1.47179i
\(355\) 8.78606 0.998522i 0.466316 0.0529960i
\(356\) 5.54275i 0.293765i
\(357\) −0.410063 + 0.00147319i −0.0217028 + 7.79696e-5i
\(358\) −22.5942 + 22.5942i −1.19414 + 1.19414i
\(359\) 27.2654 1.43901 0.719506 0.694486i \(-0.244368\pi\)
0.719506 + 0.694486i \(0.244368\pi\)
\(360\) −6.94938 + 8.86141i −0.366264 + 0.467037i
\(361\) −9.24062 −0.486349
\(362\) −15.1900 + 15.1900i −0.798369 + 0.798369i
\(363\) 0.794430 0.00285407i 0.0416968 0.000149800i
\(364\) 0.809088i 0.0424077i
\(365\) −21.3059 16.9573i −1.11520 0.887587i
\(366\) 18.1382 18.2690i 0.948101 0.954938i
\(367\) 15.9239 + 15.9239i 0.831218 + 0.831218i 0.987683 0.156465i \(-0.0500099\pi\)
−0.156465 + 0.987683i \(0.550010\pi\)
\(368\) −9.50315 9.50315i −0.495386 0.495386i
\(369\) 0.000678924 0.0944881i 3.53434e−5 0.00491885i
\(370\) 4.10960 + 36.1607i 0.213648 + 1.87990i
\(371\) 5.02457i 0.260863i
\(372\) 0.157086 + 43.7249i 0.00814453 + 2.26703i
\(373\) 23.3283 23.3283i 1.20790 1.20790i 0.236189 0.971707i \(-0.424102\pi\)
0.971707 0.236189i \(-0.0758984\pi\)
\(374\) 1.75010 0.0904954
\(375\) −6.51417 18.2364i −0.336390 0.941723i
\(376\) 8.46698 0.436651
\(377\) 0.587387 0.587387i 0.0302520 0.0302520i
\(378\) −11.3464 + 0.122294i −0.583597 + 0.00629010i
\(379\) 37.4477i 1.92356i −0.273828 0.961779i \(-0.588290\pi\)
0.273828 0.961779i \(-0.411710\pi\)
\(380\) −3.71520 32.6903i −0.190586 1.67698i
\(381\) 20.2109 + 20.0662i 1.03544 + 1.02802i
\(382\) −9.84986 9.84986i −0.503963 0.503963i
\(383\) −4.95443 4.95443i −0.253159 0.253159i 0.569105 0.822265i \(-0.307290\pi\)
−0.822265 + 0.569105i \(0.807290\pi\)
\(384\) 15.2879 + 15.1784i 0.780155 + 0.774570i
\(385\) 5.92241 + 4.71364i 0.301834 + 0.240229i
\(386\) 23.3578i 1.18888i
\(387\) −11.2247 + 11.3872i −0.570584 + 0.578843i
\(388\) 6.27841 6.27841i 0.318738 0.318738i
\(389\) 9.20279 0.466600 0.233300 0.972405i \(-0.425048\pi\)
0.233300 + 0.972405i \(0.425048\pi\)
\(390\) −2.45467 + 0.287905i −0.124297 + 0.0145787i
\(391\) −1.70011 −0.0859783
\(392\) 1.18705 1.18705i 0.0599552 0.0599552i
\(393\) 0.0790344 + 21.9992i 0.00398676 + 1.10971i
\(394\) 3.13431i 0.157904i
\(395\) −25.4280 + 2.88985i −1.27942 + 0.145404i
\(396\) 28.1164 0.202025i 1.41290 0.0101521i
\(397\) 21.9242 + 21.9242i 1.10034 + 1.10034i 0.994369 + 0.105976i \(0.0337966\pi\)
0.105976 + 0.994369i \(0.466203\pi\)
\(398\) 14.5156 + 14.5156i 0.727600 + 0.727600i
\(399\) 6.48510 6.53187i 0.324661 0.327002i
\(400\) −9.11904 + 2.09985i −0.455952 + 0.104993i
\(401\) 25.7514i 1.28596i 0.765882 + 0.642982i \(0.222303\pi\)
−0.765882 + 0.642982i \(0.777697\pi\)
\(402\) −33.9560 + 0.121990i −1.69357 + 0.00608431i
\(403\) −1.88402 + 1.88402i −0.0938497 + 0.0938497i
\(404\) −23.9117 −1.18965
\(405\) −2.55960 19.9612i −0.127188 0.991879i
\(406\) −6.20768 −0.308082
\(407\) 17.8397 17.8397i 0.884283 0.884283i
\(408\) 0.688392 0.00247311i 0.0340805 0.000122437i
\(409\) 10.9496i 0.541425i −0.962660 0.270712i \(-0.912741\pi\)
0.962660 0.270712i \(-0.0872592\pi\)
\(410\) 0.0957764 0.120337i 0.00473006 0.00594304i
\(411\) 8.96477 9.02942i 0.442200 0.445388i
\(412\) −2.66999 2.66999i −0.131541 0.131541i
\(413\) −7.29506 7.29506i −0.358967 0.358967i
\(414\) −47.0431 + 0.338019i −2.31204 + 0.0166127i
\(415\) 7.64192 9.60162i 0.375127 0.471325i
\(416\) 2.17543i 0.106659i
\(417\) 0.0766229 + 21.3280i 0.00375224 + 1.04444i
\(418\) −27.7774 + 27.7774i −1.35864 + 1.35864i
\(419\) −5.86958 −0.286748 −0.143374 0.989669i \(-0.545795\pi\)
−0.143374 + 0.989669i \(0.545795\pi\)
\(420\) 8.41419 + 6.64761i 0.410570 + 0.324370i
\(421\) 26.8842 1.31026 0.655129 0.755517i \(-0.272614\pi\)
0.655129 + 0.755517i \(0.272614\pi\)
\(422\) −12.8034 + 12.8034i −0.623257 + 0.623257i
\(423\) −10.6220 + 10.7758i −0.516460 + 0.523936i
\(424\) 8.43498i 0.409639i
\(425\) −0.627865 + 1.00353i −0.0304559 + 0.0486782i
\(426\) −10.6145 10.5385i −0.514273 0.510591i
\(427\) −4.81281 4.81281i −0.232908 0.232908i
\(428\) 8.19126 + 8.19126i 0.395940 + 0.395940i
\(429\) 1.21585 + 1.20714i 0.0587018 + 0.0582815i
\(430\) 25.8590 2.93884i 1.24703 0.141723i
\(431\) 4.18118i 0.201400i 0.994917 + 0.100700i \(0.0321083\pi\)
−0.994917 + 0.100700i \(0.967892\pi\)
\(432\) −9.72423 + 0.104809i −0.467857 + 0.00504264i
\(433\) −2.20877 + 2.20877i −0.106146 + 0.106146i −0.758185 0.652039i \(-0.773914\pi\)
0.652039 + 0.758185i \(0.273914\pi\)
\(434\) 19.9109 0.955752
\(435\) −1.28252 10.9347i −0.0614919 0.524278i
\(436\) −7.81290 −0.374170
\(437\) 26.9840 26.9840i 1.29082 1.29082i
\(438\) 0.165477 + 46.0604i 0.00790678 + 2.20085i
\(439\) 27.6028i 1.31741i −0.752401 0.658706i \(-0.771104\pi\)
0.752401 0.658706i \(-0.228896\pi\)
\(440\) −9.94222 7.91300i −0.473977 0.377238i
\(441\) 0.0215553 + 2.99992i 0.00102644 + 0.142853i
\(442\) 0.106830 + 0.106830i 0.00508138 + 0.00508138i
\(443\) 12.3040 + 12.3040i 0.584582 + 0.584582i 0.936159 0.351577i \(-0.114354\pi\)
−0.351577 + 0.936159i \(0.614354\pi\)
\(444\) 25.1825 25.3641i 1.19511 1.20373i
\(445\) −0.505479 4.44775i −0.0239620 0.210843i
\(446\) 11.9214i 0.564494i
\(447\) −32.7961 + 0.117823i −1.55120 + 0.00557285i
\(448\) 8.84854 8.84854i 0.418054 0.418054i
\(449\) −34.1859 −1.61333 −0.806666 0.591008i \(-0.798730\pi\)
−0.806666 + 0.591008i \(0.798730\pi\)
\(450\) −17.1739 + 27.8931i −0.809586 + 1.31489i
\(451\) −0.106619 −0.00502049
\(452\) 5.58726 5.58726i 0.262803 0.262803i
\(453\) 3.30000 0.0118556i 0.155048 0.000557024i
\(454\) 4.65526i 0.218482i
\(455\) 0.0737860 + 0.649248i 0.00345914 + 0.0304372i
\(456\) −10.8868 + 10.9653i −0.509823 + 0.513499i
\(457\) −9.31021 9.31021i −0.435513 0.435513i 0.454986 0.890499i \(-0.349644\pi\)
−0.890499 + 0.454986i \(0.849644\pi\)
\(458\) −9.66646 9.66646i −0.451684 0.451684i
\(459\) −0.860455 + 0.879206i −0.0401626 + 0.0410378i
\(460\) 34.7855 + 27.6858i 1.62188 + 1.29086i
\(461\) 25.6579i 1.19501i 0.801865 + 0.597505i \(0.203841\pi\)
−0.801865 + 0.597505i \(0.796159\pi\)
\(462\) −0.0459976 12.8034i −0.00214000 0.595670i
\(463\) 13.2170 13.2170i 0.614248 0.614248i −0.329802 0.944050i \(-0.606982\pi\)
0.944050 + 0.329802i \(0.106982\pi\)
\(464\) −5.32017 −0.246983
\(465\) 4.11361 + 35.0725i 0.190764 + 1.62645i
\(466\) −8.25874 −0.382579
\(467\) −19.6659 + 19.6659i −0.910031 + 0.910031i −0.996274 0.0862431i \(-0.972514\pi\)
0.0862431 + 0.996274i \(0.472514\pi\)
\(468\) 1.72862 + 1.70396i 0.0799056 + 0.0787655i
\(469\) 8.97752i 0.414543i
\(470\) 24.4706 2.78104i 1.12874 0.128280i
\(471\) 7.50457 + 7.45084i 0.345792 + 0.343317i
\(472\) 12.2466 + 12.2466i 0.563693 + 0.563693i
\(473\) −12.7575 12.7575i −0.586588 0.586588i
\(474\) 30.7196 + 30.4997i 1.41100 + 1.40090i
\(475\) −5.96248 25.8933i −0.273577 1.18807i
\(476\) 0.655505i 0.0300450i
\(477\) 10.7350 + 10.5819i 0.491524 + 0.484510i
\(478\) 3.21986 3.21986i 0.147273 0.147273i
\(479\) −26.9725 −1.23240 −0.616202 0.787588i \(-0.711330\pi\)
−0.616202 + 0.787588i \(0.711330\pi\)
\(480\) 22.6236 + 17.8737i 1.03262 + 0.815821i
\(481\) 2.17795 0.0993062
\(482\) −8.39528 + 8.39528i −0.382395 + 0.382395i
\(483\) 0.0446838 + 12.4378i 0.00203319 + 0.565937i
\(484\) 1.26993i 0.0577242i
\(485\) 4.46551 5.61064i 0.202768 0.254766i
\(486\) −23.6345 + 24.4993i −1.07208 + 1.11131i
\(487\) −28.6505 28.6505i −1.29828 1.29828i −0.929529 0.368749i \(-0.879786\pi\)
−0.368749 0.929529i \(-0.620214\pi\)
\(488\) 8.07948 + 8.07948i 0.365741 + 0.365741i
\(489\) −6.17247 + 6.21698i −0.279129 + 0.281141i
\(490\) 3.04083 3.82062i 0.137370 0.172598i
\(491\) 2.74522i 0.123890i 0.998080 + 0.0619450i \(0.0197303\pi\)
−0.998080 + 0.0619450i \(0.980270\pi\)
\(492\) −0.151046 0.000542646i −0.00680966 2.44644e-5i
\(493\) −0.475888 + 0.475888i −0.0214329 + 0.0214329i
\(494\) −3.39119 −0.152577
\(495\) 22.5435 2.72623i 1.01325 0.122535i
\(496\) 17.0642 0.766206
\(497\) −2.79628 + 2.79628i −0.125430 + 0.125430i
\(498\) −20.7574 + 0.0745730i −0.930162 + 0.00334170i
\(499\) 30.3151i 1.35709i 0.734558 + 0.678546i \(0.237389\pi\)
−0.734558 + 0.678546i \(0.762611\pi\)
\(500\) 29.1887 10.3083i 1.30536 0.461003i
\(501\) 11.0321 11.1117i 0.492879 0.496433i
\(502\) −36.0446 36.0446i −1.60875 1.60875i
\(503\) −0.331820 0.331820i −0.0147951 0.0147951i 0.699671 0.714466i \(-0.253330\pi\)
−0.714466 + 0.699671i \(0.753330\pi\)
\(504\) −0.0361859 5.03611i −0.00161185 0.224326i
\(505\) −19.1878 + 2.18067i −0.853848 + 0.0970384i
\(506\) 53.0827i 2.35982i
\(507\) −0.0803614 22.3686i −0.00356898 0.993425i
\(508\) −32.1925 + 32.1925i −1.42831 + 1.42831i
\(509\) 14.6491 0.649311 0.324656 0.945832i \(-0.394752\pi\)
0.324656 + 0.945832i \(0.394752\pi\)
\(510\) 1.98872 0.233255i 0.0880620 0.0103287i
\(511\) 12.1778 0.538713
\(512\) 14.2950 14.2950i 0.631758 0.631758i
\(513\) −0.297604 27.6117i −0.0131395 1.21909i
\(514\) 33.7466i 1.48850i
\(515\) −2.38601 1.89903i −0.105140 0.0836811i
\(516\) −18.1382 18.0084i −0.798492 0.792775i
\(517\) −12.0725 12.0725i −0.530946 0.530946i
\(518\) −11.5086 11.5086i −0.505660 0.505660i
\(519\) −6.75820 6.70982i −0.296652 0.294528i
\(520\) −0.123868 1.08992i −0.00543197 0.0477963i
\(521\) 24.6501i 1.07994i −0.841683 0.539971i \(-0.818435\pi\)
0.841683 0.539971i \(-0.181565\pi\)
\(522\) −13.0735 + 13.2628i −0.572212 + 0.580495i
\(523\) −23.4069 + 23.4069i −1.02351 + 1.02351i −0.0237950 + 0.999717i \(0.507575\pi\)
−0.999717 + 0.0237950i \(0.992425\pi\)
\(524\) −35.1668 −1.53627
\(525\) 7.35816 + 4.56699i 0.321137 + 0.199320i
\(526\) 56.1475 2.44815
\(527\) 1.52639 1.52639i 0.0664907 0.0664907i
\(528\) −0.0394214 10.9730i −0.00171560 0.477536i
\(529\) 28.5666i 1.24203i
\(530\) −2.77053 24.3781i −0.120344 1.05892i
\(531\) −30.9495 + 0.222381i −1.34310 + 0.00965053i
\(532\) 10.4041 + 10.4041i 0.451076 + 0.451076i
\(533\) −0.00650825 0.00650825i −0.000281904 0.000281904i
\(534\) −5.33487 + 5.37334i −0.230862 + 0.232527i
\(535\) 7.32005 + 5.82602i 0.316473 + 0.251881i
\(536\) 15.0710i 0.650967i
\(537\) 25.3436 0.0910493i 1.09366 0.00392907i
\(538\) 44.0273 44.0273i 1.89815 1.89815i
\(539\) −3.38507 −0.145805
\(540\) 31.9232 3.97696i 1.37375 0.171141i
\(541\) −27.2143 −1.17003 −0.585017 0.811021i \(-0.698912\pi\)
−0.585017 + 0.811021i \(0.698912\pi\)
\(542\) 4.82102 4.82102i 0.207081 0.207081i
\(543\) 17.0384 0.0612121i 0.731187 0.00262686i
\(544\) 1.76249i 0.0755660i
\(545\) −6.26942 + 0.712509i −0.268552 + 0.0305205i
\(546\) 0.778743 0.784359i 0.0333271 0.0335675i
\(547\) −3.63475 3.63475i −0.155411 0.155411i 0.625119 0.780530i \(-0.285051\pi\)
−0.780530 + 0.625119i \(0.785051\pi\)
\(548\) 14.3823 + 14.3823i 0.614380 + 0.614380i
\(549\) −20.4185 + 0.146713i −0.871440 + 0.00626154i
\(550\) −31.3333 19.6039i −1.33605 0.835914i
\(551\) 15.1065i 0.643559i
\(552\) −0.0750128 20.8798i −0.00319276 0.888705i
\(553\) 8.09279 8.09279i 0.344141 0.344141i
\(554\) 37.8227 1.60693
\(555\) 17.8945 22.6499i 0.759578 0.961433i
\(556\) −34.0938 −1.44590
\(557\) 5.91751 5.91751i 0.250733 0.250733i −0.570538 0.821271i \(-0.693265\pi\)
0.821271 + 0.570538i \(0.193265\pi\)
\(558\) 41.9328 42.5397i 1.77516 1.80085i
\(559\) 1.55749i 0.0658747i
\(560\) 2.60608 3.27439i 0.110127 0.138368i
\(561\) −0.985055 0.978002i −0.0415890 0.0412913i
\(562\) 19.6385 + 19.6385i 0.828402 + 0.828402i
\(563\) −13.8267 13.8267i −0.582728 0.582728i 0.352924 0.935652i \(-0.385187\pi\)
−0.935652 + 0.352924i \(0.885187\pi\)
\(564\) −17.1643 17.0414i −0.722749 0.717574i
\(565\) 3.97393 4.99301i 0.167185 0.210058i
\(566\) 61.2316i 2.57376i
\(567\) 6.45475 + 6.27185i 0.271074 + 0.263393i
\(568\) 4.69425 4.69425i 0.196966 0.196966i
\(569\) −6.82232 −0.286007 −0.143003 0.989722i \(-0.545676\pi\)
−0.143003 + 0.989722i \(0.545676\pi\)
\(570\) −27.8626 + 35.2670i −1.16704 + 1.47717i
\(571\) 19.7545 0.826701 0.413351 0.910572i \(-0.364358\pi\)
0.413351 + 0.910572i \(0.364358\pi\)
\(572\) −1.93663 + 1.93663i −0.0809747 + 0.0809747i
\(573\) 0.0396926 + 11.0484i 0.00165818 + 0.461555i
\(574\) 0.0687811i 0.00287087i
\(575\) 30.4383 + 19.0440i 1.26937 + 0.794189i
\(576\) −0.269737 37.5402i −0.0112390 1.56417i
\(577\) 1.10727 + 1.10727i 0.0460964 + 0.0460964i 0.729779 0.683683i \(-0.239623\pi\)
−0.683683 + 0.729779i \(0.739623\pi\)
\(578\) 26.1639 + 26.1639i 1.08827 + 1.08827i
\(579\) −13.0530 + 13.1471i −0.542463 + 0.546375i
\(580\) 17.4867 1.98734i 0.726097 0.0825197i
\(581\) 5.48799i 0.227680i
\(582\) −12.1295 + 0.0435762i −0.502782 + 0.00180629i
\(583\) −12.0268 + 12.0268i −0.498100 + 0.498100i
\(584\) −20.4434 −0.845953
\(585\) 1.54252 + 1.20969i 0.0637753 + 0.0500144i
\(586\) −20.7791 −0.858376
\(587\) 7.76708 7.76708i 0.320582 0.320582i −0.528408 0.848990i \(-0.677211\pi\)
0.848990 + 0.528408i \(0.177211\pi\)
\(588\) −4.79558 + 0.0172286i −0.197766 + 0.000710495i
\(589\) 48.4535i 1.99649i
\(590\) 39.4165 + 31.3715i 1.62275 + 1.29154i
\(591\) 1.75154 1.76417i 0.0720487 0.0725683i
\(592\) −9.86325 9.86325i −0.405377 0.405377i
\(593\) −8.01301 8.01301i −0.329055 0.329055i 0.523172 0.852227i \(-0.324748\pi\)
−0.852227 + 0.523172i \(0.824748\pi\)
\(594\) −27.4515 26.8661i −1.12635 1.10233i
\(595\) −0.0597798 0.526007i −0.00245073 0.0215642i
\(596\) 52.4261i 2.14746i
\(597\) −0.0584943 16.2819i −0.00239401 0.666373i
\(598\) 3.24029 3.24029i 0.132505 0.132505i
\(599\) −20.3742 −0.832467 −0.416233 0.909258i \(-0.636650\pi\)
−0.416233 + 0.909258i \(0.636650\pi\)
\(600\) −12.3525 7.66682i −0.504288 0.312997i
\(601\) −32.4833 −1.32502 −0.662511 0.749052i \(-0.730509\pi\)
−0.662511 + 0.749052i \(0.730509\pi\)
\(602\) −8.22998 + 8.22998i −0.335429 + 0.335429i
\(603\) 19.1805 + 18.9069i 0.781092 + 0.769947i
\(604\) 5.27521i 0.214645i
\(605\) 0.115814 + 1.01905i 0.00470849 + 0.0414303i
\(606\) 23.1809 + 23.0149i 0.941660 + 0.934918i
\(607\) −0.0701607 0.0701607i −0.00284774 0.00284774i 0.705681 0.708529i \(-0.250641\pi\)
−0.708529 + 0.705681i \(0.750641\pi\)
\(608\) 27.9740 + 27.9740i 1.13450 + 1.13450i
\(609\) 3.49404 + 3.46902i 0.141586 + 0.140572i
\(610\) 26.0044 + 20.6969i 1.05289 + 0.837992i
\(611\) 1.47386i 0.0596260i
\(612\) −1.40049 1.38051i −0.0566115 0.0558038i
\(613\) −26.6840 + 26.6840i −1.07776 + 1.07776i −0.0810445 + 0.996710i \(0.525826\pi\)
−0.996710 + 0.0810445i \(0.974174\pi\)
\(614\) 31.2239 1.26010
\(615\) −0.121156 + 0.0142103i −0.00488549 + 0.000573014i
\(616\) 5.68266 0.228961
\(617\) 6.37294 6.37294i 0.256565 0.256565i −0.567090 0.823656i \(-0.691931\pi\)
0.823656 + 0.567090i \(0.191931\pi\)
\(618\) 0.0185315 + 5.15824i 0.000745446 + 0.207495i
\(619\) 17.7676i 0.714139i −0.934078 0.357070i \(-0.883776\pi\)
0.934078 0.357070i \(-0.116224\pi\)
\(620\) −56.0879 + 6.37430i −2.25255 + 0.255998i
\(621\) 26.6675 + 26.0987i 1.07013 + 1.04731i
\(622\) −0.608631 0.608631i −0.0244039 0.0244039i
\(623\) 1.41556 + 1.41556i 0.0567130 + 0.0567130i
\(624\) 0.667407 0.672220i 0.0267177 0.0269103i
\(625\) 22.4823 10.9338i 0.899291 0.437351i
\(626\) 32.0594i 1.28135i
\(627\) 31.1575 0.111936i 1.24431 0.00447030i
\(628\) −11.9535 + 11.9535i −0.476995 + 0.476995i
\(629\) −1.76453 −0.0703565
\(630\) −1.75873 14.5431i −0.0700693 0.579409i
\(631\) 17.8248 0.709592 0.354796 0.934944i \(-0.384550\pi\)
0.354796 + 0.934944i \(0.384550\pi\)
\(632\) −13.5857 + 13.5857i −0.540412 + 0.540412i
\(633\) 14.3613 0.0515944i 0.570811 0.00205070i
\(634\) 61.1712i 2.42942i
\(635\) −22.8968 + 28.7685i −0.908633 + 1.14164i
\(636\) −16.9770 + 17.0995i −0.673183 + 0.678038i
\(637\) −0.206632 0.206632i −0.00818705 0.00818705i
\(638\) −14.8587 14.8587i −0.588262 0.588262i
\(639\) 0.0852413 + 11.8633i 0.00337210 + 0.469306i
\(640\) −17.3195 + 21.7609i −0.684614 + 0.860177i
\(641\) 14.8270i 0.585630i 0.956169 + 0.292815i \(0.0945920\pi\)
−0.956169 + 0.292815i \(0.905408\pi\)
\(642\) −0.0568527 15.8250i −0.00224380 0.624562i
\(643\) −32.7229 + 32.7229i −1.29047 + 1.29047i −0.355968 + 0.934498i \(0.615849\pi\)
−0.934498 + 0.355968i \(0.884151\pi\)
\(644\) −19.8823 −0.783474
\(645\) −16.1972 12.7966i −0.637766 0.503865i
\(646\) 2.74747 0.108098
\(647\) −27.0564 + 27.0564i −1.06370 + 1.06370i −0.0658674 + 0.997828i \(0.520981\pi\)
−0.997828 + 0.0658674i \(0.979019\pi\)
\(648\) −10.8359 10.5289i −0.425674 0.413612i
\(649\) 34.9230i 1.37085i
\(650\) −0.715985 3.10932i −0.0280833 0.121958i
\(651\) −11.2070 11.1267i −0.439236 0.436091i
\(652\) −9.90255 9.90255i −0.387814 0.387814i
\(653\) −4.04918 4.04918i −0.158457 0.158457i 0.623426 0.781883i \(-0.285740\pi\)
−0.781883 + 0.623426i \(0.785740\pi\)
\(654\) 7.57410 + 7.51988i 0.296171 + 0.294050i
\(655\) −28.2194 + 3.20709i −1.10262 + 0.125311i
\(656\) 0.0589475i 0.00230151i
\(657\) 25.6467 26.0179i 1.00057 1.01506i
\(658\) −7.78809 + 7.78809i −0.303611 + 0.303611i
\(659\) 11.5870 0.451366 0.225683 0.974201i \(-0.427539\pi\)
0.225683 + 0.974201i \(0.427539\pi\)
\(660\) 4.22849 + 36.0520i 0.164594 + 1.40332i
\(661\) −15.1550 −0.589462 −0.294731 0.955580i \(-0.595230\pi\)
−0.294731 + 0.955580i \(0.595230\pi\)
\(662\) −38.1940 + 38.1940i −1.48445 + 1.48445i
\(663\) −0.000430499 0.119829i −1.67192e−5 0.00465379i
\(664\) 9.21294i 0.357531i
\(665\) 9.29755 + 7.39991i 0.360544 + 0.286956i
\(666\) −48.8257 + 0.350827i −1.89196 + 0.0135943i
\(667\) 14.4343 + 14.4343i 0.558899 + 0.558899i
\(668\) 17.6990 + 17.6990i 0.684793 + 0.684793i
\(669\) −6.66199 + 6.71003i −0.257568 + 0.259425i
\(670\) −4.95017 43.5569i −0.191242 1.68275i
\(671\) 23.0399i 0.889445i
\(672\) −12.8941 + 0.0463233i −0.497400 + 0.00178696i
\(673\) −13.7667 + 13.7667i −0.530666 + 0.530666i −0.920770 0.390105i \(-0.872439\pi\)
0.390105 + 0.920770i \(0.372439\pi\)
\(674\) −10.5045 −0.404617
\(675\) 25.2539 6.10257i 0.972022 0.234888i
\(676\) 35.7573 1.37528
\(677\) 16.3594 16.3594i 0.628742 0.628742i −0.319009 0.947752i \(-0.603350\pi\)
0.947752 + 0.319009i \(0.103350\pi\)
\(678\) −10.7942 + 0.0387793i −0.414549 + 0.00148931i
\(679\) 3.20687i 0.123068i
\(680\) 0.100355 + 0.883031i 0.00384844 + 0.0338627i
\(681\) −2.60148 + 2.62024i −0.0996891 + 0.100408i
\(682\) 47.6587 + 47.6587i 1.82495 + 1.82495i
\(683\) 5.85622 + 5.85622i 0.224082 + 0.224082i 0.810215 0.586133i \(-0.199350\pi\)
−0.586133 + 0.810215i \(0.699350\pi\)
\(684\) 44.1398 0.317157i 1.68773 0.0121268i
\(685\) 12.8526 + 10.2294i 0.491072 + 0.390844i
\(686\) 2.18375i 0.0833758i
\(687\) 0.0389535 + 10.8427i 0.00148617 + 0.413676i
\(688\) −7.05335 + 7.05335i −0.268906 + 0.268906i
\(689\) −1.46829 −0.0559373
\(690\) −7.07492 60.3205i −0.269338 2.29636i
\(691\) 25.9095 0.985642 0.492821 0.870131i \(-0.335966\pi\)
0.492821 + 0.870131i \(0.335966\pi\)
\(692\) 10.7646 10.7646i 0.409210 0.409210i
\(693\) −7.12903 + 7.23222i −0.270809 + 0.274729i
\(694\) 74.2189i 2.81731i
\(695\) −27.3584 + 3.10923i −1.03776 + 0.117940i
\(696\) −5.86560 5.82361i −0.222335 0.220743i
\(697\) 0.00527284 + 0.00527284i 0.000199723 + 0.000199723i
\(698\) 14.4698 + 14.4698i 0.547691 + 0.547691i
\(699\) 4.64849 + 4.61521i 0.175822 + 0.174563i
\(700\) −7.34272 + 11.7360i −0.277529 + 0.443579i
\(701\) 37.9089i 1.43180i 0.698204 + 0.715899i \(0.253983\pi\)
−0.698204 + 0.715899i \(0.746017\pi\)
\(702\) −0.0357368 3.31567i −0.00134880 0.125142i
\(703\) 28.0065 28.0065i 1.05628 1.05628i
\(704\) 42.3598 1.59649
\(705\) −15.3276 12.1095i −0.577269 0.456070i
\(706\) 45.0542 1.69564
\(707\) 6.10679 6.10679i 0.229669 0.229669i
\(708\) −0.177743 49.4749i −0.00668001 1.85938i
\(709\) 16.6841i 0.626586i −0.949656 0.313293i \(-0.898568\pi\)
0.949656 0.313293i \(-0.101432\pi\)
\(710\) 12.0251 15.1088i 0.451293 0.567023i
\(711\) −0.246699 34.3339i −0.00925194 1.28762i
\(712\) −2.37636 2.37636i −0.0890578 0.0890578i
\(713\) −46.2975 46.2975i −1.73385 1.73385i
\(714\) −0.630921 + 0.635470i −0.0236116 + 0.0237819i
\(715\) −1.37743 + 1.73066i −0.0515129 + 0.0647229i
\(716\) 40.5129i 1.51404i
\(717\) −3.61167 + 0.0129753i −0.134880 + 0.000484570i
\(718\) 42.1016 42.1016i 1.57122 1.57122i
\(719\) 13.0709 0.487464 0.243732 0.969843i \(-0.421628\pi\)
0.243732 + 0.969843i \(0.421628\pi\)
\(720\) −1.50728 12.4638i −0.0561731 0.464500i
\(721\) 1.36377 0.0507895
\(722\) −14.2688 + 14.2688i −0.531031 + 0.531031i
\(723\) 9.41686 0.0338310i 0.350217 0.00125819i
\(724\) 27.2367i 1.01224i
\(725\) 13.8509 3.18946i 0.514409 0.118454i
\(726\) 1.22231 1.23112i 0.0453640 0.0456911i
\(727\) 19.4878 + 19.4878i 0.722761 + 0.722761i 0.969167 0.246406i \(-0.0792495\pi\)
−0.246406 + 0.969167i \(0.579250\pi\)
\(728\) 0.346882 + 0.346882i 0.0128563 + 0.0128563i
\(729\) 26.9937 0.581953i 0.999768 0.0215538i
\(730\) −59.0838 + 6.71478i −2.18679 + 0.248525i
\(731\) 1.26184i 0.0466709i
\(732\) −0.117264 32.6403i −0.00433418 1.20642i
\(733\) 24.5624 24.5624i 0.907232 0.907232i −0.0888162 0.996048i \(-0.528308\pi\)
0.996048 + 0.0888162i \(0.0283084\pi\)
\(734\) 49.1774 1.81517
\(735\) −3.84662 + 0.451165i −0.141885 + 0.0166415i
\(736\) −53.4585 −1.97051
\(737\) −21.4886 + 21.4886i −0.791543 + 0.791543i
\(738\) 0.146951 + 0.144855i 0.00540935 + 0.00533217i
\(739\) 25.3925i 0.934079i −0.884236 0.467040i \(-0.845321\pi\)
0.884236 0.467040i \(-0.154679\pi\)
\(740\) 36.1036 + 28.7348i 1.32720 + 1.05631i
\(741\) 1.90875 + 1.89509i 0.0701198 + 0.0696178i
\(742\) 7.75865 + 7.75865i 0.284829 + 0.284829i
\(743\) −14.4447 14.4447i −0.529923 0.529923i 0.390626 0.920549i \(-0.372258\pi\)
−0.920549 + 0.390626i \(0.872258\pi\)
\(744\) 18.8137 + 18.6790i 0.689742 + 0.684804i
\(745\) −4.78108 42.0691i −0.175165 1.54129i
\(746\) 72.0445i 2.63774i
\(747\) 11.7251 + 11.5578i 0.429000 + 0.422879i
\(748\) 1.56902 1.56902i 0.0573690 0.0573690i
\(749\) −4.18391 −0.152877
\(750\) −38.2184 18.1008i −1.39554 0.660946i
\(751\) 27.4358 1.00115 0.500573 0.865694i \(-0.333123\pi\)
0.500573 + 0.865694i \(0.333123\pi\)
\(752\) −6.67463 + 6.67463i −0.243399 + 0.243399i
\(753\) 0.145251 + 40.4307i 0.00529325 + 1.47338i
\(754\) 1.81402i 0.0660627i
\(755\) 0.481081 + 4.23306i 0.0175083 + 0.154057i
\(756\) −10.0628 + 10.2821i −0.365980 + 0.373955i
\(757\) −11.9760 11.9760i −0.435274 0.435274i 0.455144 0.890418i \(-0.349588\pi\)
−0.890418 + 0.455144i \(0.849588\pi\)
\(758\) −57.8245 57.8245i −2.10028 2.10028i
\(759\) −29.6641 + 29.8780i −1.07674 + 1.08450i
\(760\) −15.6082 12.4226i −0.566170 0.450614i
\(761\) 41.1635i 1.49217i −0.665848 0.746087i \(-0.731930\pi\)
0.665848 0.746087i \(-0.268070\pi\)
\(762\) 62.1937 0.223437i 2.25304 0.00809426i
\(763\) 1.99533 1.99533i 0.0722357 0.0722357i
\(764\) −17.6614 −0.638969
\(765\) −1.24971 0.980062i −0.0451835 0.0354342i
\(766\) −15.3007 −0.552836
\(767\) 2.13178 2.13178i 0.0769740 0.0769740i
\(768\) 3.69569 0.0132771i 0.133357 0.000479097i
\(769\) 3.96520i 0.142989i 0.997441 + 0.0714944i \(0.0227768\pi\)
−0.997441 + 0.0714944i \(0.977223\pi\)
\(770\) 16.4236 1.86651i 0.591864 0.0672644i
\(771\) −18.8585 + 18.9945i −0.679174 + 0.684071i
\(772\) −20.9410 20.9410i −0.753684 0.753684i
\(773\) −5.99943 5.99943i −0.215785 0.215785i 0.590935 0.806719i \(-0.298759\pi\)
−0.806719 + 0.590935i \(0.798759\pi\)
\(774\) 0.250881 + 34.9160i 0.00901774 + 1.25503i
\(775\) −44.4262 + 10.2301i −1.59583 + 0.367474i
\(776\) 5.38352i 0.193257i
\(777\) 0.0463770 + 12.9090i 0.00166377 + 0.463109i
\(778\) 14.2104 14.2104i 0.509468 0.509468i
\(779\) −0.167380 −0.00599702
\(780\) −1.94258 + 2.45881i −0.0695554 + 0.0880395i
\(781\) −13.3864 −0.479002
\(782\) −2.62521 + 2.62521i −0.0938774 + 0.0938774i
\(783\) 14.7701 0.159195i 0.527841 0.00568916i
\(784\) 1.87154i 0.0668406i
\(785\) −8.50188 + 10.6821i −0.303445 + 0.381261i
\(786\) 34.0920 + 33.8479i 1.21602 + 1.20731i
\(787\) 15.8108 + 15.8108i 0.563593 + 0.563593i 0.930326 0.366733i \(-0.119524\pi\)
−0.366733 + 0.930326i \(0.619524\pi\)
\(788\) 2.81001 + 2.81001i 0.100103 + 0.100103i
\(789\) −31.6030 31.3768i −1.12510 1.11704i
\(790\) −34.8021 + 43.7267i −1.23820 + 1.55573i
\(791\) 2.85385i 0.101471i
\(792\) 11.9678 12.1411i 0.425258 0.431414i
\(793\) 1.40641 1.40641i 0.0499429 0.0499429i
\(794\) 67.7082 2.40287
\(795\) −12.0637 + 15.2696i −0.427856 + 0.541558i
\(796\) 26.0274 0.922515
\(797\) 8.46554 8.46554i 0.299865 0.299865i −0.541096 0.840961i \(-0.681990\pi\)
0.840961 + 0.541096i \(0.181990\pi\)
\(798\) −0.0722114 20.1000i −0.00255625 0.711534i
\(799\) 1.19409i 0.0422438i
\(800\) −19.7427 + 31.5551i −0.698010 + 1.11564i
\(801\) 6.00554 0.0431515i 0.212195 0.00152468i
\(802\) 39.7638 + 39.7638i 1.40411 + 1.40411i
\(803\) 29.1488 + 29.1488i 1.02864 + 1.02864i
\(804\) −30.3333 + 30.5520i −1.06977 + 1.07749i
\(805\) −15.9545 + 1.81320i −0.562321 + 0.0639069i
\(806\) 5.81839i 0.204944i
\(807\) −49.3848 + 0.177420i −1.73843 + 0.00624547i
\(808\) −10.2517 + 10.2517i −0.360655 + 0.360655i
\(809\) 25.5350 0.897764 0.448882 0.893591i \(-0.351822\pi\)
0.448882 + 0.893591i \(0.351822\pi\)
\(810\) −34.7753 26.8705i −1.22188 0.944133i
\(811\) −1.94760 −0.0683895 −0.0341947 0.999415i \(-0.510887\pi\)
−0.0341947 + 0.999415i \(0.510887\pi\)
\(812\) −5.56539 + 5.56539i −0.195307 + 0.195307i
\(813\) −5.40767 + 0.0194276i −0.189655 + 0.000681355i
\(814\) 55.0942i 1.93105i
\(815\) −8.84933 7.04317i −0.309978 0.246712i
\(816\) −0.540719 + 0.544618i −0.0189289 + 0.0190654i
\(817\) −20.0278 20.0278i −0.700685 0.700685i
\(818\) −16.9078 16.9078i −0.591167 0.591167i
\(819\) −0.876642 + 0.00629893i −0.0306324 + 0.000220102i
\(820\) −0.0220197 0.193753i −0.000768962 0.00676615i
\(821\) 21.6742i 0.756434i −0.925717 0.378217i \(-0.876537\pi\)
0.925717 0.378217i \(-0.123463\pi\)
\(822\) −0.0998224 27.7856i −0.00348171 0.969133i
\(823\) 8.35207 8.35207i 0.291135 0.291135i −0.546394 0.837528i \(-0.684000\pi\)
0.837528 + 0.546394i \(0.184000\pi\)
\(824\) −2.28943 −0.0797559
\(825\) 6.68095 + 28.5441i 0.232601 + 0.993778i
\(826\) −22.5292 −0.783892
\(827\) −14.1747 + 14.1747i −0.492902 + 0.492902i −0.909219 0.416318i \(-0.863320\pi\)
0.416318 + 0.909219i \(0.363320\pi\)
\(828\) −41.8727 + 42.4788i −1.45518 + 1.47624i
\(829\) 19.3836i 0.673219i −0.941644 0.336610i \(-0.890720\pi\)
0.941644 0.336610i \(-0.109280\pi\)
\(830\) −3.02605 26.6265i −0.105036 0.924218i
\(831\) −21.2888 21.1364i −0.738500 0.733213i
\(832\) 2.58573 + 2.58573i 0.0896442 + 0.0896442i
\(833\) 0.167409 + 0.167409i 0.00580037 + 0.00580037i
\(834\) 33.0517 + 32.8151i 1.14449 + 1.13629i
\(835\) 15.8165 + 12.5884i 0.547353 + 0.435638i
\(836\) 49.8066i 1.72260i
\(837\) −47.3745 + 0.510610i −1.63750 + 0.0176493i
\(838\) −9.06346 + 9.06346i −0.313092 + 0.313092i
\(839\) 26.2528 0.906346 0.453173 0.891423i \(-0.350292\pi\)
0.453173 + 0.891423i \(0.350292\pi\)
\(840\) 6.45749 0.757391i 0.222805 0.0261325i
\(841\) −20.9192 −0.721352
\(842\) 41.5131 41.5131i 1.43063 1.43063i
\(843\) −0.0791386 22.0282i −0.00272568 0.758693i
\(844\) 22.9572i 0.790221i
\(845\) 28.6932 3.26094i 0.987077 0.112180i
\(846\) 0.237410 + 33.0412i 0.00816234 + 1.13598i
\(847\) −0.324327 0.324327i −0.0111440 0.0111440i
\(848\) 6.64940 + 6.64940i 0.228341 + 0.228341i
\(849\) 34.2179 34.4646i 1.17435 1.18282i
\(850\) 0.580076 + 2.51910i 0.0198964 + 0.0864045i
\(851\) 53.5206i 1.83466i
\(852\) −18.9643 + 0.0681311i −0.649707 + 0.00233413i
\(853\) 29.8920 29.8920i 1.02348 1.02348i 0.0237636 0.999718i \(-0.492435\pi\)
0.999718 0.0237636i \(-0.00756489\pi\)
\(854\) −14.8633 −0.508612
\(855\) 35.3908 4.27990i 1.21034 0.146369i
\(856\) 7.02373 0.240066
\(857\) 5.92367 5.92367i 0.202349 0.202349i −0.598657 0.801006i \(-0.704299\pi\)
0.801006 + 0.598657i \(0.204299\pi\)
\(858\) 3.74145 0.0134415i 0.127731 0.000458885i
\(859\) 10.3620i 0.353548i 0.984252 + 0.176774i \(0.0565661\pi\)
−0.984252 + 0.176774i \(0.943434\pi\)
\(860\) 20.5487 25.8182i 0.700705 0.880394i
\(861\) 0.0384368 0.0387139i 0.00130992 0.00131937i
\(862\) 6.45633 + 6.45633i 0.219904 + 0.219904i
\(863\) −13.2818 13.2818i −0.452118 0.452118i 0.443939 0.896057i \(-0.353581\pi\)
−0.896057 + 0.443939i \(0.853581\pi\)
\(864\) −27.0563 + 27.6459i −0.920474 + 0.940532i
\(865\) 7.65632 9.61971i 0.260323 0.327080i
\(866\) 6.82129i 0.231797i
\(867\) −0.105434 29.3476i −0.00358073 0.996696i
\(868\) 17.8507 17.8507i 0.605894 0.605894i
\(869\) 38.7419 1.31423
\(870\) −18.8651 14.9043i −0.639586 0.505303i
\(871\) −2.62342 −0.0888913
\(872\) −3.34965 + 3.34965i −0.113433 + 0.113433i
\(873\) 6.85150 + 6.75374i 0.231888 + 0.228580i
\(874\) 83.3342i 2.81882i
\(875\) −4.82184 + 10.0871i −0.163008 + 0.341007i
\(876\) 41.4430 + 41.1463i 1.40023 + 1.39020i
\(877\) 4.84197 + 4.84197i 0.163502 + 0.163502i 0.784116 0.620614i \(-0.213117\pi\)
−0.620614 + 0.784116i \(0.713117\pi\)
\(878\) −42.6227 42.6227i −1.43845 1.43845i
\(879\) 11.6957 + 11.6119i 0.394485 + 0.391660i
\(880\) 14.0755 1.59966i 0.474485 0.0539245i
\(881\) 17.0394i 0.574073i 0.957920 + 0.287036i \(0.0926701\pi\)
−0.957920 + 0.287036i \(0.907330\pi\)
\(882\) 4.66559 + 4.59902i 0.157099 + 0.154857i
\(883\) 12.2389 12.2389i 0.411871 0.411871i −0.470519 0.882390i \(-0.655933\pi\)
0.882390 + 0.470519i \(0.155933\pi\)
\(884\) 0.191553 0.00644262
\(885\) −4.65457 39.6847i −0.156462 1.33399i
\(886\) 37.9983 1.27658
\(887\) −41.0767 + 41.0767i −1.37922 + 1.37922i −0.533287 + 0.845934i \(0.679043\pi\)
−0.845934 + 0.533287i \(0.820957\pi\)
\(888\) −0.0778552 21.6710i −0.00261265 0.727231i
\(889\) 16.4432i 0.551487i
\(890\) −7.64848 6.08742i −0.256378 0.204051i
\(891\) 0.437785 + 30.4624i 0.0146664 + 1.02053i
\(892\) −10.6879 10.6879i −0.357858 0.357858i
\(893\) −18.9525 18.9525i −0.634220 0.634220i
\(894\) −50.4599 + 50.8238i −1.68763 + 1.69980i
\(895\) 3.69464 + 32.5094i 0.123498 + 1.08667i
\(896\) 12.4379i 0.415520i
\(897\) −3.63458 + 0.0130576i −0.121355 + 0.000435980i
\(898\) −52.7879 + 52.7879i −1.76155 + 1.76155i
\(899\) −25.9188 −0.864441
\(900\) 9.61009 + 40.4040i 0.320336 + 1.34680i
\(901\) 1.18958 0.0396305
\(902\) −0.164635 + 0.164635i −0.00548173 + 0.00548173i
\(903\) 9.23144 0.0331649i 0.307203 0.00110366i
\(904\) 4.79089i 0.159343i
\(905\) 2.48389 + 21.8559i 0.0825673 + 0.726515i
\(906\) 5.07736 5.11398i 0.168684 0.169901i
\(907\) 24.8992 + 24.8992i 0.826765 + 0.826765i 0.987068 0.160303i \(-0.0512470\pi\)
−0.160303 + 0.987068i \(0.551247\pi\)
\(908\) −4.17359 4.17359i −0.138505 0.138505i
\(909\) −0.186158 25.9082i −0.00617448 0.859322i
\(910\) 1.11647 + 0.888595i 0.0370105 + 0.0294566i
\(911\) 23.4322i 0.776342i 0.921587 + 0.388171i \(0.126893\pi\)
−0.921587 + 0.388171i \(0.873107\pi\)
\(912\) −0.0618874 17.2264i −0.00204930 0.570422i
\(913\) −13.1361 + 13.1361i −0.434740 + 0.434740i
\(914\) −28.7526 −0.951050
\(915\) −3.07078 26.1814i −0.101517 0.865529i
\(916\) −17.3326 −0.572685
\(917\) 8.98121 8.98121i 0.296586 0.296586i
\(918\) 0.0289532 + 2.68628i 0.000955598 + 0.0886605i
\(919\) 31.9950i 1.05542i 0.849425 + 0.527710i \(0.176949\pi\)
−0.849425 + 0.527710i \(0.823051\pi\)
\(920\) 26.7835 3.04390i 0.883026 0.100354i
\(921\) −17.5746 17.4488i −0.579103 0.574957i
\(922\) 39.6195 + 39.6195i 1.30480 + 1.30480i
\(923\) −0.817134 0.817134i −0.0268963 0.0268963i
\(924\) −11.5199 11.4375i −0.378978 0.376265i
\(925\) 31.5917 + 19.7656i 1.03873 + 0.649889i
\(926\) 40.8180i 1.34136i
\(927\) 2.87214 2.91371i 0.0943333 0.0956987i
\(928\) −14.9639 + 14.9639i −0.491214 + 0.491214i
\(929\) −49.7858 −1.63342 −0.816709 0.577050i \(-0.804204\pi\)
−0.816709 + 0.577050i \(0.804204\pi\)
\(930\) 60.5089 + 47.8049i 1.98417 + 1.56758i
\(931\) −5.31419 −0.174166
\(932\) −7.40423 + 7.40423i −0.242534 + 0.242534i
\(933\) 0.00245264 + 0.682692i 8.02958e−5 + 0.0223503i
\(934\) 60.7340i 1.98728i
\(935\) 1.11596 1.40214i 0.0364959 0.0458549i
\(936\) 1.47166 0.0105743i 0.0481027 0.000345632i
\(937\) 18.0919 + 18.0919i 0.591035 + 0.591035i 0.937911 0.346876i \(-0.112757\pi\)
−0.346876 + 0.937911i \(0.612757\pi\)
\(938\) 13.8626 + 13.8626i 0.452628 + 0.452628i
\(939\) 17.9157 18.0449i 0.584656 0.588872i
\(940\) 19.4454 24.4319i 0.634238 0.796882i
\(941\) 61.0502i 1.99018i −0.0989766 0.995090i \(-0.531557\pi\)
0.0989766 0.995090i \(-0.468443\pi\)
\(942\) 23.0933 0.0829648i 0.752419 0.00270314i
\(943\) 0.159932 0.159932i 0.00520811 0.00520811i
\(944\) −19.3082 −0.628430
\(945\) −7.13715 + 9.16849i −0.232171 + 0.298251i
\(946\) −39.3986 −1.28096
\(947\) 28.1297 28.1297i 0.914093 0.914093i −0.0824986 0.996591i \(-0.526290\pi\)
0.996591 + 0.0824986i \(0.0262900\pi\)
\(948\) 54.8851 0.197180i 1.78259 0.00640411i
\(949\) 3.55861i 0.115517i
\(950\) −49.1899 30.7761i −1.59593 0.998507i
\(951\) 34.1841 34.4306i 1.10850 1.11649i
\(952\) −0.281037 0.281037i −0.00910845 0.00910845i
\(953\) −16.4406 16.4406i −0.532564 0.532564i 0.388771 0.921335i \(-0.372900\pi\)
−0.921335 + 0.388771i \(0.872900\pi\)
\(954\) 32.9163 0.236513i 1.06571 0.00765740i
\(955\) −14.1723 + 1.61066i −0.458606 + 0.0521198i
\(956\) 5.77342i 0.186726i
\(957\) 0.0598771 + 16.6668i 0.00193555 + 0.538761i
\(958\) −41.6493 + 41.6493i −1.34563 + 1.34563i
\(959\) −7.34614 −0.237219
\(960\) 48.1355 5.64575i 1.55357 0.182216i
\(961\) 52.1335 1.68173
\(962\) 3.36307 3.36307i 0.108430 0.108430i
\(963\) −8.81142 + 8.93897i −0.283944 + 0.288054i
\(964\) 15.0533i 0.484834i
\(965\) −18.7138 14.8943i −0.602417 0.479463i
\(966\) 19.2747 + 19.1367i 0.620152 + 0.615712i
\(967\) −3.29391 3.29391i −0.105925 0.105925i 0.652158 0.758083i \(-0.273864\pi\)
−0.758083 + 0.652158i \(0.773864\pi\)
\(968\) 0.544462 + 0.544462i 0.0174997 + 0.0174997i
\(969\) −1.54643 1.53536i −0.0496785 0.0493228i
\(970\) −1.76825 15.5590i −0.0567752 0.499569i
\(971\) 32.3161i 1.03707i −0.855056 0.518536i \(-0.826477\pi\)
0.855056 0.518536i \(-0.173523\pi\)
\(972\) 0.775246 + 43.1535i 0.0248660 + 1.38415i
\(973\) 8.70717 8.70717i 0.279139 0.279139i
\(974\) −88.4809 −2.83511
\(975\) −1.33457 + 2.15021i −0.0427406 + 0.0688620i
\(976\) −12.7383 −0.407744
\(977\) −8.42742 + 8.42742i −0.269617 + 0.269617i −0.828946 0.559329i \(-0.811059\pi\)
0.559329 + 0.828946i \(0.311059\pi\)
\(978\) 0.0687302 + 19.1311i 0.00219775 + 0.611744i
\(979\) 6.77655i 0.216580i
\(980\) −0.699108 6.15151i −0.0223322 0.196503i
\(981\) −0.0608251 8.46523i −0.00194200 0.270274i
\(982\) 4.23900 + 4.23900i 0.135272 + 0.135272i
\(983\) 43.2280 + 43.2280i 1.37876 + 1.37876i 0.846718 + 0.532042i \(0.178575\pi\)
0.532042 + 0.846718i \(0.321425\pi\)
\(984\) −0.0645255 + 0.0649908i −0.00205700 + 0.00207183i
\(985\) 2.51114 + 1.99862i 0.0800117 + 0.0636812i
\(986\) 1.46968i 0.0468041i
\(987\) 8.73578 0.0313841i 0.278063 0.000998968i
\(988\) −3.04031 + 3.04031i −0.0967251 + 0.0967251i
\(989\) 38.2733 1.21702
\(990\) 30.6006 39.0200i 0.972551 1.24014i
\(991\) −25.2971 −0.803590 −0.401795 0.915730i \(-0.631614\pi\)
−0.401795 + 0.915730i \(0.631614\pi\)
\(992\) 47.9961 47.9961i 1.52388 1.52388i
\(993\) 42.8417 0.153913i 1.35954 0.00488428i
\(994\) 8.63571i 0.273908i
\(995\) 20.8855 2.37360i 0.662115 0.0752483i
\(996\) −18.5428 + 18.6765i −0.587552 + 0.591789i
\(997\) −23.3279 23.3279i −0.738803 0.738803i 0.233543 0.972346i \(-0.424968\pi\)
−0.972346 + 0.233543i \(0.924968\pi\)
\(998\) 46.8108 + 46.8108i 1.48177 + 1.48177i
\(999\) 27.6779 + 27.0877i 0.875691 + 0.857016i
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 105.2.j.a.92.11 yes 24
3.2 odd 2 inner 105.2.j.a.92.2 yes 24
5.2 odd 4 525.2.j.b.218.11 24
5.3 odd 4 inner 105.2.j.a.8.2 24
5.4 even 2 525.2.j.b.407.2 24
7.2 even 3 735.2.y.j.557.2 48
7.3 odd 6 735.2.y.g.422.11 48
7.4 even 3 735.2.y.j.422.11 48
7.5 odd 6 735.2.y.g.557.2 48
7.6 odd 2 735.2.j.h.197.11 24
15.2 even 4 525.2.j.b.218.2 24
15.8 even 4 inner 105.2.j.a.8.11 yes 24
15.14 odd 2 525.2.j.b.407.11 24
21.2 odd 6 735.2.y.j.557.11 48
21.5 even 6 735.2.y.g.557.11 48
21.11 odd 6 735.2.y.j.422.2 48
21.17 even 6 735.2.y.g.422.2 48
21.20 even 2 735.2.j.h.197.2 24
35.3 even 12 735.2.y.g.128.11 48
35.13 even 4 735.2.j.h.638.2 24
35.18 odd 12 735.2.y.j.128.11 48
35.23 odd 12 735.2.y.j.263.2 48
35.33 even 12 735.2.y.g.263.2 48
105.23 even 12 735.2.y.j.263.11 48
105.38 odd 12 735.2.y.g.128.2 48
105.53 even 12 735.2.y.j.128.2 48
105.68 odd 12 735.2.y.g.263.11 48
105.83 odd 4 735.2.j.h.638.11 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.j.a.8.2 24 5.3 odd 4 inner
105.2.j.a.8.11 yes 24 15.8 even 4 inner
105.2.j.a.92.2 yes 24 3.2 odd 2 inner
105.2.j.a.92.11 yes 24 1.1 even 1 trivial
525.2.j.b.218.2 24 15.2 even 4
525.2.j.b.218.11 24 5.2 odd 4
525.2.j.b.407.2 24 5.4 even 2
525.2.j.b.407.11 24 15.14 odd 2
735.2.j.h.197.2 24 21.20 even 2
735.2.j.h.197.11 24 7.6 odd 2
735.2.j.h.638.2 24 35.13 even 4
735.2.j.h.638.11 24 105.83 odd 4
735.2.y.g.128.2 48 105.38 odd 12
735.2.y.g.128.11 48 35.3 even 12
735.2.y.g.263.2 48 35.33 even 12
735.2.y.g.263.11 48 105.68 odd 12
735.2.y.g.422.2 48 21.17 even 6
735.2.y.g.422.11 48 7.3 odd 6
735.2.y.g.557.2 48 7.5 odd 6
735.2.y.g.557.11 48 21.5 even 6
735.2.y.j.128.2 48 105.53 even 12
735.2.y.j.128.11 48 35.18 odd 12
735.2.y.j.263.2 48 35.23 odd 12
735.2.y.j.263.11 48 105.23 even 12
735.2.y.j.422.2 48 21.11 odd 6
735.2.y.j.422.11 48 7.4 even 3
735.2.y.j.557.2 48 7.2 even 3
735.2.y.j.557.11 48 21.2 odd 6