Properties

Label 315.2.bl.i.146.4
Level $315$
Weight $2$
Character 315.146
Analytic conductor $2.515$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(41,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bl (of order \(6\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 146.4
Character \(\chi\) \(=\) 315.146
Dual form 315.2.bl.i.41.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13192 - 0.653515i) q^{2} +(-0.957531 - 1.44331i) q^{3} +(-0.145837 - 0.252598i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.140627 + 2.25947i) q^{6} +(0.709992 + 2.54871i) q^{7} +2.99529i q^{8} +(-1.16627 + 2.76402i) q^{9} +O(q^{10})\) \(q+(-1.13192 - 0.653515i) q^{2} +(-0.957531 - 1.44331i) q^{3} +(-0.145837 - 0.252598i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.140627 + 2.25947i) q^{6} +(0.709992 + 2.54871i) q^{7} +2.99529i q^{8} +(-1.16627 + 2.76402i) q^{9} -1.30703i q^{10} +(4.98971 + 2.88081i) q^{11} +(-0.224932 + 0.452359i) q^{12} +(3.14058 - 1.81321i) q^{13} +(0.861964 - 3.34892i) q^{14} +(0.771174 - 1.55090i) q^{15} +(1.66579 - 2.88523i) q^{16} -4.92433 q^{17} +(3.12645 - 2.36648i) q^{18} -3.02122i q^{19} +(0.145837 - 0.252598i) q^{20} +(2.99873 - 3.46520i) q^{21} +(-3.76530 - 6.52169i) q^{22} +(-5.93663 + 3.42751i) q^{23} +(4.32312 - 2.86808i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.73984 q^{26} +(5.10607 - 0.963357i) q^{27} +(0.540255 - 0.551040i) q^{28} +(7.16276 + 4.13542i) q^{29} +(-1.88644 + 1.25152i) q^{30} +(3.18657 - 1.83977i) q^{31} +(1.41691 - 0.818053i) q^{32} +(-0.619911 - 9.96014i) q^{33} +(5.57395 + 3.21812i) q^{34} +(-1.85225 + 1.88922i) q^{35} +(0.868272 - 0.108501i) q^{36} +2.80891 q^{37} +(-1.97441 + 3.41978i) q^{38} +(-5.62422 - 2.79661i) q^{39} +(-2.59399 + 1.49764i) q^{40} +(5.57799 + 9.66136i) q^{41} +(-5.65888 + 1.96262i) q^{42} +(-0.136193 + 0.235894i) q^{43} -1.68052i q^{44} +(-2.97685 + 0.371994i) q^{45} +8.95972 q^{46} +(1.88231 - 3.26026i) q^{47} +(-5.75931 + 0.358455i) q^{48} +(-5.99182 + 3.61912i) q^{49} +(1.13192 - 0.653515i) q^{50} +(4.71520 + 7.10732i) q^{51} +(-0.916027 - 0.528869i) q^{52} +3.51435i q^{53} +(-6.40923 - 2.24645i) q^{54} +5.76162i q^{55} +(-7.63411 + 2.12663i) q^{56} +(-4.36055 + 2.89291i) q^{57} +(-5.40512 - 9.36194i) q^{58} +(-4.33885 - 7.51511i) q^{59} +(-0.504220 + 0.0313822i) q^{60} +(7.81138 + 4.50990i) q^{61} -4.80926 q^{62} +(-7.87273 - 1.01004i) q^{63} -8.80159 q^{64} +(3.14058 + 1.81321i) q^{65} +(-5.80741 + 11.6792i) q^{66} +(1.65886 + 2.87323i) q^{67} +(0.718152 + 1.24388i) q^{68} +(10.6315 + 5.28642i) q^{69} +(3.33124 - 0.927980i) q^{70} -6.95342i q^{71} +(-8.27904 - 3.49330i) q^{72} +2.88131i q^{73} +(-3.17946 - 1.83566i) q^{74} +(1.72871 - 0.107593i) q^{75} +(-0.763154 + 0.440607i) q^{76} +(-3.79969 + 14.7627i) q^{77} +(4.53855 + 6.84105i) q^{78} +(5.15417 - 8.92729i) q^{79} +3.33158 q^{80} +(-6.27964 - 6.44718i) q^{81} -14.5812i q^{82} +(1.69417 - 2.93439i) q^{83} +(-1.31263 - 0.252116i) q^{84} +(-2.46216 - 4.26459i) q^{85} +(0.308320 - 0.178009i) q^{86} +(-0.889887 - 14.2979i) q^{87} +(-8.62884 + 14.9456i) q^{88} -4.68832 q^{89} +(3.61266 + 1.52435i) q^{90} +(6.85113 + 6.71705i) q^{91} +(1.73157 + 0.999720i) q^{92} +(-5.70659 - 2.83756i) q^{93} +(-4.26126 + 2.46024i) q^{94} +(2.61645 - 1.51061i) q^{95} +(-2.53744 - 1.26172i) q^{96} +(4.00495 + 2.31226i) q^{97} +(9.14742 - 0.180814i) q^{98} +(-13.7819 + 10.4319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13192 0.653515i −0.800389 0.462105i 0.0432184 0.999066i \(-0.486239\pi\)
−0.843607 + 0.536961i \(0.819572\pi\)
\(3\) −0.957531 1.44331i −0.552831 0.833293i
\(4\) −0.145837 0.252598i −0.0729187 0.126299i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0.140627 + 2.25947i 0.0574109 + 0.922424i
\(7\) 0.709992 + 2.54871i 0.268352 + 0.963321i
\(8\) 2.99529i 1.05899i
\(9\) −1.16627 + 2.76402i −0.388756 + 0.921341i
\(10\) 1.30703i 0.413319i
\(11\) 4.98971 + 2.88081i 1.50445 + 0.868596i 0.999987 + 0.00516464i \(0.00164396\pi\)
0.504466 + 0.863432i \(0.331689\pi\)
\(12\) −0.224932 + 0.452359i −0.0649324 + 0.130585i
\(13\) 3.14058 1.81321i 0.871039 0.502895i 0.00334565 0.999994i \(-0.498935\pi\)
0.867693 + 0.497100i \(0.165602\pi\)
\(14\) 0.861964 3.34892i 0.230369 0.895038i
\(15\) 0.771174 1.55090i 0.199116 0.400441i
\(16\) 1.66579 2.88523i 0.416447 0.721307i
\(17\) −4.92433 −1.19433 −0.597163 0.802120i \(-0.703705\pi\)
−0.597163 + 0.802120i \(0.703705\pi\)
\(18\) 3.12645 2.36648i 0.736912 0.557785i
\(19\) 3.02122i 0.693116i −0.938029 0.346558i \(-0.887350\pi\)
0.938029 0.346558i \(-0.112650\pi\)
\(20\) 0.145837 0.252598i 0.0326103 0.0564826i
\(21\) 2.99873 3.46520i 0.654376 0.756169i
\(22\) −3.76530 6.52169i −0.802765 1.39043i
\(23\) −5.93663 + 3.42751i −1.23787 + 0.714686i −0.968659 0.248394i \(-0.920097\pi\)
−0.269214 + 0.963080i \(0.586764\pi\)
\(24\) 4.32312 2.86808i 0.882452 0.585444i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −4.73984 −0.929560
\(27\) 5.10607 0.963357i 0.982663 0.185398i
\(28\) 0.540255 0.551040i 0.102099 0.104137i
\(29\) 7.16276 + 4.13542i 1.33009 + 0.767929i 0.985313 0.170755i \(-0.0546208\pi\)
0.344778 + 0.938684i \(0.387954\pi\)
\(30\) −1.88644 + 1.25152i −0.344416 + 0.228495i
\(31\) 3.18657 1.83977i 0.572325 0.330432i −0.185753 0.982597i \(-0.559472\pi\)
0.758077 + 0.652165i \(0.226139\pi\)
\(32\) 1.41691 0.818053i 0.250476 0.144613i
\(33\) −0.619911 9.96014i −0.107913 1.73384i
\(34\) 5.57395 + 3.21812i 0.955924 + 0.551903i
\(35\) −1.85225 + 1.88922i −0.313087 + 0.319337i
\(36\) 0.868272 0.108501i 0.144712 0.0180836i
\(37\) 2.80891 0.461782 0.230891 0.972980i \(-0.425836\pi\)
0.230891 + 0.972980i \(0.425836\pi\)
\(38\) −1.97441 + 3.41978i −0.320292 + 0.554762i
\(39\) −5.62422 2.79661i −0.900596 0.447815i
\(40\) −2.59399 + 1.49764i −0.410146 + 0.236798i
\(41\) 5.57799 + 9.66136i 0.871136 + 1.50885i 0.860823 + 0.508905i \(0.169949\pi\)
0.0103128 + 0.999947i \(0.496717\pi\)
\(42\) −5.65888 + 1.96262i −0.873184 + 0.302839i
\(43\) −0.136193 + 0.235894i −0.0207693 + 0.0359735i −0.876223 0.481905i \(-0.839945\pi\)
0.855454 + 0.517879i \(0.173278\pi\)
\(44\) 1.68052i 0.253348i
\(45\) −2.97685 + 0.371994i −0.443762 + 0.0554536i
\(46\) 8.95972 1.32104
\(47\) 1.88231 3.26026i 0.274564 0.475558i −0.695461 0.718564i \(-0.744800\pi\)
0.970025 + 0.243005i \(0.0781333\pi\)
\(48\) −5.75931 + 0.358455i −0.831285 + 0.0517385i
\(49\) −5.99182 + 3.61912i −0.855975 + 0.517017i
\(50\) 1.13192 0.653515i 0.160078 0.0924209i
\(51\) 4.71520 + 7.10732i 0.660260 + 0.995223i
\(52\) −0.916027 0.528869i −0.127030 0.0733409i
\(53\) 3.51435i 0.482733i 0.970434 + 0.241367i \(0.0775957\pi\)
−0.970434 + 0.241367i \(0.922404\pi\)
\(54\) −6.40923 2.24645i −0.872186 0.305703i
\(55\) 5.76162i 0.776896i
\(56\) −7.63411 + 2.12663i −1.02015 + 0.284183i
\(57\) −4.36055 + 2.89291i −0.577569 + 0.383176i
\(58\) −5.40512 9.36194i −0.709727 1.22928i
\(59\) −4.33885 7.51511i −0.564870 0.978384i −0.997062 0.0766018i \(-0.975593\pi\)
0.432192 0.901782i \(-0.357740\pi\)
\(60\) −0.504220 + 0.0313822i −0.0650946 + 0.00405143i
\(61\) 7.81138 + 4.50990i 1.00014 + 0.577434i 0.908291 0.418339i \(-0.137387\pi\)
0.0918536 + 0.995773i \(0.470721\pi\)
\(62\) −4.80926 −0.610776
\(63\) −7.87273 1.01004i −0.991870 0.127253i
\(64\) −8.80159 −1.10020
\(65\) 3.14058 + 1.81321i 0.389540 + 0.224901i
\(66\) −5.80741 + 11.6792i −0.714842 + 1.43761i
\(67\) 1.65886 + 2.87323i 0.202662 + 0.351021i 0.949385 0.314114i \(-0.101707\pi\)
−0.746723 + 0.665135i \(0.768374\pi\)
\(68\) 0.718152 + 1.24388i 0.0870887 + 0.150842i
\(69\) 10.6315 + 5.28642i 1.27988 + 0.636411i
\(70\) 3.33124 0.927980i 0.398159 0.110915i
\(71\) 6.95342i 0.825220i −0.910908 0.412610i \(-0.864617\pi\)
0.910908 0.412610i \(-0.135383\pi\)
\(72\) −8.27904 3.49330i −0.975694 0.411690i
\(73\) 2.88131i 0.337232i 0.985682 + 0.168616i \(0.0539298\pi\)
−0.985682 + 0.168616i \(0.946070\pi\)
\(74\) −3.17946 1.83566i −0.369605 0.213392i
\(75\) 1.72871 0.107593i 0.199614 0.0124238i
\(76\) −0.763154 + 0.440607i −0.0875398 + 0.0505411i
\(77\) −3.79969 + 14.7627i −0.433015 + 1.68236i
\(78\) 4.53855 + 6.84105i 0.513889 + 0.774596i
\(79\) 5.15417 8.92729i 0.579889 1.00440i −0.415602 0.909547i \(-0.636429\pi\)
0.995491 0.0948515i \(-0.0302376\pi\)
\(80\) 3.33158 0.372481
\(81\) −6.27964 6.44718i −0.697738 0.716353i
\(82\) 14.5812i 1.61022i
\(83\) 1.69417 2.93439i 0.185959 0.322091i −0.757940 0.652324i \(-0.773794\pi\)
0.943899 + 0.330233i \(0.107127\pi\)
\(84\) −1.31263 0.252116i −0.143220 0.0275081i
\(85\) −2.46216 4.26459i −0.267059 0.462560i
\(86\) 0.308320 0.178009i 0.0332470 0.0191952i
\(87\) −0.889887 14.2979i −0.0954059 1.53289i
\(88\) −8.62884 + 14.9456i −0.919838 + 1.59321i
\(89\) −4.68832 −0.496961 −0.248481 0.968637i \(-0.579931\pi\)
−0.248481 + 0.968637i \(0.579931\pi\)
\(90\) 3.61266 + 1.52435i 0.380808 + 0.160680i
\(91\) 6.85113 + 6.71705i 0.718194 + 0.704138i
\(92\) 1.73157 + 0.999720i 0.180528 + 0.104228i
\(93\) −5.70659 2.83756i −0.591746 0.294241i
\(94\) −4.26126 + 2.46024i −0.439515 + 0.253754i
\(95\) 2.61645 1.51061i 0.268443 0.154985i
\(96\) −2.53744 1.26172i −0.258976 0.128774i
\(97\) 4.00495 + 2.31226i 0.406642 + 0.234775i 0.689346 0.724433i \(-0.257898\pi\)
−0.282704 + 0.959207i \(0.591231\pi\)
\(98\) 9.14742 0.180814i 0.924029 0.0182650i
\(99\) −13.7819 + 10.4319i −1.38514 + 1.04844i
\(100\) 0.291675 0.0291675
\(101\) −4.98278 + 8.63043i −0.495805 + 0.858760i −0.999988 0.00483690i \(-0.998460\pi\)
0.504183 + 0.863597i \(0.331794\pi\)
\(102\) −0.692496 11.1264i −0.0685673 1.10167i
\(103\) −8.37044 + 4.83267i −0.824763 + 0.476177i −0.852056 0.523450i \(-0.824645\pi\)
0.0272929 + 0.999627i \(0.491311\pi\)
\(104\) 5.43109 + 9.40692i 0.532562 + 0.922425i
\(105\) 4.50032 + 0.864373i 0.439186 + 0.0843541i
\(106\) 2.29668 3.97797i 0.223073 0.386374i
\(107\) 9.46949i 0.915450i −0.889094 0.457725i \(-0.848664\pi\)
0.889094 0.457725i \(-0.151336\pi\)
\(108\) −0.987998 1.14929i −0.0950702 0.110590i
\(109\) −8.33627 −0.798470 −0.399235 0.916849i \(-0.630724\pi\)
−0.399235 + 0.916849i \(0.630724\pi\)
\(110\) 3.76530 6.52169i 0.359007 0.621819i
\(111\) −2.68962 4.05412i −0.255287 0.384800i
\(112\) 8.53630 + 2.19712i 0.806605 + 0.207608i
\(113\) 4.68004 2.70202i 0.440261 0.254185i −0.263447 0.964674i \(-0.584859\pi\)
0.703708 + 0.710489i \(0.251526\pi\)
\(114\) 6.82636 0.424867i 0.639347 0.0397924i
\(115\) −5.93663 3.42751i −0.553594 0.319617i
\(116\) 2.41240i 0.223986i
\(117\) 1.34901 + 10.7953i 0.124716 + 0.998027i
\(118\) 11.3420i 1.04412i
\(119\) −3.49623 12.5507i −0.320499 1.15052i
\(120\) 4.64539 + 2.30989i 0.424064 + 0.210863i
\(121\) 11.0981 + 19.2225i 1.00892 + 1.74750i
\(122\) −5.89457 10.2097i −0.533670 0.924343i
\(123\) 8.60321 17.3018i 0.775725 1.56005i
\(124\) −0.929443 0.536614i −0.0834664 0.0481894i
\(125\) −1.00000 −0.0894427
\(126\) 8.25122 + 6.28823i 0.735077 + 0.560200i
\(127\) 9.75881 0.865955 0.432977 0.901405i \(-0.357463\pi\)
0.432977 + 0.901405i \(0.357463\pi\)
\(128\) 7.12888 + 4.11586i 0.630110 + 0.363794i
\(129\) 0.470877 0.0293070i 0.0414584 0.00258033i
\(130\) −2.36992 4.10482i −0.207856 0.360017i
\(131\) −8.91007 15.4327i −0.778476 1.34836i −0.932820 0.360343i \(-0.882660\pi\)
0.154344 0.988017i \(-0.450674\pi\)
\(132\) −2.42550 + 1.60915i −0.211113 + 0.140059i
\(133\) 7.70021 2.14504i 0.667693 0.185999i
\(134\) 4.33636i 0.374604i
\(135\) 3.38733 + 3.94031i 0.291535 + 0.339128i
\(136\) 14.7498i 1.26478i
\(137\) 1.19435 + 0.689559i 0.102040 + 0.0589130i 0.550152 0.835065i \(-0.314570\pi\)
−0.448111 + 0.893978i \(0.647903\pi\)
\(138\) −8.57921 12.9316i −0.730311 1.10081i
\(139\) −10.5156 + 6.07121i −0.891926 + 0.514954i −0.874572 0.484896i \(-0.838858\pi\)
−0.0173539 + 0.999849i \(0.505524\pi\)
\(140\) 0.747342 + 0.192355i 0.0631619 + 0.0162569i
\(141\) −6.50793 + 0.405048i −0.548067 + 0.0341112i
\(142\) −4.54416 + 7.87072i −0.381338 + 0.660496i
\(143\) 20.8941 1.74725
\(144\) 6.03208 + 7.96922i 0.502674 + 0.664102i
\(145\) 8.27085i 0.686856i
\(146\) 1.88298 3.26142i 0.155837 0.269917i
\(147\) 10.9609 + 5.18262i 0.904037 + 0.427455i
\(148\) −0.409644 0.709525i −0.0336726 0.0583226i
\(149\) 5.61055 3.23925i 0.459634 0.265370i −0.252256 0.967661i \(-0.581173\pi\)
0.711891 + 0.702290i \(0.247839\pi\)
\(150\) −2.02707 1.00795i −0.165510 0.0822986i
\(151\) −9.46471 + 16.3934i −0.770227 + 1.33407i 0.167212 + 0.985921i \(0.446524\pi\)
−0.937438 + 0.348151i \(0.886810\pi\)
\(152\) 9.04942 0.734005
\(153\) 5.74309 13.6110i 0.464301 1.10038i
\(154\) 13.9486 14.2270i 1.12401 1.14644i
\(155\) 3.18657 + 1.83977i 0.255951 + 0.147774i
\(156\) 0.113805 + 1.82852i 0.00911172 + 0.146399i
\(157\) −0.754717 + 0.435736i −0.0602330 + 0.0347755i −0.529814 0.848114i \(-0.677738\pi\)
0.469581 + 0.882889i \(0.344405\pi\)
\(158\) −11.6682 + 6.73665i −0.928274 + 0.535939i
\(159\) 5.07229 3.36510i 0.402259 0.266870i
\(160\) 1.41691 + 0.818053i 0.112016 + 0.0646727i
\(161\) −12.9507 12.6972i −1.02066 1.00068i
\(162\) 2.89473 + 11.4015i 0.227431 + 0.895789i
\(163\) 10.7991 0.845849 0.422924 0.906165i \(-0.361004\pi\)
0.422924 + 0.906165i \(0.361004\pi\)
\(164\) 1.62696 2.81798i 0.127044 0.220047i
\(165\) 8.31578 5.51693i 0.647382 0.429492i
\(166\) −3.83533 + 2.21433i −0.297679 + 0.171865i
\(167\) −3.22089 5.57874i −0.249240 0.431696i 0.714075 0.700069i \(-0.246847\pi\)
−0.963315 + 0.268373i \(0.913514\pi\)
\(168\) 10.3793 + 8.98205i 0.800778 + 0.692980i
\(169\) 0.0754780 0.130732i 0.00580600 0.0100563i
\(170\) 6.43624i 0.493637i
\(171\) 8.35072 + 3.52355i 0.638596 + 0.269453i
\(172\) 0.0794484 0.00605788
\(173\) −2.37437 + 4.11252i −0.180520 + 0.312669i −0.942058 0.335451i \(-0.891111\pi\)
0.761538 + 0.648120i \(0.224445\pi\)
\(174\) −8.33658 + 16.7656i −0.631994 + 1.27100i
\(175\) −2.56224 0.659483i −0.193687 0.0498522i
\(176\) 16.6236 9.59763i 1.25305 0.723448i
\(177\) −6.69202 + 13.4582i −0.503003 + 1.01158i
\(178\) 5.30681 + 3.06389i 0.397762 + 0.229648i
\(179\) 19.6922i 1.47186i 0.677056 + 0.735932i \(0.263256\pi\)
−0.677056 + 0.735932i \(0.736744\pi\)
\(180\) 0.528101 + 0.697695i 0.0393623 + 0.0520031i
\(181\) 26.6033i 1.97741i −0.149883 0.988704i \(-0.547890\pi\)
0.149883 0.988704i \(-0.452110\pi\)
\(182\) −3.36525 12.0805i −0.249449 0.895464i
\(183\) −0.970470 15.5926i −0.0717392 1.15264i
\(184\) −10.2664 17.7819i −0.756848 1.31090i
\(185\) 1.40446 + 2.43259i 0.103258 + 0.178847i
\(186\) 4.60501 + 6.94123i 0.337656 + 0.508956i
\(187\) −24.5710 14.1860i −1.79681 1.03739i
\(188\) −1.09805 −0.0800833
\(189\) 6.08058 + 12.3299i 0.442297 + 0.896869i
\(190\) −3.94882 −0.286478
\(191\) −9.69208 5.59572i −0.701294 0.404892i 0.106535 0.994309i \(-0.466024\pi\)
−0.807829 + 0.589417i \(0.799358\pi\)
\(192\) 8.42780 + 12.7034i 0.608224 + 0.916788i
\(193\) −0.463712 0.803173i −0.0333787 0.0578137i 0.848853 0.528628i \(-0.177293\pi\)
−0.882232 + 0.470815i \(0.843960\pi\)
\(194\) −3.02219 5.23459i −0.216981 0.375822i
\(195\) −0.390179 6.26902i −0.0279413 0.448934i
\(196\) 1.78802 + 0.985719i 0.127715 + 0.0704085i
\(197\) 7.07291i 0.503924i 0.967737 + 0.251962i \(0.0810758\pi\)
−0.967737 + 0.251962i \(0.918924\pi\)
\(198\) 22.4174 2.80134i 1.59314 0.199082i
\(199\) 4.14124i 0.293565i 0.989169 + 0.146782i \(0.0468917\pi\)
−0.989169 + 0.146782i \(0.953108\pi\)
\(200\) −2.59399 1.49764i −0.183423 0.105899i
\(201\) 2.55854 5.14545i 0.180466 0.362932i
\(202\) 11.2802 6.51264i 0.793674 0.458228i
\(203\) −5.45448 + 21.1919i −0.382830 + 1.48738i
\(204\) 1.10764 2.22756i 0.0775504 0.155961i
\(205\) −5.57799 + 9.66136i −0.389584 + 0.674779i
\(206\) 12.6329 0.880175
\(207\) −2.55003 20.4064i −0.177239 1.41834i
\(208\) 12.0817i 0.837716i
\(209\) 8.70356 15.0750i 0.602038 1.04276i
\(210\) −4.52912 3.91942i −0.312539 0.270466i
\(211\) −7.38983 12.7996i −0.508737 0.881159i −0.999949 0.0101183i \(-0.996779\pi\)
0.491212 0.871040i \(-0.336554\pi\)
\(212\) 0.887718 0.512524i 0.0609687 0.0352003i
\(213\) −10.0359 + 6.65812i −0.687650 + 0.456207i
\(214\) −6.18845 + 10.7187i −0.423034 + 0.732716i
\(215\) −0.272387 −0.0185766
\(216\) 2.88553 + 15.2941i 0.196335 + 1.04063i
\(217\) 6.95147 + 6.81542i 0.471896 + 0.462661i
\(218\) 9.43599 + 5.44787i 0.639086 + 0.368977i
\(219\) 4.15862 2.75895i 0.281013 0.186432i
\(220\) 1.45537 0.840260i 0.0981212 0.0566503i
\(221\) −15.4652 + 8.92886i −1.04030 + 0.600620i
\(222\) 0.395010 + 6.34664i 0.0265113 + 0.425959i
\(223\) −5.55505 3.20721i −0.371994 0.214771i 0.302335 0.953202i \(-0.402234\pi\)
−0.674329 + 0.738431i \(0.735567\pi\)
\(224\) 3.09097 + 3.03048i 0.206524 + 0.202482i
\(225\) −1.81058 2.39203i −0.120705 0.159469i
\(226\) −7.06324 −0.469840
\(227\) −2.28750 + 3.96207i −0.151827 + 0.262972i −0.931899 0.362718i \(-0.881849\pi\)
0.780072 + 0.625690i \(0.215182\pi\)
\(228\) 1.36668 + 0.679570i 0.0905103 + 0.0450056i
\(229\) 5.09205 2.93990i 0.336492 0.194274i −0.322227 0.946662i \(-0.604432\pi\)
0.658720 + 0.752388i \(0.271098\pi\)
\(230\) 4.47986 + 7.75935i 0.295393 + 0.511636i
\(231\) 24.9453 8.65159i 1.64128 0.569233i
\(232\) −12.3868 + 21.4545i −0.813232 + 1.40856i
\(233\) 9.82356i 0.643563i −0.946814 0.321781i \(-0.895718\pi\)
0.946814 0.321781i \(-0.104282\pi\)
\(234\) 5.52792 13.1010i 0.361372 0.856441i
\(235\) 3.76463 0.245577
\(236\) −1.26553 + 2.19197i −0.0823792 + 0.142685i
\(237\) −17.8201 + 1.10911i −1.15754 + 0.0720443i
\(238\) −4.24459 + 16.4912i −0.275136 + 1.06897i
\(239\) 15.9544 9.21127i 1.03200 0.595827i 0.114445 0.993430i \(-0.463491\pi\)
0.917558 + 0.397602i \(0.130158\pi\)
\(240\) −3.19009 4.80848i −0.205919 0.310386i
\(241\) 3.82945 + 2.21093i 0.246677 + 0.142419i 0.618241 0.785988i \(-0.287845\pi\)
−0.371565 + 0.928407i \(0.621179\pi\)
\(242\) 29.0111i 1.86490i
\(243\) −3.29230 + 15.2368i −0.211201 + 0.977443i
\(244\) 2.63085i 0.168423i
\(245\) −6.13016 3.37951i −0.391642 0.215909i
\(246\) −21.0451 + 13.9619i −1.34179 + 0.890181i
\(247\) −5.47812 9.48838i −0.348564 0.603731i
\(248\) 5.51063 + 9.54469i 0.349925 + 0.606088i
\(249\) −5.85744 + 0.364562i −0.371200 + 0.0231032i
\(250\) 1.13192 + 0.653515i 0.0715889 + 0.0413319i
\(251\) −11.0078 −0.694809 −0.347405 0.937715i \(-0.612937\pi\)
−0.347405 + 0.937715i \(0.612937\pi\)
\(252\) 0.893004 + 2.13594i 0.0562540 + 0.134551i
\(253\) −39.4960 −2.48309
\(254\) −11.0462 6.37753i −0.693100 0.400162i
\(255\) −3.79752 + 7.63714i −0.237810 + 0.478256i
\(256\) 3.42204 + 5.92715i 0.213877 + 0.370447i
\(257\) 2.36224 + 4.09152i 0.147352 + 0.255222i 0.930248 0.366931i \(-0.119592\pi\)
−0.782896 + 0.622153i \(0.786258\pi\)
\(258\) −0.552147 0.274552i −0.0343752 0.0170928i
\(259\) 1.99430 + 7.15909i 0.123920 + 0.444844i
\(260\) 1.05774i 0.0655981i
\(261\) −19.7841 + 14.9750i −1.22461 + 0.926931i
\(262\) 23.2914i 1.43895i
\(263\) 3.45803 + 1.99649i 0.213231 + 0.123109i 0.602812 0.797883i \(-0.294047\pi\)
−0.389581 + 0.920992i \(0.627380\pi\)
\(264\) 29.8335 1.85681i 1.83612 0.114279i
\(265\) −3.04352 + 1.75718i −0.186962 + 0.107942i
\(266\) −10.1178 2.60418i −0.620365 0.159673i
\(267\) 4.48922 + 6.76669i 0.274735 + 0.414114i
\(268\) 0.483848 0.838049i 0.0295557 0.0511920i
\(269\) −21.2854 −1.29779 −0.648896 0.760877i \(-0.724769\pi\)
−0.648896 + 0.760877i \(0.724769\pi\)
\(270\) −1.25914 6.67378i −0.0766285 0.406153i
\(271\) 8.91274i 0.541411i −0.962662 0.270705i \(-0.912743\pi\)
0.962662 0.270705i \(-0.0872569\pi\)
\(272\) −8.20289 + 14.2078i −0.497373 + 0.861476i
\(273\) 3.13458 16.3201i 0.189714 0.987735i
\(274\) −0.901273 1.56105i −0.0544479 0.0943066i
\(275\) −4.98971 + 2.88081i −0.300891 + 0.173719i
\(276\) −0.215126 3.45644i −0.0129491 0.208053i
\(277\) 13.7461 23.8089i 0.825922 1.43054i −0.0752903 0.997162i \(-0.523988\pi\)
0.901212 0.433378i \(-0.142678\pi\)
\(278\) 15.8705 0.951850
\(279\) 1.36876 + 10.9534i 0.0819458 + 0.655763i
\(280\) −5.65877 5.54802i −0.338176 0.331558i
\(281\) −3.43914 1.98559i −0.205162 0.118450i 0.393899 0.919154i \(-0.371126\pi\)
−0.599061 + 0.800703i \(0.704459\pi\)
\(282\) 7.63117 + 3.79455i 0.454429 + 0.225962i
\(283\) 1.02668 0.592756i 0.0610300 0.0352357i −0.469175 0.883105i \(-0.655448\pi\)
0.530205 + 0.847870i \(0.322115\pi\)
\(284\) −1.75642 + 1.01407i −0.104224 + 0.0601740i
\(285\) −4.68561 2.32989i −0.277552 0.138011i
\(286\) −23.6504 13.6546i −1.39848 0.807412i
\(287\) −20.6637 + 21.0762i −1.21974 + 1.24409i
\(288\) 0.608621 + 4.87044i 0.0358634 + 0.286993i
\(289\) 7.24902 0.426413
\(290\) 5.40512 9.36194i 0.317399 0.549752i
\(291\) −0.497567 7.99444i −0.0291679 0.468642i
\(292\) 0.727814 0.420204i 0.0425921 0.0245906i
\(293\) −13.7335 23.7871i −0.802318 1.38966i −0.918087 0.396379i \(-0.870267\pi\)
0.115769 0.993276i \(-0.463067\pi\)
\(294\) −9.01991 13.0294i −0.526052 0.759890i
\(295\) 4.33885 7.51511i 0.252618 0.437546i
\(296\) 8.41349i 0.489024i
\(297\) 28.2530 + 9.90274i 1.63941 + 0.574615i
\(298\) −8.46760 −0.490515
\(299\) −12.4296 + 21.5287i −0.718824 + 1.24504i
\(300\) −0.279288 0.420976i −0.0161247 0.0243051i
\(301\) −0.697921 0.179634i −0.0402275 0.0103540i
\(302\) 21.4266 12.3706i 1.23296 0.711851i
\(303\) 17.2275 1.07223i 0.989696 0.0615978i
\(304\) −8.71692 5.03271i −0.499949 0.288646i
\(305\) 9.01980i 0.516473i
\(306\) −15.3957 + 11.6533i −0.880112 + 0.666177i
\(307\) 7.49498i 0.427761i 0.976860 + 0.213881i \(0.0686104\pi\)
−0.976860 + 0.213881i \(0.931390\pi\)
\(308\) 4.28315 1.19315i 0.244055 0.0679863i
\(309\) 14.9900 + 7.45367i 0.852750 + 0.424024i
\(310\) −2.40463 4.16494i −0.136574 0.236553i
\(311\) −9.95114 17.2359i −0.564278 0.977357i −0.997116 0.0758862i \(-0.975821\pi\)
0.432839 0.901471i \(-0.357512\pi\)
\(312\) 8.37663 16.8461i 0.474234 0.953725i
\(313\) 28.3246 + 16.3532i 1.60100 + 0.924339i 0.991287 + 0.131718i \(0.0420495\pi\)
0.609715 + 0.792621i \(0.291284\pi\)
\(314\) 1.13904 0.0642797
\(315\) −3.06164 7.32300i −0.172504 0.412604i
\(316\) −3.00669 −0.169139
\(317\) −7.62204 4.40059i −0.428097 0.247162i 0.270439 0.962737i \(-0.412831\pi\)
−0.698535 + 0.715575i \(0.746165\pi\)
\(318\) −7.94057 + 0.494214i −0.445285 + 0.0277142i
\(319\) 23.8267 + 41.2691i 1.33404 + 2.31063i
\(320\) −4.40079 7.62240i −0.246012 0.426105i
\(321\) −13.6674 + 9.06734i −0.762839 + 0.506089i
\(322\) 6.36133 + 22.8357i 0.354503 + 1.27258i
\(323\) 14.8775i 0.827806i
\(324\) −0.712737 + 2.52646i −0.0395965 + 0.140359i
\(325\) 3.62642i 0.201158i
\(326\) −12.2237 7.05735i −0.677007 0.390870i
\(327\) 7.98224 + 12.0318i 0.441419 + 0.665360i
\(328\) −28.9385 + 16.7077i −1.59786 + 0.922527i
\(329\) 9.64588 + 2.48271i 0.531795 + 0.136876i
\(330\) −13.0182 + 0.810241i −0.716628 + 0.0446023i
\(331\) 7.15743 12.3970i 0.393408 0.681402i −0.599489 0.800383i \(-0.704629\pi\)
0.992897 + 0.118981i \(0.0379628\pi\)
\(332\) −0.988293 −0.0542396
\(333\) −3.27594 + 7.76389i −0.179520 + 0.425459i
\(334\) 8.41959i 0.460700i
\(335\) −1.65886 + 2.87323i −0.0906332 + 0.156981i
\(336\) −5.00266 14.4243i −0.272918 0.786911i
\(337\) −13.5173 23.4126i −0.736332 1.27536i −0.954136 0.299372i \(-0.903223\pi\)
0.217804 0.975993i \(-0.430111\pi\)
\(338\) −0.170870 + 0.0986520i −0.00929412 + 0.00536596i
\(339\) −8.38113 4.16746i −0.455201 0.226345i
\(340\) −0.718152 + 1.24388i −0.0389473 + 0.0674586i
\(341\) 21.2001 1.14805
\(342\) −7.14966 9.44570i −0.386609 0.510765i
\(343\) −13.4782 12.7019i −0.727756 0.685836i
\(344\) −0.706569 0.407938i −0.0380957 0.0219945i
\(345\) 0.737555 + 11.8503i 0.0397086 + 0.638000i
\(346\) 5.37519 3.10337i 0.288972 0.166838i
\(347\) 8.99376 5.19255i 0.482811 0.278751i −0.238776 0.971075i \(-0.576746\pi\)
0.721587 + 0.692324i \(0.243413\pi\)
\(348\) −3.48183 + 2.30995i −0.186646 + 0.123826i
\(349\) −0.871278 0.503033i −0.0466385 0.0269267i 0.476499 0.879175i \(-0.341905\pi\)
−0.523138 + 0.852248i \(0.675239\pi\)
\(350\) 2.46927 + 2.42094i 0.131988 + 0.129405i
\(351\) 14.2892 12.2839i 0.762703 0.655665i
\(352\) 9.42661 0.502440
\(353\) 3.86581 6.69578i 0.205756 0.356381i −0.744617 0.667492i \(-0.767368\pi\)
0.950373 + 0.311111i \(0.100701\pi\)
\(354\) 16.3700 10.8603i 0.870055 0.577220i
\(355\) 6.02184 3.47671i 0.319606 0.184525i
\(356\) 0.683733 + 1.18426i 0.0362378 + 0.0627657i
\(357\) −14.7667 + 17.0638i −0.781538 + 0.903112i
\(358\) 12.8691 22.2900i 0.680155 1.17806i
\(359\) 19.0140i 1.00352i −0.865007 0.501760i \(-0.832686\pi\)
0.865007 0.501760i \(-0.167314\pi\)
\(360\) −1.11423 8.91651i −0.0587250 0.469941i
\(361\) 9.87222 0.519591
\(362\) −17.3856 + 30.1128i −0.913769 + 1.58269i
\(363\) 17.1171 34.4241i 0.898417 1.80680i
\(364\) 0.697560 2.71018i 0.0365621 0.142052i
\(365\) −2.49529 + 1.44066i −0.130610 + 0.0754074i
\(366\) −9.09149 + 18.2838i −0.475220 + 0.955709i
\(367\) −9.92332 5.72923i −0.517993 0.299063i 0.218120 0.975922i \(-0.430008\pi\)
−0.736113 + 0.676859i \(0.763341\pi\)
\(368\) 22.8380i 1.19052i
\(369\) −33.2097 + 4.14996i −1.72883 + 0.216038i
\(370\) 3.67133i 0.190863i
\(371\) −8.95706 + 2.49516i −0.465027 + 0.129542i
\(372\) 0.115472 + 1.85530i 0.00598695 + 0.0961926i
\(373\) −7.14969 12.3836i −0.370197 0.641200i 0.619399 0.785076i \(-0.287376\pi\)
−0.989596 + 0.143877i \(0.954043\pi\)
\(374\) 18.5416 + 32.1149i 0.958762 + 1.66062i
\(375\) 0.957531 + 1.44331i 0.0494467 + 0.0745320i
\(376\) 9.76542 + 5.63807i 0.503613 + 0.290761i
\(377\) 29.9936 1.54475
\(378\) 1.17504 17.9302i 0.0604374 0.922231i
\(379\) 6.30700 0.323969 0.161984 0.986793i \(-0.448211\pi\)
0.161984 + 0.986793i \(0.448211\pi\)
\(380\) −0.763154 0.440607i −0.0391490 0.0226027i
\(381\) −9.34437 14.0850i −0.478727 0.721594i
\(382\) 7.31377 + 12.6678i 0.374205 + 0.648142i
\(383\) −14.9406 25.8780i −0.763432 1.32230i −0.941072 0.338207i \(-0.890180\pi\)
0.177640 0.984095i \(-0.443154\pi\)
\(384\) −0.885677 14.2302i −0.0451970 0.726183i
\(385\) −14.6847 + 4.09070i −0.748400 + 0.208481i
\(386\) 1.21217i 0.0616979i
\(387\) −0.493178 0.651557i −0.0250696 0.0331205i
\(388\) 1.34886i 0.0684779i
\(389\) −6.79001 3.92022i −0.344267 0.198763i 0.317890 0.948128i \(-0.397026\pi\)
−0.662158 + 0.749365i \(0.730359\pi\)
\(390\) −3.65525 + 7.35102i −0.185091 + 0.372233i
\(391\) 29.2339 16.8782i 1.47842 0.853568i
\(392\) −10.8403 17.9472i −0.547518 0.906472i
\(393\) −13.7424 + 27.6372i −0.693214 + 1.39411i
\(394\) 4.62225 8.00598i 0.232866 0.403335i
\(395\) 10.3083 0.518669
\(396\) 4.64499 + 1.95993i 0.233420 + 0.0984904i
\(397\) 0.325200i 0.0163213i 0.999967 + 0.00816066i \(0.00259765\pi\)
−0.999967 + 0.00816066i \(0.997402\pi\)
\(398\) 2.70636 4.68756i 0.135658 0.234966i
\(399\) −10.4691 9.05982i −0.524113 0.453558i
\(400\) 1.66579 + 2.88523i 0.0832894 + 0.144261i
\(401\) −0.562380 + 0.324690i −0.0280839 + 0.0162142i −0.513976 0.857804i \(-0.671828\pi\)
0.485892 + 0.874019i \(0.338495\pi\)
\(402\) −6.25869 + 4.15220i −0.312155 + 0.207093i
\(403\) 6.67178 11.5559i 0.332345 0.575638i
\(404\) 2.90671 0.144614
\(405\) 2.44360 8.66192i 0.121423 0.430414i
\(406\) 20.0233 20.4230i 0.993738 1.01357i
\(407\) 14.0156 + 8.09193i 0.694729 + 0.401102i
\(408\) −21.2884 + 14.1234i −1.05394 + 0.699211i
\(409\) 18.7974 10.8527i 0.929470 0.536630i 0.0428259 0.999083i \(-0.486364\pi\)
0.886644 + 0.462453i \(0.153031\pi\)
\(410\) 12.6277 7.29060i 0.623637 0.360057i
\(411\) −0.148384 2.38409i −0.00731923 0.117598i
\(412\) 2.44145 + 1.40957i 0.120281 + 0.0694445i
\(413\) 16.0733 16.3941i 0.790914 0.806702i
\(414\) −10.4494 + 24.7649i −0.513562 + 1.21713i
\(415\) 3.38834 0.166327
\(416\) 2.96661 5.13831i 0.145450 0.251927i
\(417\) 18.8317 + 9.36393i 0.922192 + 0.458554i
\(418\) −19.7035 + 11.3758i −0.963728 + 0.556409i
\(419\) −1.44983 2.51117i −0.0708287 0.122679i 0.828436 0.560084i \(-0.189231\pi\)
−0.899265 + 0.437405i \(0.855898\pi\)
\(420\) −0.437976 1.26283i −0.0213711 0.0616197i
\(421\) 6.16736 10.6822i 0.300579 0.520618i −0.675688 0.737187i \(-0.736153\pi\)
0.976267 + 0.216569i \(0.0694868\pi\)
\(422\) 19.3175i 0.940359i
\(423\) 6.81616 + 9.00509i 0.331413 + 0.437843i
\(424\) −10.5265 −0.511212
\(425\) 2.46216 4.26459i 0.119433 0.206863i
\(426\) 15.7110 0.977842i 0.761203 0.0473766i
\(427\) −5.94841 + 23.1109i −0.287864 + 1.11842i
\(428\) −2.39197 + 1.38101i −0.115620 + 0.0667535i
\(429\) −20.0067 30.1565i −0.965934 1.45597i
\(430\) 0.308320 + 0.178009i 0.0148685 + 0.00858434i
\(431\) 25.3358i 1.22038i −0.792254 0.610192i \(-0.791092\pi\)
0.792254 0.610192i \(-0.208908\pi\)
\(432\) 5.72612 16.3369i 0.275498 0.786011i
\(433\) 29.9796i 1.44073i 0.693596 + 0.720365i \(0.256026\pi\)
−0.693596 + 0.720365i \(0.743974\pi\)
\(434\) −3.41453 12.2574i −0.163903 0.588374i
\(435\) 11.9374 7.91959i 0.572353 0.379715i
\(436\) 1.21574 + 2.10572i 0.0582234 + 0.100846i
\(437\) 10.3553 + 17.9359i 0.495360 + 0.857989i
\(438\) −6.51024 + 0.405192i −0.311071 + 0.0193608i
\(439\) 19.3472 + 11.1701i 0.923391 + 0.533120i 0.884715 0.466132i \(-0.154353\pi\)
0.0386756 + 0.999252i \(0.487686\pi\)
\(440\) −17.2577 −0.822728
\(441\) −3.01527 20.7824i −0.143584 0.989638i
\(442\) 23.3405 1.11020
\(443\) 11.3552 + 6.55595i 0.539504 + 0.311483i 0.744878 0.667201i \(-0.232508\pi\)
−0.205374 + 0.978684i \(0.565841\pi\)
\(444\) −0.631815 + 1.27063i −0.0299846 + 0.0603017i
\(445\) −2.34416 4.06021i −0.111124 0.192472i
\(446\) 4.19192 + 7.26062i 0.198493 + 0.343800i
\(447\) −10.0475 4.99606i −0.475231 0.236306i
\(448\) −6.24905 22.4327i −0.295240 1.05984i
\(449\) 29.0097i 1.36905i 0.728989 + 0.684526i \(0.239991\pi\)
−0.728989 + 0.684526i \(0.760009\pi\)
\(450\) 0.486207 + 3.89083i 0.0229200 + 0.183415i
\(451\) 64.2765i 3.02666i
\(452\) −1.36505 0.788112i −0.0642066 0.0370697i
\(453\) 32.7234 2.03668i 1.53748 0.0956914i
\(454\) 5.17854 2.98983i 0.243041 0.140320i
\(455\) −2.39157 + 9.29178i −0.112118 + 0.435605i
\(456\) −8.66510 13.0611i −0.405781 0.611642i
\(457\) 2.70505 4.68528i 0.126537 0.219168i −0.795796 0.605565i \(-0.792947\pi\)
0.922333 + 0.386397i \(0.126280\pi\)
\(458\) −7.68507 −0.359100
\(459\) −25.1440 + 4.74389i −1.17362 + 0.221426i
\(460\) 1.99944i 0.0932244i
\(461\) −6.99868 + 12.1221i −0.325961 + 0.564581i −0.981706 0.190401i \(-0.939021\pi\)
0.655745 + 0.754982i \(0.272354\pi\)
\(462\) −33.8901 6.50924i −1.57671 0.302837i
\(463\) −5.11805 8.86472i −0.237856 0.411978i 0.722243 0.691639i \(-0.243111\pi\)
−0.960099 + 0.279661i \(0.909778\pi\)
\(464\) 23.8633 13.7775i 1.10783 0.639603i
\(465\) −0.395893 6.36083i −0.0183591 0.294976i
\(466\) −6.41984 + 11.1195i −0.297393 + 0.515100i
\(467\) 5.78707 0.267794 0.133897 0.990995i \(-0.457251\pi\)
0.133897 + 0.990995i \(0.457251\pi\)
\(468\) 2.53014 1.91512i 0.116956 0.0885264i
\(469\) −6.14525 + 6.26792i −0.283761 + 0.289426i
\(470\) −4.26126 2.46024i −0.196557 0.113482i
\(471\) 1.35157 + 0.672057i 0.0622769 + 0.0309668i
\(472\) 22.5099 12.9961i 1.03610 0.598194i
\(473\) −1.35913 + 0.784694i −0.0624928 + 0.0360803i
\(474\) 20.8957 + 10.3903i 0.959773 + 0.477241i
\(475\) 2.61645 + 1.51061i 0.120051 + 0.0693116i
\(476\) −2.66039 + 2.71350i −0.121939 + 0.124373i
\(477\) −9.71375 4.09867i −0.444762 0.187665i
\(478\) −24.0788 −1.10134
\(479\) 5.91876 10.2516i 0.270435 0.468407i −0.698538 0.715573i \(-0.746166\pi\)
0.968973 + 0.247165i \(0.0794991\pi\)
\(480\) −0.176034 2.82834i −0.00803481 0.129096i
\(481\) 8.82160 5.09315i 0.402230 0.232228i
\(482\) −2.88975 5.00520i −0.131625 0.227981i
\(483\) −5.92530 + 30.8498i −0.269610 + 1.40371i
\(484\) 3.23704 5.60672i 0.147138 0.254851i
\(485\) 4.62452i 0.209989i
\(486\) 13.6841 15.0953i 0.620724 0.684737i
\(487\) 20.5456 0.931012 0.465506 0.885045i \(-0.345872\pi\)
0.465506 + 0.885045i \(0.345872\pi\)
\(488\) −13.5084 + 23.3973i −0.611499 + 1.05915i
\(489\) −10.3404 15.5864i −0.467611 0.704840i
\(490\) 4.73030 + 7.83149i 0.213693 + 0.353791i
\(491\) 6.02013 3.47573i 0.271685 0.156857i −0.357968 0.933734i \(-0.616530\pi\)
0.629653 + 0.776876i \(0.283197\pi\)
\(492\) −5.62507 + 0.350100i −0.253598 + 0.0157837i
\(493\) −35.2718 20.3642i −1.58856 0.917157i
\(494\) 14.3201i 0.644292i
\(495\) −15.9252 6.71958i −0.715786 0.302023i
\(496\) 12.2586i 0.550429i
\(497\) 17.7222 4.93687i 0.794951 0.221449i
\(498\) 6.86840 + 3.41527i 0.307780 + 0.153042i
\(499\) 13.4054 + 23.2188i 0.600108 + 1.03942i 0.992804 + 0.119750i \(0.0382092\pi\)
−0.392696 + 0.919668i \(0.628457\pi\)
\(500\) 0.145837 + 0.252598i 0.00652205 + 0.0112965i
\(501\) −4.96774 + 9.99055i −0.221942 + 0.446345i
\(502\) 12.4600 + 7.19379i 0.556117 + 0.321075i
\(503\) −14.8532 −0.662273 −0.331137 0.943583i \(-0.607432\pi\)
−0.331137 + 0.943583i \(0.607432\pi\)
\(504\) 3.02537 23.5811i 0.134760 1.05038i
\(505\) −9.96556 −0.443462
\(506\) 44.7064 + 25.8112i 1.98744 + 1.14745i
\(507\) −0.260959 + 0.0162418i −0.0115896 + 0.000721326i
\(508\) −1.42320 2.46506i −0.0631443 0.109369i
\(509\) 19.6497 + 34.0343i 0.870958 + 1.50854i 0.861007 + 0.508593i \(0.169834\pi\)
0.00995035 + 0.999950i \(0.496833\pi\)
\(510\) 9.28947 6.16290i 0.411345 0.272898i
\(511\) −7.34363 + 2.04571i −0.324863 + 0.0904968i
\(512\) 25.4089i 1.12292i
\(513\) −2.91051 15.4266i −0.128502 0.681100i
\(514\) 6.17503i 0.272369i
\(515\) −8.37044 4.83267i −0.368845 0.212953i
\(516\) −0.0760743 0.114668i −0.00334899 0.00504799i
\(517\) 18.7844 10.8452i 0.826136 0.476970i
\(518\) 2.42118 9.40683i 0.106380 0.413312i
\(519\) 8.20916 0.510932i 0.360342 0.0224274i
\(520\) −5.43109 + 9.40692i −0.238169 + 0.412521i
\(521\) −39.4804 −1.72967 −0.864835 0.502056i \(-0.832577\pi\)
−0.864835 + 0.502056i \(0.832577\pi\)
\(522\) 32.1804 4.02134i 1.40850 0.176009i
\(523\) 15.0977i 0.660177i 0.943950 + 0.330089i \(0.107079\pi\)
−0.943950 + 0.330089i \(0.892921\pi\)
\(524\) −2.59884 + 4.50133i −0.113531 + 0.196641i
\(525\) 1.50159 + 4.32958i 0.0655348 + 0.188958i
\(526\) −2.60948 4.51974i −0.113779 0.197070i
\(527\) −15.6917 + 9.05962i −0.683542 + 0.394643i
\(528\) −29.7699 14.8029i −1.29557 0.644213i
\(529\) 11.9957 20.7772i 0.521553 0.903356i
\(530\) 4.59336 0.199523
\(531\) 25.8322 3.22805i 1.12102 0.140086i
\(532\) −1.66481 1.63223i −0.0721788 0.0707661i
\(533\) 35.0362 + 20.2282i 1.51759 + 0.876179i
\(534\) −0.659307 10.5931i −0.0285310 0.458409i
\(535\) 8.20082 4.73475i 0.354552 0.204701i
\(536\) −8.60614 + 4.96876i −0.371729 + 0.214618i
\(537\) 28.4219 18.8559i 1.22649 0.813692i
\(538\) 24.0933 + 13.9103i 1.03874 + 0.599716i
\(539\) −40.3234 + 0.797061i −1.73685 + 0.0343319i
\(540\) 0.501314 1.43028i 0.0215731 0.0615493i
\(541\) −36.6140 −1.57416 −0.787080 0.616851i \(-0.788408\pi\)
−0.787080 + 0.616851i \(0.788408\pi\)
\(542\) −5.82461 + 10.0885i −0.250188 + 0.433339i
\(543\) −38.3967 + 25.4735i −1.64776 + 1.09317i
\(544\) −6.97733 + 4.02836i −0.299150 + 0.172715i
\(545\) −4.16813 7.21942i −0.178543 0.309246i
\(546\) −14.2135 + 16.4245i −0.608281 + 0.702904i
\(547\) 13.0028 22.5215i 0.555960 0.962951i −0.441868 0.897080i \(-0.645684\pi\)
0.997828 0.0658711i \(-0.0209826\pi\)
\(548\) 0.402254i 0.0171834i
\(549\) −21.5756 + 16.3311i −0.920825 + 0.696993i
\(550\) 7.53060 0.321106
\(551\) 12.4940 21.6403i 0.532264 0.921907i
\(552\) −15.8343 + 31.8443i −0.673955 + 1.35538i
\(553\) 26.4125 + 6.79818i 1.12317 + 0.289088i
\(554\) −31.1189 + 17.9665i −1.32212 + 0.763325i
\(555\) 2.16616 4.35634i 0.0919484 0.184916i
\(556\) 3.06715 + 1.77082i 0.130076 + 0.0750995i
\(557\) 5.40214i 0.228896i −0.993429 0.114448i \(-0.963490\pi\)
0.993429 0.114448i \(-0.0365099\pi\)
\(558\) 5.60888 13.2929i 0.237443 0.562733i
\(559\) 0.987790i 0.0417791i
\(560\) 2.36539 + 8.49121i 0.0999560 + 0.358819i
\(561\) 3.05264 + 49.0470i 0.128883 + 2.07077i
\(562\) 2.59522 + 4.49506i 0.109473 + 0.189613i
\(563\) 0.653430 + 1.13177i 0.0275388 + 0.0476986i 0.879466 0.475961i \(-0.157900\pi\)
−0.851928 + 0.523660i \(0.824566\pi\)
\(564\) 1.05141 + 1.58482i 0.0442726 + 0.0667329i
\(565\) 4.68004 + 2.70202i 0.196891 + 0.113675i
\(566\) −1.54950 −0.0651303
\(567\) 11.9735 20.5824i 0.502839 0.864380i
\(568\) 20.8275 0.873902
\(569\) 0.0109445 + 0.00631883i 0.000458818 + 0.000264899i 0.500229 0.865893i \(-0.333249\pi\)
−0.499771 + 0.866158i \(0.666582\pi\)
\(570\) 3.78112 + 5.69936i 0.158374 + 0.238720i
\(571\) −1.19240 2.06530i −0.0499004 0.0864301i 0.839996 0.542592i \(-0.182557\pi\)
−0.889897 + 0.456162i \(0.849224\pi\)
\(572\) −3.04714 5.27780i −0.127407 0.220676i
\(573\) 1.20412 + 19.3467i 0.0503030 + 0.808221i
\(574\) 37.1632 10.3525i 1.55116 0.432106i
\(575\) 6.85503i 0.285874i
\(576\) 10.2650 24.3278i 0.427709 1.01366i
\(577\) 14.0085i 0.583181i −0.956543 0.291590i \(-0.905816\pi\)
0.956543 0.291590i \(-0.0941844\pi\)
\(578\) −8.20531 4.73734i −0.341296 0.197047i
\(579\) −0.715206 + 1.43834i −0.0297229 + 0.0597755i
\(580\) 2.08920 1.20620i 0.0867493 0.0500847i
\(581\) 8.68174 + 2.23455i 0.360179 + 0.0927048i
\(582\) −4.66128 + 9.37424i −0.193216 + 0.388575i
\(583\) −10.1242 + 17.5356i −0.419300 + 0.726250i
\(584\) −8.63036 −0.357127
\(585\) −8.67451 + 6.56593i −0.358647 + 0.271468i
\(586\) 35.9001i 1.48302i
\(587\) 22.1238 38.3196i 0.913148 1.58162i 0.103558 0.994623i \(-0.466977\pi\)
0.809590 0.586996i \(-0.199689\pi\)
\(588\) −0.289387 3.52451i −0.0119341 0.145348i
\(589\) −5.55834 9.62733i −0.229028 0.396687i
\(590\) −9.82246 + 5.67100i −0.404384 + 0.233471i
\(591\) 10.2084 6.77254i 0.419917 0.278585i
\(592\) 4.67905 8.10435i 0.192308 0.333087i
\(593\) 10.0021 0.410736 0.205368 0.978685i \(-0.434161\pi\)
0.205368 + 0.978685i \(0.434161\pi\)
\(594\) −25.5086 29.6729i −1.04663 1.21749i
\(595\) 9.12109 9.30316i 0.373928 0.381393i
\(596\) −1.63646 0.944809i −0.0670319 0.0387009i
\(597\) 5.97708 3.96537i 0.244626 0.162292i
\(598\) 28.1387 16.2459i 1.15068 0.664343i
\(599\) −23.6768 + 13.6698i −0.967407 + 0.558532i −0.898445 0.439087i \(-0.855302\pi\)
−0.0689620 + 0.997619i \(0.521969\pi\)
\(600\) 0.322272 + 5.17797i 0.0131567 + 0.211390i
\(601\) −34.6432 20.0013i −1.41313 0.815869i −0.417444 0.908703i \(-0.637074\pi\)
−0.995682 + 0.0928341i \(0.970407\pi\)
\(602\) 0.672597 + 0.659433i 0.0274130 + 0.0268765i
\(603\) −9.87634 + 1.23417i −0.402196 + 0.0502594i
\(604\) 5.52124 0.224656
\(605\) −11.0981 + 19.2225i −0.451202 + 0.781505i
\(606\) −20.2009 10.0448i −0.820606 0.408041i
\(607\) −19.4976 + 11.2569i −0.791381 + 0.456904i −0.840449 0.541891i \(-0.817708\pi\)
0.0490673 + 0.998795i \(0.484375\pi\)
\(608\) −2.47152 4.28080i −0.100233 0.173609i
\(609\) 35.8093 12.4194i 1.45106 0.503260i
\(610\) 5.89457 10.2097i 0.238664 0.413379i
\(611\) 13.6521i 0.552306i
\(612\) −4.27566 + 0.534296i −0.172833 + 0.0215977i
\(613\) 31.9991 1.29243 0.646216 0.763154i \(-0.276350\pi\)
0.646216 + 0.763154i \(0.276350\pi\)
\(614\) 4.89808 8.48373i 0.197670 0.342375i
\(615\) 19.2854 1.20031i 0.777663 0.0484011i
\(616\) −44.2184 11.3812i −1.78161 0.458560i
\(617\) −0.991996 + 0.572729i −0.0399363 + 0.0230572i −0.519835 0.854267i \(-0.674007\pi\)
0.479899 + 0.877324i \(0.340673\pi\)
\(618\) −12.0964 18.2331i −0.486588 0.733444i
\(619\) −7.02781 4.05751i −0.282471 0.163085i 0.352070 0.935974i \(-0.385478\pi\)
−0.634542 + 0.772889i \(0.718811\pi\)
\(620\) 1.07323i 0.0431019i
\(621\) −27.0109 + 23.2202i −1.08391 + 0.931795i
\(622\) 26.0129i 1.04302i
\(623\) −3.32867 11.9492i −0.133360 0.478733i
\(624\) −17.4376 + 11.5686i −0.698063 + 0.463115i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −21.3741 37.0211i −0.854283 1.47966i
\(627\) −30.0918 + 1.87289i −1.20175 + 0.0747959i
\(628\) 0.220132 + 0.127093i 0.00878423 + 0.00507158i
\(629\) −13.8320 −0.551518
\(630\) −1.32015 + 10.2899i −0.0525962 + 0.409959i
\(631\) −19.8404 −0.789835 −0.394917 0.918717i \(-0.629227\pi\)
−0.394917 + 0.918717i \(0.629227\pi\)
\(632\) 26.7398 + 15.4382i 1.06365 + 0.614099i
\(633\) −11.3977 + 22.9218i −0.453018 + 0.911059i
\(634\) 5.75170 + 9.96223i 0.228429 + 0.395651i
\(635\) 4.87941 + 8.45138i 0.193633 + 0.335383i
\(636\) −1.58975 0.790491i −0.0630376 0.0313450i
\(637\) −12.2555 + 22.2306i −0.485582 + 0.880808i
\(638\) 62.2844i 2.46586i
\(639\) 19.2194 + 8.10955i 0.760309 + 0.320809i
\(640\) 8.23172i 0.325387i
\(641\) 26.4557 + 15.2742i 1.04494 + 0.603294i 0.921228 0.389024i \(-0.127188\pi\)
0.123709 + 0.992319i \(0.460521\pi\)
\(642\) 21.3960 1.33167i 0.844434 0.0525569i
\(643\) 31.1031 17.9574i 1.22658 0.708169i 0.260271 0.965536i \(-0.416188\pi\)
0.966314 + 0.257367i \(0.0828548\pi\)
\(644\) −1.31860 + 5.12305i −0.0519600 + 0.201876i
\(645\) 0.260819 + 0.393138i 0.0102697 + 0.0154798i
\(646\) 9.72266 16.8401i 0.382533 0.662566i
\(647\) 5.35102 0.210370 0.105185 0.994453i \(-0.466456\pi\)
0.105185 + 0.994453i \(0.466456\pi\)
\(648\) 19.3111 18.8093i 0.758613 0.738900i
\(649\) 49.9976i 1.96258i
\(650\) 2.36992 4.10482i 0.0929560 0.161004i
\(651\) 3.18049 16.5591i 0.124653 0.649001i
\(652\) −1.57491 2.72782i −0.0616782 0.106830i
\(653\) 29.5953 17.0869i 1.15815 0.668660i 0.207293 0.978279i \(-0.433535\pi\)
0.950861 + 0.309619i \(0.100201\pi\)
\(654\) −1.17231 18.8355i −0.0458409 0.736528i
\(655\) 8.91007 15.4327i 0.348145 0.603005i
\(656\) 37.1670 1.45113
\(657\) −7.96402 3.36038i −0.310706 0.131101i
\(658\) −9.29589 9.11395i −0.362391 0.355299i
\(659\) −16.6480 9.61174i −0.648515 0.374420i 0.139372 0.990240i \(-0.455492\pi\)
−0.787887 + 0.615820i \(0.788825\pi\)
\(660\) −2.60632 1.29597i −0.101451 0.0504457i
\(661\) −14.1032 + 8.14247i −0.548550 + 0.316705i −0.748537 0.663093i \(-0.769243\pi\)
0.199987 + 0.979799i \(0.435910\pi\)
\(662\) −16.2033 + 9.35496i −0.629758 + 0.363591i
\(663\) 27.6955 + 13.7714i 1.07560 + 0.534837i
\(664\) 8.78933 + 5.07452i 0.341092 + 0.196930i
\(665\) 5.70777 + 5.59606i 0.221338 + 0.217006i
\(666\) 8.78192 6.64723i 0.340292 0.257575i
\(667\) −56.6969 −2.19531
\(668\) −0.939453 + 1.62718i −0.0363485 + 0.0629575i
\(669\) 0.690148 + 11.0887i 0.0266827 + 0.428712i
\(670\) 3.75539 2.16818i 0.145084 0.0837640i
\(671\) 25.9843 + 45.0062i 1.00311 + 1.73744i
\(672\) 1.41420 7.36299i 0.0545541 0.284034i
\(673\) −7.55471 + 13.0851i −0.291213 + 0.504395i −0.974097 0.226131i \(-0.927392\pi\)
0.682884 + 0.730527i \(0.260725\pi\)
\(674\) 35.3349i 1.36105i
\(675\) −1.71874 + 4.90366i −0.0661545 + 0.188742i
\(676\) −0.0440301 −0.00169347
\(677\) −19.8465 + 34.3752i −0.762764 + 1.32115i 0.178656 + 0.983912i \(0.442825\pi\)
−0.941420 + 0.337235i \(0.890508\pi\)
\(678\) 6.76328 + 10.1944i 0.259742 + 0.391515i
\(679\) −3.04980 + 11.8491i −0.117040 + 0.454729i
\(680\) 12.7737 7.37489i 0.489848 0.282814i
\(681\) 7.90884 0.492240i 0.303067 0.0188627i
\(682\) −23.9968 13.8545i −0.918884 0.530518i
\(683\) 9.81578i 0.375591i −0.982208 0.187795i \(-0.939866\pi\)
0.982208 0.187795i \(-0.0601342\pi\)
\(684\) −0.327807 2.62324i −0.0125340 0.100302i
\(685\) 1.37912i 0.0526934i
\(686\) 6.95543 + 23.1857i 0.265560 + 0.885235i
\(687\) −9.11898 4.53435i −0.347911 0.172996i
\(688\) 0.453739 + 0.785898i 0.0172986 + 0.0299621i
\(689\) 6.37227 + 11.0371i 0.242764 + 0.420480i
\(690\) 6.90951 13.8956i 0.263040 0.528998i
\(691\) 33.1911 + 19.1629i 1.26265 + 0.728990i 0.973586 0.228320i \(-0.0733234\pi\)
0.289062 + 0.957310i \(0.406657\pi\)
\(692\) 1.38509 0.0526531
\(693\) −36.3728 27.7196i −1.38169 1.05298i
\(694\) −13.5736 −0.515248
\(695\) −10.5156 6.07121i −0.398881 0.230294i
\(696\) 42.8262 2.66547i 1.62332 0.101034i
\(697\) −27.4679 47.5757i −1.04042 1.80206i
\(698\) 0.657479 + 1.13879i 0.0248859 + 0.0431037i
\(699\) −14.1784 + 9.40637i −0.536277 + 0.355781i
\(700\) 0.207087 + 0.743394i 0.00782715 + 0.0280977i
\(701\) 0.509304i 0.0192362i 0.999954 + 0.00961808i \(0.00306158\pi\)
−0.999954 + 0.00961808i \(0.996938\pi\)
\(702\) −24.2020 + 4.56616i −0.913444 + 0.172339i
\(703\) 8.48634i 0.320068i
\(704\) −43.9173 25.3557i −1.65520 0.955628i
\(705\) −3.60475 5.43351i −0.135763 0.204638i
\(706\) −8.75158 + 5.05273i −0.329370 + 0.190162i
\(707\) −25.5342 6.57212i −0.960312 0.247170i
\(708\) 4.37547 0.272326i 0.164440 0.0102346i
\(709\) −8.37903 + 14.5129i −0.314681 + 0.545044i −0.979370 0.202077i \(-0.935231\pi\)
0.664688 + 0.747121i \(0.268564\pi\)
\(710\) −9.08833 −0.341079
\(711\) 18.6641 + 24.6578i 0.699958 + 0.924741i
\(712\) 14.0429i 0.526279i
\(713\) −12.6117 + 21.8440i −0.472310 + 0.818065i
\(714\) 27.8662 9.66460i 1.04287 0.361688i
\(715\) 10.4470 + 18.0948i 0.390697 + 0.676707i
\(716\) 4.97421 2.87186i 0.185895 0.107326i
\(717\) −28.5715 14.2070i −1.06702 0.530570i
\(718\) −12.4259 + 21.5223i −0.463731 + 0.803205i
\(719\) −0.103522 −0.00386073 −0.00193037 0.999998i \(-0.500614\pi\)
−0.00193037 + 0.999998i \(0.500614\pi\)
\(720\) −3.88551 + 9.20855i −0.144804 + 0.343182i
\(721\) −18.2600 17.9026i −0.680038 0.666729i
\(722\) −11.1746 6.45164i −0.415874 0.240105i
\(723\) −0.475763 7.64411i −0.0176938 0.284287i
\(724\) −6.71994 + 3.87976i −0.249745 + 0.144190i
\(725\) −7.16276 + 4.13542i −0.266018 + 0.153586i
\(726\) −41.8719 + 27.7790i −1.55401 + 1.03098i
\(727\) −42.0055 24.2519i −1.55790 0.899453i −0.997458 0.0712586i \(-0.977298\pi\)
−0.560441 0.828195i \(-0.689368\pi\)
\(728\) −20.1195 + 20.5211i −0.745677 + 0.760562i
\(729\) 25.1439 9.83793i 0.931255 0.364368i
\(730\) 3.76596 0.139384
\(731\) 0.670661 1.16162i 0.0248053 0.0429640i
\(732\) −3.79713 + 2.51912i −0.140346 + 0.0931095i
\(733\) −9.42982 + 5.44431i −0.348298 + 0.201090i −0.663936 0.747790i \(-0.731115\pi\)
0.315637 + 0.948880i \(0.397782\pi\)
\(734\) 7.48827 + 12.9701i 0.276397 + 0.478734i
\(735\) 0.992154 + 12.0837i 0.0365962 + 0.445714i
\(736\) −5.60777 + 9.71295i −0.206705 + 0.358024i
\(737\) 19.1154i 0.704126i
\(738\) 40.3027 + 17.0056i 1.48356 + 0.625984i
\(739\) −44.1464 −1.62395 −0.811975 0.583692i \(-0.801607\pi\)
−0.811975 + 0.583692i \(0.801607\pi\)
\(740\) 0.409644 0.709525i 0.0150588 0.0260827i
\(741\) −8.44917 + 16.9920i −0.310388 + 0.624217i
\(742\) 11.7693 + 3.02924i 0.432065 + 0.111207i
\(743\) −40.8891 + 23.6073i −1.50008 + 0.866069i −0.500076 + 0.865981i \(0.666695\pi\)
−1.00000 8.81124e-5i \(0.999972\pi\)
\(744\) 8.49931 17.0929i 0.311600 0.626655i
\(745\) 5.61055 + 3.23925i 0.205555 + 0.118677i
\(746\) 18.6897i 0.684278i
\(747\) 6.13486 + 8.10500i 0.224463 + 0.296546i
\(748\) 8.27543i 0.302580i
\(749\) 24.1350 6.72326i 0.881873 0.245663i
\(750\) −0.140627 2.25947i −0.00513499 0.0825041i
\(751\) 13.1860 + 22.8389i 0.481166 + 0.833403i 0.999766 0.0216131i \(-0.00688020\pi\)
−0.518601 + 0.855017i \(0.673547\pi\)
\(752\) −6.27107 10.8618i −0.228682 0.396089i
\(753\) 10.5404 + 15.8877i 0.384112 + 0.578980i
\(754\) −33.9504 19.6013i −1.23640 0.713836i
\(755\) −18.9294 −0.688912
\(756\) 2.22773 3.33410i 0.0810218 0.121260i
\(757\) −29.2002 −1.06130 −0.530649 0.847592i \(-0.678052\pi\)
−0.530649 + 0.847592i \(0.678052\pi\)
\(758\) −7.13902 4.12172i −0.259301 0.149708i
\(759\) 37.8187 + 57.0049i 1.37273 + 2.06915i
\(760\) 4.52471 + 7.83703i 0.164129 + 0.284279i
\(761\) −17.7331 30.7147i −0.642826 1.11341i −0.984799 0.173697i \(-0.944429\pi\)
0.341974 0.939710i \(-0.388905\pi\)
\(762\) 1.37236 + 22.0497i 0.0497153 + 0.798778i
\(763\) −5.91868 21.2467i −0.214271 0.769183i
\(764\) 3.26426i 0.118097i
\(765\) 14.6590 1.83182i 0.529996 0.0662296i
\(766\) 39.0557i 1.41114i
\(767\) −27.2530 15.7345i −0.984048 0.568140i
\(768\) 5.27798 10.6145i 0.190453 0.383017i
\(769\) 29.0445 16.7688i 1.04737 0.604700i 0.125459 0.992099i \(-0.459960\pi\)
0.921912 + 0.387399i \(0.126626\pi\)
\(770\) 19.2952 + 4.96630i 0.695351 + 0.178973i
\(771\) 3.64340 7.32719i 0.131214 0.263882i
\(772\) −0.135253 + 0.234265i −0.00486787 + 0.00843140i
\(773\) 29.1971 1.05015 0.525073 0.851057i \(-0.324038\pi\)
0.525073 + 0.851057i \(0.324038\pi\)
\(774\) 0.132436 + 1.05981i 0.00476033 + 0.0380941i
\(775\) 3.67953i 0.132173i
\(776\) −6.92589 + 11.9960i −0.248625 + 0.430631i
\(777\) 8.42316 9.73344i 0.302179 0.349185i
\(778\) 5.12384 + 8.87475i 0.183698 + 0.318175i
\(779\) 29.1891 16.8523i 1.04581 0.603798i
\(780\) −1.52664 + 1.01282i −0.0546625 + 0.0362647i
\(781\) 20.0315 34.6955i 0.716783 1.24150i
\(782\) −44.1206 −1.57775
\(783\) 40.5575 + 14.2155i 1.44941 + 0.508019i
\(784\) 0.460890 + 23.3165i 0.0164604 + 0.832731i
\(785\) −0.754717 0.435736i −0.0269370 0.0155521i
\(786\) 33.6167 22.3023i 1.19907 0.795496i
\(787\) 20.7541 11.9824i 0.739803 0.427126i −0.0821945 0.996616i \(-0.526193\pi\)
0.821998 + 0.569491i \(0.192860\pi\)
\(788\) 1.78660 1.03150i 0.0636451 0.0367455i
\(789\) −0.429618 6.90270i −0.0152948 0.245743i
\(790\) −11.6682 6.73665i −0.415137 0.239679i
\(791\) 10.2095 + 10.0096i 0.363006 + 0.355902i
\(792\) −31.2464 41.2809i −1.11029 1.46685i
\(793\) 32.7096 1.16155
\(794\) 0.212523 0.368100i 0.00754215 0.0130634i
\(795\) 5.45041 + 2.71018i 0.193306 + 0.0961201i
\(796\) 1.04607 0.603948i 0.0370769 0.0214064i
\(797\) 16.1948 + 28.0502i 0.573648 + 0.993588i 0.996187 + 0.0872431i \(0.0278057\pi\)
−0.422539 + 0.906345i \(0.638861\pi\)
\(798\) 5.92952 + 17.0967i 0.209903 + 0.605218i
\(799\) −9.26913 + 16.0546i −0.327918 + 0.567971i
\(800\) 1.63611i 0.0578451i
\(801\) 5.46784 12.9586i 0.193197 0.457871i
\(802\) 0.848759 0.0299707
\(803\) −8.30051 + 14.3769i −0.292919 + 0.507350i
\(804\) −1.67286 + 0.104117i −0.0589973 + 0.00367194i
\(805\) 4.52078 17.5642i 0.159336 0.619058i
\(806\) −15.1038 + 8.72020i −0.532010 + 0.307156i
\(807\) 20.3814 + 30.7213i 0.717460 + 1.08144i
\(808\) −25.8506 14.9249i −0.909421 0.525055i
\(809\) 4.89038i 0.171937i 0.996298 + 0.0859683i \(0.0273984\pi\)
−0.996298 + 0.0859683i \(0.972602\pi\)
\(810\) −8.42665 + 8.20767i −0.296082 + 0.288388i
\(811\) 8.79200i 0.308729i −0.988014 0.154364i \(-0.950667\pi\)
0.988014 0.154364i \(-0.0493330\pi\)
\(812\) 6.14850 1.71278i 0.215770 0.0601069i
\(813\) −12.8638 + 8.53423i −0.451154 + 0.299309i
\(814\) −10.5764 18.3188i −0.370702 0.642075i
\(815\) 5.39954 + 9.35227i 0.189137 + 0.327596i
\(816\) 28.3608 1.76515i 0.992825 0.0617926i
\(817\) 0.712688 + 0.411470i 0.0249338 + 0.0143955i
\(818\) −28.3695 −0.991916
\(819\) −26.5563 + 11.1028i −0.927953 + 0.387964i
\(820\) 3.25392 0.113632
\(821\) −37.8062 21.8274i −1.31945 0.761783i −0.335807 0.941931i \(-0.609009\pi\)
−0.983640 + 0.180148i \(0.942342\pi\)
\(822\) −1.39008 + 2.79557i −0.0484845 + 0.0975067i
\(823\) 0.415923 + 0.720400i 0.0144982 + 0.0251116i 0.873183 0.487392i \(-0.162052\pi\)
−0.858685 + 0.512503i \(0.828718\pi\)
\(824\) −14.4752 25.0718i −0.504269 0.873419i
\(825\) 8.93569 + 4.44321i 0.311101 + 0.154693i
\(826\) −28.9075 + 8.05273i −1.00582 + 0.280190i
\(827\) 31.2225i 1.08571i 0.839826 + 0.542856i \(0.182657\pi\)
−0.839826 + 0.542856i \(0.817343\pi\)
\(828\) −4.78272 + 3.62015i −0.166211 + 0.125809i
\(829\) 17.2401i 0.598772i 0.954132 + 0.299386i \(0.0967819\pi\)
−0.954132 + 0.299386i \(0.903218\pi\)
\(830\) −3.83533 2.21433i −0.133126 0.0768604i
\(831\) −47.5259 + 2.95797i −1.64865 + 0.102611i
\(832\) −27.6421 + 15.9591i −0.958316 + 0.553284i
\(833\) 29.5057 17.8218i 1.02231 0.617487i
\(834\) −15.1965 22.9060i −0.526212 0.793170i
\(835\) 3.22089 5.57874i 0.111463 0.193060i
\(836\) −5.07722 −0.175599
\(837\) 14.4985 12.4638i 0.501141 0.430811i
\(838\) 3.78993i 0.130921i
\(839\) 23.3177 40.3874i 0.805016 1.39433i −0.111265 0.993791i \(-0.535490\pi\)
0.916280 0.400537i \(-0.131177\pi\)
\(840\) −2.58904 + 13.4797i −0.0893305 + 0.465095i
\(841\) 19.7034 + 34.1274i 0.679429 + 1.17681i
\(842\) −13.9619 + 8.06092i −0.481160 + 0.277798i
\(843\) 0.427272 + 6.86500i 0.0147160 + 0.236443i
\(844\) −2.15543 + 3.73331i −0.0741930 + 0.128506i
\(845\) 0.150956 0.00519305
\(846\) −1.83039 14.6475i −0.0629300 0.503592i
\(847\) −41.1129 + 41.9336i −1.41266 + 1.44086i
\(848\) 10.1397 + 5.85417i 0.348199 + 0.201033i
\(849\) −1.83861 0.914236i −0.0631009 0.0313765i
\(850\) −5.57395 + 3.21812i −0.191185 + 0.110381i
\(851\) −16.6755 + 9.62758i −0.571627 + 0.330029i
\(852\) 3.14544 + 1.56405i 0.107761 + 0.0535835i
\(853\) 29.6463 + 17.1163i 1.01507 + 0.586051i 0.912672 0.408692i \(-0.134015\pi\)
0.102398 + 0.994743i \(0.467348\pi\)
\(854\) 21.8364 22.2723i 0.747228 0.762144i
\(855\) 1.12388 + 8.99371i 0.0384358 + 0.307579i
\(856\) 28.3638 0.969456
\(857\) 4.58831 7.94718i 0.156734 0.271471i −0.776955 0.629556i \(-0.783237\pi\)
0.933689 + 0.358085i \(0.116570\pi\)
\(858\) 2.93828 + 47.2095i 0.100311 + 1.61171i
\(859\) −14.7502 + 8.51605i −0.503271 + 0.290564i −0.730063 0.683379i \(-0.760510\pi\)
0.226792 + 0.973943i \(0.427176\pi\)
\(860\) 0.0397242 + 0.0688043i 0.00135458 + 0.00234621i
\(861\) 50.2055 + 9.64292i 1.71100 + 0.328630i
\(862\) −16.5573 + 28.6781i −0.563945 + 0.976781i
\(863\) 48.0982i 1.63728i −0.574307 0.818640i \(-0.694728\pi\)
0.574307 0.818640i \(-0.305272\pi\)
\(864\) 6.44676 5.54202i 0.219323 0.188543i
\(865\) −4.74873 −0.161462
\(866\) 19.5921 33.9346i 0.665768 1.15314i
\(867\) −6.94116 10.4626i −0.235734 0.355327i
\(868\) 0.707776 2.74987i 0.0240235 0.0933366i
\(869\) 51.4356 29.6963i 1.74483 1.00738i
\(870\) −18.6877 + 1.16311i −0.633573 + 0.0394331i
\(871\) 10.4195 + 6.01573i 0.353053 + 0.203835i
\(872\) 24.9695i 0.845574i
\(873\) −11.0620 + 8.37307i −0.374392 + 0.283385i
\(874\) 27.0693i 0.915633i
\(875\) −0.709992 2.54871i −0.0240021 0.0861621i
\(876\) −1.30339 0.648101i −0.0440374 0.0218973i
\(877\) 20.2172 + 35.0172i 0.682685 + 1.18245i 0.974158 + 0.225867i \(0.0725214\pi\)
−0.291473 + 0.956579i \(0.594145\pi\)
\(878\) −14.5997 25.2873i −0.492714 0.853406i
\(879\) −21.1818 + 42.5985i −0.714444 + 1.43681i
\(880\) 16.6236 + 9.59763i 0.560381 + 0.323536i
\(881\) 47.9451 1.61531 0.807656 0.589653i \(-0.200736\pi\)
0.807656 + 0.589653i \(0.200736\pi\)
\(882\) −10.1686 + 25.4945i −0.342393 + 0.858446i
\(883\) 22.4684 0.756122 0.378061 0.925781i \(-0.376591\pi\)
0.378061 + 0.925781i \(0.376591\pi\)
\(884\) 4.51082 + 2.60432i 0.151715 + 0.0875929i
\(885\) −15.0012 + 0.933661i −0.504259 + 0.0313847i
\(886\) −8.56882 14.8416i −0.287875 0.498614i
\(887\) 4.00551 + 6.93775i 0.134492 + 0.232947i 0.925403 0.378984i \(-0.123726\pi\)
−0.790911 + 0.611931i \(0.790393\pi\)
\(888\) 12.1432 8.05618i 0.407501 0.270348i
\(889\) 6.92868 + 24.8724i 0.232380 + 0.834192i
\(890\) 6.12777i 0.205403i
\(891\) −12.7605 50.2600i −0.427492 1.68377i
\(892\) 1.87093i 0.0626433i
\(893\) −9.84997 5.68689i −0.329617 0.190304i
\(894\) 8.10799 + 12.2213i 0.271172 + 0.408743i
\(895\) −17.0539 + 9.84610i −0.570050 + 0.329119i
\(896\) −5.42868 + 21.0917i −0.181360 + 0.704623i
\(897\) 42.9743 2.67469i 1.43487 0.0893052i
\(898\) 18.9582 32.8366i 0.632645 1.09577i
\(899\) 30.4329 1.01499
\(900\) −0.340171 + 0.806196i −0.0113390 + 0.0268732i
\(901\) 17.3058i 0.576541i
\(902\) 42.0056 72.7558i 1.39863 2.42250i
\(903\) 0.409013 + 1.17932i 0.0136111 + 0.0392453i
\(904\) 8.09333 + 14.0181i 0.269180 + 0.466234i
\(905\) 23.0391 13.3016i 0.765847 0.442162i
\(906\) −38.3713 19.0799i −1.27480 0.633886i
\(907\) 5.25834 9.10772i 0.174600 0.302417i −0.765423 0.643528i \(-0.777470\pi\)
0.940023 + 0.341111i \(0.110803\pi\)
\(908\) 1.33442 0.0442841
\(909\) −18.0434 23.8379i −0.598463 0.790654i
\(910\) 8.77937 8.95463i 0.291033 0.296843i
\(911\) 25.7026 + 14.8394i 0.851567 + 0.491652i 0.861179 0.508302i \(-0.169726\pi\)
−0.00961242 + 0.999954i \(0.503060\pi\)
\(912\) 1.08297 + 17.4002i 0.0358608 + 0.576177i
\(913\) 16.9068 9.76115i 0.559534 0.323047i
\(914\) −6.12380 + 3.53558i −0.202557 + 0.116947i
\(915\) 13.0183 8.63675i 0.430373 0.285522i
\(916\) −1.48523 0.857495i −0.0490732 0.0283324i
\(917\) 33.0073 33.6662i 1.09000 1.11176i
\(918\) 31.5612 + 11.0622i 1.04167 + 0.365109i
\(919\) 7.29885 0.240767 0.120383 0.992727i \(-0.461588\pi\)
0.120383 + 0.992727i \(0.461588\pi\)
\(920\) 10.2664 17.7819i 0.338473 0.586252i
\(921\) 10.8176 7.17668i 0.356451 0.236480i
\(922\) 15.8439 9.14747i 0.521791 0.301256i
\(923\) −12.6080 21.8378i −0.414999 0.718799i
\(924\) −5.82334 5.03942i −0.191574 0.165785i
\(925\) −1.40446 + 2.43259i −0.0461782 + 0.0799830i
\(926\) 13.3789i 0.439657i
\(927\) −3.59545 28.7723i −0.118090 0.945005i
\(928\) 13.5320 0.444209
\(929\) 12.1110 20.9768i 0.397348 0.688227i −0.596050 0.802948i \(-0.703264\pi\)
0.993398 + 0.114720i \(0.0365972\pi\)
\(930\) −3.70878 + 7.45868i −0.121616 + 0.244580i
\(931\) 10.9342 + 18.1026i 0.358353 + 0.593290i
\(932\) −2.48141 + 1.43264i −0.0812813 + 0.0469278i
\(933\) −15.3481 + 30.8665i −0.502475 + 1.01052i
\(934\) −6.55050 3.78193i −0.214339 0.123749i
\(935\) 28.3721i 0.927867i
\(936\) −32.3350 + 4.04067i −1.05690 + 0.132073i
\(937\) 21.2312i 0.693594i −0.937940 0.346797i \(-0.887269\pi\)
0.937940 0.346797i \(-0.112731\pi\)
\(938\) 11.0521 3.07878i 0.360864 0.100526i
\(939\) −3.51899 56.5398i −0.114838 1.84511i
\(940\) −0.549024 0.950937i −0.0179072 0.0310161i
\(941\) 2.03848 + 3.53075i 0.0664524 + 0.115099i 0.897337 0.441345i \(-0.145499\pi\)
−0.830885 + 0.556444i \(0.812165\pi\)
\(942\) −1.09067 1.64398i −0.0355358 0.0535639i
\(943\) −66.2289 38.2373i −2.15671 1.24518i
\(944\) −28.9104 −0.940954
\(945\) −7.63772 + 11.4309i −0.248455 + 0.371847i
\(946\) 2.05124 0.0666914
\(947\) −18.2207 10.5197i −0.592093 0.341845i 0.173832 0.984775i \(-0.444385\pi\)
−0.765925 + 0.642930i \(0.777718\pi\)
\(948\) 2.87900 + 4.33957i 0.0935054 + 0.140943i
\(949\) 5.22443 + 9.04899i 0.169592 + 0.293743i
\(950\) −1.97441 3.41978i −0.0640584 0.110952i
\(951\) 0.946947 + 15.2146i 0.0307069 + 0.493369i
\(952\) 37.5929 10.4722i 1.21839 0.339406i
\(953\) 45.0425i 1.45907i −0.683944 0.729535i \(-0.739737\pi\)
0.683944 0.729535i \(-0.260263\pi\)
\(954\) 8.31665 + 10.9874i 0.269261 + 0.355732i
\(955\) 11.1914i 0.362147i
\(956\) −4.65349 2.68670i −0.150505 0.0868940i
\(957\) 36.7491 73.9057i 1.18793 2.38903i
\(958\) −13.3991 + 7.73599i −0.432906 + 0.249939i
\(959\) −0.909505 + 3.53363i −0.0293694 + 0.114107i
\(960\) −6.78756 + 13.6504i −0.219068 + 0.440564i
\(961\) −8.73052 + 15.1217i −0.281630 + 0.487797i
\(962\) −13.3138 −0.429254
\(963\) 26.1739 + 11.0440i 0.843442 + 0.355887i
\(964\) 1.28975i 0.0415400i
\(965\) 0.463712 0.803173i 0.0149274 0.0258551i
\(966\) 26.8678 31.0473i 0.864456 0.998929i
\(967\) 17.2648 + 29.9034i 0.555197 + 0.961630i 0.997888 + 0.0649554i \(0.0206905\pi\)
−0.442691 + 0.896674i \(0.645976\pi\)
\(968\) −57.5768 + 33.2420i −1.85059 + 1.06844i
\(969\) 21.4728 14.2457i 0.689805 0.457637i
\(970\) 3.02219 5.23459i 0.0970368 0.168073i
\(971\) 52.4564 1.68341 0.841704 0.539940i \(-0.181553\pi\)
0.841704 + 0.539940i \(0.181553\pi\)
\(972\) 4.32893 1.39047i 0.138851 0.0445994i
\(973\) −22.9398 22.4908i −0.735415 0.721022i
\(974\) −23.2560 13.4269i −0.745171 0.430225i
\(975\) 5.23404 3.47242i 0.167624 0.111206i
\(976\) 26.0242 15.0251i 0.833014 0.480941i
\(977\) 28.8591 16.6618i 0.923286 0.533059i 0.0386041 0.999255i \(-0.487709\pi\)
0.884682 + 0.466195i \(0.154376\pi\)
\(978\) 1.51865 + 24.4002i 0.0485609 + 0.780231i
\(979\) −23.3933 13.5062i −0.747654 0.431659i
\(980\) 0.0403503 + 2.04133i 0.00128894 + 0.0652078i
\(981\) 9.72232 23.0416i 0.310410 0.735663i
\(982\) −9.08575 −0.289938
\(983\) −10.6537 + 18.4527i −0.339800 + 0.588550i −0.984395 0.175974i \(-0.943693\pi\)
0.644595 + 0.764524i \(0.277026\pi\)
\(984\) 51.8239 + 25.7691i 1.65208 + 0.821488i
\(985\) −6.12532 + 3.53646i −0.195169 + 0.112681i
\(986\) 26.6166 + 46.1013i 0.847645 + 1.46816i
\(987\) −5.65293 16.2992i −0.179935 0.518810i
\(988\) −1.59783 + 2.76752i −0.0508337 + 0.0880466i
\(989\) 1.86722i 0.0593741i
\(990\) 13.6348 + 18.0134i 0.433341 + 0.572504i
\(991\) 6.50275 0.206567 0.103283 0.994652i \(-0.467065\pi\)
0.103283 + 0.994652i \(0.467065\pi\)
\(992\) 3.01005 5.21356i 0.0955692 0.165531i
\(993\) −24.7462 + 1.54018i −0.785296 + 0.0488762i
\(994\) −23.2865 5.99360i −0.738603 0.190105i
\(995\) −3.58642 + 2.07062i −0.113697 + 0.0656431i
\(996\) 0.946322 + 1.42641i 0.0299854 + 0.0451975i
\(997\) −18.8609 10.8893i −0.597330 0.344869i 0.170660 0.985330i \(-0.445410\pi\)
−0.767991 + 0.640461i \(0.778743\pi\)
\(998\) 35.0425i 1.10925i
\(999\) 14.3425 2.70598i 0.453776 0.0856135i
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 315.2.bl.i.146.4 yes 24
3.2 odd 2 945.2.bl.i.251.9 24
7.6 odd 2 315.2.bl.j.146.4 yes 24
9.4 even 3 945.2.bl.j.881.9 24
9.5 odd 6 315.2.bl.j.41.4 yes 24
21.20 even 2 945.2.bl.j.251.9 24
63.13 odd 6 945.2.bl.i.881.9 24
63.41 even 6 inner 315.2.bl.i.41.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bl.i.41.4 24 63.41 even 6 inner
315.2.bl.i.146.4 yes 24 1.1 even 1 trivial
315.2.bl.j.41.4 yes 24 9.5 odd 6
315.2.bl.j.146.4 yes 24 7.6 odd 2
945.2.bl.i.251.9 24 3.2 odd 2
945.2.bl.i.881.9 24 63.13 odd 6
945.2.bl.j.251.9 24 21.20 even 2
945.2.bl.j.881.9 24 9.4 even 3