Properties

Label 403.2.e.a.191.14
Level $403$
Weight $2$
Character 403.191
Analytic conductor $3.218$
Analytic rank $0$
Dimension $70$
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] = [403,2,Mod(191,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.e (of order \(3\), 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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(35\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 191.14
Character \(\chi\) \(=\) 403.191
Dual form 403.2.e.a.211.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.356919 + 0.618202i) q^{2} +(-0.621239 - 1.07602i) q^{3} +(0.745217 + 1.29075i) q^{4} +(-0.797665 - 1.38160i) q^{5} +0.886928 q^{6} -1.56596 q^{7} -2.49161 q^{8} +(0.728125 - 1.26115i) q^{9} +O(q^{10})\) \(q+(-0.356919 + 0.618202i) q^{2} +(-0.621239 - 1.07602i) q^{3} +(0.745217 + 1.29075i) q^{4} +(-0.797665 - 1.38160i) q^{5} +0.886928 q^{6} -1.56596 q^{7} -2.49161 q^{8} +(0.728125 - 1.26115i) q^{9} +1.13881 q^{10} -3.65486 q^{11} +(0.925916 - 1.60373i) q^{12} +(-3.60365 - 0.117122i) q^{13} +(0.558920 - 0.968077i) q^{14} +(-0.991081 + 1.71660i) q^{15} +(-0.601132 + 1.04119i) q^{16} +5.00804 q^{17} +(0.519764 + 0.900257i) q^{18} -7.66971 q^{19} +(1.18887 - 2.05918i) q^{20} +(0.972832 + 1.68499i) q^{21} +(1.30449 - 2.25945i) q^{22} +(1.58610 - 2.74721i) q^{23} +(1.54788 + 2.68101i) q^{24} +(1.22746 - 2.12602i) q^{25} +(1.35862 - 2.18598i) q^{26} -5.53679 q^{27} +(-1.16698 - 2.02126i) q^{28} +(-0.219667 + 0.380475i) q^{29} +(-0.707472 - 1.22538i) q^{30} +(-5.20665 + 1.97251i) q^{31} +(-2.92072 - 5.05883i) q^{32} +(2.27054 + 3.93270i) q^{33} +(-1.78747 + 3.09598i) q^{34} +(1.24911 + 2.16352i) q^{35} +2.17044 q^{36} +(-2.72042 - 4.71190i) q^{37} +(2.73747 - 4.74143i) q^{38} +(2.11270 + 3.95035i) q^{39} +(1.98747 + 3.44240i) q^{40} +0.242638 q^{41} -1.38889 q^{42} -4.04007 q^{43} +(-2.72367 - 4.71753i) q^{44} -2.32320 q^{45} +(1.13222 + 1.96107i) q^{46} +11.9925 q^{47} +1.49379 q^{48} -4.54778 q^{49} +(0.876208 + 1.51764i) q^{50} +(-3.11119 - 5.38874i) q^{51} +(-2.53432 - 4.73871i) q^{52} +(-1.90660 - 3.30232i) q^{53} +(1.97619 - 3.42286i) q^{54} +(2.91536 + 5.04955i) q^{55} +3.90174 q^{56} +(4.76472 + 8.25274i) q^{57} +(-0.156807 - 0.271597i) q^{58} -2.45827 q^{59} -2.95428 q^{60} +(0.0980818 + 0.169883i) q^{61} +(0.638944 - 3.92279i) q^{62} +(-1.14021 + 1.97490i) q^{63} +1.76532 q^{64} +(2.71269 + 5.07221i) q^{65} -3.24160 q^{66} +14.4107 q^{67} +(3.73208 + 6.46415i) q^{68} -3.94139 q^{69} -1.78332 q^{70} +(0.489127 - 0.847193i) q^{71} +(-1.81420 + 3.14229i) q^{72} +(5.90111 + 10.2210i) q^{73} +3.88388 q^{74} -3.05018 q^{75} +(-5.71560 - 9.89971i) q^{76} +5.72335 q^{77} +(-3.19618 - 0.103879i) q^{78} +(-1.38093 + 2.39183i) q^{79} +1.91801 q^{80} +(1.25529 + 2.17423i) q^{81} +(-0.0866022 + 0.149999i) q^{82} +(3.01958 + 5.23007i) q^{83} +(-1.44994 + 2.51137i) q^{84} +(-3.99474 - 6.91909i) q^{85} +(1.44198 - 2.49758i) q^{86} +0.545863 q^{87} +9.10648 q^{88} +(-1.28984 + 2.23407i) q^{89} +(0.829195 - 1.43621i) q^{90} +(5.64315 + 0.183409i) q^{91} +4.72797 q^{92} +(5.35703 + 4.37705i) q^{93} +(-4.28037 + 7.41382i) q^{94} +(6.11786 + 10.5964i) q^{95} +(-3.62893 + 6.28549i) q^{96} +(0.0643701 + 0.111492i) q^{97} +(1.62319 - 2.81145i) q^{98} +(-2.66120 + 4.60933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70 q - 2 q^{2} + 4 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{7} - 6 q^{8} - 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 70 q - 2 q^{2} + 4 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{7} - 6 q^{8} - 29 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} + q^{13} - 10 q^{14} + q^{15} - 28 q^{16} - 28 q^{17} - 20 q^{18} + 4 q^{19} + 25 q^{20} - 21 q^{21} + 4 q^{22} + 2 q^{23} + 4 q^{24} - 23 q^{25} - 24 q^{26} - 38 q^{27} - 21 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} + 56 q^{36} - 12 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} + 4 q^{41} - 54 q^{42} + 2 q^{43} + 2 q^{44} + 58 q^{45} + 14 q^{46} - 2 q^{48} + 74 q^{49} + 7 q^{50} - 9 q^{51} + 5 q^{52} - 2 q^{53} + 24 q^{54} + 5 q^{55} + 26 q^{56} - q^{57} + 6 q^{58} - 42 q^{59} + 18 q^{60} - 3 q^{61} + 13 q^{62} - 32 q^{63} - 14 q^{64} + 20 q^{65} - 28 q^{66} + 4 q^{67} + 42 q^{68} - 64 q^{69} - 14 q^{70} + 43 q^{71} - 5 q^{72} + 11 q^{73} + 14 q^{74} - 74 q^{75} - 28 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} - 76 q^{80} - 11 q^{81} - 17 q^{82} + 56 q^{83} - 45 q^{84} - 5 q^{85} + 54 q^{86} + 48 q^{87} - 8 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 22 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} + 12 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.356919 + 0.618202i −0.252380 + 0.437135i −0.964181 0.265247i \(-0.914547\pi\)
0.711801 + 0.702382i \(0.247880\pi\)
\(3\) −0.621239 1.07602i −0.358672 0.621239i 0.629067 0.777351i \(-0.283437\pi\)
−0.987739 + 0.156112i \(0.950104\pi\)
\(4\) 0.745217 + 1.29075i 0.372609 + 0.645377i
\(5\) −0.797665 1.38160i −0.356727 0.617869i 0.630685 0.776039i \(-0.282774\pi\)
−0.987412 + 0.158170i \(0.949441\pi\)
\(6\) 0.886928 0.362087
\(7\) −1.56596 −0.591875 −0.295938 0.955207i \(-0.595632\pi\)
−0.295938 + 0.955207i \(0.595632\pi\)
\(8\) −2.49161 −0.880916
\(9\) 0.728125 1.26115i 0.242708 0.420383i
\(10\) 1.13881 0.360123
\(11\) −3.65486 −1.10198 −0.550991 0.834511i \(-0.685750\pi\)
−0.550991 + 0.834511i \(0.685750\pi\)
\(12\) 0.925916 1.60373i 0.267289 0.462958i
\(13\) −3.60365 0.117122i −0.999472 0.0324839i
\(14\) 0.558920 0.968077i 0.149378 0.258730i
\(15\) −0.991081 + 1.71660i −0.255896 + 0.443225i
\(16\) −0.601132 + 1.04119i −0.150283 + 0.260298i
\(17\) 5.00804 1.21463 0.607314 0.794462i \(-0.292247\pi\)
0.607314 + 0.794462i \(0.292247\pi\)
\(18\) 0.519764 + 0.900257i 0.122509 + 0.212193i
\(19\) −7.66971 −1.75955 −0.879776 0.475388i \(-0.842308\pi\)
−0.879776 + 0.475388i \(0.842308\pi\)
\(20\) 1.18887 2.05918i 0.265839 0.460447i
\(21\) 0.972832 + 1.68499i 0.212289 + 0.367696i
\(22\) 1.30449 2.25945i 0.278119 0.481715i
\(23\) 1.58610 2.74721i 0.330725 0.572833i −0.651929 0.758280i \(-0.726040\pi\)
0.982654 + 0.185447i \(0.0593733\pi\)
\(24\) 1.54788 + 2.68101i 0.315960 + 0.547259i
\(25\) 1.22746 2.12602i 0.245492 0.425205i
\(26\) 1.35862 2.18598i 0.266447 0.428706i
\(27\) −5.53679 −1.06556
\(28\) −1.16698 2.02126i −0.220538 0.381983i
\(29\) −0.219667 + 0.380475i −0.0407912 + 0.0706524i −0.885700 0.464258i \(-0.846321\pi\)
0.844909 + 0.534910i \(0.179654\pi\)
\(30\) −0.707472 1.22538i −0.129166 0.223722i
\(31\) −5.20665 + 1.97251i −0.935142 + 0.354273i
\(32\) −2.92072 5.05883i −0.516315 0.894284i
\(33\) 2.27054 + 3.93270i 0.395251 + 0.684594i
\(34\) −1.78747 + 3.09598i −0.306548 + 0.530957i
\(35\) 1.24911 + 2.16352i 0.211138 + 0.365701i
\(36\) 2.17044 0.361741
\(37\) −2.72042 4.71190i −0.447234 0.774632i 0.550971 0.834524i \(-0.314257\pi\)
−0.998205 + 0.0598926i \(0.980924\pi\)
\(38\) 2.73747 4.74143i 0.444076 0.769162i
\(39\) 2.11270 + 3.95035i 0.338303 + 0.632562i
\(40\) 1.98747 + 3.44240i 0.314246 + 0.544291i
\(41\) 0.242638 0.0378937 0.0189468 0.999820i \(-0.493969\pi\)
0.0189468 + 0.999820i \(0.493969\pi\)
\(42\) −1.38889 −0.214310
\(43\) −4.04007 −0.616105 −0.308052 0.951369i \(-0.599677\pi\)
−0.308052 + 0.951369i \(0.599677\pi\)
\(44\) −2.72367 4.71753i −0.410608 0.711194i
\(45\) −2.32320 −0.346322
\(46\) 1.13222 + 1.96107i 0.166937 + 0.289143i
\(47\) 11.9925 1.74929 0.874646 0.484762i \(-0.161094\pi\)
0.874646 + 0.484762i \(0.161094\pi\)
\(48\) 1.49379 0.215609
\(49\) −4.54778 −0.649684
\(50\) 0.876208 + 1.51764i 0.123915 + 0.214626i
\(51\) −3.11119 5.38874i −0.435653 0.754574i
\(52\) −2.53432 4.73871i −0.351448 0.657140i
\(53\) −1.90660 3.30232i −0.261891 0.453609i 0.704853 0.709353i \(-0.251013\pi\)
−0.966745 + 0.255744i \(0.917680\pi\)
\(54\) 1.97619 3.42286i 0.268925 0.465792i
\(55\) 2.91536 + 5.04955i 0.393107 + 0.680881i
\(56\) 3.90174 0.521393
\(57\) 4.76472 + 8.25274i 0.631103 + 1.09310i
\(58\) −0.156807 0.271597i −0.0205898 0.0356625i
\(59\) −2.45827 −0.320040 −0.160020 0.987114i \(-0.551156\pi\)
−0.160020 + 0.987114i \(0.551156\pi\)
\(60\) −2.95428 −0.381396
\(61\) 0.0980818 + 0.169883i 0.0125581 + 0.0217512i 0.872236 0.489085i \(-0.162669\pi\)
−0.859678 + 0.510836i \(0.829336\pi\)
\(62\) 0.638944 3.92279i 0.0811460 0.498195i
\(63\) −1.14021 + 1.97490i −0.143653 + 0.248814i
\(64\) 1.76532 0.220665
\(65\) 2.71269 + 5.07221i 0.336468 + 0.629131i
\(66\) −3.24160 −0.399014
\(67\) 14.4107 1.76055 0.880275 0.474464i \(-0.157358\pi\)
0.880275 + 0.474464i \(0.157358\pi\)
\(68\) 3.73208 + 6.46415i 0.452581 + 0.783893i
\(69\) −3.94139 −0.474488
\(70\) −1.78332 −0.213148
\(71\) 0.489127 0.847193i 0.0580487 0.100543i −0.835541 0.549429i \(-0.814845\pi\)
0.893589 + 0.448885i \(0.148179\pi\)
\(72\) −1.81420 + 3.14229i −0.213806 + 0.370322i
\(73\) 5.90111 + 10.2210i 0.690673 + 1.19628i 0.971618 + 0.236556i \(0.0760188\pi\)
−0.280945 + 0.959724i \(0.590648\pi\)
\(74\) 3.88388 0.451492
\(75\) −3.05018 −0.352205
\(76\) −5.71560 9.89971i −0.655624 1.13557i
\(77\) 5.72335 0.652236
\(78\) −3.19618 0.103879i −0.361896 0.0117620i
\(79\) −1.38093 + 2.39183i −0.155366 + 0.269102i −0.933192 0.359377i \(-0.882989\pi\)
0.777826 + 0.628480i \(0.216322\pi\)
\(80\) 1.91801 0.214440
\(81\) 1.25529 + 2.17423i 0.139477 + 0.241581i
\(82\) −0.0866022 + 0.149999i −0.00956361 + 0.0165647i
\(83\) 3.01958 + 5.23007i 0.331442 + 0.574075i 0.982795 0.184701i \(-0.0591315\pi\)
−0.651353 + 0.758775i \(0.725798\pi\)
\(84\) −1.44994 + 2.51137i −0.158202 + 0.274013i
\(85\) −3.99474 6.91909i −0.433290 0.750481i
\(86\) 1.44198 2.49758i 0.155493 0.269321i
\(87\) 0.545863 0.0585226
\(88\) 9.10648 0.970754
\(89\) −1.28984 + 2.23407i −0.136723 + 0.236811i −0.926254 0.376899i \(-0.876990\pi\)
0.789532 + 0.613710i \(0.210324\pi\)
\(90\) 0.829195 1.43621i 0.0874048 0.151390i
\(91\) 5.64315 + 0.183409i 0.591563 + 0.0192264i
\(92\) 4.72797 0.492924
\(93\) 5.35703 + 4.37705i 0.555498 + 0.453878i
\(94\) −4.28037 + 7.41382i −0.441487 + 0.764677i
\(95\) 6.11786 + 10.5964i 0.627679 + 1.08717i
\(96\) −3.62893 + 6.28549i −0.370376 + 0.641510i
\(97\) 0.0643701 + 0.111492i 0.00653580 + 0.0113203i 0.869275 0.494329i \(-0.164586\pi\)
−0.862739 + 0.505649i \(0.831253\pi\)
\(98\) 1.62319 2.81145i 0.163967 0.283999i
\(99\) −2.66120 + 4.60933i −0.267460 + 0.463255i
\(100\) 3.65890 0.365890
\(101\) 0.127849 0.221440i 0.0127214 0.0220342i −0.859595 0.510977i \(-0.829284\pi\)
0.872316 + 0.488942i \(0.162617\pi\)
\(102\) 4.44177 0.439801
\(103\) 1.12881 + 1.95515i 0.111225 + 0.192647i 0.916264 0.400574i \(-0.131189\pi\)
−0.805040 + 0.593221i \(0.797856\pi\)
\(104\) 8.97888 + 0.291823i 0.880451 + 0.0286156i
\(105\) 1.55199 2.68812i 0.151459 0.262334i
\(106\) 2.72201 0.264385
\(107\) −4.50776 7.80766i −0.435781 0.754795i 0.561578 0.827424i \(-0.310195\pi\)
−0.997359 + 0.0726287i \(0.976861\pi\)
\(108\) −4.12611 7.14663i −0.397035 0.687685i
\(109\) 14.0280 1.34364 0.671819 0.740715i \(-0.265513\pi\)
0.671819 + 0.740715i \(0.265513\pi\)
\(110\) −4.16219 −0.396849
\(111\) −3.38006 + 5.85443i −0.320821 + 0.555678i
\(112\) 0.941345 1.63046i 0.0889488 0.154064i
\(113\) −4.08609 + 7.07732i −0.384387 + 0.665778i −0.991684 0.128697i \(-0.958921\pi\)
0.607297 + 0.794475i \(0.292254\pi\)
\(114\) −6.80249 −0.637111
\(115\) −5.06072 −0.471914
\(116\) −0.654799 −0.0607965
\(117\) −2.77161 + 4.45946i −0.256236 + 0.412277i
\(118\) 0.877405 1.51971i 0.0807717 0.139901i
\(119\) −7.84237 −0.718908
\(120\) 2.46939 4.27710i 0.225423 0.390444i
\(121\) 2.35803 0.214366
\(122\) −0.140029 −0.0126776
\(123\) −0.150736 0.261083i −0.0135914 0.0235410i
\(124\) −6.42611 5.25056i −0.577082 0.471514i
\(125\) −11.8931 −1.06375
\(126\) −0.813927 1.40976i −0.0725103 0.125592i
\(127\) −8.09680 14.0241i −0.718475 1.24444i −0.961604 0.274441i \(-0.911507\pi\)
0.243129 0.969994i \(-0.421826\pi\)
\(128\) 5.21136 9.02634i 0.460624 0.797823i
\(129\) 2.50985 + 4.34718i 0.220980 + 0.382748i
\(130\) −4.10387 0.133380i −0.359933 0.0116982i
\(131\) −10.0679 + 17.4381i −0.879634 + 1.52357i −0.0278918 + 0.999611i \(0.508879\pi\)
−0.851743 + 0.523961i \(0.824454\pi\)
\(132\) −3.38409 + 5.86142i −0.294548 + 0.510172i
\(133\) 12.0104 1.04144
\(134\) −5.14347 + 8.90874i −0.444328 + 0.769598i
\(135\) 4.41651 + 7.64961i 0.380112 + 0.658374i
\(136\) −12.4781 −1.06999
\(137\) 10.1461 17.5736i 0.866843 1.50142i 0.00163788 0.999999i \(-0.499479\pi\)
0.865205 0.501418i \(-0.167188\pi\)
\(138\) 1.40676 2.43658i 0.119751 0.207415i
\(139\) 5.50170 + 9.52923i 0.466648 + 0.808259i 0.999274 0.0380920i \(-0.0121280\pi\)
−0.532626 + 0.846351i \(0.678795\pi\)
\(140\) −1.86171 + 3.22458i −0.157344 + 0.272527i
\(141\) −7.45023 12.9042i −0.627423 1.08673i
\(142\) 0.349158 + 0.604759i 0.0293007 + 0.0507503i
\(143\) 13.1708 + 0.428067i 1.10140 + 0.0357967i
\(144\) 0.875398 + 1.51623i 0.0729498 + 0.126353i
\(145\) 0.700883 0.0582052
\(146\) −8.42488 −0.697248
\(147\) 2.82526 + 4.89349i 0.233024 + 0.403609i
\(148\) 4.05460 7.02278i 0.333286 0.577269i
\(149\) 9.72953 0.797074 0.398537 0.917152i \(-0.369518\pi\)
0.398537 + 0.917152i \(0.369518\pi\)
\(150\) 1.08867 1.88563i 0.0888895 0.153961i
\(151\) −19.4285 −1.58107 −0.790534 0.612418i \(-0.790197\pi\)
−0.790534 + 0.612418i \(0.790197\pi\)
\(152\) 19.1099 1.55002
\(153\) 3.64648 6.31588i 0.294800 0.510609i
\(154\) −2.04277 + 3.53819i −0.164611 + 0.285115i
\(155\) 6.87838 + 5.62009i 0.552485 + 0.451416i
\(156\) −3.52451 + 5.67084i −0.282186 + 0.454031i
\(157\) −15.4971 −1.23681 −0.618403 0.785861i \(-0.712220\pi\)
−0.618403 + 0.785861i \(0.712220\pi\)
\(158\) −0.985758 1.70738i −0.0784227 0.135832i
\(159\) −2.36891 + 4.10306i −0.187866 + 0.325394i
\(160\) −4.65951 + 8.07051i −0.368367 + 0.638030i
\(161\) −2.48377 + 4.30201i −0.195748 + 0.339046i
\(162\) −1.79215 −0.140805
\(163\) 0.916014 + 1.58658i 0.0717477 + 0.124271i 0.899667 0.436576i \(-0.143809\pi\)
−0.827920 + 0.560847i \(0.810476\pi\)
\(164\) 0.180818 + 0.313186i 0.0141195 + 0.0244557i
\(165\) 3.62227 6.27395i 0.281993 0.488426i
\(166\) −4.31099 −0.334598
\(167\) −3.23179 5.59763i −0.250083 0.433157i 0.713465 0.700691i \(-0.247125\pi\)
−0.963549 + 0.267534i \(0.913791\pi\)
\(168\) −2.42392 4.19834i −0.187009 0.323909i
\(169\) 12.9726 + 0.844136i 0.997890 + 0.0649336i
\(170\) 5.70320 0.437415
\(171\) −5.58451 + 9.67265i −0.427058 + 0.739686i
\(172\) −3.01073 5.21473i −0.229566 0.397620i
\(173\) 6.99361 12.1133i 0.531715 0.920957i −0.467600 0.883940i \(-0.654881\pi\)
0.999315 0.0370165i \(-0.0117854\pi\)
\(174\) −0.194829 + 0.337454i −0.0147700 + 0.0255823i
\(175\) −1.92215 + 3.32926i −0.145301 + 0.251668i
\(176\) 2.19705 3.80541i 0.165609 0.286844i
\(177\) 1.52717 + 2.64514i 0.114789 + 0.198821i
\(178\) −0.920737 1.59476i −0.0690121 0.119533i
\(179\) −10.6721 18.4846i −0.797670 1.38160i −0.921130 0.389255i \(-0.872733\pi\)
0.123460 0.992349i \(-0.460601\pi\)
\(180\) −1.73129 2.99868i −0.129043 0.223508i
\(181\) −8.27077 14.3254i −0.614762 1.06480i −0.990426 0.138043i \(-0.955919\pi\)
0.375664 0.926756i \(-0.377415\pi\)
\(182\) −2.12753 + 3.42315i −0.157703 + 0.253741i
\(183\) 0.121864 0.211075i 0.00900848 0.0156031i
\(184\) −3.95195 + 6.84497i −0.291341 + 0.504618i
\(185\) −4.33997 + 7.51704i −0.319081 + 0.552664i
\(186\) −4.61793 + 1.74947i −0.338603 + 0.128278i
\(187\) −18.3037 −1.33850
\(188\) 8.93705 + 15.4794i 0.651801 + 1.12895i
\(189\) 8.67036 0.630676
\(190\) −8.73433 −0.633655
\(191\) 11.9452 20.6897i 0.864326 1.49706i −0.00338827 0.999994i \(-0.501079\pi\)
0.867715 0.497063i \(-0.165588\pi\)
\(192\) −1.09668 1.89951i −0.0791463 0.137085i
\(193\) −12.2150 21.1571i −0.879258 1.52292i −0.852156 0.523287i \(-0.824705\pi\)
−0.0271020 0.999633i \(-0.508628\pi\)
\(194\) −0.0918998 −0.00659802
\(195\) 3.77256 6.06996i 0.270159 0.434679i
\(196\) −3.38909 5.87007i −0.242078 0.419291i
\(197\) −8.86551 −0.631642 −0.315821 0.948819i \(-0.602280\pi\)
−0.315821 + 0.948819i \(0.602280\pi\)
\(198\) −1.89967 3.29032i −0.135003 0.233833i
\(199\) −0.0108343 + 0.0187656i −0.000768026 + 0.00133026i −0.866409 0.499335i \(-0.833578\pi\)
0.865641 + 0.500665i \(0.166911\pi\)
\(200\) −3.05835 + 5.29721i −0.216258 + 0.374570i
\(201\) −8.95250 15.5062i −0.631461 1.09372i
\(202\) 0.0912634 + 0.158073i 0.00642127 + 0.0111220i
\(203\) 0.343989 0.595806i 0.0241433 0.0418174i
\(204\) 4.63702 8.03156i 0.324656 0.562321i
\(205\) −0.193544 0.335228i −0.0135177 0.0234133i
\(206\) −1.61157 −0.112284
\(207\) −2.30976 4.00063i −0.160540 0.278063i
\(208\) 2.28821 3.68168i 0.158659 0.255278i
\(209\) 28.0317 1.93900
\(210\) 1.10787 + 1.91889i 0.0764503 + 0.132416i
\(211\) 10.7378 + 18.5985i 0.739223 + 1.28037i 0.952846 + 0.303456i \(0.0981404\pi\)
−0.213623 + 0.976916i \(0.568526\pi\)
\(212\) 2.84166 4.92190i 0.195166 0.338037i
\(213\) −1.21546 −0.0832819
\(214\) 6.43562 0.439930
\(215\) 3.22262 + 5.58174i 0.219781 + 0.380672i
\(216\) 13.7955 0.938665
\(217\) 8.15338 3.08886i 0.553488 0.209686i
\(218\) −5.00686 + 8.67214i −0.339108 + 0.587352i
\(219\) 7.33200 12.6994i 0.495450 0.858145i
\(220\) −4.34515 + 7.52602i −0.292950 + 0.507404i
\(221\) −18.0472 0.586554i −1.21399 0.0394559i
\(222\) −2.41282 4.17912i −0.161938 0.280484i
\(223\) −11.9539 20.7048i −0.800495 1.38650i −0.919291 0.393579i \(-0.871237\pi\)
0.118796 0.992919i \(-0.462096\pi\)
\(224\) 4.57371 + 7.92190i 0.305594 + 0.529304i
\(225\) −1.78749 3.09602i −0.119166 0.206401i
\(226\) −2.91681 5.05206i −0.194023 0.336058i
\(227\) 5.56674 9.64188i 0.369477 0.639954i −0.620006 0.784597i \(-0.712870\pi\)
0.989484 + 0.144643i \(0.0462034\pi\)
\(228\) −7.10150 + 12.3002i −0.470309 + 0.814598i
\(229\) −9.66242 + 16.7358i −0.638511 + 1.10593i 0.347249 + 0.937773i \(0.387116\pi\)
−0.985760 + 0.168160i \(0.946217\pi\)
\(230\) 1.80627 3.12855i 0.119102 0.206290i
\(231\) −3.55557 6.15842i −0.233939 0.405195i
\(232\) 0.547324 0.947993i 0.0359336 0.0622388i
\(233\) 15.8822 1.04047 0.520237 0.854022i \(-0.325844\pi\)
0.520237 + 0.854022i \(0.325844\pi\)
\(234\) −1.76761 3.30509i −0.115552 0.216060i
\(235\) −9.56604 16.5689i −0.624019 1.08083i
\(236\) −1.83195 3.17303i −0.119250 0.206546i
\(237\) 3.43154 0.222902
\(238\) 2.79909 4.84817i 0.181438 0.314260i
\(239\) −12.3475 21.3865i −0.798692 1.38338i −0.920468 0.390818i \(-0.872192\pi\)
0.121776 0.992558i \(-0.461141\pi\)
\(240\) −1.19154 2.06381i −0.0769136 0.133218i
\(241\) −0.108553 −0.00699254 −0.00349627 0.999994i \(-0.501113\pi\)
−0.00349627 + 0.999994i \(0.501113\pi\)
\(242\) −0.841625 + 1.45774i −0.0541017 + 0.0937069i
\(243\) −6.74551 + 11.6836i −0.432725 + 0.749501i
\(244\) −0.146184 + 0.253199i −0.00935850 + 0.0162094i
\(245\) 3.62761 + 6.28321i 0.231760 + 0.401419i
\(246\) 0.215203 0.0137208
\(247\) 27.6389 + 0.898296i 1.75862 + 0.0571572i
\(248\) 12.9729 4.91472i 0.823782 0.312085i
\(249\) 3.75176 6.49824i 0.237758 0.411809i
\(250\) 4.24486 7.35232i 0.268469 0.465002i
\(251\) −10.9896 −0.693656 −0.346828 0.937929i \(-0.612741\pi\)
−0.346828 + 0.937929i \(0.612741\pi\)
\(252\) −3.39882 −0.214105
\(253\) −5.79699 + 10.0407i −0.364454 + 0.631252i
\(254\) 11.5596 0.725315
\(255\) −4.96337 + 8.59682i −0.310819 + 0.538354i
\(256\) 5.48539 + 9.50097i 0.342837 + 0.593811i
\(257\) 6.37217 0.397485 0.198742 0.980052i \(-0.436314\pi\)
0.198742 + 0.980052i \(0.436314\pi\)
\(258\) −3.58325 −0.223083
\(259\) 4.26005 + 7.37863i 0.264707 + 0.458485i
\(260\) −4.52544 + 7.28132i −0.280656 + 0.451568i
\(261\) 0.319890 + 0.554066i 0.0198007 + 0.0342958i
\(262\) −7.18684 12.4480i −0.444004 0.769038i
\(263\) −11.2345 + 19.4588i −0.692752 + 1.19988i 0.278181 + 0.960529i \(0.410268\pi\)
−0.970933 + 0.239352i \(0.923065\pi\)
\(264\) −5.65730 9.79873i −0.348183 0.603070i
\(265\) −3.04165 + 5.26830i −0.186847 + 0.323629i
\(266\) −4.28675 + 7.42487i −0.262838 + 0.455248i
\(267\) 3.20519 0.196154
\(268\) 10.7391 + 18.6007i 0.655996 + 1.13622i
\(269\) 3.26244 5.65071i 0.198914 0.344530i −0.749262 0.662273i \(-0.769592\pi\)
0.948177 + 0.317743i \(0.102925\pi\)
\(270\) −6.30534 −0.383731
\(271\) −2.63065 + 4.55641i −0.159800 + 0.276782i −0.934797 0.355184i \(-0.884418\pi\)
0.774996 + 0.631966i \(0.217752\pi\)
\(272\) −3.01049 + 5.21432i −0.182538 + 0.316165i
\(273\) −3.30839 6.18607i −0.200233 0.374398i
\(274\) 7.24271 + 12.5447i 0.437548 + 0.757855i
\(275\) −4.48620 + 7.77032i −0.270528 + 0.468568i
\(276\) −2.93720 5.08737i −0.176798 0.306224i
\(277\) −4.36514 7.56064i −0.262276 0.454275i 0.704571 0.709634i \(-0.251140\pi\)
−0.966846 + 0.255359i \(0.917806\pi\)
\(278\) −7.85466 −0.471091
\(279\) −1.30346 + 8.00260i −0.0780363 + 0.479103i
\(280\) −3.11229 5.39064i −0.185995 0.322152i
\(281\) −14.0402 −0.837570 −0.418785 0.908085i \(-0.637544\pi\)
−0.418785 + 0.908085i \(0.637544\pi\)
\(282\) 10.6365 0.633396
\(283\) −12.2606 + 21.2359i −0.728815 + 1.26234i 0.228570 + 0.973528i \(0.426595\pi\)
−0.957384 + 0.288817i \(0.906738\pi\)
\(284\) 1.45802 0.0865178
\(285\) 7.60131 13.1658i 0.450263 0.779878i
\(286\) −4.96556 + 7.98946i −0.293620 + 0.472427i
\(287\) −0.379960 −0.0224283
\(288\) −8.50659 −0.501256
\(289\) 8.08046 0.475321
\(290\) −0.250159 + 0.433288i −0.0146898 + 0.0254435i
\(291\) 0.0799784 0.138527i 0.00468842 0.00812058i
\(292\) −8.79522 + 15.2338i −0.514701 + 0.891489i
\(293\) 2.81629 0.164529 0.0822646 0.996611i \(-0.473785\pi\)
0.0822646 + 0.996611i \(0.473785\pi\)
\(294\) −4.03356 −0.235242
\(295\) 1.96088 + 3.39634i 0.114167 + 0.197743i
\(296\) 6.77821 + 11.7402i 0.393976 + 0.682386i
\(297\) 20.2362 1.17422
\(298\) −3.47266 + 6.01482i −0.201166 + 0.348429i
\(299\) −6.03752 + 9.71422i −0.349159 + 0.561788i
\(300\) −2.27305 3.93704i −0.131235 0.227305i
\(301\) 6.32656 0.364657
\(302\) 6.93440 12.0107i 0.399030 0.691140i
\(303\) −0.317698 −0.0182513
\(304\) 4.61051 7.98563i 0.264431 0.458007i
\(305\) 0.156473 0.271019i 0.00895961 0.0155185i
\(306\) 2.60300 + 4.50852i 0.148803 + 0.257735i
\(307\) 8.38436 14.5221i 0.478521 0.828822i −0.521176 0.853449i \(-0.674507\pi\)
0.999697 + 0.0246272i \(0.00783988\pi\)
\(308\) 4.26514 + 7.38744i 0.243029 + 0.420938i
\(309\) 1.40252 2.42923i 0.0797865 0.138194i
\(310\) −5.92938 + 2.24631i −0.336766 + 0.127582i
\(311\) −17.9951 −1.02041 −0.510206 0.860052i \(-0.670431\pi\)
−0.510206 + 0.860052i \(0.670431\pi\)
\(312\) −5.26402 9.84272i −0.298016 0.557234i
\(313\) −10.9672 + 18.9957i −0.619900 + 1.07370i 0.369603 + 0.929190i \(0.379494\pi\)
−0.989503 + 0.144509i \(0.953840\pi\)
\(314\) 5.53123 9.58036i 0.312145 0.540651i
\(315\) 3.63803 0.204980
\(316\) −4.11636 −0.231563
\(317\) −10.3786 + 17.9763i −0.582922 + 1.00965i 0.412209 + 0.911089i \(0.364757\pi\)
−0.995131 + 0.0985608i \(0.968576\pi\)
\(318\) −1.69102 2.92893i −0.0948275 0.164246i
\(319\) 0.802853 1.39058i 0.0449512 0.0778577i
\(320\) −1.40813 2.43896i −0.0787170 0.136342i
\(321\) −5.60079 + 9.70084i −0.312605 + 0.541448i
\(322\) −1.77301 3.07094i −0.0988059 0.171137i
\(323\) −38.4102 −2.13720
\(324\) −1.87093 + 3.24055i −0.103941 + 0.180031i
\(325\) −4.67234 + 7.51768i −0.259175 + 0.417006i
\(326\) −1.30777 −0.0724308
\(327\) −8.71474 15.0944i −0.481926 0.834720i
\(328\) −0.604558 −0.0333812
\(329\) −18.7798 −1.03536
\(330\) 2.58571 + 4.47859i 0.142339 + 0.246538i
\(331\) 7.36011 12.7481i 0.404548 0.700698i −0.589721 0.807607i \(-0.700762\pi\)
0.994269 + 0.106909i \(0.0340955\pi\)
\(332\) −4.50049 + 7.79507i −0.246996 + 0.427810i
\(333\) −7.92321 −0.434189
\(334\) 4.61395 0.252464
\(335\) −11.4949 19.9098i −0.628035 1.08779i
\(336\) −2.33920 −0.127614
\(337\) 7.00984 0.381850 0.190925 0.981605i \(-0.438851\pi\)
0.190925 + 0.981605i \(0.438851\pi\)
\(338\) −5.15201 + 7.71838i −0.280232 + 0.419825i
\(339\) 10.1538 0.551476
\(340\) 5.95390 10.3125i 0.322895 0.559271i
\(341\) 19.0296 7.20925i 1.03051 0.390403i
\(342\) −3.98644 6.90471i −0.215562 0.373364i
\(343\) 18.0833 0.976407
\(344\) 10.0663 0.542736
\(345\) 3.14391 + 5.44542i 0.169263 + 0.293172i
\(346\) 4.99231 + 8.64694i 0.268388 + 0.464862i
\(347\) 0.230959 0.0123985 0.00619925 0.999981i \(-0.498027\pi\)
0.00619925 + 0.999981i \(0.498027\pi\)
\(348\) 0.406786 + 0.704575i 0.0218060 + 0.0377692i
\(349\) 4.37225 7.57296i 0.234041 0.405371i −0.724952 0.688799i \(-0.758138\pi\)
0.958994 + 0.283428i \(0.0914716\pi\)
\(350\) −1.37210 2.37655i −0.0733420 0.127032i
\(351\) 19.9526 + 0.648483i 1.06499 + 0.0346134i
\(352\) 10.6748 + 18.4893i 0.568970 + 0.985485i
\(353\) −7.51965 13.0244i −0.400230 0.693219i 0.593523 0.804817i \(-0.297737\pi\)
−0.993753 + 0.111598i \(0.964403\pi\)
\(354\) −2.18031 −0.115882
\(355\) −1.56064 −0.0828302
\(356\) −3.84484 −0.203776
\(357\) 4.87198 + 8.43852i 0.257853 + 0.446614i
\(358\) 15.2363 0.805264
\(359\) 11.7636 + 20.3752i 0.620859 + 1.07536i 0.989326 + 0.145719i \(0.0465494\pi\)
−0.368467 + 0.929641i \(0.620117\pi\)
\(360\) 5.78850 0.305081
\(361\) 39.8245 2.09602
\(362\) 11.8080 0.620615
\(363\) −1.46490 2.53728i −0.0768872 0.133172i
\(364\) 3.96864 + 7.42060i 0.208013 + 0.388945i
\(365\) 9.41422 16.3059i 0.492763 0.853490i
\(366\) 0.0869915 + 0.150674i 0.00454712 + 0.00787584i
\(367\) −8.44865 −0.441016 −0.220508 0.975385i \(-0.570771\pi\)
−0.220508 + 0.975385i \(0.570771\pi\)
\(368\) 1.90691 + 3.30287i 0.0994047 + 0.172174i
\(369\) 0.176671 0.306003i 0.00919711 0.0159299i
\(370\) −3.09804 5.36595i −0.161059 0.278963i
\(371\) 2.98565 + 5.17129i 0.155007 + 0.268480i
\(372\) −1.65754 + 10.1765i −0.0859395 + 0.527625i
\(373\) 5.00135 + 8.66259i 0.258960 + 0.448532i 0.965964 0.258678i \(-0.0832869\pi\)
−0.707004 + 0.707210i \(0.749954\pi\)
\(374\) 6.53294 11.3154i 0.337811 0.585105i
\(375\) 7.38843 + 12.7971i 0.381537 + 0.660841i
\(376\) −29.8807 −1.54098
\(377\) 0.836165 1.34537i 0.0430647 0.0692900i
\(378\) −3.09462 + 5.36004i −0.159170 + 0.275691i
\(379\) 14.1026 + 24.4264i 0.724400 + 1.25470i 0.959220 + 0.282659i \(0.0912164\pi\)
−0.234820 + 0.972039i \(0.575450\pi\)
\(380\) −9.11827 + 15.7933i −0.467758 + 0.810180i
\(381\) −10.0601 + 17.4246i −0.515394 + 0.892689i
\(382\) 8.52697 + 14.7691i 0.436277 + 0.755655i
\(383\) 3.54657 6.14284i 0.181221 0.313885i −0.761075 0.648663i \(-0.775328\pi\)
0.942297 + 0.334779i \(0.108662\pi\)
\(384\) −12.9500 −0.660852
\(385\) −4.56532 7.90737i −0.232670 0.402997i
\(386\) 17.4391 0.887629
\(387\) −2.94167 + 5.09513i −0.149534 + 0.259000i
\(388\) −0.0959394 + 0.166172i −0.00487059 + 0.00843610i
\(389\) 13.6034 23.5618i 0.689719 1.19463i −0.282209 0.959353i \(-0.591067\pi\)
0.971929 0.235276i \(-0.0755994\pi\)
\(390\) 2.40596 + 4.49869i 0.121831 + 0.227800i
\(391\) 7.94327 13.7581i 0.401708 0.695779i
\(392\) 11.3313 0.572317
\(393\) 25.0182 1.26200
\(394\) 3.16427 5.48068i 0.159414 0.276113i
\(395\) 4.40607 0.221693
\(396\) −7.93268 −0.398632
\(397\) 32.8860 1.65050 0.825251 0.564766i \(-0.191034\pi\)
0.825251 + 0.564766i \(0.191034\pi\)
\(398\) −0.00773397 0.0133956i −0.000387669 0.000671462i
\(399\) −7.46134 12.9234i −0.373534 0.646980i
\(400\) 1.47573 + 2.55604i 0.0737865 + 0.127802i
\(401\) 3.64493 6.31320i 0.182019 0.315266i −0.760549 0.649281i \(-0.775070\pi\)
0.942568 + 0.334015i \(0.108403\pi\)
\(402\) 12.7813 0.637472
\(403\) 18.9940 6.49841i 0.946157 0.323709i
\(404\) 0.381100 0.0189604
\(405\) 2.00261 3.46862i 0.0995105 0.172357i
\(406\) 0.245553 + 0.425309i 0.0121866 + 0.0211078i
\(407\) 9.94275 + 17.2214i 0.492844 + 0.853631i
\(408\) 7.75186 + 13.4266i 0.383774 + 0.664716i
\(409\) −4.82651 −0.238655 −0.119328 0.992855i \(-0.538074\pi\)
−0.119328 + 0.992855i \(0.538074\pi\)
\(410\) 0.276318 0.0136464
\(411\) −25.2127 −1.24365
\(412\) −1.68241 + 2.91403i −0.0828866 + 0.143564i
\(413\) 3.84955 0.189424
\(414\) 3.29759 0.162068
\(415\) 4.81723 8.34369i 0.236469 0.409576i
\(416\) 9.93274 + 18.5723i 0.486993 + 0.910584i
\(417\) 6.83574 11.8399i 0.334748 0.579800i
\(418\) −10.0051 + 17.3293i −0.489364 + 0.847603i
\(419\) 14.9130 25.8301i 0.728548 1.26188i −0.228948 0.973439i \(-0.573529\pi\)
0.957497 0.288444i \(-0.0931379\pi\)
\(420\) 4.62627 0.225739
\(421\) −4.75749 8.24021i −0.231866 0.401603i 0.726491 0.687176i \(-0.241150\pi\)
−0.958357 + 0.285572i \(0.907816\pi\)
\(422\) −15.3302 −0.746261
\(423\) 8.73207 15.1244i 0.424568 0.735373i
\(424\) 4.75049 + 8.22809i 0.230704 + 0.399592i
\(425\) 6.14717 10.6472i 0.298181 0.516465i
\(426\) 0.433821 0.751400i 0.0210187 0.0364055i
\(427\) −0.153592 0.266029i −0.00743282 0.0128740i
\(428\) 6.71851 11.6368i 0.324752 0.562486i
\(429\) −7.72163 14.4380i −0.372804 0.697072i
\(430\) −4.60086 −0.221873
\(431\) 2.15920 + 3.73984i 0.104005 + 0.180142i 0.913331 0.407217i \(-0.133501\pi\)
−0.809326 + 0.587359i \(0.800168\pi\)
\(432\) 3.32834 5.76485i 0.160135 0.277362i
\(433\) −14.1832 24.5660i −0.681601 1.18057i −0.974492 0.224422i \(-0.927951\pi\)
0.292891 0.956146i \(-0.405383\pi\)
\(434\) −1.00056 + 6.14291i −0.0480283 + 0.294869i
\(435\) −0.435416 0.754163i −0.0208766 0.0361593i
\(436\) 10.4539 + 18.1067i 0.500651 + 0.867153i
\(437\) −12.1650 + 21.0703i −0.581929 + 1.00793i
\(438\) 5.23386 + 9.06532i 0.250084 + 0.433158i
\(439\) −22.0253 −1.05121 −0.525606 0.850728i \(-0.676161\pi\)
−0.525606 + 0.850728i \(0.676161\pi\)
\(440\) −7.26393 12.5815i −0.346294 0.599799i
\(441\) −3.31135 + 5.73543i −0.157684 + 0.273116i
\(442\) 6.80401 10.9475i 0.323634 0.520718i
\(443\) −0.430461 0.745581i −0.0204518 0.0354236i 0.855618 0.517607i \(-0.173177\pi\)
−0.876070 + 0.482184i \(0.839844\pi\)
\(444\) −10.0755 −0.478162
\(445\) 4.11544 0.195090
\(446\) 17.0664 0.808115
\(447\) −6.04436 10.4691i −0.285889 0.495174i
\(448\) −2.76441 −0.130606
\(449\) −8.30003 14.3761i −0.391702 0.678449i 0.600972 0.799270i \(-0.294780\pi\)
−0.992674 + 0.120822i \(0.961447\pi\)
\(450\) 2.55196 0.120300
\(451\) −0.886809 −0.0417582
\(452\) −12.1801 −0.572904
\(453\) 12.0697 + 20.9054i 0.567085 + 0.982221i
\(454\) 3.97375 + 6.88274i 0.186498 + 0.323023i
\(455\) −4.24795 7.94286i −0.199147 0.372367i
\(456\) −11.8718 20.5626i −0.555949 0.962931i
\(457\) −12.7603 + 22.1015i −0.596903 + 1.03387i 0.396372 + 0.918090i \(0.370269\pi\)
−0.993275 + 0.115776i \(0.963064\pi\)
\(458\) −6.89741 11.9467i −0.322295 0.558231i
\(459\) −27.7285 −1.29425
\(460\) −3.77133 6.53214i −0.175839 0.304563i
\(461\) 1.92983 + 3.34257i 0.0898813 + 0.155679i 0.907461 0.420137i \(-0.138018\pi\)
−0.817579 + 0.575816i \(0.804685\pi\)
\(462\) 5.07620 0.236166
\(463\) −21.1658 −0.983659 −0.491829 0.870692i \(-0.663672\pi\)
−0.491829 + 0.870692i \(0.663672\pi\)
\(464\) −0.264098 0.457431i −0.0122604 0.0212357i
\(465\) 1.77420 10.8927i 0.0822765 0.505135i
\(466\) −5.66865 + 9.81838i −0.262595 + 0.454828i
\(467\) 24.2839 1.12373 0.561863 0.827230i \(-0.310085\pi\)
0.561863 + 0.827230i \(0.310085\pi\)
\(468\) −7.82152 0.254208i −0.361550 0.0117508i
\(469\) −22.5665 −1.04203
\(470\) 13.6572 0.629960
\(471\) 9.62742 + 16.6752i 0.443608 + 0.768352i
\(472\) 6.12505 0.281928
\(473\) 14.7659 0.678937
\(474\) −1.22478 + 2.12139i −0.0562561 + 0.0974385i
\(475\) −9.41426 + 16.3060i −0.431956 + 0.748170i
\(476\) −5.84427 10.1226i −0.267871 0.463967i
\(477\) −5.55296 −0.254253
\(478\) 17.6282 0.806296
\(479\) −1.74742 3.02662i −0.0798416 0.138290i 0.823340 0.567549i \(-0.192108\pi\)
−0.903181 + 0.429259i \(0.858775\pi\)
\(480\) 11.5787 0.528492
\(481\) 9.25156 + 17.2987i 0.421835 + 0.788751i
\(482\) 0.0387448 0.0671080i 0.00176478 0.00305668i
\(483\) 6.17205 0.280838
\(484\) 1.75724 + 3.04363i 0.0798746 + 0.138347i
\(485\) 0.102692 0.177867i 0.00466299 0.00807653i
\(486\) −4.81521 8.34018i −0.218422 0.378318i
\(487\) 4.68395 8.11284i 0.212250 0.367628i −0.740168 0.672422i \(-0.765254\pi\)
0.952418 + 0.304794i \(0.0985875\pi\)
\(488\) −0.244381 0.423281i −0.0110626 0.0191610i
\(489\) 1.13813 1.97129i 0.0514678 0.0891449i
\(490\) −5.17906 −0.233966
\(491\) −6.94887 −0.313598 −0.156799 0.987631i \(-0.550118\pi\)
−0.156799 + 0.987631i \(0.550118\pi\)
\(492\) 0.224662 0.389126i 0.0101286 0.0175432i
\(493\) −1.10010 + 1.90543i −0.0495461 + 0.0858163i
\(494\) −10.4202 + 16.7658i −0.468827 + 0.754331i
\(495\) 8.49098 0.381641
\(496\) 1.07612 6.60685i 0.0483194 0.296656i
\(497\) −0.765952 + 1.32667i −0.0343576 + 0.0595091i
\(498\) 2.67815 + 4.63870i 0.120011 + 0.207865i
\(499\) −15.4883 + 26.8265i −0.693350 + 1.20092i 0.277383 + 0.960759i \(0.410533\pi\)
−0.970734 + 0.240159i \(0.922801\pi\)
\(500\) −8.86291 15.3510i −0.396362 0.686518i
\(501\) −4.01543 + 6.95492i −0.179396 + 0.310723i
\(502\) 3.92240 6.79379i 0.175065 0.303222i
\(503\) −40.6947 −1.81449 −0.907245 0.420603i \(-0.861818\pi\)
−0.907245 + 0.420603i \(0.861818\pi\)
\(504\) 2.84096 4.92068i 0.126546 0.219185i
\(505\) −0.407922 −0.0181523
\(506\) −4.13812 7.16743i −0.183962 0.318631i
\(507\) −7.15075 14.4831i −0.317576 0.643218i
\(508\) 12.0678 20.9020i 0.535420 0.927375i
\(509\) −4.02227 −0.178284 −0.0891420 0.996019i \(-0.528412\pi\)
−0.0891420 + 0.996019i \(0.528412\pi\)
\(510\) −3.54305 6.13674i −0.156889 0.271739i
\(511\) −9.24087 16.0057i −0.408792 0.708049i
\(512\) 13.0141 0.575146
\(513\) 42.4656 1.87490
\(514\) −2.27435 + 3.93929i −0.100317 + 0.173755i
\(515\) 1.80082 3.11912i 0.0793537 0.137445i
\(516\) −3.74076 + 6.47919i −0.164678 + 0.285230i
\(517\) −43.8311 −1.92769
\(518\) −6.08198 −0.267227
\(519\) −17.3788 −0.762845
\(520\) −6.75896 12.6380i −0.296400 0.554211i
\(521\) −22.5036 + 38.9773i −0.985900 + 1.70763i −0.348032 + 0.937483i \(0.613150\pi\)
−0.637867 + 0.770146i \(0.720183\pi\)
\(522\) −0.456700 −0.0199892
\(523\) 7.96934 13.8033i 0.348475 0.603576i −0.637504 0.770447i \(-0.720033\pi\)
0.985979 + 0.166871i \(0.0533664\pi\)
\(524\) −30.0110 −1.31104
\(525\) 4.77645 0.208461
\(526\) −8.01965 13.8904i −0.349673 0.605652i
\(527\) −26.0751 + 9.87840i −1.13585 + 0.430310i
\(528\) −5.45958 −0.237598
\(529\) 6.46855 + 11.2039i 0.281241 + 0.487125i
\(530\) −2.17125 3.76072i −0.0943131 0.163355i
\(531\) −1.78993 + 3.10025i −0.0776763 + 0.134539i
\(532\) 8.95037 + 15.5025i 0.388048 + 0.672119i
\(533\) −0.874382 0.0284184i −0.0378737 0.00123094i
\(534\) −1.14399 + 1.98146i −0.0495055 + 0.0857460i
\(535\) −7.19136 + 12.4558i −0.310910 + 0.538511i
\(536\) −35.9059 −1.55090
\(537\) −13.2598 + 22.9667i −0.572204 + 0.991087i
\(538\) 2.32886 + 4.03370i 0.100404 + 0.173905i
\(539\) 16.6215 0.715940
\(540\) −6.58251 + 11.4012i −0.283266 + 0.490631i
\(541\) 11.8720 20.5630i 0.510418 0.884071i −0.489509 0.871998i \(-0.662824\pi\)
0.999927 0.0120722i \(-0.00384280\pi\)
\(542\) −1.87786 3.25254i −0.0806608 0.139709i
\(543\) −10.2763 + 17.7990i −0.440996 + 0.763828i
\(544\) −14.6271 25.3348i −0.627131 1.08622i
\(545\) −11.1896 19.3810i −0.479312 0.830192i
\(546\) 5.00507 + 0.162670i 0.214197 + 0.00696164i
\(547\) 1.36043 + 2.35634i 0.0581680 + 0.100750i 0.893643 0.448778i \(-0.148141\pi\)
−0.835475 + 0.549528i \(0.814807\pi\)
\(548\) 30.2443 1.29197
\(549\) 0.285663 0.0121918
\(550\) −3.20242 5.54676i −0.136552 0.236515i
\(551\) 1.68478 2.91813i 0.0717742 0.124317i
\(552\) 9.82041 0.417984
\(553\) 2.16247 3.74550i 0.0919575 0.159275i
\(554\) 6.23201 0.264773
\(555\) 10.7846 0.457782
\(556\) −8.19993 + 14.2027i −0.347754 + 0.602328i
\(557\) 4.32454 7.49032i 0.183237 0.317375i −0.759744 0.650222i \(-0.774676\pi\)
0.942981 + 0.332847i \(0.108009\pi\)
\(558\) −4.48199 3.66208i −0.189738 0.155028i
\(559\) 14.5590 + 0.473183i 0.615779 + 0.0200135i
\(560\) −3.00351 −0.126922
\(561\) 11.3710 + 19.6951i 0.480083 + 0.831528i
\(562\) 5.01123 8.67970i 0.211386 0.366131i
\(563\) −2.63030 + 4.55581i −0.110854 + 0.192005i −0.916115 0.400916i \(-0.868692\pi\)
0.805261 + 0.592921i \(0.202025\pi\)
\(564\) 11.1041 19.2328i 0.467566 0.809848i
\(565\) 13.0373 0.548485
\(566\) −8.75206 15.1590i −0.367877 0.637181i
\(567\) −1.96573 3.40475i −0.0825531 0.142986i
\(568\) −1.21871 + 2.11087i −0.0511361 + 0.0885703i
\(569\) 40.2048 1.68547 0.842737 0.538326i \(-0.180943\pi\)
0.842737 + 0.538326i \(0.180943\pi\)
\(570\) 5.42611 + 9.39829i 0.227275 + 0.393651i
\(571\) −10.3057 17.8500i −0.431280 0.746999i 0.565704 0.824609i \(-0.308605\pi\)
−0.996984 + 0.0776094i \(0.975271\pi\)
\(572\) 9.26261 + 17.3193i 0.387289 + 0.724157i
\(573\) −29.6834 −1.24004
\(574\) 0.135615 0.234892i 0.00566047 0.00980421i
\(575\) −3.89376 6.74418i −0.162381 0.281252i
\(576\) 1.28537 2.22633i 0.0535571 0.0927636i
\(577\) −16.1217 + 27.9236i −0.671155 + 1.16247i 0.306422 + 0.951896i \(0.400868\pi\)
−0.977577 + 0.210579i \(0.932465\pi\)
\(578\) −2.88407 + 4.99536i −0.119962 + 0.207780i
\(579\) −15.1769 + 26.2872i −0.630731 + 1.09246i
\(580\) 0.522310 + 0.904668i 0.0216878 + 0.0375643i
\(581\) −4.72853 8.19005i −0.196172 0.339781i
\(582\) 0.0570917 + 0.0988857i 0.00236653 + 0.00409894i
\(583\) 6.96835 + 12.0695i 0.288600 + 0.499869i
\(584\) −14.7032 25.4668i −0.608425 1.05382i
\(585\) 8.37200 + 0.272099i 0.346139 + 0.0112499i
\(586\) −1.00519 + 1.74103i −0.0415239 + 0.0719215i
\(587\) 20.9406 36.2701i 0.864310 1.49703i −0.00342145 0.999994i \(-0.501089\pi\)
0.867731 0.497034i \(-0.165578\pi\)
\(588\) −4.21086 + 7.29343i −0.173653 + 0.300776i
\(589\) 39.9335 15.1286i 1.64543 0.623362i
\(590\) −2.79950 −0.115254
\(591\) 5.50760 + 9.53945i 0.226552 + 0.392400i
\(592\) 6.54132 0.268846
\(593\) 7.42200 0.304785 0.152392 0.988320i \(-0.451302\pi\)
0.152392 + 0.988320i \(0.451302\pi\)
\(594\) −7.22269 + 12.5101i −0.296351 + 0.513295i
\(595\) 6.25558 + 10.8350i 0.256454 + 0.444191i
\(596\) 7.25062 + 12.5584i 0.296997 + 0.514414i
\(597\) 0.0269229 0.00110188
\(598\) −3.85044 7.19960i −0.157456 0.294414i
\(599\) −11.6423 20.1651i −0.475693 0.823924i 0.523920 0.851768i \(-0.324469\pi\)
−0.999612 + 0.0278439i \(0.991136\pi\)
\(600\) 7.59986 0.310263
\(601\) −6.61763 11.4621i −0.269939 0.467547i 0.698907 0.715212i \(-0.253670\pi\)
−0.968846 + 0.247665i \(0.920337\pi\)
\(602\) −2.25807 + 3.91110i −0.0920322 + 0.159404i
\(603\) 10.4928 18.1741i 0.427300 0.740105i
\(604\) −14.4784 25.0774i −0.589119 1.02038i
\(605\) −1.88092 3.25784i −0.0764701 0.132450i
\(606\) 0.113393 0.196402i 0.00460626 0.00797828i
\(607\) 0.808608 1.40055i 0.0328204 0.0568465i −0.849149 0.528154i \(-0.822884\pi\)
0.881969 + 0.471307i \(0.156218\pi\)
\(608\) 22.4011 + 38.7998i 0.908483 + 1.57354i
\(609\) −0.854797 −0.0346381
\(610\) 0.111696 + 0.193464i 0.00452246 + 0.00783312i
\(611\) −43.2169 1.40460i −1.74837 0.0568239i
\(612\) 10.8697 0.439380
\(613\) −15.0212 26.0175i −0.606700 1.05084i −0.991780 0.127952i \(-0.959160\pi\)
0.385080 0.922883i \(-0.374174\pi\)
\(614\) 5.98508 + 10.3665i 0.241538 + 0.418356i
\(615\) −0.240474 + 0.416513i −0.00969684 + 0.0167954i
\(616\) −14.2603 −0.574566
\(617\) −13.8589 −0.557938 −0.278969 0.960300i \(-0.589993\pi\)
−0.278969 + 0.960300i \(0.589993\pi\)
\(618\) 1.00117 + 1.73408i 0.0402730 + 0.0697550i
\(619\) 32.8985 1.32230 0.661151 0.750253i \(-0.270068\pi\)
0.661151 + 0.750253i \(0.270068\pi\)
\(620\) −2.12827 + 13.0665i −0.0854733 + 0.524762i
\(621\) −8.78192 + 15.2107i −0.352406 + 0.610386i
\(622\) 6.42282 11.1246i 0.257531 0.446058i
\(623\) 2.01983 3.49845i 0.0809227 0.140162i
\(624\) −5.38308 0.174956i −0.215496 0.00700384i
\(625\) 3.34938 + 5.80130i 0.133975 + 0.232052i
\(626\) −7.82878 13.5598i −0.312901 0.541961i
\(627\) −17.4144 30.1626i −0.695464 1.20458i
\(628\) −11.5487 20.0030i −0.460844 0.798206i
\(629\) −13.6240 23.5974i −0.543223 0.940889i
\(630\) −1.29848 + 2.24904i −0.0517328 + 0.0896038i
\(631\) −2.24706 + 3.89202i −0.0894540 + 0.154939i −0.907280 0.420526i \(-0.861846\pi\)
0.817826 + 0.575465i \(0.195179\pi\)
\(632\) 3.44072 5.95951i 0.136865 0.237057i
\(633\) 13.3415 23.1082i 0.530278 0.918468i
\(634\) −7.40866 12.8322i −0.294236 0.509631i
\(635\) −12.9171 + 22.3730i −0.512599 + 0.887847i
\(636\) −7.06139 −0.280003
\(637\) 16.3886 + 0.532648i 0.649341 + 0.0211043i
\(638\) 0.573108 + 0.992652i 0.0226896 + 0.0392995i
\(639\) −0.712292 1.23373i −0.0281778 0.0488054i
\(640\) −16.6277 −0.657267
\(641\) −13.5772 + 23.5163i −0.536266 + 0.928839i 0.462835 + 0.886444i \(0.346832\pi\)
−0.999101 + 0.0423951i \(0.986501\pi\)
\(642\) −3.99806 6.92484i −0.157791 0.273302i
\(643\) 11.4500 + 19.8320i 0.451545 + 0.782099i 0.998482 0.0550748i \(-0.0175397\pi\)
−0.546937 + 0.837174i \(0.684206\pi\)
\(644\) −7.40378 −0.291750
\(645\) 4.00404 6.93519i 0.157659 0.273073i
\(646\) 13.7093 23.7453i 0.539387 0.934246i
\(647\) 12.4052 21.4864i 0.487697 0.844716i −0.512203 0.858865i \(-0.671170\pi\)
0.999900 + 0.0141482i \(0.00450365\pi\)
\(648\) −3.12770 5.41733i −0.122868 0.212813i
\(649\) 8.98465 0.352679
\(650\) −2.97980 5.57166i −0.116877 0.218538i
\(651\) −8.38886 6.85426i −0.328785 0.268640i
\(652\) −1.36526 + 2.36470i −0.0534676 + 0.0926087i
\(653\) −11.5117 + 19.9388i −0.450487 + 0.780266i −0.998416 0.0562585i \(-0.982083\pi\)
0.547929 + 0.836525i \(0.315416\pi\)
\(654\) 12.4418 0.486514
\(655\) 32.1232 1.25516
\(656\) −0.145857 + 0.252632i −0.00569477 + 0.00986364i
\(657\) 17.1870 0.670528
\(658\) 6.70287 11.6097i 0.261305 0.452594i
\(659\) −6.75294 11.6964i −0.263057 0.455628i 0.703996 0.710204i \(-0.251397\pi\)
−0.967053 + 0.254576i \(0.918064\pi\)
\(660\) 10.7975 0.420292
\(661\) 22.1538 0.861683 0.430841 0.902428i \(-0.358217\pi\)
0.430841 + 0.902428i \(0.358217\pi\)
\(662\) 5.25393 + 9.10007i 0.204200 + 0.353684i
\(663\) 10.5805 + 19.7835i 0.410912 + 0.768328i
\(664\) −7.52361 13.0313i −0.291973 0.505711i
\(665\) −9.58030 16.5936i −0.371508 0.643471i
\(666\) 2.82795 4.89815i 0.109581 0.189799i
\(667\) 0.696829 + 1.20694i 0.0269813 + 0.0467331i
\(668\) 4.81677 8.34289i 0.186366 0.322796i
\(669\) −14.8525 + 25.7253i −0.574231 + 0.994596i
\(670\) 16.4111 0.634014
\(671\) −0.358476 0.620898i −0.0138388 0.0239695i
\(672\) 5.68274 9.84279i 0.219216 0.379694i
\(673\) −17.3770 −0.669834 −0.334917 0.942248i \(-0.608708\pi\)
−0.334917 + 0.942248i \(0.608708\pi\)
\(674\) −2.50195 + 4.33350i −0.0963714 + 0.166920i
\(675\) −6.79619 + 11.7713i −0.261585 + 0.453079i
\(676\) 8.57781 + 17.3735i 0.329916 + 0.668210i
\(677\) 16.5061 + 28.5895i 0.634383 + 1.09878i 0.986646 + 0.162882i \(0.0520789\pi\)
−0.352263 + 0.935901i \(0.614588\pi\)
\(678\) −3.62407 + 6.27707i −0.139182 + 0.241070i
\(679\) −0.100801 0.174592i −0.00386838 0.00670022i
\(680\) 9.95332 + 17.2397i 0.381692 + 0.661111i
\(681\) −13.8331 −0.530085
\(682\) −2.33525 + 14.3373i −0.0894215 + 0.549002i
\(683\) −11.9799 20.7499i −0.458400 0.793972i 0.540477 0.841359i \(-0.318244\pi\)
−0.998877 + 0.0473872i \(0.984911\pi\)
\(684\) −16.6467 −0.636502
\(685\) −32.3729 −1.23690
\(686\) −6.45428 + 11.1791i −0.246426 + 0.426822i
\(687\) 24.0107 0.916065
\(688\) 2.42861 4.20648i 0.0925900 0.160371i
\(689\) 6.48393 + 12.1237i 0.247018 + 0.461877i
\(690\) −4.48850 −0.170874
\(691\) 2.11812 0.0805771 0.0402886 0.999188i \(-0.487172\pi\)
0.0402886 + 0.999188i \(0.487172\pi\)
\(692\) 20.8470 0.792486
\(693\) 4.16731 7.21800i 0.158303 0.274189i
\(694\) −0.0824336 + 0.142779i −0.00312914 + 0.00541982i
\(695\) 8.77704 15.2023i 0.332932 0.576655i
\(696\) −1.36008 −0.0515535
\(697\) 1.21514 0.0460267
\(698\) 3.12108 + 5.40587i 0.118135 + 0.204615i
\(699\) −9.86661 17.0895i −0.373189 0.646383i
\(700\) −5.72967 −0.216561
\(701\) −2.56037 + 4.43469i −0.0967038 + 0.167496i −0.910318 0.413909i \(-0.864163\pi\)
0.813615 + 0.581405i \(0.197497\pi\)
\(702\) −7.52238 + 12.1033i −0.283914 + 0.456810i
\(703\) 20.8648 + 36.1389i 0.786931 + 1.36301i
\(704\) −6.45199 −0.243169
\(705\) −11.8856 + 20.5864i −0.447637 + 0.775330i
\(706\) 10.7356 0.404041
\(707\) −0.200205 + 0.346766i −0.00752950 + 0.0130415i
\(708\) −2.27615 + 3.94241i −0.0855431 + 0.148165i
\(709\) −5.50158 9.52901i −0.206616 0.357870i 0.744030 0.668146i \(-0.232912\pi\)
−0.950646 + 0.310276i \(0.899578\pi\)
\(710\) 0.557023 0.964791i 0.0209047 0.0362080i
\(711\) 2.01097 + 3.48311i 0.0754174 + 0.130627i
\(712\) 3.21377 5.56641i 0.120441 0.208610i
\(713\) −2.83938 + 17.4324i −0.106336 + 0.652847i
\(714\) −6.95562 −0.260307
\(715\) −9.91451 18.5382i −0.370782 0.693291i
\(716\) 15.9061 27.5501i 0.594437 1.02960i
\(717\) −15.3415 + 26.5722i −0.572938 + 0.992357i
\(718\) −16.7946 −0.626770
\(719\) 34.7759 1.29692 0.648461 0.761248i \(-0.275413\pi\)
0.648461 + 0.761248i \(0.275413\pi\)
\(720\) 1.39655 2.41889i 0.0520463 0.0901468i
\(721\) −1.76766 3.06168i −0.0658312 0.114023i
\(722\) −14.2141 + 24.6196i −0.528995 + 0.916246i
\(723\) 0.0674376 + 0.116805i 0.00250803 + 0.00434404i
\(724\) 12.3270 21.3511i 0.458131 0.793506i
\(725\) 0.539265 + 0.934035i 0.0200278 + 0.0346892i
\(726\) 2.09140 0.0776192
\(727\) 18.1970 31.5181i 0.674889 1.16894i −0.301613 0.953431i \(-0.597525\pi\)
0.976501 0.215511i \(-0.0691417\pi\)
\(728\) −14.0605 0.456982i −0.521117 0.0169369i
\(729\) 24.2941 0.899780
\(730\) 6.72024 + 11.6398i 0.248727 + 0.430808i
\(731\) −20.2328 −0.748338
\(732\) 0.363262 0.0134265
\(733\) −16.8198 29.1328i −0.621254 1.07604i −0.989252 0.146218i \(-0.953290\pi\)
0.367998 0.929827i \(-0.380043\pi\)
\(734\) 3.01549 5.22297i 0.111304 0.192783i
\(735\) 4.50722 7.80674i 0.166251 0.287956i
\(736\) −18.5302 −0.683034
\(737\) −52.6692 −1.94010
\(738\) 0.126114 + 0.218437i 0.00464233 + 0.00804076i
\(739\) −7.96388 −0.292956 −0.146478 0.989214i \(-0.546794\pi\)
−0.146478 + 0.989214i \(0.546794\pi\)
\(740\) −12.9369 −0.475569
\(741\) −16.2038 30.2980i −0.595261 1.11303i
\(742\) −4.26254 −0.156483
\(743\) −1.24195 + 2.15113i −0.0455629 + 0.0789173i −0.887907 0.460022i \(-0.847841\pi\)
0.842345 + 0.538939i \(0.181175\pi\)
\(744\) −13.3476 10.9059i −0.489347 0.399829i
\(745\) −7.76091 13.4423i −0.284338 0.492488i
\(746\) −7.14031 −0.261425
\(747\) 8.79453 0.321775
\(748\) −13.6402 23.6256i −0.498736 0.863837i
\(749\) 7.05894 + 12.2264i 0.257928 + 0.446745i
\(750\) −10.5483 −0.385169
\(751\) 19.8570 + 34.3933i 0.724592 + 1.25503i 0.959142 + 0.282925i \(0.0913049\pi\)
−0.234550 + 0.972104i \(0.575362\pi\)
\(752\) −7.20910 + 12.4865i −0.262889 + 0.455337i
\(753\) 6.82716 + 11.8250i 0.248795 + 0.430926i
\(754\) 0.533267 + 0.997108i 0.0194204 + 0.0363125i
\(755\) 15.4974 + 26.8423i 0.564009 + 0.976893i
\(756\) 6.46130 + 11.1913i 0.234995 + 0.407024i
\(757\) −18.8829 −0.686311 −0.343155 0.939279i \(-0.611496\pi\)
−0.343155 + 0.939279i \(0.611496\pi\)
\(758\) −20.1339 −0.731297
\(759\) 14.4053 0.522878
\(760\) −15.2433 26.4022i −0.552933 0.957708i
\(761\) −35.1999 −1.27600 −0.637998 0.770038i \(-0.720237\pi\)
−0.637998 + 0.770038i \(0.720237\pi\)
\(762\) −7.18129 12.4384i −0.260151 0.450594i
\(763\) −21.9672 −0.795267
\(764\) 35.6072 1.28822
\(765\) −11.6347 −0.420653
\(766\) 2.53168 + 4.38500i 0.0914733 + 0.158436i
\(767\) 8.85875 + 0.287919i 0.319871 + 0.0103962i
\(768\) 6.81547 11.8047i 0.245932 0.425967i
\(769\) 0.945291 + 1.63729i 0.0340881 + 0.0590422i 0.882566 0.470188i \(-0.155814\pi\)
−0.848478 + 0.529231i \(0.822481\pi\)
\(770\) 6.51780 0.234885
\(771\) −3.95864 6.85656i −0.142567 0.246933i
\(772\) 18.2057 31.5332i 0.655238 1.13491i
\(773\) −5.45444 9.44737i −0.196183 0.339798i 0.751105 0.660183i \(-0.229521\pi\)
−0.947288 + 0.320385i \(0.896188\pi\)
\(774\) −2.09988 3.63710i −0.0754786 0.130733i
\(775\) −2.19735 + 13.4906i −0.0789313 + 0.484598i
\(776\) −0.160385 0.277795i −0.00575749 0.00997226i
\(777\) 5.29302 9.16778i 0.189886 0.328892i
\(778\) 9.71062 + 16.8193i 0.348143 + 0.603001i
\(779\) −1.86096 −0.0666759
\(780\) 10.6462 + 0.346013i 0.381195 + 0.0123893i
\(781\) −1.78769 + 3.09638i −0.0639687 + 0.110797i
\(782\) 5.67021 + 9.82109i 0.202766 + 0.351202i
\(783\) 1.21625 2.10661i 0.0434653 0.0752840i
\(784\) 2.73382 4.73511i 0.0976363 0.169111i
\(785\) 12.3615 + 21.4108i 0.441202 + 0.764184i
\(786\) −8.92949 + 15.4663i −0.318504 + 0.551665i
\(787\) 8.79055 0.313349 0.156675 0.987650i \(-0.449923\pi\)
0.156675 + 0.987650i \(0.449923\pi\)
\(788\) −6.60673 11.4432i −0.235355 0.407647i
\(789\) 27.9173 0.993883
\(790\) −1.57261 + 2.72384i −0.0559510 + 0.0969099i
\(791\) 6.39863 11.0828i 0.227509 0.394058i
\(792\) 6.63066 11.4846i 0.235610 0.408089i
\(793\) −0.333555 0.623685i −0.0118449 0.0221477i
\(794\) −11.7377 + 20.3302i −0.416554 + 0.721492i
\(795\) 7.55837 0.268068
\(796\) −0.0322958 −0.00114469
\(797\) −21.5903 + 37.3955i −0.764768 + 1.32462i 0.175602 + 0.984461i \(0.443813\pi\)
−0.940369 + 0.340155i \(0.889520\pi\)
\(798\) 10.6524 0.377090
\(799\) 60.0591 2.12474
\(800\) −14.3403 −0.507005
\(801\) 1.87833 + 3.25336i 0.0663674 + 0.114952i
\(802\) 2.60189 + 4.50660i 0.0918759 + 0.159134i
\(803\) −21.5677 37.3564i −0.761109 1.31828i
\(804\) 13.3431 23.1110i 0.470575 0.815060i
\(805\) 7.92486 0.279315
\(806\) −2.76198 + 14.0615i −0.0972865 + 0.495296i
\(807\) −8.10702 −0.285380
\(808\) −0.318549 + 0.551743i −0.0112065 + 0.0194102i
\(809\) 12.4001 + 21.4776i 0.435965 + 0.755113i 0.997374 0.0724251i \(-0.0230738\pi\)
−0.561409 + 0.827539i \(0.689740\pi\)
\(810\) 1.42954 + 2.47604i 0.0502289 + 0.0869990i
\(811\) −0.832059 1.44117i −0.0292175 0.0506063i 0.851047 0.525090i \(-0.175968\pi\)
−0.880264 + 0.474483i \(0.842635\pi\)
\(812\) 1.02539 0.0359840
\(813\) 6.53703 0.229264
\(814\) −14.1950 −0.497536
\(815\) 1.46134 2.53112i 0.0511887 0.0886614i
\(816\) 7.48093 0.261885
\(817\) 30.9862 1.08407
\(818\) 1.72267 2.98376i 0.0602319 0.104325i
\(819\) 4.34022 6.98331i 0.151660 0.244017i
\(820\) 0.288464 0.499635i 0.0100736 0.0174480i
\(821\) −13.4692 + 23.3294i −0.470079 + 0.814200i −0.999415 0.0342121i \(-0.989108\pi\)
0.529336 + 0.848412i \(0.322441\pi\)
\(822\) 8.99890 15.5866i 0.313873 0.543643i
\(823\) 16.6747 0.581242 0.290621 0.956838i \(-0.406138\pi\)
0.290621 + 0.956838i \(0.406138\pi\)
\(824\) −2.81255 4.87147i −0.0979797 0.169706i
\(825\) 11.1480 0.388124
\(826\) −1.37398 + 2.37980i −0.0478068 + 0.0828038i
\(827\) 6.62472 + 11.4743i 0.230364 + 0.399002i 0.957915 0.287051i \(-0.0926750\pi\)
−0.727551 + 0.686053i \(0.759342\pi\)
\(828\) 3.44255 5.96267i 0.119637 0.207217i
\(829\) 22.3780 38.7599i 0.777221 1.34619i −0.156317 0.987707i \(-0.549962\pi\)
0.933538 0.358479i \(-0.116704\pi\)
\(830\) 3.43873 + 5.95605i 0.119360 + 0.206737i
\(831\) −5.42359 + 9.39393i −0.188142 + 0.325872i
\(832\) −6.36158 0.206758i −0.220548 0.00716805i
\(833\) −22.7755 −0.789124
\(834\) 4.87962 + 8.45175i 0.168967 + 0.292660i
\(835\) −5.15577 + 8.93006i −0.178423 + 0.309038i
\(836\) 20.8897 + 36.1821i 0.722487 + 1.25138i
\(837\) 28.8281 10.9214i 0.996446 0.377498i
\(838\) 10.6455 + 18.4385i 0.367742 + 0.636948i
\(839\) −17.5512 30.3995i −0.605934 1.04951i −0.991903 0.126996i \(-0.959466\pi\)
0.385970 0.922512i \(-0.373867\pi\)
\(840\) −3.86695 + 6.69775i −0.133422 + 0.231094i
\(841\) 14.4035 + 24.9476i 0.496672 + 0.860261i
\(842\) 6.79216 0.234073
\(843\) 8.72233 + 15.1075i 0.300413 + 0.520331i
\(844\) −16.0040 + 27.7198i −0.550882 + 0.954155i
\(845\) −9.18151 18.5962i −0.315854 0.639729i
\(846\) 6.23329 + 10.7964i 0.214305 + 0.371187i
\(847\) −3.69256 −0.126878
\(848\) 4.58447 0.157431
\(849\) 30.4670 1.04562
\(850\) 4.38809 + 7.60039i 0.150510 + 0.260691i
\(851\) −17.2594 −0.591646
\(852\) −0.905781 1.56886i −0.0310316 0.0537482i
\(853\) 22.6874 0.776803 0.388402 0.921490i \(-0.373027\pi\)
0.388402 + 0.921490i \(0.373027\pi\)
\(854\) 0.219279 0.00750359
\(855\) 17.8183 0.609372
\(856\) 11.2316 + 19.4536i 0.383887 + 0.664911i
\(857\) 22.4760 + 38.9296i 0.767767 + 1.32981i 0.938771 + 0.344541i \(0.111965\pi\)
−0.171005 + 0.985270i \(0.554701\pi\)
\(858\) 11.6816 + 0.379664i 0.398803 + 0.0129615i
\(859\) 8.30329 + 14.3817i 0.283305 + 0.490698i 0.972197 0.234166i \(-0.0752359\pi\)
−0.688892 + 0.724864i \(0.741903\pi\)
\(860\) −4.80311 + 8.31922i −0.163785 + 0.283683i
\(861\) 0.236046 + 0.408844i 0.00804443 + 0.0139334i
\(862\) −3.08264 −0.104995
\(863\) 9.24711 + 16.0165i 0.314775 + 0.545207i 0.979390 0.201980i \(-0.0647375\pi\)
−0.664614 + 0.747187i \(0.731404\pi\)
\(864\) 16.1714 + 28.0097i 0.550162 + 0.952909i
\(865\) −22.3143 −0.758707
\(866\) 20.2490 0.688090
\(867\) −5.01989 8.69471i −0.170485 0.295288i
\(868\) 10.0630 + 8.22214i 0.341560 + 0.279077i
\(869\) 5.04709 8.74182i 0.171211 0.296546i
\(870\) 0.621633 0.0210753
\(871\) −51.9312 1.68782i −1.75962 0.0571896i
\(872\) −34.9523 −1.18363
\(873\) 0.187478 0.00634517
\(874\) −8.68381 15.0408i −0.293734 0.508763i
\(875\) 18.6240 0.629606
\(876\) 21.8557 0.738436
\(877\) −1.41176 + 2.44525i −0.0476719 + 0.0825701i −0.888877 0.458146i \(-0.848514\pi\)
0.841205 + 0.540717i \(0.181847\pi\)
\(878\) 7.86127 13.6161i 0.265305 0.459522i
\(879\) −1.74959 3.03037i −0.0590121 0.102212i
\(880\) −7.01006 −0.236309
\(881\) −7.49892 −0.252645 −0.126322 0.991989i \(-0.540317\pi\)
−0.126322 + 0.991989i \(0.540317\pi\)
\(882\) −2.36377 4.09418i −0.0795924 0.137858i
\(883\) 12.9689 0.436437 0.218218 0.975900i \(-0.429975\pi\)
0.218218 + 0.975900i \(0.429975\pi\)
\(884\) −12.6920 23.7316i −0.426878 0.798181i
\(885\) 2.43635 4.21988i 0.0818970 0.141850i
\(886\) 0.614560 0.0206465
\(887\) 12.9789 + 22.4801i 0.435789 + 0.754809i 0.997360 0.0726196i \(-0.0231359\pi\)
−0.561570 + 0.827429i \(0.689803\pi\)
\(888\) 8.42177 14.5869i 0.282616 0.489506i
\(889\) 12.6792 + 21.9611i 0.425248 + 0.736551i
\(890\) −1.46888 + 2.54417i −0.0492369 + 0.0852809i
\(891\) −4.58793 7.94653i −0.153701 0.266219i
\(892\) 17.8166 30.8592i 0.596542 1.03324i
\(893\) −91.9793 −3.07797
\(894\) 8.62940 0.288610
\(895\) −17.0255 + 29.4891i −0.569100 + 0.985711i
\(896\) −8.16076 + 14.1348i −0.272632 + 0.472212i
\(897\) 14.2034 + 0.461626i 0.474238 + 0.0154132i
\(898\) 11.8498 0.395432
\(899\) 0.393240 2.41429i 0.0131153 0.0805212i
\(900\) 2.66413 4.61441i 0.0888045 0.153814i
\(901\) −9.54832 16.5382i −0.318101 0.550966i
\(902\) 0.316519 0.548227i 0.0105389 0.0182540i
\(903\) −3.93031 6.80749i −0.130792 0.226539i
\(904\) 10.1809 17.6339i 0.338613 0.586495i
\(905\) −13.1946 + 22.8538i −0.438604 + 0.759684i
\(906\) −17.2317 −0.572484
\(907\) −1.85369 + 3.21068i −0.0615507 + 0.106609i −0.895159 0.445747i \(-0.852938\pi\)
0.833608 + 0.552356i \(0.186271\pi\)
\(908\) 16.5937 0.550682
\(909\) −0.186180 0.322473i −0.00617519 0.0106957i
\(910\) 6.42647 + 0.208867i 0.213035 + 0.00692388i
\(911\) 9.51054 16.4727i 0.315098 0.545766i −0.664360 0.747413i \(-0.731296\pi\)
0.979458 + 0.201647i \(0.0646292\pi\)
\(912\) −11.4569 −0.379376
\(913\) −11.0362 19.1152i −0.365243 0.632620i
\(914\) −9.10881 15.7769i −0.301293 0.521854i
\(915\) −0.388828 −0.0128543
\(916\) −28.8024 −0.951658
\(917\) 15.7658 27.3072i 0.520634 0.901764i
\(918\) 9.89682 17.1418i 0.326644 0.565764i
\(919\) −13.3338 + 23.0949i −0.439843 + 0.761831i −0.997677 0.0681220i \(-0.978299\pi\)
0.557834 + 0.829953i \(0.311633\pi\)
\(920\) 12.6093 0.415717
\(921\) −20.8348 −0.686528
\(922\) −2.75518 −0.0907370
\(923\) −1.86187 + 2.99570i −0.0612841 + 0.0986047i
\(924\) 5.29934 9.17873i 0.174336 0.301958i
\(925\) −13.3568 −0.439169
\(926\) 7.55449 13.0848i 0.248256 0.429992i
\(927\) 3.28765 0.107981
\(928\) 2.56634 0.0842443
\(929\) −11.4190 19.7782i −0.374644 0.648903i 0.615629 0.788036i \(-0.288902\pi\)
−0.990274 + 0.139133i \(0.955568\pi\)
\(930\) 6.10063 + 4.98462i 0.200048 + 0.163452i
\(931\) 34.8802 1.14315
\(932\) 11.8357 + 20.5000i 0.387690 + 0.671498i
\(933\) 11.1793 + 19.3631i 0.365993 + 0.633919i
\(934\) −8.66740 + 15.0124i −0.283606 + 0.491220i
\(935\) 14.6002 + 25.2883i 0.477478 + 0.827017i
\(936\) 6.90577 11.1112i 0.225722 0.363182i
\(937\) 12.8570 22.2689i 0.420019 0.727494i −0.575922 0.817505i \(-0.695357\pi\)
0.995941 + 0.0900110i \(0.0286902\pi\)
\(938\) 8.05444 13.9507i 0.262987 0.455506i
\(939\) 27.2529 0.889365
\(940\) 14.2575 24.6948i 0.465030 0.805456i
\(941\) −10.6799 18.4980i −0.348153 0.603019i 0.637768 0.770228i \(-0.279858\pi\)
−0.985921 + 0.167209i \(0.946524\pi\)
\(942\) −13.7448 −0.447831
\(943\) 0.384849 0.666578i 0.0125324 0.0217068i
\(944\) 1.47775 2.55953i 0.0480965 0.0833056i
\(945\) −6.91605 11.9789i −0.224979 0.389675i
\(946\) −5.27023 + 9.12831i −0.171350 + 0.296787i
\(947\) 25.3860 + 43.9698i 0.824933 + 1.42883i 0.901971 + 0.431797i \(0.142120\pi\)
−0.0770382 + 0.997028i \(0.524546\pi\)
\(948\) 2.55724 + 4.42927i 0.0830553 + 0.143856i
\(949\) −20.0684 37.5241i −0.651448 1.21808i
\(950\) −6.72026 11.6398i −0.218034 0.377646i
\(951\) 25.7904 0.836312
\(952\) 19.5401 0.633298
\(953\) 19.6022 + 33.9521i 0.634979 + 1.09982i 0.986520 + 0.163643i \(0.0523245\pi\)
−0.351541 + 0.936173i \(0.614342\pi\)
\(954\) 1.98196 3.43286i 0.0641683 0.111143i
\(955\) −38.1132 −1.23331
\(956\) 18.4031 31.8751i 0.595199 1.03092i
\(957\) −1.99505 −0.0644910
\(958\) 2.49475 0.0806017
\(959\) −15.8884 + 27.5195i −0.513063 + 0.888651i
\(960\) −1.74957 + 3.03035i −0.0564672 + 0.0978040i
\(961\) 23.2184 20.5403i 0.748981 0.662591i
\(962\) −13.9961 0.454889i −0.451253 0.0146662i
\(963\) −13.1288 −0.423071
\(964\) −0.0808959 0.140116i −0.00260548 0.00451282i
\(965\) −19.4870 + 33.7525i −0.627310 + 1.08653i
\(966\) −2.20292 + 3.81557i −0.0708779 + 0.122764i
\(967\) −20.3071 + 35.1729i −0.653032 + 1.13108i 0.329352 + 0.944207i \(0.393170\pi\)
−0.982383 + 0.186877i \(0.940164\pi\)
\(968\) −5.87527 −0.188838
\(969\) 23.8619 + 41.3300i 0.766555 + 1.32771i
\(970\) 0.0733053 + 0.126968i 0.00235369 + 0.00407671i
\(971\) 3.95562 6.85134i 0.126942 0.219870i −0.795548 0.605890i \(-0.792817\pi\)
0.922490 + 0.386020i \(0.126150\pi\)
\(972\) −20.1075 −0.644948
\(973\) −8.61542 14.9223i −0.276198 0.478389i
\(974\) 3.34359 + 5.79126i 0.107135 + 0.185564i
\(975\) 10.9918 + 0.357245i 0.352019 + 0.0114410i
\(976\) −0.235840 −0.00754906
\(977\) −2.81457 + 4.87498i −0.0900461 + 0.155964i −0.907530 0.419987i \(-0.862035\pi\)
0.817484 + 0.575951i \(0.195368\pi\)
\(978\) 0.812438 + 1.40718i 0.0259789 + 0.0449968i
\(979\) 4.71418 8.16521i 0.150666 0.260961i
\(980\) −5.40671 + 9.36470i −0.172711 + 0.299145i
\(981\) 10.2141 17.6914i 0.326112 0.564843i
\(982\) 2.48019 4.29581i 0.0791459 0.137085i
\(983\) −6.70728 11.6173i −0.213929 0.370536i 0.739012 0.673693i \(-0.235293\pi\)
−0.952941 + 0.303157i \(0.901959\pi\)
\(984\) 0.375575 + 0.650515i 0.0119729 + 0.0207377i
\(985\) 7.07171 + 12.2486i 0.225324 + 0.390272i
\(986\) −0.785295 1.36017i −0.0250089 0.0433167i
\(987\) 11.6667 + 20.2074i 0.371356 + 0.643208i
\(988\) 19.4375 + 36.3445i 0.618390 + 1.15627i
\(989\) −6.40796 + 11.0989i −0.203761 + 0.352925i
\(990\) −3.03059 + 5.24914i −0.0963186 + 0.166829i
\(991\) 2.24466 3.88787i 0.0713040 0.123502i −0.828169 0.560478i \(-0.810617\pi\)
0.899473 + 0.436976i \(0.143951\pi\)
\(992\) 25.1858 + 20.5784i 0.799648 + 0.653366i
\(993\) −18.2895 −0.580401
\(994\) −0.546766 0.947026i −0.0173424 0.0300378i
\(995\) 0.0345687 0.00109590
\(996\) 11.1835 0.354363
\(997\) −6.57944 + 11.3959i −0.208373 + 0.360913i −0.951202 0.308568i \(-0.900150\pi\)
0.742829 + 0.669481i \(0.233483\pi\)
\(998\) −11.0561 19.1498i −0.349976 0.606176i
\(999\) 15.0624 + 26.0888i 0.476553 + 0.825413i
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 403.2.e.a.191.14 70
13.3 even 3 403.2.g.a.315.14 yes 70
31.25 even 3 403.2.g.a.87.14 yes 70
403.211 even 3 inner 403.2.e.a.211.14 yes 70
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.e.a.191.14 70 1.1 even 1 trivial
403.2.e.a.211.14 yes 70 403.211 even 3 inner
403.2.g.a.87.14 yes 70 31.25 even 3
403.2.g.a.315.14 yes 70 13.3 even 3