Properties

Label 336.2.bo.a.173.54
Level $336$
Weight $2$
Character 336.173
Analytic conductor $2.683$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(5,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bo (of order \(12\), degree \(4\), 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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(60\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 173.54
Character \(\chi\) \(=\) 336.173
Dual form 336.2.bo.a.101.54

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.32786 - 0.486611i) q^{2} +(-0.388759 - 1.68786i) q^{3} +(1.52642 - 1.29230i) q^{4} +(-0.224285 - 0.837045i) q^{5} +(-1.33755 - 2.05206i) q^{6} +(2.27219 - 1.35541i) q^{7} +(1.39802 - 2.45877i) q^{8} +(-2.69773 + 1.31234i) q^{9} +O(q^{10})\) \(q+(1.32786 - 0.486611i) q^{2} +(-0.388759 - 1.68786i) q^{3} +(1.52642 - 1.29230i) q^{4} +(-0.224285 - 0.837045i) q^{5} +(-1.33755 - 2.05206i) q^{6} +(2.27219 - 1.35541i) q^{7} +(1.39802 - 2.45877i) q^{8} +(-2.69773 + 1.31234i) q^{9} +(-0.705135 - 1.00234i) q^{10} +(-1.49644 + 5.58477i) q^{11} +(-2.77463 - 2.07398i) q^{12} +(-0.124223 + 0.124223i) q^{13} +(2.35759 - 2.90547i) q^{14} +(-1.32562 + 0.703971i) q^{15} +(0.659908 - 3.94519i) q^{16} +(-1.74467 - 3.02186i) q^{17} +(-2.94361 + 3.05535i) q^{18} +(0.346550 + 1.29334i) q^{19} +(-1.42407 - 0.987836i) q^{20} +(-3.17108 - 3.30821i) q^{21} +(0.730559 + 8.14397i) q^{22} +(-1.74815 + 3.02788i) q^{23} +(-4.69355 - 1.40379i) q^{24} +(3.67979 - 2.12453i) q^{25} +(-0.104502 + 0.225398i) q^{26} +(3.26381 + 4.04321i) q^{27} +(1.71672 - 5.00528i) q^{28} +(1.99563 - 1.99563i) q^{29} +(-1.41768 + 1.57984i) q^{30} +(4.42641 - 2.55559i) q^{31} +(-1.04351 - 5.55977i) q^{32} +(10.0081 + 0.354641i) q^{33} +(-3.78715 - 3.16363i) q^{34} +(-1.64416 - 1.59793i) q^{35} +(-2.42193 + 5.48947i) q^{36} +(2.82045 + 10.5261i) q^{37} +(1.08952 + 1.54874i) q^{38} +(0.257963 + 0.161378i) q^{39} +(-2.37165 - 0.618739i) q^{40} -7.85681i q^{41} +(-5.82056 - 2.84976i) q^{42} +(-4.53143 + 4.53143i) q^{43} +(4.93303 + 10.4585i) q^{44} +(1.70355 + 1.96378i) q^{45} +(-0.847893 + 4.87127i) q^{46} +(-5.88144 + 10.1870i) q^{47} +(-6.91547 + 0.419895i) q^{48} +(3.32573 - 6.15951i) q^{49} +(3.85242 - 4.61170i) q^{50} +(-4.42221 + 4.11953i) q^{51} +(-0.0290825 + 0.350149i) q^{52} +(-1.64946 + 6.15586i) q^{53} +(6.30135 + 3.78060i) q^{54} +5.01033 q^{55} +(-0.156068 - 7.48169i) q^{56} +(2.04825 - 1.08772i) q^{57} +(1.67882 - 3.62101i) q^{58} +(7.87208 + 2.10932i) q^{59} +(-1.11371 + 2.78766i) q^{60} +(0.443640 + 1.65569i) q^{61} +(4.63407 - 5.54740i) q^{62} +(-4.35101 + 6.63843i) q^{63} +(-4.09108 - 6.87481i) q^{64} +(0.131841 + 0.0761186i) q^{65} +(13.4619 - 4.39912i) q^{66} +(0.813578 - 3.03632i) q^{67} +(-6.56825 - 2.35798i) q^{68} +(5.79025 + 1.77351i) q^{69} +(-2.96078 - 1.32176i) q^{70} +1.67369 q^{71} +(-0.544744 + 8.46778i) q^{72} +(-5.43870 - 9.42010i) q^{73} +(8.86726 + 12.6047i) q^{74} +(-5.01645 - 5.38503i) q^{75} +(2.20037 + 1.52633i) q^{76} +(4.16947 + 14.7180i) q^{77} +(0.421066 + 0.0887590i) q^{78} +(1.17913 - 2.04231i) q^{79} +(-3.45031 + 0.332476i) q^{80} +(5.55553 - 7.08069i) q^{81} +(-3.82321 - 10.4327i) q^{82} +(-3.05874 - 3.05874i) q^{83} +(-9.11560 - 0.951729i) q^{84} +(-2.13813 + 2.13813i) q^{85} +(-3.81205 + 8.22214i) q^{86} +(-4.14416 - 2.59252i) q^{87} +(11.6396 + 11.4870i) q^{88} +(6.91129 + 3.99023i) q^{89} +(3.21767 + 1.77866i) q^{90} +(-0.113885 + 0.450630i) q^{91} +(1.24453 + 6.88095i) q^{92} +(-6.03428 - 6.47765i) q^{93} +(-2.85264 + 16.3888i) q^{94} +(1.00486 - 0.580155i) q^{95} +(-8.97844 + 3.92271i) q^{96} +5.88553i q^{97} +(1.41881 - 9.79729i) q^{98} +(-3.29214 - 17.0301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32786 0.486611i 0.938938 0.344086i
\(3\) −0.388759 1.68786i −0.224450 0.974486i
\(4\) 1.52642 1.29230i 0.763209 0.646151i
\(5\) −0.224285 0.837045i −0.100304 0.374338i 0.897467 0.441082i \(-0.145405\pi\)
−0.997770 + 0.0667446i \(0.978739\pi\)
\(6\) −1.33755 2.05206i −0.546052 0.837751i
\(7\) 2.27219 1.35541i 0.858808 0.512297i
\(8\) 1.39802 2.45877i 0.494275 0.869306i
\(9\) −2.69773 + 1.31234i −0.899244 + 0.437447i
\(10\) −0.705135 1.00234i −0.222983 0.316967i
\(11\) −1.49644 + 5.58477i −0.451192 + 1.68387i 0.247855 + 0.968797i \(0.420274\pi\)
−0.699048 + 0.715075i \(0.746392\pi\)
\(12\) −2.77463 2.07398i −0.800967 0.598708i
\(13\) −0.124223 + 0.124223i −0.0344532 + 0.0344532i −0.724123 0.689670i \(-0.757755\pi\)
0.689670 + 0.724123i \(0.257755\pi\)
\(14\) 2.35759 2.90547i 0.630094 0.776519i
\(15\) −1.32562 + 0.703971i −0.342274 + 0.181764i
\(16\) 0.659908 3.94519i 0.164977 0.986297i
\(17\) −1.74467 3.02186i −0.423145 0.732908i 0.573100 0.819485i \(-0.305741\pi\)
−0.996245 + 0.0865769i \(0.972407\pi\)
\(18\) −2.94361 + 3.05535i −0.693815 + 0.720153i
\(19\) 0.346550 + 1.29334i 0.0795039 + 0.296713i 0.994217 0.107392i \(-0.0342499\pi\)
−0.914713 + 0.404104i \(0.867583\pi\)
\(20\) −1.42407 0.987836i −0.318431 0.220887i
\(21\) −3.17108 3.30821i −0.691986 0.721911i
\(22\) 0.730559 + 8.14397i 0.155756 + 1.73630i
\(23\) −1.74815 + 3.02788i −0.364514 + 0.631357i −0.988698 0.149920i \(-0.952098\pi\)
0.624184 + 0.781278i \(0.285432\pi\)
\(24\) −4.69355 1.40379i −0.958066 0.286548i
\(25\) 3.67979 2.12453i 0.735957 0.424905i
\(26\) −0.104502 + 0.225398i −0.0204945 + 0.0442042i
\(27\) 3.26381 + 4.04321i 0.628121 + 0.778116i
\(28\) 1.71672 5.00528i 0.324429 0.945910i
\(29\) 1.99563 1.99563i 0.370579 0.370579i −0.497109 0.867688i \(-0.665605\pi\)
0.867688 + 0.497109i \(0.165605\pi\)
\(30\) −1.41768 + 1.57984i −0.258831 + 0.288437i
\(31\) 4.42641 2.55559i 0.795007 0.458997i −0.0467155 0.998908i \(-0.514875\pi\)
0.841722 + 0.539911i \(0.181542\pi\)
\(32\) −1.04351 5.55977i −0.184468 0.982839i
\(33\) 10.0081 + 0.354641i 1.74218 + 0.0617351i
\(34\) −3.78715 3.16363i −0.649490 0.542557i
\(35\) −1.64416 1.59793i −0.277914 0.270099i
\(36\) −2.42193 + 5.48947i −0.403655 + 0.914911i
\(37\) 2.82045 + 10.5261i 0.463679 + 1.73047i 0.661232 + 0.750181i \(0.270034\pi\)
−0.197553 + 0.980292i \(0.563299\pi\)
\(38\) 1.08952 + 1.54874i 0.176744 + 0.251239i
\(39\) 0.257963 + 0.161378i 0.0413071 + 0.0258411i
\(40\) −2.37165 0.618739i −0.374992 0.0978313i
\(41\) 7.85681i 1.22703i −0.789684 0.613513i \(-0.789756\pi\)
0.789684 0.613513i \(-0.210244\pi\)
\(42\) −5.82056 2.84976i −0.898131 0.439727i
\(43\) −4.53143 + 4.53143i −0.691037 + 0.691037i −0.962460 0.271423i \(-0.912506\pi\)
0.271423 + 0.962460i \(0.412506\pi\)
\(44\) 4.93303 + 10.4585i 0.743682 + 1.57669i
\(45\) 1.70355 + 1.96378i 0.253950 + 0.292744i
\(46\) −0.847893 + 4.87127i −0.125015 + 0.718230i
\(47\) −5.88144 + 10.1870i −0.857897 + 1.48592i 0.0160351 + 0.999871i \(0.494896\pi\)
−0.873932 + 0.486049i \(0.838438\pi\)
\(48\) −6.91547 + 0.419895i −0.998162 + 0.0606067i
\(49\) 3.32573 6.15951i 0.475104 0.879930i
\(50\) 3.85242 4.61170i 0.544814 0.652192i
\(51\) −4.42221 + 4.11953i −0.619234 + 0.576850i
\(52\) −0.0290825 + 0.350149i −0.00403302 + 0.0485569i
\(53\) −1.64946 + 6.15586i −0.226571 + 0.845573i 0.755199 + 0.655496i \(0.227540\pi\)
−0.981769 + 0.190077i \(0.939126\pi\)
\(54\) 6.30135 + 3.78060i 0.857506 + 0.514475i
\(55\) 5.01033 0.675593
\(56\) −0.156068 7.48169i −0.0208555 0.999783i
\(57\) 2.04825 1.08772i 0.271298 0.144073i
\(58\) 1.67882 3.62101i 0.220440 0.475462i
\(59\) 7.87208 + 2.10932i 1.02486 + 0.274610i 0.731825 0.681493i \(-0.238669\pi\)
0.293033 + 0.956102i \(0.405336\pi\)
\(60\) −1.11371 + 2.78766i −0.143779 + 0.359885i
\(61\) 0.443640 + 1.65569i 0.0568022 + 0.211989i 0.988494 0.151262i \(-0.0483336\pi\)
−0.931692 + 0.363250i \(0.881667\pi\)
\(62\) 4.63407 5.54740i 0.588527 0.704521i
\(63\) −4.35101 + 6.63843i −0.548176 + 0.836363i
\(64\) −4.09108 6.87481i −0.511385 0.859352i
\(65\) 0.131841 + 0.0761186i 0.0163529 + 0.00944135i
\(66\) 13.4619 4.39912i 1.65704 0.541494i
\(67\) 0.813578 3.03632i 0.0993944 0.370945i −0.898255 0.439475i \(-0.855164\pi\)
0.997649 + 0.0685304i \(0.0218310\pi\)
\(68\) −6.56825 2.35798i −0.796518 0.285947i
\(69\) 5.79025 + 1.77351i 0.697064 + 0.213506i
\(70\) −2.96078 1.32176i −0.353881 0.157980i
\(71\) 1.67369 0.198631 0.0993154 0.995056i \(-0.468335\pi\)
0.0993154 + 0.995056i \(0.468335\pi\)
\(72\) −0.544744 + 8.46778i −0.0641987 + 0.997937i
\(73\) −5.43870 9.42010i −0.636551 1.10254i −0.986184 0.165652i \(-0.947027\pi\)
0.349633 0.936887i \(-0.386306\pi\)
\(74\) 8.86726 + 12.6047i 1.03080 + 1.46526i
\(75\) −5.01645 5.38503i −0.579250 0.621810i
\(76\) 2.20037 + 1.52633i 0.252399 + 0.175082i
\(77\) 4.16947 + 14.7180i 0.475155 + 1.67727i
\(78\) 0.421066 + 0.0887590i 0.0476764 + 0.0100500i
\(79\) 1.17913 2.04231i 0.132662 0.229778i −0.792040 0.610470i \(-0.790981\pi\)
0.924702 + 0.380692i \(0.124314\pi\)
\(80\) −3.45031 + 0.332476i −0.385756 + 0.0371719i
\(81\) 5.55553 7.08069i 0.617281 0.786743i
\(82\) −3.82321 10.4327i −0.422203 1.15210i
\(83\) −3.05874 3.05874i −0.335740 0.335740i 0.519021 0.854761i \(-0.326297\pi\)
−0.854761 + 0.519021i \(0.826297\pi\)
\(84\) −9.11560 0.951729i −0.994594 0.103842i
\(85\) −2.13813 + 2.13813i −0.231912 + 0.231912i
\(86\) −3.81205 + 8.22214i −0.411064 + 0.886617i
\(87\) −4.14416 2.59252i −0.444301 0.277948i
\(88\) 11.6396 + 11.4870i 1.24079 + 1.22452i
\(89\) 6.91129 + 3.99023i 0.732595 + 0.422964i 0.819371 0.573264i \(-0.194323\pi\)
−0.0867758 + 0.996228i \(0.527656\pi\)
\(90\) 3.21767 + 1.77866i 0.339173 + 0.187487i
\(91\) −0.113885 + 0.450630i −0.0119384 + 0.0472389i
\(92\) 1.24453 + 6.88095i 0.129752 + 0.717389i
\(93\) −6.03428 6.47765i −0.625726 0.671701i
\(94\) −2.85264 + 16.3888i −0.294227 + 1.69038i
\(95\) 1.00486 0.580155i 0.103096 0.0595227i
\(96\) −8.97844 + 3.92271i −0.916358 + 0.400360i
\(97\) 5.88553i 0.597585i 0.954318 + 0.298793i \(0.0965839\pi\)
−0.954318 + 0.298793i \(0.903416\pi\)
\(98\) 1.41881 9.79729i 0.143321 0.989676i
\(99\) −3.29214 17.0301i −0.330872 1.71158i
\(100\) 2.87137 7.99831i 0.287137 0.799831i
\(101\) −16.7380 4.48492i −1.66549 0.446267i −0.701600 0.712571i \(-0.747531\pi\)
−0.963889 + 0.266304i \(0.914197\pi\)
\(102\) −3.86746 + 7.62206i −0.382936 + 0.754696i
\(103\) −8.51730 + 14.7524i −0.839234 + 1.45360i 0.0513016 + 0.998683i \(0.483663\pi\)
−0.890536 + 0.454913i \(0.849670\pi\)
\(104\) 0.131769 + 0.479100i 0.0129210 + 0.0469796i
\(105\) −2.05790 + 3.39632i −0.200830 + 0.331447i
\(106\) 0.805265 + 8.97676i 0.0782142 + 0.871900i
\(107\) 0.245411 0.0657577i 0.0237248 0.00635704i −0.246937 0.969032i \(-0.579424\pi\)
0.270662 + 0.962674i \(0.412757\pi\)
\(108\) 10.2070 + 1.95380i 0.982168 + 0.188004i
\(109\) 2.61921 9.77503i 0.250875 0.936278i −0.719464 0.694530i \(-0.755612\pi\)
0.970339 0.241748i \(-0.0777209\pi\)
\(110\) 6.65302 2.43809i 0.634340 0.232462i
\(111\) 16.6700 8.85262i 1.58225 0.840253i
\(112\) −3.84791 9.85868i −0.363593 0.931558i
\(113\) 2.44101i 0.229631i 0.993387 + 0.114816i \(0.0366277\pi\)
−0.993387 + 0.114816i \(0.963372\pi\)
\(114\) 2.19049 2.44105i 0.205158 0.228625i
\(115\) 2.92656 + 0.784169i 0.272903 + 0.0731241i
\(116\) 0.467210 5.62513i 0.0433793 0.522280i
\(117\) 0.172097 0.498142i 0.0159104 0.0460532i
\(118\) 11.4794 1.02977i 1.05677 0.0947978i
\(119\) −8.06009 4.50150i −0.738867 0.412652i
\(120\) −0.122342 + 4.24356i −0.0111683 + 0.387382i
\(121\) −19.4241 11.2145i −1.76583 1.01950i
\(122\) 1.39477 + 1.98264i 0.126276 + 0.179500i
\(123\) −13.2612 + 3.05440i −1.19572 + 0.275406i
\(124\) 3.45396 9.62116i 0.310175 0.864006i
\(125\) −5.66744 5.66744i −0.506912 0.506912i
\(126\) −2.54720 + 10.9321i −0.226922 + 0.973913i
\(127\) 10.2896 0.913058 0.456529 0.889708i \(-0.349092\pi\)
0.456529 + 0.889708i \(0.349092\pi\)
\(128\) −8.77774 7.13801i −0.775850 0.630917i
\(129\) 9.41005 + 5.88678i 0.828508 + 0.518302i
\(130\) 0.212107 + 0.0369193i 0.0186030 + 0.00323804i
\(131\) −11.0289 + 2.95518i −0.963597 + 0.258195i −0.706122 0.708090i \(-0.749557\pi\)
−0.257475 + 0.966285i \(0.582890\pi\)
\(132\) 15.7348 12.3921i 1.36954 1.07859i
\(133\) 2.54043 + 2.46900i 0.220284 + 0.214090i
\(134\) −0.397188 4.42769i −0.0343119 0.382495i
\(135\) 2.65232 3.63879i 0.228275 0.313177i
\(136\) −9.86913 + 0.0651232i −0.846271 + 0.00558427i
\(137\) −5.13667 8.89697i −0.438855 0.760119i 0.558746 0.829339i \(-0.311283\pi\)
−0.997601 + 0.0692192i \(0.977949\pi\)
\(138\) 8.55164 0.462626i 0.727964 0.0393814i
\(139\) −4.79178 4.79178i −0.406434 0.406434i 0.474059 0.880493i \(-0.342788\pi\)
−0.880493 + 0.474059i \(0.842788\pi\)
\(140\) −4.57468 0.314358i −0.386631 0.0265681i
\(141\) 19.4806 + 5.96677i 1.64056 + 0.502493i
\(142\) 2.22243 0.814438i 0.186502 0.0683461i
\(143\) −0.507864 0.879646i −0.0424697 0.0735597i
\(144\) 3.39717 + 11.5091i 0.283098 + 0.959091i
\(145\) −2.11802 1.22284i −0.175892 0.101551i
\(146\) −11.8057 9.86203i −0.977050 0.816187i
\(147\) −11.6893 3.21879i −0.964116 0.265481i
\(148\) 17.9080 + 12.4223i 1.47203 + 1.02111i
\(149\) 1.58785 0.425463i 0.130082 0.0348553i −0.193191 0.981161i \(-0.561884\pi\)
0.323272 + 0.946306i \(0.395217\pi\)
\(150\) −9.28155 4.70950i −0.757836 0.384529i
\(151\) −3.54744 + 2.04811i −0.288686 + 0.166673i −0.637349 0.770575i \(-0.719969\pi\)
0.348663 + 0.937248i \(0.386636\pi\)
\(152\) 3.66451 + 0.956031i 0.297231 + 0.0775443i
\(153\) 8.67236 + 5.86257i 0.701119 + 0.473960i
\(154\) 12.6984 + 17.5145i 1.02327 + 1.41136i
\(155\) −3.13192 3.13192i −0.251562 0.251562i
\(156\) 0.602308 0.0870363i 0.0482232 0.00696848i
\(157\) −2.18986 0.586771i −0.174770 0.0468295i 0.170373 0.985380i \(-0.445503\pi\)
−0.345143 + 0.938550i \(0.612169\pi\)
\(158\) 0.571905 3.28568i 0.0454983 0.261395i
\(159\) 11.0315 + 0.390906i 0.874852 + 0.0310009i
\(160\) −4.41974 + 2.12044i −0.349411 + 0.167636i
\(161\) 0.131891 + 9.24939i 0.0103945 + 0.728954i
\(162\) 3.93141 12.1055i 0.308881 0.951101i
\(163\) −19.3957 + 5.19707i −1.51919 + 0.407066i −0.919475 0.393149i \(-0.871386\pi\)
−0.599714 + 0.800214i \(0.704719\pi\)
\(164\) −10.1534 11.9928i −0.792845 0.936478i
\(165\) −1.94781 8.45673i −0.151637 0.658356i
\(166\) −5.54999 2.57316i −0.430763 0.199716i
\(167\) 7.00150i 0.541792i 0.962609 + 0.270896i \(0.0873200\pi\)
−0.962609 + 0.270896i \(0.912680\pi\)
\(168\) −12.5674 + 3.17199i −0.969593 + 0.244725i
\(169\) 12.9691i 0.997626i
\(170\) −1.79869 + 3.87957i −0.137954 + 0.297549i
\(171\) −2.63220 3.03430i −0.201289 0.232038i
\(172\) −1.06088 + 12.7728i −0.0808914 + 0.973920i
\(173\) −0.119913 + 0.0321306i −0.00911682 + 0.00244285i −0.263375 0.964694i \(-0.584836\pi\)
0.254258 + 0.967136i \(0.418169\pi\)
\(174\) −6.76441 1.42591i −0.512809 0.108098i
\(175\) 5.48158 9.81495i 0.414369 0.741941i
\(176\) 21.0455 + 9.58916i 1.58636 + 0.722810i
\(177\) 0.499888 14.1070i 0.0375739 1.06034i
\(178\) 11.1189 + 1.93536i 0.833397 + 0.145061i
\(179\) 16.9948 + 4.55374i 1.27025 + 0.340362i 0.830127 0.557575i \(-0.188268\pi\)
0.440123 + 0.897937i \(0.354935\pi\)
\(180\) 5.13813 + 0.796056i 0.382974 + 0.0593345i
\(181\) −9.08621 9.08621i −0.675372 0.675372i 0.283577 0.958949i \(-0.408479\pi\)
−0.958949 + 0.283577i \(0.908479\pi\)
\(182\) 0.0680584 + 0.653791i 0.00504482 + 0.0484622i
\(183\) 2.62210 1.39246i 0.193831 0.102934i
\(184\) 5.00092 + 8.53133i 0.368672 + 0.628938i
\(185\) 8.17820 4.72169i 0.601273 0.347145i
\(186\) −11.1648 5.66505i −0.818640 0.415382i
\(187\) 19.4872 5.22157i 1.42504 0.381839i
\(188\) 4.18709 + 23.1502i 0.305375 + 1.68840i
\(189\) 12.8962 + 4.76315i 0.938062 + 0.346468i
\(190\) 1.05200 1.25934i 0.0763201 0.0913621i
\(191\) −12.6628 7.31086i −0.916247 0.528996i −0.0338112 0.999428i \(-0.510765\pi\)
−0.882436 + 0.470433i \(0.844098\pi\)
\(192\) −10.0133 + 9.57781i −0.722645 + 0.691219i
\(193\) −4.14094 7.17232i −0.298071 0.516275i 0.677623 0.735409i \(-0.263010\pi\)
−0.975695 + 0.219135i \(0.929677\pi\)
\(194\) 2.86397 + 7.81516i 0.205621 + 0.561095i
\(195\) 0.0772229 0.252121i 0.00553005 0.0180548i
\(196\) −2.88350 13.6998i −0.205964 0.978560i
\(197\) 0.174426 + 0.174426i 0.0124273 + 0.0124273i 0.713293 0.700866i \(-0.247203\pi\)
−0.700866 + 0.713293i \(0.747203\pi\)
\(198\) −12.6585 21.0115i −0.899601 1.49322i
\(199\) 7.78849 + 13.4901i 0.552111 + 0.956285i 0.998122 + 0.0612574i \(0.0195111\pi\)
−0.446011 + 0.895028i \(0.647156\pi\)
\(200\) −0.0793021 12.0179i −0.00560750 0.849792i
\(201\) −5.44116 0.192810i −0.383790 0.0135998i
\(202\) −24.4081 + 2.18954i −1.71735 + 0.154055i
\(203\) 1.82956 7.23936i 0.128410 0.508103i
\(204\) −1.42647 + 12.0030i −0.0998727 + 0.840376i
\(205\) −6.57650 + 1.76217i −0.459323 + 0.123075i
\(206\) −4.13109 + 23.7337i −0.287827 + 1.65361i
\(207\) 0.742427 10.4626i 0.0516023 0.727200i
\(208\) 0.408106 + 0.572057i 0.0282971 + 0.0396650i
\(209\) −7.74160 −0.535498
\(210\) −1.07991 + 5.51123i −0.0745209 + 0.380311i
\(211\) −10.3013 10.3013i −0.709167 0.709167i 0.257193 0.966360i \(-0.417202\pi\)
−0.966360 + 0.257193i \(0.917202\pi\)
\(212\) 5.43747 + 11.5280i 0.373447 + 0.791748i
\(213\) −0.650663 2.82496i −0.0445827 0.193563i
\(214\) 0.293873 0.206737i 0.0200887 0.0141322i
\(215\) 4.80934 + 2.77668i 0.327995 + 0.189368i
\(216\) 14.5042 2.37247i 0.986885 0.161426i
\(217\) 6.59379 11.8064i 0.447616 0.801470i
\(218\) −1.27870 14.2544i −0.0866043 0.965430i
\(219\) −13.7854 + 12.8419i −0.931534 + 0.867775i
\(220\) 7.64787 6.47487i 0.515619 0.436535i
\(221\) 0.592111 + 0.158656i 0.0398297 + 0.0106723i
\(222\) 17.8277 19.8669i 1.19651 1.33338i
\(223\) 13.9846i 0.936476i −0.883602 0.468238i \(-0.844889\pi\)
0.883602 0.468238i \(-0.155111\pi\)
\(224\) −9.90683 11.2185i −0.661928 0.749568i
\(225\) −7.13898 + 10.5605i −0.475932 + 0.704036i
\(226\) 1.18782 + 3.24132i 0.0790129 + 0.215609i
\(227\) 4.86517 18.1571i 0.322913 1.20513i −0.593480 0.804849i \(-0.702246\pi\)
0.916393 0.400279i \(-0.131087\pi\)
\(228\) 1.72082 4.30728i 0.113964 0.285257i
\(229\) −16.9205 + 4.53383i −1.11814 + 0.299604i −0.770130 0.637888i \(-0.779808\pi\)
−0.348008 + 0.937492i \(0.613142\pi\)
\(230\) 4.26764 0.382831i 0.281400 0.0252431i
\(231\) 23.2209 12.7592i 1.52782 0.839494i
\(232\) −2.11686 7.69673i −0.138979 0.505315i
\(233\) 11.9486 20.6956i 0.782780 1.35581i −0.147537 0.989057i \(-0.547135\pi\)
0.930317 0.366757i \(-0.119532\pi\)
\(234\) −0.0138807 0.745206i −0.000907412 0.0487157i
\(235\) 9.84606 + 2.63824i 0.642286 + 0.172100i
\(236\) 14.7420 6.95341i 0.959620 0.452628i
\(237\) −3.90553 1.19624i −0.253691 0.0777039i
\(238\) −12.8931 2.05523i −0.835738 0.133221i
\(239\) 4.58228i 0.296403i 0.988957 + 0.148202i \(0.0473484\pi\)
−0.988957 + 0.148202i \(0.952652\pi\)
\(240\) 1.90251 + 5.69438i 0.122807 + 0.367571i
\(241\) −25.5960 + 14.7779i −1.64879 + 0.951927i −0.671230 + 0.741249i \(0.734234\pi\)
−0.977555 + 0.210678i \(0.932433\pi\)
\(242\) −31.2495 5.43929i −2.00880 0.349651i
\(243\) −14.1110 6.62426i −0.905218 0.424947i
\(244\) 2.81683 + 1.95395i 0.180329 + 0.125089i
\(245\) −5.90170 1.40229i −0.377046 0.0895892i
\(246\) −16.1227 + 10.5089i −1.02794 + 0.670020i
\(247\) −0.203711 0.117613i −0.0129618 0.00748353i
\(248\) −0.0953924 14.4563i −0.00605742 0.917975i
\(249\) −3.97361 + 6.35183i −0.251817 + 0.402531i
\(250\) −10.2834 4.76772i −0.650380 0.301537i
\(251\) 14.9573 14.9573i 0.944098 0.944098i −0.0544206 0.998518i \(-0.517331\pi\)
0.998518 + 0.0544206i \(0.0173312\pi\)
\(252\) 1.93739 + 15.7558i 0.122044 + 0.992525i
\(253\) −14.2940 14.2940i −0.898659 0.898659i
\(254\) 13.6632 5.00706i 0.857305 0.314171i
\(255\) 4.44007 + 2.77764i 0.278048 + 0.173943i
\(256\) −15.1290 5.20693i −0.945565 0.325433i
\(257\) −0.412351 + 0.714213i −0.0257218 + 0.0445514i −0.878600 0.477559i \(-0.841522\pi\)
0.852878 + 0.522110i \(0.174855\pi\)
\(258\) 15.3598 + 3.23778i 0.956259 + 0.201575i
\(259\) 20.6757 + 20.0944i 1.28473 + 1.24860i
\(260\) 0.299613 0.0541899i 0.0185812 0.00336072i
\(261\) −2.76473 + 8.00263i −0.171133 + 0.495350i
\(262\) −13.2068 + 9.29083i −0.815917 + 0.573990i
\(263\) 8.55527 + 14.8182i 0.527540 + 0.913727i 0.999485 + 0.0320983i \(0.0102190\pi\)
−0.471944 + 0.881628i \(0.656448\pi\)
\(264\) 14.8634 24.1117i 0.914782 1.48397i
\(265\) 5.52268 0.339256
\(266\) 4.57478 + 2.04228i 0.280498 + 0.125220i
\(267\) 4.04813 13.2165i 0.247741 0.808838i
\(268\) −2.68198 5.68608i −0.163828 0.347332i
\(269\) −5.04909 + 18.8435i −0.307848 + 1.14891i 0.622617 + 0.782526i \(0.286069\pi\)
−0.930466 + 0.366379i \(0.880597\pi\)
\(270\) 1.75123 6.12245i 0.106577 0.372600i
\(271\) 23.2129 + 13.4020i 1.41008 + 0.814111i 0.995395 0.0958531i \(-0.0305579\pi\)
0.414687 + 0.909964i \(0.363891\pi\)
\(272\) −13.0731 + 4.88891i −0.792675 + 0.296434i
\(273\) 0.804874 + 0.0170355i 0.0487132 + 0.00103104i
\(274\) −11.1501 9.31436i −0.673604 0.562701i
\(275\) 6.35843 + 23.7300i 0.383428 + 1.43097i
\(276\) 11.1303 4.77563i 0.669963 0.287459i
\(277\) 14.8501 + 3.97908i 0.892259 + 0.239080i 0.675689 0.737187i \(-0.263846\pi\)
0.216570 + 0.976267i \(0.430513\pi\)
\(278\) −8.69455 4.03108i −0.521464 0.241768i
\(279\) −8.58747 + 12.7033i −0.514118 + 0.760524i
\(280\) −6.22750 + 1.80867i −0.372165 + 0.108089i
\(281\) 9.55555 0.570036 0.285018 0.958522i \(-0.408000\pi\)
0.285018 + 0.958522i \(0.408000\pi\)
\(282\) 28.7710 1.55645i 1.71329 0.0926854i
\(283\) −6.16214 + 22.9974i −0.366301 + 1.36705i 0.499347 + 0.866402i \(0.333573\pi\)
−0.865648 + 0.500652i \(0.833094\pi\)
\(284\) 2.55476 2.16292i 0.151597 0.128346i
\(285\) −1.36987 1.47052i −0.0811439 0.0871060i
\(286\) −1.10242 0.920914i −0.0651873 0.0544548i
\(287\) −10.6492 17.8522i −0.628602 1.05378i
\(288\) 10.1114 + 13.6293i 0.595821 + 0.803117i
\(289\) 2.41225 4.17814i 0.141897 0.245773i
\(290\) −3.40749 0.593107i −0.200094 0.0348284i
\(291\) 9.93394 2.28805i 0.582338 0.134128i
\(292\) −20.4753 7.35057i −1.19823 0.430160i
\(293\) 3.12364 3.12364i 0.182485 0.182485i −0.609953 0.792438i \(-0.708812\pi\)
0.792438 + 0.609953i \(0.208812\pi\)
\(294\) −17.0880 + 1.41404i −0.996594 + 0.0824684i
\(295\) 7.06237i 0.411187i
\(296\) 29.8242 + 7.78081i 1.73350 + 0.452250i
\(297\) −27.4645 + 12.1772i −1.59365 + 0.706596i
\(298\) 1.90140 1.33762i 0.110145 0.0774862i
\(299\) −0.158972 0.593291i −0.00919358 0.0343109i
\(300\) −14.6163 1.73704i −0.843872 0.100288i
\(301\) −4.15434 + 16.4382i −0.239452 + 0.947484i
\(302\) −3.71386 + 4.44583i −0.213709 + 0.255829i
\(303\) −1.06288 + 29.9949i −0.0610611 + 1.72316i
\(304\) 5.33116 0.513717i 0.305763 0.0294637i
\(305\) 1.28638 0.742693i 0.0736580 0.0425265i
\(306\) 14.3685 + 3.56459i 0.821390 + 0.203774i
\(307\) −4.51853 + 4.51853i −0.257886 + 0.257886i −0.824194 0.566308i \(-0.808371\pi\)
0.566308 + 0.824194i \(0.308371\pi\)
\(308\) 25.3844 + 17.0776i 1.44641 + 0.973085i
\(309\) 28.2111 + 8.64087i 1.60487 + 0.491562i
\(310\) −5.68278 2.63472i −0.322760 0.149642i
\(311\) 11.9241 6.88436i 0.676152 0.390377i −0.122252 0.992499i \(-0.539012\pi\)
0.798404 + 0.602123i \(0.205678\pi\)
\(312\) 0.757427 0.408662i 0.0428809 0.0231359i
\(313\) −4.80811 + 8.32789i −0.271770 + 0.470720i −0.969315 0.245821i \(-0.920942\pi\)
0.697545 + 0.716541i \(0.254276\pi\)
\(314\) −3.19336 + 0.286461i −0.180212 + 0.0161660i
\(315\) 6.53253 + 2.15309i 0.368066 + 0.121313i
\(316\) −0.839439 4.64121i −0.0472222 0.261089i
\(317\) 3.68996 + 13.7711i 0.207249 + 0.773464i 0.988752 + 0.149563i \(0.0477866\pi\)
−0.781503 + 0.623901i \(0.785547\pi\)
\(318\) 14.8385 4.84897i 0.832099 0.271917i
\(319\) 8.15881 + 14.1315i 0.456806 + 0.791211i
\(320\) −4.83696 + 4.96634i −0.270394 + 0.277627i
\(321\) −0.206395 0.388655i −0.0115199 0.0216926i
\(322\) 4.67599 + 12.2177i 0.260583 + 0.680866i
\(323\) 3.30368 3.30368i 0.183822 0.183822i
\(324\) −0.670328 17.9875i −0.0372405 0.999306i
\(325\) −0.193199 + 0.721027i −0.0107167 + 0.0399954i
\(326\) −23.2258 + 16.3391i −1.28636 + 0.904941i
\(327\) −17.5171 0.620728i −0.968698 0.0343264i
\(328\) −19.3181 10.9840i −1.06666 0.606488i
\(329\) 0.443731 + 31.1185i 0.0244637 + 1.71562i
\(330\) −6.70156 10.2815i −0.368909 0.565979i
\(331\) −9.31527 34.7651i −0.512014 1.91086i −0.398011 0.917380i \(-0.630300\pi\)
−0.114002 0.993480i \(-0.536367\pi\)
\(332\) −8.62173 0.716101i −0.473179 0.0393011i
\(333\) −21.4226 24.6951i −1.17395 1.35328i
\(334\) 3.40701 + 9.29700i 0.186423 + 0.508709i
\(335\) −2.72401 −0.148828
\(336\) −15.1441 + 10.3274i −0.826181 + 0.563405i
\(337\) −7.79829 −0.424800 −0.212400 0.977183i \(-0.568128\pi\)
−0.212400 + 0.977183i \(0.568128\pi\)
\(338\) 6.31093 + 17.2212i 0.343269 + 0.936709i
\(339\) 4.12008 0.948965i 0.223772 0.0515407i
\(340\) −0.500570 + 6.02678i −0.0271472 + 0.326848i
\(341\) 7.64855 + 28.5448i 0.414192 + 1.54579i
\(342\) −4.97171 2.74826i −0.268840 0.148609i
\(343\) −0.791968 18.5033i −0.0427622 0.999085i
\(344\) 4.80671 + 17.4768i 0.259160 + 0.942284i
\(345\) 0.185841 5.24447i 0.0100053 0.282353i
\(346\) −0.143593 + 0.101016i −0.00771958 + 0.00543065i
\(347\) 4.08389 15.2413i 0.219235 0.818196i −0.765398 0.643557i \(-0.777458\pi\)
0.984633 0.174638i \(-0.0558756\pi\)
\(348\) −9.67605 + 1.39823i −0.518691 + 0.0749532i
\(349\) 7.97573 7.97573i 0.426931 0.426931i −0.460651 0.887582i \(-0.652384\pi\)
0.887582 + 0.460651i \(0.152384\pi\)
\(350\) 2.50270 15.7003i 0.133775 0.839215i
\(351\) −0.907697 0.0968186i −0.0484493 0.00516779i
\(352\) 32.6116 + 2.49208i 1.73820 + 0.132828i
\(353\) 8.92287 + 15.4549i 0.474917 + 0.822580i 0.999587 0.0287256i \(-0.00914491\pi\)
−0.524671 + 0.851305i \(0.675812\pi\)
\(354\) −6.20083 18.9753i −0.329571 1.00853i
\(355\) −0.375385 1.40096i −0.0199234 0.0743550i
\(356\) 15.7061 2.84071i 0.832422 0.150557i
\(357\) −4.46447 + 15.3543i −0.236285 + 0.812635i
\(358\) 24.7826 2.22313i 1.30980 0.117496i
\(359\) 8.36824 14.4942i 0.441659 0.764976i −0.556154 0.831079i \(-0.687723\pi\)
0.997813 + 0.0661035i \(0.0210568\pi\)
\(360\) 7.21009 1.44322i 0.380005 0.0760646i
\(361\) 14.9018 8.60359i 0.784308 0.452820i
\(362\) −16.4867 7.64375i −0.866519 0.401747i
\(363\) −11.3772 + 37.1448i −0.597148 + 1.94960i
\(364\) 0.408514 + 0.835025i 0.0214120 + 0.0437672i
\(365\) −6.66522 + 6.66522i −0.348874 + 0.348874i
\(366\) 2.80418 3.12494i 0.146577 0.163343i
\(367\) −26.4671 + 15.2808i −1.38157 + 0.797651i −0.992346 0.123492i \(-0.960591\pi\)
−0.389226 + 0.921142i \(0.627257\pi\)
\(368\) 10.7920 + 8.89491i 0.562569 + 0.463679i
\(369\) 10.3108 + 21.1956i 0.536759 + 1.10340i
\(370\) 8.56187 10.2493i 0.445110 0.532838i
\(371\) 4.59583 + 16.2230i 0.238604 + 0.842256i
\(372\) −17.5819 2.08949i −0.911580 0.108335i
\(373\) 8.51467 + 31.7772i 0.440873 + 1.64536i 0.726609 + 0.687051i \(0.241095\pi\)
−0.285736 + 0.958308i \(0.592238\pi\)
\(374\) 23.3353 16.4162i 1.20664 0.848861i
\(375\) −7.36257 + 11.7691i −0.380202 + 0.607754i
\(376\) 16.8250 + 28.7027i 0.867683 + 1.48023i
\(377\) 0.495805i 0.0255353i
\(378\) 19.4422 + 0.0493396i 0.999997 + 0.00253776i
\(379\) −5.96162 + 5.96162i −0.306228 + 0.306228i −0.843444 0.537217i \(-0.819476\pi\)
0.537217 + 0.843444i \(0.319476\pi\)
\(380\) 0.784098 2.18414i 0.0402234 0.112044i
\(381\) −4.00019 17.3675i −0.204936 0.889762i
\(382\) −20.3719 3.54594i −1.04232 0.181426i
\(383\) 10.9394 18.9475i 0.558975 0.968173i −0.438608 0.898679i \(-0.644528\pi\)
0.997582 0.0694940i \(-0.0221385\pi\)
\(384\) −8.63553 + 17.5906i −0.440680 + 0.897664i
\(385\) 11.3844 6.79106i 0.580205 0.346104i
\(386\) −8.98871 7.50880i −0.457513 0.382188i
\(387\) 6.27781 18.1714i 0.319119 0.923702i
\(388\) 7.60589 + 8.98379i 0.386130 + 0.456083i
\(389\) 1.03982 3.88066i 0.0527210 0.196757i −0.934542 0.355852i \(-0.884191\pi\)
0.987263 + 0.159094i \(0.0508574\pi\)
\(390\) −0.0201438 0.372359i −0.00102002 0.0188551i
\(391\) 12.1998 0.616969
\(392\) −10.4954 16.7883i −0.530096 0.847937i
\(393\) 9.27549 + 17.4663i 0.467887 + 0.881059i
\(394\) 0.316491 + 0.146735i 0.0159446 + 0.00739243i
\(395\) −1.97397 0.528923i −0.0993211 0.0266130i
\(396\) −27.0332 21.7406i −1.35847 1.09250i
\(397\) 2.77995 + 10.3749i 0.139522 + 0.520702i 0.999938 + 0.0111107i \(0.00353672\pi\)
−0.860417 + 0.509591i \(0.829797\pi\)
\(398\) 16.9064 + 14.1229i 0.847443 + 0.707919i
\(399\) 3.17971 5.24774i 0.159185 0.262716i
\(400\) −5.95334 15.9194i −0.297667 0.795972i
\(401\) −18.5751 10.7243i −0.927596 0.535548i −0.0415458 0.999137i \(-0.513228\pi\)
−0.886051 + 0.463589i \(0.846562\pi\)
\(402\) −7.31891 + 2.39170i −0.365034 + 0.119287i
\(403\) −0.232398 + 0.867322i −0.0115766 + 0.0432044i
\(404\) −31.3450 + 14.7846i −1.55947 + 0.735563i
\(405\) −7.17288 3.06213i −0.356423 0.152158i
\(406\) −1.09336 10.5031i −0.0542623 0.521262i
\(407\) −63.0063 −3.12310
\(408\) 3.94663 + 16.6324i 0.195387 + 0.823426i
\(409\) −2.15950 3.74037i −0.106780 0.184949i 0.807684 0.589616i \(-0.200721\pi\)
−0.914464 + 0.404667i \(0.867388\pi\)
\(410\) −7.87517 + 5.54011i −0.388927 + 0.273606i
\(411\) −13.0199 + 12.1287i −0.642224 + 0.598267i
\(412\) 6.06359 + 33.5253i 0.298732 + 1.65167i
\(413\) 20.7459 5.87712i 1.02084 0.289194i
\(414\) −4.10537 14.2541i −0.201768 0.700551i
\(415\) −1.87427 + 3.24633i −0.0920043 + 0.159356i
\(416\) 0.820277 + 0.561022i 0.0402174 + 0.0275064i
\(417\) −6.22500 + 9.95070i −0.304840 + 0.487288i
\(418\) −10.2798 + 3.76715i −0.502799 + 0.184257i
\(419\) −1.00684 1.00684i −0.0491873 0.0491873i 0.682085 0.731273i \(-0.261073\pi\)
−0.731273 + 0.682085i \(0.761073\pi\)
\(420\) 1.24786 + 7.84363i 0.0608892 + 0.382730i
\(421\) 20.5242 20.5242i 1.00029 1.00029i 0.000289208 1.00000i \(-0.499908\pi\)
1.00000 0.000289208i \(-9.20576e-5\pi\)
\(422\) −18.6913 8.66590i −0.909879 0.421850i
\(423\) 2.49781 35.2001i 0.121448 1.71149i
\(424\) 12.8299 + 12.6617i 0.623073 + 0.614904i
\(425\) −12.8400 7.41320i −0.622833 0.359593i
\(426\) −2.23864 3.43452i −0.108463 0.166403i
\(427\) 3.25217 + 3.16073i 0.157383 + 0.152958i
\(428\) 0.289621 0.417519i 0.0139994 0.0201815i
\(429\) −1.28728 + 1.19917i −0.0621505 + 0.0578966i
\(430\) 7.73729 + 1.34675i 0.373125 + 0.0649462i
\(431\) −0.524890 + 0.303045i −0.0252830 + 0.0145972i −0.512588 0.858635i \(-0.671313\pi\)
0.487305 + 0.873232i \(0.337980\pi\)
\(432\) 18.1050 10.2082i 0.871079 0.491143i
\(433\) 7.72438i 0.371210i 0.982624 + 0.185605i \(0.0594245\pi\)
−0.982624 + 0.185605i \(0.940576\pi\)
\(434\) 3.01050 18.8858i 0.144508 0.906549i
\(435\) −1.24058 + 4.05032i −0.0594814 + 0.194198i
\(436\) −8.63428 18.3056i −0.413507 0.876679i
\(437\) −4.52190 1.21164i −0.216312 0.0579606i
\(438\) −12.0561 + 23.7604i −0.576064 + 1.13531i
\(439\) 5.76099 9.97833i 0.274957 0.476240i −0.695167 0.718848i \(-0.744670\pi\)
0.970124 + 0.242608i \(0.0780030\pi\)
\(440\) 7.00454 12.3192i 0.333929 0.587297i
\(441\) −0.888551 + 20.9812i −0.0423120 + 0.999104i
\(442\) 0.863443 0.0774556i 0.0410698 0.00368419i
\(443\) 16.7142 4.47856i 0.794117 0.212783i 0.161118 0.986935i \(-0.448490\pi\)
0.632999 + 0.774152i \(0.281824\pi\)
\(444\) 14.0052 35.0555i 0.664656 1.66366i
\(445\) 1.78990 6.68001i 0.0848495 0.316663i
\(446\) −6.80505 18.5695i −0.322229 0.879293i
\(447\) −1.33541 2.51466i −0.0631628 0.118939i
\(448\) −18.6139 10.0758i −0.879425 0.476037i
\(449\) 26.5522i 1.25308i −0.779391 0.626538i \(-0.784471\pi\)
0.779391 0.626538i \(-0.215529\pi\)
\(450\) −4.34068 + 17.4968i −0.204622 + 0.824808i
\(451\) 43.8785 + 11.7572i 2.06616 + 0.553625i
\(452\) 3.15453 + 3.72601i 0.148376 + 0.175257i
\(453\) 4.83602 + 5.19135i 0.227216 + 0.243911i
\(454\) −2.37518 26.4775i −0.111473 1.24265i
\(455\) 0.402741 0.00574284i 0.0188808 0.000269228i
\(456\) 0.189034 6.55684i 0.00885235 0.307052i
\(457\) 25.4158 + 14.6738i 1.18890 + 0.686412i 0.958057 0.286578i \(-0.0925179\pi\)
0.230844 + 0.972991i \(0.425851\pi\)
\(458\) −20.2618 + 14.2540i −0.946772 + 0.666045i
\(459\) 6.52372 16.9168i 0.304501 0.789611i
\(460\) 5.48054 2.58503i 0.255531 0.120528i
\(461\) −3.69072 3.69072i −0.171894 0.171894i 0.615917 0.787811i \(-0.288786\pi\)
−0.787811 + 0.615917i \(0.788786\pi\)
\(462\) 24.6253 28.2420i 1.14567 1.31394i
\(463\) −2.26837 −0.105420 −0.0527101 0.998610i \(-0.516786\pi\)
−0.0527101 + 0.998610i \(0.516786\pi\)
\(464\) −6.55621 9.19008i −0.304364 0.426639i
\(465\) −4.06868 + 6.50380i −0.188680 + 0.301607i
\(466\) 5.79536 33.2952i 0.268465 1.54237i
\(467\) 3.20011 0.857468i 0.148084 0.0396789i −0.184016 0.982923i \(-0.558910\pi\)
0.332099 + 0.943244i \(0.392243\pi\)
\(468\) −0.381058 0.982774i −0.0176144 0.0454288i
\(469\) −2.26685 8.00183i −0.104673 0.369490i
\(470\) 14.3580 1.28799i 0.662284 0.0594105i
\(471\) −0.139059 + 3.92429i −0.00640751 + 0.180822i
\(472\) 16.1916 16.4068i 0.745281 0.755182i
\(473\) −18.5260 32.0880i −0.851827 1.47541i
\(474\) −5.76809 + 0.312042i −0.264937 + 0.0143326i
\(475\) 4.02296 + 4.02296i 0.184586 + 0.184586i
\(476\) −18.1204 + 3.54489i −0.830546 + 0.162480i
\(477\) −3.62879 18.7715i −0.166151 0.859489i
\(478\) 2.22979 + 6.08462i 0.101988 + 0.278304i
\(479\) −10.9507 18.9672i −0.500352 0.866635i −1.00000 0.000406431i \(-0.999871\pi\)
0.499648 0.866229i \(-0.333463\pi\)
\(480\) 5.29722 + 6.63555i 0.241784 + 0.302870i
\(481\) −1.65794 0.957211i −0.0755955 0.0436451i
\(482\) −26.7968 + 32.0783i −1.22056 + 1.46112i
\(483\) 15.5604 3.81840i 0.708023 0.173743i
\(484\) −44.1418 + 7.98377i −2.00645 + 0.362899i
\(485\) 4.92645 1.32004i 0.223699 0.0599399i
\(486\) −21.9608 1.92954i −0.996162 0.0875255i
\(487\) −1.78081 + 1.02815i −0.0806960 + 0.0465899i −0.539805 0.841790i \(-0.681502\pi\)
0.459109 + 0.888380i \(0.348169\pi\)
\(488\) 4.69117 + 1.22387i 0.212359 + 0.0554022i
\(489\) 16.3122 + 30.7168i 0.737662 + 1.38906i
\(490\) −8.51899 + 1.00978i −0.384849 + 0.0456174i
\(491\) −12.7157 12.7157i −0.573852 0.573852i 0.359351 0.933203i \(-0.382998\pi\)
−0.933203 + 0.359351i \(0.882998\pi\)
\(492\) −16.2949 + 21.7998i −0.734631 + 0.982809i
\(493\) −9.51223 2.54880i −0.428409 0.114792i
\(494\) −0.327732 0.0570450i −0.0147454 0.00256657i
\(495\) −13.5165 + 6.57526i −0.607523 + 0.295536i
\(496\) −7.16126 19.1495i −0.321550 0.859837i
\(497\) 3.80295 2.26854i 0.170586 0.101758i
\(498\) −2.18552 + 10.3679i −0.0979353 + 0.464598i
\(499\) 33.5091 8.97874i 1.50007 0.401944i 0.586949 0.809624i \(-0.300329\pi\)
0.913125 + 0.407680i \(0.133662\pi\)
\(500\) −15.9749 1.32684i −0.714421 0.0593381i
\(501\) 11.8175 2.72190i 0.527969 0.121605i
\(502\) 12.5828 27.1396i 0.561598 1.21130i
\(503\) 12.9532i 0.577555i 0.957396 + 0.288778i \(0.0932488\pi\)
−0.957396 + 0.288778i \(0.906751\pi\)
\(504\) 10.2395 + 19.9788i 0.456106 + 0.889926i
\(505\) 15.0163i 0.668218i
\(506\) −25.9361 12.0248i −1.15300 0.534569i
\(507\) 21.8901 5.04187i 0.972172 0.223917i
\(508\) 15.7063 13.2973i 0.696855 0.589974i
\(509\) 8.29819 2.22349i 0.367811 0.0985546i −0.0701794 0.997534i \(-0.522357\pi\)
0.437990 + 0.898980i \(0.355691\pi\)
\(510\) 7.24742 + 1.52772i 0.320921 + 0.0676488i
\(511\) −25.1259 14.0326i −1.11150 0.620766i
\(512\) −22.6230 + 0.447897i −0.999804 + 0.0197945i
\(513\) −4.09817 + 5.62239i −0.180939 + 0.248235i
\(514\) −0.200000 + 1.14903i −0.00882162 + 0.0506815i
\(515\) 14.2587 + 3.82061i 0.628314 + 0.168356i
\(516\) 21.9712 3.17494i 0.967227 0.139769i
\(517\) −48.0906 48.0906i −2.11502 2.11502i
\(518\) 37.2326 + 16.6215i 1.63591 + 0.730305i
\(519\) 0.100849 + 0.189905i 0.00442679 + 0.00833592i
\(520\) 0.371475 0.217752i 0.0162902 0.00954905i
\(521\) 10.6856 6.16932i 0.468143 0.270283i −0.247319 0.968934i \(-0.579550\pi\)
0.715462 + 0.698652i \(0.246216\pi\)
\(522\) 0.222993 + 11.9717i 0.00976015 + 0.523987i
\(523\) −2.98859 + 0.800789i −0.130682 + 0.0350161i −0.323567 0.946205i \(-0.604882\pi\)
0.192885 + 0.981221i \(0.438215\pi\)
\(524\) −13.0157 + 18.7635i −0.568593 + 0.819686i
\(525\) −18.6973 5.43649i −0.816016 0.237268i
\(526\) 18.5709 + 15.5133i 0.809728 + 0.676413i
\(527\) −15.4453 8.91732i −0.672806 0.388445i
\(528\) 8.00353 39.2497i 0.348309 1.70812i
\(529\) 5.38795 + 9.33220i 0.234259 + 0.405748i
\(530\) 7.33334 2.68740i 0.318540 0.116733i
\(531\) −24.0049 + 4.64047i −1.04172 + 0.201379i
\(532\) 7.06847 + 0.485723i 0.306457 + 0.0210587i
\(533\) 0.975993 + 0.975993i 0.0422749 + 0.0422749i
\(534\) −1.05597 19.5195i −0.0456961 0.844693i
\(535\) −0.110084 0.190672i −0.00475936 0.00824345i
\(536\) −6.32820 6.24523i −0.273336 0.269753i
\(537\) 1.07919 30.4551i 0.0465706 1.31423i
\(538\) 2.46496 + 27.4784i 0.106272 + 1.18468i
\(539\) 29.4227 + 27.7907i 1.26733 + 1.19703i
\(540\) −0.653866 8.98192i −0.0281379 0.386520i
\(541\) 10.0929 2.70437i 0.433926 0.116270i −0.0352425 0.999379i \(-0.511220\pi\)
0.469168 + 0.883109i \(0.344554\pi\)
\(542\) 37.3450 + 6.50026i 1.60410 + 0.279210i
\(543\) −11.8039 + 18.8686i −0.506553 + 0.809728i
\(544\) −14.9803 + 12.8533i −0.642274 + 0.551081i
\(545\) −8.76959 −0.375648
\(546\) 1.07705 0.369040i 0.0460934 0.0157935i
\(547\) −5.68276 5.68276i −0.242977 0.242977i 0.575103 0.818081i \(-0.304962\pi\)
−0.818081 + 0.575103i \(0.804962\pi\)
\(548\) −19.3383 6.94237i −0.826090 0.296563i
\(549\) −3.36964 3.88439i −0.143813 0.165782i
\(550\) 19.9904 + 28.4160i 0.852393 + 1.21166i
\(551\) 3.27262 + 1.88945i 0.139418 + 0.0804931i
\(552\) 12.4555 11.7575i 0.530143 0.500431i
\(553\) −0.0889605 6.23873i −0.00378299 0.265298i
\(554\) 21.6552 1.94259i 0.920040 0.0825326i
\(555\) −11.1489 11.9680i −0.473244 0.508015i
\(556\) −13.5067 1.12183i −0.572812 0.0475764i
\(557\) 24.7033 + 6.61922i 1.04671 + 0.280466i 0.740892 0.671624i \(-0.234403\pi\)
0.305819 + 0.952090i \(0.401070\pi\)
\(558\) −5.22140 + 21.0469i −0.221040 + 0.890986i
\(559\) 1.12581i 0.0476168i
\(560\) −7.38913 + 5.43203i −0.312248 + 0.229545i
\(561\) −16.3891 30.8617i −0.691948 1.30298i
\(562\) 12.6884 4.64984i 0.535229 0.196142i
\(563\) 0.131523 0.490851i 0.00554304 0.0206869i −0.963099 0.269148i \(-0.913258\pi\)
0.968642 + 0.248461i \(0.0799247\pi\)
\(564\) 37.4464 16.0670i 1.57678 0.676544i
\(565\) 2.04324 0.547484i 0.0859596 0.0230328i
\(566\) 3.00835 + 33.5359i 0.126450 + 1.40962i
\(567\) 3.02600 23.6187i 0.127080 0.991892i
\(568\) 2.33986 4.11522i 0.0981781 0.172671i
\(569\) 8.57445 14.8514i 0.359460 0.622603i −0.628411 0.777882i \(-0.716294\pi\)
0.987871 + 0.155279i \(0.0496277\pi\)
\(570\) −2.53456 1.28605i −0.106161 0.0538666i
\(571\) −9.93395 2.66179i −0.415723 0.111393i 0.0448939 0.998992i \(-0.485705\pi\)
−0.460617 + 0.887599i \(0.652372\pi\)
\(572\) −1.91198 0.686394i −0.0799440 0.0286996i
\(573\) −7.41693 + 24.2152i −0.309847 + 1.01160i
\(574\) −22.8277 18.5232i −0.952810 0.773142i
\(575\) 14.8560i 0.619536i
\(576\) 20.0587 + 13.1775i 0.835781 + 0.549063i
\(577\) 31.7254 18.3166i 1.32074 0.762532i 0.336897 0.941542i \(-0.390623\pi\)
0.983847 + 0.179010i \(0.0572893\pi\)
\(578\) 1.17000 6.72180i 0.0486654 0.279590i
\(579\) −10.4960 + 9.77762i −0.436200 + 0.406344i
\(580\) −4.81327 + 0.870559i −0.199860 + 0.0361480i
\(581\) −11.0959 2.80420i −0.460335 0.116338i
\(582\) 12.0775 7.87218i 0.500628 0.326312i
\(583\) −31.9108 18.4237i −1.32161 0.763032i
\(584\) −30.7652 + 0.203010i −1.27307 + 0.00840061i
\(585\) −0.455566 0.0323270i −0.0188353 0.00133656i
\(586\) 2.62775 5.66774i 0.108551 0.234132i
\(587\) 8.32984 8.32984i 0.343809 0.343809i −0.513988 0.857797i \(-0.671832\pi\)
0.857797 + 0.513988i \(0.171832\pi\)
\(588\) −22.0024 + 10.1929i −0.907364 + 0.420347i
\(589\) 4.83922 + 4.83922i 0.199396 + 0.199396i
\(590\) −3.43663 9.37784i −0.141484 0.386079i
\(591\) 0.226597 0.362216i 0.00932095 0.0148996i
\(592\) 43.3885 4.18097i 1.78326 0.171837i
\(593\) 18.2653 31.6364i 0.750065 1.29915i −0.197725 0.980258i \(-0.563355\pi\)
0.947790 0.318894i \(-0.103311\pi\)
\(594\) −30.5434 + 29.5342i −1.25321 + 1.21180i
\(595\) −1.96020 + 7.75628i −0.0803603 + 0.317976i
\(596\) 1.87390 2.70142i 0.0767578 0.110654i
\(597\) 19.7415 18.3903i 0.807965 0.752663i
\(598\) −0.499794 0.710449i −0.0204381 0.0290524i
\(599\) 9.07955 + 15.7262i 0.370980 + 0.642557i 0.989717 0.143042i \(-0.0456884\pi\)
−0.618736 + 0.785599i \(0.712355\pi\)
\(600\) −20.2536 + 4.80591i −0.826851 + 0.196200i
\(601\) 20.9059 0.852769 0.426384 0.904542i \(-0.359787\pi\)
0.426384 + 0.904542i \(0.359787\pi\)
\(602\) 2.48265 + 23.8492i 0.101185 + 0.972021i
\(603\) 1.78986 + 9.25886i 0.0728888 + 0.377050i
\(604\) −2.76809 + 7.71064i −0.112632 + 0.313741i
\(605\) −5.03050 + 18.7741i −0.204519 + 0.763275i
\(606\) 13.1845 + 40.3462i 0.535583 + 1.63895i
\(607\) −39.6809 22.9098i −1.61060 0.929879i −0.989232 0.146359i \(-0.953245\pi\)
−0.621366 0.783520i \(-0.713422\pi\)
\(608\) 6.82905 3.27635i 0.276955 0.132874i
\(609\) −12.9303 0.273675i −0.523961 0.0110899i
\(610\) 1.34673 1.61216i 0.0545275 0.0652744i
\(611\) −0.534842 1.99606i −0.0216374 0.0807519i
\(612\) 20.8139 2.25858i 0.841351 0.0912979i
\(613\) 0.614291 + 0.164599i 0.0248110 + 0.00664808i 0.271203 0.962522i \(-0.412578\pi\)
−0.246392 + 0.969170i \(0.579245\pi\)
\(614\) −3.80121 + 8.19875i −0.153404 + 0.330874i
\(615\) 5.53096 + 10.4151i 0.223030 + 0.419979i
\(616\) 42.0171 + 10.3243i 1.69292 + 0.415976i
\(617\) −33.6131 −1.35321 −0.676606 0.736345i \(-0.736550\pi\)
−0.676606 + 0.736345i \(0.736550\pi\)
\(618\) 41.6651 2.25400i 1.67602 0.0906691i
\(619\) 1.59927 5.96857i 0.0642803 0.239897i −0.926309 0.376764i \(-0.877037\pi\)
0.990589 + 0.136867i \(0.0437033\pi\)
\(620\) −8.82802 0.733234i −0.354542 0.0294474i
\(621\) −17.9480 + 2.81431i −0.720228 + 0.112934i
\(622\) 12.4835 14.9439i 0.500542 0.599194i
\(623\) 21.1122 0.301047i 0.845842 0.0120612i
\(624\) 0.806897 0.911218i 0.0323017 0.0364779i
\(625\) 7.14985 12.3839i 0.285994 0.495356i
\(626\) −2.33204 + 13.3979i −0.0932073 + 0.535489i
\(627\) 3.00962 + 13.0667i 0.120193 + 0.521835i
\(628\) −4.10093 + 1.93430i −0.163645 + 0.0771871i
\(629\) 26.8875 26.8875i 1.07208 1.07208i
\(630\) 9.72199 0.319803i 0.387334 0.0127413i
\(631\) 1.42992i 0.0569242i 0.999595 + 0.0284621i \(0.00906099\pi\)
−0.999595 + 0.0284621i \(0.990939\pi\)
\(632\) −3.37312 5.75440i −0.134176 0.228898i
\(633\) −13.3824 + 21.3918i −0.531901 + 0.850246i
\(634\) 11.6009 + 16.4905i 0.460732 + 0.654923i
\(635\) −2.30782 8.61290i −0.0915830 0.341792i
\(636\) 17.3438 13.6593i 0.687727 0.541627i
\(637\) 0.352020 + 1.17828i 0.0139475 + 0.0466852i
\(638\) 17.7103 + 14.7944i 0.701157 + 0.585717i
\(639\) −4.51518 + 2.19645i −0.178618 + 0.0868904i
\(640\) −4.00612 + 8.94832i −0.158356 + 0.353713i
\(641\) 5.17909 2.99015i 0.204562 0.118104i −0.394220 0.919016i \(-0.628985\pi\)
0.598782 + 0.800912i \(0.295652\pi\)
\(642\) −0.463188 0.415645i −0.0182806 0.0164042i
\(643\) −19.0080 + 19.0080i −0.749603 + 0.749603i −0.974405 0.224801i \(-0.927827\pi\)
0.224801 + 0.974405i \(0.427827\pi\)
\(644\) 12.1543 + 13.9480i 0.478948 + 0.549628i
\(645\) 2.81696 9.19695i 0.110918 0.362130i
\(646\) 2.77921 5.99442i 0.109347 0.235847i
\(647\) 38.2823 22.1023i 1.50503 0.868932i 0.505051 0.863089i \(-0.331474\pi\)
0.999983 0.00584236i \(-0.00185969\pi\)
\(648\) −9.64303 23.5587i −0.378814 0.925473i
\(649\) −23.5601 + 40.8073i −0.924815 + 1.60183i
\(650\) 0.0943194 + 1.05143i 0.00369951 + 0.0412407i
\(651\) −22.4909 6.53954i −0.881489 0.256305i
\(652\) −22.8898 + 32.9980i −0.896434 + 1.29230i
\(653\) −4.49506 16.7758i −0.175905 0.656487i −0.996396 0.0848271i \(-0.972966\pi\)
0.820490 0.571660i \(-0.193700\pi\)
\(654\) −23.5623 + 7.69979i −0.921359 + 0.301085i
\(655\) 4.94723 + 8.56886i 0.193304 + 0.334813i
\(656\) −30.9966 5.18477i −1.21021 0.202431i
\(657\) 27.0345 + 18.2755i 1.05472 + 0.712995i
\(658\) 15.7318 + 41.1051i 0.613291 + 1.60244i
\(659\) −35.1349 + 35.1349i −1.36866 + 1.36866i −0.506310 + 0.862351i \(0.668991\pi\)
−0.862351 + 0.506310i \(0.831009\pi\)
\(660\) −13.9018 10.3914i −0.541128 0.404483i
\(661\) 11.1353 41.5576i 0.433114 1.61640i −0.312427 0.949942i \(-0.601142\pi\)
0.745540 0.666461i \(-0.232192\pi\)
\(662\) −29.2864 41.6302i −1.13825 1.61800i
\(663\) 0.0375999 1.06108i 0.00146026 0.0412089i
\(664\) −11.7969 + 3.24455i −0.457809 + 0.125913i
\(665\) 1.49688 2.68022i 0.0580467 0.103934i
\(666\) −40.4631 22.3671i −1.56791 0.866709i
\(667\) 2.55388 + 9.53120i 0.0988865 + 0.369049i
\(668\) 9.04805 + 10.6872i 0.350080 + 0.413501i
\(669\) −23.6040 + 5.43663i −0.912583 + 0.210192i
\(670\) −3.61710 + 1.32553i −0.139741 + 0.0512098i
\(671\) −9.91051 −0.382591
\(672\) −15.0839 + 21.0826i −0.581873 + 0.813280i
\(673\) −16.3864 −0.631649 −0.315824 0.948818i \(-0.602281\pi\)
−0.315824 + 0.948818i \(0.602281\pi\)
\(674\) −10.3550 + 3.79474i −0.398861 + 0.146168i
\(675\) 20.6000 + 7.94409i 0.792896 + 0.305768i
\(676\) 16.7600 + 19.7963i 0.644617 + 0.761397i
\(677\) −3.20755 11.9707i −0.123276 0.460073i 0.876496 0.481409i \(-0.159875\pi\)
−0.999772 + 0.0213360i \(0.993208\pi\)
\(678\) 5.00911 3.26497i 0.192374 0.125390i
\(679\) 7.97731 + 13.3731i 0.306141 + 0.513211i
\(680\) 2.26801 + 8.24630i 0.0869744 + 0.316231i
\(681\) −32.5380 1.15300i −1.24686 0.0441831i
\(682\) 24.0464 + 34.1815i 0.920784 + 1.30888i
\(683\) −13.4378 + 50.1506i −0.514183 + 1.91896i −0.145683 + 0.989331i \(0.546538\pi\)
−0.368501 + 0.929628i \(0.620129\pi\)
\(684\) −7.93907 1.23001i −0.303558 0.0470305i
\(685\) −6.29508 + 6.29508i −0.240523 + 0.240523i
\(686\) −10.0555 24.1844i −0.383923 0.923365i
\(687\) 14.2305 + 26.7968i 0.542926 + 1.02236i
\(688\) 14.8870 + 20.8677i 0.567562 + 0.795573i
\(689\) −0.559797 0.969597i −0.0213266 0.0369387i
\(690\) −2.30525 7.05435i −0.0877593 0.268554i
\(691\) −9.42763 35.1844i −0.358644 1.33848i −0.875836 0.482608i \(-0.839690\pi\)
0.517192 0.855869i \(-0.326977\pi\)
\(692\) −0.141515 + 0.204009i −0.00537960 + 0.00775525i
\(693\) −30.5631 34.2334i −1.16100 1.30042i
\(694\) −1.99375 22.2256i −0.0756819 0.843671i
\(695\) −2.93621 + 5.08566i −0.111377 + 0.192910i
\(696\) −12.1680 + 6.56514i −0.461228 + 0.248851i
\(697\) −23.7422 + 13.7075i −0.899298 + 0.519210i
\(698\) 6.70956 14.4717i 0.253961 0.547763i
\(699\) −39.5764 12.1220i −1.49692 0.458495i
\(700\) −4.31670 22.0656i −0.163156 0.834001i
\(701\) 9.18394 9.18394i 0.346873 0.346873i −0.512071 0.858943i \(-0.671121\pi\)
0.858943 + 0.512071i \(0.171121\pi\)
\(702\) −1.25241 + 0.313134i −0.0472690 + 0.0118185i
\(703\) −12.6364 + 7.29560i −0.476589 + 0.275159i
\(704\) 44.5163 12.5600i 1.67777 0.473375i
\(705\) 0.625239 17.6444i 0.0235479 0.664527i
\(706\) 19.3688 + 16.1799i 0.728956 + 0.608939i
\(707\) −44.1108 + 12.4962i −1.65896 + 0.469968i
\(708\) −17.4674 22.1792i −0.656466 0.833544i
\(709\) 4.34186 + 16.2040i 0.163062 + 0.608555i 0.998279 + 0.0586356i \(0.0186750\pi\)
−0.835218 + 0.549920i \(0.814658\pi\)
\(710\) −1.18018 1.67760i −0.0442913 0.0629594i
\(711\) −0.500768 + 7.05703i −0.0187803 + 0.264659i
\(712\) 19.4732 11.4148i 0.729788 0.427789i
\(713\) 17.8702i 0.669244i
\(714\) 1.54339 + 22.5608i 0.0577598 + 0.844316i
\(715\) −0.622397 + 0.622397i −0.0232763 + 0.0232763i
\(716\) 31.8260 15.0115i 1.18939 0.561006i
\(717\) 7.73424 1.78140i 0.288840 0.0665277i
\(718\) 4.05879 23.3184i 0.151473 0.870234i
\(719\) −10.7446 + 18.6102i −0.400706 + 0.694042i −0.993811 0.111082i \(-0.964568\pi\)
0.593106 + 0.805125i \(0.297902\pi\)
\(720\) 8.87169 5.42491i 0.330628 0.202174i
\(721\) 0.642596 + 45.0647i 0.0239315 + 1.67830i
\(722\) 15.6010 18.6758i 0.580607 0.695040i
\(723\) 34.8937 + 37.4575i 1.29771 + 1.39306i
\(724\) −25.6115 2.12723i −0.951843 0.0790578i
\(725\) 3.10373 11.5833i 0.115270 0.430192i
\(726\) 2.96778 + 54.8594i 0.110145 + 2.03602i
\(727\) −27.2660 −1.01124 −0.505619 0.862757i \(-0.668736\pi\)
−0.505619 + 0.862757i \(0.668736\pi\)
\(728\) 0.948782 + 0.910007i 0.0351642 + 0.0337271i
\(729\) −5.69506 + 26.3925i −0.210928 + 0.977502i
\(730\) −5.60710 + 12.0938i −0.207528 + 0.447613i
\(731\) 21.5992 + 5.78749i 0.798875 + 0.214058i
\(732\) 2.20293 5.51402i 0.0814227 0.203804i
\(733\) −1.83153 6.83537i −0.0676491 0.252470i 0.923817 0.382834i \(-0.125052\pi\)
−0.991466 + 0.130364i \(0.958385\pi\)
\(734\) −27.7088 + 33.1699i −1.02275 + 1.22432i
\(735\) −0.0725358 + 10.5064i −0.00267552 + 0.387534i
\(736\) 18.6586 + 6.55969i 0.687763 + 0.241793i
\(737\) 15.7397 + 9.08730i 0.579778 + 0.334735i
\(738\) 24.0053 + 23.1274i 0.883647 + 0.851330i
\(739\) 10.3916 38.7821i 0.382262 1.42662i −0.460175 0.887828i \(-0.652213\pi\)
0.842438 0.538794i \(-0.181120\pi\)
\(740\) 6.38151 17.7760i 0.234589 0.653458i
\(741\) −0.119319 + 0.389559i −0.00438330 + 0.0143108i
\(742\) 13.9969 + 19.3055i 0.513843 + 0.708726i
\(743\) 11.6648 0.427942 0.213971 0.976840i \(-0.431360\pi\)
0.213971 + 0.976840i \(0.431360\pi\)
\(744\) −24.3631 + 5.78102i −0.893193 + 0.211942i
\(745\) −0.712263 1.23368i −0.0260953 0.0451984i
\(746\) 26.7694 + 38.0523i 0.980098 + 1.39319i
\(747\) 12.2658 + 4.23756i 0.448781 + 0.155044i
\(748\) 22.9977 33.1536i 0.840881 1.21222i
\(749\) 0.468493 0.482047i 0.0171184 0.0176136i
\(750\) −4.04948 + 19.2104i −0.147866 + 0.701466i
\(751\) −19.0586 + 33.0104i −0.695456 + 1.20457i 0.274570 + 0.961567i \(0.411464\pi\)
−0.970027 + 0.242999i \(0.921869\pi\)
\(752\) 36.3083 + 29.9259i 1.32403 + 1.09128i
\(753\) −31.0606 19.4310i −1.13191 0.708107i
\(754\) 0.241264 + 0.658359i 0.00878633 + 0.0239760i
\(755\) 2.51000 + 2.51000i 0.0913483 + 0.0913483i
\(756\) 25.8405 9.39526i 0.939808 0.341702i
\(757\) 15.5465 15.5465i 0.565049 0.565049i −0.365688 0.930737i \(-0.619166\pi\)
0.930737 + 0.365688i \(0.119166\pi\)
\(758\) −5.01520 + 10.8172i −0.182160 + 0.392898i
\(759\) −18.5694 + 29.6833i −0.674026 + 1.07743i
\(760\) −0.0216554 3.28178i −0.000785525 0.119043i
\(761\) 30.5621 + 17.6450i 1.10787 + 0.639631i 0.938278 0.345883i \(-0.112420\pi\)
0.169596 + 0.985514i \(0.445754\pi\)
\(762\) −13.7629 21.1150i −0.498577 0.764916i
\(763\) −7.29782 25.7609i −0.264199 0.932606i
\(764\) −28.7766 + 5.20471i −1.04110 + 0.188300i
\(765\) 2.96215 8.57404i 0.107097 0.309995i
\(766\) 5.30584 30.4828i 0.191708 1.10139i
\(767\) −1.23992 + 0.715865i −0.0447707 + 0.0258484i
\(768\) −2.90701 + 27.5599i −0.104898 + 0.994483i
\(769\) 6.22612i 0.224520i 0.993679 + 0.112260i \(0.0358089\pi\)
−0.993679 + 0.112260i \(0.964191\pi\)
\(770\) 11.8123 14.5574i 0.425687 0.524611i
\(771\) 1.36580 + 0.418334i 0.0491879 + 0.0150659i
\(772\) −15.5896 5.59661i −0.561082 0.201426i
\(773\) 9.25469 + 2.47979i 0.332868 + 0.0891917i 0.421382 0.906883i \(-0.361545\pi\)
−0.0885140 + 0.996075i \(0.528212\pi\)
\(774\) −0.506345 27.1839i −0.0182002 0.977104i
\(775\) 10.8588 18.8080i 0.390061 0.675605i
\(776\) 14.4712 + 8.22809i 0.519484 + 0.295371i
\(777\) 25.8786 42.7096i 0.928389 1.53220i
\(778\) −0.507640 5.65896i −0.0181998 0.202884i
\(779\) 10.1615 2.72277i 0.364074 0.0975535i
\(780\) −0.207942 0.484638i −0.00744553 0.0173528i
\(781\) −2.50457 + 9.34719i −0.0896206 + 0.334469i
\(782\) 16.1996 5.93655i 0.579296 0.212291i
\(783\) 14.5821 + 1.55539i 0.521122 + 0.0555850i
\(784\) −22.1058 17.1853i −0.789491 0.613762i
\(785\) 1.96462i 0.0701202i
\(786\) 20.8159 + 18.6793i 0.742477 + 0.666267i
\(787\) −20.5741 5.51281i −0.733387 0.196510i −0.127250 0.991871i \(-0.540615\pi\)
−0.606137 + 0.795360i \(0.707282\pi\)
\(788\) 0.491658 + 0.0408360i 0.0175146 + 0.00145472i
\(789\) 21.6850 20.2008i 0.772007 0.719166i
\(790\) −2.87853 + 0.258220i −0.102414 + 0.00918705i
\(791\) 3.30857 + 5.54645i 0.117639 + 0.197209i
\(792\) −46.4754 15.7138i −1.65143 0.558364i
\(793\) −0.260784 0.150564i −0.00926070 0.00534667i
\(794\) 8.73993 + 12.4237i 0.310169 + 0.440899i
\(795\) −2.14699 9.32151i −0.0761460 0.330600i
\(796\) 29.3217 + 10.5264i 1.03928 + 0.373098i
\(797\) 9.21921 + 9.21921i 0.326561 + 0.326561i 0.851277 0.524716i \(-0.175829\pi\)
−0.524716 + 0.851277i \(0.675829\pi\)
\(798\) 1.66860 8.51554i 0.0590677 0.301447i
\(799\) 41.0447 1.45206
\(800\) −15.6518 18.2418i −0.553374 0.644946i
\(801\) −23.8814 1.69463i −0.843806 0.0598766i
\(802\) −29.8837 5.20156i −1.05523 0.183673i
\(803\) 60.7477 16.2773i 2.14374 0.574414i
\(804\) −8.55465 + 6.73731i −0.301699 + 0.237607i
\(805\) 7.71258 2.18490i 0.271833 0.0770077i
\(806\) 0.113457 + 1.26477i 0.00399634 + 0.0445496i
\(807\) 33.7680 + 1.19659i 1.18869 + 0.0421218i
\(808\) −34.4274 + 34.8848i −1.21115 + 1.22724i
\(809\) −13.8920 24.0616i −0.488415 0.845960i 0.511496 0.859286i \(-0.329092\pi\)
−0.999911 + 0.0133254i \(0.995758\pi\)
\(810\) −11.0146 0.575674i −0.387015 0.0202271i
\(811\) 15.6738 + 15.6738i 0.550381 + 0.550381i 0.926551 0.376170i \(-0.122759\pi\)
−0.376170 + 0.926551i \(0.622759\pi\)
\(812\) −6.56276 13.4146i −0.230308 0.470762i
\(813\) 13.5964 44.3902i 0.476847 1.55683i
\(814\) −83.6634 + 30.6596i −2.93240 + 1.07462i
\(815\) 8.70035 + 15.0695i 0.304760 + 0.527860i
\(816\) 13.3341 + 20.1650i 0.466786 + 0.705916i
\(817\) −7.43105 4.29032i −0.259979 0.150099i
\(818\) −4.68762 3.91584i −0.163899 0.136914i
\(819\) −0.284148 1.36514i −0.00992895 0.0477017i
\(820\) −7.76124 + 11.1886i −0.271034 + 0.390724i
\(821\) −25.2310 + 6.76061i −0.880567 + 0.235947i −0.670652 0.741773i \(-0.733985\pi\)
−0.209915 + 0.977720i \(0.567319\pi\)
\(822\) −11.3866 + 22.4409i −0.397154 + 0.782716i
\(823\) −14.6550 + 8.46106i −0.510840 + 0.294934i −0.733179 0.680036i \(-0.761964\pi\)
0.222339 + 0.974970i \(0.428631\pi\)
\(824\) 24.3654 + 41.5662i 0.848808 + 1.44803i
\(825\) 37.5810 19.9574i 1.30840 0.694827i
\(826\) 24.6877 17.8992i 0.858996 0.622792i
\(827\) 6.91465 + 6.91465i 0.240446 + 0.240446i 0.817035 0.576589i \(-0.195616\pi\)
−0.576589 + 0.817035i \(0.695616\pi\)
\(828\) −12.3876 16.9297i −0.430498 0.588349i
\(829\) 23.1308 + 6.19787i 0.803365 + 0.215261i 0.637061 0.770813i \(-0.280150\pi\)
0.166304 + 0.986075i \(0.446817\pi\)
\(830\) −0.909065 + 5.22271i −0.0315541 + 0.181283i
\(831\) 0.943005 26.6118i 0.0327125 0.923155i
\(832\) 1.36221 + 0.345802i 0.0472262 + 0.0119885i
\(833\) −24.4155 + 0.696441i −0.845946 + 0.0241303i
\(834\) −3.42380 + 16.2423i −0.118557 + 0.562424i
\(835\) 5.86057 1.57033i 0.202813 0.0543437i
\(836\) −11.8169 + 10.0045i −0.408697 + 0.346013i
\(837\) 24.7797 + 9.55593i 0.856513 + 0.330301i
\(838\) −1.82688 0.847000i −0.0631085 0.0292591i
\(839\) 53.1082i 1.83350i −0.399462 0.916750i \(-0.630803\pi\)
0.399462 0.916750i \(-0.369197\pi\)
\(840\) 5.47378 + 9.80801i 0.188863 + 0.338408i
\(841\) 21.0349i 0.725342i
\(842\) 17.2659 37.2406i 0.595024 1.28340i
\(843\) −3.71480 16.1284i −0.127945 0.555492i
\(844\) −29.0364 2.41169i −0.999473 0.0830138i
\(845\) 10.8558 2.90879i 0.373449 0.100065i
\(846\) −13.8121 47.9563i −0.474868 1.64877i
\(847\) −59.3355 + 0.846089i −2.03879 + 0.0290720i
\(848\) 23.1976 + 10.5697i 0.796607 + 0.362966i
\(849\) 41.2120 + 1.46037i 1.41439 + 0.0501197i
\(850\) −20.6571 3.59557i −0.708533 0.123327i
\(851\) −36.8022 9.86113i −1.26156 0.338035i
\(852\) −4.64388 3.47121i −0.159097 0.118922i
\(853\) 25.5060 + 25.5060i 0.873310 + 0.873310i 0.992832 0.119522i \(-0.0381361\pi\)
−0.119522 + 0.992832i \(0.538136\pi\)
\(854\) 5.85647 + 2.61445i 0.200404 + 0.0894648i
\(855\) −1.94948 + 2.88382i −0.0666707 + 0.0986245i
\(856\) 0.181407 0.695339i 0.00620035 0.0237662i
\(857\) −21.1037 + 12.1842i −0.720887 + 0.416205i −0.815079 0.579350i \(-0.803307\pi\)
0.0941918 + 0.995554i \(0.469973\pi\)
\(858\) −1.12580 + 2.21874i −0.0384341 + 0.0757465i
\(859\) 6.52316 1.74788i 0.222567 0.0596368i −0.145812 0.989312i \(-0.546579\pi\)
0.368379 + 0.929676i \(0.379913\pi\)
\(860\) 10.9294 1.97676i 0.372689 0.0674069i
\(861\) −25.9920 + 24.9145i −0.885805 + 0.849085i
\(862\) −0.549514 + 0.657818i −0.0187165 + 0.0224054i
\(863\) −35.3090 20.3856i −1.20193 0.693935i −0.240947 0.970538i \(-0.577458\pi\)
−0.960984 + 0.276603i \(0.910791\pi\)
\(864\) 19.0735 22.3652i 0.648894 0.760879i
\(865\) 0.0537895 + 0.0931662i 0.00182890 + 0.00316775i
\(866\) 3.75877 + 10.2569i 0.127728 + 0.348543i
\(867\) −7.98988 2.44725i −0.271351 0.0831128i
\(868\) −5.19255 26.5427i −0.176247 0.900917i
\(869\) 9.64135 + 9.64135i 0.327061 + 0.327061i
\(870\) 0.323610 + 5.98193i 0.0109714 + 0.202806i
\(871\) 0.276114 + 0.478244i 0.00935577 + 0.0162047i
\(872\) −20.3728 20.1057i −0.689911 0.680866i
\(873\) −7.72382 15.8776i −0.261412 0.537375i
\(874\) −6.59405 + 0.591522i −0.223047 + 0.0200085i
\(875\) −20.5592 5.19582i −0.695029 0.175651i
\(876\) −4.44676 + 37.4171i −0.150242 + 1.26421i
\(877\) 30.2968 8.11801i 1.02305 0.274126i 0.291978 0.956425i \(-0.405687\pi\)
0.731073 + 0.682299i \(0.239020\pi\)
\(878\) 2.79422 16.0532i 0.0943002 0.541768i
\(879\) −6.48660 4.05791i −0.218787 0.136870i
\(880\) 3.30636 19.7667i 0.111457 0.666336i
\(881\) 14.3252 0.482627 0.241313 0.970447i \(-0.422422\pi\)
0.241313 + 0.970447i \(0.422422\pi\)
\(882\) 9.02982 + 28.2924i 0.304050 + 0.952656i
\(883\) −26.2056 26.2056i −0.881888 0.881888i 0.111838 0.993726i \(-0.464326\pi\)
−0.993726 + 0.111838i \(0.964326\pi\)
\(884\) 1.10884 0.523011i 0.0372943 0.0175908i
\(885\) −11.9203 + 2.74556i −0.400696 + 0.0922910i
\(886\) 20.0148 14.0802i 0.672411 0.473035i
\(887\) 20.7034 + 11.9531i 0.695151 + 0.401345i 0.805539 0.592543i \(-0.201876\pi\)
−0.110388 + 0.993889i \(0.535209\pi\)
\(888\) 1.53849 53.3639i 0.0516282 1.79077i
\(889\) 23.3801 13.9467i 0.784142 0.467757i
\(890\) −0.873830 9.74110i −0.0292908 0.326522i
\(891\) 31.2305 + 41.6221i 1.04626 + 1.39439i
\(892\) −18.0723 21.3463i −0.605105 0.714727i
\(893\) −15.2134 4.07642i −0.509098 0.136412i
\(894\) −2.99690 2.68929i −0.100231 0.0899433i
\(895\) 15.2467i 0.509642i
\(896\) −29.6197 4.32151i −0.989524 0.144372i
\(897\) −0.939590 + 0.498969i −0.0313720 + 0.0166601i
\(898\) −12.9206 35.2576i −0.431166 1.17656i
\(899\) 3.73347 13.9335i 0.124518 0.464708i
\(900\) 2.75033 + 25.3455i 0.0916777 + 0.844851i
\(901\) 21.4799 5.75552i 0.715599 0.191744i
\(902\) 63.9856 5.73986i 2.13049 0.191116i
\(903\) 29.3604 + 0.621427i 0.977054 + 0.0206798i
\(904\) 6.00188 + 3.41258i 0.199620 + 0.113501i
\(905\) −5.56766 + 9.64347i −0.185075 + 0.320560i
\(906\) 8.94773 + 4.54011i 0.297268 + 0.150835i
\(907\) −18.2981 4.90297i −0.607580 0.162801i −0.0581047 0.998310i \(-0.518506\pi\)
−0.549475 + 0.835510i \(0.685172\pi\)
\(908\) −16.0381 34.0026i −0.532245 1.12842i
\(909\) 51.0403 9.86677i 1.69290 0.327260i
\(910\) 0.531988 0.203604i 0.0176352 0.00674940i
\(911\) 20.0171i 0.663197i 0.943421 + 0.331598i \(0.107588\pi\)
−0.943421 + 0.331598i \(0.892412\pi\)
\(912\) −2.93962 8.79854i −0.0973405 0.291349i
\(913\) 21.6596 12.5052i 0.716827 0.413860i
\(914\) 40.8891 + 7.11715i 1.35249 + 0.235414i
\(915\) −1.75365 1.88250i −0.0579740 0.0622336i
\(916\) −19.9687 + 28.7869i −0.659784 + 0.951147i
\(917\) −21.0543 + 21.6634i −0.695273 + 0.715388i
\(918\) 0.430656 25.6377i 0.0142138 0.846170i
\(919\) −6.65546 3.84253i −0.219543 0.126753i 0.386195 0.922417i \(-0.373789\pi\)
−0.605739 + 0.795664i \(0.707122\pi\)
\(920\) 6.01948 6.09944i 0.198456 0.201093i
\(921\) 9.38327 + 5.87003i 0.309189 + 0.193424i
\(922\) −6.69670 3.10481i −0.220544 0.102251i
\(923\) −0.207910 + 0.207910i −0.00684346 + 0.00684346i
\(924\) 18.9561 49.4844i 0.623610 1.62792i
\(925\) 32.7415 + 32.7415i 1.07654 + 1.07654i
\(926\) −3.01208 + 1.10382i −0.0989831 + 0.0362736i
\(927\) 3.61724 50.9756i 0.118806 1.67426i
\(928\) −13.1777 9.01280i −0.432580 0.295860i
\(929\) −16.0903 + 27.8693i −0.527906 + 0.914361i 0.471564 + 0.881832i \(0.343690\pi\)
−0.999471 + 0.0325291i \(0.989644\pi\)
\(930\) −2.23781 + 10.6160i −0.0733806 + 0.348112i
\(931\) 9.11887 + 2.16672i 0.298859 + 0.0710114i
\(932\) −8.50639 47.0314i −0.278636 1.54056i
\(933\) −16.2554 17.4498i −0.532179 0.571280i
\(934\) 3.83204 2.69581i 0.125388 0.0882095i
\(935\) −8.74138 15.1405i −0.285874 0.495148i
\(936\) −0.984220 1.11956i −0.0321702 0.0365939i
\(937\) 18.1655 0.593440 0.296720 0.954965i \(-0.404107\pi\)
0.296720 + 0.954965i \(0.404107\pi\)
\(938\) −6.90383 9.52223i −0.225418 0.310912i
\(939\) 15.9255 + 4.87787i 0.519709 + 0.159183i
\(940\) 18.4386 8.69702i 0.601402 0.283666i
\(941\) −6.28017 + 23.4379i −0.204728 + 0.764055i 0.784805 + 0.619743i \(0.212763\pi\)
−0.989532 + 0.144311i \(0.953903\pi\)
\(942\) 1.72495 + 5.27857i 0.0562020 + 0.171985i
\(943\) 23.7895 + 13.7349i 0.774692 + 0.447269i
\(944\) 13.5165 29.6649i 0.439925 0.965510i
\(945\) 1.09453 11.8630i 0.0356051 0.385904i
\(946\) −40.2143 33.5934i −1.30748 1.09221i
\(947\) 10.6983 + 39.9267i 0.347649 + 1.29744i 0.889487 + 0.456960i \(0.151062\pi\)
−0.541839 + 0.840483i \(0.682272\pi\)
\(948\) −7.50737 + 3.22117i −0.243828 + 0.104619i
\(949\) 1.84580 + 0.494580i 0.0599171 + 0.0160547i
\(950\) 7.29955 + 3.38431i 0.236829 + 0.109801i
\(951\) 21.8092 11.5818i 0.707212 0.375565i
\(952\) −22.3363 + 13.5247i −0.723924 + 0.438338i
\(953\) 8.31415 0.269322 0.134661 0.990892i \(-0.457005\pi\)
0.134661 + 0.990892i \(0.457005\pi\)
\(954\) −13.9530 23.1601i −0.451744 0.749837i
\(955\) −3.27944 + 12.2390i −0.106120 + 0.396046i
\(956\) 5.92169 + 6.99448i 0.191521 + 0.226218i
\(957\) 20.6801 19.2647i 0.668493 0.622738i
\(958\) −23.7707 19.8571i −0.767997 0.641552i
\(959\) −23.7305 13.2533i −0.766299 0.427973i
\(960\) 10.2629 + 6.23339i 0.331233 + 0.201182i
\(961\) −2.43793 + 4.22262i −0.0786429 + 0.136214i
\(962\) −2.66730 0.464270i −0.0859971 0.0149687i
\(963\) −0.575757 + 0.499459i −0.0185535 + 0.0160949i
\(964\) −19.9728 + 55.6351i −0.643280 + 1.79188i
\(965\) −5.07480 + 5.07480i −0.163364 + 0.163364i
\(966\) 18.8039 12.6422i 0.605007 0.406755i
\(967\) 44.0766i 1.41741i 0.705506 + 0.708704i \(0.250720\pi\)
−0.705506 + 0.708704i \(0.749280\pi\)
\(968\) −54.7291 + 32.0812i −1.75906 + 1.03113i
\(969\) −6.86047 4.29181i −0.220390 0.137873i
\(970\) 5.89929 4.15009i 0.189415 0.133251i
\(971\) −7.49863 27.9853i −0.240643 0.898091i −0.975524 0.219895i \(-0.929429\pi\)
0.734881 0.678196i \(-0.237238\pi\)
\(972\) −30.0998 + 8.12423i −0.965451 + 0.260585i
\(973\) −17.3827 4.39303i −0.557263 0.140834i
\(974\) −1.86435 + 2.23180i −0.0597376 + 0.0715114i
\(975\) 1.29210 + 0.0457862i 0.0413803 + 0.00146633i
\(976\) 6.82476 0.657642i 0.218455 0.0210506i
\(977\) −41.5372 + 23.9815i −1.32889 + 0.767237i −0.985129 0.171819i \(-0.945036\pi\)
−0.343765 + 0.939056i \(0.611702\pi\)
\(978\) 36.6074 + 32.8499i 1.17058 + 1.05042i
\(979\) −32.6268 + 32.6268i −1.04276 + 1.04276i
\(980\) −10.8206 + 5.48629i −0.345653 + 0.175253i
\(981\) 5.76223 + 29.8077i 0.183974 + 0.951687i
\(982\) −23.0723 10.6971i −0.736266 0.341357i
\(983\) −29.2508 + 16.8879i −0.932955 + 0.538642i −0.887745 0.460336i \(-0.847729\pi\)
−0.0452101 + 0.998978i \(0.514396\pi\)
\(984\) −11.0293 + 36.8763i −0.351602 + 1.17557i
\(985\) 0.106881 0.185124i 0.00340552 0.00589853i
\(986\) −13.8712 + 1.24432i −0.441748 + 0.0396272i
\(987\) 52.3511 12.8466i 1.66635 0.408910i
\(988\) −0.462940 + 0.0837303i −0.0147281 + 0.00266382i
\(989\) −5.79902 21.6423i −0.184398 0.688184i
\(990\) −14.7485 + 15.3083i −0.468737 + 0.486530i
\(991\) 9.81671 + 17.0030i 0.311838 + 0.540119i 0.978760 0.205008i \(-0.0657221\pi\)
−0.666922 + 0.745127i \(0.732389\pi\)
\(992\) −18.8275 21.9431i −0.597774 0.696693i
\(993\) −55.0571 + 29.2381i −1.74718 + 0.927843i
\(994\) 3.94589 4.86286i 0.125156 0.154241i
\(995\) 9.54494 9.54494i 0.302595 0.302595i
\(996\) 2.14310 + 14.8307i 0.0679067 + 0.469927i
\(997\) −10.1300 + 37.8056i −0.320820 + 1.19732i 0.597628 + 0.801774i \(0.296110\pi\)
−0.918448 + 0.395543i \(0.870557\pi\)
\(998\) 40.1262 28.2284i 1.27017 0.893555i
\(999\) −33.3536 + 45.7587i −1.05526 + 1.44774i
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 336.2.bo.a.173.54 yes 240
3.2 odd 2 inner 336.2.bo.a.173.7 yes 240
7.3 odd 6 inner 336.2.bo.a.269.27 yes 240
16.5 even 4 inner 336.2.bo.a.5.34 yes 240
21.17 even 6 inner 336.2.bo.a.269.34 yes 240
48.5 odd 4 inner 336.2.bo.a.5.27 240
112.101 odd 12 inner 336.2.bo.a.101.7 yes 240
336.101 even 12 inner 336.2.bo.a.101.54 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bo.a.5.27 240 48.5 odd 4 inner
336.2.bo.a.5.34 yes 240 16.5 even 4 inner
336.2.bo.a.101.7 yes 240 112.101 odd 12 inner
336.2.bo.a.101.54 yes 240 336.101 even 12 inner
336.2.bo.a.173.7 yes 240 3.2 odd 2 inner
336.2.bo.a.173.54 yes 240 1.1 even 1 trivial
336.2.bo.a.269.27 yes 240 7.3 odd 6 inner
336.2.bo.a.269.34 yes 240 21.17 even 6 inner