Properties

Label 310.2.w.a.117.15
Level $310$
Weight $2$
Character 310.117
Analytic conductor $2.475$
Analytic rank $0$
Dimension $256$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [310,2,Mod(3,310)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(310, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([45, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("310.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 310 = 2 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 310.w (of order \(60\), degree \(16\), 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: \(2.47536246266\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(16\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 117.15
Character \(\chi\) \(=\) 310.117
Dual form 310.2.w.a.53.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.453990 - 0.891007i) q^{2} +(1.39807 + 0.907916i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70977 - 1.44108i) q^{5} +(1.44367 - 0.833503i) q^{6} +(-1.17558 - 3.06249i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.0899259 - 0.201977i) q^{9} +O(q^{10})\) \(q+(0.453990 - 0.891007i) q^{2} +(1.39807 + 0.907916i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70977 - 1.44108i) q^{5} +(1.44367 - 0.833503i) q^{6} +(-1.17558 - 3.06249i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.0899259 - 0.201977i) q^{9} +(-0.507792 - 2.17765i) q^{10} +(-0.643025 + 0.0675846i) q^{11} +(-0.0872443 - 1.66472i) q^{12} +(-0.164320 + 3.13541i) q^{13} +(-3.26240 - 0.342892i) q^{14} +(3.69875 - 0.462400i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.505900 + 0.624734i) q^{17} +(-0.220788 - 0.0115710i) q^{18} +(4.16895 + 3.75374i) q^{19} +(-2.17083 - 0.536186i) q^{20} +(1.13694 - 5.34890i) q^{21} +(-0.231709 + 0.603622i) q^{22} +(0.984764 + 6.21756i) q^{23} +(-1.52289 - 0.678032i) q^{24} +(0.846595 - 4.92781i) q^{25} +(2.71907 + 1.56985i) q^{26} +(0.839987 - 5.30347i) q^{27} +(-1.78662 + 2.75115i) q^{28} +(0.356381 + 1.09683i) q^{29} +(1.26719 - 3.50553i) q^{30} +(-3.10939 + 4.61863i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.960354 - 0.489325i) q^{33} +(0.786316 - 0.167137i) q^{34} +(-6.42325 - 3.54204i) q^{35} +(-0.110546 + 0.191471i) q^{36} +(3.82683 + 1.02540i) q^{37} +(5.23727 - 2.01040i) q^{38} +(-3.07642 + 4.23433i) q^{39} +(-1.46328 + 1.69080i) q^{40} +(0.464812 + 0.0987989i) q^{41} +(-4.24974 - 3.44137i) q^{42} +(-2.90784 + 0.152393i) q^{43} +(0.432638 + 0.480493i) q^{44} +(-0.444817 - 0.215743i) q^{45} +(5.98696 + 1.94528i) q^{46} +(-7.56015 + 3.85209i) q^{47} +(-1.29551 + 1.04908i) q^{48} +(-2.79485 + 2.51649i) q^{49} +(-4.00636 - 2.99150i) q^{50} +(0.140076 + 1.33274i) q^{51} +(2.63318 - 1.71001i) q^{52} +(-0.436341 - 0.167496i) q^{53} +(-4.34408 - 3.15616i) q^{54} +(-1.00203 + 1.04220i) q^{55} +(1.64019 + 2.84088i) q^{56} +(2.42040 + 9.03305i) q^{57} +(1.13907 + 0.180411i) q^{58} +(-1.40594 - 6.61443i) q^{59} +(-2.54816 - 2.72056i) q^{60} -2.83638i q^{61} +(2.70359 + 4.86730i) q^{62} +(-0.512837 + 0.512837i) q^{63} +(0.951057 - 0.309017i) q^{64} +(4.23741 + 5.59761i) q^{65} +(-0.871983 + 0.633533i) q^{66} +(-10.1476 + 2.71904i) q^{67} +(0.208060 - 0.776491i) q^{68} +(-4.26826 + 9.58666i) q^{69} +(-6.07207 + 4.11511i) q^{70} +(8.89960 - 3.96236i) q^{71} +(0.120415 + 0.185423i) q^{72} +(1.82579 - 2.25466i) q^{73} +(2.65098 - 2.94421i) q^{74} +(5.65764 - 6.12077i) q^{75} +(0.586392 - 5.57915i) q^{76} +(0.962904 + 1.88981i) q^{77} +(2.37615 + 4.66345i) q^{78} +(-1.65852 + 15.7798i) q^{79} +(0.842199 + 2.07140i) q^{80} +(5.54565 - 6.15907i) q^{81} +(0.299051 - 0.369297i) q^{82} +(-3.14438 - 4.84192i) q^{83} +(-4.99563 + 2.22420i) q^{84} +(1.76526 + 0.339109i) q^{85} +(-1.18435 + 2.66009i) q^{86} +(-0.497582 + 1.85700i) q^{87} +(0.624535 - 0.167344i) q^{88} +(14.4545 - 10.5018i) q^{89} +(-0.394171 + 0.298389i) q^{90} +(9.79532 - 3.18269i) q^{91} +(4.45128 - 4.45128i) q^{92} +(-8.54047 + 3.63409i) q^{93} +8.48496i q^{94} +(12.5374 + 0.410237i) q^{95} +(0.346590 + 1.63058i) q^{96} +(-16.1208 - 2.55328i) q^{97} +(0.973376 + 3.63269i) q^{98} +(0.0714751 + 0.123799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 24 q^{7} - 8 q^{10} + 64 q^{16} + 4 q^{20} + 32 q^{21} - 52 q^{22} + 20 q^{23} + 20 q^{25} - 180 q^{27} + 4 q^{28} + 8 q^{31} - 44 q^{33} + 48 q^{35} + 128 q^{36} - 108 q^{37} - 52 q^{38} - 32 q^{41} + 8 q^{42} - 48 q^{43} - 28 q^{45} + 40 q^{46} + 20 q^{47} + 20 q^{48} - 48 q^{50} + 16 q^{51} + 28 q^{53} - 80 q^{55} - 24 q^{57} - 20 q^{60} + 20 q^{62} - 256 q^{63} - 8 q^{65} - 56 q^{66} + 4 q^{67} - 40 q^{70} + 88 q^{71} + 32 q^{73} - 32 q^{75} - 96 q^{76} + 20 q^{77} - 112 q^{78} + 48 q^{81} + 8 q^{82} - 108 q^{83} - 120 q^{85} - 24 q^{86} + 8 q^{87} - 108 q^{88} - 32 q^{90} - 80 q^{91} - 260 q^{93} + 64 q^{95} - 88 q^{97} - 112 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/310\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(251\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{30}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.453990 0.891007i 0.321020 0.630037i
\(3\) 1.39807 + 0.907916i 0.807175 + 0.524186i 0.881017 0.473084i \(-0.156859\pi\)
−0.0738419 + 0.997270i \(0.523526\pi\)
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 1.70977 1.44108i 0.764630 0.644469i
\(6\) 1.44367 0.833503i 0.589376 0.340276i
\(7\) −1.17558 3.06249i −0.444327 1.15751i −0.954703 0.297561i \(-0.903827\pi\)
0.510375 0.859952i \(-0.329506\pi\)
\(8\) −0.987688 + 0.156434i −0.349201 + 0.0553079i
\(9\) −0.0899259 0.201977i −0.0299753 0.0673257i
\(10\) −0.507792 2.17765i −0.160578 0.688633i
\(11\) −0.643025 + 0.0675846i −0.193879 + 0.0203775i −0.200970 0.979597i \(-0.564409\pi\)
0.00709109 + 0.999975i \(0.497743\pi\)
\(12\) −0.0872443 1.66472i −0.0251853 0.480564i
\(13\) −0.164320 + 3.13541i −0.0455741 + 0.869605i 0.876217 + 0.481917i \(0.160059\pi\)
−0.921791 + 0.387688i \(0.873274\pi\)
\(14\) −3.26240 0.342892i −0.871913 0.0916418i
\(15\) 3.69875 0.462400i 0.955012 0.119391i
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 0.505900 + 0.624734i 0.122699 + 0.151520i 0.834794 0.550563i \(-0.185587\pi\)
−0.712095 + 0.702083i \(0.752253\pi\)
\(18\) −0.220788 0.0115710i −0.0520403 0.00272732i
\(19\) 4.16895 + 3.75374i 0.956423 + 0.861167i 0.990397 0.138255i \(-0.0441495\pi\)
−0.0339733 + 0.999423i \(0.510816\pi\)
\(20\) −2.17083 0.536186i −0.485412 0.119895i
\(21\) 1.13694 5.34890i 0.248101 1.16723i
\(22\) −0.231709 + 0.603622i −0.0494005 + 0.128693i
\(23\) 0.984764 + 6.21756i 0.205338 + 1.29645i 0.847875 + 0.530196i \(0.177882\pi\)
−0.642537 + 0.766254i \(0.722118\pi\)
\(24\) −1.52289 0.678032i −0.310858 0.138403i
\(25\) 0.846595 4.92781i 0.169319 0.985561i
\(26\) 2.71907 + 1.56985i 0.533253 + 0.307874i
\(27\) 0.839987 5.30347i 0.161656 1.02065i
\(28\) −1.78662 + 2.75115i −0.337639 + 0.519919i
\(29\) 0.356381 + 1.09683i 0.0661782 + 0.203676i 0.978678 0.205403i \(-0.0658504\pi\)
−0.912499 + 0.409078i \(0.865850\pi\)
\(30\) 1.26719 3.50553i 0.231357 0.640020i
\(31\) −3.10939 + 4.61863i −0.558463 + 0.829530i
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −0.960354 0.489325i −0.167176 0.0851805i
\(34\) 0.786316 0.167137i 0.134852 0.0286637i
\(35\) −6.42325 3.54204i −1.08573 0.598714i
\(36\) −0.110546 + 0.191471i −0.0184243 + 0.0319118i
\(37\) 3.82683 + 1.02540i 0.629128 + 0.168574i 0.559274 0.828983i \(-0.311080\pi\)
0.0698538 + 0.997557i \(0.477747\pi\)
\(38\) 5.23727 2.01040i 0.849598 0.326130i
\(39\) −3.07642 + 4.23433i −0.492621 + 0.678035i
\(40\) −1.46328 + 1.69080i −0.231365 + 0.267339i
\(41\) 0.464812 + 0.0987989i 0.0725915 + 0.0154298i 0.244064 0.969759i \(-0.421519\pi\)
−0.171473 + 0.985189i \(0.554853\pi\)
\(42\) −4.24974 3.44137i −0.655750 0.531016i
\(43\) −2.90784 + 0.152393i −0.443441 + 0.0232397i −0.272750 0.962085i \(-0.587933\pi\)
−0.170691 + 0.985325i \(0.554600\pi\)
\(44\) 0.432638 + 0.480493i 0.0652226 + 0.0724370i
\(45\) −0.444817 0.215743i −0.0663093 0.0321611i
\(46\) 5.98696 + 1.94528i 0.882729 + 0.286816i
\(47\) −7.56015 + 3.85209i −1.10276 + 0.561885i −0.908002 0.418966i \(-0.862393\pi\)
−0.194760 + 0.980851i \(0.562393\pi\)
\(48\) −1.29551 + 1.04908i −0.186990 + 0.151422i
\(49\) −2.79485 + 2.51649i −0.399264 + 0.359499i
\(50\) −4.00636 2.99150i −0.566585 0.423062i
\(51\) 0.140076 + 1.33274i 0.0196146 + 0.186620i
\(52\) 2.63318 1.71001i 0.365157 0.237135i
\(53\) −0.436341 0.167496i −0.0599361 0.0230073i 0.328215 0.944603i \(-0.393553\pi\)
−0.388151 + 0.921596i \(0.626886\pi\)
\(54\) −4.34408 3.15616i −0.591154 0.429499i
\(55\) −1.00203 + 1.04220i −0.135113 + 0.140530i
\(56\) 1.64019 + 2.84088i 0.219179 + 0.379629i
\(57\) 2.42040 + 9.03305i 0.320590 + 1.19646i
\(58\) 1.13907 + 0.180411i 0.149568 + 0.0236892i
\(59\) −1.40594 6.61443i −0.183038 0.861126i −0.969806 0.243877i \(-0.921581\pi\)
0.786768 0.617249i \(-0.211753\pi\)
\(60\) −2.54816 2.72056i −0.328966 0.351222i
\(61\) 2.83638i 0.363161i −0.983376 0.181580i \(-0.941879\pi\)
0.983376 0.181580i \(-0.0581212\pi\)
\(62\) 2.70359 + 4.86730i 0.343357 + 0.618147i
\(63\) −0.512837 + 0.512837i −0.0646114 + 0.0646114i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 4.23741 + 5.59761i 0.525586 + 0.694298i
\(66\) −0.871983 + 0.633533i −0.107334 + 0.0779825i
\(67\) −10.1476 + 2.71904i −1.23973 + 0.332184i −0.818360 0.574706i \(-0.805116\pi\)
−0.421367 + 0.906890i \(0.638450\pi\)
\(68\) 0.208060 0.776491i 0.0252310 0.0941634i
\(69\) −4.26826 + 9.58666i −0.513838 + 1.15410i
\(70\) −6.07207 + 4.11511i −0.725752 + 0.491849i
\(71\) 8.89960 3.96236i 1.05619 0.470245i 0.196203 0.980563i \(-0.437139\pi\)
0.859986 + 0.510318i \(0.170472\pi\)
\(72\) 0.120415 + 0.185423i 0.0141910 + 0.0218523i
\(73\) 1.82579 2.25466i 0.213692 0.263888i −0.659017 0.752128i \(-0.729028\pi\)
0.872709 + 0.488240i \(0.162361\pi\)
\(74\) 2.65098 2.94421i 0.308170 0.342258i
\(75\) 5.65764 6.12077i 0.653287 0.706766i
\(76\) 0.586392 5.57915i 0.0672638 0.639972i
\(77\) 0.962904 + 1.88981i 0.109733 + 0.215363i
\(78\) 2.37615 + 4.66345i 0.269046 + 0.528032i
\(79\) −1.65852 + 15.7798i −0.186598 + 1.77536i 0.355139 + 0.934814i \(0.384434\pi\)
−0.541737 + 0.840548i \(0.682233\pi\)
\(80\) 0.842199 + 2.07140i 0.0941607 + 0.231590i
\(81\) 5.54565 6.15907i 0.616183 0.684341i
\(82\) 0.299051 0.369297i 0.0330247 0.0407820i
\(83\) −3.14438 4.84192i −0.345141 0.531470i 0.622887 0.782311i \(-0.285959\pi\)
−0.968028 + 0.250841i \(0.919293\pi\)
\(84\) −4.99563 + 2.22420i −0.545068 + 0.242680i
\(85\) 1.76526 + 0.339109i 0.191469 + 0.0367815i
\(86\) −1.18435 + 2.66009i −0.127711 + 0.286844i
\(87\) −0.497582 + 1.85700i −0.0533464 + 0.199092i
\(88\) 0.624535 0.167344i 0.0665757 0.0178389i
\(89\) 14.4545 10.5018i 1.53218 1.11319i 0.577166 0.816627i \(-0.304158\pi\)
0.955012 0.296566i \(-0.0958415\pi\)
\(90\) −0.394171 + 0.298389i −0.0415493 + 0.0314530i
\(91\) 9.79532 3.18269i 1.02683 0.333637i
\(92\) 4.45128 4.45128i 0.464078 0.464078i
\(93\) −8.54047 + 3.63409i −0.885605 + 0.376838i
\(94\) 8.48496i 0.875156i
\(95\) 12.5374 + 0.410237i 1.28631 + 0.0420894i
\(96\) 0.346590 + 1.63058i 0.0353737 + 0.166420i
\(97\) −16.1208 2.55328i −1.63682 0.259246i −0.730832 0.682558i \(-0.760868\pi\)
−0.905984 + 0.423312i \(0.860868\pi\)
\(98\) 0.973376 + 3.63269i 0.0983258 + 0.366957i
\(99\) 0.0714751 + 0.123799i 0.00718352 + 0.0124422i
\(100\) −4.48430 + 2.21158i −0.448430 + 0.221158i
\(101\) 10.0279 + 7.28570i 0.997813 + 0.724954i 0.961618 0.274391i \(-0.0884762\pi\)
0.0361952 + 0.999345i \(0.488476\pi\)
\(102\) 1.25107 + 0.480241i 0.123874 + 0.0475509i
\(103\) −13.2016 + 8.57325i −1.30080 + 0.844748i −0.994247 0.107107i \(-0.965841\pi\)
−0.306550 + 0.951855i \(0.599175\pi\)
\(104\) −0.328189 3.12251i −0.0321816 0.306187i
\(105\) −5.76427 10.7838i −0.562535 1.05239i
\(106\) −0.347334 + 0.312741i −0.0337361 + 0.0303761i
\(107\) 1.25463 1.01598i 0.121289 0.0982182i −0.566757 0.823885i \(-0.691802\pi\)
0.688046 + 0.725667i \(0.258469\pi\)
\(108\) −4.78433 + 2.43774i −0.460372 + 0.234571i
\(109\) −1.23726 0.402010i −0.118508 0.0385055i 0.249163 0.968462i \(-0.419845\pi\)
−0.367671 + 0.929956i \(0.619845\pi\)
\(110\) 0.473698 + 1.36596i 0.0451653 + 0.130239i
\(111\) 4.41920 + 4.90802i 0.419452 + 0.465849i
\(112\) 3.27588 0.171681i 0.309541 0.0162224i
\(113\) −8.45158 6.84396i −0.795058 0.643825i 0.143227 0.989690i \(-0.454252\pi\)
−0.938284 + 0.345865i \(0.887586\pi\)
\(114\) 9.14734 + 1.94433i 0.856727 + 0.182103i
\(115\) 10.6437 + 9.21144i 0.992530 + 0.858972i
\(116\) 0.677876 0.933016i 0.0629392 0.0866284i
\(117\) 0.648057 0.248766i 0.0599128 0.0229984i
\(118\) −6.53179 1.75019i −0.601300 0.161118i
\(119\) 1.31852 2.28374i 0.120868 0.209350i
\(120\) −3.58087 + 1.03532i −0.326888 + 0.0945113i
\(121\) −10.3507 + 2.20011i −0.940974 + 0.200010i
\(122\) −2.52723 1.28769i −0.228805 0.116582i
\(123\) 0.560139 + 0.560139i 0.0505060 + 0.0505060i
\(124\) 5.56420 0.199213i 0.499680 0.0178898i
\(125\) −5.65387 9.64540i −0.505697 0.862711i
\(126\) 0.224118 + 0.689765i 0.0199660 + 0.0614491i
\(127\) −9.51897 + 14.6579i −0.844672 + 1.30068i 0.107217 + 0.994236i \(0.465806\pi\)
−0.951888 + 0.306445i \(0.900861\pi\)
\(128\) 0.156434 0.987688i 0.0138270 0.0873001i
\(129\) −4.20371 2.42702i −0.370116 0.213687i
\(130\) 6.91125 1.23430i 0.606157 0.108256i
\(131\) 5.30030 + 2.35985i 0.463090 + 0.206181i 0.625000 0.780625i \(-0.285099\pi\)
−0.161910 + 0.986805i \(0.551766\pi\)
\(132\) 0.168610 + 1.06456i 0.0146756 + 0.0926581i
\(133\) 6.59486 17.1802i 0.571847 1.48971i
\(134\) −2.18423 + 10.2760i −0.188689 + 0.887711i
\(135\) −6.20653 10.2782i −0.534173 0.884604i
\(136\) −0.597401 0.537903i −0.0512268 0.0461248i
\(137\) 1.37162 + 0.0718838i 0.117186 + 0.00614145i 0.110839 0.993838i \(-0.464646\pi\)
0.00634709 + 0.999980i \(0.497980\pi\)
\(138\) 6.60403 + 8.15529i 0.562172 + 0.694225i
\(139\) 4.69817 14.4595i 0.398494 1.22644i −0.527713 0.849422i \(-0.676951\pi\)
0.926207 0.377015i \(-0.123049\pi\)
\(140\) 0.909922 + 7.27848i 0.0769024 + 0.615144i
\(141\) −14.0670 1.47850i −1.18465 0.124512i
\(142\) 0.509848 9.72848i 0.0427855 0.816396i
\(143\) −0.106244 2.02725i −0.00888454 0.169527i
\(144\) 0.219880 0.0231103i 0.0183233 0.00192586i
\(145\) 2.18994 + 1.36174i 0.181864 + 0.113087i
\(146\) −1.18003 2.65038i −0.0976597 0.219347i
\(147\) −6.19215 + 0.980740i −0.510720 + 0.0808901i
\(148\) −1.41979 3.69869i −0.116706 0.304030i
\(149\) 11.3077 6.52850i 0.926362 0.534835i 0.0407027 0.999171i \(-0.487040\pi\)
0.885659 + 0.464336i \(0.153707\pi\)
\(150\) −2.88514 7.81976i −0.235570 0.638481i
\(151\) −9.44593 13.0012i −0.768699 1.05802i −0.996440 0.0843017i \(-0.973134\pi\)
0.227741 0.973722i \(-0.426866\pi\)
\(152\) −4.70484 3.05536i −0.381613 0.247822i
\(153\) 0.0806884 0.158360i 0.00652327 0.0128026i
\(154\) 2.12098 0.170913
\(155\) 1.33947 + 12.3776i 0.107589 + 0.994195i
\(156\) 5.23391 0.419049
\(157\) 10.0061 19.6380i 0.798572 1.56728i −0.0247392 0.999694i \(-0.507876\pi\)
0.823311 0.567591i \(-0.192124\pi\)
\(158\) 13.3069 + 8.64161i 1.05864 + 0.687490i
\(159\) −0.457963 0.630332i −0.0363188 0.0499886i
\(160\) 2.22798 + 0.189992i 0.176137 + 0.0150201i
\(161\) 17.8835 10.3251i 1.40942 0.813729i
\(162\) −2.97010 7.73737i −0.233353 0.607905i
\(163\) −4.37114 + 0.692321i −0.342374 + 0.0542267i −0.325254 0.945627i \(-0.605450\pi\)
−0.0171202 + 0.999853i \(0.505450\pi\)
\(164\) −0.193280 0.434114i −0.0150926 0.0338986i
\(165\) −2.34713 + 0.547313i −0.182724 + 0.0426083i
\(166\) −5.74171 + 0.603478i −0.445643 + 0.0468389i
\(167\) −0.665444 12.6974i −0.0514936 0.982556i −0.895176 0.445713i \(-0.852950\pi\)
0.843682 0.536843i \(-0.180383\pi\)
\(168\) −0.286194 + 5.46090i −0.0220803 + 0.421318i
\(169\) 3.12501 + 0.328452i 0.240385 + 0.0252655i
\(170\) 1.10356 1.41891i 0.0846391 0.108825i
\(171\) 0.383272 1.17959i 0.0293096 0.0902056i
\(172\) 1.83247 + 2.26291i 0.139725 + 0.172546i
\(173\) −18.3019 0.959164i −1.39147 0.0729239i −0.658191 0.752851i \(-0.728678\pi\)
−0.733280 + 0.679927i \(0.762011\pi\)
\(174\) 1.42870 + 1.28641i 0.108310 + 0.0975225i
\(175\) −16.0866 + 3.20034i −1.21603 + 0.241923i
\(176\) 0.134429 0.632438i 0.0101329 0.0476718i
\(177\) 4.03975 10.5239i 0.303646 0.791025i
\(178\) −2.79498 17.6468i −0.209493 1.32269i
\(179\) 0.0619101 + 0.0275641i 0.00462738 + 0.00206024i 0.409049 0.912512i \(-0.365860\pi\)
−0.404422 + 0.914573i \(0.632527\pi\)
\(180\) 0.0869168 + 0.486675i 0.00647840 + 0.0362746i
\(181\) −18.8109 10.8605i −1.39821 0.807254i −0.404001 0.914759i \(-0.632381\pi\)
−0.994205 + 0.107504i \(0.965714\pi\)
\(182\) 1.61118 10.1726i 0.119429 0.754044i
\(183\) 2.57519 3.96545i 0.190364 0.293134i
\(184\) −1.94528 5.98696i −0.143408 0.441364i
\(185\) 8.02066 3.76157i 0.589691 0.276556i
\(186\) −0.639290 + 9.25945i −0.0468750 + 0.678936i
\(187\) −0.367529 0.367529i −0.0268764 0.0268764i
\(188\) 7.56015 + 3.85209i 0.551381 + 0.280943i
\(189\) −17.2293 + 3.66220i −1.25325 + 0.266386i
\(190\) 6.05737 10.9846i 0.439448 0.796909i
\(191\) −0.450526 + 0.780334i −0.0325989 + 0.0564630i −0.881865 0.471503i \(-0.843712\pi\)
0.849266 + 0.527966i \(0.177045\pi\)
\(192\) 1.61020 + 0.431453i 0.116206 + 0.0311374i
\(193\) 18.0100 6.91339i 1.29639 0.497637i 0.390285 0.920694i \(-0.372377\pi\)
0.906103 + 0.423058i \(0.139043\pi\)
\(194\) −9.59366 + 13.2045i −0.688785 + 0.948031i
\(195\) 0.842036 + 11.6731i 0.0602994 + 0.835925i
\(196\) 3.67865 + 0.781922i 0.262761 + 0.0558515i
\(197\) 21.4429 + 17.3641i 1.52774 + 1.23714i 0.879694 + 0.475540i \(0.157747\pi\)
0.648047 + 0.761601i \(0.275586\pi\)
\(198\) 0.142754 0.00748144i 0.0101451 0.000531683i
\(199\) 13.5804 + 15.0826i 0.962691 + 1.06918i 0.997562 + 0.0697846i \(0.0222312\pi\)
−0.0348713 + 0.999392i \(0.511102\pi\)
\(200\) −0.0652936 + 4.99957i −0.00461696 + 0.353523i
\(201\) −16.6557 5.41177i −1.17480 0.381717i
\(202\) 11.0442 5.62729i 0.777065 0.395935i
\(203\) 2.94007 2.38082i 0.206352 0.167101i
\(204\) 0.995872 0.896687i 0.0697250 0.0627806i
\(205\) 0.937097 0.500907i 0.0654497 0.0349849i
\(206\) 1.64540 + 15.6549i 0.114640 + 1.09073i
\(207\) 1.16725 0.758020i 0.0811293 0.0526860i
\(208\) −2.93117 1.12517i −0.203240 0.0780166i
\(209\) −2.93443 2.13199i −0.202979 0.147473i
\(210\) −12.2253 + 0.240264i −0.843629 + 0.0165798i
\(211\) 7.59961 + 13.1629i 0.523179 + 0.906172i 0.999636 + 0.0269746i \(0.00858732\pi\)
−0.476457 + 0.879198i \(0.658079\pi\)
\(212\) 0.120968 + 0.451459i 0.00830812 + 0.0310063i
\(213\) 16.0397 + 2.54045i 1.09903 + 0.174069i
\(214\) −0.335653 1.57912i −0.0229448 0.107947i
\(215\) −4.75211 + 4.45097i −0.324091 + 0.303554i
\(216\) 5.36958i 0.365354i
\(217\) 17.7998 + 4.09291i 1.20833 + 0.277845i
\(218\) −0.919897 + 0.919897i −0.0623033 + 0.0623033i
\(219\) 4.59962 1.49451i 0.310814 0.100989i
\(220\) 1.43214 + 0.198066i 0.0965546 + 0.0133536i
\(221\) −2.04193 + 1.48355i −0.137355 + 0.0997941i
\(222\) 6.37935 1.70934i 0.428154 0.114724i
\(223\) −1.67580 + 6.25419i −0.112220 + 0.418811i −0.999064 0.0432580i \(-0.986226\pi\)
0.886844 + 0.462069i \(0.152893\pi\)
\(224\) 1.33425 2.99677i 0.0891481 0.200230i
\(225\) −1.07143 + 0.272145i −0.0714290 + 0.0181430i
\(226\) −9.93495 + 4.42332i −0.660863 + 0.294235i
\(227\) 6.59298 + 10.1523i 0.437592 + 0.673832i 0.986817 0.161843i \(-0.0517437\pi\)
−0.549225 + 0.835674i \(0.685077\pi\)
\(228\) 5.88522 7.26764i 0.389758 0.481311i
\(229\) −2.54456 + 2.82602i −0.168149 + 0.186749i −0.821330 0.570453i \(-0.806768\pi\)
0.653181 + 0.757202i \(0.273434\pi\)
\(230\) 13.0396 5.30169i 0.859805 0.349583i
\(231\) −0.369580 + 3.51632i −0.0243166 + 0.231357i
\(232\) −0.523574 1.02757i −0.0343743 0.0674634i
\(233\) −8.21950 16.1317i −0.538477 1.05682i −0.986647 0.162873i \(-0.947924\pi\)
0.448170 0.893949i \(-0.352076\pi\)
\(234\) 0.0725597 0.690360i 0.00474338 0.0451302i
\(235\) −7.37493 + 17.4809i −0.481087 + 1.14033i
\(236\) −4.52480 + 5.02530i −0.294539 + 0.327119i
\(237\) −16.6454 + 20.5554i −1.08124 + 1.33522i
\(238\) −1.43623 2.21160i −0.0930971 0.143357i
\(239\) 19.0551 8.48386i 1.23257 0.548775i 0.316041 0.948745i \(-0.397646\pi\)
0.916528 + 0.399970i \(0.130980\pi\)
\(240\) −0.703207 + 3.66061i −0.0453918 + 0.236291i
\(241\) −6.92738 + 15.5591i −0.446232 + 1.00225i 0.540715 + 0.841206i \(0.318154\pi\)
−0.986947 + 0.161047i \(0.948513\pi\)
\(242\) −2.73881 + 10.2214i −0.176057 + 0.657055i
\(243\) −2.21472 + 0.593433i −0.142074 + 0.0380687i
\(244\) −2.29468 + 1.66718i −0.146902 + 0.106730i
\(245\) −1.15207 + 8.33019i −0.0736033 + 0.532197i
\(246\) 0.753385 0.244790i 0.0480341 0.0156072i
\(247\) −12.4545 + 12.4545i −0.792464 + 0.792464i
\(248\) 2.34859 5.04818i 0.149136 0.320560i
\(249\) 9.62418i 0.609908i
\(250\) −11.1609 + 0.658712i −0.705878 + 0.0416606i
\(251\) −2.95649 13.9092i −0.186612 0.877940i −0.967422 0.253171i \(-0.918526\pi\)
0.780810 0.624769i \(-0.214807\pi\)
\(252\) 0.716332 + 0.113456i 0.0451247 + 0.00714705i
\(253\) −1.05344 3.93149i −0.0662292 0.247171i
\(254\) 8.73879 + 15.1360i 0.548320 + 0.949718i
\(255\) 2.16007 + 2.07681i 0.135269 + 0.130055i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 2.86246 + 1.09879i 0.178555 + 0.0685409i 0.446003 0.895031i \(-0.352847\pi\)
−0.267448 + 0.963572i \(0.586180\pi\)
\(258\) −4.07093 + 2.64370i −0.253445 + 0.164589i
\(259\) −1.35848 12.9251i −0.0844119 0.803125i
\(260\) 2.03787 6.71833i 0.126383 0.416653i
\(261\) 0.189486 0.170614i 0.0117289 0.0105607i
\(262\) 4.50893 3.65126i 0.278562 0.225575i
\(263\) −1.27866 + 0.651512i −0.0788458 + 0.0401740i −0.492969 0.870047i \(-0.664088\pi\)
0.414123 + 0.910221i \(0.364088\pi\)
\(264\) 1.02508 + 0.333068i 0.0630892 + 0.0204989i
\(265\) −0.987415 + 0.342423i −0.0606564 + 0.0210349i
\(266\) −12.3137 13.6757i −0.754999 0.838512i
\(267\) 29.7432 1.55878i 1.82026 0.0953956i
\(268\) 8.16436 + 6.61137i 0.498718 + 0.403854i
\(269\) −15.6394 3.32425i −0.953550 0.202683i −0.295234 0.955425i \(-0.595398\pi\)
−0.658316 + 0.752742i \(0.728731\pi\)
\(270\) −11.9756 + 0.863862i −0.728813 + 0.0525729i
\(271\) −2.41585 + 3.32513i −0.146752 + 0.201987i −0.876065 0.482194i \(-0.839840\pi\)
0.729312 + 0.684181i \(0.239840\pi\)
\(272\) −0.750489 + 0.288086i −0.0455051 + 0.0174678i
\(273\) 16.5842 + 4.44371i 1.00372 + 0.268946i
\(274\) 0.686753 1.18949i 0.0414883 0.0718598i
\(275\) −0.211338 + 3.22592i −0.0127442 + 0.194530i
\(276\) 10.2646 2.18181i 0.617856 0.131329i
\(277\) −14.4033 7.33883i −0.865408 0.440948i −0.0358431 0.999357i \(-0.511412\pi\)
−0.829565 + 0.558410i \(0.811412\pi\)
\(278\) −10.7506 10.7506i −0.644776 0.644776i
\(279\) 1.21247 + 0.212690i 0.0725887 + 0.0127334i
\(280\) 6.89827 + 2.49361i 0.412250 + 0.149022i
\(281\) 2.15717 + 6.63908i 0.128686 + 0.396054i 0.994555 0.104217i \(-0.0332336\pi\)
−0.865869 + 0.500271i \(0.833234\pi\)
\(282\) −7.70363 + 11.8626i −0.458745 + 0.706405i
\(283\) −1.21139 + 7.64843i −0.0720098 + 0.454652i 0.925167 + 0.379561i \(0.123925\pi\)
−0.997177 + 0.0750914i \(0.976075\pi\)
\(284\) −8.43667 4.87091i −0.500624 0.289036i
\(285\) 17.1556 + 11.9564i 1.01621 + 0.708237i
\(286\) −1.85453 0.825688i −0.109660 0.0488240i
\(287\) −0.243853 1.53963i −0.0143942 0.0908815i
\(288\) 0.0792320 0.206407i 0.00466879 0.0121626i
\(289\) 3.40014 15.9964i 0.200008 0.940965i
\(290\) 2.20753 1.33303i 0.129631 0.0782782i
\(291\) −20.2198 18.2060i −1.18530 1.06725i
\(292\) −2.89723 0.151837i −0.169548 0.00888561i
\(293\) 1.64627 + 2.03298i 0.0961763 + 0.118768i 0.822962 0.568097i \(-0.192320\pi\)
−0.726786 + 0.686864i \(0.758987\pi\)
\(294\) −1.93733 + 5.96249i −0.112987 + 0.347740i
\(295\) −11.9357 9.28306i −0.694925 0.540481i
\(296\) −3.94013 0.414124i −0.229015 0.0240705i
\(297\) −0.181699 + 3.46703i −0.0105433 + 0.201178i
\(298\) −0.683350 13.0391i −0.0395854 0.755335i
\(299\) −19.6564 + 2.06597i −1.13676 + 0.119478i
\(300\) −8.27729 0.979422i −0.477889 0.0565470i
\(301\) 3.88510 + 8.72607i 0.223933 + 0.502962i
\(302\) −15.8725 + 2.51396i −0.913361 + 0.144662i
\(303\) 7.40489 + 19.2904i 0.425400 + 1.10820i
\(304\) −4.85830 + 2.80494i −0.278642 + 0.160874i
\(305\) −4.08743 4.84954i −0.234046 0.277684i
\(306\) −0.104468 0.143788i −0.00597204 0.00821980i
\(307\) 11.2011 + 7.27410i 0.639282 + 0.415155i 0.823172 0.567792i \(-0.192202\pi\)
−0.183890 + 0.982947i \(0.558869\pi\)
\(308\) 0.962904 1.88981i 0.0548666 0.107682i
\(309\) −26.2406 −1.49278
\(310\) 11.6367 + 4.42585i 0.660918 + 0.251371i
\(311\) −2.98503 −0.169266 −0.0846329 0.996412i \(-0.526972\pi\)
−0.0846329 + 0.996412i \(0.526972\pi\)
\(312\) 2.37615 4.66345i 0.134523 0.264016i
\(313\) 17.0117 + 11.0475i 0.961559 + 0.624444i 0.927041 0.374960i \(-0.122344\pi\)
0.0345181 + 0.999404i \(0.489010\pi\)
\(314\) −12.9549 17.8310i −0.731090 1.00626i
\(315\) −0.137794 + 1.61587i −0.00776379 + 0.0910439i
\(316\) 13.7409 7.93334i 0.772989 0.446285i
\(317\) 4.44330 + 11.5752i 0.249561 + 0.650128i 0.999941 0.0108785i \(-0.00346281\pi\)
−0.750380 + 0.661007i \(0.770129\pi\)
\(318\) −0.769540 + 0.121883i −0.0431537 + 0.00683487i
\(319\) −0.303290 0.681201i −0.0169810 0.0381399i
\(320\) 1.18077 1.89889i 0.0660068 0.106151i
\(321\) 2.67648 0.281309i 0.149386 0.0157011i
\(322\) −1.08074 20.6218i −0.0602275 1.14921i
\(323\) −0.236019 + 4.50351i −0.0131324 + 0.250582i
\(324\) −8.24244 0.866316i −0.457913 0.0481286i
\(325\) 15.3116 + 3.46416i 0.849333 + 0.192157i
\(326\) −1.36759 + 4.20902i −0.0757440 + 0.233116i
\(327\) −1.36478 1.68536i −0.0754726 0.0932008i
\(328\) −0.474545 0.0248699i −0.0262024 0.00137321i
\(329\) 20.6846 + 18.6245i 1.14038 + 1.02680i
\(330\) −0.577917 + 2.33979i −0.0318133 + 0.128801i
\(331\) −3.86566 + 18.1865i −0.212476 + 0.999622i 0.734572 + 0.678531i \(0.237383\pi\)
−0.947048 + 0.321091i \(0.895950\pi\)
\(332\) −2.06898 + 5.38987i −0.113550 + 0.295808i
\(333\) −0.137025 0.865142i −0.00750893 0.0474095i
\(334\) −11.6156 5.17160i −0.635577 0.282977i
\(335\) −13.4317 + 19.2724i −0.733851 + 1.05296i
\(336\) 4.73577 + 2.73420i 0.258358 + 0.149163i
\(337\) 0.278558 1.75875i 0.0151740 0.0958051i −0.978939 0.204153i \(-0.934556\pi\)
0.994113 + 0.108348i \(0.0345560\pi\)
\(338\) 1.71138 2.63529i 0.0930867 0.143341i
\(339\) −5.60215 17.2416i −0.304267 0.936438i
\(340\) −0.763249 1.62745i −0.0413930 0.0882608i
\(341\) 1.68727 3.18004i 0.0913705 0.172209i
\(342\) −0.877021 0.877021i −0.0474239 0.0474239i
\(343\) −9.46754 4.82395i −0.511199 0.260469i
\(344\) 2.84820 0.605403i 0.153564 0.0326411i
\(345\) 6.51740 + 22.5418i 0.350885 + 1.21361i
\(346\) −9.16353 + 15.8717i −0.492634 + 0.853268i
\(347\) −3.54102 0.948813i −0.190092 0.0509349i 0.162517 0.986706i \(-0.448039\pi\)
−0.352609 + 0.935771i \(0.614705\pi\)
\(348\) 1.79482 0.688966i 0.0962124 0.0369325i
\(349\) −9.07226 + 12.4869i −0.485627 + 0.668408i −0.979574 0.201084i \(-0.935554\pi\)
0.493947 + 0.869492i \(0.335554\pi\)
\(350\) −4.45164 + 15.7862i −0.237950 + 0.843807i
\(351\) 16.4905 + 3.50517i 0.880198 + 0.187092i
\(352\) −0.502477 0.406898i −0.0267821 0.0216877i
\(353\) 22.8921 1.19972i 1.21842 0.0638549i 0.567743 0.823206i \(-0.307817\pi\)
0.650681 + 0.759351i \(0.274484\pi\)
\(354\) −7.54286 8.37720i −0.400899 0.445243i
\(355\) 9.50617 19.5997i 0.504535 1.04024i
\(356\) −16.9923 5.52114i −0.900592 0.292620i
\(357\) 3.91682 1.99572i 0.207300 0.105625i
\(358\) 0.0526664 0.0426484i 0.00278351 0.00225404i
\(359\) 23.9720 21.5845i 1.26520 1.13919i 0.281459 0.959573i \(-0.409182\pi\)
0.983737 0.179614i \(-0.0574848\pi\)
\(360\) 0.473090 + 0.143502i 0.0249340 + 0.00756323i
\(361\) 1.30355 + 12.4024i 0.0686078 + 0.652759i
\(362\) −18.2168 + 11.8301i −0.957451 + 0.621776i
\(363\) −16.4685 6.32167i −0.864373 0.331802i
\(364\) −8.33240 6.05384i −0.436736 0.317308i
\(365\) −0.127470 6.48604i −0.00667207 0.339495i
\(366\) −2.36413 4.09479i −0.123575 0.214038i
\(367\) −9.36303 34.9433i −0.488746 1.82403i −0.562563 0.826754i \(-0.690185\pi\)
0.0738166 0.997272i \(-0.476482\pi\)
\(368\) −6.21756 0.984764i −0.324113 0.0513344i
\(369\) −0.0218436 0.102766i −0.00113713 0.00534978i
\(370\) 0.289719 8.85418i 0.0150618 0.460307i
\(371\) 1.53319i 0.0795995i
\(372\) 7.96000 + 4.77332i 0.412707 + 0.247485i
\(373\) 1.42830 1.42830i 0.0739543 0.0739543i −0.669162 0.743116i \(-0.733347\pi\)
0.743116 + 0.669162i \(0.233347\pi\)
\(374\) −0.494325 + 0.160616i −0.0255609 + 0.00830525i
\(375\) 0.852723 18.6182i 0.0440344 0.961438i
\(376\) 6.86447 4.98733i 0.354008 0.257202i
\(377\) −3.49756 + 0.937168i −0.180133 + 0.0482666i
\(378\) −4.55889 + 17.0140i −0.234484 + 0.875107i
\(379\) −5.39439 + 12.1160i −0.277091 + 0.622357i −0.997460 0.0712349i \(-0.977306\pi\)
0.720369 + 0.693591i \(0.243973\pi\)
\(380\) −7.03739 10.3841i −0.361010 0.532692i
\(381\) −26.6163 + 11.8504i −1.36360 + 0.607112i
\(382\) 0.490748 + 0.755686i 0.0251089 + 0.0386643i
\(383\) −14.7483 + 18.2126i −0.753601 + 0.930619i −0.999249 0.0387395i \(-0.987666\pi\)
0.245649 + 0.969359i \(0.420999\pi\)
\(384\) 1.11544 1.23883i 0.0569223 0.0632186i
\(385\) 4.36970 + 1.84351i 0.222700 + 0.0939538i
\(386\) 2.01649 19.1856i 0.102637 0.976523i
\(387\) 0.292270 + 0.573612i 0.0148569 + 0.0291583i
\(388\) 7.40990 + 14.5428i 0.376181 + 0.738296i
\(389\) −1.00975 + 9.60715i −0.0511965 + 0.487102i 0.938641 + 0.344896i \(0.112086\pi\)
−0.989837 + 0.142205i \(0.954581\pi\)
\(390\) 10.7830 + 4.54920i 0.546021 + 0.230358i
\(391\) −3.38613 + 3.76068i −0.171244 + 0.190186i
\(392\) 2.36677 2.92272i 0.119540 0.147620i
\(393\) 5.26765 + 8.11146i 0.265718 + 0.409169i
\(394\) 25.2064 11.2226i 1.26988 0.565387i
\(395\) 19.9042 + 29.3697i 1.00149 + 1.47775i
\(396\) 0.0581431 0.130592i 0.00292180 0.00656247i
\(397\) −8.39596 + 31.3342i −0.421381 + 1.57262i 0.350319 + 0.936630i \(0.386073\pi\)
−0.771700 + 0.635986i \(0.780594\pi\)
\(398\) 19.6041 5.25289i 0.982663 0.263304i
\(399\) 24.8183 18.0315i 1.24247 0.902705i
\(400\) 4.42501 + 2.32794i 0.221251 + 0.116397i
\(401\) −7.12040 + 2.31356i −0.355576 + 0.115534i −0.481357 0.876524i \(-0.659856\pi\)
0.125782 + 0.992058i \(0.459856\pi\)
\(402\) −12.3835 + 12.3835i −0.617631 + 0.617631i
\(403\) −13.9703 10.5081i −0.695912 0.523447i
\(404\) 12.3952i 0.616683i
\(405\) 0.606070 18.5223i 0.0301159 0.920379i
\(406\) −0.786563 3.70049i −0.0390365 0.183652i
\(407\) −2.53005 0.400721i −0.125410 0.0198630i
\(408\) −0.346838 1.29442i −0.0171710 0.0640831i
\(409\) 14.3237 + 24.8093i 0.708260 + 1.22674i 0.965502 + 0.260395i \(0.0838528\pi\)
−0.257242 + 0.966347i \(0.582814\pi\)
\(410\) −0.0208786 1.06237i −0.00103112 0.0524666i
\(411\) 1.85236 + 1.34582i 0.0913702 + 0.0663843i
\(412\) 14.6956 + 5.64113i 0.724002 + 0.277918i
\(413\) −18.6038 + 12.0815i −0.915435 + 0.594491i
\(414\) −0.145481 1.38416i −0.00715000 0.0680277i
\(415\) −12.3537 3.74726i −0.606421 0.183946i
\(416\) −2.33326 + 2.10088i −0.114397 + 0.103004i
\(417\) 19.6964 15.9498i 0.964535 0.781065i
\(418\) −3.23182 + 1.64670i −0.158074 + 0.0805426i
\(419\) −32.4218 10.5345i −1.58391 0.514643i −0.620848 0.783931i \(-0.713212\pi\)
−0.963060 + 0.269288i \(0.913212\pi\)
\(420\) −5.33612 + 11.0019i −0.260376 + 0.536840i
\(421\) −19.3069 21.4425i −0.940962 1.04504i −0.998908 0.0467246i \(-0.985122\pi\)
0.0579456 0.998320i \(-0.481545\pi\)
\(422\) 15.1784 0.795466i 0.738872 0.0387227i
\(423\) 1.45789 + 1.18057i 0.0708849 + 0.0574015i
\(424\) 0.457171 + 0.0971747i 0.0222022 + 0.00471922i
\(425\) 3.50686 1.96408i 0.170108 0.0952719i
\(426\) 9.54545 13.1382i 0.462478 0.636547i
\(427\) −8.68637 + 3.33439i −0.420363 + 0.161362i
\(428\) −1.55939 0.417838i −0.0753761 0.0201970i
\(429\) 1.69204 2.93069i 0.0816923 0.141495i
\(430\) 1.80843 + 6.25486i 0.0872104 + 0.301636i
\(431\) 29.1439 6.19474i 1.40381 0.298390i 0.557104 0.830443i \(-0.311913\pi\)
0.846711 + 0.532053i \(0.178579\pi\)
\(432\) 4.78433 + 2.43774i 0.230186 + 0.117286i
\(433\) 16.4664 + 16.4664i 0.791326 + 0.791326i 0.981710 0.190384i \(-0.0609733\pi\)
−0.190384 + 0.981710i \(0.560973\pi\)
\(434\) 11.7278 14.0016i 0.562951 0.672100i
\(435\) 1.82533 + 3.89209i 0.0875181 + 0.186612i
\(436\) 0.402010 + 1.23726i 0.0192528 + 0.0592539i
\(437\) −19.2337 + 29.6173i −0.920071 + 1.41679i
\(438\) 0.756568 4.77678i 0.0361502 0.228244i
\(439\) −7.28696 4.20713i −0.347788 0.200795i 0.315923 0.948785i \(-0.397686\pi\)
−0.663711 + 0.747990i \(0.731019\pi\)
\(440\) 0.826654 1.18612i 0.0394092 0.0565462i
\(441\) 0.759602 + 0.338197i 0.0361715 + 0.0161046i
\(442\) 0.394834 + 2.49288i 0.0187803 + 0.118574i
\(443\) 9.85243 25.6665i 0.468103 1.21945i −0.472919 0.881106i \(-0.656800\pi\)
0.941022 0.338344i \(-0.109867\pi\)
\(444\) 1.37313 6.46007i 0.0651659 0.306581i
\(445\) 9.57992 38.7858i 0.454132 1.83862i
\(446\) 4.81172 + 4.33250i 0.227842 + 0.205150i
\(447\) 21.7363 + 1.13915i 1.02809 + 0.0538799i
\(448\) −2.06440 2.54933i −0.0975339 0.120444i
\(449\) −0.0507157 + 0.156087i −0.00239342 + 0.00736619i −0.952246 0.305332i \(-0.901233\pi\)
0.949853 + 0.312698i \(0.101233\pi\)
\(450\) −0.243938 + 1.07821i −0.0114994 + 0.0508271i
\(451\) −0.305563 0.0321160i −0.0143884 0.00151228i
\(452\) −0.569162 + 10.8602i −0.0267711 + 0.510823i
\(453\) −1.40205 26.7527i −0.0658740 1.25695i
\(454\) 12.0389 1.26534i 0.565014 0.0593854i
\(455\) 12.1612 19.5575i 0.570126 0.916868i
\(456\) −3.80368 8.54320i −0.178124 0.400072i
\(457\) −22.5848 + 3.57708i −1.05647 + 0.167329i −0.660417 0.750899i \(-0.729621\pi\)
−0.396054 + 0.918227i \(0.629621\pi\)
\(458\) 1.36280 + 3.55021i 0.0636794 + 0.165890i
\(459\) 3.73821 2.15826i 0.174485 0.100739i
\(460\) 1.19601 14.0253i 0.0557642 0.653932i
\(461\) −7.77308 10.6987i −0.362028 0.498289i 0.588684 0.808363i \(-0.299646\pi\)
−0.950712 + 0.310074i \(0.899646\pi\)
\(462\) 2.96527 + 1.92567i 0.137957 + 0.0895903i
\(463\) 12.8893 25.2967i 0.599018 1.17564i −0.370089 0.928996i \(-0.620673\pi\)
0.969107 0.246642i \(-0.0793271\pi\)
\(464\) −1.15327 −0.0535393
\(465\) −9.36519 + 18.5209i −0.434300 + 0.858887i
\(466\) −18.1050 −0.838698
\(467\) 16.3257 32.0409i 0.755461 1.48268i −0.116547 0.993185i \(-0.537183\pi\)
0.872008 0.489491i \(-0.162817\pi\)
\(468\) −0.582174 0.378068i −0.0269110 0.0174762i
\(469\) 20.2564 + 27.8805i 0.935352 + 1.28740i
\(470\) 12.2275 + 14.5073i 0.564011 + 0.669171i
\(471\) 31.8189 18.3706i 1.46614 0.846474i
\(472\) 2.42336 + 6.31306i 0.111544 + 0.290582i
\(473\) 1.85951 0.294518i 0.0855004 0.0135419i
\(474\) 10.7581 + 24.1631i 0.494137 + 1.10985i
\(475\) 22.0271 17.3659i 1.01067 0.796802i
\(476\) −2.62259 + 0.275645i −0.120206 + 0.0126342i
\(477\) 0.00540812 + 0.103193i 0.000247621 + 0.00472489i
\(478\) 1.09164 20.8298i 0.0499305 0.952732i
\(479\) 24.2110 + 2.54468i 1.10623 + 0.116270i 0.639986 0.768386i \(-0.278940\pi\)
0.466244 + 0.884656i \(0.345607\pi\)
\(480\) 2.94238 + 2.28844i 0.134300 + 0.104453i
\(481\) −3.84386 + 11.8302i −0.175265 + 0.539410i
\(482\) 10.7183 + 13.2360i 0.488207 + 0.602885i
\(483\) 34.3767 + 1.80161i 1.56420 + 0.0819760i
\(484\) 7.86392 + 7.08071i 0.357451 + 0.321850i
\(485\) −31.2422 + 18.8658i −1.41864 + 0.856650i
\(486\) −0.476710 + 2.24274i −0.0216240 + 0.101733i
\(487\) 10.8596 28.2902i 0.492094 1.28195i −0.432719 0.901529i \(-0.642446\pi\)
0.924814 0.380421i \(-0.124221\pi\)
\(488\) 0.443707 + 2.80145i 0.0200857 + 0.126816i
\(489\) −6.73972 3.00072i −0.304781 0.135697i
\(490\) 6.89923 + 4.80833i 0.311675 + 0.217218i
\(491\) −33.4367 19.3047i −1.50898 0.871209i −0.999945 0.0104619i \(-0.996670\pi\)
−0.509033 0.860747i \(-0.669997\pi\)
\(492\) 0.123920 0.782403i 0.00558676 0.0352734i
\(493\) −0.504932 + 0.777528i −0.0227410 + 0.0350181i
\(494\) 5.44284 + 16.7513i 0.244885 + 0.753678i
\(495\) 0.300609 + 0.108665i 0.0135114 + 0.00488414i
\(496\) −3.43172 4.38444i −0.154089 0.196867i
\(497\) −22.5969 22.5969i −1.01361 1.01361i
\(498\) −8.57521 4.36929i −0.384264 0.195792i
\(499\) −7.29727 + 1.55108i −0.326671 + 0.0694360i −0.368328 0.929696i \(-0.620070\pi\)
0.0416573 + 0.999132i \(0.486736\pi\)
\(500\) −4.48003 + 10.2435i −0.200353 + 0.458103i
\(501\) 10.5979 18.3560i 0.473478 0.820087i
\(502\) −13.7354 3.68039i −0.613041 0.164264i
\(503\) −25.8795 + 9.93422i −1.15391 + 0.442945i −0.858696 0.512485i \(-0.828725\pi\)
−0.295216 + 0.955431i \(0.595392\pi\)
\(504\) 0.426298 0.586749i 0.0189888 0.0261359i
\(505\) 27.6446 1.99414i 1.23017 0.0887382i
\(506\) −3.98123 0.846237i −0.176987 0.0376198i
\(507\) 4.07077 + 3.29645i 0.180789 + 0.146400i
\(508\) 17.4536 0.914705i 0.774379 0.0405835i
\(509\) −21.8137 24.2265i −0.966874 1.07382i −0.997237 0.0742837i \(-0.976333\pi\)
0.0303629 0.999539i \(-0.490334\pi\)
\(510\) 2.83110 0.981789i 0.125363 0.0434743i
\(511\) −9.05124 2.94092i −0.400403 0.130099i
\(512\) −0.891007 + 0.453990i −0.0393773 + 0.0200637i
\(513\) 23.4097 18.9568i 1.03356 0.836964i
\(514\) 2.27856 2.05163i 0.100503 0.0904933i
\(515\) −10.2170 + 33.6828i −0.450215 + 1.48424i
\(516\) 0.507384 + 4.82744i 0.0223364 + 0.212516i
\(517\) 4.60102 2.98794i 0.202353 0.131409i
\(518\) −12.1331 4.65745i −0.533096 0.204637i
\(519\) −24.7165 17.9576i −1.08494 0.788252i
\(520\) −5.06090 4.86581i −0.221935 0.213380i
\(521\) −12.7402 22.0667i −0.558159 0.966760i −0.997650 0.0685131i \(-0.978175\pi\)
0.439491 0.898247i \(-0.355159\pi\)
\(522\) −0.0659933 0.246290i −0.00288845 0.0107798i
\(523\) −17.4707 2.76709i −0.763942 0.120996i −0.237708 0.971337i \(-0.576396\pi\)
−0.526233 + 0.850340i \(0.676396\pi\)
\(524\) −1.20628 5.67512i −0.0526968 0.247919i
\(525\) −25.3958 10.1310i −1.10836 0.442153i
\(526\) 1.43508i 0.0625724i
\(527\) −4.45845 + 0.394021i −0.194213 + 0.0171638i
\(528\) 0.762141 0.762141i 0.0331679 0.0331679i
\(529\) −15.8140 + 5.13827i −0.687564 + 0.223403i
\(530\) −0.143176 + 1.03525i −0.00621917 + 0.0449684i
\(531\) −1.20953 + 0.878777i −0.0524892 + 0.0381357i
\(532\) −17.7754 + 4.76291i −0.770663 + 0.206498i
\(533\) −0.386153 + 1.44114i −0.0167261 + 0.0624228i
\(534\) 12.1143 27.2091i 0.524236 1.17745i
\(535\) 0.681017 3.54510i 0.0294429 0.153268i
\(536\) 9.59732 4.27300i 0.414541 0.184566i
\(537\) 0.0615286 + 0.0947457i 0.00265516 + 0.00408858i
\(538\) −10.0621 + 12.4256i −0.433807 + 0.535706i
\(539\) 1.62708 1.80705i 0.0700832 0.0778353i
\(540\) −4.66711 + 11.0625i −0.200841 + 0.476056i
\(541\) −3.20500 + 30.4936i −0.137794 + 1.31102i 0.679020 + 0.734120i \(0.262405\pi\)
−0.816814 + 0.576902i \(0.804262\pi\)
\(542\) 1.86594 + 3.66211i 0.0801490 + 0.157301i
\(543\) −16.4386 32.2625i −0.705446 1.38452i
\(544\) −0.0840286 + 0.799479i −0.00360270 + 0.0342774i
\(545\) −2.69475 + 1.09564i −0.115430 + 0.0469321i
\(546\) 11.4884 12.7592i 0.491659 0.546043i
\(547\) 12.5553 15.5045i 0.536826 0.662925i −0.434501 0.900671i \(-0.643075\pi\)
0.971327 + 0.237746i \(0.0764086\pi\)
\(548\) −0.748065 1.15192i −0.0319558 0.0492076i
\(549\) −0.572883 + 0.255064i −0.0244500 + 0.0108859i
\(550\) 2.77837 + 1.65284i 0.118470 + 0.0704773i
\(551\) −2.63147 + 5.91038i −0.112104 + 0.251791i
\(552\) 2.71602 10.1363i 0.115602 0.431431i
\(553\) 50.2751 13.4712i 2.13791 0.572852i
\(554\) −13.0779 + 9.50164i −0.555626 + 0.403686i
\(555\) 14.6286 + 2.02316i 0.620951 + 0.0858782i
\(556\) −14.4595 + 4.69817i −0.613219 + 0.199247i
\(557\) 4.91799 4.91799i 0.208382 0.208382i −0.595198 0.803579i \(-0.702926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(558\) 0.739959 0.983760i 0.0313250 0.0416459i
\(559\) 9.14229i 0.386678i
\(560\) 5.35357 5.01432i 0.226230 0.211894i
\(561\) −0.180145 0.847516i −0.00760573 0.0357821i
\(562\) 6.89480 + 1.09203i 0.290839 + 0.0460644i
\(563\) 11.2636 + 42.0364i 0.474705 + 1.77162i 0.622517 + 0.782607i \(0.286110\pi\)
−0.147812 + 0.989015i \(0.547223\pi\)
\(564\) 7.07224 + 12.2495i 0.297795 + 0.515796i
\(565\) −24.3129 + 0.477819i −1.02285 + 0.0201020i
\(566\) 6.26484 + 4.55167i 0.263331 + 0.191321i
\(567\) −25.3814 9.74302i −1.06592 0.409169i
\(568\) −8.17018 + 5.30578i −0.342813 + 0.222626i
\(569\) 3.02462 + 28.7773i 0.126799 + 1.20641i 0.854107 + 0.520097i \(0.174104\pi\)
−0.727308 + 0.686311i \(0.759229\pi\)
\(570\) 18.4417 9.85768i 0.772439 0.412893i
\(571\) 4.73109 4.25989i 0.197990 0.178271i −0.564172 0.825657i \(-0.690805\pi\)
0.762162 + 0.647386i \(0.224138\pi\)
\(572\) −1.57763 + 1.27754i −0.0659641 + 0.0534166i
\(573\) −1.33834 + 0.681921i −0.0559101 + 0.0284876i
\(574\) −1.48253 0.481702i −0.0618795 0.0201059i
\(575\) 31.4726 + 0.411027i 1.31250 + 0.0171410i
\(576\) −0.147939 0.164303i −0.00616412 0.00684595i
\(577\) 8.36369 0.438322i 0.348185 0.0182476i 0.122558 0.992461i \(-0.460890\pi\)
0.225627 + 0.974214i \(0.427557\pi\)
\(578\) −12.7093 10.2918i −0.528636 0.428081i
\(579\) 31.4560 + 6.68618i 1.30727 + 0.277868i
\(580\) −0.185539 2.57211i −0.00770409 0.106801i
\(581\) −11.1319 + 15.3217i −0.461828 + 0.635652i
\(582\) −25.4012 + 9.75062i −1.05291 + 0.404176i
\(583\) 0.291898 + 0.0782139i 0.0120892 + 0.00323929i
\(584\) −1.45060 + 2.51252i −0.0600264 + 0.103969i
\(585\) 0.749534 1.35923i 0.0309894 0.0561972i
\(586\) 2.55879 0.543887i 0.105703 0.0224678i
\(587\) −17.0665 8.69580i −0.704409 0.358914i 0.0648119 0.997898i \(-0.479355\pi\)
−0.769221 + 0.638983i \(0.779355\pi\)
\(588\) 4.43309 + 4.43309i 0.182818 + 0.182818i
\(589\) −30.3000 + 7.58299i −1.24849 + 0.312452i
\(590\) −13.6900 + 6.42040i −0.563607 + 0.264324i
\(591\) 14.2135 + 43.7445i 0.584664 + 1.79941i
\(592\) −2.15777 + 3.32267i −0.0886837 + 0.136561i
\(593\) −4.85482 + 30.6521i −0.199364 + 1.25873i 0.661519 + 0.749928i \(0.269912\pi\)
−0.860883 + 0.508803i \(0.830088\pi\)
\(594\) 3.00666 + 1.73590i 0.123365 + 0.0712246i
\(595\) −1.03669 5.80474i −0.0425001 0.237971i
\(596\) −11.9282 5.31076i −0.488596 0.217537i
\(597\) 5.29264 + 33.4164i 0.216613 + 1.36764i
\(598\) −7.08302 + 18.4519i −0.289646 + 0.754554i
\(599\) −0.786624 + 3.70078i −0.0321406 + 0.151210i −0.991292 0.131685i \(-0.957961\pi\)
0.959151 + 0.282894i \(0.0912946\pi\)
\(600\) −4.63048 + 6.93047i −0.189039 + 0.282935i
\(601\) 11.8671 + 10.6852i 0.484068 + 0.435857i 0.874682 0.484698i \(-0.161071\pi\)
−0.390614 + 0.920555i \(0.627737\pi\)
\(602\) 9.53878 + 0.499906i 0.388772 + 0.0203747i
\(603\) 1.46172 + 1.80507i 0.0595257 + 0.0735081i
\(604\) −4.96602 + 15.2838i −0.202064 + 0.621891i
\(605\) −14.5268 + 18.6778i −0.590597 + 0.759362i
\(606\) 20.5496 + 2.15985i 0.834771 + 0.0877380i
\(607\) −1.35524 + 25.8595i −0.0550075 + 1.04960i 0.822110 + 0.569329i \(0.192797\pi\)
−0.877117 + 0.480276i \(0.840536\pi\)
\(608\) 0.293598 + 5.60219i 0.0119070 + 0.227199i
\(609\) 6.27200 0.659214i 0.254154 0.0267127i
\(610\) −6.17663 + 1.44029i −0.250084 + 0.0583155i
\(611\) −10.8356 24.3371i −0.438361 0.984575i
\(612\) −0.175543 + 0.0278033i −0.00709592 + 0.00112388i
\(613\) −3.28620 8.56085i −0.132728 0.345769i 0.851069 0.525054i \(-0.175955\pi\)
−0.983797 + 0.179285i \(0.942622\pi\)
\(614\) 11.5665 6.67791i 0.466785 0.269498i
\(615\) 1.76491 + 0.150503i 0.0711680 + 0.00606886i
\(616\) −1.24668 1.71591i −0.0502302 0.0691359i
\(617\) −20.1996 13.1178i −0.813207 0.528102i 0.0697460 0.997565i \(-0.477781\pi\)
−0.882953 + 0.469462i \(0.844448\pi\)
\(618\) −11.9130 + 23.3806i −0.479211 + 0.940504i
\(619\) −9.30966 −0.374187 −0.187094 0.982342i \(-0.559907\pi\)
−0.187094 + 0.982342i \(0.559907\pi\)
\(620\) 9.22639 8.35905i 0.370541 0.335707i
\(621\) 33.8018 1.35642
\(622\) −1.35518 + 2.65968i −0.0543377 + 0.106644i
\(623\) −49.1543 31.9211i −1.96932 1.27889i
\(624\) −3.07642 4.23433i −0.123155 0.169509i
\(625\) −23.5666 8.34372i −0.942662 0.333749i
\(626\) 17.5666 10.1421i 0.702102 0.405359i
\(627\) −2.16687 5.64489i −0.0865365 0.225435i
\(628\) −21.7689 + 3.44786i −0.868674 + 0.137584i
\(629\) 1.29539 + 2.90950i 0.0516507 + 0.116009i
\(630\) 1.37719 + 0.856364i 0.0548687 + 0.0341184i
\(631\) −7.08870 + 0.745052i −0.282197 + 0.0296600i −0.244569 0.969632i \(-0.578647\pi\)
−0.0376272 + 0.999292i \(0.511980\pi\)
\(632\) −0.830398 15.8449i −0.0330315 0.630278i
\(633\) −1.32605 + 25.3025i −0.0527056 + 1.00568i
\(634\) 12.3308 + 1.29602i 0.489719 + 0.0514715i
\(635\) 4.84799 + 38.7792i 0.192387 + 1.53890i
\(636\) −0.240765 + 0.740999i −0.00954696 + 0.0293825i
\(637\) −7.43097 9.17649i −0.294426 0.363586i
\(638\) −0.744645 0.0390252i −0.0294808 0.00154502i
\(639\) −1.60061 1.44120i −0.0633192 0.0570128i
\(640\) −1.15587 1.91415i −0.0456897 0.0756634i
\(641\) 4.39333 20.6690i 0.173526 0.816376i −0.802144 0.597131i \(-0.796307\pi\)
0.975670 0.219245i \(-0.0703594\pi\)
\(642\) 0.964447 2.51247i 0.0380637 0.0991593i
\(643\) −0.443643 2.80105i −0.0174956 0.110463i 0.977395 0.211421i \(-0.0678091\pi\)
−0.994891 + 0.100958i \(0.967809\pi\)
\(644\) −18.8648 8.39917i −0.743379 0.330974i
\(645\) −10.6849 + 1.90825i −0.420717 + 0.0751372i
\(646\) 3.90550 + 2.25484i 0.153660 + 0.0887156i
\(647\) −4.60716 + 29.0885i −0.181126 + 1.14359i 0.714782 + 0.699347i \(0.246526\pi\)
−0.895908 + 0.444239i \(0.853474\pi\)
\(648\) −4.51388 + 6.95077i −0.177322 + 0.273052i
\(649\) 1.35109 + 4.15822i 0.0530349 + 0.163225i
\(650\) 10.0379 12.0700i 0.393718 0.473425i
\(651\) 21.1694 + 21.8829i 0.829693 + 0.857659i
\(652\) 3.12939 + 3.12939i 0.122556 + 0.122556i
\(653\) 17.6815 + 9.00918i 0.691931 + 0.352557i 0.764336 0.644819i \(-0.223067\pi\)
−0.0724042 + 0.997375i \(0.523067\pi\)
\(654\) −2.12127 + 0.450889i −0.0829481 + 0.0176312i
\(655\) 12.4630 3.60336i 0.486970 0.140795i
\(656\) −0.237598 + 0.411532i −0.00927666 + 0.0160676i
\(657\) −0.619575 0.166015i −0.0241719 0.00647685i
\(658\) 25.9851 9.97474i 1.01300 0.388856i
\(659\) −8.76949 + 12.0702i −0.341611 + 0.470187i −0.944911 0.327327i \(-0.893852\pi\)
0.603300 + 0.797514i \(0.293852\pi\)
\(660\) 1.82240 + 1.57717i 0.0709367 + 0.0613912i
\(661\) −12.6456 2.68790i −0.491856 0.104547i −0.0446949 0.999001i \(-0.514232\pi\)
−0.447161 + 0.894453i \(0.647565\pi\)
\(662\) 14.4493 + 11.7008i 0.561589 + 0.454766i
\(663\) −4.20169 + 0.220201i −0.163180 + 0.00855190i
\(664\) 3.86311 + 4.29042i 0.149918 + 0.166501i
\(665\) −13.4823 38.8778i −0.522822 1.50762i
\(666\) −0.833055 0.270676i −0.0322802 0.0104885i
\(667\) −6.46863 + 3.29593i −0.250466 + 0.127619i
\(668\) −9.88130 + 8.00171i −0.382319 + 0.309596i
\(669\) −8.02117 + 7.22230i −0.310116 + 0.279230i
\(670\) 11.0740 + 20.7172i 0.427825 + 0.800375i
\(671\) 0.191695 + 1.82386i 0.00740032 + 0.0704093i
\(672\) 4.58618 2.97830i 0.176916 0.114891i
\(673\) 9.77906 + 3.75383i 0.376955 + 0.144699i 0.539466 0.842007i \(-0.318626\pi\)
−0.162511 + 0.986707i \(0.551959\pi\)
\(674\) −1.44059 1.04665i −0.0554895 0.0403155i
\(675\) −25.4233 8.62919i −0.978545 0.332138i
\(676\) −1.57111 2.72125i −0.0604274 0.104663i
\(677\) −4.45787 16.6370i −0.171330 0.639411i −0.997148 0.0754746i \(-0.975953\pi\)
0.825818 0.563937i \(-0.190714\pi\)
\(678\) −17.9057 2.83599i −0.687666 0.108916i
\(679\) 11.1319 + 52.3713i 0.427202 + 2.00983i
\(680\) −1.79658 0.0587860i −0.0688955 0.00225434i
\(681\) 20.1795i 0.773280i
\(682\) −2.06743 2.94707i −0.0791661 0.112849i
\(683\) 6.90787 6.90787i 0.264322 0.264322i −0.562485 0.826807i \(-0.690155\pi\)
0.826807 + 0.562485i \(0.190155\pi\)
\(684\) −1.17959 + 0.383272i −0.0451028 + 0.0146548i
\(685\) 2.44875 1.85371i 0.0935618 0.0708267i
\(686\) −8.59634 + 6.24561i −0.328210 + 0.238458i
\(687\) −6.12327 + 1.64072i −0.233617 + 0.0625976i
\(688\) 0.753636 2.81261i 0.0287321 0.107230i
\(689\) 0.596866 1.34058i 0.0227388 0.0510722i
\(690\) 23.0437 + 4.42673i 0.877260 + 0.168523i
\(691\) −7.96733 + 3.54728i −0.303091 + 0.134945i −0.552647 0.833416i \(-0.686382\pi\)
0.249555 + 0.968361i \(0.419716\pi\)
\(692\) 9.98163 + 15.3704i 0.379445 + 0.584294i
\(693\) 0.295107 0.364427i 0.0112102 0.0138434i
\(694\) −2.45299 + 2.72432i −0.0931141 + 0.103414i
\(695\) −12.8045 31.4928i −0.485701 1.19459i
\(696\) 0.200957 1.91198i 0.00761726 0.0724734i
\(697\) 0.173425 + 0.340367i 0.00656896 + 0.0128923i
\(698\) 7.00718 + 13.7524i 0.265226 + 0.520535i
\(699\) 3.15479 30.0158i 0.119325 1.13530i
\(700\) 12.0446 + 11.1332i 0.455243 + 0.420796i
\(701\) 5.75882 6.39582i 0.217508 0.241567i −0.624510 0.781017i \(-0.714701\pi\)
0.842018 + 0.539450i \(0.181368\pi\)
\(702\) 10.6097 13.1018i 0.400436 0.494497i
\(703\) 12.1048 + 18.6398i 0.456542 + 0.703013i
\(704\) −0.590668 + 0.262982i −0.0222616 + 0.00991152i
\(705\) −26.1819 + 17.7437i −0.986067 + 0.668267i
\(706\) 9.32383 20.9417i 0.350907 0.788150i
\(707\) 10.5238 39.2753i 0.395787 1.47710i
\(708\) −10.8885 + 2.91757i −0.409216 + 0.109649i
\(709\) 19.0570 13.8457i 0.715702 0.519988i −0.169306 0.985563i \(-0.554153\pi\)
0.885008 + 0.465576i \(0.154153\pi\)
\(710\) −13.1478 17.3681i −0.493427 0.651815i
\(711\) 3.33629 1.08403i 0.125121 0.0406542i
\(712\) −12.6337 + 12.6337i −0.473469 + 0.473469i
\(713\) −31.7786 14.7845i −1.19012 0.553685i
\(714\) 4.39595i 0.164514i
\(715\) −3.10307 3.31302i −0.116048 0.123900i
\(716\) −0.0140900 0.0662881i −0.000526567 0.00247730i
\(717\) 34.3429 + 5.43938i 1.28256 + 0.203137i
\(718\) −8.34887 31.1584i −0.311577 1.16282i
\(719\) 2.65946 + 4.60632i 0.0991811 + 0.171787i 0.911346 0.411641i \(-0.135044\pi\)
−0.812165 + 0.583428i \(0.801711\pi\)
\(720\) 0.342640 0.356377i 0.0127694 0.0132814i
\(721\) 41.7751 + 30.3514i 1.55579 + 1.13034i
\(722\) 11.6424 + 4.46911i 0.433287 + 0.166323i
\(723\) −23.8114 + 15.4633i −0.885554 + 0.575085i
\(724\) 2.27046 + 21.6020i 0.0843811 + 0.802832i
\(725\) 5.70666 0.827606i 0.211940 0.0307365i
\(726\) −13.1092 + 11.8036i −0.486528 + 0.438072i
\(727\) 16.6087 13.4495i 0.615983 0.498813i −0.269798 0.962917i \(-0.586957\pi\)
0.885781 + 0.464104i \(0.153624\pi\)
\(728\) −9.17684 + 4.67584i −0.340116 + 0.173298i
\(729\) −27.2817 8.86438i −1.01044 0.328310i
\(730\) −5.83698 2.83103i −0.216036 0.104781i
\(731\) −1.56628 1.73953i −0.0579309 0.0643388i
\(732\) −4.72177 + 0.247458i −0.174522 + 0.00914630i
\(733\) 21.1588 + 17.1340i 0.781517 + 0.632860i 0.934740 0.355332i \(-0.115632\pi\)
−0.153223 + 0.988192i \(0.548965\pi\)
\(734\) −35.3855 7.52141i −1.30610 0.277620i
\(735\) −9.17380 + 10.6002i −0.338381 + 0.390994i
\(736\) −3.70014 + 5.09281i −0.136389 + 0.187724i
\(737\) 6.34139 2.43423i 0.233588 0.0896661i
\(738\) −0.101482 0.0271920i −0.00373560 0.00100095i
\(739\) −15.3599 + 26.6041i −0.565023 + 0.978648i 0.432025 + 0.901862i \(0.357799\pi\)
−0.997048 + 0.0767865i \(0.975534\pi\)
\(740\) −7.75760 4.27786i −0.285175 0.157257i
\(741\) −28.7200 + 6.10463i −1.05506 + 0.224259i
\(742\) 1.36609 + 0.696056i 0.0501506 + 0.0255530i
\(743\) −23.3224 23.3224i −0.855617 0.855617i 0.135201 0.990818i \(-0.456832\pi\)
−0.990818 + 0.135201i \(0.956832\pi\)
\(744\) 7.86682 4.92537i 0.288412 0.180573i
\(745\) 9.92543 27.4574i 0.363640 1.00596i
\(746\) −0.624188 1.92105i −0.0228531 0.0703347i
\(747\) −0.695196 + 1.07051i −0.0254359 + 0.0391678i
\(748\) −0.0813090 + 0.513365i −0.00297295 + 0.0187705i
\(749\) −4.58633 2.64792i −0.167581 0.0967529i
\(750\) −16.2018 9.21226i −0.591606 0.336384i
\(751\) 29.4413 + 13.1081i 1.07433 + 0.478322i 0.866158 0.499771i \(-0.166582\pi\)
0.208171 + 0.978093i \(0.433249\pi\)
\(752\) −1.32734 8.38049i −0.0484031 0.305605i
\(753\) 8.49501 22.1302i 0.309575 0.806471i
\(754\) −0.752835 + 3.54181i −0.0274166 + 0.128985i
\(755\) −34.8861 8.61670i −1.26963 0.313594i
\(756\) 13.0899 + 11.7862i 0.476075 + 0.428660i
\(757\) −10.8434 0.568278i −0.394110 0.0206544i −0.145748 0.989322i \(-0.546559\pi\)
−0.248362 + 0.968667i \(0.579892\pi\)
\(758\) 8.34643 + 10.3070i 0.303156 + 0.374366i
\(759\) 2.09668 6.45293i 0.0761048 0.234226i
\(760\) −12.4472 + 1.55609i −0.451507 + 0.0564453i
\(761\) 50.7601 + 5.33510i 1.84005 + 0.193397i 0.959720 0.280959i \(-0.0906525\pi\)
0.880333 + 0.474356i \(0.157319\pi\)
\(762\) −1.52482 + 29.0953i −0.0552384 + 1.05401i
\(763\) 0.223345 + 4.26169i 0.00808565 + 0.154283i
\(764\) 0.896116 0.0941856i 0.0324203 0.00340752i
\(765\) −0.0902506 0.387037i −0.00326302 0.0139933i
\(766\) 9.53196 + 21.4091i 0.344404 + 0.773543i
\(767\) 20.9700 3.32132i 0.757181 0.119926i
\(768\) −0.597401 1.55628i −0.0215569 0.0561576i
\(769\) 3.89241 2.24728i 0.140364 0.0810391i −0.428174 0.903697i \(-0.640843\pi\)
0.568537 + 0.822657i \(0.307509\pi\)
\(770\) 3.62638 3.05649i 0.130686 0.110148i
\(771\) 3.00430 + 4.13506i 0.108197 + 0.148921i
\(772\) −16.1791 10.5068i −0.582297 0.378148i
\(773\) −9.79687 + 19.2274i −0.352369 + 0.691563i −0.997359 0.0726281i \(-0.976861\pi\)
0.644990 + 0.764191i \(0.276861\pi\)
\(774\) 0.643780 0.0231402
\(775\) 20.1273 + 19.2326i 0.722994 + 0.690854i
\(776\) 16.3217 0.585915
\(777\) 9.83564 19.3035i 0.352852 0.692510i
\(778\) 8.10161 + 5.26125i 0.290457 + 0.188625i
\(779\) 1.56692 + 2.15667i 0.0561406 + 0.0772709i
\(780\) 8.94877 7.54247i 0.320417 0.270064i
\(781\) −5.45487 + 3.14937i −0.195191 + 0.112693i
\(782\) 1.81352 + 4.72438i 0.0648513 + 0.168943i
\(783\) 6.11634 0.968733i 0.218580 0.0346197i
\(784\) −1.52967 3.43569i −0.0546311 0.122703i
\(785\) −11.1919 47.9959i −0.399455 1.71305i
\(786\) 9.61883 1.01098i 0.343092 0.0360604i
\(787\) −0.825123 15.7443i −0.0294125 0.561223i −0.973100 0.230384i \(-0.926002\pi\)
0.943687 0.330839i \(-0.107332\pi\)
\(788\) 1.44404 27.5540i 0.0514419 0.981571i
\(789\) −2.37918 0.250062i −0.0847010 0.00890244i
\(790\) 35.2049 4.40116i 1.25254 0.156586i
\(791\) −11.0240 + 33.9285i −0.391970 + 1.20636i
\(792\) −0.0899615 0.111093i −0.00319664 0.00394753i
\(793\) 8.89319 + 0.466072i 0.315806 + 0.0165507i
\(794\) 24.1073 + 21.7063i 0.855534 + 0.770327i
\(795\) −1.69137 0.417760i −0.0599865 0.0148164i
\(796\) 4.21970 19.8521i 0.149563 0.703640i
\(797\) −13.5452 + 35.2864i −0.479795 + 1.24991i 0.453647 + 0.891181i \(0.350123\pi\)
−0.933442 + 0.358728i \(0.883211\pi\)
\(798\) −4.79895 30.2994i −0.169881 1.07259i
\(799\) −6.23121 2.77431i −0.220444 0.0981482i
\(800\) 4.08312 2.88585i 0.144360 0.102030i
\(801\) −3.42097 1.97510i −0.120874 0.0697866i
\(802\) −1.17120 + 7.39465i −0.0413564 + 0.261114i
\(803\) −1.02165 + 1.57320i −0.0360531 + 0.0555169i
\(804\) 5.41177 + 16.6557i 0.190858 + 0.587402i
\(805\) 15.6974 43.4250i 0.553262 1.53053i
\(806\) −15.7052 + 7.67707i −0.553192 + 0.270413i
\(807\) −18.8468 18.8468i −0.663439 0.663439i
\(808\) −11.0442 5.62729i −0.388533 0.197967i
\(809\) −8.64196 + 1.83691i −0.303835 + 0.0645821i −0.357306 0.933987i \(-0.616305\pi\)
0.0534712 + 0.998569i \(0.482971\pi\)
\(810\) −16.2283 8.94895i −0.570205 0.314434i
\(811\) 11.2196 19.4328i 0.393972 0.682379i −0.598998 0.800751i \(-0.704434\pi\)
0.992969 + 0.118372i \(0.0377674\pi\)
\(812\) −3.65425 0.979154i −0.128239 0.0343616i
\(813\) −6.39646 + 2.45537i −0.224334 + 0.0861136i
\(814\) −1.50566 + 2.07237i −0.0527735 + 0.0726364i
\(815\) −6.47594 + 7.48285i −0.226842 + 0.262113i
\(816\) −1.31079 0.278618i −0.0458870 0.00975357i
\(817\) −12.6947 10.2799i −0.444130 0.359650i
\(818\) 28.6081 1.49929i 1.00026 0.0524213i
\(819\) −1.52368 1.69222i −0.0532418 0.0591311i
\(820\) −0.956054 0.463701i −0.0333869 0.0161932i
\(821\) 37.2461 + 12.1020i 1.29990 + 0.422363i 0.875546 0.483134i \(-0.160502\pi\)
0.424352 + 0.905497i \(0.360502\pi\)
\(822\) 2.04009 1.03948i 0.0711562 0.0362559i
\(823\) −23.0068 + 18.6306i −0.801968 + 0.649421i −0.940064 0.340998i \(-0.889235\pi\)
0.138096 + 0.990419i \(0.455902\pi\)
\(824\) 11.6980 10.5329i 0.407518 0.366931i
\(825\) −3.22433 + 4.31818i −0.112257 + 0.150340i
\(826\) 2.31871 + 22.0610i 0.0806781 + 0.767601i
\(827\) 30.1208 19.5607i 1.04740 0.680192i 0.0983005 0.995157i \(-0.468659\pi\)
0.949103 + 0.314965i \(0.101993\pi\)
\(828\) −1.29934 0.498771i −0.0451552 0.0173335i
\(829\) 34.6615 + 25.1830i 1.20384 + 0.874643i 0.994657 0.103233i \(-0.0329188\pi\)
0.209185 + 0.977876i \(0.432919\pi\)
\(830\) −8.94731 + 9.30604i −0.310566 + 0.323017i
\(831\) −13.4737 23.3372i −0.467398 0.809557i
\(832\) 0.812617 + 3.03273i 0.0281724 + 0.105141i
\(833\) −2.98605 0.472944i −0.103460 0.0163865i
\(834\) −5.26942 24.7907i −0.182465 0.858430i
\(835\) −19.4357 20.7507i −0.672601 0.718106i
\(836\) 3.62716i 0.125448i
\(837\) 21.8829 + 20.3701i 0.756384 + 0.704095i
\(838\) −24.1055 + 24.1055i −0.832710 + 0.832710i
\(839\) −11.1945 + 3.63732i −0.386477 + 0.125574i −0.495810 0.868431i \(-0.665129\pi\)
0.109332 + 0.994005i \(0.465129\pi\)
\(840\) 7.38026 + 9.74929i 0.254643 + 0.336383i
\(841\) 22.3855 16.2640i 0.771913 0.560827i
\(842\) −27.8706 + 7.46790i −0.960484 + 0.257361i
\(843\) −3.01186 + 11.2404i −0.103734 + 0.387141i
\(844\) 6.18208 13.8852i 0.212796 0.477948i
\(845\) 5.81636 3.94180i 0.200089 0.135602i
\(846\) 1.71377 0.763018i 0.0589205 0.0262331i
\(847\) 18.9059 + 29.1125i 0.649615 + 1.00032i
\(848\) 0.294135 0.363226i 0.0101006 0.0124732i
\(849\) −8.63775 + 9.59319i −0.296447 + 0.329238i
\(850\) −0.157925 4.01631i −0.00541680 0.137758i
\(851\) −2.60694 + 24.8033i −0.0893646 + 0.850247i
\(852\) −7.37266 14.4697i −0.252583 0.495723i
\(853\) 17.0518 + 33.4661i 0.583843 + 1.14586i 0.974304 + 0.225236i \(0.0723155\pi\)
−0.390461 + 0.920619i \(0.627685\pi\)
\(854\) −0.972571 + 9.25339i −0.0332807 + 0.316645i
\(855\) −1.04458 2.56915i −0.0357237 0.0878630i
\(856\) −1.08025 + 1.19974i −0.0369221 + 0.0410061i
\(857\) 28.8391 35.6133i 0.985125 1.21653i 0.00885693 0.999961i \(-0.497181\pi\)
0.976268 0.216567i \(-0.0694860\pi\)
\(858\) −1.84310 2.83812i −0.0629224 0.0968919i
\(859\) 5.04028 2.24408i 0.171972 0.0765670i −0.318945 0.947773i \(-0.603328\pi\)
0.490917 + 0.871206i \(0.336662\pi\)
\(860\) 6.39413 + 1.22832i 0.218038 + 0.0418854i
\(861\) 1.05693 2.37391i 0.0360201 0.0809025i
\(862\) 7.71152 28.7798i 0.262656 0.980244i
\(863\) 37.0581 9.92969i 1.26147 0.338011i 0.434715 0.900568i \(-0.356849\pi\)
0.826758 + 0.562558i \(0.190183\pi\)
\(864\) 4.34408 3.15616i 0.147789 0.107375i
\(865\) −32.6743 + 24.7346i −1.11096 + 0.841000i
\(866\) 22.1473 7.19609i 0.752595 0.244533i
\(867\) 19.2770 19.2770i 0.654682 0.654682i
\(868\) −7.15125 16.8061i −0.242729 0.570437i
\(869\) 10.2589i 0.348008i
\(870\) 4.29656 + 0.140589i 0.145667 + 0.00476640i
\(871\) −6.85785 32.2637i −0.232369 1.09321i
\(872\) 1.28491 + 0.203510i 0.0435127 + 0.00689173i
\(873\) 0.933972 + 3.48563i 0.0316102 + 0.117971i
\(874\) 17.6573 + 30.5833i 0.597266 + 1.03449i
\(875\) −22.8924 + 28.6539i −0.773904 + 0.968677i
\(876\) −3.91267 2.84272i −0.132197 0.0960467i
\(877\) 34.2430 + 13.1447i 1.15630 + 0.443863i 0.859530 0.511084i \(-0.170756\pi\)
0.296773 + 0.954948i \(0.404089\pi\)
\(878\) −7.05679 + 4.58274i −0.238155 + 0.154660i
\(879\) 0.455829 + 4.33692i 0.0153747 + 0.146281i
\(880\) −0.681550 1.27504i −0.0229750 0.0429817i
\(881\) 3.38108 3.04433i 0.113911 0.102566i −0.610207 0.792242i \(-0.708914\pi\)
0.724118 + 0.689676i \(0.242247\pi\)
\(882\) 0.646188 0.523272i 0.0217583 0.0176195i
\(883\) −2.48055 + 1.26390i −0.0834772 + 0.0425337i −0.495231 0.868762i \(-0.664916\pi\)
0.411754 + 0.911295i \(0.364916\pi\)
\(884\) 2.40043 + 0.779946i 0.0807351 + 0.0262324i
\(885\) −8.25874 23.8150i −0.277614 0.800533i
\(886\) −18.3961 20.4309i −0.618028 0.686390i
\(887\) 27.5627 1.44450i 0.925465 0.0485015i 0.416354 0.909203i \(-0.363308\pi\)
0.509111 + 0.860701i \(0.329974\pi\)
\(888\) −5.13258 4.15628i −0.172238 0.139476i
\(889\) 56.0801 + 11.9202i 1.88086 + 0.399790i
\(890\) −30.2092 26.1442i −1.01261 0.876354i
\(891\) −3.14973 + 4.33523i −0.105520 + 0.145236i
\(892\) 6.04476 2.32037i 0.202393 0.0776916i
\(893\) −45.9777 12.3197i −1.53858 0.412262i
\(894\) 10.8830 18.8500i 0.363983 0.630438i
\(895\) 0.145574 0.0420890i 0.00486599 0.00140688i
\(896\) −3.20869 + 0.682028i −0.107195 + 0.0227849i
\(897\) −29.3567 14.9580i −0.980192 0.499433i
\(898\) 0.116050 + 0.116050i 0.00387264 + 0.00387264i
\(899\) −6.17396 1.76447i −0.205913 0.0588484i
\(900\) 0.849943 + 0.706846i 0.0283314 + 0.0235615i
\(901\) −0.116105 0.357333i −0.00386801 0.0119045i
\(902\) −0.167338 + 0.257678i −0.00557176 + 0.00857975i
\(903\) −2.49091 + 15.7270i −0.0828923 + 0.523361i
\(904\) 9.41816 + 5.43758i 0.313243 + 0.180851i
\(905\) −47.8131 + 8.53910i −1.58936 + 0.283849i
\(906\) −24.4733 10.8962i −0.813072 0.362003i
\(907\) −3.97574 25.1018i −0.132012 0.833493i −0.961467 0.274919i \(-0.911349\pi\)
0.829455 0.558573i \(-0.188651\pi\)
\(908\) 4.33813 11.3012i 0.143966 0.375044i
\(909\) 0.569775 2.68058i 0.0188982 0.0889092i
\(910\) −11.9048 19.7146i −0.394639 0.653533i
\(911\) 0.505630 + 0.455271i 0.0167523 + 0.0150838i 0.677464 0.735556i \(-0.263079\pi\)
−0.660712 + 0.750640i \(0.729746\pi\)
\(912\) −9.33889 0.489430i −0.309241 0.0162067i
\(913\) 2.34915 + 2.90096i 0.0777457 + 0.0960079i
\(914\) −7.06607 + 21.7471i −0.233725 + 0.719331i
\(915\) −1.31154 10.4910i −0.0433582 0.346823i
\(916\) 3.78196 + 0.397500i 0.124959 + 0.0131338i
\(917\) 0.996079 19.0063i 0.0328934 0.627644i
\(918\) −0.225909 4.31060i −0.00745610 0.142271i
\(919\) 32.4352 3.40908i 1.06994 0.112455i 0.446852 0.894608i \(-0.352545\pi\)
0.623087 + 0.782153i \(0.285878\pi\)
\(920\) −11.9536 7.43300i −0.394100 0.245059i
\(921\) 9.05568 + 20.3394i 0.298395 + 0.670205i
\(922\) −13.0615 + 2.06874i −0.430159 + 0.0681305i
\(923\) 10.9612 + 28.5550i 0.360793 + 0.939898i
\(924\) 3.06199 1.76784i 0.100732 0.0581577i
\(925\) 8.29274 17.9898i 0.272664 0.591501i
\(926\) −16.6879 22.9689i −0.548399 0.754806i
\(927\) 2.91877 + 1.89547i 0.0958650 + 0.0622555i
\(928\) −0.523574 + 1.02757i −0.0171872 + 0.0337317i
\(929\) −26.1037 −0.856436 −0.428218 0.903675i \(-0.640858\pi\)
−0.428218 + 0.903675i \(0.640858\pi\)
\(930\) 12.2505 + 16.7528i 0.401711 + 0.549345i
\(931\) −21.0978 −0.691453
\(932\) −8.21950 + 16.1317i −0.269239 + 0.528411i
\(933\) −4.17328 2.71016i −0.136627 0.0887267i
\(934\) −21.1370 29.0925i −0.691623 0.951937i
\(935\) −1.15802 0.0987507i −0.0378715 0.00322949i
\(936\) −0.601162 + 0.347081i −0.0196496 + 0.0113447i
\(937\) −13.1987 34.3837i −0.431182 1.12327i −0.961339 0.275367i \(-0.911201\pi\)
0.530157 0.847899i \(-0.322133\pi\)
\(938\) 34.0379 5.39107i 1.11138 0.176025i
\(939\) 13.7533 + 30.8904i 0.448822 + 1.00807i
\(940\) 18.4772 4.30859i 0.602661 0.140531i
\(941\) −27.5177 + 2.89222i −0.897050 + 0.0942838i −0.541820 0.840495i \(-0.682264\pi\)
−0.355231 + 0.934779i \(0.615598\pi\)
\(942\) −1.92289 36.6909i −0.0626511 1.19545i
\(943\) −0.156557 + 2.98729i −0.00509821 + 0.0972796i
\(944\) 6.72516 + 0.706843i 0.218885 + 0.0230058i
\(945\) −24.1805 + 31.0902i −0.786593 + 1.01137i
\(946\) 0.581783 1.79054i 0.0189154 0.0582156i
\(947\) −0.853634 1.05415i −0.0277394 0.0342553i 0.763088 0.646295i \(-0.223683\pi\)
−0.790827 + 0.612040i \(0.790349\pi\)
\(948\) 26.4136 + 1.38428i 0.857874 + 0.0449593i
\(949\) 6.76926 + 6.09507i 0.219740 + 0.197854i
\(950\) −5.47301 27.5103i −0.177568 0.892551i
\(951\) −4.29727 + 20.2171i −0.139349 + 0.655584i
\(952\) −0.945029 + 2.46188i −0.0306286 + 0.0797901i
\(953\) −1.40778 8.88836i −0.0456024 0.287922i 0.954339 0.298725i \(-0.0965613\pi\)
−0.999942 + 0.0108027i \(0.996561\pi\)
\(954\) 0.0944009 + 0.0420300i 0.00305634 + 0.00136077i
\(955\) 0.354227 + 1.98343i 0.0114625 + 0.0641823i
\(956\) −18.0639 10.4292i −0.584227 0.337304i
\(957\) 0.194453 1.22773i 0.00628577 0.0396868i
\(958\) 13.2589 20.4169i 0.428376 0.659641i
\(959\) −1.39231 4.28509i −0.0449601 0.138373i
\(960\) 3.37483 1.58274i 0.108922 0.0510829i
\(961\) −11.6634 28.7222i −0.376239 0.926523i
\(962\) 8.79570 + 8.79570i 0.283585 + 0.283585i
\(963\) −0.318027 0.162043i −0.0102483 0.00522177i
\(964\) 16.6594 3.54107i 0.536564 0.114050i
\(965\) 20.8301 37.7741i 0.670546 1.21599i
\(966\) 17.2119 29.8120i 0.553785 0.959184i
\(967\) −26.7904 7.17846i −0.861520 0.230844i −0.199103 0.979979i \(-0.563803\pi\)
−0.662417 + 0.749135i \(0.730469\pi\)
\(968\) 9.87910 3.79223i 0.317526 0.121887i
\(969\) −4.41878 + 6.08193i −0.141952 + 0.195380i
\(970\) 2.62585 + 36.4019i 0.0843109 + 1.16879i
\(971\) 51.7983 + 11.0101i 1.66229 + 0.353330i 0.940765 0.339060i \(-0.110109\pi\)
0.721523 + 0.692390i \(0.243442\pi\)
\(972\) 1.78188 + 1.44294i 0.0571538 + 0.0462822i
\(973\) −49.8051 + 2.61018i −1.59668 + 0.0836784i
\(974\) −20.2766 22.5194i −0.649703 0.721569i
\(975\) 18.2615 + 18.7448i 0.584835 + 0.600312i
\(976\) 2.69755 + 0.876488i 0.0863466 + 0.0280557i
\(977\) −17.3706 + 8.85078i −0.555736 + 0.283161i −0.709217 0.704990i \(-0.750951\pi\)
0.153482 + 0.988152i \(0.450951\pi\)
\(978\) −5.73343 + 4.64284i −0.183335 + 0.148462i
\(979\) −8.58487 + 7.72985i −0.274373 + 0.247047i
\(980\) 7.41644 3.96432i 0.236910 0.126635i
\(981\) 0.0300649 + 0.286049i 0.000959899 + 0.00913283i
\(982\) −32.3806 + 21.0282i −1.03331 + 0.671036i
\(983\) 24.4956 + 9.40299i 0.781289 + 0.299909i 0.716131 0.697966i \(-0.245911\pi\)
0.0651585 + 0.997875i \(0.479245\pi\)
\(984\) −0.640867 0.465617i −0.0204301 0.0148433i
\(985\) 61.6853 1.21230i 1.96546 0.0386269i
\(986\) 0.463548 + 0.802888i 0.0147624 + 0.0255692i
\(987\) 12.0090 + 44.8181i 0.382250 + 1.42658i
\(988\) 17.3965 + 2.75534i 0.553458 + 0.0876591i
\(989\) −3.81105 17.9296i −0.121184 0.570127i
\(990\) 0.233295 0.218512i 0.00741461 0.00694475i
\(991\) 35.6253i 1.13167i 0.824517 + 0.565837i \(0.191447\pi\)
−0.824517 + 0.565837i \(0.808553\pi\)
\(992\) −5.46453 + 1.06719i −0.173499 + 0.0338834i
\(993\) −21.9163 + 21.9163i −0.695493 + 0.695493i
\(994\) −30.3927 + 9.87520i −0.963999 + 0.313222i
\(995\) 44.9545 + 6.21725i 1.42515 + 0.197100i
\(996\) −7.78612 + 5.65695i −0.246713 + 0.179247i
\(997\) −12.4267 + 3.32972i −0.393557 + 0.105453i −0.450170 0.892943i \(-0.648637\pi\)
0.0566132 + 0.998396i \(0.481970\pi\)
\(998\) −1.93087 + 7.20609i −0.0611205 + 0.228105i
\(999\) 8.65265 19.4342i 0.273758 0.614870i
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 310.2.w.a.117.15 yes 256
5.3 odd 4 inner 310.2.w.a.303.2 yes 256
31.22 odd 30 inner 310.2.w.a.177.2 yes 256
155.53 even 60 inner 310.2.w.a.53.15 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
310.2.w.a.53.15 256 155.53 even 60 inner
310.2.w.a.117.15 yes 256 1.1 even 1 trivial
310.2.w.a.177.2 yes 256 31.22 odd 30 inner
310.2.w.a.303.2 yes 256 5.3 odd 4 inner