Properties

Label 225.2.q.a.31.8
Level $225$
Weight $2$
Character 225.31
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(16,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.q (of order \(15\), degree \(8\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 31.8
Character \(\chi\) \(=\) 225.31
Dual form 225.2.q.a.196.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.01797 + 1.13057i) q^{2} +(1.29814 + 1.14666i) q^{3} +(-0.0328678 - 0.312716i) q^{4} +(-1.82344 + 1.29424i) q^{5} +(-2.61784 + 0.300373i) q^{6} +(0.255551 + 0.442627i) q^{7} +(-2.07456 - 1.50725i) q^{8} +(0.370341 + 2.97705i) q^{9} +O(q^{10})\) \(q+(-1.01797 + 1.13057i) q^{2} +(1.29814 + 1.14666i) q^{3} +(-0.0328678 - 0.312716i) q^{4} +(-1.82344 + 1.29424i) q^{5} +(-2.61784 + 0.300373i) q^{6} +(0.255551 + 0.442627i) q^{7} +(-2.07456 - 1.50725i) q^{8} +(0.370341 + 2.97705i) q^{9} +(0.392972 - 3.37902i) q^{10} +(-0.559696 + 0.621605i) q^{11} +(0.315912 - 0.443637i) q^{12} +(-1.95815 - 2.17475i) q^{13} +(-0.760561 - 0.161662i) q^{14} +(-3.85114 - 0.410753i) q^{15} +(4.43101 - 0.941841i) q^{16} +(2.78774 + 2.02541i) q^{17} +(-3.74275 - 2.61185i) q^{18} +(4.87884 + 3.54469i) q^{19} +(0.464663 + 0.527679i) q^{20} +(-0.175802 + 0.867622i) q^{21} +(-0.133014 - 1.26555i) q^{22} +(-5.69440 - 1.21038i) q^{23} +(-0.964759 - 4.33544i) q^{24} +(1.64986 - 4.71995i) q^{25} +4.45203 q^{26} +(-2.93291 + 4.28929i) q^{27} +(0.130017 - 0.0944629i) q^{28} +(0.545297 + 0.242782i) q^{29} +(4.38472 - 3.93584i) q^{30} +(-0.811164 + 0.361154i) q^{31} +(-0.881520 + 1.52684i) q^{32} +(-1.43933 + 0.165150i) q^{33} +(-5.12769 + 1.08992i) q^{34} +(-1.03885 - 0.476358i) q^{35} +(0.918799 - 0.213661i) q^{36} +(-2.62260 + 8.07154i) q^{37} +(-8.97400 + 1.90748i) q^{38} +(-0.0482609 - 5.06846i) q^{39} +(5.73358 + 0.0634027i) q^{40} +(6.02515 + 6.69161i) q^{41} +(-0.801944 - 1.08197i) q^{42} +(-1.06736 - 1.84872i) q^{43} +(0.212782 + 0.154595i) q^{44} +(-4.52833 - 4.94916i) q^{45} +(7.16513 - 5.20577i) q^{46} +(6.64527 + 2.95867i) q^{47} +(6.83205 + 3.85822i) q^{48} +(3.36939 - 5.83595i) q^{49} +(3.65672 + 6.67004i) q^{50} +(1.29642 + 5.82586i) q^{51} +(-0.615718 + 0.683824i) q^{52} +(7.16056 - 5.20245i) q^{53} +(-1.86372 - 7.68221i) q^{54} +(0.216062 - 1.85784i) q^{55} +(0.136996 - 1.30343i) q^{56} +(2.26888 + 10.1959i) q^{57} +(-0.829576 + 0.369351i) q^{58} +(5.38582 + 5.98156i) q^{59} +(-0.00187077 + 1.21781i) q^{60} +(1.83668 - 2.03984i) q^{61} +(0.417430 - 1.28472i) q^{62} +(-1.22308 + 0.924711i) q^{63} +(1.97086 + 6.06570i) q^{64} +(6.38522 + 1.43119i) q^{65} +(1.27848 - 1.79538i) q^{66} +(-1.39886 + 0.622815i) q^{67} +(0.541751 - 0.938340i) q^{68} +(-6.00424 - 8.10079i) q^{69} +(1.59607 - 0.689571i) q^{70} +(4.04843 - 2.94135i) q^{71} +(3.71888 - 6.73426i) q^{72} +(3.39778 + 10.4573i) q^{73} +(-6.45569 - 11.1816i) q^{74} +(7.55394 - 4.23533i) q^{75} +(0.948122 - 1.64220i) q^{76} +(-0.418169 - 0.0888847i) q^{77} +(5.77936 + 5.10496i) q^{78} +(6.89241 + 3.06870i) q^{79} +(-6.86071 + 7.45220i) q^{80} +(-8.72569 + 2.20505i) q^{81} -13.6987 q^{82} +(-0.0470005 + 0.447180i) q^{83} +(0.277097 + 0.0264591i) q^{84} +(-7.70465 - 0.0851990i) q^{85} +(3.17664 + 0.675217i) q^{86} +(0.429485 + 0.940436i) q^{87} +(2.09804 - 0.445951i) q^{88} +(-5.39621 - 16.6078i) q^{89} +(10.2051 - 0.0814926i) q^{90} +(0.462194 - 1.42249i) q^{91} +(-0.191343 + 1.82051i) q^{92} +(-1.46713 - 0.461301i) q^{93} +(-10.1096 + 4.50110i) q^{94} +(-13.4840 - 0.149107i) q^{95} +(-2.89510 + 0.971246i) q^{96} +(-15.4623 - 6.88427i) q^{97} +(3.16801 + 9.75012i) q^{98} +(-2.05783 - 1.43604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.01797 + 1.13057i −0.719811 + 0.799432i −0.986397 0.164380i \(-0.947438\pi\)
0.266586 + 0.963811i \(0.414104\pi\)
\(3\) 1.29814 + 1.14666i 0.749482 + 0.662025i
\(4\) −0.0328678 0.312716i −0.0164339 0.156358i
\(5\) −1.82344 + 1.29424i −0.815467 + 0.578804i
\(6\) −2.61784 + 0.300373i −1.06873 + 0.122627i
\(7\) 0.255551 + 0.442627i 0.0965891 + 0.167297i 0.910271 0.414014i \(-0.135873\pi\)
−0.813682 + 0.581311i \(0.802540\pi\)
\(8\) −2.07456 1.50725i −0.733466 0.532894i
\(9\) 0.370341 + 2.97705i 0.123447 + 0.992351i
\(10\) 0.392972 3.37902i 0.124269 1.06854i
\(11\) −0.559696 + 0.621605i −0.168755 + 0.187421i −0.821590 0.570079i \(-0.806913\pi\)
0.652835 + 0.757500i \(0.273579\pi\)
\(12\) 0.315912 0.443637i 0.0911959 0.128067i
\(13\) −1.95815 2.17475i −0.543093 0.603166i 0.407653 0.913137i \(-0.366347\pi\)
−0.950746 + 0.309971i \(0.899681\pi\)
\(14\) −0.760561 0.161662i −0.203269 0.0432061i
\(15\) −3.85114 0.410753i −0.994360 0.106056i
\(16\) 4.43101 0.941841i 1.10775 0.235460i
\(17\) 2.78774 + 2.02541i 0.676126 + 0.491234i 0.872070 0.489381i \(-0.162777\pi\)
−0.195944 + 0.980615i \(0.562777\pi\)
\(18\) −3.74275 2.61185i −0.882175 0.615618i
\(19\) 4.87884 + 3.54469i 1.11928 + 0.813207i 0.984100 0.177614i \(-0.0568379\pi\)
0.135183 + 0.990821i \(0.456838\pi\)
\(20\) 0.464663 + 0.527679i 0.103902 + 0.117993i
\(21\) −0.175802 + 0.867622i −0.0383630 + 0.189331i
\(22\) −0.133014 1.26555i −0.0283587 0.269815i
\(23\) −5.69440 1.21038i −1.18736 0.252382i −0.428446 0.903567i \(-0.640939\pi\)
−0.758919 + 0.651185i \(0.774272\pi\)
\(24\) −0.964759 4.33544i −0.196931 0.884967i
\(25\) 1.64986 4.71995i 0.329973 0.943990i
\(26\) 4.45203 0.873115
\(27\) −2.93291 + 4.28929i −0.564439 + 0.825475i
\(28\) 0.130017 0.0944629i 0.0245709 0.0178518i
\(29\) 0.545297 + 0.242782i 0.101259 + 0.0450835i 0.456741 0.889600i \(-0.349017\pi\)
−0.355482 + 0.934683i \(0.615683\pi\)
\(30\) 4.38472 3.93584i 0.800536 0.718582i
\(31\) −0.811164 + 0.361154i −0.145689 + 0.0648651i −0.478286 0.878204i \(-0.658742\pi\)
0.332597 + 0.943069i \(0.392075\pi\)
\(32\) −0.881520 + 1.52684i −0.155832 + 0.269909i
\(33\) −1.43933 + 0.165150i −0.250556 + 0.0287490i
\(34\) −5.12769 + 1.08992i −0.879391 + 0.186920i
\(35\) −1.03885 0.476358i −0.175597 0.0805192i
\(36\) 0.918799 0.213661i 0.153133 0.0356101i
\(37\) −2.62260 + 8.07154i −0.431153 + 1.32695i 0.465825 + 0.884877i \(0.345758\pi\)
−0.896978 + 0.442075i \(0.854242\pi\)
\(38\) −8.97400 + 1.90748i −1.45578 + 0.309435i
\(39\) −0.0482609 5.06846i −0.00772793 0.811603i
\(40\) 5.73358 + 0.0634027i 0.906559 + 0.0100248i
\(41\) 6.02515 + 6.69161i 0.940970 + 1.04505i 0.998907 + 0.0467329i \(0.0148810\pi\)
−0.0579374 + 0.998320i \(0.518452\pi\)
\(42\) −0.801944 1.08197i −0.123743 0.166951i
\(43\) −1.06736 1.84872i −0.162771 0.281928i 0.773090 0.634296i \(-0.218710\pi\)
−0.935862 + 0.352368i \(0.885377\pi\)
\(44\) 0.212782 + 0.154595i 0.0320780 + 0.0233061i
\(45\) −4.52833 4.94916i −0.675043 0.737778i
\(46\) 7.16513 5.20577i 1.05644 0.767549i
\(47\) 6.64527 + 2.95867i 0.969312 + 0.431566i 0.829435 0.558603i \(-0.188662\pi\)
0.139877 + 0.990169i \(0.455329\pi\)
\(48\) 6.83205 + 3.85822i 0.986122 + 0.556887i
\(49\) 3.36939 5.83595i 0.481341 0.833707i
\(50\) 3.65672 + 6.67004i 0.517138 + 0.943286i
\(51\) 1.29642 + 5.82586i 0.181535 + 0.815783i
\(52\) −0.615718 + 0.683824i −0.0853847 + 0.0948293i
\(53\) 7.16056 5.20245i 0.983578 0.714612i 0.0250729 0.999686i \(-0.492018\pi\)
0.958505 + 0.285074i \(0.0920182\pi\)
\(54\) −1.86372 7.68221i −0.253620 1.04542i
\(55\) 0.216062 1.85784i 0.0291339 0.250511i
\(56\) 0.136996 1.30343i 0.0183069 0.174179i
\(57\) 2.26888 + 10.1959i 0.300520 + 1.35048i
\(58\) −0.829576 + 0.369351i −0.108929 + 0.0484982i
\(59\) 5.38582 + 5.98156i 0.701174 + 0.778733i 0.983563 0.180567i \(-0.0577934\pi\)
−0.282389 + 0.959300i \(0.591127\pi\)
\(60\) −0.00187077 + 1.21781i −0.000241515 + 0.157219i
\(61\) 1.83668 2.03984i 0.235163 0.261175i −0.614000 0.789306i \(-0.710440\pi\)
0.849163 + 0.528131i \(0.177107\pi\)
\(62\) 0.417430 1.28472i 0.0530137 0.163159i
\(63\) −1.22308 + 0.924711i −0.154094 + 0.116503i
\(64\) 1.97086 + 6.06570i 0.246358 + 0.758212i
\(65\) 6.38522 + 1.43119i 0.791989 + 0.177518i
\(66\) 1.27848 1.79538i 0.157370 0.220996i
\(67\) −1.39886 + 0.622815i −0.170898 + 0.0760889i −0.490403 0.871496i \(-0.663150\pi\)
0.319504 + 0.947585i \(0.396484\pi\)
\(68\) 0.541751 0.938340i 0.0656970 0.113790i
\(69\) −6.00424 8.10079i −0.722825 0.975220i
\(70\) 1.59607 0.689571i 0.190767 0.0824194i
\(71\) 4.04843 2.94135i 0.480460 0.349075i −0.321044 0.947064i \(-0.604034\pi\)
0.801504 + 0.597990i \(0.204034\pi\)
\(72\) 3.71888 6.73426i 0.438274 0.793640i
\(73\) 3.39778 + 10.4573i 0.397680 + 1.22393i 0.926855 + 0.375419i \(0.122501\pi\)
−0.529175 + 0.848512i \(0.677499\pi\)
\(74\) −6.45569 11.1816i −0.750459 1.29983i
\(75\) 7.55394 4.23533i 0.872253 0.489054i
\(76\) 0.948122 1.64220i 0.108757 0.188373i
\(77\) −0.418169 0.0888847i −0.0476548 0.0101293i
\(78\) 5.77936 + 5.10496i 0.654384 + 0.578023i
\(79\) 6.89241 + 3.06870i 0.775457 + 0.345256i 0.756014 0.654555i \(-0.227144\pi\)
0.0194429 + 0.999811i \(0.493811\pi\)
\(80\) −6.86071 + 7.45220i −0.767051 + 0.833182i
\(81\) −8.72569 + 2.20505i −0.969522 + 0.245006i
\(82\) −13.6987 −1.51277
\(83\) −0.0470005 + 0.447180i −0.00515898 + 0.0490844i −0.996799 0.0799544i \(-0.974523\pi\)
0.991640 + 0.129039i \(0.0411892\pi\)
\(84\) 0.277097 + 0.0264591i 0.0302338 + 0.00288693i
\(85\) −7.70465 0.0851990i −0.835686 0.00924113i
\(86\) 3.17664 + 0.675217i 0.342546 + 0.0728105i
\(87\) 0.429485 + 0.940436i 0.0460456 + 0.100825i
\(88\) 2.09804 0.445951i 0.223651 0.0475386i
\(89\) −5.39621 16.6078i −0.571997 1.76043i −0.646184 0.763181i \(-0.723636\pi\)
0.0741872 0.997244i \(-0.476364\pi\)
\(90\) 10.2051 0.0814926i 1.07571 0.00859007i
\(91\) 0.462194 1.42249i 0.0484511 0.149117i
\(92\) −0.191343 + 1.82051i −0.0199489 + 0.189801i
\(93\) −1.46713 0.461301i −0.152134 0.0478347i
\(94\) −10.1096 + 4.50110i −1.04273 + 0.464253i
\(95\) −13.4840 0.149107i −1.38343 0.0152981i
\(96\) −2.89510 + 0.971246i −0.295480 + 0.0991274i
\(97\) −15.4623 6.88427i −1.56996 0.698991i −0.576924 0.816798i \(-0.695747\pi\)
−0.993037 + 0.117807i \(0.962414\pi\)
\(98\) 3.16801 + 9.75012i 0.320017 + 0.984911i
\(99\) −2.05783 1.43604i −0.206820 0.144327i
\(100\) −1.53023 0.360804i −0.153023 0.0360804i
\(101\) −8.66842 15.0141i −0.862540 1.49396i −0.869469 0.493988i \(-0.835539\pi\)
0.00692858 0.999976i \(-0.497795\pi\)
\(102\) −7.90623 4.46484i −0.782834 0.442085i
\(103\) −0.876074 8.33529i −0.0863221 0.821300i −0.948943 0.315449i \(-0.897845\pi\)
0.862621 0.505852i \(-0.168822\pi\)
\(104\) 0.784399 + 7.46306i 0.0769167 + 0.731813i
\(105\) −0.802351 1.80959i −0.0783014 0.176597i
\(106\) −1.40749 + 13.3914i −0.136708 + 1.30069i
\(107\) 12.3203 1.19105 0.595524 0.803338i \(-0.296945\pi\)
0.595524 + 0.803338i \(0.296945\pi\)
\(108\) 1.43773 + 0.776189i 0.138345 + 0.0746888i
\(109\) −4.53429 + 13.9551i −0.434306 + 1.33666i 0.459490 + 0.888183i \(0.348032\pi\)
−0.893796 + 0.448474i \(0.851968\pi\)
\(110\) 1.88047 + 2.13549i 0.179296 + 0.203611i
\(111\) −12.6598 + 7.47076i −1.20162 + 0.709093i
\(112\) 1.54923 + 1.72060i 0.146389 + 0.162581i
\(113\) −8.31782 9.23787i −0.782474 0.869026i 0.211642 0.977347i \(-0.432119\pi\)
−0.994116 + 0.108322i \(0.965452\pi\)
\(114\) −13.8368 7.81395i −1.29593 0.731843i
\(115\) 11.9499 5.16289i 1.11434 0.481442i
\(116\) 0.0579991 0.178503i 0.00538508 0.0165736i
\(117\) 5.74915 6.63492i 0.531509 0.613398i
\(118\) −12.2451 −1.12726
\(119\) −0.184092 + 1.75152i −0.0168757 + 0.160562i
\(120\) 7.37030 + 6.65677i 0.672813 + 0.607678i
\(121\) 1.07668 + 10.2439i 0.0978800 + 0.931266i
\(122\) 0.436496 + 4.15298i 0.0395185 + 0.375993i
\(123\) 0.148497 + 15.5954i 0.0133895 + 1.40619i
\(124\) 0.139600 + 0.241794i 0.0125364 + 0.0217137i
\(125\) 3.10035 + 10.7419i 0.277303 + 0.960782i
\(126\) 0.199610 2.32410i 0.0177827 0.207047i
\(127\) −4.71456 14.5099i −0.418349 1.28755i −0.909221 0.416315i \(-0.863321\pi\)
0.490871 0.871232i \(-0.336679\pi\)
\(128\) −12.0852 5.38067i −1.06819 0.475589i
\(129\) 0.734272 3.62381i 0.0646491 0.319058i
\(130\) −8.11801 + 5.76201i −0.711996 + 0.505362i
\(131\) 8.42687 3.75188i 0.736259 0.327804i −0.00412177 0.999992i \(-0.501312\pi\)
0.740381 + 0.672188i \(0.234645\pi\)
\(132\) 0.0989528 + 0.444674i 0.00861273 + 0.0387039i
\(133\) −0.322181 + 3.06535i −0.0279367 + 0.265800i
\(134\) 0.719864 2.21551i 0.0621868 0.191391i
\(135\) −0.203401 11.6172i −0.0175060 0.999847i
\(136\) −2.73051 8.40365i −0.234139 0.720607i
\(137\) 9.11279 1.93698i 0.778558 0.165488i 0.198542 0.980092i \(-0.436379\pi\)
0.580016 + 0.814605i \(0.303046\pi\)
\(138\) 15.2706 + 1.45814i 1.29992 + 0.124125i
\(139\) −5.70167 1.21193i −0.483609 0.102794i −0.0403459 0.999186i \(-0.512846\pi\)
−0.443263 + 0.896391i \(0.646179\pi\)
\(140\) −0.114820 + 0.340521i −0.00970407 + 0.0287793i
\(141\) 5.23392 + 11.4606i 0.440775 + 0.965159i
\(142\) −0.795767 + 7.57122i −0.0667793 + 0.635363i
\(143\) 2.44780 0.204695
\(144\) 4.44490 + 12.8426i 0.370408 + 1.07021i
\(145\) −1.30854 + 0.263050i −0.108668 + 0.0218451i
\(146\) −15.2815 6.80375i −1.26470 0.563082i
\(147\) 11.0658 3.71235i 0.912691 0.306189i
\(148\) 2.61030 + 0.554835i 0.214565 + 0.0456072i
\(149\) −0.938800 + 1.62605i −0.0769095 + 0.133211i −0.901915 0.431913i \(-0.857839\pi\)
0.825006 + 0.565125i \(0.191172\pi\)
\(150\) −2.90133 + 12.8517i −0.236893 + 1.04933i
\(151\) −1.02623 1.77749i −0.0835138 0.144650i 0.821243 0.570578i \(-0.193281\pi\)
−0.904757 + 0.425928i \(0.859948\pi\)
\(152\) −4.77869 14.7073i −0.387603 1.19292i
\(153\) −4.99734 + 9.04934i −0.404011 + 0.731596i
\(154\) 0.526173 0.382287i 0.0424002 0.0308056i
\(155\) 1.01169 1.70839i 0.0812607 0.137221i
\(156\) −1.58340 + 0.181681i −0.126774 + 0.0145461i
\(157\) −2.99334 + 5.18462i −0.238895 + 0.413778i −0.960397 0.278634i \(-0.910118\pi\)
0.721503 + 0.692412i \(0.243452\pi\)
\(158\) −10.4856 + 4.66850i −0.834191 + 0.371406i
\(159\) 15.2609 + 1.45721i 1.21026 + 0.115564i
\(160\) −0.368702 3.92500i −0.0291485 0.310298i
\(161\) −0.919460 2.82981i −0.0724636 0.223020i
\(162\) 6.38951 12.1097i 0.502007 0.951424i
\(163\) 5.22667 16.0860i 0.409385 1.25996i −0.507793 0.861479i \(-0.669539\pi\)
0.917178 0.398478i \(-0.130461\pi\)
\(164\) 1.89454 2.10410i 0.147939 0.164302i
\(165\) 2.41079 2.16399i 0.187680 0.168466i
\(166\) −0.457722 0.508352i −0.0355261 0.0394558i
\(167\) 19.5078 8.68543i 1.50956 0.672099i 0.525638 0.850708i \(-0.323827\pi\)
0.983920 + 0.178610i \(0.0571599\pi\)
\(168\) 1.67244 1.53495i 0.129031 0.118424i
\(169\) 0.463701 4.41182i 0.0356693 0.339371i
\(170\) 7.93940 8.62389i 0.608924 0.661422i
\(171\) −8.74588 + 15.8373i −0.668814 + 1.21111i
\(172\) −0.543043 + 0.394544i −0.0414067 + 0.0300837i
\(173\) 2.21895 2.46440i 0.168704 0.187365i −0.652864 0.757475i \(-0.726433\pi\)
0.821568 + 0.570110i \(0.193100\pi\)
\(174\) −1.50043 0.471772i −0.113747 0.0357649i
\(175\) 2.51080 0.475913i 0.189799 0.0359757i
\(176\) −1.89457 + 3.28148i −0.142808 + 0.247351i
\(177\) 0.132740 + 13.9406i 0.00997733 + 1.04784i
\(178\) 24.2694 + 10.8054i 1.81907 + 0.809902i
\(179\) −2.64332 + 1.92048i −0.197571 + 0.143543i −0.682172 0.731191i \(-0.738965\pi\)
0.484602 + 0.874735i \(0.338965\pi\)
\(180\) −1.39885 + 1.57875i −0.104264 + 0.117673i
\(181\) −5.08500 3.69447i −0.377965 0.274607i 0.382541 0.923938i \(-0.375049\pi\)
−0.760506 + 0.649331i \(0.775049\pi\)
\(182\) 1.13772 + 1.97059i 0.0843333 + 0.146070i
\(183\) 4.72327 0.541953i 0.349155 0.0400623i
\(184\) 9.98900 + 11.0939i 0.736399 + 0.817854i
\(185\) −5.66438 18.1122i −0.416454 1.33164i
\(186\) 2.01502 1.18909i 0.147748 0.0871886i
\(187\) −2.81929 + 0.599258i −0.206167 + 0.0438221i
\(188\) 0.706806 2.17533i 0.0515491 0.158652i
\(189\) −2.64806 0.202055i −0.192618 0.0146973i
\(190\) 13.8948 15.0927i 1.00803 1.09494i
\(191\) −10.8485 + 2.30593i −0.784972 + 0.166851i −0.582926 0.812525i \(-0.698092\pi\)
−0.202046 + 0.979376i \(0.564759\pi\)
\(192\) −4.39683 + 10.1340i −0.317314 + 0.731361i
\(193\) −4.50515 + 7.80315i −0.324288 + 0.561683i −0.981368 0.192138i \(-0.938458\pi\)
0.657080 + 0.753821i \(0.271791\pi\)
\(194\) 23.5232 10.4732i 1.68887 0.751934i
\(195\) 6.64783 + 9.17957i 0.476061 + 0.657363i
\(196\) −1.93574 0.861846i −0.138267 0.0615604i
\(197\) −21.9807 + 15.9699i −1.56606 + 1.13781i −0.635253 + 0.772304i \(0.719104\pi\)
−0.930809 + 0.365506i \(0.880896\pi\)
\(198\) 3.71834 0.864675i 0.264251 0.0614498i
\(199\) 15.6745 1.11114 0.555569 0.831471i \(-0.312501\pi\)
0.555569 + 0.831471i \(0.312501\pi\)
\(200\) −10.5369 + 7.30504i −0.745071 + 0.516545i
\(201\) −2.53008 0.795521i −0.178458 0.0561117i
\(202\) 25.7987 + 5.48368i 1.81519 + 0.385830i
\(203\) 0.0318893 + 0.303406i 0.00223819 + 0.0212949i
\(204\) 1.77923 0.596894i 0.124571 0.0417909i
\(205\) −19.6471 4.40372i −1.37221 0.307569i
\(206\) 10.3154 + 7.49459i 0.718709 + 0.522173i
\(207\) 1.49450 17.4008i 0.103875 1.20944i
\(208\) −10.7249 7.79207i −0.743635 0.540283i
\(209\) −4.93406 + 1.04877i −0.341296 + 0.0725447i
\(210\) 2.86262 + 0.934987i 0.197540 + 0.0645202i
\(211\) 16.3896 + 3.48371i 1.12830 + 0.239829i 0.733999 0.679151i \(-0.237652\pi\)
0.394306 + 0.918979i \(0.370985\pi\)
\(212\) −1.86224 2.06823i −0.127899 0.142046i
\(213\) 8.62816 + 0.823876i 0.591192 + 0.0564511i
\(214\) −12.5416 + 13.9289i −0.857329 + 0.952161i
\(215\) 4.33897 + 1.98961i 0.295915 + 0.135690i
\(216\) 12.5495 4.47773i 0.853888 0.304671i
\(217\) −0.367150 0.266750i −0.0249237 0.0181082i
\(218\) −11.1614 19.3322i −0.755947 1.30934i
\(219\) −7.58015 + 17.4711i −0.512219 + 1.18059i
\(220\) −0.588078 0.00650305i −0.0396482 0.000438435i
\(221\) −1.05406 10.0287i −0.0709035 0.674602i
\(222\) 4.44108 21.9178i 0.298066 1.47102i
\(223\) 6.86298 7.62211i 0.459579 0.510414i −0.468160 0.883644i \(-0.655083\pi\)
0.927739 + 0.373229i \(0.121750\pi\)
\(224\) −0.901091 −0.0602067
\(225\) 14.6626 + 3.16374i 0.977504 + 0.210916i
\(226\) 18.9113 1.25796
\(227\) −3.94083 + 4.37673i −0.261562 + 0.290494i −0.859593 0.510979i \(-0.829283\pi\)
0.598031 + 0.801473i \(0.295950\pi\)
\(228\) 3.11384 1.04463i 0.206219 0.0691822i
\(229\) −1.48626 14.1408i −0.0982145 0.934449i −0.927045 0.374949i \(-0.877660\pi\)
0.828831 0.559499i \(-0.189007\pi\)
\(230\) −6.32764 + 18.7658i −0.417232 + 1.23738i
\(231\) −0.440922 0.594883i −0.0290106 0.0391404i
\(232\) −0.765316 1.32557i −0.0502454 0.0870277i
\(233\) 4.13877 + 3.00699i 0.271140 + 0.196995i 0.715044 0.699080i \(-0.246407\pi\)
−0.443904 + 0.896074i \(0.646407\pi\)
\(234\) 1.64877 + 13.2539i 0.107783 + 0.866436i
\(235\) −15.9465 + 3.20566i −1.04023 + 0.209114i
\(236\) 1.69351 1.88083i 0.110238 0.122432i
\(237\) 5.42857 + 11.8869i 0.352623 + 0.772135i
\(238\) −1.79281 1.99112i −0.116211 0.129065i
\(239\) 5.45260 + 1.15899i 0.352699 + 0.0749685i 0.380854 0.924635i \(-0.375630\pi\)
−0.0281551 + 0.999604i \(0.508963\pi\)
\(240\) −17.4513 + 1.80711i −1.12648 + 0.116648i
\(241\) −22.7925 + 4.84469i −1.46819 + 0.312074i −0.871500 0.490396i \(-0.836852\pi\)
−0.596693 + 0.802470i \(0.703519\pi\)
\(242\) −12.6775 9.21072i −0.814938 0.592087i
\(243\) −13.8556 7.14294i −0.888839 0.458220i
\(244\) −0.698258 0.507314i −0.0447014 0.0324775i
\(245\) 1.40927 + 15.0023i 0.0900350 + 0.958463i
\(246\) −17.7829 15.7078i −1.13379 1.00149i
\(247\) −1.84471 17.5513i −0.117376 1.11676i
\(248\) 2.22715 + 0.473396i 0.141424 + 0.0300607i
\(249\) −0.573777 + 0.526610i −0.0363616 + 0.0333725i
\(250\) −15.3005 7.42973i −0.967686 0.469897i
\(251\) −22.9704 −1.44988 −0.724941 0.688811i \(-0.758133\pi\)
−0.724941 + 0.688811i \(0.758133\pi\)
\(252\) 0.329372 + 0.352084i 0.0207485 + 0.0221792i
\(253\) 3.93951 2.86222i 0.247675 0.179946i
\(254\) 21.2037 + 9.44049i 1.33044 + 0.592349i
\(255\) −9.90402 8.94521i −0.620214 0.560171i
\(256\) 6.73261 2.99755i 0.420788 0.187347i
\(257\) 0.0155867 0.0269970i 0.000972274 0.00168403i −0.865539 0.500842i \(-0.833024\pi\)
0.866511 + 0.499158i \(0.166357\pi\)
\(258\) 3.34949 + 4.51906i 0.208530 + 0.281344i
\(259\) −4.24288 + 0.901853i −0.263640 + 0.0560384i
\(260\) 0.237689 2.04380i 0.0147408 0.126751i
\(261\) −0.520829 + 1.71329i −0.0322385 + 0.106050i
\(262\) −4.33652 + 13.3464i −0.267911 + 0.824545i
\(263\) 22.8282 4.85229i 1.40765 0.299205i 0.559442 0.828870i \(-0.311016\pi\)
0.848207 + 0.529665i \(0.177682\pi\)
\(264\) 3.23490 + 1.82683i 0.199094 + 0.112433i
\(265\) −6.32360 + 18.7539i −0.388456 + 1.15204i
\(266\) −3.13761 3.48467i −0.192379 0.213659i
\(267\) 12.0385 27.7469i 0.736743 1.69808i
\(268\) 0.240741 + 0.416976i 0.0147056 + 0.0254709i
\(269\) 13.1174 + 9.53037i 0.799784 + 0.581077i 0.910851 0.412736i \(-0.135427\pi\)
−0.111067 + 0.993813i \(0.535427\pi\)
\(270\) 13.3410 + 11.5959i 0.811910 + 0.705706i
\(271\) 8.23042 5.97975i 0.499962 0.363244i −0.309040 0.951049i \(-0.600008\pi\)
0.809003 + 0.587805i \(0.200008\pi\)
\(272\) 14.2601 + 6.34901i 0.864647 + 0.384966i
\(273\) 2.23110 1.31661i 0.135032 0.0796849i
\(274\) −7.08663 + 12.2744i −0.428119 + 0.741524i
\(275\) 2.01052 + 3.66730i 0.121239 + 0.221146i
\(276\) −2.33590 + 2.14388i −0.140605 + 0.129046i
\(277\) 4.60550 5.11493i 0.276718 0.307326i −0.588726 0.808333i \(-0.700370\pi\)
0.865443 + 0.501007i \(0.167037\pi\)
\(278\) 7.17427 5.21241i 0.430284 0.312620i
\(279\) −1.37558 2.28113i −0.0823539 0.136568i
\(280\) 1.43716 + 2.55404i 0.0858865 + 0.152633i
\(281\) 1.68619 16.0430i 0.100590 0.957048i −0.821536 0.570157i \(-0.806882\pi\)
0.922126 0.386891i \(-0.126451\pi\)
\(282\) −18.2850 5.74925i −1.08885 0.342363i
\(283\) 15.3146 6.81851i 0.910360 0.405318i 0.102527 0.994730i \(-0.467307\pi\)
0.807833 + 0.589412i \(0.200641\pi\)
\(284\) −1.05287 1.16933i −0.0624764 0.0693871i
\(285\) −17.3331 15.6551i −1.02672 0.927327i
\(286\) −2.49178 + 2.76740i −0.147342 + 0.163640i
\(287\) −1.42215 + 4.37693i −0.0839470 + 0.258362i
\(288\) −4.87194 2.05888i −0.287082 0.121321i
\(289\) −1.58409 4.87534i −0.0931819 0.286785i
\(290\) 1.03465 1.74716i 0.0607568 0.102597i
\(291\) −12.1784 26.6668i −0.713908 1.56323i
\(292\) 3.15848 1.40625i 0.184836 0.0822943i
\(293\) −11.7345 + 20.3247i −0.685536 + 1.18738i 0.287732 + 0.957711i \(0.407099\pi\)
−0.973268 + 0.229672i \(0.926235\pi\)
\(294\) −7.06756 + 16.2897i −0.412188 + 0.950033i
\(295\) −17.5623 3.93644i −1.02252 0.229189i
\(296\) 17.6066 12.7919i 1.02336 0.743516i
\(297\) −1.02471 4.22381i −0.0594595 0.245090i
\(298\) −0.882691 2.71664i −0.0511329 0.157371i
\(299\) 8.51822 + 14.7540i 0.492621 + 0.853245i
\(300\) −1.57274 2.22303i −0.0908020 0.128347i
\(301\) 0.545530 0.944885i 0.0314438 0.0544623i
\(302\) 3.05424 + 0.649200i 0.175752 + 0.0373572i
\(303\) 5.96329 29.4302i 0.342582 1.69072i
\(304\) 24.9567 + 11.1115i 1.43137 + 0.637286i
\(305\) −0.709024 + 6.09664i −0.0405986 + 0.349093i
\(306\) −5.14375 14.8618i −0.294049 0.849590i
\(307\) −8.91785 −0.508969 −0.254484 0.967077i \(-0.581906\pi\)
−0.254484 + 0.967077i \(0.581906\pi\)
\(308\) −0.0140513 + 0.133690i −0.000800650 + 0.00761767i
\(309\) 8.42047 11.8249i 0.479024 0.672697i
\(310\) 0.901580 + 2.88286i 0.0512063 + 0.163736i
\(311\) −19.9920 4.24944i −1.13364 0.240964i −0.397378 0.917655i \(-0.630080\pi\)
−0.736267 + 0.676691i \(0.763413\pi\)
\(312\) −7.53933 + 10.5875i −0.426831 + 0.599402i
\(313\) 22.6394 4.81215i 1.27965 0.271999i 0.482564 0.875861i \(-0.339706\pi\)
0.797089 + 0.603862i \(0.206372\pi\)
\(314\) −2.81444 8.66194i −0.158828 0.488822i
\(315\) 1.03341 3.26912i 0.0582263 0.184194i
\(316\) 0.733093 2.25623i 0.0412397 0.126923i
\(317\) −1.11960 + 10.6523i −0.0628828 + 0.598290i 0.917024 + 0.398833i \(0.130585\pi\)
−0.979906 + 0.199457i \(0.936082\pi\)
\(318\) −17.1825 + 15.7700i −0.963548 + 0.884339i
\(319\) −0.456115 + 0.203075i −0.0255375 + 0.0113700i
\(320\) −11.4442 8.50965i −0.639753 0.475704i
\(321\) 15.9935 + 14.1272i 0.892669 + 0.788503i
\(322\) 4.13527 + 1.84114i 0.230449 + 0.102603i
\(323\) 6.42149 + 19.7633i 0.357301 + 1.09966i
\(324\) 0.976348 + 2.65619i 0.0542416 + 0.147566i
\(325\) −13.4954 + 5.65434i −0.748589 + 0.313647i
\(326\) 12.8658 + 22.2842i 0.712569 + 1.23421i
\(327\) −21.8879 + 12.9164i −1.21040 + 0.714279i
\(328\) −2.41356 22.9635i −0.133267 1.26795i
\(329\) 0.388619 + 3.69746i 0.0214253 + 0.203848i
\(330\) −0.00757091 + 4.92843i −0.000416765 + 0.271301i
\(331\) −2.45698 + 23.3766i −0.135048 + 1.28489i 0.691645 + 0.722238i \(0.256886\pi\)
−0.826692 + 0.562654i \(0.809780\pi\)
\(332\) 0.141385 0.00775952
\(333\) −25.0006 4.81840i −1.37003 0.264047i
\(334\) −10.0388 + 30.8963i −0.549300 + 1.69057i
\(335\) 1.74467 2.94614i 0.0953215 0.160965i
\(336\) 0.0381826 + 4.01002i 0.00208303 + 0.218765i
\(337\) −0.833194 0.925356i −0.0453870 0.0504073i 0.720024 0.693949i \(-0.244131\pi\)
−0.765411 + 0.643542i \(0.777464\pi\)
\(338\) 4.51583 + 5.01533i 0.245629 + 0.272798i
\(339\) −0.205002 21.5298i −0.0111342 1.16934i
\(340\) 0.226591 + 2.41216i 0.0122886 + 0.130818i
\(341\) 0.229510 0.706360i 0.0124287 0.0382515i
\(342\) −9.00212 26.0097i −0.486779 1.40644i
\(343\) 7.02190 0.379147
\(344\) −0.572194 + 5.44406i −0.0308506 + 0.293524i
\(345\) 21.4328 + 7.00035i 1.15390 + 0.376886i
\(346\) 0.527345 + 5.01735i 0.0283502 + 0.269734i
\(347\) 3.45879 + 32.9082i 0.185678 + 1.76661i 0.549840 + 0.835270i \(0.314689\pi\)
−0.364162 + 0.931336i \(0.618645\pi\)
\(348\) 0.279973 0.165217i 0.0150081 0.00885654i
\(349\) −7.71967 13.3709i −0.413224 0.715726i 0.582016 0.813177i \(-0.302264\pi\)
−0.995240 + 0.0974517i \(0.968931\pi\)
\(350\) −2.01786 + 3.32309i −0.107859 + 0.177627i
\(351\) 15.0712 2.02074i 0.804442 0.107859i
\(352\) −0.455707 1.40252i −0.0242892 0.0747546i
\(353\) 22.9186 + 10.2040i 1.21983 + 0.543105i 0.912727 0.408570i \(-0.133972\pi\)
0.307107 + 0.951675i \(0.400639\pi\)
\(354\) −15.8959 14.0410i −0.844859 0.746272i
\(355\) −3.57523 + 10.6030i −0.189754 + 0.562751i
\(356\) −5.01617 + 2.23334i −0.265856 + 0.118367i
\(357\) −2.24738 + 2.06263i −0.118944 + 0.109166i
\(358\) 0.519576 4.94343i 0.0274604 0.261268i
\(359\) 0.624628 1.92241i 0.0329666 0.101461i −0.933219 0.359307i \(-0.883013\pi\)
0.966186 + 0.257847i \(0.0830130\pi\)
\(360\) 1.93463 + 17.0927i 0.101964 + 0.900862i
\(361\) 5.36697 + 16.5178i 0.282472 + 0.869360i
\(362\) 9.35320 1.98808i 0.491593 0.104491i
\(363\) −10.3486 + 14.5326i −0.543161 + 0.762766i
\(364\) −0.460026 0.0977815i −0.0241119 0.00512514i
\(365\) −19.7299 14.6707i −1.03271 0.767898i
\(366\) −4.19542 + 5.89167i −0.219298 + 0.307962i
\(367\) −3.66163 + 34.8381i −0.191135 + 1.81853i 0.307308 + 0.951610i \(0.400572\pi\)
−0.498443 + 0.866922i \(0.666095\pi\)
\(368\) −26.3720 −1.37473
\(369\) −17.6899 + 20.4154i −0.920900 + 1.06278i
\(370\) 26.2433 + 12.0337i 1.36432 + 0.625602i
\(371\) 4.13263 + 1.83996i 0.214555 + 0.0955262i
\(372\) −0.0960350 + 0.473955i −0.00497919 + 0.0245734i
\(373\) −13.4338 2.85545i −0.695577 0.147849i −0.153463 0.988154i \(-0.549043\pi\)
−0.542114 + 0.840305i \(0.682376\pi\)
\(374\) 2.19244 3.79742i 0.113368 0.196360i
\(375\) −8.29259 + 17.4995i −0.428228 + 0.903671i
\(376\) −9.32653 16.1540i −0.480979 0.833080i
\(377\) −0.539785 1.66129i −0.0278003 0.0855607i
\(378\) 2.92408 2.78813i 0.150398 0.143406i
\(379\) 20.8462 15.1457i 1.07080 0.777980i 0.0947423 0.995502i \(-0.469797\pi\)
0.976055 + 0.217522i \(0.0697973\pi\)
\(380\) 0.396559 + 4.22155i 0.0203431 + 0.216561i
\(381\) 10.5178 24.2419i 0.538842 1.24195i
\(382\) 8.43644 14.6123i 0.431646 0.747633i
\(383\) 15.1119 6.72825i 0.772182 0.343797i 0.0174642 0.999847i \(-0.494441\pi\)
0.754717 + 0.656050i \(0.227774\pi\)
\(384\) −9.51847 20.8425i −0.485738 1.06361i
\(385\) 0.877545 0.379138i 0.0447238 0.0193226i
\(386\) −4.23589 13.0367i −0.215601 0.663552i
\(387\) 5.10846 3.86225i 0.259678 0.196329i
\(388\) −1.64461 + 5.06158i −0.0834923 + 0.256963i
\(389\) −10.4226 + 11.5755i −0.528449 + 0.586902i −0.946977 0.321302i \(-0.895880\pi\)
0.418528 + 0.908204i \(0.362546\pi\)
\(390\) −17.1454 1.82869i −0.868191 0.0925991i
\(391\) −13.4230 14.9077i −0.678829 0.753916i
\(392\) −15.7862 + 7.02849i −0.797325 + 0.354992i
\(393\) 15.2414 + 4.79228i 0.768827 + 0.241738i
\(394\) 4.32058 41.1075i 0.217668 2.07097i
\(395\) −16.5395 + 3.32488i −0.832195 + 0.167293i
\(396\) −0.381435 + 0.690715i −0.0191679 + 0.0347097i
\(397\) 2.54039 1.84570i 0.127498 0.0926330i −0.522208 0.852818i \(-0.674892\pi\)
0.649707 + 0.760185i \(0.274892\pi\)
\(398\) −15.9561 + 17.7211i −0.799809 + 0.888278i
\(399\) −3.93315 + 3.60983i −0.196904 + 0.180717i
\(400\) 2.86512 22.4681i 0.143256 1.12340i
\(401\) 1.03308 1.78934i 0.0515894 0.0893554i −0.839077 0.544012i \(-0.816905\pi\)
0.890667 + 0.454656i \(0.150238\pi\)
\(402\) 3.47493 2.05061i 0.173314 0.102275i
\(403\) 2.37380 + 1.05688i 0.118247 + 0.0526471i
\(404\) −4.41025 + 3.20423i −0.219418 + 0.159417i
\(405\) 13.0569 15.3140i 0.648803 0.760957i
\(406\) −0.375483 0.272805i −0.0186349 0.0135391i
\(407\) −3.54945 6.14782i −0.175940 0.304736i
\(408\) 6.09154 14.0401i 0.301576 0.695088i
\(409\) −20.2979 22.5431i −1.00367 1.11468i −0.993396 0.114737i \(-0.963398\pi\)
−0.0102700 0.999947i \(-0.503269\pi\)
\(410\) 24.9788 17.7295i 1.23361 0.875596i
\(411\) 14.0508 + 7.93480i 0.693072 + 0.391395i
\(412\) −2.57778 + 0.547924i −0.126998 + 0.0269943i
\(413\) −1.27125 + 3.91250i −0.0625540 + 0.192521i
\(414\) 18.1514 + 19.4031i 0.892093 + 0.953609i
\(415\) −0.493058 0.876236i −0.0242033 0.0430128i
\(416\) 5.04663 1.07269i 0.247431 0.0525932i
\(417\) −6.01190 8.11113i −0.294404 0.397204i
\(418\) 3.83701 6.64589i 0.187674 0.325061i
\(419\) 21.7151 9.66820i 1.06085 0.472322i 0.199273 0.979944i \(-0.436142\pi\)
0.861580 + 0.507622i \(0.169475\pi\)
\(420\) −0.539515 + 0.310385i −0.0263256 + 0.0151452i
\(421\) 9.91682 + 4.41525i 0.483316 + 0.215186i 0.633906 0.773410i \(-0.281451\pi\)
−0.150590 + 0.988596i \(0.548117\pi\)
\(422\) −20.6226 + 14.9832i −1.00389 + 0.729371i
\(423\) −6.34709 + 20.8790i −0.308606 + 1.01517i
\(424\) −22.6964 −1.10223
\(425\) 14.1592 9.81634i 0.686823 0.476162i
\(426\) −9.71463 + 8.91604i −0.470676 + 0.431983i
\(427\) 1.37225 + 0.291681i 0.0664080 + 0.0141154i
\(428\) −0.404940 3.85275i −0.0195735 0.186230i
\(429\) 3.17759 + 2.80680i 0.153416 + 0.135513i
\(430\) −6.66631 + 2.88014i −0.321478 + 0.138893i
\(431\) −6.07997 4.41736i −0.292862 0.212777i 0.431646 0.902043i \(-0.357933\pi\)
−0.724508 + 0.689266i \(0.757933\pi\)
\(432\) −8.95595 + 21.7682i −0.430893 + 1.04733i
\(433\) −3.91359 2.84339i −0.188075 0.136644i 0.489763 0.871855i \(-0.337083\pi\)
−0.677838 + 0.735211i \(0.737083\pi\)
\(434\) 0.675325 0.143545i 0.0324166 0.00689037i
\(435\) −2.00029 1.15897i −0.0959067 0.0555684i
\(436\) 4.51301 + 0.959271i 0.216134 + 0.0459407i
\(437\) −23.4916 26.0901i −1.12376 1.24806i
\(438\) −12.0359 26.3549i −0.575099 1.25929i
\(439\) 21.3652 23.7284i 1.01970 1.13250i 0.0285746 0.999592i \(-0.490903\pi\)
0.991129 0.132904i \(-0.0424302\pi\)
\(440\) −3.24847 + 3.52854i −0.154865 + 0.168216i
\(441\) 18.6218 + 7.86955i 0.886751 + 0.374741i
\(442\) 12.4111 + 9.01718i 0.590335 + 0.428904i
\(443\) 4.66178 + 8.07443i 0.221488 + 0.383628i 0.955260 0.295768i \(-0.0955754\pi\)
−0.733772 + 0.679396i \(0.762242\pi\)
\(444\) 2.75232 + 3.71338i 0.130620 + 0.176229i
\(445\) 31.3342 + 23.2993i 1.48539 + 1.10450i
\(446\) 1.63102 + 15.5181i 0.0772310 + 0.734804i
\(447\) −3.08322 + 1.03436i −0.145831 + 0.0489234i
\(448\) −2.18118 + 2.42245i −0.103051 + 0.114450i
\(449\) −25.4208 −1.19968 −0.599840 0.800120i \(-0.704769\pi\)
−0.599840 + 0.800120i \(0.704769\pi\)
\(450\) −18.5028 + 13.3564i −0.872231 + 0.629628i
\(451\) −7.53178 −0.354658
\(452\) −2.61544 + 2.90474i −0.123020 + 0.136627i
\(453\) 0.705980 3.48418i 0.0331698 0.163701i
\(454\) −0.936557 8.91074i −0.0439548 0.418202i
\(455\) 0.998263 + 3.19201i 0.0467993 + 0.149644i
\(456\) 10.6609 24.5717i 0.499240 1.15067i
\(457\) 15.2755 + 26.4579i 0.714557 + 1.23765i 0.963130 + 0.269036i \(0.0867050\pi\)
−0.248573 + 0.968613i \(0.579962\pi\)
\(458\) 17.5000 + 12.7145i 0.817724 + 0.594111i
\(459\) −16.8638 + 6.01707i −0.787133 + 0.280853i
\(460\) −2.00728 3.56724i −0.0935901 0.166323i
\(461\) −9.77138 + 10.8522i −0.455099 + 0.505438i −0.926404 0.376532i \(-0.877116\pi\)
0.471305 + 0.881970i \(0.343783\pi\)
\(462\) 1.12140 + 0.107079i 0.0521722 + 0.00498176i
\(463\) 7.28565 + 8.09154i 0.338593 + 0.376046i 0.888262 0.459337i \(-0.151913\pi\)
−0.549669 + 0.835382i \(0.685246\pi\)
\(464\) 2.64488 + 0.562187i 0.122786 + 0.0260989i
\(465\) 3.27225 1.05766i 0.151747 0.0490480i
\(466\) −7.61274 + 1.61814i −0.352653 + 0.0749587i
\(467\) 0.134914 + 0.0980206i 0.00624307 + 0.00453585i 0.590902 0.806743i \(-0.298772\pi\)
−0.584659 + 0.811279i \(0.698772\pi\)
\(468\) −2.26381 1.57978i −0.104644 0.0730252i
\(469\) −0.633155 0.460014i −0.0292364 0.0212415i
\(470\) 12.6088 21.2918i 0.581600 0.982119i
\(471\) −9.83078 + 3.29802i −0.452978 + 0.151965i
\(472\) −2.15746 20.5269i −0.0993052 0.944826i
\(473\) 1.74657 + 0.371246i 0.0803075 + 0.0170699i
\(474\) −18.9650 5.96307i −0.871091 0.273893i
\(475\) 24.7802 17.1796i 1.13699 0.788256i
\(476\) 0.553779 0.0253824
\(477\) 18.1398 + 19.3907i 0.830565 + 0.887838i
\(478\) −6.86088 + 4.98472i −0.313809 + 0.227996i
\(479\) −26.7243 11.8984i −1.22106 0.543653i −0.307968 0.951397i \(-0.599649\pi\)
−0.913096 + 0.407744i \(0.866316\pi\)
\(480\) 4.02201 5.51797i 0.183579 0.251860i
\(481\) 22.6890 10.1018i 1.03453 0.460602i
\(482\) 17.7247 30.7001i 0.807340 1.39835i
\(483\) 2.05124 4.72780i 0.0933346 0.215122i
\(484\) 3.16805 0.673389i 0.144002 0.0306086i
\(485\) 37.1045 7.45897i 1.68483 0.338694i
\(486\) 22.1801 8.39344i 1.00611 0.380734i
\(487\) 10.0050 30.7921i 0.453369 1.39532i −0.419671 0.907676i \(-0.637855\pi\)
0.873040 0.487649i \(-0.162145\pi\)
\(488\) −6.88485 + 1.46342i −0.311663 + 0.0662459i
\(489\) 25.2302 14.8887i 1.14095 0.673292i
\(490\) −18.3957 13.6786i −0.831034 0.617936i
\(491\) 2.23539 + 2.48266i 0.100882 + 0.112041i 0.791471 0.611206i \(-0.209315\pi\)
−0.690589 + 0.723247i \(0.742649\pi\)
\(492\) 4.87206 0.559025i 0.219649 0.0252028i
\(493\) 1.02841 + 1.78126i 0.0463174 + 0.0802241i
\(494\) 21.7207 + 15.7810i 0.977262 + 0.710023i
\(495\) 5.61091 0.0448060i 0.252192 0.00201388i
\(496\) −3.25413 + 2.36426i −0.146115 + 0.106159i
\(497\) 2.33650 + 1.04028i 0.104806 + 0.0466628i
\(498\) −0.0112811 1.18476i −0.000505518 0.0530906i
\(499\) −13.0016 + 22.5194i −0.582030 + 1.00811i 0.413208 + 0.910637i \(0.364408\pi\)
−0.995239 + 0.0974695i \(0.968925\pi\)
\(500\) 3.25725 1.32259i 0.145669 0.0591479i
\(501\) 35.2831 + 11.0939i 1.57633 + 0.495639i
\(502\) 23.3832 25.9696i 1.04364 1.15908i
\(503\) −11.9885 + 8.71019i −0.534543 + 0.388368i −0.822054 0.569409i \(-0.807172\pi\)
0.287512 + 0.957777i \(0.407172\pi\)
\(504\) 3.93113 0.0748696i 0.175106 0.00333496i
\(505\) 35.2383 + 16.1583i 1.56808 + 0.719037i
\(506\) −0.774358 + 7.36753i −0.0344244 + 0.327527i
\(507\) 5.66081 5.19546i 0.251405 0.230738i
\(508\) −4.38252 + 1.95123i −0.194443 + 0.0865716i
\(509\) −25.8484 28.7076i −1.14571 1.27244i −0.956897 0.290428i \(-0.906202\pi\)
−0.188814 0.982013i \(-0.560464\pi\)
\(510\) 20.1951 2.09123i 0.894255 0.0926013i
\(511\) −3.76037 + 4.17631i −0.166349 + 0.184749i
\(512\) 4.71125 14.4997i 0.208210 0.640804i
\(513\) −29.5134 + 10.5305i −1.30305 + 0.464934i
\(514\) 0.0146551 + 0.0451039i 0.000646411 + 0.00198945i
\(515\) 12.3854 + 14.0650i 0.545764 + 0.619780i
\(516\) −1.15735 0.110512i −0.0509497 0.00486503i
\(517\) −5.55845 + 2.47478i −0.244460 + 0.108841i
\(518\) 3.29951 5.71492i 0.144972 0.251099i
\(519\) 5.70634 0.654750i 0.250480 0.0287403i
\(520\) −11.0893 12.5932i −0.486299 0.552250i
\(521\) −7.88351 + 5.72771i −0.345383 + 0.250935i −0.746929 0.664903i \(-0.768473\pi\)
0.401547 + 0.915839i \(0.368473\pi\)
\(522\) −1.40680 2.33291i −0.0615741 0.102109i
\(523\) 9.64807 + 29.6937i 0.421881 + 1.29842i 0.905950 + 0.423386i \(0.139158\pi\)
−0.484069 + 0.875030i \(0.660842\pi\)
\(524\) −1.45025 2.51190i −0.0633543 0.109733i
\(525\) 3.80508 + 2.26123i 0.166067 + 0.0986883i
\(526\) −17.7525 + 30.7483i −0.774048 + 1.34069i
\(527\) −2.99280 0.636139i −0.130368 0.0277106i
\(528\) −6.22216 + 2.08741i −0.270785 + 0.0908427i
\(529\) 9.94963 + 4.42986i 0.432593 + 0.192603i
\(530\) −14.7653 26.2401i −0.641363 1.13980i
\(531\) −15.8128 + 18.2491i −0.686218 + 0.791943i
\(532\) 0.969173 0.0420190
\(533\) 2.75440 26.2063i 0.119306 1.13512i
\(534\) 19.1150 + 41.8558i 0.827185 + 1.81128i
\(535\) −22.4653 + 15.9455i −0.971260 + 0.689383i
\(536\) 3.84076 + 0.816379i 0.165896 + 0.0352622i
\(537\) −5.63354 0.537929i −0.243105 0.0232133i
\(538\) −24.1278 + 5.12853i −1.04022 + 0.221107i
\(539\) 1.74182 + 5.36078i 0.0750257 + 0.230905i
\(540\) −3.62619 + 0.445437i −0.156046 + 0.0191686i
\(541\) −3.37778 + 10.3957i −0.145222 + 0.446948i −0.997039 0.0768912i \(-0.975501\pi\)
0.851817 + 0.523839i \(0.175501\pi\)
\(542\) −1.61779 + 15.3922i −0.0694900 + 0.661153i
\(543\) −2.36475 10.6267i −0.101481 0.456035i
\(544\) −5.54992 + 2.47098i −0.237951 + 0.105942i
\(545\) −9.79332 31.3148i −0.419500 1.34138i
\(546\) −0.782674 + 3.86268i −0.0334953 + 0.165307i
\(547\) 14.0092 + 6.23729i 0.598989 + 0.266687i 0.683753 0.729714i \(-0.260347\pi\)
−0.0847633 + 0.996401i \(0.527013\pi\)
\(548\) −0.905242 2.78605i −0.0386700 0.119014i
\(549\) 6.75291 + 4.71246i 0.288207 + 0.201123i
\(550\) −6.19277 1.46016i −0.264061 0.0622613i
\(551\) 1.79983 + 3.11740i 0.0766755 + 0.132806i
\(552\) 0.246190 + 25.8554i 0.0104786 + 1.10048i
\(553\) 0.403072 + 3.83497i 0.0171404 + 0.163080i
\(554\) 1.09452 + 10.4137i 0.0465017 + 0.442434i
\(555\) 13.4154 30.0074i 0.569453 1.27374i
\(556\) −0.191588 + 1.82283i −0.00812513 + 0.0773054i
\(557\) 22.3912 0.948745 0.474373 0.880324i \(-0.342675\pi\)
0.474373 + 0.880324i \(0.342675\pi\)
\(558\) 3.97926 + 0.766928i 0.168456 + 0.0324666i
\(559\) −1.93045 + 5.94132i −0.0816494 + 0.251291i
\(560\) −5.05180 1.13232i −0.213478 0.0478492i
\(561\) −4.34698 2.45484i −0.183530 0.103644i
\(562\) 16.4212 + 18.2376i 0.692688 + 0.769308i
\(563\) 8.98018 + 9.97350i 0.378469 + 0.420333i 0.902042 0.431648i \(-0.142068\pi\)
−0.523573 + 0.851981i \(0.675401\pi\)
\(564\) 3.41189 2.01341i 0.143667 0.0847800i
\(565\) 27.1231 + 6.07941i 1.14108 + 0.255763i
\(566\) −7.88100 + 24.2552i −0.331263 + 1.01952i
\(567\) −3.20587 3.29872i −0.134634 0.138533i
\(568\) −12.8321 −0.538421
\(569\) 1.22173 11.6240i 0.0512175 0.487302i −0.938605 0.344994i \(-0.887881\pi\)
0.989822 0.142308i \(-0.0454523\pi\)
\(570\) 35.3436 3.65988i 1.48038 0.153296i
\(571\) 4.05203 + 38.5525i 0.169572 + 1.61337i 0.666450 + 0.745550i \(0.267813\pi\)
−0.496878 + 0.867820i \(0.665520\pi\)
\(572\) −0.0804537 0.765466i −0.00336394 0.0320057i
\(573\) −16.7270 9.44616i −0.698782 0.394619i
\(574\) −3.50071 6.06341i −0.146117 0.253082i
\(575\) −15.1079 + 24.8803i −0.630044 + 1.03758i
\(576\) −17.3280 + 8.11374i −0.722000 + 0.338073i
\(577\) −10.4483 32.1567i −0.434970 1.33870i −0.893118 0.449823i \(-0.851487\pi\)
0.458148 0.888876i \(-0.348513\pi\)
\(578\) 7.12445 + 3.17201i 0.296338 + 0.131938i
\(579\) −14.7959 + 4.96372i −0.614896 + 0.206285i
\(580\) 0.125268 + 0.400554i 0.00520149 + 0.0166321i
\(581\) −0.209945 + 0.0934735i −0.00870998 + 0.00387793i
\(582\) 42.5457 + 13.3774i 1.76358 + 0.554513i
\(583\) −0.773864 + 7.36283i −0.0320502 + 0.304937i
\(584\) 8.71289 26.8155i 0.360542 1.10963i
\(585\) −1.89603 + 19.5392i −0.0783911 + 0.807846i
\(586\) −11.0331 33.9565i −0.455775 1.40273i
\(587\) −14.4709 + 3.07588i −0.597277 + 0.126955i −0.496623 0.867966i \(-0.665427\pi\)
−0.100654 + 0.994921i \(0.532094\pi\)
\(588\) −1.52462 3.33843i −0.0628741 0.137675i
\(589\) −5.23772 1.11331i −0.215816 0.0458732i
\(590\) 22.3283 15.8482i 0.919240 0.652460i
\(591\) −46.8462 4.47319i −1.92699 0.184003i
\(592\) −4.01868 + 38.2352i −0.165167 + 1.57146i
\(593\) 2.30607 0.0946989 0.0473495 0.998878i \(-0.484923\pi\)
0.0473495 + 0.998878i \(0.484923\pi\)
\(594\) 5.81842 + 3.14120i 0.238733 + 0.128885i
\(595\) −1.93122 3.43205i −0.0791721 0.140701i
\(596\) 0.539348 + 0.240133i 0.0220925 + 0.00983624i
\(597\) 20.3477 + 17.9733i 0.832778 + 0.735600i
\(598\) −25.3516 5.38866i −1.03671 0.220359i
\(599\) −4.41108 + 7.64022i −0.180232 + 0.312171i −0.941959 0.335727i \(-0.891018\pi\)
0.761727 + 0.647898i \(0.224352\pi\)
\(600\) −22.0548 2.59926i −0.900383 0.106114i
\(601\) −15.5663 26.9616i −0.634961 1.09978i −0.986523 0.163620i \(-0.947683\pi\)
0.351562 0.936165i \(-0.385651\pi\)
\(602\) 0.512925 + 1.57862i 0.0209052 + 0.0643397i
\(603\) −2.37221 3.93384i −0.0966038 0.160198i
\(604\) −0.522119 + 0.379342i −0.0212447 + 0.0154352i
\(605\) −15.2214 17.2857i −0.618838 0.702763i
\(606\) 27.2024 + 36.7009i 1.10502 + 1.49087i
\(607\) −3.13347 + 5.42734i −0.127184 + 0.220289i −0.922584 0.385795i \(-0.873927\pi\)
0.795401 + 0.606084i \(0.207260\pi\)
\(608\) −9.71295 + 4.32448i −0.393912 + 0.175381i
\(609\) −0.306507 + 0.430430i −0.0124203 + 0.0174419i
\(610\) −6.17090 7.00778i −0.249852 0.283737i
\(611\) −6.57809 20.2453i −0.266121 0.819037i
\(612\) 2.99412 + 1.26532i 0.121030 + 0.0511474i
\(613\) −8.53626 + 26.2719i −0.344776 + 1.06111i 0.616927 + 0.787020i \(0.288377\pi\)
−0.961704 + 0.274092i \(0.911623\pi\)
\(614\) 9.07808 10.0822i 0.366361 0.406886i
\(615\) −20.4551 28.2452i −0.824829 1.13895i
\(616\) 0.733544 + 0.814683i 0.0295553 + 0.0328245i
\(617\) 3.02843 1.34834i 0.121920 0.0542822i −0.344870 0.938650i \(-0.612077\pi\)
0.466790 + 0.884368i \(0.345410\pi\)
\(618\) 4.79712 + 21.5573i 0.192968 + 0.867162i
\(619\) 2.72043 25.8832i 0.109343 1.04033i −0.792973 0.609257i \(-0.791468\pi\)
0.902316 0.431075i \(-0.141866\pi\)
\(620\) −0.567491 0.260220i −0.0227910 0.0104507i
\(621\) 21.8929 20.8750i 0.878530 0.837685i
\(622\) 25.1555 18.2766i 1.00864 0.732823i
\(623\) 5.97206 6.63265i 0.239266 0.265731i
\(624\) −4.98753 22.4130i −0.199661 0.897237i
\(625\) −19.5559 15.5746i −0.782236 0.622982i
\(626\) −17.6057 + 30.4939i −0.703664 + 1.21878i
\(627\) −7.60768 4.29624i −0.303822 0.171575i
\(628\) 1.71970 + 0.765658i 0.0686234 + 0.0305531i
\(629\) −23.6593 + 17.1895i −0.943358 + 0.685390i
\(630\) 2.64398 + 4.49620i 0.105339 + 0.179133i
\(631\) −17.6953 12.8564i −0.704439 0.511805i 0.176936 0.984222i \(-0.443381\pi\)
−0.881375 + 0.472417i \(0.843381\pi\)
\(632\) −9.67339 16.7548i −0.384787 0.666470i
\(633\) 17.2813 + 23.3156i 0.686872 + 0.926713i
\(634\) −10.9034 12.1094i −0.433028 0.480927i
\(635\) 27.3761 + 20.3562i 1.08639 + 0.807810i
\(636\) −0.0458971 4.82021i −0.00181994 0.191134i
\(637\) −19.2895 + 4.10011i −0.764277 + 0.162452i
\(638\) 0.234720 0.722393i 0.00929264 0.0285998i
\(639\) 10.2559 + 10.9631i 0.405716 + 0.433693i
\(640\) 29.0005 5.82985i 1.14635 0.230445i
\(641\) 31.1679 6.62495i 1.23106 0.261670i 0.453945 0.891030i \(-0.350016\pi\)
0.777114 + 0.629360i \(0.216683\pi\)
\(642\) −32.2526 + 3.70069i −1.27291 + 0.146054i
\(643\) 6.74775 11.6875i 0.266105 0.460908i −0.701747 0.712426i \(-0.747596\pi\)
0.967853 + 0.251518i \(0.0809297\pi\)
\(644\) −0.854705 + 0.380539i −0.0336801 + 0.0149953i
\(645\) 3.35119 + 7.55812i 0.131953 + 0.297601i
\(646\) −28.8806 12.8585i −1.13629 0.505910i
\(647\) −20.1643 + 14.6502i −0.792741 + 0.575960i −0.908776 0.417285i \(-0.862982\pi\)
0.116035 + 0.993245i \(0.462982\pi\)
\(648\) 21.4255 + 8.57733i 0.841674 + 0.336949i
\(649\) −6.73259 −0.264277
\(650\) 7.34524 21.0134i 0.288104 0.824212i
\(651\) −0.170741 0.767275i −0.00669186 0.0300719i
\(652\) −5.20215 1.10575i −0.203732 0.0433046i
\(653\) −2.99391 28.4852i −0.117161 1.11471i −0.882248 0.470784i \(-0.843971\pi\)
0.765088 0.643926i \(-0.222696\pi\)
\(654\) 7.67831 37.8942i 0.300246 1.48178i
\(655\) −10.5100 + 17.7478i −0.410661 + 0.693462i
\(656\) 32.9999 + 23.9759i 1.28843 + 0.936100i
\(657\) −29.8735 + 13.9881i −1.16548 + 0.545729i
\(658\) −4.57583 3.32454i −0.178384 0.129604i
\(659\) −8.49965 + 1.80666i −0.331100 + 0.0703774i −0.370462 0.928848i \(-0.620801\pi\)
0.0393625 + 0.999225i \(0.487467\pi\)
\(660\) −0.755951 0.682767i −0.0294254 0.0265767i
\(661\) 30.0665 + 6.39082i 1.16945 + 0.248574i 0.751398 0.659849i \(-0.229380\pi\)
0.418052 + 0.908423i \(0.362713\pi\)
\(662\) −23.9276 26.5743i −0.929974 1.03284i
\(663\) 10.1312 14.2273i 0.393462 0.552542i
\(664\) 0.771519 0.856859i 0.0299407 0.0332526i
\(665\) −3.37984 6.00646i −0.131064 0.232921i
\(666\) 30.8974 23.3599i 1.19725 0.905179i
\(667\) −2.81128 2.04252i −0.108853 0.0790866i
\(668\) −3.35725 5.81492i −0.129896 0.224986i
\(669\) 17.6491 2.02507i 0.682353 0.0782938i
\(670\) 1.55479 + 4.97154i 0.0600667 + 0.192067i
\(671\) 0.239993 + 2.28338i 0.00926482 + 0.0881489i
\(672\) −1.16974 1.03325i −0.0451239 0.0398583i
\(673\) −16.5978 + 18.4338i −0.639799 + 0.710569i −0.972615 0.232423i \(-0.925335\pi\)
0.332816 + 0.942992i \(0.392001\pi\)
\(674\) 1.89434 0.0729673
\(675\) 15.4063 + 20.9200i 0.592990 + 0.805209i
\(676\) −1.39489 −0.0536495
\(677\) −4.85958 + 5.39711i −0.186769 + 0.207428i −0.829256 0.558868i \(-0.811236\pi\)
0.642488 + 0.766296i \(0.277902\pi\)
\(678\) 24.5495 + 21.6848i 0.942819 + 0.832801i
\(679\) −0.904244 8.60331i −0.0347017 0.330165i
\(680\) 15.8553 + 11.7896i 0.608023 + 0.452111i
\(681\) −10.1344 + 1.16283i −0.388350 + 0.0445596i
\(682\) 0.564953 + 0.978527i 0.0216332 + 0.0374697i
\(683\) −38.6994 28.1168i −1.48079 1.07586i −0.977301 0.211857i \(-0.932049\pi\)
−0.503491 0.864001i \(-0.667951\pi\)
\(684\) 5.24004 + 2.21444i 0.200358 + 0.0846712i
\(685\) −14.1097 + 15.3262i −0.539104 + 0.585582i
\(686\) −7.14807 + 7.93873i −0.272914 + 0.303102i
\(687\) 14.2853 20.0610i 0.545018 0.765373i
\(688\) −6.47070 7.18644i −0.246693 0.273980i
\(689\) −25.3355 5.38522i −0.965204 0.205161i
\(690\) −29.7322 + 17.1051i −1.13189 + 0.651178i
\(691\) 39.4507 8.38550i 1.50077 0.319000i 0.617019 0.786948i \(-0.288340\pi\)
0.883756 + 0.467949i \(0.155007\pi\)
\(692\) −0.843588 0.612902i −0.0320684 0.0232991i
\(693\) 0.109749 1.27783i 0.00416902 0.0485408i
\(694\) −40.7259 29.5891i −1.54593 1.12319i
\(695\) 11.9652 5.16948i 0.453865 0.196089i
\(696\) 0.526486 2.59833i 0.0199564 0.0984894i
\(697\) 3.24329 + 30.8578i 0.122848 + 1.16882i
\(698\) 22.9750 + 4.88349i 0.869617 + 0.184843i
\(699\) 1.92471 + 8.64926i 0.0727992 + 0.327145i
\(700\) −0.231350 0.769525i −0.00874421 0.0290853i
\(701\) −6.65878 −0.251498 −0.125749 0.992062i \(-0.540133\pi\)
−0.125749 + 0.992062i \(0.540133\pi\)
\(702\) −13.0574 + 19.0961i −0.492820 + 0.720734i
\(703\) −41.4063 + 30.0834i −1.56167 + 1.13462i
\(704\) −4.87355 2.16984i −0.183679 0.0817791i
\(705\) −24.3766 14.1238i −0.918075 0.531933i
\(706\) −34.8667 + 15.5237i −1.31223 + 0.584241i
\(707\) 4.43044 7.67375i 0.166624 0.288601i
\(708\) 4.35509 0.499707i 0.163674 0.0187801i
\(709\) −21.9439 + 4.66432i −0.824120 + 0.175172i −0.600623 0.799533i \(-0.705081\pi\)
−0.223497 + 0.974705i \(0.571747\pi\)
\(710\) −8.34797 14.8356i −0.313294 0.556769i
\(711\) −6.58314 + 21.6555i −0.246887 + 0.812147i
\(712\) −13.8375 + 42.5873i −0.518581 + 1.59603i
\(713\) 5.05623 1.07473i 0.189357 0.0402491i
\(714\) −0.0441859 4.64050i −0.00165362 0.173666i
\(715\) −4.46342 + 3.16805i −0.166922 + 0.118478i
\(716\) 0.687445 + 0.763485i 0.0256910 + 0.0285328i
\(717\) 5.74928 + 7.75680i 0.214711 + 0.289683i
\(718\) 1.53756 + 2.66313i 0.0573812 + 0.0993871i
\(719\) 1.49516 + 1.08630i 0.0557602 + 0.0405122i 0.615316 0.788280i \(-0.289028\pi\)
−0.559556 + 0.828793i \(0.689028\pi\)
\(720\) −24.7264 17.6649i −0.921499 0.658330i
\(721\) 3.46554 2.51786i 0.129063 0.0937700i
\(722\) −24.1379 10.7469i −0.898320 0.399958i
\(723\) −35.1431 19.8461i −1.30698 0.738085i
\(724\) −0.988185 + 1.71159i −0.0367256 + 0.0636106i
\(725\) 2.04559 2.17322i 0.0759712 0.0807114i
\(726\) −5.89558 26.4936i −0.218805 0.983268i
\(727\) −1.70712 + 1.89594i −0.0633134 + 0.0703167i −0.773969 0.633223i \(-0.781732\pi\)
0.710656 + 0.703540i \(0.248398\pi\)
\(728\) −3.10290 + 2.25439i −0.115001 + 0.0835531i
\(729\) −9.79604 25.1602i −0.362816 0.931861i
\(730\) 36.6706 7.37173i 1.35724 0.272840i
\(731\) 0.768901 7.31560i 0.0284388 0.270577i
\(732\) −0.324721 1.45923i −0.0120020 0.0539347i
\(733\) −10.4629 + 4.65840i −0.386458 + 0.172062i −0.590763 0.806845i \(-0.701173\pi\)
0.204305 + 0.978907i \(0.434507\pi\)
\(734\) −35.6594 39.6037i −1.31621 1.46180i
\(735\) −15.3731 + 21.0911i −0.567046 + 0.777956i
\(736\) 6.86778 7.62744i 0.253150 0.281151i
\(737\) 0.395794 1.21813i 0.0145792 0.0448703i
\(738\) −5.07320 40.7818i −0.186747 1.50120i
\(739\) 14.8777 + 45.7888i 0.547285 + 1.68437i 0.715495 + 0.698618i \(0.246201\pi\)
−0.168210 + 0.985751i \(0.553799\pi\)
\(740\) −5.47781 + 2.36665i −0.201368 + 0.0869998i
\(741\) 17.7306 24.8993i 0.651351 0.914698i
\(742\) −6.28708 + 2.79919i −0.230806 + 0.102761i
\(743\) 3.67273 6.36135i 0.134739 0.233375i −0.790759 0.612128i \(-0.790314\pi\)
0.925498 + 0.378753i \(0.123647\pi\)
\(744\) 2.34834 + 3.16833i 0.0860942 + 0.116156i
\(745\) −0.392660 4.18004i −0.0143860 0.153145i
\(746\) 16.9035 12.2811i 0.618880 0.449642i
\(747\) −1.34869 + 0.0256862i −0.0493458 + 0.000939808i
\(748\) 0.280061 + 0.861940i 0.0102401 + 0.0315156i
\(749\) 3.14846 + 5.45329i 0.115042 + 0.199259i
\(750\) −11.3428 27.1893i −0.414180 0.992811i
\(751\) 7.69305 13.3248i 0.280724 0.486227i −0.690840 0.723008i \(-0.742759\pi\)
0.971563 + 0.236781i \(0.0760923\pi\)
\(752\) 32.2319 + 6.85110i 1.17538 + 0.249834i
\(753\) −29.8189 26.3393i −1.08666 0.959857i
\(754\) 2.42768 + 1.08087i 0.0884109 + 0.0393631i
\(755\) 4.17178 + 1.91295i 0.151827 + 0.0696193i
\(756\) 0.0238502 + 0.834732i 0.000867424 + 0.0303589i
\(757\) −28.4272 −1.03320 −0.516602 0.856226i \(-0.672803\pi\)
−0.516602 + 0.856226i \(0.672803\pi\)
\(758\) −4.09757 + 38.9858i −0.148831 + 1.41603i
\(759\) 8.39604 + 0.801711i 0.304757 + 0.0291003i
\(760\) 27.7485 + 20.6331i 1.00654 + 0.748440i
\(761\) 33.6491 + 7.15233i 1.21978 + 0.259272i 0.772437 0.635091i \(-0.219038\pi\)
0.447341 + 0.894363i \(0.352371\pi\)
\(762\) 16.7004 + 36.5685i 0.604990 + 1.32474i
\(763\) −7.33564 + 1.55924i −0.265568 + 0.0564482i
\(764\) 1.07767 + 3.31672i 0.0389886 + 0.119995i
\(765\) −2.59971 22.9687i −0.0939926 0.830435i
\(766\) −7.77667 + 23.9341i −0.280983 + 0.864775i
\(767\) 2.46213 23.4256i 0.0889023 0.845849i
\(768\) 12.1771 + 3.82877i 0.439402 + 0.138159i
\(769\) 3.95776 1.76211i 0.142720 0.0635432i −0.334134 0.942526i \(-0.608444\pi\)
0.476854 + 0.878982i \(0.341777\pi\)
\(770\) −0.464672 + 1.37807i −0.0167456 + 0.0496623i
\(771\) 0.0511902 0.0171732i 0.00184357 0.000618479i
\(772\) 2.58824 + 1.15236i 0.0931529 + 0.0414744i
\(773\) −8.09794 24.9229i −0.291263 0.896414i −0.984451 0.175658i \(-0.943795\pi\)
0.693189 0.720756i \(-0.256205\pi\)
\(774\) −0.833714 + 9.70710i −0.0299672 + 0.348915i
\(775\) 0.366318 + 4.42451i 0.0131585 + 0.158933i
\(776\) 21.7011 + 37.5874i 0.779024 + 1.34931i
\(777\) −6.54198 3.69441i −0.234692 0.132536i
\(778\) −2.47699 23.5670i −0.0888044 0.844917i
\(779\) 5.67610 + 54.0045i 0.203368 + 1.93491i
\(780\) 2.65210 2.38059i 0.0949603 0.0852389i
\(781\) −0.437526 + 4.16279i −0.0156559 + 0.148956i
\(782\) 30.5183 1.09133
\(783\) −2.64067 + 1.62688i −0.0943699 + 0.0581400i
\(784\) 9.43327 29.0326i 0.336902 1.03688i
\(785\) −1.25199 13.3280i −0.0446853 0.475695i
\(786\) −20.9332 + 12.3530i −0.746664 + 0.440618i
\(787\) −26.2581 29.1626i −0.936000 1.03953i −0.999137 0.0415287i \(-0.986777\pi\)
0.0631371 0.998005i \(-0.479889\pi\)
\(788\) 5.71651 + 6.34882i 0.203642 + 0.226167i
\(789\) 35.1982 + 19.8773i 1.25309 + 0.707649i
\(790\) 13.0777 22.0837i 0.465284 0.785702i
\(791\) 1.96330 6.04243i 0.0698071 0.214844i
\(792\) 2.10461 + 6.08081i 0.0747840 + 0.216072i
\(793\) −8.03263 −0.285247
\(794\) −0.499344 + 4.75094i −0.0177210 + 0.168604i
\(795\) −29.7132 + 17.0941i −1.05382 + 0.606267i
\(796\) −0.515186 4.90167i −0.0182603 0.173735i
\(797\) 3.03682 + 28.8934i 0.107570 + 1.02346i 0.906549 + 0.422100i \(0.138707\pi\)
−0.798980 + 0.601358i \(0.794627\pi\)
\(798\) −0.0773302 8.12138i −0.00273746 0.287494i
\(799\) 12.5328 + 21.7074i 0.443377 + 0.767952i
\(800\) 5.75221 + 6.67980i 0.203371 + 0.236167i
\(801\) 47.4439 22.2154i 1.67635 0.784941i
\(802\) 0.971332 + 2.98945i 0.0342989 + 0.105561i
\(803\) −8.40201 3.74082i −0.296501 0.132011i
\(804\) −0.165614 + 0.817343i −0.00584075 + 0.0288255i
\(805\) 5.33904 + 3.96998i 0.188177 + 0.139923i
\(806\) −3.61133 + 1.60787i −0.127204 + 0.0566347i
\(807\) 6.10018 + 27.4130i 0.214737 + 0.964983i
\(808\) −4.64699 + 44.2132i −0.163481 + 1.55541i
\(809\) 2.52965 7.78546i 0.0889378 0.273722i −0.896689 0.442662i \(-0.854034\pi\)
0.985626 + 0.168939i \(0.0540342\pi\)
\(810\) 4.02196 + 30.3508i 0.141317 + 1.06642i
\(811\) −10.9116 33.5823i −0.383157 1.17923i −0.937809 0.347152i \(-0.887149\pi\)
0.554652 0.832082i \(-0.312851\pi\)
\(812\) 0.0938318 0.0199446i 0.00329285 0.000699917i
\(813\) 17.5410 + 1.67493i 0.615189 + 0.0587425i
\(814\) 10.5637 + 2.24539i 0.370259 + 0.0787010i
\(815\) 11.2888 + 36.0965i 0.395428 + 1.26441i
\(816\) 11.2315 + 24.5934i 0.393181 + 0.860942i
\(817\) 1.34566 12.8031i 0.0470786 0.447923i
\(818\) 46.1490 1.61356
\(819\) 4.40599 + 0.849171i 0.153958 + 0.0296724i
\(820\) −0.731359 + 6.28869i −0.0255402 + 0.219611i
\(821\) 23.7180 + 10.5599i 0.827763 + 0.368544i 0.776481 0.630141i \(-0.217003\pi\)
0.0512816 + 0.998684i \(0.483669\pi\)
\(822\) −23.2740 + 7.80795i −0.811775 + 0.272334i
\(823\) 36.8545 + 7.83366i 1.28467 + 0.273064i 0.799133 0.601154i \(-0.205292\pi\)
0.485533 + 0.874218i \(0.338625\pi\)
\(824\) −10.7459 + 18.6125i −0.374352 + 0.648396i
\(825\) −1.59520 + 7.06606i −0.0555378 + 0.246009i
\(826\) −3.12925 5.42003i −0.108881 0.188587i
\(827\) 5.57826 + 17.1681i 0.193975 + 0.596994i 0.999987 + 0.00509483i \(0.00162174\pi\)
−0.806012 + 0.591899i \(0.798378\pi\)
\(828\) −5.49062 + 0.104571i −0.190812 + 0.00363408i
\(829\) 38.5194 27.9860i 1.33783 0.971993i 0.338313 0.941034i \(-0.390144\pi\)
0.999521 0.0309591i \(-0.00985618\pi\)
\(830\) 1.49256 + 0.334545i 0.0518075 + 0.0116122i
\(831\) 11.8437 1.35895i 0.410853 0.0471416i
\(832\) 9.33210 16.1637i 0.323532 0.560375i
\(833\) 21.2132 9.44471i 0.734993 0.327240i
\(834\) 15.2901 + 1.46000i 0.529452 + 0.0505558i
\(835\) −24.3302 + 41.0852i −0.841982 + 1.42181i
\(836\) 0.490137 + 1.50849i 0.0169518 + 0.0521721i
\(837\) 0.829981 4.53855i 0.0286883 0.156875i
\(838\) −11.1747 + 34.3923i −0.386025 + 1.18806i
\(839\) −20.1621 + 22.3923i −0.696075 + 0.773069i −0.982746 0.184960i \(-0.940785\pi\)
0.286672 + 0.958029i \(0.407451\pi\)
\(840\) −1.06298 + 4.96343i −0.0366764 + 0.171255i
\(841\) −19.1664 21.2864i −0.660910 0.734015i
\(842\) −15.0867 + 6.71705i −0.519923 + 0.231485i
\(843\) 20.5848 18.8926i 0.708979 0.650697i
\(844\) 0.550723 5.23978i 0.0189567 0.180361i
\(845\) 4.86444 + 8.64483i 0.167342 + 0.297391i
\(846\) −17.1440 28.4300i −0.589424 0.977443i
\(847\) −4.25909 + 3.09441i −0.146344 + 0.106325i
\(848\) 26.8287 29.7962i 0.921300 1.02321i
\(849\) 27.6990 + 8.70928i 0.950629 + 0.298902i
\(850\) −3.31560 + 26.0007i −0.113724 + 0.891815i
\(851\) 24.7038 42.7882i 0.846835 1.46676i
\(852\) −0.0259492 2.72524i −0.000889006 0.0933653i
\(853\) −6.34609 2.82546i −0.217286 0.0967420i 0.295207 0.955433i \(-0.404611\pi\)
−0.512493 + 0.858691i \(0.671278\pi\)
\(854\) −1.72667 + 1.25450i −0.0590855 + 0.0429282i
\(855\) −4.54977 40.1977i −0.155599 1.37473i
\(856\) −25.5591 18.5698i −0.873593 0.634702i
\(857\) −16.5062 28.5897i −0.563843 0.976604i −0.997156 0.0753610i \(-0.975989\pi\)
0.433314 0.901243i \(-0.357344\pi\)
\(858\) −6.40795 + 0.735254i −0.218764 + 0.0251012i
\(859\) 16.1866 + 17.9770i 0.552279 + 0.613368i 0.953051 0.302810i \(-0.0979246\pi\)
−0.400772 + 0.916178i \(0.631258\pi\)
\(860\) 0.479570 1.42226i 0.0163532 0.0484986i
\(861\) −6.86501 + 4.05115i −0.233959 + 0.138063i
\(862\) 11.1833 2.37709i 0.380906 0.0809640i
\(863\) 10.3560 31.8723i 0.352521 1.08495i −0.604912 0.796292i \(-0.706792\pi\)
0.957433 0.288655i \(-0.0932081\pi\)
\(864\) −3.96363 8.25917i −0.134845 0.280983i
\(865\) −0.856595 + 7.36555i −0.0291251 + 0.250436i
\(866\) 7.19854 1.53010i 0.244616 0.0519948i
\(867\) 3.53398 8.14529i 0.120020 0.276629i
\(868\) −0.0713495 + 0.123581i −0.00242176 + 0.00419461i
\(869\) −5.76517 + 2.56682i −0.195570 + 0.0870734i
\(870\) 3.34653 1.08167i 0.113458 0.0366721i
\(871\) 4.09365 + 1.82261i 0.138708 + 0.0617568i
\(872\) 30.4405 22.1163i 1.03085 0.748953i
\(873\) 14.7685 48.5817i 0.499838 1.64424i
\(874\) 53.4103 1.80663
\(875\) −3.96234 + 4.11739i −0.133952 + 0.139193i
\(876\) 5.71264 + 1.79620i 0.193012 + 0.0606879i
\(877\) 42.1754 + 8.96466i 1.42416 + 0.302715i 0.854623 0.519249i \(-0.173788\pi\)
0.569539 + 0.821964i \(0.307122\pi\)
\(878\) 5.07753 + 48.3095i 0.171358 + 1.63037i
\(879\) −38.5386 + 12.9289i −1.29987 + 0.436081i
\(880\) −0.792416 8.43562i −0.0267123 0.284365i
\(881\) 1.01683 + 0.738771i 0.0342579 + 0.0248898i 0.604782 0.796391i \(-0.293260\pi\)
−0.570525 + 0.821281i \(0.693260\pi\)
\(882\) −27.8534 + 13.0422i −0.937873 + 0.439154i
\(883\) 10.5261 + 7.64764i 0.354231 + 0.257364i 0.750642 0.660709i \(-0.229744\pi\)
−0.396411 + 0.918073i \(0.629744\pi\)
\(884\) −3.10148 + 0.659240i −0.104314 + 0.0221727i
\(885\) −18.2846 25.2481i −0.614630 0.848705i
\(886\) −13.8742 2.94906i −0.466114 0.0990755i
\(887\) −20.3207 22.5685i −0.682304 0.757775i 0.298151 0.954519i \(-0.403630\pi\)
−0.980455 + 0.196743i \(0.936963\pi\)
\(888\) 37.5238 + 3.58303i 1.25922 + 0.120239i
\(889\) 5.21767 5.79481i 0.174995 0.194352i
\(890\) −58.2387 + 11.7075i −1.95217 + 0.392436i
\(891\) 3.51306 6.65809i 0.117692 0.223054i
\(892\) −2.60913 1.89564i −0.0873600 0.0634707i
\(893\) 21.9337 + 37.9903i 0.733983 + 1.27130i
\(894\) 1.96921 4.53873i 0.0658602 0.151798i
\(895\) 2.33435 6.92298i 0.0780288 0.231410i
\(896\) −0.706748 6.72426i −0.0236108 0.224642i
\(897\) −5.85996 + 28.9203i −0.195658 + 0.965620i
\(898\) 25.8775 28.7399i 0.863543 0.959062i
\(899\) −0.530007 −0.0176767
\(900\) 0.507425 4.68920i 0.0169142 0.156307i
\(901\) 30.4989 1.01606
\(902\) 7.66711 8.51518i 0.255287 0.283525i
\(903\) 1.79164 0.601057i 0.0596219 0.0200019i
\(904\) 3.33196 + 31.7015i 0.110819 + 1.05438i
\(905\) 14.0537 + 0.155408i 0.467162 + 0.00516594i
\(906\) 3.22043 + 4.34493i 0.106992 + 0.144351i
\(907\) −19.2588 33.3572i −0.639477 1.10761i −0.985548 0.169398i \(-0.945818\pi\)
0.346071 0.938208i \(-0.387516\pi\)
\(908\) 1.49820 + 1.08851i 0.0497195 + 0.0361233i
\(909\) 41.4877 31.3667i 1.37606 1.04037i
\(910\) −4.62498 2.12076i −0.153317 0.0703025i
\(911\) −13.2069 + 14.6677i −0.437563 + 0.485963i −0.921081 0.389372i \(-0.872692\pi\)
0.483518 + 0.875335i \(0.339359\pi\)
\(912\) 19.6563 + 43.0411i 0.650885 + 1.42523i
\(913\) −0.251663 0.279501i −0.00832884 0.00925012i
\(914\) −45.4624 9.66333i −1.50376 0.319634i
\(915\) −7.91119 + 7.10129i −0.261536 + 0.234761i
\(916\) −4.37319 + 0.929551i −0.144494 + 0.0307132i
\(917\) 3.81417 + 2.77116i 0.125955 + 0.0915118i
\(918\) 10.3641 25.1908i 0.342065 0.831420i
\(919\) −17.8319 12.9556i −0.588219 0.427366i 0.253459 0.967346i \(-0.418432\pi\)
−0.841678 + 0.539980i \(0.818432\pi\)
\(920\) −32.5726 7.30086i −1.07389 0.240702i
\(921\) −11.5766 10.2257i −0.381463 0.336950i
\(922\) −2.32222 22.0944i −0.0764781 0.727641i
\(923\) −14.3241 3.04469i −0.471485 0.100217i
\(924\) −0.171537 + 0.157436i −0.00564316 + 0.00517926i
\(925\) 33.7703 + 25.6955i 1.11036 + 0.844862i
\(926\) −16.5646 −0.544346
\(927\) 24.4901 5.69502i 0.804362 0.187049i
\(928\) −0.851379 + 0.618563i −0.0279479 + 0.0203053i
\(929\) −14.5062 6.45858i −0.475933 0.211899i 0.154728 0.987957i \(-0.450550\pi\)
−0.630662 + 0.776058i \(0.717216\pi\)
\(930\) −2.13528 + 4.77617i −0.0700187 + 0.156617i
\(931\) 37.1253 16.5293i 1.21673 0.541724i
\(932\) 0.804302 1.39309i 0.0263458 0.0456322i
\(933\) −21.0798 28.4405i −0.690123 0.931099i
\(934\) −0.248157 + 0.0527473i −0.00811993 + 0.00172595i
\(935\) 4.36522 4.74156i 0.142758 0.155066i
\(936\) −21.9274 + 5.09908i −0.716721 + 0.166669i
\(937\) 10.7106 32.9639i 0.349901 1.07688i −0.609007 0.793165i \(-0.708432\pi\)
0.958908 0.283718i \(-0.0915681\pi\)
\(938\) 1.16461 0.247545i 0.0380258 0.00808263i
\(939\) 34.9070 + 19.7128i 1.13915 + 0.643303i
\(940\) 1.52658 + 4.88136i 0.0497917 + 0.159212i
\(941\) −5.44265 6.04467i −0.177425 0.197051i 0.647872 0.761749i \(-0.275659\pi\)
−0.825297 + 0.564698i \(0.808992\pi\)
\(942\) 6.27877 14.4716i 0.204573 0.471511i
\(943\) −26.2102 45.3974i −0.853522 1.47834i
\(944\) 29.4983 + 21.4318i 0.960089 + 0.697545i
\(945\) 5.09009 3.05881i 0.165581 0.0995029i
\(946\) −2.19767 + 1.59670i −0.0714525 + 0.0519133i
\(947\) −34.3912 15.3119i −1.11756 0.497571i −0.237004 0.971509i \(-0.576166\pi\)
−0.880558 + 0.473938i \(0.842832\pi\)
\(948\) 3.53878 2.08829i 0.114934 0.0678246i
\(949\) 16.0886 27.8662i 0.522257 0.904576i
\(950\) −5.80265 + 45.5040i −0.188263 + 1.47634i
\(951\) −13.6679 + 12.5443i −0.443212 + 0.406778i
\(952\) 3.02190 3.35616i 0.0979402 0.108774i
\(953\) −5.31982 + 3.86508i −0.172326 + 0.125202i −0.670605 0.741814i \(-0.733965\pi\)
0.498279 + 0.867017i \(0.333965\pi\)
\(954\) −40.3882 + 0.769207i −1.30762 + 0.0249040i
\(955\) 16.7972 18.2454i 0.543545 0.590406i
\(956\) 0.183218 1.74321i 0.00592571 0.0563793i
\(957\) −0.824960 0.259388i −0.0266672 0.00838483i
\(958\) 40.6564 18.1014i 1.31355 0.584830i
\(959\) 3.18614 + 3.53857i 0.102886 + 0.114266i
\(960\) −5.09857 24.1694i −0.164556 0.780064i
\(961\) −20.2155 + 22.4516i −0.652113 + 0.724245i
\(962\) −11.6759 + 35.9347i −0.376446 + 1.15858i
\(963\) 4.56271 + 36.6782i 0.147031 + 1.18194i
\(964\) 2.26415 + 6.96833i 0.0729233 + 0.224435i
\(965\) −1.88431 20.0593i −0.0606582 0.645733i
\(966\) 3.25700 + 7.13180i 0.104792 + 0.229462i
\(967\) 16.6485 7.41240i 0.535380 0.238367i −0.121193 0.992629i \(-0.538672\pi\)
0.656573 + 0.754262i \(0.272005\pi\)
\(968\) 13.2065 22.8744i 0.424475 0.735212i
\(969\) −14.3258 + 33.0188i −0.460211 + 1.06072i
\(970\) −29.3383 + 49.5421i −0.941996 + 1.59070i
\(971\) −9.06609 + 6.58690i −0.290945 + 0.211384i −0.723677 0.690139i \(-0.757550\pi\)
0.432732 + 0.901522i \(0.357550\pi\)
\(972\) −1.77831 + 4.56765i −0.0570392 + 0.146507i
\(973\) −0.920633 2.83342i −0.0295142 0.0908352i
\(974\) 24.6278 + 42.6567i 0.789127 + 1.36681i
\(975\) −24.0025 8.13448i −0.768696 0.260512i
\(976\) 6.21715 10.7684i 0.199006 0.344689i
\(977\) −10.2147 2.17120i −0.326797 0.0694628i 0.0415918 0.999135i \(-0.486757\pi\)
−0.368389 + 0.929672i \(0.620090\pi\)
\(978\) −8.85078 + 43.6807i −0.283017 + 1.39675i
\(979\) 13.3437 + 5.94102i 0.426468 + 0.189876i
\(980\) 4.64514 0.933794i 0.148384 0.0298289i
\(981\) −43.2243 8.33067i −1.38005 0.265978i
\(982\) −5.08237 −0.162185
\(983\) −0.140774 + 1.33937i −0.00448998 + 0.0427193i −0.996537 0.0831447i \(-0.973504\pi\)
0.992048 + 0.125864i \(0.0401703\pi\)
\(984\) 23.1982 32.5774i 0.739532 1.03853i
\(985\) 19.4115 57.5686i 0.618503 1.83429i
\(986\) −3.06073 0.650578i −0.0974734 0.0207186i
\(987\) −3.73525 + 5.24544i −0.118894 + 0.166964i
\(988\) −5.42793 + 1.15374i −0.172685 + 0.0367054i
\(989\) 3.84032 + 11.8193i 0.122115 + 0.375832i
\(990\) −5.66107 + 6.38912i −0.179920 + 0.203060i
\(991\) 3.33798 10.2732i 0.106034 0.326340i −0.883937 0.467605i \(-0.845117\pi\)
0.989972 + 0.141265i \(0.0451169\pi\)
\(992\) 0.163635 1.55688i 0.00519540 0.0494310i
\(993\) −29.9945 + 27.5288i −0.951846 + 0.873599i
\(994\) −3.55458 + 1.58260i −0.112745 + 0.0501971i
\(995\) −28.5815 + 20.2867i −0.906096 + 0.643130i
\(996\) 0.183538 + 0.162121i 0.00581562 + 0.00513699i
\(997\) 17.2427 + 7.67692i 0.546080 + 0.243131i 0.661185 0.750223i \(-0.270054\pi\)
−0.115105 + 0.993353i \(0.536720\pi\)
\(998\) −12.2245 37.6231i −0.386960 1.19094i
\(999\) −26.9293 34.9222i −0.852006 1.10489i
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 225.2.q.a.31.8 224
3.2 odd 2 675.2.r.a.631.21 224
9.2 odd 6 675.2.r.a.181.8 224
9.7 even 3 inner 225.2.q.a.106.21 yes 224
25.21 even 5 inner 225.2.q.a.121.21 yes 224
75.71 odd 10 675.2.r.a.496.8 224
225.146 odd 30 675.2.r.a.46.21 224
225.196 even 15 inner 225.2.q.a.196.8 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.8 224 1.1 even 1 trivial
225.2.q.a.106.21 yes 224 9.7 even 3 inner
225.2.q.a.121.21 yes 224 25.21 even 5 inner
225.2.q.a.196.8 yes 224 225.196 even 15 inner
675.2.r.a.46.21 224 225.146 odd 30
675.2.r.a.181.8 224 9.2 odd 6
675.2.r.a.496.8 224 75.71 odd 10
675.2.r.a.631.21 224 3.2 odd 2