Properties

Label 69.2.e.c.4.2
Level $69$
Weight $2$
Character 69.4
Analytic conductor $0.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,2,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), 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: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + 4165 x^{12} - 7040 x^{11} + 10649 x^{10} - 13519 x^{9} + 15111 x^{8} - 12101 x^{7} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 4.2
Root \(2.55199 + 0.749331i\) of defining polynomial
Character \(\chi\) \(=\) 69.4
Dual form 69.2.e.c.52.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.236364 - 0.517565i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(1.09772 - 1.26683i) q^{4} +(2.27341 + 1.46103i) q^{5} +(0.372604 + 0.430008i) q^{6} +(-0.481879 - 3.35154i) q^{7} +(-2.00700 - 0.589308i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\) \(q+(-0.236364 - 0.517565i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(1.09772 - 1.26683i) q^{4} +(2.27341 + 1.46103i) q^{5} +(0.372604 + 0.430008i) q^{6} +(-0.481879 - 3.35154i) q^{7} +(-2.00700 - 0.589308i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.218827 - 1.52197i) q^{10} +(-1.86448 + 4.08263i) q^{11} +(-0.696343 + 1.52478i) q^{12} +(-0.891052 + 6.19740i) q^{13} +(-1.62074 + 1.04159i) q^{14} +(-2.59294 - 0.761356i) q^{15} +(-0.307736 - 2.14035i) q^{16} +(-2.00981 - 2.31944i) q^{17} +(-0.478659 - 0.307615i) q^{18} +(-0.686559 + 0.792332i) q^{19} +(4.34644 - 1.27623i) q^{20} +(1.40660 + 3.08002i) q^{21} +2.55372 q^{22} +(-3.18128 - 3.58879i) q^{23} +2.09173 q^{24} +(0.956704 + 2.09489i) q^{25} +(3.41817 - 1.00367i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-4.77480 - 3.06858i) q^{28} +(1.45248 + 1.67625i) q^{29} +(0.218827 + 1.52197i) q^{30} +(6.22433 + 1.82763i) q^{31} +(-4.55438 + 2.92692i) q^{32} +(0.638741 - 4.44254i) q^{33} +(-0.725416 + 1.58844i) q^{34} +(3.80120 - 8.32347i) q^{35} +(0.238557 - 1.65920i) q^{36} +(0.235181 - 0.151142i) q^{37} +(0.572361 + 0.168060i) q^{38} +(-0.891052 - 6.19740i) q^{39} +(-3.70173 - 4.27203i) q^{40} +(1.19434 + 0.767558i) q^{41} +(1.26164 - 1.45601i) q^{42} +(-1.76507 + 0.518271i) q^{43} +(3.12534 + 6.84355i) q^{44} +2.70241 q^{45} +(-1.10549 + 2.49478i) q^{46} +4.74565 q^{47} +(0.898277 + 1.96695i) q^{48} +(-4.28417 + 1.25794i) q^{49} +(0.858110 - 0.990312i) q^{50} +(2.58186 + 1.65926i) q^{51} +(6.87295 + 7.93180i) q^{52} +(-0.768306 - 5.34369i) q^{53} +(0.545935 + 0.160301i) q^{54} +(-10.2036 + 6.55744i) q^{55} +(-1.00796 + 7.01051i) q^{56} +(0.435523 - 0.953663i) q^{57} +(0.524255 - 1.14796i) q^{58} +(1.54995 - 10.7801i) q^{59} +(-3.81082 + 2.44907i) q^{60} +(-4.49474 - 1.31978i) q^{61} +(-0.525291 - 3.65348i) q^{62} +(-2.21736 - 2.55897i) q^{63} +(-1.04683 - 0.672754i) q^{64} +(-11.0803 + 12.7874i) q^{65} +(-2.45028 + 0.719467i) q^{66} +(-0.0835538 - 0.182957i) q^{67} -5.14454 q^{68} +(4.06350 + 2.54715i) q^{69} -5.20640 q^{70} +(-1.25365 - 2.74512i) q^{71} +(-2.00700 + 0.589308i) q^{72} +(7.91764 - 9.13745i) q^{73} +(-0.133814 - 0.0859970i) q^{74} +(-1.50815 - 1.74050i) q^{75} +(0.250104 + 1.73951i) q^{76} +(14.5816 + 4.28153i) q^{77} +(-2.99695 + 1.92602i) q^{78} +(-1.10543 + 7.68843i) q^{79} +(2.42751 - 5.31551i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.114961 - 0.799573i) q^{82} +(-12.4179 + 7.98047i) q^{83} +(5.44591 + 1.59906i) q^{84} +(-1.18034 - 8.20944i) q^{85} +(0.685438 + 0.791037i) q^{86} +(-1.86590 - 1.19914i) q^{87} +(6.14793 - 7.09509i) q^{88} +(0.838282 - 0.246142i) q^{89} +(-0.638752 - 1.39867i) q^{90} +21.2002 q^{91} +(-8.03854 + 0.0906751i) q^{92} -6.48711 q^{93} +(-1.12170 - 2.45618i) q^{94} +(-2.71845 + 0.798210i) q^{95} +(3.54529 - 4.09148i) q^{96} +(9.73536 + 6.25653i) q^{97} +(1.66369 + 1.92000i) q^{98} +(0.638741 + 4.44254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{2}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.236364 0.517565i −0.167135 0.365974i 0.807469 0.589910i \(-0.200837\pi\)
−0.974604 + 0.223936i \(0.928109\pi\)
\(3\) −0.959493 + 0.281733i −0.553964 + 0.162658i
\(4\) 1.09772 1.26683i 0.548858 0.633416i
\(5\) 2.27341 + 1.46103i 1.01670 + 0.653393i 0.939119 0.343593i \(-0.111644\pi\)
0.0775811 + 0.996986i \(0.475280\pi\)
\(6\) 0.372604 + 0.430008i 0.152115 + 0.175550i
\(7\) −0.481879 3.35154i −0.182133 1.26676i −0.851707 0.524018i \(-0.824432\pi\)
0.669574 0.742745i \(-0.266477\pi\)
\(8\) −2.00700 0.589308i −0.709581 0.208352i
\(9\) 0.841254 0.540641i 0.280418 0.180214i
\(10\) 0.218827 1.52197i 0.0691990 0.481290i
\(11\) −1.86448 + 4.08263i −0.562161 + 1.23096i 0.388707 + 0.921362i \(0.372922\pi\)
−0.950867 + 0.309599i \(0.899805\pi\)
\(12\) −0.696343 + 1.52478i −0.201017 + 0.440166i
\(13\) −0.891052 + 6.19740i −0.247133 + 1.71885i 0.367488 + 0.930028i \(0.380218\pi\)
−0.614621 + 0.788822i \(0.710691\pi\)
\(14\) −1.62074 + 1.04159i −0.433161 + 0.278376i
\(15\) −2.59294 0.761356i −0.669495 0.196581i
\(16\) −0.307736 2.14035i −0.0769340 0.535088i
\(17\) −2.00981 2.31944i −0.487450 0.562548i 0.457732 0.889090i \(-0.348662\pi\)
−0.945183 + 0.326542i \(0.894116\pi\)
\(18\) −0.478659 0.307615i −0.112821 0.0725056i
\(19\) −0.686559 + 0.792332i −0.157507 + 0.181773i −0.829018 0.559221i \(-0.811100\pi\)
0.671511 + 0.740995i \(0.265646\pi\)
\(20\) 4.34644 1.27623i 0.971894 0.285374i
\(21\) 1.40660 + 3.08002i 0.306945 + 0.672115i
\(22\) 2.55372 0.544455
\(23\) −3.18128 3.58879i −0.663343 0.748315i
\(24\) 2.09173 0.426972
\(25\) 0.956704 + 2.09489i 0.191341 + 0.418978i
\(26\) 3.41817 1.00367i 0.670358 0.196835i
\(27\) −0.654861 + 0.755750i −0.126028 + 0.145444i
\(28\) −4.77480 3.06858i −0.902353 0.579907i
\(29\) 1.45248 + 1.67625i 0.269719 + 0.311272i 0.874410 0.485188i \(-0.161249\pi\)
−0.604691 + 0.796460i \(0.706703\pi\)
\(30\) 0.218827 + 1.52197i 0.0399521 + 0.277873i
\(31\) 6.22433 + 1.82763i 1.11792 + 0.328252i 0.787951 0.615739i \(-0.211142\pi\)
0.329973 + 0.943990i \(0.392960\pi\)
\(32\) −4.55438 + 2.92692i −0.805108 + 0.517412i
\(33\) 0.638741 4.44254i 0.111191 0.773347i
\(34\) −0.725416 + 1.58844i −0.124408 + 0.272415i
\(35\) 3.80120 8.32347i 0.642520 1.40692i
\(36\) 0.238557 1.65920i 0.0397594 0.276533i
\(37\) 0.235181 0.151142i 0.0386635 0.0248475i −0.521166 0.853455i \(-0.674503\pi\)
0.559830 + 0.828608i \(0.310867\pi\)
\(38\) 0.572361 + 0.168060i 0.0928492 + 0.0272630i
\(39\) −0.891052 6.19740i −0.142683 0.992379i
\(40\) −3.70173 4.27203i −0.585295 0.675467i
\(41\) 1.19434 + 0.767558i 0.186525 + 0.119872i 0.630571 0.776132i \(-0.282821\pi\)
−0.444046 + 0.896004i \(0.646457\pi\)
\(42\) 1.26164 1.45601i 0.194675 0.224667i
\(43\) −1.76507 + 0.518271i −0.269171 + 0.0790356i −0.413533 0.910489i \(-0.635705\pi\)
0.144362 + 0.989525i \(0.453887\pi\)
\(44\) 3.12534 + 6.84355i 0.471163 + 1.03170i
\(45\) 2.70241 0.402851
\(46\) −1.10549 + 2.49478i −0.162996 + 0.367835i
\(47\) 4.74565 0.692225 0.346112 0.938193i \(-0.387502\pi\)
0.346112 + 0.938193i \(0.387502\pi\)
\(48\) 0.898277 + 1.96695i 0.129655 + 0.283905i
\(49\) −4.28417 + 1.25794i −0.612024 + 0.179706i
\(50\) 0.858110 0.990312i 0.121355 0.140051i
\(51\) 2.58186 + 1.65926i 0.361533 + 0.232343i
\(52\) 6.87295 + 7.93180i 0.953106 + 1.09994i
\(53\) −0.768306 5.34369i −0.105535 0.734012i −0.972035 0.234835i \(-0.924545\pi\)
0.866500 0.499177i \(-0.166364\pi\)
\(54\) 0.545935 + 0.160301i 0.0742923 + 0.0218142i
\(55\) −10.2036 + 6.55744i −1.37585 + 0.884205i
\(56\) −1.00796 + 7.01051i −0.134694 + 0.936819i
\(57\) 0.435523 0.953663i 0.0576864 0.126316i
\(58\) 0.524255 1.14796i 0.0688380 0.150734i
\(59\) 1.54995 10.7801i 0.201786 1.40346i −0.597193 0.802097i \(-0.703717\pi\)
0.798980 0.601358i \(-0.205373\pi\)
\(60\) −3.81082 + 2.44907i −0.491975 + 0.316173i
\(61\) −4.49474 1.31978i −0.575493 0.168980i −0.0189815 0.999820i \(-0.506042\pi\)
−0.556512 + 0.830840i \(0.687861\pi\)
\(62\) −0.525291 3.65348i −0.0667121 0.463993i
\(63\) −2.21736 2.55897i −0.279361 0.322400i
\(64\) −1.04683 0.672754i −0.130853 0.0840943i
\(65\) −11.0803 + 12.7874i −1.37435 + 1.58608i
\(66\) −2.45028 + 0.719467i −0.301608 + 0.0885602i
\(67\) −0.0835538 0.182957i −0.0102077 0.0223518i 0.904459 0.426560i \(-0.140275\pi\)
−0.914667 + 0.404208i \(0.867547\pi\)
\(68\) −5.14454 −0.623868
\(69\) 4.06350 + 2.54715i 0.489188 + 0.306641i
\(70\) −5.20640 −0.622284
\(71\) −1.25365 2.74512i −0.148781 0.325786i 0.820537 0.571593i \(-0.193674\pi\)
−0.969319 + 0.245807i \(0.920947\pi\)
\(72\) −2.00700 + 0.589308i −0.236527 + 0.0694506i
\(73\) 7.91764 9.13745i 0.926690 1.06946i −0.0707172 0.997496i \(-0.522529\pi\)
0.997407 0.0719611i \(-0.0229257\pi\)
\(74\) −0.133814 0.0859970i −0.0155556 0.00999695i
\(75\) −1.50815 1.74050i −0.174146 0.200975i
\(76\) 0.250104 + 1.73951i 0.0286889 + 0.199535i
\(77\) 14.5816 + 4.28153i 1.66172 + 0.487926i
\(78\) −2.99695 + 1.92602i −0.339337 + 0.218079i
\(79\) −1.10543 + 7.68843i −0.124371 + 0.865016i 0.828142 + 0.560518i \(0.189398\pi\)
−0.952513 + 0.304498i \(0.901511\pi\)
\(80\) 2.42751 5.31551i 0.271404 0.594292i
\(81\) 0.415415 0.909632i 0.0461572 0.101070i
\(82\) 0.114961 0.799573i 0.0126954 0.0882981i
\(83\) −12.4179 + 7.98047i −1.36304 + 0.875971i −0.998475 0.0552086i \(-0.982418\pi\)
−0.364562 + 0.931179i \(0.618781\pi\)
\(84\) 5.44591 + 1.59906i 0.594198 + 0.174472i
\(85\) −1.18034 8.20944i −0.128026 0.890439i
\(86\) 0.685438 + 0.791037i 0.0739127 + 0.0852997i
\(87\) −1.86590 1.19914i −0.200045 0.128561i
\(88\) 6.14793 7.09509i 0.655371 0.756339i
\(89\) 0.838282 0.246142i 0.0888577 0.0260910i −0.237002 0.971509i \(-0.576165\pi\)
0.325859 + 0.945418i \(0.394346\pi\)
\(90\) −0.638752 1.39867i −0.0673303 0.147433i
\(91\) 21.2002 2.22239
\(92\) −8.03854 + 0.0906751i −0.838076 + 0.00945354i
\(93\) −6.48711 −0.672682
\(94\) −1.12170 2.45618i −0.115695 0.253336i
\(95\) −2.71845 + 0.798210i −0.278907 + 0.0818946i
\(96\) 3.54529 4.09148i 0.361839 0.417585i
\(97\) 9.73536 + 6.25653i 0.988476 + 0.635255i 0.931737 0.363134i \(-0.118293\pi\)
0.0567390 + 0.998389i \(0.481930\pi\)
\(98\) 1.66369 + 1.92000i 0.168058 + 0.193949i
\(99\) 0.638741 + 4.44254i 0.0641959 + 0.446492i
\(100\) 3.70406 + 1.08761i 0.370406 + 0.108761i
\(101\) 7.93886 5.10200i 0.789947 0.507668i −0.0823744 0.996601i \(-0.526250\pi\)
0.872321 + 0.488934i \(0.162614\pi\)
\(102\) 0.248516 1.72847i 0.0246068 0.171144i
\(103\) 1.66695 3.65011i 0.164250 0.359656i −0.809555 0.587044i \(-0.800291\pi\)
0.973804 + 0.227388i \(0.0730186\pi\)
\(104\) 5.44052 11.9131i 0.533487 1.16817i
\(105\) −1.30223 + 9.05723i −0.127085 + 0.883895i
\(106\) −2.58410 + 1.66070i −0.250990 + 0.161302i
\(107\) −3.52529 1.03512i −0.340803 0.100069i 0.106853 0.994275i \(-0.465923\pi\)
−0.447655 + 0.894206i \(0.647741\pi\)
\(108\) 0.238557 + 1.65920i 0.0229551 + 0.159656i
\(109\) −8.78273 10.1358i −0.841233 0.970835i 0.158631 0.987338i \(-0.449292\pi\)
−0.999864 + 0.0165033i \(0.994747\pi\)
\(110\) 5.80566 + 3.73107i 0.553548 + 0.355744i
\(111\) −0.183073 + 0.211278i −0.0173765 + 0.0200536i
\(112\) −7.02518 + 2.06278i −0.663817 + 0.194914i
\(113\) 0.288666 + 0.632091i 0.0271554 + 0.0594621i 0.922724 0.385462i \(-0.125958\pi\)
−0.895568 + 0.444924i \(0.853231\pi\)
\(114\) −0.596524 −0.0558696
\(115\) −1.98902 12.8068i −0.185477 1.19424i
\(116\) 3.71794 0.345202
\(117\) 2.60097 + 5.69533i 0.240460 + 0.526533i
\(118\) −5.94578 + 1.74584i −0.547353 + 0.160717i
\(119\) −6.80522 + 7.85365i −0.623834 + 0.719943i
\(120\) 4.75535 + 3.05608i 0.434102 + 0.278981i
\(121\) −5.98816 6.91070i −0.544378 0.628246i
\(122\) 0.379326 + 2.63827i 0.0343425 + 0.238858i
\(123\) −1.36221 0.399981i −0.122826 0.0360651i
\(124\) 9.14785 5.87897i 0.821501 0.527947i
\(125\) 1.03724 7.21419i 0.0927739 0.645257i
\(126\) −0.800329 + 1.75248i −0.0712990 + 0.156123i
\(127\) −4.54632 + 9.95505i −0.403421 + 0.883368i 0.593491 + 0.804840i \(0.297749\pi\)
−0.996912 + 0.0785275i \(0.974978\pi\)
\(128\) −1.64169 + 11.4182i −0.145106 + 1.00924i
\(129\) 1.54756 0.994555i 0.136255 0.0875657i
\(130\) 9.23729 + 2.71231i 0.810164 + 0.237886i
\(131\) 0.503437 + 3.50148i 0.0439855 + 0.305926i 0.999924 + 0.0123577i \(0.00393369\pi\)
−0.955938 + 0.293568i \(0.905157\pi\)
\(132\) −4.92680 5.68583i −0.428823 0.494888i
\(133\) 2.98637 + 1.91922i 0.258951 + 0.166418i
\(134\) −0.0749432 + 0.0864890i −0.00647410 + 0.00747152i
\(135\) −2.59294 + 0.761356i −0.223165 + 0.0655271i
\(136\) 2.66682 + 5.83951i 0.228678 + 0.500734i
\(137\) 12.7925 1.09294 0.546469 0.837479i \(-0.315972\pi\)
0.546469 + 0.837479i \(0.315972\pi\)
\(138\) 0.357851 2.70518i 0.0304623 0.230280i
\(139\) 8.21741 0.696992 0.348496 0.937310i \(-0.386693\pi\)
0.348496 + 0.937310i \(0.386693\pi\)
\(140\) −6.37179 13.9523i −0.538515 1.17918i
\(141\) −4.55342 + 1.33701i −0.383467 + 0.112596i
\(142\) −1.12446 + 1.29769i −0.0943625 + 0.108900i
\(143\) −23.6404 15.1928i −1.97691 1.27048i
\(144\) −1.41605 1.63420i −0.118004 0.136184i
\(145\) 0.853026 + 5.93293i 0.0708399 + 0.492703i
\(146\) −6.60067 1.93813i −0.546275 0.160401i
\(147\) 3.75622 2.41398i 0.309808 0.199102i
\(148\) 0.0666909 0.463846i 0.00548196 0.0381279i
\(149\) −7.73403 + 16.9352i −0.633597 + 1.38738i 0.271608 + 0.962408i \(0.412445\pi\)
−0.905205 + 0.424975i \(0.860283\pi\)
\(150\) −0.544348 + 1.19196i −0.0444458 + 0.0973227i
\(151\) 0.778374 5.41371i 0.0633432 0.440562i −0.933327 0.359027i \(-0.883109\pi\)
0.996670 0.0815349i \(-0.0259822\pi\)
\(152\) 1.84485 1.18561i 0.149637 0.0961659i
\(153\) −2.94474 0.864655i −0.238068 0.0699032i
\(154\) −1.23058 8.55890i −0.0991633 0.689696i
\(155\) 11.4802 + 13.2489i 0.922115 + 1.06418i
\(156\) −8.82919 5.67418i −0.706901 0.454298i
\(157\) −10.7637 + 12.4219i −0.859033 + 0.991377i 0.140966 + 0.990014i \(0.454979\pi\)
−0.999999 + 0.00136270i \(0.999566\pi\)
\(158\) 4.24055 1.24514i 0.337360 0.0990577i
\(159\) 2.24267 + 4.91077i 0.177856 + 0.389450i
\(160\) −14.6303 −1.15663
\(161\) −10.4950 + 12.3916i −0.827121 + 0.976592i
\(162\) −0.568983 −0.0447035
\(163\) 4.16078 + 9.11084i 0.325898 + 0.713616i 0.999680 0.0253139i \(-0.00805853\pi\)
−0.673782 + 0.738930i \(0.735331\pi\)
\(164\) 2.28342 0.670472i 0.178305 0.0523551i
\(165\) 7.94282 9.16650i 0.618347 0.713611i
\(166\) 7.06554 + 4.54075i 0.548393 + 0.352430i
\(167\) 4.84536 + 5.59184i 0.374945 + 0.432709i 0.911591 0.411098i \(-0.134855\pi\)
−0.536646 + 0.843807i \(0.680309\pi\)
\(168\) −1.00796 7.01051i −0.0777657 0.540873i
\(169\) −25.1404 7.38190i −1.93388 0.567838i
\(170\) −3.96993 + 2.55132i −0.304480 + 0.195677i
\(171\) −0.149204 + 1.03773i −0.0114099 + 0.0793575i
\(172\) −1.28098 + 2.80496i −0.0976740 + 0.213876i
\(173\) 2.33259 5.10767i 0.177344 0.388329i −0.799996 0.600005i \(-0.795165\pi\)
0.977340 + 0.211677i \(0.0678923\pi\)
\(174\) −0.179602 + 1.24916i −0.0136156 + 0.0946983i
\(175\) 6.56009 4.21591i 0.495896 0.318693i
\(176\) 9.31204 + 2.73426i 0.701921 + 0.206103i
\(177\) 1.54995 + 10.7801i 0.116501 + 0.810285i
\(178\) −0.325534 0.375686i −0.0243998 0.0281589i
\(179\) 18.1247 + 11.6480i 1.35470 + 0.870614i 0.997976 0.0635946i \(-0.0202565\pi\)
0.356726 + 0.934209i \(0.383893\pi\)
\(180\) 2.96648 3.42350i 0.221108 0.255172i
\(181\) −9.84568 + 2.89095i −0.731824 + 0.214883i −0.626353 0.779540i \(-0.715453\pi\)
−0.105471 + 0.994422i \(0.533635\pi\)
\(182\) −5.01097 10.9725i −0.371438 0.813335i
\(183\) 4.68450 0.346288
\(184\) 4.26992 + 9.07745i 0.314783 + 0.669199i
\(185\) 0.755486 0.0555444
\(186\) 1.53332 + 3.35750i 0.112428 + 0.246184i
\(187\) 13.2167 3.88077i 0.966499 0.283790i
\(188\) 5.20938 6.01194i 0.379933 0.438466i
\(189\) 2.84849 + 1.83061i 0.207197 + 0.133157i
\(190\) 1.05567 + 1.21831i 0.0765863 + 0.0883853i
\(191\) −1.20256 8.36400i −0.0870143 0.605198i −0.985940 0.167097i \(-0.946561\pi\)
0.898926 0.438100i \(-0.144349\pi\)
\(192\) 1.19396 + 0.350578i 0.0861666 + 0.0253008i
\(193\) 0.329863 0.211990i 0.0237440 0.0152594i −0.528715 0.848799i \(-0.677326\pi\)
0.552459 + 0.833540i \(0.313690\pi\)
\(194\) 0.937075 6.51750i 0.0672780 0.467929i
\(195\) 7.02888 15.3911i 0.503348 1.10218i
\(196\) −3.10919 + 6.80819i −0.222085 + 0.486299i
\(197\) 3.21162 22.3373i 0.228818 1.59146i −0.474281 0.880373i \(-0.657292\pi\)
0.703099 0.711092i \(-0.251799\pi\)
\(198\) 2.14833 1.38065i 0.152675 0.0981183i
\(199\) −12.8230 3.76518i −0.908999 0.266906i −0.206380 0.978472i \(-0.566168\pi\)
−0.702620 + 0.711566i \(0.747986\pi\)
\(200\) −0.685568 4.76823i −0.0484770 0.337165i
\(201\) 0.131714 + 0.152006i 0.00929042 + 0.0107217i
\(202\) −4.51708 2.90295i −0.317820 0.204251i
\(203\) 4.91810 5.67580i 0.345183 0.398363i
\(204\) 4.93615 1.44939i 0.345600 0.101477i
\(205\) 1.59381 + 3.48995i 0.111316 + 0.243749i
\(206\) −2.28318 −0.159076
\(207\) −4.61651 1.29915i −0.320870 0.0902974i
\(208\) 13.5388 0.938749
\(209\) −1.95473 4.28025i −0.135211 0.296071i
\(210\) 4.99550 1.46681i 0.344722 0.101220i
\(211\) 0.366068 0.422465i 0.0252011 0.0290837i −0.743009 0.669281i \(-0.766602\pi\)
0.768210 + 0.640198i \(0.221148\pi\)
\(212\) −7.61293 4.89254i −0.522858 0.336021i
\(213\) 1.97626 + 2.28073i 0.135411 + 0.156273i
\(214\) 0.297510 + 2.06923i 0.0203374 + 0.141450i
\(215\) −4.76994 1.40058i −0.325307 0.0955188i
\(216\) 1.75967 1.13087i 0.119731 0.0769462i
\(217\) 3.12600 21.7418i 0.212207 1.47593i
\(218\) −3.17002 + 6.94137i −0.214701 + 0.470129i
\(219\) −5.02261 + 10.9980i −0.339396 + 0.743174i
\(220\) −2.89346 + 20.1244i −0.195077 + 1.35679i
\(221\) 16.1654 10.3889i 1.08740 0.698830i
\(222\) 0.152622 + 0.0448138i 0.0102433 + 0.00300770i
\(223\) 4.22619 + 29.3938i 0.283007 + 1.96836i 0.247049 + 0.969003i \(0.420539\pi\)
0.0359582 + 0.999353i \(0.488552\pi\)
\(224\) 12.0044 + 13.8538i 0.802075 + 0.925644i
\(225\) 1.93741 + 1.24510i 0.129161 + 0.0830066i
\(226\) 0.258918 0.298807i 0.0172229 0.0198763i
\(227\) 23.6710 6.95043i 1.57110 0.461316i 0.623778 0.781602i \(-0.285597\pi\)
0.947321 + 0.320285i \(0.103779\pi\)
\(228\) −0.730049 1.59859i −0.0483487 0.105869i
\(229\) −28.4810 −1.88207 −0.941037 0.338302i \(-0.890147\pi\)
−0.941037 + 0.338302i \(0.890147\pi\)
\(230\) −6.15819 + 4.05650i −0.406059 + 0.267478i
\(231\) −15.1972 −0.999899
\(232\) −1.92730 4.22019i −0.126533 0.277069i
\(233\) 14.4529 4.24374i 0.946839 0.278017i 0.228369 0.973575i \(-0.426661\pi\)
0.718470 + 0.695558i \(0.244843\pi\)
\(234\) 2.33293 2.69234i 0.152508 0.176004i
\(235\) 10.7888 + 6.93355i 0.703785 + 0.452295i
\(236\) −11.9552 13.7971i −0.778219 0.898112i
\(237\) −1.10543 7.68843i −0.0718054 0.499417i
\(238\) 5.67328 + 1.66583i 0.367744 + 0.107979i
\(239\) −22.6822 + 14.5770i −1.46719 + 0.942907i −0.468975 + 0.883211i \(0.655377\pi\)
−0.998217 + 0.0596958i \(0.980987\pi\)
\(240\) −0.831628 + 5.78410i −0.0536814 + 0.373362i
\(241\) 8.76904 19.2015i 0.564864 1.23688i −0.384624 0.923074i \(-0.625669\pi\)
0.949487 0.313806i \(-0.101604\pi\)
\(242\) −2.16135 + 4.73270i −0.138937 + 0.304229i
\(243\) −0.142315 + 0.989821i −0.00912950 + 0.0634971i
\(244\) −6.60589 + 4.24535i −0.422899 + 0.271780i
\(245\) −11.5776 3.39948i −0.739664 0.217185i
\(246\) 0.114961 + 0.799573i 0.00732967 + 0.0509789i
\(247\) −4.29864 4.96089i −0.273516 0.315654i
\(248\) −11.4152 7.33610i −0.724865 0.465843i
\(249\) 9.66649 11.1557i 0.612589 0.706965i
\(250\) −3.97898 + 1.16833i −0.251653 + 0.0738919i
\(251\) −0.966692 2.11676i −0.0610170 0.133609i 0.876667 0.481098i \(-0.159762\pi\)
−0.937684 + 0.347489i \(0.887034\pi\)
\(252\) −5.67582 −0.357543
\(253\) 20.5832 6.29679i 1.29405 0.395876i
\(254\) 6.22697 0.390715
\(255\) 3.44539 + 7.54436i 0.215759 + 0.472446i
\(256\) 3.90978 1.14801i 0.244361 0.0717509i
\(257\) −17.4817 + 20.1749i −1.09048 + 1.25848i −0.126651 + 0.991947i \(0.540423\pi\)
−0.963826 + 0.266531i \(0.914123\pi\)
\(258\) −0.880534 0.565885i −0.0548196 0.0352304i
\(259\) −0.619886 0.715387i −0.0385179 0.0444520i
\(260\) 4.03641 + 28.0738i 0.250327 + 1.74107i
\(261\) 2.12815 + 0.624882i 0.131729 + 0.0386792i
\(262\) 1.69325 1.08819i 0.104609 0.0672283i
\(263\) −1.42355 + 9.90102i −0.0877800 + 0.610523i 0.897684 + 0.440639i \(0.145248\pi\)
−0.985464 + 0.169884i \(0.945661\pi\)
\(264\) −3.89998 + 8.53976i −0.240027 + 0.525586i
\(265\) 6.06062 13.2709i 0.372301 0.815225i
\(266\) 0.287452 1.99927i 0.0176248 0.122583i
\(267\) −0.734979 + 0.472343i −0.0449800 + 0.0289069i
\(268\) −0.323495 0.0949866i −0.0197606 0.00580223i
\(269\) 2.49684 + 17.3659i 0.152235 + 1.05882i 0.912463 + 0.409160i \(0.134178\pi\)
−0.760228 + 0.649657i \(0.774913\pi\)
\(270\) 1.00693 + 1.16206i 0.0612797 + 0.0707206i
\(271\) 0.958576 + 0.616040i 0.0582294 + 0.0374217i 0.569432 0.822039i \(-0.307163\pi\)
−0.511202 + 0.859460i \(0.670800\pi\)
\(272\) −4.34593 + 5.01547i −0.263511 + 0.304108i
\(273\) −20.3415 + 5.97280i −1.23112 + 0.361490i
\(274\) −3.02369 6.62096i −0.182668 0.399987i
\(275\) −10.3364 −0.623309
\(276\) 7.68738 2.35172i 0.462726 0.141557i
\(277\) −21.3674 −1.28384 −0.641920 0.766772i \(-0.721862\pi\)
−0.641920 + 0.766772i \(0.721862\pi\)
\(278\) −1.94230 4.25304i −0.116491 0.255080i
\(279\) 6.22433 1.82763i 0.372641 0.109417i
\(280\) −12.5341 + 14.4651i −0.749055 + 0.864455i
\(281\) −10.4177 6.69502i −0.621465 0.399391i 0.191676 0.981458i \(-0.438608\pi\)
−0.813141 + 0.582067i \(0.802244\pi\)
\(282\) 1.76825 + 2.04067i 0.105298 + 0.121520i
\(283\) 1.01281 + 7.04422i 0.0602051 + 0.418735i 0.997528 + 0.0702729i \(0.0223870\pi\)
−0.937323 + 0.348462i \(0.886704\pi\)
\(284\) −4.85376 1.42519i −0.288018 0.0845697i
\(285\) 2.38345 1.53175i 0.141184 0.0907332i
\(286\) −2.27550 + 15.8264i −0.134553 + 0.935837i
\(287\) 1.99697 4.37276i 0.117878 0.258116i
\(288\) −2.24897 + 4.92457i −0.132522 + 0.290183i
\(289\) 1.07887 7.50369i 0.0634628 0.441393i
\(290\) 2.86905 1.84383i 0.168476 0.108273i
\(291\) −11.1037 3.26033i −0.650909 0.191124i
\(292\) −2.88429 20.0606i −0.168790 1.17396i
\(293\) 11.7773 + 13.5917i 0.688038 + 0.794038i 0.987085 0.160200i \(-0.0512140\pi\)
−0.299046 + 0.954239i \(0.596669\pi\)
\(294\) −2.13723 1.37351i −0.124646 0.0801048i
\(295\) 19.2738 22.2432i 1.12216 1.29505i
\(296\) −0.561077 + 0.164747i −0.0326119 + 0.00957573i
\(297\) −1.86448 4.08263i −0.108188 0.236898i
\(298\) 10.5931 0.613641
\(299\) 25.0759 16.5179i 1.45018 0.955255i
\(300\) −3.86044 −0.222882
\(301\) 2.58756 + 5.66596i 0.149144 + 0.326580i
\(302\) −2.98593 + 0.876747i −0.171821 + 0.0504511i
\(303\) −6.17989 + 7.13197i −0.355025 + 0.409721i
\(304\) 1.90715 + 1.22565i 0.109382 + 0.0702958i
\(305\) −8.29016 9.56736i −0.474693 0.547825i
\(306\) 0.248516 + 1.72847i 0.0142067 + 0.0988100i
\(307\) −1.75668 0.515809i −0.100259 0.0294388i 0.231218 0.972902i \(-0.425729\pi\)
−0.331477 + 0.943463i \(0.607547\pi\)
\(308\) 21.4304 13.7725i 1.22111 0.784760i
\(309\) −0.571072 + 3.97189i −0.0324871 + 0.225953i
\(310\) 4.14365 9.07333i 0.235344 0.515330i
\(311\) −3.84938 + 8.42896i −0.218278 + 0.477963i −0.986817 0.161841i \(-0.948257\pi\)
0.768539 + 0.639803i \(0.220984\pi\)
\(312\) −1.86384 + 12.9633i −0.105519 + 0.733901i
\(313\) 11.7077 7.52409i 0.661759 0.425287i −0.166187 0.986094i \(-0.553146\pi\)
0.827946 + 0.560808i \(0.189509\pi\)
\(314\) 8.97329 + 2.63479i 0.506392 + 0.148690i
\(315\) −1.30223 9.05723i −0.0733725 0.510317i
\(316\) 8.52650 + 9.84011i 0.479653 + 0.553549i
\(317\) −22.7584 14.6259i −1.27824 0.821473i −0.287568 0.957760i \(-0.592847\pi\)
−0.990669 + 0.136287i \(0.956483\pi\)
\(318\) 2.01156 2.32146i 0.112802 0.130181i
\(319\) −9.55163 + 2.80461i −0.534789 + 0.157028i
\(320\) −1.39695 3.05889i −0.0780918 0.170997i
\(321\) 3.67412 0.205069
\(322\) 8.89407 + 2.50292i 0.495647 + 0.139482i
\(323\) 3.21762 0.179033
\(324\) −0.696343 1.52478i −0.0386857 0.0847099i
\(325\) −13.8353 + 4.06242i −0.767447 + 0.225343i
\(326\) 3.73199 4.30695i 0.206696 0.238540i
\(327\) 11.2826 + 7.25086i 0.623927 + 0.400973i
\(328\) −1.94472 2.24432i −0.107379 0.123922i
\(329\) −2.28683 15.9053i −0.126077 0.876885i
\(330\) −6.62165 1.94429i −0.364510 0.107030i
\(331\) 13.8155 8.87867i 0.759367 0.488016i −0.102761 0.994706i \(-0.532768\pi\)
0.862128 + 0.506690i \(0.169131\pi\)
\(332\) −3.52136 + 24.4916i −0.193260 + 1.34415i
\(333\) 0.116134 0.254297i 0.00636408 0.0139354i
\(334\) 1.74887 3.82949i 0.0956940 0.209541i
\(335\) 0.0773544 0.538012i 0.00422632 0.0293947i
\(336\) 6.15946 3.95845i 0.336026 0.215951i
\(337\) 15.9032 + 4.66961i 0.866305 + 0.254370i 0.684543 0.728972i \(-0.260002\pi\)
0.181762 + 0.983343i \(0.441820\pi\)
\(338\) 2.12168 + 14.7566i 0.115404 + 0.802654i
\(339\) −0.455054 0.525160i −0.0247151 0.0285228i
\(340\) −11.6957 7.51634i −0.634286 0.407631i
\(341\) −19.0667 + 22.0041i −1.03252 + 1.19159i
\(342\) 0.572361 0.168060i 0.0309497 0.00908766i
\(343\) −3.56568 7.80775i −0.192529 0.421579i
\(344\) 3.84791 0.207466
\(345\) 5.51653 + 11.7276i 0.297000 + 0.631394i
\(346\) −3.19489 −0.171758
\(347\) −0.0775703 0.169855i −0.00416419 0.00911830i 0.907538 0.419969i \(-0.137959\pi\)
−0.911703 + 0.410851i \(0.865232\pi\)
\(348\) −3.56734 + 1.04746i −0.191229 + 0.0561500i
\(349\) −6.88632 + 7.94723i −0.368616 + 0.425406i −0.909508 0.415686i \(-0.863541\pi\)
0.540892 + 0.841092i \(0.318087\pi\)
\(350\) −3.73258 2.39878i −0.199515 0.128220i
\(351\) −4.10017 4.73185i −0.218851 0.252567i
\(352\) −3.45802 24.0510i −0.184313 1.28192i
\(353\) 19.8284 + 5.82213i 1.05536 + 0.309881i 0.762980 0.646422i \(-0.223736\pi\)
0.292377 + 0.956303i \(0.405554\pi\)
\(354\) 5.21307 3.35024i 0.277072 0.178063i
\(355\) 1.16064 8.07241i 0.0616002 0.428439i
\(356\) 0.608375 1.33216i 0.0322438 0.0706041i
\(357\) 4.31694 9.45277i 0.228477 0.500294i
\(358\) 1.74459 12.1339i 0.0922043 0.641295i
\(359\) 13.1887 8.47588i 0.696074 0.447340i −0.144166 0.989553i \(-0.546050\pi\)
0.840241 + 0.542214i \(0.182414\pi\)
\(360\) −5.42373 1.59255i −0.285855 0.0839347i
\(361\) 2.54756 + 17.7186i 0.134082 + 0.932560i
\(362\) 3.82342 + 4.41246i 0.200954 + 0.231914i
\(363\) 7.69256 + 4.94371i 0.403755 + 0.259478i
\(364\) 23.2718 26.8571i 1.21978 1.40770i
\(365\) 31.3502 9.20524i 1.64094 0.481824i
\(366\) −1.10725 2.42453i −0.0578767 0.126732i
\(367\) 5.44563 0.284259 0.142130 0.989848i \(-0.454605\pi\)
0.142130 + 0.989848i \(0.454605\pi\)
\(368\) −6.70228 + 7.91347i −0.349381 + 0.412518i
\(369\) 1.41972 0.0739076
\(370\) −0.178570 0.391013i −0.00928339 0.0203278i
\(371\) −17.5394 + 5.15002i −0.910598 + 0.267376i
\(372\) −7.12100 + 8.21807i −0.369207 + 0.426087i
\(373\) −3.38805 2.17737i −0.175427 0.112740i 0.449981 0.893038i \(-0.351431\pi\)
−0.625407 + 0.780298i \(0.715067\pi\)
\(374\) −5.13249 5.92321i −0.265395 0.306282i
\(375\) 1.03724 + 7.21419i 0.0535630 + 0.372539i
\(376\) −9.52451 2.79665i −0.491189 0.144226i
\(377\) −11.6826 + 7.50798i −0.601687 + 0.386681i
\(378\) 0.274181 1.90697i 0.0141023 0.0980839i
\(379\) −4.63145 + 10.1415i −0.237902 + 0.520932i −0.990494 0.137555i \(-0.956076\pi\)
0.752593 + 0.658486i \(0.228803\pi\)
\(380\) −1.97289 + 4.32003i −0.101207 + 0.221613i
\(381\) 1.55750 10.8326i 0.0797931 0.554973i
\(382\) −4.04467 + 2.59935i −0.206943 + 0.132994i
\(383\) 14.4041 + 4.22944i 0.736017 + 0.216114i 0.628195 0.778056i \(-0.283794\pi\)
0.107822 + 0.994170i \(0.465612\pi\)
\(384\) −1.64169 11.4182i −0.0837772 0.582683i
\(385\) 26.8944 + 31.0378i 1.37067 + 1.58183i
\(386\) −0.187686 0.120619i −0.00955297 0.00613932i
\(387\) −1.20467 + 1.39027i −0.0612370 + 0.0706712i
\(388\) 18.6126 5.46516i 0.944913 0.277452i
\(389\) −13.7756 30.1644i −0.698452 1.52940i −0.841838 0.539730i \(-0.818526\pi\)
0.143387 0.989667i \(-0.454201\pi\)
\(390\) −9.62726 −0.487495
\(391\) −1.93023 + 14.5916i −0.0976159 + 0.737929i
\(392\) 9.33963 0.471723
\(393\) −1.46953 3.21781i −0.0741278 0.162317i
\(394\) −12.3201 + 3.61751i −0.620677 + 0.182247i
\(395\) −13.7461 + 15.8639i −0.691643 + 0.798199i
\(396\) 6.32911 + 4.06747i 0.318050 + 0.204398i
\(397\) 4.36833 + 5.04133i 0.219240 + 0.253017i 0.854706 0.519112i \(-0.173737\pi\)
−0.635466 + 0.772129i \(0.719192\pi\)
\(398\) 1.08217 + 7.52669i 0.0542445 + 0.377279i
\(399\) −3.40611 1.00012i −0.170519 0.0500688i
\(400\) 4.18939 2.69236i 0.209469 0.134618i
\(401\) 0.886108 6.16302i 0.0442501 0.307766i −0.955661 0.294468i \(-0.904858\pi\)
0.999912 0.0132987i \(-0.00423322\pi\)
\(402\) 0.0475407 0.104100i 0.00237111 0.00519201i
\(403\) −16.8728 + 36.9462i −0.840492 + 1.84042i
\(404\) 2.25125 15.6578i 0.112004 0.779002i
\(405\) 2.27341 1.46103i 0.112967 0.0725993i
\(406\) −4.10005 1.20388i −0.203482 0.0597478i
\(407\) 0.178567 + 1.24196i 0.00885122 + 0.0615616i
\(408\) −4.20397 4.85164i −0.208128 0.240192i
\(409\) −1.64881 1.05962i −0.0815282 0.0523950i 0.499242 0.866463i \(-0.333612\pi\)
−0.580770 + 0.814068i \(0.697248\pi\)
\(410\) 1.42956 1.64980i 0.0706008 0.0814776i
\(411\) −12.2743 + 3.60407i −0.605448 + 0.177776i
\(412\) −2.79424 6.11853i −0.137662 0.301439i
\(413\) −36.8770 −1.81460
\(414\) 0.418781 + 2.69642i 0.0205820 + 0.132522i
\(415\) −39.8906 −1.95815
\(416\) −14.0811 30.8334i −0.690384 1.51173i
\(417\) −7.88455 + 2.31511i −0.386108 + 0.113372i
\(418\) −1.75328 + 2.02339i −0.0857558 + 0.0989675i
\(419\) 6.95250 + 4.46810i 0.339652 + 0.218281i 0.699336 0.714793i \(-0.253479\pi\)
−0.359684 + 0.933074i \(0.617116\pi\)
\(420\) 10.0445 + 11.5920i 0.490122 + 0.565631i
\(421\) 0.252051 + 1.75305i 0.0122842 + 0.0854385i 0.995041 0.0994630i \(-0.0317125\pi\)
−0.982757 + 0.184901i \(0.940803\pi\)
\(422\) −0.305178 0.0896084i −0.0148558 0.00436207i
\(423\) 3.99230 2.56569i 0.194112 0.124748i
\(424\) −1.60709 + 11.1775i −0.0780470 + 0.542829i
\(425\) 2.93618 6.42935i 0.142426 0.311869i
\(426\) 0.713307 1.56193i 0.0345599 0.0756755i
\(427\) −2.25736 + 15.7003i −0.109241 + 0.759790i
\(428\) −5.18109 + 3.32968i −0.250437 + 0.160946i
\(429\) 26.9631 + 7.91707i 1.30179 + 0.382240i
\(430\) 0.402550 + 2.79980i 0.0194127 + 0.135018i
\(431\) −17.5221 20.2215i −0.844008 0.974037i 0.155898 0.987773i \(-0.450173\pi\)
−0.999906 + 0.0137365i \(0.995627\pi\)
\(432\) 1.81909 + 1.16906i 0.0875212 + 0.0562465i
\(433\) −16.0940 + 18.5735i −0.773428 + 0.892583i −0.996617 0.0821919i \(-0.973808\pi\)
0.223189 + 0.974775i \(0.428353\pi\)
\(434\) −11.9917 + 3.52107i −0.575618 + 0.169017i
\(435\) −2.48997 5.45228i −0.119385 0.261417i
\(436\) −22.4813 −1.07666
\(437\) 5.02765 0.0567122i 0.240505 0.00271291i
\(438\) 6.87933 0.328707
\(439\) 2.32447 + 5.08987i 0.110941 + 0.242926i 0.956956 0.290232i \(-0.0937324\pi\)
−0.846016 + 0.533158i \(0.821005\pi\)
\(440\) 24.3429 7.14772i 1.16050 0.340754i
\(441\) −2.92397 + 3.37445i −0.139237 + 0.160688i
\(442\) −9.19781 5.91108i −0.437495 0.281161i
\(443\) −8.19690 9.45973i −0.389447 0.449445i 0.526842 0.849963i \(-0.323376\pi\)
−0.916289 + 0.400518i \(0.868830\pi\)
\(444\) 0.0666909 + 0.463846i 0.00316501 + 0.0220131i
\(445\) 2.26538 + 0.665175i 0.107389 + 0.0315323i
\(446\) 14.2143 9.13497i 0.673066 0.432553i
\(447\) 2.64956 18.4281i 0.125320 0.871620i
\(448\) −1.75032 + 3.83267i −0.0826948 + 0.181076i
\(449\) −3.38548 + 7.41317i −0.159771 + 0.349849i −0.972540 0.232737i \(-0.925232\pi\)
0.812769 + 0.582586i \(0.197959\pi\)
\(450\) 0.186485 1.29703i 0.00879100 0.0611427i
\(451\) −5.36049 + 3.44497i −0.252415 + 0.162218i
\(452\) 1.11763 + 0.328165i 0.0525687 + 0.0154356i
\(453\) 0.778374 + 5.41371i 0.0365712 + 0.254358i
\(454\) −9.19227 10.6084i −0.431414 0.497879i
\(455\) 48.1968 + 30.9742i 2.25950 + 1.45209i
\(456\) −1.43609 + 1.65734i −0.0672513 + 0.0776121i
\(457\) 17.3676 5.09960i 0.812424 0.238549i 0.150973 0.988538i \(-0.451759\pi\)
0.661451 + 0.749989i \(0.269941\pi\)
\(458\) 6.73187 + 14.7407i 0.314560 + 0.688790i
\(459\) 3.06906 0.143252
\(460\) −18.4074 11.5384i −0.858249 0.537982i
\(461\) 13.1011 0.610180 0.305090 0.952324i \(-0.401313\pi\)
0.305090 + 0.952324i \(0.401313\pi\)
\(462\) 3.59206 + 7.86551i 0.167118 + 0.365937i
\(463\) 18.6776 5.48425i 0.868023 0.254875i 0.182749 0.983160i \(-0.441501\pi\)
0.685274 + 0.728285i \(0.259682\pi\)
\(464\) 3.14079 3.62466i 0.145807 0.168271i
\(465\) −14.7479 9.47787i −0.683915 0.439526i
\(466\) −5.61255 6.47723i −0.259996 0.300052i
\(467\) 0.170185 + 1.18366i 0.00787520 + 0.0547732i 0.993380 0.114874i \(-0.0366463\pi\)
−0.985505 + 0.169647i \(0.945737\pi\)
\(468\) 10.0701 + 2.95686i 0.465493 + 0.136681i
\(469\) −0.572926 + 0.368197i −0.0264553 + 0.0170018i
\(470\) 1.03847 7.22275i 0.0479013 0.333161i
\(471\) 6.82799 14.9512i 0.314617 0.688916i
\(472\) −9.46357 + 20.7223i −0.435596 + 0.953822i
\(473\) 1.17502 8.17244i 0.0540274 0.375769i
\(474\) −3.71798 + 2.38940i −0.170772 + 0.109749i
\(475\) −2.31668 0.680239i −0.106297 0.0312115i
\(476\) 2.47905 + 17.2421i 0.113627 + 0.790293i
\(477\) −3.53535 4.08002i −0.161873 0.186811i
\(478\) 12.9058 + 8.29405i 0.590297 + 0.379361i
\(479\) 11.4506 13.2147i 0.523192 0.603796i −0.431235 0.902240i \(-0.641922\pi\)
0.954427 + 0.298444i \(0.0964675\pi\)
\(480\) 14.0377 4.12183i 0.640729 0.188135i
\(481\) 0.727128 + 1.59219i 0.0331542 + 0.0725975i
\(482\) −12.0107 −0.547073
\(483\) 6.57877 14.8464i 0.299344 0.675535i
\(484\) −15.3280 −0.696727
\(485\) 12.9915 + 28.4473i 0.589912 + 1.29173i
\(486\) 0.545935 0.160301i 0.0247641 0.00727140i
\(487\) 14.7431 17.0144i 0.668073 0.770997i −0.316001 0.948759i \(-0.602340\pi\)
0.984074 + 0.177762i \(0.0568856\pi\)
\(488\) 8.24319 + 5.29758i 0.373152 + 0.239810i
\(489\) −6.55906 7.56956i −0.296611 0.342307i
\(490\) 0.977068 + 6.79565i 0.0441394 + 0.306996i
\(491\) −28.2419 8.29258i −1.27454 0.374239i −0.426653 0.904415i \(-0.640307\pi\)
−0.847887 + 0.530176i \(0.822126\pi\)
\(492\) −2.00203 + 1.28663i −0.0902585 + 0.0580056i
\(493\) 0.968762 6.73789i 0.0436309 0.303459i
\(494\) −1.55154 + 3.39740i −0.0698071 + 0.152856i
\(495\) −5.03857 + 11.0329i −0.226467 + 0.495894i
\(496\) 1.99632 13.8847i 0.0896373 0.623441i
\(497\) −8.59627 + 5.52449i −0.385595 + 0.247807i
\(498\) −8.05862 2.36622i −0.361115 0.106033i
\(499\) 1.84778 + 12.8516i 0.0827180 + 0.575317i 0.988459 + 0.151486i \(0.0484058\pi\)
−0.905741 + 0.423831i \(0.860685\pi\)
\(500\) −8.00057 9.23315i −0.357796 0.412919i
\(501\) −6.22449 4.00024i −0.278090 0.178717i
\(502\) −0.867069 + 1.00065i −0.0386992 + 0.0446613i
\(503\) 0.705392 0.207122i 0.0314519 0.00923510i −0.265969 0.963982i \(-0.585692\pi\)
0.297421 + 0.954747i \(0.403874\pi\)
\(504\) 2.94222 + 6.44256i 0.131057 + 0.286974i
\(505\) 25.5025 1.13485
\(506\) −8.12411 9.16478i −0.361161 0.407424i
\(507\) 26.2018 1.16366
\(508\) 7.62081 + 16.6872i 0.338119 + 0.740377i
\(509\) −2.65234 + 0.778796i −0.117563 + 0.0345195i −0.339985 0.940431i \(-0.610422\pi\)
0.222422 + 0.974950i \(0.428604\pi\)
\(510\) 3.09033 3.56643i 0.136842 0.157924i
\(511\) −34.4399 22.1332i −1.52353 0.979114i
\(512\) 13.5901 + 15.6839i 0.600605 + 0.693136i
\(513\) −0.149204 1.03773i −0.00658750 0.0458171i
\(514\) 14.5739 + 4.27928i 0.642826 + 0.188751i
\(515\) 9.12259 5.86273i 0.401989 0.258343i
\(516\) 0.438845 3.05224i 0.0193191 0.134367i
\(517\) −8.84816 + 19.3748i −0.389142 + 0.852101i
\(518\) −0.223740 + 0.489923i −0.00983059 + 0.0215260i
\(519\) −0.799111 + 5.55794i −0.0350771 + 0.243966i
\(520\) 29.7739 19.1345i 1.30567 0.839104i
\(521\) 15.7236 + 4.61686i 0.688862 + 0.202268i 0.607386 0.794407i \(-0.292218\pi\)
0.0814765 + 0.996675i \(0.474036\pi\)
\(522\) −0.179602 1.24916i −0.00786095 0.0546741i
\(523\) −16.2792 18.7872i −0.711839 0.821506i 0.278462 0.960447i \(-0.410176\pi\)
−0.990301 + 0.138941i \(0.955630\pi\)
\(524\) 4.98842 + 3.20586i 0.217920 + 0.140049i
\(525\) −5.10660 + 5.89333i −0.222870 + 0.257206i
\(526\) 5.46090 1.60346i 0.238106 0.0699143i
\(527\) −8.27064 18.1102i −0.360275 0.788892i
\(528\) −9.70517 −0.422363
\(529\) −2.75887 + 22.8339i −0.119951 + 0.992780i
\(530\) −8.30107 −0.360575
\(531\) −4.52428 9.90680i −0.196337 0.429919i
\(532\) 5.70952 1.67647i 0.247539 0.0726840i
\(533\) −5.82109 + 6.71790i −0.252139 + 0.290984i
\(534\) 0.418190 + 0.268755i 0.0180969 + 0.0116302i
\(535\) −6.50209 7.50381i −0.281110 0.324418i
\(536\) 0.0598742 + 0.416434i 0.00258617 + 0.0179872i
\(537\) −20.6721 6.06989i −0.892068 0.261935i
\(538\) 8.39781 5.39695i 0.362055 0.232679i
\(539\) 2.85200 19.8361i 0.122844 0.854401i
\(540\) −1.88180 + 4.12057i −0.0809799 + 0.177321i
\(541\) 15.9154 34.8498i 0.684255 1.49831i −0.173815 0.984778i \(-0.555609\pi\)
0.858070 0.513532i \(-0.171663\pi\)
\(542\) 0.0922675 0.641735i 0.00396323 0.0275649i
\(543\) 8.63238 5.54770i 0.370451 0.238074i
\(544\) 15.9423 + 4.68107i 0.683519 + 0.200699i
\(545\) −5.15800 35.8747i −0.220945 1.53670i
\(546\) 7.89930 + 9.11628i 0.338059 + 0.390141i
\(547\) −15.8646 10.1956i −0.678323 0.435932i 0.155594 0.987821i \(-0.450271\pi\)
−0.833917 + 0.551889i \(0.813907\pi\)
\(548\) 14.0426 16.2060i 0.599868 0.692285i
\(549\) −4.49474 + 1.31978i −0.191831 + 0.0563267i
\(550\) 2.44316 + 5.34976i 0.104176 + 0.228115i
\(551\) −2.32536 −0.0990637
\(552\) −6.65438 7.50678i −0.283229 0.319510i
\(553\) 26.3008 1.11842
\(554\) 5.05047 + 11.0590i 0.214574 + 0.469851i
\(555\) −0.724883 + 0.212845i −0.0307696 + 0.00903477i
\(556\) 9.02038 10.4101i 0.382549 0.441486i
\(557\) 19.1542 + 12.3096i 0.811588 + 0.521576i 0.879378 0.476124i \(-0.157959\pi\)
−0.0677904 + 0.997700i \(0.521595\pi\)
\(558\) −2.41712 2.78951i −0.102325 0.118089i
\(559\) −1.63917 11.4007i −0.0693294 0.482196i
\(560\) −18.9849 5.57447i −0.802259 0.235564i
\(561\) −11.5880 + 7.44714i −0.489245 + 0.314418i
\(562\) −1.00275 + 6.97427i −0.0422984 + 0.294192i
\(563\) −7.56278 + 16.5602i −0.318733 + 0.697928i −0.999399 0.0346659i \(-0.988963\pi\)
0.680666 + 0.732594i \(0.261691\pi\)
\(564\) −3.30460 + 7.23607i −0.139149 + 0.304694i
\(565\) −0.267248 + 1.85875i −0.0112432 + 0.0781983i
\(566\) 3.40645 2.18919i 0.143184 0.0920186i
\(567\) −3.24885 0.953948i −0.136439 0.0400620i
\(568\) 0.898361 + 6.24824i 0.0376944 + 0.262170i
\(569\) 20.6338 + 23.8127i 0.865013 + 0.998279i 0.999972 + 0.00742738i \(0.00236423\pi\)
−0.134959 + 0.990851i \(0.543090\pi\)
\(570\) −1.35614 0.871541i −0.0568026 0.0365048i
\(571\) −3.16999 + 3.65836i −0.132660 + 0.153098i −0.818193 0.574944i \(-0.805024\pi\)
0.685533 + 0.728042i \(0.259569\pi\)
\(572\) −45.1971 + 13.2711i −1.88979 + 0.554891i
\(573\) 3.51026 + 7.68640i 0.146643 + 0.321104i
\(574\) −2.73520 −0.114165
\(575\) 4.47458 10.0978i 0.186603 0.421109i
\(576\) −1.24436 −0.0518485
\(577\) 10.4429 + 22.8667i 0.434743 + 0.951954i 0.992534 + 0.121972i \(0.0389218\pi\)
−0.557791 + 0.829982i \(0.688351\pi\)
\(578\) −4.13865 + 1.21522i −0.172145 + 0.0505464i
\(579\) −0.256776 + 0.296336i −0.0106713 + 0.0123153i
\(580\) 8.45240 + 5.43203i 0.350967 + 0.225553i
\(581\) 32.7308 + 37.7733i 1.35790 + 1.56710i
\(582\) 0.937075 + 6.51750i 0.0388430 + 0.270159i
\(583\) 23.2488 + 6.82646i 0.962867 + 0.282723i
\(584\) −21.2755 + 13.6729i −0.880385 + 0.565789i
\(585\) −2.40799 + 16.7479i −0.0995580 + 0.692441i
\(586\) 4.25088 9.30812i 0.175602 0.384515i
\(587\) 12.9330 28.3194i 0.533804 1.16887i −0.430140 0.902762i \(-0.641536\pi\)
0.963944 0.266106i \(-0.0857370\pi\)
\(588\) 1.06516 7.40837i 0.0439266 0.305516i
\(589\) −5.72146 + 3.67696i −0.235749 + 0.151507i
\(590\) −16.0679 4.71796i −0.661505 0.194235i
\(591\) 3.21162 + 22.3373i 0.132108 + 0.918833i
\(592\) −0.395870 0.456858i −0.0162702 0.0187768i
\(593\) −21.7689 13.9900i −0.893941 0.574501i 0.0110463 0.999939i \(-0.496484\pi\)
−0.904988 + 0.425438i \(0.860120\pi\)
\(594\) −1.67233 + 1.92997i −0.0686166 + 0.0791878i
\(595\) −26.9455 + 7.91191i −1.10466 + 0.324357i
\(596\) 12.9642 + 28.3877i 0.531036 + 1.16281i
\(597\) 13.3644 0.546967
\(598\) −14.4761 9.07416i −0.591972 0.371070i
\(599\) −43.7707 −1.78842 −0.894210 0.447647i \(-0.852262\pi\)
−0.894210 + 0.447647i \(0.852262\pi\)
\(600\) 2.00116 + 4.38194i 0.0816971 + 0.178892i
\(601\) −12.5602 + 3.68802i −0.512342 + 0.150437i −0.527677 0.849445i \(-0.676937\pi\)
0.0153345 + 0.999882i \(0.495119\pi\)
\(602\) 2.32090 2.67846i 0.0945927 0.109166i
\(603\) −0.169204 0.108741i −0.00689053 0.00442827i
\(604\) −6.00383 6.92879i −0.244292 0.281928i
\(605\) −3.51678 24.4597i −0.142977 0.994430i
\(606\) 5.15196 + 1.51275i 0.209284 + 0.0614513i
\(607\) 10.2332 6.57650i 0.415354 0.266932i −0.316231 0.948682i \(-0.602417\pi\)
0.731585 + 0.681750i \(0.238781\pi\)
\(608\) 0.807758 5.61808i 0.0327589 0.227843i
\(609\) −3.11983 + 6.83148i −0.126422 + 0.276825i
\(610\) −2.99223 + 6.55207i −0.121152 + 0.265286i
\(611\) −4.22862 + 29.4107i −0.171072 + 1.18983i
\(612\) −4.32787 + 2.78135i −0.174944 + 0.112429i
\(613\) −40.9582 12.0264i −1.65429 0.485742i −0.684360 0.729144i \(-0.739918\pi\)
−0.969925 + 0.243402i \(0.921736\pi\)
\(614\) 0.148252 + 1.03112i 0.00598297 + 0.0416125i
\(615\) −2.51248 2.89955i −0.101313 0.116921i
\(616\) −26.7420 17.1861i −1.07747 0.692446i
\(617\) −0.260539 + 0.300678i −0.0104889 + 0.0121048i −0.760970 0.648787i \(-0.775276\pi\)
0.750481 + 0.660892i \(0.229822\pi\)
\(618\) 2.19069 0.643245i 0.0881226 0.0258751i
\(619\) −12.4831 27.3343i −0.501740 1.09866i −0.975900 0.218219i \(-0.929975\pi\)
0.474160 0.880439i \(-0.342752\pi\)
\(620\) 29.3862 1.18018
\(621\) 4.79553 0.0540938i 0.192438 0.00217071i
\(622\) 5.27239 0.211403
\(623\) −1.22890 2.69092i −0.0492350 0.107810i
\(624\) −12.9904 + 3.81433i −0.520033 + 0.152695i
\(625\) 20.4390 23.5878i 0.817559 0.943514i
\(626\) −6.66148 4.28108i −0.266246 0.171106i
\(627\) 3.08143 + 3.55616i 0.123061 + 0.142019i
\(628\) 3.92105 + 27.2715i 0.156467 + 1.08825i
\(629\) −0.823234 0.241723i −0.0328245 0.00963814i
\(630\) −4.37990 + 2.81479i −0.174499 + 0.112144i
\(631\) 3.43513 23.8919i 0.136750 0.951120i −0.799720 0.600373i \(-0.795019\pi\)
0.936470 0.350747i \(-0.114072\pi\)
\(632\) 6.74945 14.7792i 0.268479 0.587886i
\(633\) −0.232217 + 0.508485i −0.00922981 + 0.0202105i
\(634\) −2.19060 + 15.2360i −0.0869999 + 0.605098i
\(635\) −24.8803 + 15.9896i −0.987344 + 0.634528i
\(636\) 8.68294 + 2.54954i 0.344301 + 0.101096i
\(637\) −3.97858 27.6716i −0.157637 1.09639i
\(638\) 3.70923 + 4.28068i 0.146850 + 0.169474i
\(639\) −2.53877 1.63157i −0.100432 0.0645437i
\(640\) −20.4146 + 23.5597i −0.806958 + 0.931279i
\(641\) −31.6282 + 9.28689i −1.24924 + 0.366810i −0.838479 0.544933i \(-0.816555\pi\)
−0.410761 + 0.911743i \(0.634737\pi\)
\(642\) −0.868429 1.90159i −0.0342742 0.0750499i
\(643\) 7.50786 0.296081 0.148040 0.988981i \(-0.452703\pi\)
0.148040 + 0.988981i \(0.452703\pi\)
\(644\) 4.17751 + 26.8978i 0.164617 + 1.05992i
\(645\) 4.97131 0.195745
\(646\) −0.760529 1.66533i −0.0299226 0.0655214i
\(647\) −13.2481 + 3.88998i −0.520835 + 0.152931i −0.531575 0.847011i \(-0.678400\pi\)
0.0107395 + 0.999942i \(0.496581\pi\)
\(648\) −1.36979 + 1.58082i −0.0538104 + 0.0621006i
\(649\) 41.1215 + 26.4272i 1.61416 + 1.03736i
\(650\) 5.37274 + 6.20048i 0.210736 + 0.243203i
\(651\) 3.12600 + 21.7418i 0.122518 + 0.852129i
\(652\) 16.1093 + 4.73011i 0.630888 + 0.185245i
\(653\) 20.0883 12.9100i 0.786116 0.505206i −0.0849423 0.996386i \(-0.527071\pi\)
0.871058 + 0.491180i \(0.163434\pi\)
\(654\) 1.08600 7.55329i 0.0424660 0.295357i
\(655\) −3.97126 + 8.69584i −0.155170 + 0.339775i
\(656\) 1.27530 2.79252i 0.0497922 0.109030i
\(657\) 1.72067 11.9675i 0.0671297 0.466897i
\(658\) −7.69147 + 4.94301i −0.299845 + 0.192699i
\(659\) −19.8085 5.81631i −0.771631 0.226571i −0.127863 0.991792i \(-0.540812\pi\)
−0.643768 + 0.765220i \(0.722630\pi\)
\(660\) −2.89346 20.1244i −0.112628 0.783342i
\(661\) 30.0235 + 34.6490i 1.16778 + 1.34769i 0.926076 + 0.377338i \(0.123161\pi\)
0.241703 + 0.970350i \(0.422294\pi\)
\(662\) −7.86076 5.05181i −0.305517 0.196344i
\(663\) −12.5837 + 14.5223i −0.488710 + 0.564001i
\(664\) 29.6256 8.69885i 1.14969 0.337581i
\(665\) 3.98520 + 8.72636i 0.154539 + 0.338394i
\(666\) −0.159065 −0.00616364
\(667\) 1.39497 10.5453i 0.0540134 0.408315i
\(668\) 12.4027 0.479877
\(669\) −12.3362 27.0125i −0.476945 1.04436i
\(670\) −0.296740 + 0.0871307i −0.0114641 + 0.00336615i
\(671\) 13.7685 15.8897i 0.531527 0.613415i
\(672\) −15.4212 9.91057i −0.594884 0.382309i
\(673\) −22.7553 26.2610i −0.877153 1.01229i −0.999803 0.0198386i \(-0.993685\pi\)
0.122650 0.992450i \(-0.460861\pi\)
\(674\) −1.34213 9.33469i −0.0516967 0.359559i
\(675\) −2.20972 0.648832i −0.0850521 0.0249736i
\(676\) −36.9487 + 23.7455i −1.42110 + 0.913288i
\(677\) −4.44431 + 30.9109i −0.170809 + 1.18800i 0.706372 + 0.707841i \(0.250331\pi\)
−0.877181 + 0.480161i \(0.840578\pi\)
\(678\) −0.164246 + 0.359649i −0.00630783 + 0.0138122i
\(679\) 16.2778 35.6433i 0.624683 1.36787i
\(680\) −2.46895 + 17.1719i −0.0946798 + 0.658513i
\(681\) −20.7540 + 13.3378i −0.795295 + 0.511105i
\(682\) 15.8952 + 4.66726i 0.608659 + 0.178719i
\(683\) −3.56583 24.8009i −0.136443 0.948980i −0.936902 0.349592i \(-0.886320\pi\)
0.800459 0.599387i \(-0.204589\pi\)
\(684\) 1.15085 + 1.32815i 0.0440039 + 0.0507832i
\(685\) 29.0826 + 18.6903i 1.11119 + 0.714119i
\(686\) −3.19822 + 3.69094i −0.122109 + 0.140921i
\(687\) 27.3273 8.02401i 1.04260 0.306135i
\(688\) 1.65246 + 3.61838i 0.0629994 + 0.137949i
\(689\) 33.8016 1.28774
\(690\) 4.76589 5.62715i 0.181434 0.214222i
\(691\) 47.0943 1.79155 0.895775 0.444507i \(-0.146621\pi\)
0.895775 + 0.444507i \(0.146621\pi\)
\(692\) −3.91003 8.56177i −0.148637 0.325470i
\(693\) 14.5816 4.28153i 0.553908 0.162642i
\(694\) −0.0695763 + 0.0802953i −0.00264108 + 0.00304797i
\(695\) 18.6815 + 12.0059i 0.708631 + 0.455410i
\(696\) 3.03819 + 3.50626i 0.115162 + 0.132904i
\(697\) −0.620095 4.31286i −0.0234878 0.163361i
\(698\) 5.74089 + 1.68568i 0.217296 + 0.0638038i
\(699\) −12.6718 + 8.14369i −0.479292 + 0.308023i
\(700\) 1.86026 12.9384i 0.0703113 0.489026i
\(701\) 10.6225 23.2601i 0.401207 0.878522i −0.595939 0.803030i \(-0.703220\pi\)
0.997146 0.0754920i \(-0.0240527\pi\)
\(702\) −1.47991 + 3.24054i −0.0558554 + 0.122306i
\(703\) −0.0417114 + 0.290109i −0.00157317 + 0.0109417i
\(704\) 4.69839 3.01947i 0.177077 0.113801i
\(705\) −12.3052 3.61313i −0.463441 0.136078i
\(706\) −1.67338 11.6386i −0.0629784 0.438025i
\(707\) −20.9251 24.1489i −0.786970 0.908212i
\(708\) 15.3580 + 9.87001i 0.577190 + 0.370938i
\(709\) 13.9512 16.1005i 0.523947 0.604667i −0.430668 0.902511i \(-0.641722\pi\)
0.954615 + 0.297843i \(0.0962674\pi\)
\(710\) −4.45233 + 1.30732i −0.167093 + 0.0490629i
\(711\) 3.22673 + 7.06556i 0.121012 + 0.264979i
\(712\) −1.82748 −0.0684878
\(713\) −13.2424 28.1521i −0.495931 1.05430i
\(714\) −5.91279 −0.221281
\(715\) −31.5472 69.0787i −1.17980 2.58340i
\(716\) 34.6518 10.1747i 1.29500 0.380246i
\(717\) 17.6566 20.3768i 0.659399 0.760987i
\(718\) −7.50415 4.82263i −0.280053 0.179979i
\(719\) 11.0585 + 12.7622i 0.412412 + 0.475949i 0.923510 0.383573i \(-0.125307\pi\)
−0.511098 + 0.859522i \(0.670761\pi\)
\(720\) −0.831628 5.78410i −0.0309930 0.215561i
\(721\) −13.0368 3.82794i −0.485515 0.142560i
\(722\) 8.56839 5.50657i 0.318883 0.204933i
\(723\) −3.00414 + 20.8943i −0.111725 + 0.777066i
\(724\) −7.14541 + 15.6463i −0.265557 + 0.581489i
\(725\) −2.12197 + 4.64646i −0.0788079 + 0.172565i
\(726\) 0.740446 5.14992i 0.0274805 0.191131i
\(727\) −39.3725 + 25.3032i −1.46024 + 0.938442i −0.461563 + 0.887107i \(0.652711\pi\)
−0.998681 + 0.0513351i \(0.983652\pi\)
\(728\) −42.5488 12.4935i −1.57696 0.463038i
\(729\) −0.142315 0.989821i −0.00527092 0.0366601i
\(730\) −12.1744 14.0500i −0.450593 0.520012i
\(731\) 4.74955 + 3.05235i 0.175669 + 0.112895i
\(732\) 5.14225 5.93447i 0.190063 0.219344i
\(733\) 1.17020 0.343601i 0.0432223 0.0126912i −0.260050 0.965595i \(-0.583739\pi\)
0.303272 + 0.952904i \(0.401921\pi\)
\(734\) −1.28715 2.81846i −0.0475096 0.104031i
\(735\) 12.0663 0.445074
\(736\) 24.9929 + 7.03336i 0.921250 + 0.259253i
\(737\) 0.902732 0.0332526
\(738\) −0.335570 0.734797i −0.0123525 0.0270482i
\(739\) 27.8695 8.18321i 1.02519 0.301024i 0.274439 0.961604i \(-0.411508\pi\)
0.750756 + 0.660580i \(0.229690\pi\)
\(740\) 0.829309 0.957074i 0.0304860 0.0351827i
\(741\) 5.52216 + 3.54888i 0.202862 + 0.130371i
\(742\) 6.81114 + 7.86047i 0.250045 + 0.288567i
\(743\) 3.79826 + 26.4174i 0.139344 + 0.969162i 0.932764 + 0.360487i \(0.117390\pi\)
−0.793420 + 0.608675i \(0.791701\pi\)
\(744\) 13.0196 + 3.82290i 0.477322 + 0.140154i
\(745\) −42.3255 + 27.2009i −1.55068 + 0.996565i
\(746\) −0.326116 + 2.26819i −0.0119400 + 0.0830442i
\(747\) −6.13200 + 13.4272i −0.224358 + 0.491276i
\(748\) 9.59188 21.0033i 0.350714 0.767956i
\(749\) −1.77048 + 12.3140i −0.0646919 + 0.449942i
\(750\) 3.48864 2.24201i 0.127387 0.0818668i
\(751\) −1.31007 0.384670i −0.0478050 0.0140368i 0.257743 0.966214i \(-0.417021\pi\)
−0.305548 + 0.952177i \(0.598840\pi\)
\(752\) −1.46041 10.1574i −0.0532556 0.370401i
\(753\) 1.52389 + 1.75867i 0.0555338 + 0.0640894i
\(754\) 6.64722 + 4.27191i 0.242077 + 0.155574i
\(755\) 9.67917 11.1704i 0.352261 0.406531i
\(756\) 5.44591 1.59906i 0.198066 0.0581574i
\(757\) 21.6745 + 47.4605i 0.787773 + 1.72498i 0.682918 + 0.730495i \(0.260711\pi\)
0.104855 + 0.994488i \(0.466562\pi\)
\(758\) 6.34357 0.230409
\(759\) −17.9754 + 11.8407i −0.652465 + 0.429789i
\(760\) 5.92632 0.214970
\(761\) 9.05143 + 19.8199i 0.328114 + 0.718470i 0.999749 0.0224126i \(-0.00713475\pi\)
−0.671635 + 0.740883i \(0.734407\pi\)
\(762\) −5.97473 + 1.75434i −0.216442 + 0.0635530i
\(763\) −29.7384 + 34.3199i −1.07660 + 1.24246i
\(764\) −11.9158 7.65785i −0.431100 0.277051i
\(765\) −5.43132 6.26808i −0.196370 0.226623i
\(766\) −1.21561 8.45476i −0.0439218 0.305483i
\(767\) 65.4278 + 19.2113i 2.36246 + 0.693681i
\(768\) −3.42797 + 2.20302i −0.123696 + 0.0794948i
\(769\) −5.35823 + 37.2673i −0.193223 + 1.34389i 0.630186 + 0.776444i \(0.282979\pi\)
−0.823409 + 0.567449i \(0.807931\pi\)
\(770\) 9.70721 21.2558i 0.349823 0.766007i
\(771\) 11.0896 24.2829i 0.399383 0.874526i
\(772\) 0.0935400 0.650585i 0.00336658 0.0234151i
\(773\) 1.53486 0.986395i 0.0552051 0.0354782i −0.512747 0.858540i \(-0.671372\pi\)
0.567952 + 0.823061i \(0.307736\pi\)
\(774\) 1.00429 + 0.294887i 0.0360986 + 0.0105995i
\(775\) 2.12616 + 14.7878i 0.0763740 + 0.531193i
\(776\) −15.8518 18.2940i −0.569047 0.656715i
\(777\) 0.796324 + 0.511767i 0.0285680 + 0.0183595i
\(778\) −12.3560 + 14.2596i −0.442983 + 0.511230i
\(779\) −1.42815 + 0.419342i −0.0511687 + 0.0150245i
\(780\) −11.7822 25.7995i −0.421871 0.923769i
\(781\) 13.5447 0.484668
\(782\) 8.00833 2.44991i 0.286377 0.0876085i
\(783\) −2.21800 −0.0792648
\(784\) 4.01084 + 8.78251i 0.143244 + 0.313661i
\(785\) −42.6190 + 12.5141i −1.52114 + 0.446646i
\(786\) −1.31808 + 1.52115i −0.0470145 + 0.0542576i
\(787\) −24.2453 15.5815i −0.864250 0.555420i 0.0317386 0.999496i \(-0.489896\pi\)
−0.895989 + 0.444076i \(0.853532\pi\)
\(788\) −24.7721 28.5886i −0.882471 1.01843i
\(789\) −1.42355 9.90102i −0.0506798 0.352486i
\(790\) 11.4597 + 3.36487i 0.407717 + 0.119717i
\(791\) 1.97938 1.27207i 0.0703785 0.0452295i
\(792\) 1.33607 9.29259i 0.0474753 0.330198i
\(793\) 12.1842 26.6798i 0.432675 0.947426i
\(794\) 1.57670 3.45248i 0.0559549 0.122524i
\(795\) −2.07628 + 14.4408i −0.0736379 + 0.512163i
\(796\) −18.8459 + 12.1115i −0.667974 + 0.429281i
\(797\) 0.861256 + 0.252887i 0.0305072 + 0.00895773i 0.296951 0.954893i \(-0.404030\pi\)
−0.266443 + 0.963851i \(0.585849\pi\)
\(798\) 0.287452 + 1.99927i 0.0101757 + 0.0707736i
\(799\) −9.53786 11.0073i −0.337425 0.389409i
\(800\) −10.4888 6.74072i −0.370834 0.238320i
\(801\) 0.572133 0.660277i 0.0202153 0.0233297i
\(802\) −3.39920 + 0.998096i −0.120030 + 0.0352440i
\(803\) 22.5426 + 49.3614i 0.795511 + 1.74193i
\(804\) 0.337152 0.0118904
\(805\) −41.9639 + 12.8376i −1.47903 + 0.452465i
\(806\) 23.1102 0.814021
\(807\) −7.28824 15.9590i −0.256558 0.561784i
\(808\) −18.9399 + 5.56127i −0.666304 + 0.195645i
\(809\) 24.6586 28.4575i 0.866949 1.00051i −0.133006 0.991115i \(-0.542463\pi\)
0.999956 0.00939782i \(-0.00299146\pi\)
\(810\) −1.29353 0.831302i −0.0454500 0.0292090i
\(811\) 13.4067 + 15.4722i 0.470775 + 0.543303i 0.940627 0.339442i \(-0.110238\pi\)
−0.469852 + 0.882745i \(0.655693\pi\)
\(812\) −1.79160 12.4608i −0.0628727 0.437289i
\(813\) −1.09331 0.321023i −0.0383439 0.0112588i
\(814\) 0.600587 0.385974i 0.0210506 0.0135284i
\(815\) −3.85207 + 26.7917i −0.134932 + 0.938473i
\(816\) 2.75687 6.03670i 0.0965098 0.211327i
\(817\) 0.801182 1.75434i 0.0280298 0.0613767i
\(818\) −0.158705 + 1.10382i −0.00554901 + 0.0385942i
\(819\) 17.8348 11.4617i 0.623197 0.400505i
\(820\) 6.17073 + 1.81189i 0.215491 + 0.0632739i
\(821\) 2.30296 + 16.0174i 0.0803739 + 0.559013i 0.989725 + 0.142983i \(0.0456695\pi\)
−0.909351 + 0.416029i \(0.863421\pi\)
\(822\) 4.76655 + 5.50089i 0.166252 + 0.191866i
\(823\) −15.0421 9.66699i −0.524336 0.336970i 0.251549 0.967844i \(-0.419060\pi\)
−0.775885 + 0.630874i \(0.782696\pi\)
\(824\) −5.49660 + 6.34342i −0.191483 + 0.220984i
\(825\) 9.91772 2.91210i 0.345291 0.101386i
\(826\) 8.71639 + 19.0862i 0.303282 + 0.664095i
\(827\) −8.08676 −0.281204 −0.140602 0.990066i \(-0.544904\pi\)
−0.140602 + 0.990066i \(0.544904\pi\)
\(828\) −6.71343 + 4.42225i −0.233308 + 0.153684i
\(829\) −37.2365 −1.29328 −0.646639 0.762796i \(-0.723826\pi\)
−0.646639 + 0.762796i \(0.723826\pi\)
\(830\) 9.42870 + 20.6460i 0.327275 + 0.716632i
\(831\) 20.5018 6.01988i 0.711200 0.208827i
\(832\) 5.10211 5.88814i 0.176884 0.204135i
\(833\) 11.5281 + 7.40865i 0.399425 + 0.256695i
\(834\) 3.06184 + 3.53355i 0.106023 + 0.122357i
\(835\) 2.84563 + 19.7918i 0.0984769 + 0.684922i
\(836\) −7.56809 2.22219i −0.261748 0.0768562i
\(837\) −5.45730 + 3.50720i −0.188632 + 0.121226i
\(838\) 0.669211 4.65446i 0.0231175 0.160786i
\(839\) −14.4379 + 31.6145i −0.498451 + 1.09145i 0.478519 + 0.878077i \(0.341174\pi\)
−0.976970 + 0.213377i \(0.931554\pi\)
\(840\) 7.95107 17.4104i 0.274338 0.600717i
\(841\) 3.42701 23.8354i 0.118173 0.821910i
\(842\) 0.847742 0.544810i 0.0292151 0.0187754i
\(843\) 11.8819 + 3.48883i 0.409233 + 0.120162i
\(844\) −0.133353 0.927493i −0.00459021 0.0319256i
\(845\) −46.3693 53.5131i −1.59515 1.84090i
\(846\) −2.27155 1.45984i −0.0780974 0.0501902i
\(847\) −20.2759 + 23.3997i −0.696689 + 0.804022i
\(848\) −11.2009 + 3.28889i −0.384642 + 0.112941i
\(849\) −2.95637 6.47354i −0.101462 0.222171i
\(850\) −4.02161 −0.137940
\(851\) −1.29059 0.363192i −0.0442410 0.0124501i
\(852\) 5.05867 0.173307
\(853\) −11.7305 25.6863i −0.401646 0.879482i −0.997101 0.0760933i \(-0.975755\pi\)
0.595455 0.803389i \(-0.296972\pi\)
\(854\) 8.65948 2.54265i 0.296321 0.0870078i
\(855\) −1.85536 + 2.14120i −0.0634521 + 0.0732276i
\(856\) 6.46525 + 4.15496i 0.220978 + 0.142014i
\(857\) 4.86922 + 5.61938i 0.166330 + 0.191954i 0.832795 0.553581i \(-0.186739\pi\)
−0.666466 + 0.745536i \(0.732194\pi\)
\(858\) −2.27550 15.8264i −0.0776843 0.540306i
\(859\) −39.2382 11.5214i −1.33879 0.393104i −0.467551 0.883966i \(-0.654864\pi\)
−0.871237 + 0.490862i \(0.836682\pi\)
\(860\) −7.01034 + 4.50527i −0.239051 + 0.153628i
\(861\) −0.684133 + 4.75825i −0.0233152 + 0.162161i
\(862\) −6.32437 + 13.8484i −0.215409 + 0.471680i
\(863\) −8.82000 + 19.3131i −0.300236 + 0.657426i −0.998280 0.0586297i \(-0.981327\pi\)
0.698044 + 0.716055i \(0.254054\pi\)
\(864\) 0.770464 5.35870i 0.0262117 0.182307i
\(865\) 12.7654 8.20383i 0.434037 0.278939i
\(866\) 13.4170 + 3.93959i 0.455928 + 0.133873i
\(867\) 1.07887 + 7.50369i 0.0366403 + 0.254839i
\(868\) −24.1118 27.8264i −0.818406 0.944491i
\(869\) −29.3280 18.8480i −0.994884 0.639373i
\(870\) −2.23337 + 2.57744i −0.0757182 + 0.0873835i
\(871\) 1.20831 0.354792i 0.0409421 0.0120217i
\(872\) 11.6538 + 25.5183i 0.394648 + 0.864158i
\(873\) 11.5724 0.391668
\(874\) −1.21771 2.58873i −0.0411896 0.0875651i
\(875\) −24.6785 −0.834285
\(876\) 8.41919 + 18.4355i 0.284458 + 0.622876i
\(877\) −17.9522 + 5.27124i −0.606203 + 0.177997i −0.570407 0.821362i \(-0.693215\pi\)
−0.0357955 + 0.999359i \(0.511396\pi\)
\(878\) 2.08492 2.40612i 0.0703626 0.0812028i
\(879\) −15.1295 9.72313i −0.510305 0.327953i
\(880\) 17.1752 + 19.8213i 0.578977 + 0.668175i
\(881\) −5.10803 35.5271i −0.172094 1.19694i −0.874451 0.485114i \(-0.838778\pi\)
0.702357 0.711825i \(-0.252131\pi\)
\(882\) 2.43762 + 0.715749i 0.0820788 + 0.0241005i
\(883\) 5.34188 3.43302i 0.179769 0.115530i −0.447662 0.894203i \(-0.647743\pi\)
0.627430 + 0.778673i \(0.284107\pi\)
\(884\) 4.58406 31.8828i 0.154179 1.07234i
\(885\) −12.2265 + 26.7722i −0.410988 + 0.899938i
\(886\) −2.95857 + 6.47837i −0.0993951 + 0.217645i
\(887\) −2.27527 + 15.8248i −0.0763960 + 0.531346i 0.915303 + 0.402766i \(0.131951\pi\)
−0.991699 + 0.128580i \(0.958958\pi\)
\(888\) 0.491935 0.316147i 0.0165082 0.0106092i
\(889\) 35.5555 + 10.4400i 1.19249 + 0.350148i
\(890\) −0.191183 1.32970i −0.00640845 0.0445718i
\(891\) 2.93916 + 3.39197i 0.0984657 + 0.113635i
\(892\) 41.8762 + 26.9122i 1.40212 + 0.901087i
\(893\) −3.25817 + 3.76013i −0.109031 + 0.125828i
\(894\) −10.1640 + 2.98442i −0.339935 + 0.0998139i
\(895\) 24.1867 + 52.9615i 0.808472 + 1.77031i
\(896\) 39.0597 1.30489
\(897\) −19.4065 + 22.9135i −0.647965 + 0.765059i
\(898\) 4.63700 0.154739
\(899\) 5.97715 + 13.0881i 0.199349 + 0.436514i
\(900\) 3.70406 1.08761i 0.123469 0.0362537i
\(901\) −10.8502 + 12.5218i −0.361473 + 0.417163i
\(902\) 3.05002 + 1.96013i 0.101555 + 0.0652652i
\(903\) −4.07903 4.70745i −0.135742 0.156654i
\(904\) −0.206856 1.43872i −0.00687994 0.0478511i
\(905\) −26.6070 7.81253i −0.884448 0.259697i
\(906\) 2.61797 1.68246i 0.0869761 0.0558961i
\(907\) 3.33936 23.2257i 0.110881 0.771198i −0.856184 0.516671i \(-0.827171\pi\)
0.967066 0.254527i \(-0.0819197\pi\)
\(908\) 17.1790 37.6168i 0.570105 1.24836i
\(909\) 3.92025 8.58415i 0.130026 0.284718i
\(910\) 4.63917 32.2662i 0.153787 1.06961i
\(911\) 23.3996 15.0380i 0.775263 0.498231i −0.0921956 0.995741i \(-0.529389\pi\)
0.867458 + 0.497510i \(0.165752\pi\)
\(912\) −2.17520 0.638696i −0.0720280 0.0211493i
\(913\) −9.42854 65.5770i −0.312039 2.17028i
\(914\) −6.74446 7.78352i −0.223087 0.257456i
\(915\) 10.6498 + 6.84420i 0.352071 + 0.226262i
\(916\) −31.2640 + 36.0806i −1.03299 + 1.19214i
\(917\) 11.4928 3.37458i 0.379525 0.111438i
\(918\) −0.725416 1.58844i −0.0239423 0.0524263i
\(919\) 38.7863 1.27944 0.639720 0.768608i \(-0.279050\pi\)
0.639720 + 0.768608i \(0.279050\pi\)
\(920\) −3.55516 + 26.8753i −0.117210 + 0.886051i
\(921\) 1.83085 0.0603285
\(922\) −3.09663 6.78068i −0.101982 0.223310i
\(923\) 18.1297 5.32336i 0.596746 0.175220i
\(924\) −16.6822 + 19.2522i −0.548803 + 0.633352i
\(925\) 0.541624 + 0.348080i 0.0178085 + 0.0114448i
\(926\) −7.25317 8.37060i −0.238354 0.275075i
\(927\) −0.571072 3.97189i −0.0187565 0.130454i
\(928\) −11.5214 3.38299i −0.378208 0.111052i
\(929\) −27.2494 + 17.5121i −0.894023 + 0.574554i −0.905012 0.425386i \(-0.860138\pi\)
0.0109891 + 0.999940i \(0.496502\pi\)
\(930\) −1.41955 + 9.87320i −0.0465489 + 0.323755i
\(931\) 1.94462 4.25813i 0.0637325 0.139555i
\(932\) 10.4890 22.9678i 0.343580 0.752335i
\(933\) 1.31874 9.17202i 0.0431735 0.300279i
\(934\) 0.572395 0.367856i 0.0187293 0.0120366i
\(935\) 35.7169 + 10.4874i 1.16807 + 0.342975i
\(936\) −1.86384 12.9633i −0.0609215 0.423718i
\(937\) 0.936770 + 1.08109i 0.0306029 + 0.0353177i 0.770845 0.637023i \(-0.219834\pi\)
−0.740242 + 0.672341i \(0.765289\pi\)
\(938\) 0.325985 + 0.209498i 0.0106438 + 0.00684035i
\(939\) −9.11369 + 10.5178i −0.297414 + 0.343234i
\(940\) 20.6267 6.05655i 0.672769 0.197543i
\(941\) −0.263641 0.577294i −0.00859446 0.0188192i 0.905286 0.424802i \(-0.139656\pi\)
−0.913881 + 0.405983i \(0.866929\pi\)
\(942\) −9.35211 −0.304708
\(943\) −1.04494 6.72807i −0.0340279 0.219096i
\(944\) −23.5503 −0.766496
\(945\) 3.80120 + 8.32347i 0.123653 + 0.270762i
\(946\) −4.50750 + 1.32352i −0.146551 + 0.0430314i
\(947\) 21.7906 25.1476i 0.708098 0.817188i −0.281725 0.959495i \(-0.590907\pi\)
0.989823 + 0.142307i \(0.0454520\pi\)
\(948\) −10.9534 7.03932i −0.355750 0.228627i
\(949\) 49.5734 + 57.2108i 1.60922 + 1.85714i
\(950\) 0.195512 + 1.35982i 0.00634325 + 0.0441183i
\(951\) 25.9571 + 7.62169i 0.841716 + 0.247150i
\(952\) 18.2863 11.7519i 0.592662 0.380881i
\(953\) 5.69080 39.5804i 0.184343 1.28214i −0.662003 0.749502i \(-0.730293\pi\)
0.846346 0.532634i \(-0.178798\pi\)
\(954\) −1.27604 + 2.79414i −0.0413134 + 0.0904637i
\(955\) 9.48615 20.7718i 0.306965 0.672159i
\(956\) −6.43206 + 44.7360i −0.208028 + 1.44686i
\(957\) 8.37457 5.38201i 0.270712 0.173976i
\(958\) −9.54599 2.80295i −0.308417 0.0905594i
\(959\) −6.16444 42.8746i −0.199060 1.38449i
\(960\) 2.20215 + 2.54142i 0.0710742 + 0.0820240i
\(961\) 9.32324 + 5.99169i 0.300750 + 0.193280i
\(962\) 0.652193 0.752671i 0.0210276 0.0242671i
\(963\) −3.52529 + 1.03512i −0.113601 + 0.0333562i
\(964\) −14.6992 32.1867i −0.473429 1.03666i
\(965\) 1.05964 0.0341109
\(966\) −9.23896 + 0.104216i −0.297259 + 0.00335309i
\(967\) 50.8204 1.63427 0.817136 0.576444i \(-0.195560\pi\)
0.817136 + 0.576444i \(0.195560\pi\)
\(968\) 7.94569 + 17.3986i 0.255384 + 0.559213i
\(969\) −3.08728 + 0.906509i −0.0991779 + 0.0291212i
\(970\) 11.6526 13.4478i 0.374143 0.431784i
\(971\) 36.1031 + 23.2020i 1.15860 + 0.744589i 0.971334 0.237720i \(-0.0763999\pi\)
0.187269 + 0.982309i \(0.440036\pi\)
\(972\) 1.09772 + 1.26683i 0.0352093 + 0.0406337i
\(973\) −3.95980 27.5410i −0.126945 0.882923i
\(974\) −12.2908 3.60891i −0.393823 0.115637i
\(975\) 12.1304 7.79573i 0.388484 0.249663i
\(976\) −1.44159 + 10.0265i −0.0461442 + 0.320940i
\(977\) 4.38860 9.60970i 0.140404 0.307442i −0.826347 0.563161i \(-0.809585\pi\)
0.966751 + 0.255719i \(0.0823123\pi\)
\(978\) −2.36741 + 5.18391i −0.0757015 + 0.165763i
\(979\) −0.558050 + 3.88132i −0.0178354 + 0.124048i
\(980\) −17.0155 + 10.9352i −0.543539 + 0.349311i
\(981\) −12.8683 3.77848i −0.410854 0.120638i
\(982\) 2.38343 + 16.5771i 0.0760582 + 0.528996i
\(983\) −31.0101 35.7876i −0.989068 1.14145i −0.989946 0.141446i \(-0.954825\pi\)
0.000877467 1.00000i \(-0.499721\pi\)
\(984\) 2.49824 + 1.60552i 0.0796410 + 0.0511822i
\(985\) 39.9368 46.0895i 1.27249 1.46853i
\(986\) −3.71627 + 1.09120i −0.118350 + 0.0347508i
\(987\) 6.67522 + 14.6167i 0.212475 + 0.465255i
\(988\) −11.0033 −0.350062
\(989\) 7.47516 + 4.68570i 0.237696 + 0.148997i
\(990\) 6.90120 0.219334
\(991\) 10.0139 + 21.9274i 0.318102 + 0.696546i 0.999370 0.0354879i \(-0.0112985\pi\)
−0.681268 + 0.732034i \(0.738571\pi\)
\(992\) −33.6973 + 9.89442i −1.06989 + 0.314148i
\(993\) −10.7544 + 12.4113i −0.341282 + 0.393860i
\(994\) 4.89113 + 3.14334i 0.155137 + 0.0997006i
\(995\) −23.6509 27.2946i −0.749785 0.865298i
\(996\) −3.52136 24.4916i −0.111579 0.776047i
\(997\) −27.1075 7.95949i −0.858504 0.252079i −0.177285 0.984160i \(-0.556732\pi\)
−0.681219 + 0.732080i \(0.738550\pi\)
\(998\) 6.21479 3.99400i 0.196726 0.126428i
\(999\) −0.0397856 + 0.276715i −0.00125876 + 0.00875487i
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 69.2.e.c.4.2 20
3.2 odd 2 207.2.i.d.73.1 20
23.6 even 11 inner 69.2.e.c.52.2 yes 20
23.11 odd 22 1587.2.a.t.1.6 10
23.12 even 11 1587.2.a.u.1.6 10
69.11 even 22 4761.2.a.bu.1.5 10
69.29 odd 22 207.2.i.d.190.1 20
69.35 odd 22 4761.2.a.bt.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.e.c.4.2 20 1.1 even 1 trivial
69.2.e.c.52.2 yes 20 23.6 even 11 inner
207.2.i.d.73.1 20 3.2 odd 2
207.2.i.d.190.1 20 69.29 odd 22
1587.2.a.t.1.6 10 23.11 odd 22
1587.2.a.u.1.6 10 23.12 even 11
4761.2.a.bt.1.5 10 69.35 odd 22
4761.2.a.bu.1.5 10 69.11 even 22