Properties

Label 171.3.z.a.101.17
Level $171$
Weight $3$
Character 171.101
Analytic conductor $4.659$
Analytic rank $0$
Dimension $228$
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] = [171,3,Mod(5,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([15, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.z (of order \(18\), degree \(6\), 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: \(4.65941252056\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(38\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 101.17
Character \(\chi\) \(=\) 171.101
Dual form 171.3.z.a.149.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.604348 + 0.106563i) q^{2} +(0.926188 + 2.85345i) q^{3} +(-3.40489 + 1.23928i) q^{4} +(-2.28598 - 2.72432i) q^{5} +(-0.863811 - 1.62578i) q^{6} +(-2.40415 - 4.16411i) q^{7} +(4.05149 - 2.33913i) q^{8} +(-7.28435 + 5.28566i) q^{9} +O(q^{10})\) \(q+(-0.604348 + 0.106563i) q^{2} +(0.926188 + 2.85345i) q^{3} +(-3.40489 + 1.23928i) q^{4} +(-2.28598 - 2.72432i) q^{5} +(-0.863811 - 1.62578i) q^{6} +(-2.40415 - 4.16411i) q^{7} +(4.05149 - 2.33913i) q^{8} +(-7.28435 + 5.28566i) q^{9} +(1.67184 + 1.40284i) q^{10} -6.82123i q^{11} +(-6.68979 - 8.56788i) q^{12} +(-5.99846 - 5.03331i) q^{13} +(1.89668 + 2.26037i) q^{14} +(5.65648 - 9.04616i) q^{15} +(8.90352 - 7.47094i) q^{16} +(-0.173359 - 0.206601i) q^{17} +(3.83903 - 3.97062i) q^{18} +(-10.3574 - 15.9287i) q^{19} +(11.1597 + 6.44306i) q^{20} +(9.65537 - 10.7169i) q^{21} +(0.726890 + 4.12240i) q^{22} +(1.90850 + 5.24355i) q^{23} +(10.4270 + 9.39426i) q^{24} +(2.14496 - 12.1647i) q^{25} +(4.16152 + 2.40266i) q^{26} +(-21.8290 - 15.8900i) q^{27} +(13.3463 + 11.1989i) q^{28} +(6.89453 + 18.9426i) q^{29} +(-2.45449 + 6.06980i) q^{30} -53.3648 q^{31} +(-16.6132 + 19.7989i) q^{32} +(19.4641 - 6.31774i) q^{33} +(0.126785 + 0.106385i) q^{34} +(-5.84854 + 16.0687i) q^{35} +(18.2520 - 27.0244i) q^{36} -46.1921 q^{37} +(7.95686 + 8.52279i) q^{38} +(8.80659 - 21.7781i) q^{39} +(-15.6342 - 5.69038i) q^{40} +(-37.9281 + 6.68775i) q^{41} +(-4.69318 + 7.50561i) q^{42} +(10.9148 + 3.97267i) q^{43} +(8.45341 + 23.2256i) q^{44} +(31.0517 + 7.76202i) q^{45} +(-1.71216 - 2.96555i) q^{46} +(7.00916 + 19.2575i) q^{47} +(29.5643 + 18.4863i) q^{48} +(12.9401 - 22.4130i) q^{49} +7.58028i q^{50} +(0.428964 - 0.686023i) q^{51} +(26.6618 + 9.70409i) q^{52} +(38.3467 + 6.76156i) q^{53} +(14.8856 + 7.27693i) q^{54} +(-18.5833 + 15.5932i) q^{55} +(-19.4808 - 11.2472i) q^{56} +(35.8590 - 44.3072i) q^{57} +(-6.18526 - 10.7132i) q^{58} +(-32.6473 + 89.6977i) q^{59} +(-8.04896 + 37.8111i) q^{60} +(-16.8653 - 14.1517i) q^{61} +(32.2509 - 5.68670i) q^{62} +(39.5227 + 17.6253i) q^{63} +(-15.3151 + 26.5265i) q^{64} +27.8478i q^{65} +(-11.0898 + 5.89226i) q^{66} +(-1.79263 + 10.1665i) q^{67} +(0.846305 + 0.488615i) q^{68} +(-13.1946 + 10.3023i) q^{69} +(1.82222 - 10.3343i) q^{70} +(99.4330 - 17.5327i) q^{71} +(-17.1487 + 38.4539i) q^{72} +(-4.90757 - 1.78621i) q^{73} +(27.9161 - 4.92236i) q^{74} +(36.6980 - 5.14625i) q^{75} +(55.0058 + 41.4000i) q^{76} +(-28.4043 + 16.3993i) q^{77} +(-3.00151 + 14.1000i) q^{78} +(-52.7127 + 44.2312i) q^{79} +(-40.7065 - 7.17766i) q^{80} +(25.1236 - 77.0052i) q^{81} +(22.2091 - 8.08346i) q^{82} +(75.1090 - 43.3642i) q^{83} +(-19.5943 + 48.4554i) q^{84} +(-0.166554 + 0.944573i) q^{85} +(-7.01968 - 1.23776i) q^{86} +(-47.6660 + 37.2175i) q^{87} +(-15.9558 - 27.6362i) q^{88} +(-53.3713 - 146.636i) q^{89} +(-19.5932 - 1.38200i) q^{90} +(-6.53804 + 37.0791i) q^{91} +(-12.9964 - 15.4885i) q^{92} +(-49.4258 - 152.274i) q^{93} +(-6.28811 - 10.8913i) q^{94} +(-19.7183 + 64.6296i) q^{95} +(-71.8820 - 29.0675i) q^{96} +(-14.4763 - 82.0991i) q^{97} +(-5.43196 + 14.9242i) q^{98} +(36.0547 + 49.6883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21} + 81 q^{22} + 207 q^{23} - 222 q^{24} - 3 q^{25} - 216 q^{26} - 33 q^{27} - 36 q^{28} - 9 q^{29} + 171 q^{30} - 6 q^{31} - 9 q^{32} + 30 q^{33} + 33 q^{34} + 225 q^{35} - 246 q^{36} - 24 q^{37} - 9 q^{38} - 60 q^{39} - 177 q^{40} - 9 q^{41} - 15 q^{42} + 93 q^{43} + 441 q^{44} - 57 q^{45} - 6 q^{46} - 9 q^{47} - 774 q^{48} - 543 q^{49} - 81 q^{51} + 213 q^{52} + 393 q^{54} + 63 q^{55} - 459 q^{56} + 84 q^{57} - 6 q^{58} + 126 q^{59} - 333 q^{60} - 24 q^{61} - 36 q^{62} + 369 q^{63} + 372 q^{64} + 894 q^{66} + 39 q^{67} + 747 q^{68} + 231 q^{69} + 291 q^{70} + 204 q^{72} - 51 q^{73} + 333 q^{74} + 324 q^{75} - 3 q^{76} - 18 q^{77} - 1569 q^{78} - 105 q^{79} - 756 q^{80} + 1050 q^{81} + 132 q^{82} + 99 q^{83} - 69 q^{84} - 3 q^{85} - 495 q^{86} - 483 q^{87} + 387 q^{88} - 648 q^{89} - 339 q^{90} + 225 q^{91} + 27 q^{92} + 396 q^{93} - 6 q^{94} - 1305 q^{95} - 663 q^{96} - 543 q^{97} + 1125 q^{98} - 300 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.604348 + 0.106563i −0.302174 + 0.0532814i −0.322679 0.946508i \(-0.604584\pi\)
0.0205055 + 0.999790i \(0.493472\pi\)
\(3\) 0.926188 + 2.85345i 0.308729 + 0.951150i
\(4\) −3.40489 + 1.23928i −0.851222 + 0.309820i
\(5\) −2.28598 2.72432i −0.457196 0.544865i 0.487366 0.873198i \(-0.337958\pi\)
−0.944562 + 0.328333i \(0.893513\pi\)
\(6\) −0.863811 1.62578i −0.143969 0.270963i
\(7\) −2.40415 4.16411i −0.343450 0.594872i 0.641621 0.767022i \(-0.278262\pi\)
−0.985071 + 0.172149i \(0.944929\pi\)
\(8\) 4.05149 2.33913i 0.506437 0.292391i
\(9\) −7.28435 + 5.28566i −0.809372 + 0.587296i
\(10\) 1.67184 + 1.40284i 0.167184 + 0.140284i
\(11\) 6.82123i 0.620112i −0.950718 0.310056i \(-0.899652\pi\)
0.950718 0.310056i \(-0.100348\pi\)
\(12\) −6.68979 8.56788i −0.557482 0.713990i
\(13\) −5.99846 5.03331i −0.461420 0.387178i 0.382233 0.924066i \(-0.375155\pi\)
−0.843653 + 0.536888i \(0.819600\pi\)
\(14\) 1.89668 + 2.26037i 0.135477 + 0.161455i
\(15\) 5.65648 9.04616i 0.377098 0.603077i
\(16\) 8.90352 7.47094i 0.556470 0.466934i
\(17\) −0.173359 0.206601i −0.0101976 0.0121530i 0.760922 0.648844i \(-0.224747\pi\)
−0.771119 + 0.636691i \(0.780303\pi\)
\(18\) 3.83903 3.97062i 0.213279 0.220590i
\(19\) −10.3574 15.9287i −0.545124 0.838355i
\(20\) 11.1597 + 6.44306i 0.557985 + 0.322153i
\(21\) 9.65537 10.7169i 0.459780 0.510327i
\(22\) 0.726890 + 4.12240i 0.0330405 + 0.187382i
\(23\) 1.90850 + 5.24355i 0.0829780 + 0.227980i 0.974242 0.225504i \(-0.0724029\pi\)
−0.891264 + 0.453485i \(0.850181\pi\)
\(24\) 10.4270 + 9.39426i 0.434460 + 0.391428i
\(25\) 2.14496 12.1647i 0.0857986 0.486588i
\(26\) 4.16152 + 2.40266i 0.160059 + 0.0924098i
\(27\) −21.8290 15.8900i −0.808483 0.588519i
\(28\) 13.3463 + 11.1989i 0.476655 + 0.399961i
\(29\) 6.89453 + 18.9426i 0.237742 + 0.653192i 0.999983 + 0.00589741i \(0.00187721\pi\)
−0.762240 + 0.647294i \(0.775901\pi\)
\(30\) −2.45449 + 6.06980i −0.0818164 + 0.202327i
\(31\) −53.3648 −1.72144 −0.860722 0.509076i \(-0.829987\pi\)
−0.860722 + 0.509076i \(0.829987\pi\)
\(32\) −16.6132 + 19.7989i −0.519163 + 0.618714i
\(33\) 19.4641 6.31774i 0.589820 0.191447i
\(34\) 0.126785 + 0.106385i 0.00372898 + 0.00312898i
\(35\) −5.84854 + 16.0687i −0.167101 + 0.459107i
\(36\) 18.2520 27.0244i 0.507000 0.750679i
\(37\) −46.1921 −1.24844 −0.624218 0.781251i \(-0.714582\pi\)
−0.624218 + 0.781251i \(0.714582\pi\)
\(38\) 7.95686 + 8.52279i 0.209391 + 0.224284i
\(39\) 8.80659 21.7781i 0.225810 0.558413i
\(40\) −15.6342 5.69038i −0.390855 0.142259i
\(41\) −37.9281 + 6.68775i −0.925077 + 0.163116i −0.615842 0.787870i \(-0.711184\pi\)
−0.309235 + 0.950986i \(0.600073\pi\)
\(42\) −4.69318 + 7.50561i −0.111742 + 0.178705i
\(43\) 10.9148 + 3.97267i 0.253833 + 0.0923876i 0.465803 0.884889i \(-0.345766\pi\)
−0.211970 + 0.977276i \(0.567988\pi\)
\(44\) 8.45341 + 23.2256i 0.192123 + 0.527854i
\(45\) 31.0517 + 7.76202i 0.690038 + 0.172489i
\(46\) −1.71216 2.96555i −0.0372209 0.0644685i
\(47\) 7.00916 + 19.2575i 0.149131 + 0.409734i 0.991654 0.128926i \(-0.0411529\pi\)
−0.842523 + 0.538660i \(0.818931\pi\)
\(48\) 29.5643 + 18.4863i 0.615923 + 0.385130i
\(49\) 12.9401 22.4130i 0.264085 0.457408i
\(50\) 7.58028i 0.151606i
\(51\) 0.428964 0.686023i 0.00841105 0.0134514i
\(52\) 26.6618 + 9.70409i 0.512727 + 0.186617i
\(53\) 38.3467 + 6.76156i 0.723523 + 0.127577i 0.523269 0.852167i \(-0.324712\pi\)
0.200254 + 0.979744i \(0.435823\pi\)
\(54\) 14.8856 + 7.27693i 0.275660 + 0.134758i
\(55\) −18.5833 + 15.5932i −0.337877 + 0.283513i
\(56\) −19.4808 11.2472i −0.347871 0.200843i
\(57\) 35.8590 44.3072i 0.629106 0.777320i
\(58\) −6.18526 10.7132i −0.106642 0.184710i
\(59\) −32.6473 + 89.6977i −0.553344 + 1.52030i 0.275772 + 0.961223i \(0.411067\pi\)
−0.829116 + 0.559077i \(0.811156\pi\)
\(60\) −8.04896 + 37.8111i −0.134149 + 0.630186i
\(61\) −16.8653 14.1517i −0.276481 0.231995i 0.493994 0.869465i \(-0.335536\pi\)
−0.770475 + 0.637470i \(0.779981\pi\)
\(62\) 32.2509 5.68670i 0.520175 0.0917209i
\(63\) 39.5227 + 17.6253i 0.627345 + 0.279767i
\(64\) −15.3151 + 26.5265i −0.239299 + 0.414477i
\(65\) 27.8478i 0.428428i
\(66\) −11.0898 + 5.89226i −0.168028 + 0.0892766i
\(67\) −1.79263 + 10.1665i −0.0267557 + 0.151739i −0.995259 0.0972626i \(-0.968991\pi\)
0.968503 + 0.249002i \(0.0801024\pi\)
\(68\) 0.846305 + 0.488615i 0.0124457 + 0.00718551i
\(69\) −13.1946 + 10.3023i −0.191226 + 0.149309i
\(70\) 1.82222 10.3343i 0.0260318 0.147633i
\(71\) 99.4330 17.5327i 1.40047 0.246940i 0.578131 0.815944i \(-0.303782\pi\)
0.822335 + 0.569004i \(0.192671\pi\)
\(72\) −17.1487 + 38.4539i −0.238176 + 0.534082i
\(73\) −4.90757 1.78621i −0.0672270 0.0244686i 0.308188 0.951326i \(-0.400278\pi\)
−0.375415 + 0.926857i \(0.622500\pi\)
\(74\) 27.9161 4.92236i 0.377244 0.0665184i
\(75\) 36.6980 5.14625i 0.489307 0.0686166i
\(76\) 55.0058 + 41.4000i 0.723761 + 0.544736i
\(77\) −28.4043 + 16.3993i −0.368888 + 0.212977i
\(78\) −3.00151 + 14.1000i −0.0384809 + 0.180769i
\(79\) −52.7127 + 44.2312i −0.667249 + 0.559888i −0.912250 0.409634i \(-0.865656\pi\)
0.245001 + 0.969523i \(0.421212\pi\)
\(80\) −40.7065 7.17766i −0.508832 0.0897207i
\(81\) 25.1236 77.0052i 0.310168 0.950682i
\(82\) 22.2091 8.08346i 0.270843 0.0985788i
\(83\) 75.1090 43.3642i 0.904927 0.522460i 0.0261317 0.999659i \(-0.491681\pi\)
0.878796 + 0.477199i \(0.158348\pi\)
\(84\) −19.5943 + 48.4554i −0.233266 + 0.576850i
\(85\) −0.166554 + 0.944573i −0.00195946 + 0.0111126i
\(86\) −7.01968 1.23776i −0.0816242 0.0143925i
\(87\) −47.6660 + 37.2175i −0.547885 + 0.427788i
\(88\) −15.9558 27.6362i −0.181315 0.314048i
\(89\) −53.3713 146.636i −0.599677 1.64760i −0.751918 0.659257i \(-0.770871\pi\)
0.152241 0.988343i \(-0.451351\pi\)
\(90\) −19.5932 1.38200i −0.217702 0.0153556i
\(91\) −6.53804 + 37.0791i −0.0718466 + 0.407462i
\(92\) −12.9964 15.4885i −0.141266 0.168354i
\(93\) −49.4258 152.274i −0.531460 1.63735i
\(94\) −6.28811 10.8913i −0.0668948 0.115865i
\(95\) −19.7183 + 64.6296i −0.207562 + 0.680312i
\(96\) −71.8820 29.0675i −0.748771 0.302787i
\(97\) −14.4763 82.0991i −0.149240 0.846382i −0.963864 0.266393i \(-0.914168\pi\)
0.814624 0.579989i \(-0.196943\pi\)
\(98\) −5.43196 + 14.9242i −0.0554281 + 0.152288i
\(99\) 36.0547 + 49.6883i 0.364189 + 0.501902i
\(100\) 7.77208 + 44.0777i 0.0777208 + 0.440777i
\(101\) 49.2893 + 8.69103i 0.488013 + 0.0860498i 0.412240 0.911075i \(-0.364747\pi\)
0.0757728 + 0.997125i \(0.475858\pi\)
\(102\) −0.186139 + 0.460308i −0.00182489 + 0.00451283i
\(103\) −22.3778 + 38.7594i −0.217260 + 0.376305i −0.953969 0.299904i \(-0.903045\pi\)
0.736709 + 0.676209i \(0.236379\pi\)
\(104\) −36.0763 6.36123i −0.346888 0.0611656i
\(105\) −51.2682 1.80585i −0.488268 0.0171986i
\(106\) −23.8953 −0.225427
\(107\) −167.840 96.9023i −1.56860 0.905629i −0.996333 0.0855583i \(-0.972733\pi\)
−0.572262 0.820071i \(-0.693934\pi\)
\(108\) 94.0177 + 27.0515i 0.870534 + 0.250477i
\(109\) 1.91826 + 10.8790i 0.0175987 + 0.0998072i 0.992342 0.123521i \(-0.0394188\pi\)
−0.974743 + 0.223329i \(0.928308\pi\)
\(110\) 9.56909 11.4040i 0.0869917 0.103673i
\(111\) −42.7826 131.807i −0.385429 1.18745i
\(112\) −52.5152 19.1140i −0.468885 0.170660i
\(113\) 53.7741 31.0465i 0.475877 0.274748i −0.242820 0.970071i \(-0.578072\pi\)
0.718697 + 0.695324i \(0.244739\pi\)
\(114\) −16.9498 + 30.5982i −0.148683 + 0.268405i
\(115\) 9.92234 17.1860i 0.0862812 0.149443i
\(116\) −46.9502 55.9531i −0.404743 0.482354i
\(117\) 70.2993 + 4.95855i 0.600849 + 0.0423807i
\(118\) 10.1719 57.6876i 0.0862024 0.488878i
\(119\) −0.443529 + 1.21859i −0.00372713 + 0.0102402i
\(120\) 1.75702 49.8817i 0.0146418 0.415681i
\(121\) 74.4708 0.615461
\(122\) 11.7006 + 6.75533i 0.0959064 + 0.0553716i
\(123\) −54.2118 102.032i −0.440746 0.829528i
\(124\) 181.701 66.1338i 1.46533 0.533337i
\(125\) −115.041 + 66.4191i −0.920330 + 0.531353i
\(126\) −25.7637 6.44016i −0.204473 0.0511124i
\(127\) 114.996 41.8550i 0.905477 0.329567i 0.153032 0.988221i \(-0.451096\pi\)
0.752445 + 0.658655i \(0.228874\pi\)
\(128\) 41.7877 114.811i 0.326467 0.896960i
\(129\) −1.22664 + 34.8243i −0.00950883 + 0.269956i
\(130\) −2.96754 16.8298i −0.0228272 0.129460i
\(131\) 28.9032 79.4109i 0.220635 0.606190i −0.779152 0.626835i \(-0.784350\pi\)
0.999787 + 0.0206455i \(0.00657212\pi\)
\(132\) −58.4435 + 45.6326i −0.442754 + 0.345702i
\(133\) −41.4284 + 81.4242i −0.311491 + 0.612212i
\(134\) 6.33513i 0.0472771i
\(135\) 6.61119 + 95.7936i 0.0489718 + 0.709583i
\(136\) −1.18563 0.431534i −0.00871788 0.00317305i
\(137\) −39.2676 + 46.7974i −0.286625 + 0.341587i −0.890075 0.455815i \(-0.849348\pi\)
0.603450 + 0.797401i \(0.293792\pi\)
\(138\) 6.87627 7.63222i 0.0498280 0.0553060i
\(139\) 66.6729 + 55.9452i 0.479661 + 0.402483i 0.850304 0.526292i \(-0.176418\pi\)
−0.370643 + 0.928775i \(0.620863\pi\)
\(140\) 61.9602i 0.442573i
\(141\) −48.4586 + 37.8364i −0.343678 + 0.268343i
\(142\) −58.2238 + 21.1917i −0.410027 + 0.149238i
\(143\) −34.3334 + 40.9169i −0.240094 + 0.286132i
\(144\) −25.3675 + 101.482i −0.176163 + 0.704736i
\(145\) 35.8449 62.0852i 0.247206 0.428174i
\(146\) 3.15622 + 0.556528i 0.0216180 + 0.00381183i
\(147\) 75.9394 + 16.1654i 0.516594 + 0.109969i
\(148\) 157.279 57.2449i 1.06270 0.386790i
\(149\) −13.9584 + 2.46124i −0.0936805 + 0.0165184i −0.220292 0.975434i \(-0.570701\pi\)
0.126611 + 0.991952i \(0.459590\pi\)
\(150\) −21.6300 + 7.02076i −0.144200 + 0.0468051i
\(151\) −123.233 + 213.446i −0.816113 + 1.41355i 0.0924132 + 0.995721i \(0.470542\pi\)
−0.908526 + 0.417828i \(0.862791\pi\)
\(152\) −79.2222 40.3080i −0.521199 0.265184i
\(153\) 2.35483 + 0.588640i 0.0153911 + 0.00384732i
\(154\) 15.4185 12.9377i 0.100120 0.0840110i
\(155\) 121.991 + 145.383i 0.787037 + 0.937954i
\(156\) −2.99633 + 85.0659i −0.0192072 + 0.545294i
\(157\) 9.32602 7.82546i 0.0594014 0.0498437i −0.612604 0.790390i \(-0.709878\pi\)
0.672005 + 0.740547i \(0.265433\pi\)
\(158\) 27.1434 32.3482i 0.171794 0.204736i
\(159\) 16.2225 + 115.683i 0.102028 + 0.727566i
\(160\) 91.9160 0.574475
\(161\) 17.2464 20.5534i 0.107120 0.127661i
\(162\) −6.97748 + 49.2152i −0.0430709 + 0.303797i
\(163\) −119.266 206.574i −0.731691 1.26733i −0.956160 0.292844i \(-0.905398\pi\)
0.224469 0.974481i \(-0.427935\pi\)
\(164\) 120.853 69.7746i 0.736909 0.425455i
\(165\) −61.7060 38.5841i −0.373976 0.233843i
\(166\) −40.7709 + 34.2109i −0.245608 + 0.206090i
\(167\) 44.1967 + 121.429i 0.264651 + 0.727122i 0.998839 + 0.0481758i \(0.0153408\pi\)
−0.734188 + 0.678946i \(0.762437\pi\)
\(168\) 14.0506 66.0045i 0.0836343 0.392884i
\(169\) −18.6992 106.048i −0.110646 0.627505i
\(170\) 0.588599i 0.00346235i
\(171\) 159.641 + 61.2851i 0.933571 + 0.358392i
\(172\) −42.0870 −0.244692
\(173\) −93.7130 + 16.5241i −0.541694 + 0.0955152i −0.437799 0.899073i \(-0.644242\pi\)
−0.103895 + 0.994588i \(0.533131\pi\)
\(174\) 24.8408 27.5718i 0.142763 0.158458i
\(175\) −55.8119 + 20.3139i −0.318925 + 0.116079i
\(176\) −50.9610 60.7330i −0.289551 0.345074i
\(177\) −286.185 10.0805i −1.61687 0.0569520i
\(178\) 47.8808 + 82.9320i 0.268993 + 0.465910i
\(179\) 251.151 145.002i 1.40308 0.810068i 0.408371 0.912816i \(-0.366097\pi\)
0.994707 + 0.102748i \(0.0327637\pi\)
\(180\) −115.347 + 12.0529i −0.640817 + 0.0669606i
\(181\) 24.0331 + 20.1662i 0.132779 + 0.111415i 0.706759 0.707455i \(-0.250157\pi\)
−0.573979 + 0.818870i \(0.694601\pi\)
\(182\) 23.1054i 0.126952i
\(183\) 24.7607 61.2316i 0.135304 0.334599i
\(184\) 19.9976 + 16.7800i 0.108683 + 0.0911955i
\(185\) 105.594 + 125.842i 0.570779 + 0.680228i
\(186\) 46.0971 + 86.7593i 0.247834 + 0.466448i
\(187\) −1.40928 + 1.18252i −0.00753624 + 0.00632365i
\(188\) −47.7309 56.8834i −0.253888 0.302571i
\(189\) −13.6875 + 129.100i −0.0724205 + 0.683071i
\(190\) 5.02962 41.1600i 0.0264717 0.216632i
\(191\) 189.242 + 109.259i 0.990794 + 0.572035i 0.905511 0.424322i \(-0.139487\pi\)
0.0852822 + 0.996357i \(0.472821\pi\)
\(192\) −89.8768 19.1323i −0.468108 0.0996475i
\(193\) 7.28334 + 41.3059i 0.0377375 + 0.214020i 0.997845 0.0656100i \(-0.0208993\pi\)
−0.960108 + 0.279630i \(0.909788\pi\)
\(194\) 17.4974 + 48.0738i 0.0901929 + 0.247803i
\(195\) −79.4623 + 25.7923i −0.407499 + 0.132268i
\(196\) −16.2838 + 92.3502i −0.0830808 + 0.471175i
\(197\) −282.971 163.373i −1.43640 0.829306i −0.438803 0.898583i \(-0.644597\pi\)
−0.997597 + 0.0692770i \(0.977931\pi\)
\(198\) −27.0845 26.1869i −0.136790 0.132257i
\(199\) 120.523 + 101.130i 0.605641 + 0.508193i 0.893253 0.449554i \(-0.148417\pi\)
−0.287612 + 0.957747i \(0.592861\pi\)
\(200\) −19.7645 54.3026i −0.0988226 0.271513i
\(201\) −30.6699 + 4.30092i −0.152587 + 0.0213976i
\(202\) −30.7140 −0.152050
\(203\) 62.3033 74.2502i 0.306913 0.365765i
\(204\) −0.610400 + 2.86744i −0.00299216 + 0.0140561i
\(205\) 104.923 + 88.0405i 0.511817 + 0.429466i
\(206\) 9.39363 25.8088i 0.0456002 0.125285i
\(207\) −41.6178 28.1082i −0.201052 0.135788i
\(208\) −91.0110 −0.437553
\(209\) −108.654 + 70.6500i −0.519874 + 0.338038i
\(210\) 31.1762 4.37192i 0.148458 0.0208187i
\(211\) 253.051 + 92.1030i 1.19929 + 0.436507i 0.862978 0.505242i \(-0.168597\pi\)
0.336316 + 0.941749i \(0.390819\pi\)
\(212\) −138.946 + 24.4999i −0.655405 + 0.115566i
\(213\) 142.122 + 267.489i 0.667242 + 1.25582i
\(214\) 111.760 + 40.6772i 0.522242 + 0.190080i
\(215\) −14.1282 38.8169i −0.0657126 0.180544i
\(216\) −125.609 13.3173i −0.581524 0.0616542i
\(217\) 128.297 + 222.216i 0.591229 + 1.02404i
\(218\) −2.31859 6.37028i −0.0106357 0.0292214i
\(219\) 0.551528 15.6579i 0.00251839 0.0714972i
\(220\) 43.9496 76.1230i 0.199771 0.346013i
\(221\) 2.11186i 0.00955593i
\(222\) 39.9013 + 75.0981i 0.179735 + 0.338280i
\(223\) −179.425 65.3054i −0.804597 0.292849i −0.0932068 0.995647i \(-0.529712\pi\)
−0.711390 + 0.702798i \(0.751934\pi\)
\(224\) 122.385 + 21.5798i 0.546362 + 0.0963384i
\(225\) 48.6738 + 99.9495i 0.216328 + 0.444220i
\(226\) −29.1899 + 24.4932i −0.129159 + 0.108377i
\(227\) 97.4433 + 56.2589i 0.429265 + 0.247837i 0.699034 0.715089i \(-0.253614\pi\)
−0.269768 + 0.962925i \(0.586947\pi\)
\(228\) −67.1870 + 195.301i −0.294680 + 0.856581i
\(229\) −23.1439 40.0864i −0.101065 0.175050i 0.811059 0.584965i \(-0.198892\pi\)
−0.912124 + 0.409915i \(0.865558\pi\)
\(230\) −4.16516 + 11.4437i −0.0181094 + 0.0497551i
\(231\) −73.1022 65.8616i −0.316460 0.285115i
\(232\) 72.2423 + 60.6184i 0.311389 + 0.261286i
\(233\) 63.4844 11.1940i 0.272465 0.0480430i −0.0357460 0.999361i \(-0.511381\pi\)
0.308211 + 0.951318i \(0.400270\pi\)
\(234\) −43.0136 + 4.49460i −0.183819 + 0.0192077i
\(235\) 36.4409 63.1175i 0.155068 0.268585i
\(236\) 345.870i 1.46555i
\(237\) −175.033 109.447i −0.738537 0.461800i
\(238\) 0.138190 0.783713i 0.000580629 0.00329291i
\(239\) −343.902 198.552i −1.43892 0.830762i −0.441148 0.897435i \(-0.645428\pi\)
−0.997775 + 0.0666722i \(0.978762\pi\)
\(240\) −17.2208 122.802i −0.0717533 0.511675i
\(241\) 40.4838 229.595i 0.167982 0.952676i −0.777953 0.628322i \(-0.783742\pi\)
0.945936 0.324354i \(-0.105147\pi\)
\(242\) −45.0062 + 7.93581i −0.185976 + 0.0327926i
\(243\) 243.000 + 0.367551i 0.999999 + 0.00151256i
\(244\) 74.9625 + 27.2841i 0.307224 + 0.111820i
\(245\) −90.6412 + 15.9825i −0.369964 + 0.0652346i
\(246\) 43.6356 + 55.8858i 0.177380 + 0.227178i
\(247\) −18.0460 + 147.680i −0.0730608 + 0.597894i
\(248\) −216.207 + 124.827i −0.871802 + 0.503335i
\(249\) 193.303 + 174.156i 0.776315 + 0.699423i
\(250\) 62.4471 52.3993i 0.249788 0.209597i
\(251\) 338.352 + 59.6606i 1.34802 + 0.237692i 0.800615 0.599179i \(-0.204506\pi\)
0.547401 + 0.836870i \(0.315617\pi\)
\(252\) −156.413 11.0326i −0.620687 0.0437800i
\(253\) 35.7675 13.0183i 0.141373 0.0514557i
\(254\) −65.0371 + 37.5492i −0.256052 + 0.147831i
\(255\) −2.84955 + 0.399599i −0.0111747 + 0.00156706i
\(256\) 8.25577 46.8208i 0.0322491 0.182894i
\(257\) 217.433 + 38.3393i 0.846042 + 0.149180i 0.579833 0.814735i \(-0.303118\pi\)
0.266209 + 0.963915i \(0.414229\pi\)
\(258\) −2.96966 21.1767i −0.0115103 0.0820802i
\(259\) 111.053 + 192.349i 0.428775 + 0.742659i
\(260\) −34.5112 94.8187i −0.132735 0.364687i
\(261\) −150.346 101.542i −0.576039 0.389050i
\(262\) −9.00533 + 51.0718i −0.0343715 + 0.194930i
\(263\) 314.914 + 375.300i 1.19739 + 1.42699i 0.877525 + 0.479532i \(0.159193\pi\)
0.319866 + 0.947463i \(0.396362\pi\)
\(264\) 64.0805 71.1253i 0.242729 0.269414i
\(265\) −69.2391 119.926i −0.261280 0.452550i
\(266\) 16.3603 53.6233i 0.0615050 0.201591i
\(267\) 368.988 288.105i 1.38198 1.07905i
\(268\) −6.49543 36.8374i −0.0242367 0.137453i
\(269\) 76.0980 209.078i 0.282892 0.777240i −0.714122 0.700021i \(-0.753174\pi\)
0.997014 0.0772186i \(-0.0246039\pi\)
\(270\) −14.2035 57.1882i −0.0526055 0.211808i
\(271\) 33.3616 + 189.203i 0.123105 + 0.698166i 0.982415 + 0.186710i \(0.0597824\pi\)
−0.859310 + 0.511456i \(0.829106\pi\)
\(272\) −3.08701 0.544324i −0.0113493 0.00200119i
\(273\) −111.859 + 15.6862i −0.409739 + 0.0574586i
\(274\) 18.7445 32.4663i 0.0684104 0.118490i
\(275\) −82.9783 14.6313i −0.301739 0.0532048i
\(276\) 32.1586 51.4300i 0.116517 0.186340i
\(277\) −477.806 −1.72493 −0.862466 0.506114i \(-0.831081\pi\)
−0.862466 + 0.506114i \(0.831081\pi\)
\(278\) −46.2553 26.7055i −0.166386 0.0960629i
\(279\) 388.728 282.068i 1.39329 1.01100i
\(280\) 13.8915 + 78.7829i 0.0496127 + 0.281367i
\(281\) −184.064 + 219.359i −0.655033 + 0.780638i −0.986664 0.162771i \(-0.947957\pi\)
0.331631 + 0.943409i \(0.392401\pi\)
\(282\) 25.2539 28.0302i 0.0895527 0.0993979i
\(283\) −354.901 129.174i −1.25407 0.456444i −0.372294 0.928115i \(-0.621429\pi\)
−0.881775 + 0.471671i \(0.843651\pi\)
\(284\) −316.831 + 182.922i −1.11560 + 0.644092i
\(285\) −202.680 + 3.59384i −0.711159 + 0.0126100i
\(286\) 16.3891 28.3867i 0.0573045 0.0992542i
\(287\) 119.033 + 141.858i 0.414750 + 0.494280i
\(288\) 16.3665 232.034i 0.0568280 0.805672i
\(289\) 50.1717 284.538i 0.173604 0.984560i
\(290\) −15.0468 + 41.3408i −0.0518856 + 0.142554i
\(291\) 220.858 117.347i 0.758962 0.403253i
\(292\) 18.9234 0.0648060
\(293\) 88.1762 + 50.9085i 0.300943 + 0.173749i 0.642866 0.765978i \(-0.277745\pi\)
−0.341924 + 0.939728i \(0.611078\pi\)
\(294\) −47.6164 1.67722i −0.161961 0.00570484i
\(295\) 318.997 116.105i 1.08134 0.393577i
\(296\) −187.147 + 108.049i −0.632254 + 0.365032i
\(297\) −108.390 + 148.901i −0.364948 + 0.501350i
\(298\) 8.17345 2.97489i 0.0274277 0.00998286i
\(299\) 14.9444 41.0593i 0.0499811 0.137322i
\(300\) −118.575 + 63.0014i −0.395250 + 0.210005i
\(301\) −9.69821 55.0013i −0.0322200 0.182729i
\(302\) 51.7302 142.128i 0.171292 0.470621i
\(303\) 20.8517 + 148.694i 0.0688175 + 0.490739i
\(304\) −211.220 64.4427i −0.694802 0.211982i
\(305\) 78.2972i 0.256712i
\(306\) −1.48587 0.104805i −0.00485577 0.000342501i
\(307\) −369.747 134.577i −1.20439 0.438361i −0.339634 0.940558i \(-0.610303\pi\)
−0.864754 + 0.502197i \(0.832525\pi\)
\(308\) 76.3904 91.0385i 0.248021 0.295580i
\(309\) −131.324 27.9553i −0.424997 0.0904703i
\(310\) −89.2172 74.8621i −0.287797 0.241491i
\(311\) 251.738i 0.809445i −0.914439 0.404723i \(-0.867368\pi\)
0.914439 0.404723i \(-0.132632\pi\)
\(312\) −15.2620 108.834i −0.0489167 0.348826i
\(313\) −36.8713 + 13.4201i −0.117800 + 0.0428756i −0.400247 0.916407i \(-0.631076\pi\)
0.282448 + 0.959283i \(0.408854\pi\)
\(314\) −4.80226 + 5.72311i −0.0152938 + 0.0182265i
\(315\) −42.3311 147.964i −0.134384 0.469726i
\(316\) 124.666 215.928i 0.394513 0.683316i
\(317\) −508.842 89.7226i −1.60518 0.283037i −0.701961 0.712215i \(-0.747692\pi\)
−0.903220 + 0.429179i \(0.858803\pi\)
\(318\) −22.1315 68.1840i −0.0695960 0.214415i
\(319\) 129.212 47.0292i 0.405052 0.147427i
\(320\) 107.277 18.9158i 0.335240 0.0591119i
\(321\) 121.055 568.672i 0.377118 1.77156i
\(322\) −8.23258 + 14.2592i −0.0255670 + 0.0442834i
\(323\) −1.49536 + 4.90124i −0.00462959 + 0.0151741i
\(324\) 9.88793 + 293.329i 0.0305183 + 0.905338i
\(325\) −74.0952 + 62.1732i −0.227985 + 0.191302i
\(326\) 94.0910 + 112.133i 0.288623 + 0.343967i
\(327\) −29.2660 + 15.5496i −0.0894984 + 0.0475524i
\(328\) −138.022 + 115.814i −0.420799 + 0.353092i
\(329\) 63.3393 75.4848i 0.192521 0.229437i
\(330\) 41.4035 + 16.7427i 0.125465 + 0.0507354i
\(331\) −335.690 −1.01417 −0.507084 0.861897i \(-0.669277\pi\)
−0.507084 + 0.861897i \(0.669277\pi\)
\(332\) −201.997 + 240.731i −0.608426 + 0.725094i
\(333\) 336.480 244.156i 1.01045 0.733201i
\(334\) −39.6500 68.6758i −0.118713 0.205616i
\(335\) 31.7948 18.3567i 0.0949098 0.0547962i
\(336\) 5.90181 167.552i 0.0175649 0.498668i
\(337\) −363.419 + 304.944i −1.07839 + 0.904879i −0.995786 0.0917029i \(-0.970769\pi\)
−0.0826068 + 0.996582i \(0.526325\pi\)
\(338\) 22.6016 + 62.0974i 0.0668686 + 0.183720i
\(339\) 138.395 + 124.687i 0.408244 + 0.367808i
\(340\) −0.603492 3.42257i −0.00177498 0.0100664i
\(341\) 364.014i 1.06749i
\(342\) −103.009 20.0257i −0.301196 0.0585548i
\(343\) −360.047 −1.04970
\(344\) 53.5139 9.43594i 0.155564 0.0274301i
\(345\) 58.2293 + 12.3954i 0.168781 + 0.0359288i
\(346\) 54.8744 19.9726i 0.158596 0.0577244i
\(347\) 34.5272 + 41.1479i 0.0995021 + 0.118582i 0.813498 0.581568i \(-0.197561\pi\)
−0.713995 + 0.700150i \(0.753116\pi\)
\(348\) 116.175 185.793i 0.333835 0.533888i
\(349\) −211.623 366.542i −0.606370 1.05026i −0.991833 0.127540i \(-0.959292\pi\)
0.385464 0.922723i \(-0.374042\pi\)
\(350\) 31.5651 18.2241i 0.0901860 0.0520689i
\(351\) 50.9614 + 205.188i 0.145189 + 0.584581i
\(352\) 135.053 + 113.323i 0.383672 + 0.321939i
\(353\) 18.3167i 0.0518886i −0.999663 0.0259443i \(-0.991741\pi\)
0.999663 0.0259443i \(-0.00825925\pi\)
\(354\) 174.030 24.4046i 0.491609 0.0689395i
\(355\) −275.067 230.808i −0.774836 0.650164i
\(356\) 363.447 + 433.139i 1.02092 + 1.21668i
\(357\) −3.88796 0.136948i −0.0108907 0.000383609i
\(358\) −136.331 + 114.395i −0.380812 + 0.319539i
\(359\) 383.170 + 456.645i 1.06733 + 1.27199i 0.960669 + 0.277695i \(0.0895706\pi\)
0.106658 + 0.994296i \(0.465985\pi\)
\(360\) 143.962 41.1863i 0.399895 0.114406i
\(361\) −146.450 + 329.960i −0.405679 + 0.914016i
\(362\) −16.6733 9.62634i −0.0460589 0.0265921i
\(363\) 68.9739 + 212.499i 0.190011 + 0.585396i
\(364\) −23.6900 134.353i −0.0650824 0.369100i
\(365\) 6.35240 + 17.4531i 0.0174038 + 0.0478166i
\(366\) −8.43907 + 39.6437i −0.0230576 + 0.108316i
\(367\) 42.6297 241.765i 0.116157 0.658760i −0.870014 0.493028i \(-0.835890\pi\)
0.986171 0.165733i \(-0.0529988\pi\)
\(368\) 56.1666 + 32.4278i 0.152627 + 0.0881190i
\(369\) 240.933 249.191i 0.652934 0.675315i
\(370\) −77.2257 64.8001i −0.208718 0.175135i
\(371\) −64.0353 175.936i −0.172602 0.474220i
\(372\) 356.999 + 457.223i 0.959674 + 1.22909i
\(373\) 271.540 0.727989 0.363995 0.931401i \(-0.381413\pi\)
0.363995 + 0.931401i \(0.381413\pi\)
\(374\) 0.725680 0.864832i 0.00194032 0.00231238i
\(375\) −296.073 266.748i −0.789529 0.711327i
\(376\) 73.4435 + 61.6264i 0.195328 + 0.163900i
\(377\) 53.9872 148.328i 0.143202 0.393444i
\(378\) −5.48531 79.4801i −0.0145114 0.210265i
\(379\) 241.081 0.636097 0.318049 0.948074i \(-0.396972\pi\)
0.318049 + 0.948074i \(0.396972\pi\)
\(380\) −12.9553 244.493i −0.0340929 0.643403i
\(381\) 225.939 + 289.369i 0.593015 + 0.759497i
\(382\) −126.011 45.8641i −0.329871 0.120063i
\(383\) −165.717 + 29.2204i −0.432681 + 0.0762934i −0.385747 0.922605i \(-0.626056\pi\)
−0.0469342 + 0.998898i \(0.514945\pi\)
\(384\) 366.310 + 12.9028i 0.953933 + 0.0336010i
\(385\) 109.609 + 39.8943i 0.284698 + 0.103621i
\(386\) −8.80333 24.1870i −0.0228066 0.0626605i
\(387\) −100.505 + 28.7537i −0.259704 + 0.0742989i
\(388\) 151.034 + 261.598i 0.389262 + 0.674222i
\(389\) −138.121 379.483i −0.355066 0.975536i −0.980717 0.195433i \(-0.937389\pi\)
0.625651 0.780103i \(-0.284833\pi\)
\(390\) 45.2744 24.0552i 0.116088 0.0616801i
\(391\) 0.752469 1.30331i 0.00192447 0.00333329i
\(392\) 121.075i 0.308864i
\(393\) 253.365 + 8.92443i 0.644694 + 0.0227085i
\(394\) 188.422 + 68.5801i 0.478229 + 0.174061i
\(395\) 241.000 + 42.4948i 0.610127 + 0.107582i
\(396\) −184.340 124.501i −0.465505 0.314397i
\(397\) 69.1587 58.0311i 0.174203 0.146174i −0.551517 0.834163i \(-0.685951\pi\)
0.725721 + 0.687989i \(0.241506\pi\)
\(398\) −83.6143 48.2747i −0.210086 0.121293i
\(399\) −270.710 42.7996i −0.678472 0.107267i
\(400\) −71.7840 124.334i −0.179460 0.310834i
\(401\) −76.3540 + 209.781i −0.190409 + 0.523145i −0.997758 0.0669302i \(-0.978680\pi\)
0.807349 + 0.590075i \(0.200902\pi\)
\(402\) 18.0770 5.86752i 0.0449676 0.0145958i
\(403\) 320.107 + 268.601i 0.794309 + 0.666504i
\(404\) −178.595 + 31.4912i −0.442067 + 0.0779484i
\(405\) −267.219 + 107.588i −0.659800 + 0.265648i
\(406\) −29.7406 + 51.5122i −0.0732526 + 0.126877i
\(407\) 315.087i 0.774170i
\(408\) 0.133245 3.78282i 0.000326580 0.00927162i
\(409\) 85.2158 483.283i 0.208352 1.18162i −0.683726 0.729739i \(-0.739642\pi\)
0.892078 0.451882i \(-0.149247\pi\)
\(410\) −72.7915 42.0262i −0.177540 0.102503i
\(411\) −169.903 68.7051i −0.413390 0.167166i
\(412\) 28.1601 159.704i 0.0683497 0.387631i
\(413\) 452.000 79.6997i 1.09443 0.192978i
\(414\) 28.1469 + 12.5522i 0.0679876 + 0.0303194i
\(415\) −289.836 105.492i −0.698399 0.254196i
\(416\) 199.308 35.1433i 0.479105 0.0844791i
\(417\) −97.8852 + 242.063i −0.234737 + 0.580488i
\(418\) 58.1360 54.2756i 0.139081 0.129846i
\(419\) −464.423 + 268.135i −1.10841 + 0.639939i −0.938416 0.345506i \(-0.887707\pi\)
−0.169991 + 0.985446i \(0.554374\pi\)
\(420\) 176.800 57.3868i 0.420953 0.136635i
\(421\) 79.2254 66.4780i 0.188184 0.157905i −0.543828 0.839196i \(-0.683026\pi\)
0.732012 + 0.681291i \(0.238581\pi\)
\(422\) −162.745 28.6964i −0.385653 0.0680010i
\(423\) −152.846 103.230i −0.361338 0.244044i
\(424\) 171.178 62.3036i 0.403721 0.146942i
\(425\) −2.88509 + 1.66571i −0.00678845 + 0.00391932i
\(426\) −114.396 146.511i −0.268535 0.343923i
\(427\) −18.3824 + 104.252i −0.0430502 + 0.244150i
\(428\) 691.565 + 121.942i 1.61581 + 0.284910i
\(429\) −148.554 60.0718i −0.346279 0.140028i
\(430\) 12.6748 + 21.9534i 0.0294762 + 0.0510543i
\(431\) 219.850 + 604.032i 0.510092 + 1.40147i 0.881141 + 0.472853i \(0.156776\pi\)
−0.371049 + 0.928613i \(0.621002\pi\)
\(432\) −313.069 + 21.6064i −0.724696 + 0.0500148i
\(433\) −71.8595 + 407.535i −0.165957 + 0.941190i 0.782115 + 0.623134i \(0.214141\pi\)
−0.948072 + 0.318056i \(0.896970\pi\)
\(434\) −101.216 120.624i −0.233216 0.277936i
\(435\) 210.356 + 44.7791i 0.483577 + 0.102940i
\(436\) −20.0136 34.6645i −0.0459027 0.0795057i
\(437\) 63.7562 84.7093i 0.145895 0.193843i
\(438\) 1.33523 + 9.52158i 0.00304848 + 0.0217388i
\(439\) 58.9456 + 334.297i 0.134272 + 0.761497i 0.975364 + 0.220603i \(0.0708026\pi\)
−0.841091 + 0.540893i \(0.818086\pi\)
\(440\) −38.8154 + 106.644i −0.0882168 + 0.242374i
\(441\) 24.2069 + 231.661i 0.0548909 + 0.525309i
\(442\) −0.225046 1.27630i −0.000509153 0.00288755i
\(443\) −444.822 78.4341i −1.00411 0.177052i −0.352668 0.935749i \(-0.614725\pi\)
−0.651444 + 0.758696i \(0.725837\pi\)
\(444\) 309.015 + 395.768i 0.695980 + 0.891370i
\(445\) −277.479 + 480.608i −0.623549 + 1.08002i
\(446\) 115.394 + 20.3471i 0.258732 + 0.0456213i
\(447\) −19.9511 37.5500i −0.0446334 0.0840045i
\(448\) 147.279 0.328748
\(449\) 16.0848 + 9.28656i 0.0358236 + 0.0206828i 0.517805 0.855499i \(-0.326749\pi\)
−0.481981 + 0.876182i \(0.660083\pi\)
\(450\) −40.0668 55.2174i −0.0890373 0.122705i
\(451\) 45.6187 + 258.717i 0.101150 + 0.573651i
\(452\) −144.620 + 172.351i −0.319955 + 0.381308i
\(453\) −723.194 153.948i −1.59645 0.339842i
\(454\) −64.8847 23.6161i −0.142918 0.0520179i
\(455\) 115.961 66.9502i 0.254860 0.147143i
\(456\) 41.6422 263.389i 0.0913205 0.577608i
\(457\) 299.513 518.772i 0.655390 1.13517i −0.326406 0.945230i \(-0.605838\pi\)
0.981796 0.189939i \(-0.0608290\pi\)
\(458\) 18.2587 + 21.7598i 0.0398661 + 0.0475105i
\(459\) 0.501365 + 7.26459i 0.00109230 + 0.0158270i
\(460\) −12.4862 + 70.8130i −0.0271440 + 0.153941i
\(461\) 60.5478 166.354i 0.131340 0.360854i −0.856538 0.516083i \(-0.827389\pi\)
0.987878 + 0.155229i \(0.0496117\pi\)
\(462\) 51.1975 + 32.0133i 0.110817 + 0.0692929i
\(463\) 163.476 0.353080 0.176540 0.984293i \(-0.443509\pi\)
0.176540 + 0.984293i \(0.443509\pi\)
\(464\) 202.904 + 117.147i 0.437294 + 0.252472i
\(465\) −301.856 + 482.746i −0.649154 + 1.03816i
\(466\) −37.1738 + 13.5302i −0.0797721 + 0.0290347i
\(467\) −610.974 + 352.746i −1.30830 + 0.755345i −0.981812 0.189857i \(-0.939197\pi\)
−0.326485 + 0.945203i \(0.605864\pi\)
\(468\) −245.506 + 70.2371i −0.524586 + 0.150079i
\(469\) 46.6442 16.9771i 0.0994545 0.0361985i
\(470\) −15.2970 + 42.0282i −0.0325468 + 0.0894216i
\(471\) 30.9672 + 19.3635i 0.0657478 + 0.0411114i
\(472\) 77.5444 + 439.776i 0.164289 + 0.931729i
\(473\) 27.0985 74.4525i 0.0572907 0.157405i
\(474\) 117.444 + 47.4918i 0.247772 + 0.100194i
\(475\) −215.985 + 91.8276i −0.454704 + 0.193321i
\(476\) 4.69881i 0.00987144i
\(477\) −315.070 + 153.434i −0.660525 + 0.321665i
\(478\) 228.995 + 83.3474i 0.479069 + 0.174367i
\(479\) −58.6872 + 69.9406i −0.122520 + 0.146014i −0.823818 0.566855i \(-0.808160\pi\)
0.701297 + 0.712869i \(0.252604\pi\)
\(480\) 85.1314 + 262.278i 0.177357 + 0.546412i
\(481\) 277.082 + 232.499i 0.576053 + 0.483366i
\(482\) 143.069i 0.296824i
\(483\) 74.6216 + 30.1753i 0.154496 + 0.0624748i
\(484\) −253.565 + 92.2900i −0.523894 + 0.190682i
\(485\) −190.572 + 227.115i −0.392932 + 0.468278i
\(486\) −146.895 + 25.6726i −0.302254 + 0.0528243i
\(487\) 201.846 349.608i 0.414468 0.717880i −0.580904 0.813972i \(-0.697301\pi\)
0.995372 + 0.0960919i \(0.0306343\pi\)
\(488\) −101.433 17.8853i −0.207854 0.0366502i
\(489\) 478.986 531.645i 0.979522 1.08721i
\(490\) 53.0756 19.3180i 0.108318 0.0394244i
\(491\) 706.733 124.616i 1.43937 0.253800i 0.601154 0.799133i \(-0.294708\pi\)
0.838220 + 0.545333i \(0.183597\pi\)
\(492\) 311.031 + 280.224i 0.632177 + 0.569561i
\(493\) 2.71833 4.70828i 0.00551385 0.00955027i
\(494\) −4.83111 91.1730i −0.00977956 0.184561i
\(495\) 52.9466 211.811i 0.106963 0.427901i
\(496\) −475.134 + 398.685i −0.957932 + 0.803800i
\(497\) −312.060 371.898i −0.627887 0.748287i
\(498\) −135.381 84.6521i −0.271848 0.169984i
\(499\) 681.027 571.449i 1.36478 1.14519i 0.390310 0.920683i \(-0.372368\pi\)
0.974473 0.224506i \(-0.0720767\pi\)
\(500\) 309.391 368.718i 0.618782 0.737435i
\(501\) −305.558 + 238.579i −0.609897 + 0.476206i
\(502\) −210.840 −0.420000
\(503\) −74.3723 + 88.6334i −0.147857 + 0.176210i −0.834890 0.550417i \(-0.814469\pi\)
0.687032 + 0.726627i \(0.258913\pi\)
\(504\) 201.354 21.0400i 0.399512 0.0417460i
\(505\) −88.9971 154.148i −0.176232 0.305243i
\(506\) −20.2287 + 11.6791i −0.0399777 + 0.0230811i
\(507\) 285.284 151.578i 0.562691 0.298970i
\(508\) −339.677 + 285.023i −0.668656 + 0.561069i
\(509\) −347.599 955.022i −0.682907 1.87627i −0.395533 0.918452i \(-0.629440\pi\)
−0.287373 0.957819i \(-0.592782\pi\)
\(510\) 1.67954 0.545153i 0.00329321 0.00106893i
\(511\) 4.36056 + 24.7300i 0.00853339 + 0.0483952i
\(512\) 517.892i 1.01151i
\(513\) −27.0167 + 512.288i −0.0526641 + 0.998612i
\(514\) −135.491 −0.263600
\(515\) 156.748 27.6390i 0.304366 0.0536679i
\(516\) −38.9804 120.093i −0.0755435 0.232738i
\(517\) 131.360 47.8112i 0.254081 0.0924781i
\(518\) −87.6116 104.411i −0.169134 0.201567i
\(519\) −133.947 252.101i −0.258086 0.485744i
\(520\) 65.1397 + 112.825i 0.125269 + 0.216972i
\(521\) 355.759 205.398i 0.682839 0.394237i −0.118085 0.993003i \(-0.537676\pi\)
0.800924 + 0.598766i \(0.204342\pi\)
\(522\) 101.682 + 45.3454i 0.194793 + 0.0868687i
\(523\) −541.536 454.403i −1.03544 0.868839i −0.0439539 0.999034i \(-0.513995\pi\)
−0.991489 + 0.130194i \(0.958440\pi\)
\(524\) 306.204i 0.584359i
\(525\) −109.657 140.442i −0.208870 0.267509i
\(526\) −230.310 193.253i −0.437852 0.367402i
\(527\) 9.25127 + 11.0252i 0.0175546 + 0.0209207i
\(528\) 126.099 201.665i 0.238824 0.381941i
\(529\) 381.385 320.020i 0.720955 0.604953i
\(530\) 54.6241 + 65.0985i 0.103064 + 0.122827i
\(531\) −236.297 825.952i −0.445004 1.55547i
\(532\) 40.1517 328.582i 0.0754731 0.617635i
\(533\) 261.172 + 150.788i 0.490004 + 0.282904i
\(534\) −192.296 + 213.436i −0.360104 + 0.399693i
\(535\) 119.685 + 678.766i 0.223710 + 1.26872i
\(536\) 16.5180 + 45.3827i 0.0308171 + 0.0846693i
\(537\) 646.369 + 582.348i 1.20367 + 1.08445i
\(538\) −23.7098 + 134.465i −0.0440702 + 0.249934i
\(539\) −152.884 88.2678i −0.283644 0.163762i
\(540\) −141.225 317.974i −0.261528 0.588840i
\(541\) 204.410 + 171.520i 0.377837 + 0.317043i 0.811853 0.583862i \(-0.198459\pi\)
−0.434015 + 0.900906i \(0.642904\pi\)
\(542\) −40.3240 110.789i −0.0743985 0.204408i
\(543\) −35.2840 + 87.2549i −0.0649797 + 0.160690i
\(544\) 6.97052 0.0128135
\(545\) 25.2528 30.0951i 0.0463354 0.0552204i
\(546\) 65.9300 21.3999i 0.120751 0.0391939i
\(547\) 209.405 + 175.712i 0.382825 + 0.321228i 0.813810 0.581131i \(-0.197390\pi\)
−0.430985 + 0.902359i \(0.641834\pi\)
\(548\) 75.7070 208.003i 0.138152 0.379568i
\(549\) 197.654 + 13.9415i 0.360026 + 0.0253944i
\(550\) 51.7069 0.0940125
\(551\) 230.322 306.016i 0.418007 0.555383i
\(552\) −29.3593 + 72.6036i −0.0531871 + 0.131528i
\(553\) 310.912 + 113.163i 0.562229 + 0.204634i
\(554\) 288.761 50.9164i 0.521230 0.0919068i
\(555\) −261.285 + 417.861i −0.470783 + 0.752903i
\(556\) −296.346 107.861i −0.532996 0.193995i
\(557\) −368.532 1012.53i −0.661637 1.81783i −0.569343 0.822100i \(-0.692802\pi\)
−0.0922934 0.995732i \(-0.529420\pi\)
\(558\) −204.869 + 211.891i −0.367148 + 0.379733i
\(559\) −45.4764 78.7675i −0.0813532 0.140908i
\(560\) 67.9760 + 186.762i 0.121386 + 0.333504i
\(561\) −4.67953 2.92606i −0.00834140 0.00521580i
\(562\) 87.8633 152.184i 0.156340 0.270789i
\(563\) 825.244i 1.46580i −0.680338 0.732898i \(-0.738167\pi\)
0.680338 0.732898i \(-0.261833\pi\)
\(564\) 118.106 188.882i 0.209408 0.334898i
\(565\) −207.507 75.5265i −0.367270 0.133675i
\(566\) 228.249 + 40.2465i 0.403267 + 0.0711068i
\(567\) −381.059 + 80.5147i −0.672061 + 0.142001i
\(568\) 361.841 303.621i 0.637044 0.534543i
\(569\) −289.332 167.046i −0.508492 0.293578i 0.223722 0.974653i \(-0.428179\pi\)
−0.732214 + 0.681075i \(0.761513\pi\)
\(570\) 122.106 23.7701i 0.214222 0.0417019i
\(571\) −427.909 741.161i −0.749404 1.29801i −0.948109 0.317946i \(-0.897007\pi\)
0.198705 0.980059i \(-0.436326\pi\)
\(572\) 66.1939 181.866i 0.115724 0.317948i
\(573\) −136.491 + 641.185i −0.238204 + 1.11900i
\(574\) −87.0544 73.0473i −0.151663 0.127260i
\(575\) 67.8798 11.9690i 0.118052 0.0208157i
\(576\) −28.6497 274.179i −0.0497390 0.476005i
\(577\) 516.198 894.081i 0.894624 1.54953i 0.0603548 0.998177i \(-0.480777\pi\)
0.834269 0.551357i \(-0.185890\pi\)
\(578\) 177.306i 0.306758i
\(579\) −111.118 + 59.0396i −0.191914 + 0.101968i
\(580\) −45.1071 + 255.815i −0.0777709 + 0.441061i
\(581\) −361.146 208.508i −0.621594 0.358877i
\(582\) −120.970 + 94.4534i −0.207853 + 0.162291i
\(583\) 46.1222 261.572i 0.0791118 0.448666i
\(584\) −24.0612 + 4.24264i −0.0412007 + 0.00726479i
\(585\) −147.194 202.853i −0.251614 0.346758i
\(586\) −58.7140 21.3702i −0.100195 0.0364678i
\(587\) −822.487 + 145.027i −1.40117 + 0.247064i −0.822624 0.568586i \(-0.807491\pi\)
−0.578546 + 0.815650i \(0.696380\pi\)
\(588\) −278.599 + 39.0685i −0.473807 + 0.0664431i
\(589\) 552.718 + 850.034i 0.938401 + 1.44318i
\(590\) −180.412 + 104.161i −0.305784 + 0.176544i
\(591\) 204.093 958.758i 0.345336 1.62226i
\(592\) −411.272 + 345.098i −0.694717 + 0.582937i
\(593\) −388.661 68.5314i −0.655415 0.115567i −0.163955 0.986468i \(-0.552425\pi\)
−0.491460 + 0.870900i \(0.663536\pi\)
\(594\) 49.6377 101.538i 0.0835651 0.170940i
\(595\) 4.33372 1.57735i 0.00728356 0.00265100i
\(596\) 44.4766 25.6786i 0.0746252 0.0430849i
\(597\) −176.944 + 437.571i −0.296389 + 0.732950i
\(598\) −4.65619 + 26.4066i −0.00778628 + 0.0441582i
\(599\) −47.6383 8.39991i −0.0795297 0.0140232i 0.133742 0.991016i \(-0.457301\pi\)
−0.213271 + 0.976993i \(0.568412\pi\)
\(600\) 136.644 106.691i 0.227740 0.177819i
\(601\) 274.153 + 474.848i 0.456162 + 0.790096i 0.998754 0.0499002i \(-0.0158903\pi\)
−0.542592 + 0.839996i \(0.682557\pi\)
\(602\) 11.7222 + 32.2064i 0.0194721 + 0.0534991i
\(603\) −40.6786 83.5317i −0.0674603 0.138527i
\(604\) 155.076 879.480i 0.256748 1.45609i
\(605\) −170.239 202.882i −0.281386 0.335343i
\(606\) −28.4469 87.6409i −0.0469421 0.144622i
\(607\) −547.307 947.964i −0.901659 1.56172i −0.825340 0.564636i \(-0.809016\pi\)
−0.0763194 0.997083i \(-0.524317\pi\)
\(608\) 487.440 + 59.5637i 0.801711 + 0.0979666i
\(609\) 269.574 + 109.010i 0.442650 + 0.178998i
\(610\) −8.34357 47.3187i −0.0136780 0.0775717i
\(611\) 54.8848 150.795i 0.0898279 0.246800i
\(612\) −8.74744 + 0.914042i −0.0142932 + 0.00149353i
\(613\) −77.8364 441.432i −0.126976 0.720118i −0.980114 0.198433i \(-0.936415\pi\)
0.853138 0.521685i \(-0.174696\pi\)
\(614\) 237.797 + 41.9300i 0.387291 + 0.0682898i
\(615\) −154.041 + 380.933i −0.250473 + 0.619404i
\(616\) −76.7200 + 132.883i −0.124545 + 0.215719i
\(617\) 196.579 + 34.6622i 0.318605 + 0.0561786i 0.330664 0.943749i \(-0.392727\pi\)
−0.0120589 + 0.999927i \(0.503839\pi\)
\(618\) 82.3444 + 2.90047i 0.133243 + 0.00469332i
\(619\) 702.294 1.13456 0.567281 0.823524i \(-0.307995\pi\)
0.567281 + 0.823524i \(0.307995\pi\)
\(620\) −595.535 343.832i −0.960540 0.554568i
\(621\) 41.6594 144.788i 0.0670844 0.233152i
\(622\) 26.8259 + 152.137i 0.0431284 + 0.244593i
\(623\) −482.297 + 574.779i −0.774152 + 0.922599i
\(624\) −84.2933 259.695i −0.135085 0.416178i
\(625\) 153.743 + 55.9580i 0.245989 + 0.0895328i
\(626\) 20.8530 12.0395i 0.0333115 0.0192324i
\(627\) −302.230 244.603i −0.482026 0.390116i
\(628\) −22.0562 + 38.2024i −0.0351213 + 0.0608318i
\(629\) 8.00782 + 9.54335i 0.0127310 + 0.0151723i
\(630\) 41.3501 + 84.9106i 0.0656351 + 0.134779i
\(631\) −96.9993 + 550.110i −0.153723 + 0.871807i 0.806221 + 0.591615i \(0.201509\pi\)
−0.959944 + 0.280192i \(0.909602\pi\)
\(632\) −110.103 + 302.504i −0.174213 + 0.478646i
\(633\) −28.4386 + 807.373i −0.0449267 + 1.27547i
\(634\) 317.079 0.500124
\(635\) −376.904 217.606i −0.593549 0.342686i
\(636\) −198.599 373.783i −0.312263 0.587710i
\(637\) −190.433 + 69.3118i −0.298952 + 0.108810i
\(638\) −73.0772 + 42.1911i −0.114541 + 0.0661303i
\(639\) −631.633 + 653.284i −0.988471 + 1.02235i
\(640\) −408.308 + 148.612i −0.637981 + 0.232206i
\(641\) 66.6408 183.094i 0.103964 0.285638i −0.876794 0.480866i \(-0.840322\pi\)
0.980758 + 0.195228i \(0.0625446\pi\)
\(642\) −12.5599 + 356.576i −0.0195637 + 0.555414i
\(643\) 159.049 + 902.012i 0.247355 + 1.40282i 0.814960 + 0.579517i \(0.196759\pi\)
−0.567605 + 0.823301i \(0.692130\pi\)
\(644\) −33.2506 + 91.3553i −0.0516314 + 0.141856i
\(645\) 97.6767 76.2659i 0.151437 0.118242i
\(646\) 0.381426 3.12140i 0.000590442 0.00483189i
\(647\) 96.3179i 0.148868i −0.997226 0.0744342i \(-0.976285\pi\)
0.997226 0.0744342i \(-0.0237151\pi\)
\(648\) −78.3373 370.754i −0.120891 0.572151i
\(649\) 611.849 + 222.695i 0.942757 + 0.343135i
\(650\) 38.1539 45.4700i 0.0586983 0.0699539i
\(651\) −515.257 + 571.903i −0.791485 + 0.878498i
\(652\) 662.089 + 555.559i 1.01547 + 0.852084i
\(653\) 1225.06i 1.87605i −0.346561 0.938027i \(-0.612651\pi\)
0.346561 0.938027i \(-0.387349\pi\)
\(654\) 16.0298 12.5161i 0.0245104 0.0191377i
\(655\) −282.413 + 102.790i −0.431165 + 0.156931i
\(656\) −287.730 + 342.903i −0.438613 + 0.522719i
\(657\) 45.1898 12.9284i 0.0687820 0.0196779i
\(658\) −30.2351 + 52.3687i −0.0459500 + 0.0795877i
\(659\) 916.166 + 161.545i 1.39024 + 0.245136i 0.818126 0.575039i \(-0.195013\pi\)
0.572112 + 0.820176i \(0.306124\pi\)
\(660\) 257.919 + 54.9039i 0.390786 + 0.0831877i
\(661\) −186.494 + 67.8784i −0.282140 + 0.102690i −0.479214 0.877698i \(-0.659078\pi\)
0.197074 + 0.980389i \(0.436856\pi\)
\(662\) 202.873 35.7720i 0.306455 0.0540363i
\(663\) −6.02609 + 1.95598i −0.00908912 + 0.00295020i
\(664\) 202.869 351.379i 0.305526 0.529186i
\(665\) 316.530 73.2698i 0.475985 0.110180i
\(666\) −177.333 + 183.411i −0.266265 + 0.275392i
\(667\) −86.1680 + 72.3035i −0.129187 + 0.108401i
\(668\) −300.970 358.682i −0.450553 0.536949i
\(669\) 20.1643 572.466i 0.0301410 0.855703i
\(670\) −17.2590 + 14.4820i −0.0257596 + 0.0216149i
\(671\) −96.5321 + 115.042i −0.143863 + 0.171449i
\(672\) 51.7747 + 369.207i 0.0770458 + 0.549415i
\(673\) 141.055 0.209592 0.104796 0.994494i \(-0.466581\pi\)
0.104796 + 0.994494i \(0.466581\pi\)
\(674\) 187.135 223.019i 0.277649 0.330889i
\(675\) −240.120 + 231.460i −0.355733 + 0.342904i
\(676\) 195.092 + 337.909i 0.288598 + 0.499866i
\(677\) −649.952 + 375.250i −0.960047 + 0.554284i −0.896188 0.443675i \(-0.853674\pi\)
−0.0638597 + 0.997959i \(0.520341\pi\)
\(678\) −96.9254 60.6065i −0.142958 0.0893901i
\(679\) −307.066 + 257.659i −0.452233 + 0.379469i
\(680\) 1.53469 + 4.21652i 0.00225690 + 0.00620077i
\(681\) −70.2812 + 330.156i −0.103203 + 0.484810i
\(682\) −38.7903 219.991i −0.0568773 0.322567i
\(683\) 22.7759i 0.0333469i 0.999861 + 0.0166734i \(0.00530757\pi\)
−0.999861 + 0.0166734i \(0.994692\pi\)
\(684\) −619.508 10.8297i −0.905714 0.0158329i
\(685\) 217.256 0.317162
\(686\) 217.593 38.3676i 0.317191 0.0559294i
\(687\) 92.9489 103.167i 0.135297 0.150171i
\(688\) 126.860 46.1732i 0.184389 0.0671122i
\(689\) −195.988 233.570i −0.284453 0.338998i
\(690\) −36.5117 1.28607i −0.0529154 0.00186388i
\(691\) 579.183 + 1003.17i 0.838181 + 1.45177i 0.891414 + 0.453190i \(0.149714\pi\)
−0.0532326 + 0.998582i \(0.516952\pi\)
\(692\) 298.604 172.399i 0.431509 0.249132i
\(693\) 120.226 269.594i 0.173487 0.389024i
\(694\) −25.2513 21.1883i −0.0363851 0.0305308i
\(695\) 309.528i 0.445364i
\(696\) −106.062 + 262.284i −0.152388 + 0.376844i
\(697\) 7.95689 + 6.67662i 0.0114159 + 0.00957908i
\(698\) 166.954 + 198.968i 0.239189 + 0.285054i
\(699\) 90.7401 + 170.782i 0.129814 + 0.244323i
\(700\) 164.859 138.333i 0.235513 0.197619i
\(701\) 344.587 + 410.663i 0.491565 + 0.585825i 0.953615 0.301029i \(-0.0973302\pi\)
−0.462050 + 0.886854i \(0.652886\pi\)
\(702\) −52.6638 118.574i −0.0750197 0.168909i
\(703\) 478.428 + 735.782i 0.680553 + 1.04663i
\(704\) 180.944 + 104.468i 0.257022 + 0.148392i
\(705\) 213.854 + 45.5237i 0.303339 + 0.0645726i
\(706\) 1.95188 + 11.0696i 0.00276470 + 0.0156794i
\(707\) −82.3083 226.140i −0.116419 0.319859i
\(708\) 986.923 320.341i 1.39396 0.452458i
\(709\) −182.309 + 1033.92i −0.257135 + 1.45828i 0.533397 + 0.845865i \(0.320915\pi\)
−0.790532 + 0.612420i \(0.790196\pi\)
\(710\) 190.832 + 110.177i 0.268777 + 0.155178i
\(711\) 150.187 600.817i 0.211233 0.845031i
\(712\) −559.235 469.254i −0.785443 0.659065i
\(713\) −101.846 279.821i −0.142842 0.392455i
\(714\) 2.36428 0.331548i 0.00331131 0.000464353i
\(715\) 189.956 0.265673
\(716\) −675.444 + 804.962i −0.943357 + 1.12425i
\(717\) 248.040 1165.21i 0.345942 1.62511i
\(718\) −280.230 235.141i −0.390292 0.327494i
\(719\) 321.394 883.024i 0.447002 1.22813i −0.487799 0.872956i \(-0.662200\pi\)
0.934801 0.355172i \(-0.115578\pi\)
\(720\) 334.459 162.876i 0.464527 0.226217i
\(721\) 215.198 0.298471
\(722\) 53.3453 215.017i 0.0738854 0.297807i
\(723\) 692.633 97.1296i 0.957999 0.134342i
\(724\) −106.822 38.8799i −0.147544 0.0537015i
\(725\) 245.219 43.2387i 0.338233 0.0596396i
\(726\) −64.3287 121.073i −0.0886070 0.166767i
\(727\) 37.7379 + 13.7355i 0.0519091 + 0.0188934i 0.367844 0.929887i \(-0.380096\pi\)
−0.315935 + 0.948781i \(0.602318\pi\)
\(728\) 60.2439 + 165.519i 0.0827527 + 0.227361i
\(729\) 224.015 + 693.728i 0.307290 + 0.951616i
\(730\) −5.69890 9.87079i −0.00780672 0.0135216i
\(731\) −1.07142 2.94371i −0.00146570 0.00402697i
\(732\) −8.42452 + 239.172i −0.0115089 + 0.326738i
\(733\) 629.336 1090.04i 0.858575 1.48710i −0.0147132 0.999892i \(-0.504684\pi\)
0.873288 0.487204i \(-0.161983\pi\)
\(734\) 150.653i 0.205249i
\(735\) −129.556 243.837i −0.176267 0.331751i
\(736\) −135.522 49.3261i −0.184134 0.0670192i
\(737\) 69.3481 + 12.2279i 0.0940952 + 0.0165915i
\(738\) −119.053 + 176.273i −0.161318 + 0.238852i
\(739\) −750.001 + 629.326i −1.01489 + 0.851591i −0.988976 0.148073i \(-0.952693\pi\)
−0.0259101 + 0.999664i \(0.508248\pi\)
\(740\) −515.490 297.618i −0.696608 0.402187i
\(741\) −438.111 + 85.2858i −0.591243 + 0.115096i
\(742\) 57.4478 + 99.5025i 0.0774229 + 0.134100i
\(743\) 89.9242 247.065i 0.121029 0.332523i −0.864353 0.502886i \(-0.832272\pi\)
0.985381 + 0.170362i \(0.0544939\pi\)
\(744\) −556.436 501.322i −0.747898 0.673820i
\(745\) 38.6138 + 32.4008i 0.0518306 + 0.0434911i
\(746\) −164.105 + 28.9361i −0.219979 + 0.0387883i
\(747\) −317.912 + 712.880i −0.425585 + 0.954325i
\(748\) 3.33296 5.77285i 0.00445582 0.00771771i
\(749\) 931.870i 1.24415i
\(750\) 207.357 + 129.658i 0.276475 + 0.172877i
\(751\) −0.109340 + 0.620096i −0.000145592 + 0.000825693i −0.984880 0.173235i \(-0.944578\pi\)
0.984735 + 0.174061i \(0.0556890\pi\)
\(752\) 206.278 + 119.095i 0.274306 + 0.158371i
\(753\) 143.139 + 1020.73i 0.190092 + 1.35555i
\(754\) −16.8207 + 95.3950i −0.0223086 + 0.126519i
\(755\) 863.204 152.206i 1.14332 0.201598i
\(756\) −113.387 456.535i −0.149983 0.603883i
\(757\) 1088.75 + 396.274i 1.43825 + 0.523479i 0.939283 0.343143i \(-0.111492\pi\)
0.498964 + 0.866623i \(0.333714\pi\)
\(758\) −145.697 + 25.6902i −0.192212 + 0.0338921i
\(759\) 70.2744 + 90.0033i 0.0925882 + 0.118581i
\(760\) 71.2884 + 307.970i 0.0938005 + 0.405224i
\(761\) −1177.78 + 679.992i −1.54767 + 0.893550i −0.549356 + 0.835588i \(0.685127\pi\)
−0.998319 + 0.0579619i \(0.981540\pi\)
\(762\) −167.381 150.803i −0.219661 0.197904i
\(763\) 40.6895 34.1425i 0.0533283 0.0447477i
\(764\) −779.749 137.491i −1.02061 0.179962i
\(765\) −3.77946 7.76095i −0.00494047 0.0101450i
\(766\) 97.0368 35.3185i 0.126680 0.0461077i
\(767\) 647.310 373.725i 0.843950 0.487255i
\(768\) 141.247 19.8074i 0.183916 0.0257909i
\(769\) 55.1997 313.053i 0.0717811 0.407091i −0.927653 0.373444i \(-0.878177\pi\)
0.999434 0.0336468i \(-0.0107121\pi\)
\(770\) −70.4930 12.4298i −0.0915493 0.0161426i
\(771\) 91.9845 + 655.943i 0.119305 + 0.850769i
\(772\) −75.9884 131.616i −0.0984306 0.170487i
\(773\) 407.855 + 1120.57i 0.527626 + 1.44964i 0.861859 + 0.507149i \(0.169301\pi\)
−0.334233 + 0.942490i \(0.608477\pi\)
\(774\) 57.6762 28.0874i 0.0745170 0.0362886i
\(775\) −114.466 + 649.166i −0.147697 + 0.837634i
\(776\) −250.691 298.762i −0.323056 0.385003i
\(777\) −446.002 + 495.034i −0.574005 + 0.637110i
\(778\) 123.912 + 214.621i 0.159270 + 0.275863i
\(779\) 499.363 + 534.880i 0.641031 + 0.686624i
\(780\) 238.597 186.296i 0.305893 0.238841i
\(781\) −119.595 678.256i −0.153130 0.868446i
\(782\) −0.315868 + 0.867840i −0.000403923 + 0.00110977i
\(783\) 150.497 523.052i 0.192205 0.668010i
\(784\) −52.2333 296.230i −0.0666241 0.377844i
\(785\) −42.6382 7.51826i −0.0543162 0.00957740i
\(786\) −154.071 + 21.6058i −0.196020 + 0.0274883i
\(787\) 249.132 431.510i 0.316559 0.548297i −0.663208 0.748435i \(-0.730806\pi\)
0.979768 + 0.200138i \(0.0641390\pi\)
\(788\) 1165.95 + 205.588i 1.47963 + 0.260899i
\(789\) −779.229 + 1246.19i −0.987616 + 1.57945i
\(790\) −150.176 −0.190097
\(791\) −258.562 149.281i −0.326880 0.188724i
\(792\) 262.303 + 116.975i 0.331191 + 0.147696i
\(793\) 29.9363 + 169.777i 0.0377506 + 0.214095i
\(794\) −35.6120 + 42.4407i −0.0448513 + 0.0534517i
\(795\) 278.073 308.644i 0.349778 0.388232i
\(796\) −535.695 194.977i −0.672983 0.244946i
\(797\) 300.237 173.342i 0.376709 0.217493i −0.299676 0.954041i \(-0.596879\pi\)
0.676385 + 0.736548i \(0.263545\pi\)
\(798\) 168.164 2.98181i 0.210732 0.00373661i
\(799\) 2.76353 4.78657i 0.00345873 0.00599070i
\(800\) 205.212 + 244.563i 0.256515 + 0.305703i
\(801\) 1163.85 + 786.049i 1.45299 + 0.981334i
\(802\) 23.7895 134.917i 0.0296628 0.168226i
\(803\) −12.1842 + 33.4757i −0.0151733 + 0.0416883i
\(804\) 99.0977 52.6527i 0.123256 0.0654885i
\(805\) −95.4191 −0.118533
\(806\) −222.079 128.217i −0.275532 0.159078i
\(807\) 667.073 + 23.4968i 0.826609 + 0.0291162i
\(808\) 220.025 80.0825i 0.272308 0.0991119i
\(809\) 174.494 100.744i 0.215691 0.124529i −0.388262 0.921549i \(-0.626925\pi\)
0.603953 + 0.797020i \(0.293591\pi\)
\(810\) 150.028 93.4959i 0.185220 0.115427i
\(811\) −1272.87 + 463.288i −1.56951 + 0.571255i −0.972890 0.231269i \(-0.925712\pi\)
−0.596620 + 0.802524i \(0.703490\pi\)
\(812\) −120.119 + 330.025i −0.147930 + 0.406435i
\(813\) −508.982 + 270.433i −0.626054 + 0.332636i
\(814\) −33.5766 190.422i −0.0412489 0.233934i
\(815\) −290.136 + 797.142i −0.355995 + 0.978088i
\(816\) −1.30595 9.31278i −0.00160043 0.0114127i
\(817\) −49.7691 215.006i −0.0609169 0.263165i
\(818\) 301.152i 0.368156i
\(819\) −148.362 304.655i −0.181150 0.371984i
\(820\) −466.356 169.740i −0.568727 0.207000i
\(821\) 432.802 515.794i 0.527165 0.628251i −0.435094 0.900385i \(-0.643285\pi\)
0.962259 + 0.272134i \(0.0877295\pi\)
\(822\) 110.002 + 23.4164i 0.133822 + 0.0284871i
\(823\) −233.729 196.122i −0.283997 0.238302i 0.489649 0.871919i \(-0.337125\pi\)
−0.773646 + 0.633618i \(0.781569\pi\)
\(824\) 209.378i 0.254100i
\(825\) −35.1038 250.326i −0.0425500 0.303425i
\(826\) −264.672 + 96.3327i −0.320426 + 0.116626i
\(827\) −878.002 + 1046.36i −1.06167 + 1.26525i −0.0988524 + 0.995102i \(0.531517\pi\)
−0.962819 + 0.270148i \(0.912927\pi\)
\(828\) 176.538 + 44.1293i 0.213210 + 0.0532962i
\(829\) 167.153 289.517i 0.201632 0.349237i −0.747422 0.664349i \(-0.768709\pi\)
0.949054 + 0.315112i \(0.102042\pi\)
\(830\) 186.403 + 32.8679i 0.224582 + 0.0395998i
\(831\) −442.538 1363.40i −0.532537 1.64067i
\(832\) 225.383 82.0328i 0.270893 0.0985972i
\(833\) −6.87385 + 1.21205i −0.00825192 + 0.00145504i
\(834\) 33.3617 156.721i 0.0400021 0.187915i
\(835\) 229.780 397.991i 0.275186 0.476636i
\(836\) 282.399 375.208i 0.337798 0.448813i
\(837\) 1164.90 + 847.967i 1.39176 + 1.01310i
\(838\) 252.100 211.537i 0.300835 0.252430i
\(839\) 614.843 + 732.741i 0.732828 + 0.873350i 0.995810 0.0914505i \(-0.0291503\pi\)
−0.262982 + 0.964801i \(0.584706\pi\)
\(840\) −211.937 + 112.607i −0.252306 + 0.134055i
\(841\) 332.958 279.385i 0.395907 0.332205i
\(842\) −40.7956 + 48.6183i −0.0484509 + 0.0577415i
\(843\) −796.409 322.050i −0.944731 0.382029i
\(844\) −975.752 −1.15610
\(845\) −246.164 + 293.367i −0.291318 + 0.347180i
\(846\) 103.373 + 46.0994i 0.122190 + 0.0544910i
\(847\) −179.039 310.104i −0.211380 0.366121i
\(848\) 391.936 226.284i 0.462189 0.266845i
\(849\) 39.8849 1132.33i 0.0469787 1.33372i
\(850\) 1.56610 1.31411i 0.00184247 0.00154601i
\(851\) −88.1574 242.210i −0.103593 0.284619i
\(852\) −815.404 734.640i −0.957047 0.862254i
\(853\) −98.9977 561.444i −0.116058 0.658199i −0.986221 0.165434i \(-0.947097\pi\)
0.870163 0.492765i \(-0.164014\pi\)
\(854\) 64.9633i 0.0760694i
\(855\) −197.975 575.009i −0.231549 0.672525i
\(856\) −906.669 −1.05919
\(857\) −684.385 + 120.676i −0.798582 + 0.140812i −0.558026 0.829824i \(-0.688441\pi\)
−0.240556 + 0.970635i \(0.577330\pi\)
\(858\) 96.1794 + 20.4740i 0.112097 + 0.0238624i
\(859\) −1240.17 + 451.384i −1.44373 + 0.525477i −0.940834 0.338868i \(-0.889956\pi\)
−0.502901 + 0.864344i \(0.667734\pi\)
\(860\) 96.2099 + 114.659i 0.111872 + 0.133324i
\(861\) −294.539 + 471.043i −0.342089 + 0.547089i
\(862\) −197.233 341.618i −0.228809 0.396308i
\(863\) 489.030 282.342i 0.566663 0.327163i −0.189152 0.981948i \(-0.560574\pi\)
0.755816 + 0.654785i \(0.227241\pi\)
\(864\) 677.255 168.206i 0.783860 0.194683i
\(865\) 259.243 + 217.531i 0.299703 + 0.251481i
\(866\) 253.951i 0.293245i
\(867\) 858.383 120.373i 0.990061 0.138839i
\(868\) −712.224 597.627i −0.820535 0.688511i
\(869\) 301.711 + 359.566i 0.347194 + 0.413769i
\(870\) −131.900 4.64600i −0.151609 0.00534023i
\(871\) 61.9242 51.9606i 0.0710955 0.0596562i
\(872\) 33.2192 + 39.5891i 0.0380954 + 0.0454003i
\(873\) 539.398 + 521.522i 0.617868 + 0.597391i
\(874\) −29.5040 + 57.9879i −0.0337575 + 0.0663477i
\(875\) 553.152 + 319.362i 0.632174 + 0.364986i
\(876\) 17.5266 + 53.9969i 0.0200075 + 0.0616403i
\(877\) −136.644 774.947i −0.155808 0.883634i −0.958043 0.286625i \(-0.907467\pi\)
0.802234 0.597009i \(-0.203644\pi\)
\(878\) −71.2472 195.750i −0.0811472 0.222950i
\(879\) −63.5973 + 298.757i −0.0723518 + 0.339883i
\(880\) −48.9605 + 277.669i −0.0556369 + 0.315533i
\(881\) −108.492 62.6379i −0.123146 0.0710986i 0.437161 0.899383i \(-0.355984\pi\)
−0.560308 + 0.828284i \(0.689317\pi\)
\(882\) −39.3159 137.424i −0.0445758 0.155810i
\(883\) 276.736 + 232.209i 0.313404 + 0.262977i 0.785897 0.618357i \(-0.212201\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(884\) −2.61718 7.19065i −0.00296062 0.00813422i
\(885\) 626.751 + 802.706i 0.708194 + 0.907012i
\(886\) 277.185 0.312850
\(887\) −921.114 + 1097.74i −1.03846 + 1.23759i −0.0676572 + 0.997709i \(0.521552\pi\)
−0.970803 + 0.239880i \(0.922892\pi\)
\(888\) −481.647 433.941i −0.542395 0.488672i
\(889\) −450.755 378.228i −0.507036 0.425454i
\(890\) 116.479 320.024i 0.130875 0.359577i
\(891\) −525.271 171.374i −0.589529 0.192339i
\(892\) 691.854 0.775621
\(893\) 234.152 311.104i 0.262208 0.348381i
\(894\) 16.0588 + 20.5672i 0.0179629 + 0.0230058i
\(895\) −969.159 352.745i −1.08286 0.394128i
\(896\) −578.548 + 102.014i −0.645701 + 0.113855i
\(897\) 131.002 + 4.61436i 0.146044 + 0.00514422i
\(898\) −10.7104 3.89827i −0.0119270 0.00434106i
\(899\) −367.925 1010.86i −0.409260 1.12443i
\(900\) −289.594 279.997i −0.321771 0.311107i
\(901\) −5.25081 9.09466i −0.00582775 0.0100940i
\(902\) −55.1392 151.494i −0.0611299 0.167953i
\(903\) 147.961 78.6149i 0.163855 0.0870597i
\(904\) 145.244 251.570i 0.160668 0.278285i
\(905\) 111.573i 0.123285i
\(906\) 453.466 + 15.9727i 0.500514 + 0.0176299i
\(907\) −906.462 329.925i −0.999407 0.363754i −0.210051 0.977690i \(-0.567363\pi\)
−0.789356 + 0.613936i \(0.789585\pi\)
\(908\) −401.504 70.7960i −0.442185 0.0779692i
\(909\) −404.978 + 197.218i −0.445521 + 0.216961i
\(910\) −62.9465 + 52.8184i −0.0691719 + 0.0580421i
\(911\) 1347.04 + 777.714i 1.47864 + 0.853693i 0.999708 0.0241602i \(-0.00769118\pi\)
0.478931 + 0.877853i \(0.341025\pi\)
\(912\) −11.7452 662.391i −0.0128786 0.726306i
\(913\) −295.797 512.336i −0.323984 0.561156i
\(914\) −125.728 + 345.436i −0.137558 + 0.377938i
\(915\) −223.417 + 72.5179i −0.244172 + 0.0792545i
\(916\) 128.481 + 107.808i 0.140263 + 0.117694i
\(917\) −400.163 + 70.5595i −0.436383 + 0.0769460i
\(918\) −1.07713 4.33691i −0.00117335 0.00472431i
\(919\) 269.235 466.329i 0.292966 0.507431i −0.681544 0.731777i \(-0.738691\pi\)
0.974510 + 0.224346i \(0.0720245\pi\)
\(920\) 92.8386i 0.100912i
\(921\) 41.5533 1179.70i 0.0451176 1.28089i
\(922\) −18.8648 + 106.988i −0.0204607 + 0.116039i
\(923\) −684.693 395.308i −0.741813 0.428286i
\(924\) 330.526 + 133.657i 0.357712 + 0.144651i
\(925\) −99.0804 + 561.913i −0.107114 + 0.607474i
\(926\) −98.7964 + 17.4205i −0.106692 + 0.0188126i
\(927\) −41.8617 400.618i −0.0451582 0.432167i
\(928\) −489.581 178.193i −0.527566 0.192018i
\(929\) −825.000 + 145.470i −0.888051 + 0.156587i −0.599022 0.800733i \(-0.704444\pi\)
−0.289030 + 0.957320i \(0.593333\pi\)
\(930\) 130.983 323.913i 0.140842 0.348294i
\(931\) −491.037 + 26.0192i −0.527429 + 0.0279476i
\(932\) −202.285 + 116.789i −0.217044 + 0.125310i
\(933\) 718.320 233.156i 0.769904 0.249900i
\(934\) 331.651 278.288i 0.355087 0.297953i
\(935\) 6.44315 + 1.13610i 0.00689107 + 0.00121508i
\(936\) 296.416 144.350i 0.316684 0.154220i
\(937\) −135.157 + 49.1933i −0.144245 + 0.0525008i −0.413134 0.910670i \(-0.635566\pi\)
0.268889 + 0.963171i \(0.413344\pi\)
\(938\) −26.3802 + 15.2306i −0.0281238 + 0.0162373i
\(939\) −72.4432 92.7809i −0.0771493 0.0988082i
\(940\) −45.8571 + 260.069i −0.0487842 + 0.276669i
\(941\) −765.256 134.935i −0.813237 0.143396i −0.248463 0.968641i \(-0.579925\pi\)
−0.564774 + 0.825246i \(0.691037\pi\)
\(942\) −20.7784 8.40233i −0.0220577 0.00891967i
\(943\) −107.453 186.114i −0.113948 0.197364i
\(944\) 379.450 + 1042.53i 0.401960 + 1.10438i
\(945\) 383.001 257.832i 0.405292 0.272838i
\(946\) −8.44304 + 47.8829i −0.00892499 + 0.0506161i
\(947\) 94.3776 + 112.475i 0.0996596 + 0.118770i 0.813569 0.581468i \(-0.197522\pi\)
−0.713909 + 0.700238i \(0.753077\pi\)
\(948\) 731.604 + 155.739i 0.771734 + 0.164281i
\(949\) 20.4474 + 35.4159i 0.0215462 + 0.0373191i
\(950\) 120.744 78.5117i 0.127099 0.0826439i
\(951\) −215.265 1535.06i −0.226356 1.61415i
\(952\) 1.05348 + 5.97457i 0.00110659 + 0.00627580i
\(953\) 229.840 631.480i 0.241175 0.662623i −0.758762 0.651368i \(-0.774195\pi\)
0.999937 0.0112546i \(-0.00358252\pi\)
\(954\) 174.062 126.302i 0.182455 0.132392i
\(955\) −134.946 765.318i −0.141305 0.801381i
\(956\) 1417.01 + 249.857i 1.48223 + 0.261357i
\(957\) 253.870 + 325.141i 0.265277 + 0.339750i
\(958\) 28.0144 48.5223i 0.0292426 0.0506496i
\(959\) 289.274 + 51.0069i 0.301642 + 0.0531876i
\(960\) 153.334 + 288.590i 0.159723 + 0.300614i
\(961\) 1886.80 1.96337
\(962\) −192.229 110.984i −0.199823 0.115368i
\(963\) 1734.80 181.273i 1.80145 0.188238i
\(964\) 146.689 + 831.916i 0.152167 + 0.862983i
\(965\) 95.8810 114.266i 0.0993585 0.118411i
\(966\) −48.3130 10.2845i −0.0500134 0.0106465i
\(967\) −364.704 132.741i −0.377150 0.137271i 0.146487 0.989213i \(-0.453203\pi\)
−0.523638 + 0.851941i \(0.675425\pi\)
\(968\) 301.718 174.197i 0.311692 0.179955i
\(969\) −15.3704 + 0.272542i −0.0158622 + 0.000281261i
\(970\) 90.9698 157.564i 0.0937833 0.162437i
\(971\) 369.062 + 439.831i 0.380085 + 0.452967i 0.921841 0.387568i \(-0.126685\pi\)
−0.541756 + 0.840536i \(0.682240\pi\)
\(972\) −827.843 + 299.893i −0.851690 + 0.308532i
\(973\) 72.6702 412.133i 0.0746868 0.423570i
\(974\) −84.7300 + 232.794i −0.0869918 + 0.239008i
\(975\) −246.034 153.843i −0.252343 0.157787i
\(976\) −255.887 −0.262180
\(977\) 1596.18 + 921.557i 1.63376 + 0.943252i 0.982919 + 0.184039i \(0.0589172\pi\)
0.650842 + 0.759213i \(0.274416\pi\)
\(978\) −232.821 + 372.340i −0.238058 + 0.380716i
\(979\) −1000.24 + 364.058i −1.02170 + 0.371867i
\(980\) 288.816 166.748i 0.294711 0.170151i
\(981\) −71.4759 69.1071i −0.0728603 0.0704456i
\(982\) −413.833 + 150.623i −0.421418 + 0.153384i
\(983\) −130.958 + 359.804i −0.133223 + 0.366026i −0.988310 0.152458i \(-0.951281\pi\)
0.855087 + 0.518484i \(0.173503\pi\)
\(984\) −458.305 286.573i −0.465757 0.291233i
\(985\) 201.784 + 1144.37i 0.204857 + 1.16180i
\(986\) −1.14109 + 3.13511i −0.00115729 + 0.00317963i
\(987\) 274.056 + 110.822i 0.277666 + 0.112282i
\(988\) −121.572 525.198i −0.123048 0.531577i
\(989\) 64.8141i 0.0655350i
\(990\) −9.42696 + 133.650i −0.00952218 + 0.135000i
\(991\) 852.767 + 310.382i 0.860512 + 0.313201i 0.734319 0.678805i \(-0.237502\pi\)
0.126193 + 0.992006i \(0.459724\pi\)
\(992\) 886.560 1056.56i 0.893710 1.06508i
\(993\) −310.912 957.873i −0.313103 0.964626i
\(994\) 228.223 + 191.502i 0.229601 + 0.192658i
\(995\) 559.525i 0.562336i
\(996\) −874.002 353.427i −0.877512 0.354847i
\(997\) 1538.19 559.854i 1.54281 0.561538i 0.576096 0.817382i \(-0.304575\pi\)
0.966718 + 0.255844i \(0.0823532\pi\)
\(998\) −350.682 + 417.926i −0.351384 + 0.418764i
\(999\) 1008.33 + 733.993i 1.00934 + 0.734728i
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 171.3.z.a.101.17 228
9.5 odd 6 171.3.bf.a.158.17 yes 228
19.16 even 9 171.3.bf.a.92.17 yes 228
171.149 odd 18 inner 171.3.z.a.149.17 yes 228
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.3.z.a.101.17 228 1.1 even 1 trivial
171.3.z.a.149.17 yes 228 171.149 odd 18 inner
171.3.bf.a.92.17 yes 228 19.16 even 9
171.3.bf.a.158.17 yes 228 9.5 odd 6