Properties

Label 150.3.k.a.67.1
Level $150$
Weight $3$
Character 150.67
Analytic conductor $4.087$
Analytic rank $0$
Dimension $32$
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] = [150,3,Mod(13,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.k (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 67.1
Character \(\chi\) \(=\) 150.67
Dual form 150.3.k.a.103.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.642040 - 1.26007i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-3.75559 - 3.30084i) q^{5} +(1.98168 + 1.43977i) q^{6} +(-5.04938 - 5.04938i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-2.85317 - 0.927051i) q^{9} +O(q^{10})\) \(q+(0.642040 - 1.26007i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-3.75559 - 3.30084i) q^{5} +(1.98168 + 1.43977i) q^{6} +(-5.04938 - 5.04938i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(-6.57054 + 2.61306i) q^{10} +(-1.94631 - 5.99013i) q^{11} +(3.08654 - 1.57267i) q^{12} +(-0.134649 - 0.264264i) q^{13} +(-9.60450 + 3.12069i) q^{14} +(6.66442 - 5.53042i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-3.88687 - 24.5408i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(-3.92362 + 5.40040i) q^{19} +(-0.925901 + 9.95704i) q^{20} +(10.0063 - 7.26997i) q^{21} +(-8.79761 - 1.39341i) q^{22} +(0.779906 + 0.397382i) q^{23} -4.89898i q^{24} +(3.20896 + 24.7932i) q^{25} -0.419443 q^{26} +(2.35900 - 4.62981i) q^{27} +(-2.23417 + 14.1060i) q^{28} +(0.149281 + 0.205468i) q^{29} +(-2.68992 - 11.9484i) q^{30} +(31.6948 + 23.0276i) q^{31} +(4.00000 + 4.00000i) q^{32} +(10.7748 - 1.70657i) q^{33} +(-33.4187 - 10.8584i) q^{34} +(2.29624 + 35.6306i) q^{35} +(1.85410 + 5.70634i) q^{36} +(-10.5236 + 5.36203i) q^{37} +(4.28578 + 8.41132i) q^{38} +(0.488568 - 0.158745i) q^{39} +(11.9521 + 7.55952i) q^{40} +(13.4241 - 41.3151i) q^{41} +(-2.73629 - 17.2762i) q^{42} +(-9.20095 + 9.20095i) q^{43} +(-7.40421 + 10.1910i) q^{44} +(7.65530 + 12.8995i) q^{45} +(1.00146 - 0.727604i) q^{46} +(27.3024 + 4.32428i) q^{47} +(-6.17307 - 3.14534i) q^{48} +1.99256i q^{49} +(33.3015 + 11.8747i) q^{50} +43.0357 q^{51} +(-0.269299 + 0.528529i) q^{52} +(16.2146 - 102.375i) q^{53} +(-4.31932 - 5.94504i) q^{54} +(-12.4629 + 28.9210i) q^{55} +(16.3401 + 11.8718i) q^{56} +(-8.17549 - 8.17549i) q^{57} +(0.354749 - 0.0561867i) q^{58} +(19.5696 + 6.35855i) q^{59} +(-16.7829 - 4.28185i) q^{60} +(24.2844 + 74.7398i) q^{61} +(49.3658 - 25.1531i) q^{62} +(9.72571 + 19.0878i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-0.366605 + 1.43693i) q^{65} +(4.76747 - 14.6728i) q^{66} +(-14.1042 - 89.0506i) q^{67} +(-35.1385 + 35.1385i) q^{68} +(-0.891130 + 1.22653i) q^{69} +(46.3715 + 19.9828i) q^{70} +(70.3502 - 51.1124i) q^{71} +(8.38081 + 1.32739i) q^{72} +(-126.687 - 64.5501i) q^{73} +16.7031i q^{74} +(-43.2839 - 1.22813i) q^{75} +13.3505 q^{76} +(-20.4188 + 40.0741i) q^{77} +(0.113649 - 0.717552i) q^{78} +(68.2204 + 93.8974i) q^{79} +(17.1993 - 10.2071i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-43.4413 - 43.4413i) q^{82} +(-87.8156 + 13.9086i) q^{83} +(-23.5261 - 7.64410i) q^{84} +(-66.4075 + 104.995i) q^{85} +(5.68650 + 17.5012i) q^{86} +(-0.391947 + 0.199707i) q^{87} +(8.08764 + 15.8729i) q^{88} +(-141.867 + 46.0953i) q^{89} +(21.1693 - 1.36427i) q^{90} +(-0.654476 + 2.01427i) q^{91} +(-0.273857 - 1.72907i) q^{92} +(-47.9818 + 47.9818i) q^{93} +(22.9781 - 31.6267i) q^{94} +(32.5614 - 7.33048i) q^{95} +(-7.92672 + 5.75910i) q^{96} +(-56.9694 - 9.02306i) q^{97} +(2.51077 + 1.27930i) q^{98} +18.8952i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} + 20 q^{10} + 32 q^{11} - 16 q^{13} - 60 q^{14} + 32 q^{16} + 148 q^{17} - 96 q^{18} + 180 q^{19} + 40 q^{20} - 36 q^{21} + 48 q^{22} + 48 q^{23} - 160 q^{25} - 8 q^{26} - 56 q^{28} - 200 q^{29} - 120 q^{30} + 120 q^{31} + 128 q^{32} - 156 q^{33} - 100 q^{34} - 180 q^{35} - 48 q^{36} + 444 q^{37} + 32 q^{38} - 120 q^{39} - 304 q^{41} - 24 q^{42} + 216 q^{43} + 40 q^{44} + 60 q^{45} - 16 q^{46} + 32 q^{47} + 40 q^{50} + 24 q^{51} - 32 q^{52} - 340 q^{53} + 80 q^{55} + 72 q^{56} - 24 q^{57} - 192 q^{58} - 560 q^{59} + 312 q^{61} + 40 q^{62} + 24 q^{63} - 520 q^{65} - 108 q^{66} + 688 q^{67} - 16 q^{68} + 180 q^{69} + 80 q^{70} + 212 q^{71} + 48 q^{72} - 376 q^{73} + 120 q^{75} - 64 q^{76} - 176 q^{77} - 48 q^{78} + 440 q^{79} + 80 q^{80} + 72 q^{81} - 256 q^{82} - 96 q^{83} - 240 q^{85} + 408 q^{86} + 264 q^{87} + 184 q^{88} - 560 q^{89} - 516 q^{91} + 216 q^{92} + 48 q^{93} + 80 q^{94} + 520 q^{95} - 716 q^{97} - 108 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{13}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.642040 1.26007i 0.321020 0.630037i
\(3\) −0.270952 + 1.71073i −0.0903175 + 0.570242i
\(4\) −1.17557 1.61803i −0.293893 0.404508i
\(5\) −3.75559 3.30084i −0.751119 0.660167i
\(6\) 1.98168 + 1.43977i 0.330280 + 0.239962i
\(7\) −5.04938 5.04938i −0.721341 0.721341i 0.247538 0.968878i \(-0.420379\pi\)
−0.968878 + 0.247538i \(0.920379\pi\)
\(8\) −2.79360 + 0.442463i −0.349201 + 0.0553079i
\(9\) −2.85317 0.927051i −0.317019 0.103006i
\(10\) −6.57054 + 2.61306i −0.657054 + 0.261306i
\(11\) −1.94631 5.99013i −0.176937 0.544557i 0.822779 0.568361i \(-0.192422\pi\)
−0.999717 + 0.0238037i \(0.992422\pi\)
\(12\) 3.08654 1.57267i 0.257211 0.131056i
\(13\) −0.134649 0.264264i −0.0103576 0.0203280i 0.885770 0.464125i \(-0.153631\pi\)
−0.896127 + 0.443797i \(0.853631\pi\)
\(14\) −9.60450 + 3.12069i −0.686036 + 0.222906i
\(15\) 6.66442 5.53042i 0.444294 0.368695i
\(16\) −1.23607 + 3.80423i −0.0772542 + 0.237764i
\(17\) −3.88687 24.5408i −0.228640 1.44357i −0.788524 0.615004i \(-0.789155\pi\)
0.559885 0.828571i \(-0.310845\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) −3.92362 + 5.40040i −0.206506 + 0.284232i −0.899690 0.436529i \(-0.856207\pi\)
0.693184 + 0.720761i \(0.256207\pi\)
\(20\) −0.925901 + 9.95704i −0.0462951 + 0.497852i
\(21\) 10.0063 7.26997i 0.476488 0.346189i
\(22\) −8.79761 1.39341i −0.399892 0.0633366i
\(23\) 0.779906 + 0.397382i 0.0339090 + 0.0172775i 0.470863 0.882206i \(-0.343943\pi\)
−0.436954 + 0.899484i \(0.643943\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 3.20896 + 24.7932i 0.128358 + 0.991728i
\(26\) −0.419443 −0.0161324
\(27\) 2.35900 4.62981i 0.0873705 0.171474i
\(28\) −2.23417 + 14.1060i −0.0797917 + 0.503785i
\(29\) 0.149281 + 0.205468i 0.00514763 + 0.00708510i 0.811583 0.584237i \(-0.198606\pi\)
−0.806435 + 0.591322i \(0.798606\pi\)
\(30\) −2.68992 11.9484i −0.0896640 0.398280i
\(31\) 31.6948 + 23.0276i 1.02241 + 0.742827i 0.966776 0.255624i \(-0.0822810\pi\)
0.0556371 + 0.998451i \(0.482281\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 10.7748 1.70657i 0.326510 0.0517141i
\(34\) −33.4187 10.8584i −0.982903 0.319364i
\(35\) 2.29624 + 35.6306i 0.0656069 + 1.01802i
\(36\) 1.85410 + 5.70634i 0.0515028 + 0.158509i
\(37\) −10.5236 + 5.36203i −0.284421 + 0.144920i −0.590381 0.807125i \(-0.701023\pi\)
0.305960 + 0.952044i \(0.401023\pi\)
\(38\) 4.28578 + 8.41132i 0.112784 + 0.221351i
\(39\) 0.488568 0.158745i 0.0125274 0.00407039i
\(40\) 11.9521 + 7.55952i 0.298804 + 0.188988i
\(41\) 13.4241 41.3151i 0.327417 1.00769i −0.642921 0.765933i \(-0.722278\pi\)
0.970338 0.241753i \(-0.0777225\pi\)
\(42\) −2.73629 17.2762i −0.0651497 0.411339i
\(43\) −9.20095 + 9.20095i −0.213976 + 0.213976i −0.805954 0.591978i \(-0.798347\pi\)
0.591978 + 0.805954i \(0.298347\pi\)
\(44\) −7.40421 + 10.1910i −0.168277 + 0.231614i
\(45\) 7.65530 + 12.8995i 0.170118 + 0.286655i
\(46\) 1.00146 0.727604i 0.0217709 0.0158175i
\(47\) 27.3024 + 4.32428i 0.580903 + 0.0920060i 0.439969 0.898013i \(-0.354989\pi\)
0.140934 + 0.990019i \(0.454989\pi\)
\(48\) −6.17307 3.14534i −0.128606 0.0655279i
\(49\) 1.99256i 0.0406645i
\(50\) 33.3015 + 11.8747i 0.666031 + 0.237494i
\(51\) 43.0357 0.843837
\(52\) −0.269299 + 0.528529i −0.00517882 + 0.0101640i
\(53\) 16.2146 102.375i 0.305936 1.93160i −0.0538019 0.998552i \(-0.517134\pi\)
0.359738 0.933053i \(-0.382866\pi\)
\(54\) −4.31932 5.94504i −0.0799874 0.110093i
\(55\) −12.4629 + 28.9210i −0.226598 + 0.525835i
\(56\) 16.3401 + 11.8718i 0.291788 + 0.211997i
\(57\) −8.17549 8.17549i −0.143430 0.143430i
\(58\) 0.354749 0.0561867i 0.00611636 0.000968737i
\(59\) 19.5696 + 6.35855i 0.331688 + 0.107772i 0.470126 0.882599i \(-0.344208\pi\)
−0.138438 + 0.990371i \(0.544208\pi\)
\(60\) −16.7829 4.28185i −0.279715 0.0713642i
\(61\) 24.2844 + 74.7398i 0.398105 + 1.22524i 0.926517 + 0.376254i \(0.122788\pi\)
−0.528411 + 0.848989i \(0.677212\pi\)
\(62\) 49.3658 25.1531i 0.796223 0.405696i
\(63\) 9.72571 + 19.0878i 0.154376 + 0.302981i
\(64\) 7.60845 2.47214i 0.118882 0.0386271i
\(65\) −0.366605 + 1.43693i −0.00564008 + 0.0221065i
\(66\) 4.76747 14.6728i 0.0722344 0.222315i
\(67\) −14.1042 89.0506i −0.210511 1.32911i −0.835935 0.548828i \(-0.815074\pi\)
0.625424 0.780285i \(-0.284926\pi\)
\(68\) −35.1385 + 35.1385i −0.516743 + 0.516743i
\(69\) −0.891130 + 1.22653i −0.0129149 + 0.0177759i
\(70\) 46.3715 + 19.9828i 0.662450 + 0.285469i
\(71\) 70.3502 51.1124i 0.990848 0.719893i 0.0307412 0.999527i \(-0.490213\pi\)
0.960107 + 0.279634i \(0.0902132\pi\)
\(72\) 8.38081 + 1.32739i 0.116400 + 0.0184360i
\(73\) −126.687 64.5501i −1.73544 0.884248i −0.970837 0.239742i \(-0.922937\pi\)
−0.764599 0.644507i \(-0.777063\pi\)
\(74\) 16.7031i 0.225718i
\(75\) −43.2839 1.22813i −0.577118 0.0163751i
\(76\) 13.3505 0.175665
\(77\) −20.4188 + 40.0741i −0.265179 + 0.520443i
\(78\) 0.113649 0.717552i 0.00145704 0.00919938i
\(79\) 68.2204 + 93.8974i 0.863550 + 1.18857i 0.980711 + 0.195462i \(0.0626205\pi\)
−0.117161 + 0.993113i \(0.537380\pi\)
\(80\) 17.1993 10.2071i 0.214991 0.127588i
\(81\) 7.28115 + 5.29007i 0.0898908 + 0.0653095i
\(82\) −43.4413 43.4413i −0.529772 0.529772i
\(83\) −87.8156 + 13.9086i −1.05802 + 0.167574i −0.661114 0.750286i \(-0.729916\pi\)
−0.396905 + 0.917860i \(0.629916\pi\)
\(84\) −23.5261 7.64410i −0.280073 0.0910012i
\(85\) −66.4075 + 104.995i −0.781265 + 1.23524i
\(86\) 5.68650 + 17.5012i 0.0661221 + 0.203503i
\(87\) −0.391947 + 0.199707i −0.00450514 + 0.00229549i
\(88\) 8.08764 + 15.8729i 0.0919050 + 0.180374i
\(89\) −141.867 + 46.0953i −1.59401 + 0.517925i −0.965616 0.259971i \(-0.916287\pi\)
−0.628393 + 0.777896i \(0.716287\pi\)
\(90\) 21.1693 1.36427i 0.235214 0.0151585i
\(91\) −0.654476 + 2.01427i −0.00719204 + 0.0221348i
\(92\) −0.273857 1.72907i −0.00297671 0.0187942i
\(93\) −47.9818 + 47.9818i −0.515933 + 0.515933i
\(94\) 22.9781 31.6267i 0.244448 0.336454i
\(95\) 32.5614 7.33048i 0.342751 0.0771629i
\(96\) −7.92672 + 5.75910i −0.0825700 + 0.0599906i
\(97\) −56.9694 9.02306i −0.587313 0.0930212i −0.144296 0.989535i \(-0.546092\pi\)
−0.443017 + 0.896513i \(0.646092\pi\)
\(98\) 2.51077 + 1.27930i 0.0256201 + 0.0130541i
\(99\) 18.8952i 0.190861i
\(100\) 36.3439 34.3384i 0.363439 0.343384i
\(101\) −23.7820 −0.235466 −0.117733 0.993045i \(-0.537563\pi\)
−0.117733 + 0.993045i \(0.537563\pi\)
\(102\) 27.6306 54.2281i 0.270888 0.531648i
\(103\) 23.4373 147.977i 0.227546 1.43667i −0.564107 0.825701i \(-0.690780\pi\)
0.791654 0.610970i \(-0.209220\pi\)
\(104\) 0.493085 + 0.678673i 0.00474120 + 0.00652570i
\(105\) −61.5764 5.72597i −0.586442 0.0545330i
\(106\) −118.590 86.1604i −1.11877 0.812834i
\(107\) 136.505 + 136.505i 1.27575 + 1.27575i 0.943026 + 0.332719i \(0.107966\pi\)
0.332719 + 0.943026i \(0.392034\pi\)
\(108\) −10.2644 + 1.62571i −0.0950404 + 0.0150529i
\(109\) −5.45648 1.77292i −0.0500595 0.0162653i 0.283880 0.958860i \(-0.408378\pi\)
−0.333940 + 0.942594i \(0.608378\pi\)
\(110\) 28.4409 + 34.2726i 0.258553 + 0.311569i
\(111\) −6.32157 19.4558i −0.0569511 0.175278i
\(112\) 25.4504 12.9676i 0.227236 0.115782i
\(113\) −80.2019 157.405i −0.709751 1.39297i −0.910578 0.413338i \(-0.864363\pi\)
0.200826 0.979627i \(-0.435637\pi\)
\(114\) −15.5507 + 5.05273i −0.136410 + 0.0443222i
\(115\) −1.61732 4.06675i −0.0140636 0.0353630i
\(116\) 0.156964 0.483084i 0.00135313 0.00416452i
\(117\) 0.139191 + 0.878818i 0.00118967 + 0.00751127i
\(118\) 20.5767 20.5767i 0.174379 0.174379i
\(119\) −104.289 + 143.542i −0.876382 + 1.20624i
\(120\) −16.1707 + 18.3986i −0.134756 + 0.153321i
\(121\) 65.7975 47.8047i 0.543781 0.395080i
\(122\) 109.769 + 17.3857i 0.899747 + 0.142506i
\(123\) 67.0416 + 34.1594i 0.545054 + 0.277719i
\(124\) 78.3539i 0.631886i
\(125\) 69.7868 103.705i 0.558294 0.829643i
\(126\) 30.2963 0.240447
\(127\) 26.2388 51.4965i 0.206605 0.405485i −0.764331 0.644824i \(-0.776931\pi\)
0.970936 + 0.239339i \(0.0769308\pi\)
\(128\) 1.76985 11.1744i 0.0138270 0.0873001i
\(129\) −13.2473 18.2333i −0.102692 0.141344i
\(130\) 1.57526 + 1.38451i 0.0121174 + 0.0106501i
\(131\) −192.036 139.523i −1.46593 1.06506i −0.981769 0.190077i \(-0.939126\pi\)
−0.484157 0.874981i \(-0.660874\pi\)
\(132\) −15.4279 15.4279i −0.116878 0.116878i
\(133\) 47.0806 7.45683i 0.353989 0.0560664i
\(134\) −121.266 39.4016i −0.904968 0.294042i
\(135\) −24.1417 + 9.60098i −0.178827 + 0.0711184i
\(136\) 21.7168 + 66.8374i 0.159682 + 0.491451i
\(137\) −144.912 + 73.8364i −1.05775 + 0.538952i −0.894239 0.447589i \(-0.852283\pi\)
−0.163514 + 0.986541i \(0.552283\pi\)
\(138\) 0.973383 + 1.91037i 0.00705350 + 0.0138433i
\(139\) 55.2509 17.9521i 0.397488 0.129152i −0.103450 0.994635i \(-0.532988\pi\)
0.500939 + 0.865483i \(0.332988\pi\)
\(140\) 54.9522 45.6017i 0.392515 0.325726i
\(141\) −14.7953 + 45.5353i −0.104931 + 0.322945i
\(142\) −19.2378 121.463i −0.135477 0.855370i
\(143\) −1.32091 + 1.32091i −0.00923712 + 0.00923712i
\(144\) 7.05342 9.70820i 0.0489821 0.0674181i
\(145\) 0.117577 1.26441i 0.000810874 0.00872005i
\(146\) −162.676 + 118.191i −1.11422 + 0.809527i
\(147\) −3.40872 0.539889i −0.0231886 0.00367271i
\(148\) 21.0471 + 10.7241i 0.142210 + 0.0724598i
\(149\) 23.3539i 0.156737i 0.996924 + 0.0783686i \(0.0249711\pi\)
−0.996924 + 0.0783686i \(0.975029\pi\)
\(150\) −29.3375 + 53.7523i −0.195583 + 0.358349i
\(151\) 195.405 1.29407 0.647035 0.762460i \(-0.276009\pi\)
0.647035 + 0.762460i \(0.276009\pi\)
\(152\) 8.57156 16.8226i 0.0563919 0.110675i
\(153\) −11.6606 + 73.6223i −0.0762132 + 0.481191i
\(154\) 37.3867 + 51.4584i 0.242771 + 0.334145i
\(155\) −43.0224 191.102i −0.277564 1.23291i
\(156\) −0.831201 0.603903i −0.00532821 0.00387117i
\(157\) 152.292 + 152.292i 0.970010 + 0.970010i 0.999563 0.0295532i \(-0.00940846\pi\)
−0.0295532 + 0.999563i \(0.509408\pi\)
\(158\) 162.118 25.6769i 1.02606 0.162512i
\(159\) 170.742 + 55.4775i 1.07385 + 0.348915i
\(160\) −1.81903 28.2257i −0.0113689 0.176411i
\(161\) −1.93151 5.94458i −0.0119970 0.0369229i
\(162\) 11.3407 5.77836i 0.0700041 0.0356689i
\(163\) 75.8940 + 148.950i 0.465607 + 0.913806i 0.997743 + 0.0671470i \(0.0213897\pi\)
−0.532136 + 0.846659i \(0.678610\pi\)
\(164\) −82.6303 + 26.8482i −0.503843 + 0.163709i
\(165\) −46.0990 29.1568i −0.279388 0.176708i
\(166\) −38.8552 + 119.584i −0.234067 + 0.720385i
\(167\) 1.19340 + 7.53480i 0.00714608 + 0.0451186i 0.991004 0.133834i \(-0.0427290\pi\)
−0.983858 + 0.178953i \(0.942729\pi\)
\(168\) −24.7368 + 24.7368i −0.147243 + 0.147243i
\(169\) 99.2840 136.653i 0.587479 0.808596i
\(170\) 89.6652 + 151.089i 0.527443 + 0.888761i
\(171\) 16.2012 11.7709i 0.0947439 0.0688354i
\(172\) 25.7038 + 4.07108i 0.149441 + 0.0236691i
\(173\) 131.671 + 67.0899i 0.761106 + 0.387803i 0.791052 0.611749i \(-0.209534\pi\)
−0.0299464 + 0.999552i \(0.509534\pi\)
\(174\) 0.622103i 0.00357530i
\(175\) 108.987 141.394i 0.622784 0.807964i
\(176\) 25.1936 0.143145
\(177\) −16.1802 + 31.7554i −0.0914134 + 0.179409i
\(178\) −33.0006 + 208.358i −0.185397 + 1.17055i
\(179\) 124.545 + 171.421i 0.695781 + 0.957661i 0.999987 + 0.00505444i \(0.00160889\pi\)
−0.304206 + 0.952606i \(0.598391\pi\)
\(180\) 11.8724 27.5508i 0.0659580 0.153060i
\(181\) −95.9004 69.6757i −0.529836 0.384949i 0.290460 0.956887i \(-0.406192\pi\)
−0.820297 + 0.571938i \(0.806192\pi\)
\(182\) 2.11793 + 2.11793i 0.0116370 + 0.0116370i
\(183\) −134.439 + 21.2931i −0.734641 + 0.116356i
\(184\) −2.35458 0.765048i −0.0127966 0.00415787i
\(185\) 57.2214 + 14.5990i 0.309305 + 0.0789135i
\(186\) 29.6544 + 91.2667i 0.159432 + 0.490681i
\(187\) −139.437 + 71.0469i −0.745654 + 0.379930i
\(188\) −25.0991 49.2598i −0.133506 0.262020i
\(189\) −35.2892 + 11.4662i −0.186715 + 0.0606675i
\(190\) 11.6687 45.7362i 0.0614144 0.240717i
\(191\) −47.6608 + 146.685i −0.249533 + 0.767984i 0.745325 + 0.666702i \(0.232295\pi\)
−0.994858 + 0.101282i \(0.967705\pi\)
\(192\) 2.16762 + 13.6858i 0.0112897 + 0.0712803i
\(193\) 96.7283 96.7283i 0.501183 0.501183i −0.410623 0.911805i \(-0.634689\pi\)
0.911805 + 0.410623i \(0.134689\pi\)
\(194\) −47.9463 + 65.9924i −0.247146 + 0.340167i
\(195\) −2.35885 1.01650i −0.0120967 0.00521282i
\(196\) 3.22403 2.34239i 0.0164491 0.0119510i
\(197\) 124.888 + 19.7803i 0.633949 + 0.100408i 0.465134 0.885240i \(-0.346006\pi\)
0.168815 + 0.985648i \(0.446006\pi\)
\(198\) 23.8093 + 12.1315i 0.120249 + 0.0612700i
\(199\) 188.411i 0.946788i −0.880851 0.473394i \(-0.843029\pi\)
0.880851 0.473394i \(-0.156971\pi\)
\(200\) −19.9346 67.8425i −0.0996732 0.339213i
\(201\) 156.163 0.776929
\(202\) −15.2690 + 29.9671i −0.0755891 + 0.148352i
\(203\) 0.283708 1.79126i 0.00139758 0.00882396i
\(204\) −50.5915 69.6332i −0.247997 0.341339i
\(205\) −186.790 + 110.852i −0.911170 + 0.540742i
\(206\) −171.414 124.540i −0.832109 0.604562i
\(207\) −1.85681 1.85681i −0.00897010 0.00897010i
\(208\) 1.17176 0.185588i 0.00563345 0.000892251i
\(209\) 39.9857 + 12.9921i 0.191319 + 0.0621633i
\(210\) −46.7496 + 73.9145i −0.222617 + 0.351974i
\(211\) 102.744 + 316.214i 0.486940 + 1.49865i 0.829152 + 0.559024i \(0.188824\pi\)
−0.342212 + 0.939623i \(0.611176\pi\)
\(212\) −184.708 + 94.1133i −0.871263 + 0.443931i
\(213\) 68.3778 + 134.199i 0.321022 + 0.630042i
\(214\) 259.647 84.3646i 1.21331 0.394227i
\(215\) 64.9258 4.18419i 0.301981 0.0194613i
\(216\) −4.54160 + 13.9776i −0.0210259 + 0.0647112i
\(217\) −43.7639 276.315i −0.201677 1.27334i
\(218\) −5.73729 + 5.73729i −0.0263178 + 0.0263178i
\(219\) 144.754 199.236i 0.660976 0.909755i
\(220\) 61.4461 13.8332i 0.279300 0.0628784i
\(221\) −5.96188 + 4.33156i −0.0269769 + 0.0195998i
\(222\) −28.5744 4.52575i −0.128714 0.0203863i
\(223\) −113.831 58.0000i −0.510455 0.260090i 0.179739 0.983714i \(-0.442475\pi\)
−0.690194 + 0.723625i \(0.742475\pi\)
\(224\) 40.3951i 0.180335i
\(225\) 13.8289 73.7141i 0.0614616 0.327618i
\(226\) −249.835 −1.10546
\(227\) −117.516 + 230.638i −0.517691 + 1.01603i 0.473148 + 0.880983i \(0.343118\pi\)
−0.990840 + 0.135044i \(0.956882\pi\)
\(228\) −3.61736 + 22.8391i −0.0158656 + 0.100171i
\(229\) −113.815 156.653i −0.497008 0.684073i 0.484653 0.874706i \(-0.338946\pi\)
−0.981661 + 0.190633i \(0.938946\pi\)
\(230\) −6.16278 0.573075i −0.0267947 0.00249163i
\(231\) −63.0234 45.7892i −0.272828 0.198221i
\(232\) −0.507945 0.507945i −0.00218942 0.00218942i
\(233\) 440.503 69.7689i 1.89057 0.299437i 0.899943 0.436008i \(-0.143608\pi\)
0.990630 + 0.136571i \(0.0436082\pi\)
\(234\) 1.19674 + 0.388845i 0.00511428 + 0.00166173i
\(235\) −88.2631 106.361i −0.375588 0.452600i
\(236\) −12.7171 39.1392i −0.0538860 0.165844i
\(237\) −179.117 + 91.2648i −0.755769 + 0.385083i
\(238\) 113.916 + 223.572i 0.478637 + 0.939378i
\(239\) 170.058 55.2553i 0.711541 0.231194i 0.0691891 0.997604i \(-0.477959\pi\)
0.642352 + 0.766410i \(0.277959\pi\)
\(240\) 12.8013 + 32.1889i 0.0533388 + 0.134120i
\(241\) 106.451 327.624i 0.441707 1.35943i −0.444348 0.895854i \(-0.646565\pi\)
0.886055 0.463580i \(-0.153435\pi\)
\(242\) −17.9928 113.602i −0.0743505 0.469431i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 92.3835 127.155i 0.378621 0.521127i
\(245\) 6.57711 7.48324i 0.0268453 0.0305438i
\(246\) 86.0867 62.5456i 0.349946 0.254251i
\(247\) 1.95545 + 0.309712i 0.00791679 + 0.00125390i
\(248\) −98.7317 50.3063i −0.398112 0.202848i
\(249\) 153.997i 0.618462i
\(250\) −85.8706 154.519i −0.343482 0.618078i
\(251\) −137.279 −0.546929 −0.273464 0.961882i \(-0.588170\pi\)
−0.273464 + 0.961882i \(0.588170\pi\)
\(252\) 19.4514 38.1756i 0.0771882 0.151490i
\(253\) 0.862430 5.44517i 0.00340882 0.0215224i
\(254\) −48.0431 66.1256i −0.189146 0.260337i
\(255\) −161.625 142.054i −0.633822 0.557074i
\(256\) −12.9443 9.40456i −0.0505636 0.0367366i
\(257\) 167.066 + 167.066i 0.650063 + 0.650063i 0.953008 0.302945i \(-0.0979699\pi\)
−0.302945 + 0.953008i \(0.597970\pi\)
\(258\) −31.4806 + 4.98604i −0.122018 + 0.0193257i
\(259\) 80.2125 + 26.0626i 0.309701 + 0.100628i
\(260\) 2.75596 1.09603i 0.0105999 0.00421549i
\(261\) −0.235445 0.724626i −0.000902089 0.00277635i
\(262\) −299.104 + 152.401i −1.14162 + 0.581683i
\(263\) −37.9612 74.5030i −0.144339 0.283282i 0.807507 0.589858i \(-0.200816\pi\)
−0.951846 + 0.306577i \(0.900816\pi\)
\(264\) −29.3455 + 9.53494i −0.111157 + 0.0361172i
\(265\) −398.819 + 330.957i −1.50498 + 1.24890i
\(266\) 20.8314 64.1125i 0.0783136 0.241025i
\(267\) −40.4173 255.185i −0.151376 0.955749i
\(268\) −127.506 + 127.506i −0.475770 + 0.475770i
\(269\) 63.2077 86.9980i 0.234973 0.323413i −0.675205 0.737630i \(-0.735945\pi\)
0.910178 + 0.414218i \(0.135945\pi\)
\(270\) −3.40198 + 36.5845i −0.0125999 + 0.135498i
\(271\) −116.959 + 84.9758i −0.431584 + 0.313564i −0.782282 0.622925i \(-0.785944\pi\)
0.350698 + 0.936489i \(0.385944\pi\)
\(272\) 98.1630 + 15.5475i 0.360894 + 0.0571599i
\(273\) −3.26853 1.66540i −0.0119726 0.00610037i
\(274\) 230.006i 0.839438i
\(275\) 142.269 67.4774i 0.517341 0.245372i
\(276\) 3.03216 0.0109861
\(277\) −136.261 + 267.426i −0.491915 + 0.965438i 0.502958 + 0.864311i \(0.332245\pi\)
−0.994873 + 0.101127i \(0.967755\pi\)
\(278\) 12.8523 81.1461i 0.0462312 0.291893i
\(279\) −69.0829 95.0844i −0.247609 0.340804i
\(280\) −22.1800 98.5219i −0.0792144 0.351864i
\(281\) −434.083 315.380i −1.54478 1.12235i −0.947247 0.320505i \(-0.896147\pi\)
−0.597534 0.801844i \(-0.703853\pi\)
\(282\) 47.8787 + 47.8787i 0.169782 + 0.169782i
\(283\) −84.0552 + 13.3130i −0.297015 + 0.0470425i −0.303163 0.952939i \(-0.598043\pi\)
0.00614867 + 0.999981i \(0.498043\pi\)
\(284\) −165.403 53.7428i −0.582406 0.189235i
\(285\) 3.71786 + 57.6898i 0.0130451 + 0.202420i
\(286\) 0.816367 + 2.51252i 0.00285443 + 0.00878503i
\(287\) −276.399 + 140.833i −0.963064 + 0.490706i
\(288\) −7.70447 15.1209i −0.0267516 0.0525031i
\(289\) −312.286 + 101.468i −1.08057 + 0.351100i
\(290\) −1.51776 0.959954i −0.00523364 0.00331019i
\(291\) 30.8720 95.0142i 0.106089 0.326509i
\(292\) 44.4849 + 280.867i 0.152346 + 0.961872i
\(293\) 52.5893 52.5893i 0.179486 0.179486i −0.611646 0.791132i \(-0.709492\pi\)
0.791132 + 0.611646i \(0.209492\pi\)
\(294\) −2.86883 + 3.94861i −0.00975794 + 0.0134306i
\(295\) −52.5069 88.4762i −0.177990 0.299919i
\(296\) 27.0262 19.6357i 0.0913047 0.0663368i
\(297\) −32.3245 5.11970i −0.108837 0.0172380i
\(298\) 29.4276 + 14.9941i 0.0987503 + 0.0503158i
\(299\) 0.259609i 0.000868257i
\(300\) 48.8961 + 71.4785i 0.162987 + 0.238262i
\(301\) 92.9182 0.308698
\(302\) 125.458 246.224i 0.415422 0.815312i
\(303\) 6.44380 40.6845i 0.0212667 0.134272i
\(304\) −15.6945 21.6016i −0.0516266 0.0710579i
\(305\) 155.501 360.851i 0.509841 1.18312i
\(306\) 85.2829 + 61.9617i 0.278702 + 0.202489i
\(307\) 134.703 + 134.703i 0.438771 + 0.438771i 0.891598 0.452827i \(-0.149585\pi\)
−0.452827 + 0.891598i \(0.649585\pi\)
\(308\) 88.8451 14.0717i 0.288458 0.0456873i
\(309\) 246.798 + 80.1895i 0.798699 + 0.259513i
\(310\) −268.424 68.4835i −0.865885 0.220915i
\(311\) 33.2287 + 102.267i 0.106845 + 0.328834i 0.990159 0.139947i \(-0.0446932\pi\)
−0.883314 + 0.468781i \(0.844693\pi\)
\(312\) −1.29463 + 0.659645i −0.00414944 + 0.00211425i
\(313\) 218.432 + 428.697i 0.697865 + 1.36964i 0.918946 + 0.394382i \(0.129041\pi\)
−0.221081 + 0.975255i \(0.570959\pi\)
\(314\) 289.676 94.1214i 0.922534 0.299750i
\(315\) 26.4798 103.789i 0.0840630 0.329489i
\(316\) 71.7312 220.766i 0.226998 0.698627i
\(317\) 26.4870 + 167.232i 0.0835552 + 0.527547i 0.993593 + 0.113021i \(0.0360527\pi\)
−0.910037 + 0.414526i \(0.863947\pi\)
\(318\) 179.529 179.529i 0.564557 0.564557i
\(319\) 0.940232 1.29412i 0.00294744 0.00405680i
\(320\) −36.7344 15.8299i −0.114795 0.0494685i
\(321\) −270.509 + 196.536i −0.842706 + 0.612262i
\(322\) −8.73072 1.38281i −0.0271140 0.00429444i
\(323\) 147.781 + 75.2980i 0.457525 + 0.233121i
\(324\) 18.0000i 0.0555556i
\(325\) 6.11988 4.18640i 0.0188304 0.0128812i
\(326\) 236.415 0.725201
\(327\) 4.51143 8.85417i 0.0137964 0.0270770i
\(328\) −19.2212 + 121.358i −0.0586012 + 0.369993i
\(329\) −116.025 159.695i −0.352661 0.485396i
\(330\) −66.3371 + 39.3683i −0.201021 + 0.119298i
\(331\) 12.3520 + 8.97429i 0.0373174 + 0.0271126i 0.606288 0.795245i \(-0.292658\pi\)
−0.568970 + 0.822358i \(0.692658\pi\)
\(332\) 125.738 + 125.738i 0.378729 + 0.378729i
\(333\) 34.9964 5.54289i 0.105094 0.0166453i
\(334\) 10.2606 + 3.33388i 0.0307204 + 0.00998166i
\(335\) −240.972 + 380.994i −0.719319 + 1.13729i
\(336\) 15.2882 + 47.0522i 0.0455006 + 0.140036i
\(337\) 96.0748 48.9525i 0.285088 0.145260i −0.305599 0.952160i \(-0.598857\pi\)
0.590687 + 0.806901i \(0.298857\pi\)
\(338\) −108.448 212.842i −0.320853 0.629709i
\(339\) 291.008 94.5542i 0.858430 0.278921i
\(340\) 247.952 15.9795i 0.729271 0.0469984i
\(341\) 76.2505 234.675i 0.223609 0.688197i
\(342\) −4.43034 27.9721i −0.0129542 0.0817897i
\(343\) −237.359 + 237.359i −0.692008 + 0.692008i
\(344\) 21.6327 29.7749i 0.0628858 0.0865549i
\(345\) 7.39531 1.66489i 0.0214357 0.00482577i
\(346\) 169.076 122.841i 0.488660 0.355032i
\(347\) 147.764 + 23.4036i 0.425834 + 0.0674455i 0.365673 0.930743i \(-0.380839\pi\)
0.0601607 + 0.998189i \(0.480839\pi\)
\(348\) 0.783895 + 0.399414i 0.00225257 + 0.00114774i
\(349\) 348.569i 0.998765i 0.866382 + 0.499382i \(0.166440\pi\)
−0.866382 + 0.499382i \(0.833560\pi\)
\(350\) −108.192 228.112i −0.309121 0.651749i
\(351\) −1.54113 −0.00439069
\(352\) 16.1753 31.7458i 0.0459525 0.0901869i
\(353\) −3.90486 + 24.6543i −0.0110619 + 0.0698423i −0.992602 0.121416i \(-0.961257\pi\)
0.981540 + 0.191258i \(0.0612566\pi\)
\(354\) 29.6258 + 40.7764i 0.0836887 + 0.115188i
\(355\) −432.920 40.2571i −1.21949 0.113400i
\(356\) 241.358 + 175.357i 0.677973 + 0.492576i
\(357\) −217.304 217.304i −0.608694 0.608694i
\(358\) 295.966 46.8764i 0.826721 0.130940i
\(359\) 329.183 + 106.958i 0.916945 + 0.297933i 0.729213 0.684287i \(-0.239886\pi\)
0.187732 + 0.982220i \(0.439886\pi\)
\(360\) −27.0934 32.6488i −0.0752595 0.0906912i
\(361\) 97.7856 + 300.953i 0.270874 + 0.833665i
\(362\) −149.368 + 76.1070i −0.412620 + 0.210240i
\(363\) 63.9527 + 125.514i 0.176178 + 0.345770i
\(364\) 4.02854 1.30895i 0.0110674 0.00359602i
\(365\) 262.715 + 660.596i 0.719766 + 1.80985i
\(366\) −59.4845 + 183.074i −0.162526 + 0.500203i
\(367\) −106.120 670.015i −0.289155 1.82565i −0.521771 0.853086i \(-0.674728\pi\)
0.232616 0.972569i \(-0.425272\pi\)
\(368\) −2.47575 + 2.47575i −0.00672758 + 0.00672758i
\(369\) −76.6025 + 105.434i −0.207595 + 0.285730i
\(370\) 55.1342 62.7301i 0.149011 0.169541i
\(371\) −598.805 + 435.057i −1.61403 + 1.17266i
\(372\) 134.042 + 21.2302i 0.360328 + 0.0570704i
\(373\) −121.319 61.8152i −0.325253 0.165724i 0.283738 0.958902i \(-0.408425\pi\)
−0.608991 + 0.793177i \(0.708425\pi\)
\(374\) 221.316i 0.591754i
\(375\) 158.503 + 147.485i 0.422674 + 0.393294i
\(376\) −78.1855 −0.207940
\(377\) 0.0341972 0.0671158i 9.07088e−5 0.000178026i
\(378\) −8.20886 + 51.8287i −0.0217166 + 0.137113i
\(379\) −138.277 190.322i −0.364847 0.502169i 0.586644 0.809845i \(-0.300449\pi\)
−0.951491 + 0.307676i \(0.900449\pi\)
\(380\) −50.1391 44.0679i −0.131945 0.115968i
\(381\) 80.9870 + 58.8405i 0.212564 + 0.154437i
\(382\) 154.234 + 154.234i 0.403753 + 0.403753i
\(383\) −452.560 + 71.6785i −1.18162 + 0.187150i −0.716171 0.697925i \(-0.754107\pi\)
−0.465448 + 0.885075i \(0.654107\pi\)
\(384\) 18.6368 + 6.05547i 0.0485334 + 0.0157695i
\(385\) 208.963 83.1031i 0.542761 0.215852i
\(386\) −59.7814 183.988i −0.154874 0.476653i
\(387\) 34.7816 17.7221i 0.0898750 0.0457936i
\(388\) 52.3719 + 102.786i 0.134979 + 0.264911i
\(389\) 16.3257 5.30455i 0.0419684 0.0136364i −0.287958 0.957643i \(-0.592976\pi\)
0.329926 + 0.944007i \(0.392976\pi\)
\(390\) −2.79534 + 2.31970i −0.00716754 + 0.00594794i
\(391\) 6.72066 20.6841i 0.0171884 0.0529004i
\(392\) −0.881634 5.56642i −0.00224907 0.0142000i
\(393\) 290.718 290.718i 0.739740 0.739740i
\(394\) 105.108 144.668i 0.266771 0.367178i
\(395\) 53.7317 577.825i 0.136030 1.46285i
\(396\) 30.5731 22.2126i 0.0772047 0.0560925i
\(397\) 563.879 + 89.3097i 1.42035 + 0.224961i 0.818894 0.573945i \(-0.194588\pi\)
0.601456 + 0.798906i \(0.294588\pi\)
\(398\) −237.412 120.967i −0.596511 0.303938i
\(399\) 82.5624i 0.206923i
\(400\) −98.2854 18.4385i −0.245714 0.0460962i
\(401\) 388.467 0.968745 0.484373 0.874862i \(-0.339048\pi\)
0.484373 + 0.874862i \(0.339048\pi\)
\(402\) 100.263 196.777i 0.249410 0.489494i
\(403\) 1.81769 11.4765i 0.00451041 0.0284776i
\(404\) 27.9574 + 38.4801i 0.0692016 + 0.0952478i
\(405\) −9.88340 43.9012i −0.0244035 0.108398i
\(406\) −2.07497 1.50756i −0.00511077 0.00371319i
\(407\) 52.6014 + 52.6014i 0.129242 + 0.129242i
\(408\) −120.225 + 19.0417i −0.294668 + 0.0466709i
\(409\) −139.921 45.4632i −0.342106 0.111157i 0.132925 0.991126i \(-0.457563\pi\)
−0.475031 + 0.879969i \(0.657563\pi\)
\(410\) 19.7552 + 306.540i 0.0481834 + 0.747660i
\(411\) −87.0496 267.911i −0.211800 0.651852i
\(412\) −266.984 + 136.035i −0.648020 + 0.330183i
\(413\) −66.7077 130.921i −0.161520 0.317000i
\(414\) −3.53186 + 1.14757i −0.00853107 + 0.00277191i
\(415\) 375.710 + 237.630i 0.905324 + 0.572602i
\(416\) 0.518460 1.59566i 0.00124630 0.00383571i
\(417\) 15.7408 + 99.3833i 0.0377477 + 0.238329i
\(418\) 42.0434 42.0434i 0.100582 0.100582i
\(419\) −402.320 + 553.746i −0.960191 + 1.32159i −0.0133424 + 0.999911i \(0.504247\pi\)
−0.946849 + 0.321679i \(0.895753\pi\)
\(420\) 63.1226 + 106.364i 0.150292 + 0.253248i
\(421\) 16.4207 11.9303i 0.0390040 0.0283380i −0.568112 0.822951i \(-0.692326\pi\)
0.607116 + 0.794613i \(0.292326\pi\)
\(422\) 464.419 + 73.5568i 1.10052 + 0.174305i
\(423\) −73.8896 37.6486i −0.174680 0.0890039i
\(424\) 293.170i 0.691438i
\(425\) 595.971 175.118i 1.40228 0.412043i
\(426\) 213.002 0.500004
\(427\) 254.768 500.011i 0.596647 1.17099i
\(428\) 60.3984 381.340i 0.141118 0.890982i
\(429\) −1.90181 2.61762i −0.00443312 0.00610167i
\(430\) 36.4126 84.4977i 0.0846804 0.196506i
\(431\) 170.046 + 123.546i 0.394538 + 0.286649i 0.767313 0.641273i \(-0.221593\pi\)
−0.372774 + 0.927922i \(0.621593\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 278.776 44.1537i 0.643824 0.101972i 0.174019 0.984742i \(-0.444324\pi\)
0.469804 + 0.882771i \(0.344324\pi\)
\(434\) −376.275 122.259i −0.866993 0.281703i
\(435\) 2.13120 + 0.543736i 0.00489930 + 0.00124997i
\(436\) 3.54584 + 10.9130i 0.00813266 + 0.0250297i
\(437\) −5.20608 + 2.65263i −0.0119132 + 0.00607009i
\(438\) −158.115 310.318i −0.360993 0.708489i
\(439\) −518.643 + 168.517i −1.18142 + 0.383867i −0.832894 0.553433i \(-0.813318\pi\)
−0.348526 + 0.937299i \(0.613318\pi\)
\(440\) 22.0199 86.3081i 0.0500453 0.196155i
\(441\) 1.84720 5.68511i 0.00418867 0.0128914i
\(442\) 1.63032 + 10.2934i 0.00368851 + 0.0232883i
\(443\) −289.805 + 289.805i −0.654186 + 0.654186i −0.953998 0.299812i \(-0.903076\pi\)
0.299812 + 0.953998i \(0.403076\pi\)
\(444\) −24.0487 + 33.1002i −0.0541637 + 0.0745500i
\(445\) 684.947 + 295.164i 1.53921 + 0.663290i
\(446\) −146.168 + 106.198i −0.327732 + 0.238111i
\(447\) −39.9521 6.32778i −0.0893782 0.0141561i
\(448\) −50.9008 25.9352i −0.113618 0.0578911i
\(449\) 610.887i 1.36055i −0.732957 0.680275i \(-0.761860\pi\)
0.732957 0.680275i \(-0.238140\pi\)
\(450\) −84.0065 64.7527i −0.186681 0.143895i
\(451\) −273.611 −0.606675
\(452\) −160.404 + 314.810i −0.354876 + 0.696483i
\(453\) −52.9454 + 334.284i −0.116877 + 0.737934i
\(454\) 215.171 + 296.157i 0.473945 + 0.652329i
\(455\) 9.10672 5.40446i 0.0200148 0.0118779i
\(456\) 26.4564 + 19.2217i 0.0580185 + 0.0421529i
\(457\) −69.5844 69.5844i −0.152263 0.152263i 0.626865 0.779128i \(-0.284338\pi\)
−0.779128 + 0.626865i \(0.784338\pi\)
\(458\) −270.468 + 42.8378i −0.590540 + 0.0935324i
\(459\) −122.788 39.8963i −0.267512 0.0869200i
\(460\) −4.67887 + 7.39762i −0.0101714 + 0.0160818i
\(461\) −63.0165 193.945i −0.136695 0.420705i 0.859155 0.511716i \(-0.170990\pi\)
−0.995850 + 0.0910114i \(0.970990\pi\)
\(462\) −98.1612 + 50.0156i −0.212470 + 0.108259i
\(463\) −363.761 713.922i −0.785662 1.54195i −0.839476 0.543397i \(-0.817138\pi\)
0.0538144 0.998551i \(-0.482862\pi\)
\(464\) −0.966168 + 0.313927i −0.00208226 + 0.000676567i
\(465\) 338.580 21.8200i 0.728129 0.0469248i
\(466\) 194.907 599.861i 0.418255 1.28726i
\(467\) −113.023 713.602i −0.242020 1.52806i −0.746941 0.664890i \(-0.768478\pi\)
0.504921 0.863166i \(-0.331522\pi\)
\(468\) 1.25833 1.25833i 0.00268874 0.00268874i
\(469\) −378.433 + 520.868i −0.806893 + 1.11059i
\(470\) −190.691 + 42.9299i −0.405726 + 0.0913403i
\(471\) −301.793 + 219.265i −0.640749 + 0.465532i
\(472\) −57.4831 9.10444i −0.121786 0.0192891i
\(473\) 73.0228 + 37.2070i 0.154382 + 0.0786617i
\(474\) 284.296i 0.599782i
\(475\) −146.484 79.9494i −0.308387 0.168315i
\(476\) 354.855 0.745495
\(477\) −141.170 + 277.062i −0.295954 + 0.580842i
\(478\) 39.5584 249.762i 0.0827582 0.522515i
\(479\) 8.39815 + 11.5591i 0.0175327 + 0.0241317i 0.817693 0.575654i \(-0.195252\pi\)
−0.800161 + 0.599786i \(0.795252\pi\)
\(480\) 48.7793 + 4.53597i 0.101624 + 0.00944994i
\(481\) 2.83399 + 2.05901i 0.00589186 + 0.00428069i
\(482\) −344.484 344.484i −0.714697 0.714697i
\(483\) 10.6929 1.69359i 0.0221385 0.00350640i
\(484\) −154.699 50.2648i −0.319627 0.103853i
\(485\) 184.170 + 221.933i 0.379732 + 0.457595i
\(486\) 6.81241 + 20.9664i 0.0140173 + 0.0431408i
\(487\) 404.541 206.124i 0.830680 0.423252i 0.0136910 0.999906i \(-0.495642\pi\)
0.816989 + 0.576654i \(0.195642\pi\)
\(488\) −100.911 198.048i −0.206784 0.405837i
\(489\) −275.377 + 89.4754i −0.563143 + 0.182976i
\(490\) −5.20667 13.0922i −0.0106258 0.0267187i
\(491\) −2.93885 + 9.04484i −0.00598543 + 0.0184213i −0.954005 0.299792i \(-0.903083\pi\)
0.948019 + 0.318213i \(0.103083\pi\)
\(492\) −23.5410 148.632i −0.0478477 0.302098i
\(493\) 4.46210 4.46210i 0.00905092 0.00905092i
\(494\) 1.64573 2.26516i 0.00333145 0.00458534i
\(495\) 62.3699 70.9626i 0.126000 0.143359i
\(496\) −126.779 + 92.1105i −0.255603 + 0.185707i
\(497\) −613.311 97.1390i −1.23403 0.195451i
\(498\) −194.048 98.8721i −0.389654 0.198538i
\(499\) 256.074i 0.513175i −0.966521 0.256588i \(-0.917402\pi\)
0.966521 0.256588i \(-0.0825982\pi\)
\(500\) −249.838 + 8.99566i −0.499676 + 0.0179913i
\(501\) −13.2133 −0.0263739
\(502\) −88.1386 + 172.982i −0.175575 + 0.344585i
\(503\) −50.1428 + 316.589i −0.0996874 + 0.629402i 0.886368 + 0.462982i \(0.153221\pi\)
−0.986055 + 0.166419i \(0.946779\pi\)
\(504\) −35.6154 49.0204i −0.0706656 0.0972628i
\(505\) 89.3156 + 78.5006i 0.176863 + 0.155447i
\(506\) −6.30760 4.58274i −0.0124656 0.00905680i
\(507\) 206.874 + 206.874i 0.408036 + 0.408036i
\(508\) −114.169 + 18.0825i −0.224742 + 0.0355956i
\(509\) −189.766 61.6588i −0.372822 0.121137i 0.116612 0.993178i \(-0.462797\pi\)
−0.489434 + 0.872040i \(0.662797\pi\)
\(510\) −282.768 + 112.455i −0.554446 + 0.220499i
\(511\) 313.752 + 965.629i 0.613996 + 1.88968i
\(512\) −20.1612 + 10.2726i −0.0393773 + 0.0200637i
\(513\) 15.7470 + 30.9052i 0.0306958 + 0.0602440i
\(514\) 317.779 103.253i 0.618246 0.200880i
\(515\) −576.469 + 478.379i −1.11936 + 0.928892i
\(516\) −13.9290 + 42.8691i −0.0269942 + 0.0830797i
\(517\) −27.2360 171.962i −0.0526809 0.332614i
\(518\) 84.3404 84.3404i 0.162819 0.162819i
\(519\) −150.449 + 207.075i −0.289883 + 0.398989i
\(520\) 0.388363 4.17641i 0.000746851 0.00803156i
\(521\) −16.9905 + 12.3443i −0.0326114 + 0.0236935i −0.603972 0.797006i \(-0.706416\pi\)
0.571360 + 0.820699i \(0.306416\pi\)
\(522\) −1.06425 0.168560i −0.00203879 0.000322912i
\(523\) −232.641 118.537i −0.444820 0.226647i 0.217209 0.976125i \(-0.430305\pi\)
−0.662030 + 0.749478i \(0.730305\pi\)
\(524\) 474.740i 0.905992i
\(525\) 212.355 + 224.758i 0.404487 + 0.428111i
\(526\) −118.252 −0.224814
\(527\) 441.922 867.320i 0.838561 1.64577i
\(528\) −6.82626 + 43.0993i −0.0129285 + 0.0816275i
\(529\) −310.488 427.350i −0.586934 0.807845i
\(530\) 160.973 + 715.029i 0.303723 + 1.34911i
\(531\) −49.9407 36.2840i −0.0940503 0.0683315i
\(532\) −67.4119 67.4119i −0.126714 0.126714i
\(533\) −12.7257 + 2.01555i −0.0238755 + 0.00378151i
\(534\) −347.501 112.910i −0.650752 0.211442i
\(535\) −62.0764 963.236i −0.116031 1.80044i
\(536\) 78.8033 + 242.532i 0.147021 + 0.452484i
\(537\) −327.001 + 166.615i −0.608940 + 0.310270i
\(538\) −69.0420 135.503i −0.128331 0.251863i
\(539\) 11.9357 3.87814i 0.0221441 0.00719506i
\(540\) 43.9150 + 27.7754i 0.0813240 + 0.0514360i
\(541\) 158.762 488.619i 0.293460 0.903178i −0.690274 0.723548i \(-0.742510\pi\)
0.983734 0.179630i \(-0.0574900\pi\)
\(542\) 31.9834 + 201.935i 0.0590099 + 0.372574i
\(543\) 145.181 145.181i 0.267367 0.267367i
\(544\) 82.6155 113.711i 0.151867 0.209027i
\(545\) 14.6402 + 24.6693i 0.0268628 + 0.0452648i
\(546\) −4.19705 + 3.04934i −0.00768691 + 0.00558487i
\(547\) 774.618 + 122.687i 1.41612 + 0.224291i 0.817125 0.576461i \(-0.195567\pi\)
0.598995 + 0.800752i \(0.295567\pi\)
\(548\) 289.824 + 147.673i 0.528877 + 0.269476i
\(549\) 235.758i 0.429432i
\(550\) 6.31581 222.592i 0.0114833 0.404713i
\(551\) −1.69533 −0.00307683
\(552\) 1.94677 3.82074i 0.00352675 0.00692164i
\(553\) 129.653 818.595i 0.234453 1.48028i
\(554\) 249.492 + 343.397i 0.450347 + 0.619849i
\(555\) −40.4792 + 93.9346i −0.0729354 + 0.169251i
\(556\) −93.9984 68.2939i −0.169062 0.122831i
\(557\) 20.8301 + 20.8301i 0.0373970 + 0.0373970i 0.725558 0.688161i \(-0.241582\pi\)
−0.688161 + 0.725558i \(0.741582\pi\)
\(558\) −164.167 + 26.0015i −0.294207 + 0.0465978i
\(559\) 3.67039 + 1.19258i 0.00656598 + 0.00213342i
\(560\) −138.385 35.3065i −0.247117 0.0630472i
\(561\) −83.7609 257.789i −0.149306 0.459518i
\(562\) −676.101 + 344.491i −1.20303 + 0.612972i
\(563\) −195.419 383.532i −0.347104 0.681230i 0.649779 0.760123i \(-0.274861\pi\)
−0.996883 + 0.0788934i \(0.974861\pi\)
\(564\) 91.0706 29.5906i 0.161473 0.0524657i
\(565\) −218.363 + 855.883i −0.386483 + 1.51484i
\(566\) −37.1913 + 114.463i −0.0657091 + 0.202232i
\(567\) −10.0538 63.4769i −0.0177315 0.111952i
\(568\) −173.915 + 173.915i −0.306189 + 0.306189i
\(569\) −37.6004 + 51.7525i −0.0660816 + 0.0909535i −0.840779 0.541379i \(-0.817902\pi\)
0.774697 + 0.632333i \(0.217902\pi\)
\(570\) 75.0804 + 32.3543i 0.131720 + 0.0567620i
\(571\) 693.696 504.000i 1.21488 0.882662i 0.219215 0.975677i \(-0.429651\pi\)
0.995665 + 0.0930151i \(0.0296505\pi\)
\(572\) 3.69010 + 0.584454i 0.00645122 + 0.00102177i
\(573\) −238.024 121.279i −0.415400 0.211657i
\(574\) 438.704i 0.764292i
\(575\) −7.34969 + 20.6116i −0.0127821 + 0.0358462i
\(576\) −24.0000 −0.0416667
\(577\) 115.347 226.382i 0.199908 0.392342i −0.769189 0.639022i \(-0.779339\pi\)
0.969097 + 0.246679i \(0.0793394\pi\)
\(578\) −72.6429 + 458.649i −0.125680 + 0.793511i
\(579\) 139.267 + 191.684i 0.240530 + 0.331061i
\(580\) −2.18407 + 1.29616i −0.00376564 + 0.00223475i
\(581\) 513.644 + 373.185i 0.884070 + 0.642314i
\(582\) −99.9038 99.9038i −0.171656 0.171656i
\(583\) −644.799 + 102.126i −1.10600 + 0.175173i
\(584\) 382.474 + 124.273i 0.654921 + 0.212797i
\(585\) 2.37809 3.75993i 0.00406511 0.00642723i
\(586\) −32.5020 100.031i −0.0554642 0.170701i
\(587\) 301.069 153.402i 0.512894 0.261333i −0.178333 0.983970i \(-0.557070\pi\)
0.691227 + 0.722637i \(0.257070\pi\)
\(588\) 3.13363 + 6.15010i 0.00532931 + 0.0104594i
\(589\) −248.717 + 80.8130i −0.422270 + 0.137204i
\(590\) −145.198 + 9.35738i −0.246098 + 0.0158600i
\(591\) −67.6774 + 208.290i −0.114513 + 0.352436i
\(592\) −7.39052 46.6619i −0.0124840 0.0788207i
\(593\) −48.5619 + 48.5619i −0.0818919 + 0.0818919i −0.746866 0.664974i \(-0.768442\pi\)
0.664974 + 0.746866i \(0.268442\pi\)
\(594\) −27.2048 + 37.4442i −0.0457993 + 0.0630374i
\(595\) 865.477 194.843i 1.45458 0.327468i
\(596\) 37.7873 27.4541i 0.0634016 0.0460639i
\(597\) 322.319 + 51.0504i 0.539899 + 0.0855115i
\(598\) −0.327126 0.166679i −0.000547034 0.000278728i
\(599\) 661.844i 1.10492i −0.833541 0.552458i \(-0.813690\pi\)
0.833541 0.552458i \(-0.186310\pi\)
\(600\) 121.461 15.7206i 0.202436 0.0262010i
\(601\) 74.9726 0.124746 0.0623732 0.998053i \(-0.480133\pi\)
0.0623732 + 0.998053i \(0.480133\pi\)
\(602\) 59.6572 117.084i 0.0990983 0.194491i
\(603\) −42.3127 + 267.152i −0.0701703 + 0.443038i
\(604\) −229.712 316.171i −0.380318 0.523463i
\(605\) −404.904 37.6519i −0.669263 0.0622345i
\(606\) −47.1283 34.2407i −0.0777695 0.0565029i
\(607\) 306.158 + 306.158i 0.504379 + 0.504379i 0.912796 0.408417i \(-0.133919\pi\)
−0.408417 + 0.912796i \(0.633919\pi\)
\(608\) −37.2961 + 5.90712i −0.0613422 + 0.00971566i
\(609\) 2.98749 + 0.970695i 0.00490557 + 0.00159392i
\(610\) −354.861 427.624i −0.581739 0.701023i
\(611\) −2.53350 7.79732i −0.00414649 0.0127616i
\(612\) 132.831 67.6809i 0.217045 0.110590i
\(613\) 211.737 + 415.557i 0.345411 + 0.677906i 0.996722 0.0809043i \(-0.0257808\pi\)
−0.651311 + 0.758811i \(0.725781\pi\)
\(614\) 256.220 83.2508i 0.417296 0.135588i
\(615\) −139.026 349.582i −0.226059 0.568426i
\(616\) 39.3107 120.986i 0.0638161 0.196406i
\(617\) −141.478 893.256i −0.229300 1.44774i −0.786617 0.617441i \(-0.788169\pi\)
0.557317 0.830300i \(-0.311831\pi\)
\(618\) 259.499 259.499i 0.419901 0.419901i
\(619\) 135.512 186.516i 0.218920 0.301318i −0.685405 0.728162i \(-0.740375\pi\)
0.904325 + 0.426844i \(0.140375\pi\)
\(620\) −258.633 + 294.265i −0.417151 + 0.474621i
\(621\) 3.67960 2.67339i 0.00592529 0.00430497i
\(622\) 150.199 + 23.7891i 0.241477 + 0.0382462i
\(623\) 949.093 + 483.587i 1.52342 + 0.776223i
\(624\) 2.05484i 0.00329302i
\(625\) −604.405 + 159.121i −0.967048 + 0.254593i
\(626\) 680.431 1.08695
\(627\) −33.0602 + 64.8843i −0.0527276 + 0.103484i
\(628\) 67.3835 425.442i 0.107298 0.677456i
\(629\) 172.492 + 237.415i 0.274232 + 0.377448i
\(630\) −113.781 100.003i −0.180604 0.158735i
\(631\) 385.309 + 279.944i 0.610633 + 0.443651i 0.849637 0.527368i \(-0.176821\pi\)
−0.239004 + 0.971019i \(0.576821\pi\)
\(632\) −232.127 232.127i −0.367290 0.367290i
\(633\) −568.795 + 90.0883i −0.898571 + 0.142320i
\(634\) 227.731 + 73.9942i 0.359197 + 0.116710i
\(635\) −268.524 + 106.790i −0.422872 + 0.168173i
\(636\) −110.955 341.485i −0.174458 0.536926i
\(637\) 0.526562 0.268297i 0.000826628 0.000421188i
\(638\) −1.02702 2.01564i −0.00160975 0.00315931i
\(639\) −248.105 + 80.6142i −0.388270 + 0.126157i
\(640\) −43.5318 + 36.1246i −0.0680184 + 0.0564446i
\(641\) 76.8850 236.628i 0.119945 0.369154i −0.873001 0.487718i \(-0.837829\pi\)
0.992946 + 0.118565i \(0.0378293\pi\)
\(642\) 73.9726 + 467.045i 0.115222 + 0.727484i
\(643\) −30.0966 + 30.0966i −0.0468065 + 0.0468065i −0.730123 0.683316i \(-0.760537\pi\)
0.683316 + 0.730123i \(0.260537\pi\)
\(644\) −7.34791 + 10.1135i −0.0114098 + 0.0157042i
\(645\) −10.4338 + 112.204i −0.0161764 + 0.173960i
\(646\) 189.762 137.870i 0.293749 0.213421i
\(647\) −359.915 57.0049i −0.556283 0.0881065i −0.128038 0.991769i \(-0.540868\pi\)
−0.428245 + 0.903663i \(0.640868\pi\)
\(648\) −22.6813 11.5567i −0.0350020 0.0178344i
\(649\) 129.600i 0.199692i
\(650\) −1.34597 10.3993i −0.00207073 0.0159990i
\(651\) 484.557 0.744327
\(652\) 151.788 297.901i 0.232804 0.456903i
\(653\) −176.936 + 1117.13i −0.270958 + 1.71076i 0.358334 + 0.933593i \(0.383345\pi\)
−0.629293 + 0.777169i \(0.716655\pi\)
\(654\) −8.26040 11.3695i −0.0126306 0.0173845i
\(655\) 260.669 + 1157.87i 0.397968 + 1.76774i
\(656\) 140.579 + 102.137i 0.214297 + 0.155696i
\(657\) 301.618 + 301.618i 0.459083 + 0.459083i
\(658\) −275.721 + 43.6699i −0.419029 + 0.0663676i
\(659\) 267.785 + 87.0086i 0.406350 + 0.132031i 0.505058 0.863085i \(-0.331471\pi\)
−0.0987079 + 0.995116i \(0.531471\pi\)
\(660\) 7.01592 + 108.866i 0.0106302 + 0.164948i
\(661\) −224.352 690.484i −0.339413 1.04461i −0.964507 0.264057i \(-0.914939\pi\)
0.625094 0.780549i \(-0.285061\pi\)
\(662\) 19.2388 9.80264i 0.0290616 0.0148076i
\(663\) −5.79473 11.3728i −0.00874017 0.0171535i
\(664\) 239.168 77.7104i 0.360193 0.117034i
\(665\) −201.429 127.400i −0.302901 0.191580i
\(666\) 15.4846 47.6568i 0.0232502 0.0715568i
\(667\) 0.0347761 + 0.219567i 5.21380e−5 + 0.000329186i
\(668\) 10.7886 10.7886i 0.0161507 0.0161507i
\(669\) 130.065 179.019i 0.194417 0.267592i
\(670\) 325.367 + 548.255i 0.485622 + 0.818291i
\(671\) 400.436 290.934i 0.596775 0.433582i
\(672\) 69.1049 + 10.9451i 0.102835 + 0.0162874i
\(673\) 404.407 + 206.056i 0.600902 + 0.306175i 0.727852 0.685734i \(-0.240519\pi\)
−0.126950 + 0.991909i \(0.540519\pi\)
\(674\) 152.491i 0.226247i
\(675\) 122.358 + 43.6304i 0.181271 + 0.0646376i
\(676\) −337.824 −0.499740
\(677\) −249.622 + 489.911i −0.368718 + 0.723650i −0.998592 0.0530473i \(-0.983107\pi\)
0.629874 + 0.776697i \(0.283107\pi\)
\(678\) 67.6933 427.399i 0.0998427 0.630382i
\(679\) 242.099 + 333.221i 0.356553 + 0.490753i
\(680\) 139.060 322.698i 0.204500 0.474555i
\(681\) −362.717 263.530i −0.532625 0.386974i
\(682\) −246.752 246.752i −0.361806 0.361806i
\(683\) −209.895 + 33.2441i −0.307313 + 0.0486736i −0.308186 0.951326i \(-0.599722\pi\)
0.000873363 1.00000i \(0.499722\pi\)
\(684\) −38.0913 12.3766i −0.0556890 0.0180945i
\(685\) 787.953 + 201.032i 1.15030 + 0.293477i
\(686\) 146.696 + 451.483i 0.213842 + 0.658138i
\(687\) 298.828 152.261i 0.434976 0.221631i
\(688\) −23.6295 46.3755i −0.0343452 0.0674062i
\(689\) −29.2374 + 9.49980i −0.0424345 + 0.0137878i
\(690\) 2.65020 10.3876i 0.00384086 0.0150544i
\(691\) −30.0740 + 92.5583i −0.0435225 + 0.133948i −0.970457 0.241276i \(-0.922434\pi\)
0.926934 + 0.375224i \(0.122434\pi\)
\(692\) −46.2352 291.918i −0.0668139 0.421846i
\(693\) 95.4091 95.4091i 0.137675 0.137675i
\(694\) 124.361 171.168i 0.179194 0.246640i
\(695\) −266.757 114.953i −0.383823 0.165401i
\(696\) 1.00658 0.731325i 0.00144624 0.00105075i
\(697\) −1066.08 168.851i −1.52953 0.242254i
\(698\) 439.222 + 223.795i 0.629258 + 0.320623i
\(699\) 772.485i 1.10513i
\(700\) −356.902 10.1267i −0.509860 0.0144667i
\(701\) 821.932 1.17251 0.586257 0.810125i \(-0.300601\pi\)
0.586257 + 0.810125i \(0.300601\pi\)
\(702\) −0.989467 + 1.94194i −0.00140950 + 0.00276629i
\(703\) 12.3334 77.8701i 0.0175440 0.110768i
\(704\) −29.6168 40.7641i −0.0420694 0.0579035i
\(705\) 205.870 122.175i 0.292014 0.173298i
\(706\) 28.5592 + 20.7495i 0.0404521 + 0.0293902i
\(707\) 120.085 + 120.085i 0.169851 + 0.169851i
\(708\) 70.4022 11.1506i 0.0994381 0.0157495i
\(709\) 581.552 + 188.958i 0.820242 + 0.266513i 0.688930 0.724828i \(-0.258081\pi\)
0.131313 + 0.991341i \(0.458081\pi\)
\(710\) −328.679 + 519.665i −0.462928 + 0.731922i
\(711\) −107.597 331.149i −0.151332 0.465751i
\(712\) 375.924 191.543i 0.527984 0.269021i
\(713\) 15.5682 + 30.5543i 0.0218348 + 0.0428532i
\(714\) −413.336 + 134.301i −0.578902 + 0.188097i
\(715\) 9.32090 0.600692i 0.0130362 0.000840128i
\(716\) 130.954 403.036i 0.182897 0.562899i
\(717\) 48.4490 + 305.895i 0.0675718 + 0.426631i
\(718\) 346.124 346.124i 0.482066 0.482066i
\(719\) 122.969 169.253i 0.171028 0.235400i −0.714895 0.699231i \(-0.753526\pi\)
0.885923 + 0.463832i \(0.153526\pi\)
\(720\) −58.5350 + 13.1779i −0.0812986 + 0.0183026i
\(721\) −865.537 + 628.850i −1.20047 + 0.872191i
\(722\) 442.005 + 70.0068i 0.612196 + 0.0969623i
\(723\) 531.631 + 270.879i 0.735313 + 0.374660i
\(724\) 237.079i 0.327457i
\(725\) −4.61517 + 4.36050i −0.00636575 + 0.00601448i
\(726\) 199.217 0.274404
\(727\) −556.990 + 1093.15i −0.766148 + 1.50365i 0.0951014 + 0.995468i \(0.469682\pi\)
−0.861249 + 0.508182i \(0.830318\pi\)
\(728\) 0.937106 5.91665i 0.00128723 0.00812727i
\(729\) −15.8702 21.8435i −0.0217698 0.0299636i
\(730\) 1001.07 + 93.0894i 1.37133 + 0.127520i
\(731\) 261.561 + 190.035i 0.357813 + 0.259966i
\(732\) 192.496 + 192.496i 0.262972 + 0.262972i
\(733\) 665.814 105.455i 0.908341 0.143867i 0.315256 0.949007i \(-0.397910\pi\)
0.593085 + 0.805140i \(0.297910\pi\)
\(734\) −912.402 296.457i −1.24305 0.403893i
\(735\) 11.0197 + 13.2792i 0.0149928 + 0.0180670i
\(736\) 1.53010 + 4.70915i 0.00207894 + 0.00639831i
\(737\) −505.974 + 257.806i −0.686531 + 0.349805i
\(738\) 83.6731 + 164.218i 0.113378 + 0.222517i
\(739\) −387.790 + 126.001i −0.524750 + 0.170502i −0.559400 0.828898i \(-0.688968\pi\)
0.0346499 + 0.999400i \(0.488968\pi\)
\(740\) −43.6461 109.748i −0.0589813 0.148309i
\(741\) −1.05967 + 3.26132i −0.00143005 + 0.00440124i
\(742\) 163.748 + 1033.86i 0.220684 + 1.39335i
\(743\) −125.226 + 125.226i −0.168541 + 0.168541i −0.786338 0.617797i \(-0.788025\pi\)
0.617797 + 0.786338i \(0.288025\pi\)
\(744\) 112.812 155.272i 0.151629 0.208699i
\(745\) 77.0873 87.7076i 0.103473 0.117728i
\(746\) −155.783 + 113.183i −0.208825 + 0.151720i
\(747\) 263.447 + 41.7259i 0.352673 + 0.0558579i
\(748\) 278.875 + 142.094i 0.372827 + 0.189965i
\(749\) 1378.53i 1.84049i
\(750\) 287.607 105.034i 0.383476 0.140045i
\(751\) −1206.41 −1.60641 −0.803205 0.595703i \(-0.796873\pi\)
−0.803205 + 0.595703i \(0.796873\pi\)
\(752\) −50.1982 + 98.5195i −0.0667529 + 0.131010i
\(753\) 37.1961 234.847i 0.0493972 0.311882i
\(754\) −0.0626149 0.0861821i −8.30437e−5 0.000114300i
\(755\) −733.860 644.999i −0.972001 0.854303i
\(756\) 60.0375 + 43.6198i 0.0794147 + 0.0576982i
\(757\) −146.809 146.809i −0.193935 0.193935i 0.603459 0.797394i \(-0.293789\pi\)
−0.797394 + 0.603459i \(0.793789\pi\)
\(758\) −328.599 + 52.0449i −0.433508 + 0.0686609i
\(759\) 9.08152 + 2.95076i 0.0119651 + 0.00388770i
\(760\) −87.7201 + 34.8857i −0.115421 + 0.0459022i
\(761\) −283.523 872.594i −0.372566 1.14664i −0.945106 0.326764i \(-0.894042\pi\)
0.572539 0.819877i \(-0.305958\pi\)
\(762\) 126.140 64.2717i 0.165538 0.0843460i
\(763\) 18.5997 + 36.5040i 0.0243771 + 0.0478428i
\(764\) 293.370 95.3216i 0.383992 0.124767i
\(765\) 286.808 238.006i 0.374912 0.311118i
\(766\) −200.241 + 616.280i −0.261412 + 0.804542i
\(767\) −0.954698 6.02772i −0.00124472 0.00785883i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) −416.092 + 572.701i −0.541082 + 0.744735i −0.988768 0.149456i \(-0.952248\pi\)
0.447687 + 0.894190i \(0.352248\pi\)
\(770\) 29.4465 316.664i 0.0382422 0.411252i
\(771\) −331.071 + 240.537i −0.429405 + 0.311981i
\(772\) −270.221 42.7987i −0.350027 0.0554388i
\(773\) 65.7837 + 33.5185i 0.0851019 + 0.0433616i 0.496023 0.868309i \(-0.334793\pi\)
−0.410922 + 0.911671i \(0.634793\pi\)
\(774\) 55.2057i 0.0713252i
\(775\) −469.221 + 859.710i −0.605447 + 1.10930i
\(776\) 163.142 0.210235
\(777\) −66.3198 + 130.160i −0.0853536 + 0.167516i
\(778\) 3.79764 23.9773i 0.00488128 0.0308192i
\(779\) 170.447 + 234.600i 0.218803 + 0.301156i
\(780\) 1.12827 + 5.01167i 0.00144650 + 0.00642522i
\(781\) −443.093 321.926i −0.567341 0.412197i
\(782\) −21.7485 21.7485i −0.0278114 0.0278114i
\(783\) 1.30343 0.206443i 0.00166466 0.000263657i
\(784\) −7.58014 2.46294i −0.00966855 0.00314150i
\(785\) −69.2556 1074.63i −0.0882237 1.36896i
\(786\) −179.673 552.978i −0.228592 0.703534i
\(787\) −642.057 + 327.145i −0.815829 + 0.415686i −0.811534 0.584305i \(-0.801367\pi\)
−0.00429491 + 0.999991i \(0.501367\pi\)
\(788\) −114.809 225.326i −0.145697 0.285947i
\(789\) 137.740 44.7544i 0.174575 0.0567230i
\(790\) −693.604 438.692i −0.877980 0.555307i
\(791\) −389.828 + 1199.77i −0.492830 + 1.51677i
\(792\) −8.36043 52.7857i −0.0105561 0.0666486i
\(793\) 16.4812 16.4812i 0.0207833 0.0207833i
\(794\) 474.569 653.189i 0.597694 0.822656i
\(795\) −458.116 771.944i −0.576247 0.970998i
\(796\) −304.855 + 221.490i −0.382984 + 0.278254i
\(797\) −1115.33 176.651i −1.39941 0.221645i −0.589296 0.807917i \(-0.700595\pi\)
−0.810114 + 0.586273i \(0.800595\pi\)
\(798\) 104.035 + 53.0083i 0.130369 + 0.0664265i
\(799\) 686.830i 0.859612i
\(800\) −86.3370 + 112.009i −0.107921 + 0.140011i
\(801\) 447.503 0.558680
\(802\) 249.411 489.497i 0.310986 0.610345i
\(803\) −140.092 + 884.505i −0.174461 + 1.10150i
\(804\) −183.580 252.677i −0.228334 0.314274i
\(805\) −12.3681 + 28.7010i −0.0153641 + 0.0356535i
\(806\) −13.2942 9.65877i −0.0164940 0.0119836i
\(807\) 131.703 + 131.703i 0.163201 + 0.163201i
\(808\) 66.4376 10.5227i 0.0822247 0.0130231i
\(809\) −818.752 266.029i −1.01205 0.328836i −0.244382 0.969679i \(-0.578585\pi\)
−0.767672 + 0.640843i \(0.778585\pi\)
\(810\) −61.6643 15.7325i −0.0761288 0.0194229i
\(811\) 431.556 + 1328.19i 0.532128 + 1.63772i 0.749775 + 0.661693i \(0.230162\pi\)
−0.217647 + 0.976028i \(0.569838\pi\)
\(812\) −3.23185 + 1.64671i −0.00398011 + 0.00202797i
\(813\) −113.680 223.110i −0.139828 0.274427i
\(814\) 100.054 32.5095i 0.122916 0.0399379i
\(815\) 206.634 809.911i 0.253539 0.993756i
\(816\) −53.1950 + 163.717i −0.0651900 + 0.200634i
\(817\) −13.5878 85.7898i −0.0166313 0.105006i
\(818\) −147.122 + 147.122i −0.179856 + 0.179856i
\(819\) 3.73466 5.14032i 0.00456003 0.00627634i
\(820\) 398.947 + 171.918i 0.486521 + 0.209656i
\(821\) −750.416 + 545.209i −0.914027 + 0.664080i −0.942030 0.335528i \(-0.891085\pi\)
0.0280029 + 0.999608i \(0.491085\pi\)
\(822\) −393.477 62.3207i −0.478683 0.0758159i
\(823\) −1222.48 622.885i −1.48540 0.756847i −0.491893 0.870656i \(-0.663695\pi\)
−0.993503 + 0.113809i \(0.963695\pi\)
\(824\) 423.760i 0.514272i
\(825\) 76.8872 + 261.666i 0.0931966 + 0.317171i
\(826\) −207.799 −0.251573
\(827\) 387.229 759.981i 0.468234 0.918961i −0.529277 0.848449i \(-0.677537\pi\)
0.997511 0.0705117i \(-0.0224632\pi\)
\(828\) −0.821571 + 5.18720i −0.000992236 + 0.00626473i
\(829\) −83.7870 115.323i −0.101070 0.139111i 0.755486 0.655164i \(-0.227401\pi\)
−0.856556 + 0.516053i \(0.827401\pi\)
\(830\) 540.651 320.854i 0.651387 0.386571i
\(831\) −420.573 305.564i −0.506105 0.367707i
\(832\) −1.67777 1.67777i −0.00201655 0.00201655i
\(833\) 48.8989 7.74482i 0.0587022 0.00929751i
\(834\) 135.337 + 43.9735i 0.162274 + 0.0527260i
\(835\) 20.3892 32.2369i 0.0244183 0.0386070i
\(836\) −25.9843 79.9714i −0.0310817 0.0956596i
\(837\) 181.382 92.4186i 0.216704 0.110416i
\(838\) 439.455 + 862.480i 0.524410 + 1.02921i
\(839\) 1354.47 440.096i 1.61439 0.524548i 0.643783 0.765208i \(-0.277364\pi\)
0.970609 + 0.240661i \(0.0773641\pi\)
\(840\) 174.554 11.2492i 0.207802 0.0133919i
\(841\) 259.863 799.777i 0.308993 0.950984i
\(842\) −4.49035 28.3510i −0.00533296 0.0336710i
\(843\) 657.145 657.145i 0.779531 0.779531i
\(844\) 390.863 537.976i 0.463107 0.637413i
\(845\) −823.939 + 185.492i −0.975075 + 0.219517i
\(846\) −94.8801 + 68.9344i −0.112151 + 0.0814828i
\(847\) −573.621 90.8527i −0.677239 0.107264i
\(848\) 369.416 + 188.227i 0.435632 + 0.221965i
\(849\) 147.403i 0.173619i
\(850\) 161.975 863.400i 0.190559 1.01577i
\(851\) −10.3382 −0.0121483
\(852\) 136.756 268.398i 0.160511 0.315021i
\(853\) 152.941 965.629i 0.179297 1.13204i −0.719765 0.694218i \(-0.755750\pi\)
0.899062 0.437821i \(-0.144250\pi\)
\(854\) −466.480 642.054i −0.546229 0.751820i
\(855\) −99.6988 9.27095i −0.116607 0.0108432i
\(856\) −441.739 320.942i −0.516050 0.374932i
\(857\) 66.5667 + 66.5667i 0.0776742 + 0.0776742i 0.744877 0.667202i \(-0.232508\pi\)
−0.667202 + 0.744877i \(0.732508\pi\)
\(858\) −4.51943 + 0.715807i −0.00526740 + 0.000834274i
\(859\) 1157.43 + 376.073i 1.34742 + 0.437803i 0.891824 0.452383i \(-0.149426\pi\)
0.455597 + 0.890186i \(0.349426\pi\)
\(860\) −83.0951 100.133i −0.0966222 0.116434i
\(861\) −166.035 511.003i −0.192840 0.593499i
\(862\) 264.853 134.949i 0.307254 0.156554i
\(863\) −1.25863 2.47021i −0.00145844 0.00286235i 0.890276 0.455421i \(-0.150511\pi\)
−0.891735 + 0.452559i \(0.850511\pi\)
\(864\) 27.9552 9.08321i 0.0323556 0.0105130i
\(865\) −273.051 686.588i −0.315666 0.793743i
\(866\) 123.348 379.626i 0.142434 0.438368i
\(867\) −88.9691 561.729i −0.102617 0.647899i
\(868\) −395.639 + 395.639i −0.455805 + 0.455805i
\(869\) 429.679 591.403i 0.494453 0.680556i
\(870\) 2.05346 2.33636i 0.00236030 0.00268548i
\(871\) −21.6338 + 15.7179i −0.0248379 + 0.0180458i
\(872\) 16.0277 + 2.53854i 0.0183804 + 0.00291117i
\(873\) 154.178 + 78.5578i 0.176608 + 0.0899861i
\(874\) 8.26313i 0.00945439i
\(875\) −876.028 + 171.268i −1.00118 + 0.195735i
\(876\) −492.539 −0.562260
\(877\) −602.080 + 1181.65i −0.686522 + 1.34738i 0.239866 + 0.970806i \(0.422896\pi\)
−0.926388 + 0.376569i \(0.877104\pi\)
\(878\) −120.645 + 761.724i −0.137409 + 0.867567i
\(879\) 75.7168 + 104.215i 0.0861397 + 0.118561i
\(880\) −94.6169 83.1599i −0.107519 0.0944999i
\(881\) 867.310 + 630.137i 0.984460 + 0.715252i 0.958701 0.284416i \(-0.0917996\pi\)
0.0257594 + 0.999668i \(0.491800\pi\)
\(882\) −5.97767 5.97767i −0.00677741 0.00677741i
\(883\) 1076.71 170.534i 1.21937 0.193130i 0.486615 0.873617i \(-0.338232\pi\)
0.732760 + 0.680487i \(0.238232\pi\)
\(884\) 14.0172 + 4.55447i 0.0158566 + 0.00515212i
\(885\) 165.585 65.8521i 0.187102 0.0744092i
\(886\) 179.109 + 551.241i 0.202155 + 0.622168i
\(887\) 927.623 472.647i 1.04580 0.532861i 0.155309 0.987866i \(-0.450363\pi\)
0.890489 + 0.455005i \(0.150363\pi\)
\(888\) 26.2685 + 51.5548i 0.0295816 + 0.0580572i
\(889\) −392.516 + 127.536i −0.441525 + 0.143460i
\(890\) 811.691 673.577i 0.912013 0.756828i
\(891\) 17.5168 53.9112i 0.0196597 0.0605064i
\(892\) 39.9709 + 252.366i 0.0448104 + 0.282922i
\(893\) −130.477 + 130.477i −0.146111 + 0.146111i
\(894\) −33.6243 + 46.2798i −0.0376110 + 0.0517672i
\(895\) 98.0939 1054.89i 0.109602 1.17865i
\(896\) −65.3606 + 47.4873i −0.0729471 + 0.0529992i
\(897\) 0.444120 + 0.0703416i 0.000495117 + 7.84188e-5i
\(898\) −769.762 392.214i −0.857196 0.436763i
\(899\) 9.94986i 0.0110677i
\(900\) −135.529 + 64.2805i −0.150587 + 0.0714228i
\(901\) −2575.39 −2.85836
\(902\) −175.669 + 344.769i −0.194755 + 0.382228i
\(903\) −25.1764 + 158.958i −0.0278809 + 0.176033i
\(904\) 293.698 + 404.241i 0.324888 + 0.447169i
\(905\) 130.175 + 578.225i 0.143839 + 0.638923i
\(906\) 387.229 + 281.339i 0.427405 + 0.310528i
\(907\) 634.145 + 634.145i 0.699168 + 0.699168i 0.964231 0.265063i \(-0.0853929\pi\)
−0.265063 + 0.964231i \(0.585393\pi\)
\(908\) 511.328 80.9865i 0.563137 0.0891922i
\(909\) 67.8541 + 22.0471i 0.0746470 + 0.0242543i
\(910\) −0.963141 14.9450i −0.00105840 0.0164231i
\(911\) −211.111 649.731i −0.231735 0.713207i −0.997538 0.0701314i \(-0.977658\pi\)
0.765803 0.643075i \(-0.222342\pi\)
\(912\) 41.2069 20.9960i 0.0451830 0.0230219i
\(913\) 254.231 + 498.956i 0.278457 + 0.546502i
\(914\) −132.357 + 43.0055i −0.144811 + 0.0470520i
\(915\) 575.184 + 363.794i 0.628616 + 0.397589i
\(916\) −119.672 + 368.313i −0.130646 + 0.402088i
\(917\) 265.162 + 1674.17i 0.289163 + 1.82570i
\(918\) −129.107 + 129.107i −0.140639 + 0.140639i
\(919\) 165.840 228.259i 0.180457 0.248377i −0.709200 0.705007i \(-0.750944\pi\)
0.889657 + 0.456630i \(0.150944\pi\)
\(920\) 6.31753 + 10.6453i 0.00686688 + 0.0115710i
\(921\) −266.937 + 193.941i −0.289834 + 0.210577i
\(922\) −284.844 45.1148i −0.308941 0.0489315i
\(923\) −22.9798 11.7088i −0.0248969 0.0126856i
\(924\) 155.802i 0.168617i
\(925\) −166.711 243.706i −0.180229 0.263466i
\(926\) −1133.14 −1.22370
\(927\) −204.053 + 400.476i −0.220122 + 0.432013i
\(928\) −0.224747 + 1.41900i −0.000242184 + 0.00152909i
\(929\) 614.668 + 846.018i 0.661645 + 0.910676i 0.999534 0.0305100i \(-0.00971314\pi\)
−0.337890 + 0.941186i \(0.609713\pi\)
\(930\) 189.887 440.645i 0.204179 0.473812i
\(931\) −10.7606 7.81804i −0.0115581 0.00839747i
\(932\) −630.731 630.731i −0.676750 0.676750i
\(933\) −183.955 + 29.1356i −0.197165 + 0.0312279i
\(934\) −971.757 315.743i −1.04042 0.338054i
\(935\) 758.184 + 193.437i 0.810892 + 0.206884i
\(936\) −0.777690 2.39348i −0.000830865 0.00255714i
\(937\) 948.239 483.152i 1.01199 0.515637i 0.132317 0.991207i \(-0.457758\pi\)
0.879677 + 0.475571i \(0.157758\pi\)
\(938\) 413.363 + 811.271i 0.440686 + 0.864895i
\(939\) −792.567 + 257.521i −0.844055 + 0.274250i
\(940\) −68.3364 + 267.848i −0.0726983 + 0.284944i
\(941\) −104.126 + 320.466i −0.110654 + 0.340559i −0.991016 0.133744i \(-0.957300\pi\)
0.880362 + 0.474303i \(0.157300\pi\)
\(942\) 82.5275 + 521.058i 0.0876089 + 0.553141i
\(943\) 26.8874 26.8874i 0.0285127 0.0285127i
\(944\) −48.3787 + 66.5876i −0.0512486 + 0.0705377i
\(945\) 170.380 + 73.4216i 0.180296 + 0.0776948i
\(946\) 93.7670 68.1257i 0.0991195 0.0720145i
\(947\) −535.886 84.8760i −0.565877 0.0896262i −0.133060 0.991108i \(-0.542480\pi\)
−0.432817 + 0.901482i \(0.642480\pi\)
\(948\) 358.234 + 182.530i 0.377884 + 0.192542i
\(949\) 42.1704i 0.0444367i
\(950\) −194.791 + 133.250i −0.205043 + 0.140263i
\(951\) −293.266 −0.308376
\(952\) 227.831 447.144i 0.239319 0.469689i
\(953\) −0.852072 + 5.37977i −0.000894095 + 0.00564509i −0.988131 0.153611i \(-0.950910\pi\)
0.987237 + 0.159256i \(0.0509096\pi\)
\(954\) 258.481 + 355.769i 0.270945 + 0.372924i
\(955\) 663.178 393.568i 0.694427 0.412113i
\(956\) −289.320 210.204i −0.302636 0.219878i
\(957\) 1.95912 + 1.95912i 0.00204715 + 0.00204715i
\(958\) 19.9572 3.16091i 0.0208322 0.00329949i
\(959\) 1104.55 + 358.889i 1.15177 + 0.374232i
\(960\) 37.0339 58.5533i 0.0385770 0.0609930i
\(961\) 177.324 + 545.747i 0.184520 + 0.567895i
\(962\) 4.41404 2.24906i 0.00458840 0.00233790i
\(963\) −262.924 516.018i −0.273026 0.535844i
\(964\) −655.247 + 212.903i −0.679717 + 0.220853i
\(965\) −682.556 + 43.9878i −0.707312 + 0.0455832i
\(966\) 4.73122 14.5612i 0.00489774 0.0150737i
\(967\) 210.889 + 1331.50i 0.218086 + 1.37694i 0.817237 + 0.576302i \(0.195505\pi\)
−0.599151 + 0.800636i \(0.704495\pi\)
\(968\) −162.660 + 162.660i −0.168038 + 0.168038i
\(969\) −168.856 + 232.410i −0.174258 + 0.239845i
\(970\) 397.897 89.5778i 0.410203 0.0923482i
\(971\) 1017.36 739.156i 1.04775 0.761231i 0.0759629 0.997111i \(-0.475797\pi\)
0.971782 + 0.235879i \(0.0757970\pi\)
\(972\) 30.7931 + 4.87714i 0.0316801 + 0.00501764i
\(973\) −369.630 188.336i −0.379887 0.193562i
\(974\) 642.091i 0.659231i
\(975\) 5.50360 + 11.6037i 0.00564471 + 0.0119013i
\(976\) −314.344 −0.322074
\(977\) −480.686 + 943.399i −0.492002 + 0.965608i 0.502860 + 0.864368i \(0.332281\pi\)
−0.994862 + 0.101240i \(0.967719\pi\)
\(978\) −64.0573 + 404.442i −0.0654983 + 0.413540i
\(979\) 552.234 + 760.085i 0.564080 + 0.776389i
\(980\) −19.8400 1.84491i −0.0202449 0.00188256i
\(981\) 13.9247 + 10.1169i 0.0141944 + 0.0103128i
\(982\) 9.51031 + 9.51031i 0.00968463 + 0.00968463i
\(983\) 1170.76 185.431i 1.19101 0.188638i 0.470703 0.882292i \(-0.344000\pi\)
0.720309 + 0.693654i \(0.244000\pi\)
\(984\) −202.402 65.7644i −0.205693 0.0668337i
\(985\) −403.737 486.522i −0.409885 0.493931i
\(986\) −2.75773 8.48742i −0.00279689 0.00860793i
\(987\) 304.633 155.218i 0.308645 0.157262i
\(988\) −1.79764 3.52807i −0.00181947 0.00357092i
\(989\) −10.8322 + 3.51958i −0.0109526 + 0.00355873i
\(990\) −49.3742 124.152i −0.0498729 0.125406i
\(991\) 27.3216 84.0873i 0.0275698 0.0848510i −0.936325 0.351135i \(-0.885796\pi\)
0.963895 + 0.266284i \(0.0857959\pi\)
\(992\) 34.6687 + 218.890i 0.0349483 + 0.220655i
\(993\) −18.6994 + 18.6994i −0.0188312 + 0.0188312i
\(994\) −516.172 + 710.450i −0.519288 + 0.714739i
\(995\) −621.914 + 707.595i −0.625039 + 0.711150i
\(996\) −249.172 + 181.034i −0.250173 + 0.181761i
\(997\) 652.213 + 103.300i 0.654176 + 0.103611i 0.474695 0.880150i \(-0.342558\pi\)
0.179480 + 0.983762i \(0.442558\pi\)
\(998\) −322.673 164.410i −0.323319 0.164739i
\(999\) 61.3711i 0.0614326i
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 150.3.k.a.67.1 32
25.3 odd 20 inner 150.3.k.a.103.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.k.a.67.1 32 1.1 even 1 trivial
150.3.k.a.103.1 yes 32 25.3 odd 20 inner