Properties

Label 175.2.x.a.33.18
Level $175$
Weight $2$
Character 175.33
Analytic conductor $1.397$
Analytic rank $0$
Dimension $288$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(3,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([21, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.x (of order \(60\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 33.18
Character \(\chi\) \(=\) 175.33
Dual form 175.2.x.a.122.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.03786 - 1.32340i) q^{2} +(-2.14641 + 0.823930i) q^{3} +(1.58801 - 3.56673i) q^{4} +(-0.304662 - 2.21522i) q^{5} +(-3.28370 + 4.51962i) q^{6} +(2.14884 - 1.54352i) q^{7} +(-0.723845 - 4.57018i) q^{8} +(1.69878 - 1.52959i) q^{9} +O(q^{10})\) \(q+(2.03786 - 1.32340i) q^{2} +(-2.14641 + 0.823930i) q^{3} +(1.58801 - 3.56673i) q^{4} +(-0.304662 - 2.21522i) q^{5} +(-3.28370 + 4.51962i) q^{6} +(2.14884 - 1.54352i) q^{7} +(-0.723845 - 4.57018i) q^{8} +(1.69878 - 1.52959i) q^{9} +(-3.55248 - 4.11111i) q^{10} +(0.0112005 - 0.0124395i) q^{11} +(-0.469788 + 8.96408i) q^{12} +(1.39124 + 2.73047i) q^{13} +(2.33634 - 5.98928i) q^{14} +(2.47911 + 4.50374i) q^{15} +(-2.29834 - 2.55257i) q^{16} +(-5.48928 + 4.44513i) q^{17} +(1.43762 - 5.36527i) q^{18} +(2.90112 - 1.29166i) q^{19} +(-8.38489 - 2.43114i) q^{20} +(-3.34055 + 5.08353i) q^{21} +(0.00636273 - 0.0401727i) q^{22} +(2.98285 + 4.59318i) q^{23} +(5.31918 + 9.21308i) q^{24} +(-4.81436 + 1.34978i) q^{25} +(6.44868 + 3.72315i) q^{26} +(0.745322 - 1.46278i) q^{27} +(-2.09295 - 10.1155i) q^{28} +(-0.0353871 - 0.0487062i) q^{29} +(11.0124 + 5.89714i) q^{30} +(8.96709 + 0.942479i) q^{31} +(0.877177 + 0.235039i) q^{32} +(-0.0137917 + 0.0359286i) q^{33} +(-5.30369 + 16.3231i) q^{34} +(-4.07391 - 4.28990i) q^{35} +(-2.75796 - 8.48811i) q^{36} +(-8.39052 - 0.439728i) q^{37} +(4.20270 - 6.47159i) q^{38} +(-5.23590 - 4.71442i) q^{39} +(-9.90340 + 2.99583i) q^{40} +(-5.83738 - 1.89668i) q^{41} +(-0.0800095 + 14.7804i) q^{42} +(-3.18681 - 3.18681i) q^{43} +(-0.0265816 - 0.0597034i) q^{44} +(-3.90593 - 3.29716i) q^{45} +(12.1573 + 5.41276i) q^{46} +(-2.89679 + 3.57724i) q^{47} +(7.03633 + 3.58519i) q^{48} +(2.23507 - 6.63359i) q^{49} +(-8.02470 + 9.12201i) q^{50} +(8.11977 - 14.0639i) q^{51} +(11.9482 - 0.626178i) q^{52} +(1.55951 + 4.06266i) q^{53} +(-0.416980 - 3.96730i) q^{54} +(-0.0309685 - 0.0210218i) q^{55} +(-8.60961 - 8.70333i) q^{56} +(-5.16276 + 5.16276i) q^{57} +(-0.136572 - 0.0524250i) q^{58} +(2.45075 - 0.520924i) q^{59} +(20.0005 - 1.69033i) q^{60} +(2.77436 - 13.0523i) q^{61} +(19.5210 - 9.94643i) q^{62} +(1.28946 - 5.90896i) q^{63} +(8.63203 - 2.80472i) q^{64} +(5.62472 - 3.91378i) q^{65} +(0.0194425 + 0.0914696i) q^{66} +(0.200158 + 0.247175i) q^{67} +(7.13755 + 26.6377i) q^{68} +(-10.1869 - 7.40119i) q^{69} +(-13.9793 - 3.35080i) q^{70} +(-6.35569 + 4.61768i) q^{71} +(-8.22016 - 6.65655i) q^{72} +(0.174974 + 3.33870i) q^{73} +(-17.6807 + 10.2079i) q^{74} +(9.22147 - 6.86389i) q^{75} -12.3987i q^{76} +(0.00486761 - 0.0440188i) q^{77} +(-16.9091 - 2.67814i) q^{78} +(-5.32825 + 0.560021i) q^{79} +(-4.95427 + 5.86900i) q^{80} +(-1.11138 + 10.5741i) q^{81} +(-14.4058 + 3.86003i) q^{82} +(-8.63403 + 1.36750i) q^{83} +(12.8268 + 19.9876i) q^{84} +(11.5193 + 10.8057i) q^{85} +(-10.7117 - 2.27684i) q^{86} +(0.116086 + 0.0753869i) q^{87} +(-0.0649580 - 0.0421842i) q^{88} +(8.18738 + 1.74028i) q^{89} +(-12.3232 - 1.55004i) q^{90} +(7.20412 + 3.71994i) q^{91} +(21.1194 - 3.34499i) q^{92} +(-20.0236 + 5.36531i) q^{93} +(-1.16913 + 11.1236i) q^{94} +(-3.74518 - 6.03309i) q^{95} +(-2.07644 + 0.218242i) q^{96} +(-6.79613 - 1.07640i) q^{97} +(-4.22415 - 16.4762i) q^{98} -0.0382642i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.03786 1.32340i 1.44099 0.935787i 0.441733 0.897147i \(-0.354364\pi\)
0.999253 0.0386405i \(-0.0123027\pi\)
\(3\) −2.14641 + 0.823930i −1.23923 + 0.475696i −0.887675 0.460471i \(-0.847681\pi\)
−0.351556 + 0.936167i \(0.614347\pi\)
\(4\) 1.58801 3.56673i 0.794006 1.78337i
\(5\) −0.304662 2.21522i −0.136249 0.990675i
\(6\) −3.28370 + 4.51962i −1.34056 + 1.84513i
\(7\) 2.14884 1.54352i 0.812187 0.583397i
\(8\) −0.723845 4.57018i −0.255918 1.61580i
\(9\) 1.69878 1.52959i 0.566261 0.509864i
\(10\) −3.55248 4.11111i −1.12339 1.30005i
\(11\) 0.0112005 0.0124395i 0.00337709 0.00375064i −0.741454 0.671004i \(-0.765863\pi\)
0.744831 + 0.667253i \(0.232530\pi\)
\(12\) −0.469788 + 8.96408i −0.135616 + 2.58771i
\(13\) 1.39124 + 2.73047i 0.385862 + 0.757297i 0.999478 0.0323079i \(-0.0102857\pi\)
−0.613616 + 0.789605i \(0.710286\pi\)
\(14\) 2.33634 5.98928i 0.624414 1.60070i
\(15\) 2.47911 + 4.50374i 0.640104 + 1.16286i
\(16\) −2.29834 2.55257i −0.574586 0.638142i
\(17\) −5.48928 + 4.44513i −1.33135 + 1.07810i −0.340914 + 0.940094i \(0.610737\pi\)
−0.990431 + 0.138008i \(0.955930\pi\)
\(18\) 1.43762 5.36527i 0.338850 1.26461i
\(19\) 2.90112 1.29166i 0.665563 0.296328i −0.0460087 0.998941i \(-0.514650\pi\)
0.711572 + 0.702613i \(0.247984\pi\)
\(20\) −8.38489 2.43114i −1.87492 0.543620i
\(21\) −3.34055 + 5.08353i −0.728967 + 1.10932i
\(22\) 0.00636273 0.0401727i 0.00135654 0.00856485i
\(23\) 2.98285 + 4.59318i 0.621966 + 0.957744i 0.999496 + 0.0317465i \(0.0101069\pi\)
−0.377530 + 0.925997i \(0.623226\pi\)
\(24\) 5.31918 + 9.21308i 1.08577 + 1.88061i
\(25\) −4.81436 + 1.34978i −0.962872 + 0.269957i
\(26\) 6.44868 + 3.72315i 1.26469 + 0.730169i
\(27\) 0.745322 1.46278i 0.143437 0.281512i
\(28\) −2.09295 10.1155i −0.395530 1.91165i
\(29\) −0.0353871 0.0487062i −0.00657122 0.00904451i 0.805719 0.592298i \(-0.201779\pi\)
−0.812290 + 0.583254i \(0.801779\pi\)
\(30\) 11.0124 + 5.89714i 2.01057 + 1.07667i
\(31\) 8.96709 + 0.942479i 1.61054 + 0.169274i 0.866610 0.498986i \(-0.166294\pi\)
0.743927 + 0.668260i \(0.232961\pi\)
\(32\) 0.877177 + 0.235039i 0.155065 + 0.0415494i
\(33\) −0.0137917 + 0.0359286i −0.00240083 + 0.00625437i
\(34\) −5.30369 + 16.3231i −0.909576 + 2.79939i
\(35\) −4.07391 4.28990i −0.688617 0.725126i
\(36\) −2.75796 8.48811i −0.459659 1.41469i
\(37\) −8.39052 0.439728i −1.37939 0.0722909i −0.651847 0.758350i \(-0.726006\pi\)
−0.727546 + 0.686059i \(0.759339\pi\)
\(38\) 4.20270 6.47159i 0.681768 1.04983i
\(39\) −5.23590 4.71442i −0.838415 0.754912i
\(40\) −9.90340 + 2.99583i −1.56587 + 0.473683i
\(41\) −5.83738 1.89668i −0.911646 0.296212i −0.184610 0.982812i \(-0.559102\pi\)
−0.727035 + 0.686600i \(0.759102\pi\)
\(42\) −0.0800095 + 14.7804i −0.0123457 + 2.28067i
\(43\) −3.18681 3.18681i −0.485984 0.485984i 0.421052 0.907036i \(-0.361661\pi\)
−0.907036 + 0.421052i \(0.861661\pi\)
\(44\) −0.0265816 0.0597034i −0.00400733 0.00900062i
\(45\) −3.90593 3.29716i −0.582261 0.491512i
\(46\) 12.1573 + 5.41276i 1.79249 + 0.798068i
\(47\) −2.89679 + 3.57724i −0.422541 + 0.521794i −0.943314 0.331900i \(-0.892310\pi\)
0.520774 + 0.853695i \(0.325644\pi\)
\(48\) 7.03633 + 3.58519i 1.01561 + 0.517477i
\(49\) 2.23507 6.63359i 0.319295 0.947655i
\(50\) −8.02470 + 9.12201i −1.13486 + 1.29005i
\(51\) 8.11977 14.0639i 1.13700 1.96933i
\(52\) 11.9482 0.626178i 1.65691 0.0868352i
\(53\) 1.55951 + 4.06266i 0.214215 + 0.558050i 0.998016 0.0629629i \(-0.0200550\pi\)
−0.783801 + 0.621012i \(0.786722\pi\)
\(54\) −0.416980 3.96730i −0.0567438 0.539881i
\(55\) −0.0309685 0.0210218i −0.00417579 0.00283458i
\(56\) −8.60961 8.70333i −1.15051 1.16303i
\(57\) −5.16276 + 5.16276i −0.683825 + 0.683825i
\(58\) −0.136572 0.0524250i −0.0179328 0.00688374i
\(59\) 2.45075 0.520924i 0.319061 0.0678185i −0.0455974 0.998960i \(-0.514519\pi\)
0.364658 + 0.931141i \(0.381186\pi\)
\(60\) 20.0005 1.69033i 2.58205 0.218221i
\(61\) 2.77436 13.0523i 0.355221 1.67118i −0.330878 0.943674i \(-0.607345\pi\)
0.686099 0.727509i \(-0.259322\pi\)
\(62\) 19.5210 9.94643i 2.47917 1.26320i
\(63\) 1.28946 5.90896i 0.162457 0.744460i
\(64\) 8.63203 2.80472i 1.07900 0.350590i
\(65\) 5.62472 3.91378i 0.697661 0.485444i
\(66\) 0.0194425 + 0.0914696i 0.00239320 + 0.0112591i
\(67\) 0.200158 + 0.247175i 0.0244532 + 0.0301972i 0.789226 0.614103i \(-0.210482\pi\)
−0.764773 + 0.644300i \(0.777149\pi\)
\(68\) 7.13755 + 26.6377i 0.865556 + 3.23030i
\(69\) −10.1869 7.40119i −1.22635 0.890999i
\(70\) −13.9793 3.35080i −1.67085 0.400497i
\(71\) −6.35569 + 4.61768i −0.754282 + 0.548018i −0.897151 0.441724i \(-0.854367\pi\)
0.142869 + 0.989742i \(0.454367\pi\)
\(72\) −8.22016 6.65655i −0.968755 0.784482i
\(73\) 0.174974 + 3.33870i 0.0204791 + 0.390765i 0.989569 + 0.144058i \(0.0460152\pi\)
−0.969090 + 0.246707i \(0.920651\pi\)
\(74\) −17.6807 + 10.2079i −2.05533 + 1.18665i
\(75\) 9.22147 6.86389i 1.06480 0.792573i
\(76\) 12.3987i 1.42223i
\(77\) 0.00486761 0.0440188i 0.000554716 0.00501640i
\(78\) −16.9091 2.67814i −1.91458 0.303240i
\(79\) −5.32825 + 0.560021i −0.599475 + 0.0630073i −0.399405 0.916774i \(-0.630783\pi\)
−0.200069 + 0.979782i \(0.564117\pi\)
\(80\) −4.95427 + 5.86900i −0.553905 + 0.656174i
\(81\) −1.11138 + 10.5741i −0.123486 + 1.17490i
\(82\) −14.4058 + 3.86003i −1.59086 + 0.426270i
\(83\) −8.63403 + 1.36750i −0.947708 + 0.150102i −0.611110 0.791546i \(-0.709277\pi\)
−0.336599 + 0.941648i \(0.609277\pi\)
\(84\) 12.8268 + 19.9876i 1.39952 + 2.18082i
\(85\) 11.5193 + 10.8057i 1.24944 + 1.17204i
\(86\) −10.7117 2.27684i −1.15507 0.245518i
\(87\) 0.116086 + 0.0753869i 0.0124457 + 0.00808233i
\(88\) −0.0649580 0.0421842i −0.00692455 0.00449685i
\(89\) 8.18738 + 1.74028i 0.867861 + 0.184470i 0.620264 0.784394i \(-0.287026\pi\)
0.247597 + 0.968863i \(0.420359\pi\)
\(90\) −12.3232 1.55004i −1.29898 0.163389i
\(91\) 7.20412 + 3.71994i 0.755197 + 0.389956i
\(92\) 21.1194 3.34499i 2.20185 0.348739i
\(93\) −20.0236 + 5.36531i −2.07635 + 0.556356i
\(94\) −1.16913 + 11.1236i −0.120587 + 1.14731i
\(95\) −3.74518 6.03309i −0.384247 0.618982i
\(96\) −2.07644 + 0.218242i −0.211926 + 0.0222743i
\(97\) −6.79613 1.07640i −0.690043 0.109292i −0.198442 0.980113i \(-0.563588\pi\)
−0.491601 + 0.870821i \(0.663588\pi\)
\(98\) −4.22415 16.4762i −0.426704 1.66435i
\(99\) 0.0382642i 0.00384569i
\(100\) −2.83095 + 19.3150i −0.283095 + 1.93150i
\(101\) −9.18326 + 5.30196i −0.913768 + 0.527564i −0.881642 0.471919i \(-0.843561\pi\)
−0.0321267 + 0.999484i \(0.510228\pi\)
\(102\) −2.06518 39.4059i −0.204483 3.90177i
\(103\) 0.170043 + 0.137698i 0.0167548 + 0.0135678i 0.637661 0.770317i \(-0.279902\pi\)
−0.620906 + 0.783885i \(0.713235\pi\)
\(104\) 11.4717 8.33468i 1.12489 0.817282i
\(105\) 12.2789 + 5.85127i 1.19829 + 0.571026i
\(106\) 8.55461 + 6.21528i 0.830897 + 0.603682i
\(107\) −1.26699 4.72847i −0.122485 0.457119i 0.877253 0.480028i \(-0.159374\pi\)
−0.999738 + 0.0229097i \(0.992707\pi\)
\(108\) −4.03376 4.98127i −0.388148 0.479323i
\(109\) −1.60438 7.54803i −0.153672 0.722970i −0.985737 0.168292i \(-0.946175\pi\)
0.832065 0.554678i \(-0.187158\pi\)
\(110\) −0.0909297 0.00185573i −0.00866981 0.000176937i
\(111\) 18.3718 5.96936i 1.74377 0.566587i
\(112\) −8.87874 1.93753i −0.838962 0.183079i
\(113\) −3.56746 + 1.81771i −0.335599 + 0.170996i −0.613666 0.789565i \(-0.710306\pi\)
0.278068 + 0.960561i \(0.410306\pi\)
\(114\) −3.68858 + 17.3534i −0.345467 + 1.62530i
\(115\) 9.26612 8.00701i 0.864070 0.746658i
\(116\) −0.229917 + 0.0488704i −0.0213473 + 0.00453750i
\(117\) 6.53993 + 2.51044i 0.604616 + 0.232091i
\(118\) 4.30491 4.30491i 0.396299 0.396299i
\(119\) −4.93444 + 18.0247i −0.452339 + 1.65232i
\(120\) 18.7884 14.5900i 1.71514 1.33188i
\(121\) 1.14978 + 10.9395i 0.104526 + 0.994497i
\(122\) −11.6198 30.2705i −1.05200 2.74056i
\(123\) 14.0921 0.738538i 1.27065 0.0665917i
\(124\) 17.6014 30.4866i 1.58065 2.73777i
\(125\) 4.45681 + 10.2536i 0.398630 + 0.917112i
\(126\) −5.19220 13.7481i −0.462558 1.22478i
\(127\) 6.49211 + 3.30790i 0.576082 + 0.293528i 0.717654 0.696399i \(-0.245216\pi\)
−0.141572 + 0.989928i \(0.545216\pi\)
\(128\) 12.7361 15.7278i 1.12572 1.39015i
\(129\) 9.46591 + 4.21449i 0.833427 + 0.371065i
\(130\) 6.28291 15.4195i 0.551047 1.35238i
\(131\) −4.81183 10.8075i −0.420412 0.944260i −0.992292 0.123923i \(-0.960452\pi\)
0.571880 0.820337i \(-0.306214\pi\)
\(132\) 0.106246 + 0.106246i 0.00924757 + 0.00924757i
\(133\) 4.24035 7.25354i 0.367685 0.628962i
\(134\) 0.735006 + 0.238818i 0.0634949 + 0.0206307i
\(135\) −3.46744 1.20540i −0.298430 0.103744i
\(136\) 24.2884 + 21.8694i 2.08272 + 1.87529i
\(137\) −1.79416 + 2.76276i −0.153285 + 0.236039i −0.906968 0.421200i \(-0.861609\pi\)
0.753682 + 0.657239i \(0.228276\pi\)
\(138\) −30.5542 1.60128i −2.60094 0.136310i
\(139\) 1.40509 + 4.32443i 0.119179 + 0.366794i 0.992796 0.119820i \(-0.0382318\pi\)
−0.873617 + 0.486614i \(0.838232\pi\)
\(140\) −21.7704 + 7.71814i −1.83993 + 0.652302i
\(141\) 3.27031 10.0650i 0.275410 0.847625i
\(142\) −6.84097 + 17.8213i −0.574082 + 1.49553i
\(143\) 0.0495483 + 0.0132764i 0.00414344 + 0.00111023i
\(144\) −7.80877 0.820735i −0.650731 0.0683946i
\(145\) −0.0971136 + 0.0932290i −0.00806484 + 0.00774224i
\(146\) 4.77502 + 6.57225i 0.395183 + 0.543923i
\(147\) 0.668241 + 16.0799i 0.0551156 + 1.32625i
\(148\) −14.8926 + 29.2285i −1.22417 + 2.40256i
\(149\) −15.7486 9.09246i −1.29018 0.744884i −0.311491 0.950249i \(-0.600828\pi\)
−0.978685 + 0.205366i \(0.934162\pi\)
\(150\) 9.70840 26.1914i 0.792687 2.13852i
\(151\) 9.44990 + 16.3677i 0.769022 + 1.33198i 0.938094 + 0.346381i \(0.112590\pi\)
−0.169072 + 0.985604i \(0.554077\pi\)
\(152\) −8.00310 12.3237i −0.649137 0.999583i
\(153\) −2.52586 + 15.9477i −0.204204 + 1.28929i
\(154\) −0.0483350 0.0961460i −0.00389495 0.00774766i
\(155\) −0.644136 20.1512i −0.0517382 1.61858i
\(156\) −25.1298 + 11.1885i −2.01199 + 0.895796i
\(157\) −4.20781 + 15.7038i −0.335820 + 1.25330i 0.567158 + 0.823609i \(0.308043\pi\)
−0.902978 + 0.429688i \(0.858624\pi\)
\(158\) −10.1171 + 8.19266i −0.804873 + 0.651773i
\(159\) −6.69470 7.43521i −0.530924 0.589651i
\(160\) 0.253420 2.01474i 0.0200346 0.159280i
\(161\) 13.4994 + 5.26593i 1.06390 + 0.415014i
\(162\) 11.7289 + 23.0193i 0.921510 + 1.80856i
\(163\) 0.490229 9.35413i 0.0383977 0.732672i −0.909811 0.415023i \(-0.863773\pi\)
0.948208 0.317649i \(-0.102893\pi\)
\(164\) −16.0348 + 17.8084i −1.25211 + 1.39060i
\(165\) 0.0837915 + 0.0196055i 0.00652316 + 0.00152629i
\(166\) −15.7852 + 14.2131i −1.22517 + 1.10315i
\(167\) −1.18224 7.46435i −0.0914842 0.577608i −0.990263 0.139207i \(-0.955545\pi\)
0.898779 0.438402i \(-0.144455\pi\)
\(168\) 25.6507 + 11.5872i 1.97899 + 0.893972i
\(169\) 2.12129 2.91971i 0.163177 0.224593i
\(170\) 37.7750 + 6.77580i 2.89721 + 0.519680i
\(171\) 2.95266 6.63179i 0.225796 0.507145i
\(172\) −16.4272 + 6.30581i −1.25256 + 0.480813i
\(173\) 19.6275 12.7463i 1.49225 0.969080i 0.497423 0.867508i \(-0.334280\pi\)
0.994828 0.101572i \(-0.0323871\pi\)
\(174\) 0.336334 0.0254974
\(175\) −8.26189 + 10.3316i −0.624540 + 0.780993i
\(176\) −0.0574953 −0.00433387
\(177\) −4.83112 + 3.13737i −0.363129 + 0.235819i
\(178\) 18.9878 7.28875i 1.42320 0.546315i
\(179\) 5.54190 12.4473i 0.414221 0.930356i −0.579130 0.815235i \(-0.696608\pi\)
0.993351 0.115121i \(-0.0367256\pi\)
\(180\) −17.9628 + 8.69547i −1.33887 + 0.648122i
\(181\) −3.38018 + 4.65241i −0.251247 + 0.345811i −0.915947 0.401298i \(-0.868559\pi\)
0.664701 + 0.747110i \(0.268559\pi\)
\(182\) 19.6040 1.95323i 1.45314 0.144783i
\(183\) 4.79930 + 30.3016i 0.354774 + 2.23996i
\(184\) 18.8325 16.9569i 1.38835 1.25008i
\(185\) 1.58218 + 18.7208i 0.116324 + 1.37638i
\(186\) −33.7049 + 37.4330i −2.47136 + 2.74472i
\(187\) −0.00618787 + 0.118072i −0.000452502 + 0.00863424i
\(188\) 8.15893 + 16.0128i 0.595051 + 1.16785i
\(189\) −0.656250 4.29370i −0.0477352 0.312321i
\(190\) −15.6164 7.33824i −1.13293 0.532372i
\(191\) −9.91552 11.0123i −0.717462 0.796822i 0.268591 0.963254i \(-0.413442\pi\)
−0.986053 + 0.166432i \(0.946775\pi\)
\(192\) −16.2170 + 13.1323i −1.17036 + 0.947740i
\(193\) 4.30663 16.0726i 0.309998 1.15693i −0.618558 0.785739i \(-0.712283\pi\)
0.928557 0.371191i \(-0.121050\pi\)
\(194\) −15.2741 + 6.80046i −1.09662 + 0.488245i
\(195\) −8.84829 + 13.0350i −0.633639 + 0.933452i
\(196\) −20.1109 18.5061i −1.43649 1.32186i
\(197\) 2.43376 15.3662i 0.173398 1.09479i −0.735423 0.677608i \(-0.763017\pi\)
0.908821 0.417185i \(-0.136983\pi\)
\(198\) −0.0506389 0.0779771i −0.00359875 0.00554159i
\(199\) −0.988951 1.71291i −0.0701049 0.121425i 0.828842 0.559482i \(-0.189000\pi\)
−0.898947 + 0.438057i \(0.855667\pi\)
\(200\) 9.65361 + 21.0255i 0.682613 + 1.48672i
\(201\) −0.633276 0.365622i −0.0446678 0.0257890i
\(202\) −11.6976 + 22.9578i −0.823039 + 1.61531i
\(203\) −0.151221 0.0500411i −0.0106136 0.00351220i
\(204\) −37.2677 51.2946i −2.60926 3.59134i
\(205\) −2.42313 + 13.5089i −0.169239 + 0.943503i
\(206\) 0.528754 + 0.0555743i 0.0368401 + 0.00387205i
\(207\) 12.0929 + 3.24028i 0.840514 + 0.225215i
\(208\) 3.77216 9.82681i 0.261552 0.681367i
\(209\) 0.0164266 0.0505557i 0.00113625 0.00349701i
\(210\) 32.7662 4.32579i 2.26108 0.298508i
\(211\) 2.82445 + 8.69276i 0.194443 + 0.598434i 0.999983 + 0.00589215i \(0.00187554\pi\)
−0.805540 + 0.592542i \(0.798124\pi\)
\(212\) 16.9670 + 0.889200i 1.16530 + 0.0610705i
\(213\) 9.83728 15.1481i 0.674040 1.03793i
\(214\) −8.83963 7.95924i −0.604264 0.544082i
\(215\) −6.08857 + 8.03037i −0.415237 + 0.547667i
\(216\) −7.22465 2.34743i −0.491575 0.159722i
\(217\) 20.7236 11.8157i 1.40681 0.802101i
\(218\) −13.2586 13.2586i −0.897985 0.897985i
\(219\) −3.12642 7.02205i −0.211264 0.474506i
\(220\) −0.124157 + 0.0770734i −0.00837069 + 0.00519629i
\(221\) −19.7742 8.80405i −1.33016 0.592225i
\(222\) 29.5393 36.4780i 1.98255 2.44824i
\(223\) −6.62726 3.37676i −0.443794 0.226124i 0.217789 0.975996i \(-0.430115\pi\)
−0.661584 + 0.749871i \(0.730115\pi\)
\(224\) 2.24771 0.848882i 0.150181 0.0567183i
\(225\) −6.11394 + 9.65699i −0.407596 + 0.643800i
\(226\) −4.86443 + 8.42544i −0.323577 + 0.560452i
\(227\) −11.7014 + 0.613246i −0.776651 + 0.0407026i −0.436543 0.899684i \(-0.643797\pi\)
−0.340109 + 0.940386i \(0.610464\pi\)
\(228\) 10.2157 + 26.6127i 0.676549 + 1.76247i
\(229\) 2.81607 + 26.7931i 0.186091 + 1.77054i 0.546225 + 0.837638i \(0.316064\pi\)
−0.360134 + 0.932901i \(0.617269\pi\)
\(230\) 8.28657 28.5800i 0.546401 1.88451i
\(231\) 0.0258205 + 0.0984929i 0.00169886 + 0.00648036i
\(232\) −0.196981 + 0.196981i −0.0129324 + 0.0129324i
\(233\) 20.3954 + 7.82907i 1.33615 + 0.512900i 0.918397 0.395661i \(-0.129485\pi\)
0.417753 + 0.908561i \(0.362818\pi\)
\(234\) 16.6498 3.53902i 1.08843 0.231353i
\(235\) 8.80691 + 5.32717i 0.574499 + 0.347507i
\(236\) 2.03383 9.56842i 0.132391 0.622851i
\(237\) 10.9752 5.59214i 0.712915 0.363248i
\(238\) 13.7983 + 43.2622i 0.894409 + 2.80427i
\(239\) −4.05851 + 1.31869i −0.262523 + 0.0852989i −0.437321 0.899305i \(-0.644073\pi\)
0.174798 + 0.984604i \(0.444073\pi\)
\(240\) 5.79826 16.6792i 0.374276 1.07664i
\(241\) 0.0341430 + 0.160630i 0.00219934 + 0.0103471i 0.979234 0.202735i \(-0.0649831\pi\)
−0.977034 + 0.213082i \(0.931650\pi\)
\(242\) 16.8204 + 20.7715i 1.08126 + 1.33524i
\(243\) −5.05209 18.8546i −0.324092 1.20953i
\(244\) −42.1485 30.6227i −2.69828 1.96042i
\(245\) −15.3758 2.93015i −0.982322 0.187201i
\(246\) 27.7405 20.1546i 1.76867 1.28501i
\(247\) 7.56302 + 6.12442i 0.481224 + 0.389687i
\(248\) −2.18349 41.6634i −0.138652 2.64563i
\(249\) 17.4055 10.0490i 1.10303 0.636832i
\(250\) 22.6520 + 14.9973i 1.43264 + 0.948513i
\(251\) 0.132304i 0.00835098i 0.999991 + 0.00417549i \(0.00132910\pi\)
−0.999991 + 0.00417549i \(0.998671\pi\)
\(252\) −19.0280 13.9827i −1.19865 0.880825i
\(253\) 0.0905461 + 0.0143411i 0.00569259 + 0.000901617i
\(254\) 17.6077 1.85065i 1.10481 0.116120i
\(255\) −33.6283 13.7023i −2.10588 0.858073i
\(256\) 3.24278 30.8530i 0.202674 1.92831i
\(257\) −8.87663 + 2.37849i −0.553709 + 0.148366i −0.524815 0.851217i \(-0.675865\pi\)
−0.0288944 + 0.999582i \(0.509199\pi\)
\(258\) 24.8677 3.93865i 1.54819 0.245210i
\(259\) −18.7087 + 12.0061i −1.16250 + 0.746020i
\(260\) −5.02727 26.2770i −0.311778 1.62963i
\(261\) −0.134615 0.0286134i −0.00833249 0.00177113i
\(262\) −24.1086 15.6563i −1.48943 0.967249i
\(263\) 17.5431 + 11.3926i 1.08175 + 0.702499i 0.957117 0.289703i \(-0.0935566\pi\)
0.124637 + 0.992202i \(0.460223\pi\)
\(264\) 0.174183 + 0.0370238i 0.0107202 + 0.00227866i
\(265\) 8.52455 4.69239i 0.523659 0.288251i
\(266\) −0.958107 20.3934i −0.0587453 1.25040i
\(267\) −19.0074 + 3.01047i −1.16323 + 0.184238i
\(268\) 1.19946 0.321394i 0.0732687 0.0196323i
\(269\) 0.158106 1.50428i 0.00963991 0.0917176i −0.988644 0.150276i \(-0.951984\pi\)
0.998284 + 0.0585585i \(0.0186504\pi\)
\(270\) −8.66139 + 2.13239i −0.527115 + 0.129773i
\(271\) 9.03693 0.949820i 0.548955 0.0576974i 0.174009 0.984744i \(-0.444328\pi\)
0.374946 + 0.927047i \(0.377661\pi\)
\(272\) 23.9627 + 3.79533i 1.45295 + 0.230125i
\(273\) −18.5280 2.04883i −1.12136 0.124001i
\(274\) 8.00453i 0.483571i
\(275\) −0.0371329 + 0.0750064i −0.00223920 + 0.00452305i
\(276\) −42.5749 + 24.5807i −2.56271 + 1.47958i
\(277\) −0.715125 13.6454i −0.0429677 0.819872i −0.932095 0.362213i \(-0.882021\pi\)
0.889128 0.457659i \(-0.151312\pi\)
\(278\) 8.58636 + 6.95309i 0.514975 + 0.417019i
\(279\) 16.6747 12.1149i 0.998291 0.725301i
\(280\) −16.6567 + 21.7237i −0.995430 + 1.29824i
\(281\) −3.22462 2.34282i −0.192365 0.139761i 0.487434 0.873160i \(-0.337933\pi\)
−0.679799 + 0.733399i \(0.737933\pi\)
\(282\) −6.65559 24.8390i −0.396334 1.47914i
\(283\) 11.8922 + 14.6857i 0.706920 + 0.872974i 0.996449 0.0841955i \(-0.0268320\pi\)
−0.289529 + 0.957169i \(0.593499\pi\)
\(284\) 6.37712 + 30.0020i 0.378413 + 1.78029i
\(285\) 13.0095 + 9.86374i 0.770618 + 0.584277i
\(286\) 0.118543 0.0385168i 0.00700957 0.00227755i
\(287\) −15.4712 + 4.93447i −0.913236 + 0.291272i
\(288\) 1.84965 0.942442i 0.108991 0.0555339i
\(289\) 6.83850 32.1726i 0.402265 1.89251i
\(290\) −0.0745245 + 0.318508i −0.00437623 + 0.0187034i
\(291\) 15.4742 3.28914i 0.907112 0.192813i
\(292\) 12.1861 + 4.67781i 0.713138 + 0.273748i
\(293\) −4.94524 + 4.94524i −0.288904 + 0.288904i −0.836647 0.547743i \(-0.815487\pi\)
0.547743 + 0.836647i \(0.315487\pi\)
\(294\) 22.6420 + 31.8843i 1.32051 + 1.85953i
\(295\) −1.90061 5.27024i −0.110658 0.306845i
\(296\) 4.06380 + 38.6645i 0.236204 + 2.24733i
\(297\) −0.00984815 0.0256553i −0.000571447 0.00148867i
\(298\) −44.1265 + 2.31257i −2.55618 + 0.133964i
\(299\) −8.39168 + 14.5348i −0.485303 + 0.840570i
\(300\) −9.83785 43.7905i −0.567988 2.52824i
\(301\) −11.7669 1.92904i −0.678231 0.111188i
\(302\) 40.9187 + 20.8491i 2.35460 + 1.19973i
\(303\) 15.3426 18.9465i 0.881409 1.08845i
\(304\) −9.96484 4.43663i −0.571523 0.254458i
\(305\) −29.7590 2.16926i −1.70400 0.124211i
\(306\) 15.9578 + 35.8419i 0.912248 + 2.04894i
\(307\) −4.76473 4.76473i −0.271938 0.271938i 0.557942 0.829880i \(-0.311591\pi\)
−0.829880 + 0.557942i \(0.811591\pi\)
\(308\) −0.149273 0.0872638i −0.00850564 0.00497232i
\(309\) −0.478436 0.155453i −0.0272173 0.00884342i
\(310\) −27.9808 40.2129i −1.58920 2.28394i
\(311\) 1.95368 + 1.75910i 0.110783 + 0.0997496i 0.722661 0.691203i \(-0.242919\pi\)
−0.611878 + 0.790952i \(0.709586\pi\)
\(312\) −17.7558 + 27.3415i −1.00522 + 1.54791i
\(313\) −4.34316 0.227616i −0.245490 0.0128656i −0.0708059 0.997490i \(-0.522557\pi\)
−0.174684 + 0.984625i \(0.555890\pi\)
\(314\) 12.2075 + 37.5707i 0.688908 + 2.12024i
\(315\) −13.4825 1.05619i −0.759652 0.0595098i
\(316\) −6.46387 + 19.8938i −0.363621 + 1.11911i
\(317\) 7.43621 19.3720i 0.417659 1.08804i −0.549864 0.835254i \(-0.685320\pi\)
0.967523 0.252784i \(-0.0813463\pi\)
\(318\) −23.4827 6.29216i −1.31684 0.352847i
\(319\) −0.00100223 0.000105339i −5.61143e−5 5.89785e-6i
\(320\) −8.84291 18.2673i −0.494334 1.02117i
\(321\) 6.61541 + 9.10533i 0.369236 + 0.508210i
\(322\) 34.4788 7.13384i 1.92143 0.397553i
\(323\) −10.1835 + 19.9862i −0.566623 + 1.11206i
\(324\) 35.9500 + 20.7557i 1.99722 + 1.15310i
\(325\) −10.3835 11.2676i −0.575973 0.625014i
\(326\) −11.3803 19.7112i −0.630295 1.09170i
\(327\) 9.66271 + 14.8793i 0.534349 + 0.822825i
\(328\) −4.44281 + 28.0508i −0.245313 + 1.54884i
\(329\) −0.703199 + 12.1582i −0.0387686 + 0.670304i
\(330\) 0.196702 0.0709366i 0.0108281 0.00390493i
\(331\) 14.5178 6.46376i 0.797972 0.355280i 0.0330919 0.999452i \(-0.489465\pi\)
0.764881 + 0.644172i \(0.222798\pi\)
\(332\) −8.83346 + 32.9669i −0.484799 + 1.80929i
\(333\) −14.9263 + 12.0871i −0.817955 + 0.662367i
\(334\) −12.2876 13.6467i −0.672346 0.746716i
\(335\) 0.486565 0.518698i 0.0265839 0.0283395i
\(336\) 20.6538 3.15673i 1.12676 0.172214i
\(337\) −11.6113 22.7884i −0.632508 1.24137i −0.955507 0.294967i \(-0.904691\pi\)
0.323000 0.946399i \(-0.395309\pi\)
\(338\) 0.458951 8.75730i 0.0249636 0.476334i
\(339\) 6.15957 6.84090i 0.334542 0.371547i
\(340\) 56.8337 23.9267i 3.08224 1.29761i
\(341\) 0.112160 0.100989i 0.00607382 0.00546889i
\(342\) −2.75941 17.4222i −0.149212 0.942086i
\(343\) −5.43629 17.7044i −0.293532 0.955949i
\(344\) −12.2575 + 16.8710i −0.660882 + 0.909626i
\(345\) −13.2917 + 24.8210i −0.715600 + 1.33632i
\(346\) 23.1297 51.9502i 1.24346 2.79286i
\(347\) −14.1465 + 5.43034i −0.759425 + 0.291516i −0.707099 0.707114i \(-0.749997\pi\)
−0.0523255 + 0.998630i \(0.516663\pi\)
\(348\) 0.453231 0.294331i 0.0242957 0.0157778i
\(349\) −1.48928 −0.0797192 −0.0398596 0.999205i \(-0.512691\pi\)
−0.0398596 + 0.999205i \(0.512691\pi\)
\(350\) −3.16378 + 31.9881i −0.169111 + 1.70984i
\(351\) 5.03100 0.268535
\(352\) 0.0127486 0.00827905i 0.000679504 0.000441275i
\(353\) −8.77541 + 3.36856i −0.467068 + 0.179291i −0.580509 0.814254i \(-0.697146\pi\)
0.113441 + 0.993545i \(0.463813\pi\)
\(354\) −5.69315 + 12.7870i −0.302588 + 0.679623i
\(355\) 12.1655 + 12.6724i 0.645678 + 0.672581i
\(356\) 19.2088 26.4386i 1.01806 1.40124i
\(357\) −4.25978 42.7541i −0.225451 2.26279i
\(358\) −5.17918 32.7001i −0.273728 1.72825i
\(359\) −4.56543 + 4.11073i −0.240954 + 0.216956i −0.780756 0.624836i \(-0.785166\pi\)
0.539802 + 0.841792i \(0.318499\pi\)
\(360\) −12.2413 + 20.2374i −0.645175 + 1.06661i
\(361\) −5.96536 + 6.62520i −0.313966 + 0.348695i
\(362\) −0.731315 + 13.9543i −0.0384370 + 0.733422i
\(363\) −11.4813 22.5332i −0.602610 1.18269i
\(364\) 24.7083 19.7879i 1.29506 1.03717i
\(365\) 7.34263 1.40478i 0.384331 0.0735295i
\(366\) 49.8815 + 55.3990i 2.60735 + 2.89575i
\(367\) 28.0420 22.7079i 1.46378 1.18534i 0.520267 0.854003i \(-0.325832\pi\)
0.943511 0.331341i \(-0.107501\pi\)
\(368\) 4.86880 18.1706i 0.253804 0.947209i
\(369\) −12.8176 + 5.70676i −0.667257 + 0.297082i
\(370\) 27.9994 + 36.0565i 1.45562 + 1.87449i
\(371\) 9.62196 + 6.32289i 0.499547 + 0.328268i
\(372\) −12.6611 + 79.9390i −0.656447 + 4.14464i
\(373\) 10.1248 + 15.5909i 0.524244 + 0.807264i 0.997274 0.0737815i \(-0.0235067\pi\)
−0.473031 + 0.881046i \(0.656840\pi\)
\(374\) 0.143646 + 0.248802i 0.00742777 + 0.0128653i
\(375\) −18.0144 18.3364i −0.930261 0.946887i
\(376\) 18.4455 + 10.6495i 0.951252 + 0.549206i
\(377\) 0.0837587 0.164386i 0.00431379 0.00846629i
\(378\) −7.01965 7.88149i −0.361052 0.405380i
\(379\) −13.0838 18.0083i −0.672068 0.925022i 0.327737 0.944769i \(-0.393714\pi\)
−0.999805 + 0.0197466i \(0.993714\pi\)
\(380\) −27.4658 + 3.77742i −1.40897 + 0.193777i
\(381\) −16.6602 1.75106i −0.853529 0.0897095i
\(382\) −34.7802 9.31932i −1.77951 0.476818i
\(383\) 5.51711 14.3726i 0.281911 0.734403i −0.717377 0.696685i \(-0.754658\pi\)
0.999288 0.0377184i \(-0.0120090\pi\)
\(384\) −14.3783 + 44.2520i −0.733742 + 2.25822i
\(385\) −0.0989940 + 0.00262803i −0.00504520 + 0.000133937i
\(386\) −12.4942 38.4531i −0.635937 1.95721i
\(387\) −10.2882 0.539182i −0.522979 0.0274082i
\(388\) −14.6316 + 22.5307i −0.742806 + 1.14382i
\(389\) 8.85903 + 7.97670i 0.449171 + 0.404435i 0.862428 0.506179i \(-0.168943\pi\)
−0.413258 + 0.910614i \(0.635609\pi\)
\(390\) −0.781097 + 38.2733i −0.0395524 + 1.93804i
\(391\) −36.7909 11.9541i −1.86060 0.604545i
\(392\) −31.9345 5.41296i −1.61294 0.273396i
\(393\) 19.2328 + 19.2328i 0.970168 + 0.970168i
\(394\) −15.3760 34.5350i −0.774629 1.73985i
\(395\) 2.86388 + 11.6326i 0.144098 + 0.585300i
\(396\) −0.136478 0.0607640i −0.00685828 0.00305350i
\(397\) 4.26600 5.26807i 0.214105 0.264397i −0.658767 0.752347i \(-0.728922\pi\)
0.872872 + 0.487950i \(0.162255\pi\)
\(398\) −4.28222 2.18190i −0.214648 0.109369i
\(399\) −3.12512 + 19.0628i −0.156452 + 0.954335i
\(400\) 14.5105 + 9.18673i 0.725524 + 0.459336i
\(401\) −9.14254 + 15.8353i −0.456557 + 0.790779i −0.998776 0.0494575i \(-0.984251\pi\)
0.542220 + 0.840237i \(0.317584\pi\)
\(402\) −1.77439 + 0.0929920i −0.0884987 + 0.00463802i
\(403\) 9.90201 + 25.7956i 0.493254 + 1.28497i
\(404\) 4.32754 + 41.1738i 0.215303 + 2.04847i
\(405\) 23.7624 0.759570i 1.18076 0.0377433i
\(406\) −0.374391 + 0.0981488i −0.0185807 + 0.00487104i
\(407\) −0.0994483 + 0.0994483i −0.00492947 + 0.00492947i
\(408\) −70.1518 26.9287i −3.47303 1.33317i
\(409\) −15.5613 + 3.30765i −0.769456 + 0.163553i −0.575882 0.817533i \(-0.695341\pi\)
−0.193574 + 0.981086i \(0.562008\pi\)
\(410\) 12.9397 + 30.7361i 0.639047 + 1.51795i
\(411\) 1.57468 7.40829i 0.0776732 0.365424i
\(412\) 0.761163 0.387832i 0.0374998 0.0191071i
\(413\) 4.46223 4.90218i 0.219572 0.241221i
\(414\) 28.9318 9.40052i 1.42192 0.462010i
\(415\) 5.65976 + 18.7096i 0.277827 + 0.918419i
\(416\) 0.578601 + 2.72210i 0.0283683 + 0.133462i
\(417\) −6.57894 8.12431i −0.322172 0.397849i
\(418\) −0.0334306 0.124765i −0.00163514 0.00610243i
\(419\) 28.7560 + 20.8925i 1.40482 + 1.02066i 0.994050 + 0.108926i \(0.0347411\pi\)
0.410773 + 0.911738i \(0.365259\pi\)
\(420\) 40.3689 34.5035i 1.96980 1.68360i
\(421\) −11.3679 + 8.25925i −0.554037 + 0.402531i −0.829272 0.558846i \(-0.811244\pi\)
0.275235 + 0.961377i \(0.411244\pi\)
\(422\) 17.2599 + 13.9768i 0.840197 + 0.680378i
\(423\) 0.550694 + 10.5079i 0.0267757 + 0.510910i
\(424\) 17.4383 10.0680i 0.846876 0.488944i
\(425\) 20.4274 28.8098i 0.990875 1.39748i
\(426\) 43.8884i 2.12640i
\(427\) −14.1849 32.3298i −0.686458 1.56455i
\(428\) −18.8772 2.98985i −0.912464 0.144520i
\(429\) −0.117290 + 0.0123277i −0.00566280 + 0.000595185i
\(430\) −1.78025 + 24.4224i −0.0858514 + 1.17775i
\(431\) −0.397806 + 3.78487i −0.0191616 + 0.182311i −0.999916 0.0129330i \(-0.995883\pi\)
0.980755 + 0.195244i \(0.0625498\pi\)
\(432\) −5.44685 + 1.45948i −0.262061 + 0.0702192i
\(433\) 1.22529 0.194066i 0.0588836 0.00932624i −0.126923 0.991913i \(-0.540510\pi\)
0.185807 + 0.982586i \(0.440510\pi\)
\(434\) 26.5950 51.5044i 1.27660 2.47229i
\(435\) 0.131631 0.280122i 0.00631124 0.0134308i
\(436\) −29.4696 6.26395i −1.41134 0.299989i
\(437\) 14.5864 + 9.47255i 0.697764 + 0.453133i
\(438\) −15.6642 10.1725i −0.748465 0.486059i
\(439\) −5.32727 1.13235i −0.254257 0.0540439i 0.0790199 0.996873i \(-0.474821\pi\)
−0.333277 + 0.942829i \(0.608154\pi\)
\(440\) −0.0736569 + 0.156748i −0.00351146 + 0.00747266i
\(441\) −6.34978 14.6878i −0.302371 0.699417i
\(442\) −51.9485 + 8.22783i −2.47094 + 0.391358i
\(443\) 17.6715 4.73507i 0.839599 0.224970i 0.186702 0.982417i \(-0.440220\pi\)
0.652897 + 0.757447i \(0.273553\pi\)
\(444\) 7.88353 75.0067i 0.374136 3.55966i
\(445\) 1.36072 18.6670i 0.0645042 0.884901i
\(446\) −17.9743 + 1.88917i −0.851106 + 0.0894548i
\(447\) 41.2945 + 6.54041i 1.95316 + 0.309351i
\(448\) 14.2197 19.3507i 0.671820 0.914233i
\(449\) 7.28927i 0.344002i −0.985097 0.172001i \(-0.944977\pi\)
0.985097 0.172001i \(-0.0550232\pi\)
\(450\) 0.320731 + 27.7708i 0.0151194 + 1.30913i
\(451\) −0.0889755 + 0.0513700i −0.00418969 + 0.00241892i
\(452\) 0.818124 + 15.6107i 0.0384813 + 0.734267i
\(453\) −33.7692 27.3458i −1.58662 1.28482i
\(454\) −23.0343 + 16.7354i −1.08105 + 0.785432i
\(455\) 6.04565 17.0920i 0.283424 0.801285i
\(456\) 27.3318 + 19.8577i 1.27993 + 0.929922i
\(457\) 3.05849 + 11.4145i 0.143070 + 0.533946i 0.999834 + 0.0182361i \(0.00580504\pi\)
−0.856763 + 0.515710i \(0.827528\pi\)
\(458\) 41.1969 + 50.8739i 1.92500 + 2.37718i
\(459\) 2.41095 + 11.3426i 0.112534 + 0.529429i
\(460\) −13.8442 45.7650i −0.645488 2.13381i
\(461\) −0.809532 + 0.263033i −0.0377037 + 0.0122507i −0.327808 0.944744i \(-0.606310\pi\)
0.290104 + 0.956995i \(0.406310\pi\)
\(462\) 0.182964 + 0.166544i 0.00851227 + 0.00774833i
\(463\) 34.4372 17.5466i 1.60043 0.815460i 0.600557 0.799582i \(-0.294945\pi\)
0.999874 0.0158788i \(-0.00505458\pi\)
\(464\) −0.0429941 + 0.202271i −0.00199595 + 0.00939022i
\(465\) 17.9857 + 42.7220i 0.834069 + 1.98118i
\(466\) 51.9241 11.0368i 2.40534 0.511270i
\(467\) −8.34928 3.20499i −0.386358 0.148309i 0.157433 0.987530i \(-0.449678\pi\)
−0.543791 + 0.839221i \(0.683012\pi\)
\(468\) 19.3396 19.3396i 0.893972 0.893972i
\(469\) 0.811629 + 0.222191i 0.0374775 + 0.0102598i
\(470\) 24.9973 0.799042i 1.15304 0.0368570i
\(471\) −3.90711 37.1737i −0.180030 1.71287i
\(472\) −4.15468 10.8233i −0.191235 0.498183i
\(473\) −0.0753362 + 0.00394820i −0.00346396 + 0.000181538i
\(474\) 14.9653 25.9206i 0.687377 1.19057i
\(475\) −12.2236 + 10.1344i −0.560857 + 0.464999i
\(476\) 56.4535 + 46.2233i 2.58754 + 2.11864i
\(477\) 8.86348 + 4.51617i 0.405831 + 0.206781i
\(478\) −6.52552 + 8.05835i −0.298470 + 0.368580i
\(479\) 0.885419 + 0.394214i 0.0404558 + 0.0180121i 0.426865 0.904315i \(-0.359618\pi\)
−0.386409 + 0.922328i \(0.626285\pi\)
\(480\) 1.11607 + 4.53327i 0.0509412 + 0.206914i
\(481\) −10.4726 23.5218i −0.477509 1.07250i
\(482\) 0.282157 + 0.282157i 0.0128519 + 0.0128519i
\(483\) −33.3139 0.180335i −1.51584 0.00820553i
\(484\) 40.8440 + 13.2710i 1.85655 + 0.603228i
\(485\) −0.313939 + 15.3828i −0.0142553 + 0.698499i
\(486\) −35.2477 31.7372i −1.59887 1.43963i
\(487\) −18.8835 + 29.0780i −0.855691 + 1.31765i 0.0911139 + 0.995840i \(0.470957\pi\)
−0.946805 + 0.321808i \(0.895709\pi\)
\(488\) −61.6598 3.23145i −2.79121 0.146281i
\(489\) 6.65491 + 20.4817i 0.300946 + 0.926215i
\(490\) −35.2115 + 14.3771i −1.59069 + 0.649491i
\(491\) 1.58176 4.86817i 0.0713840 0.219697i −0.908999 0.416798i \(-0.863152\pi\)
0.980383 + 0.197100i \(0.0631524\pi\)
\(492\) 19.7443 51.4357i 0.890143 2.31890i
\(493\) 0.410755 + 0.110061i 0.0184995 + 0.00495692i
\(494\) 23.5175 + 2.47179i 1.05810 + 0.111211i
\(495\) −0.0847634 + 0.0116576i −0.00380983 + 0.000523972i
\(496\) −18.2037 25.0553i −0.817371 1.12501i
\(497\) −6.52990 + 19.7329i −0.292906 + 0.885139i
\(498\) 22.1710 43.5130i 0.993506 1.94986i
\(499\) 31.5502 + 18.2155i 1.41238 + 0.815438i 0.995612 0.0935745i \(-0.0298293\pi\)
0.416768 + 0.909013i \(0.363163\pi\)
\(500\) 43.6494 + 0.386608i 1.95206 + 0.0172896i
\(501\) 8.68766 + 15.0475i 0.388136 + 0.672271i
\(502\) 0.175092 + 0.269618i 0.00781474 + 0.0120336i
\(503\) 0.209162 1.32059i 0.00932605 0.0588824i −0.982586 0.185806i \(-0.940510\pi\)
0.991912 + 0.126924i \(0.0405104\pi\)
\(504\) −27.9384 1.61588i −1.24448 0.0719772i
\(505\) 14.5428 + 18.7276i 0.647145 + 0.833367i
\(506\) 0.203500 0.0906038i 0.00904666 0.00402783i
\(507\) −2.14753 + 8.01470i −0.0953752 + 0.355945i
\(508\) 22.1079 17.9027i 0.980882 0.794302i
\(509\) −12.8202 14.2382i −0.568244 0.631098i 0.388703 0.921363i \(-0.372923\pi\)
−0.956946 + 0.290265i \(0.906257\pi\)
\(510\) −86.6634 + 16.5803i −3.83752 + 0.734188i
\(511\) 5.52935 + 6.90427i 0.244604 + 0.305427i
\(512\) −15.8470 31.1015i −0.700346 1.37451i
\(513\) 0.272856 5.20640i 0.0120469 0.229868i
\(514\) −14.9417 + 16.5944i −0.659048 + 0.731947i
\(515\) 0.253225 0.418633i 0.0111584 0.0184472i
\(516\) 30.0640 27.0697i 1.32349 1.19168i
\(517\) 0.0120533 + 0.0761016i 0.000530104 + 0.00334694i
\(518\) −22.2368 + 49.2258i −0.977028 + 2.16286i
\(519\) −31.6267 + 43.5304i −1.38826 + 1.91077i
\(520\) −21.9581 22.8730i −0.962926 1.00305i
\(521\) 5.94344 13.3492i 0.260387 0.584838i −0.735287 0.677756i \(-0.762953\pi\)
0.995674 + 0.0929175i \(0.0296193\pi\)
\(522\) −0.312195 + 0.119840i −0.0136644 + 0.00524527i
\(523\) −29.1893 + 18.9558i −1.27636 + 0.828877i −0.991552 0.129707i \(-0.958596\pi\)
−0.284807 + 0.958585i \(0.591930\pi\)
\(524\) −46.1889 −2.01777
\(525\) 9.22093 28.9830i 0.402434 1.26492i
\(526\) 50.8274 2.21618
\(527\) −53.4123 + 34.6864i −2.32668 + 1.51096i
\(528\) 0.123408 0.0473721i 0.00537066 0.00206160i
\(529\) −2.84498 + 6.38993i −0.123695 + 0.277823i
\(530\) 11.1619 20.8439i 0.484843 0.905399i
\(531\) 3.36650 4.63359i 0.146094 0.201081i
\(532\) −19.1377 26.6429i −0.829725 1.15512i
\(533\) −2.94239 18.5775i −0.127449 0.804683i
\(534\) −34.7503 + 31.2893i −1.50379 + 1.35402i
\(535\) −10.0886 + 4.24724i −0.436168 + 0.183624i
\(536\) 0.984749 1.09367i 0.0425347 0.0472395i
\(537\) −1.63948 + 31.2832i −0.0707489 + 1.34997i
\(538\) −1.66857 3.27475i −0.0719372 0.141185i
\(539\) −0.0574843 0.102103i −0.00247602 0.00439788i
\(540\) −9.80566 + 10.4532i −0.421969 + 0.449836i
\(541\) −11.5839 12.8652i −0.498029 0.553117i 0.440753 0.897628i \(-0.354711\pi\)
−0.938782 + 0.344511i \(0.888045\pi\)
\(542\) 17.1590 13.8951i 0.737043 0.596846i
\(543\) 3.42198 12.7710i 0.146851 0.548057i
\(544\) −5.85985 + 2.60897i −0.251239 + 0.111859i
\(545\) −16.2317 + 5.85365i −0.695290 + 0.250743i
\(546\) −40.4689 + 20.3447i −1.73191 + 0.870674i
\(547\) 1.54775 9.77211i 0.0661770 0.417825i −0.932253 0.361808i \(-0.882160\pi\)
0.998430 0.0560177i \(-0.0178403\pi\)
\(548\) 7.00490 + 10.7866i 0.299234 + 0.460781i
\(549\) −15.2517 26.4167i −0.650927 1.12744i
\(550\) 0.0235920 + 0.201994i 0.00100597 + 0.00861307i
\(551\) −0.165574 0.0955944i −0.00705370 0.00407246i
\(552\) −26.4511 + 51.9131i −1.12583 + 2.20957i
\(553\) −10.5852 + 9.42768i −0.450127 + 0.400906i
\(554\) −19.5157 26.8610i −0.829142 1.14122i
\(555\) −18.8206 38.8789i −0.798890 1.65032i
\(556\) 17.6554 + 1.85566i 0.748756 + 0.0786975i
\(557\) 15.6719 + 4.19928i 0.664041 + 0.177929i 0.575069 0.818105i \(-0.304975\pi\)
0.0889717 + 0.996034i \(0.471642\pi\)
\(558\) 17.9479 46.7559i 0.759796 1.97934i
\(559\) 4.26786 13.1351i 0.180511 0.555557i
\(560\) −1.58702 + 20.2586i −0.0670640 + 0.856082i
\(561\) −0.0840009 0.258528i −0.00354652 0.0109151i
\(562\) −9.67182 0.506879i −0.407981 0.0213814i
\(563\) 16.8888 26.0064i 0.711776 1.09604i −0.278969 0.960300i \(-0.589993\pi\)
0.990745 0.135739i \(-0.0433408\pi\)
\(564\) −30.7058 27.6476i −1.29295 1.16418i
\(565\) 5.11350 + 7.34891i 0.215126 + 0.309171i
\(566\) 43.6698 + 14.1892i 1.83558 + 0.596416i
\(567\) 13.9331 + 24.4374i 0.585137 + 1.02628i
\(568\) 25.7042 + 25.7042i 1.07852 + 1.07852i
\(569\) 5.42165 + 12.1772i 0.227287 + 0.510496i 0.990806 0.135290i \(-0.0431966\pi\)
−0.763519 + 0.645786i \(0.776530\pi\)
\(570\) 39.5653 + 2.88408i 1.65721 + 0.120801i
\(571\) 7.62713 + 3.39582i 0.319185 + 0.142110i 0.560075 0.828442i \(-0.310772\pi\)
−0.240889 + 0.970553i \(0.577439\pi\)
\(572\) 0.126037 0.155642i 0.00526986 0.00650774i
\(573\) 30.3562 + 15.4672i 1.26815 + 0.646153i
\(574\) −24.9979 + 30.5304i −1.04339 + 1.27431i
\(575\) −20.5603 18.0870i −0.857424 0.754281i
\(576\) 10.3739 17.9681i 0.432245 0.748670i
\(577\) 34.5559 1.81100i 1.43858 0.0753928i 0.682986 0.730432i \(-0.260681\pi\)
0.755595 + 0.655039i \(0.227348\pi\)
\(578\) −28.6414 74.6134i −1.19133 3.10351i
\(579\) 3.99887 + 38.0467i 0.166187 + 1.58117i
\(580\) 0.178305 + 0.494427i 0.00740373 + 0.0205300i
\(581\) −16.4424 + 16.2654i −0.682147 + 0.674802i
\(582\) 27.1814 27.1814i 1.12670 1.12670i
\(583\) 0.0680047 + 0.0261045i 0.00281647 + 0.00108114i
\(584\) 15.1318 3.21636i 0.626158 0.133094i
\(585\) 3.56871 15.2522i 0.147548 0.630600i
\(586\) −3.53317 + 16.6222i −0.145954 + 0.686659i
\(587\) 17.8813 9.11097i 0.738039 0.376050i −0.0442042 0.999023i \(-0.514075\pi\)
0.782244 + 0.622973i \(0.214075\pi\)
\(588\) 58.4140 + 23.1517i 2.40895 + 0.954760i
\(589\) 27.2320 8.84822i 1.12208 0.364584i
\(590\) −10.8478 8.22475i −0.446598 0.338608i
\(591\) 7.43679 + 34.9873i 0.305908 + 1.43919i
\(592\) 18.1619 + 22.4280i 0.746448 + 0.921786i
\(593\) 4.81121 + 17.9557i 0.197573 + 0.737352i 0.991586 + 0.129451i \(0.0413215\pi\)
−0.794013 + 0.607901i \(0.792012\pi\)
\(594\) −0.0540215 0.0392489i −0.00221653 0.00161040i
\(595\) 41.4320 + 5.43940i 1.69855 + 0.222994i
\(596\) −57.4394 + 41.7321i −2.35281 + 1.70942i
\(597\) 3.53401 + 2.86179i 0.144638 + 0.117125i
\(598\) 2.13433 + 40.7255i 0.0872794 + 1.66539i
\(599\) 30.6038 17.6691i 1.25044 0.721941i 0.279241 0.960221i \(-0.409917\pi\)
0.971196 + 0.238280i \(0.0765837\pi\)
\(600\) −38.0441 37.1754i −1.55314 1.51768i
\(601\) 0.819532i 0.0334294i 0.999860 + 0.0167147i \(0.00532070\pi\)
−0.999860 + 0.0167147i \(0.994679\pi\)
\(602\) −26.5322 + 11.6412i −1.08137 + 0.474460i
\(603\) 0.718101 + 0.113736i 0.0292433 + 0.00463169i
\(604\) 73.3858 7.71316i 2.98603 0.313844i
\(605\) 23.8830 5.87986i 0.970981 0.239050i
\(606\) 6.19220 58.9149i 0.251541 2.39325i
\(607\) 13.3713 3.58282i 0.542724 0.145422i 0.0229662 0.999736i \(-0.492689\pi\)
0.519757 + 0.854314i \(0.326022\pi\)
\(608\) 2.84839 0.451141i 0.115518 0.0182962i
\(609\) 0.365812 0.0171863i 0.0148234 0.000696423i
\(610\) −63.5156 + 34.9625i −2.57167 + 1.41559i
\(611\) −13.7977 2.93279i −0.558196 0.118648i
\(612\) 52.8700 + 34.3341i 2.13714 + 1.38788i
\(613\) −32.1471 20.8766i −1.29841 0.843197i −0.304406 0.952542i \(-0.598458\pi\)
−0.994004 + 0.109345i \(0.965125\pi\)
\(614\) −16.0155 3.40421i −0.646334 0.137383i
\(615\) −5.92936 30.9921i −0.239095 1.24972i
\(616\) −0.204697 + 0.00961692i −0.00824748 + 0.000387477i
\(617\) −16.5933 + 2.62812i −0.668022 + 0.105804i −0.481229 0.876595i \(-0.659809\pi\)
−0.186793 + 0.982399i \(0.559809\pi\)
\(618\) −1.18071 + 0.316371i −0.0474952 + 0.0127263i
\(619\) −0.649827 + 6.18269i −0.0261187 + 0.248503i 0.973670 + 0.227961i \(0.0732059\pi\)
−0.999789 + 0.0205421i \(0.993461\pi\)
\(620\) −72.8968 29.7029i −2.92761 1.19290i
\(621\) 8.94198 0.939840i 0.358829 0.0377145i
\(622\) 6.30933 + 0.999300i 0.252981 + 0.0400683i
\(623\) 20.2796 8.89783i 0.812484 0.356484i
\(624\) 24.2004i 0.968790i
\(625\) 21.3562 12.9967i 0.854247 0.519868i
\(626\) −9.15199 + 5.28391i −0.365787 + 0.211187i
\(627\) 0.00639625 + 0.122048i 0.000255442 + 0.00487411i
\(628\) 49.3291 + 39.9459i 1.96845 + 1.59402i
\(629\) 48.0125 34.8832i 1.91439 1.39088i
\(630\) −28.8732 + 15.6904i −1.15034 + 0.625120i
\(631\) −16.6120 12.0693i −0.661312 0.480471i 0.205794 0.978595i \(-0.434022\pi\)
−0.867106 + 0.498124i \(0.834022\pi\)
\(632\) 6.41622 + 23.9457i 0.255224 + 0.952508i
\(633\) −13.2246 16.3311i −0.525632 0.649102i
\(634\) −10.4830 49.3185i −0.416332 1.95869i
\(635\) 5.34981 15.3892i 0.212301 0.610703i
\(636\) −37.1507 + 12.0710i −1.47312 + 0.478646i
\(637\) 21.2223 3.12616i 0.840860 0.123863i
\(638\) −0.00218182 + 0.00111169i −8.63790e−5 + 4.40123e-5i
\(639\) −3.73378 + 17.5661i −0.147706 + 0.694902i
\(640\) −38.7207 23.4216i −1.53057 0.925820i
\(641\) −9.09717 + 1.93366i −0.359317 + 0.0763751i −0.384033 0.923319i \(-0.625465\pi\)
0.0247163 + 0.999695i \(0.492132\pi\)
\(642\) 25.5313 + 9.80055i 1.00764 + 0.386797i
\(643\) −10.6811 + 10.6811i −0.421223 + 0.421223i −0.885625 0.464402i \(-0.846269\pi\)
0.464402 + 0.885625i \(0.346269\pi\)
\(644\) 40.2193 39.7862i 1.58486 1.56780i
\(645\) 6.45211 22.2530i 0.254052 0.876212i
\(646\) 5.69727 + 54.2059i 0.224156 + 2.13270i
\(647\) −5.43005 14.1458i −0.213477 0.556127i 0.784470 0.620167i \(-0.212935\pi\)
−0.997947 + 0.0640393i \(0.979602\pi\)
\(648\) 49.1298 2.57478i 1.93000 0.101147i
\(649\) 0.0209698 0.0363207i 0.000823135 0.00142571i
\(650\) −36.0717 9.22025i −1.41485 0.361648i
\(651\) −34.7461 + 42.4361i −1.36181 + 1.66320i
\(652\) −32.5852 16.6030i −1.27614 0.650223i
\(653\) −22.6948 + 28.0257i −0.888116 + 1.09673i 0.106624 + 0.994299i \(0.465996\pi\)
−0.994740 + 0.102432i \(0.967337\pi\)
\(654\) 39.3825 + 17.5342i 1.53998 + 0.685643i
\(655\) −22.4751 + 13.9519i −0.878174 + 0.545145i
\(656\) 8.57490 + 19.2595i 0.334794 + 0.751959i
\(657\) 5.40409 + 5.40409i 0.210833 + 0.210833i
\(658\) 14.6572 + 25.7074i 0.571397 + 1.00218i
\(659\) 30.6779 + 9.96786i 1.19504 + 0.388293i 0.837935 0.545771i \(-0.183763\pi\)
0.357107 + 0.934063i \(0.383763\pi\)
\(660\) 0.202990 0.267728i 0.00790136 0.0104213i
\(661\) −13.5393 12.1908i −0.526618 0.474169i 0.362412 0.932018i \(-0.381953\pi\)
−0.889030 + 0.457849i \(0.848620\pi\)
\(662\) 21.0312 32.3852i 0.817400 1.25869i
\(663\) 49.6975 + 2.60454i 1.93009 + 0.101152i
\(664\) 12.4994 + 38.4692i 0.485071 + 1.49290i
\(665\) −17.3600 7.18341i −0.673193 0.278561i
\(666\) −14.4216 + 44.3852i −0.558827 + 1.71989i
\(667\) 0.118162 0.307822i 0.00457525 0.0119189i
\(668\) −28.5007 7.63675i −1.10273 0.295475i
\(669\) 17.0070 + 1.78751i 0.657530 + 0.0691092i
\(670\) 0.305105 1.70096i 0.0117872 0.0657137i
\(671\) −0.131290 0.180705i −0.00506839 0.00697604i
\(672\) −4.12508 + 3.67400i −0.159128 + 0.141728i
\(673\) −8.71675 + 17.1076i −0.336006 + 0.659449i −0.995756 0.0920367i \(-0.970662\pi\)
0.659750 + 0.751485i \(0.270662\pi\)
\(674\) −53.8205 31.0733i −2.07309 1.19690i
\(675\) −1.61382 + 8.04836i −0.0621159 + 0.309782i
\(676\) −7.04519 12.2026i −0.270969 0.469332i
\(677\) 19.3296 + 29.7649i 0.742895 + 1.14396i 0.984806 + 0.173660i \(0.0555593\pi\)
−0.241911 + 0.970299i \(0.577774\pi\)
\(678\) 3.49909 22.0924i 0.134382 0.848453i
\(679\) −16.2653 + 8.17698i −0.624204 + 0.313804i
\(680\) 41.0457 60.4669i 1.57403 2.31880i
\(681\) 24.6108 10.9574i 0.943088 0.419890i
\(682\) 0.0949172 0.354236i 0.00363457 0.0135644i
\(683\) −7.41808 + 6.00704i −0.283845 + 0.229853i −0.760660 0.649151i \(-0.775124\pi\)
0.476815 + 0.879004i \(0.341791\pi\)
\(684\) −18.9650 21.0627i −0.725143 0.805353i
\(685\) 6.66673 + 3.13274i 0.254723 + 0.119696i
\(686\) −34.5085 28.8848i −1.31754 1.10283i
\(687\) −28.1201 55.1888i −1.07285 2.10558i
\(688\) −0.810168 + 15.4589i −0.0308874 + 0.589366i
\(689\) −8.92332 + 9.91036i −0.339952 + 0.377554i
\(690\) 5.76152 + 68.1720i 0.219337 + 2.59526i
\(691\) −37.4522 + 33.7221i −1.42475 + 1.28285i −0.521823 + 0.853054i \(0.674748\pi\)
−0.902926 + 0.429796i \(0.858585\pi\)
\(692\) −14.2938 90.2473i −0.543367 3.43069i
\(693\) −0.0590617 0.0822238i −0.00224357 0.00312342i
\(694\) −21.6421 + 29.7878i −0.821524 + 1.13073i
\(695\) 9.15148 4.43008i 0.347135 0.168042i
\(696\) 0.260504 0.585101i 0.00987437 0.0221782i
\(697\) 40.4740 15.5365i 1.53306 0.588487i
\(698\) −3.03494 + 1.97091i −0.114874 + 0.0746002i
\(699\) −50.2276 −1.89978
\(700\) 23.7299 + 45.8746i 0.896907 + 1.73390i
\(701\) 41.2864 1.55936 0.779682 0.626176i \(-0.215381\pi\)
0.779682 + 0.626176i \(0.215381\pi\)
\(702\) 10.2525 6.65804i 0.386955 0.251291i
\(703\) −24.9099 + 9.56202i −0.939495 + 0.360638i
\(704\) 0.0617943 0.138792i 0.00232896 0.00523093i
\(705\) −23.2925 4.17803i −0.877244 0.157354i
\(706\) −13.4251 + 18.4781i −0.505261 + 0.695431i
\(707\) −11.5497 + 25.5677i −0.434371 + 0.961571i
\(708\) 3.51827 + 22.2135i 0.132225 + 0.834834i
\(709\) 1.43178 1.28918i 0.0537715 0.0484161i −0.641807 0.766866i \(-0.721815\pi\)
0.695578 + 0.718450i \(0.255148\pi\)
\(710\) 41.5623 + 9.72475i 1.55981 + 0.364963i
\(711\) −8.19493 + 9.10139i −0.307334 + 0.341329i
\(712\) 2.02700 38.6775i 0.0759651 1.44950i
\(713\) 22.4185 + 43.9987i 0.839578 + 1.64777i
\(714\) −65.2617 81.4895i −2.44236 3.04967i
\(715\) 0.0143147 0.113805i 0.000535338 0.00425606i
\(716\) −35.5957 39.5330i −1.33027 1.47742i
\(717\) 7.62472 6.17437i 0.284750 0.230586i
\(718\) −3.86356 + 14.4190i −0.144187 + 0.538112i
\(719\) 44.2991 19.7232i 1.65208 0.735552i 0.652327 0.757938i \(-0.273793\pi\)
0.999749 + 0.0223865i \(0.00712643\pi\)
\(720\) 0.560930 + 17.5482i 0.0209046 + 0.653981i
\(721\) 0.577936 + 0.0334263i 0.0215235 + 0.00124486i
\(722\) −3.38876 + 21.3958i −0.126117 + 0.796270i
\(723\) −0.205633 0.316647i −0.00764756 0.0117762i
\(724\) 11.2262 + 19.4443i 0.417217 + 0.722641i
\(725\) 0.236109 + 0.186724i 0.00876887 + 0.00693476i
\(726\) −53.2178 30.7253i −1.97510 1.14032i
\(727\) −3.31875 + 6.51342i −0.123086 + 0.241569i −0.944325 0.329015i \(-0.893283\pi\)
0.821239 + 0.570584i \(0.193283\pi\)
\(728\) 11.7861 35.6168i 0.436823 1.32005i
\(729\) 7.63022 + 10.5021i 0.282601 + 0.388967i
\(730\) 13.1042 12.5800i 0.485007 0.465607i
\(731\) 31.6591 + 3.32750i 1.17095 + 0.123072i
\(732\) 115.699 + 31.0015i 4.27636 + 1.14585i
\(733\) 3.69327 9.62129i 0.136414 0.355371i −0.848308 0.529503i \(-0.822379\pi\)
0.984722 + 0.174132i \(0.0557119\pi\)
\(734\) 27.0939 83.3864i 1.00005 3.07785i
\(735\) 35.4169 6.37924i 1.30637 0.235302i
\(736\) 1.53691 + 4.73012i 0.0566512 + 0.174354i
\(737\) 0.00531660 0.000278631i 0.000195839 1.02635e-5i
\(738\) −18.5681 + 28.5924i −0.683502 + 1.05250i
\(739\) 16.3525 + 14.7239i 0.601537 + 0.541626i 0.912648 0.408747i \(-0.134034\pi\)
−0.311111 + 0.950374i \(0.600701\pi\)
\(740\) 69.2845 + 24.0856i 2.54695 + 0.885405i
\(741\) −21.2794 6.91411i −0.781720 0.253996i
\(742\) 27.9760 + 0.151440i 1.02703 + 0.00555953i
\(743\) −32.3075 32.3075i −1.18525 1.18525i −0.978366 0.206883i \(-0.933668\pi\)
−0.206883 0.978366i \(-0.566332\pi\)
\(744\) 39.0144 + 87.6278i 1.43034 + 3.21259i
\(745\) −15.3438 + 37.6567i −0.562152 + 1.37963i
\(746\) 41.2660 + 18.3728i 1.51086 + 0.672676i
\(747\) −12.5756 + 15.5296i −0.460119 + 0.568199i
\(748\) 0.411303 + 0.209569i 0.0150387 + 0.00766262i
\(749\) −10.0211 8.20512i −0.366162 0.299809i
\(750\) −60.9773 13.5267i −2.22658 0.493924i
\(751\) −11.0388 + 19.1197i −0.402810 + 0.697687i −0.994064 0.108798i \(-0.965300\pi\)
0.591254 + 0.806485i \(0.298633\pi\)
\(752\) 15.7890 0.827466i 0.575765 0.0301746i
\(753\) −0.109010 0.283980i −0.00397253 0.0103488i
\(754\) −0.0468599 0.445842i −0.00170654 0.0162366i
\(755\) 33.3790 25.9202i 1.21479 0.943332i
\(756\) −16.3566 4.47778i −0.594885 0.162855i
\(757\) 2.36580 2.36580i 0.0859865 0.0859865i −0.662805 0.748792i \(-0.730634\pi\)
0.748792 + 0.662805i \(0.230634\pi\)
\(758\) −50.4951 19.3833i −1.83406 0.704032i
\(759\) −0.206165 + 0.0438218i −0.00748332 + 0.00159063i
\(760\) −24.8614 + 21.4831i −0.901818 + 0.779276i
\(761\) −7.78209 + 36.6118i −0.282101 + 1.32718i 0.577575 + 0.816338i \(0.303999\pi\)
−0.859675 + 0.510841i \(0.829334\pi\)
\(762\) −36.2686 + 18.4798i −1.31387 + 0.669451i
\(763\) −15.0981 13.7431i −0.546589 0.497535i
\(764\) −55.0239 + 17.8784i −1.99070 + 0.646816i
\(765\) 36.0970 + 0.736683i 1.30509 + 0.0266348i
\(766\) −7.77758 36.5906i −0.281015 1.32207i
\(767\) 4.83197 + 5.96698i 0.174472 + 0.215455i
\(768\) 18.4604 + 68.8951i 0.666132 + 2.48604i
\(769\) −31.5396 22.9148i −1.13735 0.826330i −0.150599 0.988595i \(-0.548120\pi\)
−0.986747 + 0.162264i \(0.948120\pi\)
\(770\) −0.198258 + 0.136365i −0.00714473 + 0.00491424i
\(771\) 17.0932 12.4189i 0.615596 0.447257i
\(772\) −50.4876 40.8841i −1.81709 1.47145i
\(773\) −1.21669 23.2158i −0.0437612 0.835014i −0.929046 0.369964i \(-0.879370\pi\)
0.885285 0.465049i \(-0.153963\pi\)
\(774\) −21.6795 + 12.5167i −0.779254 + 0.449902i
\(775\) −44.4430 + 7.56620i −1.59644 + 0.271786i
\(776\) 31.8387i 1.14294i
\(777\) 30.2643 41.1845i 1.08573 1.47749i
\(778\) 28.6099 + 4.53136i 1.02571 + 0.162457i
\(779\) −19.3848 + 2.03743i −0.694534 + 0.0729984i
\(780\) 32.4410 + 52.2592i 1.16157 + 1.87118i
\(781\) −0.0137457 + 0.130782i −0.000491861 + 0.00467975i
\(782\) −90.7949 + 24.3284i −3.24682 + 0.869983i
\(783\) −0.0976210 + 0.0154617i −0.00348869 + 0.000552554i
\(784\) −22.0696 + 9.54110i −0.788201 + 0.340754i
\(785\) 36.0692 + 4.53687i 1.28736 + 0.161928i
\(786\) 64.6466 + 13.7411i 2.30587 + 0.490127i
\(787\) −13.8453 8.99124i −0.493531 0.320503i 0.273764 0.961797i \(-0.411731\pi\)
−0.767295 + 0.641294i \(0.778398\pi\)
\(788\) −50.9422 33.0822i −1.81474 1.17851i
\(789\) −47.0414 9.99896i −1.67472 0.355972i
\(790\) 21.2308 + 19.9156i 0.755358 + 0.708564i
\(791\) −4.86024 + 9.41245i −0.172810 + 0.334668i
\(792\) −0.174874 + 0.0276973i −0.00621388 + 0.000984182i
\(793\) 39.4989 10.5837i 1.40265 0.375838i
\(794\) 1.72174 16.3812i 0.0611022 0.581349i
\(795\) −14.4310 + 17.0954i −0.511814 + 0.606312i
\(796\) −7.67997 + 0.807198i −0.272209 + 0.0286104i
\(797\) −43.0687 6.82142i −1.52557 0.241627i −0.663409 0.748257i \(-0.730891\pi\)
−0.862164 + 0.506630i \(0.830891\pi\)
\(798\) 18.8592 + 42.9832i 0.667609 + 1.52159i
\(799\) 32.5131i 1.15023i
\(800\) −4.54030 + 0.0524369i −0.160524 + 0.00185393i
\(801\) 16.5705 9.56698i 0.585490 0.338033i
\(802\) 2.32531 + 44.3695i 0.0821095 + 1.56674i
\(803\) 0.0434914 + 0.0352186i 0.00153478 + 0.00124284i
\(804\) −2.30973 + 1.67811i −0.0814578 + 0.0591825i
\(805\) 7.55244 31.5083i 0.266189 1.11052i
\(806\) 54.3169 + 39.4635i 1.91323 + 1.39004i
\(807\) 0.900061 + 3.35907i 0.0316836 + 0.118245i
\(808\) 30.8782 + 38.1313i 1.08629 + 1.34146i
\(809\) 3.06134 + 14.4025i 0.107631 + 0.506364i 0.998628 + 0.0523559i \(0.0166730\pi\)
−0.890997 + 0.454008i \(0.849994\pi\)
\(810\) 47.4193 32.9951i 1.66614 1.15933i
\(811\) 24.6251 8.00118i 0.864704 0.280959i 0.157112 0.987581i \(-0.449782\pi\)
0.707592 + 0.706621i \(0.249782\pi\)
\(812\) −0.418623 + 0.459897i −0.0146908 + 0.0161392i
\(813\) −18.6144 + 9.48450i −0.652835 + 0.332636i
\(814\) −0.0710517 + 0.334272i −0.00249036 + 0.0117162i
\(815\) −20.8708 + 1.76388i −0.731071 + 0.0617862i
\(816\) −54.5610 + 11.5973i −1.91002 + 0.405986i
\(817\) −13.3616 5.12904i −0.467464 0.179442i
\(818\) −27.3344 + 27.3344i −0.955725 + 0.955725i
\(819\) 17.9282 4.69998i 0.626463 0.164231i
\(820\) 44.3347 + 30.0950i 1.54823 + 1.05096i
\(821\) −5.12351 48.7470i −0.178812 1.70128i −0.604657 0.796486i \(-0.706690\pi\)
0.425846 0.904796i \(-0.359977\pi\)
\(822\) −6.59517 17.1810i −0.230033 0.599256i
\(823\) −52.8866 + 2.77167i −1.84351 + 0.0966142i −0.941891 0.335918i \(-0.890953\pi\)
−0.901618 + 0.432533i \(0.857620\pi\)
\(824\) 0.506220 0.876799i 0.0176350 0.0305447i
\(825\) 0.0179024 0.191589i 0.000623282 0.00667028i
\(826\) 2.60585 15.8953i 0.0906690 0.553068i
\(827\) 4.78458 + 2.43786i 0.166376 + 0.0847728i 0.535196 0.844728i \(-0.320238\pi\)
−0.368819 + 0.929501i \(0.620238\pi\)
\(828\) 30.7609 37.9865i 1.06901 1.32012i
\(829\) −32.0214 14.2568i −1.11215 0.495161i −0.233369 0.972388i \(-0.574975\pi\)
−0.878780 + 0.477228i \(0.841642\pi\)
\(830\) 36.2942 + 30.6375i 1.25979 + 1.06344i
\(831\) 12.7778 + 28.6994i 0.443257 + 0.995571i
\(832\) 19.6675 + 19.6675i 0.681847 + 0.681847i
\(833\) 17.2183 + 46.3488i 0.596577 + 1.60589i
\(834\) −24.1587 7.84964i −0.836548 0.271811i
\(835\) −16.1750 + 4.89301i −0.559757 + 0.169330i
\(836\) −0.154233 0.138872i −0.00533427 0.00480300i
\(837\) 8.06201 12.4144i 0.278664 0.429105i
\(838\) 86.2499 + 4.52017i 2.97945 + 0.156147i
\(839\) −4.17081 12.8364i −0.143992 0.443163i 0.852888 0.522095i \(-0.174849\pi\)
−0.996880 + 0.0789314i \(0.974849\pi\)
\(840\) 17.8534 60.3520i 0.616000 2.08234i
\(841\) 8.96037 27.5772i 0.308978 0.950938i
\(842\) −12.2359 + 31.8755i −0.421675 + 1.09850i
\(843\) 8.85167 + 2.37180i 0.304868 + 0.0816891i
\(844\) 35.4900 + 3.73015i 1.22162 + 0.128397i
\(845\) −7.11407 3.80960i −0.244731 0.131054i
\(846\) 15.0284 + 20.6848i 0.516686 + 0.711158i
\(847\) 19.3560 + 21.7325i 0.665081 + 0.746737i
\(848\) 6.78594 13.3182i 0.233030 0.457347i
\(849\) −37.6256 21.7232i −1.29131 0.745537i
\(850\) 3.50126 85.7441i 0.120092 2.94100i
\(851\) −23.0079 39.8508i −0.788699 1.36607i
\(852\) −38.4075 59.1423i −1.31582 2.02618i
\(853\) 5.33840 33.7053i 0.182783 1.15405i −0.710214 0.703986i \(-0.751402\pi\)
0.892997 0.450063i \(-0.148598\pi\)
\(854\) −71.6923 47.1112i −2.45326 1.61211i
\(855\) −15.5904 4.52033i −0.533181 0.154592i
\(856\) −20.6929 + 9.21306i −0.707268 + 0.314896i
\(857\) 1.77688 6.63141i 0.0606971 0.226525i −0.928914 0.370296i \(-0.879256\pi\)
0.989611 + 0.143771i \(0.0459230\pi\)
\(858\) −0.222706 + 0.180344i −0.00760305 + 0.00615683i
\(859\) 29.6526 + 32.9326i 1.01174 + 1.12365i 0.992303 + 0.123834i \(0.0395192\pi\)
0.0194321 + 0.999811i \(0.493814\pi\)
\(860\) 18.9735 + 34.4686i 0.646990 + 1.17537i
\(861\) 29.1419 23.3386i 0.993152 0.795376i
\(862\) 4.19824 + 8.23950i 0.142993 + 0.280639i
\(863\) 0.105676 2.01642i 0.00359726 0.0686398i −0.996241 0.0866249i \(-0.972392\pi\)
0.999838 + 0.0179852i \(0.00572516\pi\)
\(864\) 0.997589 1.10794i 0.0339387 0.0376927i
\(865\) −34.2154 39.5959i −1.16336 1.34630i
\(866\) 2.24014 2.01703i 0.0761230 0.0685415i
\(867\) 11.8297 + 74.6900i 0.401759 + 2.53661i
\(868\) −9.23402 92.6791i −0.313423 3.14573i
\(869\) −0.0527129 + 0.0725531i −0.00178816 + 0.00246119i
\(870\) −0.102468 0.745052i −0.00347399 0.0252596i
\(871\) −0.396434 + 0.890406i −0.0134327 + 0.0301703i
\(872\) −33.3345 + 12.7959i −1.12885 + 0.433324i
\(873\) −13.1916 + 8.56673i −0.446468 + 0.289940i
\(874\) 42.2612 1.42950
\(875\) 25.4037 + 15.1542i 0.858802 + 0.512307i
\(876\) −30.0106 −1.01396
\(877\) −39.3610 + 25.5614i −1.32913 + 0.863146i −0.996794 0.0800162i \(-0.974503\pi\)
−0.332334 + 0.943162i \(0.607836\pi\)
\(878\) −12.3548 + 4.74256i −0.416954 + 0.160054i
\(879\) 6.53998 14.6890i 0.220588 0.495449i
\(880\) 0.0175166 + 0.127364i 0.000590485 + 0.00429345i
\(881\) −12.9945 + 17.8855i −0.437797 + 0.602576i −0.969721 0.244216i \(-0.921469\pi\)
0.531924 + 0.846792i \(0.321469\pi\)
\(882\) −32.3778 21.5283i −1.09022 0.724896i
\(883\) 2.48456 + 15.6869i 0.0836122 + 0.527906i 0.993571 + 0.113208i \(0.0361128\pi\)
−0.909959 + 0.414698i \(0.863887\pi\)
\(884\) −62.8034 + 56.5485i −2.11231 + 1.90193i
\(885\) 8.42180 + 9.74614i 0.283096 + 0.327613i
\(886\) 29.7457 33.0360i 0.999327 1.10986i
\(887\) 0.918554 17.5270i 0.0308420 0.588501i −0.938873 0.344263i \(-0.888129\pi\)
0.969715 0.244238i \(-0.0785378\pi\)
\(888\) −40.5794 79.6415i −1.36175 2.67259i
\(889\) 19.0564 2.91258i 0.639130 0.0976848i
\(890\) −21.9310 39.8416i −0.735130 1.33549i
\(891\) 0.119088 + 0.132260i 0.00398958 + 0.00443088i
\(892\) −22.5682 + 18.2753i −0.755638 + 0.611904i
\(893\) −3.78336 + 14.1197i −0.126605 + 0.472498i
\(894\) 92.8081 41.3208i 3.10397 1.38198i
\(895\) −29.2619 8.48429i −0.978117 0.283598i
\(896\) 3.09170 53.4551i 0.103287 1.78581i
\(897\) 6.03632 38.1118i 0.201547 1.27252i
\(898\) −9.64664 14.8545i −0.321912 0.495702i
\(899\) −0.271415 0.470104i −0.00905219 0.0156789i
\(900\) 24.7349 + 37.1422i 0.824497 + 1.23807i
\(901\) −26.6196 15.3689i −0.886829 0.512011i
\(902\) −0.113336 + 0.222435i −0.00377369 + 0.00740629i
\(903\) 26.8459 5.55457i 0.893377 0.184844i
\(904\) 10.8896 + 14.9882i 0.362182 + 0.498500i
\(905\) 11.3359 + 6.07041i 0.376818 + 0.201787i
\(906\) −105.006 11.0366i −3.48860 0.366667i
\(907\) −28.7163 7.69450i −0.953508 0.255492i −0.251658 0.967816i \(-0.580976\pi\)
−0.701850 + 0.712325i \(0.747642\pi\)
\(908\) −16.3947 + 42.7097i −0.544078 + 1.41737i
\(909\) −7.49054 + 23.0535i −0.248445 + 0.764636i
\(910\) −10.2994 42.8320i −0.341422 1.41987i
\(911\) 12.1969 + 37.5382i 0.404101 + 1.24370i 0.921643 + 0.388038i \(0.126847\pi\)
−0.517542 + 0.855658i \(0.673153\pi\)
\(912\) 25.0441 + 1.31251i 0.829293 + 0.0434614i
\(913\) −0.0796949 + 0.122719i −0.00263752 + 0.00406142i
\(914\) 21.3387 + 19.2135i 0.705822 + 0.635525i
\(915\) 65.6624 19.8632i 2.17073 0.656658i
\(916\) 100.036 + 32.5036i 3.30528 + 1.07395i
\(917\) −27.0216 15.7966i −0.892331 0.521648i
\(918\) 19.9241 + 19.9241i 0.657593 + 0.657593i
\(919\) 6.01760 + 13.5158i 0.198502 + 0.445844i 0.985181 0.171519i \(-0.0548676\pi\)
−0.786678 + 0.617363i \(0.788201\pi\)
\(920\) −43.3007 36.5520i −1.42758 1.20508i
\(921\) 14.1529 + 6.30127i 0.466353 + 0.207634i
\(922\) −1.30162 + 1.60736i −0.0428664 + 0.0529356i
\(923\) −21.4508 10.9297i −0.706061 0.359756i
\(924\) 0.392301 + 0.0643132i 0.0129058 + 0.00211575i
\(925\) 40.9885 9.20837i 1.34769 0.302769i
\(926\) 46.9570 81.3318i 1.54310 2.67273i
\(927\) 0.499488 0.0261771i 0.0164053 0.000859767i
\(928\) −0.0195929 0.0510413i −0.000643169 0.00167551i
\(929\) 1.81026 + 17.2234i 0.0593925 + 0.565082i 0.983239 + 0.182320i \(0.0583606\pi\)
−0.923847 + 0.382763i \(0.874973\pi\)
\(930\) 93.1908 + 63.2591i 3.05585 + 2.07435i
\(931\) −2.08416 22.1318i −0.0683056 0.725341i
\(932\) 60.3124 60.3124i 1.97560 1.97560i
\(933\) −5.64278 2.16606i −0.184736 0.0709136i
\(934\) −21.2562 + 4.51814i −0.695523 + 0.147838i
\(935\) 0.263439 0.0222644i 0.00861538 0.000728125i
\(936\) 6.73928 31.7058i 0.220280 1.03634i
\(937\) 29.8820 15.2256i 0.976202 0.497400i 0.108291 0.994119i \(-0.465462\pi\)
0.867911 + 0.496719i \(0.165462\pi\)
\(938\) 1.94804 0.621317i 0.0636056 0.0202867i
\(939\) 9.50975 3.08990i 0.310339 0.100835i
\(940\) 32.9861 22.9523i 1.07589 0.748621i
\(941\) 9.06149 + 42.6310i 0.295396 + 1.38973i 0.836128 + 0.548534i \(0.184814\pi\)
−0.540732 + 0.841195i \(0.681853\pi\)
\(942\) −57.1579 70.5841i −1.86230 2.29975i
\(943\) −8.70021 32.4696i −0.283318 1.05736i
\(944\) −6.96237 5.05846i −0.226606 0.164639i
\(945\) −9.31155 + 2.76186i −0.302905 + 0.0898434i
\(946\) −0.148300 + 0.107746i −0.00482164 + 0.00350312i
\(947\) −4.28310 3.46839i −0.139182 0.112707i 0.557201 0.830378i \(-0.311875\pi\)
−0.696383 + 0.717670i \(0.745209\pi\)
\(948\) −2.51693 48.0259i −0.0817462 1.55981i
\(949\) −8.87279 + 5.12271i −0.288023 + 0.166290i
\(950\) −11.4981 + 36.8293i −0.373047 + 1.19490i
\(951\) 47.7071i 1.54701i
\(952\) 85.9480 + 9.50416i 2.78559 + 0.308032i
\(953\) −6.68823 1.05931i −0.216653 0.0343145i 0.0471642 0.998887i \(-0.484982\pi\)
−0.263817 + 0.964573i \(0.584982\pi\)
\(954\) 24.0393 2.52663i 0.778300 0.0818026i
\(955\) −21.3738 + 25.3201i −0.691638 + 0.819338i
\(956\) −1.74155 + 16.5697i −0.0563257 + 0.535903i
\(957\) 0.00223799 0.000599669i 7.23441e−5 1.93845e-5i
\(958\) 2.32607 0.368413i 0.0751518 0.0119029i
\(959\) 0.409023 + 8.70608i 0.0132080 + 0.281134i
\(960\) 34.0315 + 31.9232i 1.09836 + 1.03032i
\(961\) 49.1979 + 10.4573i 1.58703 + 0.337333i
\(962\) −52.4706 34.0748i −1.69172 1.09862i
\(963\) −9.38497 6.09467i −0.302426 0.196398i
\(964\) 0.627144 + 0.133304i 0.0201989 + 0.00429342i
\(965\) −36.9163 4.64342i −1.18838 0.149477i
\(966\) −68.1278 + 43.7202i −2.19198 + 1.40668i
\(967\) −57.0421 + 9.03458i −1.83435 + 0.290533i −0.975222 0.221228i \(-0.928994\pi\)
−0.859128 + 0.511760i \(0.828994\pi\)
\(968\) 49.1630 13.1732i 1.58016 0.423403i
\(969\) 5.39069 51.2890i 0.173174 1.64764i
\(970\) 19.7179 + 31.7636i 0.633105 + 1.01987i
\(971\) −19.5233 + 2.05199i −0.626534 + 0.0658514i −0.412474 0.910969i \(-0.635335\pi\)
−0.214060 + 0.976821i \(0.568669\pi\)
\(972\) −75.2723 11.9220i −2.41436 0.382397i
\(973\) 9.69420 + 7.12374i 0.310782 + 0.228377i
\(974\) 84.2473i 2.69946i
\(975\) 31.5710 + 15.6296i 1.01108 + 0.500548i
\(976\) −39.6935 + 22.9170i −1.27056 + 0.733556i
\(977\) −1.28796 24.5758i −0.0412056 0.786249i −0.938597 0.345014i \(-0.887874\pi\)
0.897392 0.441235i \(-0.145459\pi\)
\(978\) 40.6674 + 32.9318i 1.30040 + 1.05304i
\(979\) 0.113351 0.0823545i 0.00362272 0.00263206i
\(980\) −34.8680 + 50.1882i −1.11382 + 1.60320i
\(981\) −14.2709 10.3684i −0.455634 0.331038i
\(982\) −3.21913 12.0140i −0.102727 0.383381i
\(983\) −28.2657 34.9053i −0.901537 1.11331i −0.993072 0.117504i \(-0.962511\pi\)
0.0915351 0.995802i \(-0.470823\pi\)
\(984\) −13.5758 63.8690i −0.432780 2.03607i
\(985\) −34.7808 0.709822i −1.10821 0.0226168i
\(986\) 0.982717 0.319304i 0.0312961 0.0101687i
\(987\) −8.50816 26.6759i −0.270818 0.849103i
\(988\) 33.8543 17.2496i 1.07705 0.548784i
\(989\) 5.13183 24.1433i 0.163183 0.767714i
\(990\) −0.157308 + 0.135933i −0.00499959 + 0.00432023i
\(991\) 45.3163 9.63229i 1.43952 0.305980i 0.578972 0.815347i \(-0.303454\pi\)
0.860549 + 0.509368i \(0.170121\pi\)
\(992\) 7.64421 + 2.93434i 0.242704 + 0.0931653i
\(993\) −25.8356 + 25.8356i −0.819867 + 0.819867i
\(994\) 12.8075 + 48.8545i 0.406229 + 1.54957i
\(995\) −3.49318 + 2.71260i −0.110741 + 0.0859952i
\(996\) −8.20219 78.0386i −0.259896 2.47275i
\(997\) 8.86960 + 23.1061i 0.280903 + 0.731778i 0.999345 + 0.0361906i \(0.0115223\pi\)
−0.718442 + 0.695587i \(0.755144\pi\)
\(998\) 88.4014 4.63292i 2.79830 0.146653i
\(999\) −6.89686 + 11.9457i −0.218207 + 0.377946i
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 175.2.x.a.33.18 288
5.2 odd 4 875.2.bb.b.607.18 288
5.3 odd 4 875.2.bb.a.607.1 288
5.4 even 2 875.2.bb.c.768.1 288
7.3 odd 6 inner 175.2.x.a.108.18 yes 288
25.3 odd 20 875.2.bb.c.257.1 288
25.4 even 10 875.2.bb.a.243.18 288
25.21 even 5 875.2.bb.b.243.1 288
25.22 odd 20 inner 175.2.x.a.47.18 yes 288
35.3 even 12 875.2.bb.a.857.18 288
35.17 even 12 875.2.bb.b.857.1 288
35.24 odd 6 875.2.bb.c.143.1 288
175.3 even 60 875.2.bb.c.507.1 288
175.122 even 60 inner 175.2.x.a.122.18 yes 288
175.129 odd 30 875.2.bb.a.493.1 288
175.171 odd 30 875.2.bb.b.493.18 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.x.a.33.18 288 1.1 even 1 trivial
175.2.x.a.47.18 yes 288 25.22 odd 20 inner
175.2.x.a.108.18 yes 288 7.3 odd 6 inner
175.2.x.a.122.18 yes 288 175.122 even 60 inner
875.2.bb.a.243.18 288 25.4 even 10
875.2.bb.a.493.1 288 175.129 odd 30
875.2.bb.a.607.1 288 5.3 odd 4
875.2.bb.a.857.18 288 35.3 even 12
875.2.bb.b.243.1 288 25.21 even 5
875.2.bb.b.493.18 288 175.171 odd 30
875.2.bb.b.607.18 288 5.2 odd 4
875.2.bb.b.857.1 288 35.17 even 12
875.2.bb.c.143.1 288 35.24 odd 6
875.2.bb.c.257.1 288 25.3 odd 20
875.2.bb.c.507.1 288 175.3 even 60
875.2.bb.c.768.1 288 5.4 even 2