Properties

Label 175.2.t.a.39.14
Level $175$
Weight $2$
Character 175.39
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(4,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([3, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.t (of order \(30\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 39.14
Character \(\chi\) \(=\) 175.39
Dual form 175.2.t.a.9.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.616889 - 1.38556i) q^{2} +(2.15328 - 1.93883i) q^{3} +(-0.200952 - 0.223180i) q^{4} +(-1.69368 + 1.45995i) q^{5} +(-1.35801 - 4.17954i) q^{6} +(-2.50069 + 0.864026i) q^{7} +(2.45170 - 0.796607i) q^{8} +(0.564002 - 5.36612i) q^{9} +O(q^{10})\) \(q+(0.616889 - 1.38556i) q^{2} +(2.15328 - 1.93883i) q^{3} +(-0.200952 - 0.223180i) q^{4} +(-1.69368 + 1.45995i) q^{5} +(-1.35801 - 4.17954i) q^{6} +(-2.50069 + 0.864026i) q^{7} +(2.45170 - 0.796607i) q^{8} +(0.564002 - 5.36612i) q^{9} +(0.978032 + 3.24731i) q^{10} +(0.0311666 + 0.296530i) q^{11} +(-0.865413 - 0.0909585i) q^{12} +(-0.705999 + 0.971725i) q^{13} +(-0.345493 + 3.99786i) q^{14} +(-0.816379 + 6.42744i) q^{15} +(0.471470 - 4.48574i) q^{16} +(-1.37395 + 6.46391i) q^{17} +(-7.08713 - 4.09176i) q^{18} +(2.07257 - 2.30182i) q^{19} +(0.666179 + 0.0846145i) q^{20} +(-3.70950 + 6.70890i) q^{21} +(0.430086 + 0.139743i) q^{22} +(-2.69533 + 6.05382i) q^{23} +(3.73473 - 6.46875i) q^{24} +(0.737087 - 4.94537i) q^{25} +(0.910856 + 1.57765i) q^{26} +(-4.08014 - 5.61583i) q^{27} +(0.695352 + 0.384476i) q^{28} +(1.97373 - 6.07451i) q^{29} +(8.40196 + 5.09615i) q^{30} +(1.12021 + 0.238107i) q^{31} +(-1.45939 - 0.842577i) q^{32} +(0.642032 + 0.578088i) q^{33} +(8.10853 + 5.89119i) q^{34} +(2.97393 - 5.11427i) q^{35} +(-1.31095 + 0.952458i) q^{36} +(-2.74736 - 0.288759i) q^{37} +(-1.91076 - 4.29163i) q^{38} +(0.363788 + 3.46121i) q^{39} +(-2.98939 + 4.92856i) q^{40} +(-7.69071 - 5.58763i) q^{41} +(7.00720 + 9.27837i) q^{42} -2.00893i q^{43} +(0.0599166 - 0.0665441i) q^{44} +(6.87904 + 9.91189i) q^{45} +(6.72518 + 7.46907i) q^{46} +(1.56037 + 7.34097i) q^{47} +(-7.68185 - 10.5732i) q^{48} +(5.50692 - 4.32133i) q^{49} +(-6.39739 - 4.07202i) q^{50} +(9.57389 + 16.5825i) q^{51} +(0.358741 - 0.0377052i) q^{52} +(5.45461 - 4.91135i) q^{53} +(-10.2980 + 2.18892i) q^{54} +(-0.485706 - 0.456725i) q^{55} +(-5.44267 + 4.11040i) q^{56} -8.97484i q^{57} +(-7.19900 - 6.48201i) q^{58} +(-11.2461 + 5.00707i) q^{59} +(1.59853 - 1.10941i) q^{60} +(-8.55099 - 3.80715i) q^{61} +(1.02096 - 1.40522i) q^{62} +(3.22607 + 13.9063i) q^{63} +(5.23034 - 3.80006i) q^{64} +(-0.222935 - 2.67651i) q^{65} +(1.19704 - 0.532954i) q^{66} +(1.71355 - 8.06160i) q^{67} +(1.71871 - 0.992297i) q^{68} +(5.93348 + 18.2614i) q^{69} +(-5.25152 - 7.27548i) q^{70} +(-1.15037 + 3.54049i) q^{71} +(-2.89192 - 13.6054i) q^{72} +(8.30494 - 0.872884i) q^{73} +(-2.09491 + 3.62849i) q^{74} +(-8.00106 - 12.0779i) q^{75} -0.930207 q^{76} +(-0.334148 - 0.714602i) q^{77} +(5.02012 + 1.63113i) q^{78} +(7.57630 - 1.61039i) q^{79} +(5.75044 + 8.28571i) q^{80} +(-3.84052 - 0.816327i) q^{81} +(-12.4863 + 7.20896i) q^{82} +(1.86230 - 0.605097i) q^{83} +(2.24272 - 0.520280i) q^{84} +(-7.10996 - 12.9537i) q^{85} +(-2.78349 - 1.23929i) q^{86} +(-7.52742 - 16.9069i) q^{87} +(0.312629 + 0.702177i) q^{88} +(-3.79878 - 1.69132i) q^{89} +(17.9771 - 3.41675i) q^{90} +(0.925891 - 3.03999i) q^{91} +(1.89272 - 0.614983i) q^{92} +(2.87377 - 1.65917i) q^{93} +(11.1339 + 2.36658i) q^{94} +(-0.149718 + 6.92440i) q^{95} +(-4.77608 + 1.01519i) q^{96} +(-3.80086 - 1.23497i) q^{97} +(-2.59028 - 10.2959i) q^{98} +1.60880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.616889 1.38556i 0.436207 0.979736i −0.552996 0.833184i \(-0.686516\pi\)
0.989203 0.146552i \(-0.0468177\pi\)
\(3\) 2.15328 1.93883i 1.24320 1.11938i 0.254882 0.966972i \(-0.417963\pi\)
0.988317 0.152409i \(-0.0487032\pi\)
\(4\) −0.200952 0.223180i −0.100476 0.111590i
\(5\) −1.69368 + 1.45995i −0.757436 + 0.652910i
\(6\) −1.35801 4.17954i −0.554407 1.70629i
\(7\) −2.50069 + 0.864026i −0.945173 + 0.326571i
\(8\) 2.45170 0.796607i 0.866808 0.281643i
\(9\) 0.564002 5.36612i 0.188001 1.78871i
\(10\) 0.978032 + 3.24731i 0.309281 + 1.02689i
\(11\) 0.0311666 + 0.296530i 0.00939709 + 0.0894073i 0.998215 0.0597192i \(-0.0190205\pi\)
−0.988818 + 0.149126i \(0.952354\pi\)
\(12\) −0.865413 0.0909585i −0.249823 0.0262575i
\(13\) −0.705999 + 0.971725i −0.195809 + 0.269508i −0.895620 0.444820i \(-0.853268\pi\)
0.699811 + 0.714328i \(0.253268\pi\)
\(14\) −0.345493 + 3.99786i −0.0923369 + 1.06847i
\(15\) −0.816379 + 6.42744i −0.210788 + 1.65956i
\(16\) 0.471470 4.48574i 0.117867 1.12143i
\(17\) −1.37395 + 6.46391i −0.333231 + 1.56773i 0.418475 + 0.908228i \(0.362565\pi\)
−0.751705 + 0.659499i \(0.770768\pi\)
\(18\) −7.08713 4.09176i −1.67045 0.964437i
\(19\) 2.07257 2.30182i 0.475481 0.528075i −0.456917 0.889509i \(-0.651046\pi\)
0.932397 + 0.361435i \(0.117713\pi\)
\(20\) 0.666179 + 0.0846145i 0.148962 + 0.0189204i
\(21\) −3.70950 + 6.70890i −0.809480 + 1.46400i
\(22\) 0.430086 + 0.139743i 0.0916946 + 0.0297934i
\(23\) −2.69533 + 6.05382i −0.562016 + 1.26231i 0.379453 + 0.925211i \(0.376112\pi\)
−0.941470 + 0.337098i \(0.890555\pi\)
\(24\) 3.73473 6.46875i 0.762349 1.32043i
\(25\) 0.737087 4.94537i 0.147417 0.989074i
\(26\) 0.910856 + 1.57765i 0.178634 + 0.309402i
\(27\) −4.08014 5.61583i −0.785224 1.08077i
\(28\) 0.695352 + 0.384476i 0.131409 + 0.0726591i
\(29\) 1.97373 6.07451i 0.366512 1.12801i −0.582517 0.812818i \(-0.697932\pi\)
0.949029 0.315189i \(-0.102068\pi\)
\(30\) 8.40196 + 5.09615i 1.53398 + 0.930426i
\(31\) 1.12021 + 0.238107i 0.201195 + 0.0427654i 0.307407 0.951578i \(-0.400539\pi\)
−0.106212 + 0.994344i \(0.533872\pi\)
\(32\) −1.45939 0.842577i −0.257985 0.148948i
\(33\) 0.642032 + 0.578088i 0.111763 + 0.100632i
\(34\) 8.10853 + 5.89119i 1.39060 + 1.01033i
\(35\) 2.97393 5.11427i 0.502686 0.864469i
\(36\) −1.31095 + 0.952458i −0.218491 + 0.158743i
\(37\) −2.74736 0.288759i −0.451663 0.0474717i −0.124034 0.992278i \(-0.539583\pi\)
−0.327629 + 0.944806i \(0.606250\pi\)
\(38\) −1.91076 4.29163i −0.309966 0.696195i
\(39\) 0.363788 + 3.46121i 0.0582527 + 0.554237i
\(40\) −2.98939 + 4.92856i −0.472664 + 0.779274i
\(41\) −7.69071 5.58763i −1.20109 0.872641i −0.206695 0.978405i \(-0.566271\pi\)
−0.994391 + 0.105765i \(0.966271\pi\)
\(42\) 7.00720 + 9.27837i 1.08123 + 1.43168i
\(43\) 2.00893i 0.306359i −0.988198 0.153180i \(-0.951049\pi\)
0.988198 0.153180i \(-0.0489513\pi\)
\(44\) 0.0599166 0.0665441i 0.00903276 0.0100319i
\(45\) 6.87904 + 9.91189i 1.02547 + 1.47758i
\(46\) 6.72518 + 7.46907i 0.991574 + 1.10125i
\(47\) 1.56037 + 7.34097i 0.227604 + 1.07079i 0.932413 + 0.361394i \(0.117699\pi\)
−0.704810 + 0.709397i \(0.748968\pi\)
\(48\) −7.68185 10.5732i −1.10878 1.52610i
\(49\) 5.50692 4.32133i 0.786702 0.617332i
\(50\) −6.39739 4.07202i −0.904727 0.575871i
\(51\) 9.57389 + 16.5825i 1.34061 + 2.32201i
\(52\) 0.358741 0.0377052i 0.0497484 0.00522877i
\(53\) 5.45461 4.91135i 0.749248 0.674626i −0.203265 0.979124i \(-0.565155\pi\)
0.952513 + 0.304498i \(0.0984887\pi\)
\(54\) −10.2980 + 2.18892i −1.40139 + 0.297874i
\(55\) −0.485706 0.456725i −0.0654926 0.0615848i
\(56\) −5.44267 + 4.11040i −0.727307 + 0.549276i
\(57\) 8.97484i 1.18875i
\(58\) −7.19900 6.48201i −0.945275 0.851129i
\(59\) −11.2461 + 5.00707i −1.46411 + 0.651865i −0.975372 0.220565i \(-0.929210\pi\)
−0.488740 + 0.872429i \(0.662543\pi\)
\(60\) 1.59853 1.10941i 0.206369 0.143224i
\(61\) −8.55099 3.80715i −1.09484 0.487455i −0.221796 0.975093i \(-0.571192\pi\)
−0.873046 + 0.487638i \(0.837859\pi\)
\(62\) 1.02096 1.40522i 0.129661 0.178464i
\(63\) 3.22607 + 13.9063i 0.406447 + 1.75203i
\(64\) 5.23034 3.80006i 0.653792 0.475008i
\(65\) −0.222935 2.67651i −0.0276517 0.331981i
\(66\) 1.19704 0.532954i 0.147345 0.0656022i
\(67\) 1.71355 8.06160i 0.209343 0.984881i −0.740477 0.672082i \(-0.765400\pi\)
0.949819 0.312799i \(-0.101266\pi\)
\(68\) 1.71871 0.992297i 0.208424 0.120334i
\(69\) 5.93348 + 18.2614i 0.714307 + 2.19841i
\(70\) −5.25152 7.27548i −0.627677 0.869587i
\(71\) −1.15037 + 3.54049i −0.136524 + 0.420179i −0.995824 0.0912938i \(-0.970900\pi\)
0.859300 + 0.511472i \(0.170900\pi\)
\(72\) −2.89192 13.6054i −0.340816 1.60341i
\(73\) 8.30494 0.872884i 0.972019 0.102163i 0.394813 0.918762i \(-0.370809\pi\)
0.577206 + 0.816598i \(0.304143\pi\)
\(74\) −2.09491 + 3.62849i −0.243528 + 0.421803i
\(75\) −8.00106 12.0779i −0.923882 1.39463i
\(76\) −0.930207 −0.106702
\(77\) −0.334148 0.714602i −0.0380797 0.0814365i
\(78\) 5.02012 + 1.63113i 0.568416 + 0.184690i
\(79\) 7.57630 1.61039i 0.852400 0.181183i 0.239063 0.971004i \(-0.423160\pi\)
0.613338 + 0.789821i \(0.289827\pi\)
\(80\) 5.75044 + 8.28571i 0.642918 + 0.926371i
\(81\) −3.84052 0.816327i −0.426724 0.0907030i
\(82\) −12.4863 + 7.20896i −1.37888 + 0.796096i
\(83\) 1.86230 0.605097i 0.204414 0.0664180i −0.205021 0.978758i \(-0.565726\pi\)
0.409434 + 0.912340i \(0.365726\pi\)
\(84\) 2.24272 0.520280i 0.244701 0.0567672i
\(85\) −7.10996 12.9537i −0.771184 1.40502i
\(86\) −2.78349 1.23929i −0.300151 0.133636i
\(87\) −7.52742 16.9069i −0.807024 1.81260i
\(88\) 0.312629 + 0.702177i 0.0333264 + 0.0748524i
\(89\) −3.79878 1.69132i −0.402669 0.179280i 0.195401 0.980723i \(-0.437399\pi\)
−0.598071 + 0.801443i \(0.704066\pi\)
\(90\) 17.9771 3.41675i 1.89495 0.360157i
\(91\) 0.925891 3.03999i 0.0970598 0.318677i
\(92\) 1.89272 0.614983i 0.197330 0.0641164i
\(93\) 2.87377 1.65917i 0.297997 0.172048i
\(94\) 11.1339 + 2.36658i 1.14837 + 0.244095i
\(95\) −0.149718 + 6.92440i −0.0153608 + 0.710428i
\(96\) −4.77608 + 1.01519i −0.487457 + 0.103612i
\(97\) −3.80086 1.23497i −0.385919 0.125393i 0.109630 0.993972i \(-0.465033\pi\)
−0.495549 + 0.868580i \(0.665033\pi\)
\(98\) −2.59028 10.2959i −0.261658 1.04005i
\(99\) 1.60880 0.161690
\(100\) −1.25183 + 0.829279i −0.125183 + 0.0829279i
\(101\) 1.53118 2.65208i 0.152358 0.263892i −0.779736 0.626108i \(-0.784647\pi\)
0.932094 + 0.362217i \(0.117980\pi\)
\(102\) 28.8820 3.03562i 2.85974 0.300571i
\(103\) 1.78729 + 8.40853i 0.176107 + 0.828517i 0.974147 + 0.225913i \(0.0725366\pi\)
−0.798041 + 0.602604i \(0.794130\pi\)
\(104\) −0.956819 + 2.94479i −0.0938238 + 0.288760i
\(105\) −3.51196 16.7784i −0.342732 1.63740i
\(106\) −3.44006 10.5874i −0.334128 1.02834i
\(107\) −13.5997 + 7.85178i −1.31473 + 0.759060i −0.982876 0.184270i \(-0.941008\pi\)
−0.331856 + 0.943330i \(0.607675\pi\)
\(108\) −0.433428 + 2.03912i −0.0417066 + 0.196214i
\(109\) −12.8122 + 5.70436i −1.22719 + 0.546379i −0.914928 0.403618i \(-0.867752\pi\)
−0.312259 + 0.949997i \(0.601086\pi\)
\(110\) −0.932445 + 0.391224i −0.0889052 + 0.0373018i
\(111\) −6.47570 + 4.70487i −0.614646 + 0.446567i
\(112\) 2.69679 + 11.6248i 0.254823 + 1.09844i
\(113\) 3.13291 4.31207i 0.294719 0.405646i −0.635821 0.771837i \(-0.719338\pi\)
0.930540 + 0.366191i \(0.119338\pi\)
\(114\) −12.4351 5.53648i −1.16466 0.518539i
\(115\) −4.27325 14.1883i −0.398483 1.32306i
\(116\) −1.75233 + 0.780188i −0.162700 + 0.0724386i
\(117\) 4.81621 + 4.33653i 0.445259 + 0.400913i
\(118\) 18.6709i 1.71879i
\(119\) −2.14917 17.3514i −0.197014 1.59060i
\(120\) 3.11862 + 16.4085i 0.284690 + 1.49788i
\(121\) 10.6727 2.26854i 0.970242 0.206231i
\(122\) −10.5500 + 9.49929i −0.955154 + 0.860025i
\(123\) −27.3937 + 2.87920i −2.47001 + 0.259608i
\(124\) −0.171967 0.297856i −0.0154431 0.0267482i
\(125\) 5.97161 + 9.45198i 0.534117 + 0.845410i
\(126\) 21.2581 + 4.10876i 1.89382 + 0.366037i
\(127\) −5.51739 7.59404i −0.489590 0.673862i 0.490723 0.871316i \(-0.336733\pi\)
−0.980312 + 0.197454i \(0.936733\pi\)
\(128\) −2.73939 12.8878i −0.242130 1.13913i
\(129\) −3.89497 4.32580i −0.342933 0.380866i
\(130\) −3.84599 1.34222i −0.337315 0.117721i
\(131\) 4.77072 5.29843i 0.416820 0.462926i −0.497769 0.867309i \(-0.665847\pi\)
0.914589 + 0.404384i \(0.132514\pi\)
\(132\) 0.259456i 0.0225828i
\(133\) −3.19403 + 7.54691i −0.276957 + 0.654400i
\(134\) −10.1127 7.34733i −0.873606 0.634712i
\(135\) 15.1093 + 3.55460i 1.30040 + 0.305932i
\(136\) 1.78068 + 16.9421i 0.152692 + 1.45277i
\(137\) 6.36641 + 14.2992i 0.543919 + 1.22166i 0.951261 + 0.308386i \(0.0997888\pi\)
−0.407343 + 0.913275i \(0.633545\pi\)
\(138\) 28.9625 + 3.04408i 2.46545 + 0.259129i
\(139\) 5.33788 3.87820i 0.452753 0.328944i −0.337929 0.941172i \(-0.609726\pi\)
0.790682 + 0.612227i \(0.209726\pi\)
\(140\) −1.73902 + 0.364001i −0.146974 + 0.0307637i
\(141\) 17.5928 + 12.7819i 1.48158 + 1.07643i
\(142\) 4.19589 + 3.77800i 0.352111 + 0.317042i
\(143\) −0.310150 0.179065i −0.0259360 0.0149742i
\(144\) −23.8051 5.05993i −1.98376 0.421661i
\(145\) 5.52562 + 13.1698i 0.458878 + 1.09369i
\(146\) 3.91380 12.0454i 0.323908 0.996887i
\(147\) 3.47966 19.9820i 0.286998 1.64809i
\(148\) 0.487642 + 0.671181i 0.0400839 + 0.0551708i
\(149\) 5.90514 + 10.2280i 0.483768 + 0.837911i 0.999826 0.0186424i \(-0.00593442\pi\)
−0.516058 + 0.856554i \(0.672601\pi\)
\(150\) −21.6703 + 3.63520i −1.76938 + 0.296813i
\(151\) 0.789055 1.36668i 0.0642124 0.111219i −0.832132 0.554578i \(-0.812880\pi\)
0.896344 + 0.443359i \(0.146213\pi\)
\(152\) 3.24768 7.29442i 0.263422 0.591655i
\(153\) 33.9112 + 11.0184i 2.74156 + 0.890786i
\(154\) −1.19625 + 0.0221504i −0.0963969 + 0.00178493i
\(155\) −2.24490 + 1.23217i −0.180314 + 0.0989703i
\(156\) 0.699368 0.776726i 0.0559942 0.0621879i
\(157\) 10.8421 + 6.25969i 0.865294 + 0.499578i 0.865782 0.500422i \(-0.166822\pi\)
−0.000487578 1.00000i \(0.500155\pi\)
\(158\) 2.44245 11.4908i 0.194311 0.914161i
\(159\) 2.22307 21.1511i 0.176301 1.67739i
\(160\) 3.70185 0.703578i 0.292657 0.0556227i
\(161\) 1.50954 17.4676i 0.118969 1.37664i
\(162\) −3.50024 + 4.81767i −0.275005 + 0.378512i
\(163\) 0.557776 + 0.0586246i 0.0436884 + 0.00459183i 0.126347 0.991986i \(-0.459675\pi\)
−0.0826591 + 0.996578i \(0.526341\pi\)
\(164\) 0.298417 + 2.83925i 0.0233025 + 0.221708i
\(165\) −1.93137 0.0417598i −0.150357 0.00325100i
\(166\) 0.310435 2.95360i 0.0240945 0.229243i
\(167\) −16.7998 + 5.45858i −1.30001 + 0.422397i −0.875583 0.483067i \(-0.839523\pi\)
−0.424422 + 0.905465i \(0.639523\pi\)
\(168\) −3.75025 + 19.4033i −0.289338 + 1.49699i
\(169\) 3.57141 + 10.9917i 0.274724 + 0.845512i
\(170\) −22.3341 + 1.86028i −1.71295 + 0.142677i
\(171\) −11.1829 12.4199i −0.855180 0.949774i
\(172\) −0.448353 + 0.403699i −0.0341866 + 0.0307817i
\(173\) 5.18708 11.6504i 0.394366 0.885761i −0.601830 0.798624i \(-0.705562\pi\)
0.996196 0.0871369i \(-0.0277718\pi\)
\(174\) −28.0690 −2.12790
\(175\) 2.42970 + 13.0037i 0.183668 + 0.982988i
\(176\) 1.34485 0.101372
\(177\) −14.5081 + 32.5858i −1.09050 + 2.44930i
\(178\) −4.68685 + 4.22006i −0.351294 + 0.316307i
\(179\) 4.72778 + 5.25073i 0.353371 + 0.392458i 0.893455 0.449153i \(-0.148274\pi\)
−0.540084 + 0.841611i \(0.681608\pi\)
\(180\) 0.829778 3.52707i 0.0618480 0.262893i
\(181\) −3.42377 10.5373i −0.254487 0.783231i −0.993930 0.110012i \(-0.964911\pi\)
0.739443 0.673219i \(-0.235089\pi\)
\(182\) −3.64090 3.15821i −0.269881 0.234102i
\(183\) −25.7941 + 8.38101i −1.90675 + 0.619542i
\(184\) −1.78565 + 16.9893i −0.131640 + 1.25247i
\(185\) 5.07472 3.52195i 0.373101 0.258939i
\(186\) −0.526078 5.00530i −0.0385739 0.367007i
\(187\) −1.95957 0.205959i −0.143298 0.0150612i
\(188\) 1.32480 1.82342i 0.0966206 0.132987i
\(189\) 15.0554 + 10.5181i 1.09512 + 0.765081i
\(190\) 9.50178 + 4.47903i 0.689332 + 0.324943i
\(191\) −0.135216 + 1.28650i −0.00978390 + 0.0930876i −0.998324 0.0578701i \(-0.981569\pi\)
0.988540 + 0.150958i \(0.0482357\pi\)
\(192\) 3.89474 18.3233i 0.281079 1.32237i
\(193\) −0.709630 0.409705i −0.0510803 0.0294912i 0.474242 0.880394i \(-0.342722\pi\)
−0.525323 + 0.850903i \(0.676055\pi\)
\(194\) −4.05584 + 4.50446i −0.291192 + 0.323402i
\(195\) −5.66934 5.33106i −0.405990 0.381765i
\(196\) −2.07106 0.360653i −0.147933 0.0257609i
\(197\) 21.3985 + 6.95278i 1.52458 + 0.495365i 0.947072 0.321021i \(-0.104026\pi\)
0.577506 + 0.816387i \(0.304026\pi\)
\(198\) 0.992449 2.22908i 0.0705303 0.158414i
\(199\) −0.379861 + 0.657939i −0.0269276 + 0.0466400i −0.879175 0.476499i \(-0.841906\pi\)
0.852248 + 0.523139i \(0.175239\pi\)
\(200\) −2.13240 12.7118i −0.150783 0.898857i
\(201\) −11.9403 20.6812i −0.842203 1.45874i
\(202\) −2.73004 3.75757i −0.192085 0.264382i
\(203\) 0.312851 + 16.8958i 0.0219578 + 1.18585i
\(204\) 1.77698 5.46897i 0.124413 0.382905i
\(205\) 21.1832 1.76442i 1.47950 0.123232i
\(206\) 12.7530 + 2.71074i 0.888547 + 0.188866i
\(207\) 30.9654 + 17.8779i 2.15224 + 1.24260i
\(208\) 4.02604 + 3.62507i 0.279156 + 0.251353i
\(209\) 0.747156 + 0.542841i 0.0516819 + 0.0375491i
\(210\) −25.4139 5.48440i −1.75373 0.378460i
\(211\) 8.51968 6.18991i 0.586519 0.426131i −0.254550 0.967060i \(-0.581927\pi\)
0.841068 + 0.540929i \(0.181927\pi\)
\(212\) −2.19223 0.230412i −0.150563 0.0158248i
\(213\) 4.38731 + 9.85405i 0.300613 + 0.675189i
\(214\) 2.48958 + 23.6868i 0.170184 + 1.61920i
\(215\) 2.93294 + 3.40248i 0.200025 + 0.232047i
\(216\) −14.4769 10.5181i −0.985029 0.715665i
\(217\) −3.00702 + 0.372455i −0.204130 + 0.0252839i
\(218\) 21.2710i 1.44065i
\(219\) 16.1905 17.9814i 1.09405 1.21507i
\(220\) −0.00432824 + 0.200179i −0.000291810 + 0.0134961i
\(221\) −5.31113 5.89861i −0.357266 0.396784i
\(222\) 2.52407 + 11.8748i 0.169405 + 0.796987i
\(223\) −4.68314 6.44579i −0.313606 0.431642i 0.622895 0.782305i \(-0.285956\pi\)
−0.936502 + 0.350663i \(0.885956\pi\)
\(224\) 4.37748 + 0.846077i 0.292483 + 0.0565309i
\(225\) −26.1217 6.74450i −1.74145 0.449633i
\(226\) −4.04196 7.00089i −0.268867 0.465692i
\(227\) 1.61336 0.169571i 0.107083 0.0112548i −0.0508356 0.998707i \(-0.516188\pi\)
0.157918 + 0.987452i \(0.449522\pi\)
\(228\) −2.00300 + 1.80351i −0.132652 + 0.119440i
\(229\) 8.32102 1.76869i 0.549869 0.116878i 0.0754045 0.997153i \(-0.475975\pi\)
0.474464 + 0.880275i \(0.342642\pi\)
\(230\) −22.2948 2.83176i −1.47007 0.186721i
\(231\) −2.10501 0.890887i −0.138499 0.0586161i
\(232\) 16.4652i 1.08099i
\(233\) −12.2006 10.9855i −0.799290 0.719684i 0.164491 0.986379i \(-0.447402\pi\)
−0.963781 + 0.266695i \(0.914068\pi\)
\(234\) 8.97958 3.99797i 0.587013 0.261355i
\(235\) −13.3602 10.1552i −0.871525 0.662450i
\(236\) 3.37739 + 1.50371i 0.219849 + 0.0978833i
\(237\) 13.1917 18.1568i 0.856890 1.17941i
\(238\) −25.3671 7.72607i −1.64430 0.500807i
\(239\) −14.8595 + 10.7960i −0.961178 + 0.698337i −0.953424 0.301633i \(-0.902468\pi\)
−0.00775395 + 0.999970i \(0.502468\pi\)
\(240\) 28.4469 + 6.69240i 1.83624 + 0.431993i
\(241\) 7.73006 3.44164i 0.497937 0.221696i −0.142372 0.989813i \(-0.545473\pi\)
0.640309 + 0.768117i \(0.278806\pi\)
\(242\) 3.44066 16.1870i 0.221174 1.04054i
\(243\) 8.18224 4.72402i 0.524891 0.303046i
\(244\) 0.868659 + 2.67346i 0.0556102 + 0.171151i
\(245\) −3.01802 + 15.3588i −0.192814 + 0.981235i
\(246\) −12.9096 + 39.7317i −0.823086 + 2.53320i
\(247\) 0.773505 + 3.63906i 0.0492170 + 0.231548i
\(248\) 2.93610 0.308596i 0.186442 0.0195959i
\(249\) 2.83688 4.91362i 0.179780 0.311388i
\(250\) 16.7801 2.44318i 1.06126 0.154520i
\(251\) 28.8626 1.82179 0.910895 0.412638i \(-0.135392\pi\)
0.910895 + 0.412638i \(0.135392\pi\)
\(252\) 2.45532 3.51450i 0.154671 0.221392i
\(253\) −1.87915 0.610572i −0.118141 0.0383863i
\(254\) −13.9256 + 2.95998i −0.873769 + 0.185725i
\(255\) −40.4247 14.1079i −2.53149 0.883474i
\(256\) −6.89912 1.46645i −0.431195 0.0916533i
\(257\) 24.1450 13.9401i 1.50612 0.869560i 0.506148 0.862447i \(-0.331069\pi\)
0.999975 0.00711374i \(-0.00226439\pi\)
\(258\) −8.39641 + 2.72816i −0.522738 + 0.169848i
\(259\) 7.11980 1.65169i 0.442403 0.102631i
\(260\) −0.552544 + 0.587605i −0.0342673 + 0.0364417i
\(261\) −31.4834 14.0173i −1.94877 0.867649i
\(262\) −4.39826 9.87865i −0.271725 0.610305i
\(263\) −2.80742 6.30557i −0.173113 0.388818i 0.806063 0.591829i \(-0.201594\pi\)
−0.979176 + 0.203011i \(0.934927\pi\)
\(264\) 2.03458 + 0.905853i 0.125220 + 0.0557514i
\(265\) −2.06802 + 16.2817i −0.127037 + 1.00018i
\(266\) 8.48630 + 9.08111i 0.520329 + 0.556799i
\(267\) −11.4590 + 3.72326i −0.701281 + 0.227860i
\(268\) −2.14352 + 1.23756i −0.130937 + 0.0755963i
\(269\) 17.1166 + 3.63825i 1.04362 + 0.221828i 0.697665 0.716424i \(-0.254222\pi\)
0.345953 + 0.938252i \(0.387556\pi\)
\(270\) 14.2459 18.7420i 0.866975 1.14060i
\(271\) −11.5918 + 2.46392i −0.704153 + 0.149672i −0.546053 0.837751i \(-0.683870\pi\)
−0.158100 + 0.987423i \(0.550537\pi\)
\(272\) 28.3476 + 9.21069i 1.71883 + 0.558480i
\(273\) −3.90030 8.34110i −0.236057 0.504826i
\(274\) 23.7397 1.43417
\(275\) 1.48943 + 0.0644383i 0.0898158 + 0.00388578i
\(276\) 2.88322 4.99389i 0.173550 0.300597i
\(277\) −13.7020 + 1.44014i −0.823274 + 0.0865296i −0.506791 0.862069i \(-0.669169\pi\)
−0.316483 + 0.948598i \(0.602502\pi\)
\(278\) −2.08058 9.78835i −0.124785 0.587066i
\(279\) 1.90951 5.87688i 0.114320 0.351839i
\(280\) 3.21713 14.9077i 0.192260 0.890907i
\(281\) −2.06261 6.34806i −0.123045 0.378694i 0.870495 0.492178i \(-0.163799\pi\)
−0.993540 + 0.113484i \(0.963799\pi\)
\(282\) 28.5629 16.4908i 1.70089 0.982011i
\(283\) −0.760794 + 3.57925i −0.0452245 + 0.212765i −0.994958 0.100296i \(-0.968021\pi\)
0.949733 + 0.313061i \(0.101354\pi\)
\(284\) 1.02133 0.454727i 0.0606050 0.0269831i
\(285\) 13.1028 + 15.2005i 0.776144 + 0.900399i
\(286\) −0.439433 + 0.319266i −0.0259842 + 0.0188786i
\(287\) 24.0599 + 7.32796i 1.42021 + 0.432556i
\(288\) −5.34446 + 7.35602i −0.314926 + 0.433458i
\(289\) −24.3641 10.8476i −1.43318 0.638093i
\(290\) 21.6562 + 0.468246i 1.27170 + 0.0274964i
\(291\) −10.5787 + 4.70996i −0.620136 + 0.276102i
\(292\) −1.86370 1.67808i −0.109065 0.0982025i
\(293\) 29.0587i 1.69763i −0.528693 0.848813i \(-0.677318\pi\)
0.528693 0.848813i \(-0.322682\pi\)
\(294\) −25.5396 17.1479i −1.48950 1.00009i
\(295\) 11.7371 24.8991i 0.683362 1.44968i
\(296\) −6.96574 + 1.48061i −0.404875 + 0.0860589i
\(297\) 1.53810 1.38491i 0.0892497 0.0803608i
\(298\) 17.8143 1.87236i 1.03195 0.108463i
\(299\) −3.97974 6.89312i −0.230155 0.398639i
\(300\) −1.08771 + 4.21274i −0.0627989 + 0.243223i
\(301\) 1.73577 + 5.02372i 0.100048 + 0.289562i
\(302\) −1.40686 1.93637i −0.0809555 0.111426i
\(303\) −1.84486 8.67936i −0.105984 0.498616i
\(304\) −9.34822 10.3823i −0.536157 0.595463i
\(305\) 20.0409 6.03595i 1.14754 0.345617i
\(306\) 36.1861 40.1887i 2.06862 2.29744i
\(307\) 27.1407i 1.54900i 0.632571 + 0.774502i \(0.282000\pi\)
−0.632571 + 0.774502i \(0.718000\pi\)
\(308\) −0.0923370 + 0.218176i −0.00526139 + 0.0124317i
\(309\) 20.1512 + 14.6407i 1.14636 + 0.832881i
\(310\) 0.322390 + 3.87054i 0.0183105 + 0.219832i
\(311\) 2.28225 + 21.7142i 0.129415 + 1.23130i 0.845764 + 0.533557i \(0.179145\pi\)
−0.716349 + 0.697742i \(0.754188\pi\)
\(312\) 3.64912 + 8.19607i 0.206591 + 0.464011i
\(313\) −11.1989 1.17706i −0.633001 0.0665311i −0.217407 0.976081i \(-0.569760\pi\)
−0.415594 + 0.909550i \(0.636426\pi\)
\(314\) 15.3615 11.1608i 0.866901 0.629841i
\(315\) −25.7665 18.8429i −1.45178 1.06168i
\(316\) −1.88188 1.36726i −0.105864 0.0769146i
\(317\) 1.89050 + 1.70221i 0.106181 + 0.0956057i 0.720511 0.693443i \(-0.243907\pi\)
−0.614330 + 0.789049i \(0.710574\pi\)
\(318\) −27.9346 16.1280i −1.56649 0.904416i
\(319\) 1.86279 + 0.395948i 0.104296 + 0.0221689i
\(320\) −3.31060 + 14.0721i −0.185068 + 0.786655i
\(321\) −14.0608 + 43.2745i −0.784795 + 2.41535i
\(322\) −23.2711 12.8671i −1.29685 0.717056i
\(323\) 12.0312 + 16.5595i 0.669432 + 0.921395i
\(324\) 0.589571 + 1.02117i 0.0327540 + 0.0567315i
\(325\) 4.28516 + 4.20768i 0.237698 + 0.233400i
\(326\) 0.425313 0.736665i 0.0235559 0.0408001i
\(327\) −16.5286 + 37.1238i −0.914031 + 2.05295i
\(328\) −23.3065 7.57273i −1.28688 0.418134i
\(329\) −10.2448 17.0093i −0.564814 0.937753i
\(330\) −1.24930 + 2.65027i −0.0687719 + 0.145892i
\(331\) 2.36394 2.62543i 0.129934 0.144306i −0.674667 0.738122i \(-0.735713\pi\)
0.804601 + 0.593816i \(0.202379\pi\)
\(332\) −0.509277 0.294031i −0.0279502 0.0161371i
\(333\) −3.09903 + 14.5798i −0.169826 + 0.798968i
\(334\) −2.80043 + 26.6444i −0.153233 + 1.45791i
\(335\) 8.86734 + 16.1554i 0.484475 + 0.882666i
\(336\) 28.3454 + 19.8029i 1.54637 + 1.08034i
\(337\) −6.84062 + 9.41531i −0.372633 + 0.512885i −0.953614 0.301032i \(-0.902669\pi\)
0.580981 + 0.813917i \(0.302669\pi\)
\(338\) 17.4327 + 1.83225i 0.948215 + 0.0996614i
\(339\) −1.61433 15.3593i −0.0876781 0.834202i
\(340\) −1.46223 + 4.18986i −0.0793008 + 0.227227i
\(341\) −0.0356930 + 0.339597i −0.00193289 + 0.0183902i
\(342\) −24.1071 + 7.83287i −1.30356 + 0.423553i
\(343\) −10.0374 + 15.5644i −0.541967 + 0.840400i
\(344\) −1.60033 4.92531i −0.0862840 0.265555i
\(345\) −36.7101 22.2663i −1.97641 1.19878i
\(346\) −12.9424 14.3740i −0.695787 0.772750i
\(347\) −21.8134 + 19.6409i −1.17100 + 1.05438i −0.173424 + 0.984847i \(0.555483\pi\)
−0.997580 + 0.0695298i \(0.977850\pi\)
\(348\) −2.26062 + 5.07743i −0.121182 + 0.272179i
\(349\) −10.2072 −0.546381 −0.273190 0.961960i \(-0.588079\pi\)
−0.273190 + 0.961960i \(0.588079\pi\)
\(350\) 19.5162 + 4.65536i 1.04319 + 0.248839i
\(351\) 8.33762 0.445029
\(352\) 0.204366 0.459012i 0.0108927 0.0244654i
\(353\) −17.9649 + 16.1757i −0.956177 + 0.860945i −0.990367 0.138470i \(-0.955782\pi\)
0.0341900 + 0.999415i \(0.489115\pi\)
\(354\) 36.1995 + 40.2037i 1.92398 + 2.13680i
\(355\) −3.22058 7.67593i −0.170930 0.407396i
\(356\) 0.385902 + 1.18768i 0.0204528 + 0.0629471i
\(357\) −38.2690 33.1955i −2.02541 1.75689i
\(358\) 10.1917 3.31148i 0.538648 0.175017i
\(359\) 1.10371 10.5011i 0.0582518 0.554228i −0.926008 0.377503i \(-0.876783\pi\)
0.984260 0.176726i \(-0.0565505\pi\)
\(360\) 24.7612 + 18.8211i 1.30503 + 0.991961i
\(361\) 0.983200 + 9.35453i 0.0517474 + 0.492343i
\(362\) −16.7121 1.75651i −0.878368 0.0923202i
\(363\) 18.5830 25.5773i 0.975353 1.34246i
\(364\) −0.864522 + 0.404251i −0.0453133 + 0.0211885i
\(365\) −12.7915 + 13.6032i −0.669538 + 0.712023i
\(366\) −4.29974 + 40.9093i −0.224751 + 2.13836i
\(367\) 3.09703 14.5704i 0.161664 0.760568i −0.820366 0.571839i \(-0.806230\pi\)
0.982029 0.188728i \(-0.0604366\pi\)
\(368\) 25.8851 + 14.9448i 1.34935 + 0.779049i
\(369\) −34.3215 + 38.1178i −1.78670 + 1.98434i
\(370\) −1.74932 9.20395i −0.0909426 0.478491i
\(371\) −9.39675 + 16.9947i −0.487855 + 0.882321i
\(372\) −0.947784 0.307954i −0.0491403 0.0159667i
\(373\) −3.69394 + 8.29672i −0.191265 + 0.429588i −0.983568 0.180540i \(-0.942215\pi\)
0.792303 + 0.610128i \(0.208882\pi\)
\(374\) −1.49420 + 2.58804i −0.0772634 + 0.133824i
\(375\) 31.1843 + 8.77488i 1.61035 + 0.453133i
\(376\) 9.67344 + 16.7549i 0.498869 + 0.864067i
\(377\) 4.50930 + 6.20652i 0.232241 + 0.319652i
\(378\) 23.8610 14.3716i 1.22728 0.739195i
\(379\) −4.37202 + 13.4557i −0.224576 + 0.691173i 0.773759 + 0.633480i \(0.218374\pi\)
−0.998334 + 0.0576924i \(0.981626\pi\)
\(380\) 1.57547 1.35806i 0.0808200 0.0696668i
\(381\) −26.6040 5.65486i −1.36297 0.289707i
\(382\) 1.69910 + 0.980975i 0.0869335 + 0.0501911i
\(383\) 4.77086 + 4.29570i 0.243780 + 0.219500i 0.781958 0.623331i \(-0.214221\pi\)
−0.538179 + 0.842831i \(0.680888\pi\)
\(384\) −30.8859 22.4399i −1.57614 1.14513i
\(385\) 1.60922 + 0.722466i 0.0820136 + 0.0368203i
\(386\) −1.00543 + 0.730489i −0.0511751 + 0.0371809i
\(387\) −10.7802 1.13304i −0.547987 0.0575958i
\(388\) 0.488169 + 1.09644i 0.0247830 + 0.0556636i
\(389\) 1.61619 + 15.3770i 0.0819440 + 0.779645i 0.955910 + 0.293659i \(0.0948730\pi\)
−0.873966 + 0.485987i \(0.838460\pi\)
\(390\) −10.8838 + 4.56651i −0.551124 + 0.231234i
\(391\) −35.4281 25.7400i −1.79168 1.30173i
\(392\) 10.0589 14.9815i 0.508053 0.756678i
\(393\) 20.6586i 1.04209i
\(394\) 22.8340 25.3597i 1.15036 1.27760i
\(395\) −10.4807 + 13.7885i −0.527342 + 0.693775i
\(396\) −0.323291 0.359051i −0.0162460 0.0180430i
\(397\) −4.82019 22.6772i −0.241918 1.13814i −0.916531 0.399964i \(-0.869023\pi\)
0.674613 0.738172i \(-0.264311\pi\)
\(398\) 0.677278 + 0.932194i 0.0339489 + 0.0467267i
\(399\) 7.75449 + 22.4433i 0.388210 + 1.12357i
\(400\) −21.8361 5.63797i −1.09181 0.281899i
\(401\) −0.524412 0.908308i −0.0261879 0.0453588i 0.852634 0.522508i \(-0.175003\pi\)
−0.878822 + 0.477149i \(0.841670\pi\)
\(402\) −36.0208 + 3.78593i −1.79655 + 0.188825i
\(403\) −1.02224 + 0.920430i −0.0509214 + 0.0458499i
\(404\) −0.899583 + 0.191212i −0.0447559 + 0.00951316i
\(405\) 7.69640 4.22437i 0.382437 0.209911i
\(406\) 23.6031 + 9.98938i 1.17140 + 0.495764i
\(407\) 0.823676i 0.0408281i
\(408\) 36.6821 + 33.0287i 1.81603 + 1.63516i
\(409\) −5.20370 + 2.31684i −0.257307 + 0.114560i −0.531336 0.847161i \(-0.678310\pi\)
0.274030 + 0.961721i \(0.411643\pi\)
\(410\) 10.6230 30.4390i 0.524633 1.50328i
\(411\) 41.4323 + 18.4468i 2.04370 + 0.909916i
\(412\) 1.51745 2.08860i 0.0747596 0.102898i
\(413\) 23.7967 22.2380i 1.17096 1.09426i
\(414\) 43.8730 31.8756i 2.15624 1.56660i
\(415\) −2.27072 + 3.74370i −0.111465 + 0.183771i
\(416\) 1.84908 0.823263i 0.0906585 0.0403638i
\(417\) 3.97482 18.7001i 0.194648 0.915747i
\(418\) 1.21305 0.700354i 0.0593321 0.0342554i
\(419\) 6.28785 + 19.3520i 0.307182 + 0.945407i 0.978854 + 0.204559i \(0.0655762\pi\)
−0.671673 + 0.740848i \(0.734424\pi\)
\(420\) −3.03886 + 4.15545i −0.148281 + 0.202765i
\(421\) 9.00232 27.7063i 0.438746 1.35032i −0.450452 0.892801i \(-0.648737\pi\)
0.889198 0.457522i \(-0.151263\pi\)
\(422\) −3.32077 15.6230i −0.161652 0.760515i
\(423\) 40.2726 4.23282i 1.95812 0.205807i
\(424\) 9.46066 16.3864i 0.459450 0.795792i
\(425\) 30.9537 + 11.5591i 1.50148 + 0.560700i
\(426\) 16.3598 0.792636
\(427\) 24.6729 + 2.13222i 1.19400 + 0.103185i
\(428\) 4.48524 + 1.45734i 0.216802 + 0.0704433i
\(429\) −1.01502 + 0.215748i −0.0490054 + 0.0104164i
\(430\) 6.52363 1.96480i 0.314598 0.0947511i
\(431\) −17.9763 3.82098i −0.865888 0.184050i −0.246507 0.969141i \(-0.579283\pi\)
−0.619381 + 0.785091i \(0.712616\pi\)
\(432\) −27.1148 + 15.6547i −1.30456 + 0.753189i
\(433\) 12.4459 4.04392i 0.598112 0.194338i 0.00571375 0.999984i \(-0.498181\pi\)
0.592398 + 0.805645i \(0.298181\pi\)
\(434\) −1.33894 + 4.39616i −0.0642714 + 0.211023i
\(435\) 37.4322 + 17.6451i 1.79474 + 0.846018i
\(436\) 3.84773 + 1.71312i 0.184273 + 0.0820436i
\(437\) 8.34856 + 18.7512i 0.399366 + 0.896990i
\(438\) −14.9265 33.5254i −0.713214 1.60191i
\(439\) −11.2173 4.99428i −0.535374 0.238364i 0.121197 0.992629i \(-0.461327\pi\)
−0.656570 + 0.754265i \(0.727994\pi\)
\(440\) −1.55464 0.732838i −0.0741145 0.0349367i
\(441\) −20.0828 31.9880i −0.956326 1.52324i
\(442\) −11.4492 + 3.72008i −0.544585 + 0.176946i
\(443\) 0.710842 0.410405i 0.0337731 0.0194989i −0.483018 0.875610i \(-0.660460\pi\)
0.516792 + 0.856111i \(0.327126\pi\)
\(444\) 2.35134 + 0.499792i 0.111589 + 0.0237191i
\(445\) 8.90315 2.68147i 0.422050 0.127114i
\(446\) −11.8200 + 2.51241i −0.559692 + 0.118966i
\(447\) 32.5458 + 10.5748i 1.53936 + 0.500169i
\(448\) −9.79611 + 14.0219i −0.462823 + 0.662474i
\(449\) −31.7045 −1.49623 −0.748114 0.663570i \(-0.769040\pi\)
−0.748114 + 0.663570i \(0.769040\pi\)
\(450\) −25.4591 + 32.0325i −1.20015 + 1.51003i
\(451\) 1.41721 2.45468i 0.0667337 0.115586i
\(452\) −1.59193 + 0.167319i −0.0748781 + 0.00787000i
\(453\) −0.950701 4.47270i −0.0446678 0.210146i
\(454\) 0.760315 2.34001i 0.0356834 0.109822i
\(455\) 2.87007 + 6.50051i 0.134551 + 0.304749i
\(456\) −7.14942 22.0036i −0.334802 1.03041i
\(457\) −1.22234 + 0.705719i −0.0571787 + 0.0330121i −0.528317 0.849047i \(-0.677177\pi\)
0.471138 + 0.882059i \(0.343843\pi\)
\(458\) 2.68253 12.6203i 0.125347 0.589709i
\(459\) 41.9061 18.6578i 1.95601 0.870872i
\(460\) −2.30782 + 3.80486i −0.107602 + 0.177403i
\(461\) −8.04550 + 5.84539i −0.374716 + 0.272247i −0.759164 0.650900i \(-0.774392\pi\)
0.384448 + 0.923147i \(0.374392\pi\)
\(462\) −2.53293 + 2.36702i −0.117843 + 0.110124i
\(463\) −7.20026 + 9.91031i −0.334624 + 0.460571i −0.942862 0.333184i \(-0.891877\pi\)
0.608237 + 0.793755i \(0.291877\pi\)
\(464\) −26.3181 11.7176i −1.22179 0.543974i
\(465\) −2.44493 + 7.00568i −0.113381 + 0.324880i
\(466\) −22.7475 + 10.1278i −1.05376 + 0.469162i
\(467\) −26.2816 23.6640i −1.21617 1.09504i −0.992735 0.120320i \(-0.961608\pi\)
−0.223430 0.974720i \(-0.571726\pi\)
\(468\) 1.94631i 0.0899684i
\(469\) 2.68038 + 21.6401i 0.123769 + 0.999248i
\(470\) −22.3123 + 12.2467i −1.02919 + 0.564899i
\(471\) 35.4826 7.54205i 1.63495 0.347520i
\(472\) −23.5833 + 21.2345i −1.08551 + 0.977399i
\(473\) 0.595710 0.0626116i 0.0273908 0.00287889i
\(474\) −17.0194 29.4785i −0.781728 1.35399i
\(475\) −9.85571 11.9463i −0.452211 0.548133i
\(476\) −3.44059 + 3.96644i −0.157699 + 0.181801i
\(477\) −23.2785 32.0401i −1.06585 1.46702i
\(478\) 5.79186 + 27.2486i 0.264913 + 1.24632i
\(479\) −14.9312 16.5827i −0.682222 0.757685i 0.298219 0.954498i \(-0.403608\pi\)
−0.980441 + 0.196813i \(0.936941\pi\)
\(480\) 6.60702 8.69224i 0.301568 0.396745i
\(481\) 2.22023 2.46581i 0.101234 0.112431i
\(482\) 12.8335i 0.584552i
\(483\) −30.6161 40.5394i −1.39308 1.84461i
\(484\) −2.65098 1.92605i −0.120499 0.0875479i
\(485\) 8.24043 3.45742i 0.374179 0.156993i
\(486\) −1.49786 14.2511i −0.0679441 0.646445i
\(487\) −4.58024 10.2874i −0.207550 0.466166i 0.779535 0.626358i \(-0.215455\pi\)
−0.987086 + 0.160192i \(0.948789\pi\)
\(488\) −23.9973 2.52222i −1.08631 0.114175i
\(489\) 1.31471 0.955195i 0.0594534 0.0431954i
\(490\) 19.4186 + 13.6563i 0.877245 + 0.616928i
\(491\) 28.1497 + 20.4520i 1.27038 + 0.922985i 0.999218 0.0395486i \(-0.0125920\pi\)
0.271162 + 0.962534i \(0.412592\pi\)
\(492\) 6.14739 + 5.53514i 0.277146 + 0.249543i
\(493\) 36.5532 + 21.1040i 1.64628 + 0.950478i
\(494\) 5.51928 + 1.17316i 0.248324 + 0.0527830i
\(495\) −2.72478 + 2.34876i −0.122470 + 0.105569i
\(496\) 1.59623 4.91270i 0.0716729 0.220587i
\(497\) −0.182343 9.84762i −0.00817920 0.441726i
\(498\) −5.05805 6.96181i −0.226657 0.311966i
\(499\) 18.7370 + 32.4534i 0.838784 + 1.45282i 0.890912 + 0.454176i \(0.150066\pi\)
−0.0521285 + 0.998640i \(0.516601\pi\)
\(500\) 0.909482 3.23213i 0.0406733 0.144545i
\(501\) −25.5915 + 44.3257i −1.14334 + 1.98033i
\(502\) 17.8050 39.9907i 0.794677 1.78487i
\(503\) −7.49603 2.43561i −0.334231 0.108598i 0.137093 0.990558i \(-0.456224\pi\)
−0.471325 + 0.881960i \(0.656224\pi\)
\(504\) 18.9873 + 31.5243i 0.845759 + 1.40420i
\(505\) 1.27858 + 6.72721i 0.0568961 + 0.299357i
\(506\) −2.00521 + 2.22701i −0.0891423 + 0.0990026i
\(507\) 29.0012 + 16.7438i 1.28799 + 0.743620i
\(508\) −0.586105 + 2.75741i −0.0260042 + 0.122340i
\(509\) 2.82188 26.8484i 0.125078 1.19003i −0.734348 0.678773i \(-0.762512\pi\)
0.859425 0.511261i \(-0.170821\pi\)
\(510\) −44.4849 + 47.3076i −1.96982 + 2.09482i
\(511\) −20.0139 + 9.35850i −0.885362 + 0.413995i
\(512\) 9.20115 12.6643i 0.406637 0.559688i
\(513\) −21.3830 2.24745i −0.944085 0.0992273i
\(514\) −4.42003 42.0537i −0.194959 1.85491i
\(515\) −15.3031 11.6320i −0.674336 0.512566i
\(516\) −0.182730 + 1.73856i −0.00804422 + 0.0765357i
\(517\) −2.12819 + 0.691491i −0.0935977 + 0.0304117i
\(518\) 2.10361 10.8838i 0.0924274 0.478206i
\(519\) −11.4188 35.1434i −0.501229 1.54262i
\(520\) −2.67870 6.38443i −0.117469 0.279976i
\(521\) 16.9031 + 18.7727i 0.740536 + 0.822449i 0.989266 0.146124i \(-0.0466799\pi\)
−0.248730 + 0.968573i \(0.580013\pi\)
\(522\) −38.8435 + 34.9748i −1.70013 + 1.53081i
\(523\) 4.25741 9.56231i 0.186164 0.418131i −0.796220 0.605008i \(-0.793170\pi\)
0.982383 + 0.186877i \(0.0598367\pi\)
\(524\) −2.14119 −0.0935381
\(525\) 30.4438 + 23.2899i 1.32868 + 1.01646i
\(526\) −10.4686 −0.456452
\(527\) −3.07821 + 6.91377i −0.134089 + 0.301169i
\(528\) 2.89585 2.60743i 0.126026 0.113474i
\(529\) −13.9939 15.5418i −0.608431 0.675731i
\(530\) 21.2835 + 12.9094i 0.924495 + 0.560747i
\(531\) 20.5257 + 63.1717i 0.890741 + 2.74142i
\(532\) 2.32616 0.803723i 0.100852 0.0348458i
\(533\) 10.8593 3.52839i 0.470367 0.152832i
\(534\) −1.91016 + 18.1740i −0.0826607 + 0.786464i
\(535\) 11.5703 33.1533i 0.500226 1.43334i
\(536\) −2.22082 21.1297i −0.0959247 0.912663i
\(537\) 20.3605 + 2.13998i 0.878621 + 0.0923468i
\(538\) 15.6000 21.4716i 0.672566 0.925707i
\(539\) 1.45304 + 1.49829i 0.0625867 + 0.0645358i
\(540\) −2.24292 4.08639i −0.0965200 0.175850i
\(541\) 2.44752 23.2866i 0.105227 1.00117i −0.806740 0.590907i \(-0.798770\pi\)
0.911967 0.410263i \(-0.134563\pi\)
\(542\) −3.73697 + 17.5811i −0.160517 + 0.755172i
\(543\) −27.8023 16.0517i −1.19311 0.688844i
\(544\) 7.45145 8.27568i 0.319478 0.354817i
\(545\) 13.3717 28.3665i 0.572779 1.21509i
\(546\) −13.9631 + 0.258547i −0.597566 + 0.0110648i
\(547\) −33.2127 10.7915i −1.42007 0.461409i −0.504447 0.863443i \(-0.668303\pi\)
−0.915625 + 0.402034i \(0.868303\pi\)
\(548\) 1.91194 4.29430i 0.0816742 0.183443i
\(549\) −25.2524 + 43.7384i −1.07775 + 1.86671i
\(550\) 1.00809 2.02393i 0.0429853 0.0863007i
\(551\) −9.89175 17.1330i −0.421403 0.729891i
\(552\) 29.0943 + 40.0448i 1.23833 + 1.70442i
\(553\) −17.5546 + 10.5732i −0.746496 + 0.449619i
\(554\) −6.45723 + 19.8733i −0.274341 + 0.844336i
\(555\) 4.09887 17.4227i 0.173987 0.739554i
\(556\) −1.93819 0.411975i −0.0821976 0.0174716i
\(557\) −20.3983 11.7770i −0.864304 0.499006i 0.00114721 0.999999i \(-0.499635\pi\)
−0.865451 + 0.500993i \(0.832968\pi\)
\(558\) −6.96478 6.27112i −0.294843 0.265478i
\(559\) 1.95213 + 1.41831i 0.0825663 + 0.0599879i
\(560\) −21.5391 15.7515i −0.910195 0.665622i
\(561\) −4.61882 + 3.35577i −0.195007 + 0.141681i
\(562\) −10.0680 1.05819i −0.424693 0.0446370i
\(563\) −0.712014 1.59921i −0.0300078 0.0673986i 0.897920 0.440159i \(-0.145078\pi\)
−0.927928 + 0.372761i \(0.878411\pi\)
\(564\) −0.682641 6.49490i −0.0287444 0.273485i
\(565\) 0.989285 + 11.8772i 0.0416195 + 0.499676i
\(566\) 4.48993 + 3.26213i 0.188726 + 0.137117i
\(567\) 10.3093 1.27693i 0.432949 0.0536258i
\(568\) 9.59662i 0.402665i
\(569\) 5.88851 6.53985i 0.246859 0.274165i −0.606963 0.794730i \(-0.707612\pi\)
0.853822 + 0.520566i \(0.174279\pi\)
\(570\) 29.1441 8.77768i 1.22071 0.367657i
\(571\) 1.04634 + 1.16208i 0.0437882 + 0.0486317i 0.764641 0.644456i \(-0.222916\pi\)
−0.720853 + 0.693088i \(0.756250\pi\)
\(572\) 0.0223615 + 0.105202i 0.000934981 + 0.00439874i
\(573\) 2.20313 + 3.03235i 0.0920372 + 0.126678i
\(574\) 24.9956 28.8159i 1.04330 1.20275i
\(575\) 27.9517 + 17.7916i 1.16567 + 0.741962i
\(576\) −17.4417 30.2099i −0.726736 1.25874i
\(577\) −14.6098 + 1.53555i −0.608214 + 0.0639259i −0.403629 0.914923i \(-0.632251\pi\)
−0.204585 + 0.978849i \(0.565585\pi\)
\(578\) −30.0599 + 27.0660i −1.25033 + 1.12580i
\(579\) −2.32238 + 0.493637i −0.0965149 + 0.0205149i
\(580\) 1.82885 3.87970i 0.0759387 0.161096i
\(581\) −4.13421 + 3.12224i −0.171516 + 0.129532i
\(582\) 17.5629i 0.728008i
\(583\) 1.62637 + 1.46439i 0.0673572 + 0.0606487i
\(584\) 19.6659 8.75582i 0.813781 0.362318i
\(585\) −14.4882 0.313262i −0.599015 0.0129518i
\(586\) −40.2624 17.9260i −1.66323 0.740516i
\(587\) 4.57144 6.29204i 0.188683 0.259700i −0.704187 0.710015i \(-0.748688\pi\)
0.892870 + 0.450315i \(0.148688\pi\)
\(588\) −5.15882 + 3.23883i −0.212746 + 0.133567i
\(589\) 2.86979 2.08503i 0.118248 0.0859120i
\(590\) −27.2585 31.6224i −1.12222 1.30187i
\(591\) 59.5572 26.5166i 2.44986 1.09075i
\(592\) −2.59059 + 12.1878i −0.106473 + 0.500915i
\(593\) −9.65143 + 5.57226i −0.396337 + 0.228825i −0.684902 0.728635i \(-0.740155\pi\)
0.288565 + 0.957460i \(0.406822\pi\)
\(594\) −0.970036 2.98546i −0.0398011 0.122495i
\(595\) 28.9721 + 26.2499i 1.18774 + 1.07614i
\(596\) 1.09603 3.37324i 0.0448953 0.138173i
\(597\) 0.457680 + 2.15321i 0.0187316 + 0.0881251i
\(598\) −12.0059 + 1.26187i −0.490956 + 0.0516016i
\(599\) 8.65074 14.9835i 0.353460 0.612210i −0.633393 0.773830i \(-0.718338\pi\)
0.986853 + 0.161620i \(0.0516718\pi\)
\(600\) −29.2375 23.2377i −1.19362 0.948674i
\(601\) 5.91240 0.241172 0.120586 0.992703i \(-0.461523\pi\)
0.120586 + 0.992703i \(0.461523\pi\)
\(602\) 8.03142 + 0.694073i 0.327336 + 0.0282883i
\(603\) −42.2931 13.7418i −1.72231 0.559611i
\(604\) −0.463578 + 0.0985365i −0.0188627 + 0.00400939i
\(605\) −14.7641 + 19.4237i −0.600246 + 0.789688i
\(606\) −13.1638 2.79806i −0.534744 0.113663i
\(607\) −33.6092 + 19.4043i −1.36415 + 0.787595i −0.990174 0.139842i \(-0.955341\pi\)
−0.373980 + 0.927437i \(0.622007\pi\)
\(608\) −4.96414 + 1.61295i −0.201323 + 0.0654137i
\(609\) 33.4317 + 35.7749i 1.35472 + 1.44967i
\(610\) 3.99985 31.4912i 0.161949 1.27504i
\(611\) −8.23503 3.66647i −0.333154 0.148329i
\(612\) −4.35543 9.78246i −0.176058 0.395432i
\(613\) −4.85190 10.8976i −0.195967 0.440148i 0.788658 0.614832i \(-0.210776\pi\)
−0.984625 + 0.174684i \(0.944110\pi\)
\(614\) 37.6050 + 16.7428i 1.51762 + 0.675686i
\(615\) 42.1926 44.8699i 1.70137 1.80933i
\(616\) −1.38849 1.48581i −0.0559438 0.0598649i
\(617\) 24.8966 8.08939i 1.00230 0.325667i 0.238515 0.971139i \(-0.423339\pi\)
0.763784 + 0.645472i \(0.223339\pi\)
\(618\) 32.7166 18.8889i 1.31605 0.759824i
\(619\) −23.8295 5.06511i −0.957787 0.203584i −0.297605 0.954689i \(-0.596188\pi\)
−0.660182 + 0.751105i \(0.729521\pi\)
\(620\) 0.726111 + 0.253408i 0.0291613 + 0.0101771i
\(621\) 44.9946 9.56390i 1.80557 0.383786i
\(622\) 31.4941 + 10.2331i 1.26280 + 0.410308i
\(623\) 10.9609 + 0.947238i 0.439140 + 0.0379503i
\(624\) 15.6976 0.628407
\(625\) −23.9134 7.29034i −0.956536 0.291614i
\(626\) −8.53938 + 14.7906i −0.341302 + 0.591153i
\(627\) 2.66131 0.279715i 0.106283 0.0111708i
\(628\) −0.781705 3.67763i −0.0311934 0.146753i
\(629\) 5.64124 17.3619i 0.224931 0.692266i
\(630\) −42.0030 + 24.0769i −1.67344 + 0.959247i
\(631\) 4.79933 + 14.7708i 0.191058 + 0.588017i 1.00000 0.000127907i \(4.07141e-5\pi\)
−0.808942 + 0.587889i \(0.799959\pi\)
\(632\) 17.2920 9.98354i 0.687839 0.397124i
\(633\) 6.34413 29.8468i 0.252157 1.18630i
\(634\) 3.52474 1.56931i 0.139985 0.0623254i
\(635\) 20.4316 + 4.80673i 0.810804 + 0.190749i
\(636\) −5.16722 + 3.75420i −0.204893 + 0.148864i
\(637\) 0.311260 + 8.40206i 0.0123326 + 0.332902i
\(638\) 1.69774 2.33674i 0.0672143 0.0925126i
\(639\) 18.3499 + 8.16989i 0.725910 + 0.323196i
\(640\) 23.4552 + 17.8284i 0.927148 + 0.704730i
\(641\) −26.9427 + 11.9957i −1.06417 + 0.473800i −0.862712 0.505696i \(-0.831236\pi\)
−0.201461 + 0.979496i \(0.564569\pi\)
\(642\) 51.2854 + 46.1776i 2.02407 + 1.82248i
\(643\) 36.3038i 1.43168i 0.698264 + 0.715840i \(0.253956\pi\)
−0.698264 + 0.715840i \(0.746044\pi\)
\(644\) −4.20175 + 3.17324i −0.165572 + 0.125043i
\(645\) 12.9123 + 1.64005i 0.508421 + 0.0645769i
\(646\) 30.3660 6.45449i 1.19473 0.253949i
\(647\) 11.9145 10.7279i 0.468408 0.421757i −0.400828 0.916153i \(-0.631278\pi\)
0.869237 + 0.494396i \(0.164611\pi\)
\(648\) −10.0661 + 1.05799i −0.395434 + 0.0415618i
\(649\) −1.83525 3.17875i −0.0720399 0.124777i
\(650\) 8.47344 3.34166i 0.332356 0.131071i
\(651\) −5.75285 + 6.63210i −0.225472 + 0.259932i
\(652\) −0.0990022 0.136265i −0.00387723 0.00533654i
\(653\) 3.79695 + 17.8633i 0.148586 + 0.699044i 0.987862 + 0.155337i \(0.0496463\pi\)
−0.839275 + 0.543707i \(0.817020\pi\)
\(654\) 41.2407 + 45.8025i 1.61264 + 1.79102i
\(655\) −0.344627 + 15.9388i −0.0134657 + 0.622782i
\(656\) −28.6906 + 31.8641i −1.12018 + 1.24408i
\(657\) 45.0576i 1.75786i
\(658\) −29.8873 + 3.70189i −1.16513 + 0.144315i
\(659\) −3.05262 2.21786i −0.118913 0.0863955i 0.526739 0.850027i \(-0.323414\pi\)
−0.645652 + 0.763632i \(0.723414\pi\)
\(660\) 0.378793 + 0.439435i 0.0147445 + 0.0171050i
\(661\) −0.186726 1.77658i −0.00726282 0.0691011i 0.990290 0.139016i \(-0.0443939\pi\)
−0.997553 + 0.0699148i \(0.977727\pi\)
\(662\) −2.17938 4.89497i −0.0847041 0.190249i
\(663\) −22.8728 2.40402i −0.888304 0.0933646i
\(664\) 4.08378 2.96704i 0.158481 0.115143i
\(665\) −5.60846 17.4452i −0.217487 0.676494i
\(666\) 18.2894 + 13.2880i 0.708699 + 0.514900i
\(667\) 31.4541 + 28.3214i 1.21791 + 1.09661i
\(668\) 4.59419 + 2.65245i 0.177754 + 0.102627i
\(669\) −22.5814 4.79982i −0.873047 0.185572i
\(670\) 27.8544 2.32008i 1.07611 0.0896326i
\(671\) 0.862429 2.65428i 0.0332937 0.102468i
\(672\) 11.0664 6.66533i 0.426894 0.257121i
\(673\) 16.1740 + 22.2615i 0.623460 + 0.858119i 0.997599 0.0692535i \(-0.0220617\pi\)
−0.374139 + 0.927373i \(0.622062\pi\)
\(674\) 8.82553 + 15.2863i 0.339947 + 0.588805i
\(675\) −30.7798 + 16.0385i −1.18472 + 0.617321i
\(676\) 1.73543 3.00586i 0.0667474 0.115610i
\(677\) 11.9469 26.8331i 0.459156 1.03128i −0.524531 0.851391i \(-0.675759\pi\)
0.983687 0.179889i \(-0.0575740\pi\)
\(678\) −22.2770 7.23824i −0.855543 0.277983i
\(679\) 10.5718 0.195753i 0.405710 0.00751230i
\(680\) −27.7505 26.0947i −1.06418 1.00069i
\(681\) 3.14526 3.49316i 0.120527 0.133858i
\(682\) 0.448512 + 0.258948i 0.0171744 + 0.00991564i
\(683\) −4.10929 + 19.3327i −0.157238 + 0.739746i 0.826901 + 0.562347i \(0.190101\pi\)
−0.984139 + 0.177399i \(0.943232\pi\)
\(684\) −0.524639 + 4.99160i −0.0200601 + 0.190859i
\(685\) −31.6587 14.9236i −1.20962 0.570200i
\(686\) 15.3734 + 23.5089i 0.586961 + 0.897572i
\(687\) 14.4883 19.9415i 0.552765 0.760816i
\(688\) −9.01154 0.947151i −0.343562 0.0361098i
\(689\) 0.921532 + 8.76779i 0.0351076 + 0.334026i
\(690\) −53.4973 + 37.1281i −2.03661 + 1.41344i
\(691\) −3.53308 + 33.6150i −0.134405 + 1.27877i 0.694545 + 0.719450i \(0.255606\pi\)
−0.828949 + 0.559324i \(0.811061\pi\)
\(692\) −3.64248 + 1.18351i −0.138466 + 0.0449904i
\(693\) −4.02310 + 1.39004i −0.152825 + 0.0528033i
\(694\) 13.7571 + 42.3399i 0.522211 + 1.60720i
\(695\) −3.37867 + 14.3615i −0.128160 + 0.544761i
\(696\) −31.9231 35.4542i −1.21004 1.34389i
\(697\) 46.6845 42.0349i 1.76830 1.59219i
\(698\) −6.29674 + 14.1427i −0.238335 + 0.535309i
\(699\) −47.5704 −1.79928
\(700\) 2.41391 3.15538i 0.0912372 0.119262i
\(701\) −39.9977 −1.51069 −0.755347 0.655325i \(-0.772532\pi\)
−0.755347 + 0.655325i \(0.772532\pi\)
\(702\) 5.14339 11.5522i 0.194125 0.436011i
\(703\) −6.35877 + 5.72547i −0.239826 + 0.215940i
\(704\) 1.28985 + 1.43252i 0.0486129 + 0.0539901i
\(705\) −48.4575 + 4.03617i −1.82501 + 0.152011i
\(706\) 11.3300 + 34.8700i 0.426409 + 1.31235i
\(707\) −1.53754 + 7.95501i −0.0578251 + 0.299179i
\(708\) 10.1879 3.31026i 0.382885 0.124407i
\(709\) −1.65323 + 15.7294i −0.0620884 + 0.590732i 0.918605 + 0.395178i \(0.129317\pi\)
−0.980693 + 0.195554i \(0.937350\pi\)
\(710\) −12.6222 0.272914i −0.473702 0.0102423i
\(711\) −4.36851 41.5636i −0.163832 1.55876i
\(712\) −10.6608 1.12049i −0.399530 0.0419923i
\(713\) −4.46079 + 6.13976i −0.167058 + 0.229936i
\(714\) −69.6021 + 32.5459i −2.60479 + 1.21800i
\(715\) 0.786720 0.149525i 0.0294216 0.00559191i
\(716\) 0.221800 2.11029i 0.00828907 0.0788652i
\(717\) −11.0650 + 52.0568i −0.413231 + 1.94410i
\(718\) −13.8690 8.00729i −0.517588 0.298829i
\(719\) 0.704671 0.782616i 0.0262798 0.0291867i −0.729862 0.683595i \(-0.760416\pi\)
0.756141 + 0.654408i \(0.227082\pi\)
\(720\) 47.7054 26.1844i 1.77788 0.975834i
\(721\) −11.7346 19.4829i −0.437021 0.725580i
\(722\) 13.5677 + 4.40843i 0.504939 + 0.164065i
\(723\) 9.97226 22.3981i 0.370872 0.832993i
\(724\) −1.66370 + 2.88160i −0.0618307 + 0.107094i
\(725\) −28.5859 14.2383i −1.06165 0.528795i
\(726\) −23.9751 41.5261i −0.889799 1.54118i
\(727\) −14.7472 20.2978i −0.546944 0.752804i 0.442650 0.896695i \(-0.354039\pi\)
−0.989594 + 0.143891i \(0.954039\pi\)
\(728\) −0.151663 8.19072i −0.00562101 0.303568i
\(729\) 12.0995 37.2385i 0.448131 1.37921i
\(730\) 10.9570 + 26.1150i 0.405538 + 0.966560i
\(731\) 12.9856 + 2.76016i 0.480288 + 0.102088i
\(732\) 7.05384 + 4.07254i 0.260718 + 0.150525i
\(733\) 9.63402 + 8.67451i 0.355841 + 0.320400i 0.827591 0.561332i \(-0.189711\pi\)
−0.471750 + 0.881732i \(0.656378\pi\)
\(734\) −18.2776 13.2794i −0.674637 0.490152i
\(735\) 23.2793 + 38.9232i 0.858670 + 1.43570i
\(736\) 9.03434 6.56383i 0.333010 0.241946i
\(737\) 2.44391 + 0.256866i 0.0900227 + 0.00946177i
\(738\) 31.6419 + 71.0688i 1.16475 + 2.61608i
\(739\) 3.94087 + 37.4949i 0.144967 + 1.37927i 0.789056 + 0.614322i \(0.210570\pi\)
−0.644088 + 0.764951i \(0.722763\pi\)
\(740\) −1.80580 0.424832i −0.0663825 0.0156171i
\(741\) 8.72107 + 6.33623i 0.320377 + 0.232767i
\(742\) 17.7503 + 23.5036i 0.651636 + 0.862843i
\(743\) 15.1585i 0.556113i 0.960565 + 0.278057i \(0.0896903\pi\)
−0.960565 + 0.278057i \(0.910310\pi\)
\(744\) 5.72393 6.35707i 0.209850 0.233062i
\(745\) −24.9338 8.70173i −0.913504 0.318807i
\(746\) 9.21682 + 10.2363i 0.337452 + 0.374778i
\(747\) −2.19668 10.3346i −0.0803725 0.378123i
\(748\) 0.347813 + 0.478723i 0.0127173 + 0.0175038i
\(749\) 27.2245 31.3854i 0.994761 1.14680i
\(750\) 31.3954 37.7945i 1.14640 1.38006i
\(751\) 1.14689 + 1.98648i 0.0418508 + 0.0724877i 0.886192 0.463318i \(-0.153341\pi\)
−0.844341 + 0.535806i \(0.820008\pi\)
\(752\) 33.6653 3.53837i 1.22765 0.129031i
\(753\) 62.1494 55.9595i 2.26485 2.03928i
\(754\) 11.3812 2.41915i 0.414479 0.0881003i
\(755\) 0.658886 + 3.46670i 0.0239793 + 0.126166i
\(756\) −0.677981 5.47369i −0.0246579 0.199076i
\(757\) 46.5833i 1.69310i 0.532311 + 0.846549i \(0.321324\pi\)
−0.532311 + 0.846549i \(0.678676\pi\)
\(758\) 15.9466 + 14.3584i 0.579206 + 0.521519i
\(759\) −5.23013 + 2.32860i −0.189842 + 0.0845230i
\(760\) 5.14896 + 17.0958i 0.186772 + 0.620131i
\(761\) 0.852466 + 0.379543i 0.0309019 + 0.0137584i 0.422129 0.906536i \(-0.361283\pi\)
−0.391228 + 0.920294i \(0.627949\pi\)
\(762\) −24.2469 + 33.3730i −0.878372 + 1.20897i
\(763\) 27.1107 25.3349i 0.981472 0.917186i
\(764\) 0.314292 0.228346i 0.0113707 0.00826128i
\(765\) −73.5210 + 30.8470i −2.65816 + 1.11528i
\(766\) 8.89503 3.96032i 0.321390 0.143092i
\(767\) 3.07422 14.4631i 0.111004 0.522231i
\(768\) −17.6990 + 10.2185i −0.638656 + 0.368728i
\(769\) −9.05322 27.8629i −0.326467 1.00476i −0.970774 0.239996i \(-0.922854\pi\)
0.644307 0.764767i \(-0.277146\pi\)
\(770\) 1.99373 1.78399i 0.0718491 0.0642905i
\(771\) 24.9636 76.8299i 0.899041 2.76696i
\(772\) 0.0511636 + 0.240706i 0.00184142 + 0.00866319i
\(773\) −45.9166 + 4.82603i −1.65150 + 0.173580i −0.884008 0.467472i \(-0.845165\pi\)
−0.767497 + 0.641052i \(0.778498\pi\)
\(774\) −8.22007 + 14.2376i −0.295464 + 0.511759i
\(775\) 2.00322 5.36434i 0.0719578 0.192693i
\(776\) −10.3024 −0.369834
\(777\) 12.1286 17.3606i 0.435111 0.622808i
\(778\) 22.3027 + 7.24659i 0.799591 + 0.259803i
\(779\) −28.8013 + 6.12190i −1.03191 + 0.219340i
\(780\) −0.0505208 + 2.33657i −0.00180893 + 0.0836625i
\(781\) −1.08572 0.230776i −0.0388500 0.00825782i
\(782\) −57.5194 + 33.2089i −2.05689 + 1.18755i
\(783\) −42.1665 + 13.7007i −1.50691 + 0.489624i
\(784\) −16.7880 26.7400i −0.599571 0.954998i
\(785\) −27.5019 + 5.22704i −0.981584 + 0.186561i
\(786\) −28.6237 12.7441i −1.02097 0.454566i
\(787\) −6.24373 14.0236i −0.222565 0.499889i 0.767406 0.641162i \(-0.221547\pi\)
−0.989971 + 0.141273i \(0.954881\pi\)
\(788\) −2.74834 6.17288i −0.0979056 0.219900i
\(789\) −18.2706 8.13459i −0.650450 0.289599i
\(790\) 12.6393 + 23.0276i 0.449687 + 0.819285i
\(791\) −4.10869 + 13.4901i −0.146088 + 0.479652i
\(792\) 3.94429 1.28158i 0.140154 0.0455389i
\(793\) 9.73649 5.62137i 0.345753 0.199621i
\(794\) −34.3940 7.31068i −1.22060 0.259446i
\(795\) 27.1144 + 39.0687i 0.961647 + 1.38562i
\(796\) 0.223172 0.0474367i 0.00791013 0.00168135i
\(797\) −4.26542 1.38592i −0.151089 0.0490918i 0.232496 0.972597i \(-0.425311\pi\)
−0.383585 + 0.923506i \(0.625311\pi\)
\(798\) 35.8801 + 3.10075i 1.27014 + 0.109765i
\(799\) −49.5952 −1.75455
\(800\) −5.24255 + 6.59615i −0.185352 + 0.233209i
\(801\) −11.2184 + 19.4308i −0.396381 + 0.686553i
\(802\) −1.58202 + 0.166277i −0.0558629 + 0.00587143i
\(803\) 0.517673 + 2.43546i 0.0182683 + 0.0859456i
\(804\) −2.21619 + 6.82075i −0.0781592 + 0.240549i
\(805\) 22.9451 + 31.7883i 0.808710 + 1.12039i
\(806\) 0.644698 + 1.98418i 0.0227085 + 0.0698896i
\(807\) 43.9108 25.3519i 1.54573 0.892430i
\(808\) 1.64133 7.72186i 0.0577418 0.271654i
\(809\) 28.5118 12.6943i 1.00242 0.446307i 0.161156 0.986929i \(-0.448478\pi\)
0.841266 + 0.540622i \(0.181811\pi\)
\(810\) −1.10528 13.2698i −0.0388356 0.466252i
\(811\) 21.7660 15.8139i 0.764308 0.555302i −0.135921 0.990720i \(-0.543399\pi\)
0.900229 + 0.435418i \(0.143399\pi\)
\(812\) 3.70793 3.46507i 0.130123 0.121600i
\(813\) −20.1834 + 27.7800i −0.707862 + 0.974289i
\(814\) −1.14125 0.508117i −0.0400007 0.0178095i
\(815\) −1.03028 + 0.715034i −0.0360892 + 0.0250465i
\(816\) 78.8984 35.1278i 2.76200 1.22972i
\(817\) −4.62421 4.16366i −0.161781 0.145668i
\(818\) 8.63926i 0.302065i
\(819\) −15.7907 6.68300i −0.551773 0.233523i
\(820\) −4.65059 4.37310i −0.162406 0.152715i
\(821\) 13.8680 2.94774i 0.483998 0.102877i 0.0405509 0.999177i \(-0.487089\pi\)
0.443447 + 0.896301i \(0.353755\pi\)
\(822\) 51.1183 46.0271i 1.78295 1.60538i
\(823\) 34.8244 3.66019i 1.21390 0.127586i 0.524146 0.851628i \(-0.324384\pi\)
0.689756 + 0.724042i \(0.257718\pi\)
\(824\) 11.0802 + 19.1915i 0.385997 + 0.668566i
\(825\) 3.33209 2.74898i 0.116009 0.0957073i
\(826\) −16.1321 46.6900i −0.561308 1.62455i
\(827\) 8.81071 + 12.1269i 0.306378 + 0.421694i 0.934248 0.356625i \(-0.116073\pi\)
−0.627869 + 0.778319i \(0.716073\pi\)
\(828\) −2.23257 10.5034i −0.0775872 0.365019i
\(829\) 11.4129 + 12.6753i 0.396387 + 0.440232i 0.907991 0.418989i \(-0.137615\pi\)
−0.511605 + 0.859221i \(0.670949\pi\)
\(830\) 3.78633 + 5.45566i 0.131425 + 0.189369i
\(831\) −26.7121 + 29.6668i −0.926634 + 1.02913i
\(832\) 7.76529i 0.269213i
\(833\) 20.3664 + 41.5335i 0.705655 + 1.43905i
\(834\) −23.4580 17.0432i −0.812283 0.590158i
\(835\) 20.4841 33.7719i 0.708883 1.16872i
\(836\) −0.0289914 0.275835i −0.00100269 0.00953994i
\(837\) −3.23343 7.26241i −0.111764 0.251026i
\(838\) 30.6922 + 3.22588i 1.06024 + 0.111436i
\(839\) 5.30538 3.85458i 0.183162 0.133075i −0.492426 0.870354i \(-0.663890\pi\)
0.675588 + 0.737279i \(0.263890\pi\)
\(840\) −21.9761 38.3380i −0.758247 1.32279i
\(841\) −9.54254 6.93306i −0.329053 0.239071i
\(842\) −32.8352 29.5649i −1.13158 1.01888i
\(843\) −16.7492 9.67014i −0.576872 0.333057i
\(844\) −3.09351 0.657545i −0.106483 0.0226336i
\(845\) −22.0961 13.4022i −0.760129 0.461051i
\(846\) 18.9789 58.4111i 0.652509 2.00822i
\(847\) −24.7290 + 14.8944i −0.849697 + 0.511777i
\(848\) −19.4593 26.7835i −0.668236 0.919748i
\(849\) 5.30135 + 9.18220i 0.181942 + 0.315132i
\(850\) 35.1108 35.7574i 1.20429 1.22647i
\(851\) 9.15315 15.8537i 0.313766 0.543459i
\(852\) 1.31759 2.95935i 0.0451398 0.101386i
\(853\) 32.0356 + 10.4090i 1.09688 + 0.356398i 0.800901 0.598797i \(-0.204354\pi\)
0.295979 + 0.955195i \(0.404354\pi\)
\(854\) 18.1747 32.8703i 0.621926 1.12480i
\(855\) 37.0727 + 4.70878i 1.26786 + 0.161037i
\(856\) −27.0876 + 30.0838i −0.925836 + 1.02824i
\(857\) −12.4752 7.20257i −0.426145 0.246035i 0.271558 0.962422i \(-0.412461\pi\)
−0.697703 + 0.716387i \(0.745795\pi\)
\(858\) −0.327221 + 1.53945i −0.0111711 + 0.0525561i
\(859\) −1.32709 + 12.6264i −0.0452796 + 0.430807i 0.948275 + 0.317451i \(0.102827\pi\)
−0.993554 + 0.113356i \(0.963840\pi\)
\(860\) 0.169985 1.33831i 0.00579643 0.0456359i
\(861\) 66.0155 30.8689i 2.24980 1.05201i
\(862\) −16.3836 + 22.5501i −0.558027 + 0.768058i
\(863\) −33.6200 3.53361i −1.14444 0.120285i −0.486727 0.873554i \(-0.661809\pi\)
−0.657713 + 0.753269i \(0.728476\pi\)
\(864\) 1.22273 + 11.6335i 0.0415981 + 0.395780i
\(865\) 8.22373 + 27.3048i 0.279615 + 0.928393i
\(866\) 2.07467 19.7391i 0.0705001 0.670763i
\(867\) −73.4944 + 23.8798i −2.49600 + 0.811000i
\(868\) 0.687392 + 0.596261i 0.0233316 + 0.0202384i
\(869\) 0.713658 + 2.19641i 0.0242092 + 0.0745082i
\(870\) 47.5398 40.9793i 1.61175 1.38933i
\(871\) 6.62389 + 7.35658i 0.224442 + 0.249268i
\(872\) −26.8676 + 24.1917i −0.909852 + 0.819234i
\(873\) −8.77072 + 19.6993i −0.296844 + 0.666722i
\(874\) 31.1309 1.05302
\(875\) −23.0999 18.4768i −0.780920 0.624631i
\(876\) −7.26659 −0.245515
\(877\) 2.76804 6.21711i 0.0934699 0.209937i −0.860760 0.509011i \(-0.830011\pi\)
0.954230 + 0.299074i \(0.0966778\pi\)
\(878\) −13.8397 + 12.4613i −0.467067 + 0.420549i
\(879\) −56.3397 62.5716i −1.90029 2.11049i
\(880\) −2.27774 + 1.96342i −0.0767828 + 0.0661868i
\(881\) −9.86492 30.3611i −0.332358 1.02289i −0.968009 0.250915i \(-0.919268\pi\)
0.635651 0.771976i \(-0.280732\pi\)
\(882\) −56.7101 + 8.09284i −1.90953 + 0.272500i
\(883\) 28.3455 9.21002i 0.953903 0.309942i 0.209603 0.977787i \(-0.432783\pi\)
0.744301 + 0.667845i \(0.232783\pi\)
\(884\) −0.249168 + 2.37067i −0.00838042 + 0.0797344i
\(885\) −23.0016 76.3710i −0.773189 2.56718i
\(886\) −0.130128 1.23809i −0.00437174 0.0415943i
\(887\) 13.2561 + 1.39327i 0.445095 + 0.0467814i 0.324425 0.945911i \(-0.394829\pi\)
0.120670 + 0.992693i \(0.461496\pi\)
\(888\) −12.1286 + 16.6935i −0.407008 + 0.560199i
\(889\) 20.3588 + 14.2232i 0.682811 + 0.477030i
\(890\) 1.77693 13.9900i 0.0595629 0.468945i
\(891\) 0.122370 1.16427i 0.00409955 0.0390046i
\(892\) −0.497483 + 2.34047i −0.0166570 + 0.0783648i
\(893\) 20.1316 + 11.6230i 0.673679 + 0.388948i
\(894\) 34.7291 38.5705i 1.16151 1.28999i
\(895\) −15.6731 1.99072i −0.523896 0.0665424i
\(896\) 17.9858 + 29.8615i 0.600862 + 0.997603i
\(897\) −21.9341 7.12681i −0.732357 0.237957i
\(898\) −19.5582 + 43.9284i −0.652665 + 1.46591i
\(899\) 3.65737 6.33475i 0.121980 0.211276i
\(900\) 3.74398 + 7.18516i 0.124799 + 0.239505i
\(901\) 24.2522 + 42.0060i 0.807957 + 1.39942i
\(902\) −2.52683 3.47788i −0.0841343 0.115801i
\(903\) 13.4777 + 7.45214i 0.448511 + 0.247992i
\(904\) 4.24593 13.0676i 0.141217 0.434623i
\(905\) 21.1827 + 12.8482i 0.704137 + 0.427090i
\(906\) −6.78365 1.44191i −0.225372 0.0479042i
\(907\) 28.4092 + 16.4021i 0.943312 + 0.544622i 0.890997 0.454009i \(-0.150007\pi\)
0.0523151 + 0.998631i \(0.483340\pi\)
\(908\) −0.362053 0.325994i −0.0120151 0.0108185i
\(909\) −13.3678 9.71226i −0.443381 0.322135i
\(910\) 10.7773 + 0.0334541i 0.357265 + 0.00110899i
\(911\) −14.0742 + 10.2255i −0.466300 + 0.338787i −0.795997 0.605300i \(-0.793053\pi\)
0.329698 + 0.944087i \(0.393053\pi\)
\(912\) −40.2588 4.23137i −1.33310 0.140115i
\(913\) 0.237471 + 0.533369i 0.00785915 + 0.0176519i
\(914\) 0.223764 + 2.12897i 0.00740146 + 0.0704202i
\(915\) 31.4510 51.8529i 1.03974 1.71420i
\(916\) −2.06686 1.50166i −0.0682910 0.0496163i
\(917\) −7.35213 + 17.3718i −0.242789 + 0.573666i
\(918\) 69.5731i 2.29625i
\(919\) 0.110059 0.122233i 0.00363053 0.00403211i −0.741327 0.671144i \(-0.765803\pi\)
0.744957 + 0.667112i \(0.232470\pi\)
\(920\) −21.7792 31.3813i −0.718040 1.03461i
\(921\) 52.6212 + 58.4417i 1.73393 + 1.92572i
\(922\) 3.13594 + 14.7534i 0.103277 + 0.485879i
\(923\) −2.62822 3.61743i −0.0865088 0.119069i
\(924\) 0.224177 + 0.648820i 0.00737488 + 0.0213446i
\(925\) −3.45307 + 13.3739i −0.113536 + 0.439730i
\(926\) 9.28952 + 16.0899i 0.305273 + 0.528748i
\(927\) 46.1292 4.84838i 1.51508 0.159242i
\(928\) −7.99866 + 7.20203i −0.262569 + 0.236418i
\(929\) −50.8083 + 10.7996i −1.66697 + 0.354325i −0.942299 0.334773i \(-0.891340\pi\)
−0.724668 + 0.689098i \(0.758007\pi\)
\(930\) 8.19850 + 7.70932i 0.268839 + 0.252799i
\(931\) 1.46655 21.6322i 0.0480642 0.708967i
\(932\) 4.93049i 0.161503i
\(933\) 47.0144 + 42.3319i 1.53918 + 1.38589i
\(934\) −49.0006 + 21.8165i −1.60335 + 0.713857i
\(935\) 3.61956 2.51204i 0.118372 0.0821526i
\(936\) 15.2624 + 6.79527i 0.498868 + 0.222110i
\(937\) −34.6594 + 47.7045i −1.13227 + 1.55844i −0.348592 + 0.937275i \(0.613340\pi\)
−0.783681 + 0.621164i \(0.786660\pi\)
\(938\) 31.6371 + 9.63573i 1.03299 + 0.314618i
\(939\) −26.3966 + 19.1782i −0.861420 + 0.625858i
\(940\) 0.418334 + 5.02243i 0.0136445 + 0.163814i
\(941\) 38.4799 17.1323i 1.25441 0.558499i 0.331477 0.943463i \(-0.392453\pi\)
0.922931 + 0.384965i \(0.125786\pi\)
\(942\) 11.4389 53.8157i 0.372699 1.75341i
\(943\) 54.5555 31.4976i 1.77657 1.02570i
\(944\) 17.1582 + 52.8075i 0.558452 + 1.71874i
\(945\) −40.8549 + 4.16585i −1.32901 + 0.135515i
\(946\) 0.280735 0.864014i 0.00912748 0.0280915i
\(947\) 5.17386 + 24.3411i 0.168128 + 0.790980i 0.978693 + 0.205331i \(0.0658270\pi\)
−0.810565 + 0.585649i \(0.800840\pi\)
\(948\) −6.70311 + 0.704525i −0.217707 + 0.0228819i
\(949\) −5.01508 + 8.68637i −0.162796 + 0.281971i
\(950\) −22.6321 + 6.28610i −0.734283 + 0.203948i
\(951\) 7.37107 0.239023
\(952\) −19.0913 40.8284i −0.618754 1.32325i
\(953\) −44.6274 14.5003i −1.44562 0.469712i −0.521978 0.852959i \(-0.674806\pi\)
−0.923646 + 0.383247i \(0.874806\pi\)
\(954\) −58.7536 + 12.4885i −1.90222 + 0.404329i
\(955\) −1.64921 2.37632i −0.0533671 0.0768959i
\(956\) 5.39549 + 1.14685i 0.174502 + 0.0370916i
\(957\) 4.77879 2.75904i 0.154476 0.0891870i
\(958\) −32.1872 + 10.4583i −1.03992 + 0.337891i
\(959\) −28.2753 30.2571i −0.913056 0.977053i
\(960\) 20.1547 + 36.7199i 0.650491 + 1.18513i
\(961\) −27.1217 12.0754i −0.874895 0.389528i
\(962\) −2.04689 4.59739i −0.0659943 0.148226i
\(963\) 34.4634 + 77.4060i 1.11057 + 2.49437i
\(964\) −2.32147 1.03359i −0.0747696 0.0332896i
\(965\) 1.80003 0.342117i 0.0579451 0.0110131i
\(966\) −75.0564 + 17.4120i −2.41490 + 0.560223i
\(967\) 57.5816 18.7094i 1.85170 0.601654i 0.855178 0.518335i \(-0.173448\pi\)
0.996523 0.0833195i \(-0.0265522\pi\)
\(968\) 24.3591 14.0637i 0.782930 0.452025i
\(969\) 58.0125 + 12.3309i 1.86363 + 0.396127i
\(970\) 0.292985 13.5504i 0.00940717 0.435078i
\(971\) −25.6956 + 5.46178i −0.824612 + 0.175277i −0.600845 0.799366i \(-0.705169\pi\)
−0.223768 + 0.974643i \(0.571836\pi\)
\(972\) −2.69854 0.876809i −0.0865557 0.0281237i
\(973\) −9.99753 + 14.3102i −0.320506 + 0.458765i
\(974\) −17.0792 −0.547254
\(975\) 17.3851 + 0.752147i 0.556769 + 0.0240880i
\(976\) −21.1094 + 36.5625i −0.675695 + 1.17034i
\(977\) 4.21689 0.443213i 0.134910 0.0141796i −0.0368326 0.999321i \(-0.511727\pi\)
0.171743 + 0.985142i \(0.445060\pi\)
\(978\) −0.512443 2.41086i −0.0163861 0.0770907i
\(979\) 0.383134 1.17917i 0.0122450 0.0376863i
\(980\) 4.03424 2.41281i 0.128869 0.0770744i
\(981\) 23.3842 + 71.9691i 0.746600 + 2.29780i
\(982\) 45.7026 26.3864i 1.45843 0.842025i
\(983\) 7.09667 33.3872i 0.226349 1.06489i −0.707360 0.706853i \(-0.750114\pi\)
0.933709 0.358034i \(-0.116553\pi\)
\(984\) −64.8677 + 28.8810i −2.06791 + 0.920691i
\(985\) −46.3928 + 19.4649i −1.47820 + 0.620204i
\(986\) 51.7901 37.6277i 1.64933 1.19831i
\(987\) −55.0380 16.7630i −1.75188 0.533572i
\(988\) 0.656726 0.903905i 0.0208932 0.0287571i
\(989\) 12.1617 + 5.41475i 0.386720 + 0.172179i
\(990\) 1.57345 + 5.22427i 0.0500077 + 0.166038i
\(991\) 7.10897 3.16512i 0.225824 0.100543i −0.290706 0.956812i \(-0.593890\pi\)
0.516530 + 0.856269i \(0.327224\pi\)
\(992\) −1.43419 1.29135i −0.0455356 0.0410004i
\(993\) 10.2366i 0.324848i
\(994\) −13.7569 5.82225i −0.436343 0.184670i
\(995\) −0.317196 1.66891i −0.0100558 0.0529081i
\(996\) −1.66669 + 0.354267i −0.0528112 + 0.0112254i
\(997\) 36.5888 32.9447i 1.15878 1.04337i 0.160366 0.987058i \(-0.448733\pi\)
0.998413 0.0563118i \(-0.0179341\pi\)
\(998\) 56.5247 5.94099i 1.78926 0.188059i
\(999\) 9.58800 + 16.6069i 0.303351 + 0.525419i
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.t.a.39.14 yes 144
5.2 odd 4 875.2.q.b.676.27 288
5.3 odd 4 875.2.q.b.676.10 288
5.4 even 2 875.2.u.a.74.5 144
7.2 even 3 inner 175.2.t.a.114.5 yes 144
25.9 even 10 inner 175.2.t.a.109.5 yes 144
25.12 odd 20 875.2.q.b.326.10 288
25.13 odd 20 875.2.q.b.326.27 288
25.16 even 5 875.2.u.a.424.14 144
35.2 odd 12 875.2.q.b.51.10 288
35.9 even 6 875.2.u.a.324.14 144
35.23 odd 12 875.2.q.b.51.27 288
175.9 even 30 inner 175.2.t.a.9.14 144
175.16 even 15 875.2.u.a.674.5 144
175.37 odd 60 875.2.q.b.576.27 288
175.163 odd 60 875.2.q.b.576.10 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.t.a.9.14 144 175.9 even 30 inner
175.2.t.a.39.14 yes 144 1.1 even 1 trivial
175.2.t.a.109.5 yes 144 25.9 even 10 inner
175.2.t.a.114.5 yes 144 7.2 even 3 inner
875.2.q.b.51.10 288 35.2 odd 12
875.2.q.b.51.27 288 35.23 odd 12
875.2.q.b.326.10 288 25.12 odd 20
875.2.q.b.326.27 288 25.13 odd 20
875.2.q.b.576.10 288 175.163 odd 60
875.2.q.b.576.27 288 175.37 odd 60
875.2.q.b.676.10 288 5.3 odd 4
875.2.q.b.676.27 288 5.2 odd 4
875.2.u.a.74.5 144 5.4 even 2
875.2.u.a.324.14 144 35.9 even 6
875.2.u.a.424.14 144 25.16 even 5
875.2.u.a.674.5 144 175.16 even 15