Properties

Label 144.2.x.e.61.9
Level $144$
Weight $2$
Character 144.61
Analytic conductor $1.150$
Analytic rank $0$
Dimension $72$
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] = [144,2,Mod(13,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\), degree \(4\), 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: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 61.9
Character \(\chi\) \(=\) 144.61
Dual form 144.2.x.e.85.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.174715 - 1.40338i) q^{2} +(-1.22967 - 1.21980i) q^{3} +(-1.93895 + 0.490384i) q^{4} +(0.174734 + 0.0468197i) q^{5} +(-1.49700 + 1.93881i) q^{6} +(-4.04791 - 2.33706i) q^{7} +(1.02696 + 2.63540i) q^{8} +(0.0241875 + 2.99990i) q^{9} +O(q^{10})\) \(q+(-0.174715 - 1.40338i) q^{2} +(-1.22967 - 1.21980i) q^{3} +(-1.93895 + 0.490384i) q^{4} +(0.174734 + 0.0468197i) q^{5} +(-1.49700 + 1.93881i) q^{6} +(-4.04791 - 2.33706i) q^{7} +(1.02696 + 2.63540i) q^{8} +(0.0241875 + 2.99990i) q^{9} +(0.0351772 - 0.253398i) q^{10} +(0.160430 + 0.598734i) q^{11} +(2.98244 + 1.76211i) q^{12} +(1.18229 - 4.41237i) q^{13} +(-2.57255 + 6.08908i) q^{14} +(-0.157754 - 0.270713i) q^{15} +(3.51905 - 1.90166i) q^{16} -4.34691 q^{17} +(4.20578 - 0.558073i) q^{18} +(-1.23918 - 1.23918i) q^{19} +(-0.361759 - 0.00509454i) q^{20} +(2.12686 + 7.81146i) q^{21} +(0.812222 - 0.329753i) q^{22} +(3.86311 - 2.23037i) q^{23} +(1.95184 - 4.49337i) q^{24} +(-4.30179 - 2.48364i) q^{25} +(-6.39880 - 0.888296i) q^{26} +(3.62953 - 3.71840i) q^{27} +(8.99475 + 2.54642i) q^{28} +(8.64910 - 2.31752i) q^{29} +(-0.352350 + 0.268687i) q^{30} +(-2.25376 - 3.90364i) q^{31} +(-3.28358 - 4.60631i) q^{32} +(0.533058 - 0.931939i) q^{33} +(0.759472 + 6.10037i) q^{34} +(-0.597886 - 0.597886i) q^{35} +(-1.51800 - 5.80480i) q^{36} +(2.79692 - 2.79692i) q^{37} +(-1.52254 + 1.95554i) q^{38} +(-6.83604 + 3.98362i) q^{39} +(0.0560553 + 0.508576i) q^{40} +(-3.67211 + 2.12009i) q^{41} +(10.5908 - 4.34957i) q^{42} +(0.00351694 + 0.0131254i) q^{43} +(-0.604676 - 1.08224i) q^{44} +(-0.136228 + 0.525316i) q^{45} +(-3.80500 - 5.03173i) q^{46} +(-1.17465 + 2.03456i) q^{47} +(-6.64691 - 1.95411i) q^{48} +(7.42373 + 12.8583i) q^{49} +(-2.73390 + 6.47097i) q^{50} +(5.34528 + 5.30235i) q^{51} +(-0.128647 + 9.13515i) q^{52} +(-0.519418 + 0.519418i) q^{53} +(-5.85246 - 4.44395i) q^{54} +0.112130i q^{55} +(2.00207 - 13.0680i) q^{56} +(0.0122364 + 3.03533i) q^{57} +(-4.76349 - 11.7331i) q^{58} +(11.0349 + 2.95679i) q^{59} +(0.438631 + 0.447538i) q^{60} +(-2.19745 + 0.588805i) q^{61} +(-5.08451 + 3.84491i) q^{62} +(6.91305 - 12.1999i) q^{63} +(-5.89071 + 5.41290i) q^{64} +(0.413172 - 0.715636i) q^{65} +(-1.40100 - 0.585258i) q^{66} +(-1.88714 + 7.04291i) q^{67} +(8.42844 - 2.13166i) q^{68} +(-7.47096 - 1.96959i) q^{69} +(-0.734601 + 0.943520i) q^{70} +7.55145i q^{71} +(-7.88112 + 3.14452i) q^{72} +2.92707i q^{73} +(-4.41380 - 3.43647i) q^{74} +(2.26025 + 8.30137i) q^{75} +(3.01038 + 1.79503i) q^{76} +(0.749872 - 2.79856i) q^{77} +(6.78489 + 8.89756i) q^{78} +(1.45885 - 2.52680i) q^{79} +(0.703931 - 0.167523i) q^{80} +(-8.99883 + 0.145120i) q^{81} +(3.61687 + 4.78295i) q^{82} +(-7.44148 + 1.99394i) q^{83} +(-7.95449 - 14.1030i) q^{84} +(-0.759552 - 0.203521i) q^{85} +(0.0178055 - 0.00722882i) q^{86} +(-13.4625 - 7.70036i) q^{87} +(-1.41315 + 1.03767i) q^{88} -3.18821i q^{89} +(0.761019 + 0.0993992i) q^{90} +(-15.0978 + 15.0978i) q^{91} +(-6.39664 + 6.21898i) q^{92} +(-1.99025 + 7.54933i) q^{93} +(3.06049 + 1.29301i) q^{94} +(-0.158508 - 0.274544i) q^{95} +(-1.58104 + 9.66956i) q^{96} +(8.03868 - 13.9234i) q^{97} +(16.7480 - 12.6648i) q^{98} +(-1.79226 + 0.495757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22} - 40 q^{24} - 4 q^{26} + 8 q^{27} - 16 q^{28} + 4 q^{29} + 18 q^{30} + 28 q^{31} - 46 q^{32} - 32 q^{33} - 14 q^{34} - 16 q^{35} + 14 q^{36} + 16 q^{37} + 2 q^{38} - 10 q^{40} + 26 q^{42} - 10 q^{43} + 60 q^{44} + 40 q^{45} + 20 q^{46} - 56 q^{47} + 2 q^{48} + 4 q^{49} - 36 q^{50} - 54 q^{51} + 6 q^{52} - 8 q^{53} + 92 q^{54} + 52 q^{56} - 14 q^{58} - 14 q^{59} + 18 q^{60} - 32 q^{61} + 16 q^{62} - 108 q^{63} - 44 q^{64} - 64 q^{65} + 26 q^{66} - 18 q^{67} + 16 q^{68} + 32 q^{69} + 14 q^{70} + 114 q^{72} + 38 q^{74} + 86 q^{75} + 10 q^{76} - 36 q^{77} + 16 q^{78} + 44 q^{79} + 144 q^{80} - 44 q^{81} - 88 q^{82} + 20 q^{83} - 58 q^{84} - 8 q^{85} + 76 q^{86} - 42 q^{88} - 80 q^{91} - 68 q^{92} - 4 q^{93} + 20 q^{94} + 48 q^{95} + 94 q^{96} + 40 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.174715 1.40338i −0.123542 0.992339i
\(3\) −1.22967 1.21980i −0.709952 0.704250i
\(4\) −1.93895 + 0.490384i −0.969475 + 0.245192i
\(5\) 0.174734 + 0.0468197i 0.0781432 + 0.0209384i 0.297679 0.954666i \(-0.403788\pi\)
−0.219536 + 0.975604i \(0.570454\pi\)
\(6\) −1.49700 + 1.93881i −0.611146 + 0.791518i
\(7\) −4.04791 2.33706i −1.52997 0.883327i −0.999362 0.0357075i \(-0.988632\pi\)
−0.530605 0.847619i \(-0.678035\pi\)
\(8\) 1.02696 + 2.63540i 0.363085 + 0.931756i
\(9\) 0.0241875 + 2.99990i 0.00806251 + 0.999967i
\(10\) 0.0351772 0.253398i 0.0111240 0.0801314i
\(11\) 0.160430 + 0.598734i 0.0483716 + 0.180525i 0.985885 0.167424i \(-0.0535449\pi\)
−0.937513 + 0.347949i \(0.886878\pi\)
\(12\) 2.98244 + 1.76211i 0.860957 + 0.508679i
\(13\) 1.18229 4.41237i 0.327909 1.22377i −0.583446 0.812152i \(-0.698296\pi\)
0.911355 0.411621i \(-0.135037\pi\)
\(14\) −2.57255 + 6.08908i −0.687544 + 1.62737i
\(15\) −0.157754 0.270713i −0.0407320 0.0698977i
\(16\) 3.51905 1.90166i 0.879762 0.475415i
\(17\) −4.34691 −1.05428 −0.527141 0.849778i \(-0.676736\pi\)
−0.527141 + 0.849778i \(0.676736\pi\)
\(18\) 4.20578 0.558073i 0.991311 0.131539i
\(19\) −1.23918 1.23918i −0.284287 0.284287i 0.550529 0.834816i \(-0.314426\pi\)
−0.834816 + 0.550529i \(0.814426\pi\)
\(20\) −0.361759 0.00509454i −0.0808918 0.00113917i
\(21\) 2.12686 + 7.81146i 0.464119 + 1.70460i
\(22\) 0.812222 0.329753i 0.173166 0.0703035i
\(23\) 3.86311 2.23037i 0.805515 0.465064i −0.0398812 0.999204i \(-0.512698\pi\)
0.845396 + 0.534140i \(0.179365\pi\)
\(24\) 1.95184 4.49337i 0.398417 0.917204i
\(25\) −4.30179 2.48364i −0.860357 0.496728i
\(26\) −6.39880 0.888296i −1.25491 0.174209i
\(27\) 3.62953 3.71840i 0.698504 0.715607i
\(28\) 8.99475 + 2.54642i 1.69985 + 0.481227i
\(29\) 8.64910 2.31752i 1.60610 0.430353i 0.659221 0.751949i \(-0.270886\pi\)
0.946877 + 0.321597i \(0.104220\pi\)
\(30\) −0.352350 + 0.268687i −0.0643301 + 0.0490553i
\(31\) −2.25376 3.90364i −0.404788 0.701114i 0.589509 0.807762i \(-0.299321\pi\)
−0.994297 + 0.106648i \(0.965988\pi\)
\(32\) −3.28358 4.60631i −0.580460 0.814288i
\(33\) 0.533058 0.931939i 0.0927935 0.162230i
\(34\) 0.759472 + 6.10037i 0.130248 + 1.04620i
\(35\) −0.597886 0.597886i −0.101061 0.101061i
\(36\) −1.51800 5.80480i −0.253000 0.967466i
\(37\) 2.79692 2.79692i 0.459811 0.459811i −0.438783 0.898593i \(-0.644590\pi\)
0.898593 + 0.438783i \(0.144590\pi\)
\(38\) −1.52254 + 1.95554i −0.246988 + 0.317231i
\(39\) −6.83604 + 3.98362i −1.09464 + 0.637889i
\(40\) 0.0560553 + 0.508576i 0.00886312 + 0.0804129i
\(41\) −3.67211 + 2.12009i −0.573487 + 0.331103i −0.758541 0.651626i \(-0.774087\pi\)
0.185054 + 0.982728i \(0.440754\pi\)
\(42\) 10.5908 4.34957i 1.63420 0.671154i
\(43\) 0.00351694 + 0.0131254i 0.000536329 + 0.00200161i 0.966193 0.257818i \(-0.0830035\pi\)
−0.965657 + 0.259820i \(0.916337\pi\)
\(44\) −0.604676 1.08224i −0.0911583 0.163154i
\(45\) −0.136228 + 0.525316i −0.0203077 + 0.0783095i
\(46\) −3.80500 5.03173i −0.561017 0.741889i
\(47\) −1.17465 + 2.03456i −0.171341 + 0.296771i −0.938889 0.344221i \(-0.888143\pi\)
0.767548 + 0.640991i \(0.221477\pi\)
\(48\) −6.64691 1.95411i −0.959399 0.282051i
\(49\) 7.42373 + 12.8583i 1.06053 + 1.83690i
\(50\) −2.73390 + 6.47097i −0.386632 + 0.915133i
\(51\) 5.34528 + 5.30235i 0.748489 + 0.742478i
\(52\) −0.128647 + 9.13515i −0.0178402 + 1.26682i
\(53\) −0.519418 + 0.519418i −0.0713476 + 0.0713476i −0.741880 0.670533i \(-0.766066\pi\)
0.670533 + 0.741880i \(0.266066\pi\)
\(54\) −5.85246 4.44395i −0.796419 0.604745i
\(55\) 0.112130i 0.0151196i
\(56\) 2.00207 13.0680i 0.267538 1.74628i
\(57\) 0.0122364 + 3.03533i 0.00162075 + 0.402040i
\(58\) −4.76349 11.7331i −0.625477 1.54063i
\(59\) 11.0349 + 2.95679i 1.43662 + 0.384942i 0.891350 0.453317i \(-0.149759\pi\)
0.545273 + 0.838258i \(0.316426\pi\)
\(60\) 0.438631 + 0.447538i 0.0566270 + 0.0577769i
\(61\) −2.19745 + 0.588805i −0.281355 + 0.0753887i −0.396737 0.917932i \(-0.629857\pi\)
0.115382 + 0.993321i \(0.463191\pi\)
\(62\) −5.08451 + 3.84491i −0.645734 + 0.488304i
\(63\) 6.91305 12.1999i 0.870963 1.53704i
\(64\) −5.89071 + 5.41290i −0.736339 + 0.676613i
\(65\) 0.413172 0.715636i 0.0512477 0.0887637i
\(66\) −1.40100 0.585258i −0.172451 0.0720403i
\(67\) −1.88714 + 7.04291i −0.230551 + 0.860428i 0.749553 + 0.661944i \(0.230268\pi\)
−0.980104 + 0.198484i \(0.936398\pi\)
\(68\) 8.42844 2.13166i 1.02210 0.258501i
\(69\) −7.47096 1.96959i −0.899398 0.237111i
\(70\) −0.734601 + 0.943520i −0.0878016 + 0.112772i
\(71\) 7.55145i 0.896193i 0.893985 + 0.448096i \(0.147898\pi\)
−0.893985 + 0.448096i \(0.852102\pi\)
\(72\) −7.88112 + 3.14452i −0.928798 + 0.370585i
\(73\) 2.92707i 0.342588i 0.985220 + 0.171294i \(0.0547948\pi\)
−0.985220 + 0.171294i \(0.945205\pi\)
\(74\) −4.41380 3.43647i −0.513094 0.399482i
\(75\) 2.26025 + 8.30137i 0.260991 + 0.958560i
\(76\) 3.01038 + 1.79503i 0.345314 + 0.205904i
\(77\) 0.749872 2.79856i 0.0854558 0.318925i
\(78\) 6.78489 + 8.89756i 0.768237 + 1.00745i
\(79\) 1.45885 2.52680i 0.164133 0.284287i −0.772214 0.635362i \(-0.780851\pi\)
0.936347 + 0.351076i \(0.114184\pi\)
\(80\) 0.703931 0.167523i 0.0787019 0.0187296i
\(81\) −8.99883 + 0.145120i −0.999870 + 0.0161245i
\(82\) 3.61687 + 4.78295i 0.399416 + 0.528188i
\(83\) −7.44148 + 1.99394i −0.816808 + 0.218863i −0.642950 0.765908i \(-0.722290\pi\)
−0.173858 + 0.984771i \(0.555623\pi\)
\(84\) −7.95449 14.1030i −0.867906 1.53877i
\(85\) −0.759552 0.203521i −0.0823850 0.0220750i
\(86\) 0.0178055 0.00722882i 0.00192001 0.000779503i
\(87\) −13.4625 7.70036i −1.44333 0.825566i
\(88\) −1.41315 + 1.03767i −0.150642 + 0.110616i
\(89\) 3.18821i 0.337950i −0.985620 0.168975i \(-0.945954\pi\)
0.985620 0.168975i \(-0.0540457\pi\)
\(90\) 0.761019 + 0.0993992i 0.0802185 + 0.0104776i
\(91\) −15.0978 + 15.0978i −1.58268 + 1.58268i
\(92\) −6.39664 + 6.21898i −0.666896 + 0.648373i
\(93\) −1.99025 + 7.54933i −0.206380 + 0.782829i
\(94\) 3.06049 + 1.29301i 0.315665 + 0.133364i
\(95\) −0.158508 0.274544i −0.0162626 0.0281676i
\(96\) −1.58104 + 9.66956i −0.161364 + 0.986895i
\(97\) 8.03868 13.9234i 0.816204 1.41371i −0.0922553 0.995735i \(-0.529408\pi\)
0.908460 0.417972i \(-0.137259\pi\)
\(98\) 16.7480 12.6648i 1.69180 1.27934i
\(99\) −1.79226 + 0.495757i −0.180129 + 0.0498255i
\(100\) 9.55888 + 2.70612i 0.955888 + 0.270612i
\(101\) −4.56339 17.0308i −0.454074 1.69463i −0.690795 0.723051i \(-0.742739\pi\)
0.236720 0.971578i \(-0.423928\pi\)
\(102\) 6.50731 8.42786i 0.644320 0.834482i
\(103\) 8.05916 4.65296i 0.794093 0.458470i −0.0473086 0.998880i \(-0.515064\pi\)
0.841401 + 0.540411i \(0.181731\pi\)
\(104\) 12.8426 1.41551i 1.25932 0.138802i
\(105\) 0.00590388 + 1.46450i 0.000576159 + 0.142921i
\(106\) 0.819691 + 0.638191i 0.0796155 + 0.0619866i
\(107\) 9.51927 9.51927i 0.920263 0.920263i −0.0767848 0.997048i \(-0.524465\pi\)
0.997048 + 0.0767848i \(0.0244654\pi\)
\(108\) −5.21403 + 8.98965i −0.501721 + 0.865030i
\(109\) −6.35255 6.35255i −0.608464 0.608464i 0.334081 0.942544i \(-0.391574\pi\)
−0.942544 + 0.334081i \(0.891574\pi\)
\(110\) 0.157361 0.0195909i 0.0150038 0.00186792i
\(111\) −6.85097 + 0.0276184i −0.650265 + 0.00262143i
\(112\) −18.6891 0.526489i −1.76595 0.0497486i
\(113\) 5.34598 + 9.25951i 0.502908 + 0.871062i 0.999994 + 0.00336088i \(0.00106980\pi\)
−0.497087 + 0.867701i \(0.665597\pi\)
\(114\) 4.25759 0.547491i 0.398759 0.0512773i
\(115\) 0.779441 0.208851i 0.0726832 0.0194754i
\(116\) −15.6337 + 8.73493i −1.45155 + 0.811018i
\(117\) 13.2653 + 3.44004i 1.22638 + 0.318032i
\(118\) 2.22154 16.0028i 0.204509 1.47317i
\(119\) 17.5959 + 10.1590i 1.61302 + 0.931275i
\(120\) 0.551430 0.693757i 0.0503384 0.0633311i
\(121\) 9.19353 5.30789i 0.835776 0.482535i
\(122\) 1.21024 + 2.98098i 0.109570 + 0.269885i
\(123\) 7.10157 + 1.87221i 0.640327 + 0.168811i
\(124\) 6.28421 + 6.46374i 0.564339 + 0.580461i
\(125\) −1.27495 1.27495i −0.114035 0.114035i
\(126\) −18.3289 7.57013i −1.63287 0.674401i
\(127\) −11.5283 −1.02297 −0.511484 0.859293i \(-0.670904\pi\)
−0.511484 + 0.859293i \(0.670904\pi\)
\(128\) 8.62556 + 7.32119i 0.762399 + 0.647108i
\(129\) 0.0116857 0.0204299i 0.00102886 0.00179875i
\(130\) −1.07650 0.454805i −0.0944149 0.0398891i
\(131\) 0.917160 3.42289i 0.0801327 0.299059i −0.914215 0.405229i \(-0.867192\pi\)
0.994348 + 0.106169i \(0.0338586\pi\)
\(132\) −0.576564 + 2.06839i −0.0501835 + 0.180030i
\(133\) 2.12005 + 7.91213i 0.183832 + 0.686069i
\(134\) 10.2136 + 1.41787i 0.882320 + 0.122486i
\(135\) 0.808296 0.479796i 0.0695670 0.0412943i
\(136\) −4.46410 11.4559i −0.382793 0.982333i
\(137\) −13.0194 7.51678i −1.11233 0.642202i −0.172895 0.984940i \(-0.555312\pi\)
−0.939431 + 0.342739i \(0.888646\pi\)
\(138\) −1.45879 + 10.8287i −0.124181 + 0.921801i
\(139\) −9.76161 2.61562i −0.827969 0.221854i −0.180142 0.983641i \(-0.557656\pi\)
−0.647828 + 0.761787i \(0.724322\pi\)
\(140\) 1.45246 + 0.866076i 0.122756 + 0.0731968i
\(141\) 3.92619 1.06900i 0.330645 0.0900261i
\(142\) 10.5976 1.31935i 0.889327 0.110718i
\(143\) 2.83152 0.236783
\(144\) 5.78991 + 10.5108i 0.482492 + 0.875900i
\(145\) 1.61979 0.134517
\(146\) 4.10780 0.511405i 0.339964 0.0423242i
\(147\) 6.55574 24.8669i 0.540708 2.05099i
\(148\) −4.05152 + 6.79465i −0.333033 + 0.558516i
\(149\) −5.14811 1.37943i −0.421749 0.113007i 0.0417013 0.999130i \(-0.486722\pi\)
−0.463451 + 0.886123i \(0.653389\pi\)
\(150\) 11.2551 4.62237i 0.918973 0.377415i
\(151\) 9.86458 + 5.69532i 0.802768 + 0.463479i 0.844438 0.535653i \(-0.179934\pi\)
−0.0416699 + 0.999131i \(0.513268\pi\)
\(152\) 1.99315 4.53832i 0.161666 0.368107i
\(153\) −0.105141 13.0403i −0.00850015 1.05425i
\(154\) −4.05846 0.563404i −0.327040 0.0454004i
\(155\) −0.211041 0.787617i −0.0169512 0.0632629i
\(156\) 11.3012 11.0763i 0.904822 0.886815i
\(157\) 1.46607 5.47145i 0.117005 0.436670i −0.882424 0.470455i \(-0.844090\pi\)
0.999429 + 0.0337857i \(0.0107564\pi\)
\(158\) −3.80094 1.60584i −0.302386 0.127754i
\(159\) 1.27230 0.00512904i 0.100900 0.000406760i
\(160\) −0.358086 0.958614i −0.0283092 0.0757851i
\(161\) −20.8501 −1.64321
\(162\) 1.77589 + 12.6034i 0.139527 + 0.990218i
\(163\) 15.0117 + 15.0117i 1.17581 + 1.17581i 0.980802 + 0.195004i \(0.0624721\pi\)
0.195004 + 0.980802i \(0.437528\pi\)
\(164\) 6.08037 5.91149i 0.474797 0.461610i
\(165\) 0.136776 0.137884i 0.0106480 0.0107342i
\(166\) 4.09839 + 10.0948i 0.318097 + 0.783512i
\(167\) −7.81918 + 4.51441i −0.605066 + 0.349335i −0.771032 0.636796i \(-0.780259\pi\)
0.165966 + 0.986132i \(0.446926\pi\)
\(168\) −18.4021 + 13.6272i −1.41976 + 1.05136i
\(169\) −6.81291 3.93343i −0.524070 0.302572i
\(170\) −0.152912 + 1.10150i −0.0117278 + 0.0844810i
\(171\) 3.68744 3.74739i 0.281986 0.286570i
\(172\) −0.0132557 0.0237249i −0.00101073 0.00180900i
\(173\) 5.00520 1.34114i 0.380539 0.101965i −0.0634788 0.997983i \(-0.520220\pi\)
0.444017 + 0.896018i \(0.353553\pi\)
\(174\) −8.45444 + 20.2383i −0.640929 + 1.53426i
\(175\) 11.6088 + 20.1071i 0.877546 + 1.51995i
\(176\) 1.70315 + 1.80189i 0.128380 + 0.135823i
\(177\) −9.96263 17.0962i −0.748837 1.28503i
\(178\) −4.47427 + 0.557029i −0.335361 + 0.0417511i
\(179\) 1.96093 + 1.96093i 0.146566 + 0.146566i 0.776582 0.630016i \(-0.216952\pi\)
−0.630016 + 0.776582i \(0.716952\pi\)
\(180\) 0.00653306 1.08537i 0.000486946 0.0808984i
\(181\) −0.224256 + 0.224256i −0.0166688 + 0.0166688i −0.715392 0.698723i \(-0.753752\pi\)
0.698723 + 0.715392i \(0.253752\pi\)
\(182\) 23.8258 + 18.5501i 1.76608 + 1.37503i
\(183\) 3.42037 + 1.95641i 0.252841 + 0.144622i
\(184\) 9.84518 + 7.89037i 0.725796 + 0.581685i
\(185\) 0.619667 0.357765i 0.0455588 0.0263034i
\(186\) 10.9423 + 1.47410i 0.802329 + 0.108086i
\(187\) −0.697377 2.60265i −0.0509972 0.190324i
\(188\) 1.27988 4.52093i 0.0933446 0.329723i
\(189\) −23.3822 + 6.56932i −1.70080 + 0.477847i
\(190\) −0.357596 + 0.270414i −0.0259427 + 0.0196179i
\(191\) −10.3893 + 17.9947i −0.751741 + 1.30205i 0.195237 + 0.980756i \(0.437452\pi\)
−0.946978 + 0.321298i \(0.895881\pi\)
\(192\) 13.8463 + 0.529379i 0.999270 + 0.0382047i
\(193\) 7.69572 + 13.3294i 0.553950 + 0.959469i 0.997984 + 0.0634596i \(0.0202134\pi\)
−0.444035 + 0.896010i \(0.646453\pi\)
\(194\) −20.9443 8.84869i −1.50371 0.635299i
\(195\) −1.38100 + 0.376010i −0.0988953 + 0.0269267i
\(196\) −20.6997 21.2911i −1.47855 1.52079i
\(197\) −0.905158 + 0.905158i −0.0644898 + 0.0644898i −0.738616 0.674126i \(-0.764520\pi\)
0.674126 + 0.738616i \(0.264520\pi\)
\(198\) 1.00887 + 2.42861i 0.0716974 + 0.172594i
\(199\) 16.5201i 1.17108i −0.810645 0.585538i \(-0.800883\pi\)
0.810645 0.585538i \(-0.199117\pi\)
\(200\) 2.12763 13.8875i 0.150446 0.981998i
\(201\) 10.9115 6.35854i 0.769637 0.448497i
\(202\) −23.1034 + 9.37971i −1.62555 + 0.659954i
\(203\) −40.4270 10.8324i −2.83742 0.760284i
\(204\) −12.9644 7.65976i −0.907690 0.536290i
\(205\) −0.740902 + 0.198524i −0.0517469 + 0.0138655i
\(206\) −7.93793 10.4971i −0.553062 0.731369i
\(207\) 6.78433 + 11.5350i 0.471543 + 0.801739i
\(208\) −4.23029 17.7757i −0.293318 1.23252i
\(209\) 0.543137 0.940741i 0.0375696 0.0650724i
\(210\) 2.05422 0.264156i 0.141755 0.0182285i
\(211\) 6.75305 25.2027i 0.464899 1.73503i −0.192325 0.981331i \(-0.561603\pi\)
0.657224 0.753695i \(-0.271730\pi\)
\(212\) 0.752411 1.26184i 0.0516758 0.0866635i
\(213\) 9.21125 9.28581i 0.631144 0.636253i
\(214\) −15.0223 11.6960i −1.02690 0.799522i
\(215\) 0.00245811i 0.000167642i
\(216\) 13.5269 + 5.74664i 0.920387 + 0.391009i
\(217\) 21.0688i 1.43024i
\(218\) −7.80515 + 10.0249i −0.528631 + 0.678974i
\(219\) 3.57044 3.59934i 0.241268 0.243221i
\(220\) −0.0549869 0.217415i −0.00370721 0.0146581i
\(221\) −5.13932 + 19.1802i −0.345708 + 1.29020i
\(222\) 1.23573 + 9.60968i 0.0829366 + 0.644960i
\(223\) 6.47927 11.2224i 0.433884 0.751510i −0.563320 0.826239i \(-0.690476\pi\)
0.997204 + 0.0747295i \(0.0238093\pi\)
\(224\) 2.52641 + 26.3199i 0.168803 + 1.75857i
\(225\) 7.34662 12.9650i 0.489775 0.864334i
\(226\) 12.0606 9.12022i 0.802258 0.606668i
\(227\) −13.1401 + 3.52089i −0.872142 + 0.233690i −0.667014 0.745045i \(-0.732428\pi\)
−0.205128 + 0.978735i \(0.565761\pi\)
\(228\) −1.51220 5.87935i −0.100148 0.389370i
\(229\) −16.2371 4.35071i −1.07298 0.287503i −0.321260 0.946991i \(-0.604106\pi\)
−0.751715 + 0.659488i \(0.770773\pi\)
\(230\) −0.429277 1.05736i −0.0283057 0.0697204i
\(231\) −4.33577 + 2.52662i −0.285273 + 0.166239i
\(232\) 14.9899 + 20.4139i 0.984133 + 1.34024i
\(233\) 10.0493i 0.658351i 0.944269 + 0.329176i \(0.106771\pi\)
−0.944269 + 0.329176i \(0.893229\pi\)
\(234\) 2.51003 19.2173i 0.164086 1.25627i
\(235\) −0.300509 + 0.300509i −0.0196030 + 0.0196030i
\(236\) −22.8461 0.321734i −1.48715 0.0209431i
\(237\) −4.87608 + 1.32763i −0.316735 + 0.0862390i
\(238\) 11.1827 26.4687i 0.724865 1.71571i
\(239\) −3.38365 5.86066i −0.218870 0.379094i 0.735593 0.677424i \(-0.236904\pi\)
−0.954463 + 0.298330i \(0.903570\pi\)
\(240\) −1.06995 0.652655i −0.0690649 0.0421287i
\(241\) −1.07804 + 1.86722i −0.0694428 + 0.120278i −0.898656 0.438654i \(-0.855455\pi\)
0.829213 + 0.558932i \(0.188789\pi\)
\(242\) −9.05524 11.9747i −0.582093 0.769760i
\(243\) 11.2426 + 10.7983i 0.721215 + 0.692711i
\(244\) 3.97200 2.21926i 0.254281 0.142073i
\(245\) 0.695154 + 2.59435i 0.0444118 + 0.165747i
\(246\) 1.38667 10.2933i 0.0884107 0.656277i
\(247\) −6.93279 + 4.00265i −0.441123 + 0.254683i
\(248\) 7.97313 9.94845i 0.506294 0.631727i
\(249\) 11.5828 + 6.62520i 0.734029 + 0.419855i
\(250\) −1.56649 + 2.01200i −0.0990735 + 0.127250i
\(251\) 3.65289 3.65289i 0.230568 0.230568i −0.582362 0.812930i \(-0.697871\pi\)
0.812930 + 0.582362i \(0.197871\pi\)
\(252\) −7.42144 + 27.0450i −0.467507 + 1.70367i
\(253\) 1.95516 + 1.95516i 0.122920 + 0.122920i
\(254\) 2.01417 + 16.1785i 0.126380 + 1.01513i
\(255\) 0.685745 + 1.17676i 0.0429430 + 0.0736918i
\(256\) 8.76739 13.3841i 0.547962 0.836503i
\(257\) −5.09689 8.82807i −0.317935 0.550680i 0.662122 0.749396i \(-0.269656\pi\)
−0.980057 + 0.198716i \(0.936323\pi\)
\(258\) −0.0307126 0.0128300i −0.00191208 0.000798761i
\(259\) −17.8583 + 4.78511i −1.10966 + 0.297332i
\(260\) −0.450184 + 1.59019i −0.0279192 + 0.0986196i
\(261\) 7.16153 + 25.8904i 0.443288 + 1.60258i
\(262\) −4.96385 0.689093i −0.306668 0.0425723i
\(263\) −14.5937 8.42569i −0.899888 0.519550i −0.0227239 0.999742i \(-0.507234\pi\)
−0.877164 + 0.480191i \(0.840567\pi\)
\(264\) 3.00347 + 0.447760i 0.184851 + 0.0275577i
\(265\) −0.115079 + 0.0664408i −0.00706924 + 0.00408143i
\(266\) 10.7333 4.35760i 0.658102 0.267182i
\(267\) −3.88897 + 3.92045i −0.238001 + 0.239928i
\(268\) 0.205343 14.5813i 0.0125433 0.890692i
\(269\) 18.2219 + 18.2219i 1.11101 + 1.11101i 0.993014 + 0.117993i \(0.0376461\pi\)
0.117993 + 0.993014i \(0.462354\pi\)
\(270\) −0.814557 1.05052i −0.0495724 0.0639325i
\(271\) 9.95663 0.604822 0.302411 0.953178i \(-0.402208\pi\)
0.302411 + 0.953178i \(0.402208\pi\)
\(272\) −15.2970 + 8.26634i −0.927516 + 0.501221i
\(273\) 36.9816 0.149085i 2.23823 0.00902302i
\(274\) −8.27420 + 19.5845i −0.499863 + 1.18314i
\(275\) 0.796902 2.97408i 0.0480550 0.179344i
\(276\) 15.4517 + 0.155301i 0.930081 + 0.00934805i
\(277\) −0.706690 2.63740i −0.0424609 0.158466i 0.941440 0.337180i \(-0.109473\pi\)
−0.983901 + 0.178714i \(0.942806\pi\)
\(278\) −1.96520 + 14.1562i −0.117865 + 0.849035i
\(279\) 11.6560 6.85549i 0.697827 0.410428i
\(280\) 0.961666 2.18967i 0.0574706 0.130858i
\(281\) 21.8517 + 12.6161i 1.30356 + 0.752612i 0.981013 0.193941i \(-0.0621271\pi\)
0.322549 + 0.946553i \(0.395460\pi\)
\(282\) −2.18618 5.32316i −0.130185 0.316989i
\(283\) 8.63704 + 2.31429i 0.513419 + 0.137570i 0.506221 0.862404i \(-0.331042\pi\)
0.00719814 + 0.999974i \(0.497709\pi\)
\(284\) −3.70311 14.6419i −0.219739 0.868836i
\(285\) −0.139975 + 0.530947i −0.00829142 + 0.0314506i
\(286\) −0.494709 3.97369i −0.0292528 0.234969i
\(287\) 19.8192 1.16989
\(288\) 13.7391 9.96184i 0.809582 0.587007i
\(289\) 1.89565 0.111509
\(290\) −0.283003 2.27319i −0.0166185 0.133486i
\(291\) −26.8687 + 7.31566i −1.57507 + 0.428852i
\(292\) −1.43539 5.67545i −0.0839998 0.332130i
\(293\) 20.1100 + 5.38845i 1.17484 + 0.314796i 0.792876 0.609383i \(-0.208583\pi\)
0.381960 + 0.924179i \(0.375249\pi\)
\(294\) −36.0431 4.85556i −2.10208 0.283182i
\(295\) 1.78973 + 1.03330i 0.104202 + 0.0601612i
\(296\) 10.2433 + 4.49869i 0.595382 + 0.261481i
\(297\) 2.80862 + 1.57658i 0.162973 + 0.0914825i
\(298\) −1.03641 + 7.46576i −0.0600378 + 0.432480i
\(299\) −5.27390 19.6824i −0.304997 1.13827i
\(300\) −8.45337 14.9875i −0.488056 0.865306i
\(301\) 0.0164386 0.0613498i 0.000947507 0.00353615i
\(302\) 6.26920 14.8388i 0.360752 0.853878i
\(303\) −15.1627 + 26.5087i −0.871072 + 1.52289i
\(304\) −6.71723 2.00423i −0.385259 0.114951i
\(305\) −0.411536 −0.0235645
\(306\) −18.2821 + 2.42590i −1.04512 + 0.138679i
\(307\) 11.4523 + 11.4523i 0.653619 + 0.653619i 0.953863 0.300243i \(-0.0970679\pi\)
−0.300243 + 0.953863i \(0.597068\pi\)
\(308\) −0.0815949 + 5.79399i −0.00464930 + 0.330143i
\(309\) −15.5858 4.10893i −0.886645 0.233749i
\(310\) −1.06845 + 0.433780i −0.0606841 + 0.0246370i
\(311\) 15.6387 9.02903i 0.886792 0.511989i 0.0138999 0.999903i \(-0.495575\pi\)
0.872892 + 0.487914i \(0.162242\pi\)
\(312\) −17.5188 13.9247i −0.991805 0.788331i
\(313\) 22.1825 + 12.8070i 1.25383 + 0.723897i 0.971867 0.235529i \(-0.0756823\pi\)
0.281959 + 0.959426i \(0.409016\pi\)
\(314\) −7.93467 1.10151i −0.447779 0.0621617i
\(315\) 1.77914 1.80806i 0.100243 0.101873i
\(316\) −1.58953 + 5.61472i −0.0894180 + 0.315853i
\(317\) 3.31301 0.887719i 0.186077 0.0498593i −0.164577 0.986364i \(-0.552626\pi\)
0.350654 + 0.936505i \(0.385959\pi\)
\(318\) −0.229488 1.78462i −0.0128691 0.100077i
\(319\) 2.77516 + 4.80671i 0.155379 + 0.269124i
\(320\) −1.28274 + 0.670015i −0.0717071 + 0.0374550i
\(321\) −23.3172 + 0.0939989i −1.30144 + 0.00524651i
\(322\) 3.64282 + 29.2605i 0.203007 + 1.63063i
\(323\) 5.38660 + 5.38660i 0.299719 + 0.299719i
\(324\) 17.3771 4.69426i 0.965395 0.260792i
\(325\) −16.0447 + 16.0447i −0.890001 + 0.890001i
\(326\) 18.4443 23.6899i 1.02154 1.31206i
\(327\) 0.0627288 + 15.5604i 0.00346891 + 0.860491i
\(328\) −9.35840 7.50024i −0.516731 0.414131i
\(329\) 9.50978 5.49047i 0.524291 0.302700i
\(330\) −0.217400 0.167859i −0.0119675 0.00924032i
\(331\) −4.07910 15.2234i −0.224207 0.836753i −0.982721 0.185096i \(-0.940741\pi\)
0.758513 0.651658i \(-0.225926\pi\)
\(332\) 13.4508 7.51532i 0.738211 0.412457i
\(333\) 8.45813 + 8.32283i 0.463503 + 0.456088i
\(334\) 7.70156 + 10.1845i 0.421410 + 0.557273i
\(335\) −0.659494 + 1.14228i −0.0360320 + 0.0624093i
\(336\) 22.3392 + 23.4443i 1.21871 + 1.27899i
\(337\) −8.67225 15.0208i −0.472407 0.818233i 0.527094 0.849807i \(-0.323282\pi\)
−0.999501 + 0.0315734i \(0.989948\pi\)
\(338\) −4.32978 + 10.2483i −0.235509 + 0.557436i
\(339\) 4.72093 17.9072i 0.256406 0.972585i
\(340\) 1.57254 + 0.0221455i 0.0852827 + 0.00120101i
\(341\) 1.97567 1.97567i 0.106988 0.106988i
\(342\) −5.90326 4.52016i −0.319212 0.244422i
\(343\) 36.6800i 1.98053i
\(344\) −0.0309790 + 0.0227478i −0.00167028 + 0.00122648i
\(345\) −1.21321 0.693942i −0.0653171 0.0373606i
\(346\) −2.75661 6.78988i −0.148197 0.365026i
\(347\) 6.92193 + 1.85473i 0.371589 + 0.0995669i 0.439780 0.898105i \(-0.355056\pi\)
−0.0681917 + 0.997672i \(0.521723\pi\)
\(348\) 29.8792 + 8.32884i 1.60169 + 0.446473i
\(349\) −1.10009 + 0.294768i −0.0588865 + 0.0157786i −0.288142 0.957588i \(-0.593038\pi\)
0.229256 + 0.973366i \(0.426371\pi\)
\(350\) 26.1897 19.8046i 1.39990 1.05860i
\(351\) −12.1158 20.4111i −0.646694 1.08946i
\(352\) 2.23117 2.70498i 0.118922 0.144176i
\(353\) −12.2507 + 21.2188i −0.652037 + 1.12936i 0.330591 + 0.943774i \(0.392752\pi\)
−0.982628 + 0.185587i \(0.940581\pi\)
\(354\) −22.2519 + 16.9683i −1.18268 + 0.901856i
\(355\) −0.353557 + 1.31949i −0.0187649 + 0.0700314i
\(356\) 1.56345 + 6.18178i 0.0828625 + 0.327634i
\(357\) −9.24528 33.9557i −0.489312 1.79713i
\(358\) 2.40932 3.09453i 0.127336 0.163551i
\(359\) 11.6859i 0.616757i 0.951264 + 0.308378i \(0.0997863\pi\)
−0.951264 + 0.308378i \(0.900214\pi\)
\(360\) −1.52432 + 0.180462i −0.0803388 + 0.00951116i
\(361\) 15.9289i 0.838362i
\(362\) 0.353898 + 0.275536i 0.0186005 + 0.0144818i
\(363\) −17.7796 4.68729i −0.933186 0.246019i
\(364\) 21.8702 36.6776i 1.14631 1.92243i
\(365\) −0.137045 + 0.511458i −0.00717325 + 0.0267709i
\(366\) 2.14799 5.14189i 0.112277 0.268771i
\(367\) −5.61911 + 9.73258i −0.293315 + 0.508037i −0.974592 0.223990i \(-0.928092\pi\)
0.681276 + 0.732026i \(0.261425\pi\)
\(368\) 9.35307 15.1951i 0.487563 0.792099i
\(369\) −6.44889 10.9647i −0.335716 0.570798i
\(370\) −0.610345 0.807121i −0.0317303 0.0419602i
\(371\) 3.31647 0.888646i 0.172183 0.0461362i
\(372\) 0.156931 15.6138i 0.00813647 0.809535i
\(373\) −11.5685 3.09978i −0.598996 0.160501i −0.0534347 0.998571i \(-0.517017\pi\)
−0.545561 + 0.838071i \(0.683684\pi\)
\(374\) −3.53066 + 1.43341i −0.182566 + 0.0741197i
\(375\) 0.0125896 + 3.12296i 0.000650126 + 0.161269i
\(376\) −6.56820 1.00628i −0.338729 0.0518948i
\(377\) 40.9031i 2.10661i
\(378\) 13.3045 + 31.6663i 0.684308 + 1.62874i
\(379\) 11.6135 11.6135i 0.596544 0.596544i −0.342847 0.939391i \(-0.611391\pi\)
0.939391 + 0.342847i \(0.111391\pi\)
\(380\) 0.441971 + 0.454597i 0.0226727 + 0.0233204i
\(381\) 14.1760 + 14.0622i 0.726258 + 0.720426i
\(382\) 27.0686 + 11.4361i 1.38495 + 0.585124i
\(383\) −14.5294 25.1657i −0.742418 1.28591i −0.951391 0.307985i \(-0.900345\pi\)
0.208973 0.977921i \(-0.432988\pi\)
\(384\) −1.67624 19.5241i −0.0855402 0.996335i
\(385\) 0.262056 0.453894i 0.0133556 0.0231326i
\(386\) 17.3616 13.1289i 0.883683 0.668241i
\(387\) −0.0392899 + 0.0108680i −0.00199722 + 0.000552449i
\(388\) −8.75878 + 30.9388i −0.444660 + 1.57068i
\(389\) 3.65693 + 13.6478i 0.185414 + 0.691973i 0.994542 + 0.104341i \(0.0332732\pi\)
−0.809128 + 0.587632i \(0.800060\pi\)
\(390\) 0.768967 + 1.87237i 0.0389381 + 0.0948111i
\(391\) −16.7926 + 9.69522i −0.849239 + 0.490308i
\(392\) −26.2629 + 32.7694i −1.32648 + 1.65511i
\(393\) −5.30304 + 3.09028i −0.267503 + 0.155884i
\(394\) 1.42843 + 1.11214i 0.0719630 + 0.0560286i
\(395\) 0.373213 0.373213i 0.0187784 0.0187784i
\(396\) 3.23200 1.84015i 0.162414 0.0924708i
\(397\) −1.83996 1.83996i −0.0923450 0.0923450i 0.659425 0.751770i \(-0.270800\pi\)
−0.751770 + 0.659425i \(0.770800\pi\)
\(398\) −23.1839 + 2.88631i −1.16211 + 0.144678i
\(399\) 7.04423 12.3154i 0.352653 0.616539i
\(400\) −19.8612 0.559510i −0.993061 0.0279755i
\(401\) 14.5786 + 25.2509i 0.728021 + 1.26097i 0.957718 + 0.287708i \(0.0928931\pi\)
−0.229697 + 0.973262i \(0.573774\pi\)
\(402\) −10.8298 14.2020i −0.540144 0.708333i
\(403\) −19.8889 + 5.32922i −0.990737 + 0.265467i
\(404\) 17.1998 + 30.7841i 0.855723 + 1.53156i
\(405\) −1.57919 0.395965i −0.0784707 0.0196757i
\(406\) −8.13873 + 58.6270i −0.403918 + 2.90961i
\(407\) 2.12332 + 1.22590i 0.105249 + 0.0607656i
\(408\) −8.48447 + 19.5323i −0.420044 + 0.966991i
\(409\) −9.18277 + 5.30167i −0.454059 + 0.262151i −0.709543 0.704662i \(-0.751099\pi\)
0.255484 + 0.966813i \(0.417765\pi\)
\(410\) 0.408052 + 1.00508i 0.0201522 + 0.0496375i
\(411\) 6.84070 + 25.1243i 0.337427 + 1.23929i
\(412\) −13.3446 + 12.9739i −0.657440 + 0.639180i
\(413\) −37.7581 37.7581i −1.85796 1.85796i
\(414\) 15.0027 11.5363i 0.737341 0.566980i
\(415\) −1.39363 −0.0684107
\(416\) −24.2069 + 9.04238i −1.18684 + 0.443339i
\(417\) 8.81306 + 15.1235i 0.431577 + 0.740603i
\(418\) −1.41511 0.597866i −0.0692153 0.0292426i
\(419\) 3.70507 13.8275i 0.181005 0.675519i −0.814446 0.580240i \(-0.802959\pi\)
0.995451 0.0952792i \(-0.0303744\pi\)
\(420\) −0.729616 2.83670i −0.0356016 0.138417i
\(421\) 5.16753 + 19.2855i 0.251850 + 0.939918i 0.969816 + 0.243839i \(0.0784068\pi\)
−0.717966 + 0.696079i \(0.754926\pi\)
\(422\) −36.5488 5.07379i −1.77917 0.246988i
\(423\) −6.13189 3.47463i −0.298143 0.168942i
\(424\) −1.90230 0.835456i −0.0923838 0.0405733i
\(425\) 18.6995 + 10.7962i 0.907059 + 0.523691i
\(426\) −14.6409 11.3045i −0.709352 0.547705i
\(427\) 10.2712 + 2.75215i 0.497056 + 0.133186i
\(428\) −13.7893 + 23.1255i −0.666530 + 1.11781i
\(429\) −3.48184 3.45388i −0.168105 0.166755i
\(430\) 0.00344967 0.000429470i 0.000166358 2.07109e-5i
\(431\) −8.92159 −0.429738 −0.214869 0.976643i \(-0.568932\pi\)
−0.214869 + 0.976643i \(0.568932\pi\)
\(432\) 5.70136 19.9874i 0.274307 0.961642i
\(433\) −29.8178 −1.43295 −0.716476 0.697612i \(-0.754246\pi\)
−0.716476 + 0.697612i \(0.754246\pi\)
\(434\) 29.5675 3.68104i 1.41928 0.176695i
\(435\) −1.99182 1.97582i −0.0955003 0.0947334i
\(436\) 15.4325 + 9.20208i 0.739080 + 0.440700i
\(437\) −7.55091 2.02326i −0.361209 0.0967857i
\(438\) −5.67505 4.38182i −0.271165 0.209371i
\(439\) 27.0574 + 15.6216i 1.29138 + 0.745579i 0.978899 0.204345i \(-0.0655065\pi\)
0.312481 + 0.949924i \(0.398840\pi\)
\(440\) −0.295509 + 0.115153i −0.0140878 + 0.00548971i
\(441\) −38.3940 + 22.5815i −1.82829 + 1.07531i
\(442\) 27.8150 + 3.86134i 1.32303 + 0.183665i
\(443\) 2.84043 + 10.6006i 0.134953 + 0.503651i 0.999998 + 0.00195701i \(0.000622937\pi\)
−0.865045 + 0.501694i \(0.832710\pi\)
\(444\) 13.2701 3.41315i 0.629773 0.161981i
\(445\) 0.149271 0.557087i 0.00707613 0.0264085i
\(446\) −16.8814 7.13215i −0.799356 0.337717i
\(447\) 4.64786 + 7.97590i 0.219836 + 0.377247i
\(448\) 36.4954 8.14399i 1.72424 0.384767i
\(449\) 27.4967 1.29765 0.648824 0.760938i \(-0.275261\pi\)
0.648824 + 0.760938i \(0.275261\pi\)
\(450\) −19.4784 8.04491i −0.918221 0.379241i
\(451\) −1.85849 1.85849i −0.0875128 0.0875128i
\(452\) −14.9063 15.3321i −0.701134 0.721163i
\(453\) −5.18307 19.0362i −0.243522 0.894397i
\(454\) 7.23693 + 17.8255i 0.339646 + 0.836590i
\(455\) −3.34497 + 1.93122i −0.156815 + 0.0905370i
\(456\) −7.98676 + 3.14941i −0.374014 + 0.147485i
\(457\) −16.8184 9.71008i −0.786729 0.454218i 0.0520805 0.998643i \(-0.483415\pi\)
−0.838810 + 0.544424i \(0.816748\pi\)
\(458\) −3.26883 + 23.5469i −0.152742 + 1.10027i
\(459\) −15.7773 + 16.1636i −0.736419 + 0.754451i
\(460\) −1.40888 + 0.787176i −0.0656893 + 0.0367023i
\(461\) 4.03437 1.08101i 0.187900 0.0503475i −0.163642 0.986520i \(-0.552324\pi\)
0.351542 + 0.936172i \(0.385658\pi\)
\(462\) 4.30333 + 5.64330i 0.200209 + 0.262550i
\(463\) −0.773244 1.33930i −0.0359357 0.0622425i 0.847498 0.530798i \(-0.178108\pi\)
−0.883434 + 0.468556i \(0.844774\pi\)
\(464\) 26.0295 24.6031i 1.20839 1.14217i
\(465\) −0.701222 + 1.22594i −0.0325184 + 0.0568515i
\(466\) 14.1030 1.75577i 0.653308 0.0813343i
\(467\) −2.13196 2.13196i −0.0986553 0.0986553i 0.656056 0.754712i \(-0.272223\pi\)
−0.754712 + 0.656056i \(0.772223\pi\)
\(468\) −27.4077 0.164973i −1.26692 0.00762588i
\(469\) 24.0987 24.0987i 1.11277 1.11277i
\(470\) 0.474231 + 0.369224i 0.0218747 + 0.0170310i
\(471\) −8.47685 + 4.93978i −0.390593 + 0.227613i
\(472\) 3.54005 + 32.1180i 0.162944 + 1.47835i
\(473\) −0.00729441 + 0.00421143i −0.000335397 + 0.000193642i
\(474\) 2.71510 + 6.61103i 0.124709 + 0.303655i
\(475\) 2.25301 + 8.40836i 0.103375 + 0.385802i
\(476\) −39.0994 11.0690i −1.79212 0.507349i
\(477\) −1.57077 1.54564i −0.0719205 0.0707700i
\(478\) −7.63355 + 5.77250i −0.349151 + 0.264028i
\(479\) 14.5113 25.1343i 0.663037 1.14841i −0.316777 0.948500i \(-0.602601\pi\)
0.979814 0.199914i \(-0.0640661\pi\)
\(480\) −0.728987 + 1.61557i −0.0332735 + 0.0737405i
\(481\) −9.03428 15.6478i −0.411928 0.713480i
\(482\) 2.80877 + 1.18667i 0.127936 + 0.0540513i
\(483\) 25.6387 + 25.4328i 1.16660 + 1.15723i
\(484\) −15.2229 + 14.8001i −0.691950 + 0.672731i
\(485\) 2.05652 2.05652i 0.0933817 0.0933817i
\(486\) 13.1899 17.6643i 0.598304 0.801269i
\(487\) 3.59517i 0.162913i −0.996677 0.0814564i \(-0.974043\pi\)
0.996677 0.0814564i \(-0.0259571\pi\)
\(488\) −3.80843 5.18649i −0.172399 0.234781i
\(489\) −0.148234 36.7707i −0.00670339 1.66283i
\(490\) 3.51940 1.42884i 0.158990 0.0645483i
\(491\) 19.9964 + 5.35801i 0.902424 + 0.241804i 0.680057 0.733159i \(-0.261955\pi\)
0.222367 + 0.974963i \(0.428622\pi\)
\(492\) −14.6877 0.147623i −0.662172 0.00665535i
\(493\) −37.5969 + 10.0741i −1.69328 + 0.453713i
\(494\) 6.82850 + 9.03002i 0.307229 + 0.406280i
\(495\) −0.336380 + 0.00271215i −0.0151192 + 0.000121902i
\(496\) −15.3545 9.45119i −0.689437 0.424371i
\(497\) 17.6482 30.5676i 0.791631 1.37115i
\(498\) 7.27399 17.4126i 0.325955 0.780275i
\(499\) 3.94988 14.7412i 0.176821 0.659905i −0.819413 0.573203i \(-0.805701\pi\)
0.996234 0.0867019i \(-0.0276328\pi\)
\(500\) 3.09728 + 1.84685i 0.138515 + 0.0825938i
\(501\) 15.1217 + 3.98658i 0.675587 + 0.178107i
\(502\) −5.76461 4.48817i −0.257287 0.200317i
\(503\) 11.1260i 0.496085i −0.968749 0.248042i \(-0.920213\pi\)
0.968749 0.248042i \(-0.0797872\pi\)
\(504\) 39.2510 + 5.68993i 1.74838 + 0.253449i
\(505\) 3.18951i 0.141931i
\(506\) 2.40223 3.08543i 0.106792 0.137164i
\(507\) 3.57965 + 13.1472i 0.158978 + 0.583888i
\(508\) 22.3527 5.65328i 0.991742 0.250824i
\(509\) 6.47918 24.1806i 0.287185 1.07179i −0.660044 0.751227i \(-0.729462\pi\)
0.947228 0.320560i \(-0.103871\pi\)
\(510\) 1.53164 1.16796i 0.0678220 0.0517181i
\(511\) 6.84076 11.8485i 0.302617 0.524149i
\(512\) −20.3147 9.96558i −0.897792 0.440420i
\(513\) −9.10540 + 0.110125i −0.402013 + 0.00486214i
\(514\) −11.4986 + 8.69527i −0.507183 + 0.383532i
\(515\) 1.62606 0.435701i 0.0716526 0.0191993i
\(516\) −0.0126394 + 0.0453430i −0.000556418 + 0.00199611i
\(517\) −1.40661 0.376900i −0.0618626 0.0165760i
\(518\) 9.83543 + 24.2259i 0.432144 + 1.06442i
\(519\) −7.79068 4.45617i −0.341973 0.195604i
\(520\) 2.31030 + 0.353948i 0.101313 + 0.0155216i
\(521\) 44.7974i 1.96261i 0.192458 + 0.981305i \(0.438354\pi\)
−0.192458 + 0.981305i \(0.561646\pi\)
\(522\) 35.0828 14.5738i 1.53553 0.637878i
\(523\) 7.02267 7.02267i 0.307080 0.307080i −0.536696 0.843776i \(-0.680328\pi\)
0.843776 + 0.536696i \(0.180328\pi\)
\(524\) −0.0997979 + 7.08657i −0.00435969 + 0.309578i
\(525\) 10.2515 38.8856i 0.447413 1.69711i
\(526\) −9.27470 + 21.9526i −0.404396 + 0.957180i
\(527\) 9.79692 + 16.9688i 0.426761 + 0.739171i
\(528\) 0.103625 4.29323i 0.00450971 0.186839i
\(529\) −1.55091 + 2.68626i −0.0674309 + 0.116794i
\(530\) 0.113348 + 0.149891i 0.00492351 + 0.00651085i
\(531\) −8.60319 + 33.1752i −0.373347 + 1.43968i
\(532\) −7.99065 14.3016i −0.346438 0.620052i
\(533\) 5.01314 + 18.7093i 0.217143 + 0.810389i
\(534\) 6.18135 + 4.77274i 0.267493 + 0.206537i
\(535\) 2.10903 1.21765i 0.0911812 0.0526435i
\(536\) −20.4989 + 2.25940i −0.885419 + 0.0975910i
\(537\) −0.0193633 4.80323i −0.000835590 0.207275i
\(538\) 22.3886 28.7559i 0.965240 1.23975i
\(539\) −6.50770 + 6.50770i −0.280306 + 0.280306i
\(540\) −1.33196 + 1.32667i −0.0573184 + 0.0570910i
\(541\) 14.9663 + 14.9663i 0.643452 + 0.643452i 0.951402 0.307950i \(-0.0996431\pi\)
−0.307950 + 0.951402i \(0.599643\pi\)
\(542\) −1.73958 13.9729i −0.0747212 0.600189i
\(543\) 0.549309 0.00221444i 0.0235731 9.50308e-5i
\(544\) 14.2734 + 20.0232i 0.611969 + 0.858489i
\(545\) −0.812579 1.40743i −0.0348071 0.0602876i
\(546\) −6.67048 51.8732i −0.285470 2.21997i
\(547\) −5.15670 + 1.38173i −0.220485 + 0.0590787i −0.367370 0.930075i \(-0.619742\pi\)
0.146885 + 0.989154i \(0.453075\pi\)
\(548\) 28.9301 + 8.19013i 1.23583 + 0.349865i
\(549\) −1.81951 6.57789i −0.0776547 0.280738i
\(550\) −4.31299 0.598739i −0.183907 0.0255303i
\(551\) −13.5896 7.84596i −0.578937 0.334249i
\(552\) −2.48170 21.7117i −0.105628 0.924111i
\(553\) −11.8106 + 6.81883i −0.502236 + 0.289966i
\(554\) −3.57781 + 1.45255i −0.152007 + 0.0617129i
\(555\) −1.19839 0.315935i −0.0508687 0.0134107i
\(556\) 20.2099 + 0.284610i 0.857092 + 0.0120702i
\(557\) 7.66230 + 7.66230i 0.324662 + 0.324662i 0.850552 0.525890i \(-0.176268\pi\)
−0.525890 + 0.850552i \(0.676268\pi\)
\(558\) −11.6573 15.1601i −0.493495 0.641776i
\(559\) 0.0620723 0.00262538
\(560\) −3.24096 0.967014i −0.136956 0.0408638i
\(561\) −2.31716 + 4.05106i −0.0978304 + 0.171036i
\(562\) 13.8873 32.8704i 0.585801 1.38655i
\(563\) 5.71152 21.3157i 0.240712 0.898349i −0.734779 0.678307i \(-0.762714\pi\)
0.975490 0.220042i \(-0.0706194\pi\)
\(564\) −7.08845 + 3.99808i −0.298478 + 0.168349i
\(565\) 0.500595 + 1.86825i 0.0210602 + 0.0785977i
\(566\) 1.73880 12.5254i 0.0730873 0.526482i
\(567\) 36.7656 + 20.4434i 1.54401 + 0.858542i
\(568\) −19.9011 + 7.75503i −0.835033 + 0.325394i
\(569\) −38.6354 22.3061i −1.61968 0.935122i −0.987002 0.160706i \(-0.948623\pi\)
−0.632676 0.774416i \(-0.718044\pi\)
\(570\) 0.769577 + 0.103674i 0.0322340 + 0.00434242i
\(571\) 9.47469 + 2.53873i 0.396503 + 0.106243i 0.451561 0.892240i \(-0.350867\pi\)
−0.0550573 + 0.998483i \(0.517534\pi\)
\(572\) −5.49016 + 1.38853i −0.229555 + 0.0580573i
\(573\) 34.7253 9.45483i 1.45067 0.394981i
\(574\) −3.46271 27.8138i −0.144531 1.16093i
\(575\) −22.1577 −0.924041
\(576\) −16.3807 17.5406i −0.682528 0.730860i
\(577\) −0.565932 −0.0235600 −0.0117800 0.999931i \(-0.503750\pi\)
−0.0117800 + 0.999931i \(0.503750\pi\)
\(578\) −0.331200 2.66032i −0.0137761 0.110655i
\(579\) 6.79593 25.7780i 0.282429 1.07130i
\(580\) −3.14070 + 0.794321i −0.130410 + 0.0329824i
\(581\) 34.7824 + 9.31992i 1.44302 + 0.386655i
\(582\) 14.9610 + 36.4288i 0.620154 + 1.51002i
\(583\) −0.394324 0.227663i −0.0163312 0.00942884i
\(584\) −7.71402 + 3.00598i −0.319209 + 0.124389i
\(585\) 2.15683 + 1.22217i 0.0891740 + 0.0505304i
\(586\) 4.04852 29.1633i 0.167243 1.20473i
\(587\) 10.6937 + 39.9093i 0.441375 + 1.64723i 0.725334 + 0.688397i \(0.241685\pi\)
−0.283960 + 0.958836i \(0.591648\pi\)
\(588\) −0.516917 + 51.4305i −0.0213173 + 2.12096i
\(589\) −2.04448 + 7.63012i −0.0842415 + 0.314394i
\(590\) 1.13742 2.69221i 0.0468269 0.110836i
\(591\) 2.21716 0.00893807i 0.0912017 0.000367663i
\(592\) 4.52370 15.1613i 0.185923 0.623124i
\(593\) −12.9281 −0.530893 −0.265447 0.964126i \(-0.585519\pi\)
−0.265447 + 0.964126i \(0.585519\pi\)
\(594\) 1.72183 4.21701i 0.0706476 0.173026i
\(595\) 2.59896 + 2.59896i 0.106547 + 0.106547i
\(596\) 10.6584 + 0.150098i 0.436584 + 0.00614827i
\(597\) −20.1511 + 20.3143i −0.824731 + 0.831408i
\(598\) −26.7005 + 10.8401i −1.09187 + 0.443285i
\(599\) −39.9617 + 23.0719i −1.63279 + 0.942692i −0.649563 + 0.760308i \(0.725048\pi\)
−0.983227 + 0.182384i \(0.941619\pi\)
\(600\) −19.5563 + 14.4818i −0.798382 + 0.591219i
\(601\) −28.4107 16.4029i −1.15890 0.669090i −0.207858 0.978159i \(-0.566649\pi\)
−0.951040 + 0.309069i \(0.899983\pi\)
\(602\) −0.0889692 0.0123509i −0.00362611 0.000503385i
\(603\) −21.1737 5.49089i −0.862259 0.223606i
\(604\) −21.9198 6.20550i −0.891905 0.252498i
\(605\) 1.85493 0.497028i 0.0754138 0.0202071i
\(606\) 39.8510 + 16.6475i 1.61883 + 0.676258i
\(607\) −6.36706 11.0281i −0.258431 0.447616i 0.707391 0.706823i \(-0.249872\pi\)
−0.965822 + 0.259207i \(0.916539\pi\)
\(608\) −1.63910 + 9.77699i −0.0664743 + 0.396509i
\(609\) 36.4986 + 62.6330i 1.47900 + 2.53802i
\(610\) 0.0719016 + 0.577541i 0.00291121 + 0.0233840i
\(611\) 7.58845 + 7.58845i 0.306996 + 0.306996i
\(612\) 6.59862 + 25.2329i 0.266734 + 1.01998i
\(613\) 29.9303 29.9303i 1.20888 1.20888i 0.237483 0.971392i \(-0.423677\pi\)
0.971392 0.237483i \(-0.0763225\pi\)
\(614\) 14.0711 18.0729i 0.567862 0.729362i
\(615\) 1.15323 + 0.659631i 0.0465026 + 0.0265989i
\(616\) 8.14542 0.897790i 0.328188 0.0361730i
\(617\) −2.50740 + 1.44765i −0.100944 + 0.0582802i −0.549622 0.835413i \(-0.685228\pi\)
0.448678 + 0.893693i \(0.351895\pi\)
\(618\) −3.04331 + 22.5907i −0.122420 + 0.908731i
\(619\) 1.48762 + 5.55188i 0.0597926 + 0.223149i 0.989356 0.145512i \(-0.0464830\pi\)
−0.929564 + 0.368661i \(0.879816\pi\)
\(620\) 0.795433 + 1.42366i 0.0319454 + 0.0571755i
\(621\) 5.72788 22.4598i 0.229852 0.901280i
\(622\) −15.4035 20.3696i −0.617624 0.816746i
\(623\) −7.45105 + 12.9056i −0.298520 + 0.517052i
\(624\) −16.4809 + 27.0183i −0.659762 + 1.08160i
\(625\) 12.2551 + 21.2265i 0.490204 + 0.849059i
\(626\) 14.0975 33.3680i 0.563451 1.33365i
\(627\) −1.81539 + 0.494286i −0.0724999 + 0.0197399i
\(628\) −0.159526 + 11.3278i −0.00636578 + 0.452029i
\(629\) −12.1580 + 12.1580i −0.484770 + 0.484770i
\(630\) −2.84824 2.18091i −0.113476 0.0868895i
\(631\) 33.4420i 1.33130i 0.746262 + 0.665652i \(0.231846\pi\)
−0.746262 + 0.665652i \(0.768154\pi\)
\(632\) 8.15730 + 1.24973i 0.324480 + 0.0497118i
\(633\) −39.0462 + 22.7537i −1.55195 + 0.904379i
\(634\) −1.82464 4.49432i −0.0724657 0.178492i
\(635\) −2.01438 0.539750i −0.0799381 0.0214193i
\(636\) −2.46441 + 0.633860i −0.0977202 + 0.0251342i
\(637\) 65.5126 17.5540i 2.59570 0.695516i
\(638\) 6.26078 4.73440i 0.247867 0.187437i
\(639\) −22.6536 + 0.182651i −0.896164 + 0.00722556i
\(640\) 1.16440 + 1.68310i 0.0460269 + 0.0665305i
\(641\) 9.42170 16.3189i 0.372135 0.644557i −0.617759 0.786368i \(-0.711959\pi\)
0.989894 + 0.141811i \(0.0452925\pi\)
\(642\) 4.20578 + 32.7064i 0.165989 + 1.29082i
\(643\) 3.18391 11.8825i 0.125561 0.468601i −0.874298 0.485390i \(-0.838678\pi\)
0.999859 + 0.0167890i \(0.00534435\pi\)
\(644\) 40.4272 10.2245i 1.59305 0.402903i
\(645\) 0.00299840 0.00302267i 0.000118062 0.000119018i
\(646\) 6.61833 8.50057i 0.260395 0.334451i
\(647\) 8.72393i 0.342973i −0.985186 0.171487i \(-0.945143\pi\)
0.985186 0.171487i \(-0.0548570\pi\)
\(648\) −9.62388 23.5665i −0.378062 0.925780i
\(649\) 7.08134i 0.277967i
\(650\) 25.3201 + 19.7136i 0.993135 + 0.773230i
\(651\) 25.6996 25.9077i 1.00725 1.01540i
\(652\) −36.4684 21.7454i −1.42821 0.851616i
\(653\) −5.07099 + 18.9252i −0.198443 + 0.740600i 0.792906 + 0.609345i \(0.208567\pi\)
−0.991349 + 0.131255i \(0.958099\pi\)
\(654\) 21.8262 2.80667i 0.853470 0.109749i
\(655\) 0.320517 0.555152i 0.0125237 0.0216916i
\(656\) −8.89063 + 14.4438i −0.347121 + 0.563935i
\(657\) −8.78094 + 0.0707987i −0.342577 + 0.00276212i
\(658\) −9.36672 12.3866i −0.365153 0.482878i
\(659\) 37.3628 10.0113i 1.45545 0.389986i 0.557533 0.830155i \(-0.311748\pi\)
0.897915 + 0.440168i \(0.145081\pi\)
\(660\) −0.197586 + 0.334422i −0.00769104 + 0.0130174i
\(661\) −26.6308 7.13570i −1.03582 0.277546i −0.299438 0.954116i \(-0.596799\pi\)
−0.736379 + 0.676569i \(0.763466\pi\)
\(662\) −20.6515 + 8.38428i −0.802644 + 0.325864i
\(663\) 29.7157 17.3164i 1.15406 0.672515i
\(664\) −12.8969 17.5636i −0.500498 0.681600i
\(665\) 1.48177i 0.0574608i
\(666\) 10.2023 13.3241i 0.395332 0.516298i
\(667\) 28.2435 28.2435i 1.09359 1.09359i
\(668\) 12.9472 12.5876i 0.500942 0.487029i
\(669\) −21.6565 + 5.89651i −0.837288 + 0.227972i
\(670\) 1.71827 + 0.725947i 0.0663827 + 0.0280458i
\(671\) −0.705075 1.22123i −0.0272191 0.0471449i
\(672\) 28.9983 35.4465i 1.11863 1.36738i
\(673\) 10.0608 17.4258i 0.387815 0.671716i −0.604340 0.796726i \(-0.706563\pi\)
0.992155 + 0.125011i \(0.0398965\pi\)
\(674\) −19.5647 + 14.7948i −0.753603 + 0.569875i
\(675\) −24.8486 + 6.98133i −0.956424 + 0.268711i
\(676\) 15.1388 + 4.28579i 0.582261 + 0.164838i
\(677\) −5.24998 19.5932i −0.201773 0.753027i −0.990409 0.138167i \(-0.955879\pi\)
0.788636 0.614860i \(-0.210788\pi\)
\(678\) −25.9554 3.49659i −0.996811 0.134286i
\(679\) −65.0798 + 37.5738i −2.49753 + 1.44195i
\(680\) −0.243667 2.21073i −0.00934422 0.0847778i
\(681\) 20.4528 + 11.6988i 0.783755 + 0.448298i
\(682\) −3.11779 2.42743i −0.119386 0.0929512i
\(683\) −18.4322 + 18.4322i −0.705287 + 0.705287i −0.965540 0.260253i \(-0.916194\pi\)
0.260253 + 0.965540i \(0.416194\pi\)
\(684\) −5.31211 + 9.07426i −0.203113 + 0.346963i
\(685\) −1.92300 1.92300i −0.0734741 0.0734741i
\(686\) −51.4760 + 6.40856i −1.96536 + 0.244680i
\(687\) 14.6593 + 25.1559i 0.559286 + 0.959756i
\(688\) 0.0373363 + 0.0395009i 0.00142343 + 0.00150596i
\(689\) 1.67776 + 2.90597i 0.0639177 + 0.110709i
\(690\) −0.761898 + 1.82384i −0.0290050 + 0.0694324i
\(691\) 15.6519 4.19392i 0.595427 0.159544i 0.0514946 0.998673i \(-0.483601\pi\)
0.543932 + 0.839129i \(0.316935\pi\)
\(692\) −9.04716 + 5.05487i −0.343921 + 0.192157i
\(693\) 8.41354 + 2.18185i 0.319604 + 0.0828817i
\(694\) 1.39352 10.0381i 0.0528972 0.381043i
\(695\) −1.58322 0.914072i −0.0600549 0.0346727i
\(696\) 6.46817 43.3870i 0.245176 1.64458i
\(697\) 15.9623 9.21585i 0.604616 0.349075i
\(698\) 0.605875 + 1.49234i 0.0229327 + 0.0564861i
\(699\) 12.2581 12.3573i 0.463644 0.467397i
\(700\) −32.3691 33.2939i −1.22344 1.25839i
\(701\) 2.97647 + 2.97647i 0.112420 + 0.112420i 0.761079 0.648659i \(-0.224670\pi\)
−0.648659 + 0.761079i \(0.724670\pi\)
\(702\) −26.5277 + 20.5692i −1.00122 + 0.776335i
\(703\) −6.93177 −0.261437
\(704\) −4.18594 2.65858i −0.157764 0.100199i
\(705\) 0.736087 0.00296740i 0.0277226 0.000111759i
\(706\) 31.9184 + 13.4851i 1.20126 + 0.507518i
\(707\) −21.3299 + 79.6042i −0.802192 + 2.99382i
\(708\) 27.7008 + 28.2632i 1.04106 + 1.06220i
\(709\) 10.0033 + 37.3329i 0.375682 + 1.40207i 0.852345 + 0.522980i \(0.175180\pi\)
−0.476663 + 0.879086i \(0.658154\pi\)
\(710\) 1.91352 + 0.265639i 0.0718132 + 0.00996926i
\(711\) 7.61542 + 4.31528i 0.285601 + 0.161836i
\(712\) 8.40222 3.27416i 0.314887 0.122704i
\(713\) −17.4131 10.0535i −0.652125 0.376505i
\(714\) −46.0375 + 18.9072i −1.72291 + 0.707585i
\(715\) 0.494761 + 0.132571i 0.0185030 + 0.00495787i
\(716\) −4.76374 2.84053i −0.178029 0.106156i
\(717\) −2.98803 + 11.3341i −0.111590 + 0.423278i
\(718\) 16.3997 2.04170i 0.612032 0.0761956i
\(719\) 38.3674 1.43086 0.715431 0.698683i \(-0.246230\pi\)
0.715431 + 0.698683i \(0.246230\pi\)
\(720\) 0.519578 + 2.10767i 0.0193635 + 0.0785483i
\(721\) −43.4970 −1.61991
\(722\) −22.3543 + 2.78302i −0.831939 + 0.103573i
\(723\) 3.60327 0.981080i 0.134007 0.0364867i
\(724\) 0.324850 0.544794i 0.0120730 0.0202471i
\(725\) −42.9625 11.5118i −1.59559 0.427536i
\(726\) −3.47168 + 25.7704i −0.128846 + 0.956431i
\(727\) −14.8899 8.59667i −0.552235 0.318833i 0.197788 0.980245i \(-0.436624\pi\)
−0.750023 + 0.661412i \(0.769958\pi\)
\(728\) −55.2937 24.2840i −2.04932 0.900025i
\(729\) −0.653006 26.9921i −0.0241854 0.999707i
\(730\) 0.741714 + 0.102966i 0.0274521 + 0.00381096i
\(731\) −0.0152878 0.0570550i −0.000565441 0.00211026i
\(732\) −7.59130 2.11608i −0.280583 0.0782126i
\(733\) 3.41130 12.7311i 0.125999 0.470235i −0.873874 0.486152i \(-0.838400\pi\)
0.999873 + 0.0159168i \(0.00506670\pi\)
\(734\) 14.6403 + 6.18531i 0.540382 + 0.228304i
\(735\) 2.30977 4.03815i 0.0851972 0.148949i
\(736\) −22.9586 10.4711i −0.846266 0.385970i
\(737\) −4.51959 −0.166481
\(738\) −14.2609 + 10.9659i −0.524951 + 0.403662i
\(739\) −15.2048 15.2048i −0.559316 0.559316i 0.369797 0.929113i \(-0.379427\pi\)
−0.929113 + 0.369797i \(0.879427\pi\)
\(740\) −1.02606 + 0.997562i −0.0377187 + 0.0366711i
\(741\) 13.4075 + 3.53466i 0.492536 + 0.129849i
\(742\) −1.82655 4.49901i −0.0670546 0.165164i
\(743\) 36.6127 21.1384i 1.34319 0.775491i 0.355916 0.934518i \(-0.384169\pi\)
0.987274 + 0.159027i \(0.0508356\pi\)
\(744\) −21.9394 + 2.50773i −0.804339 + 0.0919378i
\(745\) −0.834963 0.482066i −0.0305907 0.0176615i
\(746\) −2.32897 + 16.7766i −0.0852696 + 0.614236i
\(747\) −6.16161 22.2755i −0.225441 0.815017i
\(748\) 2.62847 + 4.70442i 0.0961065 + 0.172010i
\(749\) −60.7803 + 16.2860i −2.22086 + 0.595079i
\(750\) 4.38050 0.563297i 0.159953 0.0205687i
\(751\) −9.72823 16.8498i −0.354988 0.614857i 0.632128 0.774864i \(-0.282182\pi\)
−0.987116 + 0.160007i \(0.948848\pi\)
\(752\) −0.264624 + 9.39349i −0.00964983 + 0.342545i
\(753\) −8.94764 + 0.0360708i −0.326070 + 0.00131449i
\(754\) −57.4025 + 7.14639i −2.09048 + 0.260256i
\(755\) 1.45702 + 1.45702i 0.0530264 + 0.0530264i
\(756\) 42.1153 24.2038i 1.53172 0.880284i
\(757\) 26.9716 26.9716i 0.980300 0.980300i −0.0195093 0.999810i \(-0.506210\pi\)
0.999810 + 0.0195093i \(0.00621039\pi\)
\(758\) −18.3272 14.2691i −0.665673 0.518276i
\(759\) −0.0193064 4.78910i −0.000700778 0.173833i
\(760\) 0.560754 0.699679i 0.0203407 0.0253800i
\(761\) −15.0417 + 8.68435i −0.545263 + 0.314808i −0.747209 0.664589i \(-0.768607\pi\)
0.201946 + 0.979397i \(0.435273\pi\)
\(762\) 17.2578 22.3512i 0.625183 0.809698i
\(763\) 10.8683 + 40.5609i 0.393457 + 1.46840i
\(764\) 11.3199 39.9856i 0.409541 1.44663i
\(765\) 0.592172 2.28350i 0.0214100 0.0825603i
\(766\) −32.7785 + 24.7871i −1.18434 + 0.895595i
\(767\) 26.0930 45.1944i 0.942163 1.63187i
\(768\) −27.1069 + 5.76356i −0.978134 + 0.207974i
\(769\) 15.0664 + 26.0957i 0.543307 + 0.941036i 0.998711 + 0.0507510i \(0.0161615\pi\)
−0.455404 + 0.890285i \(0.650505\pi\)
\(770\) −0.682770 0.288461i −0.0246053 0.0103954i
\(771\) −4.50096 + 17.0728i −0.162098 + 0.614862i
\(772\) −21.4581 22.0711i −0.772294 0.794357i
\(773\) −9.37945 + 9.37945i −0.337355 + 0.337355i −0.855371 0.518016i \(-0.826671\pi\)
0.518016 + 0.855371i \(0.326671\pi\)
\(774\) 0.0221164 + 0.0532398i 0.000794958 + 0.00191367i
\(775\) 22.3901i 0.804278i
\(776\) 44.9492 + 6.88641i 1.61358 + 0.247208i
\(777\) 27.7967 + 15.8993i 0.997200 + 0.570386i
\(778\) 18.5142 7.51655i 0.663766 0.269481i
\(779\) 7.17757 + 1.92322i 0.257163 + 0.0689067i
\(780\) 2.49329 1.40628i 0.0892742 0.0503530i
\(781\) −4.52131 + 1.21148i −0.161785 + 0.0433502i
\(782\) 16.5400 + 21.8725i 0.591469 + 0.782159i
\(783\) 22.7747 40.5723i 0.813902 1.44994i
\(784\) 50.5765 + 31.1315i 1.80630 + 1.11184i
\(785\) 0.512344 0.887406i 0.0182863 0.0316729i
\(786\) 5.26336 + 6.90226i 0.187738 + 0.246195i
\(787\) −3.39895 + 12.6850i −0.121159 + 0.452173i −0.999674 0.0255430i \(-0.991869\pi\)
0.878514 + 0.477716i \(0.158535\pi\)
\(788\) 1.31118 2.19893i 0.0467089 0.0783337i
\(789\) 7.66786 + 28.1622i 0.272983 + 1.00260i
\(790\) −0.588966 0.458554i −0.0209545 0.0163146i
\(791\) 49.9756i 1.77693i
\(792\) −3.14710 4.21422i −0.111827 0.149746i
\(793\) 10.3921i 0.369035i
\(794\) −2.26069 + 2.90363i −0.0802291 + 0.103046i
\(795\) 0.222554 + 0.0586725i 0.00789316 + 0.00208090i
\(796\) 8.10117 + 32.0316i 0.287138 + 1.13533i
\(797\) 4.30559 16.0687i 0.152512 0.569181i −0.846794 0.531921i \(-0.821470\pi\)
0.999306 0.0372602i \(-0.0118630\pi\)
\(798\) −18.5139 7.73405i −0.655383 0.273782i
\(799\) 5.10611 8.84405i 0.180641 0.312880i
\(800\) 2.68486 + 27.9706i 0.0949240 + 0.988910i
\(801\) 9.56432 0.0771149i 0.337939 0.00272472i
\(802\) 32.8895 24.8710i 1.16137 0.878227i
\(803\) −1.75254 + 0.469592i −0.0618458 + 0.0165715i
\(804\) −18.0387 + 17.6797i −0.636176 + 0.623515i
\(805\) −3.64320 0.976194i −0.128406 0.0344063i
\(806\) 10.9538 + 26.9806i 0.385832 + 0.950351i
\(807\) −0.179934 44.6339i −0.00633396 1.57119i
\(808\) 40.1967 29.5163i 1.41411 1.03838i
\(809\) 6.67548i 0.234697i 0.993091 + 0.117349i \(0.0374395\pi\)
−0.993091 + 0.117349i \(0.962560\pi\)
\(810\) −0.279781 + 2.28539i −0.00983049 + 0.0803003i
\(811\) −18.4521 + 18.4521i −0.647940 + 0.647940i −0.952495 0.304555i \(-0.901492\pi\)
0.304555 + 0.952495i \(0.401492\pi\)
\(812\) 83.6979 + 1.17869i 2.93722 + 0.0413639i
\(813\) −12.2434 12.1451i −0.429395 0.425947i
\(814\) 1.34943 3.19401i 0.0472974 0.111950i
\(815\) 1.92020 + 3.32589i 0.0672618 + 0.116501i
\(816\) 28.8936 + 8.49434i 1.01148 + 0.297361i
\(817\) 0.0119066 0.0206229i 0.000416560 0.000721502i
\(818\) 9.04463 + 11.9606i 0.316238 + 0.418194i
\(819\) −45.6572 44.9268i −1.59539 1.56987i
\(820\) 1.33922 0.748255i 0.0467676 0.0261302i
\(821\) −3.30305 12.3271i −0.115277 0.430220i 0.884030 0.467430i \(-0.154820\pi\)
−0.999307 + 0.0372093i \(0.988153\pi\)
\(822\) 34.0637 13.9897i 1.18811 0.487946i
\(823\) 7.14088 4.12279i 0.248915 0.143711i −0.370352 0.928891i \(-0.620763\pi\)
0.619268 + 0.785180i \(0.287430\pi\)
\(824\) 20.5389 + 16.4608i 0.715505 + 0.573438i
\(825\) −4.60770 + 2.68508i −0.160420 + 0.0934826i
\(826\) −46.3921 + 59.5859i −1.61419 + 2.07326i
\(827\) −24.9396 + 24.9396i −0.867236 + 0.867236i −0.992166 0.124930i \(-0.960130\pi\)
0.124930 + 0.992166i \(0.460130\pi\)
\(828\) −18.8111 19.0389i −0.653729 0.661647i
\(829\) 22.7949 + 22.7949i 0.791701 + 0.791701i 0.981771 0.190069i \(-0.0608713\pi\)
−0.190069 + 0.981771i \(0.560871\pi\)
\(830\) 0.243489 + 1.95579i 0.00845162 + 0.0678866i
\(831\) −2.34810 + 4.10516i −0.0814548 + 0.142407i
\(832\) 16.9192 + 32.3917i 0.586568 + 1.12298i
\(833\) −32.2703 55.8938i −1.11810 1.93661i
\(834\) 19.6843 15.0104i 0.681611 0.519767i
\(835\) −1.57764 + 0.422726i −0.0545964 + 0.0146291i
\(836\) −0.591791 + 2.09039i −0.0204675 + 0.0722978i
\(837\) −22.6954 5.78797i −0.784467 0.200061i
\(838\) −20.0526 2.78375i −0.692706 0.0961629i
\(839\) −29.5746 17.0749i −1.02103 0.589492i −0.106628 0.994299i \(-0.534005\pi\)
−0.914402 + 0.404807i \(0.867339\pi\)
\(840\) −3.85349 + 1.51954i −0.132958 + 0.0524292i
\(841\) 44.3213 25.5889i 1.52832 0.882377i
\(842\) 26.1620 10.6215i 0.901603 0.366040i
\(843\) −11.4813 42.1683i −0.395439 1.45235i
\(844\) −0.734811 + 52.1784i −0.0252932 + 1.79605i
\(845\) −1.00628 1.00628i −0.0346171 0.0346171i
\(846\) −3.80489 + 9.21244i −0.130815 + 0.316730i
\(847\) −49.6195 −1.70495
\(848\) −0.840101 + 2.81561i −0.0288492 + 0.0966886i
\(849\) −7.79777 13.3813i −0.267619 0.459244i
\(850\) 11.8840 28.1287i 0.407619 0.964808i
\(851\) 4.56665 17.0430i 0.156543 0.584225i
\(852\) −13.3065 + 22.5218i −0.455874 + 0.771583i
\(853\) 5.84290 + 21.8060i 0.200057 + 0.746624i 0.990900 + 0.134604i \(0.0429761\pi\)
−0.790842 + 0.612020i \(0.790357\pi\)
\(854\) 2.06778 14.8952i 0.0707580 0.509702i
\(855\) 0.819772 0.482150i 0.0280356 0.0164892i
\(856\) 34.8630 + 15.3112i 1.19159 + 0.523327i
\(857\) 44.1400 + 25.4842i 1.50779 + 0.870525i 0.999959 + 0.00907074i \(0.00288735\pi\)
0.507835 + 0.861454i \(0.330446\pi\)
\(858\) −4.23877 + 5.48978i −0.144709 + 0.187418i
\(859\) 17.4277 + 4.66973i 0.594624 + 0.159329i 0.543566 0.839367i \(-0.317074\pi\)
0.0510584 + 0.998696i \(0.483741\pi\)
\(860\) −0.00120542 0.00476615i −4.11044e−5 0.000162525i
\(861\) −24.3711 24.1754i −0.830564 0.823894i
\(862\) 1.55874 + 12.5204i 0.0530908 + 0.426446i
\(863\) −45.5523 −1.55062 −0.775309 0.631583i \(-0.782406\pi\)
−0.775309 + 0.631583i \(0.782406\pi\)
\(864\) −29.0460 4.50908i −0.988164 0.153402i
\(865\) 0.937369 0.0318715
\(866\) 5.20963 + 41.8457i 0.177030 + 1.42197i
\(867\) −2.33103 2.31231i −0.0791660 0.0785303i
\(868\) −10.3318 40.8513i −0.350683 1.38658i
\(869\) 1.74692 + 0.468086i 0.0592603 + 0.0158787i
\(870\) −2.42483 + 3.14048i −0.0822093 + 0.106472i
\(871\) 28.8448 + 16.6536i 0.977369 + 0.564284i
\(872\) 10.2177 23.2653i 0.346016 0.787864i
\(873\) 41.9633 + 23.7785i 1.42024 + 0.804780i
\(874\) −1.52014 + 10.9503i −0.0514196 + 0.370399i
\(875\) 2.18125 + 8.14054i 0.0737398 + 0.275201i
\(876\) −5.15784 + 8.72983i −0.174267 + 0.294954i
\(877\) −5.03203 + 18.7798i −0.169919 + 0.634148i 0.827442 + 0.561551i \(0.189795\pi\)
−0.997361 + 0.0725968i \(0.976871\pi\)
\(878\) 17.1957 40.7012i 0.580327 1.37360i
\(879\) −18.1558 31.1561i −0.612381 1.05087i
\(880\) 0.213234 + 0.394592i 0.00718810 + 0.0133017i
\(881\) 51.8921 1.74829 0.874145 0.485666i \(-0.161423\pi\)
0.874145 + 0.485666i \(0.161423\pi\)
\(882\) 38.3984 + 49.9361i 1.29294 + 1.68143i
\(883\) −1.40472 1.40472i −0.0472726 0.0472726i 0.683075 0.730348i \(-0.260642\pi\)
−0.730348 + 0.683075i \(0.760642\pi\)
\(884\) 0.559219 39.7097i 0.0188086 1.33558i
\(885\) −0.940365 3.45374i −0.0316100 0.116096i
\(886\) 14.3804 5.83829i 0.483120 0.196141i
\(887\) −6.52145 + 3.76516i −0.218969 + 0.126422i −0.605473 0.795866i \(-0.707016\pi\)
0.386504 + 0.922288i \(0.373683\pi\)
\(888\) −7.10845 18.0267i −0.238544 0.604937i
\(889\) 46.6654 + 26.9423i 1.56511 + 0.903616i
\(890\) −0.807885 0.112152i −0.0270804 0.00375936i
\(891\) −1.53057 5.36463i −0.0512762 0.179722i
\(892\) −7.05968 + 24.9371i −0.236376 + 0.834954i
\(893\) 3.97679 1.06558i 0.133078 0.0356582i
\(894\) 10.3812 7.91622i 0.347198 0.264758i
\(895\) 0.250830 + 0.434449i 0.00838431 + 0.0145220i
\(896\) −17.8054 49.7940i −0.594837 1.66350i
\(897\) −17.5234 + 30.6360i −0.585091 + 1.02291i
\(898\) −4.80409 38.5883i −0.160315 1.28771i
\(899\) −28.5398 28.5398i −0.951855 0.951855i
\(900\) −7.88689 + 28.7412i −0.262896 + 0.958039i
\(901\) 2.25787 2.25787i 0.0752204 0.0752204i
\(902\) −2.28346 + 2.93287i −0.0760309 + 0.0976539i
\(903\) −0.0950485 + 0.0553884i −0.00316302 + 0.00184321i
\(904\) −18.9125 + 23.5980i −0.629019 + 0.784857i
\(905\) −0.0496848 + 0.0286855i −0.00165158 + 0.000953539i
\(906\) −25.8094 + 10.5997i −0.857460 + 0.352152i
\(907\) −5.17036 19.2960i −0.171679 0.640714i −0.997094 0.0761873i \(-0.975725\pi\)
0.825415 0.564527i \(-0.190941\pi\)
\(908\) 23.7515 13.2705i 0.788221 0.440398i
\(909\) 50.9804 14.1017i 1.69091 0.467723i
\(910\) 3.29465 + 4.35685i 0.109217 + 0.144428i
\(911\) −20.6774 + 35.8143i −0.685073 + 1.18658i 0.288341 + 0.957528i \(0.406896\pi\)
−0.973414 + 0.229053i \(0.926437\pi\)
\(912\) 5.81523 + 10.6582i 0.192561 + 0.352929i
\(913\) −2.38768 4.13558i −0.0790206 0.136868i
\(914\) −10.6885 + 25.2990i −0.353544 + 0.836818i
\(915\) 0.506054 + 0.501991i 0.0167296 + 0.0165953i
\(916\) 33.6164 + 0.473408i 1.11072 + 0.0156419i
\(917\) −11.7121 + 11.7121i −0.386767 + 0.386767i
\(918\) 25.4401 + 19.3175i 0.839650 + 0.637571i
\(919\) 8.25699i 0.272373i 0.990683 + 0.136187i \(0.0434847\pi\)
−0.990683 + 0.136187i \(0.956515\pi\)
\(920\) 1.35086 + 1.83966i 0.0445365 + 0.0606518i
\(921\) −0.113087 28.0521i −0.00372635 0.924350i
\(922\) −2.22193 5.47289i −0.0731754 0.180240i
\(923\) 33.3198 + 8.92803i 1.09674 + 0.293870i
\(924\) 7.16783 7.02518i 0.235804 0.231111i
\(925\) −18.9783 + 5.08522i −0.624002 + 0.167201i
\(926\) −1.74445 + 1.31915i −0.0573261 + 0.0433500i
\(927\) 14.1534 + 24.0642i 0.464857 + 0.790371i
\(928\) −39.0752 32.2307i −1.28271 1.05802i
\(929\) −2.79783 + 4.84599i −0.0917939 + 0.158992i −0.908266 0.418393i \(-0.862593\pi\)
0.816472 + 0.577385i \(0.195927\pi\)
\(930\) 1.84297 + 0.769890i 0.0604334 + 0.0252457i
\(931\) 6.73438 25.1330i 0.220710 0.823702i
\(932\) −4.92801 19.4851i −0.161422 0.638255i
\(933\) −30.2441 7.97335i −0.990148 0.261036i
\(934\) −2.61946 + 3.36443i −0.0857114 + 0.110088i
\(935\) 0.487421i 0.0159404i
\(936\) 4.55702 + 38.4922i 0.148951 + 1.25816i
\(937\) 3.12869i 0.102210i −0.998693 0.0511049i \(-0.983726\pi\)
0.998693 0.0511049i \(-0.0162743\pi\)
\(938\) −38.0300 29.6092i −1.24173 0.966775i
\(939\) −11.6551 42.8066i −0.380351 1.39694i
\(940\) 0.435306 0.730036i 0.0141981 0.0238111i
\(941\) −3.45992 + 12.9126i −0.112790 + 0.420939i −0.999112 0.0421307i \(-0.986585\pi\)
0.886322 + 0.463070i \(0.153252\pi\)
\(942\) 8.41343 + 11.0332i 0.274124 + 0.359481i
\(943\) −9.45717 + 16.3803i −0.307968 + 0.533416i
\(944\) 44.4552 10.5795i 1.44689 0.344334i
\(945\) −4.39322 + 0.0531337i −0.142912 + 0.00172844i
\(946\) 0.00718468 + 0.00950102i 0.000233594 + 0.000308905i
\(947\) −21.8316 + 5.84975i −0.709431 + 0.190091i −0.595451 0.803392i \(-0.703027\pi\)
−0.113980 + 0.993483i \(0.536360\pi\)
\(948\) 8.80342 4.96536i 0.285922 0.161268i
\(949\) 12.9154 + 3.46066i 0.419250 + 0.112338i
\(950\) 11.4065 4.63090i 0.370075 0.150246i
\(951\) −5.15676 2.94960i −0.167219 0.0956474i
\(952\) −8.70281 + 56.8053i −0.282060 + 1.84107i
\(953\) 13.2051i 0.427754i −0.976861 0.213877i \(-0.931391\pi\)
0.976861 0.213877i \(-0.0686092\pi\)
\(954\) −1.89468 + 2.47443i −0.0613427 + 0.0801127i
\(955\) −2.65786 + 2.65786i −0.0860065 + 0.0860065i
\(956\) 9.43470 + 9.70423i 0.305140 + 0.313857i
\(957\) 2.45068 9.29581i 0.0792193 0.300491i
\(958\) −37.8083 15.9735i −1.22153 0.516080i
\(959\) 35.1344 + 60.8545i 1.13455 + 1.96509i
\(960\) 2.39463 + 0.740780i 0.0772862 + 0.0239086i
\(961\) 5.34109 9.25104i 0.172293 0.298421i
\(962\) −20.3814 + 15.4124i −0.657123 + 0.496917i
\(963\) 28.7871 + 28.3266i 0.927653 + 0.912813i
\(964\) 1.17461 4.14911i 0.0378317 0.133634i
\(965\) 0.720623 + 2.68940i 0.0231977 + 0.0865749i
\(966\) 31.2125 40.4244i 1.00424 1.30063i
\(967\) 26.0110 15.0175i 0.836457 0.482929i −0.0196013 0.999808i \(-0.506240\pi\)
0.856058 + 0.516879i \(0.172906\pi\)
\(968\) 23.4298 + 18.7777i 0.753063 + 0.603538i
\(969\) −0.0531905 13.1943i −0.00170873 0.423863i
\(970\) −3.24538 2.52677i −0.104203 0.0811297i
\(971\) 29.4184 29.4184i 0.944081 0.944081i −0.0544362 0.998517i \(-0.517336\pi\)
0.998517 + 0.0544362i \(0.0173361\pi\)
\(972\) −27.0942 15.4242i −0.869047 0.494730i
\(973\) 33.4013 + 33.4013i 1.07080 + 1.07080i
\(974\) −5.04539 + 0.628131i −0.161665 + 0.0201266i
\(975\) 39.3010 0.158435i 1.25864 0.00507398i
\(976\) −6.61322 + 6.25083i −0.211684 + 0.200084i
\(977\) −1.26388 2.18911i −0.0404352 0.0700358i 0.845100 0.534609i \(-0.179541\pi\)
−0.885535 + 0.464573i \(0.846208\pi\)
\(978\) −51.5773 + 6.63243i −1.64926 + 0.212082i
\(979\) 1.90889 0.511486i 0.0610084 0.0163472i
\(980\) −2.62010 4.68942i −0.0836959 0.149798i
\(981\) 18.9034 19.2107i 0.603538 0.613350i
\(982\) 4.02565 28.9986i 0.128464 0.925383i
\(983\) −17.8779 10.3218i −0.570215 0.329214i 0.187020 0.982356i \(-0.440117\pi\)
−0.757235 + 0.653142i \(0.773450\pi\)
\(984\) 2.35899 + 20.6382i 0.0752019 + 0.657921i
\(985\) −0.200541 + 0.115782i −0.00638976 + 0.00368913i
\(986\) 20.7065 + 51.0026i 0.659429 + 1.62425i
\(987\) −18.3912 4.84852i −0.585398 0.154330i
\(988\) 11.4795 11.1607i 0.365212 0.355068i
\(989\) 0.0428609 + 0.0428609i 0.00136290 + 0.00136290i
\(990\) 0.0625769 + 0.471595i 0.00198882 + 0.0149883i
\(991\) 32.9680 1.04726 0.523631 0.851945i \(-0.324577\pi\)
0.523631 + 0.851945i \(0.324577\pi\)
\(992\) −10.5809 + 23.1994i −0.335945 + 0.736583i
\(993\) −13.5535 + 23.6955i −0.430108 + 0.751953i
\(994\) −45.9814 19.4265i −1.45844 0.616172i
\(995\) 0.773465 2.88661i 0.0245205 0.0915117i
\(996\) −25.7073 7.16593i −0.814567 0.227061i
\(997\) 2.23491 + 8.34081i 0.0707804 + 0.264156i 0.992243 0.124310i \(-0.0396717\pi\)
−0.921463 + 0.388466i \(0.873005\pi\)
\(998\) −21.3776 2.96768i −0.676695 0.0939402i
\(999\) −0.248561 20.5516i −0.00786411 0.650223i
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 144.2.x.e.61.9 yes 72
3.2 odd 2 432.2.y.e.397.10 72
4.3 odd 2 576.2.bb.e.529.14 72
9.4 even 3 inner 144.2.x.e.13.17 72
9.5 odd 6 432.2.y.e.253.2 72
12.11 even 2 1728.2.bc.e.721.8 72
16.5 even 4 inner 144.2.x.e.133.17 yes 72
16.11 odd 4 576.2.bb.e.241.15 72
36.23 even 6 1728.2.bc.e.145.11 72
36.31 odd 6 576.2.bb.e.337.15 72
48.5 odd 4 432.2.y.e.181.2 72
48.11 even 4 1728.2.bc.e.1585.11 72
144.5 odd 12 432.2.y.e.37.10 72
144.59 even 12 1728.2.bc.e.1009.8 72
144.85 even 12 inner 144.2.x.e.85.9 yes 72
144.139 odd 12 576.2.bb.e.49.14 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.17 72 9.4 even 3 inner
144.2.x.e.61.9 yes 72 1.1 even 1 trivial
144.2.x.e.85.9 yes 72 144.85 even 12 inner
144.2.x.e.133.17 yes 72 16.5 even 4 inner
432.2.y.e.37.10 72 144.5 odd 12
432.2.y.e.181.2 72 48.5 odd 4
432.2.y.e.253.2 72 9.5 odd 6
432.2.y.e.397.10 72 3.2 odd 2
576.2.bb.e.49.14 72 144.139 odd 12
576.2.bb.e.241.15 72 16.11 odd 4
576.2.bb.e.337.15 72 36.31 odd 6
576.2.bb.e.529.14 72 4.3 odd 2
1728.2.bc.e.145.11 72 36.23 even 6
1728.2.bc.e.721.8 72 12.11 even 2
1728.2.bc.e.1009.8 72 144.59 even 12
1728.2.bc.e.1585.11 72 48.11 even 4