Properties

Label 90.2.l.a.47.1
Level $90$
Weight $2$
Character 90.47
Analytic conductor $0.719$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [90,2,Mod(23,90)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(90, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("90.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 90.l (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: \(0.718653618192\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 47.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 90.47
Dual form 90.2.l.a.23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(1.62484 - 0.599900i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.20711 + 0.358719i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-4.40508 + 1.18034i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.28024 - 1.94949i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(1.62484 - 0.599900i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.20711 + 0.358719i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-4.40508 + 1.18034i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.28024 - 1.94949i) q^{9} +(-0.224745 - 2.22474i) q^{10} +(-0.550510 - 0.317837i) q^{11} +(-1.10721 + 1.33195i) q^{12} +(-3.34607 - 0.896575i) q^{13} +(2.28024 + 3.94949i) q^{14} +(3.80140 - 0.741181i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.317837 - 0.317837i) q^{17} +(-2.47323 - 1.69798i) q^{18} +6.44949i q^{19} +(-2.09077 + 0.792893i) q^{20} +(-6.44949 + 4.56048i) q^{21} +(-0.164525 + 0.614014i) q^{22} +(-0.258819 + 0.965926i) q^{23} +(1.57313 + 0.724745i) q^{24} +(4.74264 + 1.58346i) q^{25} +3.46410i q^{26} +(2.53553 - 4.53553i) q^{27} +(3.22474 - 3.22474i) q^{28} +(-0.158919 + 0.275255i) q^{29} +(-1.69980 - 3.48004i) q^{30} +(-0.224745 - 0.389270i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.08516 - 0.186185i) q^{33} +(-0.389270 - 0.224745i) q^{34} +(-10.1459 + 1.02494i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(-3.00000 - 3.00000i) q^{37} +(6.22973 - 1.66925i) q^{38} +(-5.97469 + 0.550510i) q^{39} +(1.30701 + 1.81431i) q^{40} +(6.39898 - 3.69445i) q^{41} +(6.07433 + 5.04939i) q^{42} +(-0.896575 - 3.34607i) q^{43} +0.635674 q^{44} +(5.73205 - 3.48477i) q^{45} +1.00000 q^{46} +(-2.32937 - 8.69333i) q^{47} +(0.292893 - 1.70711i) q^{48} +(11.9494 - 6.89898i) q^{49} +(0.302023 - 4.99087i) q^{50} +(0.325765 - 0.707107i) q^{51} +(3.34607 - 0.896575i) q^{52} +(3.78194 + 3.78194i) q^{53} +(-5.03723 - 1.27526i) q^{54} +(-1.10102 - 0.898979i) q^{55} +(-3.94949 - 2.28024i) q^{56} +(3.86905 + 10.4794i) q^{57} +(0.307007 + 0.0822623i) q^{58} +(-4.48905 - 7.77526i) q^{59} +(-2.92152 + 2.54258i) q^{60} +(0.275255 - 0.476756i) q^{61} +(-0.317837 + 0.317837i) q^{62} +(-7.74358 + 11.2791i) q^{63} +1.00000i q^{64} +(-7.06350 - 3.17914i) q^{65} +(0.101021 + 1.09638i) q^{66} +(-1.71089 + 6.38512i) q^{67} +(-0.116337 + 0.434174i) q^{68} +(0.158919 + 1.72474i) q^{69} +(3.61597 + 9.53491i) q^{70} +6.29253i q^{71} +(2.99087 + 0.233875i) q^{72} +(-6.89898 + 6.89898i) q^{73} +(-2.12132 + 3.67423i) q^{74} +(8.65597 - 0.272229i) q^{75} +(-3.22474 - 5.58542i) q^{76} +(2.80020 + 0.750311i) q^{77} +(2.07812 + 5.62863i) q^{78} +(-2.12132 - 1.22474i) q^{79} +(1.41421 - 1.73205i) q^{80} +(1.39898 - 8.89060i) q^{81} +(-5.22474 - 5.22474i) q^{82} +(5.26380 - 1.41043i) q^{83} +(3.30518 - 7.17423i) q^{84} +(0.815515 - 0.587486i) q^{85} +(-3.00000 + 1.73205i) q^{86} +(-0.0930924 + 0.542582i) q^{87} +(-0.164525 - 0.614014i) q^{88} -8.02458 q^{89} +(-4.84959 - 4.63481i) q^{90} +15.7980 q^{91} +(-0.258819 - 0.965926i) q^{92} +(-0.598698 - 0.497678i) q^{93} +(-7.79423 + 4.50000i) q^{94} +(-2.31356 + 14.2347i) q^{95} +(-1.72474 + 0.158919i) q^{96} +(-2.59405 + 0.695075i) q^{97} +(-9.75663 - 9.75663i) q^{98} +(-1.87492 + 0.348469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{10} - 24 q^{11} - 4 q^{12} + 16 q^{15} + 4 q^{16} - 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{25} - 8 q^{27} + 16 q^{28} - 12 q^{30} + 8 q^{31} + 16 q^{33} - 8 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{40} + 12 q^{41} + 20 q^{42} + 32 q^{45} + 8 q^{46} + 8 q^{48} + 24 q^{50} + 32 q^{51} - 48 q^{55} - 12 q^{56} + 28 q^{57} - 4 q^{58} - 8 q^{60} + 12 q^{61} - 32 q^{63} - 24 q^{65} + 40 q^{66} + 4 q^{67} - 12 q^{68} - 16 q^{70} + 8 q^{72} - 16 q^{73} + 8 q^{75} - 16 q^{76} + 24 q^{77} - 24 q^{78} - 28 q^{81} - 32 q^{82} + 12 q^{83} - 20 q^{85} - 24 q^{86} - 8 q^{87} - 8 q^{88} - 20 q^{90} + 48 q^{91} - 20 q^{93} - 24 q^{95} - 4 q^{96} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) 1.62484 0.599900i 0.938104 0.346353i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 2.20711 + 0.358719i 0.987048 + 0.160424i
\(6\) −1.00000 1.41421i −0.408248 0.577350i
\(7\) −4.40508 + 1.18034i −1.66497 + 0.446126i −0.963746 0.266820i \(-0.914027\pi\)
−0.701219 + 0.712946i \(0.747360\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.28024 1.94949i 0.760080 0.649830i
\(10\) −0.224745 2.22474i −0.0710706 0.703526i
\(11\) −0.550510 0.317837i −0.165985 0.0958315i 0.414706 0.909955i \(-0.363884\pi\)
−0.580691 + 0.814124i \(0.697218\pi\)
\(12\) −1.10721 + 1.33195i −0.319623 + 0.384501i
\(13\) −3.34607 0.896575i −0.928032 0.248665i −0.237016 0.971506i \(-0.576170\pi\)
−0.691015 + 0.722840i \(0.742836\pi\)
\(14\) 2.28024 + 3.94949i 0.609419 + 1.05555i
\(15\) 3.80140 0.741181i 0.981518 0.191372i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.317837 0.317837i 0.0770869 0.0770869i −0.667512 0.744599i \(-0.732641\pi\)
0.744599 + 0.667512i \(0.232641\pi\)
\(18\) −2.47323 1.69798i −0.582946 0.400217i
\(19\) 6.44949i 1.47961i 0.672819 + 0.739807i \(0.265083\pi\)
−0.672819 + 0.739807i \(0.734917\pi\)
\(20\) −2.09077 + 0.792893i −0.467510 + 0.177296i
\(21\) −6.44949 + 4.56048i −1.40739 + 0.995178i
\(22\) −0.164525 + 0.614014i −0.0350768 + 0.130908i
\(23\) −0.258819 + 0.965926i −0.0539675 + 0.201409i −0.987646 0.156704i \(-0.949913\pi\)
0.933678 + 0.358113i \(0.116580\pi\)
\(24\) 1.57313 + 0.724745i 0.321114 + 0.147938i
\(25\) 4.74264 + 1.58346i 0.948528 + 0.316693i
\(26\) 3.46410i 0.679366i
\(27\) 2.53553 4.53553i 0.487964 0.872864i
\(28\) 3.22474 3.22474i 0.609419 0.609419i
\(29\) −0.158919 + 0.275255i −0.0295104 + 0.0511136i −0.880403 0.474225i \(-0.842728\pi\)
0.850893 + 0.525339i \(0.176061\pi\)
\(30\) −1.69980 3.48004i −0.310340 0.635365i
\(31\) −0.224745 0.389270i −0.0403654 0.0699149i 0.845137 0.534550i \(-0.179519\pi\)
−0.885502 + 0.464635i \(0.846186\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) −1.08516 0.186185i −0.188903 0.0324106i
\(34\) −0.389270 0.224745i −0.0667592 0.0385434i
\(35\) −10.1459 + 1.02494i −1.71497 + 0.173247i
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) −3.00000 3.00000i −0.493197 0.493197i 0.416115 0.909312i \(-0.363391\pi\)
−0.909312 + 0.416115i \(0.863391\pi\)
\(38\) 6.22973 1.66925i 1.01060 0.270788i
\(39\) −5.97469 + 0.550510i −0.956716 + 0.0881522i
\(40\) 1.30701 + 1.81431i 0.206656 + 0.286868i
\(41\) 6.39898 3.69445i 0.999353 0.576977i 0.0912960 0.995824i \(-0.470899\pi\)
0.908057 + 0.418847i \(0.137566\pi\)
\(42\) 6.07433 + 5.04939i 0.937290 + 0.779138i
\(43\) −0.896575 3.34607i −0.136726 0.510270i −0.999985 0.00550783i \(-0.998247\pi\)
0.863258 0.504762i \(-0.168420\pi\)
\(44\) 0.635674 0.0958315
\(45\) 5.73205 3.48477i 0.854484 0.519478i
\(46\) 1.00000 0.147442
\(47\) −2.32937 8.69333i −0.339774 1.26805i −0.898600 0.438768i \(-0.855415\pi\)
0.558827 0.829285i \(-0.311252\pi\)
\(48\) 0.292893 1.70711i 0.0422755 0.246400i
\(49\) 11.9494 6.89898i 1.70705 0.985568i
\(50\) 0.302023 4.99087i 0.0427126 0.705816i
\(51\) 0.325765 0.707107i 0.0456163 0.0990148i
\(52\) 3.34607 0.896575i 0.464016 0.124333i
\(53\) 3.78194 + 3.78194i 0.519489 + 0.519489i 0.917417 0.397928i \(-0.130270\pi\)
−0.397928 + 0.917417i \(0.630270\pi\)
\(54\) −5.03723 1.27526i −0.685481 0.173540i
\(55\) −1.10102 0.898979i −0.148462 0.121218i
\(56\) −3.94949 2.28024i −0.527773 0.304710i
\(57\) 3.86905 + 10.4794i 0.512468 + 1.38803i
\(58\) 0.307007 + 0.0822623i 0.0403120 + 0.0108016i
\(59\) −4.48905 7.77526i −0.584424 1.01225i −0.994947 0.100402i \(-0.967987\pi\)
0.410523 0.911850i \(-0.365346\pi\)
\(60\) −2.92152 + 2.54258i −0.377167 + 0.328246i
\(61\) 0.275255 0.476756i 0.0352428 0.0610423i −0.847866 0.530211i \(-0.822113\pi\)
0.883109 + 0.469168i \(0.155446\pi\)
\(62\) −0.317837 + 0.317837i −0.0403654 + 0.0403654i
\(63\) −7.74358 + 11.2791i −0.975600 + 1.42104i
\(64\) 1.00000i 0.125000i
\(65\) −7.06350 3.17914i −0.876120 0.394323i
\(66\) 0.101021 + 1.09638i 0.0124348 + 0.134955i
\(67\) −1.71089 + 6.38512i −0.209018 + 0.780067i 0.779169 + 0.626814i \(0.215642\pi\)
−0.988187 + 0.153253i \(0.951025\pi\)
\(68\) −0.116337 + 0.434174i −0.0141079 + 0.0526513i
\(69\) 0.158919 + 1.72474i 0.0191316 + 0.207635i
\(70\) 3.61597 + 9.53491i 0.432191 + 1.13964i
\(71\) 6.29253i 0.746786i 0.927673 + 0.373393i \(0.121806\pi\)
−0.927673 + 0.373393i \(0.878194\pi\)
\(72\) 2.99087 + 0.233875i 0.352477 + 0.0275624i
\(73\) −6.89898 + 6.89898i −0.807464 + 0.807464i −0.984249 0.176785i \(-0.943430\pi\)
0.176785 + 0.984249i \(0.443430\pi\)
\(74\) −2.12132 + 3.67423i −0.246598 + 0.427121i
\(75\) 8.65597 0.272229i 0.999506 0.0314343i
\(76\) −3.22474 5.58542i −0.369904 0.640692i
\(77\) 2.80020 + 0.750311i 0.319112 + 0.0855059i
\(78\) 2.07812 + 5.62863i 0.235300 + 0.637316i
\(79\) −2.12132 1.22474i −0.238667 0.137795i 0.375897 0.926662i \(-0.377335\pi\)
−0.614564 + 0.788867i \(0.710668\pi\)
\(80\) 1.41421 1.73205i 0.158114 0.193649i
\(81\) 1.39898 8.89060i 0.155442 0.987845i
\(82\) −5.22474 5.22474i −0.576977 0.576977i
\(83\) 5.26380 1.41043i 0.577777 0.154815i 0.0419163 0.999121i \(-0.486654\pi\)
0.535861 + 0.844306i \(0.319987\pi\)
\(84\) 3.30518 7.17423i 0.360625 0.782773i
\(85\) 0.815515 0.587486i 0.0884550 0.0637218i
\(86\) −3.00000 + 1.73205i −0.323498 + 0.186772i
\(87\) −0.0930924 + 0.542582i −0.00998055 + 0.0581709i
\(88\) −0.164525 0.614014i −0.0175384 0.0654542i
\(89\) −8.02458 −0.850604 −0.425302 0.905052i \(-0.639832\pi\)
−0.425302 + 0.905052i \(0.639832\pi\)
\(90\) −4.84959 4.63481i −0.511192 0.488552i
\(91\) 15.7980 1.65608
\(92\) −0.258819 0.965926i −0.0269838 0.100705i
\(93\) −0.598698 0.497678i −0.0620821 0.0516068i
\(94\) −7.79423 + 4.50000i −0.803913 + 0.464140i
\(95\) −2.31356 + 14.2347i −0.237366 + 1.46045i
\(96\) −1.72474 + 0.158919i −0.176031 + 0.0162196i
\(97\) −2.59405 + 0.695075i −0.263386 + 0.0705741i −0.388095 0.921619i \(-0.626867\pi\)
0.124709 + 0.992193i \(0.460200\pi\)
\(98\) −9.75663 9.75663i −0.985568 0.985568i
\(99\) −1.87492 + 0.348469i −0.188436 + 0.0350225i
\(100\) −4.89898 + 1.00000i −0.489898 + 0.100000i
\(101\) 10.8990 + 6.29253i 1.08449 + 0.626130i 0.932104 0.362191i \(-0.117971\pi\)
0.152385 + 0.988321i \(0.451305\pi\)
\(102\) −0.767327 0.131652i −0.0759767 0.0130355i
\(103\) 9.42418 + 2.52520i 0.928592 + 0.248816i 0.691254 0.722612i \(-0.257058\pi\)
0.237338 + 0.971427i \(0.423725\pi\)
\(104\) −1.73205 3.00000i −0.169842 0.294174i
\(105\) −15.8706 + 7.75190i −1.54882 + 0.756508i
\(106\) 2.67423 4.63191i 0.259745 0.449891i
\(107\) 13.6100 13.6100i 1.31573 1.31573i 0.398606 0.917122i \(-0.369494\pi\)
0.917122 0.398606i \(-0.130506\pi\)
\(108\) 0.0719302 + 5.19565i 0.00692148 + 0.499952i
\(109\) 5.65153i 0.541318i −0.962675 0.270659i \(-0.912758\pi\)
0.962675 0.270659i \(-0.0872417\pi\)
\(110\) −0.583382 + 1.29618i −0.0556233 + 0.123586i
\(111\) −6.67423 3.07483i −0.633490 0.291850i
\(112\) −1.18034 + 4.40508i −0.111532 + 0.416241i
\(113\) −1.50062 + 5.60040i −0.141167 + 0.526841i 0.858729 + 0.512429i \(0.171254\pi\)
−0.999896 + 0.0144120i \(0.995412\pi\)
\(114\) 9.12096 6.44949i 0.854256 0.604050i
\(115\) −0.917738 + 2.03906i −0.0855795 + 0.190143i
\(116\) 0.317837i 0.0295104i
\(117\) −9.37769 + 4.47871i −0.866968 + 0.414057i
\(118\) −6.34847 + 6.34847i −0.584424 + 0.584424i
\(119\) −1.02494 + 1.77526i −0.0939565 + 0.162737i
\(120\) 3.21209 + 2.16390i 0.293222 + 0.197536i
\(121\) −5.29796 9.17633i −0.481633 0.834212i
\(122\) −0.531752 0.142483i −0.0481426 0.0128998i
\(123\) 8.18104 9.84166i 0.737660 0.887393i
\(124\) 0.389270 + 0.224745i 0.0349574 + 0.0201827i
\(125\) 9.89949 + 5.19615i 0.885438 + 0.464758i
\(126\) 12.8990 + 4.56048i 1.14913 + 0.406280i
\(127\) 1.87628 + 1.87628i 0.166493 + 0.166493i 0.785436 0.618943i \(-0.212439\pi\)
−0.618943 + 0.785436i \(0.712439\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −3.46410 4.89898i −0.304997 0.431331i
\(130\) −1.24264 + 7.64564i −0.108987 + 0.670567i
\(131\) −3.12372 + 1.80348i −0.272921 + 0.157571i −0.630214 0.776421i \(-0.717033\pi\)
0.357293 + 0.933992i \(0.383700\pi\)
\(132\) 1.03287 0.381341i 0.0899000 0.0331915i
\(133\) −7.61258 28.4105i −0.660095 2.46351i
\(134\) 6.61037 0.571049
\(135\) 7.22318 9.10086i 0.621672 0.783278i
\(136\) 0.449490 0.0385434
\(137\) 5.64173 + 21.0552i 0.482005 + 1.79887i 0.593183 + 0.805068i \(0.297871\pi\)
−0.111178 + 0.993801i \(0.535462\pi\)
\(138\) 1.62484 0.599900i 0.138316 0.0510669i
\(139\) 2.68556 1.55051i 0.227786 0.131513i −0.381764 0.924260i \(-0.624683\pi\)
0.609550 + 0.792747i \(0.291350\pi\)
\(140\) 8.27414 5.96058i 0.699292 0.503761i
\(141\) −9.00000 12.7279i −0.757937 1.07188i
\(142\) 6.07812 1.62863i 0.510064 0.136671i
\(143\) 1.55708 + 1.55708i 0.130209 + 0.130209i
\(144\) −0.548188 2.94949i −0.0456823 0.245791i
\(145\) −0.449490 + 0.550510i −0.0373281 + 0.0457174i
\(146\) 8.44949 + 4.87832i 0.699285 + 0.403732i
\(147\) 15.2772 18.3782i 1.26004 1.51581i
\(148\) 4.09808 + 1.09808i 0.336860 + 0.0902613i
\(149\) 2.20881 + 3.82577i 0.180952 + 0.313419i 0.942205 0.335036i \(-0.108749\pi\)
−0.761253 + 0.648455i \(0.775415\pi\)
\(150\) −2.50328 8.29057i −0.204392 0.676922i
\(151\) −8.79796 + 15.2385i −0.715968 + 1.24009i 0.246617 + 0.969113i \(0.420681\pi\)
−0.962585 + 0.270980i \(0.912652\pi\)
\(152\) −4.56048 + 4.56048i −0.369904 + 0.369904i
\(153\) 0.105124 1.34437i 0.00849881 0.108685i
\(154\) 2.89898i 0.233606i
\(155\) −0.356397 0.939780i −0.0286265 0.0754849i
\(156\) 4.89898 3.46410i 0.392232 0.277350i
\(157\) −3.78780 + 14.1363i −0.302300 + 1.12820i 0.632945 + 0.774196i \(0.281846\pi\)
−0.935245 + 0.354001i \(0.884821\pi\)
\(158\) −0.633975 + 2.36603i −0.0504363 + 0.188231i
\(159\) 8.41385 + 3.87628i 0.667262 + 0.307409i
\(160\) −2.03906 0.917738i −0.161202 0.0725535i
\(161\) 4.56048i 0.359416i
\(162\) −8.94975 + 0.949747i −0.703159 + 0.0746192i
\(163\) 4.44949 4.44949i 0.348511 0.348511i −0.511044 0.859555i \(-0.670741\pi\)
0.859555 + 0.511044i \(0.170741\pi\)
\(164\) −3.69445 + 6.39898i −0.288488 + 0.499676i
\(165\) −2.32829 0.800199i −0.181257 0.0622954i
\(166\) −2.72474 4.71940i −0.211481 0.366296i
\(167\) −8.49818 2.27708i −0.657609 0.176206i −0.0854420 0.996343i \(-0.527230\pi\)
−0.572167 + 0.820137i \(0.693897\pi\)
\(168\) −7.78522 1.33573i −0.600643 0.103054i
\(169\) −0.866025 0.500000i −0.0666173 0.0384615i
\(170\) −0.778539 0.635674i −0.0597112 0.0487540i
\(171\) 12.5732 + 14.7064i 0.961498 + 1.12462i
\(172\) 2.44949 + 2.44949i 0.186772 + 0.186772i
\(173\) −12.4595 + 3.33850i −0.947275 + 0.253822i −0.699206 0.714921i \(-0.746463\pi\)
−0.248069 + 0.968742i \(0.579796\pi\)
\(174\) 0.548188 0.0505103i 0.0415580 0.00382917i
\(175\) −22.7608 1.37737i −1.72055 0.104119i
\(176\) −0.550510 + 0.317837i −0.0414963 + 0.0239579i
\(177\) −11.9584 9.94060i −0.898847 0.747181i
\(178\) 2.07691 + 7.75115i 0.155671 + 0.580973i
\(179\) 10.6780 0.798114 0.399057 0.916926i \(-0.369338\pi\)
0.399057 + 0.916926i \(0.369338\pi\)
\(180\) −3.22172 + 5.88392i −0.240133 + 0.438562i
\(181\) −15.4495 −1.14835 −0.574176 0.818732i \(-0.694677\pi\)
−0.574176 + 0.818732i \(0.694677\pi\)
\(182\) −4.08881 15.2597i −0.303083 1.13112i
\(183\) 0.161241 0.939780i 0.0119193 0.0694705i
\(184\) −0.866025 + 0.500000i −0.0638442 + 0.0368605i
\(185\) −5.54516 7.69748i −0.407688 0.565930i
\(186\) −0.325765 + 0.707107i −0.0238863 + 0.0518476i
\(187\) −0.275993 + 0.0739521i −0.0201826 + 0.00540792i
\(188\) 6.36396 + 6.36396i 0.464140 + 0.464140i
\(189\) −5.81577 + 22.9722i −0.423035 + 1.67098i
\(190\) 14.3485 1.44949i 1.04095 0.105157i
\(191\) −15.1237 8.73169i −1.09431 0.631803i −0.159593 0.987183i \(-0.551018\pi\)
−0.934722 + 0.355380i \(0.884351\pi\)
\(192\) 0.599900 + 1.62484i 0.0432941 + 0.117263i
\(193\) 16.7303 + 4.48288i 1.20428 + 0.322685i 0.804513 0.593934i \(-0.202426\pi\)
0.399762 + 0.916619i \(0.369093\pi\)
\(194\) 1.34278 + 2.32577i 0.0964061 + 0.166980i
\(195\) −13.3843 0.928203i −0.958467 0.0664700i
\(196\) −6.89898 + 11.9494i −0.492784 + 0.853527i
\(197\) 6.92820 6.92820i 0.493614 0.493614i −0.415829 0.909443i \(-0.636508\pi\)
0.909443 + 0.415829i \(0.136508\pi\)
\(198\) 0.821859 + 1.72084i 0.0584070 + 0.122295i
\(199\) 8.44949i 0.598968i 0.954101 + 0.299484i \(0.0968146\pi\)
−0.954101 + 0.299484i \(0.903185\pi\)
\(200\) 2.23388 + 4.47323i 0.157959 + 0.316305i
\(201\) 1.05051 + 11.4012i 0.0740973 + 0.804178i
\(202\) 3.25725 12.1562i 0.229179 0.855310i
\(203\) 0.375156 1.40010i 0.0263308 0.0982677i
\(204\) 0.0714323 + 0.775255i 0.00500126 + 0.0542787i
\(205\) 15.4485 5.85861i 1.07897 0.409183i
\(206\) 9.75663i 0.679777i
\(207\) 1.29289 + 2.70711i 0.0898623 + 0.188157i
\(208\) −2.44949 + 2.44949i −0.169842 + 0.169842i
\(209\) 2.04989 3.55051i 0.141794 0.245594i
\(210\) 11.5954 + 13.3235i 0.800158 + 0.919411i
\(211\) −4.55051 7.88171i −0.313270 0.542600i 0.665798 0.746132i \(-0.268091\pi\)
−0.979068 + 0.203532i \(0.934758\pi\)
\(212\) −5.16622 1.38429i −0.354818 0.0950731i
\(213\) 3.77489 + 10.2244i 0.258651 + 0.700563i
\(214\) −16.6688 9.62372i −1.13945 0.657864i
\(215\) −0.778539 7.70674i −0.0530959 0.525595i
\(216\) 5.00000 1.41421i 0.340207 0.0962250i
\(217\) 1.44949 + 1.44949i 0.0983978 + 0.0983978i
\(218\) −5.45896 + 1.46272i −0.369727 + 0.0990682i
\(219\) −7.07107 + 15.3485i −0.477818 + 1.03715i
\(220\) 1.40300 + 0.228029i 0.0945903 + 0.0153737i
\(221\) −1.34847 + 0.778539i −0.0907079 + 0.0523702i
\(222\) −1.24264 + 7.24264i −0.0834006 + 0.486094i
\(223\) 6.63374 + 24.7575i 0.444228 + 1.65788i 0.717966 + 0.696078i \(0.245073\pi\)
−0.273738 + 0.961804i \(0.588260\pi\)
\(224\) 4.56048 0.304710
\(225\) 13.9013 5.63505i 0.926753 0.375670i
\(226\) 5.79796 0.385674
\(227\) 6.44433 + 24.0506i 0.427725 + 1.59629i 0.757899 + 0.652372i \(0.226226\pi\)
−0.330174 + 0.943920i \(0.607107\pi\)
\(228\) −8.59041 7.14092i −0.568914 0.472919i
\(229\) −1.43027 + 0.825765i −0.0945147 + 0.0545681i −0.546512 0.837451i \(-0.684045\pi\)
0.451998 + 0.892019i \(0.350712\pi\)
\(230\) 2.20711 + 0.358719i 0.145532 + 0.0236533i
\(231\) 5.00000 0.460702i 0.328976 0.0303120i
\(232\) −0.307007 + 0.0822623i −0.0201560 + 0.00540079i
\(233\) −14.4600 14.4600i −0.947304 0.947304i 0.0513751 0.998679i \(-0.483640\pi\)
−0.998679 + 0.0513751i \(0.983640\pi\)
\(234\) 6.75323 + 7.89898i 0.441472 + 0.516372i
\(235\) −2.02270 20.0227i −0.131947 1.30614i
\(236\) 7.77526 + 4.48905i 0.506126 + 0.292212i
\(237\) −4.18154 0.717439i −0.271620 0.0466027i
\(238\) 1.98004 + 0.530550i 0.128347 + 0.0343905i
\(239\) −8.48528 14.6969i −0.548867 0.950666i −0.998353 0.0573782i \(-0.981726\pi\)
0.449485 0.893288i \(-0.351607\pi\)
\(240\) 1.25882 3.66270i 0.0812564 0.236426i
\(241\) −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i \(0.376281\pi\)
−0.990912 + 0.134515i \(0.957053\pi\)
\(242\) −7.49245 + 7.49245i −0.481633 + 0.481633i
\(243\) −3.06035 15.2851i −0.196322 0.980540i
\(244\) 0.550510i 0.0352428i
\(245\) 28.8484 10.9403i 1.84305 0.698951i
\(246\) −11.6237 5.35507i −0.741102 0.341427i
\(247\) 5.78245 21.5804i 0.367929 1.37313i
\(248\) 0.116337 0.434174i 0.00738738 0.0275701i
\(249\) 7.70674 5.44949i 0.488395 0.345347i
\(250\) 2.45692 10.9070i 0.155389 0.689822i
\(251\) 2.68556i 0.169511i 0.996402 + 0.0847556i \(0.0270110\pi\)
−0.996402 + 0.0847556i \(0.972989\pi\)
\(252\) 1.06658 13.6398i 0.0671883 0.859226i
\(253\) 0.449490 0.449490i 0.0282592 0.0282592i
\(254\) 1.32673 2.29796i 0.0832463 0.144187i
\(255\) 0.972652 1.44380i 0.0609098 0.0904144i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −17.4305 4.67050i −1.08729 0.291337i −0.329709 0.944083i \(-0.606951\pi\)
−0.757578 + 0.652745i \(0.773617\pi\)
\(258\) −3.83548 + 4.61401i −0.238786 + 0.287256i
\(259\) 16.7563 + 9.67423i 1.04118 + 0.601128i
\(260\) 7.70674 0.778539i 0.477952 0.0482829i
\(261\) 0.174235 + 0.937458i 0.0107849 + 0.0580272i
\(262\) 2.55051 + 2.55051i 0.157571 + 0.157571i
\(263\) 16.1280 4.32149i 0.994495 0.266474i 0.275358 0.961342i \(-0.411204\pi\)
0.719138 + 0.694868i \(0.244537\pi\)
\(264\) −0.635674 0.898979i −0.0391231 0.0553284i
\(265\) 6.99049 + 9.70380i 0.429422 + 0.596100i
\(266\) −25.4722 + 14.7064i −1.56180 + 0.901706i
\(267\) −13.0387 + 4.81395i −0.797955 + 0.294609i
\(268\) −1.71089 6.38512i −0.104509 0.390033i
\(269\) −15.0956 −0.920398 −0.460199 0.887816i \(-0.652222\pi\)
−0.460199 + 0.887816i \(0.652222\pi\)
\(270\) −10.6603 4.62158i −0.648762 0.281260i
\(271\) 28.0454 1.70364 0.851819 0.523837i \(-0.175500\pi\)
0.851819 + 0.523837i \(0.175500\pi\)
\(272\) −0.116337 0.434174i −0.00705394 0.0263257i
\(273\) 25.6692 9.47720i 1.55357 0.573586i
\(274\) 18.8776 10.8990i 1.14044 0.658431i
\(275\) −2.10759 2.37910i −0.127092 0.143465i
\(276\) −1.00000 1.41421i −0.0601929 0.0851257i
\(277\) 27.1825 7.28353i 1.63324 0.437625i 0.678386 0.734705i \(-0.262680\pi\)
0.954852 + 0.297080i \(0.0960129\pi\)
\(278\) −2.19275 2.19275i −0.131513 0.131513i
\(279\) −1.27135 0.449490i −0.0761137 0.0269102i
\(280\) −7.89898 6.44949i −0.472054 0.385431i
\(281\) −14.8485 8.57277i −0.885785 0.511408i −0.0132238 0.999913i \(-0.504209\pi\)
−0.872562 + 0.488504i \(0.837543\pi\)
\(282\) −9.96486 + 11.9876i −0.593399 + 0.713849i
\(283\) −23.3914 6.26772i −1.39048 0.372577i −0.515561 0.856853i \(-0.672417\pi\)
−0.874916 + 0.484275i \(0.839083\pi\)
\(284\) −3.14626 5.44949i −0.186696 0.323368i
\(285\) 4.78024 + 24.5171i 0.283157 + 1.45227i
\(286\) 1.10102 1.90702i 0.0651047 0.112765i
\(287\) −23.8273 + 23.8273i −1.40648 + 1.40648i
\(288\) −2.70711 + 1.29289i −0.159518 + 0.0761845i
\(289\) 16.7980i 0.988115i
\(290\) 0.648089 + 0.291691i 0.0380571 + 0.0171287i
\(291\) −3.79796 + 2.68556i −0.222640 + 0.157430i
\(292\) 2.52520 9.42418i 0.147776 0.551508i
\(293\) 5.70577 21.2942i 0.333335 1.24402i −0.572329 0.820024i \(-0.693960\pi\)
0.905663 0.423998i \(-0.139374\pi\)
\(294\) −21.7060 10.0000i −1.26592 0.583212i
\(295\) −7.11867 18.7711i −0.414465 1.09290i
\(296\) 4.24264i 0.246598i
\(297\) −2.83740 + 1.69097i −0.164643 + 0.0981201i
\(298\) 3.12372 3.12372i 0.180952 0.180952i
\(299\) 1.73205 3.00000i 0.100167 0.173494i
\(300\) −7.36018 + 4.56374i −0.424940 + 0.263488i
\(301\) 7.89898 + 13.6814i 0.455290 + 0.788585i
\(302\) 16.9964 + 4.55416i 0.978030 + 0.262062i
\(303\) 21.4840 + 3.68608i 1.23423 + 0.211760i
\(304\) 5.58542 + 3.22474i 0.320346 + 0.184952i
\(305\) 0.778539 0.953512i 0.0445790 0.0545979i
\(306\) −1.32577 + 0.246405i −0.0757890 + 0.0140860i
\(307\) −6.67423 6.67423i −0.380919 0.380919i 0.490514 0.871433i \(-0.336809\pi\)
−0.871433 + 0.490514i \(0.836809\pi\)
\(308\) −2.80020 + 0.750311i −0.159556 + 0.0427529i
\(309\) 16.8277 1.55051i 0.957294 0.0882054i
\(310\) −0.815515 + 0.587486i −0.0463181 + 0.0333670i
\(311\) 23.8207 13.7529i 1.35075 0.779853i 0.362392 0.932026i \(-0.381960\pi\)
0.988354 + 0.152172i \(0.0486269\pi\)
\(312\) −4.61401 3.83548i −0.261217 0.217141i
\(313\) 3.09273 + 11.5422i 0.174811 + 0.652405i 0.996584 + 0.0825888i \(0.0263188\pi\)
−0.821772 + 0.569816i \(0.807015\pi\)
\(314\) 14.6349 0.825898
\(315\) −21.1370 + 22.1164i −1.19093 + 1.24612i
\(316\) 2.44949 0.137795
\(317\) −2.82086 10.5276i −0.158435 0.591289i −0.998787 0.0492469i \(-0.984318\pi\)
0.840351 0.542042i \(-0.182349\pi\)
\(318\) 1.56653 9.13041i 0.0878467 0.512008i
\(319\) 0.174973 0.101021i 0.00979659 0.00565606i
\(320\) −0.358719 + 2.20711i −0.0200530 + 0.123381i
\(321\) 13.9495 30.2788i 0.778585 1.69000i
\(322\) −4.40508 + 1.18034i −0.245486 + 0.0657777i
\(323\) 2.04989 + 2.04989i 0.114059 + 0.114059i
\(324\) 3.23375 + 8.39898i 0.179653 + 0.466610i
\(325\) −14.4495 9.55051i −0.801513 0.529767i
\(326\) −5.44949 3.14626i −0.301819 0.174255i
\(327\) −3.39036 9.18286i −0.187487 0.507813i
\(328\) 7.13713 + 1.91239i 0.394082 + 0.105594i
\(329\) 20.5222 + 35.5454i 1.13142 + 1.95968i
\(330\) −0.170328 + 2.45606i −0.00937627 + 0.135202i
\(331\) −0.224745 + 0.389270i −0.0123531 + 0.0213962i −0.872136 0.489264i \(-0.837266\pi\)
0.859783 + 0.510660i \(0.170599\pi\)
\(332\) −3.85337 + 3.85337i −0.211481 + 0.211481i
\(333\) −12.6892 0.992248i −0.695363 0.0543748i
\(334\) 8.79796i 0.481403i
\(335\) −6.06658 + 13.4789i −0.331453 + 0.736432i
\(336\) 0.724745 + 7.86566i 0.0395381 + 0.429107i
\(337\) −0.806003 + 3.00804i −0.0439058 + 0.163859i −0.984398 0.175957i \(-0.943698\pi\)
0.940492 + 0.339816i \(0.110365\pi\)
\(338\) −0.258819 + 0.965926i −0.0140779 + 0.0525394i
\(339\) 0.921404 + 10.0000i 0.0500438 + 0.543125i
\(340\) −0.412514 + 0.916536i −0.0223717 + 0.0497061i
\(341\) 0.285729i 0.0154731i
\(342\) 10.9511 15.9511i 0.592167 0.862536i
\(343\) −21.9217 + 21.9217i −1.18366 + 1.18366i
\(344\) 1.73205 3.00000i 0.0933859 0.161749i
\(345\) −0.267949 + 3.86370i −0.0144259 + 0.208015i
\(346\) 6.44949 + 11.1708i 0.346727 + 0.600548i
\(347\) 22.9871 + 6.15937i 1.23401 + 0.330652i 0.816140 0.577855i \(-0.196110\pi\)
0.417870 + 0.908507i \(0.362777\pi\)
\(348\) −0.190671 0.516436i −0.0102210 0.0276839i
\(349\) −25.1541 14.5227i −1.34647 0.777383i −0.358719 0.933446i \(-0.616786\pi\)
−0.987747 + 0.156063i \(0.950120\pi\)
\(350\) 4.56048 + 22.3417i 0.243768 + 1.19421i
\(351\) −12.5505 + 12.9029i −0.669897 + 0.688706i
\(352\) 0.449490 + 0.449490i 0.0239579 + 0.0239579i
\(353\) −33.1244 + 8.87564i −1.76303 + 0.472403i −0.987328 0.158694i \(-0.949272\pi\)
−0.775704 + 0.631097i \(0.782605\pi\)
\(354\) −6.50683 + 14.1237i −0.345834 + 0.750667i
\(355\) −2.25725 + 13.8883i −0.119803 + 0.737114i
\(356\) 6.94949 4.01229i 0.368322 0.212651i
\(357\) −0.600398 + 3.49938i −0.0317764 + 0.185207i
\(358\) −2.76368 10.3142i −0.146065 0.545122i
\(359\) 3.32124 0.175288 0.0876441 0.996152i \(-0.472066\pi\)
0.0876441 + 0.996152i \(0.472066\pi\)
\(360\) 6.51727 + 1.58907i 0.343490 + 0.0837514i
\(361\) −22.5959 −1.18926
\(362\) 3.99862 + 14.9231i 0.210163 + 0.784339i
\(363\) −14.1132 11.7319i −0.740753 0.615763i
\(364\) −13.6814 + 7.89898i −0.717102 + 0.414019i
\(365\) −17.7016 + 12.7520i −0.926543 + 0.667469i
\(366\) −0.949490 + 0.0874863i −0.0496306 + 0.00457298i
\(367\) 3.96008 1.06110i 0.206714 0.0553890i −0.153976 0.988075i \(-0.549208\pi\)
0.360690 + 0.932686i \(0.382541\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) 7.38891 20.8990i 0.384651 1.08796i
\(370\) −6.00000 + 7.34847i −0.311925 + 0.382029i
\(371\) −21.1237 12.1958i −1.09669 0.633174i
\(372\) 0.767327 + 0.131652i 0.0397841 + 0.00682586i
\(373\) 0.476018 + 0.127549i 0.0246473 + 0.00660422i 0.271122 0.962545i \(-0.412605\pi\)
−0.246474 + 0.969149i \(0.579272\pi\)
\(374\) 0.142865 + 0.247449i 0.00738735 + 0.0127953i
\(375\) 19.2023 + 2.50423i 0.991603 + 0.129318i
\(376\) 4.50000 7.79423i 0.232070 0.401957i
\(377\) 0.778539 0.778539i 0.0400968 0.0400968i
\(378\) 23.6947 0.328036i 1.21872 0.0168724i
\(379\) 21.3485i 1.09660i −0.836283 0.548299i \(-0.815276\pi\)
0.836283 0.548299i \(-0.184724\pi\)
\(380\) −5.11376 13.4844i −0.262330 0.691735i
\(381\) 4.17423 + 1.92308i 0.213853 + 0.0985222i
\(382\) −4.51985 + 16.8683i −0.231256 + 0.863058i
\(383\) −2.12284 + 7.92256i −0.108472 + 0.404824i −0.998716 0.0506606i \(-0.983867\pi\)
0.890244 + 0.455485i \(0.150534\pi\)
\(384\) 1.41421 1.00000i 0.0721688 0.0510310i
\(385\) 5.91119 + 2.66050i 0.301262 + 0.135592i
\(386\) 17.3205i 0.881591i
\(387\) −8.56753 5.88196i −0.435512 0.298997i
\(388\) 1.89898 1.89898i 0.0964061 0.0964061i
\(389\) 18.4008 31.8712i 0.932959 1.61593i 0.154726 0.987957i \(-0.450551\pi\)
0.778233 0.627975i \(-0.216116\pi\)
\(390\) 2.56753 + 13.1684i 0.130012 + 0.666810i
\(391\) 0.224745 + 0.389270i 0.0113658 + 0.0196862i
\(392\) 13.3278 + 3.57117i 0.673156 + 0.180372i
\(393\) −3.99366 + 4.80430i −0.201453 + 0.242345i
\(394\) −8.48528 4.89898i −0.427482 0.246807i
\(395\) −4.24264 3.46410i −0.213470 0.174298i
\(396\) 1.44949 1.23924i 0.0728396 0.0622742i
\(397\) 10.5505 + 10.5505i 0.529515 + 0.529515i 0.920428 0.390913i \(-0.127841\pi\)
−0.390913 + 0.920428i \(0.627841\pi\)
\(398\) 8.16158 2.18689i 0.409103 0.109619i
\(399\) −29.4128 41.5959i −1.47248 2.08240i
\(400\) 3.74264 3.31552i 0.187132 0.165776i
\(401\) 7.65153 4.41761i 0.382099 0.220605i −0.296632 0.954992i \(-0.595863\pi\)
0.678731 + 0.734387i \(0.262530\pi\)
\(402\) 10.7408 3.96556i 0.535703 0.197784i
\(403\) 0.403001 + 1.50402i 0.0200749 + 0.0749207i
\(404\) −12.5851 −0.626130
\(405\) 6.27693 19.1207i 0.311903 0.950114i
\(406\) −1.44949 −0.0719370
\(407\) 0.698019 + 2.60504i 0.0345995 + 0.129127i
\(408\) 0.730351 0.269649i 0.0361578 0.0133496i
\(409\) −25.0273 + 14.4495i −1.23752 + 0.714481i −0.968586 0.248678i \(-0.920004\pi\)
−0.268932 + 0.963159i \(0.586671\pi\)
\(410\) −9.65735 13.4058i −0.476943 0.662065i
\(411\) 21.7980 + 30.8270i 1.07521 + 1.52058i
\(412\) −9.42418 + 2.52520i −0.464296 + 0.124408i
\(413\) 28.9521 + 28.9521i 1.42464 + 1.42464i
\(414\) 2.28024 1.94949i 0.112068 0.0958122i
\(415\) 12.1237 1.22474i 0.595130 0.0601204i
\(416\) 3.00000 + 1.73205i 0.147087 + 0.0849208i
\(417\) 3.43347 4.13041i 0.168138 0.202267i
\(418\) −3.96008 1.06110i −0.193694 0.0519001i
\(419\) 2.51059 + 4.34847i 0.122650 + 0.212437i 0.920812 0.390007i \(-0.127527\pi\)
−0.798162 + 0.602443i \(0.794194\pi\)
\(420\) 9.86843 14.6487i 0.481530 0.714782i
\(421\) 2.55051 4.41761i 0.124304 0.215301i −0.797157 0.603773i \(-0.793663\pi\)
0.921461 + 0.388471i \(0.126997\pi\)
\(422\) −6.43539 + 6.43539i −0.313270 + 0.313270i
\(423\) −22.2591 15.2818i −1.08227 0.743026i
\(424\) 5.34847i 0.259745i
\(425\) 2.01067 1.00410i 0.0975319 0.0487062i
\(426\) 8.89898 6.29253i 0.431157 0.304874i
\(427\) −0.649788 + 2.42504i −0.0314455 + 0.117356i
\(428\) −4.98161 + 18.5916i −0.240795 + 0.898659i
\(429\) 3.46410 + 1.59592i 0.167248 + 0.0770516i
\(430\) −7.24264 + 2.74666i −0.349271 + 0.132456i
\(431\) 15.5563i 0.749323i −0.927162 0.374661i \(-0.877759\pi\)
0.927162 0.374661i \(-0.122241\pi\)
\(432\) −2.66012 4.46360i −0.127985 0.214755i
\(433\) 13.4495 13.4495i 0.646341 0.646341i −0.305766 0.952107i \(-0.598912\pi\)
0.952107 + 0.305766i \(0.0989124\pi\)
\(434\) 1.02494 1.77526i 0.0491989 0.0852150i
\(435\) −0.400100 + 1.16414i −0.0191833 + 0.0558164i
\(436\) 2.82577 + 4.89437i 0.135330 + 0.234398i
\(437\) −6.22973 1.66925i −0.298008 0.0798511i
\(438\) 16.6556 + 2.85765i 0.795836 + 0.136544i
\(439\) −25.8058 14.8990i −1.23164 0.711089i −0.264271 0.964449i \(-0.585131\pi\)
−0.967372 + 0.253359i \(0.918465\pi\)
\(440\) −0.142865 1.41421i −0.00681080 0.0674200i
\(441\) 13.7980 39.0265i 0.657046 1.85841i
\(442\) 1.10102 + 1.10102i 0.0523702 + 0.0523702i
\(443\) −5.26380 + 1.41043i −0.250091 + 0.0670116i −0.381687 0.924292i \(-0.624657\pi\)
0.131596 + 0.991303i \(0.457990\pi\)
\(444\) 7.31747 0.674235i 0.347272 0.0319978i
\(445\) −17.7111 2.87857i −0.839587 0.136457i
\(446\) 22.1969 12.8154i 1.05106 0.606827i
\(447\) 5.88405 + 4.89121i 0.278306 + 0.231346i
\(448\) −1.18034 4.40508i −0.0557658 0.208121i
\(449\) 0.921404 0.0434837 0.0217419 0.999764i \(-0.493079\pi\)
0.0217419 + 0.999764i \(0.493079\pi\)
\(450\) −9.04096 11.9692i −0.426195 0.564232i
\(451\) −4.69694 −0.221170
\(452\) −1.50062 5.60040i −0.0705833 0.263421i
\(453\) −5.15373 + 30.0381i −0.242143 + 1.41131i
\(454\) 21.5631 12.4495i 1.01201 0.584284i
\(455\) 34.8678 + 5.66704i 1.63463 + 0.265675i
\(456\) −4.67423 + 10.1459i −0.218891 + 0.475125i
\(457\) 14.1363 3.78780i 0.661267 0.177186i 0.0874492 0.996169i \(-0.472128\pi\)
0.573818 + 0.818983i \(0.305462\pi\)
\(458\) 1.16781 + 1.16781i 0.0545681 + 0.0545681i
\(459\) −0.635674 2.24745i −0.0296707 0.104902i
\(460\) −0.224745 2.22474i −0.0104788 0.103729i
\(461\) 28.6237 + 16.5259i 1.33314 + 0.769689i 0.985780 0.168043i \(-0.0537448\pi\)
0.347360 + 0.937732i \(0.387078\pi\)
\(462\) −1.73910 4.71039i −0.0809102 0.219147i
\(463\) 11.8182 + 3.16668i 0.549239 + 0.147168i 0.522758 0.852481i \(-0.324903\pi\)
0.0264810 + 0.999649i \(0.491570\pi\)
\(464\) 0.158919 + 0.275255i 0.00737761 + 0.0127784i
\(465\) −1.14286 1.31319i −0.0529991 0.0608979i
\(466\) −10.2247 + 17.7098i −0.473652 + 0.820390i
\(467\) 2.82843 2.82843i 0.130884 0.130884i −0.638630 0.769514i \(-0.720499\pi\)
0.769514 + 0.638630i \(0.220499\pi\)
\(468\) 5.88196 8.56753i 0.271894 0.396034i
\(469\) 30.1464i 1.39203i
\(470\) −18.8169 + 7.13604i −0.867960 + 0.329161i
\(471\) 2.32577 + 25.2415i 0.107166 + 1.16307i
\(472\) 2.32370 8.67217i 0.106957 0.399169i
\(473\) −0.569930 + 2.12701i −0.0262054 + 0.0977999i
\(474\) 0.389270 + 4.22474i 0.0178797 + 0.194049i
\(475\) −10.2125 + 30.5876i −0.468583 + 1.40346i
\(476\) 2.04989i 0.0939565i
\(477\) 15.9966 + 1.25087i 0.732433 + 0.0572736i
\(478\) −12.0000 + 12.0000i −0.548867 + 0.548867i
\(479\) −3.53553 + 6.12372i −0.161543 + 0.279800i −0.935422 0.353533i \(-0.884980\pi\)
0.773879 + 0.633333i \(0.218314\pi\)
\(480\) −3.86370 0.267949i −0.176353 0.0122302i
\(481\) 7.34847 + 12.7279i 0.335061 + 0.580343i
\(482\) 18.3526 + 4.91756i 0.835938 + 0.223989i
\(483\) −2.73583 7.41007i −0.124485 0.337170i
\(484\) 9.17633 + 5.29796i 0.417106 + 0.240816i
\(485\) −5.97469 + 0.603566i −0.271297 + 0.0274065i
\(486\) −13.9722 + 6.91215i −0.633792 + 0.313541i
\(487\) −12.0000 12.0000i −0.543772 0.543772i 0.380861 0.924632i \(-0.375628\pi\)
−0.924632 + 0.380861i \(0.875628\pi\)
\(488\) 0.531752 0.142483i 0.0240713 0.00644988i
\(489\) 4.56048 9.89898i 0.206232 0.447647i
\(490\) −18.0340 25.0338i −0.814695 1.13091i
\(491\) −24.2474 + 13.9993i −1.09427 + 0.631778i −0.934711 0.355410i \(-0.884341\pi\)
−0.159561 + 0.987188i \(0.551008\pi\)
\(492\) −2.16416 + 12.6136i −0.0975679 + 0.568667i
\(493\) 0.0369761 + 0.137997i 0.00166532 + 0.00621505i
\(494\) −22.3417 −1.00520
\(495\) −4.26314 + 0.0965401i −0.191614 + 0.00433916i
\(496\) −0.449490 −0.0201827
\(497\) −7.42731 27.7191i −0.333161 1.24337i
\(498\) −7.25845 6.03371i −0.325259 0.270377i
\(499\) 0.778539 0.449490i 0.0348522 0.0201219i −0.482473 0.875911i \(-0.660261\pi\)
0.517325 + 0.855789i \(0.326928\pi\)
\(500\) −11.1713 + 0.449747i −0.499595 + 0.0201133i
\(501\) −15.1742 + 1.39816i −0.677935 + 0.0624652i
\(502\) 2.59405 0.695075i 0.115778 0.0310227i
\(503\) 4.02834 + 4.02834i 0.179615 + 0.179615i 0.791188 0.611573i \(-0.209463\pi\)
−0.611573 + 0.791188i \(0.709463\pi\)
\(504\) −13.4511 + 2.50000i −0.599159 + 0.111359i
\(505\) 21.7980 + 17.7980i 0.969996 + 0.791999i
\(506\) −0.550510 0.317837i −0.0244732 0.0141296i
\(507\) −1.70711 0.292893i −0.0758153 0.0130078i
\(508\) −2.56304 0.686765i −0.113717 0.0304702i
\(509\) −4.22659 7.32066i −0.187340 0.324483i 0.757022 0.653389i \(-0.226653\pi\)
−0.944363 + 0.328906i \(0.893320\pi\)
\(510\) −1.64635 0.565826i −0.0729014 0.0250552i
\(511\) 22.2474 38.5337i 0.984169 1.70463i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 29.2519 + 16.3529i 1.29150 + 0.721998i
\(514\) 18.0454i 0.795949i
\(515\) 19.8943 + 8.95403i 0.876649 + 0.394562i
\(516\) 5.44949 + 2.51059i 0.239900 + 0.110523i
\(517\) −1.48072 + 5.52613i −0.0651221 + 0.243039i
\(518\) 5.00775 18.6892i 0.220028 0.821156i
\(519\) −18.2419 + 12.8990i −0.800731 + 0.566202i
\(520\) −2.74666 7.24264i −0.120449 0.317611i
\(521\) 29.4449i 1.29000i 0.764181 + 0.645001i \(0.223143\pi\)
−0.764181 + 0.645001i \(0.776857\pi\)
\(522\) 0.860419 0.410930i 0.0376595 0.0179859i
\(523\) 4.22474 4.22474i 0.184735 0.184735i −0.608680 0.793416i \(-0.708301\pi\)
0.793416 + 0.608680i \(0.208301\pi\)
\(524\) 1.80348 3.12372i 0.0787855 0.136461i
\(525\) −37.8090 + 11.4162i −1.65012 + 0.498243i
\(526\) −8.34847 14.4600i −0.364011 0.630485i
\(527\) −0.195157 0.0522921i −0.00850116 0.00227788i
\(528\) −0.703823 + 0.846687i −0.0306300 + 0.0368473i
\(529\) 19.0526 + 11.0000i 0.828372 + 0.478261i
\(530\) 7.56388 9.26382i 0.328554 0.402395i
\(531\) −25.3939 8.97809i −1.10200 0.389616i
\(532\) 20.7980 + 20.7980i 0.901706 + 0.901706i
\(533\) −24.7238 + 6.62471i −1.07090 + 0.286948i
\(534\) 8.02458 + 11.3485i 0.347258 + 0.491096i
\(535\) 34.9209 25.1566i 1.50976 1.08761i
\(536\) −5.72474 + 3.30518i −0.247271 + 0.142762i
\(537\) 17.3501 6.40576i 0.748714 0.276429i
\(538\) 3.90704 + 14.5813i 0.168444 + 0.628643i
\(539\) −8.77101 −0.377794
\(540\) −1.70502 + 11.4932i −0.0733726 + 0.494587i
\(541\) 27.9444 1.20142 0.600712 0.799466i \(-0.294884\pi\)
0.600712 + 0.799466i \(0.294884\pi\)
\(542\) −7.25869 27.0898i −0.311787 1.16361i
\(543\) −25.1030 + 9.26816i −1.07727 + 0.397735i
\(544\) −0.389270 + 0.224745i −0.0166898 + 0.00963586i
\(545\) 2.02731 12.4735i 0.0868406 0.534307i
\(546\) −15.7980 22.3417i −0.676090 0.956136i
\(547\) 3.92907 1.05279i 0.167995 0.0450140i −0.173841 0.984774i \(-0.555618\pi\)
0.341836 + 0.939760i \(0.388951\pi\)
\(548\) −15.4135 15.4135i −0.658431 0.658431i
\(549\) −0.301783 1.62372i −0.0128798 0.0692989i
\(550\) −1.75255 + 2.65153i −0.0747290 + 0.113062i
\(551\) −1.77526 1.02494i −0.0756284 0.0436641i
\(552\) −1.10721 + 1.33195i −0.0471258 + 0.0566916i
\(553\) 10.7902 + 2.89123i 0.458846 + 0.122947i
\(554\) −14.0707 24.3712i −0.597807 1.03543i
\(555\) −13.6277 9.18066i −0.578466 0.389697i
\(556\) −1.55051 + 2.68556i −0.0657563 + 0.113893i
\(557\) −7.88171 + 7.88171i −0.333959 + 0.333959i −0.854088 0.520129i \(-0.825884\pi\)
0.520129 + 0.854088i \(0.325884\pi\)
\(558\) −0.105124 + 1.34437i −0.00445027 + 0.0569115i
\(559\) 12.0000i 0.507546i
\(560\) −4.18532 + 9.29908i −0.176862 + 0.392958i
\(561\) −0.404082 + 0.285729i −0.0170604 + 0.0120635i
\(562\) −4.43759 + 16.5613i −0.187188 + 0.698597i
\(563\) 5.08619 18.9819i 0.214357 0.799993i −0.772034 0.635581i \(-0.780761\pi\)
0.986392 0.164412i \(-0.0525726\pi\)
\(564\) 14.1582 + 6.52270i 0.596167 + 0.274655i
\(565\) −5.32101 + 11.8224i −0.223856 + 0.497371i
\(566\) 24.2166i 1.01790i
\(567\) 4.33130 + 40.8151i 0.181898 + 1.71407i
\(568\) −4.44949 + 4.44949i −0.186696 + 0.186696i
\(569\) −9.58166 + 16.5959i −0.401684 + 0.695737i −0.993929 0.110021i \(-0.964908\pi\)
0.592245 + 0.805758i \(0.298242\pi\)
\(570\) 22.4445 10.9628i 0.940096 0.459183i
\(571\) −18.4495 31.9555i −0.772087 1.33729i −0.936417 0.350889i \(-0.885880\pi\)
0.164330 0.986405i \(-0.447454\pi\)
\(572\) −2.12701 0.569930i −0.0889347 0.0238300i
\(573\) −29.8118 5.11490i −1.24541 0.213678i
\(574\) 29.1824 + 16.8485i 1.21805 + 0.703242i
\(575\) −2.75699 + 4.17121i −0.114975 + 0.173951i
\(576\) 1.94949 + 2.28024i 0.0812287 + 0.0950100i
\(577\) −17.0000 17.0000i −0.707719 0.707719i 0.258336 0.966055i \(-0.416826\pi\)
−0.966055 + 0.258336i \(0.916826\pi\)
\(578\) 16.2256 4.34763i 0.674895 0.180838i
\(579\) 29.8735 2.75255i 1.24150 0.114392i
\(580\) 0.114014 0.701501i 0.00473419 0.0291282i
\(581\) −21.5227 + 12.4261i −0.892912 + 0.515523i
\(582\) 3.57704 + 2.97347i 0.148273 + 0.123254i
\(583\) −0.879955 3.28404i −0.0364440 0.136011i
\(584\) −9.75663 −0.403732
\(585\) −22.3042 + 6.52104i −0.922164 + 0.269612i
\(586\) −22.0454 −0.910687
\(587\) 3.37640 + 12.6009i 0.139359 + 0.520095i 0.999942 + 0.0107843i \(0.00343281\pi\)
−0.860583 + 0.509310i \(0.829901\pi\)
\(588\) −4.04133 + 23.5546i −0.166662 + 0.971375i
\(589\) 2.51059 1.44949i 0.103447 0.0597252i
\(590\) −16.2891 + 11.7344i −0.670610 + 0.483099i
\(591\) 7.10102 15.4135i 0.292097 0.634026i
\(592\) −4.09808 + 1.09808i −0.168430 + 0.0451307i
\(593\) −7.24604 7.24604i −0.297559 0.297559i 0.542498 0.840057i \(-0.317479\pi\)
−0.840057 + 0.542498i \(0.817479\pi\)
\(594\) 2.36773 + 2.30306i 0.0971489 + 0.0944958i
\(595\) −2.89898 + 3.55051i −0.118847 + 0.145557i
\(596\) −3.82577 2.20881i −0.156709 0.0904762i
\(597\) 5.06885 + 13.7291i 0.207454 + 0.561895i
\(598\) −3.34607 0.896575i −0.136831 0.0366637i
\(599\) 9.97093 + 17.2702i 0.407401 + 0.705639i 0.994598 0.103805i \(-0.0331018\pi\)
−0.587197 + 0.809444i \(0.699768\pi\)
\(600\) 6.31319 + 5.92820i 0.257735 + 0.242018i
\(601\) −2.65153 + 4.59259i −0.108158 + 0.187335i −0.915024 0.403399i \(-0.867829\pi\)
0.806866 + 0.590735i \(0.201162\pi\)
\(602\) 11.1708 11.1708i 0.455290 0.455290i
\(603\) 8.54650 + 17.8950i 0.348040 + 0.728739i
\(604\) 17.5959i 0.715968i
\(605\) −8.40143 22.1536i −0.341567 0.900673i
\(606\) −2.00000 21.7060i −0.0812444 0.881747i
\(607\) 3.04744 11.3732i 0.123692 0.461624i −0.876098 0.482133i \(-0.839862\pi\)
0.999790 + 0.0205092i \(0.00652872\pi\)
\(608\) 1.66925 6.22973i 0.0676971 0.252649i
\(609\) −0.230351 2.50000i −0.00933429 0.101305i
\(610\) −1.12252 0.505224i −0.0454496 0.0204559i
\(611\) 31.1769i 1.26128i
\(612\) 0.581142 + 1.21682i 0.0234913 + 0.0491869i
\(613\) 6.79796 6.79796i 0.274567 0.274567i −0.556369 0.830936i \(-0.687806\pi\)
0.830936 + 0.556369i \(0.187806\pi\)
\(614\) −4.71940 + 8.17423i −0.190459 + 0.329885i
\(615\) 21.5868 18.7869i 0.870465 0.757561i
\(616\) 1.44949 + 2.51059i 0.0584016 + 0.101155i
\(617\) −16.3232 4.37378i −0.657146 0.176082i −0.0851882 0.996365i \(-0.527149\pi\)
−0.571958 + 0.820283i \(0.693816\pi\)
\(618\) −5.85301 15.8530i −0.235442 0.637701i
\(619\) 42.2121 + 24.3712i 1.69665 + 0.979560i 0.948900 + 0.315578i \(0.102198\pi\)
0.747748 + 0.663982i \(0.231135\pi\)
\(620\) 0.778539 + 0.635674i 0.0312669 + 0.0255293i
\(621\) 3.72474 + 3.62302i 0.149469 + 0.145387i
\(622\) −19.4495 19.4495i −0.779853 0.779853i
\(623\) 35.3489 9.47172i 1.41623 0.379476i
\(624\) −2.51059 + 5.44949i −0.100504 + 0.218154i
\(625\) 19.9853 + 15.0196i 0.799411 + 0.600784i
\(626\) 10.3485 5.97469i 0.413608 0.238797i
\(627\) 1.20080 6.99876i 0.0479552 0.279503i
\(628\) −3.78780 14.1363i −0.151150 0.564099i
\(629\) −1.90702 −0.0760380
\(630\) 26.8335 + 14.6926i 1.06907 + 0.585366i
\(631\) −3.10102 −0.123450 −0.0617248 0.998093i \(-0.519660\pi\)
−0.0617248 + 0.998093i \(0.519660\pi\)
\(632\) −0.633975 2.36603i −0.0252182 0.0941154i
\(633\) −12.1221 10.0767i −0.481811 0.400513i
\(634\) −9.43879 + 5.44949i −0.374862 + 0.216427i
\(635\) 3.46808 + 4.81420i 0.137627 + 0.191046i
\(636\) −9.22474 + 0.849971i −0.365785 + 0.0337036i
\(637\) −46.1689 + 12.3709i −1.82928 + 0.490153i
\(638\) −0.142865 0.142865i −0.00565606 0.00565606i
\(639\) 12.2672 + 14.3485i 0.485284 + 0.567617i
\(640\) 2.22474 0.224745i 0.0879408 0.00888382i
\(641\) 16.7474 + 9.66914i 0.661484 + 0.381908i 0.792842 0.609427i \(-0.208600\pi\)
−0.131358 + 0.991335i \(0.541934\pi\)
\(642\) −32.8575 5.63745i −1.29678 0.222492i
\(643\) −6.10913 1.63694i −0.240921 0.0645545i 0.136338 0.990662i \(-0.456467\pi\)
−0.377259 + 0.926108i \(0.623133\pi\)
\(644\) 2.28024 + 3.94949i 0.0898540 + 0.155632i
\(645\) −5.88828 12.0552i −0.231851 0.474673i
\(646\) 1.44949 2.51059i 0.0570294 0.0987778i
\(647\) 23.5416 23.5416i 0.925516 0.925516i −0.0718961 0.997412i \(-0.522905\pi\)
0.997412 + 0.0718961i \(0.0229050\pi\)
\(648\) 7.27583 5.29738i 0.285822 0.208101i
\(649\) 5.70714i 0.224025i
\(650\) −5.48528 + 16.4290i −0.215150 + 0.644398i
\(651\) 3.22474 + 1.48565i 0.126388 + 0.0582271i
\(652\) −1.62863 + 6.07812i −0.0637819 + 0.238037i
\(653\) 6.84563 25.5482i 0.267890 0.999780i −0.692567 0.721353i \(-0.743520\pi\)
0.960457 0.278427i \(-0.0898129\pi\)
\(654\) −7.99247 + 5.65153i −0.312530 + 0.220992i
\(655\) −7.54134 + 2.85994i −0.294664 + 0.111747i
\(656\) 7.38891i 0.288488i
\(657\) −2.28183 + 29.1808i −0.0890227 + 1.13845i
\(658\) 29.0227 29.0227i 1.13142 1.13142i
\(659\) 5.65685 9.79796i 0.220360 0.381674i −0.734557 0.678546i \(-0.762610\pi\)
0.954917 + 0.296872i \(0.0959435\pi\)
\(660\) 2.41645 0.471150i 0.0940603 0.0183395i
\(661\) 0.651531 + 1.12848i 0.0253416 + 0.0438930i 0.878418 0.477893i \(-0.158599\pi\)
−0.853076 + 0.521786i \(0.825266\pi\)
\(662\) 0.434174 + 0.116337i 0.0168746 + 0.00452155i
\(663\) −1.72401 + 2.07395i −0.0669549 + 0.0805456i
\(664\) 4.71940 + 2.72474i 0.183148 + 0.105741i
\(665\) −6.61037 65.4359i −0.256339 2.53749i
\(666\) 2.32577 + 12.5136i 0.0901216 + 0.484893i
\(667\) −0.224745 0.224745i −0.00870216 0.00870216i
\(668\) 8.49818 2.27708i 0.328804 0.0881028i
\(669\) 25.6308 + 36.2474i 0.990945 + 1.40141i
\(670\) 14.5898 + 2.37127i 0.563653 + 0.0916100i
\(671\) −0.303062 + 0.174973i −0.0116996 + 0.00675474i
\(672\) 7.41007 2.73583i 0.285850 0.105537i
\(673\) −6.02093 22.4704i −0.232090 0.866171i −0.979439 0.201740i \(-0.935340\pi\)
0.747349 0.664431i \(-0.231326\pi\)
\(674\) 3.11416 0.119953
\(675\) 19.2070 17.4955i 0.739277 0.673401i
\(676\) 1.00000 0.0384615
\(677\) −11.8011 44.0423i −0.453553 1.69268i −0.692308 0.721602i \(-0.743406\pi\)
0.238755 0.971080i \(-0.423261\pi\)
\(678\) 9.42078 3.47820i 0.361803 0.133579i
\(679\) 10.6066 6.12372i 0.407044 0.235007i
\(680\) 0.992072 + 0.161241i 0.0380442 + 0.00618330i
\(681\) 24.8990 + 35.2125i 0.954131 + 1.34934i
\(682\) 0.275993 0.0739521i 0.0105683 0.00283177i
\(683\) −13.8564 13.8564i −0.530201 0.530201i 0.390431 0.920632i \(-0.372326\pi\)
−0.920632 + 0.390431i \(0.872326\pi\)
\(684\) −18.2419 6.44949i −0.697497 0.246602i
\(685\) 4.89898 + 48.4949i 0.187180 + 1.85289i
\(686\) 26.8485 + 15.5010i 1.02508 + 0.591830i
\(687\) −1.82859 + 2.19976i −0.0697649 + 0.0839260i
\(688\) −3.34607 0.896575i −0.127568 0.0341816i
\(689\) −9.26382 16.0454i −0.352923 0.611281i
\(690\) 3.80140 0.741181i 0.144717 0.0282163i
\(691\) 10.4722 18.1384i 0.398381 0.690016i −0.595145 0.803618i \(-0.702906\pi\)
0.993526 + 0.113602i \(0.0362388\pi\)
\(692\) 9.12096 9.12096i 0.346727 0.346727i
\(693\) 7.84785 3.74807i 0.298115 0.142377i
\(694\) 23.7980i 0.903358i
\(695\) 6.48352 2.45878i 0.245934 0.0932668i
\(696\) −0.449490 + 0.317837i −0.0170379 + 0.0120476i
\(697\) 0.859599 3.20807i 0.0325596 0.121514i
\(698\) −7.51750 + 28.0557i −0.284542 + 1.06192i
\(699\) −32.1698 14.8207i −1.21677 0.560569i
\(700\) 20.4001 10.1875i 0.771050 0.385053i
\(701\) 21.1024i 0.797028i −0.917162 0.398514i \(-0.869526\pi\)
0.917162 0.398514i \(-0.130474\pi\)
\(702\) 15.7116 + 8.78335i 0.592994 + 0.331506i
\(703\) 19.3485 19.3485i 0.729741 0.729741i
\(704\) 0.317837 0.550510i 0.0119789 0.0207481i
\(705\) −15.2982 31.3204i −0.576164 1.17959i
\(706\) 17.1464 + 29.6985i 0.645314 + 1.11772i
\(707\) −55.4382 14.8546i −2.08497 0.558666i
\(708\) 15.3266 + 2.62962i 0.576007 + 0.0988272i
\(709\) −25.6790 14.8258i −0.964394 0.556793i −0.0668716 0.997762i \(-0.521302\pi\)
−0.897523 + 0.440968i \(0.854635\pi\)
\(710\) 13.9993 1.41421i 0.525383 0.0530745i
\(711\) −7.22474 + 1.34278i −0.270949 + 0.0503582i
\(712\) −5.67423 5.67423i −0.212651 0.212651i
\(713\) 0.434174 0.116337i 0.0162599 0.00435684i
\(714\) 3.53553 0.325765i 0.132314 0.0121915i
\(715\) 2.87808 + 3.99519i 0.107634 + 0.149412i
\(716\) −9.24745 + 5.33902i −0.345593 + 0.199528i
\(717\) −22.6040 18.7899i −0.844160 0.701722i
\(718\) −0.859599 3.20807i −0.0320800 0.119724i
\(719\) 32.5269 1.21305 0.606525 0.795065i \(-0.292563\pi\)
0.606525 + 0.795065i \(0.292563\pi\)
\(720\) −0.151870 6.70648i −0.00565988 0.249936i
\(721\) −44.4949 −1.65708
\(722\) 5.84825 + 21.8260i 0.217649 + 0.812279i
\(723\) −5.56497 + 32.4350i −0.206964 + 1.20627i
\(724\) 13.3797 7.72474i 0.497251 0.287088i
\(725\) −1.18955 + 1.05379i −0.0441788 + 0.0391369i
\(726\) −7.67934 + 16.6688i −0.285007 + 0.618636i
\(727\) −46.6759 + 12.5068i −1.73111 + 0.463850i −0.980439 0.196822i \(-0.936938\pi\)
−0.750674 + 0.660673i \(0.770271\pi\)
\(728\) 11.1708 + 11.1708i 0.414019 + 0.414019i
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) 16.8990 + 13.7980i 0.625459 + 0.510685i
\(731\) −1.34847 0.778539i −0.0498749 0.0287953i
\(732\) 0.330251 + 0.894494i 0.0122064 + 0.0330614i
\(733\) −32.9846 8.83821i −1.21832 0.326447i −0.408296 0.912850i \(-0.633877\pi\)
−0.810019 + 0.586403i \(0.800543\pi\)
\(734\) −2.04989 3.55051i −0.0756627 0.131052i
\(735\) 40.3110 35.0824i 1.48689 1.29404i
\(736\) 0.500000 0.866025i 0.0184302 0.0319221i
\(737\) 2.97129 2.97129i 0.109449 0.109449i
\(738\) −22.0993 1.72808i −0.813485 0.0636115i
\(739\) 28.9444i 1.06474i 0.846513 + 0.532368i \(0.178698\pi\)
−0.846513 + 0.532368i \(0.821302\pi\)
\(740\) 8.65099 + 3.89363i 0.318017 + 0.143133i
\(741\) −3.55051 38.5337i −0.130431 1.41557i
\(742\) −6.31300 + 23.5605i −0.231758 + 0.864931i
\(743\) −2.56204 + 9.56168i −0.0939923 + 0.350784i −0.996865 0.0791245i \(-0.974788\pi\)
0.902872 + 0.429909i \(0.141454\pi\)
\(744\) −0.0714323 0.775255i −0.00261883 0.0284222i
\(745\) 3.50270 + 9.23621i 0.128329 + 0.338389i
\(746\) 0.492810i 0.0180431i
\(747\) 9.25311 13.4779i 0.338553 0.493129i
\(748\) 0.202041 0.202041i 0.00738735 0.00738735i
\(749\) −43.8888 + 76.0176i −1.60366 + 2.77762i
\(750\) −2.55103 19.1962i −0.0931503 0.700944i
\(751\) −10.3485 17.9241i −0.377621 0.654059i 0.613095 0.790010i \(-0.289924\pi\)
−0.990716 + 0.135951i \(0.956591\pi\)
\(752\) −8.69333 2.32937i −0.317013 0.0849434i
\(753\) 1.61107 + 4.36362i 0.0587107 + 0.159019i
\(754\) −0.953512 0.550510i −0.0347248 0.0200484i
\(755\) −24.8844 + 30.4770i −0.905636 + 1.10917i
\(756\) −6.44949 22.8024i −0.234566 0.829315i
\(757\) 22.0454 + 22.0454i 0.801254 + 0.801254i 0.983292 0.182038i \(-0.0582693\pi\)
−0.182038 + 0.983292i \(0.558269\pi\)
\(758\) −20.6210 + 5.52539i −0.748990 + 0.200691i
\(759\) 0.460702 1.00000i 0.0167224 0.0362977i
\(760\) −11.7014 + 8.42953i −0.424454 + 0.305771i
\(761\) −5.60102 + 3.23375i −0.203037 + 0.117223i −0.598071 0.801443i \(-0.704066\pi\)
0.395034 + 0.918666i \(0.370733\pi\)
\(762\) 0.777179 4.52973i 0.0281542 0.164095i
\(763\) 6.67072 + 24.8955i 0.241496 + 0.901276i
\(764\) 17.4634 0.631803
\(765\) 0.714271 2.92945i 0.0258245 0.105914i
\(766\) 8.20204 0.296352
\(767\) 8.04954 + 30.0413i 0.290652 + 1.08473i
\(768\) −1.33195 1.10721i −0.0480627 0.0399529i
\(769\) −8.39780 + 4.84847i −0.302832 + 0.174840i −0.643715 0.765266i \(-0.722608\pi\)
0.340882 + 0.940106i \(0.389274\pi\)
\(770\) 1.03992 6.39836i 0.0374761 0.230581i
\(771\) −31.1237 + 2.86775i −1.12089 + 0.103280i
\(772\) −16.7303 + 4.48288i −0.602138 + 0.161342i
\(773\) 30.8270 + 30.8270i 1.10877 + 1.10877i 0.993313 + 0.115456i \(0.0368331\pi\)
0.115456 + 0.993313i \(0.463167\pi\)
\(774\) −3.46410 + 9.79796i −0.124515 + 0.352180i
\(775\) −0.449490 2.20204i −0.0161461 0.0790996i
\(776\) −2.32577 1.34278i −0.0834901 0.0482030i
\(777\) 33.0299 + 5.66704i 1.18494 + 0.203304i
\(778\) −35.5477 9.52497i −1.27445 0.341487i
\(779\) 23.8273 + 41.2702i 0.853703 + 1.47866i
\(780\) 12.0552 5.88828i 0.431646 0.210834i
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 0.317837 0.317837i 0.0113658 0.0113658i
\(783\) 0.845485 + 1.41870i 0.0302152 + 0.0507002i
\(784\) 13.7980i 0.492784i
\(785\) −13.4310 + 29.8415i −0.479374 + 1.06509i
\(786\) 5.67423 + 2.61413i 0.202393 + 0.0932429i
\(787\) −2.52520 + 9.42418i −0.0900137 + 0.335936i −0.996216 0.0869079i \(-0.972301\pi\)
0.906203 + 0.422844i \(0.138968\pi\)
\(788\) −2.53590 + 9.46410i −0.0903376 + 0.337145i
\(789\) 23.6130 16.6969i 0.840646 0.594427i
\(790\) −2.24799 + 4.99465i −0.0799799 + 0.177702i
\(791\) 26.4415i 0.940150i
\(792\) −1.57217 1.07936i −0.0558646 0.0383534i
\(793\) −1.34847 + 1.34847i −0.0478855 + 0.0478855i
\(794\) 7.46034 12.9217i 0.264757 0.458573i
\(795\) 17.1798 + 11.5736i 0.609304 + 0.410472i
\(796\) −4.22474 7.31747i −0.149742 0.259361i
\(797\) 38.4419 + 10.3005i 1.36168 + 0.364861i 0.864433 0.502747i \(-0.167677\pi\)
0.497248 + 0.867609i \(0.334344\pi\)
\(798\) −32.5660 + 39.1764i −1.15282 + 1.38683i
\(799\) −3.50343 2.02270i −0.123942 0.0715581i
\(800\) −4.17121 2.75699i −0.147474 0.0974745i
\(801\) −18.2980 + 15.6438i −0.646527 + 0.552748i
\(802\) −6.24745 6.24745i −0.220605 0.220605i
\(803\) 5.99071 1.60521i 0.211408 0.0566465i
\(804\) −6.61037 9.34847i −0.233130 0.329695i
\(805\) 1.63593 10.0655i 0.0576590 0.354761i
\(806\) 1.34847 0.778539i 0.0474978 0.0274229i
\(807\) −24.5281 + 9.05589i −0.863429 + 0.318782i
\(808\) 3.25725 + 12.1562i 0.114590 + 0.427655i
\(809\) −19.4490 −0.683792 −0.341896 0.939738i \(-0.611069\pi\)
−0.341896 + 0.939738i \(0.611069\pi\)
\(810\) −20.0937 1.11425i −0.706022 0.0391509i
\(811\) −39.6413 −1.39200 −0.695998 0.718044i \(-0.745038\pi\)
−0.695998 + 0.718044i \(0.745038\pi\)
\(812\) 0.375156 + 1.40010i 0.0131654 + 0.0491339i
\(813\) 45.5694 16.8245i 1.59819 0.590059i
\(814\) 2.33562 1.34847i 0.0818633 0.0472638i
\(815\) 11.4166 8.22438i 0.399907 0.288087i
\(816\) −0.449490 0.635674i −0.0157353 0.0222531i
\(817\) 21.5804 5.78245i 0.755003 0.202302i
\(818\) 20.4347 + 20.4347i 0.714481 + 0.714481i
\(819\) 36.0231 30.7980i 1.25875 1.07617i
\(820\) −10.4495 + 12.7980i −0.364912 + 0.446924i
\(821\) 19.3207 + 11.1548i 0.674296 + 0.389305i 0.797702 0.603051i \(-0.206049\pi\)
−0.123407 + 0.992356i \(0.539382\pi\)
\(822\) 24.1348 29.0338i 0.841799 1.01267i
\(823\) −3.23908 0.867910i −0.112907 0.0302534i 0.201923 0.979401i \(-0.435281\pi\)
−0.314830 + 0.949148i \(0.601948\pi\)
\(824\) 4.87832 + 8.44949i 0.169944 + 0.294352i
\(825\) −4.85173 2.60133i −0.168915 0.0905666i
\(826\) 20.4722 35.4589i 0.712319 1.23377i
\(827\) 31.5662 31.5662i 1.09766 1.09766i 0.102980 0.994683i \(-0.467162\pi\)
0.994683 0.102980i \(-0.0328379\pi\)
\(828\) −2.47323 1.69798i −0.0859507 0.0590088i
\(829\) 10.5505i 0.366434i −0.983072 0.183217i \(-0.941349\pi\)
0.983072 0.183217i \(-0.0586512\pi\)
\(830\) −4.32086 11.3936i −0.149979 0.395479i
\(831\) 39.7980 28.1414i 1.38058 0.976215i
\(832\) 0.896575 3.34607i 0.0310832 0.116004i
\(833\) 1.60521 5.99071i 0.0556171 0.207566i
\(834\) −4.87832 2.24745i −0.168922 0.0778228i
\(835\) −17.9395 8.07422i −0.620824 0.279420i
\(836\) 4.09978i 0.141794i
\(837\) −2.33539 + 0.0323319i −0.0807230 + 0.00111755i
\(838\) 3.55051 3.55051i 0.122650 0.122650i
\(839\) 0.246405 0.426786i 0.00850684 0.0147343i −0.861741 0.507349i \(-0.830625\pi\)
0.870247 + 0.492615i \(0.163959\pi\)
\(840\) −16.7037 5.74082i −0.576331 0.198077i
\(841\) 14.4495 + 25.0273i 0.498258 + 0.863009i
\(842\) −4.92721 1.32024i −0.169803 0.0454985i
\(843\) −29.2693 5.02181i −1.00809 0.172960i
\(844\) 7.88171 + 4.55051i 0.271300 + 0.156635i
\(845\) −1.73205 1.41421i −0.0595844 0.0486504i
\(846\) −9.00000 + 25.4558i −0.309426 + 0.875190i
\(847\) 34.1691 + 34.1691i 1.17407 + 1.17407i
\(848\) 5.16622 1.38429i 0.177409 0.0475366i
\(849\) −41.7675 + 3.84847i −1.43346 + 0.132079i
\(850\) −1.49029 1.68228i −0.0511165 0.0577017i
\(851\) 3.67423 2.12132i 0.125951 0.0727179i
\(852\) −8.38134 6.96713i −0.287140 0.238690i
\(853\) −0.641478 2.39403i −0.0219638 0.0819700i 0.954074 0.299571i \(-0.0968435\pi\)
−0.976038 + 0.217601i \(0.930177\pi\)
\(854\) 2.51059 0.0859106
\(855\) 22.4750 + 36.9688i 0.768627 + 1.26431i
\(856\) 19.2474 0.657864
\(857\) 4.08881 + 15.2597i 0.139671 + 0.521260i 0.999935 + 0.0114106i \(0.00363219\pi\)
−0.860264 + 0.509849i \(0.829701\pi\)
\(858\) 0.644963 3.75912i 0.0220187 0.128334i
\(859\) −40.2658 + 23.2474i −1.37385 + 0.793193i −0.991410 0.130788i \(-0.958249\pi\)
−0.382440 + 0.923980i \(0.624916\pi\)
\(860\) 4.52761 + 6.28497i 0.154390 + 0.214316i
\(861\) −24.4217 + 53.0097i −0.832289 + 1.80657i
\(862\) −15.0263 + 4.02628i −0.511797 + 0.137136i
\(863\) −20.7132 20.7132i −0.705085 0.705085i 0.260413 0.965497i \(-0.416141\pi\)
−0.965497 + 0.260413i \(0.916141\pi\)
\(864\) −3.62302 + 3.72474i −0.123258 + 0.126718i
\(865\) −28.6969 + 2.89898i −0.975725 + 0.0985683i
\(866\) −16.4722 9.51023i −0.559748 0.323171i
\(867\) 10.0771 + 27.2941i 0.342236 + 0.926955i
\(868\) −1.98004 0.530550i −0.0672069 0.0180080i
\(869\) 0.778539 + 1.34847i 0.0264101 + 0.0457437i
\(870\) 1.22803 + 0.0851642i 0.0416341 + 0.00288734i
\(871\) 11.4495 19.8311i 0.387951 0.671951i
\(872\) 3.99624 3.99624i 0.135330 0.135330i
\(873\) −4.56002 + 6.64202i −0.154333 + 0.224798i
\(874\) 6.44949i 0.218157i
\(875\) −49.7413 11.2047i −1.68156 0.378789i
\(876\) −1.55051 16.8277i −0.0523869 0.568555i
\(877\) 11.0713 41.3188i 0.373852 1.39524i −0.481162 0.876632i \(-0.659785\pi\)
0.855014 0.518604i \(-0.173548\pi\)
\(878\) −7.71228 + 28.7826i −0.260277 + 0.971366i
\(879\) −3.50343 38.0227i −0.118168 1.28247i
\(880\) −1.32905 + 0.504022i −0.0448022 + 0.0169906i
\(881\) 54.8365i 1.84749i 0.383010 + 0.923744i \(0.374887\pi\)
−0.383010 + 0.923744i \(0.625113\pi\)
\(882\) −41.2679 3.22700i −1.38956 0.108659i
\(883\) 6.27015 6.27015i 0.211007 0.211007i −0.593688 0.804695i \(-0.702329\pi\)
0.804695 + 0.593688i \(0.202329\pi\)
\(884\) 0.778539 1.34847i 0.0261851 0.0453539i
\(885\) −22.8275 26.2297i −0.767339 0.881701i
\(886\) 2.72474 + 4.71940i 0.0915396 + 0.158551i
\(887\) −7.92256 2.12284i −0.266014 0.0712781i 0.123347 0.992364i \(-0.460637\pi\)
−0.389360 + 0.921085i \(0.627304\pi\)
\(888\) −2.54516 6.89363i −0.0854100 0.231335i
\(889\) −10.4798 6.05051i −0.351481 0.202928i
\(890\) 1.80348 + 17.8526i 0.0604529 + 0.598422i
\(891\) −3.59592 + 4.44972i −0.120468 + 0.149071i
\(892\) −18.1237 18.1237i −0.606827 0.606827i
\(893\) 56.0676 15.0233i 1.87623 0.502734i
\(894\) 3.20164 6.94949i 0.107079 0.232426i
\(895\) 23.5676 + 3.83042i 0.787777 + 0.128037i
\(896\) −3.94949 + 2.28024i −0.131943 + 0.0761774i
\(897\) 1.01461 5.91359i 0.0338769 0.197449i
\(898\) −0.238477 0.890008i −0.00795807 0.0296999i
\(899\) 0.142865 0.00476480
\(900\) −9.22135 + 11.8307i −0.307378 + 0.394358i
\(901\) 2.40408 0.0800916
\(902\) 1.21566 + 4.53689i 0.0404770 + 0.151062i
\(903\) 21.0421 + 17.4916i 0.700238 + 0.582084i
\(904\) −5.02118 + 2.89898i −0.167002 + 0.0964186i
\(905\) −34.0987 5.54203i −1.13348 0.184223i
\(906\) 30.3485 2.79632i 1.00826 0.0929015i
\(907\) 3.65307 0.978838i 0.121298 0.0325018i −0.197659 0.980271i \(-0.563334\pi\)
0.318957 + 0.947769i \(0.396667\pi\)
\(908\) −17.6062 17.6062i −0.584284 0.584284i
\(909\) 37.1195 6.89898i 1.23118 0.228825i
\(910\) −3.55051 35.1464i −0.117698 1.16509i
\(911\) −6.12372 3.53553i −0.202888 0.117137i 0.395114 0.918632i \(-0.370705\pi\)
−0.598002 + 0.801495i \(0.704038\pi\)
\(912\) 11.0100 + 1.88901i 0.364576 + 0.0625514i
\(913\) −3.34607 0.896575i −0.110739 0.0296723i
\(914\) −7.31747 12.6742i −0.242040 0.419226i
\(915\) 0.692993 2.01635i 0.0229096 0.0666586i
\(916\) 0.825765 1.43027i 0.0272841 0.0472574i
\(917\) 11.6315 11.6315i 0.384107 0.384107i
\(918\) −2.00634 + 1.19570i −0.0662192 + 0.0394639i
\(919\) 12.6515i 0.417335i 0.977987 + 0.208668i \(0.0669127\pi\)
−0.977987 + 0.208668i \(0.933087\pi\)
\(920\) −2.09077 + 0.792893i −0.0689307 + 0.0261409i
\(921\) −14.8485 6.84072i −0.489274 0.225409i
\(922\) 8.55444 31.9256i 0.281726 1.05141i
\(923\) 5.64173 21.0552i 0.185700 0.693041i
\(924\) −4.09978 + 2.89898i −0.134873 + 0.0953694i
\(925\) −9.47753 18.9783i −0.311619 0.624003i
\(926\) 12.2351i 0.402071i
\(927\) 26.4122 12.6143i 0.867492 0.414307i
\(928\) 0.224745 0.224745i 0.00737761 0.00737761i
\(929\) 21.1024 36.5505i 0.692349 1.19918i −0.278717 0.960373i \(-0.589909\pi\)
0.971066 0.238810i \(-0.0767574\pi\)
\(930\) −0.972652 + 1.44380i −0.0318945 + 0.0473441i
\(931\) 44.4949 + 77.0674i 1.45826 + 2.52578i
\(932\) 19.7527 + 5.29272i 0.647021 + 0.173369i
\(933\) 30.4545 36.6363i 0.997036 1.19942i
\(934\) −3.46410 2.00000i −0.113349 0.0654420i
\(935\) −0.635674 + 0.0642162i −0.0207888 + 0.00210009i
\(936\) −9.79796 3.46410i −0.320256 0.113228i
\(937\) −3.10102 3.10102i −0.101306 0.101306i 0.654637 0.755943i \(-0.272821\pi\)
−0.755943 + 0.654637i \(0.772821\pi\)
\(938\) −29.1192 + 7.80247i −0.950776 + 0.254760i
\(939\) 11.9494 + 16.8990i 0.389953 + 0.551477i
\(940\) 11.7631 + 16.3288i 0.383669 + 0.532587i
\(941\) 27.5227 15.8902i 0.897215 0.518007i 0.0209191 0.999781i \(-0.493341\pi\)
0.876295 + 0.481774i \(0.160007\pi\)
\(942\) 23.7795 8.77951i 0.774778 0.286052i
\(943\) 1.91239 + 7.13713i 0.0622760 + 0.232417i
\(944\) −8.97809 −0.292212
\(945\) −21.0766 + 48.6159i −0.685622 + 1.58147i
\(946\) 2.20204 0.0715945
\(947\) 0.788210 + 2.94164i 0.0256134 + 0.0955904i 0.977549 0.210707i \(-0.0675765\pi\)
−0.951936 + 0.306297i \(0.900910\pi\)
\(948\) 3.98004 1.46945i 0.129266 0.0477255i
\(949\) 29.2699 16.8990i 0.950141 0.548564i
\(950\) 32.1886 + 1.94790i 1.04433 + 0.0631981i
\(951\) −10.8990 15.4135i −0.353424 0.499816i
\(952\) −1.98004 + 0.530550i −0.0641735 + 0.0171952i
\(953\) −5.79972 5.79972i −0.187871 0.187871i 0.606904 0.794775i \(-0.292411\pi\)
−0.794775 + 0.606904i \(0.792411\pi\)
\(954\) −2.93197 15.7753i −0.0949260 0.510743i
\(955\) −30.2474 24.6969i −0.978784 0.799174i
\(956\) 14.6969 + 8.48528i 0.475333 + 0.274434i
\(957\) 0.223701 0.269109i 0.00723123 0.00869905i
\(958\) 6.83013 + 1.83013i 0.220671 + 0.0591287i
\(959\) −49.7046 86.0908i −1.60504 2.78002i
\(960\) 0.741181 + 3.80140i 0.0239215 + 0.122690i
\(961\) 15.3990 26.6718i 0.496741 0.860381i
\(962\) 10.3923 10.3923i 0.335061 0.335061i
\(963\) 4.50150 57.5666i 0.145059 1.85506i
\(964\) 19.0000i 0.611949i
\(965\) 35.3175 + 15.8957i 1.13691 + 0.511700i
\(966\) −6.44949 + 4.56048i −0.207509 + 0.146731i
\(967\) −10.3679 + 38.6937i −0.333411 + 1.24431i 0.572171 + 0.820134i \(0.306101\pi\)
−0.905582 + 0.424172i \(0.860565\pi\)
\(968\) 2.74243 10.2349i 0.0881449 0.328961i
\(969\) 4.56048 + 2.10102i 0.146504 + 0.0674945i
\(970\) 2.12936 + 5.61489i 0.0683698 + 0.180283i
\(971\) 21.4989i 0.689934i −0.938615 0.344967i \(-0.887890\pi\)
0.938615 0.344967i \(-0.112110\pi\)
\(972\) 10.2929 + 11.7071i 0.330145 + 0.375506i
\(973\) −10.0000 + 10.0000i −0.320585 + 0.320585i
\(974\) −8.48528 + 14.6969i −0.271886 + 0.470920i
\(975\) −29.2075 6.84984i −0.935390 0.219370i
\(976\) −0.275255 0.476756i −0.00881070 0.0152606i
\(977\) 6.27359 + 1.68100i 0.200710 + 0.0537801i 0.357773 0.933808i \(-0.383536\pi\)
−0.157063 + 0.987589i \(0.550203\pi\)
\(978\) −10.7420 1.84304i −0.343492 0.0589339i
\(979\) 4.41761 + 2.55051i 0.141188 + 0.0815147i
\(980\) −19.5133 + 23.8988i −0.623328 + 0.763418i
\(981\) −11.0176 12.8868i −0.351765 0.411445i
\(982\) 19.7980 + 19.7980i 0.631778 + 0.631778i
\(983\) −26.2752 + 7.04041i −0.838047 + 0.224554i −0.652221 0.758029i \(-0.726163\pi\)
−0.185826 + 0.982583i \(0.559496\pi\)
\(984\) 12.7440 1.17423i 0.406263 0.0374332i
\(985\) 17.7766 12.8060i 0.566408 0.408033i
\(986\) 0.123724 0.0714323i 0.00394019 0.00227487i
\(987\) 54.6690 + 45.4445i 1.74013 + 1.44651i
\(988\) 5.78245 + 21.5804i 0.183964 + 0.686564i
\(989\) 3.46410 0.110152
\(990\) 1.19663 + 4.09289i 0.0380315 + 0.130081i
\(991\) 16.7423 0.531838 0.265919 0.963995i \(-0.414325\pi\)
0.265919 + 0.963995i \(0.414325\pi\)
\(992\) 0.116337 + 0.434174i 0.00369369 + 0.0137850i
\(993\) −0.131652 + 0.767327i −0.00417787 + 0.0243504i
\(994\) −24.8523 + 14.3485i −0.788266 + 0.455106i
\(995\) −3.03100 + 18.6489i −0.0960890 + 0.591211i
\(996\) −3.94949 + 8.57277i −0.125144 + 0.271639i
\(997\) 6.49211 1.73955i 0.205607 0.0550922i −0.154545 0.987986i \(-0.549391\pi\)
0.360153 + 0.932893i \(0.382725\pi\)
\(998\) −0.635674 0.635674i −0.0201219 0.0201219i
\(999\) −21.2132 + 6.00000i −0.671156 + 0.189832i
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 90.2.l.a.47.1 yes 8
3.2 odd 2 270.2.m.a.197.2 8
4.3 odd 2 720.2.cu.a.497.1 8
5.2 odd 4 450.2.p.a.443.2 8
5.3 odd 4 inner 90.2.l.a.83.1 yes 8
5.4 even 2 450.2.p.a.407.2 8
9.2 odd 6 810.2.f.b.647.3 8
9.4 even 3 270.2.m.a.17.2 8
9.5 odd 6 inner 90.2.l.a.77.1 yes 8
9.7 even 3 810.2.f.b.647.2 8
15.2 even 4 1350.2.q.g.143.1 8
15.8 even 4 270.2.m.a.143.2 8
15.14 odd 2 1350.2.q.g.1007.1 8
20.3 even 4 720.2.cu.a.353.1 8
36.23 even 6 720.2.cu.a.257.1 8
45.4 even 6 1350.2.q.g.557.1 8
45.13 odd 12 270.2.m.a.233.2 8
45.14 odd 6 450.2.p.a.257.2 8
45.22 odd 12 1350.2.q.g.1043.1 8
45.23 even 12 inner 90.2.l.a.23.1 8
45.32 even 12 450.2.p.a.293.2 8
45.38 even 12 810.2.f.b.323.1 8
45.43 odd 12 810.2.f.b.323.4 8
180.23 odd 12 720.2.cu.a.113.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.l.a.23.1 8 45.23 even 12 inner
90.2.l.a.47.1 yes 8 1.1 even 1 trivial
90.2.l.a.77.1 yes 8 9.5 odd 6 inner
90.2.l.a.83.1 yes 8 5.3 odd 4 inner
270.2.m.a.17.2 8 9.4 even 3
270.2.m.a.143.2 8 15.8 even 4
270.2.m.a.197.2 8 3.2 odd 2
270.2.m.a.233.2 8 45.13 odd 12
450.2.p.a.257.2 8 45.14 odd 6
450.2.p.a.293.2 8 45.32 even 12
450.2.p.a.407.2 8 5.4 even 2
450.2.p.a.443.2 8 5.2 odd 4
720.2.cu.a.113.1 8 180.23 odd 12
720.2.cu.a.257.1 8 36.23 even 6
720.2.cu.a.353.1 8 20.3 even 4
720.2.cu.a.497.1 8 4.3 odd 2
810.2.f.b.323.1 8 45.38 even 12
810.2.f.b.323.4 8 45.43 odd 12
810.2.f.b.647.2 8 9.7 even 3
810.2.f.b.647.3 8 9.2 odd 6
1350.2.q.g.143.1 8 15.2 even 4
1350.2.q.g.557.1 8 45.4 even 6
1350.2.q.g.1007.1 8 15.14 odd 2
1350.2.q.g.1043.1 8 45.22 odd 12