Properties

Label 187.2.r.a.9.4
Level $187$
Weight $2$
Character 187.9
Analytic conductor $1.493$
Analytic rank $0$
Dimension $256$
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] = [187,2,Mod(9,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([24, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.r (of order \(40\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(16\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 9.4
Character \(\chi\) \(=\) 187.9
Dual form 187.2.r.a.104.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766568 - 1.50447i) q^{2} +(2.49633 - 0.599317i) q^{3} +(-0.500247 + 0.688531i) q^{4} +(1.08364 + 0.0852843i) q^{5} +(-2.81527 - 3.29625i) q^{6} +(-0.0461198 + 0.192103i) q^{7} +(-1.91609 - 0.303480i) q^{8} +(3.19948 - 1.63022i) q^{9} +O(q^{10})\) \(q+(-0.766568 - 1.50447i) q^{2} +(2.49633 - 0.599317i) q^{3} +(-0.500247 + 0.688531i) q^{4} +(1.08364 + 0.0852843i) q^{5} +(-2.81527 - 3.29625i) q^{6} +(-0.0461198 + 0.192103i) q^{7} +(-1.91609 - 0.303480i) q^{8} +(3.19948 - 1.63022i) q^{9} +(-0.702375 - 1.69568i) q^{10} +(0.477308 + 3.28210i) q^{11} +(-0.836136 + 2.01861i) q^{12} +(0.391287 + 0.127137i) q^{13} +(0.324368 - 0.0778739i) q^{14} +(2.75624 - 0.436545i) q^{15} +(1.53823 + 4.73419i) q^{16} +(-3.93671 - 1.22570i) q^{17} +(-4.90524 - 3.56386i) q^{18} +(0.00230718 - 0.0145670i) q^{19} +(-0.600808 + 0.703456i) q^{20} +0.507193i q^{21} +(4.57195 - 3.23405i) q^{22} +(-4.95498 + 2.05242i) q^{23} +(-4.96509 + 0.390761i) q^{24} +(-3.77144 - 0.597338i) q^{25} +(-0.108674 - 0.686141i) q^{26} +(1.15345 - 0.985142i) q^{27} +(-0.109198 - 0.127854i) q^{28} +(0.0229170 - 0.0140435i) q^{29} +(-2.76961 - 3.81205i) q^{30} +(5.44810 - 6.37891i) q^{31} +(3.19976 - 3.19976i) q^{32} +(3.15854 + 7.90715i) q^{33} +(1.17373 + 6.86226i) q^{34} +(-0.0663606 + 0.204237i) q^{35} +(-0.478076 + 3.01845i) q^{36} +(0.580754 + 0.947704i) q^{37} +(-0.0236842 + 0.00769547i) q^{38} +(1.05298 + 0.0828712i) q^{39} +(-2.05047 - 0.492275i) q^{40} +(-2.10772 - 1.29161i) q^{41} +(0.763060 - 0.388798i) q^{42} +(7.70774 + 7.70774i) q^{43} +(-2.49860 - 1.31322i) q^{44} +(3.60611 - 1.49370i) q^{45} +(6.88614 + 5.88132i) q^{46} +(-3.14737 - 4.33198i) q^{47} +(6.67721 + 10.8962i) q^{48} +(6.20227 + 3.16021i) q^{49} +(1.99239 + 6.13194i) q^{50} +(-10.5619 - 0.700410i) q^{51} +(-0.283278 + 0.205813i) q^{52} +(3.67165 + 7.20601i) q^{53} +(-2.36632 - 0.980163i) q^{54} +(0.237319 + 3.59732i) q^{55} +(0.146669 - 0.354091i) q^{56} +(-0.00297073 - 0.0377467i) q^{57} +(-0.0386956 - 0.0237127i) q^{58} +(-0.693237 - 4.37693i) q^{59} +(-1.07822 + 2.11614i) q^{60} +(7.07956 - 6.04652i) q^{61} +(-13.7732 - 3.30666i) q^{62} +(0.165610 + 0.689815i) q^{63} +(2.20158 + 0.715335i) q^{64} +(0.413171 + 0.171141i) q^{65} +(9.47488 - 10.8133i) q^{66} -0.975391 q^{67} +(2.81326 - 2.09740i) q^{68} +(-11.1392 + 8.09312i) q^{69} +(0.358139 - 0.0567237i) q^{70} +(0.464812 - 5.90600i) q^{71} +(-6.62524 + 2.15267i) q^{72} +(-5.69278 + 3.48854i) q^{73} +(0.980610 - 1.60021i) q^{74} +(-9.77277 + 0.769133i) q^{75} +(0.00887565 + 0.00887565i) q^{76} +(-0.652514 - 0.0596775i) q^{77} +(-0.682502 - 1.64771i) q^{78} +(-0.416643 - 5.29395i) q^{79} +(1.26314 + 5.26134i) q^{80} +(-4.04297 + 5.56467i) q^{81} +(-0.327487 + 4.16112i) q^{82} +(3.15832 + 1.60925i) q^{83} +(-0.349218 - 0.253722i) q^{84} +(-4.16144 - 1.66395i) q^{85} +(5.68759 - 17.5046i) q^{86} +(0.0487919 - 0.0487919i) q^{87} +(0.0814820 - 6.43367i) q^{88} -7.19606i q^{89} +(-5.01157 - 4.28028i) q^{90} +(-0.0424695 + 0.0693039i) q^{91} +(1.06556 - 4.43837i) q^{92} +(9.77729 - 19.1890i) q^{93} +(-4.10468 + 8.05589i) q^{94} +(0.00374248 - 0.0155886i) q^{95} +(6.07000 - 9.90535i) q^{96} +(-13.5216 - 11.5486i) q^{97} -11.7537i q^{98} +(6.87767 + 9.72289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 12 q^{2} - 12 q^{3} - 20 q^{5} - 12 q^{6} - 12 q^{7} - 28 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 12 q^{2} - 12 q^{3} - 20 q^{5} - 12 q^{6} - 12 q^{7} - 28 q^{8} - 36 q^{9} - 32 q^{10} - 16 q^{11} - 32 q^{12} - 12 q^{14} + 12 q^{15} + 16 q^{16} + 12 q^{17} - 16 q^{18} - 12 q^{19} - 44 q^{20} + 88 q^{22} - 48 q^{23} - 80 q^{24} - 4 q^{25} - 12 q^{26} - 48 q^{27} - 28 q^{28} - 12 q^{29} + 44 q^{31} - 8 q^{32} - 56 q^{33} - 64 q^{34} - 88 q^{35} + 56 q^{36} - 28 q^{37} + 12 q^{39} + 120 q^{40} - 48 q^{41} + 44 q^{42} + 8 q^{43} - 16 q^{44} - 32 q^{45} - 44 q^{46} + 60 q^{48} + 64 q^{49} + 32 q^{50} - 28 q^{51} - 232 q^{52} - 20 q^{53} + 48 q^{54} - 64 q^{56} + 128 q^{57} + 124 q^{58} + 104 q^{59} + 4 q^{60} + 64 q^{61} - 52 q^{62} - 12 q^{63} - 88 q^{65} - 208 q^{66} - 96 q^{67} + 44 q^{68} + 48 q^{69} + 92 q^{70} - 44 q^{71} + 28 q^{73} - 12 q^{74} + 104 q^{75} + 176 q^{76} - 148 q^{77} - 12 q^{79} + 32 q^{80} - 72 q^{82} - 16 q^{83} + 216 q^{84} + 80 q^{85} - 24 q^{86} - 128 q^{87} - 32 q^{88} - 28 q^{90} - 108 q^{91} + 76 q^{92} + 164 q^{93} - 88 q^{94} - 32 q^{95} - 44 q^{96} + 128 q^{97} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766568 1.50447i −0.542046 1.06382i −0.985839 0.167695i \(-0.946368\pi\)
0.443793 0.896129i \(-0.353632\pi\)
\(3\) 2.49633 0.599317i 1.44126 0.346016i 0.563897 0.825845i \(-0.309302\pi\)
0.877362 + 0.479830i \(0.159302\pi\)
\(4\) −0.500247 + 0.688531i −0.250124 + 0.344266i
\(5\) 1.08364 + 0.0852843i 0.484618 + 0.0381403i 0.318415 0.947951i \(-0.396849\pi\)
0.166203 + 0.986092i \(0.446849\pi\)
\(6\) −2.81527 3.29625i −1.14933 1.34569i
\(7\) −0.0461198 + 0.192103i −0.0174317 + 0.0726081i −0.980408 0.196979i \(-0.936887\pi\)
0.962976 + 0.269587i \(0.0868871\pi\)
\(8\) −1.91609 0.303480i −0.677442 0.107296i
\(9\) 3.19948 1.63022i 1.06649 0.543405i
\(10\) −0.702375 1.69568i −0.222111 0.536222i
\(11\) 0.477308 + 3.28210i 0.143914 + 0.989590i
\(12\) −0.836136 + 2.01861i −0.241372 + 0.582722i
\(13\) 0.391287 + 0.127137i 0.108523 + 0.0352614i 0.362775 0.931877i \(-0.381829\pi\)
−0.254252 + 0.967138i \(0.581829\pi\)
\(14\) 0.324368 0.0778739i 0.0866910 0.0208127i
\(15\) 2.75624 0.436545i 0.711657 0.112715i
\(16\) 1.53823 + 4.73419i 0.384558 + 1.18355i
\(17\) −3.93671 1.22570i −0.954792 0.297275i
\(18\) −4.90524 3.56386i −1.15618 0.840011i
\(19\) 0.00230718 0.0145670i 0.000529303 0.00334189i −0.987422 0.158105i \(-0.949461\pi\)
0.987952 + 0.154763i \(0.0494615\pi\)
\(20\) −0.600808 + 0.703456i −0.134345 + 0.157298i
\(21\) 0.507193i 0.110679i
\(22\) 4.57195 3.23405i 0.974742 0.689502i
\(23\) −4.95498 + 2.05242i −1.03318 + 0.427959i −0.833861 0.551975i \(-0.813874\pi\)
−0.199323 + 0.979934i \(0.563874\pi\)
\(24\) −4.96509 + 0.390761i −1.01349 + 0.0797638i
\(25\) −3.77144 0.597338i −0.754288 0.119468i
\(26\) −0.108674 0.686141i −0.0213127 0.134563i
\(27\) 1.15345 0.985142i 0.221982 0.189591i
\(28\) −0.109198 0.127854i −0.0206364 0.0241621i
\(29\) 0.0229170 0.0140435i 0.00425557 0.00260782i −0.520369 0.853941i \(-0.674206\pi\)
0.524625 + 0.851334i \(0.324206\pi\)
\(30\) −2.76961 3.81205i −0.505660 0.695981i
\(31\) 5.44810 6.37891i 0.978508 1.14569i −0.0108145 0.999942i \(-0.503442\pi\)
0.989322 0.145744i \(-0.0465576\pi\)
\(32\) 3.19976 3.19976i 0.565644 0.565644i
\(33\) 3.15854 + 7.90715i 0.549831 + 1.37646i
\(34\) 1.17373 + 6.86226i 0.201293 + 1.17687i
\(35\) −0.0663606 + 0.204237i −0.0112170 + 0.0345224i
\(36\) −0.478076 + 3.01845i −0.0796793 + 0.503075i
\(37\) 0.580754 + 0.947704i 0.0954754 + 0.155802i 0.896812 0.442412i \(-0.145877\pi\)
−0.801336 + 0.598214i \(0.795877\pi\)
\(38\) −0.0236842 + 0.00769547i −0.00384209 + 0.00124837i
\(39\) 1.05298 + 0.0828712i 0.168611 + 0.0132700i
\(40\) −2.05047 0.492275i −0.324208 0.0778355i
\(41\) −2.10772 1.29161i −0.329171 0.201716i 0.348087 0.937462i \(-0.386832\pi\)
−0.677257 + 0.735746i \(0.736832\pi\)
\(42\) 0.763060 0.388798i 0.117743 0.0599929i
\(43\) 7.70774 + 7.70774i 1.17542 + 1.17542i 0.980898 + 0.194520i \(0.0623151\pi\)
0.194520 + 0.980898i \(0.437685\pi\)
\(44\) −2.49860 1.31322i −0.376678 0.197975i
\(45\) 3.60611 1.49370i 0.537567 0.222668i
\(46\) 6.88614 + 5.88132i 1.01531 + 0.867153i
\(47\) −3.14737 4.33198i −0.459091 0.631884i 0.515229 0.857052i \(-0.327707\pi\)
−0.974320 + 0.225168i \(0.927707\pi\)
\(48\) 6.67721 + 10.8962i 0.963773 + 1.57273i
\(49\) 6.20227 + 3.16021i 0.886038 + 0.451459i
\(50\) 1.99239 + 6.13194i 0.281766 + 0.867187i
\(51\) −10.5619 0.700410i −1.47896 0.0980770i
\(52\) −0.283278 + 0.205813i −0.0392836 + 0.0285412i
\(53\) 3.67165 + 7.20601i 0.504340 + 0.989822i 0.993085 + 0.117396i \(0.0374546\pi\)
−0.488746 + 0.872426i \(0.662545\pi\)
\(54\) −2.36632 0.980163i −0.322016 0.133383i
\(55\) 0.237319 + 3.59732i 0.0320000 + 0.485062i
\(56\) 0.146669 0.354091i 0.0195995 0.0473174i
\(57\) −0.00297073 0.0377467i −0.000393483 0.00499967i
\(58\) −0.0386956 0.0237127i −0.00508098 0.00311363i
\(59\) −0.693237 4.37693i −0.0902517 0.569827i −0.990828 0.135129i \(-0.956855\pi\)
0.900576 0.434698i \(-0.143145\pi\)
\(60\) −1.07822 + 2.11614i −0.139198 + 0.273192i
\(61\) 7.07956 6.04652i 0.906445 0.774177i −0.0682609 0.997668i \(-0.521745\pi\)
0.974706 + 0.223490i \(0.0717450\pi\)
\(62\) −13.7732 3.30666i −1.74920 0.419947i
\(63\) 0.165610 + 0.689815i 0.0208649 + 0.0869085i
\(64\) 2.20158 + 0.715335i 0.275197 + 0.0894169i
\(65\) 0.413171 + 0.171141i 0.0512476 + 0.0212274i
\(66\) 9.47488 10.8133i 1.16628 1.33103i
\(67\) −0.975391 −0.119163 −0.0595815 0.998223i \(-0.518977\pi\)
−0.0595815 + 0.998223i \(0.518977\pi\)
\(68\) 2.81326 2.09740i 0.341158 0.254347i
\(69\) −11.1392 + 8.09312i −1.34100 + 0.974297i
\(70\) 0.358139 0.0567237i 0.0428058 0.00677978i
\(71\) 0.464812 5.90600i 0.0551631 0.700913i −0.905705 0.423908i \(-0.860658\pi\)
0.960868 0.277005i \(-0.0893420\pi\)
\(72\) −6.62524 + 2.15267i −0.780792 + 0.253695i
\(73\) −5.69278 + 3.48854i −0.666289 + 0.408303i −0.814109 0.580712i \(-0.802774\pi\)
0.147820 + 0.989014i \(0.452774\pi\)
\(74\) 0.980610 1.60021i 0.113994 0.186021i
\(75\) −9.77277 + 0.769133i −1.12846 + 0.0888119i
\(76\) 0.00887565 + 0.00887565i 0.00101811 + 0.00101811i
\(77\) −0.652514 0.0596775i −0.0743609 0.00680089i
\(78\) −0.682502 1.64771i −0.0772781 0.186566i
\(79\) −0.416643 5.29395i −0.0468760 0.595616i −0.974834 0.222932i \(-0.928437\pi\)
0.927958 0.372685i \(-0.121563\pi\)
\(80\) 1.26314 + 5.26134i 0.141223 + 0.588236i
\(81\) −4.04297 + 5.56467i −0.449219 + 0.618297i
\(82\) −0.327487 + 4.16112i −0.0361649 + 0.459519i
\(83\) 3.15832 + 1.60925i 0.346671 + 0.176638i 0.618652 0.785665i \(-0.287679\pi\)
−0.271981 + 0.962303i \(0.587679\pi\)
\(84\) −0.349218 0.253722i −0.0381029 0.0276833i
\(85\) −4.16144 1.66395i −0.451371 0.180481i
\(86\) 5.68759 17.5046i 0.613309 1.88757i
\(87\) 0.0487919 0.0487919i 0.00523104 0.00523104i
\(88\) 0.0814820 6.43367i 0.00868602 0.685831i
\(89\) 7.19606i 0.762781i −0.924414 0.381391i \(-0.875445\pi\)
0.924414 0.381391i \(-0.124555\pi\)
\(90\) −5.01157 4.28028i −0.528265 0.451181i
\(91\) −0.0424695 + 0.0693039i −0.00445201 + 0.00726502i
\(92\) 1.06556 4.43837i 0.111092 0.462732i
\(93\) 9.77729 19.1890i 1.01386 1.98981i
\(94\) −4.10468 + 8.05589i −0.423366 + 0.830902i
\(95\) 0.00374248 0.0155886i 0.000383971 0.00159935i
\(96\) 6.07000 9.90535i 0.619517 1.01096i
\(97\) −13.5216 11.5486i −1.37291 1.17258i −0.965827 0.259189i \(-0.916545\pi\)
−0.407086 0.913390i \(-0.633455\pi\)
\(98\) 11.7537i 1.18730i
\(99\) 6.87767 + 9.72289i 0.691232 + 0.977187i
\(100\) 2.29794 2.29794i 0.229794 0.229794i
\(101\) 1.71175 5.26824i 0.170326 0.524209i −0.829063 0.559155i \(-0.811126\pi\)
0.999389 + 0.0349454i \(0.0111257\pi\)
\(102\) 7.04268 + 16.4270i 0.697329 + 1.62652i
\(103\) −0.544832 0.395844i −0.0536839 0.0390037i 0.560620 0.828073i \(-0.310563\pi\)
−0.614304 + 0.789070i \(0.710563\pi\)
\(104\) −0.711160 0.362354i −0.0697349 0.0355317i
\(105\) −0.0432556 + 0.549615i −0.00422132 + 0.0536369i
\(106\) 8.02670 11.0478i 0.779622 1.07306i
\(107\) −3.13770 13.0695i −0.303333 1.26347i −0.890863 0.454271i \(-0.849900\pi\)
0.587530 0.809202i \(-0.300100\pi\)
\(108\) 0.101289 + 1.28700i 0.00974657 + 0.123842i
\(109\) 4.11984 + 9.94617i 0.394609 + 0.952670i 0.988922 + 0.148436i \(0.0474240\pi\)
−0.594313 + 0.804234i \(0.702576\pi\)
\(110\) 5.23015 3.11463i 0.498676 0.296968i
\(111\) 2.01773 + 2.01773i 0.191514 + 0.191514i
\(112\) −0.980395 + 0.0771587i −0.0926386 + 0.00729081i
\(113\) −5.23167 + 8.53731i −0.492154 + 0.803123i −0.998236 0.0593624i \(-0.981093\pi\)
0.506082 + 0.862485i \(0.331093\pi\)
\(114\) −0.0545117 + 0.0334048i −0.00510549 + 0.00312865i
\(115\) −5.54445 + 1.80150i −0.517022 + 0.167991i
\(116\) −0.00179474 + 0.0228043i −0.000166637 + 0.00211733i
\(117\) 1.45917 0.231111i 0.134901 0.0213662i
\(118\) −6.05356 + 4.39817i −0.557275 + 0.404884i
\(119\) 0.417020 0.699724i 0.0382282 0.0641436i
\(120\) −5.41369 −0.494200
\(121\) −10.5444 + 3.13315i −0.958578 + 0.284832i
\(122\) −14.5238 6.01596i −1.31492 0.544659i
\(123\) −6.03566 1.96110i −0.544217 0.176827i
\(124\) 1.66668 + 6.94222i 0.149672 + 0.623430i
\(125\) −9.32072 2.23771i −0.833671 0.200147i
\(126\) 0.910857 0.777946i 0.0811456 0.0693049i
\(127\) 3.85259 7.56114i 0.341862 0.670943i −0.654509 0.756054i \(-0.727125\pi\)
0.996371 + 0.0851114i \(0.0271246\pi\)
\(128\) −2.02723 12.7994i −0.179184 1.13132i
\(129\) 23.8605 + 14.6217i 2.10080 + 1.28737i
\(130\) −0.0592464 0.752797i −0.00519625 0.0660247i
\(131\) −5.27092 + 12.7251i −0.460523 + 1.11180i 0.507661 + 0.861557i \(0.330510\pi\)
−0.968183 + 0.250243i \(0.919490\pi\)
\(132\) −7.02437 1.78078i −0.611393 0.154997i
\(133\) 0.00269195 + 0.00111504i 0.000233422 + 9.66864e-5i
\(134\) 0.747704 + 1.46745i 0.0645918 + 0.126768i
\(135\) 1.33394 0.969167i 0.114808 0.0834126i
\(136\) 7.17113 + 3.54326i 0.614919 + 0.303832i
\(137\) 6.55447 + 20.1726i 0.559986 + 1.72346i 0.682398 + 0.730981i \(0.260937\pi\)
−0.122412 + 0.992479i \(0.539063\pi\)
\(138\) 20.7149 + 10.5548i 1.76337 + 0.898480i
\(139\) 9.61714 + 15.6937i 0.815715 + 1.33113i 0.940794 + 0.338979i \(0.110082\pi\)
−0.125079 + 0.992147i \(0.539918\pi\)
\(140\) −0.107427 0.147860i −0.00907923 0.0124965i
\(141\) −10.4531 8.92779i −0.880310 0.751856i
\(142\) −9.24174 + 3.82805i −0.775550 + 0.321243i
\(143\) −0.230511 + 1.34493i −0.0192763 + 0.112468i
\(144\) 12.6393 + 12.6393i 1.05327 + 1.05327i
\(145\) 0.0260314 0.0132637i 0.00216179 0.00110149i
\(146\) 9.61232 + 5.89044i 0.795522 + 0.487496i
\(147\) 17.3769 + 4.17182i 1.43322 + 0.344086i
\(148\) −0.943045 0.0742192i −0.0775178 0.00610078i
\(149\) −4.52465 + 1.47015i −0.370674 + 0.120439i −0.488429 0.872603i \(-0.662430\pi\)
0.117756 + 0.993043i \(0.462430\pi\)
\(150\) 8.64863 + 14.1133i 0.706158 + 1.15235i
\(151\) 1.73163 10.9331i 0.140918 0.889723i −0.811372 0.584530i \(-0.801279\pi\)
0.952290 0.305193i \(-0.0987210\pi\)
\(152\) −0.00884155 + 0.0272115i −0.000717144 + 0.00220714i
\(153\) −14.5936 + 2.49610i −1.17982 + 0.201797i
\(154\) 0.410413 + 1.02744i 0.0330721 + 0.0827934i
\(155\) 6.44780 6.44780i 0.517899 0.517899i
\(156\) −0.583809 + 0.683552i −0.0467421 + 0.0547280i
\(157\) −10.6721 14.6889i −0.851729 1.17230i −0.983479 0.181021i \(-0.942060\pi\)
0.131750 0.991283i \(-0.457940\pi\)
\(158\) −7.64523 + 4.68501i −0.608222 + 0.372719i
\(159\) 13.4843 + 15.7881i 1.06938 + 1.25208i
\(160\) 3.74028 3.19450i 0.295695 0.252547i
\(161\) −0.165753 1.04652i −0.0130632 0.0824776i
\(162\) 11.4711 + 1.81685i 0.901256 + 0.142745i
\(163\) −5.12514 + 0.403357i −0.401432 + 0.0315934i −0.277568 0.960706i \(-0.589529\pi\)
−0.123864 + 0.992299i \(0.539529\pi\)
\(164\) 1.94370 0.805106i 0.151777 0.0628682i
\(165\) 2.74836 + 8.83788i 0.213959 + 0.688028i
\(166\) 5.98521i 0.464543i
\(167\) 10.0469 11.7635i 0.777455 0.910283i −0.220422 0.975405i \(-0.570743\pi\)
0.997877 + 0.0651214i \(0.0207435\pi\)
\(168\) 0.153923 0.971830i 0.0118754 0.0749784i
\(169\) −10.3803 7.54171i −0.798483 0.580132i
\(170\) 0.686654 + 7.53631i 0.0526640 + 0.578009i
\(171\) −0.0163655 0.0503679i −0.00125150 0.00385173i
\(172\) −9.16279 + 1.45124i −0.698656 + 0.110656i
\(173\) −20.1326 + 4.83340i −1.53065 + 0.367477i −0.909329 0.416079i \(-0.863404\pi\)
−0.621322 + 0.783555i \(0.713404\pi\)
\(174\) −0.110808 0.0360038i −0.00840037 0.00272944i
\(175\) 0.288689 0.696956i 0.0218228 0.0526849i
\(176\) −14.8039 + 7.30830i −1.11588 + 0.550883i
\(177\) −4.35371 10.5108i −0.327245 0.790040i
\(178\) −10.8263 + 5.51627i −0.811465 + 0.413462i
\(179\) 10.3923 + 1.64598i 0.776760 + 0.123027i 0.532213 0.846611i \(-0.321361\pi\)
0.244547 + 0.969637i \(0.421361\pi\)
\(180\) −0.775488 + 3.23014i −0.0578015 + 0.240760i
\(181\) 11.2183 + 13.1350i 0.833852 + 0.976315i 0.999952 0.00979371i \(-0.00311748\pi\)
−0.166100 + 0.986109i \(0.553117\pi\)
\(182\) 0.136822 + 0.0107681i 0.0101419 + 0.000798184i
\(183\) 14.0492 19.3370i 1.03854 1.42943i
\(184\) 10.1171 2.42889i 0.745840 0.179060i
\(185\) 0.548504 + 1.07650i 0.0403268 + 0.0791458i
\(186\) −36.3643 −2.66636
\(187\) 2.14383 13.5057i 0.156772 0.987635i
\(188\) 4.55716 0.332365
\(189\) 0.136052 + 0.267016i 0.00989630 + 0.0194226i
\(190\) −0.0263215 + 0.00631922i −0.00190956 + 0.000458445i
\(191\) 15.2942 21.0506i 1.10665 1.52317i 0.280382 0.959889i \(-0.409539\pi\)
0.826265 0.563281i \(-0.190461\pi\)
\(192\) 5.92458 + 0.466274i 0.427570 + 0.0336505i
\(193\) −13.8181 16.1789i −0.994645 1.16458i −0.986358 0.164614i \(-0.947362\pi\)
−0.00828743 0.999966i \(-0.502638\pi\)
\(194\) −7.00927 + 29.1957i −0.503236 + 2.09613i
\(195\) 1.13398 + 0.179605i 0.0812060 + 0.0128618i
\(196\) −5.27857 + 2.68957i −0.377041 + 0.192112i
\(197\) −4.96202 11.9794i −0.353529 0.853494i −0.996179 0.0873346i \(-0.972165\pi\)
0.642650 0.766160i \(-0.277835\pi\)
\(198\) 9.35564 17.8005i 0.664877 1.26503i
\(199\) 0.206327 0.498118i 0.0146262 0.0353107i −0.916398 0.400269i \(-0.868917\pi\)
0.931024 + 0.364958i \(0.118917\pi\)
\(200\) 7.04516 + 2.28911i 0.498168 + 0.161865i
\(201\) −2.43490 + 0.584568i −0.171745 + 0.0412322i
\(202\) −9.23811 + 1.46317i −0.649991 + 0.102949i
\(203\) 0.00164088 + 0.00505010i 0.000115167 + 0.000354448i
\(204\) 5.76582 6.92183i 0.403688 0.484625i
\(205\) −2.17385 1.57940i −0.151829 0.110310i
\(206\) −0.177886 + 1.12313i −0.0123939 + 0.0782520i
\(207\) −12.5075 + 14.6443i −0.869328 + 1.01785i
\(208\) 2.04799i 0.142003i
\(209\) 0.0489114 0.000619461i 0.00338327 4.28490e-5i
\(210\) 0.860040 0.356240i 0.0593484 0.0245829i
\(211\) −11.0034 + 0.865990i −0.757508 + 0.0596172i −0.451330 0.892357i \(-0.649050\pi\)
−0.306178 + 0.951974i \(0.599050\pi\)
\(212\) −6.79830 1.07674i −0.466909 0.0739511i
\(213\) −2.37924 15.0219i −0.163023 1.02928i
\(214\) −17.2574 + 14.7392i −1.17969 + 1.00755i
\(215\) 7.69506 + 9.00975i 0.524799 + 0.614460i
\(216\) −2.50910 + 1.53758i −0.170722 + 0.104619i
\(217\) 0.974141 + 1.34079i 0.0661290 + 0.0910188i
\(218\) 11.8056 13.8226i 0.799577 0.936185i
\(219\) −12.1203 + 12.1203i −0.819016 + 0.819016i
\(220\) −2.59558 1.63615i −0.174994 0.110309i
\(221\) −1.38455 0.980099i −0.0931350 0.0659286i
\(222\) 1.48890 4.58235i 0.0999282 0.307547i
\(223\) 2.26414 14.2952i 0.151618 0.957279i −0.788154 0.615478i \(-0.788963\pi\)
0.939772 0.341801i \(-0.111037\pi\)
\(224\) 0.467111 + 0.762257i 0.0312102 + 0.0509304i
\(225\) −13.0404 + 4.23709i −0.869362 + 0.282473i
\(226\) 16.8546 + 1.32649i 1.12115 + 0.0882366i
\(227\) 26.5459 + 6.37312i 1.76192 + 0.422999i 0.979775 0.200103i \(-0.0641277\pi\)
0.782141 + 0.623102i \(0.214128\pi\)
\(228\) 0.0274759 + 0.0168372i 0.00181964 + 0.00111507i
\(229\) −23.6136 + 12.0317i −1.56043 + 0.795078i −0.999463 0.0327608i \(-0.989570\pi\)
−0.560966 + 0.827839i \(0.689570\pi\)
\(230\) 6.96051 + 6.96051i 0.458962 + 0.458962i
\(231\) −1.66466 + 0.242088i −0.109527 + 0.0159282i
\(232\) −0.0481730 + 0.0199539i −0.00316271 + 0.00131004i
\(233\) 15.8877 + 13.5693i 1.04084 + 0.888958i 0.993938 0.109942i \(-0.0350665\pi\)
0.0468976 + 0.998900i \(0.485067\pi\)
\(234\) −1.46626 2.01813i −0.0958522 0.131929i
\(235\) −3.04116 4.96272i −0.198383 0.323732i
\(236\) 3.36044 + 1.71223i 0.218746 + 0.111457i
\(237\) −4.21283 12.9658i −0.273653 0.842217i
\(238\) −1.37239 0.0910098i −0.0889590 0.00589929i
\(239\) 13.4588 9.77836i 0.870575 0.632510i −0.0601664 0.998188i \(-0.519163\pi\)
0.930741 + 0.365679i \(0.119163\pi\)
\(240\) 6.30641 + 12.3770i 0.407077 + 0.798934i
\(241\) 8.85045 + 3.66597i 0.570107 + 0.236146i 0.649067 0.760732i \(-0.275160\pi\)
−0.0789592 + 0.996878i \(0.525160\pi\)
\(242\) 12.7967 + 13.4619i 0.822604 + 0.865366i
\(243\) −8.49907 + 20.5186i −0.545215 + 1.31627i
\(244\) 0.621685 + 7.89926i 0.0397993 + 0.505698i
\(245\) 6.45151 + 3.95349i 0.412172 + 0.252579i
\(246\) 1.67631 + 10.5838i 0.106878 + 0.674799i
\(247\) 0.00275477 0.00540653i 0.000175282 0.000344009i
\(248\) −12.3749 + 10.5692i −0.785810 + 0.671145i
\(249\) 8.84867 + 2.12438i 0.560762 + 0.134627i
\(250\) 3.77839 + 15.7381i 0.238967 + 0.995368i
\(251\) −0.753832 0.244935i −0.0475815 0.0154602i 0.285130 0.958489i \(-0.407963\pi\)
−0.332711 + 0.943029i \(0.607963\pi\)
\(252\) −0.557805 0.231050i −0.0351384 0.0145548i
\(253\) −9.10129 15.2831i −0.572193 0.960840i
\(254\) −14.3288 −0.899070
\(255\) −11.3856 1.65976i −0.712992 0.103938i
\(256\) −13.9569 + 10.1403i −0.872305 + 0.633767i
\(257\) −23.2372 + 3.68041i −1.44950 + 0.229578i −0.831028 0.556231i \(-0.812247\pi\)
−0.618469 + 0.785809i \(0.712247\pi\)
\(258\) 3.70732 47.1060i 0.230808 2.93269i
\(259\) −0.208841 + 0.0678566i −0.0129768 + 0.00421640i
\(260\) −0.324524 + 0.198868i −0.0201261 + 0.0123333i
\(261\) 0.0504284 0.0822916i 0.00312144 0.00509372i
\(262\) 23.1852 1.82471i 1.43238 0.112731i
\(263\) 18.5850 + 18.5850i 1.14600 + 1.14600i 0.987331 + 0.158672i \(0.0507211\pi\)
0.158672 + 0.987331i \(0.449279\pi\)
\(264\) −3.65240 16.1094i −0.224789 0.991466i
\(265\) 3.36418 + 8.12185i 0.206660 + 0.498922i
\(266\) −0.000386010 0.00490472i −2.36678e−5 0.000300728i
\(267\) −4.31272 17.9638i −0.263934 1.09936i
\(268\) 0.487937 0.671587i 0.0298055 0.0410237i
\(269\) −0.127959 + 1.62587i −0.00780177 + 0.0991309i −0.999585 0.0287966i \(-0.990832\pi\)
0.991784 + 0.127927i \(0.0408325\pi\)
\(270\) −2.48065 1.26395i −0.150967 0.0769217i
\(271\) −11.3248 8.22794i −0.687932 0.499812i 0.188048 0.982160i \(-0.439784\pi\)
−0.875980 + 0.482348i \(0.839784\pi\)
\(272\) −0.252893 20.5225i −0.0153339 1.24436i
\(273\) −0.0644830 + 0.198458i −0.00390269 + 0.0120112i
\(274\) 25.3247 25.3247i 1.52992 1.52992i
\(275\) 0.160381 12.6634i 0.00967132 0.763629i
\(276\) 11.7183i 0.705357i
\(277\) 21.0788 + 18.0030i 1.26650 + 1.08170i 0.992788 + 0.119884i \(0.0382523\pi\)
0.273714 + 0.961811i \(0.411748\pi\)
\(278\) 16.2387 26.4991i 0.973930 1.58931i
\(279\) 7.03209 29.2908i 0.421000 1.75359i
\(280\) 0.189135 0.371198i 0.0113030 0.0221833i
\(281\) −10.5026 + 20.6126i −0.626534 + 1.22964i 0.331627 + 0.943411i \(0.392403\pi\)
−0.958161 + 0.286231i \(0.907597\pi\)
\(282\) −5.41862 + 22.5702i −0.322674 + 1.34404i
\(283\) −1.63094 + 2.66145i −0.0969493 + 0.158207i −0.897438 0.441142i \(-0.854574\pi\)
0.800488 + 0.599349i \(0.204574\pi\)
\(284\) 3.83394 + 3.27450i 0.227503 + 0.194306i
\(285\) 0.0411572i 0.00243794i
\(286\) 2.20011 0.684179i 0.130095 0.0404564i
\(287\) 0.345330 0.345330i 0.0203842 0.0203842i
\(288\) 5.02127 15.4539i 0.295881 0.910629i
\(289\) 13.9953 + 9.65041i 0.823255 + 0.567671i
\(290\) −0.0399097 0.0289961i −0.00234358 0.00170271i
\(291\) −40.6757 20.7253i −2.38445 1.21494i
\(292\) 0.445829 5.66479i 0.0260901 0.331507i
\(293\) 6.64169 9.14151i 0.388012 0.534053i −0.569673 0.821872i \(-0.692930\pi\)
0.957685 + 0.287819i \(0.0929301\pi\)
\(294\) −7.04417 29.3411i −0.410825 1.71121i
\(295\) −0.377936 4.80213i −0.0220043 0.279591i
\(296\) −0.825171 1.99214i −0.0479621 0.115791i
\(297\) 3.78389 + 3.31553i 0.219563 + 0.192387i
\(298\) 5.68025 + 5.68025i 0.329048 + 0.329048i
\(299\) −2.19976 + 0.173125i −0.127215 + 0.0100121i
\(300\) 4.35923 7.11361i 0.251680 0.410705i
\(301\) −1.83616 + 1.12520i −0.105834 + 0.0648554i
\(302\) −17.7760 + 5.77577i −1.02289 + 0.332358i
\(303\) 1.11577 14.1772i 0.0640991 0.814457i
\(304\) 0.0725117 0.0114847i 0.00415883 0.000658694i
\(305\) 8.18737 5.94847i 0.468807 0.340608i
\(306\) 14.9423 + 20.0422i 0.854193 + 1.14574i
\(307\) 18.8755 1.07728 0.538641 0.842536i \(-0.318938\pi\)
0.538641 + 0.842536i \(0.318938\pi\)
\(308\) 0.367508 0.419423i 0.0209407 0.0238988i
\(309\) −1.59732 0.661631i −0.0908683 0.0376389i
\(310\) −14.6432 4.75787i −0.831679 0.270229i
\(311\) 6.98715 + 29.1036i 0.396205 + 1.65031i 0.712516 + 0.701656i \(0.247556\pi\)
−0.316311 + 0.948656i \(0.602444\pi\)
\(312\) −1.99246 0.478346i −0.112801 0.0270810i
\(313\) 9.14291 7.80879i 0.516788 0.441379i −0.352408 0.935847i \(-0.614637\pi\)
0.869196 + 0.494468i \(0.164637\pi\)
\(314\) −13.9182 + 27.3160i −0.785450 + 1.54153i
\(315\) 0.120631 + 0.761634i 0.00679679 + 0.0429132i
\(316\) 3.85348 + 2.36141i 0.216775 + 0.132840i
\(317\) 1.01011 + 12.8347i 0.0567337 + 0.720870i 0.957846 + 0.287283i \(0.0927521\pi\)
−0.901112 + 0.433586i \(0.857248\pi\)
\(318\) 13.4162 32.3895i 0.752342 1.81631i
\(319\) 0.0570308 + 0.0685127i 0.00319311 + 0.00383597i
\(320\) 2.32471 + 0.962925i 0.129955 + 0.0538291i
\(321\) −15.6655 30.7453i −0.874363 1.71603i
\(322\) −1.44741 + 1.05160i −0.0806608 + 0.0586035i
\(323\) −0.0269373 + 0.0545180i −0.00149883 + 0.00303346i
\(324\) −1.80897 5.56742i −0.100498 0.309301i
\(325\) −1.39977 0.713220i −0.0776454 0.0395623i
\(326\) 4.53561 + 7.40145i 0.251204 + 0.409928i
\(327\) 16.2454 + 22.3599i 0.898372 + 1.23650i
\(328\) 3.64661 + 3.11450i 0.201351 + 0.171970i
\(329\) 0.977342 0.404828i 0.0538826 0.0223189i
\(330\) 11.1896 10.9097i 0.615965 0.600558i
\(331\) −1.42328 1.42328i −0.0782307 0.0782307i 0.666909 0.745139i \(-0.267617\pi\)
−0.745139 + 0.666909i \(0.767617\pi\)
\(332\) −2.68796 + 1.36958i −0.147521 + 0.0751657i
\(333\) 3.40307 + 2.08541i 0.186487 + 0.114280i
\(334\) −25.3995 6.09788i −1.38980 0.333661i
\(335\) −1.05697 0.0831855i −0.0577485 0.00454491i
\(336\) −2.40115 + 0.780181i −0.130993 + 0.0425623i
\(337\) −10.3060 16.8179i −0.561406 0.916131i −0.999849 0.0173721i \(-0.994470\pi\)
0.438443 0.898759i \(-0.355530\pi\)
\(338\) −3.38913 + 21.3981i −0.184344 + 1.16390i
\(339\) −7.94344 + 24.4474i −0.431429 + 1.32780i
\(340\) 3.22743 2.03289i 0.175032 0.110249i
\(341\) 23.5366 + 14.8365i 1.27458 + 0.803442i
\(342\) −0.0632319 + 0.0632319i −0.00341919 + 0.00341919i
\(343\) −1.79128 + 2.09731i −0.0967198 + 0.113244i
\(344\) −12.4296 17.1079i −0.670160 0.922396i
\(345\) −12.7611 + 7.82002i −0.687035 + 0.421016i
\(346\) 22.7047 + 26.5838i 1.22061 + 1.42915i
\(347\) −15.9323 + 13.6075i −0.855291 + 0.730488i −0.964656 0.263514i \(-0.915119\pi\)
0.109364 + 0.994002i \(0.465119\pi\)
\(348\) 0.00918673 + 0.0580027i 0.000492460 + 0.00310927i
\(349\) 12.9247 + 2.04708i 0.691845 + 0.109577i 0.492449 0.870341i \(-0.336102\pi\)
0.199396 + 0.979919i \(0.436102\pi\)
\(350\) −1.26985 + 0.0999395i −0.0678765 + 0.00534199i
\(351\) 0.576579 0.238827i 0.0307755 0.0127476i
\(352\) 12.0292 + 8.97467i 0.641159 + 0.478351i
\(353\) 17.3665i 0.924324i −0.886795 0.462162i \(-0.847074\pi\)
0.886795 0.462162i \(-0.152926\pi\)
\(354\) −12.4758 + 14.6073i −0.663082 + 0.776369i
\(355\) 1.00738 6.36033i 0.0534661 0.337571i
\(356\) 4.95472 + 3.59981i 0.262599 + 0.190790i
\(357\) 0.621665 1.99667i 0.0329020 0.105675i
\(358\) −5.49009 16.8968i −0.290160 0.893022i
\(359\) −6.54950 + 1.03734i −0.345669 + 0.0547486i −0.326855 0.945074i \(-0.605989\pi\)
−0.0188139 + 0.999823i \(0.505989\pi\)
\(360\) −7.36296 + 1.76769i −0.388062 + 0.0931655i
\(361\) 18.0699 + 5.87126i 0.951046 + 0.309013i
\(362\) 11.1616 26.9466i 0.586642 1.41628i
\(363\) −24.4445 + 14.1408i −1.28300 + 0.742199i
\(364\) −0.0264726 0.0639106i −0.00138754 0.00334983i
\(365\) −6.46644 + 3.29481i −0.338469 + 0.172458i
\(366\) −39.8617 6.31348i −2.08361 0.330011i
\(367\) −3.32261 + 13.8397i −0.173439 + 0.722424i 0.816070 + 0.577953i \(0.196148\pi\)
−0.989509 + 0.144471i \(0.953852\pi\)
\(368\) −17.3384 20.3007i −0.903828 1.05825i
\(369\) −8.84921 0.696448i −0.460672 0.0362556i
\(370\) 1.19910 1.65042i 0.0623382 0.0858012i
\(371\) −1.55363 + 0.372994i −0.0806606 + 0.0193649i
\(372\) 8.32117 + 16.3312i 0.431433 + 0.846734i
\(373\) −15.0645 −0.780011 −0.390005 0.920813i \(-0.627527\pi\)
−0.390005 + 0.920813i \(0.627527\pi\)
\(374\) −21.9624 + 7.12770i −1.13565 + 0.368565i
\(375\) −24.6087 −1.27079
\(376\) 4.71598 + 9.25564i 0.243208 + 0.477323i
\(377\) 0.0107526 0.00258146i 0.000553785 0.000132952i
\(378\) 0.297427 0.409373i 0.0152980 0.0210559i
\(379\) 7.82494 + 0.615836i 0.401940 + 0.0316334i 0.277818 0.960634i \(-0.410389\pi\)
0.124122 + 0.992267i \(0.460389\pi\)
\(380\) 0.00886104 + 0.0103750i 0.000454562 + 0.000532224i
\(381\) 5.08584 21.1841i 0.260556 1.08529i
\(382\) −43.3942 6.87296i −2.22024 0.351651i
\(383\) 14.1849 7.22758i 0.724816 0.369312i −0.0523324 0.998630i \(-0.516666\pi\)
0.777148 + 0.629318i \(0.216666\pi\)
\(384\) −12.7316 30.7367i −0.649705 1.56853i
\(385\) −0.702001 0.120318i −0.0357773 0.00613198i
\(386\) −13.7482 + 33.1911i −0.699766 + 1.68938i
\(387\) 37.2260 + 12.0955i 1.89230 + 0.614847i
\(388\) 14.7157 3.53293i 0.747076 0.179357i
\(389\) 11.1239 1.76185i 0.564003 0.0893293i 0.132079 0.991239i \(-0.457835\pi\)
0.431924 + 0.901910i \(0.357835\pi\)
\(390\) −0.599062 1.84372i −0.0303347 0.0933606i
\(391\) 22.0219 2.00648i 1.11370 0.101472i
\(392\) −10.9251 7.93753i −0.551800 0.400906i
\(393\) −5.53159 + 34.9251i −0.279032 + 1.76174i
\(394\) −14.2189 + 16.6482i −0.716339 + 0.838726i
\(395\) 5.77227i 0.290434i
\(396\) −10.1350 0.128360i −0.509305 0.00645033i
\(397\) 0.529585 0.219361i 0.0265791 0.0110094i −0.369354 0.929289i \(-0.620421\pi\)
0.395933 + 0.918279i \(0.370421\pi\)
\(398\) −0.907570 + 0.0714273i −0.0454924 + 0.00358033i
\(399\) 0.00738826 + 0.00117019i 0.000369876 + 5.85826e-5i
\(400\) −2.97344 18.7736i −0.148672 0.938678i
\(401\) 3.90986 3.33933i 0.195249 0.166758i −0.546449 0.837492i \(-0.684021\pi\)
0.741698 + 0.670734i \(0.234021\pi\)
\(402\) 2.74599 + 3.21514i 0.136957 + 0.160356i
\(403\) 2.94277 1.80333i 0.146590 0.0898302i
\(404\) 2.77105 + 3.81402i 0.137865 + 0.189755i
\(405\) −4.85570 + 5.68529i −0.241282 + 0.282505i
\(406\) 0.00633991 0.00633991i 0.000314644 0.000314644i
\(407\) −2.83326 + 2.35844i −0.140440 + 0.116904i
\(408\) 20.0251 + 4.54738i 0.991389 + 0.225129i
\(409\) −6.53807 + 20.1221i −0.323287 + 0.994975i 0.648921 + 0.760856i \(0.275221\pi\)
−0.972208 + 0.234119i \(0.924779\pi\)
\(410\) −0.709756 + 4.48122i −0.0350524 + 0.221312i
\(411\) 28.4519 + 46.4293i 1.40343 + 2.29019i
\(412\) 0.545102 0.177114i 0.0268552 0.00872580i
\(413\) 0.872792 + 0.0686902i 0.0429473 + 0.00338003i
\(414\) 31.6199 + 7.59126i 1.55403 + 0.373090i
\(415\) 3.28524 + 2.01320i 0.161266 + 0.0988240i
\(416\) 1.65883 0.845218i 0.0813310 0.0414402i
\(417\) 33.4131 + 33.4131i 1.63625 + 1.63625i
\(418\) −0.0365620 0.0740609i −0.00178831 0.00362244i
\(419\) −6.84721 + 2.83621i −0.334508 + 0.138558i −0.543614 0.839335i \(-0.682945\pi\)
0.209106 + 0.977893i \(0.432945\pi\)
\(420\) −0.356788 0.304726i −0.0174095 0.0148691i
\(421\) 0.0803200 + 0.110551i 0.00391456 + 0.00538792i 0.810970 0.585088i \(-0.198940\pi\)
−0.807055 + 0.590476i \(0.798940\pi\)
\(422\) 9.73775 + 15.8906i 0.474026 + 0.773540i
\(423\) −17.1320 8.72918i −0.832986 0.424427i
\(424\) −4.84835 14.9217i −0.235457 0.724661i
\(425\) 14.1149 + 6.97418i 0.684674 + 0.338298i
\(426\) −20.7762 + 15.0948i −1.00661 + 0.731347i
\(427\) 0.835046 + 1.63887i 0.0404107 + 0.0793105i
\(428\) 10.5684 + 4.37756i 0.510841 + 0.211597i
\(429\) 0.230604 + 3.49553i 0.0111337 + 0.168766i
\(430\) 7.65616 18.4836i 0.369213 0.891359i
\(431\) 0.748734 + 9.51357i 0.0360653 + 0.458253i 0.988262 + 0.152768i \(0.0488186\pi\)
−0.952197 + 0.305485i \(0.901181\pi\)
\(432\) 6.43813 + 3.94529i 0.309754 + 0.189818i
\(433\) 1.93215 + 12.1991i 0.0928533 + 0.586253i 0.989615 + 0.143740i \(0.0459129\pi\)
−0.896762 + 0.442513i \(0.854087\pi\)
\(434\) 1.27044 2.49338i 0.0609831 0.119686i
\(435\) 0.0570340 0.0487116i 0.00273457 0.00233554i
\(436\) −8.90918 2.13891i −0.426673 0.102435i
\(437\) 0.0184655 + 0.0769142i 0.000883323 + 0.00367931i
\(438\) 27.5258 + 8.94367i 1.31523 + 0.427345i
\(439\) −16.9955 7.03977i −0.811152 0.335990i −0.0617383 0.998092i \(-0.519664\pi\)
−0.749413 + 0.662102i \(0.769664\pi\)
\(440\) 0.636988 6.96482i 0.0303672 0.332035i
\(441\) 24.9959 1.19028
\(442\) −0.413182 + 2.83434i −0.0196530 + 0.134816i
\(443\) 23.7303 17.2411i 1.12746 0.819148i 0.142137 0.989847i \(-0.454603\pi\)
0.985323 + 0.170699i \(0.0546026\pi\)
\(444\) −2.39863 + 0.379906i −0.113834 + 0.0180296i
\(445\) 0.613711 7.79794i 0.0290927 0.369658i
\(446\) −23.2424 + 7.55192i −1.10056 + 0.357594i
\(447\) −10.4139 + 6.38167i −0.492563 + 0.301843i
\(448\) −0.238954 + 0.389938i −0.0112895 + 0.0184228i
\(449\) −0.385546 + 0.0303431i −0.0181950 + 0.00143198i −0.0875533 0.996160i \(-0.527905\pi\)
0.0693583 + 0.997592i \(0.477905\pi\)
\(450\) 16.3710 + 16.3710i 0.771736 + 0.771736i
\(451\) 3.23317 7.53424i 0.152244 0.354774i
\(452\) −3.26108 7.87294i −0.153388 0.370312i
\(453\) −2.22966 28.3305i −0.104758 1.33108i
\(454\) −10.7611 44.8231i −0.505042 2.10365i
\(455\) −0.0519321 + 0.0714784i −0.00243461 + 0.00335096i
\(456\) −0.00576315 + 0.0732278i −0.000269884 + 0.00342921i
\(457\) −8.71659 4.44132i −0.407745 0.207756i 0.238074 0.971247i \(-0.423484\pi\)
−0.645819 + 0.763491i \(0.723484\pi\)
\(458\) 36.2028 + 26.3029i 1.69165 + 1.22905i
\(459\) −5.74829 + 2.46443i −0.268307 + 0.115030i
\(460\) 1.53320 4.71872i 0.0714861 0.220011i
\(461\) 13.3054 13.3054i 0.619696 0.619696i −0.325757 0.945453i \(-0.605619\pi\)
0.945453 + 0.325757i \(0.105619\pi\)
\(462\) 1.64029 + 2.31886i 0.0763132 + 0.107883i
\(463\) 35.2670i 1.63900i 0.573082 + 0.819498i \(0.305748\pi\)
−0.573082 + 0.819498i \(0.694252\pi\)
\(464\) 0.101736 + 0.0868911i 0.00472299 + 0.00403382i
\(465\) 12.2316 19.9601i 0.567226 0.925628i
\(466\) 8.23576 34.3044i 0.381514 1.58912i
\(467\) 14.7042 28.8586i 0.680428 1.33542i −0.249751 0.968310i \(-0.580349\pi\)
0.930179 0.367106i \(-0.119651\pi\)
\(468\) −0.570821 + 1.12030i −0.0263862 + 0.0517859i
\(469\) 0.0449849 0.187376i 0.00207721 0.00865220i
\(470\) −5.13503 + 8.37961i −0.236861 + 0.386523i
\(471\) −35.4445 30.2725i −1.63320 1.39488i
\(472\) 8.59699i 0.395708i
\(473\) −21.6186 + 28.9765i −0.994024 + 1.33234i
\(474\) −16.2772 + 16.2772i −0.747639 + 0.747639i
\(475\) −0.0174028 + 0.0535603i −0.000798494 + 0.00245751i
\(476\) 0.273169 + 0.637167i 0.0125207 + 0.0292045i
\(477\) 23.4947 + 17.0699i 1.07575 + 0.781578i
\(478\) −25.0284 12.7526i −1.14477 0.583290i
\(479\) −0.0997815 + 1.26784i −0.00455913 + 0.0579293i −0.998776 0.0494613i \(-0.984250\pi\)
0.994217 + 0.107391i \(0.0342495\pi\)
\(480\) 7.42246 10.2161i 0.338788 0.466301i
\(481\) 0.106753 + 0.444660i 0.00486753 + 0.0202747i
\(482\) −1.26910 16.1255i −0.0578061 0.734496i
\(483\) −1.04097 2.51313i −0.0473659 0.114351i
\(484\) 3.11751 8.82747i 0.141705 0.401248i
\(485\) −13.6677 13.6677i −0.620616 0.620616i
\(486\) 37.3848 2.94225i 1.69581 0.133463i
\(487\) −7.22846 + 11.7958i −0.327553 + 0.534518i −0.973448 0.228908i \(-0.926484\pi\)
0.645895 + 0.763426i \(0.276484\pi\)
\(488\) −15.4001 + 9.43720i −0.697130 + 0.427202i
\(489\) −12.5523 + 4.07850i −0.567636 + 0.184436i
\(490\) 1.00240 12.7367i 0.0452840 0.575388i
\(491\) −8.55786 + 1.35543i −0.386211 + 0.0611698i −0.346521 0.938042i \(-0.612637\pi\)
−0.0396899 + 0.999212i \(0.512637\pi\)
\(492\) 4.36960 3.17470i 0.196997 0.143127i
\(493\) −0.107431 + 0.0271961i −0.00483843 + 0.00122485i
\(494\) −0.0102457 −0.000460976
\(495\) 6.62370 + 11.1227i 0.297713 + 0.499926i
\(496\) 38.5794 + 15.9801i 1.73227 + 0.717528i
\(497\) 1.11312 + 0.361676i 0.0499304 + 0.0162234i
\(498\) −3.58704 14.9411i −0.160739 0.669526i
\(499\) −15.8527 3.80590i −0.709666 0.170376i −0.137486 0.990504i \(-0.543902\pi\)
−0.572180 + 0.820128i \(0.693902\pi\)
\(500\) 6.20340 5.29820i 0.277424 0.236943i
\(501\) 18.0305 35.3868i 0.805542 1.58096i
\(502\) 0.209365 + 1.32188i 0.00934444 + 0.0589984i
\(503\) −25.5374 15.6493i −1.13866 0.697769i −0.180375 0.983598i \(-0.557731\pi\)
−0.958281 + 0.285828i \(0.907731\pi\)
\(504\) −0.107979 1.37201i −0.00480979 0.0611141i
\(505\) 2.30422 5.56289i 0.102537 0.247545i
\(506\) −16.0163 + 25.4082i −0.712010 + 1.12953i
\(507\) −30.4325 12.6056i −1.35156 0.559832i
\(508\) 3.27883 + 6.43507i 0.145475 + 0.285510i
\(509\) 28.1091 20.4224i 1.24591 0.905209i 0.247936 0.968776i \(-0.420248\pi\)
0.997978 + 0.0635675i \(0.0202478\pi\)
\(510\) 6.23075 + 18.4016i 0.275902 + 0.814837i
\(511\) −0.407609 1.25449i −0.0180315 0.0554954i
\(512\) 2.86160 + 1.45806i 0.126466 + 0.0644376i
\(513\) −0.0116893 0.0190752i −0.000516095 0.000842191i
\(514\) 23.3500 + 32.1385i 1.02992 + 1.41757i
\(515\) −0.556642 0.475418i −0.0245286 0.0209494i
\(516\) −22.0036 + 9.11420i −0.968656 + 0.401230i
\(517\) 12.7157 12.3977i 0.559237 0.545248i
\(518\) 0.262180 + 0.262180i 0.0115195 + 0.0115195i
\(519\) −47.3608 + 24.1316i −2.07891 + 1.05926i
\(520\) −0.739737 0.453312i −0.0324396 0.0198790i
\(521\) −5.34186 1.28247i −0.234031 0.0561859i 0.114733 0.993396i \(-0.463399\pi\)
−0.348764 + 0.937210i \(0.613399\pi\)
\(522\) −0.162462 0.0127861i −0.00711079 0.000559631i
\(523\) 42.6367 13.8535i 1.86437 0.605772i 0.870936 0.491396i \(-0.163513\pi\)
0.993438 0.114376i \(-0.0364869\pi\)
\(524\) −6.12489 9.99491i −0.267567 0.436630i
\(525\) 0.302966 1.91285i 0.0132225 0.0834836i
\(526\) 13.7140 42.2074i 0.597960 1.84033i
\(527\) −29.2662 + 18.4342i −1.27485 + 0.803005i
\(528\) −32.5754 + 27.1161i −1.41766 + 1.18008i
\(529\) 4.07591 4.07591i 0.177214 0.177214i
\(530\) 9.64025 11.2873i 0.418746 0.490288i
\(531\) −9.35333 12.8738i −0.405900 0.558673i
\(532\) −0.00211438 + 0.00129569i −9.16700e−5 + 5.61755e-5i
\(533\) −0.660512 0.773360i −0.0286099 0.0334979i
\(534\) −23.7200 + 20.2588i −1.02647 + 0.876686i
\(535\) −2.28552 14.4302i −0.0988115 0.623871i
\(536\) 1.86894 + 0.296011i 0.0807260 + 0.0127857i
\(537\) 26.9292 2.11937i 1.16208 0.0914577i
\(538\) 2.54417 1.05383i 0.109687 0.0454337i
\(539\) −7.41174 + 21.8649i −0.319246 + 0.941786i
\(540\) 1.40329i 0.0603878i
\(541\) 2.27100 2.65900i 0.0976378 0.114319i −0.709436 0.704770i \(-0.751050\pi\)
0.807073 + 0.590451i \(0.201050\pi\)
\(542\) −3.69751 + 23.3451i −0.158822 + 1.00276i
\(543\) 35.8767 + 26.0659i 1.53962 + 1.11860i
\(544\) −16.5185 + 8.67460i −0.708224 + 0.371920i
\(545\) 3.61617 + 11.1294i 0.154900 + 0.476732i
\(546\) 0.348006 0.0551187i 0.0148933 0.00235886i
\(547\) −26.6328 + 6.39396i −1.13873 + 0.273386i −0.758607 0.651548i \(-0.774120\pi\)
−0.380127 + 0.924934i \(0.624120\pi\)
\(548\) −17.1683 5.57832i −0.733394 0.238294i
\(549\) 12.7938 30.8869i 0.546025 1.31822i
\(550\) −19.1746 + 9.46604i −0.817610 + 0.403633i
\(551\) −0.000151698 0 0.000366231i −6.46255e−6 0 1.56020e-5i
\(552\) 23.7999 12.1267i 1.01299 0.516145i
\(553\) 1.03620 + 0.164118i 0.0440637 + 0.00697900i
\(554\) 10.9267 45.5131i 0.464232 1.93366i
\(555\) 2.01441 + 2.35857i 0.0855070 + 0.100116i
\(556\) −15.6166 1.22905i −0.662291 0.0521234i
\(557\) 4.43702 6.10703i 0.188002 0.258763i −0.704603 0.709602i \(-0.748875\pi\)
0.892606 + 0.450838i \(0.148875\pi\)
\(558\) −49.4578 + 11.8738i −2.09371 + 0.502656i
\(559\) 2.03600 + 3.99587i 0.0861136 + 0.169007i
\(560\) −1.06897 −0.0451724
\(561\) −2.74247 34.9996i −0.115787 1.47768i
\(562\) 39.0621 1.64773
\(563\) 5.72829 + 11.2424i 0.241418 + 0.473810i 0.979644 0.200744i \(-0.0643359\pi\)
−0.738225 + 0.674554i \(0.764336\pi\)
\(564\) 11.3762 2.73118i 0.479024 0.115004i
\(565\) −6.39734 + 8.80519i −0.269138 + 0.370437i
\(566\) 5.25432 + 0.413524i 0.220855 + 0.0173817i
\(567\) −0.882529 1.03331i −0.0370627 0.0433949i
\(568\) −2.68297 + 11.1754i −0.112575 + 0.468909i
\(569\) 18.7319 + 2.96684i 0.785281 + 0.124376i 0.536183 0.844102i \(-0.319866\pi\)
0.249098 + 0.968478i \(0.419866\pi\)
\(570\) −0.0619199 + 0.0315498i −0.00259354 + 0.00132147i
\(571\) −6.75015 16.2963i −0.282485 0.681979i 0.717408 0.696654i \(-0.245329\pi\)
−0.999892 + 0.0146751i \(0.995329\pi\)
\(572\) −0.810711 0.831510i −0.0338975 0.0347672i
\(573\) 25.5634 61.7154i 1.06792 2.57820i
\(574\) −0.784260 0.254822i −0.0327344 0.0106360i
\(575\) 19.9134 4.78078i 0.830446 0.199372i
\(576\) 8.21004 1.30034i 0.342085 0.0541810i
\(577\) 0.905279 + 2.78616i 0.0376873 + 0.115989i 0.968130 0.250447i \(-0.0805776\pi\)
−0.930443 + 0.366437i \(0.880578\pi\)
\(578\) 3.79042 28.4533i 0.157661 1.18350i
\(579\) −44.1907 32.1064i −1.83650 1.33430i
\(580\) −0.00388969 + 0.0245586i −0.000161511 + 0.00101974i
\(581\) −0.454802 + 0.532505i −0.0188684 + 0.0220920i
\(582\) 77.0830i 3.19519i
\(583\) −21.8983 + 15.4902i −0.906937 + 0.641539i
\(584\) 11.9666 4.95673i 0.495182 0.205111i
\(585\) 1.60093 0.125996i 0.0661903 0.00520929i
\(586\) −18.8445 2.98467i −0.778458 0.123296i
\(587\) −3.26234 20.5976i −0.134651 0.850154i −0.958862 0.283872i \(-0.908381\pi\)
0.824211 0.566283i \(-0.191619\pi\)
\(588\) −11.5652 + 9.87759i −0.476940 + 0.407345i
\(589\) −0.0803515 0.0940795i −0.00331083 0.00387648i
\(590\) −6.93497 + 4.24976i −0.285508 + 0.174960i
\(591\) −19.5663 26.9307i −0.804849 1.10778i
\(592\) −3.59328 + 4.20719i −0.147683 + 0.172914i
\(593\) −14.6581 + 14.6581i −0.601935 + 0.601935i −0.940826 0.338890i \(-0.889948\pi\)
0.338890 + 0.940826i \(0.389948\pi\)
\(594\) 2.08753 8.23434i 0.0856522 0.337859i
\(595\) 0.511575 0.722684i 0.0209725 0.0296271i
\(596\) 1.25120 3.85080i 0.0512512 0.157735i
\(597\) 0.216531 1.36712i 0.00886203 0.0559527i
\(598\) 1.94672 + 3.17677i 0.0796075 + 0.129908i
\(599\) −2.84763 + 0.925250i −0.116351 + 0.0378047i −0.366614 0.930373i \(-0.619483\pi\)
0.250263 + 0.968178i \(0.419483\pi\)
\(600\) 18.9590 + 1.49210i 0.773996 + 0.0609148i
\(601\) 16.6371 + 3.99421i 0.678641 + 0.162927i 0.558091 0.829780i \(-0.311534\pi\)
0.120551 + 0.992707i \(0.461534\pi\)
\(602\) 3.10038 + 1.89991i 0.126362 + 0.0774347i
\(603\) −3.12074 + 1.59010i −0.127086 + 0.0647538i
\(604\) 6.66154 + 6.66154i 0.271054 + 0.271054i
\(605\) −11.6935 + 2.49593i −0.475408 + 0.101474i
\(606\) −22.1845 + 9.18912i −0.901184 + 0.373283i
\(607\) −4.26015 3.63851i −0.172914 0.147682i 0.558780 0.829316i \(-0.311270\pi\)
−0.731694 + 0.681634i \(0.761270\pi\)
\(608\) −0.0392284 0.0539932i −0.00159092 0.00218972i
\(609\) 0.00712279 + 0.0116233i 0.000288630 + 0.000471001i
\(610\) −15.2255 7.75778i −0.616462 0.314103i
\(611\) −0.680769 2.09519i −0.0275410 0.0847624i
\(612\) 5.58175 11.2968i 0.225629 0.456646i
\(613\) −27.5003 + 19.9801i −1.11072 + 0.806989i −0.982778 0.184792i \(-0.940839\pi\)
−0.127947 + 0.991781i \(0.540839\pi\)
\(614\) −14.4694 28.3977i −0.583936 1.14604i
\(615\) −6.37322 2.63988i −0.256993 0.106450i
\(616\) 1.23217 + 0.312373i 0.0496455 + 0.0125859i
\(617\) 3.76683 9.09392i 0.151647 0.366108i −0.829740 0.558150i \(-0.811511\pi\)
0.981387 + 0.192043i \(0.0615112\pi\)
\(618\) 0.229046 + 2.91031i 0.00921360 + 0.117070i
\(619\) 10.1521 + 6.22122i 0.408048 + 0.250052i 0.711344 0.702844i \(-0.248087\pi\)
−0.303296 + 0.952896i \(0.598087\pi\)
\(620\) 1.21402 + 7.66500i 0.0487561 + 0.307834i
\(621\) −3.69341 + 7.24872i −0.148211 + 0.290881i
\(622\) 38.4295 32.8219i 1.54088 1.31604i
\(623\) 1.38239 + 0.331881i 0.0553841 + 0.0132965i
\(624\) 1.22740 + 5.11247i 0.0491351 + 0.204663i
\(625\) 8.24836 + 2.68006i 0.329935 + 0.107202i
\(626\) −18.7568 7.76932i −0.749672 0.310524i
\(627\) 0.122470 0.0277670i 0.00489100 0.00110891i
\(628\) 15.4525 0.616622
\(629\) −1.12466 4.44266i −0.0448432 0.177141i
\(630\) 1.05339 0.765331i 0.0419680 0.0304915i
\(631\) −5.45658 + 0.864237i −0.217223 + 0.0344047i −0.264097 0.964496i \(-0.585074\pi\)
0.0468743 + 0.998901i \(0.485074\pi\)
\(632\) −0.808279 + 10.2702i −0.0321516 + 0.408525i
\(633\) −26.9492 + 8.75634i −1.07114 + 0.348033i
\(634\) 18.5352 11.3584i 0.736127 0.451099i
\(635\) 4.81967 7.86498i 0.191263 0.312112i
\(636\) −17.6161 + 1.38642i −0.698525 + 0.0549751i
\(637\) 2.02509 + 2.02509i 0.0802369 + 0.0802369i
\(638\) 0.0593576 0.138321i 0.00234999 0.00547618i
\(639\) −8.14090 19.6539i −0.322049 0.777495i
\(640\) −1.10520 14.0429i −0.0436868 0.555093i
\(641\) 10.3144 + 42.9624i 0.407393 + 1.69691i 0.678697 + 0.734419i \(0.262545\pi\)
−0.271304 + 0.962494i \(0.587455\pi\)
\(642\) −34.2468 + 47.1367i −1.35161 + 1.86034i
\(643\) 0.798143 10.1414i 0.0314757 0.399937i −0.960918 0.276833i \(-0.910715\pi\)
0.992394 0.123104i \(-0.0392848\pi\)
\(644\) 0.803481 + 0.409394i 0.0316616 + 0.0161324i
\(645\) 24.6091 + 17.8796i 0.968983 + 0.704007i
\(646\) 0.102670 0.00126517i 0.00403951 4.97776e-5i
\(647\) 10.7778 33.1706i 0.423718 1.30407i −0.480498 0.876996i \(-0.659544\pi\)
0.904216 0.427075i \(-0.140456\pi\)
\(648\) 9.43548 9.43548i 0.370661 0.370661i
\(649\) 14.0346 4.36442i 0.550907 0.171318i
\(650\) 2.65265i 0.104046i
\(651\) 3.23534 + 2.76324i 0.126803 + 0.108300i
\(652\) 2.28611 3.73060i 0.0895311 0.146102i
\(653\) 3.65949 15.2429i 0.143207 0.596500i −0.853896 0.520443i \(-0.825767\pi\)
0.997103 0.0760571i \(-0.0242331\pi\)
\(654\) 21.1866 41.5811i 0.828463 1.62595i
\(655\) −6.79703 + 13.3399i −0.265582 + 0.521234i
\(656\) 2.87258 11.9651i 0.112155 0.467160i
\(657\) −12.5269 + 20.4420i −0.488719 + 0.797517i
\(658\) −1.35825 1.16006i −0.0529502 0.0452238i
\(659\) 0.780281i 0.0303954i 0.999885 + 0.0151977i \(0.00483777\pi\)
−0.999885 + 0.0151977i \(0.995162\pi\)
\(660\) −7.46001 2.52879i −0.290381 0.0984331i
\(661\) 26.8920 26.8920i 1.04598 1.04598i 0.0470851 0.998891i \(-0.485007\pi\)
0.998891 0.0470851i \(-0.0149932\pi\)
\(662\) −1.05025 + 3.23234i −0.0408191 + 0.125628i
\(663\) −4.04369 1.61687i −0.157044 0.0627940i
\(664\) −5.56327 4.04195i −0.215897 0.156858i
\(665\) 0.00282201 + 0.00143788i 0.000109433 + 5.57587e-5i
\(666\) 0.528753 6.71844i 0.0204888 0.260334i
\(667\) −0.0847298 + 0.116621i −0.00328075 + 0.00451557i
\(668\) 3.07355 + 12.8023i 0.118919 + 0.495334i
\(669\) −2.91531 37.0426i −0.112713 1.43215i
\(670\) 0.685091 + 1.65396i 0.0264674 + 0.0638979i
\(671\) 23.2244 + 20.3498i 0.896569 + 0.785595i
\(672\) 1.62290 + 1.62290i 0.0626047 + 0.0626047i
\(673\) −48.0716 + 3.78331i −1.85302 + 0.145836i −0.955473 0.295077i \(-0.904655\pi\)
−0.897550 + 0.440913i \(0.854655\pi\)
\(674\) −17.4019 + 28.3973i −0.670295 + 1.09382i
\(675\) −4.93864 + 3.02640i −0.190088 + 0.116486i
\(676\) 10.3854 3.37443i 0.399439 0.129786i
\(677\) −0.356163 + 4.52549i −0.0136885 + 0.173929i 0.986273 + 0.165124i \(0.0528025\pi\)
−0.999961 + 0.00880426i \(0.997197\pi\)
\(678\) 42.8697 6.78989i 1.64640 0.260764i
\(679\) 2.84213 2.06493i 0.109071 0.0792446i
\(680\) 7.46874 + 4.45120i 0.286413 + 0.170696i
\(681\) 70.0870 2.68574
\(682\) 4.27871 46.7835i 0.163840 1.79143i
\(683\) 0.0916550 + 0.0379648i 0.00350708 + 0.00145268i 0.384436 0.923152i \(-0.374396\pi\)
−0.380929 + 0.924604i \(0.624396\pi\)
\(684\) 0.0428666 + 0.0139282i 0.00163905 + 0.000532559i
\(685\) 5.38228 + 22.4188i 0.205646 + 0.856578i
\(686\) 4.52849 + 1.08719i 0.172899 + 0.0415093i
\(687\) −51.7365 + 44.1872i −1.97387 + 1.68585i
\(688\) −24.6336 + 48.3462i −0.939147 + 1.84318i
\(689\) 0.520518 + 3.28642i 0.0198302 + 0.125203i
\(690\) 21.5473 + 13.2042i 0.820291 + 0.502675i
\(691\) 1.14632 + 14.5654i 0.0436082 + 0.554095i 0.979452 + 0.201679i \(0.0646397\pi\)
−0.935844 + 0.352416i \(0.885360\pi\)
\(692\) 6.74331 16.2798i 0.256342 0.618865i
\(693\) −2.18499 + 0.872802i −0.0830010 + 0.0331550i
\(694\) 32.6853 + 13.5387i 1.24072 + 0.513922i
\(695\) 9.08308 + 17.8265i 0.344541 + 0.676200i
\(696\) −0.108297 + 0.0786825i −0.00410499 + 0.00298245i
\(697\) 6.71435 + 7.66812i 0.254324 + 0.290451i
\(698\) −6.82791 21.0142i −0.258440 0.795398i
\(699\) 47.7932 + 24.3519i 1.80771 + 0.921072i
\(700\) 0.335460 + 0.547421i 0.0126792 + 0.0206906i
\(701\) −7.32590 10.0832i −0.276695 0.380839i 0.647940 0.761691i \(-0.275631\pi\)
−0.924636 + 0.380852i \(0.875631\pi\)
\(702\) −0.801296 0.684372i −0.0302430 0.0258299i
\(703\) 0.0151451 0.00627329i 0.000571207 0.000236602i
\(704\) −1.29697 + 7.56723i −0.0488814 + 0.285201i
\(705\) −10.5660 10.5660i −0.397938 0.397938i
\(706\) −26.1274 + 13.3126i −0.983319 + 0.501026i
\(707\) 0.933099 + 0.571804i 0.0350928 + 0.0215049i
\(708\) 9.41494 + 2.26033i 0.353835 + 0.0849483i
\(709\) 32.4207 + 2.55156i 1.21758 + 0.0958259i 0.670922 0.741528i \(-0.265898\pi\)
0.546661 + 0.837354i \(0.315898\pi\)
\(710\) −10.3412 + 3.36005i −0.388098 + 0.126101i
\(711\) −9.96333 16.2587i −0.373654 0.609748i
\(712\) −2.18386 + 13.7883i −0.0818436 + 0.516740i
\(713\) −13.9030 + 42.7891i −0.520672 + 1.60246i
\(714\) −3.48049 + 0.595307i −0.130254 + 0.0222788i
\(715\) −0.364492 + 1.43776i −0.0136312 + 0.0537690i
\(716\) −6.33205 + 6.33205i −0.236640 + 0.236640i
\(717\) 27.7372 32.4761i 1.03587 1.21284i
\(718\) 6.58129 + 9.05837i 0.245612 + 0.338055i
\(719\) −4.98416 + 3.05430i −0.185878 + 0.113906i −0.612324 0.790607i \(-0.709765\pi\)
0.426446 + 0.904513i \(0.359765\pi\)
\(720\) 12.6185 + 14.7744i 0.470263 + 0.550608i
\(721\) 0.101170 0.0864077i 0.00376778 0.00321799i
\(722\) −5.01863 31.6864i −0.186774 1.17924i
\(723\) 24.2907 + 3.84728i 0.903382 + 0.143082i
\(724\) −14.6558 + 1.15344i −0.544678 + 0.0428671i
\(725\) −0.0948187 + 0.0392752i −0.00352148 + 0.00145864i
\(726\) 40.0128 + 25.9362i 1.48501 + 0.962583i
\(727\) 26.5958i 0.986385i 0.869920 + 0.493192i \(0.164170\pi\)
−0.869920 + 0.493192i \(0.835830\pi\)
\(728\) 0.102408 0.119904i 0.00379549 0.00444394i
\(729\) −5.69137 + 35.9339i −0.210792 + 1.33089i
\(730\) 9.91393 + 7.20289i 0.366931 + 0.266591i
\(731\) −20.8958 39.7905i −0.772858 1.47170i
\(732\) 6.28609 + 19.3466i 0.232340 + 0.715071i
\(733\) −15.8375 + 2.50841i −0.584971 + 0.0926503i −0.441903 0.897063i \(-0.645697\pi\)
−0.143068 + 0.989713i \(0.545697\pi\)
\(734\) 23.3684 5.61026i 0.862544 0.207078i
\(735\) 18.4745 + 6.00273i 0.681442 + 0.221414i
\(736\) −9.28750 + 22.4220i −0.342342 + 0.826486i
\(737\) −0.465562 3.20133i −0.0171492 0.117923i
\(738\) 5.73574 + 13.8473i 0.211135 + 0.509726i
\(739\) −27.5888 + 14.0572i −1.01487 + 0.517103i −0.880610 0.473843i \(-0.842867\pi\)
−0.134263 + 0.990946i \(0.542867\pi\)
\(740\) −1.01559 0.160854i −0.0373339 0.00591310i
\(741\) 0.00363659 0.0151475i 0.000133593 0.000556457i
\(742\) 1.75213 + 2.05148i 0.0643226 + 0.0753120i
\(743\) 41.8203 + 3.29133i 1.53424 + 0.120747i 0.817227 0.576316i \(-0.195510\pi\)
0.717010 + 0.697063i \(0.245510\pi\)
\(744\) −24.5577 + 33.8008i −0.900329 + 1.23920i
\(745\) −5.02847 + 1.20723i −0.184229 + 0.0442294i
\(746\) 11.5480 + 22.6642i 0.422801 + 0.829794i
\(747\) 12.7284 0.465708
\(748\) 8.22665 + 8.23229i 0.300796 + 0.301002i
\(749\) 2.65539 0.0970260
\(750\) 18.8643 + 37.0232i 0.688825 + 1.35190i
\(751\) −33.6721 + 8.08395i −1.22871 + 0.294987i −0.795304 0.606211i \(-0.792689\pi\)
−0.433407 + 0.901198i \(0.642689\pi\)
\(752\) 15.6670 21.5638i 0.571318 0.786351i
\(753\) −2.02861 0.159655i −0.0739267 0.00581815i
\(754\) −0.0121263 0.0141981i −0.000441614 0.000517064i
\(755\) 2.80889 11.6999i 0.102226 0.425801i
\(756\) −0.251909 0.0398984i −0.00916183 0.00145109i
\(757\) 10.4832 5.34146i 0.381018 0.194139i −0.252983 0.967471i \(-0.581412\pi\)
0.634001 + 0.773332i \(0.281412\pi\)
\(758\) −5.07184 12.2445i −0.184217 0.444740i
\(759\) −31.8793 32.6971i −1.15714 1.18683i
\(760\) −0.0119018 + 0.0287334i −0.000431722 + 0.00104227i
\(761\) −31.8389 10.3451i −1.15416 0.375009i −0.331450 0.943473i \(-0.607538\pi\)
−0.822708 + 0.568464i \(0.807538\pi\)
\(762\) −35.7695 + 8.58750i −1.29579 + 0.311092i
\(763\) −2.10069 + 0.332717i −0.0760502 + 0.0120452i
\(764\) 6.84314 + 21.0610i 0.247576 + 0.761961i
\(765\) −16.0270 + 1.46027i −0.579459 + 0.0527961i
\(766\) −21.7474 15.8004i −0.785766 0.570893i
\(767\) 0.285214 1.80077i 0.0102985 0.0650220i
\(768\) −28.7638 + 33.6781i −1.03792 + 1.21525i
\(769\) 14.7283i 0.531116i 0.964095 + 0.265558i \(0.0855562\pi\)
−0.964095 + 0.265558i \(0.914444\pi\)
\(770\) 0.357116 + 1.14837i 0.0128696 + 0.0413845i
\(771\) −55.8021 + 23.1140i −2.00966 + 0.832429i
\(772\) 18.0521 1.42073i 0.649709 0.0511332i
\(773\) −30.9389 4.90024i −1.11280 0.176249i −0.427147 0.904182i \(-0.640481\pi\)
−0.685649 + 0.727933i \(0.740481\pi\)
\(774\) −10.3390 65.2776i −0.371626 2.34635i
\(775\) −24.3576 + 20.8033i −0.874949 + 0.747277i
\(776\) 22.4040 + 26.2317i 0.804255 + 0.941662i
\(777\) −0.480669 + 0.294555i −0.0172439 + 0.0105671i
\(778\) −11.1779 15.3850i −0.400746 0.551579i
\(779\) −0.0236778 + 0.0277231i −0.000848343 + 0.000993283i
\(780\) −0.690934 + 0.690934i −0.0247394 + 0.0247394i
\(781\) 19.6059 1.29342i 0.701556 0.0462823i
\(782\) −19.9000 31.5933i −0.711623 1.12978i
\(783\) 0.0125988 0.0387750i 0.000450243 0.00138571i
\(784\) −5.42053 + 34.2239i −0.193590 + 1.22228i
\(785\) −10.3120 16.8277i −0.368051 0.600605i
\(786\) 56.7843 18.4503i 2.02543 0.658102i
\(787\) −29.5646 2.32679i −1.05387 0.0829410i −0.460329 0.887748i \(-0.652269\pi\)
−0.593536 + 0.804807i \(0.702269\pi\)
\(788\) 10.7304 + 2.57614i 0.382255 + 0.0917712i
\(789\) 57.5328 + 35.2561i 2.04822 + 1.25515i
\(790\) −8.68423 + 4.42484i −0.308971 + 0.157429i
\(791\) −1.39876 1.39876i −0.0497342 0.0497342i
\(792\) −10.2276 20.7172i −0.363421 0.736154i
\(793\) 3.53888 1.46585i 0.125669 0.0520539i
\(794\) −0.735986 0.628592i −0.0261192 0.0223079i
\(795\) 13.2657 + 18.2586i 0.470485 + 0.647567i
\(796\) 0.239755 + 0.391245i 0.00849790 + 0.0138673i
\(797\) −5.30196 2.70148i −0.187805 0.0956915i 0.357560 0.933890i \(-0.383609\pi\)
−0.545365 + 0.838199i \(0.683609\pi\)
\(798\) −0.00390309 0.0120125i −0.000138168 0.000425237i
\(799\) 7.08058 + 20.9114i 0.250493 + 0.739794i
\(800\) −13.9791 + 10.1564i −0.494234 + 0.359082i
\(801\) −11.7311 23.0237i −0.414499 0.813501i
\(802\) −8.02111 3.32245i −0.283235 0.117320i
\(803\) −14.1669 17.0192i −0.499941 0.600593i
\(804\) 0.815559 1.96893i 0.0287626 0.0694389i
\(805\) −0.0903645 1.14819i −0.00318493 0.0404684i
\(806\) −4.96889 3.04494i −0.175022 0.107253i
\(807\) 0.654982 + 4.13539i 0.0230565 + 0.145573i
\(808\) −4.87869 + 9.57496i −0.171632 + 0.336846i
\(809\) 5.86886 5.01248i 0.206338 0.176229i −0.540274 0.841489i \(-0.681679\pi\)
0.746612 + 0.665260i \(0.231679\pi\)
\(810\) 12.2756 + 2.94711i 0.431321 + 0.103551i
\(811\) −5.48469 22.8454i −0.192594 0.802210i −0.982083 0.188446i \(-0.939655\pi\)
0.789490 0.613763i \(-0.210345\pi\)
\(812\) −0.00429800 0.00139650i −0.000150830 4.90077e-5i
\(813\) −33.2016 13.7525i −1.16443 0.482323i
\(814\) 5.72010 + 2.45467i 0.200489 + 0.0860360i
\(815\) −5.58821 −0.195746
\(816\) −12.9308 51.0795i −0.452668 1.78814i
\(817\) 0.130061 0.0944951i 0.00455027 0.00330597i
\(818\) 35.2851 5.58861i 1.23371 0.195401i
\(819\) −0.0228999 + 0.290971i −0.000800187 + 0.0101673i
\(820\) 2.17493 0.706677i 0.0759518 0.0246782i
\(821\) −34.1107 + 20.9031i −1.19047 + 0.729522i −0.969340 0.245722i \(-0.920975\pi\)
−0.221131 + 0.975244i \(0.570975\pi\)
\(822\) 48.0414 78.3964i 1.67563 2.73439i
\(823\) −50.4013 + 3.96667i −1.75688 + 0.138269i −0.915537 0.402234i \(-0.868234\pi\)
−0.841342 + 0.540504i \(0.818234\pi\)
\(824\) 0.923820 + 0.923820i 0.0321828 + 0.0321828i
\(825\) −7.18900 31.7081i −0.250289 1.10393i
\(826\) −0.565712 1.36575i −0.0196836 0.0475205i
\(827\) 1.94380 + 24.6983i 0.0675926 + 0.858845i 0.933485 + 0.358616i \(0.116751\pi\)
−0.865893 + 0.500230i \(0.833249\pi\)
\(828\) −3.82627 15.9376i −0.132972 0.553869i
\(829\) −17.9998 + 24.7746i −0.625160 + 0.860459i −0.997716 0.0675507i \(-0.978482\pi\)
0.372556 + 0.928010i \(0.378482\pi\)
\(830\) 0.510445 6.48581i 0.0177178 0.225126i
\(831\) 63.4092 + 32.3086i 2.19964 + 1.12077i
\(832\) 0.770502 + 0.559803i 0.0267124 + 0.0194077i
\(833\) −20.5431 20.0429i −0.711775 0.694447i
\(834\) 24.6558 75.8826i 0.853759 2.62760i
\(835\) 11.8905 11.8905i 0.411487 0.411487i
\(836\) −0.0248943 + 0.0333672i −0.000860988 + 0.00115403i
\(837\) 12.7249i 0.439838i
\(838\) 9.51586 + 8.12731i 0.328720 + 0.280753i
\(839\) 21.3948 34.9131i 0.738629 1.20533i −0.233834 0.972276i \(-0.575127\pi\)
0.972463 0.233056i \(-0.0748727\pi\)
\(840\) 0.249679 1.03999i 0.00861473 0.0358829i
\(841\) −13.1654 + 25.8385i −0.453979 + 0.890984i
\(842\) 0.104750 0.205584i 0.00360994 0.00708490i
\(843\) −13.8646 + 57.7502i −0.477522 + 1.98902i
\(844\) 4.90818 8.00942i 0.168947 0.275696i
\(845\) −10.6053 9.05777i −0.364833 0.311597i
\(846\) 32.4662i 1.11621i
\(847\) −0.115583 2.17010i −0.00397148 0.0745656i
\(848\) −28.4668 + 28.4668i −0.977554 + 0.977554i
\(849\) −2.47632 + 7.62132i −0.0849870 + 0.261563i
\(850\) −0.327558 26.5817i −0.0112352 0.911745i
\(851\) −4.82271 3.50390i −0.165320 0.120112i
\(852\) 11.5333 + 5.87649i 0.395123 + 0.201325i
\(853\) 1.38443 17.5909i 0.0474020 0.602299i −0.926643 0.375943i \(-0.877319\pi\)
0.974045 0.226356i \(-0.0726813\pi\)
\(854\) 1.82552 2.51261i 0.0624680 0.0859798i
\(855\) −0.0134387 0.0559763i −0.000459595 0.00191435i
\(856\) 2.04582 + 25.9946i 0.0699246 + 0.888476i
\(857\) 7.81972 + 18.8785i 0.267117 + 0.644877i 0.999345 0.0361823i \(-0.0115197\pi\)
−0.732229 + 0.681059i \(0.761520\pi\)
\(858\) 5.08217 3.02650i 0.173502 0.103323i
\(859\) −11.3157 11.3157i −0.386088 0.386088i 0.487202 0.873289i \(-0.338018\pi\)
−0.873289 + 0.487202i \(0.838018\pi\)
\(860\) −10.0529 + 0.791183i −0.342802 + 0.0269791i
\(861\) 0.655097 1.06902i 0.0223257 0.0364322i
\(862\) 13.7390 8.41925i 0.467951 0.286761i
\(863\) 37.5160 12.1897i 1.27706 0.414942i 0.409516 0.912303i \(-0.365698\pi\)
0.867544 + 0.497361i \(0.165698\pi\)
\(864\) 0.538556 6.84300i 0.0183220 0.232804i
\(865\) −22.2286 + 3.52067i −0.755797 + 0.119706i
\(866\) 16.8722 12.2583i 0.573339 0.416555i
\(867\) 40.7207 + 15.7030i 1.38295 + 0.533302i
\(868\) −1.41049 −0.0478751
\(869\) 17.1764 3.89431i 0.582670 0.132105i
\(870\) −0.117006 0.0484654i −0.00396687 0.00164313i
\(871\) −0.381658 0.124008i −0.0129320 0.00420186i
\(872\) −4.87554 20.3081i −0.165107 0.687718i
\(873\) −62.0888 14.9062i −2.10139 0.504498i
\(874\) 0.101560 0.0867408i 0.00343533 0.00293405i
\(875\) 0.859740 1.68734i 0.0290645 0.0570423i
\(876\) −2.28207 14.4084i −0.0771038 0.486814i
\(877\) −4.01923 2.46299i −0.135720 0.0831691i 0.452981 0.891520i \(-0.350360\pi\)
−0.588701 + 0.808351i \(0.700360\pi\)
\(878\) 2.43706 + 30.9658i 0.0822468 + 1.04504i
\(879\) 11.1012 26.8007i 0.374435 0.903966i
\(880\) −16.6653 + 6.65702i −0.561788 + 0.224408i
\(881\) 19.3770 + 8.02620i 0.652826 + 0.270409i 0.684416 0.729091i \(-0.260057\pi\)
−0.0315901 + 0.999501i \(0.510057\pi\)
\(882\) −19.1610 37.6056i −0.645185 1.26625i
\(883\) 33.1096 24.0555i 1.11423 0.809533i 0.130902 0.991395i \(-0.458213\pi\)
0.983324 + 0.181863i \(0.0582126\pi\)
\(884\) 1.36745 0.463015i 0.0459922 0.0155729i
\(885\) −3.82145 11.7612i −0.128457 0.395349i
\(886\) −44.1297 22.4852i −1.48256 0.755404i
\(887\) −19.6755 32.1075i −0.660638 1.07806i −0.990955 0.134193i \(-0.957156\pi\)
0.330318 0.943870i \(-0.392844\pi\)
\(888\) −3.25382 4.47850i −0.109191 0.150289i
\(889\) 1.27484 + 1.08881i 0.0427567 + 0.0365176i
\(890\) −12.2023 + 5.05434i −0.409020 + 0.169422i
\(891\) −20.1935 10.6134i −0.676509 0.355561i
\(892\) 8.71008 + 8.71008i 0.291635 + 0.291635i
\(893\) −0.0703653 + 0.0358529i −0.00235468 + 0.00119977i
\(894\) 17.5841 + 10.7755i 0.588099 + 0.360388i
\(895\) 11.1212 + 2.66996i 0.371740 + 0.0892468i
\(896\) 2.55231 + 0.200871i 0.0852666 + 0.00671063i
\(897\) −5.38757 + 1.75053i −0.179886 + 0.0584484i
\(898\) 0.341197 + 0.556784i 0.0113859 + 0.0185801i
\(899\) 0.0352716 0.222696i 0.00117637 0.00742732i
\(900\) 3.60607 11.0983i 0.120202 0.369945i
\(901\) −5.62183 32.8683i −0.187290 1.09500i
\(902\) −13.8135 + 0.911292i −0.459940 + 0.0303427i
\(903\) −3.90931 + 3.90931i −0.130094 + 0.130094i
\(904\) 12.6153 14.7706i 0.419578 0.491263i
\(905\) 11.0364 + 15.1903i 0.366863 + 0.504943i
\(906\) −40.9133 + 25.0717i −1.35925 + 0.832951i
\(907\) 36.7787 + 43.0624i 1.22122 + 1.42986i 0.869628 + 0.493708i \(0.164359\pi\)
0.351590 + 0.936154i \(0.385641\pi\)
\(908\) −17.6676 + 15.0896i −0.586321 + 0.500765i
\(909\) −3.11164 19.6461i −0.103207 0.651622i
\(910\) 0.147347 + 0.0233375i 0.00488450 + 0.000773629i
\(911\) −15.1587 + 1.19302i −0.502231 + 0.0395264i −0.327045 0.945009i \(-0.606053\pi\)
−0.175186 + 0.984535i \(0.556053\pi\)
\(912\) 0.174130 0.0721271i 0.00576603 0.00238837i
\(913\) −3.77421 + 11.1340i −0.124908 + 0.368483i
\(914\) 16.5185i 0.546382i
\(915\) 16.8734 19.7562i 0.557817 0.653119i
\(916\) 3.52841 22.2775i 0.116582 0.736070i
\(917\) −2.20144 1.59944i −0.0726980 0.0528182i
\(918\) 8.11414 + 6.75900i 0.267806 + 0.223080i
\(919\) −4.33209 13.3328i −0.142902 0.439808i 0.853833 0.520547i \(-0.174272\pi\)
−0.996735 + 0.0807390i \(0.974272\pi\)
\(920\) 11.1704 1.76922i 0.368277 0.0583294i
\(921\) 47.1195 11.3124i 1.55264 0.372756i
\(922\) −30.2172 9.81817i −0.995151 0.323344i
\(923\) 0.932745 2.25185i 0.0307017 0.0741204i
\(924\) 0.666056 1.26727i 0.0219116 0.0416902i
\(925\) −1.62418 3.92112i −0.0534027 0.128926i
\(926\) 53.0583 27.0346i 1.74360 0.888411i
\(927\) −2.38849 0.378300i −0.0784483 0.0124250i
\(928\) 0.0283929 0.118265i 0.000932042 0.00388224i
\(929\) −16.2365 19.0104i −0.532701 0.623712i 0.427165 0.904174i \(-0.359512\pi\)
−0.959865 + 0.280462i \(0.909512\pi\)
\(930\) −39.4058 3.10131i −1.29217 0.101696i
\(931\) 0.0603444 0.0830570i 0.00197771 0.00272208i
\(932\) −17.2907 + 4.15113i −0.566375 + 0.135975i
\(933\) 34.8845 + 68.4647i 1.14207 + 2.24143i
\(934\) −54.6888 −1.78947
\(935\) 3.47496 14.4525i 0.113643 0.472646i
\(936\) −2.86605 −0.0936799
\(937\) −5.09326 9.99609i −0.166390 0.326558i 0.792723 0.609582i \(-0.208663\pi\)
−0.959113 + 0.283024i \(0.908663\pi\)
\(938\) −0.316386 + 0.0759575i −0.0103304 + 0.00248010i
\(939\) 18.1438 24.9728i 0.592101 0.814957i
\(940\) 4.93832 + 0.388654i 0.161070 + 0.0126765i
\(941\) −26.7271 31.2934i −0.871278 1.02014i −0.999597 0.0284025i \(-0.990958\pi\)
0.128319 0.991733i \(-0.459042\pi\)
\(942\) −18.3735 + 76.5313i −0.598642 + 2.49352i
\(943\) 13.0946 + 2.07399i 0.426420 + 0.0675383i
\(944\) 19.6548 10.0146i 0.639710 0.325949i
\(945\) 0.124659 + 0.300952i 0.00405514 + 0.00978998i
\(946\) 60.1666 + 10.3121i 1.95618 + 0.335277i
\(947\) 12.9172 31.1848i 0.419752 1.01337i −0.562668 0.826683i \(-0.690225\pi\)
0.982419 0.186687i \(-0.0597750\pi\)
\(948\) 11.0348 + 3.58542i 0.358393 + 0.116449i
\(949\) −2.67103 + 0.641258i −0.0867054 + 0.0208161i
\(950\) 0.0939205 0.0148755i 0.00304718 0.000482626i
\(951\) 10.2136 + 31.4344i 0.331200 + 1.01933i
\(952\) −1.01140 + 1.21418i −0.0327797 + 0.0393518i
\(953\) 33.1125 + 24.0577i 1.07262 + 0.779304i 0.976381 0.216054i \(-0.0693187\pi\)
0.0962389 + 0.995358i \(0.469319\pi\)
\(954\) 7.67095 48.4325i 0.248356 1.56806i
\(955\) 18.3687 21.5069i 0.594396 0.695948i
\(956\) 14.1584i 0.457915i
\(957\) 0.183429 + 0.136851i 0.00592940 + 0.00442376i
\(958\) 1.98393 0.821770i 0.0640978 0.0265502i
\(959\) −4.17750 + 0.328777i −0.134899 + 0.0106168i
\(960\) 6.38034 + 1.01055i 0.205925 + 0.0326152i
\(961\) −6.15918 38.8875i −0.198683 1.25444i
\(962\) 0.587146 0.501470i 0.0189303 0.0161680i
\(963\) −31.3451 36.7004i −1.01008 1.18265i
\(964\) −6.95155 + 4.25992i −0.223894 + 0.137203i
\(965\) −13.5940 18.7105i −0.437606 0.602313i
\(966\) −2.98297 + 3.49260i −0.0959753 + 0.112373i
\(967\) −17.8002 + 17.8002i −0.572416 + 0.572416i −0.932803 0.360387i \(-0.882645\pi\)
0.360387 + 0.932803i \(0.382645\pi\)
\(968\) 21.1548 2.80341i 0.679942 0.0901050i
\(969\) −0.0345711 + 0.152239i −0.00111058 + 0.00489062i
\(970\) −10.0855 + 31.0398i −0.323824 + 0.996629i
\(971\) −1.81217 + 11.4416i −0.0581553 + 0.367178i 0.941398 + 0.337297i \(0.109513\pi\)
−0.999553 + 0.0298808i \(0.990487\pi\)
\(972\) −9.87604 16.1162i −0.316774 0.516928i
\(973\) −3.45836 + 1.12369i −0.110870 + 0.0360238i
\(974\) 23.2876 + 1.83277i 0.746182 + 0.0587258i
\(975\) −3.92174 0.941527i −0.125596 0.0301530i
\(976\) 39.5154 + 24.2150i 1.26486 + 0.775105i
\(977\) 8.53071 4.34662i 0.272922 0.139061i −0.312174 0.950025i \(-0.601057\pi\)
0.585095 + 0.810965i \(0.301057\pi\)
\(978\) 15.7582 + 15.7582i 0.503892 + 0.503892i
\(979\) 23.6182 3.43474i 0.754841 0.109775i
\(980\) −5.94945 + 2.46434i −0.190048 + 0.0787205i
\(981\) 29.3957 + 25.1063i 0.938533 + 0.801583i
\(982\) 8.59940 + 11.8361i 0.274418 + 0.377704i
\(983\) 17.2317 + 28.1196i 0.549607 + 0.896877i 0.999992 + 0.00404228i \(0.00128670\pi\)
−0.450385 + 0.892834i \(0.648713\pi\)
\(984\) 10.9697 + 5.58936i 0.349702 + 0.178182i
\(985\) −4.35538 13.4045i −0.138774 0.427103i
\(986\) 0.123269 + 0.140779i 0.00392567 + 0.00448331i
\(987\) 2.19715 1.59632i 0.0699361 0.0508115i
\(988\) 0.00234450 + 0.00460135i 7.45886e−5 + 0.000146388i
\(989\) −54.0112 22.3722i −1.71745 0.711393i
\(990\) 11.6562 18.4915i 0.370460 0.587698i
\(991\) −14.7891 + 35.7041i −0.469792 + 1.13418i 0.494462 + 0.869199i \(0.335365\pi\)
−0.964254 + 0.264980i \(0.914635\pi\)
\(992\) −2.97836 37.8436i −0.0945630 1.20154i
\(993\) −4.40598 2.69999i −0.139820 0.0856816i
\(994\) −0.309153 1.95191i −0.00980574 0.0619110i
\(995\) 0.266066 0.522184i 0.00843486 0.0165543i
\(996\) −5.88923 + 5.02987i −0.186607 + 0.159378i
\(997\) 41.8417 + 10.0453i 1.32514 + 0.318138i 0.833432 0.552623i \(-0.186373\pi\)
0.491708 + 0.870760i \(0.336373\pi\)
\(998\) 6.42631 + 26.7675i 0.203421 + 0.847311i
\(999\) 1.60350 + 0.521007i 0.0507324 + 0.0164839i
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 187.2.r.a.9.4 256
11.5 even 5 inner 187.2.r.a.60.13 yes 256
17.2 even 8 inner 187.2.r.a.53.13 yes 256
187.104 even 40 inner 187.2.r.a.104.4 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.r.a.9.4 256 1.1 even 1 trivial
187.2.r.a.53.13 yes 256 17.2 even 8 inner
187.2.r.a.60.13 yes 256 11.5 even 5 inner
187.2.r.a.104.4 yes 256 187.104 even 40 inner