Properties

Label 231.2.j.a.169.1
Level $231$
Weight $2$
Character 231.169
Analytic conductor $1.845$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(64,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.j (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 169.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 231.169
Dual form 231.2.j.a.190.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-1.30902 + 0.951057i) q^{5} +(2.11803 - 1.53884i) q^{6} +(0.309017 + 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-1.30902 + 0.951057i) q^{5} +(2.11803 - 1.53884i) q^{6} +(0.309017 + 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.809017 - 0.587785i) q^{9} +4.23607 q^{10} +(-2.54508 - 2.12663i) q^{11} -4.85410 q^{12} +(-4.42705 - 3.21644i) q^{13} +(0.809017 - 2.48990i) q^{14} +(-0.500000 - 1.53884i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(2.42705 - 1.76336i) q^{17} +(0.809017 + 2.48990i) q^{18} +(1.23607 - 3.80423i) q^{19} +(-6.35410 - 4.61653i) q^{20} -1.00000 q^{21} +(2.11803 + 8.42075i) q^{22} -7.23607 q^{23} +(6.04508 + 4.39201i) q^{24} +(-0.736068 + 2.26538i) q^{25} +(4.42705 + 13.6251i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.92705 + 2.85317i) q^{28} +(0.927051 + 2.85317i) q^{29} +(-1.30902 + 4.02874i) q^{30} +(-0.190983 - 0.138757i) q^{31} +10.8541 q^{32} +(2.80902 - 1.76336i) q^{33} -7.85410 q^{34} +(-1.30902 - 0.951057i) q^{35} +(1.50000 - 4.61653i) q^{36} +(-2.61803 - 8.05748i) q^{37} +(-8.47214 + 6.15537i) q^{38} +(4.42705 - 3.21644i) q^{39} +(3.73607 + 11.4984i) q^{40} +(-0.954915 + 2.93893i) q^{41} +(2.11803 + 1.53884i) q^{42} -9.00000 q^{43} +(6.00000 - 14.9394i) q^{44} +1.61803 q^{45} +(15.3262 + 11.1352i) q^{46} +(3.11803 - 9.59632i) q^{47} +(-3.04508 - 9.37181i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(5.04508 - 3.66547i) q^{50} +(0.927051 + 2.85317i) q^{51} +(8.20820 - 25.2623i) q^{52} +(-3.30902 - 2.40414i) q^{53} -2.61803 q^{54} +(5.35410 + 0.363271i) q^{55} +7.47214 q^{56} +(3.23607 + 2.35114i) q^{57} +(2.42705 - 7.46969i) q^{58} +(3.89919 + 12.0005i) q^{59} +(6.35410 - 4.61653i) q^{60} +(5.42705 - 3.94298i) q^{61} +(0.190983 + 0.587785i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-7.04508 - 5.11855i) q^{64} +8.85410 q^{65} +(-8.66312 - 0.587785i) q^{66} -3.70820 q^{67} +(11.7812 + 8.55951i) q^{68} +(2.23607 - 6.88191i) q^{69} +(1.30902 + 4.02874i) q^{70} +(-9.89919 + 7.19218i) q^{71} +(-6.04508 + 4.39201i) q^{72} +(-1.19098 - 3.66547i) q^{73} +(-6.85410 + 21.0948i) q^{74} +(-1.92705 - 1.40008i) q^{75} +19.4164 q^{76} +(1.23607 - 3.07768i) q^{77} -14.3262 q^{78} +(-5.54508 - 4.02874i) q^{79} +(4.92705 - 15.1639i) q^{80} +(0.309017 + 0.951057i) q^{81} +(6.54508 - 4.75528i) q^{82} +(-2.38197 + 1.73060i) q^{83} +(-1.50000 - 4.61653i) q^{84} +(-1.50000 + 4.61653i) q^{85} +(19.0623 + 13.8496i) q^{86} -3.00000 q^{87} +(-20.9894 + 13.1760i) q^{88} +2.67376 q^{89} +(-3.42705 - 2.48990i) q^{90} +(1.69098 - 5.20431i) q^{91} +(-10.8541 - 33.4055i) q^{92} +(0.190983 - 0.138757i) q^{93} +(-21.3713 + 15.5272i) q^{94} +(2.00000 + 6.15537i) q^{95} +(-3.35410 + 10.3229i) q^{96} +(13.2812 + 9.64932i) q^{97} +2.61803 q^{98} +(0.809017 + 3.21644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + q^{3} + 6 q^{4} - 3 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + q^{3} + 6 q^{4} - 3 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9} + 8 q^{10} + q^{11} - 6 q^{12} - 11 q^{13} + q^{14} - 2 q^{15} - 14 q^{16} + 3 q^{17} + q^{18} - 4 q^{19} - 12 q^{20} - 4 q^{21} + 4 q^{22} - 20 q^{23} + 13 q^{24} + 6 q^{25} + 11 q^{26} + q^{27} - 9 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 30 q^{32} + 9 q^{33} - 18 q^{34} - 3 q^{35} + 6 q^{36} - 6 q^{37} - 16 q^{38} + 11 q^{39} + 6 q^{40} - 15 q^{41} + 4 q^{42} - 36 q^{43} + 24 q^{44} + 2 q^{45} + 30 q^{46} + 8 q^{47} - q^{48} - q^{49} + 9 q^{50} - 3 q^{51} + 6 q^{52} - 11 q^{53} - 6 q^{54} + 8 q^{55} + 12 q^{56} + 4 q^{57} + 3 q^{58} - 9 q^{59} + 12 q^{60} + 15 q^{61} + 3 q^{62} - q^{63} - 17 q^{64} + 22 q^{65} - 19 q^{66} + 12 q^{67} + 27 q^{68} + 3 q^{70} - 15 q^{71} - 13 q^{72} - 7 q^{73} - 14 q^{74} - q^{75} + 24 q^{76} - 4 q^{77} - 26 q^{78} - 11 q^{79} + 13 q^{80} - q^{81} + 15 q^{82} - 14 q^{83} - 6 q^{84} - 6 q^{85} + 36 q^{86} - 12 q^{87} - 37 q^{88} + 42 q^{89} - 7 q^{90} + 9 q^{91} - 30 q^{92} + 3 q^{93} - 43 q^{94} + 8 q^{95} + 33 q^{97} + 6 q^{98} + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11803 1.53884i −1.49768 1.08813i −0.971295 0.237877i \(-0.923549\pi\)
−0.526381 0.850249i \(-0.676451\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) 1.50000 + 4.61653i 0.750000 + 2.30826i
\(5\) −1.30902 + 0.951057i −0.585410 + 0.425325i −0.840670 0.541547i \(-0.817839\pi\)
0.255260 + 0.966872i \(0.417839\pi\)
\(6\) 2.11803 1.53884i 0.864684 0.628230i
\(7\) 0.309017 + 0.951057i 0.116797 + 0.359466i
\(8\) 2.30902 7.10642i 0.816361 2.51250i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 4.23607 1.33956
\(11\) −2.54508 2.12663i −0.767372 0.641202i
\(12\) −4.85410 −1.40126
\(13\) −4.42705 3.21644i −1.22784 0.892080i −0.231116 0.972926i \(-0.574238\pi\)
−0.996727 + 0.0808459i \(0.974238\pi\)
\(14\) 0.809017 2.48990i 0.216219 0.665453i
\(15\) −0.500000 1.53884i −0.129099 0.397327i
\(16\) −7.97214 + 5.79210i −1.99303 + 1.44802i
\(17\) 2.42705 1.76336i 0.588646 0.427677i −0.253185 0.967418i \(-0.581478\pi\)
0.841831 + 0.539741i \(0.181478\pi\)
\(18\) 0.809017 + 2.48990i 0.190687 + 0.586875i
\(19\) 1.23607 3.80423i 0.283573 0.872749i −0.703249 0.710943i \(-0.748268\pi\)
0.986823 0.161806i \(-0.0517318\pi\)
\(20\) −6.35410 4.61653i −1.42082 1.03229i
\(21\) −1.00000 −0.218218
\(22\) 2.11803 + 8.42075i 0.451566 + 1.79531i
\(23\) −7.23607 −1.50882 −0.754412 0.656401i \(-0.772078\pi\)
−0.754412 + 0.656401i \(0.772078\pi\)
\(24\) 6.04508 + 4.39201i 1.23395 + 0.896516i
\(25\) −0.736068 + 2.26538i −0.147214 + 0.453077i
\(26\) 4.42705 + 13.6251i 0.868216 + 2.67209i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) −3.92705 + 2.85317i −0.742143 + 0.539198i
\(29\) 0.927051 + 2.85317i 0.172149 + 0.529820i 0.999492 0.0318771i \(-0.0101485\pi\)
−0.827343 + 0.561697i \(0.810149\pi\)
\(30\) −1.30902 + 4.02874i −0.238993 + 0.735544i
\(31\) −0.190983 0.138757i −0.0343016 0.0249215i 0.570502 0.821296i \(-0.306749\pi\)
−0.604804 + 0.796374i \(0.706749\pi\)
\(32\) 10.8541 1.91875
\(33\) 2.80902 1.76336i 0.488987 0.306961i
\(34\) −7.85410 −1.34697
\(35\) −1.30902 0.951057i −0.221264 0.160758i
\(36\) 1.50000 4.61653i 0.250000 0.769421i
\(37\) −2.61803 8.05748i −0.430402 1.32464i −0.897726 0.440555i \(-0.854782\pi\)
0.467323 0.884086i \(-0.345218\pi\)
\(38\) −8.47214 + 6.15537i −1.37436 + 0.998532i
\(39\) 4.42705 3.21644i 0.708896 0.515043i
\(40\) 3.73607 + 11.4984i 0.590724 + 1.81806i
\(41\) −0.954915 + 2.93893i −0.149133 + 0.458983i −0.997519 0.0703940i \(-0.977574\pi\)
0.848387 + 0.529377i \(0.177574\pi\)
\(42\) 2.11803 + 1.53884i 0.326820 + 0.237448i
\(43\) −9.00000 −1.37249 −0.686244 0.727372i \(-0.740742\pi\)
−0.686244 + 0.727372i \(0.740742\pi\)
\(44\) 6.00000 14.9394i 0.904534 2.25220i
\(45\) 1.61803 0.241202
\(46\) 15.3262 + 11.1352i 2.25973 + 1.64179i
\(47\) 3.11803 9.59632i 0.454812 1.39977i −0.416544 0.909116i \(-0.636759\pi\)
0.871356 0.490652i \(-0.163241\pi\)
\(48\) −3.04508 9.37181i −0.439520 1.35270i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 5.04508 3.66547i 0.713483 0.518376i
\(51\) 0.927051 + 2.85317i 0.129813 + 0.399524i
\(52\) 8.20820 25.2623i 1.13827 3.50324i
\(53\) −3.30902 2.40414i −0.454528 0.330234i 0.336853 0.941557i \(-0.390638\pi\)
−0.791381 + 0.611323i \(0.790638\pi\)
\(54\) −2.61803 −0.356269
\(55\) 5.35410 + 0.363271i 0.721947 + 0.0489835i
\(56\) 7.47214 0.998506
\(57\) 3.23607 + 2.35114i 0.428628 + 0.311416i
\(58\) 2.42705 7.46969i 0.318687 0.980819i
\(59\) 3.89919 + 12.0005i 0.507631 + 1.56233i 0.796302 + 0.604899i \(0.206787\pi\)
−0.288671 + 0.957428i \(0.593213\pi\)
\(60\) 6.35410 4.61653i 0.820311 0.595991i
\(61\) 5.42705 3.94298i 0.694863 0.504847i −0.183392 0.983040i \(-0.558708\pi\)
0.878255 + 0.478193i \(0.158708\pi\)
\(62\) 0.190983 + 0.587785i 0.0242549 + 0.0746488i
\(63\) 0.309017 0.951057i 0.0389325 0.119822i
\(64\) −7.04508 5.11855i −0.880636 0.639819i
\(65\) 8.85410 1.09822
\(66\) −8.66312 0.587785i −1.06636 0.0723514i
\(67\) −3.70820 −0.453029 −0.226515 0.974008i \(-0.572733\pi\)
−0.226515 + 0.974008i \(0.572733\pi\)
\(68\) 11.7812 + 8.55951i 1.42867 + 1.03799i
\(69\) 2.23607 6.88191i 0.269191 0.828485i
\(70\) 1.30902 + 4.02874i 0.156457 + 0.481527i
\(71\) −9.89919 + 7.19218i −1.17482 + 0.853555i −0.991578 0.129513i \(-0.958658\pi\)
−0.183240 + 0.983068i \(0.558658\pi\)
\(72\) −6.04508 + 4.39201i −0.712420 + 0.517603i
\(73\) −1.19098 3.66547i −0.139394 0.429011i 0.856854 0.515560i \(-0.172416\pi\)
−0.996248 + 0.0865492i \(0.972416\pi\)
\(74\) −6.85410 + 21.0948i −0.796773 + 2.45222i
\(75\) −1.92705 1.40008i −0.222517 0.161668i
\(76\) 19.4164 2.22721
\(77\) 1.23607 3.07768i 0.140863 0.350735i
\(78\) −14.3262 −1.62213
\(79\) −5.54508 4.02874i −0.623871 0.453269i 0.230401 0.973096i \(-0.425996\pi\)
−0.854271 + 0.519827i \(0.825996\pi\)
\(80\) 4.92705 15.1639i 0.550861 1.69538i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 6.54508 4.75528i 0.722784 0.525133i
\(83\) −2.38197 + 1.73060i −0.261455 + 0.189958i −0.710788 0.703406i \(-0.751662\pi\)
0.449333 + 0.893364i \(0.351662\pi\)
\(84\) −1.50000 4.61653i −0.163663 0.503704i
\(85\) −1.50000 + 4.61653i −0.162698 + 0.500732i
\(86\) 19.0623 + 13.8496i 2.05554 + 1.49344i
\(87\) −3.00000 −0.321634
\(88\) −20.9894 + 13.1760i −2.23747 + 1.40457i
\(89\) 2.67376 0.283418 0.141709 0.989908i \(-0.454740\pi\)
0.141709 + 0.989908i \(0.454740\pi\)
\(90\) −3.42705 2.48990i −0.361243 0.262458i
\(91\) 1.69098 5.20431i 0.177263 0.545560i
\(92\) −10.8541 33.4055i −1.13162 3.48276i
\(93\) 0.190983 0.138757i 0.0198040 0.0143885i
\(94\) −21.3713 + 15.5272i −2.20428 + 1.60151i
\(95\) 2.00000 + 6.15537i 0.205196 + 0.631527i
\(96\) −3.35410 + 10.3229i −0.342327 + 1.05357i
\(97\) 13.2812 + 9.64932i 1.34850 + 0.979740i 0.999085 + 0.0427710i \(0.0136186\pi\)
0.349412 + 0.936969i \(0.386381\pi\)
\(98\) 2.61803 0.264461
\(99\) 0.809017 + 3.21644i 0.0813093 + 0.323264i
\(100\) −11.5623 −1.15623
\(101\) −2.61803 1.90211i −0.260504 0.189267i 0.449865 0.893096i \(-0.351472\pi\)
−0.710369 + 0.703829i \(0.751472\pi\)
\(102\) 2.42705 7.46969i 0.240314 0.739610i
\(103\) 3.78115 + 11.6372i 0.372568 + 1.14665i 0.945105 + 0.326768i \(0.105959\pi\)
−0.572537 + 0.819879i \(0.694041\pi\)
\(104\) −33.0795 + 24.0337i −3.24371 + 2.35670i
\(105\) 1.30902 0.951057i 0.127747 0.0928136i
\(106\) 3.30902 + 10.1841i 0.321400 + 0.989168i
\(107\) −4.92705 + 15.1639i −0.476316 + 1.46595i 0.367859 + 0.929882i \(0.380091\pi\)
−0.844175 + 0.536068i \(0.819909\pi\)
\(108\) 3.92705 + 2.85317i 0.377881 + 0.274546i
\(109\) 0.437694 0.0419235 0.0209617 0.999780i \(-0.493327\pi\)
0.0209617 + 0.999780i \(0.493327\pi\)
\(110\) −10.7812 9.00854i −1.02794 0.858930i
\(111\) 8.47214 0.804140
\(112\) −7.97214 5.79210i −0.753296 0.547302i
\(113\) −0.454915 + 1.40008i −0.0427948 + 0.131709i −0.970171 0.242421i \(-0.922059\pi\)
0.927376 + 0.374130i \(0.122059\pi\)
\(114\) −3.23607 9.95959i −0.303086 0.932801i
\(115\) 9.47214 6.88191i 0.883281 0.641741i
\(116\) −11.7812 + 8.55951i −1.09385 + 0.794730i
\(117\) 1.69098 + 5.20431i 0.156331 + 0.481139i
\(118\) 10.2082 31.4176i 0.939741 2.89223i
\(119\) 2.42705 + 1.76336i 0.222487 + 0.161647i
\(120\) −12.0902 −1.10368
\(121\) 1.95492 + 10.8249i 0.177720 + 0.984081i
\(122\) −17.5623 −1.59002
\(123\) −2.50000 1.81636i −0.225417 0.163775i
\(124\) 0.354102 1.08981i 0.0317993 0.0978682i
\(125\) −3.69098 11.3597i −0.330132 1.01604i
\(126\) −2.11803 + 1.53884i −0.188689 + 0.137091i
\(127\) −5.30902 + 3.85723i −0.471099 + 0.342274i −0.797869 0.602830i \(-0.794040\pi\)
0.326770 + 0.945104i \(0.394040\pi\)
\(128\) 0.336881 + 1.03681i 0.0297764 + 0.0916422i
\(129\) 2.78115 8.55951i 0.244867 0.753623i
\(130\) −18.7533 13.6251i −1.64477 1.19500i
\(131\) −1.32624 −0.115874 −0.0579370 0.998320i \(-0.518452\pi\)
−0.0579370 + 0.998320i \(0.518452\pi\)
\(132\) 12.3541 + 10.3229i 1.07529 + 0.898490i
\(133\) 4.00000 0.346844
\(134\) 7.85410 + 5.70634i 0.678491 + 0.492953i
\(135\) −0.500000 + 1.53884i −0.0430331 + 0.132442i
\(136\) −6.92705 21.3193i −0.593990 1.82811i
\(137\) 8.47214 6.15537i 0.723823 0.525888i −0.163780 0.986497i \(-0.552369\pi\)
0.887603 + 0.460608i \(0.152369\pi\)
\(138\) −15.3262 + 11.1352i −1.30466 + 0.947888i
\(139\) −5.42705 16.7027i −0.460316 1.41671i −0.864778 0.502154i \(-0.832541\pi\)
0.404462 0.914555i \(-0.367459\pi\)
\(140\) 2.42705 7.46969i 0.205123 0.631304i
\(141\) 8.16312 + 5.93085i 0.687459 + 0.499468i
\(142\) 32.0344 2.68827
\(143\) 4.42705 + 17.6008i 0.370209 + 1.47185i
\(144\) 9.85410 0.821175
\(145\) −3.92705 2.85317i −0.326124 0.236943i
\(146\) −3.11803 + 9.59632i −0.258050 + 0.794197i
\(147\) −0.309017 0.951057i −0.0254873 0.0784418i
\(148\) 33.2705 24.1724i 2.73482 1.98696i
\(149\) 16.4443 11.9475i 1.34717 0.978774i 0.348020 0.937487i \(-0.386854\pi\)
0.999147 0.0412872i \(-0.0131458\pi\)
\(150\) 1.92705 + 5.93085i 0.157343 + 0.484252i
\(151\) −3.28115 + 10.0984i −0.267016 + 0.821792i 0.724206 + 0.689584i \(0.242207\pi\)
−0.991222 + 0.132208i \(0.957793\pi\)
\(152\) −24.1803 17.5680i −1.96128 1.42496i
\(153\) −3.00000 −0.242536
\(154\) −7.35410 + 4.61653i −0.592610 + 0.372010i
\(155\) 0.381966 0.0306802
\(156\) 21.4894 + 15.6129i 1.72053 + 1.25003i
\(157\) −4.98936 + 15.3557i −0.398194 + 1.22552i 0.528252 + 0.849088i \(0.322848\pi\)
−0.926446 + 0.376428i \(0.877152\pi\)
\(158\) 5.54508 + 17.0660i 0.441143 + 1.35770i
\(159\) 3.30902 2.40414i 0.262422 0.190661i
\(160\) −14.2082 + 10.3229i −1.12326 + 0.816094i
\(161\) −2.23607 6.88191i −0.176227 0.542370i
\(162\) 0.809017 2.48990i 0.0635624 0.195625i
\(163\) −9.82624 7.13918i −0.769650 0.559184i 0.132205 0.991222i \(-0.457794\pi\)
−0.901855 + 0.432039i \(0.857794\pi\)
\(164\) −15.0000 −1.17130
\(165\) −2.00000 + 4.97980i −0.155700 + 0.387677i
\(166\) 7.70820 0.598273
\(167\) −12.2082 8.86978i −0.944699 0.686364i 0.00484803 0.999988i \(-0.498457\pi\)
−0.949547 + 0.313624i \(0.898457\pi\)
\(168\) −2.30902 + 7.10642i −0.178145 + 0.548272i
\(169\) 5.23607 + 16.1150i 0.402774 + 1.23961i
\(170\) 10.2812 7.46969i 0.788528 0.572899i
\(171\) −3.23607 + 2.35114i −0.247468 + 0.179796i
\(172\) −13.5000 41.5487i −1.02937 3.16806i
\(173\) 3.89919 12.0005i 0.296450 0.912378i −0.686281 0.727337i \(-0.740758\pi\)
0.982731 0.185042i \(-0.0592421\pi\)
\(174\) 6.35410 + 4.61653i 0.481703 + 0.349978i
\(175\) −2.38197 −0.180060
\(176\) 32.6074 + 2.21238i 2.45787 + 0.166765i
\(177\) −12.6180 −0.948430
\(178\) −5.66312 4.11450i −0.424469 0.308395i
\(179\) 3.87132 11.9147i 0.289356 0.890547i −0.695703 0.718330i \(-0.744907\pi\)
0.985059 0.172217i \(-0.0550931\pi\)
\(180\) 2.42705 + 7.46969i 0.180902 + 0.556758i
\(181\) −6.28115 + 4.56352i −0.466874 + 0.339204i −0.796222 0.605005i \(-0.793171\pi\)
0.329348 + 0.944209i \(0.393171\pi\)
\(182\) −11.5902 + 8.42075i −0.859121 + 0.624188i
\(183\) 2.07295 + 6.37988i 0.153237 + 0.471614i
\(184\) −16.7082 + 51.4226i −1.23175 + 3.79092i
\(185\) 11.0902 + 8.05748i 0.815366 + 0.592398i
\(186\) −0.618034 −0.0453165
\(187\) −9.92705 0.673542i −0.725938 0.0492543i
\(188\) 48.9787 3.57214
\(189\) 0.809017 + 0.587785i 0.0588473 + 0.0427551i
\(190\) 5.23607 16.1150i 0.379864 1.16910i
\(191\) 5.10739 + 15.7189i 0.369558 + 1.13738i 0.947077 + 0.321005i \(0.104021\pi\)
−0.577520 + 0.816377i \(0.695979\pi\)
\(192\) 7.04508 5.11855i 0.508435 0.369400i
\(193\) 17.3262 12.5882i 1.24717 0.906122i 0.249116 0.968474i \(-0.419860\pi\)
0.998054 + 0.0623518i \(0.0198601\pi\)
\(194\) −13.2812 40.8752i −0.953531 2.93467i
\(195\) −2.73607 + 8.42075i −0.195934 + 0.603023i
\(196\) −3.92705 2.85317i −0.280504 0.203798i
\(197\) −2.18034 −0.155343 −0.0776714 0.996979i \(-0.524748\pi\)
−0.0776714 + 0.996979i \(0.524748\pi\)
\(198\) 3.23607 8.05748i 0.229977 0.572620i
\(199\) −11.5623 −0.819630 −0.409815 0.912169i \(-0.634407\pi\)
−0.409815 + 0.912169i \(0.634407\pi\)
\(200\) 14.3992 + 10.4616i 1.01818 + 0.739748i
\(201\) 1.14590 3.52671i 0.0808254 0.248755i
\(202\) 2.61803 + 8.05748i 0.184204 + 0.566922i
\(203\) −2.42705 + 1.76336i −0.170346 + 0.123763i
\(204\) −11.7812 + 8.55951i −0.824846 + 0.599285i
\(205\) −1.54508 4.75528i −0.107913 0.332123i
\(206\) 9.89919 30.4666i 0.689709 2.12271i
\(207\) 5.85410 + 4.25325i 0.406888 + 0.295622i
\(208\) 53.9230 3.73889
\(209\) −11.2361 + 7.05342i −0.777215 + 0.487895i
\(210\) −4.23607 −0.292316
\(211\) −11.0451 8.02472i −0.760375 0.552445i 0.138650 0.990341i \(-0.455724\pi\)
−0.899025 + 0.437897i \(0.855724\pi\)
\(212\) 6.13525 18.8824i 0.421371 1.29685i
\(213\) −3.78115 11.6372i −0.259080 0.797367i
\(214\) 33.7705 24.5357i 2.30850 1.67723i
\(215\) 11.7812 8.55951i 0.803468 0.583754i
\(216\) −2.30902 7.10642i −0.157109 0.483531i
\(217\) 0.0729490 0.224514i 0.00495210 0.0152410i
\(218\) −0.927051 0.673542i −0.0627878 0.0456180i
\(219\) 3.85410 0.260436
\(220\) 6.35410 + 25.2623i 0.428393 + 1.70318i
\(221\) −16.4164 −1.10429
\(222\) −17.9443 13.0373i −1.20434 0.875005i
\(223\) −4.69098 + 14.4374i −0.314131 + 0.966797i 0.661979 + 0.749522i \(0.269717\pi\)
−0.976110 + 0.217275i \(0.930283\pi\)
\(224\) 3.35410 + 10.3229i 0.224105 + 0.689725i
\(225\) 1.92705 1.40008i 0.128470 0.0933390i
\(226\) 3.11803 2.26538i 0.207409 0.150691i
\(227\) −0.190983 0.587785i −0.0126760 0.0390127i 0.944518 0.328458i \(-0.106529\pi\)
−0.957194 + 0.289446i \(0.906529\pi\)
\(228\) −6.00000 + 18.4661i −0.397360 + 1.22295i
\(229\) −22.7082 16.4985i −1.50060 1.09025i −0.970142 0.242539i \(-0.922020\pi\)
−0.530459 0.847711i \(-0.677980\pi\)
\(230\) −30.6525 −2.02116
\(231\) 2.54508 + 2.12663i 0.167454 + 0.139922i
\(232\) 22.4164 1.47171
\(233\) −3.57295 2.59590i −0.234072 0.170063i 0.464566 0.885538i \(-0.346210\pi\)
−0.698638 + 0.715475i \(0.746210\pi\)
\(234\) 4.42705 13.6251i 0.289405 0.890698i
\(235\) 5.04508 + 15.5272i 0.329105 + 1.01288i
\(236\) −49.5517 + 36.0014i −3.22554 + 2.34349i
\(237\) 5.54508 4.02874i 0.360192 0.261695i
\(238\) −2.42705 7.46969i −0.157322 0.484188i
\(239\) −0.118034 + 0.363271i −0.00763498 + 0.0234981i −0.954801 0.297244i \(-0.903932\pi\)
0.947166 + 0.320742i \(0.103932\pi\)
\(240\) 12.8992 + 9.37181i 0.832639 + 0.604948i
\(241\) −0.708204 −0.0456194 −0.0228097 0.999740i \(-0.507261\pi\)
−0.0228097 + 0.999740i \(0.507261\pi\)
\(242\) 12.5172 25.9358i 0.804637 1.66722i
\(243\) −1.00000 −0.0641500
\(244\) 26.3435 + 19.1396i 1.68647 + 1.22529i
\(245\) 0.500000 1.53884i 0.0319438 0.0983130i
\(246\) 2.50000 + 7.69421i 0.159394 + 0.490565i
\(247\) −17.7082 + 12.8658i −1.12675 + 0.818629i
\(248\) −1.42705 + 1.03681i −0.0906178 + 0.0658377i
\(249\) −0.909830 2.80017i −0.0576581 0.177453i
\(250\) −9.66312 + 29.7400i −0.611149 + 1.88092i
\(251\) 8.42705 + 6.12261i 0.531911 + 0.386456i 0.821072 0.570825i \(-0.193376\pi\)
−0.289161 + 0.957280i \(0.593376\pi\)
\(252\) 4.85410 0.305780
\(253\) 18.4164 + 15.3884i 1.15783 + 0.967462i
\(254\) 17.1803 1.07799
\(255\) −3.92705 2.85317i −0.245921 0.178672i
\(256\) −4.50000 + 13.8496i −0.281250 + 0.865598i
\(257\) −0.145898 0.449028i −0.00910087 0.0280096i 0.946403 0.322988i \(-0.104687\pi\)
−0.955504 + 0.294979i \(0.904687\pi\)
\(258\) −19.0623 + 13.8496i −1.18677 + 0.862237i
\(259\) 6.85410 4.97980i 0.425893 0.309430i
\(260\) 13.2812 + 40.8752i 0.823662 + 2.53497i
\(261\) 0.927051 2.85317i 0.0573830 0.176607i
\(262\) 2.80902 + 2.04087i 0.173542 + 0.126085i
\(263\) −15.0000 −0.924940 −0.462470 0.886635i \(-0.653037\pi\)
−0.462470 + 0.886635i \(0.653037\pi\)
\(264\) −6.04508 24.0337i −0.372049 1.47917i
\(265\) 6.61803 0.406543
\(266\) −8.47214 6.15537i −0.519460 0.377410i
\(267\) −0.826238 + 2.54290i −0.0505649 + 0.155623i
\(268\) −5.56231 17.1190i −0.339772 1.04571i
\(269\) 16.2812 11.8290i 0.992679 0.721224i 0.0321732 0.999482i \(-0.489757\pi\)
0.960506 + 0.278258i \(0.0897572\pi\)
\(270\) 3.42705 2.48990i 0.208564 0.151530i
\(271\) −5.21885 16.0620i −0.317022 0.975695i −0.974914 0.222582i \(-0.928552\pi\)
0.657892 0.753113i \(-0.271448\pi\)
\(272\) −9.13525 + 28.1154i −0.553906 + 1.70475i
\(273\) 4.42705 + 3.21644i 0.267937 + 0.194668i
\(274\) −27.4164 −1.65629
\(275\) 6.69098 4.20025i 0.403481 0.253285i
\(276\) 35.1246 2.11425
\(277\) 10.0902 + 7.33094i 0.606260 + 0.440473i 0.848095 0.529844i \(-0.177749\pi\)
−0.241836 + 0.970317i \(0.577749\pi\)
\(278\) −14.2082 + 43.7284i −0.852151 + 2.62265i
\(279\) 0.0729490 + 0.224514i 0.00436734 + 0.0134413i
\(280\) −9.78115 + 7.10642i −0.584536 + 0.424690i
\(281\) −9.30902 + 6.76340i −0.555329 + 0.403470i −0.829747 0.558140i \(-0.811515\pi\)
0.274417 + 0.961611i \(0.411515\pi\)
\(282\) −8.16312 25.1235i −0.486107 1.49608i
\(283\) −6.39919 + 19.6947i −0.380392 + 1.17073i 0.559376 + 0.828914i \(0.311041\pi\)
−0.939768 + 0.341813i \(0.888959\pi\)
\(284\) −48.0517 34.9116i −2.85134 2.07162i
\(285\) −6.47214 −0.383376
\(286\) 17.7082 44.0916i 1.04711 2.60719i
\(287\) −3.09017 −0.182407
\(288\) −8.78115 6.37988i −0.517434 0.375938i
\(289\) −2.47214 + 7.60845i −0.145420 + 0.447556i
\(290\) 3.92705 + 12.0862i 0.230604 + 0.709727i
\(291\) −13.2812 + 9.64932i −0.778555 + 0.565653i
\(292\) 15.1353 10.9964i 0.885724 0.643516i
\(293\) 0.201626 + 0.620541i 0.0117791 + 0.0362524i 0.956773 0.290835i \(-0.0939330\pi\)
−0.944994 + 0.327087i \(0.893933\pi\)
\(294\) −0.809017 + 2.48990i −0.0471828 + 0.145214i
\(295\) −16.5172 12.0005i −0.961670 0.698694i
\(296\) −63.3050 −3.67953
\(297\) −3.30902 0.224514i −0.192009 0.0130276i
\(298\) −53.2148 −3.08265
\(299\) 32.0344 + 23.2744i 1.85260 + 1.34599i
\(300\) 3.57295 10.9964i 0.206284 0.634878i
\(301\) −2.78115 8.55951i −0.160303 0.493362i
\(302\) 22.4894 16.3395i 1.29412 0.940231i
\(303\) 2.61803 1.90211i 0.150402 0.109274i
\(304\) 12.1803 + 37.4872i 0.698590 + 2.15004i
\(305\) −3.35410 + 10.3229i −0.192055 + 0.591085i
\(306\) 6.35410 + 4.61653i 0.363240 + 0.263909i
\(307\) −6.70820 −0.382857 −0.191429 0.981507i \(-0.561312\pi\)
−0.191429 + 0.981507i \(0.561312\pi\)
\(308\) 16.0623 + 1.08981i 0.915235 + 0.0620979i
\(309\) −12.2361 −0.696086
\(310\) −0.809017 0.587785i −0.0459491 0.0333840i
\(311\) 7.42705 22.8581i 0.421149 1.29616i −0.485484 0.874246i \(-0.661357\pi\)
0.906633 0.421919i \(-0.138643\pi\)
\(312\) −12.6353 38.8873i −0.715330 2.20156i
\(313\) 1.07295 0.779543i 0.0606467 0.0440624i −0.557049 0.830480i \(-0.688066\pi\)
0.617696 + 0.786417i \(0.288066\pi\)
\(314\) 34.1976 24.8460i 1.92988 1.40214i
\(315\) 0.500000 + 1.53884i 0.0281718 + 0.0867039i
\(316\) 10.2812 31.6421i 0.578360 1.78001i
\(317\) −11.5172 8.36775i −0.646872 0.469980i 0.215333 0.976541i \(-0.430916\pi\)
−0.862204 + 0.506561i \(0.830916\pi\)
\(318\) −10.7082 −0.600486
\(319\) 3.70820 9.23305i 0.207620 0.516952i
\(320\) 14.0902 0.787664
\(321\) −12.8992 9.37181i −0.719962 0.523083i
\(322\) −5.85410 + 18.0171i −0.326236 + 1.00405i
\(323\) −3.70820 11.4127i −0.206330 0.635018i
\(324\) −3.92705 + 2.85317i −0.218169 + 0.158509i
\(325\) 10.5451 7.66145i 0.584936 0.424981i
\(326\) 9.82624 + 30.2421i 0.544225 + 1.67495i
\(327\) −0.135255 + 0.416272i −0.00747961 + 0.0230199i
\(328\) 18.6803 + 13.5721i 1.03145 + 0.749392i
\(329\) 10.0902 0.556289
\(330\) 11.8992 7.46969i 0.655029 0.411193i
\(331\) 31.5410 1.73365 0.866826 0.498611i \(-0.166157\pi\)
0.866826 + 0.498611i \(0.166157\pi\)
\(332\) −11.5623 8.40051i −0.634564 0.461038i
\(333\) −2.61803 + 8.05748i −0.143467 + 0.441547i
\(334\) 12.2082 + 37.5730i 0.668003 + 2.05590i
\(335\) 4.85410 3.52671i 0.265208 0.192685i
\(336\) 7.97214 5.79210i 0.434916 0.315985i
\(337\) −0.0729490 0.224514i −0.00397379 0.0122301i 0.949050 0.315126i \(-0.102047\pi\)
−0.953024 + 0.302896i \(0.902047\pi\)
\(338\) 13.7082 42.1895i 0.745628 2.29481i
\(339\) −1.19098 0.865300i −0.0646853 0.0469966i
\(340\) −23.5623 −1.27785
\(341\) 0.190983 + 0.759299i 0.0103423 + 0.0411183i
\(342\) 10.4721 0.566268
\(343\) −0.809017 0.587785i −0.0436828 0.0317374i
\(344\) −20.7812 + 63.9578i −1.12044 + 3.44837i
\(345\) 3.61803 + 11.1352i 0.194788 + 0.599497i
\(346\) −26.7254 + 19.4172i −1.43677 + 1.04387i
\(347\) 19.3262 14.0413i 1.03749 0.753778i 0.0676934 0.997706i \(-0.478436\pi\)
0.969793 + 0.243928i \(0.0784360\pi\)
\(348\) −4.50000 13.8496i −0.241225 0.742415i
\(349\) 0.791796 2.43690i 0.0423839 0.130444i −0.927626 0.373512i \(-0.878154\pi\)
0.970009 + 0.243067i \(0.0781536\pi\)
\(350\) 5.04508 + 3.66547i 0.269671 + 0.195928i
\(351\) −5.47214 −0.292081
\(352\) −27.6246 23.0826i −1.47240 1.23031i
\(353\) 24.7082 1.31509 0.657543 0.753417i \(-0.271596\pi\)
0.657543 + 0.753417i \(0.271596\pi\)
\(354\) 26.7254 + 19.4172i 1.42044 + 1.03201i
\(355\) 6.11803 18.8294i 0.324712 0.999359i
\(356\) 4.01064 + 12.3435i 0.212564 + 0.654204i
\(357\) −2.42705 + 1.76336i −0.128453 + 0.0933267i
\(358\) −26.5344 + 19.2784i −1.40239 + 1.01890i
\(359\) 4.93769 + 15.1967i 0.260602 + 0.802049i 0.992674 + 0.120822i \(0.0385532\pi\)
−0.732073 + 0.681227i \(0.761447\pi\)
\(360\) 3.73607 11.4984i 0.196908 0.606021i
\(361\) 2.42705 + 1.76336i 0.127740 + 0.0928082i
\(362\) 20.3262 1.06832
\(363\) −10.8992 1.48584i −0.572059 0.0779864i
\(364\) 26.5623 1.39224
\(365\) 5.04508 + 3.66547i 0.264072 + 0.191859i
\(366\) 5.42705 16.7027i 0.283676 0.873066i
\(367\) −7.63525 23.4989i −0.398557 1.22663i −0.926157 0.377139i \(-0.876908\pi\)
0.527599 0.849493i \(-0.323092\pi\)
\(368\) 57.6869 41.9120i 3.00714 2.18481i
\(369\) 2.50000 1.81636i 0.130145 0.0945557i
\(370\) −11.0902 34.1320i −0.576550 1.77444i
\(371\) 1.26393 3.88998i 0.0656201 0.201958i
\(372\) 0.927051 + 0.673542i 0.0480654 + 0.0349215i
\(373\) −34.1803 −1.76979 −0.884895 0.465790i \(-0.845770\pi\)
−0.884895 + 0.465790i \(0.845770\pi\)
\(374\) 19.9894 + 16.7027i 1.03363 + 0.863678i
\(375\) 11.9443 0.616800
\(376\) −60.9959 44.3161i −3.14563 2.28543i
\(377\) 5.07295 15.6129i 0.261270 0.804107i
\(378\) −0.809017 2.48990i −0.0416113 0.128067i
\(379\) 9.54508 6.93491i 0.490298 0.356222i −0.315001 0.949091i \(-0.602005\pi\)
0.805299 + 0.592869i \(0.202005\pi\)
\(380\) −25.4164 + 18.4661i −1.30383 + 0.947291i
\(381\) −2.02786 6.24112i −0.103891 0.319742i
\(382\) 13.3713 41.1527i 0.684136 2.10556i
\(383\) 5.07295 + 3.68571i 0.259216 + 0.188331i 0.709801 0.704402i \(-0.248785\pi\)
−0.450586 + 0.892733i \(0.648785\pi\)
\(384\) −1.09017 −0.0556325
\(385\) 1.30902 + 5.20431i 0.0667137 + 0.265236i
\(386\) −56.0689 −2.85383
\(387\) 7.28115 + 5.29007i 0.370122 + 0.268909i
\(388\) −24.6246 + 75.7868i −1.25013 + 3.84749i
\(389\) −8.67376 26.6951i −0.439777 1.35350i −0.888111 0.459629i \(-0.847982\pi\)
0.448334 0.893866i \(-0.352018\pi\)
\(390\) 18.7533 13.6251i 0.949610 0.689932i
\(391\) −17.5623 + 12.7598i −0.888164 + 0.645289i
\(392\) 2.30902 + 7.10642i 0.116623 + 0.358929i
\(393\) 0.409830 1.26133i 0.0206732 0.0636255i
\(394\) 4.61803 + 3.35520i 0.232653 + 0.169032i
\(395\) 11.0902 0.558007
\(396\) −13.6353 + 8.55951i −0.685197 + 0.430131i
\(397\) 18.2705 0.916971 0.458485 0.888702i \(-0.348392\pi\)
0.458485 + 0.888702i \(0.348392\pi\)
\(398\) 24.4894 + 17.7926i 1.22754 + 0.891860i
\(399\) −1.23607 + 3.80423i −0.0618808 + 0.190450i
\(400\) −7.25329 22.3233i −0.362664 1.11617i
\(401\) −2.64590 + 1.92236i −0.132130 + 0.0959979i −0.651887 0.758316i \(-0.726022\pi\)
0.519757 + 0.854314i \(0.326022\pi\)
\(402\) −7.85410 + 5.70634i −0.391727 + 0.284606i
\(403\) 0.399187 + 1.22857i 0.0198849 + 0.0611995i
\(404\) 4.85410 14.9394i 0.241501 0.743262i
\(405\) −1.30902 0.951057i −0.0650456 0.0472584i
\(406\) 7.85410 0.389793
\(407\) −10.4721 + 26.0746i −0.519085 + 1.29247i
\(408\) 22.4164 1.10978
\(409\) −7.78115 5.65334i −0.384753 0.279540i 0.378549 0.925581i \(-0.376423\pi\)
−0.763302 + 0.646042i \(0.776423\pi\)
\(410\) −4.04508 + 12.4495i −0.199773 + 0.614837i
\(411\) 3.23607 + 9.95959i 0.159623 + 0.491271i
\(412\) −48.0517 + 34.9116i −2.36734 + 1.71997i
\(413\) −10.2082 + 7.41669i −0.502313 + 0.364952i
\(414\) −5.85410 18.0171i −0.287713 0.885491i
\(415\) 1.47214 4.53077i 0.0722643 0.222407i
\(416\) −48.0517 34.9116i −2.35593 1.71168i
\(417\) 17.5623 0.860030
\(418\) 34.6525 + 2.35114i 1.69491 + 0.114998i
\(419\) −13.3262 −0.651029 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(420\) 6.35410 + 4.61653i 0.310048 + 0.225263i
\(421\) 1.42705 4.39201i 0.0695502 0.214054i −0.910240 0.414081i \(-0.864103\pi\)
0.979790 + 0.200027i \(0.0641031\pi\)
\(422\) 11.0451 + 33.9933i 0.537666 + 1.65477i
\(423\) −8.16312 + 5.93085i −0.396904 + 0.288368i
\(424\) −24.7254 + 17.9641i −1.20077 + 0.872412i
\(425\) 2.20820 + 6.79615i 0.107114 + 0.329662i
\(426\) −9.89919 + 30.4666i −0.479617 + 1.47611i
\(427\) 5.42705 + 3.94298i 0.262633 + 0.190814i
\(428\) −77.3951 −3.74103
\(429\) −18.1074 1.22857i −0.874233 0.0593160i
\(430\) −38.1246 −1.83853
\(431\) −15.8713 11.5312i −0.764495 0.555438i 0.135791 0.990738i \(-0.456642\pi\)
−0.900286 + 0.435300i \(0.856642\pi\)
\(432\) −3.04508 + 9.37181i −0.146507 + 0.450901i
\(433\) 5.85410 + 18.0171i 0.281330 + 0.865845i 0.987475 + 0.157778i \(0.0504329\pi\)
−0.706144 + 0.708068i \(0.749567\pi\)
\(434\) −0.500000 + 0.363271i −0.0240008 + 0.0174376i
\(435\) 3.92705 2.85317i 0.188288 0.136799i
\(436\) 0.656541 + 2.02063i 0.0314426 + 0.0967704i
\(437\) −8.94427 + 27.5276i −0.427863 + 1.31683i
\(438\) −8.16312 5.93085i −0.390049 0.283387i
\(439\) 29.8328 1.42384 0.711921 0.702259i \(-0.247825\pi\)
0.711921 + 0.702259i \(0.247825\pi\)
\(440\) 14.9443 37.2097i 0.712440 1.77390i
\(441\) 1.00000 0.0476190
\(442\) 34.7705 + 25.2623i 1.65386 + 1.20160i
\(443\) 2.27051 6.98791i 0.107875 0.332006i −0.882519 0.470276i \(-0.844154\pi\)
0.990395 + 0.138270i \(0.0441543\pi\)
\(444\) 12.7082 + 39.1118i 0.603105 + 1.85617i
\(445\) −3.50000 + 2.54290i −0.165916 + 0.120545i
\(446\) 32.1525 23.3601i 1.52246 1.10613i
\(447\) 6.28115 + 19.3314i 0.297088 + 0.914344i
\(448\) 2.69098 8.28199i 0.127137 0.391287i
\(449\) −10.8992 7.91872i −0.514364 0.373708i 0.300112 0.953904i \(-0.402976\pi\)
−0.814477 + 0.580196i \(0.802976\pi\)
\(450\) −6.23607 −0.293971
\(451\) 8.68034 5.44907i 0.408741 0.256587i
\(452\) −7.14590 −0.336115
\(453\) −8.59017 6.24112i −0.403601 0.293234i
\(454\) −0.500000 + 1.53884i −0.0234662 + 0.0722214i
\(455\) 2.73607 + 8.42075i 0.128269 + 0.394771i
\(456\) 24.1803 17.5680i 1.13235 0.822699i
\(457\) 9.01722 6.55139i 0.421808 0.306461i −0.356557 0.934274i \(-0.616049\pi\)
0.778365 + 0.627812i \(0.216049\pi\)
\(458\) 22.7082 + 69.8887i 1.06108 + 3.26568i
\(459\) 0.927051 2.85317i 0.0432710 0.133175i
\(460\) 45.9787 + 33.4055i 2.14377 + 1.55754i
\(461\) 4.41641 0.205693 0.102846 0.994697i \(-0.467205\pi\)
0.102846 + 0.994697i \(0.467205\pi\)
\(462\) −2.11803 8.42075i −0.0985399 0.391769i
\(463\) 30.6869 1.42614 0.713071 0.701092i \(-0.247304\pi\)
0.713071 + 0.701092i \(0.247304\pi\)
\(464\) −23.9164 17.3763i −1.11029 0.806674i
\(465\) −0.118034 + 0.363271i −0.00547370 + 0.0168463i
\(466\) 3.57295 + 10.9964i 0.165514 + 0.509399i
\(467\) −22.3713 + 16.2537i −1.03522 + 0.752132i −0.969347 0.245696i \(-0.920984\pi\)
−0.0658743 + 0.997828i \(0.520984\pi\)
\(468\) −21.4894 + 15.6129i −0.993346 + 0.721708i
\(469\) −1.14590 3.52671i −0.0529127 0.162848i
\(470\) 13.2082 40.6507i 0.609249 1.87508i
\(471\) −13.0623 9.49032i −0.601879 0.437291i
\(472\) 94.2837 4.33976
\(473\) 22.9058 + 19.1396i 1.05321 + 0.880042i
\(474\) −17.9443 −0.824208
\(475\) 7.70820 + 5.60034i 0.353677 + 0.256961i
\(476\) −4.50000 + 13.8496i −0.206257 + 0.634794i
\(477\) 1.26393 + 3.88998i 0.0578715 + 0.178110i
\(478\) 0.809017 0.587785i 0.0370036 0.0268847i
\(479\) −3.78115 + 2.74717i −0.172765 + 0.125521i −0.670808 0.741631i \(-0.734052\pi\)
0.498042 + 0.867153i \(0.334052\pi\)
\(480\) −5.42705 16.7027i −0.247710 0.762373i
\(481\) −14.3262 + 44.0916i −0.653220 + 2.01041i
\(482\) 1.50000 + 1.08981i 0.0683231 + 0.0496397i
\(483\) 7.23607 0.329252
\(484\) −47.0410 + 25.2623i −2.13823 + 1.14828i
\(485\) −26.5623 −1.20613
\(486\) 2.11803 + 1.53884i 0.0960760 + 0.0698033i
\(487\) −6.57295 + 20.2295i −0.297849 + 0.916684i 0.684401 + 0.729106i \(0.260064\pi\)
−0.982250 + 0.187578i \(0.939936\pi\)
\(488\) −15.4894 47.6713i −0.701170 2.15798i
\(489\) 9.82624 7.13918i 0.444358 0.322845i
\(490\) −3.42705 + 2.48990i −0.154818 + 0.112482i
\(491\) −12.5623 38.6628i −0.566929 1.74483i −0.662150 0.749372i \(-0.730356\pi\)
0.0952207 0.995456i \(-0.469644\pi\)
\(492\) 4.63525 14.2658i 0.208973 0.643154i
\(493\) 7.28115 + 5.29007i 0.327927 + 0.238253i
\(494\) 57.3050 2.57827
\(495\) −4.11803 3.44095i −0.185092 0.154659i
\(496\) 2.32624 0.104451
\(497\) −9.89919 7.19218i −0.444039 0.322613i
\(498\) −2.38197 + 7.33094i −0.106738 + 0.328507i
\(499\) −1.54508 4.75528i −0.0691675 0.212876i 0.910498 0.413514i \(-0.135699\pi\)
−0.979665 + 0.200638i \(0.935699\pi\)
\(500\) 46.9058 34.0790i 2.09769 1.52406i
\(501\) 12.2082 8.86978i 0.545422 0.396273i
\(502\) −8.42705 25.9358i −0.376118 1.15757i
\(503\) 7.34346 22.6008i 0.327429 1.00772i −0.642904 0.765947i \(-0.722270\pi\)
0.970332 0.241775i \(-0.0777295\pi\)
\(504\) −6.04508 4.39201i −0.269269 0.195636i
\(505\) 5.23607 0.233002
\(506\) −15.3262 60.9331i −0.681334 2.70881i
\(507\) −16.9443 −0.752522
\(508\) −25.7705 18.7234i −1.14338 0.830715i
\(509\) 1.48936 4.58377i 0.0660146 0.203172i −0.912608 0.408835i \(-0.865935\pi\)
0.978623 + 0.205663i \(0.0659351\pi\)
\(510\) 3.92705 + 12.0862i 0.173893 + 0.535187i
\(511\) 3.11803 2.26538i 0.137934 0.100215i
\(512\) 32.6074 23.6907i 1.44106 1.04699i
\(513\) −1.23607 3.80423i −0.0545737 0.167961i
\(514\) −0.381966 + 1.17557i −0.0168478 + 0.0518522i
\(515\) −16.0172 11.6372i −0.705803 0.512796i
\(516\) 43.6869 1.92321
\(517\) −28.3435 + 17.7926i −1.24654 + 0.782516i
\(518\) −22.1803 −0.974548
\(519\) 10.2082 + 7.41669i 0.448090 + 0.325557i
\(520\) 20.4443 62.9210i 0.896541 2.75927i
\(521\) −7.83688 24.1194i −0.343340 1.05669i −0.962466 0.271401i \(-0.912513\pi\)
0.619126 0.785291i \(-0.287487\pi\)
\(522\) −6.35410 + 4.61653i −0.278111 + 0.202060i
\(523\) −6.13525 + 4.45752i −0.268276 + 0.194914i −0.713788 0.700362i \(-0.753022\pi\)
0.445512 + 0.895276i \(0.353022\pi\)
\(524\) −1.98936 6.12261i −0.0869055 0.267468i
\(525\) 0.736068 2.26538i 0.0321246 0.0988695i
\(526\) 31.7705 + 23.0826i 1.38526 + 1.00645i
\(527\) −0.708204 −0.0308498
\(528\) −12.1803 + 30.3278i −0.530081 + 1.31985i
\(529\) 29.3607 1.27655
\(530\) −14.0172 10.1841i −0.608869 0.442369i
\(531\) 3.89919 12.0005i 0.169210 0.520776i
\(532\) 6.00000 + 18.4661i 0.260133 + 0.800607i
\(533\) 13.6803 9.93935i 0.592561 0.430521i
\(534\) 5.66312 4.11450i 0.245067 0.178052i
\(535\) −7.97214 24.5357i −0.344665 1.06077i
\(536\) −8.56231 + 26.3521i −0.369835 + 1.13824i
\(537\) 10.1353 + 7.36369i 0.437369 + 0.317767i
\(538\) −52.6869 −2.27149
\(539\) 3.30902 + 0.224514i 0.142529 + 0.00967050i
\(540\) −7.85410 −0.337987
\(541\) −13.3090 9.66957i −0.572199 0.415727i 0.263704 0.964604i \(-0.415056\pi\)
−0.835903 + 0.548876i \(0.815056\pi\)
\(542\) −13.6631 + 42.0508i −0.586881 + 1.80623i
\(543\) −2.39919 7.38394i −0.102959 0.316875i
\(544\) 26.3435 19.1396i 1.12947 0.820605i
\(545\) −0.572949 + 0.416272i −0.0245424 + 0.0178311i
\(546\) −4.42705 13.6251i −0.189460 0.583099i
\(547\) 6.98278 21.4908i 0.298562 0.918880i −0.683440 0.730007i \(-0.739517\pi\)
0.982002 0.188872i \(-0.0604833\pi\)
\(548\) 41.1246 + 29.8788i 1.75676 + 1.27636i
\(549\) −6.70820 −0.286299
\(550\) −20.6353 1.40008i −0.879890 0.0596998i
\(551\) 12.0000 0.511217
\(552\) −43.7426 31.7809i −1.86181 1.35268i
\(553\) 2.11803 6.51864i 0.0900680 0.277201i
\(554\) −10.0902 31.0543i −0.428690 1.31937i
\(555\) −11.0902 + 8.05748i −0.470751 + 0.342021i
\(556\) 68.9681 50.1082i 2.92490 2.12506i
\(557\) 2.52786 + 7.77997i 0.107109 + 0.329648i 0.990220 0.139517i \(-0.0445550\pi\)
−0.883111 + 0.469165i \(0.844555\pi\)
\(558\) 0.190983 0.587785i 0.00808496 0.0248829i
\(559\) 39.8435 + 28.9480i 1.68520 + 1.22437i
\(560\) 15.9443 0.673768
\(561\) 3.70820 9.23305i 0.156560 0.389820i
\(562\) 30.1246 1.27073
\(563\) 14.8090 + 10.7594i 0.624126 + 0.453454i 0.854360 0.519681i \(-0.173949\pi\)
−0.230235 + 0.973135i \(0.573949\pi\)
\(564\) −15.1353 + 46.5815i −0.637309 + 1.96144i
\(565\) −0.736068 2.26538i −0.0309666 0.0953054i
\(566\) 43.8607 31.8666i 1.84360 1.33946i
\(567\) −0.809017 + 0.587785i −0.0339755 + 0.0246847i
\(568\) 28.2533 + 86.9547i 1.18548 + 3.64854i
\(569\) −3.54508 + 10.9106i −0.148618 + 0.457398i −0.997458 0.0712504i \(-0.977301\pi\)
0.848841 + 0.528649i \(0.177301\pi\)
\(570\) 13.7082 + 9.95959i 0.574173 + 0.417161i
\(571\) −22.8885 −0.957856 −0.478928 0.877854i \(-0.658974\pi\)
−0.478928 + 0.877854i \(0.658974\pi\)
\(572\) −74.6140 + 46.8388i −3.11977 + 1.95843i
\(573\) −16.5279 −0.690461
\(574\) 6.54508 + 4.75528i 0.273187 + 0.198482i
\(575\) 5.32624 16.3925i 0.222119 0.683613i
\(576\) 2.69098 + 8.28199i 0.112124 + 0.345083i
\(577\) 20.1074 14.6089i 0.837082 0.608175i −0.0844723 0.996426i \(-0.526920\pi\)
0.921554 + 0.388250i \(0.126920\pi\)
\(578\) 16.9443 12.3107i 0.704789 0.512059i
\(579\) 6.61803 + 20.3682i 0.275036 + 0.846474i
\(580\) 7.28115 22.4091i 0.302333 0.930487i
\(581\) −2.38197 1.73060i −0.0988206 0.0717974i
\(582\) 42.9787 1.78153
\(583\) 3.30902 + 13.1558i 0.137045 + 0.544857i
\(584\) −28.7984 −1.19169
\(585\) −7.16312 5.20431i −0.296159 0.215172i
\(586\) 0.527864 1.62460i 0.0218059 0.0671115i
\(587\) 1.85410 + 5.70634i 0.0765270 + 0.235526i 0.982001 0.188876i \(-0.0604844\pi\)
−0.905474 + 0.424402i \(0.860484\pi\)
\(588\) 3.92705 2.85317i 0.161949 0.117663i
\(589\) −0.763932 + 0.555029i −0.0314773 + 0.0228696i
\(590\) 16.5172 + 50.8348i 0.680003 + 2.09283i
\(591\) 0.673762 2.07363i 0.0277149 0.0852976i
\(592\) 67.5410 + 49.0714i 2.77592 + 2.01682i
\(593\) −26.3607 −1.08250 −0.541252 0.840861i \(-0.682049\pi\)
−0.541252 + 0.840861i \(0.682049\pi\)
\(594\) 6.66312 + 5.56758i 0.273391 + 0.228441i
\(595\) −4.85410 −0.198999
\(596\) 79.8222 + 57.9942i 3.26964 + 2.37554i
\(597\) 3.57295 10.9964i 0.146231 0.450053i
\(598\) −32.0344 98.5919i −1.30999 4.03172i
\(599\) −13.1074 + 9.52308i −0.535553 + 0.389102i −0.822431 0.568865i \(-0.807383\pi\)
0.286878 + 0.957967i \(0.407383\pi\)
\(600\) −14.3992 + 10.4616i −0.587844 + 0.427094i
\(601\) 4.29180 + 13.2088i 0.175066 + 0.538798i 0.999636 0.0269615i \(-0.00858315\pi\)
−0.824570 + 0.565759i \(0.808583\pi\)
\(602\) −7.28115 + 22.4091i −0.296758 + 0.913326i
\(603\) 3.00000 + 2.17963i 0.122169 + 0.0887613i
\(604\) −51.5410 −2.09717
\(605\) −12.8541 12.3107i −0.522594 0.500503i
\(606\) −8.47214 −0.344157
\(607\) −29.0066 21.0745i −1.17734 0.855388i −0.185471 0.982650i \(-0.559381\pi\)
−0.991869 + 0.127262i \(0.959381\pi\)
\(608\) 13.4164 41.2915i 0.544107 1.67459i
\(609\) −0.927051 2.85317i −0.0375660 0.115616i
\(610\) 22.9894 16.7027i 0.930812 0.676274i
\(611\) −44.6697 + 32.4544i −1.80714 + 1.31297i
\(612\) −4.50000 13.8496i −0.181902 0.559836i
\(613\) 4.93769 15.1967i 0.199432 0.613787i −0.800465 0.599380i \(-0.795414\pi\)
0.999896 0.0144073i \(-0.00458615\pi\)
\(614\) 14.2082 + 10.3229i 0.573396 + 0.416597i
\(615\) 5.00000 0.201619
\(616\) −19.0172 15.8904i −0.766226 0.640244i
\(617\) 13.7984 0.555502 0.277751 0.960653i \(-0.410411\pi\)
0.277751 + 0.960653i \(0.410411\pi\)
\(618\) 25.9164 + 18.8294i 1.04251 + 0.757428i
\(619\) 9.79837 30.1563i 0.393830 1.21208i −0.536039 0.844193i \(-0.680080\pi\)
0.929869 0.367891i \(-0.119920\pi\)
\(620\) 0.572949 + 1.76336i 0.0230102 + 0.0708181i
\(621\) −5.85410 + 4.25325i −0.234917 + 0.170677i
\(622\) −50.9058 + 36.9852i −2.04114 + 1.48297i
\(623\) 0.826238 + 2.54290i 0.0331025 + 0.101879i
\(624\) −16.6631 + 51.2838i −0.667059 + 2.05300i
\(625\) 6.00000 + 4.35926i 0.240000 + 0.174370i
\(626\) −3.47214 −0.138774
\(627\) −3.23607 12.8658i −0.129236 0.513809i
\(628\) −78.3738 −3.12746
\(629\) −20.5623 14.9394i −0.819873 0.595672i
\(630\) 1.30902 4.02874i 0.0521525 0.160509i
\(631\) −7.30902 22.4948i −0.290967 0.895505i −0.984546 0.175125i \(-0.943967\pi\)
0.693579 0.720381i \(-0.256033\pi\)
\(632\) −41.4336 + 30.1033i −1.64814 + 1.19744i
\(633\) 11.0451 8.02472i 0.439003 0.318954i
\(634\) 11.5172 + 35.4464i 0.457407 + 1.40775i
\(635\) 3.28115 10.0984i 0.130209 0.400741i
\(636\) 16.0623 + 11.6699i 0.636912 + 0.462744i
\(637\) 5.47214 0.216814
\(638\) −22.0623 + 13.8496i −0.873455 + 0.548310i
\(639\) 12.2361 0.484051
\(640\) −1.42705 1.03681i −0.0564091 0.0409836i
\(641\) −0.152476 + 0.469272i −0.00602243 + 0.0185351i −0.954023 0.299735i \(-0.903102\pi\)
0.948000 + 0.318270i \(0.103102\pi\)
\(642\) 12.8992 + 39.6996i 0.509090 + 1.56682i
\(643\) 25.8885 18.8091i 1.02094 0.741760i 0.0544682 0.998516i \(-0.482654\pi\)
0.966476 + 0.256756i \(0.0826536\pi\)
\(644\) 28.4164 20.6457i 1.11976 0.813556i
\(645\) 4.50000 + 13.8496i 0.177187 + 0.545327i
\(646\) −9.70820 + 29.8788i −0.381964 + 1.17556i
\(647\) 3.28115 + 2.38390i 0.128995 + 0.0937207i 0.650412 0.759582i \(-0.274596\pi\)
−0.521417 + 0.853302i \(0.674596\pi\)
\(648\) 7.47214 0.293533
\(649\) 15.5967 38.8343i 0.612226 1.52438i
\(650\) −34.1246 −1.33848
\(651\) 0.190983 + 0.138757i 0.00748521 + 0.00543833i
\(652\) 18.2188 56.0718i 0.713505 2.19594i
\(653\) 9.72542 + 29.9318i 0.380585 + 1.17132i 0.939633 + 0.342185i \(0.111167\pi\)
−0.559047 + 0.829136i \(0.688833\pi\)
\(654\) 0.927051 0.673542i 0.0362506 0.0263376i
\(655\) 1.73607 1.26133i 0.0678338 0.0492841i
\(656\) −9.40983 28.9605i −0.367392 1.13072i
\(657\) −1.19098 + 3.66547i −0.0464647 + 0.143004i
\(658\) −21.3713 15.5272i −0.833141 0.605312i
\(659\) −8.12461 −0.316490 −0.158245 0.987400i \(-0.550584\pi\)
−0.158245 + 0.987400i \(0.550584\pi\)
\(660\) −25.9894 1.76336i −1.01163 0.0686385i
\(661\) −18.4164 −0.716315 −0.358158 0.933661i \(-0.616595\pi\)
−0.358158 + 0.933661i \(0.616595\pi\)
\(662\) −66.8050 48.5366i −2.59645 1.88643i
\(663\) 5.07295 15.6129i 0.197017 0.606356i
\(664\) 6.79837 + 20.9232i 0.263828 + 0.811979i
\(665\) −5.23607 + 3.80423i −0.203046 + 0.147522i
\(666\) 17.9443 13.0373i 0.695326 0.505184i
\(667\) −6.70820 20.6457i −0.259743 0.799406i
\(668\) 22.6353 69.6642i 0.875784 2.69539i
\(669\) −12.2812 8.92278i −0.474817 0.344975i
\(670\) −15.7082 −0.606861
\(671\) −22.1976 1.50609i −0.856927 0.0581418i
\(672\) −10.8541 −0.418706
\(673\) 8.42705 + 6.12261i 0.324839 + 0.236009i 0.738238 0.674541i \(-0.235658\pi\)
−0.413399 + 0.910550i \(0.635658\pi\)
\(674\) −0.190983 + 0.587785i −0.00735639 + 0.0226406i
\(675\) 0.736068 + 2.26538i 0.0283313 + 0.0871947i
\(676\) −66.5410 + 48.3449i −2.55927 + 1.85942i
\(677\) −18.5344 + 13.4661i −0.712336 + 0.517543i −0.883927 0.467626i \(-0.845110\pi\)
0.171590 + 0.985168i \(0.445110\pi\)
\(678\) 1.19098 + 3.66547i 0.0457394 + 0.140771i
\(679\) −5.07295 + 15.6129i −0.194682 + 0.599169i
\(680\) 29.3435 + 21.3193i 1.12527 + 0.817557i
\(681\) 0.618034 0.0236831
\(682\) 0.763932 1.90211i 0.0292525 0.0728357i
\(683\) 0.347524 0.0132976 0.00664882 0.999978i \(-0.497884\pi\)
0.00664882 + 0.999978i \(0.497884\pi\)
\(684\) −15.7082 11.4127i −0.600618 0.436375i
\(685\) −5.23607 + 16.1150i −0.200060 + 0.615721i
\(686\) 0.809017 + 2.48990i 0.0308884 + 0.0950648i
\(687\) 22.7082 16.4985i 0.866372 0.629456i
\(688\) 71.7492 52.1289i 2.73541 1.98739i
\(689\) 6.91641 + 21.2865i 0.263494 + 0.810952i
\(690\) 9.47214 29.1522i 0.360598 1.10981i
\(691\) −3.78115 2.74717i −0.143842 0.104507i 0.513537 0.858067i \(-0.328335\pi\)
−0.657379 + 0.753560i \(0.728335\pi\)
\(692\) 61.2492 2.32835
\(693\) −2.80902 + 1.76336i −0.106706 + 0.0669843i
\(694\) −62.5410 −2.37402
\(695\) 22.9894 + 16.7027i 0.872036 + 0.633571i
\(696\) −6.92705 + 21.3193i −0.262569 + 0.808105i
\(697\) 2.86475 + 8.81678i 0.108510 + 0.333959i
\(698\) −5.42705 + 3.94298i −0.205417 + 0.149244i
\(699\) 3.57295 2.59590i 0.135141 0.0981859i
\(700\) −3.57295 10.9964i −0.135045 0.415625i
\(701\) −3.45492 + 10.6331i −0.130490 + 0.401608i −0.994861 0.101247i \(-0.967717\pi\)
0.864371 + 0.502855i \(0.167717\pi\)
\(702\) 11.5902 + 8.42075i 0.437443 + 0.317821i
\(703\) −33.8885 −1.27813
\(704\) 7.04508 + 28.0094i 0.265522 + 1.05564i
\(705\) −16.3262 −0.614882
\(706\) −52.3328 38.0220i −1.96957 1.43098i
\(707\) 1.00000 3.07768i 0.0376089 0.115748i
\(708\) −18.9271 58.2515i −0.711322 2.18922i
\(709\) −3.38197 + 2.45714i −0.127012 + 0.0922799i −0.649478 0.760381i \(-0.725012\pi\)
0.522465 + 0.852661i \(0.325012\pi\)
\(710\) −41.9336 + 30.4666i −1.57374 + 1.14339i
\(711\) 2.11803 + 6.51864i 0.0794325 + 0.244468i
\(712\) 6.17376 19.0009i 0.231372 0.712088i
\(713\) 1.38197 + 1.00406i 0.0517550 + 0.0376022i
\(714\) 7.85410 0.293932
\(715\) −22.5344 18.8294i −0.842740 0.704179i
\(716\) 60.8115 2.27263
\(717\) −0.309017 0.224514i −0.0115405 0.00838463i
\(718\) 12.9271 39.7854i 0.482433 1.48478i
\(719\) −2.13525 6.57164i −0.0796316 0.245081i 0.903313 0.428982i \(-0.141127\pi\)
−0.982945 + 0.183901i \(0.941127\pi\)
\(720\) −12.8992 + 9.37181i −0.480724 + 0.349267i
\(721\) −9.89919 + 7.19218i −0.368665 + 0.267851i
\(722\) −2.42705 7.46969i −0.0903255 0.277993i
\(723\) 0.218847 0.673542i 0.00813901 0.0250493i
\(724\) −30.4894 22.1518i −1.13313 0.823266i
\(725\) −7.14590 −0.265392
\(726\) 20.7984 + 19.9192i 0.771900 + 0.739270i
\(727\) 36.3951 1.34982 0.674910 0.737900i \(-0.264182\pi\)
0.674910 + 0.737900i \(0.264182\pi\)
\(728\) −33.0795 24.0337i −1.22601 0.890748i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −5.04508 15.5272i −0.186727 0.574687i
\(731\) −21.8435 + 15.8702i −0.807910 + 0.586981i
\(732\) −26.3435 + 19.1396i −0.973682 + 0.707422i
\(733\) 7.74671 + 23.8419i 0.286131 + 0.880622i 0.986057 + 0.166406i \(0.0532163\pi\)
−0.699926 + 0.714215i \(0.746784\pi\)
\(734\) −19.9894 + 61.5209i −0.737821 + 2.27078i
\(735\) 1.30902 + 0.951057i 0.0482838 + 0.0350802i
\(736\) −78.5410 −2.89506
\(737\) 9.43769 + 7.88597i 0.347642 + 0.290483i
\(738\) −8.09017 −0.297803
\(739\) 9.35410 + 6.79615i 0.344096 + 0.250001i 0.746388 0.665511i \(-0.231786\pi\)
−0.402292 + 0.915511i \(0.631786\pi\)
\(740\) −20.5623 + 63.2843i −0.755885 + 2.32638i
\(741\) −6.76393 20.8172i −0.248479 0.764741i
\(742\) −8.66312 + 6.29412i −0.318033 + 0.231065i
\(743\) −3.16312 + 2.29814i −0.116044 + 0.0843106i −0.644293 0.764778i \(-0.722848\pi\)
0.528250 + 0.849089i \(0.322848\pi\)
\(744\) −0.545085 1.67760i −0.0199838 0.0615038i
\(745\) −10.1631 + 31.2789i −0.372348 + 1.14597i
\(746\) 72.3951 + 52.5981i 2.65057 + 1.92575i
\(747\) 2.94427 0.107725
\(748\) −11.7812 46.8388i −0.430762 1.71260i
\(749\) −15.9443 −0.582591
\(750\) −25.2984 18.3803i −0.923766 0.671155i
\(751\) 8.20820 25.2623i 0.299522 0.921833i −0.682143 0.731218i \(-0.738952\pi\)
0.981665 0.190614i \(-0.0610480\pi\)
\(752\) 30.7254 + 94.5631i 1.12044 + 3.44836i
\(753\) −8.42705 + 6.12261i −0.307099 + 0.223120i
\(754\) −34.7705 + 25.2623i −1.26627 + 0.919997i
\(755\) −5.30902 16.3395i −0.193215 0.594654i
\(756\) −1.50000 + 4.61653i −0.0545545 + 0.167901i
\(757\) 12.2361 + 8.89002i 0.444727 + 0.323113i 0.787511 0.616301i \(-0.211370\pi\)
−0.342783 + 0.939415i \(0.611370\pi\)
\(758\) −30.8885 −1.12192
\(759\) −20.3262 + 12.7598i −0.737796 + 0.463150i
\(760\) 48.3607 1.75423
\(761\) 30.4894 + 22.1518i 1.10524 + 0.803003i 0.981907 0.189363i \(-0.0606423\pi\)
0.123331 + 0.992366i \(0.460642\pi\)
\(762\) −5.30902 + 16.3395i −0.192325 + 0.591917i
\(763\) 0.135255 + 0.416272i 0.00489656 + 0.0150701i
\(764\) −64.9058 + 47.1568i −2.34821 + 1.70607i
\(765\) 3.92705 2.85317i 0.141983 0.103157i
\(766\) −5.07295 15.6129i −0.183293 0.564118i
\(767\) 21.3369 65.6682i 0.770430 2.37114i
\(768\) −11.7812 8.55951i −0.425116 0.308865i
\(769\) 23.5279 0.848436 0.424218 0.905560i \(-0.360549\pi\)
0.424218 + 0.905560i \(0.360549\pi\)
\(770\) 5.23607 13.0373i 0.188695 0.469831i
\(771\) 0.472136 0.0170036
\(772\) 84.1033 + 61.1046i 3.02694 + 2.19920i
\(773\) 5.85410 18.0171i 0.210557 0.648029i −0.788882 0.614545i \(-0.789340\pi\)
0.999439 0.0334842i \(-0.0106603\pi\)
\(774\) −7.28115 22.4091i −0.261716 0.805478i
\(775\) 0.454915 0.330515i 0.0163410 0.0118725i
\(776\) 99.2386 72.1010i 3.56246 2.58828i
\(777\) 2.61803 + 8.05748i 0.0939214 + 0.289060i
\(778\) −22.7082 + 69.8887i −0.814129 + 2.50563i
\(779\) 10.0000 + 7.26543i 0.358287 + 0.260311i
\(780\) −42.9787 −1.53888
\(781\) 40.4894 + 2.74717i 1.44882 + 0.0983014i
\(782\) 56.8328 2.03234
\(783\) 2.42705 + 1.76336i 0.0867357 + 0.0630172i
\(784\) 3.04508 9.37181i 0.108753 0.334707i
\(785\) −8.07295 24.8460i −0.288136 0.886791i
\(786\) −2.80902 + 2.04087i −0.100194 + 0.0727954i
\(787\) 15.9271 11.5717i 0.567738 0.412486i −0.266545 0.963823i \(-0.585882\pi\)
0.834283 + 0.551337i \(0.185882\pi\)
\(788\) −3.27051 10.0656i −0.116507 0.358572i
\(789\) 4.63525 14.2658i 0.165019 0.507878i
\(790\) −23.4894 17.0660i −0.835714 0.607182i
\(791\) −1.47214 −0.0523431
\(792\) 24.7254 + 1.67760i 0.878580 + 0.0596109i
\(793\) −36.7082 −1.30355
\(794\) −38.6976 28.1154i −1.37333 0.997779i
\(795\) −2.04508 + 6.29412i −0.0725317 + 0.223230i
\(796\) −17.3435 53.3777i −0.614723 1.89192i
\(797\) −37.9058 + 27.5402i −1.34269 + 0.975522i −0.343351 + 0.939207i \(0.611562\pi\)
−0.999340 + 0.0363149i \(0.988438\pi\)
\(798\) 8.47214 6.15537i 0.299910 0.217898i
\(799\) −9.35410 28.7890i −0.330924 1.01848i
\(800\) −7.98936 + 24.5887i −0.282466 + 0.869342i
\(801\) −2.16312 1.57160i −0.0764301 0.0555297i
\(802\) 8.56231 0.302346
\(803\) −4.76393 + 11.8617i −0.168116 + 0.418591i
\(804\) 18.0000 0.634811
\(805\) 9.47214 + 6.88191i 0.333849 + 0.242555i
\(806\) 1.04508 3.21644i 0.0368115 0.113294i
\(807\) 6.21885 + 19.1396i 0.218914 + 0.673747i
\(808\) −19.5623 + 14.2128i −0.688200 + 0.500006i
\(809\) −12.7361 + 9.25330i −0.447776 + 0.325329i −0.788717 0.614756i \(-0.789254\pi\)
0.340941 + 0.940085i \(0.389254\pi\)
\(810\) 1.30902 + 4.02874i 0.0459942 + 0.141555i
\(811\) −11.0344 + 33.9605i −0.387472 + 1.19252i 0.547200 + 0.837002i \(0.315694\pi\)
−0.934671 + 0.355513i \(0.884306\pi\)
\(812\) −11.7812 8.55951i −0.413437 0.300380i
\(813\) 16.8885 0.592307
\(814\) 62.3050 39.1118i 2.18379 1.37087i
\(815\) 19.6525 0.688396
\(816\) −23.9164 17.3763i −0.837242 0.608292i
\(817\) −11.1246 + 34.2380i −0.389201 + 1.19784i
\(818\) 7.78115 + 23.9479i 0.272062 + 0.837320i
\(819\) −4.42705 + 3.21644i −0.154694 + 0.112392i
\(820\) 19.6353 14.2658i 0.685693 0.498185i
\(821\) 3.72949 + 11.4782i 0.130160 + 0.400592i 0.994806 0.101790i \(-0.0324571\pi\)
−0.864646 + 0.502382i \(0.832457\pi\)
\(822\) 8.47214 26.0746i 0.295500 0.909454i
\(823\) −37.8885 27.5276i −1.32071 0.959553i −0.999923 0.0124023i \(-0.996052\pi\)
−0.320789 0.947151i \(-0.603948\pi\)
\(824\) 91.4296 3.18510
\(825\) 1.92705 + 7.66145i 0.0670913 + 0.266738i
\(826\) 33.0344 1.14942
\(827\) −31.1353 22.6211i −1.08268 0.786612i −0.104531 0.994522i \(-0.533334\pi\)
−0.978148 + 0.207909i \(0.933334\pi\)
\(828\) −10.8541 + 33.4055i −0.377206 + 1.16092i
\(829\) 2.29837 + 7.07367i 0.0798258 + 0.245679i 0.983003 0.183589i \(-0.0587716\pi\)
−0.903177 + 0.429268i \(0.858772\pi\)
\(830\) −10.0902 + 7.33094i −0.350235 + 0.254461i
\(831\) −10.0902 + 7.33094i −0.350024 + 0.254307i
\(832\) 14.7254 + 45.3202i 0.510512 + 1.57120i
\(833\) −0.927051 + 2.85317i −0.0321204 + 0.0988565i
\(834\) −37.1976 27.0256i −1.28805 0.935820i
\(835\) 24.4164 0.844965
\(836\) −49.4164 41.2915i −1.70910 1.42809i
\(837\) −0.236068 −0.00815970
\(838\) 28.2254 + 20.5070i 0.975031 + 0.708402i
\(839\) −4.63525 + 14.2658i −0.160027 + 0.492512i −0.998635 0.0522225i \(-0.983369\pi\)
0.838609 + 0.544734i \(0.183369\pi\)
\(840\) −3.73607 11.4984i −0.128907 0.396734i
\(841\) 16.1803 11.7557i 0.557943 0.405369i
\(842\) −9.78115 + 7.10642i −0.337081 + 0.244904i
\(843\) −3.55573 10.9434i −0.122466 0.376911i
\(844\) 20.4787 63.0270i 0.704906 2.16948i
\(845\) −22.1803 16.1150i −0.763027 0.554371i
\(846\) 26.4164 0.908215
\(847\) −9.69098 + 5.20431i −0.332986 + 0.178822i
\(848\) 40.3050 1.38408
\(849\) −16.7533 12.1720i −0.574971 0.417741i
\(850\) 5.78115 17.7926i 0.198292 0.610280i
\(851\) 18.9443 + 58.3045i 0.649401 + 1.99865i
\(852\) 48.0517 34.9116i 1.64622 1.19605i
\(853\) −5.44427 + 3.95550i −0.186408 + 0.135434i −0.677076 0.735913i \(-0.736753\pi\)
0.490667 + 0.871347i \(0.336753\pi\)
\(854\) −5.42705 16.7027i −0.185710 0.571556i
\(855\) 2.00000 6.15537i 0.0683986 0.210509i
\(856\) 96.3845 + 70.0274i 3.29435 + 2.39349i
\(857\) 23.9443 0.817921 0.408960 0.912552i \(-0.365891\pi\)
0.408960 + 0.912552i \(0.365891\pi\)
\(858\) 36.4615 + 30.4666i 1.24477 + 1.04011i
\(859\) 40.4164 1.37899 0.689495 0.724290i \(-0.257833\pi\)
0.689495 + 0.724290i \(0.257833\pi\)
\(860\) 57.1869 + 41.5487i 1.95006 + 1.41680i
\(861\) 0.954915 2.93893i 0.0325434 0.100158i
\(862\) 15.8713 + 48.8469i 0.540579 + 1.66373i
\(863\) 1.80902 1.31433i 0.0615797 0.0447402i −0.556570 0.830801i \(-0.687883\pi\)
0.618149 + 0.786061i \(0.287883\pi\)
\(864\) 8.78115 6.37988i 0.298741 0.217048i
\(865\) 6.30902 + 19.4172i 0.214513 + 0.660203i
\(866\) 15.3262 47.1693i 0.520807 1.60288i
\(867\) −6.47214 4.70228i −0.219805 0.159698i
\(868\) 1.14590 0.0388943
\(869\) 5.54508 + 22.0458i 0.188104 + 0.747853i
\(870\) −12.7082 −0.430848
\(871\) 16.4164 + 11.9272i 0.556249 + 0.404138i
\(872\) 1.01064 3.11044i 0.0342247 0.105333i
\(873\) −5.07295 15.6129i −0.171693 0.528418i
\(874\) 61.3050 44.5407i 2.07367 1.50661i
\(875\) 9.66312 7.02067i 0.326673 0.237342i
\(876\) 5.78115 + 17.7926i 0.195327 + 0.601155i
\(877\) −2.92047 + 8.98829i −0.0986174 + 0.303513i −0.988180 0.153301i \(-0.951010\pi\)
0.889562 + 0.456814i \(0.151010\pi\)
\(878\) −63.1869 45.9080i −2.13246 1.54932i
\(879\) −0.652476 −0.0220075
\(880\) −44.7877 + 28.1154i −1.50979 + 0.947771i
\(881\) 1.06888 0.0360116 0.0180058 0.999838i \(-0.494268\pi\)
0.0180058 + 0.999838i \(0.494268\pi\)
\(882\) −2.11803 1.53884i −0.0713179 0.0518155i
\(883\) −1.37539 + 4.23301i −0.0462855 + 0.142452i −0.971528 0.236923i \(-0.923861\pi\)
0.925243 + 0.379375i \(0.123861\pi\)
\(884\) −24.6246 75.7868i −0.828215 2.54898i
\(885\) 16.5172 12.0005i 0.555220 0.403391i
\(886\) −15.5623 + 11.3067i −0.522826 + 0.379855i
\(887\) 9.52380 + 29.3112i 0.319778 + 0.984175i 0.973743 + 0.227650i \(0.0731043\pi\)
−0.653965 + 0.756525i \(0.726896\pi\)
\(888\) 19.5623 60.2066i 0.656468 2.02040i
\(889\) −5.30902 3.85723i −0.178059 0.129367i
\(890\) 11.3262 0.379656
\(891\) 1.23607 3.07768i 0.0414098 0.103106i
\(892\) −73.6869 −2.46722
\(893\) −32.6525 23.7234i −1.09267 0.793874i
\(894\) 16.4443 50.6103i 0.549979 1.69266i
\(895\) 6.26393 + 19.2784i 0.209380 + 0.644406i
\(896\) −0.881966 + 0.640786i −0.0294644 + 0.0214072i
\(897\) −32.0344 + 23.2744i −1.06960 + 0.777109i
\(898\) 10.8992 + 33.5442i 0.363711 + 1.11939i
\(899\) 0.218847 0.673542i 0.00729896 0.0224639i
\(900\) 9.35410 + 6.79615i 0.311803 + 0.226538i
\(901\) −12.2705 −0.408790
\(902\) −26.7705 1.81636i −0.891360 0.0604781i
\(903\) 9.00000 0.299501
\(904\) 8.89919 + 6.46564i 0.295983 + 0.215044i
\(905\) 3.88197 11.9475i 0.129041 0.397147i
\(906\) 8.59017 + 26.4378i 0.285389 + 0.878338i
\(907\) 2.17376 1.57933i 0.0721786 0.0524408i −0.551111 0.834432i \(-0.685796\pi\)
0.623289 + 0.781991i \(0.285796\pi\)
\(908\) 2.42705 1.76336i 0.0805445 0.0585190i
\(909\) 1.00000 + 3.07768i 0.0331679 + 0.102080i
\(910\) 7.16312 22.0458i 0.237455 0.730812i
\(911\) −18.7812 13.6453i −0.622247 0.452089i 0.231458 0.972845i \(-0.425650\pi\)
−0.853706 + 0.520756i \(0.825650\pi\)
\(912\) −39.4164 −1.30521
\(913\) 9.74265 + 0.661030i 0.322435 + 0.0218769i
\(914\) −29.1803 −0.965200
\(915\) −8.78115 6.37988i −0.290296 0.210912i
\(916\) 42.1033 129.581i 1.39113 4.28147i
\(917\) −0.409830 1.26133i −0.0135338 0.0416527i
\(918\) −6.35410 + 4.61653i −0.209717 + 0.152368i
\(919\) 17.4164 12.6538i 0.574514 0.417409i −0.262228 0.965006i \(-0.584457\pi\)
0.836742 + 0.547597i \(0.184457\pi\)
\(920\) −27.0344 83.2035i −0.891299 2.74314i
\(921\) 2.07295 6.37988i 0.0683060 0.210224i
\(922\) −9.35410 6.79615i −0.308061 0.223819i
\(923\) 66.9574 2.20393
\(924\) −6.00000 + 14.9394i −0.197386 + 0.491470i
\(925\) 20.1803 0.663525
\(926\) −64.9959 47.2223i −2.13590 1.55182i
\(927\) 3.78115 11.6372i 0.124189 0.382216i
\(928\) 10.0623 + 30.9686i 0.330311 + 1.01659i
\(929\) −29.1246 + 21.1603i −0.955548 + 0.694246i −0.952112 0.305748i \(-0.901093\pi\)
−0.00343511 + 0.999994i \(0.501093\pi\)
\(930\) 0.809017 0.587785i 0.0265287 0.0192742i
\(931\) 1.23607 + 3.80423i 0.0405105 + 0.124678i
\(932\) 6.62461 20.3885i 0.216996 0.667846i
\(933\) 19.4443 + 14.1271i 0.636577 + 0.462500i
\(934\) 72.3951 2.36884
\(935\) 13.6353 8.55951i 0.445921 0.279926i
\(936\) 40.8885 1.33648
\(937\) 16.6074 + 12.0660i 0.542540 + 0.394178i 0.825027 0.565093i \(-0.191160\pi\)
−0.282488 + 0.959271i \(0.591160\pi\)
\(938\) −3.00000 + 9.23305i −0.0979535 + 0.301470i
\(939\) 0.409830 + 1.26133i 0.0133743 + 0.0411619i
\(940\) −64.1140 + 46.5815i −2.09117 + 1.51932i
\(941\) −13.7639 + 10.0001i −0.448691 + 0.325993i −0.789079 0.614292i \(-0.789442\pi\)
0.340388 + 0.940285i \(0.389442\pi\)
\(942\) 13.0623 + 40.2016i 0.425593 + 1.30984i
\(943\) 6.90983 21.2663i 0.225015 0.692525i
\(944\) −100.593 73.0849i −3.27401 2.37871i
\(945\) −1.61803 −0.0526346
\(946\) −19.0623 75.7868i −0.619769 2.46404i
\(947\) 11.5623 0.375724 0.187862 0.982195i \(-0.439844\pi\)
0.187862 + 0.982195i \(0.439844\pi\)
\(948\) 26.9164 + 19.5559i 0.874204 + 0.635147i
\(949\) −6.51722 + 20.0579i −0.211558 + 0.651108i
\(950\) −7.70820 23.7234i −0.250087 0.769689i
\(951\) 11.5172 8.36775i 0.373471 0.271343i
\(952\) 18.1353 13.1760i 0.587767 0.427038i
\(953\) 12.1697 + 37.4545i 0.394215 + 1.21327i 0.929571 + 0.368643i \(0.120177\pi\)
−0.535356 + 0.844627i \(0.679823\pi\)
\(954\) 3.30902 10.1841i 0.107133 0.329723i
\(955\) −21.6353 15.7189i −0.700100 0.508653i
\(956\) −1.85410 −0.0599659
\(957\) 7.63525 + 6.37988i 0.246813 + 0.206232i
\(958\) 12.2361 0.395329
\(959\) 8.47214 + 6.15537i 0.273580 + 0.198767i
\(960\) −4.35410 + 13.4005i −0.140528 + 0.432501i
\(961\) −9.56231 29.4298i −0.308461 0.949347i
\(962\) 98.1935 71.3418i 3.16589 2.30015i
\(963\) 12.8992 9.37181i 0.415670 0.302002i
\(964\) −1.06231 3.26944i −0.0342146 0.105302i
\(965\) −10.7082 + 32.9565i −0.344709 + 1.06091i
\(966\) −15.3262 11.1352i −0.493114 0.358268i
\(967\) −32.6525 −1.05003 −0.525016 0.851092i \(-0.675941\pi\)
−0.525016 + 0.851092i \(0.675941\pi\)
\(968\) 81.4402 + 11.1024i 2.61759 + 0.356845i
\(969\) 12.0000 0.385496
\(970\) 56.2599 + 40.8752i 1.80640 + 1.31242i
\(971\) −12.4894 + 38.4383i −0.400803 + 1.23354i 0.523547 + 0.851997i \(0.324608\pi\)
−0.924350 + 0.381547i \(0.875392\pi\)
\(972\) −1.50000 4.61653i −0.0481125 0.148075i
\(973\) 14.2082 10.3229i 0.455494 0.330936i
\(974\) 45.0517 32.7319i 1.44355 1.04880i
\(975\) 4.02786 + 12.3965i 0.128995 + 0.397005i
\(976\) −20.4271 + 62.8680i −0.653854 + 2.01236i
\(977\) −44.1697 32.0912i −1.41311 1.02669i −0.992861 0.119280i \(-0.961941\pi\)
−0.420253 0.907407i \(-0.638059\pi\)
\(978\) −31.7984 −1.01680
\(979\) −6.80495 5.68609i −0.217487 0.181728i
\(980\) 7.85410 0.250890
\(981\) −0.354102 0.257270i −0.0113056 0.00821400i
\(982\) −32.8885 + 101.221i −1.04952 + 3.23008i
\(983\) 14.3647 + 44.2101i 0.458164 + 1.41008i 0.867380 + 0.497647i \(0.165802\pi\)
−0.409216 + 0.912438i \(0.634198\pi\)
\(984\) −18.6803 + 13.5721i −0.595507 + 0.432662i
\(985\) 2.85410 2.07363i 0.0909393 0.0660712i
\(986\) −7.28115 22.4091i −0.231879 0.713651i
\(987\) −3.11803 + 9.59632i −0.0992481 + 0.305454i
\(988\) −85.9574 62.4517i −2.73467 1.98685i
\(989\) 65.1246 2.07084
\(990\) 3.42705 + 13.6251i 0.108919 + 0.433033i
\(991\) 42.7984 1.35954 0.679768 0.733428i \(-0.262081\pi\)
0.679768 + 0.733428i \(0.262081\pi\)
\(992\) −2.07295 1.50609i −0.0658162 0.0478183i
\(993\) −9.74671 + 29.9973i −0.309303 + 0.951935i
\(994\) 9.89919 + 30.4666i 0.313983 + 0.966341i
\(995\) 15.1353 10.9964i 0.479820 0.348610i
\(996\) 11.5623 8.40051i 0.366366 0.266180i
\(997\) 11.4508 + 35.2421i 0.362652 + 1.11613i 0.951438 + 0.307839i \(0.0996060\pi\)
−0.588786 + 0.808289i \(0.700394\pi\)
\(998\) −4.04508 + 12.4495i −0.128045 + 0.394082i
\(999\) −6.85410 4.97980i −0.216854 0.157554i
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 231.2.j.a.169.1 4
3.2 odd 2 693.2.m.e.631.1 4
11.3 even 5 inner 231.2.j.a.190.1 yes 4
11.5 even 5 2541.2.a.bf.1.2 2
11.6 odd 10 2541.2.a.m.1.1 2
33.5 odd 10 7623.2.a.u.1.1 2
33.14 odd 10 693.2.m.e.190.1 4
33.17 even 10 7623.2.a.by.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.j.a.169.1 4 1.1 even 1 trivial
231.2.j.a.190.1 yes 4 11.3 even 5 inner
693.2.m.e.190.1 4 33.14 odd 10
693.2.m.e.631.1 4 3.2 odd 2
2541.2.a.m.1.1 2 11.6 odd 10
2541.2.a.bf.1.2 2 11.5 even 5
7623.2.a.u.1.1 2 33.5 odd 10
7623.2.a.by.1.2 2 33.17 even 10