Properties

Label 273.2.r.b.269.28
Level $273$
Weight $2$
Character 273.269
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
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] = [273,2,Mod(68,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.r (of order \(6\), degree \(2\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.28
Character \(\chi\) \(=\) 273.269
Dual form 273.2.r.b.68.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.97104i q^{2} +(1.69142 + 0.372976i) q^{3} -1.88498 q^{4} +(-0.272603 - 0.472162i) q^{5} +(-0.735148 + 3.33384i) q^{6} +(2.35644 - 1.20299i) q^{7} +0.226699i q^{8} +(2.72178 + 1.26171i) q^{9} +O(q^{10})\) \(q+1.97104i q^{2} +(1.69142 + 0.372976i) q^{3} -1.88498 q^{4} +(-0.272603 - 0.472162i) q^{5} +(-0.735148 + 3.33384i) q^{6} +(2.35644 - 1.20299i) q^{7} +0.226699i q^{8} +(2.72178 + 1.26171i) q^{9} +(0.930648 - 0.537310i) q^{10} +(0.383707 - 0.221534i) q^{11} +(-3.18829 - 0.703053i) q^{12} +(-2.64192 + 2.45362i) q^{13} +(2.37115 + 4.64463i) q^{14} +(-0.284980 - 0.900296i) q^{15} -4.21680 q^{16} -3.83879 q^{17} +(-2.48688 + 5.36472i) q^{18} +(0.0717668 + 0.0414346i) q^{19} +(0.513852 + 0.890018i) q^{20} +(4.43441 - 1.15587i) q^{21} +(0.436651 + 0.756301i) q^{22} -7.16086i q^{23} +(-0.0845531 + 0.383442i) q^{24} +(2.35138 - 4.07270i) q^{25} +(-4.83618 - 5.20732i) q^{26} +(4.13307 + 3.14924i) q^{27} +(-4.44185 + 2.26763i) q^{28} +(-3.66493 - 2.11595i) q^{29} +(1.77452 - 0.561706i) q^{30} +(5.32612 + 3.07503i) q^{31} -7.85807i q^{32} +(0.731636 - 0.231592i) q^{33} -7.56640i q^{34} +(-1.21038 - 0.784680i) q^{35} +(-5.13051 - 2.37831i) q^{36} -3.94217 q^{37} +(-0.0816691 + 0.141455i) q^{38} +(-5.38373 + 3.16473i) q^{39} +(0.107038 - 0.0617987i) q^{40} +(-2.97274 + 5.14894i) q^{41} +(2.27826 + 8.74038i) q^{42} +(-3.19077 - 5.52657i) q^{43} +(-0.723283 + 0.417588i) q^{44} +(-0.146231 - 1.62907i) q^{45} +14.1143 q^{46} +(-0.322950 - 0.559365i) q^{47} +(-7.13237 - 1.57276i) q^{48} +(4.10561 - 5.66957i) q^{49} +(8.02744 + 4.63465i) q^{50} +(-6.49300 - 1.43178i) q^{51} +(4.97998 - 4.62504i) q^{52} +(7.39479 + 4.26939i) q^{53} +(-6.20727 + 8.14644i) q^{54} +(-0.209199 - 0.120781i) q^{55} +(0.272718 + 0.534202i) q^{56} +(0.105933 + 0.0968504i) q^{57} +(4.17061 - 7.22371i) q^{58} -5.84841 q^{59} +(0.537183 + 1.69704i) q^{60} +(-4.76950 - 2.75367i) q^{61} +(-6.06101 + 10.4980i) q^{62} +(7.93154 - 0.301135i) q^{63} +7.05494 q^{64} +(1.87870 + 0.578549i) q^{65} +(0.456476 + 1.44208i) q^{66} +(5.03321 + 8.71777i) q^{67} +7.23607 q^{68} +(2.67082 - 12.1120i) q^{69} +(1.54663 - 2.38570i) q^{70} +(7.56167 - 4.36573i) q^{71} +(-0.286029 + 0.617024i) q^{72} +(12.7809 + 7.37904i) q^{73} -7.77015i q^{74} +(5.49617 - 6.01163i) q^{75} +(-0.135279 - 0.0781036i) q^{76} +(0.637679 - 0.983629i) q^{77} +(-6.23779 - 10.6115i) q^{78} +(-5.78537 - 10.0206i) q^{79} +(1.14951 + 1.99101i) q^{80} +(5.81616 + 6.86821i) q^{81} +(-10.1488 - 5.85939i) q^{82} -1.87826 q^{83} +(-8.35879 + 2.17880i) q^{84} +(1.04647 + 1.81253i) q^{85} +(10.8931 - 6.28912i) q^{86} +(-5.40973 - 4.94588i) q^{87} +(0.0502214 + 0.0869860i) q^{88} -13.2339 q^{89} +(3.21095 - 0.288227i) q^{90} +(-3.27382 + 8.96003i) q^{91} +13.4981i q^{92} +(7.86177 + 7.18768i) q^{93} +(1.10253 - 0.636546i) q^{94} -0.0451807i q^{95} +(2.93087 - 13.2913i) q^{96} +(1.99439 - 1.15146i) q^{97} +(11.1749 + 8.09230i) q^{98} +(1.32388 - 0.118836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31} - 45 q^{33} + 33 q^{39} + 90 q^{40} + 3 q^{42} - 20 q^{43} - 6 q^{48} - 6 q^{49} - 10 q^{51} - 48 q^{52} - 18 q^{55} + 4 q^{57} + 30 q^{58} + 55 q^{60} - 18 q^{61} + 31 q^{63} - 84 q^{64} + 75 q^{66} + 44 q^{67} + 33 q^{69} + 20 q^{70} + 17 q^{72} + 84 q^{73} - 18 q^{76} - 71 q^{78} + 20 q^{79} + 16 q^{81} - 18 q^{82} - 135 q^{84} - 2 q^{85} - 46 q^{88} - 10 q^{91} - 56 q^{93} + 36 q^{94} + 30 q^{96} - 24 q^{97} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.97104i 1.39373i 0.717201 + 0.696867i \(0.245423\pi\)
−0.717201 + 0.696867i \(0.754577\pi\)
\(3\) 1.69142 + 0.372976i 0.976540 + 0.215338i
\(4\) −1.88498 −0.942492
\(5\) −0.272603 0.472162i −0.121912 0.211157i 0.798610 0.601849i \(-0.205569\pi\)
−0.920521 + 0.390692i \(0.872236\pi\)
\(6\) −0.735148 + 3.33384i −0.300123 + 1.36104i
\(7\) 2.35644 1.20299i 0.890650 0.454689i
\(8\) 0.226699i 0.0801501i
\(9\) 2.72178 + 1.26171i 0.907260 + 0.420571i
\(10\) 0.930648 0.537310i 0.294297 0.169912i
\(11\) 0.383707 0.221534i 0.115692 0.0667949i −0.441037 0.897489i \(-0.645389\pi\)
0.556729 + 0.830694i \(0.312056\pi\)
\(12\) −3.18829 0.703053i −0.920381 0.202954i
\(13\) −2.64192 + 2.45362i −0.732737 + 0.680512i
\(14\) 2.37115 + 4.64463i 0.633716 + 1.24133i
\(15\) −0.284980 0.900296i −0.0735815 0.232455i
\(16\) −4.21680 −1.05420
\(17\) −3.83879 −0.931044 −0.465522 0.885036i \(-0.654133\pi\)
−0.465522 + 0.885036i \(0.654133\pi\)
\(18\) −2.48688 + 5.36472i −0.586164 + 1.26448i
\(19\) 0.0717668 + 0.0414346i 0.0164644 + 0.00950575i 0.508210 0.861233i \(-0.330308\pi\)
−0.491745 + 0.870739i \(0.663641\pi\)
\(20\) 0.513852 + 0.890018i 0.114901 + 0.199014i
\(21\) 4.43441 1.15587i 0.967667 0.252232i
\(22\) 0.436651 + 0.756301i 0.0930943 + 0.161244i
\(23\) 7.16086i 1.49314i −0.665306 0.746571i \(-0.731699\pi\)
0.665306 0.746571i \(-0.268301\pi\)
\(24\) −0.0845531 + 0.383442i −0.0172593 + 0.0782698i
\(25\) 2.35138 4.07270i 0.470275 0.814540i
\(26\) −4.83618 5.20732i −0.948453 1.02124i
\(27\) 4.13307 + 3.14924i 0.795410 + 0.606072i
\(28\) −4.44185 + 2.26763i −0.839431 + 0.428541i
\(29\) −3.66493 2.11595i −0.680560 0.392922i 0.119506 0.992834i \(-0.461869\pi\)
−0.800066 + 0.599912i \(0.795202\pi\)
\(30\) 1.77452 0.561706i 0.323981 0.102553i
\(31\) 5.32612 + 3.07503i 0.956599 + 0.552293i 0.895125 0.445816i \(-0.147086\pi\)
0.0614742 + 0.998109i \(0.480420\pi\)
\(32\) 7.85807i 1.38912i
\(33\) 0.731636 0.231592i 0.127361 0.0403150i
\(34\) 7.56640i 1.29763i
\(35\) −1.21038 0.784680i −0.204591 0.132635i
\(36\) −5.13051 2.37831i −0.855085 0.396385i
\(37\) −3.94217 −0.648088 −0.324044 0.946042i \(-0.605043\pi\)
−0.324044 + 0.946042i \(0.605043\pi\)
\(38\) −0.0816691 + 0.141455i −0.0132485 + 0.0229470i
\(39\) −5.38373 + 3.16473i −0.862086 + 0.506762i
\(40\) 0.107038 0.0617987i 0.0169243 0.00977123i
\(41\) −2.97274 + 5.14894i −0.464265 + 0.804130i −0.999168 0.0407834i \(-0.987015\pi\)
0.534903 + 0.844913i \(0.320348\pi\)
\(42\) 2.27826 + 8.74038i 0.351544 + 1.34867i
\(43\) −3.19077 5.52657i −0.486588 0.842795i 0.513293 0.858213i \(-0.328425\pi\)
−0.999881 + 0.0154185i \(0.995092\pi\)
\(44\) −0.723283 + 0.417588i −0.109039 + 0.0629537i
\(45\) −0.146231 1.62907i −0.0217989 0.242847i
\(46\) 14.1143 2.08104
\(47\) −0.322950 0.559365i −0.0471071 0.0815918i 0.841510 0.540241i \(-0.181667\pi\)
−0.888618 + 0.458649i \(0.848334\pi\)
\(48\) −7.13237 1.57276i −1.02947 0.227009i
\(49\) 4.10561 5.66957i 0.586515 0.809938i
\(50\) 8.02744 + 4.63465i 1.13525 + 0.655438i
\(51\) −6.49300 1.43178i −0.909202 0.200489i
\(52\) 4.97998 4.62504i 0.690599 0.641378i
\(53\) 7.39479 + 4.26939i 1.01575 + 0.586445i 0.912871 0.408248i \(-0.133860\pi\)
0.102882 + 0.994694i \(0.467194\pi\)
\(54\) −6.20727 + 8.14644i −0.844702 + 1.10859i
\(55\) −0.209199 0.120781i −0.0282084 0.0162861i
\(56\) 0.272718 + 0.534202i 0.0364434 + 0.0713857i
\(57\) 0.105933 + 0.0968504i 0.0140312 + 0.0128281i
\(58\) 4.17061 7.22371i 0.547628 0.948520i
\(59\) −5.84841 −0.761398 −0.380699 0.924699i \(-0.624317\pi\)
−0.380699 + 0.924699i \(0.624317\pi\)
\(60\) 0.537183 + 1.69704i 0.0693500 + 0.219087i
\(61\) −4.76950 2.75367i −0.610672 0.352572i 0.162556 0.986699i \(-0.448026\pi\)
−0.773228 + 0.634128i \(0.781359\pi\)
\(62\) −6.06101 + 10.4980i −0.769749 + 1.33324i
\(63\) 7.93154 0.301135i 0.999280 0.0379394i
\(64\) 7.05494 0.881868
\(65\) 1.87870 + 0.578549i 0.233024 + 0.0717601i
\(66\) 0.456476 + 1.44208i 0.0561884 + 0.177508i
\(67\) 5.03321 + 8.71777i 0.614904 + 1.06505i 0.990401 + 0.138222i \(0.0441386\pi\)
−0.375497 + 0.926824i \(0.622528\pi\)
\(68\) 7.23607 0.877502
\(69\) 2.67082 12.1120i 0.321529 1.45811i
\(70\) 1.54663 2.38570i 0.184858 0.285146i
\(71\) 7.56167 4.36573i 0.897405 0.518117i 0.0210474 0.999778i \(-0.493300\pi\)
0.876357 + 0.481662i \(0.159967\pi\)
\(72\) −0.286029 + 0.617024i −0.0337088 + 0.0727170i
\(73\) 12.7809 + 7.37904i 1.49589 + 0.863651i 0.999989 0.00472968i \(-0.00150551\pi\)
0.495898 + 0.868381i \(0.334839\pi\)
\(74\) 7.77015i 0.903262i
\(75\) 5.49617 6.01163i 0.634643 0.694163i
\(76\) −0.135279 0.0781036i −0.0155176 0.00895909i
\(77\) 0.637679 0.983629i 0.0726703 0.112095i
\(78\) −6.23779 10.6115i −0.706291 1.20152i
\(79\) −5.78537 10.0206i −0.650905 1.12740i −0.982904 0.184120i \(-0.941056\pi\)
0.331999 0.943280i \(-0.392277\pi\)
\(80\) 1.14951 + 1.99101i 0.128519 + 0.222602i
\(81\) 5.81616 + 6.86821i 0.646240 + 0.763135i
\(82\) −10.1488 5.85939i −1.12074 0.647061i
\(83\) −1.87826 −0.206166 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(84\) −8.35879 + 2.17880i −0.912019 + 0.237727i
\(85\) 1.04647 + 1.81253i 0.113505 + 0.196597i
\(86\) 10.8931 6.28912i 1.17463 0.678174i
\(87\) −5.40973 4.94588i −0.579984 0.530254i
\(88\) 0.0502214 + 0.0869860i 0.00535362 + 0.00927274i
\(89\) −13.2339 −1.40279 −0.701397 0.712771i \(-0.747440\pi\)
−0.701397 + 0.712771i \(0.747440\pi\)
\(90\) 3.21095 0.288227i 0.338464 0.0303818i
\(91\) −3.27382 + 8.96003i −0.343190 + 0.939266i
\(92\) 13.4981i 1.40727i
\(93\) 7.86177 + 7.18768i 0.815227 + 0.745327i
\(94\) 1.10253 0.636546i 0.113717 0.0656547i
\(95\) 0.0451807i 0.00463544i
\(96\) 2.93087 13.2913i 0.299131 1.35653i
\(97\) 1.99439 1.15146i 0.202499 0.116913i −0.395321 0.918543i \(-0.629367\pi\)
0.597821 + 0.801630i \(0.296033\pi\)
\(98\) 11.1749 + 8.09230i 1.12884 + 0.817446i
\(99\) 1.32388 0.118836i 0.133055 0.0119435i
\(100\) −4.43231 + 7.67698i −0.443231 + 0.767698i
\(101\) −6.72115 11.6414i −0.668779 1.15836i −0.978246 0.207450i \(-0.933484\pi\)
0.309466 0.950910i \(-0.399850\pi\)
\(102\) 2.82208 12.7979i 0.279428 1.26718i
\(103\) −3.33506 + 1.92550i −0.328613 + 0.189725i −0.655225 0.755434i \(-0.727426\pi\)
0.326612 + 0.945159i \(0.394093\pi\)
\(104\) −0.556233 0.598920i −0.0545432 0.0587289i
\(105\) −1.75459 1.77866i −0.171230 0.173580i
\(106\) −8.41512 + 14.5754i −0.817348 + 1.41569i
\(107\) 0.766743i 0.0741238i −0.999313 0.0370619i \(-0.988200\pi\)
0.999313 0.0370619i \(-0.0117999\pi\)
\(108\) −7.79078 5.93627i −0.749668 0.571218i
\(109\) 1.63804 2.83717i 0.156896 0.271752i −0.776852 0.629683i \(-0.783185\pi\)
0.933748 + 0.357932i \(0.116518\pi\)
\(110\) 0.238064 0.412340i 0.0226985 0.0393150i
\(111\) −6.66784 1.47033i −0.632884 0.139558i
\(112\) −9.93663 + 5.07279i −0.938924 + 0.479334i
\(113\) 17.1700 9.91313i 1.61522 0.932548i 0.627088 0.778948i \(-0.284247\pi\)
0.988133 0.153600i \(-0.0490868\pi\)
\(114\) −0.190896 + 0.208799i −0.0178790 + 0.0195558i
\(115\) −3.38108 + 1.95207i −0.315287 + 0.182031i
\(116\) 6.90834 + 3.98853i 0.641423 + 0.370326i
\(117\) −10.2865 + 3.34487i −0.950986 + 0.309233i
\(118\) 11.5274i 1.06119i
\(119\) −9.04588 + 4.61805i −0.829235 + 0.423336i
\(120\) 0.204096 0.0646046i 0.0186313 0.00589757i
\(121\) −5.40185 + 9.35627i −0.491077 + 0.850570i
\(122\) 5.42759 9.40086i 0.491391 0.851114i
\(123\) −6.94858 + 7.60025i −0.626532 + 0.685291i
\(124\) −10.0396 5.79639i −0.901587 0.520532i
\(125\) −5.28999 −0.473151
\(126\) 0.593548 + 15.6334i 0.0528774 + 1.39273i
\(127\) −2.52619 + 4.37549i −0.224163 + 0.388262i −0.956068 0.293145i \(-0.905298\pi\)
0.731905 + 0.681407i \(0.238631\pi\)
\(128\) 1.81059i 0.160035i
\(129\) −3.33564 10.5378i −0.293687 0.927803i
\(130\) −1.14034 + 3.70299i −0.100014 + 0.324773i
\(131\) 9.22290 + 15.9745i 0.805808 + 1.39570i 0.915744 + 0.401762i \(0.131602\pi\)
−0.109936 + 0.993939i \(0.535065\pi\)
\(132\) −1.37912 + 0.436548i −0.120037 + 0.0379966i
\(133\) 0.218960 + 0.0113029i 0.0189862 + 0.000980090i
\(134\) −17.1830 + 9.92063i −1.48439 + 0.857012i
\(135\) 0.360264 2.80997i 0.0310066 0.241844i
\(136\) 0.870250i 0.0746233i
\(137\) 11.8546i 1.01280i 0.862298 + 0.506402i \(0.169025\pi\)
−0.862298 + 0.506402i \(0.830975\pi\)
\(138\) 23.8732 + 5.26429i 2.03222 + 0.448126i
\(139\) −13.1770 + 7.60777i −1.11766 + 0.645282i −0.940803 0.338954i \(-0.889927\pi\)
−0.176859 + 0.984236i \(0.556594\pi\)
\(140\) 2.28155 + 1.47911i 0.192826 + 0.125008i
\(141\) −0.337613 1.06657i −0.0284321 0.0898216i
\(142\) 8.60501 + 14.9043i 0.722117 + 1.25074i
\(143\) −0.470164 + 1.52675i −0.0393171 + 0.127673i
\(144\) −11.4772 5.32040i −0.956433 0.443366i
\(145\) 2.30725i 0.191607i
\(146\) −14.5444 + 25.1916i −1.20370 + 2.08487i
\(147\) 9.05890 8.05831i 0.747165 0.664638i
\(148\) 7.43092 0.610818
\(149\) −4.00950 2.31488i −0.328471 0.189643i 0.326691 0.945131i \(-0.394066\pi\)
−0.655162 + 0.755488i \(0.727400\pi\)
\(150\) 11.8491 + 10.8332i 0.967478 + 0.884524i
\(151\) −6.21552 + 10.7656i −0.505812 + 0.876091i 0.494166 + 0.869368i \(0.335474\pi\)
−0.999977 + 0.00672369i \(0.997860\pi\)
\(152\) −0.00939317 + 0.0162695i −0.000761887 + 0.00131963i
\(153\) −10.4483 4.84346i −0.844699 0.391570i
\(154\) 1.93877 + 1.25689i 0.156230 + 0.101283i
\(155\) 3.35305i 0.269323i
\(156\) 10.1482 5.96546i 0.812510 0.477619i
\(157\) −7.76199 4.48138i −0.619474 0.357653i 0.157190 0.987568i \(-0.449756\pi\)
−0.776664 + 0.629915i \(0.783090\pi\)
\(158\) 19.7509 11.4032i 1.57129 0.907188i
\(159\) 10.9153 + 9.97939i 0.865640 + 0.791417i
\(160\) −3.71028 + 2.14213i −0.293323 + 0.169350i
\(161\) −8.61447 16.8741i −0.678916 1.32987i
\(162\) −13.5375 + 11.4639i −1.06361 + 0.900686i
\(163\) −9.84836 + 17.0579i −0.771383 + 1.33607i 0.165422 + 0.986223i \(0.447101\pi\)
−0.936805 + 0.349852i \(0.886232\pi\)
\(164\) 5.60358 9.70568i 0.437566 0.757886i
\(165\) −0.308795 0.282318i −0.0240396 0.0219784i
\(166\) 3.70212i 0.287340i
\(167\) 5.40460 9.36105i 0.418221 0.724380i −0.577540 0.816362i \(-0.695987\pi\)
0.995761 + 0.0919829i \(0.0293205\pi\)
\(168\) 0.262035 + 1.00527i 0.0202164 + 0.0775586i
\(169\) 0.959472 12.9645i 0.0738056 0.997273i
\(170\) −3.57256 + 2.06262i −0.274003 + 0.158196i
\(171\) 0.143055 + 0.203325i 0.0109397 + 0.0155486i
\(172\) 6.01455 + 10.4175i 0.458605 + 0.794328i
\(173\) 1.34374 2.32743i 0.102163 0.176951i −0.810413 0.585859i \(-0.800757\pi\)
0.912575 + 0.408908i \(0.134090\pi\)
\(174\) 9.74851 10.6628i 0.739033 0.808342i
\(175\) 0.641432 12.4258i 0.0484877 0.939300i
\(176\) −1.61802 + 0.934163i −0.121963 + 0.0704152i
\(177\) −9.89209 2.18131i −0.743535 0.163957i
\(178\) 26.0846i 1.95512i
\(179\) −2.65933 + 1.53536i −0.198767 + 0.114758i −0.596080 0.802925i \(-0.703276\pi\)
0.397313 + 0.917683i \(0.369943\pi\)
\(180\) 0.275644 + 3.07076i 0.0205453 + 0.228881i
\(181\) 14.8814i 1.10613i 0.833139 + 0.553063i \(0.186541\pi\)
−0.833139 + 0.553063i \(0.813459\pi\)
\(182\) −17.6605 6.45283i −1.30909 0.478315i
\(183\) −7.04016 6.43651i −0.520424 0.475801i
\(184\) 1.62336 0.119675
\(185\) 1.07464 + 1.86134i 0.0790095 + 0.136848i
\(186\) −14.1672 + 15.4958i −1.03879 + 1.13621i
\(187\) −1.47297 + 0.850422i −0.107715 + 0.0621890i
\(188\) 0.608755 + 1.05440i 0.0443980 + 0.0768997i
\(189\) 13.5279 + 2.44893i 0.984006 + 0.178133i
\(190\) 0.0890528 0.00646057
\(191\) 1.86007 + 1.07391i 0.134590 + 0.0777054i 0.565783 0.824554i \(-0.308574\pi\)
−0.431193 + 0.902260i \(0.641907\pi\)
\(192\) 11.9328 + 2.63132i 0.861179 + 0.189899i
\(193\) −7.16502 12.4102i −0.515749 0.893304i −0.999833 0.0182823i \(-0.994180\pi\)
0.484084 0.875022i \(-0.339153\pi\)
\(194\) 2.26957 + 3.93101i 0.162946 + 0.282230i
\(195\) 2.96188 + 1.67928i 0.212105 + 0.120255i
\(196\) −7.73901 + 10.6871i −0.552786 + 0.763361i
\(197\) 11.1575 + 6.44181i 0.794942 + 0.458960i 0.841700 0.539946i \(-0.181555\pi\)
−0.0467573 + 0.998906i \(0.514889\pi\)
\(198\) 0.234231 + 2.60941i 0.0166461 + 0.185443i
\(199\) 0.594301i 0.0421289i −0.999778 0.0210644i \(-0.993294\pi\)
0.999778 0.0210644i \(-0.00670551\pi\)
\(200\) 0.923277 + 0.533054i 0.0652855 + 0.0376926i
\(201\) 5.26173 + 16.6226i 0.371134 + 1.17247i
\(202\) 22.9456 13.2476i 1.61444 0.932100i
\(203\) −11.1817 0.577210i −0.784799 0.0405122i
\(204\) 12.2392 + 2.69888i 0.856916 + 0.188959i
\(205\) 3.24151 0.226397
\(206\) −3.79523 6.57353i −0.264426 0.457999i
\(207\) 9.03495 19.4903i 0.627972 1.35467i
\(208\) 11.1404 10.3464i 0.772451 0.717397i
\(209\) 0.0367166 0.00253974
\(210\) 3.50581 3.45836i 0.241924 0.238649i
\(211\) −0.381963 + 0.661579i −0.0262954 + 0.0455450i −0.878874 0.477055i \(-0.841704\pi\)
0.852578 + 0.522600i \(0.175038\pi\)
\(212\) −13.9391 8.04773i −0.957340 0.552720i
\(213\) 14.4182 4.56395i 0.987921 0.312717i
\(214\) 1.51128 0.103309
\(215\) −1.73962 + 3.01312i −0.118641 + 0.205493i
\(216\) −0.713929 + 0.936963i −0.0485767 + 0.0637522i
\(217\) 16.2499 + 0.838839i 1.10312 + 0.0569441i
\(218\) 5.59217 + 3.22864i 0.378749 + 0.218671i
\(219\) 18.8656 + 17.2480i 1.27482 + 1.16551i
\(220\) 0.394338 + 0.227671i 0.0265862 + 0.0153496i
\(221\) 10.1418 9.41895i 0.682210 0.633587i
\(222\) 2.89808 13.1426i 0.194506 0.882071i
\(223\) −2.67954 1.54704i −0.179435 0.103597i 0.407592 0.913164i \(-0.366369\pi\)
−0.587027 + 0.809567i \(0.699702\pi\)
\(224\) −9.45322 18.5171i −0.631620 1.23722i
\(225\) 11.5385 8.11823i 0.769234 0.541215i
\(226\) 19.5391 + 33.8428i 1.29972 + 2.25119i
\(227\) 4.64073 0.308016 0.154008 0.988070i \(-0.450782\pi\)
0.154008 + 0.988070i \(0.450782\pi\)
\(228\) −0.199683 0.182562i −0.0132243 0.0120904i
\(229\) 12.0558 6.96041i 0.796669 0.459957i −0.0456363 0.998958i \(-0.514532\pi\)
0.842305 + 0.539001i \(0.181198\pi\)
\(230\) −3.84760 6.66423i −0.253703 0.439427i
\(231\) 1.44545 1.42589i 0.0951037 0.0938164i
\(232\) 0.479683 0.830835i 0.0314927 0.0545470i
\(233\) −22.1345 + 12.7794i −1.45008 + 0.837205i −0.998485 0.0550173i \(-0.982479\pi\)
−0.451596 + 0.892222i \(0.649145\pi\)
\(234\) −6.59286 20.2750i −0.430989 1.32542i
\(235\) −0.176074 + 0.304969i −0.0114858 + 0.0198940i
\(236\) 11.0242 0.717612
\(237\) −6.04804 19.1067i −0.392863 1.24112i
\(238\) −9.10234 17.8298i −0.590017 1.15573i
\(239\) 15.5619i 1.00662i 0.864106 + 0.503309i \(0.167884\pi\)
−0.864106 + 0.503309i \(0.832116\pi\)
\(240\) 1.20170 + 3.79637i 0.0775696 + 0.245055i
\(241\) 4.85425i 0.312689i 0.987703 + 0.156345i \(0.0499711\pi\)
−0.987703 + 0.156345i \(0.950029\pi\)
\(242\) −18.4416 10.6472i −1.18547 0.684430i
\(243\) 7.27587 + 13.7863i 0.466747 + 0.884391i
\(244\) 8.99044 + 5.19063i 0.575554 + 0.332296i
\(245\) −3.79615 0.392970i −0.242527 0.0251060i
\(246\) −14.9804 13.6959i −0.955113 0.873219i
\(247\) −0.291267 + 0.0666218i −0.0185329 + 0.00423905i
\(248\) −0.697107 + 1.20742i −0.0442663 + 0.0766715i
\(249\) −3.17692 0.700545i −0.201329 0.0443952i
\(250\) 10.4268i 0.659447i
\(251\) 12.6213 + 21.8608i 0.796650 + 1.37984i 0.921786 + 0.387699i \(0.126730\pi\)
−0.125136 + 0.992140i \(0.539937\pi\)
\(252\) −14.9508 + 0.567634i −0.941814 + 0.0357576i
\(253\) −1.58637 2.74767i −0.0997342 0.172745i
\(254\) −8.62424 4.97921i −0.541133 0.312423i
\(255\) 1.09398 + 3.45605i 0.0685076 + 0.216426i
\(256\) 17.6786 1.10491
\(257\) 15.3352 0.956582 0.478291 0.878201i \(-0.341256\pi\)
0.478291 + 0.878201i \(0.341256\pi\)
\(258\) 20.7704 6.57467i 1.29311 0.409321i
\(259\) −9.28947 + 4.74241i −0.577220 + 0.294679i
\(260\) −3.54132 1.09056i −0.219623 0.0676334i
\(261\) −7.30541 10.3832i −0.452193 0.642706i
\(262\) −31.4864 + 18.1787i −1.94523 + 1.12308i
\(263\) 5.77676 3.33522i 0.356211 0.205658i −0.311207 0.950342i \(-0.600733\pi\)
0.667417 + 0.744684i \(0.267400\pi\)
\(264\) 0.0525016 + 0.165861i 0.00323125 + 0.0102080i
\(265\) 4.65538i 0.285978i
\(266\) −0.0222785 + 0.431578i −0.00136598 + 0.0264617i
\(267\) −22.3841 4.93593i −1.36988 0.302074i
\(268\) −9.48752 16.4329i −0.579543 1.00380i
\(269\) −0.524532 −0.0319813 −0.0159906 0.999872i \(-0.505090\pi\)
−0.0159906 + 0.999872i \(0.505090\pi\)
\(270\) 5.53855 + 0.710093i 0.337066 + 0.0432149i
\(271\) 28.7873i 1.74871i 0.485290 + 0.874353i \(0.338714\pi\)
−0.485290 + 0.874353i \(0.661286\pi\)
\(272\) 16.1874 0.981507
\(273\) −8.87927 + 13.9341i −0.537398 + 0.843329i
\(274\) −23.3658 −1.41158
\(275\) 2.08363i 0.125648i
\(276\) −5.03446 + 22.8309i −0.303039 + 1.37426i
\(277\) 17.4150 1.04637 0.523184 0.852220i \(-0.324744\pi\)
0.523184 + 0.852220i \(0.324744\pi\)
\(278\) −14.9952 25.9724i −0.899352 1.55772i
\(279\) 10.6167 + 15.0896i 0.635605 + 0.903391i
\(280\) 0.177886 0.274392i 0.0106307 0.0163980i
\(281\) 20.8248i 1.24230i −0.783690 0.621152i \(-0.786665\pi\)
0.783690 0.621152i \(-0.213335\pi\)
\(282\) 2.10225 0.665447i 0.125187 0.0396268i
\(283\) −23.7740 + 13.7259i −1.41322 + 0.815922i −0.995690 0.0927422i \(-0.970437\pi\)
−0.417528 + 0.908664i \(0.637103\pi\)
\(284\) −14.2536 + 8.22934i −0.845797 + 0.488321i
\(285\) 0.0168513 0.0764194i 0.000998185 0.00452669i
\(286\) −3.00927 0.926711i −0.177942 0.0547976i
\(287\) −0.810935 + 15.7094i −0.0478680 + 0.927294i
\(288\) 9.91464 21.3879i 0.584226 1.26030i
\(289\) −2.26366 −0.133157
\(290\) −4.54768 −0.267049
\(291\) 3.80281 1.20374i 0.222924 0.0705645i
\(292\) −24.0917 13.9094i −1.40986 0.813984i
\(293\) −11.5362 19.9814i −0.673955 1.16732i −0.976773 0.214276i \(-0.931261\pi\)
0.302818 0.953048i \(-0.402072\pi\)
\(294\) 15.8832 + 17.8554i 0.926328 + 1.04135i
\(295\) 1.59429 + 2.76139i 0.0928232 + 0.160775i
\(296\) 0.893684i 0.0519444i
\(297\) 2.28355 + 0.292773i 0.132505 + 0.0169884i
\(298\) 4.56272 7.90286i 0.264311 0.457801i
\(299\) 17.5700 + 18.9184i 1.01610 + 1.09408i
\(300\) −10.3602 + 11.3318i −0.598147 + 0.654244i
\(301\) −14.1673 9.18455i −0.816589 0.529389i
\(302\) −21.2194 12.2510i −1.22104 0.704966i
\(303\) −7.02632 22.1972i −0.403651 1.27520i
\(304\) −0.302626 0.174721i −0.0173568 0.0100210i
\(305\) 3.00263i 0.171930i
\(306\) 9.54663 20.5941i 0.545745 1.17728i
\(307\) 7.55190i 0.431010i −0.976503 0.215505i \(-0.930860\pi\)
0.976503 0.215505i \(-0.0691397\pi\)
\(308\) −1.20202 + 1.85412i −0.0684912 + 0.105649i
\(309\) −6.35914 + 2.01292i −0.361759 + 0.114511i
\(310\) 6.60898 0.375365
\(311\) −4.74562 + 8.21965i −0.269099 + 0.466094i −0.968629 0.248509i \(-0.920059\pi\)
0.699530 + 0.714603i \(0.253393\pi\)
\(312\) −0.717440 1.22048i −0.0406170 0.0690963i
\(313\) −5.53459 + 3.19540i −0.312834 + 0.180615i −0.648194 0.761475i \(-0.724475\pi\)
0.335360 + 0.942090i \(0.391142\pi\)
\(314\) 8.83297 15.2992i 0.498474 0.863381i
\(315\) −2.30434 3.66288i −0.129835 0.206380i
\(316\) 10.9053 + 18.8886i 0.613473 + 1.06257i
\(317\) 16.6710 9.62501i 0.936337 0.540595i 0.0475271 0.998870i \(-0.484866\pi\)
0.888810 + 0.458275i \(0.151533\pi\)
\(318\) −19.6697 + 21.5145i −1.10302 + 1.20647i
\(319\) −1.87501 −0.104981
\(320\) −1.92320 3.33107i −0.107510 0.186213i
\(321\) 0.285976 1.29688i 0.0159616 0.0723848i
\(322\) 33.2595 16.9794i 1.85348 0.946227i
\(323\) −0.275498 0.159059i −0.0153291 0.00885027i
\(324\) −10.9634 12.9465i −0.609076 0.719249i
\(325\) 3.78073 + 16.5291i 0.209717 + 0.916872i
\(326\) −33.6217 19.4115i −1.86213 1.07510i
\(327\) 3.82880 4.18789i 0.211733 0.231591i
\(328\) −1.16726 0.673917i −0.0644511 0.0372109i
\(329\) −1.43392 0.929603i −0.0790548 0.0512507i
\(330\) 0.556458 0.608646i 0.0306320 0.0335048i
\(331\) −4.58154 + 7.93547i −0.251824 + 0.436173i −0.964028 0.265800i \(-0.914364\pi\)
0.712204 + 0.701973i \(0.247697\pi\)
\(332\) 3.54049 0.194310
\(333\) −10.7297 4.97389i −0.587984 0.272567i
\(334\) 18.4510 + 10.6527i 1.00959 + 0.582888i
\(335\) 2.74413 4.75297i 0.149928 0.259683i
\(336\) −18.6990 + 4.87408i −1.02011 + 0.265903i
\(337\) 29.6751 1.61651 0.808253 0.588836i \(-0.200413\pi\)
0.808253 + 0.588836i \(0.200413\pi\)
\(338\) 25.5536 + 1.89115i 1.38993 + 0.102865i
\(339\) 32.7390 10.3632i 1.77814 0.562853i
\(340\) −1.97257 3.41659i −0.106978 0.185291i
\(341\) 2.72489 0.147561
\(342\) −0.400761 + 0.281966i −0.0216707 + 0.0152470i
\(343\) 2.85415 18.2990i 0.154109 0.988054i
\(344\) 1.25287 0.723344i 0.0675501 0.0390001i
\(345\) −6.44689 + 2.04070i −0.347089 + 0.109868i
\(346\) 4.58744 + 2.64856i 0.246622 + 0.142387i
\(347\) 24.1021i 1.29387i 0.762547 + 0.646933i \(0.223949\pi\)
−0.762547 + 0.646933i \(0.776051\pi\)
\(348\) 10.1973 + 9.32291i 0.546630 + 0.499760i
\(349\) 8.15072 + 4.70582i 0.436298 + 0.251897i 0.702026 0.712151i \(-0.252279\pi\)
−0.265728 + 0.964048i \(0.585612\pi\)
\(350\) 24.4916 + 1.26429i 1.30913 + 0.0675789i
\(351\) −18.6463 + 1.82096i −0.995265 + 0.0971958i
\(352\) −1.74083 3.01520i −0.0927864 0.160711i
\(353\) 17.6164 + 30.5125i 0.937627 + 1.62402i 0.769881 + 0.638187i \(0.220315\pi\)
0.167745 + 0.985830i \(0.446351\pi\)
\(354\) 4.29945 19.4977i 0.228513 1.03629i
\(355\) −4.12266 2.38022i −0.218808 0.126329i
\(356\) 24.9458 1.32212
\(357\) −17.0228 + 4.43715i −0.900941 + 0.234839i
\(358\) −3.02626 5.24163i −0.159943 0.277029i
\(359\) −15.9685 + 9.21941i −0.842784 + 0.486582i −0.858210 0.513299i \(-0.828423\pi\)
0.0154255 + 0.999881i \(0.495090\pi\)
\(360\) 0.369307 0.0331504i 0.0194642 0.00174718i
\(361\) −9.49657 16.4485i −0.499819 0.865712i
\(362\) −29.3318 −1.54164
\(363\) −12.6264 + 13.8106i −0.662716 + 0.724868i
\(364\) 6.17111 16.8895i 0.323454 0.885251i
\(365\) 8.04618i 0.421156i
\(366\) 12.6866 13.8764i 0.663139 0.725332i
\(367\) 10.1844 5.87995i 0.531620 0.306931i −0.210056 0.977689i \(-0.567365\pi\)
0.741676 + 0.670759i \(0.234031\pi\)
\(368\) 30.1959i 1.57407i
\(369\) −14.5876 + 10.2635i −0.759402 + 0.534298i
\(370\) −3.66877 + 2.11816i −0.190730 + 0.110118i
\(371\) 22.5614 + 1.16465i 1.17133 + 0.0604654i
\(372\) −14.8193 13.5487i −0.768346 0.702465i
\(373\) 12.7164 22.0254i 0.658429 1.14043i −0.322593 0.946538i \(-0.604555\pi\)
0.981022 0.193895i \(-0.0621121\pi\)
\(374\) −1.67621 2.90328i −0.0866749 0.150125i
\(375\) −8.94758 1.97304i −0.462051 0.101887i
\(376\) 0.126807 0.0732123i 0.00653959 0.00377564i
\(377\) 14.8742 3.40219i 0.766060 0.175222i
\(378\) −4.82692 + 26.6639i −0.248270 + 1.37144i
\(379\) 5.01100 8.67931i 0.257398 0.445826i −0.708146 0.706066i \(-0.750468\pi\)
0.965544 + 0.260240i \(0.0838016\pi\)
\(380\) 0.0851650i 0.00436887i
\(381\) −5.90478 + 6.45856i −0.302511 + 0.330882i
\(382\) −2.11672 + 3.66626i −0.108301 + 0.187582i
\(383\) 10.1434 17.5690i 0.518306 0.897732i −0.481468 0.876464i \(-0.659896\pi\)
0.999774 0.0212681i \(-0.00677036\pi\)
\(384\) 0.675306 3.06246i 0.0344616 0.156281i
\(385\) −0.638265 0.0329479i −0.0325290 0.00167918i
\(386\) 24.4609 14.1225i 1.24503 0.718817i
\(387\) −1.71161 19.0680i −0.0870061 0.969278i
\(388\) −3.75939 + 2.17049i −0.190854 + 0.110190i
\(389\) 0.485213 + 0.280138i 0.0246013 + 0.0142036i 0.512250 0.858836i \(-0.328812\pi\)
−0.487649 + 0.873040i \(0.662145\pi\)
\(390\) −3.30991 + 5.83797i −0.167604 + 0.295617i
\(391\) 27.4890i 1.39018i
\(392\) 1.28528 + 0.930736i 0.0649167 + 0.0470093i
\(393\) 9.64165 + 30.4595i 0.486357 + 1.53648i
\(394\) −12.6970 + 21.9919i −0.639668 + 1.10794i
\(395\) −3.15421 + 5.46326i −0.158706 + 0.274886i
\(396\) −2.49549 + 0.224005i −0.125403 + 0.0112567i
\(397\) −32.4132 18.7137i −1.62677 0.939216i −0.985048 0.172278i \(-0.944887\pi\)
−0.641722 0.766938i \(-0.721780\pi\)
\(398\) 1.17139 0.0587164
\(399\) 0.366136 + 0.100785i 0.0183297 + 0.00504554i
\(400\) −9.91528 + 17.1738i −0.495764 + 0.858689i
\(401\) 36.6930i 1.83236i 0.400763 + 0.916182i \(0.368745\pi\)
−0.400763 + 0.916182i \(0.631255\pi\)
\(402\) −32.7638 + 10.3711i −1.63411 + 0.517262i
\(403\) −21.6161 + 4.94429i −1.07678 + 0.246292i
\(404\) 12.6693 + 21.9438i 0.630320 + 1.09175i
\(405\) 1.65741 4.61846i 0.0823572 0.229493i
\(406\) 1.13770 22.0395i 0.0564632 1.09380i
\(407\) −1.51264 + 0.873322i −0.0749787 + 0.0432890i
\(408\) 0.324582 1.47195i 0.0160692 0.0728726i
\(409\) 23.3881i 1.15647i −0.815871 0.578234i \(-0.803742\pi\)
0.815871 0.578234i \(-0.196258\pi\)
\(410\) 6.38914i 0.315537i
\(411\) −4.42146 + 20.0510i −0.218095 + 0.989043i
\(412\) 6.28654 3.62954i 0.309716 0.178814i
\(413\) −13.7814 + 7.03560i −0.678139 + 0.346199i
\(414\) 38.4160 + 17.8082i 1.88804 + 0.875226i
\(415\) 0.512019 + 0.886842i 0.0251340 + 0.0435334i
\(416\) 19.2807 + 20.7604i 0.945316 + 1.01786i
\(417\) −25.1254 + 7.95319i −1.23039 + 0.389469i
\(418\) 0.0723698i 0.00353972i
\(419\) −3.06783 + 5.31364i −0.149873 + 0.259588i −0.931180 0.364559i \(-0.881220\pi\)
0.781307 + 0.624147i \(0.214553\pi\)
\(420\) 3.30737 + 3.35275i 0.161383 + 0.163598i
\(421\) 11.6799 0.569243 0.284622 0.958640i \(-0.408132\pi\)
0.284622 + 0.958640i \(0.408132\pi\)
\(422\) −1.30400 0.752863i −0.0634776 0.0366488i
\(423\) −0.173239 1.92994i −0.00842315 0.0938368i
\(424\) −0.967865 + 1.67639i −0.0470037 + 0.0814128i
\(425\) −9.02645 + 15.6343i −0.437847 + 0.758373i
\(426\) 8.99571 + 28.4189i 0.435844 + 1.37690i
\(427\) −14.5517 0.751175i −0.704206 0.0363519i
\(428\) 1.44530i 0.0698611i
\(429\) −1.36468 + 2.40701i −0.0658875 + 0.116211i
\(430\) −5.93897 3.42886i −0.286402 0.165354i
\(431\) 10.8897 6.28715i 0.524537 0.302841i −0.214252 0.976778i \(-0.568731\pi\)
0.738789 + 0.673937i \(0.235398\pi\)
\(432\) −17.4283 13.2797i −0.838522 0.638921i
\(433\) 33.2740 19.2107i 1.59905 0.923209i 0.607374 0.794416i \(-0.292223\pi\)
0.991671 0.128794i \(-0.0411105\pi\)
\(434\) −1.65338 + 32.0292i −0.0793649 + 1.53745i
\(435\) −0.860549 + 3.90252i −0.0412602 + 0.187112i
\(436\) −3.08768 + 5.34802i −0.147873 + 0.256124i
\(437\) 0.296707 0.513912i 0.0141934 0.0245837i
\(438\) −33.9964 + 37.1847i −1.62441 + 1.77675i
\(439\) 5.47622i 0.261366i −0.991424 0.130683i \(-0.958283\pi\)
0.991424 0.130683i \(-0.0417169\pi\)
\(440\) 0.0273810 0.0474252i 0.00130534 0.00226091i
\(441\) 18.3279 10.2512i 0.872758 0.488153i
\(442\) 18.5651 + 19.9898i 0.883052 + 0.950819i
\(443\) 32.4866 18.7562i 1.54349 0.891133i 0.544872 0.838519i \(-0.316578\pi\)
0.998615 0.0526134i \(-0.0167551\pi\)
\(444\) 12.5688 + 2.77155i 0.596488 + 0.131532i
\(445\) 3.60760 + 6.24856i 0.171017 + 0.296210i
\(446\) 3.04926 5.28148i 0.144387 0.250085i
\(447\) −5.91833 5.41088i −0.279928 0.255926i
\(448\) 16.6245 8.48706i 0.785436 0.400976i
\(449\) −8.43932 + 4.87244i −0.398276 + 0.229945i −0.685740 0.727847i \(-0.740521\pi\)
0.287464 + 0.957791i \(0.407188\pi\)
\(450\) 16.0013 + 22.7428i 0.754310 + 1.07211i
\(451\) 2.63425i 0.124042i
\(452\) −32.3653 + 18.6861i −1.52233 + 0.878920i
\(453\) −14.5283 + 15.8909i −0.682600 + 0.746618i
\(454\) 9.14705i 0.429293i
\(455\) 5.12303 0.896753i 0.240172 0.0420404i
\(456\) −0.0219559 + 0.0240150i −0.00102818 + 0.00112460i
\(457\) −2.53174 −0.118430 −0.0592148 0.998245i \(-0.518860\pi\)
−0.0592148 + 0.998245i \(0.518860\pi\)
\(458\) 13.7192 + 23.7624i 0.641057 + 1.11034i
\(459\) −15.8660 12.0893i −0.740562 0.564279i
\(460\) 6.37329 3.67962i 0.297156 0.171563i
\(461\) −6.39308 11.0731i −0.297755 0.515727i 0.677867 0.735185i \(-0.262905\pi\)
−0.975622 + 0.219457i \(0.929571\pi\)
\(462\) 2.81047 + 2.84904i 0.130755 + 0.132549i
\(463\) 8.19368 0.380792 0.190396 0.981707i \(-0.439023\pi\)
0.190396 + 0.981707i \(0.439023\pi\)
\(464\) 15.4543 + 8.92254i 0.717447 + 0.414218i
\(465\) 1.25061 5.67140i 0.0579955 0.263005i
\(466\) −25.1886 43.6280i −1.16684 2.02103i
\(467\) −17.8200 30.8651i −0.824610 1.42827i −0.902217 0.431282i \(-0.858061\pi\)
0.0776075 0.996984i \(-0.475272\pi\)
\(468\) 19.3899 6.30503i 0.896297 0.291450i
\(469\) 22.3479 + 14.4880i 1.03193 + 0.668992i
\(470\) −0.601105 0.347048i −0.0277269 0.0160081i
\(471\) −11.4573 10.4749i −0.527925 0.482659i
\(472\) 1.32583i 0.0610261i
\(473\) −2.44864 1.41373i −0.112589 0.0650032i
\(474\) 37.6600 11.9209i 1.72978 0.547546i
\(475\) 0.337501 0.194857i 0.0154856 0.00894063i
\(476\) 17.0514 8.70495i 0.781547 0.398991i
\(477\) 14.7402 + 20.9504i 0.674910 + 0.959255i
\(478\) −30.6732 −1.40296
\(479\) −4.85613 8.41107i −0.221882 0.384312i 0.733497 0.679693i \(-0.237887\pi\)
−0.955380 + 0.295381i \(0.904553\pi\)
\(480\) −7.07459 + 2.23939i −0.322909 + 0.102214i
\(481\) 10.4149 9.67259i 0.474878 0.441032i
\(482\) −9.56790 −0.435806
\(483\) −8.27703 31.7541i −0.376618 1.44486i
\(484\) 10.1824 17.6364i 0.462836 0.801656i
\(485\) −1.08735 0.627782i −0.0493740 0.0285061i
\(486\) −27.1733 + 14.3410i −1.23260 + 0.650521i
\(487\) 21.1622 0.958952 0.479476 0.877555i \(-0.340827\pi\)
0.479476 + 0.877555i \(0.340827\pi\)
\(488\) 0.624254 1.08124i 0.0282587 0.0489454i
\(489\) −23.0198 + 25.1787i −1.04099 + 1.13862i
\(490\) 0.774559 7.48235i 0.0349910 0.338018i
\(491\) −8.34337 4.81705i −0.376531 0.217390i 0.299777 0.954009i \(-0.403088\pi\)
−0.676308 + 0.736619i \(0.736421\pi\)
\(492\) 13.0980 14.3263i 0.590502 0.645882i
\(493\) 14.0689 + 8.12269i 0.633632 + 0.365828i
\(494\) −0.131314 0.574098i −0.00590810 0.0258299i
\(495\) −0.417003 0.592690i −0.0187429 0.0266394i
\(496\) −22.4592 12.9668i −1.00845 0.582227i
\(497\) 12.5667 19.3842i 0.563691 0.869501i
\(498\) 1.38080 6.26183i 0.0618751 0.280599i
\(499\) −14.6610 25.3936i −0.656316 1.13677i −0.981562 0.191143i \(-0.938780\pi\)
0.325246 0.945629i \(-0.394553\pi\)
\(500\) 9.97155 0.445941
\(501\) 12.6329 13.8176i 0.564395 0.617327i
\(502\) −43.0883 + 24.8771i −1.92313 + 1.11032i
\(503\) −1.57235 2.72340i −0.0701078 0.121430i 0.828841 0.559485i \(-0.189001\pi\)
−0.898948 + 0.438055i \(0.855668\pi\)
\(504\) 0.0682669 + 1.79807i 0.00304085 + 0.0800924i
\(505\) −3.66441 + 6.34694i −0.163064 + 0.282435i
\(506\) 5.41577 3.12679i 0.240760 0.139003i
\(507\) 6.45832 21.5706i 0.286824 0.957983i
\(508\) 4.76183 8.24772i 0.211272 0.365934i
\(509\) −29.0330 −1.28686 −0.643432 0.765504i \(-0.722490\pi\)
−0.643432 + 0.765504i \(0.722490\pi\)
\(510\) −6.81200 + 2.15627i −0.301640 + 0.0954813i
\(511\) 38.9943 + 2.01293i 1.72500 + 0.0890467i
\(512\) 31.2240i 1.37992i
\(513\) 0.166130 + 0.397263i 0.00733482 + 0.0175396i
\(514\) 30.2262i 1.33322i
\(515\) 1.81829 + 1.04979i 0.0801236 + 0.0462594i
\(516\) 6.28764 + 19.8636i 0.276798 + 0.874447i
\(517\) −0.247836 0.143088i −0.0108998 0.00629302i
\(518\) −9.34746 18.3099i −0.410704 0.804490i
\(519\) 3.14090 3.43546i 0.137870 0.150800i
\(520\) −0.131156 + 0.425899i −0.00575159 + 0.0186769i
\(521\) 0.304773 0.527883i 0.0133524 0.0231270i −0.859272 0.511519i \(-0.829083\pi\)
0.872624 + 0.488392i \(0.162416\pi\)
\(522\) 20.4657 14.3992i 0.895761 0.630237i
\(523\) 26.6694i 1.16617i 0.812411 + 0.583086i \(0.198155\pi\)
−0.812411 + 0.583086i \(0.801845\pi\)
\(524\) −17.3850 30.1117i −0.759468 1.31544i
\(525\) 5.71944 20.7779i 0.249617 0.906822i
\(526\) 6.57383 + 11.3862i 0.286633 + 0.496463i
\(527\) −20.4459 11.8044i −0.890636 0.514209i
\(528\) −3.08516 + 0.976578i −0.134264 + 0.0425001i
\(529\) −28.2778 −1.22947
\(530\) 9.17593 0.398577
\(531\) −15.9181 7.37901i −0.690785 0.320222i
\(532\) −0.412736 0.0213059i −0.0178944 0.000923727i
\(533\) −4.77981 20.8971i −0.207037 0.905153i
\(534\) 9.72890 44.1199i 0.421011 1.90925i
\(535\) −0.362026 + 0.209016i −0.0156518 + 0.00903655i
\(536\) −1.97631 + 1.14102i −0.0853635 + 0.0492846i
\(537\) −5.07068 + 1.60507i −0.218816 + 0.0692640i
\(538\) 1.03387i 0.0445733i
\(539\) 0.319352 3.08499i 0.0137555 0.132880i
\(540\) −0.679092 + 5.29675i −0.0292235 + 0.227936i
\(541\) −10.7583 18.6339i −0.462534 0.801133i 0.536552 0.843867i \(-0.319726\pi\)
−0.999086 + 0.0427343i \(0.986393\pi\)
\(542\) −56.7409 −2.43723
\(543\) −5.55040 + 25.1706i −0.238190 + 1.08018i
\(544\) 30.1655i 1.29334i
\(545\) −1.78614 −0.0765097
\(546\) −27.4646 17.5014i −1.17538 0.748989i
\(547\) −18.1656 −0.776705 −0.388353 0.921511i \(-0.626956\pi\)
−0.388353 + 0.921511i \(0.626956\pi\)
\(548\) 22.3457i 0.954560i
\(549\) −9.50718 13.5126i −0.405757 0.576705i
\(550\) 4.10692 0.175120
\(551\) −0.175347 0.303710i −0.00747003 0.0129385i
\(552\) 2.74577 + 0.605473i 0.116868 + 0.0257706i
\(553\) −25.6875 16.6530i −1.09235 0.708159i
\(554\) 34.3257i 1.45836i
\(555\) 1.12344 + 3.54912i 0.0476873 + 0.150652i
\(556\) 24.8385 14.3405i 1.05339 0.608174i
\(557\) 28.7566 16.6026i 1.21845 0.703475i 0.253868 0.967239i \(-0.418297\pi\)
0.964587 + 0.263764i \(0.0849639\pi\)
\(558\) −29.7421 + 20.9259i −1.25909 + 0.885864i
\(559\) 21.9899 + 6.77182i 0.930073 + 0.286417i
\(560\) 5.10393 + 3.30884i 0.215680 + 0.139824i
\(561\) −2.80860 + 0.889034i −0.118579 + 0.0375351i
\(562\) 41.0465 1.73144
\(563\) 22.5352 0.949744 0.474872 0.880055i \(-0.342494\pi\)
0.474872 + 0.880055i \(0.342494\pi\)
\(564\) 0.636395 + 2.01047i 0.0267971 + 0.0846561i
\(565\) −9.36120 5.40469i −0.393828 0.227377i
\(566\) −27.0543 46.8594i −1.13718 1.96965i
\(567\) 21.9678 + 9.18771i 0.922563 + 0.385848i
\(568\) 0.989706 + 1.71422i 0.0415271 + 0.0719271i
\(569\) 25.8988i 1.08573i −0.839819 0.542867i \(-0.817339\pi\)
0.839819 0.542867i \(-0.182661\pi\)
\(570\) 0.150625 + 0.0332145i 0.00630900 + 0.00139120i
\(571\) 5.54250 9.59990i 0.231947 0.401743i −0.726434 0.687236i \(-0.758824\pi\)
0.958381 + 0.285493i \(0.0921572\pi\)
\(572\) 0.886252 2.87790i 0.0370561 0.120331i
\(573\) 2.74560 + 2.51019i 0.114699 + 0.104865i
\(574\) −30.9637 1.59838i −1.29240 0.0667152i
\(575\) −29.1640 16.8379i −1.21622 0.702187i
\(576\) 19.2020 + 8.90132i 0.800083 + 0.370888i
\(577\) −15.6001 9.00673i −0.649441 0.374955i 0.138801 0.990320i \(-0.455675\pi\)
−0.788242 + 0.615365i \(0.789009\pi\)
\(578\) 4.46177i 0.185585i
\(579\) −7.49034 23.6632i −0.311288 0.983407i
\(580\) 4.34914i 0.180588i
\(581\) −4.42601 + 2.25954i −0.183622 + 0.0937414i
\(582\) 2.37262 + 7.49547i 0.0983481 + 0.310697i
\(583\) 3.78325 0.156686
\(584\) −1.67282 + 2.89741i −0.0692217 + 0.119896i
\(585\) 4.38344 + 3.94506i 0.181233 + 0.163108i
\(586\) 39.3840 22.7384i 1.62694 0.939313i
\(587\) 5.52925 9.57695i 0.228217 0.395283i −0.729063 0.684447i \(-0.760044\pi\)
0.957280 + 0.289164i \(0.0933772\pi\)
\(588\) −17.0759 + 15.1898i −0.704198 + 0.626416i
\(589\) 0.254826 + 0.441371i 0.0104999 + 0.0181864i
\(590\) −5.44281 + 3.14241i −0.224077 + 0.129371i
\(591\) 16.4694 + 15.0573i 0.677461 + 0.619374i
\(592\) 16.6233 0.683215
\(593\) −6.34378 10.9878i −0.260508 0.451213i 0.705869 0.708342i \(-0.250557\pi\)
−0.966377 + 0.257129i \(0.917223\pi\)
\(594\) −0.577065 + 4.50097i −0.0236773 + 0.184677i
\(595\) 4.64640 + 3.01223i 0.190484 + 0.123489i
\(596\) 7.55784 + 4.36352i 0.309581 + 0.178737i
\(597\) 0.221660 1.00521i 0.00907193 0.0411405i
\(598\) −37.2889 + 34.6312i −1.52485 + 1.41617i
\(599\) −31.3527 18.1015i −1.28104 0.739607i −0.303999 0.952672i \(-0.598322\pi\)
−0.977038 + 0.213066i \(0.931655\pi\)
\(600\) 1.36283 + 1.24598i 0.0556373 + 0.0508668i
\(601\) 40.7500 + 23.5270i 1.66223 + 0.959687i 0.971649 + 0.236428i \(0.0759768\pi\)
0.690577 + 0.723258i \(0.257356\pi\)
\(602\) 18.1031 27.9243i 0.737827 1.13811i
\(603\) 2.69994 + 30.0783i 0.109950 + 1.22488i
\(604\) 11.7162 20.2930i 0.476724 0.825710i
\(605\) 5.89023 0.239472
\(606\) 43.7516 13.8491i 1.77729 0.562582i
\(607\) −16.6623 9.61998i −0.676302 0.390463i 0.122158 0.992511i \(-0.461018\pi\)
−0.798460 + 0.602048i \(0.794352\pi\)
\(608\) 0.325596 0.563949i 0.0132047 0.0228711i
\(609\) −18.6976 5.14679i −0.757663 0.208558i
\(610\) −5.91830 −0.239625
\(611\) 2.22568 + 0.685401i 0.0900413 + 0.0277284i
\(612\) 19.6950 + 9.12985i 0.796122 + 0.369052i
\(613\) 7.03355 + 12.1825i 0.284082 + 0.492045i 0.972386 0.233377i \(-0.0749777\pi\)
−0.688304 + 0.725423i \(0.741644\pi\)
\(614\) 14.8851 0.600712
\(615\) 5.48274 + 1.20900i 0.221086 + 0.0487518i
\(616\) 0.222987 + 0.144561i 0.00898442 + 0.00582453i
\(617\) −9.60577 + 5.54589i −0.386714 + 0.223269i −0.680735 0.732530i \(-0.738340\pi\)
0.294022 + 0.955799i \(0.405006\pi\)
\(618\) −3.96755 12.5341i −0.159598 0.504195i
\(619\) 11.7915 + 6.80781i 0.473939 + 0.273629i 0.717887 0.696159i \(-0.245109\pi\)
−0.243948 + 0.969788i \(0.578443\pi\)
\(620\) 6.32045i 0.253835i
\(621\) 22.5513 29.5963i 0.904951 1.18766i
\(622\) −16.2012 9.35378i −0.649610 0.375053i
\(623\) −31.1850 + 15.9204i −1.24940 + 0.637836i
\(624\) 22.7021 13.3450i 0.908812 0.534228i
\(625\) −10.3148 17.8658i −0.412593 0.714631i
\(626\) −6.29825 10.9089i −0.251729 0.436007i
\(627\) 0.0621031 + 0.0136944i 0.00248016 + 0.000546902i
\(628\) 14.6312 + 8.44734i 0.583850 + 0.337086i
\(629\) 15.1332 0.603399
\(630\) 7.21967 4.54194i 0.287638 0.180955i
\(631\) −12.1974 21.1265i −0.485571 0.841034i 0.514291 0.857616i \(-0.328055\pi\)
−0.999863 + 0.0165816i \(0.994722\pi\)
\(632\) 2.27165 1.31154i 0.0903613 0.0521701i
\(633\) −0.892811 + 0.976543i −0.0354861 + 0.0388141i
\(634\) 18.9713 + 32.8592i 0.753445 + 1.30500i
\(635\) 2.75458 0.109312
\(636\) −20.5752 18.8110i −0.815859 0.745905i
\(637\) 3.06430 + 25.0521i 0.121412 + 0.992602i
\(638\) 3.69572i 0.146315i
\(639\) 26.0895 2.34189i 1.03208 0.0926438i
\(640\) −0.854892 + 0.493572i −0.0337926 + 0.0195101i
\(641\) 4.15171i 0.163983i 0.996633 + 0.0819914i \(0.0261280\pi\)
−0.996633 + 0.0819914i \(0.973872\pi\)
\(642\) 2.55620 + 0.563670i 0.100885 + 0.0222463i
\(643\) −6.06294 + 3.50044i −0.239099 + 0.138044i −0.614762 0.788712i \(-0.710748\pi\)
0.375664 + 0.926756i \(0.377415\pi\)
\(644\) 16.2382 + 31.8075i 0.639873 + 1.25339i
\(645\) −4.06625 + 4.44760i −0.160108 + 0.175124i
\(646\) 0.313511 0.543017i 0.0123349 0.0213647i
\(647\) 3.62396 + 6.27689i 0.142473 + 0.246770i 0.928427 0.371514i \(-0.121161\pi\)
−0.785955 + 0.618284i \(0.787828\pi\)
\(648\) −1.55702 + 1.31852i −0.0611653 + 0.0517962i
\(649\) −2.24408 + 1.29562i −0.0880877 + 0.0508575i
\(650\) −32.5795 + 7.45196i −1.27787 + 0.292290i
\(651\) 27.1725 + 7.47965i 1.06497 + 0.293151i
\(652\) 18.5640 32.1538i 0.727023 1.25924i
\(653\) 11.2380i 0.439775i 0.975525 + 0.219888i \(0.0705691\pi\)
−0.975525 + 0.219888i \(0.929431\pi\)
\(654\) 8.25448 + 7.54671i 0.322776 + 0.295100i
\(655\) 5.02837 8.70940i 0.196475 0.340304i
\(656\) 12.5355 21.7121i 0.489428 0.847714i
\(657\) 25.4765 + 36.2099i 0.993931 + 1.41268i
\(658\) 1.83228 2.82632i 0.0714298 0.110181i
\(659\) −13.9778 + 8.07010i −0.544499 + 0.314366i −0.746900 0.664936i \(-0.768459\pi\)
0.202402 + 0.979303i \(0.435125\pi\)
\(660\) 0.582073 + 0.532165i 0.0226572 + 0.0207145i
\(661\) 35.4897 20.4900i 1.38039 0.796967i 0.388182 0.921583i \(-0.373103\pi\)
0.992205 + 0.124615i \(0.0397697\pi\)
\(662\) −15.6411 9.03039i −0.607908 0.350976i
\(663\) 20.6670 12.1487i 0.802640 0.471818i
\(664\) 0.425799i 0.0165242i
\(665\) −0.0543522 0.106466i −0.00210769 0.00412856i
\(666\) 9.80371 21.1486i 0.379886 0.819493i
\(667\) −15.1520 + 26.2440i −0.586688 + 1.01617i
\(668\) −10.1876 + 17.6454i −0.394170 + 0.682722i
\(669\) −3.95522 3.61608i −0.152918 0.139806i
\(670\) 9.36829 + 5.40878i 0.361928 + 0.208959i
\(671\) −2.44012 −0.0942000
\(672\) −9.08292 34.8459i −0.350381 1.34421i
\(673\) −12.9872 + 22.4945i −0.500621 + 0.867100i 0.499379 + 0.866384i \(0.333562\pi\)
−1.00000 0.000716818i \(0.999772\pi\)
\(674\) 58.4907i 2.25298i
\(675\) 22.5443 9.42773i 0.867731 0.362873i
\(676\) −1.80859 + 24.4380i −0.0695612 + 0.939922i
\(677\) 14.1017 + 24.4249i 0.541974 + 0.938727i 0.998791 + 0.0491659i \(0.0156563\pi\)
−0.456816 + 0.889561i \(0.651010\pi\)
\(678\) 20.4263 + 64.5298i 0.784467 + 2.47825i
\(679\) 3.31445 5.11258i 0.127197 0.196203i
\(680\) −0.410899 + 0.237232i −0.0157572 + 0.00909745i
\(681\) 7.84941 + 1.73088i 0.300790 + 0.0663275i
\(682\) 5.37087i 0.205661i
\(683\) 18.1673i 0.695152i 0.937652 + 0.347576i \(0.112995\pi\)
−0.937652 + 0.347576i \(0.887005\pi\)
\(684\) −0.269656 0.383264i −0.0103106 0.0146545i
\(685\) 5.59727 3.23158i 0.213861 0.123472i
\(686\) 36.0680 + 5.62563i 1.37708 + 0.214787i
\(687\) 22.9874 7.27644i 0.877024 0.277613i
\(688\) 13.4548 + 23.3045i 0.512961 + 0.888475i
\(689\) −30.0119 + 6.86466i −1.14336 + 0.261523i
\(690\) −4.02229 12.7071i −0.153126 0.483749i
\(691\) 16.9791i 0.645916i −0.946413 0.322958i \(-0.895323\pi\)
0.946413 0.322958i \(-0.104677\pi\)
\(692\) −2.53293 + 4.38716i −0.0962875 + 0.166775i
\(693\) 2.97668 1.87265i 0.113075 0.0711361i
\(694\) −47.5060 −1.80330
\(695\) 7.18419 + 4.14780i 0.272512 + 0.157335i
\(696\) 1.12122 1.22638i 0.0424999 0.0464858i
\(697\) 11.4117 19.7657i 0.432251 0.748680i
\(698\) −9.27534 + 16.0654i −0.351077 + 0.608083i
\(699\) −42.2051 + 13.3596i −1.59634 + 0.505307i
\(700\) −1.20909 + 23.4224i −0.0456993 + 0.885283i
\(701\) 15.1990i 0.574057i 0.957922 + 0.287029i \(0.0926675\pi\)
−0.957922 + 0.287029i \(0.907333\pi\)
\(702\) −3.58918 36.7525i −0.135465 1.38713i
\(703\) −0.282917 0.163342i −0.0106704 0.00616056i
\(704\) 2.70703 1.56291i 0.102025 0.0589043i
\(705\) −0.411560 + 0.450158i −0.0155003 + 0.0169539i
\(706\) −60.1413 + 34.7226i −2.26345 + 1.30680i
\(707\) −29.8425 19.3467i −1.12234 0.727607i
\(708\) 18.6464 + 4.11174i 0.700776 + 0.154529i
\(709\) −1.99144 + 3.44927i −0.0747899 + 0.129540i −0.900995 0.433830i \(-0.857162\pi\)
0.826205 + 0.563370i \(0.190495\pi\)
\(710\) 4.69150 8.12591i 0.176069 0.304960i
\(711\) −3.10342 34.5732i −0.116387 1.29660i
\(712\) 3.00012i 0.112434i
\(713\) 22.0199 38.1395i 0.824651 1.42834i
\(714\) −8.74579 33.5525i −0.327303 1.25567i
\(715\) 0.849039 0.194202i 0.0317523 0.00726274i
\(716\) 5.01279 2.89414i 0.187337 0.108159i
\(717\) −5.80422 + 26.3217i −0.216763 + 0.983003i
\(718\) −18.1718 31.4745i −0.678165 1.17462i
\(719\) 19.2400 33.3246i 0.717530 1.24280i −0.244445 0.969663i \(-0.578606\pi\)
0.961976 0.273136i \(-0.0880608\pi\)
\(720\) 0.616628 + 6.86945i 0.0229804 + 0.256009i
\(721\) −5.54250 + 8.54938i −0.206414 + 0.318396i
\(722\) 32.4207 18.7181i 1.20657 0.696615i
\(723\) −1.81051 + 8.21055i −0.0673338 + 0.305354i
\(724\) 28.0512i 1.04252i
\(725\) −17.2353 + 9.95078i −0.640101 + 0.369563i
\(726\) −27.2212 24.8872i −1.01027 0.923649i
\(727\) 46.7806i 1.73500i −0.497439 0.867499i \(-0.665726\pi\)
0.497439 0.867499i \(-0.334274\pi\)
\(728\) −2.03123 0.742172i −0.0752823 0.0275067i
\(729\) 7.16457 + 26.0321i 0.265355 + 0.964151i
\(730\) 15.8593 0.586979
\(731\) 12.2487 + 21.2154i 0.453035 + 0.784679i
\(732\) 13.2706 + 12.1327i 0.490495 + 0.448439i
\(733\) −24.6315 + 14.2210i −0.909784 + 0.525264i −0.880362 0.474303i \(-0.842700\pi\)
−0.0294225 + 0.999567i \(0.509367\pi\)
\(734\) 11.5896 + 20.0738i 0.427780 + 0.740936i
\(735\) −6.27430 2.08055i −0.231431 0.0767422i
\(736\) −56.2705 −2.07416
\(737\) 3.86256 + 2.23005i 0.142279 + 0.0821449i
\(738\) −20.2298 28.7528i −0.744669 1.05840i
\(739\) 13.6727 + 23.6818i 0.502959 + 0.871151i 0.999994 + 0.00342014i \(0.00108867\pi\)
−0.497035 + 0.867730i \(0.665578\pi\)
\(740\) −2.02569 3.50860i −0.0744658 0.128979i
\(741\) −0.517502 + 0.00404983i −0.0190109 + 0.000148774i
\(742\) −2.29556 + 44.4694i −0.0842727 + 1.63252i
\(743\) −46.2640 26.7105i −1.69726 0.979914i −0.948340 0.317256i \(-0.897239\pi\)
−0.748921 0.662659i \(-0.769428\pi\)
\(744\) −1.62944 + 1.78225i −0.0597381 + 0.0653406i
\(745\) 2.52417i 0.0924786i
\(746\) 43.4129 + 25.0644i 1.58946 + 0.917675i
\(747\) −5.11221 2.36983i −0.187046 0.0867074i
\(748\) 2.77653 1.60303i 0.101520 0.0586127i
\(749\) −0.922388 1.80678i −0.0337033 0.0660184i
\(750\) 3.88893 17.6360i 0.142004 0.643976i
\(751\) −9.92940 −0.362329 −0.181164 0.983453i \(-0.557987\pi\)
−0.181164 + 0.983453i \(0.557987\pi\)
\(752\) 1.36181 + 2.35873i 0.0496603 + 0.0860141i
\(753\) 13.1944 + 41.6831i 0.480829 + 1.51902i
\(754\) 6.70584 + 29.3176i 0.244212 + 1.06768i
\(755\) 6.77747 0.246657
\(756\) −25.4998 4.61619i −0.927419 0.167889i
\(757\) 19.0677 33.0262i 0.693028 1.20036i −0.277814 0.960635i \(-0.589610\pi\)
0.970841 0.239724i \(-0.0770569\pi\)
\(758\) 17.1072 + 9.87686i 0.621363 + 0.358744i
\(759\) −1.65840 5.23914i −0.0601960 0.190169i
\(760\) 0.0102424 0.000371531
\(761\) −20.1162 + 34.8423i −0.729211 + 1.26303i 0.228006 + 0.973660i \(0.426779\pi\)
−0.957217 + 0.289371i \(0.906554\pi\)
\(762\) −12.7301 11.6385i −0.461161 0.421620i
\(763\) 0.446841 8.65617i 0.0161767 0.313374i
\(764\) −3.50620 2.02430i −0.126850 0.0732367i
\(765\) 0.561351 + 6.25365i 0.0202957 + 0.226101i
\(766\) 34.6291 + 19.9931i 1.25120 + 0.722380i
\(767\) 15.4510 14.3498i 0.557904 0.518141i
\(768\) 29.9019 + 6.59370i 1.07899 + 0.237930i
\(769\) −16.6964 9.63964i −0.602086 0.347614i 0.167776 0.985825i \(-0.446342\pi\)
−0.769862 + 0.638211i \(0.779675\pi\)
\(770\) 0.0649416 1.25804i 0.00234033 0.0453367i
\(771\) 25.9382 + 5.71965i 0.934140 + 0.205988i
\(772\) 13.5060 + 23.3930i 0.486090 + 0.841932i
\(773\) −7.51951 −0.270458 −0.135229 0.990814i \(-0.543177\pi\)
−0.135229 + 0.990814i \(0.543177\pi\)
\(774\) 37.5836 3.37365i 1.35092 0.121263i
\(775\) 25.0474 14.4611i 0.899729 0.519459i
\(776\) 0.261035 + 0.452125i 0.00937060 + 0.0162304i
\(777\) −17.4812 + 4.55664i −0.627133 + 0.163468i
\(778\) −0.552162 + 0.956373i −0.0197960 + 0.0342876i
\(779\) −0.426689 + 0.246349i −0.0152877 + 0.00882636i
\(780\) −5.58310 3.16541i −0.199907 0.113340i
\(781\) 1.93431 3.35033i 0.0692151 0.119884i
\(782\) −54.1819 −1.93754
\(783\) −8.48379 20.2871i −0.303186 0.725002i
\(784\) −17.3125 + 23.9074i −0.618305 + 0.853837i
\(785\) 4.88655i 0.174408i
\(786\) −60.0368 + 19.0040i −2.14144 + 0.677852i
\(787\) 15.7870i 0.562745i 0.959599 + 0.281372i \(0.0907896\pi\)
−0.959599 + 0.281372i \(0.909210\pi\)
\(788\) −21.0318 12.1427i −0.749227 0.432566i
\(789\) 11.0149 3.48665i 0.392140 0.124128i
\(790\) −10.7683 6.21707i −0.383118 0.221193i
\(791\) 28.5347 44.0151i 1.01458 1.56500i
\(792\) 0.0269401 + 0.300122i 0.000957274 + 0.0106644i
\(793\) 19.3571 4.42758i 0.687391 0.157228i
\(794\) 36.8855 63.8875i 1.30902 2.26728i
\(795\) 1.73634 7.87419i 0.0615818 0.279269i
\(796\) 1.12025i 0.0397061i
\(797\) 19.7148 + 34.1470i 0.698333 + 1.20955i 0.969044 + 0.246888i \(0.0794078\pi\)
−0.270711 + 0.962661i \(0.587259\pi\)
\(798\) −0.198650 + 0.721668i −0.00703214 + 0.0255468i
\(799\) 1.23974 + 2.14729i 0.0438587 + 0.0759656i
\(800\) −32.0036 18.4773i −1.13150 0.653270i
\(801\) −36.0198 16.6974i −1.27270 0.589975i
\(802\) −72.3233 −2.55383
\(803\) 6.53882 0.230750
\(804\) −9.91829 31.3334i −0.349791 1.10504i
\(805\) −5.61898 + 8.66735i −0.198043 + 0.305484i
\(806\) −9.74537 42.6062i −0.343266 1.50074i
\(807\) −0.887201 0.195637i −0.0312310 0.00688676i
\(808\) 2.63909 1.52368i 0.0928427 0.0536028i
\(809\) 20.7823 11.9987i 0.730668 0.421851i −0.0879985 0.996121i \(-0.528047\pi\)
0.818667 + 0.574269i \(0.194714\pi\)
\(810\) 9.10315 + 3.26681i 0.319852 + 0.114784i
\(811\) 50.3082i 1.76656i 0.468845 + 0.883280i \(0.344670\pi\)
−0.468845 + 0.883280i \(0.655330\pi\)
\(812\) 21.0773 + 1.08803i 0.739667 + 0.0381824i
\(813\) −10.7370 + 48.6914i −0.376562 + 1.70768i
\(814\) −1.72135 2.98147i −0.0603333 0.104500i
\(815\) 10.7388 0.376162
\(816\) 27.3797 + 6.03752i 0.958481 + 0.211355i
\(817\) 0.528833i 0.0185015i
\(818\) 46.0988 1.61181
\(819\) −20.2156 + 20.2566i −0.706391 + 0.707822i
\(820\) −6.11020 −0.213377
\(821\) 38.8168i 1.35472i 0.735654 + 0.677358i \(0.236875\pi\)
−0.735654 + 0.677358i \(0.763125\pi\)
\(822\) −39.5212 8.71486i −1.37846 0.303966i
\(823\) 35.5039 1.23759 0.618794 0.785554i \(-0.287622\pi\)
0.618794 + 0.785554i \(0.287622\pi\)
\(824\) −0.436508 0.756054i −0.0152065 0.0263384i
\(825\) 0.777145 3.52429i 0.0270567 0.122700i
\(826\) −13.8674 27.1637i −0.482510 0.945145i
\(827\) 53.7244i 1.86818i 0.357037 + 0.934090i \(0.383787\pi\)
−0.357037 + 0.934090i \(0.616213\pi\)
\(828\) −17.0307 + 36.7389i −0.591859 + 1.27676i
\(829\) −1.02755 + 0.593257i −0.0356884 + 0.0206047i −0.517738 0.855539i \(-0.673226\pi\)
0.482050 + 0.876144i \(0.339892\pi\)
\(830\) −1.74800 + 1.00921i −0.0606739 + 0.0350301i
\(831\) 29.4561 + 6.49539i 1.02182 + 0.225322i
\(832\) −18.6386 + 17.3102i −0.646177 + 0.600122i
\(833\) −15.7606 + 21.7643i −0.546072 + 0.754088i
\(834\) −15.6760 49.5230i −0.542816 1.71484i
\(835\) −5.89324 −0.203944
\(836\) −0.0692103 −0.00239369
\(837\) 12.3292 + 29.4826i 0.426160 + 1.01907i
\(838\) −10.4734 6.04680i −0.361797 0.208883i
\(839\) 19.6280 + 33.9966i 0.677632 + 1.17369i 0.975692 + 0.219146i \(0.0703272\pi\)
−0.298060 + 0.954547i \(0.596339\pi\)
\(840\) 0.403221 0.397763i 0.0139124 0.0137241i
\(841\) −5.54552 9.60513i −0.191225 0.331211i
\(842\) 23.0215i 0.793373i
\(843\) 7.76715 35.2234i 0.267515 1.21316i
\(844\) 0.719994 1.24707i 0.0247832 0.0429258i
\(845\) −6.38291 + 3.08114i −0.219579 + 0.105995i
\(846\) 3.80398 0.341460i 0.130784 0.0117396i
\(847\) −1.47357 + 28.5459i −0.0506325 + 0.980848i
\(848\) −31.1824 18.0032i −1.07081 0.618231i
\(849\) −45.3312 + 14.3491i −1.55576 + 0.492461i
\(850\) −30.8157 17.7915i −1.05697 0.610242i
\(851\) 28.2293i 0.967687i
\(852\) −27.1782 + 8.60298i −0.931108 + 0.294733i
\(853\) 15.9126i 0.544837i −0.962179 0.272419i \(-0.912176\pi\)
0.962179 0.272419i \(-0.0878236\pi\)
\(854\) 1.48059 28.6819i 0.0506649 0.981475i
\(855\) 0.0570051 0.122972i 0.00194953 0.00420555i
\(856\) 0.173820 0.00594103
\(857\) 22.9820 39.8060i 0.785051 1.35975i −0.143918 0.989590i \(-0.545970\pi\)
0.928969 0.370158i \(-0.120697\pi\)
\(858\) −4.74430 2.68984i −0.161968 0.0918296i
\(859\) 22.1304 12.7770i 0.755079 0.435945i −0.0724471 0.997372i \(-0.523081\pi\)
0.827526 + 0.561427i \(0.189748\pi\)
\(860\) 3.27917 5.67968i 0.111819 0.193676i
\(861\) −7.23084 + 26.2686i −0.246426 + 0.895232i
\(862\) 12.3922 + 21.4639i 0.422080 + 0.731064i
\(863\) −23.8124 + 13.7481i −0.810582 + 0.467990i −0.847158 0.531341i \(-0.821688\pi\)
0.0365758 + 0.999331i \(0.488355\pi\)
\(864\) 24.7470 32.4780i 0.841909 1.10492i
\(865\) −1.46523 −0.0498193
\(866\) 37.8651 + 65.5842i 1.28671 + 2.22864i
\(867\) −3.82880 0.844292i −0.130033 0.0286736i
\(868\) −30.6309 1.58120i −1.03968 0.0536694i
\(869\) −4.43978 2.56331i −0.150609 0.0869542i
\(870\) −7.69202 1.69617i −0.260784 0.0575057i
\(871\) −34.6874 10.6821i −1.17534 0.361948i
\(872\) 0.643183 + 0.371342i 0.0217809 + 0.0125752i
\(873\) 6.88109 0.617673i 0.232890 0.0209051i
\(874\) 1.01294 + 0.584820i 0.0342632 + 0.0197818i
\(875\) −12.4655 + 6.36383i −0.421412 + 0.215137i
\(876\) −35.5613 32.5122i −1.20151 1.09848i
\(877\) −6.52932 + 11.3091i −0.220479 + 0.381882i −0.954954 0.296755i \(-0.904096\pi\)
0.734474 + 0.678637i \(0.237429\pi\)
\(878\) 10.7938 0.364274
\(879\) −12.0600 38.0995i −0.406775 1.28507i
\(880\) 0.882152 + 0.509311i 0.0297373 + 0.0171689i
\(881\) 5.11869 8.86583i 0.172453 0.298698i −0.766824 0.641858i \(-0.778164\pi\)
0.939277 + 0.343160i \(0.111497\pi\)
\(882\) 20.2055 + 36.1250i 0.680355 + 1.21639i
\(883\) −15.5517 −0.523357 −0.261679 0.965155i \(-0.584276\pi\)
−0.261679 + 0.965155i \(0.584276\pi\)
\(884\) −19.1171 + 17.7546i −0.642978 + 0.597151i
\(885\) 1.66668 + 5.26530i 0.0560248 + 0.176991i
\(886\) 36.9691 + 64.0324i 1.24200 + 2.15121i
\(887\) 17.1468 0.575732 0.287866 0.957671i \(-0.407054\pi\)
0.287866 + 0.957671i \(0.407054\pi\)
\(888\) 0.333322 1.51159i 0.0111856 0.0507257i
\(889\) −0.689119 + 13.3496i −0.0231123 + 0.447730i
\(890\) −12.3161 + 7.11072i −0.412838 + 0.238352i
\(891\) 3.75324 + 1.34691i 0.125738 + 0.0451232i
\(892\) 5.05090 + 2.91614i 0.169117 + 0.0976395i
\(893\) 0.0535251i 0.00179115i
\(894\) 10.6650 11.6653i 0.356692 0.390144i
\(895\) 1.44988 + 0.837088i 0.0484641 + 0.0279808i
\(896\) −2.17813 4.26655i −0.0727663 0.142535i
\(897\) 22.6621 + 38.5521i 0.756667 + 1.28722i
\(898\) −9.60376 16.6342i −0.320482 0.555091i
\(899\) −13.0132 22.5396i −0.434016 0.751737i
\(900\) −21.7499 + 15.3027i −0.724997 + 0.510091i
\(901\) −28.3871 16.3893i −0.945711 0.546007i
\(902\) −5.19220 −0.172881
\(903\) −20.5372 20.8190i −0.683435 0.692812i
\(904\) 2.24729 + 3.89243i 0.0747439 + 0.129460i
\(905\) 7.02643 4.05671i 0.233566 0.134850i
\(906\) −31.3215 28.6359i −1.04059 0.951363i
\(907\) −17.4511 30.2261i −0.579453 1.00364i −0.995542 0.0943177i \(-0.969933\pi\)
0.416090 0.909324i \(-0.363400\pi\)
\(908\) −8.74771 −0.290303
\(909\) −3.60540 40.1654i −0.119584 1.33220i
\(910\) 1.76753 + 10.0977i 0.0585931 + 0.334735i
\(911\) 57.9344i 1.91945i −0.280940 0.959725i \(-0.590646\pi\)
0.280940 0.959725i \(-0.409354\pi\)
\(912\) −0.446700 0.408399i −0.0147917 0.0135234i
\(913\) −0.720703 + 0.416098i −0.0238518 + 0.0137708i
\(914\) 4.99014i 0.165059i
\(915\) −1.11991 + 5.07870i −0.0370230 + 0.167897i
\(916\) −22.7250 + 13.1203i −0.750854 + 0.433506i
\(917\) 40.9505 + 26.5479i 1.35230 + 0.876689i
\(918\) 23.8284 31.2725i 0.786455 1.03215i
\(919\) 6.65431 11.5256i 0.219505 0.380195i −0.735151 0.677903i \(-0.762889\pi\)
0.954657 + 0.297708i \(0.0962223\pi\)
\(920\) −0.442532 0.766487i −0.0145898 0.0252703i
\(921\) 2.81667 12.7734i 0.0928125 0.420898i
\(922\) 21.8256 12.6010i 0.718786 0.414992i
\(923\) −9.26546 + 30.0874i −0.304976 + 0.990338i
\(924\) −2.72465 + 2.68777i −0.0896345 + 0.0884213i
\(925\) −9.26951 + 16.0553i −0.304780 + 0.527894i
\(926\) 16.1500i 0.530723i
\(927\) −11.5067 + 1.03289i −0.377930 + 0.0339245i
\(928\) −16.6273 + 28.7993i −0.545817 + 0.945383i
\(929\) −11.7687 + 20.3840i −0.386118 + 0.668776i −0.991924 0.126837i \(-0.959518\pi\)
0.605806 + 0.795613i \(0.292851\pi\)
\(930\) 11.1785 + 2.46499i 0.366559 + 0.0808302i
\(931\) 0.529562 0.236773i 0.0173557 0.00775991i
\(932\) 41.7233 24.0889i 1.36669 0.789059i
\(933\) −11.0925 + 12.1329i −0.363154 + 0.397212i
\(934\) 60.8362 35.1238i 1.99062 1.14929i
\(935\) 0.803073 + 0.463654i 0.0262633 + 0.0151631i
\(936\) −0.758278 2.33193i −0.0247851 0.0762217i
\(937\) 46.5554i 1.52090i −0.649398 0.760449i \(-0.724979\pi\)
0.649398 0.760449i \(-0.275021\pi\)
\(938\) −28.5563 + 44.0485i −0.932397 + 1.43823i
\(939\) −10.5531 + 3.34048i −0.344388 + 0.109012i
\(940\) 0.331897 0.574862i 0.0108253 0.0187499i
\(941\) −11.8519 + 20.5282i −0.386362 + 0.669199i −0.991957 0.126574i \(-0.959602\pi\)
0.605595 + 0.795773i \(0.292935\pi\)
\(942\) 20.6464 22.5828i 0.672698 0.735786i
\(943\) 36.8708 + 21.2874i 1.20068 + 0.693213i
\(944\) 24.6616 0.802666
\(945\) −2.53144 7.05492i −0.0823477 0.229496i
\(946\) 2.78650 4.82637i 0.0905971 0.156919i
\(947\) 38.0657i 1.23697i −0.785798 0.618484i \(-0.787747\pi\)
0.785798 0.618484i \(-0.212253\pi\)
\(948\) 11.4005 + 36.0159i 0.370270 + 1.16974i
\(949\) −51.8714 + 11.8646i −1.68382 + 0.385141i
\(950\) 0.384069 + 0.665228i 0.0124609 + 0.0215828i
\(951\) 31.7875 10.0620i 1.03078 0.326284i
\(952\) −1.04691 2.05069i −0.0339304 0.0664633i
\(953\) 29.5240 17.0457i 0.956378 0.552165i 0.0613213 0.998118i \(-0.480469\pi\)
0.895056 + 0.445953i \(0.147135\pi\)
\(954\) −41.2941 + 29.0536i −1.33695 + 0.940644i
\(955\) 1.17100i 0.0378928i
\(956\) 29.3340i 0.948730i
\(957\) −3.17143 0.699335i −0.102518 0.0226063i
\(958\) 16.5785 9.57162i 0.535628 0.309245i
\(959\) 14.2610 + 27.9345i 0.460511 + 0.902053i
\(960\) −2.01052 6.35154i −0.0648892 0.204995i
\(961\) 3.41168 + 5.90920i 0.110054 + 0.190619i
\(962\) 19.0650 + 20.5281i 0.614681 + 0.661853i
\(963\) 0.967410 2.08690i 0.0311743 0.0672495i
\(964\) 9.15018i 0.294707i
\(965\) −3.90641 + 6.76609i −0.125752 + 0.217808i
\(966\) 62.5886 16.3143i 2.01375 0.524905i
\(967\) 54.2984 1.74612 0.873059 0.487615i \(-0.162133\pi\)
0.873059 + 0.487615i \(0.162133\pi\)
\(968\) −2.12106 1.22459i −0.0681733 0.0393599i
\(969\) −0.406657 0.371789i −0.0130637 0.0119436i
\(970\) 1.23738 2.14321i 0.0397299 0.0688143i
\(971\) 9.56957 16.5750i 0.307102 0.531917i −0.670625 0.741797i \(-0.733974\pi\)
0.977727 + 0.209880i \(0.0673073\pi\)
\(972\) −13.7149 25.9869i −0.439906 0.833532i
\(973\) −21.8988 + 33.7792i −0.702043 + 1.08291i
\(974\) 41.7115i 1.33652i
\(975\) 0.229824 + 29.3678i 0.00736027 + 0.940521i
\(976\) 20.1120 + 11.6117i 0.643771 + 0.371681i
\(977\) −26.1300 + 15.0862i −0.835973 + 0.482649i −0.855893 0.517152i \(-0.826992\pi\)
0.0199203 + 0.999802i \(0.493659\pi\)
\(978\) −49.6282 45.3729i −1.58694 1.45087i
\(979\) −5.07796 + 2.93176i −0.162292 + 0.0936995i
\(980\) 7.15569 + 0.740743i 0.228580 + 0.0236622i
\(981\) 8.03808 5.65541i 0.256636 0.180563i
\(982\) 9.49458 16.4451i 0.302984 0.524784i
\(983\) 22.8267 39.5370i 0.728059 1.26104i −0.229643 0.973275i \(-0.573756\pi\)
0.957702 0.287760i \(-0.0929107\pi\)
\(984\) −1.72297 1.57523i −0.0549262 0.0502166i
\(985\) 7.02422i 0.223810i
\(986\) −16.0101 + 27.7303i −0.509866 + 0.883114i
\(987\) −2.07864 2.10716i −0.0661640 0.0670718i
\(988\) 0.549034 0.125581i 0.0174671 0.00399527i
\(989\) −39.5750 + 22.8486i −1.25841 + 0.726544i
\(990\) 1.16821 0.821928i 0.0371282 0.0261226i
\(991\) 0.845446 + 1.46436i 0.0268565 + 0.0465168i 0.879141 0.476561i \(-0.158117\pi\)
−0.852285 + 0.523078i \(0.824784\pi\)
\(992\) 24.1638 41.8530i 0.767203 1.32883i
\(993\) −10.7090 + 11.7134i −0.339841 + 0.371713i
\(994\) 38.2070 + 24.7693i 1.21185 + 0.785635i
\(995\) −0.280606 + 0.162008i −0.00889581 + 0.00513600i
\(996\) 5.98845 + 1.32052i 0.189751 + 0.0418422i
\(997\) 25.1803i 0.797469i −0.917066 0.398735i \(-0.869449\pi\)
0.917066 0.398735i \(-0.130551\pi\)
\(998\) 50.0517 28.8974i 1.58436 0.914730i
\(999\) −16.2933 12.4148i −0.515496 0.392788i
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 273.2.r.b.269.28 yes 64
3.2 odd 2 inner 273.2.r.b.269.5 yes 64
7.5 odd 6 273.2.bf.b.152.28 yes 64
13.3 even 3 273.2.bf.b.185.5 yes 64
21.5 even 6 273.2.bf.b.152.5 yes 64
39.29 odd 6 273.2.bf.b.185.28 yes 64
91.68 odd 6 inner 273.2.r.b.68.28 yes 64
273.68 even 6 inner 273.2.r.b.68.5 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.r.b.68.5 64 273.68 even 6 inner
273.2.r.b.68.28 yes 64 91.68 odd 6 inner
273.2.r.b.269.5 yes 64 3.2 odd 2 inner
273.2.r.b.269.28 yes 64 1.1 even 1 trivial
273.2.bf.b.152.5 yes 64 21.5 even 6
273.2.bf.b.152.28 yes 64 7.5 odd 6
273.2.bf.b.185.5 yes 64 13.3 even 3
273.2.bf.b.185.28 yes 64 39.29 odd 6