Properties

Label 585.2.i.h.196.5
Level $585$
Weight $2$
Character 585.196
Analytic conductor $4.671$
Analytic rank $0$
Dimension $30$
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] = [585,2,Mod(196,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.196");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.i (of order \(3\), 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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 196.5
Character \(\chi\) \(=\) 585.196
Dual form 585.2.i.h.391.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.644173 + 1.11574i) q^{2} +(-0.971694 - 1.43381i) q^{3} +(0.170081 + 0.294590i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.22570 - 0.160537i) q^{6} +(1.40888 - 2.44026i) q^{7} -3.01494 q^{8} +(-1.11162 + 2.78645i) q^{9} +O(q^{10})\) \(q+(-0.644173 + 1.11574i) q^{2} +(-0.971694 - 1.43381i) q^{3} +(0.170081 + 0.294590i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.22570 - 0.160537i) q^{6} +(1.40888 - 2.44026i) q^{7} -3.01494 q^{8} +(-1.11162 + 2.78645i) q^{9} -1.28835 q^{10} +(2.57577 - 4.46137i) q^{11} +(0.257118 - 0.530116i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(1.81513 + 3.14390i) q^{14} +(0.755868 - 1.55842i) q^{15} +(1.60198 - 2.77471i) q^{16} -6.95944 q^{17} +(-2.39288 - 3.03524i) q^{18} +5.29545 q^{19} +(-0.170081 + 0.294590i) q^{20} +(-4.86787 + 0.351114i) q^{21} +(3.31849 + 5.74779i) q^{22} +(-0.178608 - 0.309358i) q^{23} +(2.92960 + 4.32285i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.28835 q^{26} +(5.07539 - 1.11373i) q^{27} +0.958499 q^{28} +(2.41921 - 4.19019i) q^{29} +(1.25188 + 1.84724i) q^{30} +(-3.69084 - 6.39272i) q^{31} +(-0.951033 - 1.64724i) q^{32} +(-8.89962 + 0.641920i) q^{33} +(4.48308 - 7.76493i) q^{34} +2.81777 q^{35} +(-1.00993 + 0.146452i) q^{36} +5.70885 q^{37} +(-3.41119 + 5.90835i) q^{38} +(-0.755868 + 1.55842i) q^{39} +(-1.50747 - 2.61102i) q^{40} +(3.03414 + 5.25529i) q^{41} +(2.74400 - 5.65746i) q^{42} +(4.89119 - 8.47179i) q^{43} +1.75236 q^{44} +(-2.96895 + 0.430534i) q^{45} +0.460217 q^{46} +(3.06257 - 5.30452i) q^{47} +(-5.53505 + 0.399237i) q^{48} +(-0.469900 - 0.813891i) q^{49} +(-0.644173 - 1.11574i) q^{50} +(6.76245 + 9.97851i) q^{51} +(0.170081 - 0.294590i) q^{52} +3.26565 q^{53} +(-2.02680 + 6.38026i) q^{54} +5.15154 q^{55} +(-4.24770 + 7.35723i) q^{56} +(-5.14556 - 7.59267i) q^{57} +(3.11678 + 5.39842i) q^{58} +(-0.656449 - 1.13700i) q^{59} +(0.587653 - 0.0423868i) q^{60} +(4.58881 - 7.94805i) q^{61} +9.51016 q^{62} +(5.23351 + 6.63842i) q^{63} +8.85845 q^{64} +(0.500000 - 0.866025i) q^{65} +(5.01668 - 10.3432i) q^{66} +(-0.894026 - 1.54850i) q^{67} +(-1.18367 - 2.05018i) q^{68} +(-0.270008 + 0.556691i) q^{69} +(-1.81513 + 3.14390i) q^{70} -4.91564 q^{71} +(3.35147 - 8.40098i) q^{72} +4.67778 q^{73} +(-3.67749 + 6.36960i) q^{74} +(1.72756 - 0.124607i) q^{75} +(0.900658 + 1.55999i) q^{76} +(-7.25792 - 12.5711i) q^{77} +(-1.25188 - 1.84724i) q^{78} +(-4.43554 + 7.68258i) q^{79} +3.20396 q^{80} +(-6.52860 - 6.19494i) q^{81} -7.81806 q^{82} +(-7.47911 + 12.9542i) q^{83} +(-0.931368 - 1.37431i) q^{84} +(-3.47972 - 6.02705i) q^{85} +(6.30155 + 10.9146i) q^{86} +(-8.35866 + 0.602902i) q^{87} +(-7.76580 + 13.4508i) q^{88} +6.44960 q^{89} +(1.43215 - 3.58991i) q^{90} -2.81777 q^{91} +(0.0607557 - 0.105232i) q^{92} +(-5.57958 + 11.5037i) q^{93} +(3.94565 + 6.83406i) q^{94} +(2.64773 + 4.58600i) q^{95} +(-1.43771 + 2.96421i) q^{96} +(-5.62800 + 9.74798i) q^{97} +1.21079 q^{98} +(9.56810 + 12.1366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.644173 + 1.11574i −0.455499 + 0.788948i −0.998717 0.0506441i \(-0.983873\pi\)
0.543217 + 0.839592i \(0.317206\pi\)
\(3\) −0.971694 1.43381i −0.561008 0.827810i
\(4\) 0.170081 + 0.294590i 0.0850407 + 0.147295i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 2.22570 0.160537i 0.908638 0.0655391i
\(7\) 1.40888 2.44026i 0.532508 0.922330i −0.466772 0.884378i \(-0.654583\pi\)
0.999280 0.0379524i \(-0.0120835\pi\)
\(8\) −3.01494 −1.06594
\(9\) −1.11162 + 2.78645i −0.370540 + 0.928817i
\(10\) −1.28835 −0.407411
\(11\) 2.57577 4.46137i 0.776625 1.34515i −0.157252 0.987558i \(-0.550264\pi\)
0.933877 0.357595i \(-0.116403\pi\)
\(12\) 0.257118 0.530116i 0.0742237 0.153031i
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 1.81513 + 3.14390i 0.485114 + 0.840242i
\(15\) 0.755868 1.55842i 0.195164 0.402382i
\(16\) 1.60198 2.77471i 0.400495 0.693678i
\(17\) −6.95944 −1.68791 −0.843956 0.536413i \(-0.819779\pi\)
−0.843956 + 0.536413i \(0.819779\pi\)
\(18\) −2.39288 3.03524i −0.564007 0.715412i
\(19\) 5.29545 1.21486 0.607430 0.794373i \(-0.292200\pi\)
0.607430 + 0.794373i \(0.292200\pi\)
\(20\) −0.170081 + 0.294590i −0.0380314 + 0.0658723i
\(21\) −4.86787 + 0.351114i −1.06226 + 0.0766194i
\(22\) 3.31849 + 5.74779i 0.707504 + 1.22543i
\(23\) −0.178608 0.309358i −0.0372423 0.0645055i 0.846803 0.531906i \(-0.178524\pi\)
−0.884046 + 0.467400i \(0.845191\pi\)
\(24\) 2.92960 + 4.32285i 0.598002 + 0.882398i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.28835 0.252666
\(27\) 5.07539 1.11373i 0.976760 0.214337i
\(28\) 0.958499 0.181139
\(29\) 2.41921 4.19019i 0.449235 0.778099i −0.549101 0.835756i \(-0.685030\pi\)
0.998336 + 0.0576574i \(0.0183631\pi\)
\(30\) 1.25188 + 1.84724i 0.228561 + 0.337259i
\(31\) −3.69084 6.39272i −0.662894 1.14817i −0.979852 0.199727i \(-0.935994\pi\)
0.316957 0.948440i \(-0.397339\pi\)
\(32\) −0.951033 1.64724i −0.168121 0.291193i
\(33\) −8.89962 + 0.641920i −1.54922 + 0.111744i
\(34\) 4.48308 7.76493i 0.768843 1.33167i
\(35\) 2.81777 0.476289
\(36\) −1.00993 + 0.146452i −0.168321 + 0.0244086i
\(37\) 5.70885 0.938530 0.469265 0.883058i \(-0.344519\pi\)
0.469265 + 0.883058i \(0.344519\pi\)
\(38\) −3.41119 + 5.90835i −0.553368 + 0.958461i
\(39\) −0.755868 + 1.55842i −0.121036 + 0.249546i
\(40\) −1.50747 2.61102i −0.238352 0.412838i
\(41\) 3.03414 + 5.25529i 0.473854 + 0.820739i 0.999552 0.0299323i \(-0.00952917\pi\)
−0.525698 + 0.850671i \(0.676196\pi\)
\(42\) 2.74400 5.65746i 0.423408 0.872964i
\(43\) 4.89119 8.47179i 0.745900 1.29194i −0.203873 0.978997i \(-0.565353\pi\)
0.949773 0.312939i \(-0.101314\pi\)
\(44\) 1.75236 0.264179
\(45\) −2.96895 + 0.430534i −0.442584 + 0.0641802i
\(46\) 0.460217 0.0678553
\(47\) 3.06257 5.30452i 0.446721 0.773744i −0.551449 0.834208i \(-0.685925\pi\)
0.998170 + 0.0604648i \(0.0192583\pi\)
\(48\) −5.53505 + 0.399237i −0.798915 + 0.0576249i
\(49\) −0.469900 0.813891i −0.0671286 0.116270i
\(50\) −0.644173 1.11574i −0.0910999 0.157790i
\(51\) 6.76245 + 9.97851i 0.946932 + 1.39727i
\(52\) 0.170081 0.294590i 0.0235861 0.0408522i
\(53\) 3.26565 0.448572 0.224286 0.974523i \(-0.427995\pi\)
0.224286 + 0.974523i \(0.427995\pi\)
\(54\) −2.02680 + 6.38026i −0.275813 + 0.868243i
\(55\) 5.15154 0.694634
\(56\) −4.24770 + 7.35723i −0.567623 + 0.983151i
\(57\) −5.14556 7.59267i −0.681546 1.00567i
\(58\) 3.11678 + 5.39842i 0.409253 + 0.708847i
\(59\) −0.656449 1.13700i −0.0854624 0.148025i 0.820126 0.572183i \(-0.193903\pi\)
−0.905588 + 0.424158i \(0.860570\pi\)
\(60\) 0.587653 0.0423868i 0.0758657 0.00547211i
\(61\) 4.58881 7.94805i 0.587537 1.01764i −0.407017 0.913421i \(-0.633431\pi\)
0.994554 0.104223i \(-0.0332356\pi\)
\(62\) 9.51016 1.20779
\(63\) 5.23351 + 6.63842i 0.659360 + 0.836362i
\(64\) 8.85845 1.10731
\(65\) 0.500000 0.866025i 0.0620174 0.107417i
\(66\) 5.01668 10.3432i 0.617510 1.27316i
\(67\) −0.894026 1.54850i −0.109223 0.189179i 0.806233 0.591598i \(-0.201503\pi\)
−0.915456 + 0.402419i \(0.868169\pi\)
\(68\) −1.18367 2.05018i −0.143541 0.248621i
\(69\) −0.270008 + 0.556691i −0.0325051 + 0.0670177i
\(70\) −1.81513 + 3.14390i −0.216949 + 0.375767i
\(71\) −4.91564 −0.583379 −0.291689 0.956513i \(-0.594217\pi\)
−0.291689 + 0.956513i \(0.594217\pi\)
\(72\) 3.35147 8.40098i 0.394974 0.990065i
\(73\) 4.67778 0.547493 0.273746 0.961802i \(-0.411737\pi\)
0.273746 + 0.961802i \(0.411737\pi\)
\(74\) −3.67749 + 6.36960i −0.427500 + 0.740451i
\(75\) 1.72756 0.124607i 0.199482 0.0143884i
\(76\) 0.900658 + 1.55999i 0.103313 + 0.178943i
\(77\) −7.25792 12.5711i −0.827117 1.43261i
\(78\) −1.25188 1.84724i −0.141747 0.209159i
\(79\) −4.43554 + 7.68258i −0.499037 + 0.864358i −0.999999 0.00111120i \(-0.999646\pi\)
0.500962 + 0.865469i \(0.332980\pi\)
\(80\) 3.20396 0.358214
\(81\) −6.52860 6.19494i −0.725400 0.688327i
\(82\) −7.81806 −0.863360
\(83\) −7.47911 + 12.9542i −0.820939 + 1.42191i 0.0840448 + 0.996462i \(0.473216\pi\)
−0.904984 + 0.425446i \(0.860117\pi\)
\(84\) −0.931368 1.37431i −0.101621 0.149949i
\(85\) −3.47972 6.02705i −0.377429 0.653725i
\(86\) 6.30155 + 10.9146i 0.679514 + 1.17695i
\(87\) −8.35866 + 0.602902i −0.896143 + 0.0646379i
\(88\) −7.76580 + 13.4508i −0.827837 + 1.43386i
\(89\) 6.44960 0.683656 0.341828 0.939763i \(-0.388954\pi\)
0.341828 + 0.939763i \(0.388954\pi\)
\(90\) 1.43215 3.58991i 0.150962 0.378410i
\(91\) −2.81777 −0.295382
\(92\) 0.0607557 0.105232i 0.00633422 0.0109712i
\(93\) −5.57958 + 11.5037i −0.578575 + 1.19288i
\(94\) 3.94565 + 6.83406i 0.406962 + 0.704879i
\(95\) 2.64773 + 4.58600i 0.271651 + 0.470513i
\(96\) −1.43771 + 2.96421i −0.146736 + 0.302534i
\(97\) −5.62800 + 9.74798i −0.571437 + 0.989757i 0.424982 + 0.905202i \(0.360280\pi\)
−0.996419 + 0.0845556i \(0.973053\pi\)
\(98\) 1.21079 0.122308
\(99\) 9.56810 + 12.1366i 0.961630 + 1.21977i
\(100\) −0.340163 −0.0340163
\(101\) −4.87922 + 8.45106i −0.485501 + 0.840912i −0.999861 0.0166623i \(-0.994696\pi\)
0.514361 + 0.857574i \(0.328029\pi\)
\(102\) −15.4896 + 1.11725i −1.53370 + 0.110624i
\(103\) −3.96888 6.87431i −0.391066 0.677345i 0.601525 0.798854i \(-0.294560\pi\)
−0.992590 + 0.121509i \(0.961227\pi\)
\(104\) 1.50747 + 2.61102i 0.147820 + 0.256031i
\(105\) −2.73801 4.04014i −0.267202 0.394277i
\(106\) −2.10365 + 3.64362i −0.204324 + 0.353900i
\(107\) 4.45095 0.430290 0.215145 0.976582i \(-0.430978\pi\)
0.215145 + 0.976582i \(0.430978\pi\)
\(108\) 1.19132 + 1.30573i 0.114635 + 0.125644i
\(109\) −8.58876 −0.822654 −0.411327 0.911488i \(-0.634935\pi\)
−0.411327 + 0.911488i \(0.634935\pi\)
\(110\) −3.31849 + 5.74779i −0.316405 + 0.548030i
\(111\) −5.54726 8.18541i −0.526523 0.776924i
\(112\) −4.51401 7.81849i −0.426534 0.738778i
\(113\) −9.61749 16.6580i −0.904738 1.56705i −0.821269 0.570541i \(-0.806733\pi\)
−0.0834690 0.996510i \(-0.526600\pi\)
\(114\) 11.7861 0.850118i 1.10387 0.0796209i
\(115\) 0.178608 0.309358i 0.0166553 0.0288477i
\(116\) 1.64585 0.152813
\(117\) 2.96895 0.430534i 0.274479 0.0398029i
\(118\) 1.69147 0.155712
\(119\) −9.80503 + 16.9828i −0.898826 + 1.55681i
\(120\) −2.27890 + 4.69854i −0.208034 + 0.428916i
\(121\) −7.76921 13.4567i −0.706291 1.22333i
\(122\) 5.91198 + 10.2398i 0.535245 + 0.927072i
\(123\) 4.58683 9.45693i 0.413580 0.852702i
\(124\) 1.25549 2.17457i 0.112746 0.195282i
\(125\) −1.00000 −0.0894427
\(126\) −10.7780 + 1.56295i −0.960184 + 0.139239i
\(127\) 7.98997 0.708995 0.354497 0.935057i \(-0.384652\pi\)
0.354497 + 0.935057i \(0.384652\pi\)
\(128\) −3.80431 + 6.58926i −0.336257 + 0.582414i
\(129\) −16.8997 + 1.21896i −1.48793 + 0.107323i
\(130\) 0.644173 + 1.11574i 0.0564977 + 0.0978570i
\(131\) 1.73503 + 3.00516i 0.151590 + 0.262562i 0.931812 0.362941i \(-0.118227\pi\)
−0.780222 + 0.625503i \(0.784894\pi\)
\(132\) −1.70276 2.51256i −0.148206 0.218690i
\(133\) 7.46067 12.9223i 0.646922 1.12050i
\(134\) 2.30363 0.199003
\(135\) 3.50221 + 3.83856i 0.301422 + 0.330370i
\(136\) 20.9823 1.79922
\(137\) −2.87915 + 4.98683i −0.245982 + 0.426054i −0.962407 0.271610i \(-0.912444\pi\)
0.716425 + 0.697664i \(0.245777\pi\)
\(138\) −0.447191 0.659864i −0.0380674 0.0561713i
\(139\) 3.79217 + 6.56823i 0.321647 + 0.557110i 0.980828 0.194875i \(-0.0624301\pi\)
−0.659181 + 0.751985i \(0.729097\pi\)
\(140\) 0.479250 + 0.830085i 0.0405040 + 0.0701550i
\(141\) −10.5815 + 0.763236i −0.891127 + 0.0642761i
\(142\) 3.16652 5.48458i 0.265729 0.460256i
\(143\) −5.15154 −0.430794
\(144\) 5.95081 + 7.54827i 0.495900 + 0.629022i
\(145\) 4.83841 0.401808
\(146\) −3.01330 + 5.21919i −0.249383 + 0.431943i
\(147\) −0.710365 + 1.46460i −0.0585899 + 0.120798i
\(148\) 0.970970 + 1.68177i 0.0798132 + 0.138241i
\(149\) −3.00953 5.21267i −0.246551 0.427038i 0.716016 0.698084i \(-0.245964\pi\)
−0.962566 + 0.271046i \(0.912631\pi\)
\(150\) −0.973820 + 2.00778i −0.0795121 + 0.163935i
\(151\) −4.91595 + 8.51467i −0.400054 + 0.692914i −0.993732 0.111789i \(-0.964342\pi\)
0.593678 + 0.804703i \(0.297675\pi\)
\(152\) −15.9655 −1.29497
\(153\) 7.73625 19.3921i 0.625439 1.56776i
\(154\) 18.7014 1.50700
\(155\) 3.69084 6.39272i 0.296455 0.513476i
\(156\) −0.587653 + 0.0423868i −0.0470499 + 0.00339366i
\(157\) 1.25443 + 2.17274i 0.100115 + 0.173403i 0.911732 0.410786i \(-0.134746\pi\)
−0.811617 + 0.584190i \(0.801412\pi\)
\(158\) −5.71451 9.89783i −0.454622 0.787429i
\(159\) −3.17322 4.68233i −0.251653 0.371333i
\(160\) 0.951033 1.64724i 0.0751858 0.130226i
\(161\) −1.00655 −0.0793272
\(162\) 11.1175 3.29361i 0.873474 0.258771i
\(163\) −19.8235 −1.55269 −0.776347 0.630306i \(-0.782929\pi\)
−0.776347 + 0.630306i \(0.782929\pi\)
\(164\) −1.03210 + 1.78766i −0.0805938 + 0.139592i
\(165\) −5.00573 7.38633i −0.389695 0.575025i
\(166\) −9.63569 16.6895i −0.747874 1.29536i
\(167\) 11.8886 + 20.5916i 0.919964 + 1.59342i 0.799467 + 0.600710i \(0.205115\pi\)
0.120497 + 0.992714i \(0.461551\pi\)
\(168\) 14.6763 1.05859i 1.13230 0.0816719i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 8.96617 0.687674
\(171\) −5.88653 + 14.7555i −0.450154 + 1.12838i
\(172\) 3.32760 0.253727
\(173\) 2.89292 5.01068i 0.219944 0.380955i −0.734846 0.678234i \(-0.762746\pi\)
0.954791 + 0.297279i \(0.0960791\pi\)
\(174\) 4.71175 9.71448i 0.357197 0.736452i
\(175\) 1.40888 + 2.44026i 0.106502 + 0.184466i
\(176\) −8.25268 14.2941i −0.622069 1.07746i
\(177\) −0.992378 + 2.04604i −0.0745917 + 0.153790i
\(178\) −4.15466 + 7.19608i −0.311405 + 0.539369i
\(179\) −20.1982 −1.50969 −0.754844 0.655905i \(-0.772287\pi\)
−0.754844 + 0.655905i \(0.772287\pi\)
\(180\) −0.631794 0.801395i −0.0470911 0.0597325i
\(181\) −10.0801 −0.749249 −0.374625 0.927177i \(-0.622228\pi\)
−0.374625 + 0.927177i \(0.622228\pi\)
\(182\) 1.81513 3.14390i 0.134546 0.233041i
\(183\) −15.8549 + 1.14360i −1.17203 + 0.0845372i
\(184\) 0.538492 + 0.932695i 0.0396981 + 0.0687592i
\(185\) 2.85443 + 4.94401i 0.209862 + 0.363491i
\(186\) −9.24097 13.6358i −0.677581 0.999823i
\(187\) −17.9259 + 31.0486i −1.31087 + 2.27050i
\(188\) 2.08354 0.151958
\(189\) 4.43285 13.9544i 0.322443 1.01503i
\(190\) −6.82238 −0.494947
\(191\) 9.12892 15.8118i 0.660545 1.14410i −0.319927 0.947442i \(-0.603658\pi\)
0.980473 0.196656i \(-0.0630082\pi\)
\(192\) −8.60770 12.7013i −0.621208 0.916639i
\(193\) 1.08415 + 1.87780i 0.0780388 + 0.135167i 0.902404 0.430892i \(-0.141801\pi\)
−0.824365 + 0.566059i \(0.808468\pi\)
\(194\) −7.25081 12.5588i −0.520578 0.901668i
\(195\) −1.72756 + 0.124607i −0.123713 + 0.00892332i
\(196\) 0.159843 0.276856i 0.0114173 0.0197754i
\(197\) 14.9589 1.06578 0.532890 0.846185i \(-0.321106\pi\)
0.532890 + 0.846185i \(0.321106\pi\)
\(198\) −19.7048 + 2.85744i −1.40036 + 0.203070i
\(199\) 4.81279 0.341170 0.170585 0.985343i \(-0.445434\pi\)
0.170585 + 0.985343i \(0.445434\pi\)
\(200\) 1.50747 2.61102i 0.106594 0.184627i
\(201\) −1.35153 + 2.78653i −0.0953297 + 0.196547i
\(202\) −6.28613 10.8879i −0.442290 0.766069i
\(203\) −6.81676 11.8070i −0.478443 0.828687i
\(204\) −1.78940 + 3.68931i −0.125283 + 0.258303i
\(205\) −3.03414 + 5.25529i −0.211914 + 0.367046i
\(206\) 10.2266 0.712520
\(207\) 1.06055 0.153793i 0.0737135 0.0106894i
\(208\) −3.20396 −0.222155
\(209\) 13.6399 23.6250i 0.943490 1.63417i
\(210\) 6.27150 0.452357i 0.432775 0.0312156i
\(211\) −4.80298 8.31901i −0.330651 0.572704i 0.651989 0.758229i \(-0.273935\pi\)
−0.982640 + 0.185524i \(0.940602\pi\)
\(212\) 0.555427 + 0.962028i 0.0381469 + 0.0660724i
\(213\) 4.77650 + 7.04809i 0.327280 + 0.482927i
\(214\) −2.86718 + 4.96611i −0.195997 + 0.339476i
\(215\) 9.78238 0.667153
\(216\) −15.3020 + 3.35782i −1.04117 + 0.228471i
\(217\) −20.7998 −1.41199
\(218\) 5.53265 9.58283i 0.374718 0.649031i
\(219\) −4.54537 6.70704i −0.307148 0.453220i
\(220\) 0.876182 + 1.51759i 0.0590722 + 0.102316i
\(221\) 3.47972 + 6.02705i 0.234071 + 0.405423i
\(222\) 12.7062 0.916484i 0.852784 0.0615104i
\(223\) 3.17548 5.50009i 0.212646 0.368313i −0.739896 0.672721i \(-0.765125\pi\)
0.952542 + 0.304408i \(0.0984587\pi\)
\(224\) −5.35958 −0.358102
\(225\) −1.85733 2.35592i −0.123822 0.157061i
\(226\) 24.7813 1.64843
\(227\) −2.84962 + 4.93569i −0.189136 + 0.327593i −0.944962 0.327179i \(-0.893902\pi\)
0.755826 + 0.654772i \(0.227235\pi\)
\(228\) 1.36156 2.80720i 0.0901714 0.185912i
\(229\) 10.9728 + 19.0054i 0.725102 + 1.25591i 0.958932 + 0.283636i \(0.0915407\pi\)
−0.233830 + 0.972277i \(0.575126\pi\)
\(230\) 0.230109 + 0.398560i 0.0151729 + 0.0262803i
\(231\) −10.9721 + 22.6217i −0.721909 + 1.48840i
\(232\) −7.29377 + 12.6332i −0.478859 + 0.829408i
\(233\) 25.7672 1.68806 0.844031 0.536294i \(-0.180176\pi\)
0.844031 + 0.536294i \(0.180176\pi\)
\(234\) −1.43215 + 3.58991i −0.0936227 + 0.234680i
\(235\) 6.12513 0.399560
\(236\) 0.223300 0.386766i 0.0145356 0.0251763i
\(237\) 15.3254 1.10540i 0.995489 0.0718036i
\(238\) −12.6323 21.8797i −0.818829 1.41825i
\(239\) 2.97550 + 5.15372i 0.192469 + 0.333366i 0.946068 0.323968i \(-0.105017\pi\)
−0.753599 + 0.657335i \(0.771684\pi\)
\(240\) −3.11327 4.59387i −0.200961 0.296533i
\(241\) −11.6495 + 20.1774i −0.750407 + 1.29974i 0.197218 + 0.980360i \(0.436809\pi\)
−0.947625 + 0.319384i \(0.896524\pi\)
\(242\) 20.0189 1.28686
\(243\) −2.53856 + 15.3804i −0.162849 + 0.986651i
\(244\) 3.12189 0.199858
\(245\) 0.469900 0.813891i 0.0300208 0.0519976i
\(246\) 7.59677 + 11.2096i 0.484352 + 0.714699i
\(247\) −2.64773 4.58600i −0.168471 0.291800i
\(248\) 11.1277 + 19.2737i 0.706607 + 1.22388i
\(249\) 25.8413 1.86390i 1.63762 0.118120i
\(250\) 0.644173 1.11574i 0.0407411 0.0705657i
\(251\) 16.6483 1.05083 0.525417 0.850845i \(-0.323909\pi\)
0.525417 + 0.850845i \(0.323909\pi\)
\(252\) −1.06549 + 2.67081i −0.0671194 + 0.168245i
\(253\) −1.84021 −0.115693
\(254\) −5.14692 + 8.91473i −0.322947 + 0.559360i
\(255\) −5.26042 + 10.8457i −0.329420 + 0.679184i
\(256\) 3.95718 + 6.85404i 0.247324 + 0.428377i
\(257\) 3.29768 + 5.71175i 0.205704 + 0.356289i 0.950357 0.311163i \(-0.100718\pi\)
−0.744653 + 0.667452i \(0.767385\pi\)
\(258\) 9.52628 19.6409i 0.593081 1.22279i
\(259\) 8.04310 13.9311i 0.499774 0.865634i
\(260\) 0.340163 0.0210960
\(261\) 8.98651 + 11.3989i 0.556251 + 0.705574i
\(262\) −4.47064 −0.276197
\(263\) 8.83438 15.3016i 0.544751 0.943536i −0.453872 0.891067i \(-0.649958\pi\)
0.998623 0.0524693i \(-0.0167092\pi\)
\(264\) 26.8318 1.93535i 1.65138 0.119113i
\(265\) 1.63283 + 2.82814i 0.100304 + 0.173731i
\(266\) 9.61193 + 16.6484i 0.589345 + 1.02078i
\(267\) −6.26704 9.24750i −0.383537 0.565938i
\(268\) 0.304115 0.526742i 0.0185768 0.0321759i
\(269\) −6.09803 −0.371804 −0.185902 0.982568i \(-0.559521\pi\)
−0.185902 + 0.982568i \(0.559521\pi\)
\(270\) −6.53887 + 1.43487i −0.397943 + 0.0873232i
\(271\) −19.9160 −1.20981 −0.604906 0.796297i \(-0.706789\pi\)
−0.604906 + 0.796297i \(0.706789\pi\)
\(272\) −11.1489 + 19.3104i −0.676001 + 1.17087i
\(273\) 2.73801 + 4.04014i 0.165712 + 0.244520i
\(274\) −3.70934 6.42477i −0.224090 0.388134i
\(275\) 2.57577 + 4.46137i 0.155325 + 0.269031i
\(276\) −0.209919 + 0.0151412i −0.0126356 + 0.000911394i
\(277\) −16.1804 + 28.0254i −0.972189 + 1.68388i −0.283272 + 0.959040i \(0.591420\pi\)
−0.688916 + 0.724841i \(0.741913\pi\)
\(278\) −9.77125 −0.586041
\(279\) 21.9158 3.17806i 1.31207 0.190266i
\(280\) −8.49540 −0.507697
\(281\) 16.0058 27.7228i 0.954825 1.65381i 0.220057 0.975487i \(-0.429376\pi\)
0.734768 0.678319i \(-0.237291\pi\)
\(282\) 5.96478 12.2979i 0.355197 0.732331i
\(283\) 14.4870 + 25.0921i 0.861160 + 1.49157i 0.870810 + 0.491620i \(0.163595\pi\)
−0.00965008 + 0.999953i \(0.503072\pi\)
\(284\) −0.836059 1.44810i −0.0496110 0.0859287i
\(285\) 4.00266 8.25252i 0.237097 0.488837i
\(286\) 3.31849 5.74779i 0.196226 0.339874i
\(287\) 17.0990 1.00932
\(288\) 5.64713 0.818904i 0.332761 0.0482544i
\(289\) 31.4338 1.84905
\(290\) −3.11678 + 5.39842i −0.183023 + 0.317006i
\(291\) 19.4454 1.40258i 1.13991 0.0822207i
\(292\) 0.795603 + 1.37803i 0.0465592 + 0.0806429i
\(293\) −2.02909 3.51448i −0.118541 0.205318i 0.800649 0.599134i \(-0.204488\pi\)
−0.919190 + 0.393815i \(0.871155\pi\)
\(294\) −1.17652 1.73604i −0.0686158 0.101248i
\(295\) 0.656449 1.13700i 0.0382199 0.0661989i
\(296\) −17.2119 −1.00042
\(297\) 8.10431 25.5119i 0.470260 1.48035i
\(298\) 7.75465 0.449215
\(299\) −0.178608 + 0.309358i −0.0103292 + 0.0178906i
\(300\) 0.330534 + 0.487729i 0.0190834 + 0.0281590i
\(301\) −13.7822 23.8715i −0.794395 1.37593i
\(302\) −6.33345 10.9698i −0.364449 0.631244i
\(303\) 16.8583 1.21597i 0.968485 0.0698558i
\(304\) 8.48322 14.6934i 0.486546 0.842722i
\(305\) 9.17762 0.525509
\(306\) 16.6531 + 21.1235i 0.951994 + 1.20755i
\(307\) 10.2358 0.584185 0.292093 0.956390i \(-0.405648\pi\)
0.292093 + 0.956390i \(0.405648\pi\)
\(308\) 2.46888 4.27622i 0.140677 0.243660i
\(309\) −5.99990 + 12.3703i −0.341323 + 0.703724i
\(310\) 4.75508 + 8.23604i 0.270070 + 0.467776i
\(311\) −11.1128 19.2479i −0.630149 1.09145i −0.987521 0.157488i \(-0.949660\pi\)
0.357372 0.933962i \(-0.383673\pi\)
\(312\) 2.27890 4.69854i 0.129017 0.266002i
\(313\) 4.81602 8.34160i 0.272218 0.471495i −0.697212 0.716865i \(-0.745576\pi\)
0.969429 + 0.245370i \(0.0789096\pi\)
\(314\) −3.23228 −0.182408
\(315\) −3.13228 + 7.85156i −0.176484 + 0.442385i
\(316\) −3.01761 −0.169754
\(317\) −15.3523 + 26.5910i −0.862273 + 1.49350i 0.00745758 + 0.999972i \(0.497626\pi\)
−0.869730 + 0.493528i \(0.835707\pi\)
\(318\) 7.26837 0.524260i 0.407590 0.0293990i
\(319\) −12.4627 21.5859i −0.697775 1.20858i
\(320\) 4.42922 + 7.67164i 0.247601 + 0.428858i
\(321\) −4.32496 6.38181i −0.241396 0.356198i
\(322\) 0.648392 1.12305i 0.0361335 0.0625850i
\(323\) −36.8534 −2.05058
\(324\) 0.714573 2.97690i 0.0396985 0.165384i
\(325\) 1.00000 0.0554700
\(326\) 12.7697 22.1179i 0.707251 1.22499i
\(327\) 8.34565 + 12.3146i 0.461516 + 0.681002i
\(328\) −9.14777 15.8444i −0.505101 0.874861i
\(329\) −8.62959 14.9469i −0.475765 0.824049i
\(330\) 11.4658 0.827016i 0.631171 0.0455257i
\(331\) 1.75825 3.04538i 0.0966424 0.167389i −0.813651 0.581354i \(-0.802523\pi\)
0.910293 + 0.413965i \(0.135856\pi\)
\(332\) −5.08823 −0.279253
\(333\) −6.34607 + 15.9074i −0.347763 + 0.871722i
\(334\) −30.6331 −1.67617
\(335\) 0.894026 1.54850i 0.0488459 0.0846035i
\(336\) −6.82399 + 14.0694i −0.372279 + 0.767549i
\(337\) 9.81302 + 16.9967i 0.534549 + 0.925867i 0.999185 + 0.0403646i \(0.0128520\pi\)
−0.464636 + 0.885502i \(0.653815\pi\)
\(338\) −0.644173 1.11574i −0.0350384 0.0606883i
\(339\) −14.5391 + 29.9761i −0.789656 + 1.62808i
\(340\) 1.18367 2.05018i 0.0641936 0.111187i
\(341\) −38.0271 −2.05928
\(342\) −12.6714 16.0729i −0.685190 0.869126i
\(343\) 17.0762 0.922029
\(344\) −14.7467 + 25.5420i −0.795086 + 1.37713i
\(345\) −0.617112 + 0.0445117i −0.0332242 + 0.00239643i
\(346\) 3.72708 + 6.45549i 0.200369 + 0.347049i
\(347\) −12.6960 21.9902i −0.681559 1.18049i −0.974505 0.224366i \(-0.927969\pi\)
0.292946 0.956129i \(-0.405364\pi\)
\(348\) −1.59926 2.35983i −0.0857295 0.126500i
\(349\) 6.09864 10.5632i 0.326453 0.565433i −0.655352 0.755323i \(-0.727480\pi\)
0.981805 + 0.189890i \(0.0608132\pi\)
\(350\) −3.63026 −0.194045
\(351\) −3.50221 3.83856i −0.186934 0.204887i
\(352\) −9.79858 −0.522266
\(353\) 8.97537 15.5458i 0.477711 0.827419i −0.521963 0.852968i \(-0.674800\pi\)
0.999674 + 0.0255491i \(0.00813343\pi\)
\(354\) −1.64359 2.42524i −0.0873558 0.128900i
\(355\) −2.45782 4.25707i −0.130447 0.225942i
\(356\) 1.09696 + 1.89999i 0.0581386 + 0.100699i
\(357\) 33.8776 2.44356i 1.79299 0.129327i
\(358\) 13.0112 22.5360i 0.687662 1.19106i
\(359\) 20.1656 1.06430 0.532149 0.846651i \(-0.321385\pi\)
0.532149 + 0.846651i \(0.321385\pi\)
\(360\) 8.95120 1.29803i 0.471770 0.0684124i
\(361\) 9.04182 0.475885
\(362\) 6.49334 11.2468i 0.341283 0.591119i
\(363\) −11.7450 + 24.2153i −0.616452 + 1.27097i
\(364\) −0.479250 0.830085i −0.0251195 0.0435083i
\(365\) 2.33889 + 4.05108i 0.122423 + 0.212043i
\(366\) 8.93735 18.4266i 0.467163 0.963176i
\(367\) −14.9418 + 25.8799i −0.779953 + 1.35092i 0.152015 + 0.988378i \(0.451424\pi\)
−0.931968 + 0.362540i \(0.881910\pi\)
\(368\) −1.14451 −0.0596615
\(369\) −18.0164 + 2.61260i −0.937898 + 0.136007i
\(370\) −7.35498 −0.382367
\(371\) 4.60092 7.96903i 0.238868 0.413732i
\(372\) −4.33786 + 0.312886i −0.224908 + 0.0162224i
\(373\) 1.82808 + 3.16632i 0.0946542 + 0.163946i 0.909464 0.415782i \(-0.136492\pi\)
−0.814810 + 0.579728i \(0.803159\pi\)
\(374\) −23.0948 40.0014i −1.19420 2.06842i
\(375\) 0.971694 + 1.43381i 0.0501781 + 0.0740416i
\(376\) −9.23346 + 15.9928i −0.476179 + 0.824766i
\(377\) −4.83841 −0.249191
\(378\) 12.7139 + 13.9349i 0.653934 + 0.716736i
\(379\) 24.0635 1.23606 0.618028 0.786156i \(-0.287932\pi\)
0.618028 + 0.786156i \(0.287932\pi\)
\(380\) −0.900658 + 1.55999i −0.0462028 + 0.0800256i
\(381\) −7.76381 11.4561i −0.397752 0.586913i
\(382\) 11.7612 + 20.3710i 0.601756 + 1.04227i
\(383\) 14.8405 + 25.7045i 0.758314 + 1.31344i 0.943710 + 0.330775i \(0.107310\pi\)
−0.185396 + 0.982664i \(0.559357\pi\)
\(384\) 13.1444 0.948089i 0.670771 0.0483820i
\(385\) 7.25792 12.5711i 0.369898 0.640682i
\(386\) −2.79352 −0.142187
\(387\) 18.1691 + 23.0465i 0.923586 + 1.17152i
\(388\) −3.82887 −0.194382
\(389\) −2.84354 + 4.92516i −0.144173 + 0.249715i −0.929064 0.369919i \(-0.879386\pi\)
0.784891 + 0.619634i \(0.212719\pi\)
\(390\) 0.973820 2.00778i 0.0493113 0.101668i
\(391\) 1.24301 + 2.15296i 0.0628617 + 0.108880i
\(392\) 1.41672 + 2.45383i 0.0715552 + 0.123937i
\(393\) 2.62291 5.40780i 0.132308 0.272788i
\(394\) −9.63614 + 16.6903i −0.485462 + 0.840845i
\(395\) −8.87108 −0.446353
\(396\) −1.94796 + 4.88288i −0.0978888 + 0.245374i
\(397\) −1.64080 −0.0823496 −0.0411748 0.999152i \(-0.513110\pi\)
−0.0411748 + 0.999152i \(0.513110\pi\)
\(398\) −3.10027 + 5.36983i −0.155403 + 0.269165i
\(399\) −25.7776 + 1.85931i −1.29049 + 0.0930818i
\(400\) 1.60198 + 2.77471i 0.0800991 + 0.138736i
\(401\) 6.65233 + 11.5222i 0.332201 + 0.575390i 0.982943 0.183909i \(-0.0588753\pi\)
−0.650742 + 0.759299i \(0.725542\pi\)
\(402\) −2.23843 3.30297i −0.111643 0.164737i
\(403\) −3.69084 + 6.39272i −0.183854 + 0.318444i
\(404\) −3.31946 −0.165149
\(405\) 2.10068 8.75141i 0.104384 0.434861i
\(406\) 17.5647 0.871721
\(407\) 14.7047 25.4693i 0.728885 1.26247i
\(408\) −20.3884 30.0846i −1.00938 1.48941i
\(409\) −5.27938 9.14416i −0.261049 0.452150i 0.705472 0.708738i \(-0.250735\pi\)
−0.966521 + 0.256588i \(0.917402\pi\)
\(410\) −3.90903 6.77064i −0.193053 0.334378i
\(411\) 9.94782 0.717526i 0.490690 0.0353930i
\(412\) 1.35007 2.33838i 0.0665130 0.115204i
\(413\) −3.69944 −0.182037
\(414\) −0.511587 + 1.28237i −0.0251431 + 0.0630252i
\(415\) −14.9582 −0.734270
\(416\) −0.951033 + 1.64724i −0.0466282 + 0.0807625i
\(417\) 5.73276 11.8196i 0.280734 0.578806i
\(418\) 17.5729 + 30.4371i 0.859518 + 1.48873i
\(419\) −10.2745 17.7960i −0.501944 0.869393i −0.999997 0.00224654i \(-0.999285\pi\)
0.498053 0.867146i \(-0.334048\pi\)
\(420\) 0.724499 1.49374i 0.0353519 0.0728871i
\(421\) 18.1358 31.4121i 0.883885 1.53093i 0.0368980 0.999319i \(-0.488252\pi\)
0.846987 0.531614i \(-0.178414\pi\)
\(422\) 12.3758 0.602445
\(423\) 11.3764 + 14.4303i 0.553138 + 0.701625i
\(424\) −9.84576 −0.478152
\(425\) 3.47972 6.02705i 0.168791 0.292355i
\(426\) −10.9407 + 0.789144i −0.530080 + 0.0382341i
\(427\) −12.9302 22.3957i −0.625736 1.08381i
\(428\) 0.757024 + 1.31120i 0.0365921 + 0.0633794i
\(429\) 5.00573 + 7.38633i 0.241679 + 0.356616i
\(430\) −6.30155 + 10.9146i −0.303888 + 0.526349i
\(431\) 15.4318 0.743323 0.371661 0.928368i \(-0.378788\pi\)
0.371661 + 0.928368i \(0.378788\pi\)
\(432\) 5.04041 15.8669i 0.242507 0.763398i
\(433\) −23.3484 −1.12205 −0.561027 0.827797i \(-0.689594\pi\)
−0.561027 + 0.827797i \(0.689594\pi\)
\(434\) 13.3987 23.2072i 0.643158 1.11398i
\(435\) −4.70146 6.93736i −0.225418 0.332621i
\(436\) −1.46079 2.53016i −0.0699591 0.121173i
\(437\) −0.945809 1.63819i −0.0452442 0.0783652i
\(438\) 10.4113 0.750959i 0.497473 0.0358822i
\(439\) −6.22486 + 10.7818i −0.297096 + 0.514586i −0.975470 0.220131i \(-0.929352\pi\)
0.678374 + 0.734717i \(0.262685\pi\)
\(440\) −15.5316 −0.740440
\(441\) 2.79022 0.404616i 0.132867 0.0192674i
\(442\) −8.96617 −0.426477
\(443\) 3.63184 6.29053i 0.172554 0.298872i −0.766758 0.641936i \(-0.778131\pi\)
0.939312 + 0.343064i \(0.111465\pi\)
\(444\) 1.46785 3.02635i 0.0696611 0.143624i
\(445\) 3.22480 + 5.58552i 0.152870 + 0.264779i
\(446\) 4.09111 + 7.08602i 0.193720 + 0.335533i
\(447\) −4.54962 + 9.38022i −0.215190 + 0.443669i
\(448\) 12.4805 21.6169i 0.589649 1.02130i
\(449\) −14.7385 −0.695555 −0.347777 0.937577i \(-0.613064\pi\)
−0.347777 + 0.937577i \(0.613064\pi\)
\(450\) 3.82503 0.554677i 0.180314 0.0261477i
\(451\) 31.2611 1.47203
\(452\) 3.27152 5.66643i 0.153879 0.266526i
\(453\) 16.9852 1.22513i 0.798035 0.0575615i
\(454\) −3.67130 6.35888i −0.172303 0.298437i
\(455\) −1.40888 2.44026i −0.0660494 0.114401i
\(456\) 15.5136 + 22.8915i 0.726489 + 1.07199i
\(457\) −3.70139 + 6.41099i −0.173143 + 0.299893i −0.939517 0.342502i \(-0.888726\pi\)
0.766374 + 0.642395i \(0.222059\pi\)
\(458\) −28.2735 −1.32113
\(459\) −35.3219 + 7.75091i −1.64868 + 0.361782i
\(460\) 0.121511 0.00566550
\(461\) 1.52205 2.63626i 0.0708888 0.122783i −0.828402 0.560134i \(-0.810750\pi\)
0.899291 + 0.437351i \(0.144083\pi\)
\(462\) −18.1721 26.8143i −0.845442 1.24751i
\(463\) −6.99042 12.1078i −0.324872 0.562695i 0.656614 0.754227i \(-0.271988\pi\)
−0.981487 + 0.191531i \(0.938655\pi\)
\(464\) −7.75105 13.4252i −0.359833 0.623250i
\(465\) −12.7523 + 0.919811i −0.591374 + 0.0426552i
\(466\) −16.5985 + 28.7495i −0.768911 + 1.33179i
\(467\) 30.6445 1.41806 0.709030 0.705178i \(-0.249133\pi\)
0.709030 + 0.705178i \(0.249133\pi\)
\(468\) 0.631794 + 0.801395i 0.0292047 + 0.0370445i
\(469\) −5.03831 −0.232648
\(470\) −3.94565 + 6.83406i −0.181999 + 0.315232i
\(471\) 1.89637 3.90985i 0.0873801 0.180157i
\(472\) 1.97915 + 3.42800i 0.0910980 + 0.157786i
\(473\) −25.1972 43.6428i −1.15857 2.00670i
\(474\) −8.63884 + 17.8112i −0.396795 + 0.818095i
\(475\) −2.64773 + 4.58600i −0.121486 + 0.210420i
\(476\) −6.67062 −0.305747
\(477\) −3.63017 + 9.09958i −0.166214 + 0.416641i
\(478\) −7.66695 −0.350678
\(479\) 1.48202 2.56693i 0.0677152 0.117286i −0.830180 0.557495i \(-0.811762\pi\)
0.897895 + 0.440209i \(0.145096\pi\)
\(480\) −3.28594 + 0.237011i −0.149982 + 0.0108180i
\(481\) −2.85443 4.94401i −0.130151 0.225428i
\(482\) −15.0085 25.9955i −0.683620 1.18406i
\(483\) 0.978058 + 1.44320i 0.0445032 + 0.0656679i
\(484\) 2.64280 4.57746i 0.120127 0.208066i
\(485\) −11.2560 −0.511109
\(486\) −15.5252 12.7400i −0.704239 0.577898i
\(487\) −17.5341 −0.794546 −0.397273 0.917700i \(-0.630043\pi\)
−0.397273 + 0.917700i \(0.630043\pi\)
\(488\) −13.8350 + 23.9629i −0.626281 + 1.08475i
\(489\) 19.2624 + 28.4231i 0.871074 + 1.28534i
\(490\) 0.605394 + 1.04857i 0.0273489 + 0.0473697i
\(491\) 10.5572 + 18.2856i 0.476439 + 0.825216i 0.999636 0.0269956i \(-0.00859399\pi\)
−0.523197 + 0.852212i \(0.675261\pi\)
\(492\) 3.56605 0.257215i 0.160770 0.0115962i
\(493\) −16.8363 + 29.1614i −0.758270 + 1.31336i
\(494\) 6.82238 0.306953
\(495\) −5.72656 + 14.3545i −0.257390 + 0.645188i
\(496\) −23.6506 −1.06194
\(497\) −6.92556 + 11.9954i −0.310654 + 0.538068i
\(498\) −14.5666 + 30.0328i −0.652746 + 1.34580i
\(499\) −16.5523 28.6694i −0.740981 1.28342i −0.952049 0.305945i \(-0.901028\pi\)
0.211068 0.977471i \(-0.432306\pi\)
\(500\) −0.170081 0.294590i −0.00760627 0.0131745i
\(501\) 17.9724 37.0546i 0.802946 1.65548i
\(502\) −10.7244 + 18.5752i −0.478654 + 0.829053i
\(503\) 20.4002 0.909601 0.454800 0.890593i \(-0.349711\pi\)
0.454800 + 0.890593i \(0.349711\pi\)
\(504\) −15.7787 20.0144i −0.702840 0.891514i
\(505\) −9.75844 −0.434245
\(506\) 1.18541 2.05320i 0.0526981 0.0912758i
\(507\) 1.72756 0.124607i 0.0767238 0.00553401i
\(508\) 1.35895 + 2.35376i 0.0602934 + 0.104431i
\(509\) 15.9675 + 27.6564i 0.707745 + 1.22585i 0.965692 + 0.259691i \(0.0836207\pi\)
−0.257947 + 0.966159i \(0.583046\pi\)
\(510\) −8.71238 12.8558i −0.385791 0.569263i
\(511\) 6.59044 11.4150i 0.291544 0.504969i
\(512\) −25.4137 −1.12314
\(513\) 26.8765 5.89769i 1.18663 0.260389i
\(514\) −8.49711 −0.374791
\(515\) 3.96888 6.87431i 0.174890 0.302918i
\(516\) −3.23341 4.77115i −0.142343 0.210038i
\(517\) −15.7769 27.3265i −0.693869 1.20182i
\(518\) 10.3623 + 17.9480i 0.455294 + 0.788591i
\(519\) −9.99539 + 0.720957i −0.438749 + 0.0316465i
\(520\) −1.50747 + 2.61102i −0.0661070 + 0.114501i
\(521\) −20.4121 −0.894270 −0.447135 0.894467i \(-0.647556\pi\)
−0.447135 + 0.894467i \(0.647556\pi\)
\(522\) −18.5071 + 2.68376i −0.810033 + 0.117465i
\(523\) 16.5405 0.723264 0.361632 0.932321i \(-0.382220\pi\)
0.361632 + 0.932321i \(0.382220\pi\)
\(524\) −0.590193 + 1.02224i −0.0257827 + 0.0446570i
\(525\) 2.12986 4.39125i 0.0929547 0.191650i
\(526\) 11.3817 + 19.7138i 0.496267 + 0.859560i
\(527\) 25.6862 + 44.4898i 1.11891 + 1.93800i
\(528\) −12.4759 + 25.7222i −0.542943 + 1.11942i
\(529\) 11.4362 19.8081i 0.497226 0.861221i
\(530\) −4.20729 −0.182753
\(531\) 3.89792 0.565247i 0.169155 0.0245296i
\(532\) 5.07569 0.220059
\(533\) 3.03414 5.25529i 0.131423 0.227632i
\(534\) 14.3549 1.03540i 0.621196 0.0448062i
\(535\) 2.22547 + 3.85464i 0.0962157 + 0.166650i
\(536\) 2.69544 + 4.66863i 0.116425 + 0.201654i
\(537\) 19.6265 + 28.9604i 0.846947 + 1.24973i
\(538\) 3.92819 6.80382i 0.169356 0.293334i
\(539\) −4.84142 −0.208535
\(540\) −0.535138 + 1.68458i −0.0230287 + 0.0724929i
\(541\) 13.3791 0.575211 0.287606 0.957749i \(-0.407141\pi\)
0.287606 + 0.957749i \(0.407141\pi\)
\(542\) 12.8294 22.2211i 0.551069 0.954479i
\(543\) 9.79480 + 14.4530i 0.420335 + 0.620236i
\(544\) 6.61866 + 11.4639i 0.283773 + 0.491509i
\(545\) −4.29438 7.43809i −0.183951 0.318613i
\(546\) −6.27150 + 0.452357i −0.268395 + 0.0193591i
\(547\) −13.9133 + 24.0986i −0.594892 + 1.03038i 0.398671 + 0.917094i \(0.369472\pi\)
−0.993562 + 0.113288i \(0.963862\pi\)
\(548\) −1.95876 −0.0836741
\(549\) 17.0458 + 21.6217i 0.727498 + 0.922791i
\(550\) −6.63698 −0.283002
\(551\) 12.8108 22.1889i 0.545758 0.945281i
\(552\) 0.814058 1.67839i 0.0346486 0.0714370i
\(553\) 12.4983 + 21.6477i 0.531482 + 0.920554i
\(554\) −20.8460 36.1064i −0.885663 1.53401i
\(555\) 4.31514 8.89677i 0.183168 0.377647i
\(556\) −1.28995 + 2.23427i −0.0547063 + 0.0947540i
\(557\) −6.61513 −0.280292 −0.140146 0.990131i \(-0.544757\pi\)
−0.140146 + 0.990131i \(0.544757\pi\)
\(558\) −10.5717 + 26.4996i −0.447535 + 1.12182i
\(559\) −9.78238 −0.413751
\(560\) 4.51401 7.81849i 0.190752 0.330392i
\(561\) 61.9363 4.46740i 2.61495 0.188614i
\(562\) 20.6210 + 35.7166i 0.869844 + 1.50661i
\(563\) −8.40891 14.5647i −0.354393 0.613827i 0.632621 0.774462i \(-0.281979\pi\)
−0.987014 + 0.160634i \(0.948646\pi\)
\(564\) −2.02457 2.98740i −0.0852496 0.125792i
\(565\) 9.61749 16.6580i 0.404611 0.700807i
\(566\) −37.3284 −1.56903
\(567\) −24.3153 + 7.20351i −1.02115 + 0.302519i
\(568\) 14.8204 0.621848
\(569\) 14.8185 25.6664i 0.621223 1.07599i −0.368035 0.929812i \(-0.619969\pi\)
0.989258 0.146178i \(-0.0466972\pi\)
\(570\) 6.62927 + 9.78199i 0.277669 + 0.409723i
\(571\) −12.4637 21.5878i −0.521590 0.903421i −0.999685 0.0251123i \(-0.992006\pi\)
0.478094 0.878308i \(-0.341328\pi\)
\(572\) −0.876182 1.51759i −0.0366350 0.0634537i
\(573\) −31.5416 + 2.27506i −1.31767 + 0.0950420i
\(574\) −11.0147 + 19.0781i −0.459746 + 0.796303i
\(575\) 0.357215 0.0148969
\(576\) −9.84723 + 24.6836i −0.410301 + 1.02848i
\(577\) 25.6134 1.06630 0.533151 0.846020i \(-0.321008\pi\)
0.533151 + 0.846020i \(0.321008\pi\)
\(578\) −20.2488 + 35.0720i −0.842239 + 1.45880i
\(579\) 1.63895 3.37912i 0.0681124 0.140431i
\(580\) 0.822924 + 1.42535i 0.0341701 + 0.0591843i
\(581\) 21.0744 + 36.5019i 0.874312 + 1.51435i
\(582\) −10.9613 + 22.5996i −0.454361 + 0.936783i
\(583\) 8.41158 14.5693i 0.348372 0.603398i
\(584\) −14.1032 −0.583596
\(585\) 1.85733 + 2.35592i 0.0767910 + 0.0974051i
\(586\) 5.22834 0.215981
\(587\) −13.1566 + 22.7878i −0.543029 + 0.940554i 0.455699 + 0.890134i \(0.349389\pi\)
−0.998728 + 0.0504202i \(0.983944\pi\)
\(588\) −0.552276 + 0.0398351i −0.0227755 + 0.00164277i
\(589\) −19.5447 33.8524i −0.805324 1.39486i
\(590\) 0.845734 + 1.46485i 0.0348183 + 0.0603071i
\(591\) −14.5355 21.4483i −0.597911 0.882263i
\(592\) 9.14548 15.8404i 0.375877 0.651038i
\(593\) −28.9470 −1.18871 −0.594356 0.804202i \(-0.702593\pi\)
−0.594356 + 0.804202i \(0.702593\pi\)
\(594\) 23.2441 + 25.4764i 0.953717 + 1.04531i
\(595\) −19.6101 −0.803934
\(596\) 1.02373 1.77316i 0.0419337 0.0726313i
\(597\) −4.67656 6.90063i −0.191399 0.282424i
\(598\) −0.230109 0.398560i −0.00940984 0.0162983i
\(599\) 17.8935 + 30.9925i 0.731110 + 1.26632i 0.956409 + 0.292031i \(0.0943309\pi\)
−0.225299 + 0.974290i \(0.572336\pi\)
\(600\) −5.20850 + 0.375684i −0.212636 + 0.0153372i
\(601\) −23.1849 + 40.1574i −0.945731 + 1.63805i −0.191450 + 0.981502i \(0.561319\pi\)
−0.754281 + 0.656552i \(0.772014\pi\)
\(602\) 35.5126 1.44738
\(603\) 5.30863 0.769817i 0.216184 0.0313494i
\(604\) −3.34445 −0.136084
\(605\) 7.76921 13.4567i 0.315863 0.547091i
\(606\) −9.50297 + 19.5928i −0.386032 + 0.795904i
\(607\) −1.97001 3.41216i −0.0799603 0.138495i 0.823272 0.567647i \(-0.192146\pi\)
−0.903233 + 0.429151i \(0.858813\pi\)
\(608\) −5.03615 8.72287i −0.204243 0.353759i
\(609\) −10.3051 + 21.2467i −0.417585 + 0.860960i
\(610\) −5.91198 + 10.2398i −0.239369 + 0.414599i
\(611\) −6.12513 −0.247796
\(612\) 7.02851 1.01922i 0.284111 0.0411996i
\(613\) −36.4623 −1.47270 −0.736349 0.676602i \(-0.763452\pi\)
−0.736349 + 0.676602i \(0.763452\pi\)
\(614\) −6.59360 + 11.4205i −0.266096 + 0.460892i
\(615\) 10.4834 0.756153i 0.422730 0.0304910i
\(616\) 21.8822 + 37.9011i 0.881659 + 1.52708i
\(617\) −6.07505 10.5223i −0.244572 0.423612i 0.717439 0.696621i \(-0.245314\pi\)
−0.962011 + 0.273010i \(0.911981\pi\)
\(618\) −9.93712 14.6630i −0.399730 0.589832i
\(619\) −4.37235 + 7.57314i −0.175740 + 0.304390i −0.940417 0.340023i \(-0.889565\pi\)
0.764677 + 0.644413i \(0.222898\pi\)
\(620\) 2.51097 0.100843
\(621\) −1.25104 1.37119i −0.0502027 0.0550240i
\(622\) 28.6343 1.14813
\(623\) 9.08673 15.7387i 0.364052 0.630557i
\(624\) 3.11327 + 4.59387i 0.124631 + 0.183902i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 6.20471 + 10.7469i 0.247990 + 0.429531i
\(627\) −47.1275 + 3.39926i −1.88209 + 0.135753i
\(628\) −0.426711 + 0.739085i −0.0170276 + 0.0294927i
\(629\) −39.7304 −1.58415
\(630\) −6.74257 8.55258i −0.268631 0.340743i
\(631\) 8.53562 0.339798 0.169899 0.985462i \(-0.445656\pi\)
0.169899 + 0.985462i \(0.445656\pi\)
\(632\) 13.3729 23.1625i 0.531945 0.921356i
\(633\) −7.26085 + 14.9701i −0.288593 + 0.595008i
\(634\) −19.7791 34.2584i −0.785529 1.36058i
\(635\) 3.99498 + 6.91951i 0.158536 + 0.274592i
\(636\) 0.839660 1.73117i 0.0332947 0.0686455i
\(637\) −0.469900 + 0.813891i −0.0186181 + 0.0322475i
\(638\) 32.1124 1.27134
\(639\) 5.46432 13.6972i 0.216165 0.541852i
\(640\) −7.60862 −0.300757
\(641\) −9.66780 + 16.7451i −0.381855 + 0.661393i −0.991327 0.131415i \(-0.958048\pi\)
0.609472 + 0.792807i \(0.291381\pi\)
\(642\) 9.90648 0.714544i 0.390977 0.0282008i
\(643\) 19.7501 + 34.2082i 0.778868 + 1.34904i 0.932594 + 0.360926i \(0.117539\pi\)
−0.153726 + 0.988113i \(0.549127\pi\)
\(644\) −0.171195 0.296519i −0.00674604 0.0116845i
\(645\) −9.50549 14.0261i −0.374278 0.552276i
\(646\) 23.7400 41.1188i 0.934036 1.61780i
\(647\) 35.0901 1.37954 0.689768 0.724031i \(-0.257713\pi\)
0.689768 + 0.724031i \(0.257713\pi\)
\(648\) 19.6834 + 18.6774i 0.773235 + 0.733717i
\(649\) −6.76345 −0.265489
\(650\) −0.644173 + 1.11574i −0.0252666 + 0.0437630i
\(651\) 20.2111 + 29.8230i 0.792135 + 1.16886i
\(652\) −3.37160 5.83979i −0.132042 0.228704i
\(653\) 5.16552 + 8.94694i 0.202142 + 0.350121i 0.949218 0.314618i \(-0.101876\pi\)
−0.747076 + 0.664738i \(0.768543\pi\)
\(654\) −19.1160 + 1.37882i −0.747495 + 0.0539160i
\(655\) −1.73503 + 3.00516i −0.0677933 + 0.117421i
\(656\) 19.4426 0.759105
\(657\) −5.19991 + 13.0344i −0.202868 + 0.508520i
\(658\) 22.2358 0.866842
\(659\) −16.6368 + 28.8158i −0.648078 + 1.12250i 0.335504 + 0.942039i \(0.391094\pi\)
−0.983581 + 0.180465i \(0.942240\pi\)
\(660\) 1.32456 2.73091i 0.0515583 0.106301i
\(661\) 10.6134 + 18.3829i 0.412812 + 0.715011i 0.995196 0.0979025i \(-0.0312133\pi\)
−0.582384 + 0.812914i \(0.697880\pi\)
\(662\) 2.26524 + 3.92351i 0.0880411 + 0.152492i
\(663\) 5.26042 10.8457i 0.204298 0.421212i
\(664\) 22.5491 39.0561i 0.875074 1.51567i
\(665\) 14.9213 0.578625
\(666\) −13.6606 17.3277i −0.529337 0.671435i
\(667\) −1.72836 −0.0669222
\(668\) −4.04404 + 7.00449i −0.156469 + 0.271012i
\(669\) −10.9717 + 0.791375i −0.424189 + 0.0305963i
\(670\) 1.15182 + 1.99500i 0.0444985 + 0.0770737i
\(671\) −23.6395 40.9447i −0.912591 1.58065i
\(672\) 5.20787 + 7.68461i 0.200898 + 0.296440i
\(673\) 0.618753 1.07171i 0.0238512 0.0413115i −0.853853 0.520513i \(-0.825741\pi\)
0.877705 + 0.479202i \(0.159074\pi\)
\(674\) −25.2851 −0.973947
\(675\) −1.57318 + 4.95228i −0.0605518 + 0.190613i
\(676\) −0.340163 −0.0130832
\(677\) −11.3996 + 19.7446i −0.438121 + 0.758848i −0.997545 0.0700341i \(-0.977689\pi\)
0.559424 + 0.828882i \(0.311023\pi\)
\(678\) −24.0799 35.5317i −0.924782 1.36459i
\(679\) 15.8584 + 27.4675i 0.608589 + 1.05411i
\(680\) 10.4911 + 18.1712i 0.402317 + 0.696834i
\(681\) 9.84581 0.710168i 0.377292 0.0272137i
\(682\) 24.4960 42.4283i 0.938001 1.62467i
\(683\) 2.63501 0.100826 0.0504130 0.998728i \(-0.483946\pi\)
0.0504130 + 0.998728i \(0.483946\pi\)
\(684\) −5.34801 + 0.775528i −0.204486 + 0.0296531i
\(685\) −5.75830 −0.220013
\(686\) −11.0000 + 19.0526i −0.419984 + 0.727433i
\(687\) 16.5880 34.2003i 0.632870 1.30482i
\(688\) −15.6712 27.1433i −0.597459 1.03483i
\(689\) −1.63283 2.82814i −0.0622058 0.107744i
\(690\) 0.347864 0.717210i 0.0132429 0.0273037i
\(691\) 11.8570 20.5370i 0.451063 0.781264i −0.547389 0.836878i \(-0.684378\pi\)
0.998452 + 0.0556138i \(0.0177116\pi\)
\(692\) 1.96813 0.0748169
\(693\) 43.0968 6.24956i 1.63711 0.237401i
\(694\) 32.7138 1.24180
\(695\) −3.79217 + 6.56823i −0.143845 + 0.249147i
\(696\) 25.2009 1.81771i 0.955237 0.0689002i
\(697\) −21.1159 36.5739i −0.799823 1.38533i
\(698\) 7.85717 + 13.6090i 0.297398 + 0.515109i
\(699\) −25.0378 36.9452i −0.947017 1.39740i
\(700\) −0.479250 + 0.830085i −0.0181139 + 0.0313743i
\(701\) 36.6440 1.38403 0.692013 0.721885i \(-0.256724\pi\)
0.692013 + 0.721885i \(0.256724\pi\)
\(702\) 6.53887 1.43487i 0.246794 0.0541555i
\(703\) 30.2310 1.14018
\(704\) 22.8173 39.5208i 0.859961 1.48950i
\(705\) −5.95176 8.78227i −0.224156 0.330760i
\(706\) 11.5634 + 20.0284i 0.435194 + 0.753778i
\(707\) 13.7485 + 23.8131i 0.517065 + 0.895584i
\(708\) −0.771528 + 0.0556495i −0.0289958 + 0.00209144i
\(709\) −12.7783 + 22.1327i −0.479900 + 0.831211i −0.999734 0.0230560i \(-0.992660\pi\)
0.519834 + 0.854267i \(0.325994\pi\)
\(710\) 6.33305 0.237675
\(711\) −16.4765 20.8995i −0.617917 0.783793i
\(712\) −19.4452 −0.728738
\(713\) −1.31842 + 2.28358i −0.0493754 + 0.0855207i
\(714\) −19.0967 + 39.3727i −0.714675 + 1.47349i
\(715\) −2.57577 4.46137i −0.0963284 0.166846i
\(716\) −3.43535 5.95019i −0.128385 0.222369i
\(717\) 4.49817 9.27414i 0.167987 0.346349i
\(718\) −12.9901 + 22.4996i −0.484787 + 0.839676i
\(719\) 3.51637 0.131139 0.0655693 0.997848i \(-0.479114\pi\)
0.0655693 + 0.997848i \(0.479114\pi\)
\(720\) −3.56159 + 8.92768i −0.132733 + 0.332715i
\(721\) −22.3668 −0.832981
\(722\) −5.82450 + 10.0883i −0.216765 + 0.375449i
\(723\) 40.2503 2.90321i 1.49693 0.107972i
\(724\) −1.71444 2.96950i −0.0637167 0.110361i
\(725\) 2.41921 + 4.19019i 0.0898471 + 0.155620i
\(726\) −19.4522 28.7032i −0.721939 1.06528i
\(727\) 9.54123 16.5259i 0.353865 0.612912i −0.633058 0.774104i \(-0.718201\pi\)
0.986923 + 0.161192i \(0.0515340\pi\)
\(728\) 8.49540 0.314860
\(729\) 24.5192 11.3052i 0.908119 0.418711i
\(730\) −6.02660 −0.223054
\(731\) −34.0399 + 58.9589i −1.25901 + 2.18067i
\(732\) −3.03352 4.47619i −0.112122 0.165445i
\(733\) 8.11234 + 14.0510i 0.299636 + 0.518985i 0.976053 0.217534i \(-0.0698014\pi\)
−0.676417 + 0.736519i \(0.736468\pi\)
\(734\) −19.2502 33.3423i −0.710536 1.23068i
\(735\) −1.62356 + 0.117106i −0.0598861 + 0.00431952i
\(736\) −0.339724 + 0.588419i −0.0125224 + 0.0216894i
\(737\) −9.21123 −0.339300
\(738\) 8.69071 21.7846i 0.319909 0.801903i
\(739\) 17.3100 0.636760 0.318380 0.947963i \(-0.396861\pi\)
0.318380 + 0.947963i \(0.396861\pi\)
\(740\) −0.970970 + 1.68177i −0.0356936 + 0.0618231i
\(741\) −4.00266 + 8.25252i −0.147042 + 0.303164i
\(742\) 5.92758 + 10.2669i 0.217608 + 0.376909i
\(743\) 22.3620 + 38.7321i 0.820381 + 1.42094i 0.905399 + 0.424562i \(0.139572\pi\)
−0.0850183 + 0.996379i \(0.527095\pi\)
\(744\) 16.8221 34.6831i 0.616728 1.27154i
\(745\) 3.00953 5.21267i 0.110261 0.190977i
\(746\) −4.71039 −0.172460
\(747\) −27.7823 35.2403i −1.01650 1.28938i
\(748\) −12.1955 −0.445911
\(749\) 6.27086 10.8615i 0.229132 0.396869i
\(750\) −2.22570 + 0.160537i −0.0812711 + 0.00586200i
\(751\) −14.4998 25.1143i −0.529104 0.916435i −0.999424 0.0339392i \(-0.989195\pi\)
0.470320 0.882496i \(-0.344139\pi\)
\(752\) −9.81235 16.9955i −0.357820 0.619762i
\(753\) −16.1771 23.8705i −0.589526 0.869891i
\(754\) 3.11678 5.39842i 0.113506 0.196599i
\(755\) −9.83190 −0.357819
\(756\) 4.86476 1.06751i 0.176930 0.0388248i
\(757\) 32.0762 1.16583 0.582914 0.812534i \(-0.301912\pi\)
0.582914 + 0.812534i \(0.301912\pi\)
\(758\) −15.5010 + 26.8486i −0.563023 + 0.975184i
\(759\) 1.78812 + 2.63851i 0.0649048 + 0.0957719i
\(760\) −7.98274 13.8265i −0.289564 0.501540i
\(761\) 12.4399 + 21.5465i 0.450944 + 0.781059i 0.998445 0.0557467i \(-0.0177539\pi\)
−0.547501 + 0.836805i \(0.684421\pi\)
\(762\) 17.7833 1.28269i 0.644220 0.0464669i
\(763\) −12.1006 + 20.9588i −0.438070 + 0.758759i
\(764\) 6.21064 0.224693
\(765\) 20.6622 2.99627i 0.747043 0.108331i
\(766\) −38.2394 −1.38165
\(767\) −0.656449 + 1.13700i −0.0237030 + 0.0410548i
\(768\) 5.98221 12.3339i 0.215864 0.445060i
\(769\) 20.1005 + 34.8150i 0.724842 + 1.25546i 0.959039 + 0.283273i \(0.0914204\pi\)
−0.234198 + 0.972189i \(0.575246\pi\)
\(770\) 9.35072 + 16.1959i 0.336977 + 0.583660i
\(771\) 4.98522 10.2783i 0.179538 0.370165i
\(772\) −0.368788 + 0.638759i −0.0132730 + 0.0229894i
\(773\) −2.03131 −0.0730612 −0.0365306 0.999333i \(-0.511631\pi\)
−0.0365306 + 0.999333i \(0.511631\pi\)
\(774\) −37.4179 + 5.42606i −1.34496 + 0.195036i
\(775\) 7.38168 0.265158
\(776\) 16.9681 29.3896i 0.609119 1.05502i
\(777\) −27.7899 + 2.00446i −0.996958 + 0.0719096i
\(778\) −3.66346 6.34531i −0.131342 0.227490i
\(779\) 16.0672 + 27.8292i 0.575666 + 0.997083i
\(780\) −0.330534 0.487729i −0.0118350 0.0174635i
\(781\) −12.6616 + 21.9305i −0.453066 + 0.784734i
\(782\) −3.20285 −0.114534
\(783\) 7.61170 23.9612i 0.272020 0.856303i
\(784\) −3.01109 −0.107539
\(785\) −1.25443 + 2.17274i −0.0447726 + 0.0775484i
\(786\) 4.34410 + 6.41005i 0.154949 + 0.228639i
\(787\) −18.7372 32.4537i −0.667908 1.15685i −0.978488 0.206303i \(-0.933857\pi\)
0.310580 0.950547i \(-0.399477\pi\)
\(788\) 2.54424 + 4.40675i 0.0906347 + 0.156984i
\(789\) −30.5239 + 2.20166i −1.08668 + 0.0783810i
\(790\) 5.71451 9.89783i 0.203313 0.352149i
\(791\) −54.1997 −1.92712
\(792\) −28.8473 36.5911i −1.02504 1.30021i
\(793\) −9.17762 −0.325907
\(794\) 1.05696 1.83071i 0.0375102 0.0649696i
\(795\) 2.46840 5.08925i 0.0875453 0.180497i
\(796\) 0.818567 + 1.41780i 0.0290133 + 0.0502526i
\(797\) 6.95827 + 12.0521i 0.246475 + 0.426907i 0.962545 0.271121i \(-0.0873944\pi\)
−0.716070 + 0.698028i \(0.754061\pi\)
\(798\) 14.5307 29.9588i 0.514381 1.06053i
\(799\) −21.3137 + 36.9165i −0.754026 + 1.30601i
\(800\) 1.90207 0.0672482
\(801\) −7.16950 + 17.9715i −0.253322 + 0.634991i
\(802\) −17.1410 −0.605270
\(803\) 12.0489 20.8693i 0.425196 0.736461i
\(804\) −1.05075 + 0.0757898i −0.0370572 + 0.00267290i
\(805\) −0.503275 0.871697i −0.0177381 0.0307233i
\(806\) −4.75508 8.23604i −0.167491 0.290102i
\(807\) 5.92542 + 8.74342i 0.208585 + 0.307783i
\(808\) 14.7106 25.4794i 0.517516 0.896364i
\(809\) 7.77442 0.273334 0.136667 0.990617i \(-0.456361\pi\)
0.136667 + 0.990617i \(0.456361\pi\)
\(810\) 8.41110 + 7.98124i 0.295536 + 0.280432i
\(811\) −29.5307 −1.03696 −0.518482 0.855089i \(-0.673503\pi\)
−0.518482 + 0.855089i \(0.673503\pi\)
\(812\) 2.31881 4.01629i 0.0813742 0.140944i
\(813\) 19.3523 + 28.5558i 0.678714 + 1.00150i
\(814\) 18.9448 + 32.8133i 0.664013 + 1.15010i
\(815\) −9.91173 17.1676i −0.347193 0.601356i
\(816\) 38.5208 2.77847i 1.34850 0.0972658i
\(817\) 25.9011 44.8620i 0.906164 1.56952i
\(818\) 13.6034 0.475630
\(819\) 3.13228 7.85156i 0.109451 0.274356i
\(820\) −2.06421 −0.0720852
\(821\) 9.69370 16.7900i 0.338312 0.585974i −0.645803 0.763504i \(-0.723477\pi\)
0.984115 + 0.177530i \(0.0568106\pi\)
\(822\) −5.60755 + 11.5614i −0.195586 + 0.403250i
\(823\) −19.9843 34.6138i −0.696609 1.20656i −0.969635 0.244555i \(-0.921358\pi\)
0.273027 0.962006i \(-0.411975\pi\)
\(824\) 11.9659 + 20.7256i 0.416853 + 0.722011i
\(825\) 3.89389 8.02825i 0.135568 0.279508i
\(826\) 2.38308 4.12761i 0.0829179 0.143618i
\(827\) 39.8289 1.38499 0.692494 0.721424i \(-0.256512\pi\)
0.692494 + 0.721424i \(0.256512\pi\)
\(828\) 0.225686 + 0.286271i 0.00784314 + 0.00994860i
\(829\) 32.8078 1.13946 0.569731 0.821831i \(-0.307047\pi\)
0.569731 + 0.821831i \(0.307047\pi\)
\(830\) 9.63569 16.6895i 0.334460 0.579301i
\(831\) 55.9055 4.03240i 1.93934 0.139883i
\(832\) −4.42922 7.67164i −0.153556 0.265966i
\(833\) 3.27024 + 5.66422i 0.113307 + 0.196254i
\(834\) 9.49467 + 14.0101i 0.328774 + 0.485131i
\(835\) −11.8886 + 20.5916i −0.411420 + 0.712601i
\(836\) 9.27956 0.320940
\(837\) −25.8522 28.3350i −0.893583 0.979400i
\(838\) 26.4743 0.914541
\(839\) −24.7549 + 42.8767i −0.854633 + 1.48027i 0.0223528 + 0.999750i \(0.492884\pi\)
−0.876985 + 0.480517i \(0.840449\pi\)
\(840\) 8.25493 + 12.1808i 0.284822 + 0.420277i
\(841\) 2.79488 + 4.84087i 0.0963751 + 0.166927i
\(842\) 23.3652 + 40.4697i 0.805218 + 1.39468i
\(843\) −55.3020 + 3.98888i −1.90470 + 0.137384i
\(844\) 1.63380 2.82982i 0.0562376 0.0974064i
\(845\) −1.00000 −0.0344010
\(846\) −23.4288 + 3.39747i −0.805499 + 0.116807i
\(847\) −43.7836 −1.50442
\(848\) 5.23152 9.06126i 0.179651 0.311165i
\(849\) 21.9005 45.1534i 0.751622 1.54966i
\(850\) 4.48308 + 7.76493i 0.153769 + 0.266335i
\(851\) −1.01965 1.76608i −0.0349530 0.0605403i
\(852\) −1.26390 + 2.60586i −0.0433005 + 0.0892752i
\(853\) 9.43866 16.3482i 0.323174 0.559753i −0.657967 0.753046i \(-0.728584\pi\)
0.981141 + 0.193293i \(0.0619168\pi\)
\(854\) 33.3171 1.14009
\(855\) −15.7219 + 2.27987i −0.537678 + 0.0779700i
\(856\) −13.4193 −0.458664
\(857\) 19.0881 33.0616i 0.652037 1.12936i −0.330591 0.943774i \(-0.607248\pi\)
0.982628 0.185587i \(-0.0594187\pi\)
\(858\) −11.4658 + 0.827016i −0.391436 + 0.0282338i
\(859\) −17.1791 29.7551i −0.586144 1.01523i −0.994732 0.102512i \(-0.967312\pi\)
0.408588 0.912719i \(-0.366021\pi\)
\(860\) 1.66380 + 2.88179i 0.0567352 + 0.0982682i
\(861\) −16.6150 24.5167i −0.566238 0.835528i
\(862\) −9.94074 + 17.2179i −0.338583 + 0.586443i
\(863\) 38.0198 1.29421 0.647105 0.762401i \(-0.275980\pi\)
0.647105 + 0.762401i \(0.275980\pi\)
\(864\) −6.66144 7.30119i −0.226627 0.248392i
\(865\) 5.78584 0.196724
\(866\) 15.0404 26.0508i 0.511095 0.885243i
\(867\) −30.5440 45.0700i −1.03733 1.53066i
\(868\) −3.53767 6.12742i −0.120076 0.207978i
\(869\) 22.8499 + 39.5772i 0.775129 + 1.34256i
\(870\) 10.7689 0.776746i 0.365098 0.0263342i
\(871\) −0.894026 + 1.54850i −0.0302929 + 0.0524689i
\(872\) 25.8946 0.876902
\(873\) −20.9061 26.5182i −0.707563 0.897504i
\(874\) 2.43706 0.0824347
\(875\) −1.40888 + 2.44026i −0.0476289 + 0.0824957i
\(876\) 1.20274 2.47976i 0.0406369 0.0837835i
\(877\) 15.8916 + 27.5251i 0.536622 + 0.929456i 0.999083 + 0.0428167i \(0.0136331\pi\)
−0.462461 + 0.886640i \(0.653034\pi\)
\(878\) −8.01978 13.8907i −0.270654 0.468787i
\(879\) −3.06745 + 6.32433i −0.103462 + 0.213314i
\(880\) 8.25268 14.2941i 0.278198 0.481853i
\(881\) −9.08373 −0.306039 −0.153019 0.988223i \(-0.548900\pi\)
−0.153019 + 0.988223i \(0.548900\pi\)
\(882\) −1.34594 + 3.37380i −0.0453200 + 0.113602i
\(883\) 49.6414 1.67057 0.835283 0.549820i \(-0.185304\pi\)
0.835283 + 0.549820i \(0.185304\pi\)
\(884\) −1.18367 + 2.05018i −0.0398112 + 0.0689550i
\(885\) −2.26811 + 0.163597i −0.0762418 + 0.00549924i
\(886\) 4.67907 + 8.10438i 0.157196 + 0.272272i
\(887\) −14.9338 25.8661i −0.501429 0.868500i −0.999999 0.00165060i \(-0.999475\pi\)
0.498570 0.866850i \(-0.333859\pi\)
\(888\) 16.7247 + 24.6785i 0.561243 + 0.828157i
\(889\) 11.2569 19.4976i 0.377545 0.653927i
\(890\) −8.30932 −0.278529
\(891\) −44.4541 + 13.1697i −1.48927 + 0.441203i
\(892\) 2.16036 0.0723342
\(893\) 16.2177 28.0898i 0.542704 0.939990i
\(894\) −7.53515 11.1187i −0.252013 0.371865i
\(895\) −10.0991 17.4922i −0.337576 0.584699i
\(896\) 10.7196 + 18.5670i 0.358118 + 0.620279i
\(897\) 0.617112 0.0445117i 0.0206048 0.00148620i
\(898\) 9.49418 16.4444i 0.316825 0.548757i
\(899\) −35.7156 −1.19118
\(900\) 0.378132 0.947847i 0.0126044 0.0315949i
\(901\) −22.7271 −0.757150
\(902\) −20.1375 + 34.8793i −0.670507 + 1.16135i
\(903\) −20.8351 + 42.9569i −0.693349 + 1.42952i
\(904\) 28.9962 + 50.2229i 0.964399 + 1.67039i
\(905\) −5.04006 8.72964i −0.167537 0.290183i
\(906\) −9.57450 + 19.7403i −0.318091 + 0.655827i
\(907\) 9.22113 15.9715i 0.306183 0.530324i −0.671341 0.741148i \(-0.734282\pi\)
0.977524 + 0.210824i \(0.0676148\pi\)
\(908\) −1.93867 −0.0643371
\(909\) −18.1246 22.9901i −0.601155 0.762532i
\(910\) 3.63026 0.120342
\(911\) 4.10456 7.10930i 0.135990 0.235542i −0.789985 0.613126i \(-0.789912\pi\)
0.925975 + 0.377584i \(0.123245\pi\)
\(912\) −29.3106 + 2.11414i −0.970570 + 0.0700062i
\(913\) 38.5290 + 66.7341i 1.27512 + 2.20858i
\(914\) −4.76867 8.25957i −0.157733 0.273202i
\(915\) −8.91784 13.1590i −0.294815 0.435022i
\(916\) −3.73253 + 6.46494i −0.123326 + 0.213608i
\(917\) 9.77782 0.322892
\(918\) 14.1054 44.4030i 0.465548 1.46552i
\(919\) −1.11177 −0.0366738 −0.0183369 0.999832i \(-0.505837\pi\)
−0.0183369 + 0.999832i \(0.505837\pi\)
\(920\) −0.538492 + 0.932695i −0.0177535 + 0.0307500i
\(921\) −9.94603 14.6761i −0.327733 0.483595i
\(922\) 1.96093 + 3.39642i 0.0645796 + 0.111855i
\(923\) 2.45782 + 4.25707i 0.0809001 + 0.140123i
\(924\) −8.53028 + 0.615280i −0.280625 + 0.0202412i
\(925\) −2.85443 + 4.94401i −0.0938530 + 0.162558i
\(926\) 18.0122 0.591916
\(927\) 23.5668 3.41748i 0.774035 0.112245i
\(928\) −9.20299 −0.302103
\(929\) −5.88119 + 10.1865i −0.192956 + 0.334209i −0.946228 0.323499i \(-0.895141\pi\)
0.753273 + 0.657708i \(0.228474\pi\)
\(930\) 7.18843 14.8208i 0.235718 0.485993i
\(931\) −2.48833 4.30992i −0.0815519 0.141252i
\(932\) 4.38252 + 7.59074i 0.143554 + 0.248643i
\(933\) −16.7996 + 34.6368i −0.549995 + 1.13396i
\(934\) −19.7404 + 34.1914i −0.645926 + 1.11878i
\(935\) −35.8519 −1.17248
\(936\) −8.95120 + 1.29803i −0.292579 + 0.0424276i
\(937\) −50.7176 −1.65687 −0.828436 0.560084i \(-0.810769\pi\)
−0.828436 + 0.560084i \(0.810769\pi\)
\(938\) 3.24555 5.62145i 0.105971 0.183547i
\(939\) −16.6400 + 1.20022i −0.543025 + 0.0391678i
\(940\) 1.04177 + 1.80440i 0.0339788 + 0.0588531i
\(941\) −13.3852 23.1839i −0.436345 0.755772i 0.561059 0.827776i \(-0.310394\pi\)
−0.997404 + 0.0720035i \(0.977061\pi\)
\(942\) 3.14079 + 4.63448i 0.102333 + 0.151000i
\(943\) 1.08384 1.87727i 0.0352948 0.0611324i
\(944\) −4.20648 −0.136909
\(945\) 14.3013 3.13822i 0.465220 0.102086i
\(946\) 64.9254 2.11091
\(947\) 11.4159 19.7730i 0.370968 0.642536i −0.618746 0.785591i \(-0.712359\pi\)
0.989715 + 0.143055i \(0.0456925\pi\)
\(948\) 2.93220 + 4.32668i 0.0952334 + 0.140524i
\(949\) −2.33889 4.05108i −0.0759236 0.131503i
\(950\) −3.41119 5.90835i −0.110674 0.191692i
\(951\) 53.0442 3.82602i 1.72008 0.124067i
\(952\) 29.5616 51.2022i 0.958097 1.65947i
\(953\) −4.98857 −0.161596 −0.0807979 0.996731i \(-0.525747\pi\)
−0.0807979 + 0.996731i \(0.525747\pi\)
\(954\) −7.81432 9.91203i −0.252998 0.320914i
\(955\) 18.2578 0.590810
\(956\) −1.01216 + 1.75310i −0.0327354 + 0.0566994i
\(957\) −18.8402 + 38.8440i −0.609019 + 1.25565i
\(958\) 1.90936 + 3.30710i 0.0616885 + 0.106848i
\(959\) 8.11277 + 14.0517i 0.261975 + 0.453754i
\(960\) 6.69582 13.8052i 0.216107 0.445559i
\(961\) −11.7446 + 20.3422i −0.378858 + 0.656201i
\(962\) 7.35498 0.237134
\(963\) −4.94776 + 12.4023i −0.159439 + 0.399660i
\(964\) −7.92542 −0.255261
\(965\) −1.08415 + 1.87780i −0.0349000 + 0.0604486i
\(966\) −2.24028 + 0.161589i −0.0720797 + 0.00519903i
\(967\) 8.44142 + 14.6210i 0.271458 + 0.470179i 0.969235 0.246136i \(-0.0791610\pi\)
−0.697778 + 0.716314i \(0.745828\pi\)
\(968\) 23.4237 + 40.5710i 0.752866 + 1.30400i
\(969\) 35.8102 + 52.8407i 1.15039 + 1.69749i
\(970\) 7.25081 12.5588i 0.232810 0.403238i
\(971\) −12.3303 −0.395699 −0.197850 0.980232i \(-0.563396\pi\)
−0.197850 + 0.980232i \(0.563396\pi\)
\(972\) −4.96266 + 1.86808i −0.159177 + 0.0599187i
\(973\) 21.3709 0.685119
\(974\) 11.2950 19.5635i 0.361915 0.626856i
\(975\) −0.971694 1.43381i −0.0311191 0.0459187i
\(976\) −14.7024 25.4653i −0.470612 0.815123i
\(977\) −30.0983 52.1317i −0.962929 1.66784i −0.715079 0.699044i \(-0.753609\pi\)
−0.247850 0.968798i \(-0.579724\pi\)
\(978\) −44.1211 + 3.18241i −1.41084 + 0.101762i
\(979\) 16.6127 28.7740i 0.530944 0.919622i
\(980\) 0.319685 0.0102120
\(981\) 9.54744 23.9322i 0.304826 0.764095i
\(982\) −27.2026 −0.868070
\(983\) 1.13564 1.96698i 0.0362212 0.0627370i −0.847346 0.531040i \(-0.821801\pi\)
0.883568 + 0.468303i \(0.155135\pi\)
\(984\) −13.8290 + 28.5121i −0.440853 + 0.908932i
\(985\) 7.47946 + 12.9548i 0.238316 + 0.412775i
\(986\) −21.6910 37.5699i −0.690783 1.19647i
\(987\) −13.0457 + 26.8970i −0.415248 + 0.856141i
\(988\) 0.900658 1.55999i 0.0286538 0.0496298i
\(989\) −3.49442 −0.111116
\(990\) −12.3270 15.6362i −0.391779 0.496950i
\(991\) 55.9580 1.77756 0.888782 0.458331i \(-0.151552\pi\)
0.888782 + 0.458331i \(0.151552\pi\)
\(992\) −7.02022 + 12.1594i −0.222892 + 0.386061i
\(993\) −6.07499 + 0.438183i −0.192784 + 0.0139053i
\(994\) −8.92252 15.4543i −0.283005 0.490179i
\(995\) 2.40640 + 4.16800i 0.0762879 + 0.132135i
\(996\) 4.94421 + 7.29556i 0.156663 + 0.231169i
\(997\) −1.41267 + 2.44682i −0.0447397 + 0.0774915i −0.887528 0.460754i \(-0.847579\pi\)
0.842788 + 0.538245i \(0.180913\pi\)
\(998\) 42.6501 1.35007
\(999\) 28.9747 6.35810i 0.916718 0.201161i
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 585.2.i.h.196.5 30
3.2 odd 2 1755.2.i.h.586.11 30
9.2 odd 6 5265.2.a.bl.1.5 15
9.4 even 3 inner 585.2.i.h.391.5 yes 30
9.5 odd 6 1755.2.i.h.1171.11 30
9.7 even 3 5265.2.a.bk.1.11 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.i.h.196.5 30 1.1 even 1 trivial
585.2.i.h.391.5 yes 30 9.4 even 3 inner
1755.2.i.h.586.11 30 3.2 odd 2
1755.2.i.h.1171.11 30 9.5 odd 6
5265.2.a.bk.1.11 15 9.7 even 3
5265.2.a.bl.1.5 15 9.2 odd 6