Properties

Label 441.2.h.f.214.3
Level $441$
Weight $2$
Character 441.214
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
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] = [441,2,Mod(214,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 214.3
Root \(0.247934 - 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.f.373.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.495868 q^{2} +(0.221298 + 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 + 3.19787i) q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 + 0.760316i) q^{9} +O(q^{10})\) \(q-0.495868 q^{2} +(0.221298 + 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 + 3.19787i) q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 + 0.760316i) q^{9} +(0.915516 - 1.58572i) q^{10} +(0.446284 + 0.772987i) q^{11} +(-0.388182 - 3.01332i) q^{12} +(-0.598355 - 1.03638i) q^{13} +(-5.90205 - 2.46398i) q^{15} +2.58515 q^{16} +(0.124991 - 0.216492i) q^{17} +(1.43904 - 0.377017i) q^{18} +(-1.40414 - 2.43204i) q^{19} +(3.23860 - 5.60943i) q^{20} +(-0.221298 - 0.383300i) q^{22} +(-1.23886 + 2.14576i) q^{23} +(0.411957 + 3.19787i) q^{24} +(-4.31757 - 7.47825i) q^{25} +(0.296705 + 0.513909i) q^{26} +(-1.94833 - 4.81705i) q^{27} +(2.07128 - 3.58755i) q^{29} +(2.92664 + 1.22181i) q^{30} -3.58515 q^{31} -5.00499 q^{32} +(-1.22912 + 0.937712i) q^{33} +(-0.0619793 + 0.107351i) q^{34} +(5.09054 - 1.33368i) q^{36} +(-2.36568 - 4.09747i) q^{37} +(0.696267 + 1.20597i) q^{38} +(1.64794 - 1.25724i) q^{39} +(-3.43695 + 5.95298i) q^{40} +(2.39093 + 4.14121i) q^{41} +(-4.98928 + 8.64169i) q^{43} +(-0.782834 - 1.35591i) q^{44} +(2.92664 - 10.6841i) q^{45} +(0.614310 - 1.06402i) q^{46} +10.1731 q^{47} +(0.572088 + 4.44091i) q^{48} +(2.14095 + 3.70823i) q^{50} +(0.399562 + 0.166808i) q^{51} +(1.04958 + 1.81793i) q^{52} +(-4.94465 + 8.56438i) q^{53} +(0.966116 + 2.38862i) q^{54} -3.29588 q^{55} +(3.86715 - 2.95031i) q^{57} +(-1.02708 + 1.77895i) q^{58} -1.81237 q^{59} +(10.3529 + 4.32210i) q^{60} -10.8041 q^{61} +1.77776 q^{62} -2.68848 q^{64} +4.41895 q^{65} +(0.609480 - 0.464982i) q^{66} +1.02937 q^{67} +(-0.219249 + 0.379751i) q^{68} +(-3.96027 - 1.65332i) q^{69} -4.94533 q^{71} +(-5.40231 + 1.41536i) q^{72} +(0.915262 - 1.58528i) q^{73} +(1.17306 + 2.03181i) q^{74} +(11.8911 - 9.07189i) q^{75} +(2.46302 + 4.26607i) q^{76} +(-0.817161 + 0.623424i) q^{78} -1.79912 q^{79} +(-4.77293 + 8.26696i) q^{80} +(7.84384 - 4.41296i) q^{81} +(-1.18559 - 2.05350i) q^{82} +(-6.16156 + 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} +(2.47403 - 4.28514i) q^{86} +(6.62127 + 2.76423i) q^{87} +(0.830779 + 1.43895i) q^{88} +(1.20370 + 2.08488i) q^{89} +(-1.45123 + 5.29793i) q^{90} +(2.17310 - 3.76392i) q^{92} +(-0.793387 - 6.15877i) q^{93} -5.04450 q^{94} +10.3698 q^{95} +(-1.10759 - 8.59784i) q^{96} +(-5.52210 + 9.56456i) q^{97} +(-1.88286 - 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + 7 q^{10} + 4 q^{11} + 20 q^{12} + 8 q^{13} - 19 q^{15} - 4 q^{16} - 12 q^{17} + 4 q^{18} - q^{19} - 5 q^{20} - q^{22} + 3 q^{23} - 6 q^{24} - q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + 16 q^{45} + 3 q^{46} + 54 q^{47} + 5 q^{48} + 19 q^{50} - 9 q^{51} + 10 q^{52} - 21 q^{53} - q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} + 60 q^{59} + 10 q^{60} - 28 q^{61} + 12 q^{62} - 50 q^{64} + 22 q^{65} - 19 q^{66} + 4 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 36 q^{72} - 15 q^{73} - 36 q^{74} + 14 q^{75} - 5 q^{76} - 20 q^{78} + 8 q^{79} - 20 q^{80} + 23 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} - 2 q^{87} - 18 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 6 q^{93} - 6 q^{94} + 28 q^{95} - 59 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.495868 −0.350632 −0.175316 0.984512i \(-0.556095\pi\)
−0.175316 + 0.984512i \(0.556095\pi\)
\(3\) 0.221298 + 1.71786i 0.127767 + 0.991804i
\(4\) −1.75411 −0.877057
\(5\) −1.84629 + 3.19787i −0.825686 + 1.43013i 0.0757082 + 0.997130i \(0.475878\pi\)
−0.901394 + 0.433000i \(0.857455\pi\)
\(6\) −0.109735 0.851830i −0.0447990 0.347758i
\(7\) 0 0
\(8\) 1.86155 0.658156
\(9\) −2.90205 + 0.760316i −0.967351 + 0.253439i
\(10\) 0.915516 1.58572i 0.289512 0.501449i
\(11\) 0.446284 + 0.772987i 0.134560 + 0.233064i 0.925429 0.378921i \(-0.123705\pi\)
−0.790869 + 0.611985i \(0.790371\pi\)
\(12\) −0.388182 3.01332i −0.112059 0.869869i
\(13\) −0.598355 1.03638i −0.165954 0.287441i 0.771040 0.636787i \(-0.219737\pi\)
−0.936994 + 0.349346i \(0.886404\pi\)
\(14\) 0 0
\(15\) −5.90205 2.46398i −1.52390 0.636196i
\(16\) 2.58515 0.646287
\(17\) 0.124991 0.216492i 0.0303149 0.0525069i −0.850470 0.526024i \(-0.823682\pi\)
0.880785 + 0.473517i \(0.157016\pi\)
\(18\) 1.43904 0.377017i 0.339184 0.0888637i
\(19\) −1.40414 2.43204i −0.322131 0.557948i 0.658796 0.752321i \(-0.271066\pi\)
−0.980928 + 0.194374i \(0.937733\pi\)
\(20\) 3.23860 5.60943i 0.724174 1.25431i
\(21\) 0 0
\(22\) −0.221298 0.383300i −0.0471809 0.0817198i
\(23\) −1.23886 + 2.14576i −0.258320 + 0.447423i −0.965792 0.259318i \(-0.916502\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(24\) 0.411957 + 3.19787i 0.0840903 + 0.652762i
\(25\) −4.31757 7.47825i −0.863514 1.49565i
\(26\) 0.296705 + 0.513909i 0.0581887 + 0.100786i
\(27\) −1.94833 4.81705i −0.374957 0.927042i
\(28\) 0 0
\(29\) 2.07128 3.58755i 0.384626 0.666192i −0.607091 0.794632i \(-0.707664\pi\)
0.991717 + 0.128440i \(0.0409970\pi\)
\(30\) 2.92664 + 1.22181i 0.534329 + 0.223071i
\(31\) −3.58515 −0.643912 −0.321956 0.946755i \(-0.604340\pi\)
−0.321956 + 0.946755i \(0.604340\pi\)
\(32\) −5.00499 −0.884765
\(33\) −1.22912 + 0.937712i −0.213962 + 0.163235i
\(34\) −0.0619793 + 0.107351i −0.0106294 + 0.0184106i
\(35\) 0 0
\(36\) 5.09054 1.33368i 0.848423 0.222280i
\(37\) −2.36568 4.09747i −0.388915 0.673621i 0.603389 0.797447i \(-0.293817\pi\)
−0.992304 + 0.123826i \(0.960483\pi\)
\(38\) 0.696267 + 1.20597i 0.112949 + 0.195634i
\(39\) 1.64794 1.25724i 0.263882 0.201319i
\(40\) −3.43695 + 5.95298i −0.543430 + 0.941249i
\(41\) 2.39093 + 4.14121i 0.373400 + 0.646748i 0.990086 0.140461i \(-0.0448584\pi\)
−0.616686 + 0.787209i \(0.711525\pi\)
\(42\) 0 0
\(43\) −4.98928 + 8.64169i −0.760859 + 1.31785i 0.181550 + 0.983382i \(0.441889\pi\)
−0.942408 + 0.334464i \(0.891445\pi\)
\(44\) −0.782834 1.35591i −0.118017 0.204411i
\(45\) 2.92664 10.6841i 0.436278 1.59270i
\(46\) 0.614310 1.06402i 0.0905751 0.156881i
\(47\) 10.1731 1.48389 0.741947 0.670459i \(-0.233903\pi\)
0.741947 + 0.670459i \(0.233903\pi\)
\(48\) 0.572088 + 4.44091i 0.0825738 + 0.640990i
\(49\) 0 0
\(50\) 2.14095 + 3.70823i 0.302776 + 0.524423i
\(51\) 0.399562 + 0.166808i 0.0559498 + 0.0233578i
\(52\) 1.04958 + 1.81793i 0.145551 + 0.252102i
\(53\) −4.94465 + 8.56438i −0.679199 + 1.17641i 0.296023 + 0.955181i \(0.404339\pi\)
−0.975222 + 0.221227i \(0.928994\pi\)
\(54\) 0.966116 + 2.38862i 0.131472 + 0.325051i
\(55\) −3.29588 −0.444416
\(56\) 0 0
\(57\) 3.86715 2.95031i 0.512217 0.390778i
\(58\) −1.02708 + 1.77895i −0.134862 + 0.233588i
\(59\) −1.81237 −0.235951 −0.117975 0.993017i \(-0.537640\pi\)
−0.117975 + 0.993017i \(0.537640\pi\)
\(60\) 10.3529 + 4.32210i 1.33655 + 0.557980i
\(61\) −10.8041 −1.38332 −0.691662 0.722221i \(-0.743121\pi\)
−0.691662 + 0.722221i \(0.743121\pi\)
\(62\) 1.77776 0.225776
\(63\) 0 0
\(64\) −2.68848 −0.336060
\(65\) 4.41895 0.548103
\(66\) 0.609480 0.464982i 0.0750219 0.0572353i
\(67\) 1.02937 0.125757 0.0628787 0.998021i \(-0.479972\pi\)
0.0628787 + 0.998021i \(0.479972\pi\)
\(68\) −0.219249 + 0.379751i −0.0265879 + 0.0460516i
\(69\) −3.96027 1.65332i −0.476761 0.199037i
\(70\) 0 0
\(71\) −4.94533 −0.586903 −0.293451 0.955974i \(-0.594804\pi\)
−0.293451 + 0.955974i \(0.594804\pi\)
\(72\) −5.40231 + 1.41536i −0.636668 + 0.166802i
\(73\) 0.915262 1.58528i 0.107123 0.185543i −0.807480 0.589894i \(-0.799169\pi\)
0.914604 + 0.404351i \(0.132503\pi\)
\(74\) 1.17306 + 2.03181i 0.136366 + 0.236193i
\(75\) 11.8911 9.07189i 1.37306 1.04753i
\(76\) 2.46302 + 4.26607i 0.282527 + 0.489352i
\(77\) 0 0
\(78\) −0.817161 + 0.623424i −0.0925253 + 0.0705889i
\(79\) −1.79912 −0.202417 −0.101209 0.994865i \(-0.532271\pi\)
−0.101209 + 0.994865i \(0.532271\pi\)
\(80\) −4.77293 + 8.26696i −0.533630 + 0.924274i
\(81\) 7.84384 4.41296i 0.871538 0.490329i
\(82\) −1.18559 2.05350i −0.130926 0.226771i
\(83\) −6.16156 + 10.6721i −0.676319 + 1.17142i 0.299763 + 0.954014i \(0.403092\pi\)
−0.976082 + 0.217405i \(0.930241\pi\)
\(84\) 0 0
\(85\) 0.461541 + 0.799412i 0.0500611 + 0.0867084i
\(86\) 2.47403 4.28514i 0.266781 0.462079i
\(87\) 6.62127 + 2.76423i 0.709875 + 0.296357i
\(88\) 0.830779 + 1.43895i 0.0885613 + 0.153393i
\(89\) 1.20370 + 2.08488i 0.127592 + 0.220997i 0.922743 0.385415i \(-0.125942\pi\)
−0.795151 + 0.606412i \(0.792608\pi\)
\(90\) −1.45123 + 5.29793i −0.152973 + 0.558451i
\(91\) 0 0
\(92\) 2.17310 3.76392i 0.226561 0.392416i
\(93\) −0.793387 6.15877i −0.0822704 0.638634i
\(94\) −5.04450 −0.520300
\(95\) 10.3698 1.06392
\(96\) −1.10759 8.59784i −0.113043 0.877513i
\(97\) −5.52210 + 9.56456i −0.560684 + 0.971134i 0.436752 + 0.899582i \(0.356129\pi\)
−0.997437 + 0.0715522i \(0.977205\pi\)
\(98\) 0 0
\(99\) −1.88286 1.90393i −0.189234 0.191352i
\(100\) 7.57351 + 13.1177i 0.757351 + 1.31177i
\(101\) −1.29982 2.25136i −0.129337 0.224018i 0.794083 0.607810i \(-0.207952\pi\)
−0.923420 + 0.383791i \(0.874618\pi\)
\(102\) −0.198130 0.0827148i −0.0196178 0.00818999i
\(103\) 4.85578 8.41045i 0.478454 0.828706i −0.521241 0.853409i \(-0.674531\pi\)
0.999695 + 0.0247032i \(0.00786408\pi\)
\(104\) −1.11387 1.92927i −0.109224 0.189181i
\(105\) 0 0
\(106\) 2.45189 4.24680i 0.238149 0.412486i
\(107\) −5.45025 9.44012i −0.526896 0.912610i −0.999509 0.0313403i \(-0.990022\pi\)
0.472613 0.881270i \(-0.343311\pi\)
\(108\) 3.41760 + 8.44966i 0.328859 + 0.813069i
\(109\) −1.06096 + 1.83764i −0.101622 + 0.176014i −0.912353 0.409404i \(-0.865737\pi\)
0.810731 + 0.585419i \(0.199070\pi\)
\(110\) 1.63432 0.155826
\(111\) 6.51535 4.97066i 0.618410 0.471794i
\(112\) 0 0
\(113\) 7.91318 + 13.7060i 0.744409 + 1.28935i 0.950470 + 0.310816i \(0.100602\pi\)
−0.206061 + 0.978539i \(0.566065\pi\)
\(114\) −1.91760 + 1.46297i −0.179600 + 0.137019i
\(115\) −4.57458 7.92341i −0.426582 0.738861i
\(116\) −3.63325 + 6.29298i −0.337339 + 0.584289i
\(117\) 2.52444 + 2.55270i 0.233384 + 0.235997i
\(118\) 0.898698 0.0827318
\(119\) 0 0
\(120\) −10.9869 4.58681i −1.00297 0.418716i
\(121\) 5.10166 8.83634i 0.463787 0.803303i
\(122\) 5.35741 0.485038
\(123\) −6.58489 + 5.02371i −0.593740 + 0.452973i
\(124\) 6.28876 0.564747
\(125\) 13.4230 1.20059
\(126\) 0 0
\(127\) −1.26946 −0.112647 −0.0563233 0.998413i \(-0.517938\pi\)
−0.0563233 + 0.998413i \(0.517938\pi\)
\(128\) 11.3431 1.00260
\(129\) −15.9493 6.65848i −1.40426 0.586246i
\(130\) −2.19122 −0.192182
\(131\) −7.51444 + 13.0154i −0.656540 + 1.13716i 0.324965 + 0.945726i \(0.394647\pi\)
−0.981505 + 0.191435i \(0.938686\pi\)
\(132\) 2.15601 1.64485i 0.187657 0.143166i
\(133\) 0 0
\(134\) −0.510432 −0.0440946
\(135\) 19.0015 + 2.66316i 1.63539 + 0.229209i
\(136\) 0.232677 0.403009i 0.0199519 0.0345577i
\(137\) 0.244246 + 0.423047i 0.0208674 + 0.0361433i 0.876271 0.481819i \(-0.160024\pi\)
−0.855403 + 0.517963i \(0.826691\pi\)
\(138\) 1.96377 + 0.819831i 0.167167 + 0.0697887i
\(139\) 4.93487 + 8.54745i 0.418570 + 0.724985i 0.995796 0.0915997i \(-0.0291980\pi\)
−0.577226 + 0.816585i \(0.695865\pi\)
\(140\) 0 0
\(141\) 2.25128 + 17.4759i 0.189592 + 1.47173i
\(142\) 2.45223 0.205787
\(143\) 0.534073 0.925042i 0.0446614 0.0773559i
\(144\) −7.50224 + 1.96553i −0.625187 + 0.163794i
\(145\) 7.64835 + 13.2473i 0.635161 + 1.10013i
\(146\) −0.453849 + 0.786090i −0.0375609 + 0.0650573i
\(147\) 0 0
\(148\) 4.14967 + 7.18744i 0.341101 + 0.590804i
\(149\) −10.5120 + 18.2073i −0.861175 + 1.49160i 0.00962096 + 0.999954i \(0.496938\pi\)
−0.870796 + 0.491645i \(0.836396\pi\)
\(150\) −5.89641 + 4.49846i −0.481440 + 0.367298i
\(151\) −0.749191 1.29764i −0.0609683 0.105600i 0.833930 0.551870i \(-0.186086\pi\)
−0.894898 + 0.446270i \(0.852752\pi\)
\(152\) −2.61387 4.52735i −0.212013 0.367217i
\(153\) −0.198130 + 0.723303i −0.0160179 + 0.0584756i
\(154\) 0 0
\(155\) 6.61922 11.4648i 0.531669 0.920877i
\(156\) −2.89068 + 2.20534i −0.231439 + 0.176568i
\(157\) 16.6796 1.33118 0.665590 0.746317i \(-0.268180\pi\)
0.665590 + 0.746317i \(0.268180\pi\)
\(158\) 0.892128 0.0709739
\(159\) −15.8066 6.59890i −1.25355 0.523327i
\(160\) 9.24065 16.0053i 0.730538 1.26533i
\(161\) 0 0
\(162\) −3.88951 + 2.18825i −0.305589 + 0.171925i
\(163\) −3.34135 5.78738i −0.261714 0.453303i 0.704983 0.709224i \(-0.250954\pi\)
−0.966698 + 0.255921i \(0.917621\pi\)
\(164\) −4.19396 7.26416i −0.327494 0.567236i
\(165\) −0.729372 5.66184i −0.0567815 0.440774i
\(166\) 3.05532 5.29197i 0.237139 0.410737i
\(167\) −8.81549 15.2689i −0.682163 1.18154i −0.974319 0.225170i \(-0.927706\pi\)
0.292156 0.956371i \(-0.405627\pi\)
\(168\) 0 0
\(169\) 5.78394 10.0181i 0.444919 0.770622i
\(170\) −0.228863 0.396403i −0.0175530 0.0304027i
\(171\) 5.92400 + 5.99031i 0.453020 + 0.458091i
\(172\) 8.75178 15.1585i 0.667317 1.15583i
\(173\) 3.88685 0.295511 0.147756 0.989024i \(-0.452795\pi\)
0.147756 + 0.989024i \(0.452795\pi\)
\(174\) −3.28328 1.37070i −0.248905 0.103912i
\(175\) 0 0
\(176\) 1.15371 + 1.99829i 0.0869642 + 0.150626i
\(177\) −0.401075 3.11339i −0.0301466 0.234017i
\(178\) −0.596879 1.03382i −0.0447380 0.0774884i
\(179\) 3.66758 6.35244i 0.274128 0.474804i −0.695787 0.718248i \(-0.744944\pi\)
0.969915 + 0.243445i \(0.0782775\pi\)
\(180\) −5.13366 + 18.7412i −0.382641 + 1.39689i
\(181\) −11.2566 −0.836693 −0.418346 0.908288i \(-0.637390\pi\)
−0.418346 + 0.908288i \(0.637390\pi\)
\(182\) 0 0
\(183\) −2.39093 18.5599i −0.176743 1.37199i
\(184\) −2.30619 + 3.99444i −0.170015 + 0.294474i
\(185\) 17.4709 1.28449
\(186\) 0.393415 + 3.05394i 0.0288466 + 0.223925i
\(187\) 0.223127 0.0163167
\(188\) −17.8447 −1.30146
\(189\) 0 0
\(190\) −5.14204 −0.373043
\(191\) −23.8459 −1.72543 −0.862715 0.505690i \(-0.831238\pi\)
−0.862715 + 0.505690i \(0.831238\pi\)
\(192\) −0.594956 4.61842i −0.0429373 0.333306i
\(193\) 5.93456 0.427179 0.213589 0.976924i \(-0.431485\pi\)
0.213589 + 0.976924i \(0.431485\pi\)
\(194\) 2.73823 4.74276i 0.196594 0.340510i
\(195\) 0.977905 + 7.59112i 0.0700293 + 0.543611i
\(196\) 0 0
\(197\) −15.4682 −1.10206 −0.551032 0.834484i \(-0.685766\pi\)
−0.551032 + 0.834484i \(0.685766\pi\)
\(198\) 0.933648 + 0.944100i 0.0663515 + 0.0670942i
\(199\) −7.74818 + 13.4202i −0.549254 + 0.951336i 0.449072 + 0.893496i \(0.351755\pi\)
−0.998326 + 0.0578402i \(0.981579\pi\)
\(200\) −8.03736 13.9211i −0.568327 0.984371i
\(201\) 0.227798 + 1.76831i 0.0160676 + 0.124727i
\(202\) 0.644540 + 1.11638i 0.0453497 + 0.0785480i
\(203\) 0 0
\(204\) −0.700877 0.292600i −0.0490712 0.0204861i
\(205\) −17.6574 −1.23325
\(206\) −2.40783 + 4.17048i −0.167761 + 0.290571i
\(207\) 1.96377 7.16905i 0.136492 0.498283i
\(208\) −1.54684 2.67920i −0.107254 0.185769i
\(209\) 1.25329 2.17076i 0.0866918 0.150155i
\(210\) 0 0
\(211\) 0.771898 + 1.33697i 0.0531397 + 0.0920406i 0.891372 0.453273i \(-0.149744\pi\)
−0.838232 + 0.545314i \(0.816410\pi\)
\(212\) 8.67347 15.0229i 0.595697 1.03178i
\(213\) −1.09439 8.49536i −0.0749866 0.582093i
\(214\) 2.70261 + 4.68105i 0.184746 + 0.319990i
\(215\) −18.4233 31.9101i −1.25646 2.17625i
\(216\) −3.62691 8.96717i −0.246780 0.610138i
\(217\) 0 0
\(218\) 0.526098 0.911229i 0.0356319 0.0617162i
\(219\) 2.92583 + 1.22147i 0.197709 + 0.0825392i
\(220\) 5.78135 0.389779
\(221\) −0.299157 −0.0201235
\(222\) −3.23075 + 2.46479i −0.216834 + 0.165426i
\(223\) 2.72171 4.71414i 0.182259 0.315682i −0.760390 0.649466i \(-0.774992\pi\)
0.942649 + 0.333784i \(0.108326\pi\)
\(224\) 0 0
\(225\) 18.2157 + 18.4196i 1.21438 + 1.22797i
\(226\) −3.92389 6.79638i −0.261014 0.452089i
\(227\) −8.03818 13.9225i −0.533513 0.924072i −0.999234 0.0391399i \(-0.987538\pi\)
0.465721 0.884932i \(-0.345795\pi\)
\(228\) −6.78343 + 5.17518i −0.449244 + 0.342735i
\(229\) −4.98420 + 8.63289i −0.329365 + 0.570477i −0.982386 0.186863i \(-0.940168\pi\)
0.653021 + 0.757340i \(0.273501\pi\)
\(230\) 2.26839 + 3.92897i 0.149573 + 0.259068i
\(231\) 0 0
\(232\) 3.85578 6.67840i 0.253144 0.438458i
\(233\) 8.27045 + 14.3248i 0.541815 + 0.938451i 0.998800 + 0.0489765i \(0.0155959\pi\)
−0.456985 + 0.889474i \(0.651071\pi\)
\(234\) −1.25179 1.26580i −0.0818320 0.0827480i
\(235\) −18.7824 + 32.5321i −1.22523 + 2.12216i
\(236\) 3.17911 0.206942
\(237\) −0.398143 3.09063i −0.0258621 0.200758i
\(238\) 0 0
\(239\) −11.0119 19.0732i −0.712303 1.23375i −0.963990 0.265937i \(-0.914319\pi\)
0.251687 0.967809i \(-0.419015\pi\)
\(240\) −15.2577 6.36974i −0.984879 0.411165i
\(241\) 8.36004 + 14.4800i 0.538517 + 0.932739i 0.998984 + 0.0450623i \(0.0143486\pi\)
−0.460467 + 0.887677i \(0.652318\pi\)
\(242\) −2.52975 + 4.38166i −0.162619 + 0.281664i
\(243\) 9.31665 + 12.4980i 0.597664 + 0.801747i
\(244\) 18.9516 1.21325
\(245\) 0 0
\(246\) 3.26524 2.49110i 0.208184 0.158827i
\(247\) −1.68035 + 2.91045i −0.106918 + 0.185187i
\(248\) −6.67392 −0.423794
\(249\) −19.6967 8.22294i −1.24823 0.521108i
\(250\) −6.65606 −0.420966
\(251\) 8.53099 0.538471 0.269236 0.963074i \(-0.413229\pi\)
0.269236 + 0.963074i \(0.413229\pi\)
\(252\) 0 0
\(253\) −2.21153 −0.139038
\(254\) 0.629487 0.0394975
\(255\) −1.27114 + 0.969769i −0.0796017 + 0.0607293i
\(256\) −0.247722 −0.0154826
\(257\) −8.55986 + 14.8261i −0.533950 + 0.924828i 0.465264 + 0.885172i \(0.345959\pi\)
−0.999213 + 0.0396557i \(0.987374\pi\)
\(258\) 7.90875 + 3.30173i 0.492377 + 0.205557i
\(259\) 0 0
\(260\) −7.75135 −0.480718
\(261\) −3.28328 + 11.9861i −0.203230 + 0.741921i
\(262\) 3.72617 6.45392i 0.230204 0.398725i
\(263\) −10.2763 17.7991i −0.633666 1.09754i −0.986796 0.161967i \(-0.948216\pi\)
0.353130 0.935574i \(-0.385117\pi\)
\(264\) −2.28806 + 1.74559i −0.140820 + 0.107434i
\(265\) −18.2585 31.6246i −1.12161 1.94269i
\(266\) 0 0
\(267\) −3.31514 + 2.52917i −0.202883 + 0.154783i
\(268\) −1.80563 −0.110297
\(269\) −9.92267 + 17.1866i −0.604996 + 1.04788i 0.387057 + 0.922056i \(0.373492\pi\)
−0.992052 + 0.125827i \(0.959842\pi\)
\(270\) −9.42223 1.32058i −0.573419 0.0803679i
\(271\) −5.32056 9.21548i −0.323201 0.559801i 0.657946 0.753065i \(-0.271426\pi\)
−0.981147 + 0.193265i \(0.938092\pi\)
\(272\) 0.323121 0.559663i 0.0195921 0.0339345i
\(273\) 0 0
\(274\) −0.121114 0.209776i −0.00731676 0.0126730i
\(275\) 3.85373 6.67485i 0.232388 0.402509i
\(276\) 6.94677 + 2.90012i 0.418146 + 0.174567i
\(277\) 12.4407 + 21.5479i 0.747487 + 1.29469i 0.949024 + 0.315205i \(0.102073\pi\)
−0.201536 + 0.979481i \(0.564593\pi\)
\(278\) −2.44705 4.23841i −0.146764 0.254203i
\(279\) 10.4043 2.72585i 0.622889 0.163192i
\(280\) 0 0
\(281\) −6.83733 + 11.8426i −0.407881 + 0.706470i −0.994652 0.103282i \(-0.967065\pi\)
0.586771 + 0.809753i \(0.300399\pi\)
\(282\) −1.11634 8.66572i −0.0664770 0.516036i
\(283\) −6.32179 −0.375791 −0.187896 0.982189i \(-0.560167\pi\)
−0.187896 + 0.982189i \(0.560167\pi\)
\(284\) 8.67468 0.514747
\(285\) 2.29481 + 17.8138i 0.135933 + 1.05520i
\(286\) −0.264830 + 0.458699i −0.0156597 + 0.0271234i
\(287\) 0 0
\(288\) 14.5247 3.80537i 0.855878 0.224234i
\(289\) 8.46875 + 14.6683i 0.498162 + 0.862842i
\(290\) −3.79257 6.56893i −0.222708 0.385741i
\(291\) −17.6526 7.36955i −1.03481 0.432011i
\(292\) −1.60547 + 2.78076i −0.0939533 + 0.162732i
\(293\) 1.31508 + 2.27778i 0.0768277 + 0.133069i 0.901880 0.431987i \(-0.142188\pi\)
−0.825052 + 0.565057i \(0.808854\pi\)
\(294\) 0 0
\(295\) 3.34616 5.79573i 0.194821 0.337440i
\(296\) −4.40382 7.62764i −0.255967 0.443348i
\(297\) 2.85401 3.65581i 0.165606 0.212132i
\(298\) 5.21256 9.02841i 0.301955 0.523002i
\(299\) 2.96511 0.171477
\(300\) −20.8583 + 15.9131i −1.20426 + 0.918745i
\(301\) 0 0
\(302\) 0.371500 + 0.643457i 0.0213774 + 0.0370268i
\(303\) 3.57986 2.73113i 0.205657 0.156899i
\(304\) −3.62990 6.28717i −0.208189 0.360594i
\(305\) 19.9475 34.5501i 1.14219 1.97833i
\(306\) 0.0982463 0.358663i 0.00561637 0.0205034i
\(307\) 2.79496 0.159517 0.0797583 0.996814i \(-0.474585\pi\)
0.0797583 + 0.996814i \(0.474585\pi\)
\(308\) 0 0
\(309\) 15.5225 + 6.48030i 0.883045 + 0.368652i
\(310\) −3.28226 + 5.68504i −0.186420 + 0.322889i
\(311\) 15.1003 0.856258 0.428129 0.903718i \(-0.359173\pi\)
0.428129 + 0.903718i \(0.359173\pi\)
\(312\) 3.06772 2.34041i 0.173675 0.132499i
\(313\) 25.4785 1.44013 0.720064 0.693908i \(-0.244112\pi\)
0.720064 + 0.693908i \(0.244112\pi\)
\(314\) −8.27090 −0.466754
\(315\) 0 0
\(316\) 3.15587 0.177531
\(317\) 32.5209 1.82656 0.913278 0.407337i \(-0.133543\pi\)
0.913278 + 0.407337i \(0.133543\pi\)
\(318\) 7.83799 + 3.27219i 0.439533 + 0.183495i
\(319\) 3.69751 0.207021
\(320\) 4.96372 8.59741i 0.277480 0.480610i
\(321\) 15.0106 11.4518i 0.837811 0.639179i
\(322\) 0 0
\(323\) −0.702021 −0.0390615
\(324\) −13.7590 + 7.74084i −0.764388 + 0.430046i
\(325\) −5.16688 + 8.94931i −0.286607 + 0.496418i
\(326\) 1.65687 + 2.86978i 0.0917654 + 0.158942i
\(327\) −3.39159 1.41591i −0.187556 0.0783003i
\(328\) 4.45083 + 7.70906i 0.245756 + 0.425661i
\(329\) 0 0
\(330\) 0.361672 + 2.80753i 0.0199094 + 0.154549i
\(331\) 18.0948 0.994582 0.497291 0.867584i \(-0.334328\pi\)
0.497291 + 0.867584i \(0.334328\pi\)
\(332\) 10.8081 18.7201i 0.593170 1.02740i
\(333\) 9.98070 + 10.0924i 0.546939 + 0.553062i
\(334\) 4.37132 + 7.57135i 0.239188 + 0.414286i
\(335\) −1.90051 + 3.29179i −0.103836 + 0.179850i
\(336\) 0 0
\(337\) −12.5086 21.6656i −0.681389 1.18020i −0.974557 0.224139i \(-0.928043\pi\)
0.293168 0.956061i \(-0.405290\pi\)
\(338\) −2.86807 + 4.96765i −0.156003 + 0.270204i
\(339\) −21.7938 + 16.6268i −1.18368 + 0.903045i
\(340\) −0.809596 1.40226i −0.0439065 0.0760483i
\(341\) −1.59999 2.77127i −0.0866446 0.150073i
\(342\) −2.93752 2.97041i −0.158843 0.160621i
\(343\) 0 0
\(344\) −9.28778 + 16.0869i −0.500764 + 0.867348i
\(345\) 12.5989 9.61190i 0.678303 0.517488i
\(346\) −1.92736 −0.103616
\(347\) 10.7489 0.577030 0.288515 0.957475i \(-0.406838\pi\)
0.288515 + 0.957475i \(0.406838\pi\)
\(348\) −11.6145 4.84878i −0.622601 0.259922i
\(349\) 1.64301 2.84577i 0.0879482 0.152331i −0.818695 0.574228i \(-0.805302\pi\)
0.906644 + 0.421897i \(0.138636\pi\)
\(350\) 0 0
\(351\) −3.82651 + 4.90153i −0.204244 + 0.261624i
\(352\) −2.23365 3.86879i −0.119054 0.206207i
\(353\) 8.40960 + 14.5658i 0.447598 + 0.775262i 0.998229 0.0594866i \(-0.0189463\pi\)
−0.550631 + 0.834748i \(0.685613\pi\)
\(354\) 0.198880 + 1.54383i 0.0105704 + 0.0820538i
\(355\) 9.13051 15.8145i 0.484597 0.839347i
\(356\) −2.11144 3.65711i −0.111906 0.193827i
\(357\) 0 0
\(358\) −1.81864 + 3.14997i −0.0961180 + 0.166481i
\(359\) 11.8921 + 20.5978i 0.627642 + 1.08711i 0.988024 + 0.154303i \(0.0493131\pi\)
−0.360382 + 0.932805i \(0.617354\pi\)
\(360\) 5.44808 19.8890i 0.287139 1.04824i
\(361\) 5.55680 9.62466i 0.292463 0.506561i
\(362\) 5.58177 0.293371
\(363\) 16.3085 + 6.80845i 0.855976 + 0.357351i
\(364\) 0 0
\(365\) 3.37968 + 5.85377i 0.176900 + 0.306401i
\(366\) 1.18559 + 9.20326i 0.0619716 + 0.481062i
\(367\) −0.344992 0.597544i −0.0180084 0.0311915i 0.856881 0.515515i \(-0.172399\pi\)
−0.874889 + 0.484323i \(0.839066\pi\)
\(368\) −3.20263 + 5.54712i −0.166949 + 0.289164i
\(369\) −10.0872 10.2002i −0.525121 0.530999i
\(370\) −8.66327 −0.450382
\(371\) 0 0
\(372\) 1.39169 + 10.8032i 0.0721558 + 0.560119i
\(373\) 1.88006 3.25636i 0.0973457 0.168608i −0.813239 0.581929i \(-0.802298\pi\)
0.910585 + 0.413321i \(0.135631\pi\)
\(374\) −0.110642 −0.00572114
\(375\) 2.97050 + 23.0589i 0.153396 + 1.19075i
\(376\) 18.9376 0.976634
\(377\) −4.95744 −0.255321
\(378\) 0 0
\(379\) 32.8735 1.68860 0.844300 0.535872i \(-0.180017\pi\)
0.844300 + 0.535872i \(0.180017\pi\)
\(380\) −18.1898 −0.933116
\(381\) −0.280930 2.18075i −0.0143925 0.111723i
\(382\) 11.8244 0.604991
\(383\) −0.536335 + 0.928960i −0.0274055 + 0.0474676i −0.879403 0.476078i \(-0.842058\pi\)
0.851997 + 0.523546i \(0.175391\pi\)
\(384\) 2.51021 + 19.4858i 0.128099 + 0.994381i
\(385\) 0 0
\(386\) −2.94276 −0.149782
\(387\) 7.90875 28.8721i 0.402024 1.46765i
\(388\) 9.68640 16.7773i 0.491752 0.851740i
\(389\) 11.8718 + 20.5626i 0.601925 + 1.04256i 0.992529 + 0.122006i \(0.0389326\pi\)
−0.390605 + 0.920559i \(0.627734\pi\)
\(390\) −0.484912 3.76419i −0.0245545 0.190607i
\(391\) 0.309693 + 0.536405i 0.0156619 + 0.0271271i
\(392\) 0 0
\(393\) −24.0215 10.0284i −1.21172 0.505868i
\(394\) 7.67019 0.386419
\(395\) 3.32170 5.75336i 0.167133 0.289483i
\(396\) 3.30274 + 3.33972i 0.165969 + 0.167827i
\(397\) 0.0160489 + 0.0277975i 0.000805471 + 0.00139512i 0.866428 0.499302i \(-0.166410\pi\)
−0.865622 + 0.500697i \(0.833077\pi\)
\(398\) 3.84208 6.65467i 0.192586 0.333569i
\(399\) 0 0
\(400\) −11.1616 19.3324i −0.558078 0.966619i
\(401\) −12.2628 + 21.2398i −0.612374 + 1.06066i 0.378465 + 0.925616i \(0.376452\pi\)
−0.990839 + 0.135048i \(0.956881\pi\)
\(402\) −0.112958 0.876848i −0.00563381 0.0437332i
\(403\) 2.14519 + 3.71558i 0.106860 + 0.185086i
\(404\) 2.28004 + 3.94914i 0.113436 + 0.196477i
\(405\) −0.369938 + 33.2312i −0.0183824 + 1.65127i
\(406\) 0 0
\(407\) 2.11153 3.65728i 0.104665 0.181284i
\(408\) 0.743802 + 0.310521i 0.0368237 + 0.0153731i
\(409\) −26.7897 −1.32467 −0.662333 0.749210i \(-0.730433\pi\)
−0.662333 + 0.749210i \(0.730433\pi\)
\(410\) 8.75574 0.432415
\(411\) −0.672682 + 0.513199i −0.0331810 + 0.0253143i
\(412\) −8.51759 + 14.7529i −0.419631 + 0.726823i
\(413\) 0 0
\(414\) −0.973773 + 3.55490i −0.0478583 + 0.174714i
\(415\) −22.7520 39.4077i −1.11685 1.93445i
\(416\) 2.99476 + 5.18708i 0.146830 + 0.254317i
\(417\) −13.5912 + 10.3689i −0.665564 + 0.507769i
\(418\) −0.621466 + 1.07641i −0.0303969 + 0.0526490i
\(419\) 10.5262 + 18.2320i 0.514240 + 0.890689i 0.999864 + 0.0165215i \(0.00525920\pi\)
−0.485624 + 0.874168i \(0.661407\pi\)
\(420\) 0 0
\(421\) −7.44533 + 12.8957i −0.362863 + 0.628498i −0.988431 0.151672i \(-0.951534\pi\)
0.625568 + 0.780170i \(0.284867\pi\)
\(422\) −0.382760 0.662959i −0.0186325 0.0322724i
\(423\) −29.5228 + 7.73475i −1.43545 + 0.376076i
\(424\) −9.20469 + 15.9430i −0.447019 + 0.774260i
\(425\) −2.15864 −0.104709
\(426\) 0.542675 + 4.21258i 0.0262927 + 0.204100i
\(427\) 0 0
\(428\) 9.56037 + 16.5590i 0.462118 + 0.800412i
\(429\) 1.70728 + 0.712750i 0.0824281 + 0.0344119i
\(430\) 9.13554 + 15.8232i 0.440555 + 0.763064i
\(431\) −7.95192 + 13.7731i −0.383031 + 0.663428i −0.991494 0.130154i \(-0.958453\pi\)
0.608463 + 0.793582i \(0.291786\pi\)
\(432\) −5.03673 12.4528i −0.242330 0.599135i
\(433\) 16.3658 0.786490 0.393245 0.919434i \(-0.371352\pi\)
0.393245 + 0.919434i \(0.371352\pi\)
\(434\) 0 0
\(435\) −21.0644 + 16.0704i −1.00996 + 0.770515i
\(436\) 1.86105 3.22344i 0.0891282 0.154375i
\(437\) 6.95811 0.332851
\(438\) −1.45083 0.605687i −0.0693231 0.0289409i
\(439\) 15.5447 0.741909 0.370954 0.928651i \(-0.379031\pi\)
0.370954 + 0.928651i \(0.379031\pi\)
\(440\) −6.13543 −0.292495
\(441\) 0 0
\(442\) 0.148343 0.00705594
\(443\) 1.79005 0.0850480 0.0425240 0.999095i \(-0.486460\pi\)
0.0425240 + 0.999095i \(0.486460\pi\)
\(444\) −11.4287 + 8.71910i −0.542381 + 0.413790i
\(445\) −8.88955 −0.421405
\(446\) −1.34961 + 2.33759i −0.0639058 + 0.110688i
\(447\) −33.6038 14.0288i −1.58940 0.663540i
\(448\) 0 0
\(449\) 13.5666 0.640250 0.320125 0.947375i \(-0.396275\pi\)
0.320125 + 0.947375i \(0.396275\pi\)
\(450\) −9.03257 9.13368i −0.425799 0.430566i
\(451\) −2.13407 + 3.69631i −0.100489 + 0.174053i
\(452\) −13.8806 24.0419i −0.652890 1.13084i
\(453\) 2.06336 1.57417i 0.0969450 0.0739608i
\(454\) 3.98588 + 6.90375i 0.187067 + 0.324009i
\(455\) 0 0
\(456\) 7.19889 5.49214i 0.337119 0.257193i
\(457\) 2.56917 0.120181 0.0600905 0.998193i \(-0.480861\pi\)
0.0600905 + 0.998193i \(0.480861\pi\)
\(458\) 2.47151 4.28078i 0.115486 0.200028i
\(459\) −1.28638 0.180293i −0.0600429 0.00841535i
\(460\) 8.02434 + 13.8986i 0.374137 + 0.648024i
\(461\) −18.0934 + 31.3388i −0.842695 + 1.45959i 0.0449122 + 0.998991i \(0.485699\pi\)
−0.887608 + 0.460600i \(0.847634\pi\)
\(462\) 0 0
\(463\) 8.19224 + 14.1894i 0.380726 + 0.659436i 0.991166 0.132626i \(-0.0423409\pi\)
−0.610440 + 0.792062i \(0.709008\pi\)
\(464\) 5.35455 9.27436i 0.248579 0.430551i
\(465\) 21.1597 + 8.83372i 0.981259 + 0.409654i
\(466\) −4.10105 7.10323i −0.189978 0.329051i
\(467\) 4.35022 + 7.53480i 0.201304 + 0.348669i 0.948949 0.315430i \(-0.102149\pi\)
−0.747645 + 0.664099i \(0.768815\pi\)
\(468\) −4.42815 4.47772i −0.204692 0.206983i
\(469\) 0 0
\(470\) 9.31361 16.1316i 0.429605 0.744097i
\(471\) 3.69117 + 28.6532i 0.170080 + 1.32027i
\(472\) −3.37381 −0.155292
\(473\) −8.90655 −0.409524
\(474\) 0.197426 + 1.53255i 0.00906809 + 0.0703922i
\(475\) −12.1249 + 21.0010i −0.556330 + 0.963591i
\(476\) 0 0
\(477\) 7.83799 28.6138i 0.358877 1.31014i
\(478\) 5.46047 + 9.45782i 0.249756 + 0.432591i
\(479\) −8.88370 15.3870i −0.405907 0.703051i 0.588520 0.808483i \(-0.299711\pi\)
−0.994427 + 0.105432i \(0.966378\pi\)
\(480\) 29.5397 + 12.3322i 1.34830 + 0.562884i
\(481\) −2.83103 + 4.90349i −0.129084 + 0.223580i
\(482\) −4.14548 7.18018i −0.188821 0.327048i
\(483\) 0 0
\(484\) −8.94890 + 15.4999i −0.406768 + 0.704543i
\(485\) −20.3908 35.3179i −0.925898 1.60370i
\(486\) −4.61983 6.19736i −0.209560 0.281118i
\(487\) 8.32763 14.4239i 0.377361 0.653608i −0.613316 0.789837i \(-0.710165\pi\)
0.990677 + 0.136229i \(0.0434983\pi\)
\(488\) −20.1123 −0.910443
\(489\) 9.20245 7.02068i 0.416149 0.317486i
\(490\) 0 0
\(491\) −3.21021 5.56025i −0.144875 0.250930i 0.784451 0.620190i \(-0.212945\pi\)
−0.929326 + 0.369260i \(0.879611\pi\)
\(492\) 11.5507 8.81217i 0.520744 0.397283i
\(493\) −0.517784 0.896827i −0.0233198 0.0403911i
\(494\) 0.833230 1.44320i 0.0374888 0.0649325i
\(495\) 9.56482 2.50591i 0.429907 0.112632i
\(496\) −9.26814 −0.416152
\(497\) 0 0
\(498\) 9.76698 + 4.07750i 0.437669 + 0.182717i
\(499\) −5.57296 + 9.65264i −0.249480 + 0.432112i −0.963382 0.268134i \(-0.913593\pi\)
0.713902 + 0.700246i \(0.246926\pi\)
\(500\) −23.5456 −1.05299
\(501\) 24.2789 18.5227i 1.08470 0.827533i
\(502\) −4.23025 −0.188805
\(503\) 17.7223 0.790200 0.395100 0.918638i \(-0.370710\pi\)
0.395100 + 0.918638i \(0.370710\pi\)
\(504\) 0 0
\(505\) 9.59939 0.427167
\(506\) 1.09663 0.0487511
\(507\) 18.4896 + 7.71899i 0.821151 + 0.342812i
\(508\) 2.22678 0.0987976
\(509\) 15.5411 26.9180i 0.688848 1.19312i −0.283362 0.959013i \(-0.591450\pi\)
0.972211 0.234107i \(-0.0752167\pi\)
\(510\) 0.630316 0.480878i 0.0279109 0.0212936i
\(511\) 0 0
\(512\) −22.5634 −0.997169
\(513\) −8.97952 + 11.5022i −0.396456 + 0.507835i
\(514\) 4.24456 7.35180i 0.187220 0.324274i
\(515\) 17.9303 + 31.0563i 0.790105 + 1.36850i
\(516\) 27.9769 + 11.6797i 1.23161 + 0.514172i
\(517\) 4.54008 + 7.86365i 0.199672 + 0.345843i
\(518\) 0 0
\(519\) 0.860152 + 6.67704i 0.0377565 + 0.293089i
\(520\) 8.22608 0.360737
\(521\) 2.37986 4.12203i 0.104263 0.180590i −0.809174 0.587570i \(-0.800085\pi\)
0.913437 + 0.406980i \(0.133418\pi\)
\(522\) 1.62807 5.94353i 0.0712588 0.260141i
\(523\) −20.1258 34.8588i −0.880038 1.52427i −0.851298 0.524683i \(-0.824184\pi\)
−0.0287402 0.999587i \(-0.509150\pi\)
\(524\) 13.1812 22.8305i 0.575823 0.997355i
\(525\) 0 0
\(526\) 5.09571 + 8.82602i 0.222183 + 0.384833i
\(527\) −0.448113 + 0.776154i −0.0195201 + 0.0338098i
\(528\) −3.17745 + 2.42412i −0.138281 + 0.105496i
\(529\) 8.43046 + 14.6020i 0.366542 + 0.634869i
\(530\) 9.05381 + 15.6817i 0.393272 + 0.681168i
\(531\) 5.25960 1.37798i 0.228247 0.0597991i
\(532\) 0 0
\(533\) 2.86125 4.95583i 0.123935 0.214661i
\(534\) 1.64387 1.25413i 0.0711373 0.0542717i
\(535\) 40.2510 1.74020
\(536\) 1.91622 0.0827680
\(537\) 11.7242 + 4.89459i 0.505937 + 0.211217i
\(538\) 4.92033 8.52227i 0.212131 0.367421i
\(539\) 0 0
\(540\) −33.3308 4.67150i −1.43433 0.201029i
\(541\) 12.0547 + 20.8794i 0.518273 + 0.897675i 0.999775 + 0.0212301i \(0.00675826\pi\)
−0.481502 + 0.876445i \(0.659908\pi\)
\(542\) 2.63830 + 4.56966i 0.113325 + 0.196284i
\(543\) −2.49105 19.3371i −0.106901 0.829836i
\(544\) −0.625580 + 1.08354i −0.0268215 + 0.0464563i
\(545\) −3.91769 6.78564i −0.167815 0.290665i
\(546\) 0 0
\(547\) −6.17751 + 10.6998i −0.264131 + 0.457489i −0.967336 0.253499i \(-0.918419\pi\)
0.703204 + 0.710988i \(0.251752\pi\)
\(548\) −0.428436 0.742073i −0.0183019 0.0316998i
\(549\) 31.3541 8.21454i 1.33816 0.350588i
\(550\) −1.91094 + 3.30985i −0.0814828 + 0.141132i
\(551\) −11.6334 −0.495600
\(552\) −7.37223 3.07774i −0.313783 0.130997i
\(553\) 0 0
\(554\) −6.16893 10.6849i −0.262093 0.453958i
\(555\) 3.86628 + 30.0125i 0.164114 + 1.27396i
\(556\) −8.65633 14.9932i −0.367110 0.635853i
\(557\) 4.03845 6.99479i 0.171114 0.296379i −0.767695 0.640815i \(-0.778597\pi\)
0.938810 + 0.344436i \(0.111930\pi\)
\(558\) −5.15916 + 1.35166i −0.218405 + 0.0572204i
\(559\) 11.9415 0.505070
\(560\) 0 0
\(561\) 0.0493776 + 0.383300i 0.00208472 + 0.0161829i
\(562\) 3.39041 5.87237i 0.143016 0.247711i
\(563\) −45.2127 −1.90549 −0.952744 0.303774i \(-0.901753\pi\)
−0.952744 + 0.303774i \(0.901753\pi\)
\(564\) −3.94900 30.6547i −0.166283 1.29079i
\(565\) −58.4401 −2.45859
\(566\) 3.13477 0.131764
\(567\) 0 0
\(568\) −9.20596 −0.386274
\(569\) 22.4299 0.940309 0.470155 0.882584i \(-0.344198\pi\)
0.470155 + 0.882584i \(0.344198\pi\)
\(570\) −1.13792 8.83329i −0.0476624 0.369986i
\(571\) −21.8269 −0.913426 −0.456713 0.889614i \(-0.650973\pi\)
−0.456713 + 0.889614i \(0.650973\pi\)
\(572\) −0.936826 + 1.62263i −0.0391706 + 0.0678455i
\(573\) −5.27706 40.9638i −0.220452 1.71129i
\(574\) 0 0
\(575\) 21.3954 0.892251
\(576\) 7.80212 2.04410i 0.325088 0.0851707i
\(577\) 16.1022 27.8898i 0.670342 1.16107i −0.307465 0.951559i \(-0.599481\pi\)
0.977807 0.209508i \(-0.0671861\pi\)
\(578\) −4.19939 7.27355i −0.174671 0.302540i
\(579\) 1.31331 + 10.1947i 0.0545791 + 0.423678i
\(580\) −13.4161 23.2373i −0.557072 0.964878i
\(581\) 0 0
\(582\) 8.75335 + 3.65433i 0.362838 + 0.151477i
\(583\) −8.82687 −0.365571
\(584\) 1.70380 2.95107i 0.0705039 0.122116i
\(585\) −12.8240 + 3.35980i −0.530209 + 0.138911i
\(586\) −0.652105 1.12948i −0.0269382 0.0466584i
\(587\) 9.72304 16.8408i 0.401313 0.695094i −0.592572 0.805518i \(-0.701887\pi\)
0.993885 + 0.110424i \(0.0352208\pi\)
\(588\) 0 0
\(589\) 5.03404 + 8.71921i 0.207424 + 0.359269i
\(590\) −1.65926 + 2.87392i −0.0683105 + 0.118317i
\(591\) −3.42309 26.5721i −0.140807 1.09303i
\(592\) −6.11563 10.5926i −0.251351 0.435352i
\(593\) 14.4202 + 24.9766i 0.592168 + 1.02566i 0.993940 + 0.109925i \(0.0350611\pi\)
−0.401772 + 0.915740i \(0.631606\pi\)
\(594\) −1.41521 + 1.81280i −0.0580669 + 0.0743801i
\(595\) 0 0
\(596\) 18.4392 31.9377i 0.755300 1.30822i
\(597\) −24.7687 10.3404i −1.01372 0.423204i
\(598\) −1.47030 −0.0601252
\(599\) −46.9989 −1.92032 −0.960161 0.279447i \(-0.909849\pi\)
−0.960161 + 0.279447i \(0.909849\pi\)
\(600\) 22.1358 16.8877i 0.903690 0.689439i
\(601\) 7.80843 13.5246i 0.318512 0.551680i −0.661665 0.749799i \(-0.730150\pi\)
0.980178 + 0.198119i \(0.0634834\pi\)
\(602\) 0 0
\(603\) −2.98729 + 0.782646i −0.121652 + 0.0318718i
\(604\) 1.31417 + 2.27620i 0.0534727 + 0.0926174i
\(605\) 18.8383 + 32.6289i 0.765885 + 1.32655i
\(606\) −1.77514 + 1.35428i −0.0721100 + 0.0550138i
\(607\) −14.3266 + 24.8144i −0.581500 + 1.00719i 0.413802 + 0.910367i \(0.364200\pi\)
−0.995302 + 0.0968200i \(0.969133\pi\)
\(608\) 7.02769 + 12.1723i 0.285010 + 0.493652i
\(609\) 0 0
\(610\) −9.89134 + 17.1323i −0.400489 + 0.693667i
\(611\) −6.08711 10.5432i −0.246258 0.426531i
\(612\) 0.347543 1.26876i 0.0140486 0.0512865i
\(613\) 14.6734 25.4151i 0.592653 1.02651i −0.401220 0.915982i \(-0.631414\pi\)
0.993873 0.110524i \(-0.0352529\pi\)
\(614\) −1.38593 −0.0559316
\(615\) −3.90755 30.3328i −0.157568 1.22314i
\(616\) 0 0
\(617\) 2.06401 + 3.57497i 0.0830938 + 0.143923i 0.904577 0.426310i \(-0.140187\pi\)
−0.821484 + 0.570232i \(0.806853\pi\)
\(618\) −7.69712 3.21338i −0.309624 0.129261i
\(619\) 11.3565 + 19.6700i 0.456456 + 0.790605i 0.998771 0.0495708i \(-0.0157853\pi\)
−0.542315 + 0.840175i \(0.682452\pi\)
\(620\) −11.6109 + 20.1106i −0.466304 + 0.807662i
\(621\) 12.7500 + 1.78698i 0.511639 + 0.0717090i
\(622\) −7.48774 −0.300231
\(623\) 0 0
\(624\) 4.26017 3.25014i 0.170543 0.130110i
\(625\) −3.19498 + 5.53387i −0.127799 + 0.221355i
\(626\) −12.6340 −0.504955
\(627\) 4.00640 + 1.67258i 0.160000 + 0.0667965i
\(628\) −29.2580 −1.16752
\(629\) −1.18276 −0.0471597
\(630\) 0 0
\(631\) −38.6411 −1.53828 −0.769138 0.639082i \(-0.779314\pi\)
−0.769138 + 0.639082i \(0.779314\pi\)
\(632\) −3.34915 −0.133222
\(633\) −2.12590 + 1.62188i −0.0844968 + 0.0644639i
\(634\) −16.1261 −0.640449
\(635\) 2.34380 4.05958i 0.0930107 0.161099i
\(636\) 27.7266 + 11.5752i 1.09943 + 0.458988i
\(637\) 0 0
\(638\) −1.83348 −0.0725881
\(639\) 14.3516 3.76002i 0.567741 0.148744i
\(640\) −20.9427 + 36.2737i −0.827831 + 1.43385i
\(641\) 14.2363 + 24.6580i 0.562301 + 0.973933i 0.997295 + 0.0735002i \(0.0234169\pi\)
−0.434995 + 0.900433i \(0.643250\pi\)
\(642\) −7.44329 + 5.67860i −0.293763 + 0.224116i
\(643\) 8.52125 + 14.7592i 0.336045 + 0.582048i 0.983685 0.179899i \(-0.0575771\pi\)
−0.647640 + 0.761947i \(0.724244\pi\)
\(644\) 0 0
\(645\) 50.7400 38.7103i 1.99788 1.52422i
\(646\) 0.348110 0.0136962
\(647\) −1.68809 + 2.92386i −0.0663657 + 0.114949i −0.897299 0.441423i \(-0.854474\pi\)
0.830933 + 0.556372i \(0.187807\pi\)
\(648\) 14.6017 8.21493i 0.573608 0.322713i
\(649\) −0.808833 1.40094i −0.0317495 0.0549917i
\(650\) 2.56209 4.43768i 0.100494 0.174060i
\(651\) 0 0
\(652\) 5.86110 + 10.1517i 0.229538 + 0.397572i
\(653\) 9.17255 15.8873i 0.358950 0.621719i −0.628836 0.777538i \(-0.716468\pi\)
0.987786 + 0.155819i \(0.0498017\pi\)
\(654\) 1.68178 + 0.702107i 0.0657629 + 0.0274546i
\(655\) −27.7477 48.0604i −1.08419 1.87787i
\(656\) 6.18090 + 10.7056i 0.241324 + 0.417985i
\(657\) −1.45083 + 5.29646i −0.0566021 + 0.206635i
\(658\) 0 0
\(659\) −13.9248 + 24.1184i −0.542432 + 0.939519i 0.456332 + 0.889810i \(0.349163\pi\)
−0.998764 + 0.0497098i \(0.984170\pi\)
\(660\) 1.27940 + 9.93152i 0.0498007 + 0.386584i
\(661\) −39.0141 −1.51747 −0.758737 0.651397i \(-0.774183\pi\)
−0.758737 + 0.651397i \(0.774183\pi\)
\(662\) −8.97265 −0.348732
\(663\) −0.0662030 0.513909i −0.00257111 0.0199586i
\(664\) −11.4700 + 19.8667i −0.445123 + 0.770976i
\(665\) 0 0
\(666\) −4.94911 5.00452i −0.191774 0.193921i
\(667\) 5.13203 + 8.88894i 0.198713 + 0.344181i
\(668\) 15.4634 + 26.7834i 0.598296 + 1.03628i
\(669\) 8.70051 + 3.63227i 0.336381 + 0.140432i
\(670\) 0.942405 1.63229i 0.0364083 0.0630610i
\(671\) −4.82170 8.35143i −0.186140 0.322404i
\(672\) 0 0
\(673\) 24.6154 42.6352i 0.948856 1.64347i 0.201014 0.979588i \(-0.435576\pi\)
0.747841 0.663878i \(-0.231090\pi\)
\(674\) 6.20264 + 10.7433i 0.238917 + 0.413816i
\(675\) −27.6111 + 35.3681i −1.06275 + 1.36132i
\(676\) −10.1457 + 17.5729i −0.390219 + 0.675879i
\(677\) 23.3915 0.899010 0.449505 0.893278i \(-0.351600\pi\)
0.449505 + 0.893278i \(0.351600\pi\)
\(678\) 10.8069 8.24471i 0.415035 0.316636i
\(679\) 0 0
\(680\) 0.859180 + 1.48814i 0.0329480 + 0.0570677i
\(681\) 22.1381 16.8895i 0.848333 0.647206i
\(682\) 0.793387 + 1.37419i 0.0303803 + 0.0526203i
\(683\) −15.1632 + 26.2634i −0.580204 + 1.00494i 0.415251 + 0.909707i \(0.363694\pi\)
−0.995455 + 0.0952356i \(0.969640\pi\)
\(684\) −10.3914 10.5077i −0.397324 0.401772i
\(685\) −1.80380 −0.0689196
\(686\) 0 0
\(687\) −15.9330 6.65169i −0.607884 0.253778i
\(688\) −12.8980 + 22.3401i −0.491733 + 0.851707i
\(689\) 11.8346 0.450863
\(690\) −6.24741 + 4.76624i −0.237835 + 0.181448i
\(691\) 4.11330 0.156477 0.0782387 0.996935i \(-0.475070\pi\)
0.0782387 + 0.996935i \(0.475070\pi\)
\(692\) −6.81797 −0.259180
\(693\) 0 0
\(694\) −5.33003 −0.202325
\(695\) −36.4448 −1.38243
\(696\) 12.3258 + 5.14575i 0.467208 + 0.195049i
\(697\) 1.19538 0.0452784
\(698\) −0.814716 + 1.41113i −0.0308375 + 0.0534120i
\(699\) −22.7778 + 17.3775i −0.861534 + 0.657277i
\(700\) 0 0
\(701\) 29.1835 1.10225 0.551123 0.834424i \(-0.314200\pi\)
0.551123 + 0.834424i \(0.314200\pi\)
\(702\) 1.89745 2.43051i 0.0716145 0.0917338i
\(703\) −6.64347 + 11.5068i −0.250563 + 0.433988i
\(704\) −1.19983 2.07816i −0.0452202 0.0783236i
\(705\) −60.0420 25.0662i −2.26131 0.944047i
\(706\) −4.17005 7.22274i −0.156942 0.271831i
\(707\) 0 0
\(708\) 0.703531 + 5.46125i 0.0264403 + 0.205246i
\(709\) −42.4617 −1.59468 −0.797342 0.603528i \(-0.793761\pi\)
−0.797342 + 0.603528i \(0.793761\pi\)
\(710\) −4.52753 + 7.84192i −0.169915 + 0.294302i
\(711\) 5.22115 1.36790i 0.195809 0.0513004i
\(712\) 2.24075 + 3.88109i 0.0839757 + 0.145450i
\(713\) 4.44149 7.69288i 0.166335 0.288101i
\(714\) 0 0
\(715\) 1.97211 + 3.41579i 0.0737526 + 0.127743i
\(716\) −6.43336 + 11.1429i −0.240426 + 0.416430i
\(717\) 30.3282 23.1378i 1.13263 0.864097i
\(718\) −5.89692 10.2138i −0.220071 0.381175i
\(719\) 5.57126 + 9.64970i 0.207773 + 0.359873i 0.951013 0.309152i \(-0.100045\pi\)
−0.743240 + 0.669025i \(0.766712\pi\)
\(720\) 7.56580 27.6201i 0.281961 1.02934i
\(721\) 0 0
\(722\) −2.75544 + 4.77256i −0.102547 + 0.177616i
\(723\) −23.0245 + 17.5657i −0.856290 + 0.653277i
\(724\) 19.7453 0.733828
\(725\) −35.7715 −1.32852
\(726\) −8.08689 3.37609i −0.300132 0.125299i
\(727\) 14.3410 24.8393i 0.531878 0.921239i −0.467430 0.884030i \(-0.654820\pi\)
0.999308 0.0372089i \(-0.0118467\pi\)
\(728\) 0 0
\(729\) −19.4080 + 18.7704i −0.718815 + 0.695202i
\(730\) −1.67588 2.90270i −0.0620269 0.107434i
\(731\) 1.24724 + 2.16028i 0.0461307 + 0.0799007i
\(732\) 4.19396 + 32.5562i 0.155013 + 1.20331i
\(733\) −12.5264 + 21.6964i −0.462674 + 0.801375i −0.999093 0.0425768i \(-0.986443\pi\)
0.536419 + 0.843952i \(0.319777\pi\)
\(734\) 0.171071 + 0.296303i 0.00631433 + 0.0109367i
\(735\) 0 0
\(736\) 6.20047 10.7395i 0.228552 0.395864i
\(737\) 0.459391 + 0.795689i 0.0169219 + 0.0293096i
\(738\) 5.00194 + 5.05793i 0.184124 + 0.186185i
\(739\) 13.7608 23.8344i 0.506198 0.876761i −0.493776 0.869589i \(-0.664384\pi\)
0.999974 0.00717223i \(-0.00228301\pi\)
\(740\) −30.6460 −1.12657
\(741\) −5.37158 2.24252i −0.197330 0.0823809i
\(742\) 0 0
\(743\) −7.00608 12.1349i −0.257028 0.445186i 0.708416 0.705795i \(-0.249410\pi\)
−0.965444 + 0.260609i \(0.916077\pi\)
\(744\) −1.47693 11.4648i −0.0541467 0.420321i
\(745\) −38.8163 67.2318i −1.42212 2.46318i
\(746\) −0.932261 + 1.61472i −0.0341325 + 0.0591192i
\(747\) 9.76698 35.6558i 0.357355 1.30458i
\(748\) −0.391390 −0.0143106
\(749\) 0 0
\(750\) −1.47297 11.4342i −0.0537854 0.417516i
\(751\) 26.1297 45.2580i 0.953486 1.65149i 0.215692 0.976461i \(-0.430799\pi\)
0.737795 0.675025i \(-0.235867\pi\)
\(752\) 26.2989 0.959021
\(753\) 1.88789 + 14.6550i 0.0687986 + 0.534058i
\(754\) 2.45824 0.0895237
\(755\) 5.53289 0.201363
\(756\) 0 0
\(757\) −43.3447 −1.57539 −0.787694 0.616066i \(-0.788725\pi\)
−0.787694 + 0.616066i \(0.788725\pi\)
\(758\) −16.3009 −0.592077
\(759\) −0.489408 3.79909i −0.0177644 0.137898i
\(760\) 19.3038 0.700223
\(761\) −8.62550 + 14.9398i −0.312674 + 0.541568i −0.978940 0.204146i \(-0.934558\pi\)
0.666266 + 0.745714i \(0.267891\pi\)
\(762\) 0.139304 + 1.08137i 0.00504646 + 0.0391738i
\(763\) 0 0
\(764\) 41.8285 1.51330
\(765\) −1.94722 1.96902i −0.0704020 0.0711901i
\(766\) 0.265952 0.460642i 0.00960922 0.0166437i
\(767\) 1.08444 + 1.87831i 0.0391570 + 0.0678218i
\(768\) −0.0548204 0.425550i −0.00197816 0.0153557i
\(769\) 10.6727 + 18.4856i 0.384867 + 0.666609i 0.991751 0.128182i \(-0.0409141\pi\)
−0.606884 + 0.794790i \(0.707581\pi\)
\(770\) 0 0
\(771\) −27.3634 11.4236i −0.985469 0.411411i
\(772\) −10.4099 −0.374660
\(773\) 6.57357 11.3858i 0.236435 0.409517i −0.723254 0.690582i \(-0.757354\pi\)
0.959689 + 0.281065i \(0.0906877\pi\)
\(774\) −3.92170 + 14.3168i −0.140963 + 0.514605i
\(775\) 15.4791 + 26.8106i 0.556027 + 0.963066i
\(776\) −10.2796 + 17.8049i −0.369018 + 0.639158i
\(777\) 0 0
\(778\) −5.88685 10.1963i −0.211054 0.365556i
\(779\) 6.71439 11.6297i 0.240568 0.416676i
\(780\) −1.71536 13.3157i −0.0614197 0.476778i
\(781\) −2.20702 3.82268i −0.0789735 0.136786i
\(782\) −0.153567 0.265986i −0.00549155 0.00951164i
\(783\) −21.3170 2.98769i −0.761807 0.106771i
\(784\) 0 0
\(785\) −30.7954 + 53.3393i −1.09914 + 1.90376i
\(786\) 11.9115 + 4.97279i 0.424869 + 0.177373i
\(787\) 28.1301 1.00273 0.501364 0.865236i \(-0.332832\pi\)
0.501364 + 0.865236i \(0.332832\pi\)
\(788\) 27.1330 0.966573
\(789\) 28.3022 21.5922i 1.00758 0.768701i
\(790\) −1.64713 + 2.85291i −0.0586021 + 0.101502i
\(791\) 0 0
\(792\) −3.50502 3.54426i −0.124546 0.125940i
\(793\) 6.46470 + 11.1972i 0.229568 + 0.397624i
\(794\) −0.00795814 0.0137839i −0.000282424 0.000489172i
\(795\) 50.2860 38.3639i 1.78346 1.36063i
\(796\) 13.5912 23.5406i 0.481727 0.834376i
\(797\) −12.8683 22.2885i −0.455817 0.789499i 0.542917 0.839786i \(-0.317320\pi\)
−0.998735 + 0.0502873i \(0.983986\pi\)
\(798\) 0 0
\(799\) 1.27155 2.20238i 0.0449841 0.0779147i
\(800\) 21.6094 + 37.4285i 0.764007 + 1.32330i
\(801\) −5.07838 5.13523i −0.179436 0.181444i
\(802\) 6.08073 10.5321i 0.214718 0.371902i
\(803\) 1.63387 0.0576580
\(804\) −0.399583 3.10181i −0.0140922 0.109393i
\(805\) 0 0
\(806\) −1.06373 1.84244i −0.0374684 0.0648972i
\(807\) −31.7199 13.2423i −1.11659 0.466153i
\(808\) −2.41968 4.19100i −0.0851240 0.147439i
\(809\) 15.9353 27.6007i 0.560254 0.970388i −0.437220 0.899355i \(-0.644037\pi\)
0.997474 0.0710338i \(-0.0226298\pi\)
\(810\) 0.183441 16.4783i 0.00644544 0.578988i
\(811\) −43.3860 −1.52349 −0.761744 0.647878i \(-0.775657\pi\)
−0.761744 + 0.647878i \(0.775657\pi\)
\(812\) 0 0
\(813\) 14.6534 11.1793i 0.513918 0.392076i
\(814\) −1.04704 + 1.81353i −0.0366987 + 0.0635641i
\(815\) 24.6764 0.864375
\(816\) 1.03293 + 0.431223i 0.0361596 + 0.0150958i
\(817\) 28.0226 0.980385
\(818\) 13.2842 0.464470
\(819\) 0 0
\(820\) 30.9731 1.08163
\(821\) −16.3935 −0.572139 −0.286069 0.958209i \(-0.592349\pi\)
−0.286069 + 0.958209i \(0.592349\pi\)
\(822\) 0.333562 0.254479i 0.0116343 0.00887598i
\(823\) −26.3780 −0.919478 −0.459739 0.888054i \(-0.652057\pi\)
−0.459739 + 0.888054i \(0.652057\pi\)
\(824\) 9.03925 15.6564i 0.314897 0.545418i
\(825\) 12.3193 + 5.14301i 0.428901 + 0.179057i
\(826\) 0 0
\(827\) 36.7225 1.27697 0.638484 0.769635i \(-0.279562\pi\)
0.638484 + 0.769635i \(0.279562\pi\)
\(828\) −3.44468 + 12.5753i −0.119711 + 0.437023i
\(829\) −12.1579 + 21.0581i −0.422261 + 0.731377i −0.996160 0.0875485i \(-0.972097\pi\)
0.573899 + 0.818926i \(0.305430\pi\)
\(830\) 11.2820 + 19.5410i 0.391604 + 0.678279i
\(831\) −34.2630 + 26.1398i −1.18857 + 0.906779i
\(832\) 1.60867 + 2.78629i 0.0557705 + 0.0965974i
\(833\) 0 0
\(834\) 6.73944 5.14162i 0.233368 0.178040i
\(835\) 65.1038 2.25301
\(836\) −2.19841 + 3.80776i −0.0760337 + 0.131694i
\(837\) 6.98506 + 17.2698i 0.241439 + 0.596933i
\(838\) −5.21962 9.04065i −0.180309 0.312304i
\(839\) 12.8405 22.2404i 0.443303 0.767824i −0.554629 0.832098i \(-0.687140\pi\)
0.997932 + 0.0642741i \(0.0204732\pi\)
\(840\) 0 0
\(841\) 5.91963 + 10.2531i 0.204125 + 0.353555i
\(842\) 3.69190 6.39456i 0.127231 0.220371i
\(843\) −21.8570 9.12480i −0.752794 0.314275i
\(844\) −1.35400 2.34519i −0.0466065 0.0807249i
\(845\) 21.3577 + 36.9926i 0.734726 + 1.27258i
\(846\) 14.6394 3.83542i 0.503313 0.131864i
\(847\) 0 0
\(848\) −12.7826 + 22.1402i −0.438958 + 0.760297i
\(849\) −1.39900 10.8599i −0.0480135 0.372711i
\(850\) 1.07040 0.0367144
\(851\) 11.7230 0.401858
\(852\) 1.91969 + 14.9018i 0.0657675 + 0.510529i
\(853\) −14.4872 + 25.0925i −0.496031 + 0.859150i −0.999990 0.00457743i \(-0.998543\pi\)
0.503959 + 0.863728i \(0.331876\pi\)
\(854\) 0 0
\(855\) −30.0937 + 7.88431i −1.02918 + 0.269638i
\(856\) −10.1459 17.5732i −0.346780 0.600640i
\(857\) −12.6934 21.9856i −0.433598 0.751015i 0.563582 0.826060i \(-0.309423\pi\)
−0.997180 + 0.0750458i \(0.976090\pi\)
\(858\) −0.846585 0.353430i −0.0289019 0.0120659i
\(859\) −2.97891 + 5.15963i −0.101639 + 0.176044i −0.912360 0.409388i \(-0.865742\pi\)
0.810721 + 0.585433i \(0.199075\pi\)
\(860\) 32.3166 + 55.9740i 1.10199 + 1.90870i
\(861\) 0 0
\(862\) 3.94310 6.82966i 0.134303 0.232619i
\(863\) 8.19545 + 14.1949i 0.278977 + 0.483201i 0.971131 0.238548i \(-0.0766715\pi\)
−0.692154 + 0.721750i \(0.743338\pi\)
\(864\) 9.75138 + 24.1093i 0.331749 + 0.820214i
\(865\) −7.17624 + 12.4296i −0.244000 + 0.422620i
\(866\) −8.11528 −0.275768
\(867\) −23.3239 + 17.7942i −0.792122 + 0.604322i
\(868\) 0 0
\(869\) −0.802920 1.39070i −0.0272372 0.0471762i
\(870\) 10.4452 7.96879i 0.354125 0.270167i
\(871\) −0.615929 1.06682i −0.0208700 0.0361478i
\(872\) −1.97503 + 3.42086i −0.0668830 + 0.115845i
\(873\) 8.75335 31.9554i 0.296256 1.08153i
\(874\) −3.45030 −0.116708
\(875\) 0 0
\(876\) −5.13224 2.14260i −0.173402 0.0723916i
\(877\) −17.6270 + 30.5308i −0.595220 + 1.03095i 0.398295 + 0.917257i \(0.369602\pi\)
−0.993516 + 0.113695i \(0.963731\pi\)
\(878\) −7.70813 −0.260137
\(879\) −3.62188 + 2.76318i −0.122163 + 0.0931998i
\(880\) −8.52033 −0.287220
\(881\) −26.2582 −0.884661 −0.442331 0.896852i \(-0.645848\pi\)
−0.442331 + 0.896852i \(0.645848\pi\)
\(882\) 0 0
\(883\) 10.0087 0.336821 0.168410 0.985717i \(-0.446137\pi\)
0.168410 + 0.985717i \(0.446137\pi\)
\(884\) 0.524756 0.0176495
\(885\) 10.6967 + 4.46564i 0.359566 + 0.150111i
\(886\) −0.887631 −0.0298205
\(887\) −7.95282 + 13.7747i −0.267030 + 0.462509i −0.968093 0.250590i \(-0.919376\pi\)
0.701064 + 0.713099i \(0.252709\pi\)
\(888\) 12.1286 9.25311i 0.407010 0.310514i
\(889\) 0 0
\(890\) 4.40804 0.147758
\(891\) 6.91174 + 4.09375i 0.231552 + 0.137146i
\(892\) −4.77419 + 8.26914i −0.159852 + 0.276871i
\(893\) −14.2844 24.7413i −0.478009 0.827935i
\(894\) 16.6630 + 6.95645i 0.557295 + 0.232658i
\(895\) 13.5428 + 23.4569i 0.452687 + 0.784077i
\(896\) 0 0
\(897\) 0.656173 + 5.09363i 0.0219090 + 0.170071i
\(898\) −6.72727 −0.224492
\(899\) −7.42583 + 12.8619i −0.247665 + 0.428969i
\(900\) −31.9524 32.3100i −1.06508 1.07700i
\(901\) 1.23608 + 2.14095i 0.0411797 + 0.0713253i
\(902\) 1.05822 1.83288i 0.0352348 0.0610284i
\(903\) 0 0
\(904\) 14.7307 + 25.5144i 0.489937 + 0.848597i
\(905\) 20.7829 35.9970i 0.690846 1.19658i
\(906\) −1.02315 + 0.780579i −0.0339920 + 0.0259330i
\(907\) 8.54624 + 14.8025i 0.283773 + 0.491510i 0.972311 0.233691i \(-0.0750804\pi\)
−0.688538 + 0.725201i \(0.741747\pi\)
\(908\) 14.0999 + 24.4217i 0.467922 + 0.810464i
\(909\) 5.48390 + 5.54528i 0.181889 + 0.183925i
\(910\) 0 0
\(911\) 14.9435 25.8829i 0.495099 0.857537i −0.504885 0.863187i \(-0.668465\pi\)
0.999984 + 0.00564955i \(0.00179832\pi\)
\(912\) 9.99717 7.62699i 0.331039 0.252555i
\(913\) −10.9992 −0.364021
\(914\) −1.27397 −0.0421393
\(915\) 63.7664 + 26.6211i 2.10805 + 0.880065i
\(916\) 8.74286 15.1431i 0.288872 0.500341i
\(917\) 0 0
\(918\) 0.637873 + 0.0894015i 0.0210530 + 0.00295069i
\(919\) 11.8283 + 20.4873i 0.390181 + 0.675813i 0.992473 0.122462i \(-0.0390791\pi\)
−0.602292 + 0.798276i \(0.705746\pi\)
\(920\) −8.51579 14.7498i −0.280757 0.486286i
\(921\) 0.618519 + 4.80133i 0.0203809 + 0.158209i
\(922\) 8.97196 15.5399i 0.295476 0.511779i
\(923\) 2.95907 + 5.12525i 0.0973989 + 0.168700i
\(924\) 0 0
\(925\) −20.4280 + 35.3823i −0.671667 + 1.16336i
\(926\) −4.06227 7.03606i −0.133495 0.231219i
\(927\) −7.69712 + 28.0995i −0.252807 + 0.922909i
\(928\) −10.3667 + 17.9557i −0.340304 + 0.589423i
\(929\) −12.6176 −0.413970 −0.206985 0.978344i \(-0.566365\pi\)
−0.206985 + 0.978344i \(0.566365\pi\)
\(930\) −10.4924 4.38036i −0.344061 0.143638i
\(931\) 0 0
\(932\) −14.5073 25.1274i −0.475203 0.823075i
\(933\) 3.34166 + 25.9401i 0.109401 + 0.849240i
\(934\) −2.15714 3.73627i −0.0705836 0.122254i
\(935\) −0.411957 + 0.713530i −0.0134724 + 0.0233349i
\(936\) 4.69936 + 4.75196i 0.153603 + 0.155323i
\(937\) 26.3440 0.860622 0.430311 0.902681i \(-0.358404\pi\)
0.430311 + 0.902681i \(0.358404\pi\)
\(938\) 0 0
\(939\) 5.63834 + 43.7683i 0.184000 + 1.42833i
\(940\) 32.9465 57.0651i 1.07460 1.86126i
\(941\) −50.9397 −1.66059 −0.830294 0.557326i \(-0.811827\pi\)
−0.830294 + 0.557326i \(0.811827\pi\)
\(942\) −1.83034 14.2082i −0.0596356 0.462929i
\(943\) −11.8481 −0.385827
\(944\) −4.68525 −0.152492
\(945\) 0 0
\(946\) 4.41648 0.143592
\(947\) 27.6798 0.899474 0.449737 0.893161i \(-0.351518\pi\)
0.449737 + 0.893161i \(0.351518\pi\)
\(948\) 0.698388 + 5.42133i 0.0226826 + 0.176076i
\(949\) −2.19061 −0.0711102
\(950\) 6.01236 10.4137i 0.195067 0.337866i
\(951\) 7.19682 + 55.8662i 0.233373 + 1.81159i
\(952\) 0 0
\(953\) −27.4017 −0.887628 −0.443814 0.896119i \(-0.646375\pi\)
−0.443814 + 0.896119i \(0.646375\pi\)
\(954\) −3.88661 + 14.1887i −0.125834 + 0.459375i
\(955\) 44.0265 76.2561i 1.42466 2.46759i
\(956\) 19.3162 + 33.4567i 0.624731 + 1.08207i
\(957\) 0.818252 + 6.35179i 0.0264503 + 0.205324i
\(958\) 4.40515 + 7.62994i 0.142324 + 0.246512i
\(959\) 0 0
\(960\) 15.8676 + 6.62436i 0.512123 + 0.213800i
\(961\) −18.1467 −0.585378
\(962\) 1.40382 2.43149i 0.0452610 0.0783943i
\(963\) 22.9944 + 23.2518i 0.740984 + 0.749279i
\(964\) −14.6645 25.3996i −0.472310 0.818066i
\(965\) −10.9569 + 18.9779i −0.352715 + 0.610921i
\(966\) 0 0
\(967\) 9.09069 + 15.7455i 0.292337 + 0.506342i 0.974362 0.224986i \(-0.0722338\pi\)
−0.682025 + 0.731329i \(0.738900\pi\)
\(968\) 9.49698 16.4492i 0.305244 0.528699i
\(969\) −0.155356 1.20597i −0.00499075 0.0387413i
\(970\) 10.1111 + 17.5130i 0.324649 + 0.562309i
\(971\) −19.7416 34.1935i −0.633538 1.09732i −0.986823 0.161804i \(-0.948269\pi\)
0.353285 0.935516i \(-0.385065\pi\)
\(972\) −16.3425 21.9229i −0.524185 0.703178i
\(973\) 0 0
\(974\) −4.12941 + 7.15234i −0.132315 + 0.229176i
\(975\) −16.5170 6.89549i −0.528968 0.220833i
\(976\) −27.9302 −0.894024
\(977\) 11.9156 0.381215 0.190608 0.981666i \(-0.438954\pi\)
0.190608 + 0.981666i \(0.438954\pi\)
\(978\) −4.56320 + 3.48133i −0.145915 + 0.111321i
\(979\) −1.07439 + 1.86090i −0.0343376 + 0.0594745i
\(980\) 0 0
\(981\) 1.68178 6.13961i 0.0536952 0.196023i
\(982\) 1.59184 + 2.75715i 0.0507977 + 0.0879842i
\(983\) −9.23896 16.0024i −0.294677 0.510396i 0.680233 0.732996i \(-0.261879\pi\)
−0.974910 + 0.222601i \(0.928545\pi\)
\(984\) −12.2581 + 9.35187i −0.390773 + 0.298127i
\(985\) 28.5588 49.4653i 0.909959 1.57609i
\(986\) 0.256752 + 0.444708i 0.00817666 + 0.0141624i
\(987\) 0 0
\(988\) 2.94752 5.10525i 0.0937731 0.162420i
\(989\) −12.3620 21.4117i −0.393090 0.680851i
\(990\) −4.74289 + 1.24260i −0.150739 + 0.0394925i
\(991\) −6.34850 + 10.9959i −0.201667 + 0.349297i −0.949066 0.315079i \(-0.897969\pi\)
0.747399 + 0.664376i \(0.231302\pi\)
\(992\) 17.9436 0.569710
\(993\) 4.00435 + 31.0843i 0.127074 + 0.986430i
\(994\) 0 0
\(995\) −28.6108 49.5553i −0.907023 1.57101i
\(996\) 34.5503 + 14.4240i 1.09477 + 0.457041i
\(997\) 20.9767 + 36.3327i 0.664338 + 1.15067i 0.979464 + 0.201617i \(0.0646197\pi\)
−0.315127 + 0.949050i \(0.602047\pi\)
\(998\) 2.76345 4.78644i 0.0874755 0.151512i
\(999\) −15.1286 + 19.3788i −0.478648 + 0.613119i
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 441.2.h.f.214.3 10
3.2 odd 2 1323.2.h.f.802.3 10
7.2 even 3 441.2.g.f.79.3 10
7.3 odd 6 441.2.f.e.295.3 10
7.4 even 3 441.2.f.f.295.3 10
7.5 odd 6 63.2.g.b.16.3 yes 10
7.6 odd 2 63.2.h.b.25.3 yes 10
9.4 even 3 441.2.g.f.67.3 10
9.5 odd 6 1323.2.g.f.361.3 10
21.2 odd 6 1323.2.g.f.667.3 10
21.5 even 6 189.2.g.b.100.3 10
21.11 odd 6 1323.2.f.f.883.3 10
21.17 even 6 1323.2.f.e.883.3 10
21.20 even 2 189.2.h.b.46.3 10
28.19 even 6 1008.2.t.i.961.1 10
28.27 even 2 1008.2.q.i.529.3 10
63.4 even 3 441.2.f.f.148.3 10
63.5 even 6 189.2.h.b.37.3 10
63.11 odd 6 3969.2.a.bb.1.3 5
63.13 odd 6 63.2.g.b.4.3 10
63.20 even 6 567.2.e.e.487.3 10
63.23 odd 6 1323.2.h.f.226.3 10
63.25 even 3 3969.2.a.ba.1.3 5
63.31 odd 6 441.2.f.e.148.3 10
63.32 odd 6 1323.2.f.f.442.3 10
63.34 odd 6 567.2.e.f.487.3 10
63.38 even 6 3969.2.a.bc.1.3 5
63.40 odd 6 63.2.h.b.58.3 yes 10
63.41 even 6 189.2.g.b.172.3 10
63.47 even 6 567.2.e.e.163.3 10
63.52 odd 6 3969.2.a.z.1.3 5
63.58 even 3 inner 441.2.h.f.373.3 10
63.59 even 6 1323.2.f.e.442.3 10
63.61 odd 6 567.2.e.f.163.3 10
84.47 odd 6 3024.2.t.i.289.5 10
84.83 odd 2 3024.2.q.i.2881.1 10
252.103 even 6 1008.2.q.i.625.3 10
252.131 odd 6 3024.2.q.i.2305.1 10
252.139 even 6 1008.2.t.i.193.1 10
252.167 odd 6 3024.2.t.i.1873.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.3 10 63.13 odd 6
63.2.g.b.16.3 yes 10 7.5 odd 6
63.2.h.b.25.3 yes 10 7.6 odd 2
63.2.h.b.58.3 yes 10 63.40 odd 6
189.2.g.b.100.3 10 21.5 even 6
189.2.g.b.172.3 10 63.41 even 6
189.2.h.b.37.3 10 63.5 even 6
189.2.h.b.46.3 10 21.20 even 2
441.2.f.e.148.3 10 63.31 odd 6
441.2.f.e.295.3 10 7.3 odd 6
441.2.f.f.148.3 10 63.4 even 3
441.2.f.f.295.3 10 7.4 even 3
441.2.g.f.67.3 10 9.4 even 3
441.2.g.f.79.3 10 7.2 even 3
441.2.h.f.214.3 10 1.1 even 1 trivial
441.2.h.f.373.3 10 63.58 even 3 inner
567.2.e.e.163.3 10 63.47 even 6
567.2.e.e.487.3 10 63.20 even 6
567.2.e.f.163.3 10 63.61 odd 6
567.2.e.f.487.3 10 63.34 odd 6
1008.2.q.i.529.3 10 28.27 even 2
1008.2.q.i.625.3 10 252.103 even 6
1008.2.t.i.193.1 10 252.139 even 6
1008.2.t.i.961.1 10 28.19 even 6
1323.2.f.e.442.3 10 63.59 even 6
1323.2.f.e.883.3 10 21.17 even 6
1323.2.f.f.442.3 10 63.32 odd 6
1323.2.f.f.883.3 10 21.11 odd 6
1323.2.g.f.361.3 10 9.5 odd 6
1323.2.g.f.667.3 10 21.2 odd 6
1323.2.h.f.226.3 10 63.23 odd 6
1323.2.h.f.802.3 10 3.2 odd 2
3024.2.q.i.2305.1 10 252.131 odd 6
3024.2.q.i.2881.1 10 84.83 odd 2
3024.2.t.i.289.5 10 84.47 odd 6
3024.2.t.i.1873.5 10 252.167 odd 6
3969.2.a.z.1.3 5 63.52 odd 6
3969.2.a.ba.1.3 5 63.25 even 3
3969.2.a.bb.1.3 5 63.11 odd 6
3969.2.a.bc.1.3 5 63.38 even 6