Properties

Label 375.2.i.d.274.6
Level $375$
Weight $2$
Character 375.274
Analytic conductor $2.994$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [375,2,Mod(49,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.i (of order \(10\), degree \(4\), 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: \(2.99439007580\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 274.6
Character \(\chi\) \(=\) 375.274
Dual form 375.2.i.d.349.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.55553 + 0.830342i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(4.22323 + 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} -1.68704i q^{7} +(5.08599 + 7.00026i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(2.55553 + 0.830342i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(4.22323 + 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} -1.68704i q^{7} +(5.08599 + 7.00026i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.333373 - 1.02602i) q^{11} +(-4.96470 + 1.61313i) q^{12} +(-2.54620 + 0.827310i) q^{13} +(1.40082 - 4.31129i) q^{14} +(3.95852 + 12.1831i) q^{16} +(-2.31098 - 3.18079i) q^{17} -2.68704i q^{18} +(-0.952655 + 0.692144i) q^{19} +(1.36485 + 0.991619i) q^{21} +(1.70389 - 2.34520i) q^{22} +(-3.86409 - 1.25552i) q^{23} -8.65280 q^{24} -7.19384 q^{26} +(0.951057 + 0.309017i) q^{27} +(5.17644 - 7.12476i) q^{28} +(4.81846 + 3.50082i) q^{29} +(5.74653 - 4.17510i) q^{31} +17.1155i q^{32} +(0.634113 + 0.872782i) q^{33} +(-3.26463 - 10.0475i) q^{34} +(1.61313 - 4.96470i) q^{36} +(-4.35761 + 1.41587i) q^{37} +(-3.00925 + 0.977766i) q^{38} +(0.827310 - 2.54620i) q^{39} +(-3.47998 - 10.7103i) q^{41} +(2.66452 + 3.66740i) q^{42} +2.58587i q^{43} +(4.55609 - 3.31019i) q^{44} +(-8.83229 - 6.41703i) q^{46} +(1.12727 - 1.55155i) q^{47} +(-12.1831 - 3.95852i) q^{48} +4.15389 q^{49} +3.93167 q^{51} +(-13.2917 - 4.31872i) q^{52} +(-1.49803 + 2.06187i) q^{53} +(2.17386 + 1.57940i) q^{54} +(11.8097 - 8.58028i) q^{56} -1.17755i q^{57} +(9.40685 + 12.9474i) q^{58} +(-0.412843 - 1.27060i) q^{59} +(-2.24997 + 6.92470i) q^{61} +(18.1522 - 5.89800i) q^{62} +(-1.60447 + 0.521325i) q^{63} +(-6.29470 + 19.3731i) q^{64} +(0.895787 + 2.75695i) q^{66} +(7.31502 + 10.0683i) q^{67} -20.5241i q^{68} +(3.28699 - 2.38814i) q^{69} +(4.84181 + 3.51778i) q^{71} +(5.08599 - 7.00026i) q^{72} +(-3.13911 - 1.01996i) q^{73} -12.3117 q^{74} -6.14702 q^{76} +(-1.73093 - 0.562414i) q^{77} +(4.22843 - 5.81994i) q^{78} +(-3.23934 - 2.35351i) q^{79} +(-0.809017 + 0.587785i) q^{81} -30.2600i q^{82} +(-5.21649 - 7.17988i) q^{83} +(2.72142 + 8.37566i) q^{84} +(-2.14716 + 6.60827i) q^{86} +(-5.66445 + 1.84049i) q^{87} +(8.87792 - 2.88461i) q^{88} +(-4.77234 + 14.6877i) q^{89} +(1.39571 + 4.29555i) q^{91} +(-12.4666 - 17.1587i) q^{92} +7.10310i q^{93} +(4.16908 - 3.02901i) q^{94} +(-13.8468 - 10.0603i) q^{96} +(-6.32939 + 8.71166i) q^{97} +(10.6154 + 3.44915i) q^{98} -1.07882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.55553 + 0.830342i 1.80703 + 0.587140i 0.999994 0.00335992i \(-0.00106950\pi\)
0.807038 + 0.590500i \(0.201069\pi\)
\(3\) −0.587785 + 0.809017i −0.339358 + 0.467086i
\(4\) 4.22323 + 3.06835i 2.11161 + 1.53418i
\(5\) 0 0
\(6\) −2.17386 + 1.57940i −0.887476 + 0.644789i
\(7\) 1.68704i 0.637642i −0.947815 0.318821i \(-0.896713\pi\)
0.947815 0.318821i \(-0.103287\pi\)
\(8\) 5.08599 + 7.00026i 1.79817 + 2.47497i
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) 0.333373 1.02602i 0.100516 0.309356i −0.888136 0.459581i \(-0.848000\pi\)
0.988652 + 0.150225i \(0.0479998\pi\)
\(12\) −4.96470 + 1.61313i −1.43319 + 0.465670i
\(13\) −2.54620 + 0.827310i −0.706189 + 0.229455i −0.640025 0.768354i \(-0.721076\pi\)
−0.0661638 + 0.997809i \(0.521076\pi\)
\(14\) 1.40082 4.31129i 0.374385 1.15224i
\(15\) 0 0
\(16\) 3.95852 + 12.1831i 0.989631 + 3.04577i
\(17\) −2.31098 3.18079i −0.560494 0.771454i 0.430895 0.902402i \(-0.358198\pi\)
−0.991389 + 0.130948i \(0.958198\pi\)
\(18\) 2.68704i 0.633342i
\(19\) −0.952655 + 0.692144i −0.218554 + 0.158789i −0.691676 0.722208i \(-0.743127\pi\)
0.473121 + 0.880997i \(0.343127\pi\)
\(20\) 0 0
\(21\) 1.36485 + 0.991619i 0.297834 + 0.216389i
\(22\) 1.70389 2.34520i 0.363270 0.499999i
\(23\) −3.86409 1.25552i −0.805719 0.261794i −0.122935 0.992415i \(-0.539231\pi\)
−0.682783 + 0.730621i \(0.739231\pi\)
\(24\) −8.65280 −1.76625
\(25\) 0 0
\(26\) −7.19384 −1.41083
\(27\) 0.951057 + 0.309017i 0.183031 + 0.0594703i
\(28\) 5.17644 7.12476i 0.978256 1.34645i
\(29\) 4.81846 + 3.50082i 0.894766 + 0.650086i 0.937116 0.349017i \(-0.113484\pi\)
−0.0423500 + 0.999103i \(0.513484\pi\)
\(30\) 0 0
\(31\) 5.74653 4.17510i 1.03211 0.749870i 0.0633776 0.997990i \(-0.479813\pi\)
0.968729 + 0.248120i \(0.0798128\pi\)
\(32\) 17.1155i 3.02563i
\(33\) 0.634113 + 0.872782i 0.110385 + 0.151932i
\(34\) −3.26463 10.0475i −0.559879 1.72313i
\(35\) 0 0
\(36\) 1.61313 4.96470i 0.268855 0.827450i
\(37\) −4.35761 + 1.41587i −0.716387 + 0.232768i −0.644456 0.764641i \(-0.722916\pi\)
−0.0719311 + 0.997410i \(0.522916\pi\)
\(38\) −3.00925 + 0.977766i −0.488165 + 0.158615i
\(39\) 0.827310 2.54620i 0.132476 0.407718i
\(40\) 0 0
\(41\) −3.47998 10.7103i −0.543481 1.67266i −0.724574 0.689197i \(-0.757963\pi\)
0.181093 0.983466i \(-0.442037\pi\)
\(42\) 2.66452 + 3.66740i 0.411144 + 0.565892i
\(43\) 2.58587i 0.394342i 0.980369 + 0.197171i \(0.0631754\pi\)
−0.980369 + 0.197171i \(0.936825\pi\)
\(44\) 4.55609 3.31019i 0.686857 0.499031i
\(45\) 0 0
\(46\) −8.83229 6.41703i −1.30225 0.946140i
\(47\) 1.12727 1.55155i 0.164429 0.226317i −0.718850 0.695166i \(-0.755331\pi\)
0.883278 + 0.468849i \(0.155331\pi\)
\(48\) −12.1831 3.95852i −1.75848 0.571364i
\(49\) 4.15389 0.593413
\(50\) 0 0
\(51\) 3.93167 0.550544
\(52\) −13.2917 4.31872i −1.84322 0.598899i
\(53\) −1.49803 + 2.06187i −0.205771 + 0.283219i −0.899412 0.437101i \(-0.856005\pi\)
0.693642 + 0.720320i \(0.256005\pi\)
\(54\) 2.17386 + 1.57940i 0.295825 + 0.214930i
\(55\) 0 0
\(56\) 11.8097 8.58028i 1.57814 1.14659i
\(57\) 1.17755i 0.155970i
\(58\) 9.40685 + 12.9474i 1.23518 + 1.70008i
\(59\) −0.412843 1.27060i −0.0537476 0.165418i 0.920579 0.390555i \(-0.127717\pi\)
−0.974327 + 0.225137i \(0.927717\pi\)
\(60\) 0 0
\(61\) −2.24997 + 6.92470i −0.288079 + 0.886617i 0.697379 + 0.716702i \(0.254349\pi\)
−0.985459 + 0.169915i \(0.945651\pi\)
\(62\) 18.1522 5.89800i 2.30533 0.749047i
\(63\) −1.60447 + 0.521325i −0.202145 + 0.0656807i
\(64\) −6.29470 + 19.3731i −0.786838 + 2.42164i
\(65\) 0 0
\(66\) 0.895787 + 2.75695i 0.110264 + 0.339357i
\(67\) 7.31502 + 10.0683i 0.893672 + 1.23003i 0.972443 + 0.233141i \(0.0749004\pi\)
−0.0787711 + 0.996893i \(0.525100\pi\)
\(68\) 20.5241i 2.48891i
\(69\) 3.28699 2.38814i 0.395707 0.287498i
\(70\) 0 0
\(71\) 4.84181 + 3.51778i 0.574617 + 0.417484i 0.836779 0.547540i \(-0.184436\pi\)
−0.262162 + 0.965024i \(0.584436\pi\)
\(72\) 5.08599 7.00026i 0.599390 0.824989i
\(73\) −3.13911 1.01996i −0.367405 0.119377i 0.119495 0.992835i \(-0.461872\pi\)
−0.486900 + 0.873458i \(0.661872\pi\)
\(74\) −12.3117 −1.43120
\(75\) 0 0
\(76\) −6.14702 −0.705112
\(77\) −1.73093 0.562414i −0.197258 0.0640931i
\(78\) 4.22843 5.81994i 0.478776 0.658978i
\(79\) −3.23934 2.35351i −0.364454 0.264791i 0.390454 0.920623i \(-0.372318\pi\)
−0.754907 + 0.655831i \(0.772318\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 30.2600i 3.34166i
\(83\) −5.21649 7.17988i −0.572584 0.788094i 0.420274 0.907397i \(-0.361934\pi\)
−0.992858 + 0.119303i \(0.961934\pi\)
\(84\) 2.72142 + 8.37566i 0.296931 + 0.913859i
\(85\) 0 0
\(86\) −2.14716 + 6.60827i −0.231534 + 0.712588i
\(87\) −5.66445 + 1.84049i −0.607292 + 0.197321i
\(88\) 8.87792 2.88461i 0.946389 0.307501i
\(89\) −4.77234 + 14.6877i −0.505867 + 1.55690i 0.293442 + 0.955977i \(0.405199\pi\)
−0.799309 + 0.600920i \(0.794801\pi\)
\(90\) 0 0
\(91\) 1.39571 + 4.29555i 0.146310 + 0.450296i
\(92\) −12.4666 17.1587i −1.29973 1.78892i
\(93\) 7.10310i 0.736557i
\(94\) 4.16908 3.02901i 0.430008 0.312419i
\(95\) 0 0
\(96\) −13.8468 10.0603i −1.41323 1.02677i
\(97\) −6.32939 + 8.71166i −0.642652 + 0.884535i −0.998754 0.0499122i \(-0.984106\pi\)
0.356101 + 0.934447i \(0.384106\pi\)
\(98\) 10.6154 + 3.44915i 1.07232 + 0.348416i
\(99\) −1.07882 −0.108425
\(100\) 0 0
\(101\) −13.5654 −1.34981 −0.674905 0.737905i \(-0.735815\pi\)
−0.674905 + 0.737905i \(0.735815\pi\)
\(102\) 10.0475 + 3.26463i 0.994850 + 0.323246i
\(103\) 0.804700 1.10757i 0.0792894 0.109133i −0.767530 0.641013i \(-0.778514\pi\)
0.846819 + 0.531880i \(0.178514\pi\)
\(104\) −18.7413 13.6164i −1.83774 1.33520i
\(105\) 0 0
\(106\) −5.54032 + 4.02528i −0.538124 + 0.390970i
\(107\) 11.0115i 1.06452i −0.846579 0.532262i \(-0.821342\pi\)
0.846579 0.532262i \(-0.178658\pi\)
\(108\) 3.06835 + 4.22323i 0.295253 + 0.406380i
\(109\) −1.06577 3.28010i −0.102082 0.314176i 0.886952 0.461861i \(-0.152818\pi\)
−0.989035 + 0.147684i \(0.952818\pi\)
\(110\) 0 0
\(111\) 1.41587 4.35761i 0.134389 0.413606i
\(112\) 20.5534 6.67820i 1.94211 0.631030i
\(113\) −5.75574 + 1.87015i −0.541455 + 0.175929i −0.566960 0.823745i \(-0.691881\pi\)
0.0255053 + 0.999675i \(0.491881\pi\)
\(114\) 0.977766 3.00925i 0.0915762 0.281842i
\(115\) 0 0
\(116\) 9.60772 + 29.5695i 0.892054 + 2.74546i
\(117\) 1.57364 + 2.16593i 0.145483 + 0.200240i
\(118\) 3.58986i 0.330473i
\(119\) −5.36612 + 3.89872i −0.491912 + 0.357395i
\(120\) 0 0
\(121\) 7.95761 + 5.78155i 0.723419 + 0.525595i
\(122\) −11.4997 + 15.8280i −1.04114 + 1.43300i
\(123\) 10.7103 + 3.47998i 0.965713 + 0.313779i
\(124\) 37.0796 3.32984
\(125\) 0 0
\(126\) −4.53315 −0.403845
\(127\) 19.2457 + 6.25332i 1.70778 + 0.554893i 0.989962 0.141334i \(-0.0451392\pi\)
0.717822 + 0.696227i \(0.245139\pi\)
\(128\) −12.0521 + 16.5882i −1.06526 + 1.46621i
\(129\) −2.09201 1.51994i −0.184192 0.133823i
\(130\) 0 0
\(131\) 2.46759 1.79281i 0.215595 0.156639i −0.474747 0.880122i \(-0.657460\pi\)
0.690341 + 0.723484i \(0.257460\pi\)
\(132\) 5.63164i 0.490171i
\(133\) 1.16768 + 1.60717i 0.101250 + 0.139359i
\(134\) 10.3336 + 31.8037i 0.892691 + 2.74742i
\(135\) 0 0
\(136\) 10.5127 32.3549i 0.901460 2.77441i
\(137\) −19.5062 + 6.33795i −1.66653 + 0.541487i −0.982224 0.187711i \(-0.939893\pi\)
−0.684302 + 0.729199i \(0.739893\pi\)
\(138\) 10.3830 3.37363i 0.883858 0.287183i
\(139\) −5.66068 + 17.4218i −0.480133 + 1.47770i 0.358775 + 0.933424i \(0.383194\pi\)
−0.838908 + 0.544273i \(0.816806\pi\)
\(140\) 0 0
\(141\) 0.592639 + 1.82396i 0.0499092 + 0.153605i
\(142\) 9.45242 + 13.0101i 0.793230 + 1.09179i
\(143\) 2.88825i 0.241527i
\(144\) 10.3635 7.52956i 0.863629 0.627463i
\(145\) 0 0
\(146\) −7.17517 5.21306i −0.593821 0.431436i
\(147\) −2.44159 + 3.36057i −0.201379 + 0.277175i
\(148\) −22.7476 7.39114i −1.86984 0.607548i
\(149\) −0.705938 −0.0578327 −0.0289163 0.999582i \(-0.509206\pi\)
−0.0289163 + 0.999582i \(0.509206\pi\)
\(150\) 0 0
\(151\) 7.04538 0.573345 0.286673 0.958029i \(-0.407451\pi\)
0.286673 + 0.958029i \(0.407451\pi\)
\(152\) −9.69039 3.14860i −0.785994 0.255385i
\(153\) −2.31098 + 3.18079i −0.186831 + 0.257151i
\(154\) −3.95645 2.87453i −0.318820 0.231636i
\(155\) 0 0
\(156\) 11.3066 8.21470i 0.905249 0.657702i
\(157\) 5.12880i 0.409323i 0.978833 + 0.204662i \(0.0656094\pi\)
−0.978833 + 0.204662i \(0.934391\pi\)
\(158\) −6.32399 8.70423i −0.503110 0.692471i
\(159\) −0.787563 2.42387i −0.0624578 0.192225i
\(160\) 0 0
\(161\) −2.11811 + 6.51888i −0.166931 + 0.513760i
\(162\) −2.55553 + 0.830342i −0.200781 + 0.0652378i
\(163\) 23.0739 7.49715i 1.80728 0.587222i 0.807289 0.590157i \(-0.200934\pi\)
0.999996 + 0.00293441i \(0.000934052\pi\)
\(164\) 18.1662 55.9097i 1.41854 4.36581i
\(165\) 0 0
\(166\) −7.36913 22.6799i −0.571955 1.76030i
\(167\) 2.67377 + 3.68013i 0.206903 + 0.284777i 0.899840 0.436221i \(-0.143683\pi\)
−0.692937 + 0.720998i \(0.743683\pi\)
\(168\) 14.5976i 1.12623i
\(169\) −4.71853 + 3.42821i −0.362964 + 0.263709i
\(170\) 0 0
\(171\) 0.952655 + 0.692144i 0.0728513 + 0.0529296i
\(172\) −7.93437 + 10.9207i −0.604990 + 0.832697i
\(173\) −2.54625 0.827327i −0.193588 0.0629005i 0.210618 0.977568i \(-0.432452\pi\)
−0.404206 + 0.914668i \(0.632452\pi\)
\(174\) −16.0039 −1.21325
\(175\) 0 0
\(176\) 13.8197 1.04170
\(177\) 1.27060 + 0.412843i 0.0955042 + 0.0310312i
\(178\) −24.3917 + 33.5723i −1.82823 + 2.51635i
\(179\) −12.6422 9.18511i −0.944924 0.686528i 0.00467674 0.999989i \(-0.498511\pi\)
−0.949601 + 0.313461i \(0.898511\pi\)
\(180\) 0 0
\(181\) −0.164103 + 0.119228i −0.0121977 + 0.00886215i −0.593867 0.804563i \(-0.702400\pi\)
0.581670 + 0.813425i \(0.302400\pi\)
\(182\) 12.1363i 0.899603i
\(183\) −4.27970 5.89050i −0.316365 0.435439i
\(184\) −10.8638 33.4352i −0.800887 2.46488i
\(185\) 0 0
\(186\) −5.89800 + 18.1522i −0.432462 + 1.33098i
\(187\) −4.03396 + 1.31071i −0.294992 + 0.0958488i
\(188\) 9.52141 3.09369i 0.694420 0.225631i
\(189\) 0.521325 1.60447i 0.0379208 0.116708i
\(190\) 0 0
\(191\) −2.44734 7.53213i −0.177083 0.545006i 0.822639 0.568563i \(-0.192501\pi\)
−0.999722 + 0.0235578i \(0.992501\pi\)
\(192\) −11.9732 16.4798i −0.864094 1.18932i
\(193\) 16.4269i 1.18243i −0.806513 0.591216i \(-0.798648\pi\)
0.806513 0.591216i \(-0.201352\pi\)
\(194\) −23.4086 + 17.0073i −1.68064 + 1.22106i
\(195\) 0 0
\(196\) 17.5428 + 12.7456i 1.25306 + 0.910400i
\(197\) 10.0728 13.8640i 0.717657 0.987770i −0.281942 0.959432i \(-0.590978\pi\)
0.999598 0.0283382i \(-0.00902154\pi\)
\(198\) −2.75695 0.895787i −0.195928 0.0636608i
\(199\) 2.01848 0.143086 0.0715430 0.997438i \(-0.477208\pi\)
0.0715430 + 0.997438i \(0.477208\pi\)
\(200\) 0 0
\(201\) −12.4451 −0.877806
\(202\) −34.6668 11.2639i −2.43915 0.792528i
\(203\) 5.90603 8.12895i 0.414522 0.570541i
\(204\) 16.6043 + 12.0638i 1.16254 + 0.844632i
\(205\) 0 0
\(206\) 2.97610 2.16226i 0.207355 0.150652i
\(207\) 4.06295i 0.282394i
\(208\) −20.1584 27.7456i −1.39773 1.92381i
\(209\) 0.392562 + 1.20818i 0.0271541 + 0.0835717i
\(210\) 0 0
\(211\) −7.36119 + 22.6554i −0.506765 + 1.55966i 0.291018 + 0.956718i \(0.406006\pi\)
−0.797783 + 0.602945i \(0.793994\pi\)
\(212\) −12.6531 + 4.11123i −0.869017 + 0.282361i
\(213\) −5.69189 + 1.84941i −0.390002 + 0.126719i
\(214\) 9.14333 28.1403i 0.625025 1.92363i
\(215\) 0 0
\(216\) 2.67386 + 8.22930i 0.181933 + 0.559933i
\(217\) −7.04356 9.69463i −0.478148 0.658115i
\(218\) 9.26733i 0.627663i
\(219\) 2.67028 1.94007i 0.180441 0.131098i
\(220\) 0 0
\(221\) 8.51571 + 6.18702i 0.572828 + 0.416184i
\(222\) 7.23662 9.96035i 0.485690 0.668495i
\(223\) 12.4695 + 4.05158i 0.835017 + 0.271314i 0.695157 0.718858i \(-0.255335\pi\)
0.139860 + 0.990171i \(0.455335\pi\)
\(224\) 28.8746 1.92927
\(225\) 0 0
\(226\) −16.2618 −1.08172
\(227\) 24.9944 + 8.12118i 1.65894 + 0.539022i 0.980649 0.195774i \(-0.0627218\pi\)
0.678289 + 0.734795i \(0.262722\pi\)
\(228\) 3.61313 4.97305i 0.239285 0.329348i
\(229\) 1.61484 + 1.17325i 0.106711 + 0.0775304i 0.639861 0.768490i \(-0.278992\pi\)
−0.533150 + 0.846021i \(0.678992\pi\)
\(230\) 0 0
\(231\) 1.47242 1.06978i 0.0968781 0.0703861i
\(232\) 51.5357i 3.38348i
\(233\) 0.308910 + 0.425178i 0.0202373 + 0.0278543i 0.819016 0.573771i \(-0.194520\pi\)
−0.798778 + 0.601625i \(0.794520\pi\)
\(234\) 2.22302 + 6.84175i 0.145323 + 0.447259i
\(235\) 0 0
\(236\) 2.15512 6.63278i 0.140286 0.431757i
\(237\) 3.80807 1.23732i 0.247361 0.0803723i
\(238\) −16.9505 + 5.50757i −1.09874 + 0.357002i
\(239\) 2.16612 6.66663i 0.140115 0.431229i −0.856236 0.516585i \(-0.827203\pi\)
0.996350 + 0.0853565i \(0.0272029\pi\)
\(240\) 0 0
\(241\) 0.715542 + 2.20221i 0.0460921 + 0.141857i 0.971454 0.237228i \(-0.0762388\pi\)
−0.925362 + 0.379085i \(0.876239\pi\)
\(242\) 15.5353 + 21.3824i 0.998644 + 1.37452i
\(243\) 1.00000i 0.0641500i
\(244\) −30.7496 + 22.3409i −1.96854 + 1.43023i
\(245\) 0 0
\(246\) 24.4808 + 17.7864i 1.56084 + 1.13402i
\(247\) 1.85303 2.55048i 0.117906 0.162283i
\(248\) 58.4536 + 18.9927i 3.71180 + 1.20604i
\(249\) 8.87482 0.562419
\(250\) 0 0
\(251\) −6.17885 −0.390005 −0.195003 0.980803i \(-0.562472\pi\)
−0.195003 + 0.980803i \(0.562472\pi\)
\(252\) −8.37566 2.72142i −0.527617 0.171433i
\(253\) −2.57637 + 3.54607i −0.161975 + 0.222939i
\(254\) 43.9907 + 31.9611i 2.76022 + 2.00542i
\(255\) 0 0
\(256\) −11.6138 + 8.43794i −0.725864 + 0.527371i
\(257\) 13.2239i 0.824882i −0.910984 0.412441i \(-0.864676\pi\)
0.910984 0.412441i \(-0.135324\pi\)
\(258\) −4.08413 5.62133i −0.254267 0.349969i
\(259\) 2.38864 + 7.35148i 0.148423 + 0.456799i
\(260\) 0 0
\(261\) 1.84049 5.66445i 0.113923 0.350620i
\(262\) 7.79465 2.53264i 0.481555 0.156467i
\(263\) 6.63498 2.15583i 0.409130 0.132934i −0.0972190 0.995263i \(-0.530995\pi\)
0.506349 + 0.862329i \(0.330995\pi\)
\(264\) −2.88461 + 8.87792i −0.177536 + 0.546398i
\(265\) 0 0
\(266\) 1.64953 + 5.07674i 0.101139 + 0.311275i
\(267\) −9.07752 12.4941i −0.555535 0.764629i
\(268\) 64.9656i 3.96841i
\(269\) 19.1898 13.9422i 1.17002 0.850070i 0.179010 0.983847i \(-0.442711\pi\)
0.991011 + 0.133777i \(0.0427107\pi\)
\(270\) 0 0
\(271\) −23.4542 17.0405i −1.42474 1.03514i −0.990966 0.134114i \(-0.957181\pi\)
−0.433775 0.901021i \(-0.642819\pi\)
\(272\) 29.6037 40.7460i 1.79499 2.47059i
\(273\) −4.29555 1.39571i −0.259978 0.0844721i
\(274\) −55.1113 −3.32940
\(275\) 0 0
\(276\) 21.2094 1.27665
\(277\) 8.16641 + 2.65343i 0.490672 + 0.159429i 0.543894 0.839154i \(-0.316949\pi\)
−0.0532223 + 0.998583i \(0.516949\pi\)
\(278\) −28.9321 + 39.8216i −1.73523 + 2.38834i
\(279\) −5.74653 4.17510i −0.344036 0.249957i
\(280\) 0 0
\(281\) −13.8877 + 10.0900i −0.828471 + 0.601919i −0.919126 0.393963i \(-0.871104\pi\)
0.0906557 + 0.995882i \(0.471104\pi\)
\(282\) 5.15327i 0.306872i
\(283\) 5.65452 + 7.78278i 0.336126 + 0.462638i 0.943305 0.331927i \(-0.107699\pi\)
−0.607179 + 0.794565i \(0.707699\pi\)
\(284\) 9.65426 + 29.7128i 0.572875 + 1.76313i
\(285\) 0 0
\(286\) −2.39823 + 7.38100i −0.141810 + 0.436447i
\(287\) −18.0687 + 5.87087i −1.06656 + 0.346546i
\(288\) 16.2779 5.28899i 0.959182 0.311657i
\(289\) 0.476498 1.46651i 0.0280293 0.0862654i
\(290\) 0 0
\(291\) −3.32756 10.2412i −0.195065 0.600348i
\(292\) −10.1276 13.9394i −0.592671 0.815742i
\(293\) 16.8202i 0.982649i 0.870977 + 0.491324i \(0.163487\pi\)
−0.870977 + 0.491324i \(0.836513\pi\)
\(294\) −9.02998 + 6.56067i −0.526639 + 0.382626i
\(295\) 0 0
\(296\) −32.0743 23.3033i −1.86428 1.35448i
\(297\) 0.634113 0.872782i 0.0367950 0.0506439i
\(298\) −1.80404 0.586170i −0.104505 0.0339559i
\(299\) 10.8775 0.629059
\(300\) 0 0
\(301\) 4.36247 0.251449
\(302\) 18.0047 + 5.85008i 1.03605 + 0.336634i
\(303\) 7.97356 10.9747i 0.458069 0.630478i
\(304\) −12.2036 8.86641i −0.699922 0.508523i
\(305\) 0 0
\(306\) −8.54691 + 6.20969i −0.488594 + 0.354984i
\(307\) 11.3212i 0.646134i −0.946376 0.323067i \(-0.895286\pi\)
0.946376 0.323067i \(-0.104714\pi\)
\(308\) −5.58444 7.68632i −0.318203 0.437969i
\(309\) 0.423056 + 1.30203i 0.0240668 + 0.0740700i
\(310\) 0 0
\(311\) 5.73642 17.6549i 0.325283 1.00112i −0.646030 0.763312i \(-0.723572\pi\)
0.971313 0.237805i \(-0.0764280\pi\)
\(312\) 22.0318 7.15855i 1.24730 0.405273i
\(313\) 9.22478 2.99731i 0.521416 0.169418i −0.0364720 0.999335i \(-0.511612\pi\)
0.557888 + 0.829916i \(0.311612\pi\)
\(314\) −4.25866 + 13.1068i −0.240330 + 0.739660i
\(315\) 0 0
\(316\) −6.45903 19.8789i −0.363349 1.11827i
\(317\) 4.39456 + 6.04859i 0.246823 + 0.339723i 0.914395 0.404822i \(-0.132667\pi\)
−0.667573 + 0.744545i \(0.732667\pi\)
\(318\) 6.84822i 0.384029i
\(319\) 5.19825 3.77675i 0.291046 0.211457i
\(320\) 0 0
\(321\) 8.90851 + 6.47241i 0.497225 + 0.361255i
\(322\) −10.8258 + 14.9004i −0.603298 + 0.830369i
\(323\) 4.40313 + 1.43066i 0.244997 + 0.0796042i
\(324\) −5.22020 −0.290011
\(325\) 0 0
\(326\) 65.1911 3.61060
\(327\) 3.28010 + 1.06577i 0.181390 + 0.0589371i
\(328\) 57.2756 78.8331i 3.16252 4.35283i
\(329\) −2.61753 1.90175i −0.144309 0.104847i
\(330\) 0 0
\(331\) 20.4333 14.8457i 1.12312 0.815993i 0.138439 0.990371i \(-0.455791\pi\)
0.984679 + 0.174378i \(0.0557914\pi\)
\(332\) 46.3283i 2.54259i
\(333\) 2.69315 + 3.70681i 0.147584 + 0.203132i
\(334\) 3.77714 + 11.6248i 0.206676 + 0.636083i
\(335\) 0 0
\(336\) −6.67820 + 20.5534i −0.364325 + 1.12128i
\(337\) −12.3866 + 4.02464i −0.674739 + 0.219236i −0.626291 0.779590i \(-0.715428\pi\)
−0.0484485 + 0.998826i \(0.515428\pi\)
\(338\) −14.9049 + 4.84291i −0.810721 + 0.263419i
\(339\) 1.87015 5.75574i 0.101573 0.312609i
\(340\) 0 0
\(341\) −2.36798 7.28790i −0.128233 0.394662i
\(342\) 1.85982 + 2.55982i 0.100568 + 0.138419i
\(343\) 18.8171i 1.01603i
\(344\) −18.1018 + 13.1517i −0.975983 + 0.709093i
\(345\) 0 0
\(346\) −5.82005 4.22852i −0.312888 0.227326i
\(347\) 3.52759 4.85531i 0.189371 0.260647i −0.703766 0.710432i \(-0.748500\pi\)
0.893137 + 0.449785i \(0.148500\pi\)
\(348\) −29.5695 9.60772i −1.58509 0.515028i
\(349\) 22.7183 1.21608 0.608042 0.793905i \(-0.291955\pi\)
0.608042 + 0.793905i \(0.291955\pi\)
\(350\) 0 0
\(351\) −2.67723 −0.142900
\(352\) 17.5608 + 5.70586i 0.935996 + 0.304123i
\(353\) −2.85366 + 3.92772i −0.151885 + 0.209052i −0.878179 0.478333i \(-0.841241\pi\)
0.726294 + 0.687385i \(0.241241\pi\)
\(354\) 2.90425 + 2.11006i 0.154359 + 0.112149i
\(355\) 0 0
\(356\) −65.2218 + 47.3864i −3.45675 + 2.51148i
\(357\) 6.63289i 0.351050i
\(358\) −24.6808 33.9702i −1.30442 1.79538i
\(359\) −8.92780 27.4769i −0.471191 1.45018i −0.851026 0.525123i \(-0.824019\pi\)
0.379835 0.925054i \(-0.375981\pi\)
\(360\) 0 0
\(361\) −5.44284 + 16.7513i −0.286465 + 0.881649i
\(362\) −0.518371 + 0.168429i −0.0272450 + 0.00885242i
\(363\) −9.35474 + 3.03954i −0.490996 + 0.159534i
\(364\) −7.28587 + 22.4236i −0.381883 + 1.17532i
\(365\) 0 0
\(366\) −6.04577 18.6070i −0.316018 0.972602i
\(367\) −8.64570 11.8998i −0.451302 0.621163i 0.521375 0.853328i \(-0.325419\pi\)
−0.972677 + 0.232164i \(0.925419\pi\)
\(368\) 52.0465i 2.71311i
\(369\) −9.11070 + 6.61931i −0.474284 + 0.344588i
\(370\) 0 0
\(371\) 3.47846 + 2.52725i 0.180592 + 0.131208i
\(372\) −21.7948 + 29.9980i −1.13001 + 1.55532i
\(373\) −31.4220 10.2096i −1.62697 0.528635i −0.653399 0.757013i \(-0.726658\pi\)
−0.973572 + 0.228378i \(0.926658\pi\)
\(374\) −11.3972 −0.589337
\(375\) 0 0
\(376\) 16.5945 0.855797
\(377\) −15.1650 4.92742i −0.781039 0.253775i
\(378\) 2.66452 3.66740i 0.137048 0.188631i
\(379\) −12.2612 8.90826i −0.629814 0.457587i 0.226522 0.974006i \(-0.427265\pi\)
−0.856336 + 0.516419i \(0.827265\pi\)
\(380\) 0 0
\(381\) −16.3714 + 11.8945i −0.838733 + 0.609375i
\(382\) 21.2807i 1.08882i
\(383\) 4.70705 + 6.47870i 0.240519 + 0.331046i 0.912163 0.409828i \(-0.134411\pi\)
−0.671644 + 0.740874i \(0.734411\pi\)
\(384\) −6.33615 19.5007i −0.323340 0.995139i
\(385\) 0 0
\(386\) 13.6399 41.9793i 0.694253 2.13669i
\(387\) 2.45931 0.799078i 0.125014 0.0406194i
\(388\) −53.4609 + 17.3705i −2.71407 + 0.881854i
\(389\) −0.332078 + 1.02203i −0.0168370 + 0.0518191i −0.959122 0.282993i \(-0.908673\pi\)
0.942285 + 0.334812i \(0.108673\pi\)
\(390\) 0 0
\(391\) 4.93629 + 15.1923i 0.249639 + 0.768309i
\(392\) 21.1266 + 29.0783i 1.06706 + 1.46868i
\(393\) 3.05011i 0.153858i
\(394\) 37.2532 27.0660i 1.87679 1.36357i
\(395\) 0 0
\(396\) −4.55609 3.31019i −0.228952 0.166344i
\(397\) 14.2326 19.5894i 0.714312 0.983166i −0.285382 0.958414i \(-0.592120\pi\)
0.999694 0.0247517i \(-0.00787952\pi\)
\(398\) 5.15828 + 1.67603i 0.258561 + 0.0840116i
\(399\) −1.98657 −0.0994529
\(400\) 0 0
\(401\) −1.99317 −0.0995340 −0.0497670 0.998761i \(-0.515848\pi\)
−0.0497670 + 0.998761i \(0.515848\pi\)
\(402\) −31.8037 10.3336i −1.58622 0.515395i
\(403\) −11.1777 + 15.3848i −0.556801 + 0.766371i
\(404\) −57.2899 41.6235i −2.85028 2.07085i
\(405\) 0 0
\(406\) 21.8428 15.8698i 1.08404 0.787603i
\(407\) 4.94300i 0.245015i
\(408\) 19.9964 + 27.5227i 0.989971 + 1.36258i
\(409\) −2.05953 6.33858i −0.101837 0.313423i 0.887138 0.461504i \(-0.152690\pi\)
−0.988975 + 0.148082i \(0.952690\pi\)
\(410\) 0 0
\(411\) 6.33795 19.5062i 0.312628 0.962169i
\(412\) 6.79686 2.20843i 0.334857 0.108802i
\(413\) −2.14356 + 0.696484i −0.105477 + 0.0342717i
\(414\) −3.37363 + 10.3830i −0.165805 + 0.510295i
\(415\) 0 0
\(416\) −14.1599 43.5796i −0.694245 2.13667i
\(417\) −10.7673 14.8199i −0.527275 0.725732i
\(418\) 3.41351i 0.166960i
\(419\) 17.2758 12.5516i 0.843977 0.613185i −0.0795021 0.996835i \(-0.525333\pi\)
0.923479 + 0.383650i \(0.125333\pi\)
\(420\) 0 0
\(421\) −18.0708 13.1292i −0.880717 0.639878i 0.0527243 0.998609i \(-0.483210\pi\)
−0.933441 + 0.358731i \(0.883210\pi\)
\(422\) −37.6235 + 51.7842i −1.83148 + 2.52082i
\(423\) −1.82396 0.592639i −0.0886838 0.0288151i
\(424\) −22.0526 −1.07097
\(425\) 0 0
\(426\) −16.0814 −0.779147
\(427\) 11.6823 + 3.79580i 0.565344 + 0.183692i
\(428\) 33.7873 46.5042i 1.63317 2.24786i
\(429\) −2.33664 1.69767i −0.112814 0.0819642i
\(430\) 0 0
\(431\) 24.6046 17.8763i 1.18516 0.861070i 0.192416 0.981313i \(-0.438368\pi\)
0.992744 + 0.120244i \(0.0383677\pi\)
\(432\) 12.8101i 0.616324i
\(433\) −0.338940 0.466511i −0.0162884 0.0224191i 0.800795 0.598938i \(-0.204411\pi\)
−0.817084 + 0.576519i \(0.804411\pi\)
\(434\) −9.95017 30.6235i −0.477624 1.46997i
\(435\) 0 0
\(436\) 5.56352 17.1227i 0.266444 0.820031i
\(437\) 4.55015 1.47843i 0.217663 0.0707230i
\(438\) 8.43491 2.74067i 0.403036 0.130954i
\(439\) −3.95681 + 12.1778i −0.188848 + 0.581215i −0.999993 0.00363006i \(-0.998845\pi\)
0.811145 + 0.584845i \(0.198845\pi\)
\(440\) 0 0
\(441\) −1.28362 3.95058i −0.0611249 0.188123i
\(442\) 16.6248 + 22.8821i 0.790761 + 1.08839i
\(443\) 14.3147i 0.680110i 0.940405 + 0.340055i \(0.110446\pi\)
−0.940405 + 0.340055i \(0.889554\pi\)
\(444\) 19.3503 14.0588i 0.918323 0.667200i
\(445\) 0 0
\(446\) 28.5019 + 20.7078i 1.34960 + 0.980545i
\(447\) 0.414940 0.571116i 0.0196260 0.0270128i
\(448\) 32.6833 + 10.6194i 1.54414 + 0.501721i
\(449\) 11.9663 0.564724 0.282362 0.959308i \(-0.408882\pi\)
0.282362 + 0.959308i \(0.408882\pi\)
\(450\) 0 0
\(451\) −12.1490 −0.572076
\(452\) −30.0461 9.76257i −1.41325 0.459193i
\(453\) −4.14117 + 5.69983i −0.194569 + 0.267802i
\(454\) 57.1306 + 41.5078i 2.68127 + 1.94806i
\(455\) 0 0
\(456\) 8.24313 5.98899i 0.386020 0.280460i
\(457\) 8.22154i 0.384587i 0.981337 + 0.192294i \(0.0615926\pi\)
−0.981337 + 0.192294i \(0.938407\pi\)
\(458\) 3.15257 + 4.33913i 0.147310 + 0.202754i
\(459\) −1.21495 3.73924i −0.0567091 0.174533i
\(460\) 0 0
\(461\) 0.393120 1.20990i 0.0183094 0.0563506i −0.941484 0.337057i \(-0.890569\pi\)
0.959794 + 0.280706i \(0.0905686\pi\)
\(462\) 4.65109 1.51123i 0.216388 0.0703088i
\(463\) −31.0771 + 10.0976i −1.44428 + 0.469273i −0.923227 0.384254i \(-0.874459\pi\)
−0.521048 + 0.853527i \(0.674459\pi\)
\(464\) −23.5768 + 72.5618i −1.09452 + 3.36860i
\(465\) 0 0
\(466\) 0.436385 + 1.34305i 0.0202151 + 0.0622158i
\(467\) 8.48450 + 11.6779i 0.392616 + 0.540389i 0.958872 0.283840i \(-0.0916085\pi\)
−0.566256 + 0.824230i \(0.691609\pi\)
\(468\) 13.9757i 0.646026i
\(469\) 16.9856 12.3407i 0.784321 0.569843i
\(470\) 0 0
\(471\) −4.14929 3.01464i −0.191189 0.138907i
\(472\) 6.79482 9.35227i 0.312757 0.430473i
\(473\) 2.65315 + 0.862060i 0.121992 + 0.0396375i
\(474\) 10.7590 0.494178
\(475\) 0 0
\(476\) −34.6250 −1.58703
\(477\) 2.42387 + 0.787563i 0.110981 + 0.0360600i
\(478\) 11.0712 15.2382i 0.506383 0.696977i
\(479\) −13.6415 9.91113i −0.623296 0.452851i 0.230775 0.973007i \(-0.425874\pi\)
−0.854071 + 0.520156i \(0.825874\pi\)
\(480\) 0 0
\(481\) 9.92398 7.21020i 0.452495 0.328757i
\(482\) 6.22196i 0.283403i
\(483\) −4.02889 5.54529i −0.183321 0.252320i
\(484\) 15.8670 + 48.8336i 0.721227 + 2.21971i
\(485\) 0 0
\(486\) 0.830342 2.55553i 0.0376651 0.115921i
\(487\) 37.8744 12.3061i 1.71625 0.557644i 0.724898 0.688856i \(-0.241887\pi\)
0.991354 + 0.131212i \(0.0418868\pi\)
\(488\) −59.9181 + 19.4686i −2.71236 + 0.881301i
\(489\) −7.49715 + 23.0739i −0.339033 + 1.04344i
\(490\) 0 0
\(491\) 4.33411 + 13.3390i 0.195596 + 0.601981i 0.999969 + 0.00785739i \(0.00250111\pi\)
−0.804374 + 0.594124i \(0.797499\pi\)
\(492\) 34.5541 + 47.5596i 1.55782 + 2.14415i
\(493\) 23.4168i 1.05464i
\(494\) 6.85324 4.97917i 0.308342 0.224024i
\(495\) 0 0
\(496\) 73.6133 + 53.4832i 3.30534 + 2.40147i
\(497\) 5.93464 8.16834i 0.266205 0.366400i
\(498\) 22.6799 + 7.36913i 1.01631 + 0.330219i
\(499\) −15.2315 −0.681857 −0.340929 0.940089i \(-0.610741\pi\)
−0.340929 + 0.940089i \(0.610741\pi\)
\(500\) 0 0
\(501\) −4.54890 −0.203230
\(502\) −15.7902 5.13055i −0.704752 0.228988i
\(503\) 13.9499 19.2004i 0.621996 0.856104i −0.375501 0.926822i \(-0.622529\pi\)
0.997496 + 0.0707185i \(0.0225292\pi\)
\(504\) −11.8097 8.58028i −0.526048 0.382196i
\(505\) 0 0
\(506\) −9.52843 + 6.92281i −0.423590 + 0.307756i
\(507\) 5.83243i 0.259027i
\(508\) 62.0918 + 85.4620i 2.75488 + 3.79176i
\(509\) 3.86570 + 11.8974i 0.171344 + 0.527343i 0.999448 0.0332320i \(-0.0105800\pi\)
−0.828103 + 0.560575i \(0.810580\pi\)
\(510\) 0 0
\(511\) −1.72071 + 5.29581i −0.0761198 + 0.234273i
\(512\) 2.31548 0.752345i 0.102331 0.0332493i
\(513\) −1.11991 + 0.363882i −0.0494454 + 0.0160658i
\(514\) 10.9803 33.7940i 0.484321 1.49059i
\(515\) 0 0
\(516\) −4.17134 12.8381i −0.183633 0.565165i
\(517\) −1.21612 1.67384i −0.0534847 0.0736154i
\(518\) 20.7703i 0.912595i
\(519\) 2.16597 1.57367i 0.0950755 0.0690764i
\(520\) 0 0
\(521\) 22.6232 + 16.4367i 0.991141 + 0.720106i 0.960171 0.279414i \(-0.0901403\pi\)
0.0309702 + 0.999520i \(0.490140\pi\)
\(522\) 9.40685 12.9474i 0.411727 0.566693i
\(523\) 14.9328 + 4.85196i 0.652966 + 0.212162i 0.616722 0.787181i \(-0.288460\pi\)
0.0362446 + 0.999343i \(0.488460\pi\)
\(524\) 15.9222 0.695564
\(525\) 0 0
\(526\) 18.7460 0.817362
\(527\) −26.5602 8.62993i −1.15698 0.375926i
\(528\) −8.12302 + 11.1804i −0.353509 + 0.486564i
\(529\) −5.25252 3.81618i −0.228370 0.165921i
\(530\) 0 0
\(531\) −1.08084 + 0.785274i −0.0469043 + 0.0340780i
\(532\) 10.3703i 0.449609i
\(533\) 17.7214 + 24.3915i 0.767601 + 1.05651i
\(534\) −12.8235 39.4666i −0.554926 1.70789i
\(535\) 0 0
\(536\) −33.2764 + 102.414i −1.43732 + 4.42362i
\(537\) 14.8618 4.82890i 0.641335 0.208382i
\(538\) 60.6168 19.6956i 2.61338 0.849137i
\(539\) 1.38479 4.26196i 0.0596473 0.183576i
\(540\) 0 0
\(541\) −7.40971 22.8048i −0.318569 0.980453i −0.974261 0.225425i \(-0.927623\pi\)
0.655692 0.755028i \(-0.272377\pi\)
\(542\) −45.7885 63.0224i −1.96678 2.70705i
\(543\) 0.202843i 0.00870482i
\(544\) 54.4409 39.5536i 2.33413 1.69585i
\(545\) 0 0
\(546\) −9.81848 7.13354i −0.420192 0.305287i
\(547\) 3.30736 4.55219i 0.141412 0.194637i −0.732436 0.680836i \(-0.761617\pi\)
0.873848 + 0.486198i \(0.161617\pi\)
\(548\) −101.826 33.0853i −4.34980 1.41333i
\(549\) 7.28106 0.310748
\(550\) 0 0
\(551\) −7.01341 −0.298781
\(552\) 33.4352 + 10.8638i 1.42310 + 0.462392i
\(553\) −3.97048 + 5.46490i −0.168842 + 0.232391i
\(554\) 18.6663 + 13.5618i 0.793053 + 0.576187i
\(555\) 0 0
\(556\) −77.3626 + 56.2072i −3.28090 + 2.38372i
\(557\) 42.4247i 1.79759i 0.438366 + 0.898796i \(0.355557\pi\)
−0.438366 + 0.898796i \(0.644443\pi\)
\(558\) −11.2187 15.4412i −0.474924 0.653677i
\(559\) −2.13932 6.58414i −0.0904835 0.278480i
\(560\) 0 0
\(561\) 1.31071 4.03396i 0.0553383 0.170314i
\(562\) −43.8686 + 14.2538i −1.85048 + 0.601259i
\(563\) −5.50279 + 1.78796i −0.231915 + 0.0753537i −0.422669 0.906284i \(-0.638907\pi\)
0.190754 + 0.981638i \(0.438907\pi\)
\(564\) −3.09369 + 9.52141i −0.130268 + 0.400924i
\(565\) 0 0
\(566\) 7.98793 + 24.5843i 0.335758 + 1.03336i
\(567\) 0.991619 + 1.36485i 0.0416441 + 0.0573181i
\(568\) 51.7853i 2.17286i
\(569\) −17.8029 + 12.9346i −0.746336 + 0.542245i −0.894689 0.446690i \(-0.852603\pi\)
0.148353 + 0.988934i \(0.452603\pi\)
\(570\) 0 0
\(571\) −27.1946 19.7580i −1.13806 0.826847i −0.151210 0.988502i \(-0.548317\pi\)
−0.986847 + 0.161654i \(0.948317\pi\)
\(572\) −8.86216 + 12.1977i −0.370546 + 0.510012i
\(573\) 7.53213 + 2.44734i 0.314659 + 0.102239i
\(574\) −51.0499 −2.13078
\(575\) 0 0
\(576\) 20.3701 0.848754
\(577\) −38.2658 12.4333i −1.59303 0.517605i −0.627656 0.778491i \(-0.715985\pi\)
−0.965370 + 0.260886i \(0.915985\pi\)
\(578\) 2.43541 3.35205i 0.101300 0.139427i
\(579\) 13.2896 + 9.65547i 0.552297 + 0.401268i
\(580\) 0 0
\(581\) −12.1128 + 8.80043i −0.502522 + 0.365103i
\(582\) 28.9346i 1.19938i
\(583\) 1.61611 + 2.22438i 0.0669323 + 0.0921243i
\(584\) −8.82549 27.1621i −0.365201 1.12397i
\(585\) 0 0
\(586\) −13.9665 + 42.9846i −0.576952 + 1.77568i
\(587\) −2.68483 + 0.872353i −0.110815 + 0.0360059i −0.363899 0.931438i \(-0.618555\pi\)
0.253085 + 0.967444i \(0.418555\pi\)
\(588\) −20.6228 + 6.70076i −0.850471 + 0.276335i
\(589\) −2.58469 + 7.95485i −0.106500 + 0.327774i
\(590\) 0 0
\(591\) 5.29558 + 16.2981i 0.217831 + 0.670415i
\(592\) −34.4994 47.4844i −1.41792 1.95160i
\(593\) 24.6805i 1.01351i −0.862091 0.506754i \(-0.830845\pi\)
0.862091 0.506754i \(-0.169155\pi\)
\(594\) 2.34520 1.70389i 0.0962248 0.0699114i
\(595\) 0 0
\(596\) −2.98134 2.16607i −0.122120 0.0887256i
\(597\) −1.18643 + 1.63298i −0.0485574 + 0.0668335i
\(598\) 27.7976 + 9.03200i 1.13673 + 0.369346i
\(599\) 7.71547 0.315245 0.157623 0.987499i \(-0.449617\pi\)
0.157623 + 0.987499i \(0.449617\pi\)
\(600\) 0 0
\(601\) 22.6506 0.923938 0.461969 0.886896i \(-0.347143\pi\)
0.461969 + 0.886896i \(0.347143\pi\)
\(602\) 11.1484 + 3.62234i 0.454376 + 0.147636i
\(603\) 7.31502 10.0683i 0.297891 0.410011i
\(604\) 29.7543 + 21.6177i 1.21068 + 0.879613i
\(605\) 0 0
\(606\) 29.4894 21.4253i 1.19792 0.870343i
\(607\) 24.6423i 1.00020i 0.865968 + 0.500099i \(0.166703\pi\)
−0.865968 + 0.500099i \(0.833297\pi\)
\(608\) −11.8464 16.3052i −0.480436 0.661264i
\(609\) 3.10498 + 9.55616i 0.125820 + 0.387235i
\(610\) 0 0
\(611\) −1.58663 + 4.88315i −0.0641883 + 0.197551i
\(612\) −19.5196 + 6.34229i −0.789031 + 0.256372i
\(613\) 39.7574 12.9180i 1.60579 0.521751i 0.637256 0.770652i \(-0.280069\pi\)
0.968529 + 0.248901i \(0.0800694\pi\)
\(614\) 9.40045 28.9316i 0.379371 1.16758i
\(615\) 0 0
\(616\) −4.86646 14.9774i −0.196075 0.603458i
\(617\) 9.36871 + 12.8949i 0.377170 + 0.519130i 0.954832 0.297146i \(-0.0960348\pi\)
−0.577662 + 0.816276i \(0.696035\pi\)
\(618\) 3.67866i 0.147977i
\(619\) −38.1613 + 27.7258i −1.53383 + 1.11440i −0.579775 + 0.814777i \(0.696859\pi\)
−0.954059 + 0.299619i \(0.903141\pi\)
\(620\) 0 0
\(621\) −3.28699 2.38814i −0.131902 0.0958327i
\(622\) 29.3192 40.3544i 1.17559 1.61806i
\(623\) 24.7788 + 8.05113i 0.992743 + 0.322562i
\(624\) 34.2955 1.37292
\(625\) 0 0
\(626\) 26.0630 1.04169
\(627\) −1.20818 0.392562i −0.0482501 0.0156774i
\(628\) −15.7370 + 21.6601i −0.627974 + 0.864332i
\(629\) 14.5739 + 10.5886i 0.581101 + 0.422195i
\(630\) 0 0
\(631\) −26.1825 + 19.0227i −1.04231 + 0.757282i −0.970735 0.240153i \(-0.922802\pi\)
−0.0715741 + 0.997435i \(0.522802\pi\)
\(632\) 34.6462i 1.37815i
\(633\) −14.0018 19.2718i −0.556522 0.765987i
\(634\) 6.20802 + 19.1063i 0.246552 + 0.758809i
\(635\) 0 0
\(636\) 4.11123 12.6531i 0.163021 0.501727i
\(637\) −10.5766 + 3.43656i −0.419061 + 0.136161i
\(638\) 16.4203 5.33526i 0.650084 0.211225i
\(639\) 1.84941 5.69189i 0.0731614 0.225168i
\(640\) 0 0
\(641\) 5.56360 + 17.1230i 0.219749 + 0.676317i 0.998782 + 0.0493350i \(0.0157102\pi\)
−0.779033 + 0.626982i \(0.784290\pi\)
\(642\) 17.3916 + 23.9376i 0.686394 + 0.944740i
\(643\) 21.8891i 0.863224i 0.902059 + 0.431612i \(0.142055\pi\)
−0.902059 + 0.431612i \(0.857945\pi\)
\(644\) −28.9475 + 21.0316i −1.14069 + 0.828761i
\(645\) 0 0
\(646\) 10.0644 + 7.31220i 0.395978 + 0.287695i
\(647\) −11.1834 + 15.3926i −0.439665 + 0.605147i −0.970138 0.242555i \(-0.922015\pi\)
0.530473 + 0.847702i \(0.322015\pi\)
\(648\) −8.22930 2.67386i −0.323278 0.105039i
\(649\) −1.44129 −0.0565755
\(650\) 0 0
\(651\) 11.9832 0.469660
\(652\) 120.450 + 39.1366i 4.71719 + 1.53271i
\(653\) −1.36349 + 1.87669i −0.0533576 + 0.0734405i −0.834862 0.550459i \(-0.814453\pi\)
0.781504 + 0.623900i \(0.214453\pi\)
\(654\) 7.49743 + 5.44720i 0.293173 + 0.213002i
\(655\) 0 0
\(656\) 116.709 84.7937i 4.55670 3.31064i
\(657\) 3.30065i 0.128771i
\(658\) −5.11007 7.03341i −0.199211 0.274191i
\(659\) −2.22239 6.83980i −0.0865719 0.266441i 0.898394 0.439191i \(-0.144735\pi\)
−0.984966 + 0.172750i \(0.944735\pi\)
\(660\) 0 0
\(661\) 13.2943 40.9158i 0.517090 1.59144i −0.262358 0.964971i \(-0.584500\pi\)
0.779447 0.626468i \(-0.215500\pi\)
\(662\) 64.5450 20.9719i 2.50861 0.815098i
\(663\) −10.0108 + 3.25271i −0.388788 + 0.126325i
\(664\) 23.7300 73.0336i 0.920904 2.83425i
\(665\) 0 0
\(666\) 3.80451 + 11.7091i 0.147422 + 0.453718i
\(667\) −14.2236 19.5772i −0.550742 0.758031i
\(668\) 23.7461i 0.918765i
\(669\) −10.6072 + 7.70656i −0.410097 + 0.297953i
\(670\) 0 0
\(671\) 6.35478 + 4.61702i 0.245324 + 0.178238i
\(672\) −16.9721 + 23.3601i −0.654713 + 0.901135i
\(673\) −28.3444 9.20966i −1.09260 0.355006i −0.293348 0.956006i \(-0.594769\pi\)
−0.799250 + 0.600999i \(0.794769\pi\)
\(674\) −34.9961 −1.34800
\(675\) 0 0
\(676\) −30.4464 −1.17102
\(677\) 25.4261 + 8.26144i 0.977204 + 0.317513i 0.753721 0.657195i \(-0.228257\pi\)
0.223483 + 0.974708i \(0.428257\pi\)
\(678\) 9.55846 13.1561i 0.367091 0.505257i
\(679\) 14.6969 + 10.6780i 0.564017 + 0.409782i
\(680\) 0 0
\(681\) −21.2615 + 15.4474i −0.814743 + 0.591946i
\(682\) 20.5907i 0.788457i
\(683\) −16.7489 23.0529i −0.640880 0.882096i 0.357782 0.933805i \(-0.383533\pi\)
−0.998662 + 0.0517093i \(0.983533\pi\)
\(684\) 1.89953 + 5.84617i 0.0726305 + 0.223534i
\(685\) 0 0
\(686\) 15.6246 48.0876i 0.596550 1.83599i
\(687\) −1.89835 + 0.616813i −0.0724267 + 0.0235329i
\(688\) −31.5039 + 10.2362i −1.20107 + 0.390253i
\(689\) 2.10849 6.48926i 0.0803270 0.247221i
\(690\) 0 0
\(691\) 10.7065 + 32.9512i 0.407294 + 1.25352i 0.918965 + 0.394340i \(0.129027\pi\)
−0.511671 + 0.859182i \(0.670973\pi\)
\(692\) −8.21486 11.3068i −0.312282 0.429820i
\(693\) 1.82001i 0.0691365i
\(694\) 13.0464 9.47878i 0.495235 0.359810i
\(695\) 0 0
\(696\) −41.6932 30.2919i −1.58038 1.14821i
\(697\) −26.0249 + 35.8203i −0.985765 + 1.35679i
\(698\) 58.0574 + 18.8640i 2.19750 + 0.714012i
\(699\) −0.525548 −0.0198781
\(700\) 0 0
\(701\) 0.973305 0.0367612 0.0183806 0.999831i \(-0.494149\pi\)
0.0183806 + 0.999831i \(0.494149\pi\)
\(702\) −6.84175 2.22302i −0.258225 0.0839024i
\(703\) 3.17131 4.36494i 0.119608 0.164627i
\(704\) 17.7786 + 12.9169i 0.670058 + 0.486826i
\(705\) 0 0
\(706\) −10.5540 + 7.66790i −0.397204 + 0.288585i
\(707\) 22.8854i 0.860696i
\(708\) 4.09928 + 5.64218i 0.154061 + 0.212046i
\(709\) 3.49938 + 10.7700i 0.131422 + 0.404475i 0.995016 0.0997119i \(-0.0317921\pi\)
−0.863594 + 0.504187i \(0.831792\pi\)
\(710\) 0 0
\(711\) −1.23732 + 3.80807i −0.0464030 + 0.142814i
\(712\) −127.090 + 41.2941i −4.76290 + 1.54756i
\(713\) −27.4470 + 8.91808i −1.02790 + 0.333985i
\(714\) 5.50757 16.9505i 0.206115 0.634358i
\(715\) 0 0
\(716\) −25.2078 77.5816i −0.942060 2.89936i
\(717\) 4.12021 + 5.67098i 0.153872 + 0.211787i
\(718\) 77.6312i 2.89717i
\(719\) −24.8627 + 18.0638i −0.927224 + 0.673667i −0.945311 0.326169i \(-0.894242\pi\)
0.0180878 + 0.999836i \(0.494242\pi\)
\(720\) 0 0
\(721\) −1.86852 1.35756i −0.0695875 0.0505583i
\(722\) −27.8186 + 38.2891i −1.03530 + 1.42497i
\(723\) −2.20221 0.715542i −0.0819011 0.0266113i
\(724\) −1.05888 −0.0393529
\(725\) 0 0
\(726\) −26.4302 −0.980915
\(727\) 6.24688 + 2.02973i 0.231684 + 0.0752787i 0.422558 0.906336i \(-0.361132\pi\)
−0.190874 + 0.981615i \(0.561132\pi\)
\(728\) −22.9714 + 31.6174i −0.851377 + 1.17182i
\(729\) 0.809017 + 0.587785i 0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) 8.22510 5.97589i 0.304216 0.221026i
\(732\) 38.0086i 1.40484i
\(733\) 18.7666 + 25.8300i 0.693159 + 0.954051i 0.999997 + 0.00228977i \(0.000728857\pi\)
−0.306838 + 0.951762i \(0.599271\pi\)
\(734\) −12.2134 37.5891i −0.450806 1.38744i
\(735\) 0 0
\(736\) 21.4889 66.1360i 0.792091 2.43781i
\(737\) 12.7688 4.14885i 0.470346 0.152825i
\(738\) −28.7789 + 9.35085i −1.05937 + 0.344209i
\(739\) 4.73017 14.5580i 0.174002 0.535524i −0.825584 0.564279i \(-0.809154\pi\)
0.999586 + 0.0287550i \(0.00915426\pi\)
\(740\) 0 0
\(741\) 0.974196 + 2.99827i 0.0357880 + 0.110144i
\(742\) 6.79082 + 9.34676i 0.249299 + 0.343130i
\(743\) 16.5455i 0.606995i 0.952832 + 0.303498i \(0.0981545\pi\)
−0.952832 + 0.303498i \(0.901846\pi\)
\(744\) −49.7236 + 36.1263i −1.82295 + 1.32445i
\(745\) 0 0
\(746\) −71.8225 52.1821i −2.62961 1.91052i
\(747\) −5.21649 + 7.17988i −0.190861 + 0.262698i
\(748\) −21.0580 6.84217i −0.769959 0.250175i
\(749\) −18.5769 −0.678786
\(750\) 0 0
\(751\) 46.0279 1.67958 0.839791 0.542911i \(-0.182678\pi\)
0.839791 + 0.542911i \(0.182678\pi\)
\(752\) 23.3650 + 7.59174i 0.852033 + 0.276842i
\(753\) 3.63184 4.99879i 0.132351 0.182166i
\(754\) −34.6632 25.1843i −1.26236 0.917159i
\(755\) 0 0
\(756\) 7.12476 5.17644i 0.259125 0.188265i
\(757\) 26.5282i 0.964184i 0.876121 + 0.482092i \(0.160123\pi\)
−0.876121 + 0.482092i \(0.839877\pi\)
\(758\) −23.9369 32.9463i −0.869427 1.19666i
\(759\) −1.35448 4.16865i −0.0491644 0.151312i
\(760\) 0 0
\(761\) −8.78353 + 27.0329i −0.318403 + 0.979943i 0.655928 + 0.754823i \(0.272277\pi\)
−0.974331 + 0.225120i \(0.927723\pi\)
\(762\) −51.7141 + 16.8029i −1.87341 + 0.608706i
\(763\) −5.53366 + 1.79800i −0.200332 + 0.0650918i
\(764\) 12.7756 39.3192i 0.462204 1.42252i
\(765\) 0 0
\(766\) 6.64947 + 20.4650i 0.240255 + 0.739429i
\(767\) 2.10236 + 2.89365i 0.0759119 + 0.104484i
\(768\) 14.3555i 0.518009i
\(769\) −7.24841 + 5.26628i −0.261384 + 0.189907i −0.710757 0.703438i \(-0.751647\pi\)
0.449373 + 0.893344i \(0.351647\pi\)
\(770\) 0 0
\(771\) 10.6983 + 7.77279i 0.385291 + 0.279930i
\(772\) 50.4034 69.3744i 1.81406 2.49684i
\(773\) 21.9734 + 7.13959i 0.790329 + 0.256793i 0.676244 0.736678i \(-0.263607\pi\)
0.114085 + 0.993471i \(0.463607\pi\)
\(774\) 6.94834 0.249753
\(775\) 0 0
\(776\) −93.1752 −3.34479
\(777\) −7.35148 2.38864i −0.263733 0.0856920i
\(778\) −1.69727 + 2.33609i −0.0608501 + 0.0837530i
\(779\) 10.7283 + 7.79455i 0.384380 + 0.279269i
\(780\) 0 0
\(781\) 5.22343 3.79504i 0.186909 0.135797i
\(782\) 42.9232i 1.53493i
\(783\) 3.50082 + 4.81846i 0.125109 + 0.172198i
\(784\) 16.4433 + 50.6072i 0.587260 + 1.80740i
\(785\) 0 0
\(786\) −2.53264 + 7.79465i −0.0903361 + 0.278026i
\(787\) −1.93436 + 0.628511i −0.0689524 + 0.0224040i −0.343290 0.939229i \(-0.611541\pi\)
0.274338 + 0.961633i \(0.411541\pi\)
\(788\) 85.0794 27.6440i 3.03083 0.984776i
\(789\) −2.15583 + 6.63498i −0.0767497 + 0.236211i
\(790\) 0 0
\(791\) 3.15503 + 9.71018i 0.112180 + 0.345254i
\(792\) −5.48686 7.55201i −0.194967 0.268349i
\(793\) 19.4931i 0.692220i
\(794\) 52.6376 38.2435i 1.86804 1.35721i
\(795\) 0 0
\(796\) 8.52449 + 6.19340i 0.302142 + 0.219519i
\(797\) 7.16646 9.86379i 0.253849 0.349393i −0.663006 0.748614i \(-0.730719\pi\)
0.916855 + 0.399221i \(0.130719\pi\)
\(798\) −5.07674 1.64953i −0.179715 0.0583928i
\(799\) −7.54024 −0.266754
\(800\) 0 0
\(801\) 15.4436 0.545673
\(802\) −5.09359 1.65501i −0.179861 0.0584404i
\(803\) −2.09299 + 2.88075i −0.0738599 + 0.101659i
\(804\) −52.5583 38.1858i −1.85359 1.34671i
\(805\) 0 0
\(806\) −41.3396 + 30.0350i −1.45612 + 1.05794i
\(807\) 23.7199i 0.834979i
\(808\) −68.9936 94.9616i −2.42719 3.34074i
\(809\) −2.72972 8.40121i −0.0959718 0.295371i 0.891534 0.452954i \(-0.149630\pi\)
−0.987506 + 0.157583i \(0.949630\pi\)
\(810\) 0 0
\(811\) −4.30102 + 13.2372i −0.151029 + 0.464820i −0.997737 0.0672381i \(-0.978581\pi\)
0.846708 + 0.532058i \(0.178581\pi\)
\(812\) 49.8850 16.2086i 1.75062 0.568811i
\(813\) 27.5721 8.95871i 0.966995 0.314196i
\(814\) −4.10438 + 12.6320i −0.143858 + 0.442750i
\(815\) 0 0
\(816\) 15.5636 + 47.8998i 0.544835 + 1.67683i
\(817\) −1.78980 2.46344i −0.0626170 0.0861850i
\(818\) 17.9085i 0.626158i
\(819\) 3.65401 2.65479i 0.127681 0.0927660i
\(820\) 0 0
\(821\) 23.8603 + 17.3355i 0.832731 + 0.605015i 0.920331 0.391141i \(-0.127920\pi\)
−0.0875994 + 0.996156i \(0.527920\pi\)
\(822\) 32.3936 44.5860i 1.12986 1.55511i
\(823\) −39.9121 12.9682i −1.39125 0.452044i −0.484898 0.874571i \(-0.661143\pi\)
−0.906350 + 0.422527i \(0.861143\pi\)
\(824\) 11.8460 0.412675
\(825\) 0 0
\(826\) −6.05624 −0.210724
\(827\) −35.6336 11.5781i −1.23910 0.402609i −0.385099 0.922875i \(-0.625833\pi\)
−0.854004 + 0.520266i \(0.825833\pi\)
\(828\) −12.4666 + 17.1587i −0.433243 + 0.596307i
\(829\) −7.73108 5.61696i −0.268512 0.195085i 0.445379 0.895342i \(-0.353069\pi\)
−0.713891 + 0.700257i \(0.753069\pi\)
\(830\) 0 0
\(831\) −6.94677 + 5.04712i −0.240981 + 0.175083i
\(832\) 54.5355i 1.89068i
\(833\) −9.59954 13.2126i −0.332604 0.457791i
\(834\) −15.2105 46.8131i −0.526696 1.62100i
\(835\) 0 0
\(836\) −2.04925 + 6.30695i −0.0708748 + 0.218130i
\(837\) 6.75545 2.19498i 0.233502 0.0758695i
\(838\) 54.5708 17.7311i 1.88512 0.612512i
\(839\) −16.9128 + 52.0522i −0.583895 + 1.79704i 0.0197702 + 0.999805i \(0.493707\pi\)
−0.603665 + 0.797238i \(0.706293\pi\)
\(840\) 0 0
\(841\) 2.00037 + 6.15651i 0.0689783 + 0.212294i
\(842\) −35.2787 48.5570i −1.21579 1.67338i
\(843\) 17.1661i 0.591233i
\(844\) −100.603 + 73.0922i −3.46289 + 2.51594i
\(845\) 0 0
\(846\) −4.16908 3.02901i −0.143336 0.104140i
\(847\) 9.75371 13.4248i 0.335141 0.461283i
\(848\) −31.0499 10.0887i −1.06626 0.346448i
\(849\) −9.62005 −0.330159
\(850\) 0 0
\(851\) 18.6159 0.638144
\(852\) −29.7128 9.65426i −1.01794 0.330750i
\(853\) −8.99706 + 12.3834i −0.308053 + 0.423999i −0.934773 0.355246i \(-0.884397\pi\)
0.626720 + 0.779245i \(0.284397\pi\)
\(854\) 26.7026 + 19.4005i 0.913743 + 0.663873i
\(855\) 0 0
\(856\) 77.0836 56.0045i 2.63466 1.91419i
\(857\) 8.66910i 0.296131i 0.988978 + 0.148065i \(0.0473046\pi\)
−0.988978 + 0.148065i \(0.952695\pi\)
\(858\) −4.56171 6.27865i −0.155734 0.214350i
\(859\) 9.39653 + 28.9195i 0.320605 + 0.986722i 0.973385 + 0.229174i \(0.0736026\pi\)
−0.652780 + 0.757547i \(0.726397\pi\)
\(860\) 0 0
\(861\) 5.87087 18.0687i 0.200079 0.615779i
\(862\) 77.7211 25.2531i 2.64719 0.860125i
\(863\) 17.1595 5.57545i 0.584115 0.189791i −0.00202803 0.999998i \(-0.500646\pi\)
0.586143 + 0.810207i \(0.300646\pi\)
\(864\) −5.28899 + 16.2779i −0.179935 + 0.553784i
\(865\) 0 0
\(866\) −0.478808 1.47362i −0.0162706 0.0500756i
\(867\) 0.906354 + 1.24749i 0.0307814 + 0.0423669i
\(868\) 62.5548i 2.12325i
\(869\) −3.49465 + 2.53901i −0.118548 + 0.0861301i
\(870\) 0 0
\(871\) −26.9551 19.5840i −0.913338 0.663579i
\(872\) 17.5411 24.1432i 0.594015 0.817591i
\(873\) 10.2412 + 3.32756i 0.346611 + 0.112621i
\(874\) 12.8556 0.434848
\(875\) 0 0
\(876\) 17.2301 0.582149
\(877\) −21.2140 6.89285i −0.716346 0.232755i −0.0719076 0.997411i \(-0.522909\pi\)
−0.644438 + 0.764656i \(0.722909\pi\)
\(878\) −20.2235 + 27.8352i −0.682509 + 0.939393i
\(879\) −13.6079 9.88669i −0.458982 0.333470i
\(880\) 0 0
\(881\) −6.27761 + 4.56095i −0.211498 + 0.153662i −0.688491 0.725245i \(-0.741727\pi\)
0.476993 + 0.878907i \(0.341727\pi\)
\(882\) 11.1617i 0.375833i
\(883\) 11.7279 + 16.1421i 0.394675 + 0.543224i 0.959398 0.282057i \(-0.0910167\pi\)
−0.564722 + 0.825281i \(0.691017\pi\)
\(884\) 16.9798 + 52.2584i 0.571092 + 1.75764i
\(885\) 0 0
\(886\) −11.8861 + 36.5816i −0.399320 + 1.22898i
\(887\) 8.18183 2.65844i 0.274719 0.0892616i −0.168418 0.985716i \(-0.553866\pi\)
0.443137 + 0.896454i \(0.353866\pi\)
\(888\) 37.7056 12.2513i 1.26532 0.411126i
\(889\) 10.5496 32.4684i 0.353823 1.08895i
\(890\) 0 0
\(891\) 0.333373 + 1.02602i 0.0111684 + 0.0343729i
\(892\) 40.2297 + 55.3715i 1.34699 + 1.85397i
\(893\) 2.25832i 0.0755719i
\(894\) 1.53461 1.11496i 0.0513251 0.0372899i
\(895\) 0 0
\(896\) 27.9851 + 20.3323i 0.934916 + 0.679256i
\(897\) −6.39360 + 8.80004i −0.213476 + 0.293825i
\(898\) 30.5802 + 9.93611i 1.02047 + 0.331572i
\(899\) 42.3057 1.41097
\(900\) 0 0
\(901\) 10.0203 0.333824
\(902\) −31.0472 10.0879i −1.03376 0.335889i
\(903\) −2.56420 + 3.52932i −0.0853312 + 0.117448i
\(904\) −42.3652 30.7801i −1.40905 1.02373i
\(905\) 0 0
\(906\) −15.3157 + 11.1275i −0.508830 + 0.369687i
\(907\) 6.26125i 0.207902i −0.994582 0.103951i \(-0.966852\pi\)
0.994582 0.103951i \(-0.0331484\pi\)
\(908\) 80.6385 + 110.989i 2.67608 + 3.68331i
\(909\) 4.19195 + 12.9015i 0.139038 + 0.427915i
\(910\) 0 0
\(911\) 0.279838 0.861253i 0.00927145 0.0285346i −0.946314 0.323250i \(-0.895225\pi\)
0.955585 + 0.294715i \(0.0952247\pi\)
\(912\) 14.3461 4.66135i 0.475048 0.154353i
\(913\) −9.10571 + 2.95862i −0.301355 + 0.0979162i
\(914\) −6.82669 + 21.0104i −0.225807 + 0.694962i
\(915\) 0 0
\(916\) 3.21988 + 9.90978i 0.106388 + 0.327428i
\(917\) −3.02455 4.16293i −0.0998794 0.137472i
\(918\) 10.5646i 0.348682i
\(919\) 35.5913 25.8586i 1.17405 0.852997i 0.182561 0.983194i \(-0.441561\pi\)
0.991488 + 0.130198i \(0.0415612\pi\)
\(920\) 0 0
\(921\) 9.15903 + 6.65443i 0.301800 + 0.219271i
\(922\) 2.00926 2.76551i 0.0661714 0.0910771i
\(923\) −15.2385 4.95129i −0.501582 0.162974i
\(924\) 9.50081 0.312554
\(925\) 0 0
\(926\) −87.8029 −2.88538
\(927\) −1.30203 0.423056i −0.0427643 0.0138950i
\(928\) −59.9184 + 82.4707i −1.96692 + 2.70723i
\(929\) −29.7271 21.5980i −0.975313 0.708606i −0.0186568 0.999826i \(-0.505939\pi\)
−0.956656 + 0.291220i \(0.905939\pi\)
\(930\) 0 0
\(931\) −3.95722 + 2.87509i −0.129693 + 0.0942273i
\(932\) 2.74347i 0.0898652i
\(933\) 10.9113 + 15.0181i 0.357221 + 0.491672i
\(934\) 11.9857 + 36.8883i 0.392185 + 1.20702i
\(935\) 0 0
\(936\) −7.15855 + 22.0318i −0.233985 + 0.720131i
\(937\) 23.4426 7.61696i 0.765836 0.248835i 0.100055 0.994982i \(-0.468098\pi\)
0.665782 + 0.746147i \(0.268098\pi\)
\(938\) 53.6542 17.4333i 1.75187 0.569217i
\(939\) −2.99731 + 9.22478i −0.0978137 + 0.301039i
\(940\) 0 0
\(941\) −18.2777 56.2530i −0.595836 1.83379i −0.550520 0.834822i \(-0.685571\pi\)
−0.0453159 0.998973i \(-0.514429\pi\)
\(942\) −8.10045 11.1493i −0.263927 0.363264i
\(943\) 45.7546i 1.48998i
\(944\) 13.8456 10.0594i 0.450635 0.327406i
\(945\) 0 0
\(946\) 6.06439 + 4.40604i 0.197170 + 0.143253i
\(947\) 17.6900 24.3482i 0.574848 0.791210i −0.418271 0.908322i \(-0.637364\pi\)
0.993119 + 0.117112i \(0.0373638\pi\)
\(948\) 19.8789 + 6.45903i 0.645635 + 0.209780i
\(949\) 8.83661 0.286849
\(950\) 0 0
\(951\) −7.47647 −0.242441
\(952\) −54.5841 17.7354i −1.76908 0.574809i
\(953\) −12.1315 + 16.6975i −0.392977 + 0.540886i −0.958964 0.283528i \(-0.908495\pi\)
0.565987 + 0.824414i \(0.308495\pi\)
\(954\) 5.54032 + 4.02528i 0.179375 + 0.130323i
\(955\) 0 0
\(956\) 29.6036 21.5083i 0.957449 0.695628i
\(957\) 6.42538i 0.207703i
\(958\) −26.6316 36.6553i −0.860429 1.18428i
\(959\) 10.6924 + 32.9078i 0.345275 + 1.06265i
\(960\) 0 0
\(961\) 6.01162 18.5019i 0.193923 0.596834i
\(962\) 31.3480 10.1856i 1.01070 0.328396i
\(963\) −10.4726 + 3.40275i −0.337474 + 0.109652i
\(964\) −3.73527 + 11.4960i −0.120305 + 0.370260i
\(965\) 0 0
\(966\) −5.69146 17.5165i −0.183120 0.563585i
\(967\) −13.2849 18.2850i −0.427212 0.588007i 0.540098 0.841602i \(-0.318387\pi\)
−0.967311 + 0.253595i \(0.918387\pi\)
\(968\) 85.1103i 2.73555i
\(969\) −3.74552 + 2.72128i −0.120324 + 0.0874202i
\(970\) 0 0
\(971\) −19.5281 14.1880i −0.626687 0.455315i 0.228564 0.973529i \(-0.426597\pi\)
−0.855251 + 0.518214i \(0.826597\pi\)
\(972\) 3.06835 4.22323i 0.0984175 0.135460i
\(973\) 29.3913 + 9.54981i 0.942242 + 0.306153i
\(974\) 107.007 3.42874
\(975\) 0 0
\(976\) −93.2708 −2.98553
\(977\) −21.9224 7.12302i −0.701360 0.227886i −0.0634371 0.997986i \(-0.520206\pi\)
−0.637923 + 0.770100i \(0.720206\pi\)
\(978\) −38.3184 + 52.7407i −1.22529 + 1.68646i
\(979\) 13.4789 + 9.79299i 0.430787 + 0.312985i
\(980\) 0 0
\(981\) −2.79022 + 2.02721i −0.0890847 + 0.0647239i
\(982\) 37.6870i 1.20264i
\(983\) −17.5579 24.1664i −0.560010 0.770787i 0.431318 0.902200i \(-0.358049\pi\)
−0.991328 + 0.131413i \(0.958049\pi\)
\(984\) 30.1116 + 92.6738i 0.959921 + 2.95433i
\(985\) 0 0
\(986\) 19.4440 59.8424i 0.619222 1.90577i
\(987\) 3.07709 0.999807i 0.0979449 0.0318242i
\(988\) 15.6515 5.08550i 0.497942 0.161791i
\(989\) 3.24661 9.99204i 0.103236 0.317728i
\(990\) 0 0
\(991\) 5.14700 + 15.8408i 0.163500 + 0.503201i 0.998923 0.0464072i \(-0.0147772\pi\)
−0.835423 + 0.549608i \(0.814777\pi\)
\(992\) 71.4591 + 98.3550i 2.26883 + 3.12277i
\(993\) 25.2570i 0.801507i
\(994\) 21.9487 15.9466i 0.696169 0.505797i
\(995\) 0 0
\(996\) 37.4804 + 27.2311i 1.18761 + 0.862850i
\(997\) −7.34343 + 10.1074i −0.232569 + 0.320103i −0.909311 0.416116i \(-0.863391\pi\)
0.676743 + 0.736220i \(0.263391\pi\)
\(998\) −38.9246 12.6474i −1.23214 0.400346i
\(999\) −4.58187 −0.144964
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 375.2.i.d.274.6 24
5.2 odd 4 75.2.g.c.46.1 yes 12
5.3 odd 4 375.2.g.c.226.3 12
5.4 even 2 inner 375.2.i.d.274.1 24
15.2 even 4 225.2.h.d.46.3 12
25.6 even 5 inner 375.2.i.d.349.1 24
25.8 odd 20 375.2.g.c.151.3 12
25.9 even 10 1875.2.b.f.1249.1 12
25.12 odd 20 1875.2.a.j.1.1 6
25.13 odd 20 1875.2.a.k.1.6 6
25.16 even 5 1875.2.b.f.1249.12 12
25.17 odd 20 75.2.g.c.31.1 12
25.19 even 10 inner 375.2.i.d.349.6 24
75.17 even 20 225.2.h.d.181.3 12
75.38 even 20 5625.2.a.q.1.1 6
75.62 even 20 5625.2.a.p.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.c.31.1 12 25.17 odd 20
75.2.g.c.46.1 yes 12 5.2 odd 4
225.2.h.d.46.3 12 15.2 even 4
225.2.h.d.181.3 12 75.17 even 20
375.2.g.c.151.3 12 25.8 odd 20
375.2.g.c.226.3 12 5.3 odd 4
375.2.i.d.274.1 24 5.4 even 2 inner
375.2.i.d.274.6 24 1.1 even 1 trivial
375.2.i.d.349.1 24 25.6 even 5 inner
375.2.i.d.349.6 24 25.19 even 10 inner
1875.2.a.j.1.1 6 25.12 odd 20
1875.2.a.k.1.6 6 25.13 odd 20
1875.2.b.f.1249.1 12 25.9 even 10
1875.2.b.f.1249.12 12 25.16 even 5
5625.2.a.p.1.6 6 75.62 even 20
5625.2.a.q.1.1 6 75.38 even 20