Properties

Label 475.2.e.f.201.1
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
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] = [475,2,Mod(26,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(-0.975939 - 1.69038i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.f.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.08504 + 1.87935i) q^{2} +(-1.47594 + 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +O(q^{10})\) \(q+(-1.08504 + 1.87935i) q^{2} +(-1.47594 + 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +2.58045 q^{11} +7.99745 q^{12} +(-3.43332 - 5.94669i) q^{13} +(-0.641933 + 1.11186i) q^{14} +(1.03919 - 1.79993i) q^{16} +(2.61787 - 4.53429i) q^{17} +12.3990 q^{18} +(-2.26423 + 3.72468i) q^{19} +(-0.873195 + 1.51242i) q^{21} +(-2.79990 + 4.84957i) q^{22} +(-1.45072 - 2.51271i) q^{23} +(-2.27175 + 3.93478i) q^{24} +14.9012 q^{26} +8.01017 q^{27} +(-0.801431 - 1.38812i) q^{28} +(-3.52494 - 6.10538i) q^{29} -6.81421 q^{31} +(3.79432 + 6.57195i) q^{32} +(-3.80859 + 6.59667i) q^{33} +(5.68101 + 9.83980i) q^{34} +(-7.73984 + 13.4058i) q^{36} -4.82538 q^{37} +(-4.54320 - 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 + 5.39393i) q^{41} +(-1.89491 - 3.28208i) q^{42} +(-2.18013 + 3.77609i) q^{43} +(-3.49558 - 6.05452i) q^{44} +6.29636 q^{46} +(-1.27941 - 2.21600i) q^{47} +(3.06756 + 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 + 13.3847i) q^{51} +(-9.30181 + 16.1112i) q^{52} +(4.79573 + 8.30645i) q^{53} +(-8.69138 + 15.0539i) q^{54} +0.910615 q^{56} +(-6.17993 - 11.2857i) q^{57} +15.2989 q^{58} +(1.46221 - 2.53263i) q^{59} +(-1.16586 - 2.01932i) q^{61} +(7.39371 - 12.8063i) q^{62} +(-1.69013 - 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 - 14.3153i) q^{66} +(-2.15122 - 3.72603i) q^{67} -14.1851 q^{68} +8.56468 q^{69} +(6.74645 - 11.6852i) q^{71} +(-4.39714 - 7.61607i) q^{72} +(4.21337 - 7.29777i) q^{73} +(5.23574 - 9.06858i) q^{74} +(11.8064 + 0.266962i) q^{76} +1.52665 q^{77} +(-21.9933 + 38.0935i) q^{78} +(-2.93630 + 5.08583i) q^{79} +(-3.25215 + 5.63288i) q^{81} +(-6.75806 - 11.7053i) q^{82} -4.02036 q^{83} +4.73145 q^{84} +(-4.73107 - 8.19445i) q^{86} +20.8104 q^{87} +3.97180 q^{88} +(-1.85823 - 3.21855i) q^{89} +(-2.03122 - 3.51818i) q^{91} +(-3.93039 + 6.80764i) q^{92} +(10.0574 - 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(-1.26285 + 2.18732i) q^{97} +(7.21552 - 12.4977i) q^{98} +(-7.37182 - 12.7684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.08504 + 1.87935i −0.767241 + 1.32890i 0.171812 + 0.985130i \(0.445038\pi\)
−0.939053 + 0.343771i \(0.888295\pi\)
\(3\) −1.47594 + 2.55640i −0.852134 + 1.47594i 0.0271449 + 0.999632i \(0.491358\pi\)
−0.879279 + 0.476308i \(0.841975\pi\)
\(4\) −1.35464 2.34630i −0.677319 1.17315i
\(5\) 0 0
\(6\) −3.20292 5.54761i −1.30758 2.26480i
\(7\) 0.591620 0.223611 0.111806 0.993730i \(-0.464337\pi\)
0.111806 + 0.993730i \(0.464337\pi\)
\(8\) 1.53919 0.544185
\(9\) −2.85679 4.94811i −0.952264 1.64937i
\(10\) 0 0
\(11\) 2.58045 0.778036 0.389018 0.921230i \(-0.372814\pi\)
0.389018 + 0.921230i \(0.372814\pi\)
\(12\) 7.99745 2.30867
\(13\) −3.43332 5.94669i −0.952232 1.64931i −0.740579 0.671969i \(-0.765449\pi\)
−0.211653 0.977345i \(-0.567885\pi\)
\(14\) −0.641933 + 1.11186i −0.171564 + 0.297157i
\(15\) 0 0
\(16\) 1.03919 1.79993i 0.259797 0.449982i
\(17\) 2.61787 4.53429i 0.634927 1.09973i −0.351603 0.936149i \(-0.614363\pi\)
0.986531 0.163577i \(-0.0523033\pi\)
\(18\) 12.3990 2.92247
\(19\) −2.26423 + 3.72468i −0.519449 + 0.854501i
\(20\) 0 0
\(21\) −0.873195 + 1.51242i −0.190547 + 0.330037i
\(22\) −2.79990 + 4.84957i −0.596941 + 1.03393i
\(23\) −1.45072 2.51271i −0.302495 0.523937i 0.674205 0.738544i \(-0.264486\pi\)
−0.976701 + 0.214607i \(0.931153\pi\)
\(24\) −2.27175 + 3.93478i −0.463719 + 0.803185i
\(25\) 0 0
\(26\) 14.9012 2.92237
\(27\) 8.01017 1.54156
\(28\) −0.801431 1.38812i −0.151456 0.262330i
\(29\) −3.52494 6.10538i −0.654565 1.13374i −0.982003 0.188867i \(-0.939518\pi\)
0.327438 0.944873i \(-0.393815\pi\)
\(30\) 0 0
\(31\) −6.81421 −1.22387 −0.611934 0.790909i \(-0.709608\pi\)
−0.611934 + 0.790909i \(0.709608\pi\)
\(32\) 3.79432 + 6.57195i 0.670747 + 1.16177i
\(33\) −3.80859 + 6.59667i −0.662990 + 1.14833i
\(34\) 5.68101 + 9.83980i 0.974285 + 1.68751i
\(35\) 0 0
\(36\) −7.73984 + 13.4058i −1.28997 + 2.23430i
\(37\) −4.82538 −0.793287 −0.396644 0.917973i \(-0.629825\pi\)
−0.396644 + 0.917973i \(0.629825\pi\)
\(38\) −4.54320 8.29672i −0.737005 1.34591i
\(39\) 20.2695 3.24572
\(40\) 0 0
\(41\) −3.11419 + 5.39393i −0.486355 + 0.842391i −0.999877 0.0156852i \(-0.995007\pi\)
0.513522 + 0.858076i \(0.328340\pi\)
\(42\) −1.89491 3.28208i −0.292391 0.506436i
\(43\) −2.18013 + 3.77609i −0.332467 + 0.575849i −0.982995 0.183633i \(-0.941214\pi\)
0.650528 + 0.759482i \(0.274548\pi\)
\(44\) −3.49558 6.05452i −0.526978 0.912753i
\(45\) 0 0
\(46\) 6.29636 0.928348
\(47\) −1.27941 2.21600i −0.186621 0.323237i 0.757501 0.652834i \(-0.226420\pi\)
−0.944121 + 0.329598i \(0.893087\pi\)
\(48\) 3.06756 + 5.31317i 0.442764 + 0.766890i
\(49\) −6.64999 −0.949998
\(50\) 0 0
\(51\) 7.72764 + 13.3847i 1.08209 + 1.87423i
\(52\) −9.30181 + 16.1112i −1.28993 + 2.23422i
\(53\) 4.79573 + 8.30645i 0.658745 + 1.14098i 0.980941 + 0.194306i \(0.0622456\pi\)
−0.322196 + 0.946673i \(0.604421\pi\)
\(54\) −8.69138 + 15.0539i −1.18275 + 2.04858i
\(55\) 0 0
\(56\) 0.910615 0.121686
\(57\) −6.17993 11.2857i −0.818551 1.49483i
\(58\) 15.2989 2.00884
\(59\) 1.46221 2.53263i 0.190364 0.329720i −0.755007 0.655717i \(-0.772367\pi\)
0.945371 + 0.325997i \(0.105700\pi\)
\(60\) 0 0
\(61\) −1.16586 2.01932i −0.149273 0.258548i 0.781686 0.623672i \(-0.214360\pi\)
−0.930959 + 0.365124i \(0.881027\pi\)
\(62\) 7.39371 12.8063i 0.939003 1.62640i
\(63\) −1.69013 2.92740i −0.212937 0.368818i
\(64\) −12.3112 −1.53891
\(65\) 0 0
\(66\) −8.26497 14.3153i −1.01735 1.76210i
\(67\) −2.15122 3.72603i −0.262814 0.455207i 0.704175 0.710027i \(-0.251317\pi\)
−0.966989 + 0.254820i \(0.917984\pi\)
\(68\) −14.1851 −1.72019
\(69\) 8.56468 1.03107
\(70\) 0 0
\(71\) 6.74645 11.6852i 0.800656 1.38678i −0.118528 0.992951i \(-0.537818\pi\)
0.919185 0.393827i \(-0.128849\pi\)
\(72\) −4.39714 7.61607i −0.518208 0.897563i
\(73\) 4.21337 7.29777i 0.493137 0.854139i −0.506831 0.862045i \(-0.669183\pi\)
0.999969 + 0.00790620i \(0.00251665\pi\)
\(74\) 5.23574 9.06858i 0.608643 1.05420i
\(75\) 0 0
\(76\) 11.8064 + 0.266962i 1.35429 + 0.0306226i
\(77\) 1.52665 0.173978
\(78\) −21.9933 + 38.0935i −2.49025 + 4.31324i
\(79\) −2.93630 + 5.08583i −0.330360 + 0.572200i −0.982582 0.185827i \(-0.940503\pi\)
0.652222 + 0.758028i \(0.273837\pi\)
\(80\) 0 0
\(81\) −3.25215 + 5.63288i −0.361350 + 0.625876i
\(82\) −6.75806 11.7053i −0.746303 1.29263i
\(83\) −4.02036 −0.441292 −0.220646 0.975354i \(-0.570816\pi\)
−0.220646 + 0.975354i \(0.570816\pi\)
\(84\) 4.73145 0.516244
\(85\) 0 0
\(86\) −4.73107 8.19445i −0.510164 0.883630i
\(87\) 20.8104 2.23111
\(88\) 3.97180 0.423396
\(89\) −1.85823 3.21855i −0.196972 0.341166i 0.750573 0.660787i \(-0.229778\pi\)
−0.947545 + 0.319622i \(0.896444\pi\)
\(90\) 0 0
\(91\) −2.03122 3.51818i −0.212930 0.368805i
\(92\) −3.93039 + 6.80764i −0.409772 + 0.709745i
\(93\) 10.0574 17.4199i 1.04290 1.80636i
\(94\) 5.55285 0.572733
\(95\) 0 0
\(96\) −22.4007 −2.28627
\(97\) −1.26285 + 2.18732i −0.128223 + 0.222089i −0.922988 0.384828i \(-0.874261\pi\)
0.794765 + 0.606917i \(0.207594\pi\)
\(98\) 7.21552 12.4977i 0.728878 1.26245i
\(99\) −7.37182 12.7684i −0.740895 1.28327i
\(100\) 0 0
\(101\) −0.692736 1.19985i −0.0689298 0.119390i 0.829501 0.558506i \(-0.188625\pi\)
−0.898430 + 0.439116i \(0.855292\pi\)
\(102\) −33.5393 −3.32088
\(103\) 0.166774 0.0164328 0.00821638 0.999966i \(-0.497385\pi\)
0.00821638 + 0.999966i \(0.497385\pi\)
\(104\) −5.28453 9.15307i −0.518191 0.897533i
\(105\) 0 0
\(106\) −20.8143 −2.02166
\(107\) −4.51729 −0.436703 −0.218351 0.975870i \(-0.570068\pi\)
−0.218351 + 0.975870i \(0.570068\pi\)
\(108\) −10.8509 18.7943i −1.04413 1.80848i
\(109\) 5.35464 9.27450i 0.512881 0.888336i −0.487007 0.873398i \(-0.661911\pi\)
0.999888 0.0149384i \(-0.00475523\pi\)
\(110\) 0 0
\(111\) 7.12196 12.3356i 0.675987 1.17084i
\(112\) 0.614805 1.06487i 0.0580936 0.100621i
\(113\) 13.2065 1.24237 0.621183 0.783665i \(-0.286652\pi\)
0.621183 + 0.783665i \(0.286652\pi\)
\(114\) 27.9152 + 0.631206i 2.61450 + 0.0591178i
\(115\) 0 0
\(116\) −9.55004 + 16.5411i −0.886699 + 1.53581i
\(117\) −19.6166 + 33.9769i −1.81355 + 3.14117i
\(118\) 3.17313 + 5.49602i 0.292110 + 0.505950i
\(119\) 1.54879 2.68257i 0.141977 0.245911i
\(120\) 0 0
\(121\) −4.34127 −0.394661
\(122\) 5.06002 0.458113
\(123\) −9.19271 15.9222i −0.828879 1.43566i
\(124\) 9.23079 + 15.9882i 0.828949 + 1.43578i
\(125\) 0 0
\(126\) 7.33548 0.653496
\(127\) −0.860805 1.49096i −0.0763841 0.132301i 0.825303 0.564690i \(-0.191004\pi\)
−0.901687 + 0.432389i \(0.857671\pi\)
\(128\) 5.76959 9.99323i 0.509965 0.883285i
\(129\) −6.43548 11.1466i −0.566612 0.981401i
\(130\) 0 0
\(131\) −1.64201 + 2.84405i −0.143463 + 0.248486i −0.928799 0.370585i \(-0.879157\pi\)
0.785335 + 0.619071i \(0.212491\pi\)
\(132\) 20.6370 1.79622
\(133\) −1.33956 + 2.20360i −0.116155 + 0.191076i
\(134\) 9.33668 0.806567
\(135\) 0 0
\(136\) 4.02940 6.97913i 0.345518 0.598455i
\(137\) −4.07541 7.05882i −0.348186 0.603075i 0.637741 0.770251i \(-0.279869\pi\)
−0.985927 + 0.167175i \(0.946536\pi\)
\(138\) −9.29304 + 16.0960i −0.791076 + 1.37018i
\(139\) 7.81401 + 13.5343i 0.662776 + 1.14796i 0.979883 + 0.199571i \(0.0639550\pi\)
−0.317108 + 0.948390i \(0.602712\pi\)
\(140\) 0 0
\(141\) 7.55331 0.636103
\(142\) 14.6404 + 25.3579i 1.22859 + 2.12799i
\(143\) −8.85952 15.3451i −0.740870 1.28323i
\(144\) −11.8750 −0.989582
\(145\) 0 0
\(146\) 9.14337 + 15.8368i 0.756711 + 1.31066i
\(147\) 9.81497 17.0000i 0.809525 1.40214i
\(148\) 6.53664 + 11.3218i 0.537308 + 0.930646i
\(149\) −1.61005 + 2.78869i −0.131900 + 0.228458i −0.924409 0.381402i \(-0.875441\pi\)
0.792509 + 0.609861i \(0.208775\pi\)
\(150\) 0 0
\(151\) −11.1226 −0.905142 −0.452571 0.891728i \(-0.649493\pi\)
−0.452571 + 0.891728i \(0.649493\pi\)
\(152\) −3.48507 + 5.73299i −0.282677 + 0.465007i
\(153\) −29.9149 −2.41847
\(154\) −1.65648 + 2.86910i −0.133483 + 0.231199i
\(155\) 0 0
\(156\) −27.4578 47.5583i −2.19838 3.80771i
\(157\) −10.7157 + 18.5602i −0.855209 + 1.48127i 0.0212418 + 0.999774i \(0.493238\pi\)
−0.876451 + 0.481491i \(0.840095\pi\)
\(158\) −6.37203 11.0367i −0.506932 0.878032i
\(159\) −28.3128 −2.24535
\(160\) 0 0
\(161\) −0.858273 1.48657i −0.0676414 0.117158i
\(162\) −7.05744 12.2238i −0.554485 0.960396i
\(163\) 10.3129 0.807768 0.403884 0.914810i \(-0.367660\pi\)
0.403884 + 0.914810i \(0.367660\pi\)
\(164\) 16.8744 1.31767
\(165\) 0 0
\(166\) 4.36226 7.55566i 0.338577 0.586433i
\(167\) −3.25342 5.63509i −0.251757 0.436056i 0.712252 0.701923i \(-0.247675\pi\)
−0.964010 + 0.265867i \(0.914342\pi\)
\(168\) −1.34401 + 2.32790i −0.103693 + 0.179601i
\(169\) −17.0754 + 29.5754i −1.31349 + 2.27503i
\(170\) 0 0
\(171\) 24.8986 + 0.562995i 1.90404 + 0.0430533i
\(172\) 11.8131 0.900744
\(173\) −3.13027 + 5.42179i −0.237990 + 0.412211i −0.960137 0.279528i \(-0.909822\pi\)
0.722147 + 0.691739i \(0.243155\pi\)
\(174\) −22.5802 + 39.1100i −1.71180 + 2.96492i
\(175\) 0 0
\(176\) 2.68158 4.64463i 0.202131 0.350102i
\(177\) 4.31628 + 7.47601i 0.324431 + 0.561931i
\(178\) 8.06505 0.604501
\(179\) 23.1893 1.73325 0.866624 0.498961i \(-0.166285\pi\)
0.866624 + 0.498961i \(0.166285\pi\)
\(180\) 0 0
\(181\) 1.59948 + 2.77039i 0.118889 + 0.205921i 0.919328 0.393493i \(-0.128733\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(182\) 8.81585 0.653474
\(183\) 6.88294 0.508801
\(184\) −2.23293 3.86754i −0.164614 0.285119i
\(185\) 0 0
\(186\) 21.8253 + 37.8026i 1.60031 + 2.77182i
\(187\) 6.75529 11.7005i 0.493996 0.855626i
\(188\) −3.46627 + 6.00375i −0.252803 + 0.437868i
\(189\) 4.73898 0.344710
\(190\) 0 0
\(191\) 18.9443 1.37076 0.685382 0.728184i \(-0.259635\pi\)
0.685382 + 0.728184i \(0.259635\pi\)
\(192\) 18.1706 31.4725i 1.31135 2.27133i
\(193\) 0.515269 0.892472i 0.0370899 0.0642415i −0.846885 0.531777i \(-0.821525\pi\)
0.883974 + 0.467535i \(0.154858\pi\)
\(194\) −2.74049 4.74667i −0.196756 0.340791i
\(195\) 0 0
\(196\) 9.00832 + 15.6029i 0.643452 + 1.11449i
\(197\) −18.5515 −1.32174 −0.660868 0.750502i \(-0.729812\pi\)
−0.660868 + 0.750502i \(0.729812\pi\)
\(198\) 31.9950 2.27378
\(199\) −11.3166 19.6010i −0.802215 1.38948i −0.918155 0.396221i \(-0.870321\pi\)
0.115940 0.993256i \(-0.463012\pi\)
\(200\) 0 0
\(201\) 12.7003 0.895810
\(202\) 3.00659 0.211543
\(203\) −2.08542 3.61206i −0.146368 0.253517i
\(204\) 20.9363 36.2627i 1.46583 2.53890i
\(205\) 0 0
\(206\) −0.180957 + 0.313427i −0.0126079 + 0.0218375i
\(207\) −8.28879 + 14.3566i −0.576111 + 0.997853i
\(208\) −14.2715 −0.989549
\(209\) −5.84273 + 9.61137i −0.404150 + 0.664832i
\(210\) 0 0
\(211\) −6.21978 + 10.7730i −0.428187 + 0.741642i −0.996712 0.0810240i \(-0.974181\pi\)
0.568525 + 0.822666i \(0.307514\pi\)
\(212\) 12.9930 22.5045i 0.892360 1.54561i
\(213\) 19.9147 + 34.4933i 1.36453 + 2.36344i
\(214\) 4.90145 8.48956i 0.335056 0.580335i
\(215\) 0 0
\(216\) 12.3292 0.838893
\(217\) −4.03142 −0.273671
\(218\) 11.6200 + 20.1265i 0.787008 + 1.36314i
\(219\) 12.4373 + 21.5421i 0.840438 + 1.45568i
\(220\) 0 0
\(221\) −35.9520 −2.41839
\(222\) 15.4553 + 26.7693i 1.03729 + 1.79664i
\(223\) 9.58654 16.6044i 0.641962 1.11191i −0.343032 0.939324i \(-0.611454\pi\)
0.984994 0.172588i \(-0.0552128\pi\)
\(224\) 2.24479 + 3.88810i 0.149987 + 0.259784i
\(225\) 0 0
\(226\) −14.3297 + 24.8197i −0.953195 + 1.65098i
\(227\) −26.5208 −1.76025 −0.880123 0.474745i \(-0.842540\pi\)
−0.880123 + 0.474745i \(0.842540\pi\)
\(228\) −18.1080 + 29.7880i −1.19923 + 1.97276i
\(229\) −8.81023 −0.582196 −0.291098 0.956693i \(-0.594021\pi\)
−0.291098 + 0.956693i \(0.594021\pi\)
\(230\) 0 0
\(231\) −2.25324 + 3.90272i −0.148252 + 0.256780i
\(232\) −5.42555 9.39733i −0.356205 0.616965i
\(233\) 2.25616 3.90778i 0.147806 0.256007i −0.782610 0.622512i \(-0.786112\pi\)
0.930416 + 0.366505i \(0.119446\pi\)
\(234\) −42.5697 73.7328i −2.78287 4.82006i
\(235\) 0 0
\(236\) −7.92308 −0.515749
\(237\) −8.66761 15.0127i −0.563022 0.975182i
\(238\) 3.36100 + 5.82142i 0.217861 + 0.377347i
\(239\) −7.82431 −0.506112 −0.253056 0.967452i \(-0.581436\pi\)
−0.253056 + 0.967452i \(0.581436\pi\)
\(240\) 0 0
\(241\) −13.6697 23.6766i −0.880541 1.52514i −0.850740 0.525586i \(-0.823846\pi\)
−0.0298010 0.999556i \(-0.509487\pi\)
\(242\) 4.71046 8.15876i 0.302800 0.524465i
\(243\) 2.41531 + 4.18345i 0.154942 + 0.268368i
\(244\) −3.15863 + 5.47091i −0.202210 + 0.350239i
\(245\) 0 0
\(246\) 39.8979 2.54380
\(247\) 29.9233 + 0.676612i 1.90398 + 0.0430518i
\(248\) −10.4884 −0.666011
\(249\) 5.93380 10.2777i 0.376040 0.651320i
\(250\) 0 0
\(251\) 8.11886 + 14.0623i 0.512458 + 0.887603i 0.999896 + 0.0144451i \(0.00459818\pi\)
−0.487438 + 0.873158i \(0.662068\pi\)
\(252\) −4.57904 + 7.93113i −0.288452 + 0.499614i
\(253\) −3.74350 6.48394i −0.235352 0.407642i
\(254\) 3.73604 0.234420
\(255\) 0 0
\(256\) 0.209275 + 0.362476i 0.0130797 + 0.0226547i
\(257\) 4.57174 + 7.91848i 0.285177 + 0.493941i 0.972652 0.232267i \(-0.0746143\pi\)
−0.687475 + 0.726208i \(0.741281\pi\)
\(258\) 27.9311 1.73891
\(259\) −2.85479 −0.177388
\(260\) 0 0
\(261\) −20.1400 + 34.8836i −1.24664 + 2.15924i
\(262\) −3.56331 6.17183i −0.220142 0.381297i
\(263\) 7.64861 13.2478i 0.471634 0.816894i −0.527840 0.849344i \(-0.676998\pi\)
0.999473 + 0.0324505i \(0.0103311\pi\)
\(264\) −5.86214 + 10.1535i −0.360790 + 0.624906i
\(265\) 0 0
\(266\) −2.68785 4.90850i −0.164803 0.300960i
\(267\) 10.9705 0.671386
\(268\) −5.82826 + 10.0948i −0.356017 + 0.616640i
\(269\) 7.07334 12.2514i 0.431269 0.746981i −0.565714 0.824602i \(-0.691399\pi\)
0.996983 + 0.0776213i \(0.0247325\pi\)
\(270\) 0 0
\(271\) 5.68158 9.84078i 0.345131 0.597785i −0.640246 0.768170i \(-0.721168\pi\)
0.985378 + 0.170385i \(0.0545010\pi\)
\(272\) −5.44093 9.42396i −0.329905 0.571412i
\(273\) 11.9918 0.725779
\(274\) 17.6880 1.06857
\(275\) 0 0
\(276\) −11.6020 20.0953i −0.698360 1.20960i
\(277\) 18.9102 1.13620 0.568101 0.822959i \(-0.307678\pi\)
0.568101 + 0.822959i \(0.307678\pi\)
\(278\) −33.9142 −2.03404
\(279\) 19.4668 + 33.7175i 1.16545 + 2.01861i
\(280\) 0 0
\(281\) 13.9438 + 24.1513i 0.831816 + 1.44075i 0.896596 + 0.442849i \(0.146032\pi\)
−0.0647802 + 0.997900i \(0.520635\pi\)
\(282\) −8.19567 + 14.1953i −0.488045 + 0.845318i
\(283\) −7.19798 + 12.4673i −0.427876 + 0.741102i −0.996684 0.0813677i \(-0.974071\pi\)
0.568809 + 0.822470i \(0.307405\pi\)
\(284\) −36.5560 −2.16920
\(285\) 0 0
\(286\) 38.4519 2.27371
\(287\) −1.84242 + 3.19116i −0.108754 + 0.188368i
\(288\) 21.6792 37.5494i 1.27746 2.21262i
\(289\) −5.20651 9.01794i −0.306265 0.530467i
\(290\) 0 0
\(291\) −3.72778 6.45670i −0.218526 0.378498i
\(292\) −22.8303 −1.33605
\(293\) 2.63178 0.153750 0.0768752 0.997041i \(-0.475506\pi\)
0.0768752 + 0.997041i \(0.475506\pi\)
\(294\) 21.2993 + 36.8915i 1.24220 + 2.15156i
\(295\) 0 0
\(296\) −7.42717 −0.431695
\(297\) 20.6699 1.19939
\(298\) −3.49395 6.05169i −0.202399 0.350565i
\(299\) −9.96155 + 17.2539i −0.576091 + 0.997819i
\(300\) 0 0
\(301\) −1.28981 + 2.23401i −0.0743433 + 0.128766i
\(302\) 12.0685 20.9032i 0.694463 1.20284i
\(303\) 4.08974 0.234950
\(304\) 4.35120 + 7.94610i 0.249559 + 0.455740i
\(305\) 0 0
\(306\) 32.4589 56.2205i 1.85555 3.21391i
\(307\) 8.41257 14.5710i 0.480131 0.831611i −0.519609 0.854404i \(-0.673923\pi\)
0.999740 + 0.0227929i \(0.00725584\pi\)
\(308\) −2.06805 3.58197i −0.117838 0.204102i
\(309\) −0.246149 + 0.426342i −0.0140029 + 0.0242538i
\(310\) 0 0
\(311\) −18.3273 −1.03924 −0.519622 0.854396i \(-0.673927\pi\)
−0.519622 + 0.854396i \(0.673927\pi\)
\(312\) 31.1986 1.76627
\(313\) 11.7527 + 20.3562i 0.664299 + 1.15060i 0.979475 + 0.201567i \(0.0646033\pi\)
−0.315176 + 0.949033i \(0.602063\pi\)
\(314\) −23.2541 40.2772i −1.31230 2.27298i
\(315\) 0 0
\(316\) 15.9105 0.895036
\(317\) 1.94177 + 3.36324i 0.109061 + 0.188899i 0.915390 0.402568i \(-0.131882\pi\)
−0.806329 + 0.591467i \(0.798549\pi\)
\(318\) 30.7207 53.2097i 1.72273 2.98385i
\(319\) −9.09594 15.7546i −0.509275 0.882090i
\(320\) 0 0
\(321\) 6.66724 11.5480i 0.372129 0.644546i
\(322\) 3.72505 0.207589
\(323\) 10.9613 + 20.0174i 0.609905 + 1.11380i
\(324\) 17.6219 0.978996
\(325\) 0 0
\(326\) −11.1899 + 19.3815i −0.619753 + 1.07344i
\(327\) 15.8062 + 27.3772i 0.874087 + 1.51396i
\(328\) −4.79333 + 8.30228i −0.264667 + 0.458417i
\(329\) −0.756923 1.31103i −0.0417305 0.0722793i
\(330\) 0 0
\(331\) 3.25821 0.179087 0.0895437 0.995983i \(-0.471459\pi\)
0.0895437 + 0.995983i \(0.471459\pi\)
\(332\) 5.44613 + 9.43297i 0.298895 + 0.517702i
\(333\) 13.7851 + 23.8765i 0.755419 + 1.30842i
\(334\) 14.1204 0.772635
\(335\) 0 0
\(336\) 1.81483 + 3.14338i 0.0990070 + 0.171485i
\(337\) 11.0987 19.2234i 0.604582 1.04717i −0.387535 0.921855i \(-0.626673\pi\)
0.992117 0.125312i \(-0.0399933\pi\)
\(338\) −37.0551 64.1813i −2.01553 3.49100i
\(339\) −19.4921 + 33.7612i −1.05866 + 1.83366i
\(340\) 0 0
\(341\) −17.5837 −0.952213
\(342\) −28.0741 + 46.1823i −1.51807 + 2.49725i
\(343\) −8.07560 −0.436042
\(344\) −3.35563 + 5.81212i −0.180923 + 0.313369i
\(345\) 0 0
\(346\) −6.79296 11.7658i −0.365192 0.632531i
\(347\) 1.49728 2.59336i 0.0803780 0.139219i −0.823034 0.567992i \(-0.807721\pi\)
0.903412 + 0.428773i \(0.141054\pi\)
\(348\) −28.1905 48.8274i −1.51117 2.61743i
\(349\) 15.1407 0.810461 0.405230 0.914215i \(-0.367191\pi\)
0.405230 + 0.914215i \(0.367191\pi\)
\(350\) 0 0
\(351\) −27.5015 47.6340i −1.46792 2.54251i
\(352\) 9.79106 + 16.9586i 0.521865 + 0.903897i
\(353\) −34.4369 −1.83289 −0.916446 0.400159i \(-0.868955\pi\)
−0.916446 + 0.400159i \(0.868955\pi\)
\(354\) −18.7334 −0.995668
\(355\) 0 0
\(356\) −5.03446 + 8.71994i −0.266826 + 0.462156i
\(357\) 4.57182 + 7.91863i 0.241967 + 0.419098i
\(358\) −25.1614 + 43.5808i −1.32982 + 2.30332i
\(359\) −1.58165 + 2.73950i −0.0834763 + 0.144585i −0.904741 0.425962i \(-0.859936\pi\)
0.821265 + 0.570548i \(0.193269\pi\)
\(360\) 0 0
\(361\) −8.74655 16.8671i −0.460345 0.887740i
\(362\) −6.94204 −0.364865
\(363\) 6.40744 11.0980i 0.336304 0.582495i
\(364\) −5.50314 + 9.53171i −0.288443 + 0.499597i
\(365\) 0 0
\(366\) −7.46829 + 12.9354i −0.390374 + 0.676147i
\(367\) −10.7270 18.5797i −0.559945 0.969853i −0.997500 0.0706615i \(-0.977489\pi\)
0.437556 0.899191i \(-0.355844\pi\)
\(368\) −6.03027 −0.314350
\(369\) 35.5864 1.85255
\(370\) 0 0
\(371\) 2.83725 + 4.91426i 0.147303 + 0.255136i
\(372\) −54.4963 −2.82550
\(373\) −33.1587 −1.71689 −0.858446 0.512904i \(-0.828570\pi\)
−0.858446 + 0.512904i \(0.828570\pi\)
\(374\) 14.6596 + 25.3911i 0.758028 + 1.31294i
\(375\) 0 0
\(376\) −1.96925 3.41084i −0.101556 0.175901i
\(377\) −24.2045 + 41.9234i −1.24660 + 2.15917i
\(378\) −5.14199 + 8.90619i −0.264476 + 0.458085i
\(379\) −14.1646 −0.727589 −0.363795 0.931479i \(-0.618519\pi\)
−0.363795 + 0.931479i \(0.618519\pi\)
\(380\) 0 0
\(381\) 5.08198 0.260358
\(382\) −20.5554 + 35.6030i −1.05171 + 1.82161i
\(383\) −5.41036 + 9.37102i −0.276457 + 0.478837i −0.970502 0.241095i \(-0.922494\pi\)
0.694045 + 0.719932i \(0.255827\pi\)
\(384\) 17.0311 + 29.4988i 0.869117 + 1.50535i
\(385\) 0 0
\(386\) 1.11818 + 1.93674i 0.0569138 + 0.0985775i
\(387\) 24.9127 1.26638
\(388\) 6.84281 0.347391
\(389\) −5.38703 9.33061i −0.273133 0.473081i 0.696529 0.717529i \(-0.254727\pi\)
−0.969662 + 0.244448i \(0.921393\pi\)
\(390\) 0 0
\(391\) −15.1912 −0.768250
\(392\) −10.2356 −0.516975
\(393\) −4.84702 8.39529i −0.244500 0.423486i
\(394\) 20.1291 34.8647i 1.01409 1.75646i
\(395\) 0 0
\(396\) −19.9723 + 34.5930i −1.00364 + 1.73836i
\(397\) 1.55107 2.68653i 0.0778461 0.134833i −0.824474 0.565899i \(-0.808529\pi\)
0.902320 + 0.431066i \(0.141862\pi\)
\(398\) 49.1162 2.46197
\(399\) −3.65617 6.67683i −0.183037 0.334260i
\(400\) 0 0
\(401\) 5.65671 9.79771i 0.282483 0.489274i −0.689513 0.724273i \(-0.742175\pi\)
0.971996 + 0.234999i \(0.0755088\pi\)
\(402\) −13.7804 + 23.8683i −0.687303 + 1.19044i
\(403\) 23.3954 + 40.5220i 1.16541 + 2.01854i
\(404\) −1.87681 + 3.25074i −0.0933749 + 0.161730i
\(405\) 0 0
\(406\) 9.05110 0.449199
\(407\) −12.4517 −0.617206
\(408\) 11.8943 + 20.6015i 0.588855 + 1.01993i
\(409\) −7.11186 12.3181i −0.351659 0.609091i 0.634882 0.772609i \(-0.281049\pi\)
−0.986540 + 0.163519i \(0.947716\pi\)
\(410\) 0 0
\(411\) 24.0602 1.18680
\(412\) −0.225919 0.391303i −0.0111302 0.0192781i
\(413\) 0.865075 1.49835i 0.0425675 0.0737291i
\(414\) −17.9874 31.1551i −0.884032 1.53119i
\(415\) 0 0
\(416\) 26.0542 45.1272i 1.27741 2.21255i
\(417\) −46.1320 −2.25909
\(418\) −11.7235 21.4093i −0.573416 1.04716i
\(419\) −11.0053 −0.537643 −0.268821 0.963190i \(-0.586634\pi\)
−0.268821 + 0.963190i \(0.586634\pi\)
\(420\) 0 0
\(421\) 11.4625 19.8536i 0.558646 0.967604i −0.438963 0.898505i \(-0.644654\pi\)
0.997610 0.0690991i \(-0.0220125\pi\)
\(422\) −13.4975 23.3783i −0.657046 1.13804i
\(423\) −7.31000 + 12.6613i −0.355424 + 0.615613i
\(424\) 7.38154 + 12.7852i 0.358479 + 0.620904i
\(425\) 0 0
\(426\) −86.4332 −4.18770
\(427\) −0.689744 1.19467i −0.0333791 0.0578142i
\(428\) 6.11929 + 10.5989i 0.295787 + 0.512318i
\(429\) 52.3045 2.52528
\(430\) 0 0
\(431\) 8.49811 + 14.7192i 0.409340 + 0.708997i 0.994816 0.101693i \(-0.0324258\pi\)
−0.585476 + 0.810690i \(0.699092\pi\)
\(432\) 8.32408 14.4177i 0.400492 0.693673i
\(433\) −15.7493 27.2786i −0.756863 1.31093i −0.944443 0.328676i \(-0.893398\pi\)
0.187580 0.982249i \(-0.439936\pi\)
\(434\) 4.37427 7.57645i 0.209972 0.363681i
\(435\) 0 0
\(436\) −29.0144 −1.38954
\(437\) 12.6438 + 0.285896i 0.604836 + 0.0136763i
\(438\) −53.9802 −2.57928
\(439\) −1.57963 + 2.73600i −0.0753916 + 0.130582i −0.901256 0.433286i \(-0.857354\pi\)
0.825865 + 0.563868i \(0.190687\pi\)
\(440\) 0 0
\(441\) 18.9976 + 32.9049i 0.904649 + 1.56690i
\(442\) 39.0095 67.5664i 1.85549 3.21380i
\(443\) 5.94720 + 10.3008i 0.282560 + 0.489408i 0.972015 0.234921i \(-0.0754831\pi\)
−0.689455 + 0.724329i \(0.742150\pi\)
\(444\) −38.5907 −1.83143
\(445\) 0 0
\(446\) 20.8036 + 36.0329i 0.985080 + 1.70621i
\(447\) −4.75267 8.23186i −0.224794 0.389354i
\(448\) −7.28358 −0.344117
\(449\) 21.2175 1.00132 0.500659 0.865645i \(-0.333091\pi\)
0.500659 + 0.865645i \(0.333091\pi\)
\(450\) 0 0
\(451\) −8.03602 + 13.9188i −0.378401 + 0.655410i
\(452\) −17.8901 30.9865i −0.841479 1.45748i
\(453\) 16.4162 28.4338i 0.771302 1.33593i
\(454\) 28.7762 49.8418i 1.35053 2.33919i
\(455\) 0 0
\(456\) −9.51208 17.3708i −0.445444 0.813462i
\(457\) −9.41670 −0.440495 −0.220247 0.975444i \(-0.570686\pi\)
−0.220247 + 0.975444i \(0.570686\pi\)
\(458\) 9.55948 16.5575i 0.446685 0.773682i
\(459\) 20.9696 36.3204i 0.978777 1.69529i
\(460\) 0 0
\(461\) −1.16004 + 2.00924i −0.0540282 + 0.0935797i −0.891775 0.452480i \(-0.850539\pi\)
0.837746 + 0.546060i \(0.183873\pi\)
\(462\) −4.88972 8.46924i −0.227490 0.394025i
\(463\) −14.7160 −0.683909 −0.341955 0.939716i \(-0.611089\pi\)
−0.341955 + 0.939716i \(0.611089\pi\)
\(464\) −14.6523 −0.680217
\(465\) 0 0
\(466\) 4.89606 + 8.48023i 0.226806 + 0.392839i
\(467\) 11.7747 0.544867 0.272434 0.962175i \(-0.412172\pi\)
0.272434 + 0.962175i \(0.412172\pi\)
\(468\) 106.293 4.91341
\(469\) −1.27271 2.20439i −0.0587681 0.101789i
\(470\) 0 0
\(471\) −31.6316 54.7875i −1.45751 2.52447i
\(472\) 2.25062 3.89819i 0.103593 0.179429i
\(473\) −5.62572 + 9.74403i −0.258671 + 0.448031i
\(474\) 37.6189 1.72789
\(475\) 0 0
\(476\) −8.39217 −0.384655
\(477\) 27.4008 47.4596i 1.25460 2.17303i
\(478\) 8.48971 14.7046i 0.388310 0.672573i
\(479\) −5.69219 9.85915i −0.260083 0.450476i 0.706181 0.708031i \(-0.250416\pi\)
−0.966264 + 0.257555i \(0.917083\pi\)
\(480\) 0 0
\(481\) 16.5671 + 28.6950i 0.755394 + 1.30838i
\(482\) 59.3288 2.70235
\(483\) 5.06703 0.230558
\(484\) 5.88084 + 10.1859i 0.267311 + 0.462996i
\(485\) 0 0
\(486\) −10.4829 −0.475513
\(487\) 4.77063 0.216178 0.108089 0.994141i \(-0.465527\pi\)
0.108089 + 0.994141i \(0.465527\pi\)
\(488\) −1.79447 3.10812i −0.0812321 0.140698i
\(489\) −15.2212 + 26.3639i −0.688326 + 1.19222i
\(490\) 0 0
\(491\) 2.50665 4.34165i 0.113124 0.195936i −0.803904 0.594758i \(-0.797248\pi\)
0.917028 + 0.398822i \(0.130581\pi\)
\(492\) −24.9056 + 43.1377i −1.12283 + 1.94480i
\(493\) −36.9114 −1.66240
\(494\) −33.7397 + 55.5023i −1.51802 + 2.49717i
\(495\) 0 0
\(496\) −7.08125 + 12.2651i −0.317958 + 0.550719i
\(497\) 3.99133 6.91319i 0.179036 0.310099i
\(498\) 12.8769 + 22.3034i 0.577026 + 0.999439i
\(499\) −10.9112 + 18.8987i −0.488450 + 0.846021i −0.999912 0.0132853i \(-0.995771\pi\)
0.511461 + 0.859306i \(0.329104\pi\)
\(500\) 0 0
\(501\) 19.2074 0.858124
\(502\) −35.2372 −1.57272
\(503\) 7.58583 + 13.1391i 0.338236 + 0.585841i 0.984101 0.177610i \(-0.0568366\pi\)
−0.645865 + 0.763451i \(0.723503\pi\)
\(504\) −2.60144 4.50582i −0.115877 0.200705i
\(505\) 0 0
\(506\) 16.2475 0.722288
\(507\) −50.4045 87.3031i −2.23854 3.87727i
\(508\) −2.33216 + 4.03941i −0.103473 + 0.179220i
\(509\) −2.59122 4.48812i −0.114854 0.198933i 0.802868 0.596157i \(-0.203307\pi\)
−0.917721 + 0.397225i \(0.869973\pi\)
\(510\) 0 0
\(511\) 2.49271 4.31750i 0.110271 0.190995i
\(512\) 22.1701 0.979789
\(513\) −18.1368 + 29.8354i −0.800761 + 1.31726i
\(514\) −19.8421 −0.875199
\(515\) 0 0
\(516\) −17.4355 + 30.1991i −0.767554 + 1.32944i
\(517\) −3.30145 5.71828i −0.145198 0.251490i
\(518\) 3.09757 5.36515i 0.136099 0.235731i
\(519\) −9.24018 16.0045i −0.405599 0.702518i
\(520\) 0 0
\(521\) 11.2091 0.491079 0.245540 0.969387i \(-0.421035\pi\)
0.245540 + 0.969387i \(0.421035\pi\)
\(522\) −43.7056 75.7004i −1.91294 3.31332i
\(523\) −2.71940 4.71014i −0.118911 0.205960i 0.800425 0.599433i \(-0.204607\pi\)
−0.919336 + 0.393472i \(0.871274\pi\)
\(524\) 8.89733 0.388682
\(525\) 0 0
\(526\) 16.5982 + 28.7488i 0.723714 + 1.25351i
\(527\) −17.8387 + 30.8976i −0.777067 + 1.34592i
\(528\) 7.91569 + 13.7104i 0.344486 + 0.596668i
\(529\) 7.29084 12.6281i 0.316993 0.549048i
\(530\) 0 0
\(531\) −16.7090 −0.725107
\(532\) 6.98492 + 0.157940i 0.302835 + 0.00684756i
\(533\) 42.7680 1.85249
\(534\) −11.9035 + 20.6175i −0.515116 + 0.892206i
\(535\) 0 0
\(536\) −3.31114 5.73506i −0.143019 0.247717i
\(537\) −34.2260 + 59.2811i −1.47696 + 2.55817i
\(538\) 15.3498 + 26.5866i 0.661776 + 1.14623i
\(539\) −17.1600 −0.739132
\(540\) 0 0
\(541\) −7.14111 12.3688i −0.307020 0.531775i 0.670689 0.741739i \(-0.265999\pi\)
−0.977709 + 0.209964i \(0.932665\pi\)
\(542\) 12.3295 + 21.3554i 0.529598 + 0.917291i
\(543\) −9.44296 −0.405236
\(544\) 39.7322 1.70350
\(545\) 0 0
\(546\) −13.0117 + 22.5369i −0.556848 + 0.964488i
\(547\) 12.5122 + 21.6717i 0.534982 + 0.926616i 0.999164 + 0.0408766i \(0.0130151\pi\)
−0.464182 + 0.885740i \(0.653652\pi\)
\(548\) −11.0414 + 19.1243i −0.471666 + 0.816949i
\(549\) −6.66122 + 11.5376i −0.284294 + 0.492412i
\(550\) 0 0
\(551\) 30.7219 + 0.694668i 1.30880 + 0.0295939i
\(552\) 13.1827 0.561091
\(553\) −1.73718 + 3.00888i −0.0738722 + 0.127950i
\(554\) −20.5184 + 35.5388i −0.871741 + 1.50990i
\(555\) 0 0
\(556\) 21.1703 36.6680i 0.897821 1.55507i
\(557\) 3.57846 + 6.19807i 0.151624 + 0.262621i 0.931825 0.362909i \(-0.118216\pi\)
−0.780201 + 0.625529i \(0.784883\pi\)
\(558\) −84.4892 −3.57671
\(559\) 29.9403 1.26634
\(560\) 0 0
\(561\) 19.9408 + 34.5385i 0.841901 + 1.45822i
\(562\) −60.5184 −2.55282
\(563\) 28.9386 1.21962 0.609809 0.792548i \(-0.291246\pi\)
0.609809 + 0.792548i \(0.291246\pi\)
\(564\) −10.2320 17.7223i −0.430845 0.746245i
\(565\) 0 0
\(566\) −15.6202 27.0551i −0.656568 1.13721i
\(567\) −1.92403 + 3.33253i −0.0808019 + 0.139953i
\(568\) 10.3841 17.9857i 0.435706 0.754664i
\(569\) 38.8864 1.63020 0.815100 0.579320i \(-0.196682\pi\)
0.815100 + 0.579320i \(0.196682\pi\)
\(570\) 0 0
\(571\) 15.1613 0.634480 0.317240 0.948345i \(-0.397244\pi\)
0.317240 + 0.948345i \(0.397244\pi\)
\(572\) −24.0029 + 41.5742i −1.00361 + 1.73831i
\(573\) −27.9607 + 48.4293i −1.16807 + 2.02316i
\(574\) −3.99820 6.92509i −0.166882 0.289048i
\(575\) 0 0
\(576\) 35.1707 + 60.9174i 1.46544 + 2.53822i
\(577\) 20.6412 0.859303 0.429651 0.902995i \(-0.358636\pi\)
0.429651 + 0.902995i \(0.358636\pi\)
\(578\) 22.5972 0.939918
\(579\) 1.52101 + 2.63447i 0.0632111 + 0.109485i
\(580\) 0 0
\(581\) −2.37852 −0.0986778
\(582\) 16.1792 0.670649
\(583\) 12.3752 + 21.4344i 0.512527 + 0.887723i
\(584\) 6.48517 11.2326i 0.268358 0.464810i
\(585\) 0 0
\(586\) −2.85560 + 4.94604i −0.117964 + 0.204319i
\(587\) −3.58942 + 6.21706i −0.148151 + 0.256606i −0.930544 0.366180i \(-0.880666\pi\)
0.782393 + 0.622785i \(0.213999\pi\)
\(588\) −53.1829 −2.19323
\(589\) 15.4289 25.3808i 0.635738 1.04580i
\(590\) 0 0
\(591\) 27.3808 47.4250i 1.12630 1.95080i
\(592\) −5.01448 + 8.68533i −0.206094 + 0.356965i
\(593\) −18.3743 31.8253i −0.754543 1.30691i −0.945601 0.325328i \(-0.894525\pi\)
0.191058 0.981579i \(-0.438808\pi\)
\(594\) −22.4277 + 38.8459i −0.920219 + 1.59387i
\(595\) 0 0
\(596\) 8.72413 0.357354
\(597\) 66.8107 2.73438
\(598\) −21.6174 37.4425i −0.884002 1.53114i
\(599\) 0.926876 + 1.60540i 0.0378711 + 0.0655947i 0.884340 0.466844i \(-0.154609\pi\)
−0.846469 + 0.532439i \(0.821276\pi\)
\(600\) 0 0
\(601\) −38.1633 −1.55671 −0.778356 0.627823i \(-0.783946\pi\)
−0.778356 + 0.627823i \(0.783946\pi\)
\(602\) −2.79899 4.84800i −0.114078 0.197590i
\(603\) −12.2912 + 21.2890i −0.500536 + 0.866954i
\(604\) 15.0671 + 26.0969i 0.613070 + 1.06187i
\(605\) 0 0
\(606\) −4.43755 + 7.68606i −0.180263 + 0.312225i
\(607\) 7.44914 0.302351 0.151176 0.988507i \(-0.451694\pi\)
0.151176 + 0.988507i \(0.451694\pi\)
\(608\) −33.0696 0.747755i −1.34115 0.0303255i
\(609\) 12.3118 0.498901
\(610\) 0 0
\(611\) −8.78523 + 15.2165i −0.355412 + 0.615592i
\(612\) 40.5238 + 70.1893i 1.63808 + 2.83723i
\(613\) 10.6049 18.3682i 0.428326 0.741883i −0.568398 0.822754i \(-0.692437\pi\)
0.996725 + 0.0808706i \(0.0257700\pi\)
\(614\) 18.2560 + 31.6203i 0.736753 + 1.27609i
\(615\) 0 0
\(616\) 2.34980 0.0946760
\(617\) 15.4076 + 26.6868i 0.620287 + 1.07437i 0.989432 + 0.144997i \(0.0463172\pi\)
−0.369145 + 0.929372i \(0.620349\pi\)
\(618\) −0.534164 0.925199i −0.0214872 0.0372170i
\(619\) 7.32036 0.294230 0.147115 0.989119i \(-0.453001\pi\)
0.147115 + 0.989119i \(0.453001\pi\)
\(620\) 0 0
\(621\) −11.6205 20.1273i −0.466314 0.807680i
\(622\) 19.8859 34.4434i 0.797352 1.38105i
\(623\) −1.09937 1.90416i −0.0440452 0.0762885i
\(624\) 21.0638 36.4836i 0.843228 1.46051i
\(625\) 0 0
\(626\) −51.0086 −2.03871
\(627\) −15.9470 29.1222i −0.636862 1.16303i
\(628\) 58.0638 2.31700
\(629\) −12.6322 + 21.8797i −0.503680 + 0.872399i
\(630\) 0 0
\(631\) −2.25414 3.90429i −0.0897360 0.155427i 0.817664 0.575696i \(-0.195269\pi\)
−0.907399 + 0.420269i \(0.861936\pi\)
\(632\) −4.51953 + 7.82805i −0.179777 + 0.311383i
\(633\) −18.3600 31.8005i −0.729746 1.26396i
\(634\) −8.42762 −0.334704
\(635\) 0 0
\(636\) 38.3536 + 66.4305i 1.52082 + 2.63414i
\(637\) 22.8315 + 39.5454i 0.904618 + 1.56685i
\(638\) 39.4780 1.56295
\(639\) −77.0928 −3.04975
\(640\) 0 0
\(641\) 8.48158 14.6905i 0.335002 0.580241i −0.648483 0.761229i \(-0.724596\pi\)
0.983485 + 0.180988i \(0.0579296\pi\)
\(642\) 14.4685 + 25.0602i 0.571026 + 0.989046i
\(643\) −4.64306 + 8.04202i −0.183104 + 0.317146i −0.942936 0.332974i \(-0.891948\pi\)
0.759832 + 0.650120i \(0.225281\pi\)
\(644\) −2.32530 + 4.02753i −0.0916295 + 0.158707i
\(645\) 0 0
\(646\) −49.5132 1.11957i −1.94807 0.0440489i
\(647\) 39.2779 1.54418 0.772088 0.635516i \(-0.219213\pi\)
0.772088 + 0.635516i \(0.219213\pi\)
\(648\) −5.00567 + 8.67007i −0.196641 + 0.340593i
\(649\) 3.77317 6.53533i 0.148110 0.256534i
\(650\) 0 0
\(651\) 5.95013 10.3059i 0.233204 0.403921i
\(652\) −13.9702 24.1972i −0.547116 0.947634i
\(653\) 26.5513 1.03903 0.519517 0.854460i \(-0.326112\pi\)
0.519517 + 0.854460i \(0.326112\pi\)
\(654\) −68.6018 −2.68254
\(655\) 0 0
\(656\) 6.47246 + 11.2106i 0.252707 + 0.437702i
\(657\) −48.1469 −1.87839
\(658\) 3.28518 0.128069
\(659\) −16.3143 28.2573i −0.635517 1.10075i −0.986405 0.164330i \(-0.947454\pi\)
0.350889 0.936417i \(-0.385880\pi\)
\(660\) 0 0
\(661\) −3.13332 5.42707i −0.121872 0.211088i 0.798634 0.601817i \(-0.205556\pi\)
−0.920506 + 0.390729i \(0.872223\pi\)
\(662\) −3.53530 + 6.12332i −0.137403 + 0.237989i
\(663\) 53.0629 91.9077i 2.06079 3.56940i
\(664\) −6.18809 −0.240145
\(665\) 0 0
\(666\) −59.8297 −2.31836
\(667\) −10.2274 + 17.7143i −0.396006 + 0.685902i
\(668\) −8.81442 + 15.2670i −0.341040 + 0.590699i
\(669\) 28.2983 + 49.0141i 1.09408 + 1.89499i
\(670\) 0 0
\(671\) −3.00844 5.21077i −0.116140 0.201160i
\(672\) −13.2527 −0.511235
\(673\) −7.39044 −0.284881 −0.142440 0.989803i \(-0.545495\pi\)
−0.142440 + 0.989803i \(0.545495\pi\)
\(674\) 24.0850 + 41.7165i 0.927721 + 1.60686i
\(675\) 0 0
\(676\) 92.5238 3.55861
\(677\) −20.2751 −0.779234 −0.389617 0.920977i \(-0.627393\pi\)
−0.389617 + 0.920977i \(0.627393\pi\)
\(678\) −42.2994 73.2648i −1.62450 2.81372i
\(679\) −0.747127 + 1.29406i −0.0286721 + 0.0496615i
\(680\) 0 0
\(681\) 39.1431 67.7978i 1.49997 2.59802i
\(682\) 19.0791 33.0460i 0.730577 1.26540i
\(683\) 24.6563 0.943448 0.471724 0.881746i \(-0.343632\pi\)
0.471724 + 0.881746i \(0.343632\pi\)
\(684\) −32.4076 59.1822i −1.23914 2.26289i
\(685\) 0 0
\(686\) 8.76238 15.1769i 0.334549 0.579456i
\(687\) 13.0034 22.5225i 0.496109 0.859286i
\(688\) 4.53113 + 7.84815i 0.172748 + 0.299208i
\(689\) 32.9306 57.0374i 1.25456 2.17295i
\(690\) 0 0
\(691\) −41.7299 −1.58748 −0.793739 0.608258i \(-0.791869\pi\)
−0.793739 + 0.608258i \(0.791869\pi\)
\(692\) 16.9615 0.644781
\(693\) −4.36131 7.55402i −0.165673 0.286953i
\(694\) 3.24922 + 5.62782i 0.123339 + 0.213629i
\(695\) 0 0
\(696\) 32.0311 1.21414
\(697\) 16.3051 + 28.2413i 0.617600 + 1.06971i
\(698\) −16.4283 + 28.4546i −0.621819 + 1.07702i
\(699\) 6.65991 + 11.5353i 0.251901 + 0.436305i
\(700\) 0 0
\(701\) 3.60840 6.24993i 0.136287 0.236057i −0.789801 0.613363i \(-0.789816\pi\)
0.926089 + 0.377306i \(0.123150\pi\)
\(702\) 119.361 4.50500
\(703\) 10.9258 17.9730i 0.412073 0.677865i
\(704\) −31.7686 −1.19732
\(705\) 0 0
\(706\) 37.3655 64.7190i 1.40627 2.43573i
\(707\) −0.409836 0.709857i −0.0154135 0.0266969i
\(708\) 11.6940 20.2546i 0.439487 0.761213i
\(709\) 10.3172 + 17.8700i 0.387472 + 0.671122i 0.992109 0.125380i \(-0.0400149\pi\)
−0.604636 + 0.796502i \(0.706682\pi\)
\(710\) 0 0
\(711\) 33.5536 1.25836
\(712\) −2.86017 4.95396i −0.107189 0.185657i
\(713\) 9.88549 + 17.1222i 0.370214 + 0.641230i
\(714\) −19.8425 −0.742587
\(715\) 0 0
\(716\) −31.4131 54.4091i −1.17396 2.03336i
\(717\) 11.5482 20.0021i 0.431275 0.746991i
\(718\) −3.43232 5.94495i −0.128093 0.221864i
\(719\) −0.748958 + 1.29723i −0.0279314 + 0.0483787i −0.879653 0.475616i \(-0.842225\pi\)
0.851722 + 0.523994i \(0.175559\pi\)
\(720\) 0 0
\(721\) 0.0986670 0.00367455
\(722\) 41.1895 + 1.86367i 1.53291 + 0.0693585i
\(723\) 80.7024 3.00136
\(724\) 4.33344 7.50574i 0.161051 0.278949i
\(725\) 0 0
\(726\) 13.9047 + 24.0837i 0.516052 + 0.893828i
\(727\) 5.68222 9.84190i 0.210742 0.365016i −0.741205 0.671279i \(-0.765745\pi\)
0.951947 + 0.306263i \(0.0990787\pi\)
\(728\) −3.12643 5.41514i −0.115873 0.200698i
\(729\) −33.7723 −1.25083
\(730\) 0 0
\(731\) 11.4146 + 19.7707i 0.422184 + 0.731244i
\(732\) −9.32389 16.1494i −0.344621 0.596901i
\(733\) 45.6910 1.68764 0.843818 0.536630i \(-0.180303\pi\)
0.843818 + 0.536630i \(0.180303\pi\)
\(734\) 46.5570 1.71845
\(735\) 0 0
\(736\) 11.0090 19.0681i 0.405796 0.702859i
\(737\) −5.55113 9.61484i −0.204479 0.354167i
\(738\) −38.6127 + 66.8792i −1.42135 + 2.46186i
\(739\) 1.78276 3.08783i 0.0655799 0.113588i −0.831371 0.555718i \(-0.812444\pi\)
0.896951 + 0.442130i \(0.145777\pi\)
\(740\) 0 0
\(741\) −45.8947 + 75.4975i −1.68599 + 2.77347i
\(742\) −12.3142 −0.452067
\(743\) −21.2482 + 36.8030i −0.779522 + 1.35017i 0.152696 + 0.988273i \(0.451205\pi\)
−0.932218 + 0.361898i \(0.882129\pi\)
\(744\) 15.4802 26.8125i 0.567531 0.982992i
\(745\) 0 0
\(746\) 35.9786 62.3168i 1.31727 2.28158i
\(747\) 11.4853 + 19.8932i 0.420226 + 0.727853i
\(748\) −36.6039 −1.33837
\(749\) −2.67252 −0.0976516
\(750\) 0 0
\(751\) 6.38588 + 11.0607i 0.233024 + 0.403610i 0.958697 0.284431i \(-0.0918045\pi\)
−0.725672 + 0.688040i \(0.758471\pi\)
\(752\) −5.31818 −0.193934
\(753\) −47.9317 −1.74673
\(754\) −52.5259 90.9775i −1.91288 3.31320i
\(755\) 0 0
\(756\) −6.41960 11.1191i −0.233478 0.404396i
\(757\) 5.67306 9.82603i 0.206191 0.357133i −0.744321 0.667822i \(-0.767227\pi\)
0.950512 + 0.310689i \(0.100560\pi\)
\(758\) 15.3693 26.6203i 0.558237 0.966894i
\(759\) 22.1007 0.802206
\(760\) 0 0
\(761\) −36.9214 −1.33840 −0.669199 0.743083i \(-0.733363\pi\)
−0.669199 + 0.743083i \(0.733363\pi\)
\(762\) −5.51417 + 9.55082i −0.199757 + 0.345990i
\(763\) 3.16791 5.48698i 0.114686 0.198642i
\(764\) −25.6627 44.4491i −0.928444 1.60811i
\(765\) 0 0
\(766\) −11.7410 20.3359i −0.424218 0.734767i
\(767\) −20.0810 −0.725083
\(768\) −1.23551 −0.0445827
\(769\) −14.2528 24.6866i −0.513971 0.890223i −0.999869 0.0162076i \(-0.994841\pi\)
0.485898 0.874015i \(-0.338493\pi\)
\(770\) 0 0
\(771\) −26.9904 −0.972036
\(772\) −2.79201 −0.100487
\(773\) 7.60956 + 13.1801i 0.273697 + 0.474057i 0.969805 0.243880i \(-0.0784202\pi\)
−0.696109 + 0.717936i \(0.745087\pi\)
\(774\) −27.0314 + 46.8197i −0.971622 + 1.68290i
\(775\) 0 0
\(776\) −1.94376 + 3.36670i −0.0697770 + 0.120857i
\(777\) 4.21350 7.29799i 0.151158 0.261814i
\(778\) 23.3807 0.838237
\(779\) −13.0395 23.8125i −0.467188 0.853170i
\(780\) 0 0
\(781\) 17.4089 30.1531i 0.622939 1.07896i
\(782\) 16.4831 28.5495i 0.589433 1.02093i
\(783\) −28.2354 48.9051i −1.00905 1.74773i
\(784\) −6.91059 + 11.9695i −0.246807 + 0.427482i
\(785\) 0 0
\(786\) 21.0369 0.750362
\(787\) −46.5712 −1.66008 −0.830042 0.557700i \(-0.811684\pi\)
−0.830042 + 0.557700i \(0.811684\pi\)
\(788\) 25.1305 + 43.5273i 0.895237 + 1.55060i
\(789\) 22.5778 + 39.1059i 0.803790 + 1.39221i
\(790\) 0 0
\(791\) 7.81325 0.277807
\(792\) −11.3466 19.6529i −0.403184 0.698336i
\(793\) −8.00553 + 13.8660i −0.284285 + 0.492395i
\(794\) 3.36596 + 5.83001i 0.119453 + 0.206899i
\(795\) 0 0
\(796\) −30.6599 + 53.1045i −1.08671 + 1.88224i
\(797\) −8.32080 −0.294738 −0.147369 0.989082i \(-0.547080\pi\)
−0.147369 + 0.989082i \(0.547080\pi\)
\(798\) 16.5152 + 0.373434i 0.584632 + 0.0132194i
\(799\) −13.3973 −0.473962
\(800\) 0 0
\(801\) −10.6172 + 18.3895i −0.375139 + 0.649760i
\(802\) 12.2755 + 21.2619i 0.433465 + 0.750783i
\(803\) 10.8724 18.8315i 0.383678 0.664551i
\(804\) −17.2043 29.7987i −0.606749 1.05092i
\(805\) 0 0
\(806\) −101.540 −3.57659
\(807\) 20.8796 + 36.1646i 0.734998 + 1.27305i
\(808\) −1.06625 1.84680i −0.0375106 0.0649703i
\(809\) −14.2469 −0.500893 −0.250447 0.968130i \(-0.580577\pi\)
−0.250447 + 0.968130i \(0.580577\pi\)
\(810\) 0 0
\(811\) 16.4331 + 28.4630i 0.577045 + 0.999471i 0.995816 + 0.0913794i \(0.0291276\pi\)
−0.418771 + 0.908092i \(0.637539\pi\)
\(812\) −5.64999 + 9.78607i −0.198276 + 0.343424i
\(813\) 16.7713 + 29.0488i 0.588196 + 1.01879i
\(814\) 13.5106 23.4010i 0.473546 0.820206i
\(815\) 0 0
\(816\) 32.1219 1.12449
\(817\) −9.12845 16.6702i −0.319364 0.583218i
\(818\) 30.8667 1.07923
\(819\) −11.6056 + 20.1014i −0.405531 + 0.702400i
\(820\) 0 0
\(821\) −6.58734 11.4096i −0.229900 0.398198i 0.727878 0.685706i \(-0.240507\pi\)
−0.957778 + 0.287508i \(0.907173\pi\)
\(822\) −26.1064 + 45.2176i −0.910565 + 1.57714i
\(823\) −15.5045 26.8545i −0.540452 0.936090i −0.998878 0.0473572i \(-0.984920\pi\)
0.458426 0.888732i \(-0.348413\pi\)
\(824\) 0.256697 0.00894247
\(825\) 0 0
\(826\) 1.87729 + 3.25156i 0.0653192 + 0.113136i
\(827\) −9.79469 16.9649i −0.340595 0.589927i 0.643949 0.765069i \(-0.277295\pi\)
−0.984543 + 0.175141i \(0.943962\pi\)
\(828\) 44.9132 1.56084
\(829\) −14.9634 −0.519699 −0.259850 0.965649i \(-0.583673\pi\)
−0.259850 + 0.965649i \(0.583673\pi\)
\(830\) 0 0
\(831\) −27.9103 + 48.3420i −0.968196 + 1.67697i
\(832\) 42.2685 + 73.2111i 1.46539 + 2.53814i
\(833\) −17.4088 + 30.1529i −0.603180 + 1.04474i
\(834\) 50.0552 86.6982i 1.73327 3.00211i
\(835\) 0 0
\(836\) 30.4660 + 0.688881i 1.05369 + 0.0238255i
\(837\) −54.5830 −1.88666
\(838\) 11.9412 20.6828i 0.412502 0.714474i
\(839\) 13.2661 22.9776i 0.457997 0.793274i −0.540858 0.841114i \(-0.681900\pi\)
0.998855 + 0.0478399i \(0.0152337\pi\)
\(840\) 0 0
\(841\) −10.3504 + 17.9274i −0.356911 + 0.618188i
\(842\) 24.8745 + 43.0840i 0.857233 + 1.48477i
\(843\) −82.3207 −2.83528
\(844\) 33.7022 1.16008
\(845\) 0 0
\(846\) −15.8633 27.4761i −0.545393 0.944648i
\(847\) −2.56838 −0.0882505
\(848\) 19.9347 0.684560
\(849\) −21.2476 36.8019i −0.729215 1.26304i
\(850\) 0 0
\(851\) 7.00026 + 12.1248i 0.239966 + 0.415633i
\(852\) 53.9544 93.4518i 1.84845 3.20160i
\(853\) 3.10745 5.38226i 0.106397 0.184285i −0.807911 0.589304i \(-0.799402\pi\)
0.914308 + 0.405019i \(0.132735\pi\)
\(854\) 2.99361 0.102439
\(855\) 0 0
\(856\) −6.95296 −0.237647
\(857\) −18.6965 + 32.3832i −0.638659 + 1.10619i 0.347068 + 0.937840i \(0.387177\pi\)
−0.985727 + 0.168350i \(0.946156\pi\)
\(858\) −56.7526 + 98.2984i −1.93750 + 3.35585i
\(859\) 21.4745 + 37.1950i 0.732701 + 1.26908i 0.955725 + 0.294263i \(0.0950741\pi\)
−0.223023 + 0.974813i \(0.571593\pi\)
\(860\) 0 0
\(861\) −5.43859 9.41991i −0.185347 0.321030i
\(862\) −36.8833 −1.25625
\(863\) −37.3005 −1.26972 −0.634862 0.772625i \(-0.718943\pi\)
−0.634862 + 0.772625i \(0.718943\pi\)
\(864\) 30.3931 + 52.6425i 1.03400 + 1.79093i
\(865\) 0 0
\(866\) 68.3547 2.32279
\(867\) 30.7380 1.04392
\(868\) 5.46112 + 9.45893i 0.185362 + 0.321057i
\(869\) −7.57699 + 13.1237i −0.257032 + 0.445192i
\(870\) 0 0
\(871\) −14.7717 + 25.5853i −0.500519 + 0.866925i
\(872\) 8.24180 14.2752i 0.279103 0.483420i
\(873\) 14.4308 0.488408
\(874\) −14.2564 + 23.4520i −0.482230 + 0.793274i
\(875\) 0 0
\(876\) 33.6962 58.3635i 1.13849 1.97192i
\(877\) 18.7681 32.5073i 0.633754 1.09769i −0.353024 0.935614i \(-0.614847\pi\)
0.986778 0.162079i \(-0.0518200\pi\)
\(878\) −3.42793 5.93735i −0.115687 0.200376i
\(879\) −3.88435 + 6.72789i −0.131016 + 0.226926i
\(880\) 0 0
\(881\) 24.1432 0.813404 0.406702 0.913561i \(-0.366679\pi\)
0.406702 + 0.913561i \(0.366679\pi\)
\(882\) −82.4530 −2.77634
\(883\) −15.5062 26.8575i −0.521825 0.903827i −0.999678 0.0253873i \(-0.991918\pi\)
0.477853 0.878440i \(-0.341415\pi\)
\(884\) 48.7019 + 84.3542i 1.63802 + 2.83714i
\(885\) 0 0
\(886\) −25.8119 −0.867167
\(887\) −18.6066 32.2276i −0.624750 1.08210i −0.988589 0.150637i \(-0.951868\pi\)
0.363839 0.931462i \(-0.381466\pi\)
\(888\) 10.9620 18.9868i 0.367862 0.637156i
\(889\) −0.509269 0.882080i −0.0170803 0.0295840i
\(890\) 0 0
\(891\) −8.39201 + 14.5354i −0.281143 + 0.486954i
\(892\) −51.9452 −1.73925
\(893\) 11.1508 + 0.252136i 0.373146 + 0.00843740i
\(894\) 20.6274 0.689884
\(895\) 0 0
\(896\) 3.41341 5.91219i 0.114034 0.197513i
\(897\) −29.4053 50.9314i −0.981814 1.70055i
\(898\) −23.0219 + 39.8752i −0.768252 + 1.33065i
\(899\) 24.0197 + 41.6033i 0.801102 + 1.38755i
\(900\) 0 0
\(901\) 50.2185 1.67302
\(902\) −17.4389 30.2050i −0.580650 1.00572i
\(903\) −3.80735 6.59453i −0.126701 0.219452i
\(904\) 20.3274 0.676078
\(905\) 0 0
\(906\) 35.6247 + 61.7037i 1.18355 + 2.04997i
\(907\) −4.44080 + 7.69168i −0.147454 + 0.255398i −0.930286 0.366835i \(-0.880441\pi\)
0.782832 + 0.622234i \(0.213775\pi\)
\(908\) 35.9261 + 62.2258i 1.19225 + 2.06503i
\(909\) −3.95801 + 6.85547i −0.131279 + 0.227382i
\(910\) 0 0
\(911\) −7.31703 −0.242424 −0.121212 0.992627i \(-0.538678\pi\)
−0.121212 + 0.992627i \(0.538678\pi\)
\(912\) −26.7355 0.604531i −0.885302 0.0200180i
\(913\) −10.3743 −0.343341
\(914\) 10.2175 17.6973i 0.337966 0.585374i
\(915\) 0 0
\(916\) 11.9347 + 20.6715i 0.394333 + 0.683004i
\(917\) −0.971448 + 1.68260i −0.0320800 + 0.0555642i
\(918\) 45.5059 + 78.8184i 1.50192 + 2.60140i
\(919\) −18.1725 −0.599454 −0.299727 0.954025i \(-0.596896\pi\)
−0.299727 + 0.954025i \(0.596896\pi\)
\(920\) 0 0
\(921\) 24.8329 + 43.0118i 0.818271 + 1.41729i
\(922\) −2.51738 4.36023i −0.0829054 0.143596i
\(923\) −92.6509 −3.04964
\(924\) 12.2093 0.401656
\(925\) 0 0
\(926\) 15.9675 27.6565i 0.524724 0.908848i
\(927\) −0.476440 0.825218i −0.0156483 0.0271037i
\(928\) 26.7495 46.3315i 0.878095 1.52091i
\(929\) −3.62348 + 6.27605i −0.118882 + 0.205910i −0.919325 0.393499i \(-0.871265\pi\)
0.800443 + 0.599409i \(0.204598\pi\)
\(930\) 0 0
\(931\) 15.0571 24.7691i 0.493476 0.811774i
\(932\) −12.2251 −0.400447
\(933\) 27.0500 46.8519i 0.885576 1.53386i
\(934\) −12.7760 + 22.1287i −0.418045 + 0.724074i
\(935\) 0 0
\(936\) −30.1936 + 52.2969i −0.986909 + 1.70938i
\(937\) 0.874288 + 1.51431i 0.0285618 + 0.0494704i 0.879953 0.475061i \(-0.157574\pi\)
−0.851391 + 0.524531i \(0.824241\pi\)
\(938\) 5.52377 0.180357
\(939\) −69.3848 −2.26429
\(940\) 0 0
\(941\) −14.2280 24.6436i −0.463819 0.803359i 0.535328 0.844644i \(-0.320188\pi\)
−0.999147 + 0.0412856i \(0.986855\pi\)
\(942\) 137.286 4.47303
\(943\) 18.0712 0.588480
\(944\) −3.03903 5.26376i −0.0989121 0.171321i
\(945\) 0 0
\(946\) −12.2083 21.1454i −0.396926 0.687496i
\(947\) −5.53560 + 9.58793i −0.179883 + 0.311566i −0.941840 0.336061i \(-0.890905\pi\)
0.761957 + 0.647627i \(0.224238\pi\)
\(948\) −23.4829 + 40.6737i −0.762691 + 1.32102i
\(949\) −57.8634 −1.87832
\(950\) 0 0
\(951\) −11.4637 −0.371737
\(952\) 2.38387 4.12899i 0.0772618 0.133821i
\(953\) 26.2385 45.4464i 0.849949 1.47215i −0.0313045 0.999510i \(-0.509966\pi\)
0.881253 0.472644i \(-0.156701\pi\)
\(954\) 59.4622 + 102.992i 1.92516 + 3.33447i
\(955\) 0 0
\(956\) 10.5991 + 18.3582i 0.342799 + 0.593746i
\(957\) 53.7002 1.73588
\(958\) 24.7051 0.798185
\(959\) −2.41109 4.17614i −0.0778583 0.134854i
\(960\) 0 0
\(961\) 15.4335 0.497854
\(962\) −71.9040 −2.31828
\(963\) 12.9050 + 22.3520i 0.415856 + 0.720284i
\(964\) −37.0349 + 64.1464i −1.19281 + 2.06602i
\(965\) 0 0
\(966\) −5.49795 + 9.52273i −0.176894 + 0.306389i
\(967\) −7.63706 + 13.2278i −0.245591 + 0.425376i −0.962298 0.271999i \(-0.912315\pi\)
0.716707 + 0.697375i \(0.245649\pi\)
\(968\) −6.68203 −0.214769
\(969\) −67.3508 1.52290i −2.16362 0.0489227i
\(970\) 0 0
\(971\) −26.3376 + 45.6181i −0.845215 + 1.46396i 0.0402194 + 0.999191i \(0.487194\pi\)
−0.885434 + 0.464764i \(0.846139\pi\)
\(972\) 6.54375 11.3341i 0.209891 0.363542i
\(973\) 4.62292 + 8.00714i 0.148204 + 0.256697i
\(974\) −5.17634 + 8.96568i −0.165861 + 0.287279i
\(975\) 0 0
\(976\) −4.84618 −0.155123
\(977\) 56.5695 1.80982 0.904909 0.425605i \(-0.139939\pi\)
0.904909 + 0.425605i \(0.139939\pi\)
\(978\) −33.0313 57.2119i −1.05623 1.82944i
\(979\) −4.79508 8.30532i −0.153251 0.265439i
\(980\) 0 0
\(981\) −61.1883 −1.95359
\(982\) 5.43965 + 9.42176i 0.173586 + 0.300660i
\(983\) −30.8770 + 53.4806i −0.984825 + 1.70577i −0.342111 + 0.939659i \(0.611142\pi\)
−0.642713 + 0.766107i \(0.722191\pi\)
\(984\) −14.1493 24.5073i −0.451064 0.781265i
\(985\) 0 0
\(986\) 40.0504 69.3694i 1.27547 2.20917i
\(987\) 4.46869 0.142240
\(988\) −38.9478 71.1258i −1.23909 2.26281i
\(989\) 12.6510 0.402278
\(990\) 0 0
\(991\) 28.5967 49.5310i 0.908404 1.57340i 0.0921233 0.995748i \(-0.470635\pi\)
0.816281 0.577655i \(-0.196032\pi\)
\(992\) −25.8553 44.7827i −0.820906 1.42185i
\(993\) −4.80892 + 8.32929i −0.152606 + 0.264322i
\(994\) 8.66154 + 15.0022i 0.274727 + 0.475842i
\(995\) 0 0
\(996\) −32.1526 −1.01879
\(997\) 15.4592 + 26.7761i 0.489597 + 0.848007i 0.999928 0.0119712i \(-0.00381063\pi\)
−0.510332 + 0.859978i \(0.670477\pi\)
\(998\) −23.6782 41.0118i −0.749519 1.29820i
\(999\) −38.6521 −1.22290
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 475.2.e.f.201.1 yes 12
5.2 odd 4 475.2.j.d.49.2 24
5.3 odd 4 475.2.j.d.49.11 24
5.4 even 2 475.2.e.h.201.6 yes 12
19.7 even 3 inner 475.2.e.f.26.1 12
19.8 odd 6 9025.2.a.bs.1.1 6
19.11 even 3 9025.2.a.bz.1.6 6
95.7 odd 12 475.2.j.d.349.11 24
95.49 even 6 9025.2.a.br.1.1 6
95.64 even 6 475.2.e.h.26.6 yes 12
95.83 odd 12 475.2.j.d.349.2 24
95.84 odd 6 9025.2.a.by.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.1 12 19.7 even 3 inner
475.2.e.f.201.1 yes 12 1.1 even 1 trivial
475.2.e.h.26.6 yes 12 95.64 even 6
475.2.e.h.201.6 yes 12 5.4 even 2
475.2.j.d.49.2 24 5.2 odd 4
475.2.j.d.49.11 24 5.3 odd 4
475.2.j.d.349.2 24 95.83 odd 12
475.2.j.d.349.11 24 95.7 odd 12
9025.2.a.br.1.1 6 95.49 even 6
9025.2.a.bs.1.1 6 19.8 odd 6
9025.2.a.by.1.6 6 95.84 odd 6
9025.2.a.bz.1.6 6 19.11 even 3