Properties

Label 475.2.l.b.176.1
Level $475$
Weight $2$
Character 475.176
Analytic conductor $3.793$
Analytic rank $0$
Dimension $18$
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(101,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\), degree \(6\), 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: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} - 1294 x^{9} + 3333 x^{8} - 2616 x^{7} + 5113 x^{6} - 3126 x^{5} + 4032 x^{4} + \cdots + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 176.1
Root \(1.01081 - 1.75077i\) of defining polynomial
Character \(\chi\) \(=\) 475.176
Dual form 475.2.l.b.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.89970 + 0.691434i) q^{2} +(0.330026 - 1.87167i) q^{3} +(1.59869 - 1.34146i) q^{4} +(0.667187 + 3.78381i) q^{6} +(1.54609 + 2.67790i) q^{7} +(-0.0878797 + 0.152212i) q^{8} +(-0.575162 - 0.209342i) q^{9} +O(q^{10})\) \(q+(-1.89970 + 0.691434i) q^{2} +(0.330026 - 1.87167i) q^{3} +(1.59869 - 1.34146i) q^{4} +(0.667187 + 3.78381i) q^{6} +(1.54609 + 2.67790i) q^{7} +(-0.0878797 + 0.152212i) q^{8} +(-0.575162 - 0.209342i) q^{9} +(-0.481594 + 0.834145i) q^{11} +(-1.98316 - 3.43494i) q^{12} +(0.513859 + 2.91424i) q^{13} +(-4.78870 - 4.01819i) q^{14} +(-0.663086 + 3.76055i) q^{16} +(0.0366124 - 0.0133258i) q^{17} +1.23738 q^{18} +(-4.31788 + 0.596607i) q^{19} +(5.52241 - 2.00999i) q^{21} +(0.338127 - 1.91762i) q^{22} +(-2.97348 + 2.49504i) q^{23} +(0.255888 + 0.214716i) q^{24} +(-2.99118 - 5.18088i) q^{26} +(2.26918 - 3.93034i) q^{27} +(6.06401 + 2.20712i) q^{28} +(8.76529 + 3.19030i) q^{29} +(4.68894 + 8.12148i) q^{31} +(-1.40155 - 7.94857i) q^{32} +(1.40231 + 1.17668i) q^{33} +(-0.0603386 + 0.0506301i) q^{34} +(-1.20033 + 0.436884i) q^{36} +1.11739 q^{37} +(7.79016 - 4.11890i) q^{38} +5.62409 q^{39} +(2.09674 - 11.8912i) q^{41} +(-9.10114 + 7.63676i) q^{42} +(3.79459 + 3.18404i) q^{43} +(0.349053 + 1.97958i) q^{44} +(3.92356 - 6.79580i) q^{46} +(7.53217 + 2.74148i) q^{47} +(6.81968 + 2.48216i) q^{48} +(-1.28078 + 2.21837i) q^{49} +(-0.0128585 - 0.0729242i) q^{51} +(4.73083 + 3.96964i) q^{52} +(-4.64208 + 3.89517i) q^{53} +(-1.59319 + 9.03545i) q^{54} -0.543479 q^{56} +(-0.308361 + 8.27855i) q^{57} -18.8573 q^{58} +(-2.60732 + 0.948987i) q^{59} +(-7.68360 + 6.44731i) q^{61} +(-14.5230 - 12.1863i) q^{62} +(-0.328654 - 1.86389i) q^{63} +(4.33987 + 7.51688i) q^{64} +(-3.47756 - 1.26573i) q^{66} +(8.78501 + 3.19748i) q^{67} +(0.0406557 - 0.0704178i) q^{68} +(3.68858 + 6.38881i) q^{69} +(9.64404 + 8.09231i) q^{71} +(0.0824094 - 0.0691497i) q^{72} +(-0.155782 + 0.883486i) q^{73} +(-2.12271 + 0.772603i) q^{74} +(-6.10262 + 6.74604i) q^{76} -2.97835 q^{77} +(-10.6841 + 3.88869i) q^{78} +(1.54415 - 8.75731i) q^{79} +(-8.01404 - 6.72458i) q^{81} +(4.23882 + 24.0395i) q^{82} +(-4.80224 - 8.31772i) q^{83} +(6.13229 - 10.6214i) q^{84} +(-9.41012 - 3.42500i) q^{86} +(8.86398 - 15.3529i) q^{87} +(-0.0846446 - 0.146609i) q^{88} +(-1.51886 - 8.61386i) q^{89} +(-7.00958 + 5.88173i) q^{91} +(-1.40667 + 7.97760i) q^{92} +(16.7482 - 6.09585i) q^{93} -16.2044 q^{94} -15.3397 q^{96} +(7.31855 - 2.66374i) q^{97} +(0.899233 - 5.09981i) q^{98} +(0.451616 - 0.378951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26} - 6 q^{27} + 24 q^{28} - 9 q^{29} + 30 q^{31} - 45 q^{32} + 3 q^{33} + 24 q^{34} - 21 q^{36} + 60 q^{37} + 15 q^{38} + 12 q^{39} - 6 q^{41} - 39 q^{42} + 6 q^{43} - 30 q^{44} + 21 q^{46} - 33 q^{47} + 63 q^{48} - 3 q^{49} + 27 q^{51} - 9 q^{52} - 24 q^{53} + 30 q^{54} - 72 q^{56} + 30 q^{57} - 36 q^{58} + 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{63} - 24 q^{64} - 33 q^{66} + 24 q^{67} + 3 q^{68} + 27 q^{69} + 24 q^{71} - 18 q^{72} - 6 q^{73} - 39 q^{74} + 27 q^{76} - 24 q^{77} - 72 q^{78} + 9 q^{79} + 15 q^{81} + 57 q^{82} - 12 q^{84} - 33 q^{86} + 45 q^{87} - 39 q^{88} - 6 q^{89} - 6 q^{91} + 66 q^{92} + 72 q^{93} - 66 q^{94} - 18 q^{96} + 87 q^{97} - 39 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.89970 + 0.691434i −1.34329 + 0.488918i −0.910847 0.412743i \(-0.864571\pi\)
−0.432443 + 0.901661i \(0.642348\pi\)
\(3\) 0.330026 1.87167i 0.190541 1.08061i −0.728086 0.685485i \(-0.759590\pi\)
0.918627 0.395125i \(-0.129299\pi\)
\(4\) 1.59869 1.34146i 0.799344 0.670730i
\(5\) 0 0
\(6\) 0.667187 + 3.78381i 0.272378 + 1.54473i
\(7\) 1.54609 + 2.67790i 0.584366 + 1.01215i 0.994954 + 0.100331i \(0.0319902\pi\)
−0.410588 + 0.911821i \(0.634676\pi\)
\(8\) −0.0878797 + 0.152212i −0.0310701 + 0.0538151i
\(9\) −0.575162 0.209342i −0.191721 0.0697806i
\(10\) 0 0
\(11\) −0.481594 + 0.834145i −0.145206 + 0.251504i −0.929450 0.368949i \(-0.879718\pi\)
0.784244 + 0.620453i \(0.213051\pi\)
\(12\) −1.98316 3.43494i −0.572490 0.991581i
\(13\) 0.513859 + 2.91424i 0.142519 + 0.808264i 0.969326 + 0.245779i \(0.0790437\pi\)
−0.826807 + 0.562486i \(0.809845\pi\)
\(14\) −4.78870 4.01819i −1.27983 1.07391i
\(15\) 0 0
\(16\) −0.663086 + 3.76055i −0.165772 + 0.940137i
\(17\) 0.0366124 0.0133258i 0.00887980 0.00323198i −0.337576 0.941298i \(-0.609607\pi\)
0.346456 + 0.938066i \(0.387385\pi\)
\(18\) 1.23738 0.291654
\(19\) −4.31788 + 0.596607i −0.990589 + 0.136871i
\(20\) 0 0
\(21\) 5.52241 2.00999i 1.20509 0.438616i
\(22\) 0.338127 1.91762i 0.0720890 0.408837i
\(23\) −2.97348 + 2.49504i −0.620013 + 0.520253i −0.897808 0.440388i \(-0.854841\pi\)
0.277795 + 0.960641i \(0.410397\pi\)
\(24\) 0.255888 + 0.214716i 0.0522330 + 0.0438287i
\(25\) 0 0
\(26\) −2.99118 5.18088i −0.586619 1.01605i
\(27\) 2.26918 3.93034i 0.436704 0.756394i
\(28\) 6.06401 + 2.20712i 1.14599 + 0.417106i
\(29\) 8.76529 + 3.19030i 1.62767 + 0.592425i 0.984822 0.173566i \(-0.0555291\pi\)
0.642851 + 0.765991i \(0.277751\pi\)
\(30\) 0 0
\(31\) 4.68894 + 8.12148i 0.842158 + 1.45866i 0.888067 + 0.459715i \(0.152048\pi\)
−0.0459085 + 0.998946i \(0.514618\pi\)
\(32\) −1.40155 7.94857i −0.247761 1.40512i
\(33\) 1.40231 + 1.17668i 0.244110 + 0.204833i
\(34\) −0.0603386 + 0.0506301i −0.0103480 + 0.00868299i
\(35\) 0 0
\(36\) −1.20033 + 0.436884i −0.200055 + 0.0728140i
\(37\) 1.11739 0.183698 0.0918491 0.995773i \(-0.470722\pi\)
0.0918491 + 0.995773i \(0.470722\pi\)
\(38\) 7.79016 4.11890i 1.26373 0.668174i
\(39\) 5.62409 0.900575
\(40\) 0 0
\(41\) 2.09674 11.8912i 0.327456 1.85710i −0.164362 0.986400i \(-0.552557\pi\)
0.491818 0.870698i \(-0.336332\pi\)
\(42\) −9.10114 + 7.63676i −1.40434 + 1.17838i
\(43\) 3.79459 + 3.18404i 0.578669 + 0.485561i 0.884510 0.466522i \(-0.154493\pi\)
−0.305841 + 0.952083i \(0.598938\pi\)
\(44\) 0.349053 + 1.97958i 0.0526217 + 0.298432i
\(45\) 0 0
\(46\) 3.92356 6.79580i 0.578497 1.00199i
\(47\) 7.53217 + 2.74148i 1.09868 + 0.399887i 0.826829 0.562453i \(-0.190142\pi\)
0.271850 + 0.962340i \(0.412364\pi\)
\(48\) 6.81968 + 2.48216i 0.984336 + 0.358269i
\(49\) −1.28078 + 2.21837i −0.182968 + 0.316910i
\(50\) 0 0
\(51\) −0.0128585 0.0729242i −0.00180055 0.0102114i
\(52\) 4.73083 + 3.96964i 0.656048 + 0.550490i
\(53\) −4.64208 + 3.89517i −0.637639 + 0.535043i −0.903292 0.429026i \(-0.858857\pi\)
0.265653 + 0.964069i \(0.414412\pi\)
\(54\) −1.59319 + 9.03545i −0.216806 + 1.22957i
\(55\) 0 0
\(56\) −0.543479 −0.0726254
\(57\) −0.308361 + 8.27855i −0.0408434 + 1.09652i
\(58\) −18.8573 −2.47609
\(59\) −2.60732 + 0.948987i −0.339444 + 0.123548i −0.506117 0.862465i \(-0.668920\pi\)
0.166673 + 0.986012i \(0.446698\pi\)
\(60\) 0 0
\(61\) −7.68360 + 6.44731i −0.983784 + 0.825493i −0.984656 0.174507i \(-0.944167\pi\)
0.000871917 1.00000i \(0.499722\pi\)
\(62\) −14.5230 12.1863i −1.84443 1.54766i
\(63\) −0.328654 1.86389i −0.0414065 0.234828i
\(64\) 4.33987 + 7.51688i 0.542484 + 0.939610i
\(65\) 0 0
\(66\) −3.47756 1.26573i −0.428058 0.155800i
\(67\) 8.78501 + 3.19748i 1.07326 + 0.390635i 0.817395 0.576078i \(-0.195418\pi\)
0.255865 + 0.966713i \(0.417640\pi\)
\(68\) 0.0406557 0.0704178i 0.00493023 0.00853941i
\(69\) 3.68858 + 6.38881i 0.444053 + 0.769122i
\(70\) 0 0
\(71\) 9.64404 + 8.09231i 1.14454 + 0.960381i 0.999578 0.0290571i \(-0.00925045\pi\)
0.144959 + 0.989438i \(0.453695\pi\)
\(72\) 0.0824094 0.0691497i 0.00971204 0.00814937i
\(73\) −0.155782 + 0.883486i −0.0182330 + 0.103404i −0.992566 0.121707i \(-0.961163\pi\)
0.974333 + 0.225111i \(0.0722744\pi\)
\(74\) −2.12271 + 0.772603i −0.246760 + 0.0898133i
\(75\) 0 0
\(76\) −6.10262 + 6.74604i −0.700018 + 0.773824i
\(77\) −2.97835 −0.339414
\(78\) −10.6841 + 3.88869i −1.20973 + 0.440307i
\(79\) 1.54415 8.75731i 0.173731 0.985275i −0.765868 0.642997i \(-0.777691\pi\)
0.939599 0.342277i \(-0.111198\pi\)
\(80\) 0 0
\(81\) −8.01404 6.72458i −0.890449 0.747176i
\(82\) 4.23882 + 24.0395i 0.468099 + 2.65472i
\(83\) −4.80224 8.31772i −0.527114 0.912988i −0.999501 0.0315966i \(-0.989941\pi\)
0.472387 0.881391i \(-0.343393\pi\)
\(84\) 6.13229 10.6214i 0.669087 1.15889i
\(85\) 0 0
\(86\) −9.41012 3.42500i −1.01472 0.369328i
\(87\) 8.86398 15.3529i 0.950319 1.64600i
\(88\) −0.0846446 0.146609i −0.00902315 0.0156285i
\(89\) −1.51886 8.61386i −0.160998 0.913068i −0.953095 0.302672i \(-0.902121\pi\)
0.792096 0.610396i \(-0.208990\pi\)
\(90\) 0 0
\(91\) −7.00958 + 5.88173i −0.734803 + 0.616573i
\(92\) −1.40667 + 7.97760i −0.146655 + 0.831722i
\(93\) 16.7482 6.09585i 1.73671 0.632111i
\(94\) −16.2044 −1.67136
\(95\) 0 0
\(96\) −15.3397 −1.56560
\(97\) 7.31855 2.66374i 0.743087 0.270461i 0.0573929 0.998352i \(-0.481721\pi\)
0.685694 + 0.727890i \(0.259499\pi\)
\(98\) 0.899233 5.09981i 0.0908363 0.515158i
\(99\) 0.451616 0.378951i 0.0453891 0.0380860i
\(100\) 0 0
\(101\) −0.528521 2.99739i −0.0525898 0.298251i 0.947157 0.320771i \(-0.103942\pi\)
−0.999746 + 0.0225200i \(0.992831\pi\)
\(102\) 0.0748496 + 0.129643i 0.00741121 + 0.0128366i
\(103\) −0.164287 + 0.284553i −0.0161876 + 0.0280378i −0.874006 0.485916i \(-0.838486\pi\)
0.857818 + 0.513953i \(0.171820\pi\)
\(104\) −0.488740 0.177887i −0.0479249 0.0174432i
\(105\) 0 0
\(106\) 6.12531 10.6093i 0.594943 1.03047i
\(107\) −6.39366 11.0741i −0.618099 1.07058i −0.989832 0.142239i \(-0.954570\pi\)
0.371734 0.928339i \(-0.378763\pi\)
\(108\) −1.64467 9.32740i −0.158259 0.897529i
\(109\) −11.6754 9.79682i −1.11830 0.938366i −0.119783 0.992800i \(-0.538220\pi\)
−0.998517 + 0.0544346i \(0.982664\pi\)
\(110\) 0 0
\(111\) 0.368769 2.09139i 0.0350020 0.198506i
\(112\) −11.0956 + 4.03846i −1.04843 + 0.381598i
\(113\) −2.56380 −0.241182 −0.120591 0.992702i \(-0.538479\pi\)
−0.120591 + 0.992702i \(0.538479\pi\)
\(114\) −5.13828 15.9400i −0.481244 1.49291i
\(115\) 0 0
\(116\) 18.2926 6.65797i 1.69843 0.618177i
\(117\) 0.314520 1.78373i 0.0290774 0.164906i
\(118\) 4.29697 3.60558i 0.395568 0.331921i
\(119\) 0.0922912 + 0.0774415i 0.00846032 + 0.00709905i
\(120\) 0 0
\(121\) 5.03613 + 8.72284i 0.457830 + 0.792986i
\(122\) 10.1386 17.5606i 0.917910 1.58987i
\(123\) −21.5645 7.84884i −1.94441 0.707706i
\(124\) 18.3908 + 6.69370i 1.65154 + 0.601112i
\(125\) 0 0
\(126\) 1.91310 + 3.31359i 0.170433 + 0.295198i
\(127\) 2.68740 + 15.2410i 0.238468 + 1.35242i 0.835186 + 0.549968i \(0.185360\pi\)
−0.596718 + 0.802451i \(0.703529\pi\)
\(128\) −1.07610 0.902953i −0.0951145 0.0798105i
\(129\) 7.21178 6.05141i 0.634962 0.532797i
\(130\) 0 0
\(131\) −0.791413 + 0.288051i −0.0691461 + 0.0251671i −0.376362 0.926473i \(-0.622825\pi\)
0.307216 + 0.951640i \(0.400603\pi\)
\(132\) 3.82032 0.332516
\(133\) −8.27347 10.6404i −0.717401 0.922644i
\(134\) −18.8997 −1.63269
\(135\) 0 0
\(136\) −0.00118913 + 0.00674391i −0.000101967 + 0.000578285i
\(137\) 3.88675 3.26137i 0.332068 0.278638i −0.461474 0.887154i \(-0.652679\pi\)
0.793542 + 0.608516i \(0.208235\pi\)
\(138\) −11.4246 9.58641i −0.972529 0.816049i
\(139\) 0.474127 + 2.68891i 0.0402150 + 0.228070i 0.998291 0.0584449i \(-0.0186142\pi\)
−0.958076 + 0.286515i \(0.907503\pi\)
\(140\) 0 0
\(141\) 7.61698 13.1930i 0.641465 1.11105i
\(142\) −23.9161 8.70474i −2.00699 0.730486i
\(143\) −2.67837 0.974847i −0.223977 0.0815208i
\(144\) 1.16862 2.02411i 0.0973852 0.168676i
\(145\) 0 0
\(146\) −0.314933 1.78607i −0.0260640 0.147816i
\(147\) 3.72937 + 3.12931i 0.307593 + 0.258101i
\(148\) 1.78636 1.49894i 0.146838 0.123212i
\(149\) −1.15401 + 6.54471i −0.0945401 + 0.536164i 0.900347 + 0.435172i \(0.143313\pi\)
−0.994887 + 0.100991i \(0.967799\pi\)
\(150\) 0 0
\(151\) −5.19059 −0.422404 −0.211202 0.977442i \(-0.567738\pi\)
−0.211202 + 0.977442i \(0.567738\pi\)
\(152\) 0.288643 0.709662i 0.0234120 0.0575612i
\(153\) −0.0238477 −0.00192797
\(154\) 5.65796 2.05933i 0.455932 0.165946i
\(155\) 0 0
\(156\) 8.99116 7.54448i 0.719869 0.604042i
\(157\) −8.92275 7.48708i −0.712113 0.597534i 0.213078 0.977035i \(-0.431651\pi\)
−0.925191 + 0.379501i \(0.876096\pi\)
\(158\) 3.12168 + 17.7039i 0.248348 + 1.40845i
\(159\) 5.75847 + 9.97396i 0.456676 + 0.790987i
\(160\) 0 0
\(161\) −11.2787 4.10513i −0.888890 0.323529i
\(162\) 19.8739 + 7.23350i 1.56144 + 0.568317i
\(163\) −0.278398 + 0.482199i −0.0218058 + 0.0377688i −0.876722 0.480997i \(-0.840275\pi\)
0.854917 + 0.518765i \(0.173608\pi\)
\(164\) −12.5996 21.8231i −0.983860 1.70410i
\(165\) 0 0
\(166\) 14.8740 + 12.4807i 1.15444 + 0.968693i
\(167\) −16.9727 + 14.2418i −1.31339 + 1.10206i −0.325727 + 0.945464i \(0.605609\pi\)
−0.987662 + 0.156600i \(0.949947\pi\)
\(168\) −0.179362 + 1.01721i −0.0138381 + 0.0784798i
\(169\) 3.98727 1.45125i 0.306713 0.111634i
\(170\) 0 0
\(171\) 2.60837 + 0.560767i 0.199467 + 0.0428829i
\(172\) 10.3376 0.788236
\(173\) −10.7653 + 3.91823i −0.818467 + 0.297898i −0.717117 0.696953i \(-0.754539\pi\)
−0.101350 + 0.994851i \(0.532316\pi\)
\(174\) −6.22341 + 35.2947i −0.471795 + 2.67568i
\(175\) 0 0
\(176\) −2.81751 2.36417i −0.212377 0.178206i
\(177\) 0.915709 + 5.19324i 0.0688289 + 0.390348i
\(178\) 8.84129 + 15.3136i 0.662683 + 1.14780i
\(179\) −2.98306 + 5.16681i −0.222964 + 0.386185i −0.955707 0.294321i \(-0.904907\pi\)
0.732743 + 0.680506i \(0.238240\pi\)
\(180\) 0 0
\(181\) 5.80527 + 2.11294i 0.431502 + 0.157054i 0.548634 0.836062i \(-0.315148\pi\)
−0.117132 + 0.993116i \(0.537370\pi\)
\(182\) 9.24926 16.0202i 0.685601 1.18750i
\(183\) 9.53145 + 16.5090i 0.704585 + 1.22038i
\(184\) −0.118468 0.671863i −0.00873354 0.0495304i
\(185\) 0 0
\(186\) −27.6017 + 23.1606i −2.02386 + 1.69822i
\(187\) −0.00651663 + 0.0369577i −0.000476543 + 0.00270261i
\(188\) 15.7192 5.72131i 1.14644 0.417270i
\(189\) 14.0334 1.02078
\(190\) 0 0
\(191\) −18.6639 −1.35047 −0.675235 0.737602i \(-0.735958\pi\)
−0.675235 + 0.737602i \(0.735958\pi\)
\(192\) 15.5014 5.64205i 1.11872 0.407180i
\(193\) 4.15136 23.5435i 0.298821 1.69470i −0.352431 0.935838i \(-0.614645\pi\)
0.651252 0.758861i \(-0.274244\pi\)
\(194\) −12.0613 + 10.1206i −0.865948 + 0.726616i
\(195\) 0 0
\(196\) 0.928289 + 5.26459i 0.0663064 + 0.376042i
\(197\) −3.35076 5.80368i −0.238732 0.413495i 0.721619 0.692290i \(-0.243398\pi\)
−0.960351 + 0.278795i \(0.910065\pi\)
\(198\) −0.595916 + 1.03216i −0.0423499 + 0.0733521i
\(199\) −2.96836 1.08040i −0.210422 0.0765872i 0.234659 0.972078i \(-0.424603\pi\)
−0.445080 + 0.895491i \(0.646825\pi\)
\(200\) 0 0
\(201\) 8.88392 15.3874i 0.626624 1.08534i
\(202\) 3.07653 + 5.32870i 0.216464 + 0.374926i
\(203\) 5.00858 + 28.4051i 0.351534 + 1.99365i
\(204\) −0.118382 0.0993340i −0.00828837 0.00695477i
\(205\) 0 0
\(206\) 0.115346 0.654158i 0.00803652 0.0455774i
\(207\) 2.23255 0.812582i 0.155173 0.0564783i
\(208\) −11.2999 −0.783505
\(209\) 1.58181 3.88906i 0.109416 0.269012i
\(210\) 0 0
\(211\) 10.7670 3.91887i 0.741231 0.269786i 0.0563198 0.998413i \(-0.482063\pi\)
0.684911 + 0.728627i \(0.259841\pi\)
\(212\) −2.19603 + 12.4543i −0.150824 + 0.855367i
\(213\) 18.3289 15.3798i 1.25588 1.05381i
\(214\) 19.8031 + 16.6168i 1.35371 + 1.13590i
\(215\) 0 0
\(216\) 0.398830 + 0.690793i 0.0271369 + 0.0470025i
\(217\) −14.4990 + 25.1130i −0.984258 + 1.70478i
\(218\) 28.9536 + 10.5383i 1.96099 + 0.713741i
\(219\) 1.60218 + 0.583148i 0.108266 + 0.0394055i
\(220\) 0 0
\(221\) 0.0576482 + 0.0998496i 0.00387784 + 0.00671661i
\(222\) 0.745510 + 4.22800i 0.0500354 + 0.283765i
\(223\) 5.75623 + 4.83005i 0.385465 + 0.323444i 0.814844 0.579681i \(-0.196823\pi\)
−0.429378 + 0.903125i \(0.641267\pi\)
\(224\) 19.1186 16.0424i 1.27741 1.07188i
\(225\) 0 0
\(226\) 4.87044 1.77270i 0.323977 0.117918i
\(227\) 4.20184 0.278886 0.139443 0.990230i \(-0.455469\pi\)
0.139443 + 0.990230i \(0.455469\pi\)
\(228\) 10.6124 + 13.6485i 0.702821 + 0.903892i
\(229\) 22.5758 1.49185 0.745927 0.666028i \(-0.232007\pi\)
0.745927 + 0.666028i \(0.232007\pi\)
\(230\) 0 0
\(231\) −0.982933 + 5.57449i −0.0646722 + 0.366774i
\(232\) −1.25589 + 1.05382i −0.0824534 + 0.0691867i
\(233\) 8.41032 + 7.05710i 0.550978 + 0.462326i 0.875272 0.483631i \(-0.160682\pi\)
−0.324294 + 0.945956i \(0.605127\pi\)
\(234\) 0.635840 + 3.60603i 0.0415661 + 0.235733i
\(235\) 0 0
\(236\) −2.89527 + 5.01475i −0.188466 + 0.326432i
\(237\) −15.8812 5.78029i −1.03160 0.375470i
\(238\) −0.228871 0.0833023i −0.0148355 0.00539969i
\(239\) 1.36280 2.36043i 0.0881520 0.152684i −0.818578 0.574395i \(-0.805237\pi\)
0.906730 + 0.421712i \(0.138571\pi\)
\(240\) 0 0
\(241\) 1.93687 + 10.9846i 0.124765 + 0.707577i 0.981447 + 0.191733i \(0.0614107\pi\)
−0.856682 + 0.515845i \(0.827478\pi\)
\(242\) −15.5984 13.0886i −1.00270 0.841369i
\(243\) −4.80130 + 4.02877i −0.308003 + 0.258445i
\(244\) −3.63489 + 20.6145i −0.232700 + 1.31971i
\(245\) 0 0
\(246\) 46.3930 2.95791
\(247\) −3.95743 12.2768i −0.251805 0.781151i
\(248\) −1.64825 −0.104664
\(249\) −17.1529 + 6.24315i −1.08702 + 0.395643i
\(250\) 0 0
\(251\) −20.9654 + 17.5920i −1.32332 + 1.11040i −0.337732 + 0.941242i \(0.609660\pi\)
−0.985589 + 0.169156i \(0.945896\pi\)
\(252\) −3.02575 2.53890i −0.190604 0.159936i
\(253\) −0.649220 3.68191i −0.0408161 0.231480i
\(254\) −15.6434 27.0951i −0.981553 1.70010i
\(255\) 0 0
\(256\) −13.6440 4.96601i −0.852749 0.310375i
\(257\) −19.0408 6.93029i −1.18773 0.432300i −0.328806 0.944397i \(-0.606646\pi\)
−0.858927 + 0.512098i \(0.828869\pi\)
\(258\) −9.51608 + 16.4823i −0.592445 + 1.02614i
\(259\) 1.72759 + 2.99227i 0.107347 + 0.185931i
\(260\) 0 0
\(261\) −4.37360 3.66989i −0.270719 0.227160i
\(262\) 1.30428 1.09442i 0.0805786 0.0676135i
\(263\) −1.66049 + 9.41708i −0.102390 + 0.580682i 0.889841 + 0.456271i \(0.150815\pi\)
−0.992231 + 0.124411i \(0.960296\pi\)
\(264\) −0.302339 + 0.110042i −0.0186077 + 0.00677263i
\(265\) 0 0
\(266\) 23.0743 + 14.4931i 1.41477 + 0.888629i
\(267\) −16.6236 −1.01735
\(268\) 18.3338 6.67295i 1.11991 0.407615i
\(269\) 0.794363 4.50506i 0.0484332 0.274678i −0.950968 0.309290i \(-0.899909\pi\)
0.999401 + 0.0346123i \(0.0110196\pi\)
\(270\) 0 0
\(271\) −16.9571 14.2287i −1.03007 0.864330i −0.0392098 0.999231i \(-0.512484\pi\)
−0.990859 + 0.134901i \(0.956928\pi\)
\(272\) 0.0258352 + 0.146519i 0.00156649 + 0.00888400i
\(273\) 8.69533 + 15.0608i 0.526265 + 0.911518i
\(274\) −5.12864 + 8.88306i −0.309832 + 0.536645i
\(275\) 0 0
\(276\) 14.4672 + 5.26564i 0.870824 + 0.316954i
\(277\) 11.7771 20.3985i 0.707617 1.22563i −0.258122 0.966112i \(-0.583104\pi\)
0.965739 0.259516i \(-0.0835629\pi\)
\(278\) −2.75990 4.78029i −0.165528 0.286703i
\(279\) −0.996734 5.65276i −0.0596729 0.338422i
\(280\) 0 0
\(281\) 7.90783 6.63545i 0.471741 0.395838i −0.375688 0.926746i \(-0.622594\pi\)
0.847429 + 0.530908i \(0.178149\pi\)
\(282\) −5.34788 + 30.3294i −0.318462 + 1.80609i
\(283\) −29.0110 + 10.5592i −1.72453 + 0.627676i −0.998217 0.0596910i \(-0.980988\pi\)
−0.726310 + 0.687367i \(0.758766\pi\)
\(284\) 26.2733 1.55903
\(285\) 0 0
\(286\) 5.76214 0.340722
\(287\) 35.0853 12.7700i 2.07102 0.753790i
\(288\) −0.857852 + 4.86512i −0.0505494 + 0.286680i
\(289\) −13.0216 + 10.9264i −0.765976 + 0.642730i
\(290\) 0 0
\(291\) −2.57033 14.5770i −0.150675 0.854521i
\(292\) 0.936113 + 1.62140i 0.0547819 + 0.0948850i
\(293\) 3.18052 5.50882i 0.185808 0.321828i −0.758041 0.652207i \(-0.773843\pi\)
0.943848 + 0.330379i \(0.107176\pi\)
\(294\) −9.24839 3.36614i −0.539377 0.196317i
\(295\) 0 0
\(296\) −0.0981961 + 0.170081i −0.00570753 + 0.00988573i
\(297\) 2.18565 + 3.78565i 0.126824 + 0.219666i
\(298\) −2.33297 13.2309i −0.135145 0.766446i
\(299\) −8.79910 7.38332i −0.508865 0.426989i
\(300\) 0 0
\(301\) −2.65977 + 15.0843i −0.153307 + 0.869446i
\(302\) 9.86055 3.58895i 0.567411 0.206521i
\(303\) −5.78456 −0.332314
\(304\) 0.619557 16.6332i 0.0355340 0.953979i
\(305\) 0 0
\(306\) 0.0453035 0.0164891i 0.00258983 0.000942620i
\(307\) 1.02217 5.79702i 0.0583384 0.330854i −0.941645 0.336608i \(-0.890720\pi\)
0.999983 + 0.00575393i \(0.00183154\pi\)
\(308\) −4.76145 + 3.99533i −0.271309 + 0.227655i
\(309\) 0.478371 + 0.401401i 0.0272136 + 0.0228349i
\(310\) 0 0
\(311\) 12.6942 + 21.9871i 0.719825 + 1.24677i 0.961069 + 0.276308i \(0.0891111\pi\)
−0.241245 + 0.970464i \(0.577556\pi\)
\(312\) −0.494243 + 0.856054i −0.0279810 + 0.0484645i
\(313\) 5.67434 + 2.06529i 0.320733 + 0.116737i 0.497369 0.867539i \(-0.334299\pi\)
−0.176637 + 0.984276i \(0.556522\pi\)
\(314\) 22.1274 + 8.05371i 1.24872 + 0.454497i
\(315\) 0 0
\(316\) −9.27896 16.0716i −0.521982 0.904100i
\(317\) −2.75679 15.6346i −0.154837 0.878124i −0.958935 0.283627i \(-0.908462\pi\)
0.804098 0.594497i \(-0.202649\pi\)
\(318\) −17.8357 14.9659i −1.00018 0.839248i
\(319\) −6.88249 + 5.77509i −0.385345 + 0.323343i
\(320\) 0 0
\(321\) −22.8373 + 8.31208i −1.27465 + 0.463935i
\(322\) 24.2647 1.35222
\(323\) −0.150137 + 0.0793824i −0.00835387 + 0.00441695i
\(324\) −21.8327 −1.21293
\(325\) 0 0
\(326\) 0.195463 1.10853i 0.0108257 0.0613956i
\(327\) −22.1896 + 18.6193i −1.22709 + 1.02965i
\(328\) 1.62573 + 1.36415i 0.0897657 + 0.0753224i
\(329\) 4.30396 + 24.4090i 0.237285 + 1.34571i
\(330\) 0 0
\(331\) 7.08478 12.2712i 0.389414 0.674486i −0.602956 0.797774i \(-0.706011\pi\)
0.992371 + 0.123288i \(0.0393440\pi\)
\(332\) −18.8352 6.85544i −1.03371 0.376241i
\(333\) −0.642682 0.233917i −0.0352188 0.0128186i
\(334\) 22.3958 38.7907i 1.22544 2.12253i
\(335\) 0 0
\(336\) 3.89684 + 22.1001i 0.212590 + 1.20566i
\(337\) 1.64694 + 1.38195i 0.0897147 + 0.0752796i 0.686542 0.727090i \(-0.259128\pi\)
−0.596827 + 0.802370i \(0.703572\pi\)
\(338\) −6.57117 + 5.51387i −0.357425 + 0.299915i
\(339\) −0.846120 + 4.79859i −0.0459550 + 0.260623i
\(340\) 0 0
\(341\) −9.03266 −0.489146
\(342\) −5.34286 + 0.738230i −0.288909 + 0.0399189i
\(343\) 13.7245 0.741051
\(344\) −0.818115 + 0.297770i −0.0441098 + 0.0160547i
\(345\) 0 0
\(346\) 17.7415 14.8869i 0.953791 0.800326i
\(347\) 8.46670 + 7.10441i 0.454516 + 0.381385i 0.841109 0.540866i \(-0.181903\pi\)
−0.386592 + 0.922251i \(0.626348\pi\)
\(348\) −6.42450 36.4351i −0.344389 1.95313i
\(349\) −17.6725 30.6097i −0.945989 1.63850i −0.753759 0.657151i \(-0.771762\pi\)
−0.192229 0.981350i \(-0.561572\pi\)
\(350\) 0 0
\(351\) 12.6200 + 4.59330i 0.673604 + 0.245172i
\(352\) 7.30524 + 2.65889i 0.389371 + 0.141719i
\(353\) 11.0952 19.2174i 0.590538 1.02284i −0.403622 0.914926i \(-0.632249\pi\)
0.994160 0.107916i \(-0.0344176\pi\)
\(354\) −5.33036 9.23245i −0.283305 0.490699i
\(355\) 0 0
\(356\) −13.9833 11.7334i −0.741115 0.621869i
\(357\) 0.175404 0.147181i 0.00928334 0.00778965i
\(358\) 2.09441 11.8780i 0.110693 0.627770i
\(359\) 8.93517 3.25214i 0.471580 0.171641i −0.0952879 0.995450i \(-0.530377\pi\)
0.566868 + 0.823809i \(0.308155\pi\)
\(360\) 0 0
\(361\) 18.2881 5.15215i 0.962533 0.271166i
\(362\) −12.4892 −0.656419
\(363\) 17.9884 6.54723i 0.944144 0.343640i
\(364\) −3.31603 + 18.8061i −0.173807 + 0.985709i
\(365\) 0 0
\(366\) −29.5218 24.7717i −1.54313 1.29484i
\(367\) 0.379110 + 2.15004i 0.0197894 + 0.112231i 0.993102 0.117250i \(-0.0374080\pi\)
−0.973313 + 0.229482i \(0.926297\pi\)
\(368\) −7.41107 12.8363i −0.386328 0.669141i
\(369\) −3.69530 + 6.40045i −0.192370 + 0.333194i
\(370\) 0 0
\(371\) −17.6079 6.40877i −0.914159 0.332727i
\(372\) 18.5979 32.2124i 0.964254 1.67014i
\(373\) −6.17035 10.6874i −0.319488 0.553370i 0.660893 0.750480i \(-0.270178\pi\)
−0.980381 + 0.197110i \(0.936844\pi\)
\(374\) −0.0131741 0.0747143i −0.000681219 0.00386338i
\(375\) 0 0
\(376\) −1.07921 + 0.905566i −0.0556561 + 0.0467010i
\(377\) −4.79319 + 27.1835i −0.246862 + 1.40002i
\(378\) −26.6593 + 9.70318i −1.37120 + 0.499078i
\(379\) −18.5014 −0.950352 −0.475176 0.879891i \(-0.657616\pi\)
−0.475176 + 0.879891i \(0.657616\pi\)
\(380\) 0 0
\(381\) 29.4130 1.50688
\(382\) 35.4558 12.9048i 1.81407 0.660269i
\(383\) 1.98517 11.2585i 0.101438 0.575282i −0.891146 0.453717i \(-0.850098\pi\)
0.992584 0.121565i \(-0.0387912\pi\)
\(384\) −2.04517 + 1.71610i −0.104367 + 0.0875746i
\(385\) 0 0
\(386\) 8.39246 + 47.5960i 0.427165 + 2.42257i
\(387\) −1.51595 2.62570i −0.0770601 0.133472i
\(388\) 8.12680 14.0760i 0.412576 0.714602i
\(389\) −11.7685 4.28337i −0.596684 0.217175i 0.0259826 0.999662i \(-0.491729\pi\)
−0.622667 + 0.782487i \(0.713951\pi\)
\(390\) 0 0
\(391\) −0.0756176 + 0.130974i −0.00382415 + 0.00662361i
\(392\) −0.225108 0.389899i −0.0113697 0.0196929i
\(393\) 0.277949 + 1.57633i 0.0140207 + 0.0795153i
\(394\) 10.3783 + 8.70843i 0.522851 + 0.438724i
\(395\) 0 0
\(396\) 0.213646 1.21165i 0.0107361 0.0608877i
\(397\) 11.0417 4.01886i 0.554168 0.201701i −0.0497292 0.998763i \(-0.515836\pi\)
0.603898 + 0.797062i \(0.293614\pi\)
\(398\) 6.38602 0.320102
\(399\) −22.6459 + 11.9736i −1.13371 + 0.599430i
\(400\) 0 0
\(401\) 13.7588 5.00780i 0.687083 0.250078i 0.0251970 0.999683i \(-0.491979\pi\)
0.661886 + 0.749605i \(0.269756\pi\)
\(402\) −6.23741 + 35.3741i −0.311094 + 1.76430i
\(403\) −21.2585 + 17.8380i −1.05896 + 0.888573i
\(404\) −4.86582 4.08290i −0.242083 0.203132i
\(405\) 0 0
\(406\) −29.1551 50.4980i −1.44694 2.50618i
\(407\) −0.538130 + 0.932068i −0.0266741 + 0.0462009i
\(408\) 0.0122299 + 0.00445134i 0.000605472 + 0.000220374i
\(409\) −11.9790 4.36001i −0.592324 0.215588i 0.0284271 0.999596i \(-0.490950\pi\)
−0.620751 + 0.784007i \(0.713172\pi\)
\(410\) 0 0
\(411\) −4.82149 8.35106i −0.237827 0.411928i
\(412\) 0.119073 + 0.675295i 0.00586630 + 0.0332694i
\(413\) −6.57244 5.51494i −0.323409 0.271372i
\(414\) −3.67933 + 3.08732i −0.180829 + 0.151734i
\(415\) 0 0
\(416\) 22.4438 8.16889i 1.10040 0.400513i
\(417\) 5.18923 0.254118
\(418\) −0.315930 + 8.48176i −0.0154527 + 0.414856i
\(419\) 2.84601 0.139037 0.0695184 0.997581i \(-0.477854\pi\)
0.0695184 + 0.997581i \(0.477854\pi\)
\(420\) 0 0
\(421\) 1.93626 10.9811i 0.0943677 0.535186i −0.900572 0.434708i \(-0.856852\pi\)
0.994939 0.100478i \(-0.0320372\pi\)
\(422\) −17.7444 + 14.8893i −0.863785 + 0.724802i
\(423\) −3.75831 3.15360i −0.182735 0.153333i
\(424\) −0.184947 1.04889i −0.00898182 0.0509384i
\(425\) 0 0
\(426\) −24.1854 + 41.8903i −1.17178 + 2.02959i
\(427\) −29.1448 10.6078i −1.41041 0.513349i
\(428\) −25.0770 9.12728i −1.21214 0.441184i
\(429\) −2.70853 + 4.69131i −0.130769 + 0.226498i
\(430\) 0 0
\(431\) −2.59366 14.7094i −0.124932 0.708525i −0.981348 0.192239i \(-0.938425\pi\)
0.856416 0.516286i \(-0.172686\pi\)
\(432\) 13.2756 + 11.1395i 0.638721 + 0.535950i
\(433\) 29.6894 24.9123i 1.42678 1.19721i 0.479195 0.877708i \(-0.340929\pi\)
0.947585 0.319503i \(-0.103516\pi\)
\(434\) 10.1798 57.7323i 0.488645 2.77124i
\(435\) 0 0
\(436\) −31.8074 −1.52330
\(437\) 11.3506 12.5473i 0.542971 0.600218i
\(438\) −3.44688 −0.164698
\(439\) 29.5331 10.7492i 1.40954 0.513030i 0.478544 0.878064i \(-0.341165\pi\)
0.930994 + 0.365034i \(0.118943\pi\)
\(440\) 0 0
\(441\) 1.20105 1.00780i 0.0571929 0.0479906i
\(442\) −0.178554 0.149824i −0.00849293 0.00712641i
\(443\) −1.84950 10.4890i −0.0878722 0.498348i −0.996700 0.0811761i \(-0.974132\pi\)
0.908828 0.417172i \(-0.136979\pi\)
\(444\) −2.21597 3.83817i −0.105165 0.182152i
\(445\) 0 0
\(446\) −14.2748 5.19559i −0.675930 0.246018i
\(447\) 11.8687 + 4.31985i 0.561370 + 0.204322i
\(448\) −13.4196 + 23.2435i −0.634019 + 1.09815i
\(449\) −2.05200 3.55417i −0.0968399 0.167732i 0.813535 0.581516i \(-0.197540\pi\)
−0.910375 + 0.413784i \(0.864207\pi\)
\(450\) 0 0
\(451\) 8.90923 + 7.47573i 0.419519 + 0.352019i
\(452\) −4.09871 + 3.43923i −0.192787 + 0.161768i
\(453\) −1.71303 + 9.71508i −0.0804852 + 0.456454i
\(454\) −7.98224 + 2.90530i −0.374625 + 0.136352i
\(455\) 0 0
\(456\) −1.23300 0.774452i −0.0577403 0.0362670i
\(457\) −9.25947 −0.433140 −0.216570 0.976267i \(-0.569487\pi\)
−0.216570 + 0.976267i \(0.569487\pi\)
\(458\) −42.8873 + 15.6097i −2.00399 + 0.729394i
\(459\) 0.0307052 0.174138i 0.00143319 0.00812805i
\(460\) 0 0
\(461\) 5.09121 + 4.27203i 0.237121 + 0.198968i 0.753603 0.657330i \(-0.228314\pi\)
−0.516482 + 0.856298i \(0.672759\pi\)
\(462\) −1.98711 11.2695i −0.0924489 0.524304i
\(463\) 11.1474 + 19.3079i 0.518064 + 0.897313i 0.999780 + 0.0209853i \(0.00668032\pi\)
−0.481716 + 0.876327i \(0.659986\pi\)
\(464\) −17.8094 + 30.8469i −0.826783 + 1.43203i
\(465\) 0 0
\(466\) −20.8566 7.59118i −0.966163 0.351655i
\(467\) −7.73697 + 13.4008i −0.358024 + 0.620116i −0.987631 0.156798i \(-0.949883\pi\)
0.629606 + 0.776914i \(0.283216\pi\)
\(468\) −1.88998 3.27355i −0.0873645 0.151320i
\(469\) 5.01985 + 28.4690i 0.231795 + 1.31458i
\(470\) 0 0
\(471\) −16.9581 + 14.2295i −0.781388 + 0.655663i
\(472\) 0.0846832 0.480262i 0.00389786 0.0221059i
\(473\) −4.48340 + 1.63182i −0.206147 + 0.0750313i
\(474\) 34.1662 1.56931
\(475\) 0 0
\(476\) 0.251429 0.0115242
\(477\) 3.48537 1.26857i 0.159584 0.0580839i
\(478\) −0.956820 + 5.42640i −0.0437639 + 0.248198i
\(479\) 24.6710 20.7014i 1.12725 0.945872i 0.128299 0.991736i \(-0.459048\pi\)
0.998948 + 0.0458635i \(0.0146039\pi\)
\(480\) 0 0
\(481\) 0.574182 + 3.25635i 0.0261805 + 0.148477i
\(482\) −11.2746 19.5281i −0.513543 0.889482i
\(483\) −11.4057 + 19.7553i −0.518979 + 0.898898i
\(484\) 19.7525 + 7.18934i 0.897843 + 0.326788i
\(485\) 0 0
\(486\) 6.33539 10.9732i 0.287379 0.497755i
\(487\) −1.82569 3.16219i −0.0827301 0.143293i 0.821692 0.569932i \(-0.193031\pi\)
−0.904422 + 0.426640i \(0.859697\pi\)
\(488\) −0.306125 1.73612i −0.0138576 0.0785906i
\(489\) 0.810640 + 0.680208i 0.0366584 + 0.0307601i
\(490\) 0 0
\(491\) 0.789859 4.47952i 0.0356459 0.202158i −0.961784 0.273810i \(-0.911716\pi\)
0.997430 + 0.0716523i \(0.0228272\pi\)
\(492\) −45.0038 + 16.3801i −2.02893 + 0.738470i
\(493\) 0.363431 0.0163681
\(494\) 16.0065 + 20.5858i 0.720166 + 0.926201i
\(495\) 0 0
\(496\) −33.6504 + 12.2477i −1.51095 + 0.549940i
\(497\) −6.75989 + 38.3372i −0.303222 + 1.71966i
\(498\) 28.2686 23.7202i 1.26675 1.06293i
\(499\) −16.7177 14.0278i −0.748387 0.627972i 0.186689 0.982419i \(-0.440224\pi\)
−0.935076 + 0.354448i \(0.884669\pi\)
\(500\) 0 0
\(501\) 21.0545 + 36.4675i 0.940648 + 1.62925i
\(502\) 27.6641 47.9157i 1.23471 2.13858i
\(503\) −23.2469 8.46117i −1.03653 0.377265i −0.232964 0.972485i \(-0.574842\pi\)
−0.803562 + 0.595221i \(0.797065\pi\)
\(504\) 0.312588 + 0.113773i 0.0139238 + 0.00506785i
\(505\) 0 0
\(506\) 3.77912 + 6.54563i 0.168003 + 0.290989i
\(507\) −1.40036 7.94181i −0.0621920 0.352708i
\(508\) 24.7415 + 20.7606i 1.09773 + 0.921101i
\(509\) −13.2902 + 11.1518i −0.589078 + 0.494295i −0.887914 0.460009i \(-0.847846\pi\)
0.298836 + 0.954305i \(0.403402\pi\)
\(510\) 0 0
\(511\) −2.60674 + 0.948777i −0.115316 + 0.0419714i
\(512\) 32.1626 1.42140
\(513\) −7.45318 + 18.3245i −0.329066 + 0.809047i
\(514\) 40.9637 1.80683
\(515\) 0 0
\(516\) 3.41168 19.3486i 0.150191 0.851776i
\(517\) −5.91424 + 4.96264i −0.260108 + 0.218257i
\(518\) −5.35085 4.48990i −0.235103 0.197275i
\(519\) 3.78083 + 21.4421i 0.165960 + 0.941206i
\(520\) 0 0
\(521\) −0.228337 + 0.395492i −0.0100036 + 0.0173268i −0.870984 0.491312i \(-0.836518\pi\)
0.860980 + 0.508638i \(0.169851\pi\)
\(522\) 10.8460 + 3.94762i 0.474717 + 0.172783i
\(523\) −35.5171 12.9272i −1.55305 0.565265i −0.583922 0.811810i \(-0.698483\pi\)
−0.969132 + 0.246544i \(0.920705\pi\)
\(524\) −0.878815 + 1.52215i −0.0383912 + 0.0664955i
\(525\) 0 0
\(526\) −3.35687 19.0377i −0.146366 0.830085i
\(527\) 0.279898 + 0.234863i 0.0121926 + 0.0102308i
\(528\) −5.35480 + 4.49321i −0.233038 + 0.195542i
\(529\) −1.37758 + 7.81265i −0.0598949 + 0.339681i
\(530\) 0 0
\(531\) 1.69830 0.0736998
\(532\) −27.5004 5.91224i −1.19229 0.256328i
\(533\) 35.7313 1.54769
\(534\) 31.5798 11.4941i 1.36659 0.497399i
\(535\) 0 0
\(536\) −1.25872 + 1.05619i −0.0543684 + 0.0456205i
\(537\) 8.68608 + 7.28849i 0.374832 + 0.314522i
\(538\) 1.60590 + 9.10750i 0.0692352 + 0.392652i
\(539\) −1.23363 2.13671i −0.0531361 0.0920344i
\(540\) 0 0
\(541\) 19.8556 + 7.22684i 0.853658 + 0.310706i 0.731531 0.681808i \(-0.238806\pi\)
0.122127 + 0.992514i \(0.461028\pi\)
\(542\) 42.0515 + 15.3055i 1.80627 + 0.657428i
\(543\) 5.87063 10.1682i 0.251933 0.436361i
\(544\) −0.157235 0.272339i −0.00674140 0.0116765i
\(545\) 0 0
\(546\) −26.9320 22.5987i −1.15258 0.967134i
\(547\) 9.60806 8.06212i 0.410811 0.344711i −0.413843 0.910348i \(-0.635814\pi\)
0.824655 + 0.565637i \(0.191369\pi\)
\(548\) 1.83871 10.4278i 0.0785458 0.445455i
\(549\) 5.76901 2.09975i 0.246215 0.0896150i
\(550\) 0 0
\(551\) −39.7508 8.54591i −1.69344 0.364068i
\(552\) −1.29660 −0.0551872
\(553\) 25.8386 9.40449i 1.09877 0.399920i
\(554\) −8.26870 + 46.8941i −0.351303 + 1.99234i
\(555\) 0 0
\(556\) 4.36504 + 3.66271i 0.185119 + 0.155333i
\(557\) 5.56111 + 31.5386i 0.235632 + 1.33633i 0.841279 + 0.540601i \(0.181803\pi\)
−0.605647 + 0.795733i \(0.707086\pi\)
\(558\) 5.80201 + 10.0494i 0.245618 + 0.425424i
\(559\) −7.32916 + 12.6945i −0.309990 + 0.536919i
\(560\) 0 0
\(561\) 0.0670220 + 0.0243940i 0.00282967 + 0.00102992i
\(562\) −10.4345 + 18.0731i −0.440153 + 0.762368i
\(563\) 9.79034 + 16.9574i 0.412614 + 0.714668i 0.995175 0.0981190i \(-0.0312826\pi\)
−0.582561 + 0.812787i \(0.697949\pi\)
\(564\) −5.52068 31.3093i −0.232463 1.31836i
\(565\) 0 0
\(566\) 47.8113 40.1184i 2.00966 1.68630i
\(567\) 5.61736 31.8576i 0.235907 1.33789i
\(568\) −2.07926 + 0.756789i −0.0872439 + 0.0317542i
\(569\) −18.6525 −0.781953 −0.390977 0.920401i \(-0.627863\pi\)
−0.390977 + 0.920401i \(0.627863\pi\)
\(570\) 0 0
\(571\) −0.460181 −0.0192580 −0.00962899 0.999954i \(-0.503065\pi\)
−0.00962899 + 0.999954i \(0.503065\pi\)
\(572\) −5.58960 + 2.03445i −0.233713 + 0.0850645i
\(573\) −6.15957 + 34.9327i −0.257320 + 1.45933i
\(574\) −57.8219 + 48.5184i −2.41344 + 2.02512i
\(575\) 0 0
\(576\) −0.922533 5.23194i −0.0384389 0.217998i
\(577\) 5.87392 + 10.1739i 0.244534 + 0.423546i 0.962001 0.273047i \(-0.0880316\pi\)
−0.717466 + 0.696593i \(0.754698\pi\)
\(578\) 17.1822 29.7605i 0.714686 1.23787i
\(579\) −42.6957 15.5400i −1.77437 0.645819i
\(580\) 0 0
\(581\) 14.8494 25.7198i 0.616055 1.06704i
\(582\) 14.9619 + 25.9148i 0.620191 + 1.07420i
\(583\) −1.01354 5.74806i −0.0419765 0.238060i
\(584\) −0.120787 0.101352i −0.00499821 0.00419399i
\(585\) 0 0
\(586\) −2.23304 + 12.6642i −0.0922461 + 0.523154i
\(587\) −4.60486 + 1.67603i −0.190063 + 0.0691773i −0.435298 0.900286i \(-0.643357\pi\)
0.245235 + 0.969464i \(0.421135\pi\)
\(588\) 10.1599 0.418989
\(589\) −25.0916 32.2701i −1.03388 1.32967i
\(590\) 0 0
\(591\) −11.9684 + 4.35615i −0.492316 + 0.179188i
\(592\) −0.740928 + 4.20201i −0.0304519 + 0.172702i
\(593\) 14.1700 11.8900i 0.581892 0.488265i −0.303676 0.952775i \(-0.598214\pi\)
0.885568 + 0.464510i \(0.153770\pi\)
\(594\) −6.76960 5.68037i −0.277760 0.233068i
\(595\) 0 0
\(596\) 6.93456 + 12.0110i 0.284051 + 0.491990i
\(597\) −3.00178 + 5.19924i −0.122855 + 0.212791i
\(598\) 21.8207 + 7.94210i 0.892316 + 0.324777i
\(599\) 20.1336 + 7.32805i 0.822638 + 0.299416i 0.718834 0.695182i \(-0.244676\pi\)
0.103804 + 0.994598i \(0.466898\pi\)
\(600\) 0 0
\(601\) −15.0195 26.0146i −0.612659 1.06116i −0.990790 0.135404i \(-0.956767\pi\)
0.378132 0.925752i \(-0.376567\pi\)
\(602\) −5.37705 30.4948i −0.219152 1.24287i
\(603\) −4.38344 3.67814i −0.178507 0.149785i
\(604\) −8.29813 + 6.96296i −0.337646 + 0.283319i
\(605\) 0 0
\(606\) 10.9889 3.99964i 0.446394 0.162474i
\(607\) −29.3882 −1.19283 −0.596415 0.802676i \(-0.703409\pi\)
−0.596415 + 0.802676i \(0.703409\pi\)
\(608\) 10.7939 + 33.4848i 0.437750 + 1.35799i
\(609\) 54.8180 2.22134
\(610\) 0 0
\(611\) −4.11887 + 23.3593i −0.166632 + 0.945015i
\(612\) −0.0381250 + 0.0319907i −0.00154111 + 0.00129315i
\(613\) 4.22183 + 3.54254i 0.170518 + 0.143082i 0.724053 0.689744i \(-0.242277\pi\)
−0.553535 + 0.832826i \(0.686721\pi\)
\(614\) 2.06644 + 11.7194i 0.0833948 + 0.472955i
\(615\) 0 0
\(616\) 0.261736 0.453340i 0.0105456 0.0182656i
\(617\) 43.1381 + 15.7010i 1.73667 + 0.632098i 0.999069 0.0431340i \(-0.0137342\pi\)
0.737606 + 0.675232i \(0.235956\pi\)
\(618\) −1.18630 0.431779i −0.0477201 0.0173687i
\(619\) 0.239303 0.414484i 0.00961839 0.0166595i −0.861176 0.508307i \(-0.830272\pi\)
0.870795 + 0.491647i \(0.163605\pi\)
\(620\) 0 0
\(621\) 3.05900 + 17.3485i 0.122754 + 0.696170i
\(622\) −39.3179 32.9916i −1.57650 1.32284i
\(623\) 20.7188 17.3851i 0.830081 0.696521i
\(624\) −3.72925 + 21.1497i −0.149290 + 0.846664i
\(625\) 0 0
\(626\) −12.2075 −0.487912
\(627\) −6.75701 4.24412i −0.269849 0.169494i
\(628\) −24.3083 −0.970008
\(629\) 0.0409104 0.0148902i 0.00163120 0.000593710i
\(630\) 0 0
\(631\) 12.9110 10.8336i 0.513980 0.431281i −0.348547 0.937291i \(-0.613325\pi\)
0.862527 + 0.506011i \(0.168880\pi\)
\(632\) 1.19727 + 1.00463i 0.0476248 + 0.0399620i
\(633\) −3.78144 21.4456i −0.150299 0.852387i
\(634\) 16.0473 + 27.7948i 0.637321 + 1.10387i
\(635\) 0 0
\(636\) 22.5857 + 8.22051i 0.895580 + 0.325964i
\(637\) −7.12299 2.59256i −0.282223 0.102721i
\(638\) 9.08156 15.7297i 0.359543 0.622746i
\(639\) −3.85283 6.67329i −0.152416 0.263991i
\(640\) 0 0
\(641\) 17.5433 + 14.7206i 0.692920 + 0.581429i 0.919750 0.392506i \(-0.128392\pi\)
−0.226830 + 0.973934i \(0.572836\pi\)
\(642\) 37.6367 31.5809i 1.48540 1.24640i
\(643\) 1.49019 8.45131i 0.0587675 0.333287i −0.941222 0.337788i \(-0.890321\pi\)
0.999990 + 0.00450051i \(0.00143256\pi\)
\(644\) −23.5381 + 8.56716i −0.927530 + 0.337593i
\(645\) 0 0
\(646\) 0.230328 0.254613i 0.00906215 0.0100176i
\(647\) 27.2647 1.07188 0.535942 0.844255i \(-0.319957\pi\)
0.535942 + 0.844255i \(0.319957\pi\)
\(648\) 1.72783 0.628880i 0.0678757 0.0247047i
\(649\) 0.464077 2.63191i 0.0182166 0.103312i
\(650\) 0 0
\(651\) 42.2183 + 35.4254i 1.65467 + 1.38843i
\(652\) 0.201779 + 1.14435i 0.00790228 + 0.0448160i
\(653\) −13.1299 22.7417i −0.513813 0.889950i −0.999872 0.0160238i \(-0.994899\pi\)
0.486059 0.873926i \(-0.338434\pi\)
\(654\) 29.2796 50.7138i 1.14492 1.98307i
\(655\) 0 0
\(656\) 43.3272 + 15.7698i 1.69164 + 0.615708i
\(657\) 0.274551 0.475536i 0.0107113 0.0185524i
\(658\) −25.0534 43.3938i −0.976685 1.69167i
\(659\) −3.99590 22.6619i −0.155658 0.882781i −0.958182 0.286160i \(-0.907621\pi\)
0.802524 0.596620i \(-0.203490\pi\)
\(660\) 0 0
\(661\) 23.4408 19.6692i 0.911742 0.765042i −0.0607080 0.998156i \(-0.519336\pi\)
0.972450 + 0.233114i \(0.0748914\pi\)
\(662\) −4.97423 + 28.2102i −0.193329 + 1.09642i
\(663\) 0.205911 0.0749455i 0.00799693 0.00291064i
\(664\) 1.68807 0.0655100
\(665\) 0 0
\(666\) 1.38264 0.0535763
\(667\) −34.0234 + 12.3835i −1.31739 + 0.479491i
\(668\) −8.02930 + 45.5364i −0.310663 + 1.76186i
\(669\) 10.9400 9.17973i 0.422964 0.354909i
\(670\) 0 0
\(671\) −1.67761 9.51422i −0.0647636 0.367292i
\(672\) −23.7165 41.0781i −0.914883 1.58462i
\(673\) −18.9334 + 32.7936i −0.729828 + 1.26410i 0.227128 + 0.973865i \(0.427066\pi\)
−0.956956 + 0.290234i \(0.906267\pi\)
\(674\) −4.08422 1.48654i −0.157318 0.0572592i
\(675\) 0 0
\(676\) 4.42761 7.66885i 0.170293 0.294956i
\(677\) −21.8471 37.8403i −0.839654 1.45432i −0.890184 0.455600i \(-0.849425\pi\)
0.0505308 0.998723i \(-0.483909\pi\)
\(678\) −1.71053 9.70091i −0.0656926 0.372561i
\(679\) 18.4484 + 15.4800i 0.707983 + 0.594068i
\(680\) 0 0
\(681\) 1.38672 7.86447i 0.0531392 0.301367i
\(682\) 17.1593 6.24549i 0.657065 0.239152i
\(683\) −15.0878 −0.577320 −0.288660 0.957432i \(-0.593210\pi\)
−0.288660 + 0.957432i \(0.593210\pi\)
\(684\) 4.92222 2.60254i 0.188206 0.0995104i
\(685\) 0 0
\(686\) −26.0724 + 9.48956i −0.995447 + 0.362313i
\(687\) 7.45062 42.2546i 0.284259 1.61211i
\(688\) −14.4899 + 12.1584i −0.552421 + 0.463536i
\(689\) −13.7368 11.5266i −0.523331 0.439127i
\(690\) 0 0
\(691\) −5.36034 9.28438i −0.203917 0.353194i 0.745870 0.666091i \(-0.232034\pi\)
−0.949787 + 0.312897i \(0.898701\pi\)
\(692\) −11.9541 + 20.7052i −0.454428 + 0.787093i
\(693\) 1.71303 + 0.623493i 0.0650727 + 0.0236845i
\(694\) −20.9964 7.64207i −0.797013 0.290089i
\(695\) 0 0
\(696\) 1.55793 + 2.69841i 0.0590531 + 0.102283i
\(697\) −0.0816935 0.463307i −0.00309436 0.0175490i
\(698\) 54.7371 + 45.9299i 2.07183 + 1.73847i
\(699\) 15.9842 13.4123i 0.604578 0.507301i
\(700\) 0 0
\(701\) −23.0611 + 8.39354i −0.871005 + 0.317020i −0.738574 0.674172i \(-0.764500\pi\)
−0.132431 + 0.991192i \(0.542278\pi\)
\(702\) −27.1501 −1.02472
\(703\) −4.82476 + 0.666644i −0.181969 + 0.0251429i
\(704\) −8.36023 −0.315088
\(705\) 0 0
\(706\) −7.78994 + 44.1790i −0.293178 + 1.66270i
\(707\) 7.20958 6.04956i 0.271144 0.227517i
\(708\) 8.43046 + 7.07399i 0.316836 + 0.265857i
\(709\) −7.43295 42.1543i −0.279150 1.58314i −0.725462 0.688262i \(-0.758374\pi\)
0.446312 0.894878i \(-0.352737\pi\)
\(710\) 0 0
\(711\) −2.72141 + 4.71362i −0.102061 + 0.176775i
\(712\) 1.44461 + 0.525795i 0.0541391 + 0.0197050i
\(713\) −34.2059 12.4499i −1.28102 0.466254i
\(714\) −0.231448 + 0.400880i −0.00866173 + 0.0150026i
\(715\) 0 0
\(716\) 2.16208 + 12.2618i 0.0808007 + 0.458244i
\(717\) −3.96820 3.32971i −0.148195 0.124350i
\(718\) −14.7255 + 12.3562i −0.549551 + 0.461128i
\(719\) 3.69371 20.9481i 0.137752 0.781231i −0.835152 0.550020i \(-0.814620\pi\)
0.972904 0.231211i \(-0.0742688\pi\)
\(720\) 0 0
\(721\) −1.01601 −0.0378381
\(722\) −31.1796 + 22.4326i −1.16038 + 0.834854i
\(723\) 21.1987 0.788388
\(724\) 12.1152 4.40959i 0.450259 0.163881i
\(725\) 0 0
\(726\) −29.6455 + 24.8755i −1.10025 + 0.923217i
\(727\) 8.06976 + 6.77133i 0.299291 + 0.251135i 0.780049 0.625718i \(-0.215194\pi\)
−0.480758 + 0.876853i \(0.659639\pi\)
\(728\) −0.279271 1.58383i −0.0103505 0.0587005i
\(729\) −9.73641 16.8640i −0.360608 0.624591i
\(730\) 0 0
\(731\) 0.181359 + 0.0660091i 0.00670779 + 0.00244144i
\(732\) 37.3839 + 13.6066i 1.38175 + 0.502916i
\(733\) −12.5446 + 21.7279i −0.463346 + 0.802538i −0.999125 0.0418196i \(-0.986685\pi\)
0.535779 + 0.844358i \(0.320018\pi\)
\(734\) −2.20681 3.82230i −0.0814548 0.141084i
\(735\) 0 0
\(736\) 23.9995 + 20.1380i 0.884634 + 0.742296i
\(737\) −6.89797 + 5.78809i −0.254090 + 0.213207i
\(738\) 2.59447 14.7140i 0.0955039 0.541629i
\(739\) −26.7511 + 9.73660i −0.984054 + 0.358166i −0.783415 0.621499i \(-0.786524\pi\)
−0.200639 + 0.979665i \(0.564302\pi\)
\(740\) 0 0
\(741\) −24.2841 + 3.35537i −0.892099 + 0.123262i
\(742\) 37.8811 1.39066
\(743\) −9.54830 + 3.47530i −0.350293 + 0.127496i −0.511173 0.859478i \(-0.670789\pi\)
0.160880 + 0.986974i \(0.448567\pi\)
\(744\) −0.543966 + 3.08498i −0.0199427 + 0.113101i
\(745\) 0 0
\(746\) 19.1114 + 16.0364i 0.699718 + 0.587133i
\(747\) 1.02082 + 5.78934i 0.0373498 + 0.211821i
\(748\) 0.0391591 + 0.0678256i 0.00143180 + 0.00247995i
\(749\) 19.7703 34.2432i 0.722392 1.25122i
\(750\) 0 0
\(751\) 24.1407 + 8.78648i 0.880905 + 0.320623i 0.742575 0.669763i \(-0.233604\pi\)
0.138330 + 0.990386i \(0.455826\pi\)
\(752\) −15.3040 + 26.5072i −0.558078 + 0.966620i
\(753\) 26.0074 + 45.0461i 0.947762 + 1.64157i
\(754\) −9.68999 54.9547i −0.352889 2.00133i
\(755\) 0 0
\(756\) 22.4351 18.8252i 0.815955 0.684668i
\(757\) 5.48348 31.0983i 0.199300 1.13029i −0.706860 0.707354i \(-0.749889\pi\)
0.906160 0.422935i \(-0.139000\pi\)
\(758\) 35.1471 12.7925i 1.27660 0.464644i
\(759\) −7.10559 −0.257917
\(760\) 0 0
\(761\) −3.42183 −0.124041 −0.0620207 0.998075i \(-0.519754\pi\)
−0.0620207 + 0.998075i \(0.519754\pi\)
\(762\) −55.8760 + 20.3372i −2.02417 + 0.736738i
\(763\) 8.18375 46.4123i 0.296272 1.68024i
\(764\) −29.8377 + 25.0368i −1.07949 + 0.905801i
\(765\) 0 0
\(766\) 4.01327 + 22.7604i 0.145005 + 0.822365i
\(767\) −4.10537 7.11071i −0.148236 0.256753i
\(768\) −13.7976 + 23.8982i −0.497878 + 0.862351i
\(769\) 26.7893 + 9.75052i 0.966048 + 0.351613i 0.776401 0.630239i \(-0.217043\pi\)
0.189648 + 0.981852i \(0.439265\pi\)
\(770\) 0 0
\(771\) −19.2552 + 33.3510i −0.693459 + 1.20111i
\(772\) −24.9459 43.2076i −0.897824 1.55508i
\(773\) −0.247597 1.40419i −0.00890545 0.0505053i 0.980031 0.198844i \(-0.0637186\pi\)
−0.988937 + 0.148338i \(0.952608\pi\)
\(774\) 4.69535 + 3.93987i 0.168771 + 0.141616i
\(775\) 0 0
\(776\) −0.237699 + 1.34806i −0.00853291 + 0.0483925i
\(777\) 6.17070 2.24595i 0.221372 0.0805730i
\(778\) 25.3182 0.907701
\(779\) −1.95910 + 52.5958i −0.0701920 + 1.88444i
\(780\) 0 0
\(781\) −11.3947 + 4.14732i −0.407733 + 0.148403i
\(782\) 0.0530912 0.301095i 0.00189854 0.0107671i
\(783\) 32.4290 27.2112i 1.15892 0.972448i
\(784\) −7.49302 6.28739i −0.267608 0.224550i
\(785\) 0 0
\(786\) −1.61795 2.80237i −0.0577103 0.0999572i
\(787\) 12.1600 21.0617i 0.433456 0.750768i −0.563712 0.825971i \(-0.690627\pi\)
0.997168 + 0.0752034i \(0.0239606\pi\)
\(788\) −13.1422 4.78338i −0.468172 0.170401i
\(789\) 17.0777 + 6.21577i 0.607982 + 0.221287i
\(790\) 0 0
\(791\) −3.96386 6.86560i −0.140938 0.244113i
\(792\) 0.0179930 + 0.102043i 0.000639354 + 0.00362596i
\(793\) −22.7373 19.0788i −0.807424 0.677509i
\(794\) −18.1972 + 15.2693i −0.645794 + 0.541885i
\(795\) 0 0
\(796\) −6.19479 + 2.25472i −0.219569 + 0.0799164i
\(797\) −33.5714 −1.18916 −0.594580 0.804037i \(-0.702681\pi\)
−0.594580 + 0.804037i \(0.702681\pi\)
\(798\) 34.7414 38.4044i 1.22983 1.35950i
\(799\) 0.312303 0.0110485
\(800\) 0 0
\(801\) −0.929654 + 5.27233i −0.0328477 + 0.186289i
\(802\) −22.6751 + 19.0266i −0.800684 + 0.671854i
\(803\) −0.661932 0.555427i −0.0233591 0.0196006i
\(804\) −6.43895 36.5171i −0.227084 1.28786i
\(805\) 0 0
\(806\) 28.0509 48.5856i 0.988052 1.71136i
\(807\) −8.16983 2.97357i −0.287592 0.104675i
\(808\) 0.502685 + 0.182962i 0.0176844 + 0.00643659i
\(809\) −9.12037 + 15.7970i −0.320655 + 0.555391i −0.980623 0.195902i \(-0.937236\pi\)
0.659968 + 0.751294i \(0.270570\pi\)
\(810\) 0 0
\(811\) −6.34578 35.9887i −0.222830 1.26373i −0.866790 0.498674i \(-0.833820\pi\)
0.643959 0.765060i \(-0.277291\pi\)
\(812\) 46.1114 + 38.6921i 1.61819 + 1.35783i
\(813\) −32.2277 + 27.0422i −1.13027 + 0.948413i
\(814\) 0.377821 2.14273i 0.0132426 0.0751026i
\(815\) 0 0
\(816\) 0.282761 0.00989863
\(817\) −18.2842 11.4844i −0.639682 0.401788i
\(818\) 25.7712 0.901069
\(819\) 5.26294 1.91555i 0.183902 0.0669348i
\(820\) 0 0
\(821\) 8.13847 6.82899i 0.284035 0.238333i −0.489628 0.871932i \(-0.662867\pi\)
0.773662 + 0.633598i \(0.218423\pi\)
\(822\) 14.9336 + 12.5308i 0.520869 + 0.437061i
\(823\) 6.43574 + 36.4989i 0.224336 + 1.27227i 0.863951 + 0.503577i \(0.167983\pi\)
−0.639615 + 0.768696i \(0.720906\pi\)
\(824\) −0.0288749 0.0500128i −0.00100591 0.00174228i
\(825\) 0 0
\(826\) 16.2989 + 5.93231i 0.567111 + 0.206411i
\(827\) 26.1420 + 9.51490i 0.909045 + 0.330865i 0.753871 0.657022i \(-0.228184\pi\)
0.155174 + 0.987887i \(0.450406\pi\)
\(828\) 2.47911 4.29394i 0.0861549 0.149225i
\(829\) 6.90991 + 11.9683i 0.239991 + 0.415677i 0.960711 0.277549i \(-0.0895221\pi\)
−0.720720 + 0.693226i \(0.756189\pi\)
\(830\) 0 0
\(831\) −34.2926 28.7749i −1.18960 0.998190i
\(832\) −19.6759 + 16.5100i −0.682139 + 0.572383i
\(833\) −0.0173307 + 0.0982871i −0.000600472 + 0.00340545i
\(834\) −9.85798 + 3.58801i −0.341354 + 0.124243i
\(835\) 0 0
\(836\) −2.68820 8.33932i −0.0929732 0.288422i
\(837\) 42.5602 1.47110
\(838\) −5.40657 + 1.96783i −0.186767 + 0.0679776i
\(839\) −1.11616 + 6.33006i −0.0385341 + 0.218538i −0.997994 0.0633071i \(-0.979835\pi\)
0.959460 + 0.281845i \(0.0909464\pi\)
\(840\) 0 0
\(841\) 44.4370 + 37.2871i 1.53231 + 1.28576i
\(842\) 3.91439 + 22.1996i 0.134899 + 0.765048i
\(843\) −9.80960 16.9907i −0.337861 0.585192i
\(844\) 11.9561 20.7085i 0.411545 0.712817i
\(845\) 0 0
\(846\) 9.32017 + 3.39226i 0.320434 + 0.116628i
\(847\) −15.5726 + 26.9726i −0.535081 + 0.926788i
\(848\) −11.5699 20.0396i −0.397311 0.688163i
\(849\) 10.1889 + 57.7839i 0.349681 + 1.98314i
\(850\) 0 0
\(851\) −3.32254 + 2.78794i −0.113895 + 0.0955695i
\(852\) 8.67089 49.1751i 0.297060 1.68471i
\(853\) 24.8033 9.02767i 0.849250 0.309102i 0.119515 0.992832i \(-0.461866\pi\)
0.729734 + 0.683731i \(0.239644\pi\)
\(854\) 62.7009 2.14558
\(855\) 0 0
\(856\) 2.24749 0.0768177
\(857\) 16.0036 5.82483i 0.546672 0.198973i −0.0538950 0.998547i \(-0.517164\pi\)
0.600567 + 0.799574i \(0.294941\pi\)
\(858\) 1.90166 10.7848i 0.0649215 0.368188i
\(859\) 18.9375 15.8905i 0.646140 0.542176i −0.259757 0.965674i \(-0.583642\pi\)
0.905897 + 0.423498i \(0.139198\pi\)
\(860\) 0 0
\(861\) −12.3222 69.8826i −0.419939 2.38159i
\(862\) 15.0977 + 26.1500i 0.514230 + 0.890673i
\(863\) −0.519450 + 0.899714i −0.0176823 + 0.0306266i −0.874731 0.484609i \(-0.838962\pi\)
0.857049 + 0.515235i \(0.172295\pi\)
\(864\) −34.4209 12.5282i −1.17102 0.426218i
\(865\) 0 0
\(866\) −39.1757 + 67.8542i −1.33124 + 2.30578i
\(867\) 16.1532 + 27.9782i 0.548591 + 0.950188i
\(868\) 10.5087 + 59.5978i 0.356688 + 2.02288i
\(869\) 6.56122 + 5.50552i 0.222574 + 0.186762i
\(870\) 0 0
\(871\) −4.80397 + 27.2447i −0.162776 + 0.923150i
\(872\) 2.51722 0.916195i 0.0852440 0.0310263i
\(873\) −4.76699 −0.161338
\(874\) −12.8870 + 31.6842i −0.435910 + 1.07174i
\(875\) 0 0
\(876\) 3.34366 1.21699i 0.112972 0.0411184i
\(877\) −3.68173 + 20.8801i −0.124323 + 0.705071i 0.857385 + 0.514676i \(0.172088\pi\)
−0.981708 + 0.190395i \(0.939023\pi\)
\(878\) −48.6717 + 40.8404i −1.64259 + 1.37830i
\(879\) −9.26105 7.77094i −0.312367 0.262107i
\(880\) 0 0
\(881\) −7.84097 13.5810i −0.264169 0.457554i 0.703176 0.711015i \(-0.251764\pi\)
−0.967346 + 0.253461i \(0.918431\pi\)
\(882\) −1.58481 + 2.74497i −0.0533633 + 0.0924279i
\(883\) 18.4562 + 6.71750i 0.621100 + 0.226062i 0.633353 0.773863i \(-0.281678\pi\)
−0.0122532 + 0.999925i \(0.503900\pi\)
\(884\) 0.226106 + 0.0822957i 0.00760476 + 0.00276790i
\(885\) 0 0
\(886\) 10.7659 + 18.6472i 0.361689 + 0.626464i
\(887\) −4.30310 24.4041i −0.144484 0.819408i −0.967780 0.251797i \(-0.918979\pi\)
0.823296 0.567612i \(-0.192133\pi\)
\(888\) 0.285928 + 0.239922i 0.00959511 + 0.00805125i
\(889\) −36.6589 + 30.7605i −1.22950 + 1.03167i
\(890\) 0 0
\(891\) 9.46879 3.44636i 0.317216 0.115457i
\(892\) 15.6817 0.525063
\(893\) −34.1586 7.34365i −1.14307 0.245746i
\(894\) −25.5339 −0.853980
\(895\) 0 0
\(896\) 0.754279 4.27773i 0.0251987 0.142909i
\(897\) −16.7231 + 14.0323i −0.558368 + 0.468526i
\(898\) 6.35566 + 5.33303i 0.212091 + 0.177966i
\(899\) 15.1899 + 86.1463i 0.506612 + 2.87314i
\(900\) 0 0
\(901\) −0.118051 + 0.204471i −0.00393286 + 0.00681191i
\(902\) −22.0938 8.04150i −0.735644 0.267753i
\(903\) 27.3551 + 9.95645i 0.910322 + 0.331330i
\(904\) 0.225306 0.390241i 0.00749355 0.0129792i
\(905\) 0 0
\(906\) −3.46309 19.6402i −0.115054 0.652501i
\(907\) 16.3342 + 13.7060i 0.542368 + 0.455100i 0.872347 0.488888i \(-0.162597\pi\)
−0.329979 + 0.943988i \(0.607042\pi\)
\(908\) 6.71744 5.63660i 0.222926 0.187057i
\(909\) −0.323494 + 1.83463i −0.0107296 + 0.0608507i
\(910\) 0 0
\(911\) −34.0175 −1.12705 −0.563524 0.826100i \(-0.690555\pi\)
−0.563524 + 0.826100i \(0.690555\pi\)
\(912\) −30.9274 6.64900i −1.02411 0.220170i
\(913\) 9.25091 0.306160
\(914\) 17.5902 6.40232i 0.581833 0.211770i
\(915\) 0 0
\(916\) 36.0917 30.2846i 1.19250 1.00063i
\(917\) −1.99497 1.67397i −0.0658796 0.0552795i
\(918\) 0.0620741 + 0.352040i 0.00204875 + 0.0116190i
\(919\) 20.8710 + 36.1496i 0.688470 + 1.19246i 0.972333 + 0.233600i \(0.0750505\pi\)
−0.283863 + 0.958865i \(0.591616\pi\)
\(920\) 0 0
\(921\) −10.5128 3.82634i −0.346408 0.126082i
\(922\) −12.6256 4.59534i −0.415802 0.151340i
\(923\) −18.6272 + 32.2633i −0.613123 + 1.06196i
\(924\) 5.90655 + 10.2304i 0.194311 + 0.336557i
\(925\) 0 0
\(926\) −34.5268 28.9715i −1.13462 0.952061i
\(927\) 0.154060 0.129272i 0.00506001 0.00424585i
\(928\) 13.0734 74.1429i 0.429155 2.43386i
\(929\) 21.5234 7.83389i 0.706161 0.257022i 0.0361220 0.999347i \(-0.488500\pi\)
0.670039 + 0.742326i \(0.266277\pi\)
\(930\) 0 0
\(931\) 4.20674 10.3428i 0.137870 0.338970i
\(932\) 22.9123 0.750517
\(933\) 45.3420 16.5032i 1.48443 0.540289i
\(934\) 5.43213 30.8071i 0.177745 1.00804i
\(935\) 0 0
\(936\) 0.243866 + 0.204627i 0.00797099 + 0.00668846i
\(937\) −2.02604 11.4902i −0.0661877 0.375369i −0.999852 0.0172191i \(-0.994519\pi\)
0.933664 0.358150i \(-0.116592\pi\)
\(938\) −29.2206 50.6116i −0.954088 1.65253i
\(939\) 5.73823 9.93890i 0.187260 0.324344i
\(940\) 0 0
\(941\) −52.0967 18.9616i −1.69830 0.618132i −0.702672 0.711514i \(-0.748010\pi\)
−0.995630 + 0.0933820i \(0.970232\pi\)
\(942\) 22.3765 38.7573i 0.729066 1.26278i
\(943\) 23.4345 + 40.5898i 0.763133 + 1.32179i
\(944\) −1.83983 10.4342i −0.0598815 0.339605i
\(945\) 0 0
\(946\) 7.38881 6.19995i 0.240231 0.201578i
\(947\) 1.61575 9.16340i 0.0525049 0.297770i −0.947236 0.320537i \(-0.896137\pi\)
0.999741 + 0.0227671i \(0.00724762\pi\)
\(948\) −33.1431 + 12.0631i −1.07644 + 0.391792i
\(949\) −2.65474 −0.0861765
\(950\) 0 0
\(951\) −30.1726 −0.978413
\(952\) −0.0198980 + 0.00724229i −0.000644899 + 0.000234724i
\(953\) 2.99473 16.9840i 0.0970090 0.550165i −0.897104 0.441819i \(-0.854333\pi\)
0.994113 0.108346i \(-0.0345555\pi\)
\(954\) −5.74403 + 4.81981i −0.185970 + 0.156047i
\(955\) 0 0
\(956\) −0.987737 5.60173i −0.0319457 0.181173i
\(957\) 8.53768 + 14.7877i 0.275984 + 0.478018i
\(958\) −32.5538 + 56.3848i −1.05177 + 1.82171i
\(959\) 14.7429 + 5.36598i 0.476073 + 0.173276i
\(960\) 0 0
\(961\) −28.4723 + 49.3154i −0.918460 + 1.59082i
\(962\) −3.34232 5.78908i −0.107761 0.186647i
\(963\) 1.35911 + 7.70789i 0.0437967 + 0.248383i
\(964\) 17.8318 + 14.9626i 0.574323 + 0.481914i
\(965\) 0 0
\(966\) 8.00798 45.4155i 0.257652 1.46122i
\(967\) 3.46405 1.26081i 0.111396 0.0405449i −0.285721 0.958313i \(-0.592233\pi\)
0.397117 + 0.917768i \(0.370011\pi\)
\(968\) −1.77029 −0.0568994
\(969\) 0.0990285 + 0.307206i 0.00318125 + 0.00986889i
\(970\) 0 0
\(971\) 21.3740 7.77948i 0.685923 0.249656i 0.0245344 0.999699i \(-0.492190\pi\)
0.661389 + 0.750043i \(0.269967\pi\)
\(972\) −2.27135 + 12.8815i −0.0728537 + 0.413174i
\(973\) −6.46760 + 5.42696i −0.207342 + 0.173980i
\(974\) 5.65472 + 4.74487i 0.181189 + 0.152036i
\(975\) 0 0
\(976\) −19.1505 33.1697i −0.612993 1.06174i
\(977\) −22.5088 + 38.9865i −0.720122 + 1.24729i 0.240829 + 0.970568i \(0.422581\pi\)
−0.960951 + 0.276720i \(0.910753\pi\)
\(978\) −2.01029 0.731686i −0.0642820 0.0233968i
\(979\) 7.91669 + 2.88144i 0.253018 + 0.0920911i
\(980\) 0 0
\(981\) 4.66436 + 8.07891i 0.148922 + 0.257940i
\(982\) 1.59679 + 9.05587i 0.0509557 + 0.288984i
\(983\) −32.4157 27.2000i −1.03390 0.867544i −0.0425891 0.999093i \(-0.513561\pi\)
−0.991310 + 0.131548i \(0.958005\pi\)
\(984\) 3.08977 2.59262i 0.0984982 0.0826498i
\(985\) 0 0
\(986\) −0.690411 + 0.251289i −0.0219872 + 0.00800267i
\(987\) 47.1061 1.49940
\(988\) −22.7955 14.3180i −0.725220 0.455515i
\(989\) −19.2274 −0.611397
\(990\) 0 0
\(991\) 5.41069 30.6856i 0.171876 0.974759i −0.769812 0.638271i \(-0.779650\pi\)
0.941688 0.336488i \(-0.109239\pi\)
\(992\) 57.9824 48.6530i 1.84094 1.54473i
\(993\) −20.6295 17.3102i −0.654657 0.549322i
\(994\) −13.6659 77.5032i −0.433456 2.45825i
\(995\) 0 0
\(996\) −19.0472 + 32.9908i −0.603534 + 1.04535i
\(997\) 36.5451 + 13.3013i 1.15740 + 0.421258i 0.848166 0.529730i \(-0.177707\pi\)
0.309229 + 0.950987i \(0.399929\pi\)
\(998\) 41.4579 + 15.0895i 1.31233 + 0.477648i
\(999\) 2.53557 4.39173i 0.0802218 0.138948i
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.l.b.176.1 18
5.2 odd 4 475.2.u.c.24.1 36
5.3 odd 4 475.2.u.c.24.6 36
5.4 even 2 95.2.k.b.81.3 yes 18
15.14 odd 2 855.2.bs.b.271.1 18
19.2 odd 18 9025.2.a.cd.1.1 9
19.4 even 9 inner 475.2.l.b.251.1 18
19.17 even 9 9025.2.a.ce.1.9 9
95.4 even 18 95.2.k.b.61.3 18
95.23 odd 36 475.2.u.c.99.1 36
95.42 odd 36 475.2.u.c.99.6 36
95.59 odd 18 1805.2.a.u.1.9 9
95.74 even 18 1805.2.a.t.1.1 9
285.194 odd 18 855.2.bs.b.631.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.b.61.3 18 95.4 even 18
95.2.k.b.81.3 yes 18 5.4 even 2
475.2.l.b.176.1 18 1.1 even 1 trivial
475.2.l.b.251.1 18 19.4 even 9 inner
475.2.u.c.24.1 36 5.2 odd 4
475.2.u.c.24.6 36 5.3 odd 4
475.2.u.c.99.1 36 95.23 odd 36
475.2.u.c.99.6 36 95.42 odd 36
855.2.bs.b.271.1 18 15.14 odd 2
855.2.bs.b.631.1 18 285.194 odd 18
1805.2.a.t.1.1 9 95.74 even 18
1805.2.a.u.1.9 9 95.59 odd 18
9025.2.a.cd.1.1 9 19.2 odd 18
9025.2.a.ce.1.9 9 19.17 even 9