Properties

Label 855.2.bs.b.631.1
Level $855$
Weight $2$
Character 855.631
Analytic conductor $6.827$
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] = [855,2,Mod(226,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.bs (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: \(6.82720937282\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 631.1
Root \(1.01081 + 1.75077i\) of defining polynomial
Character \(\chi\) \(=\) 855.631
Dual form 855.2.bs.b.271.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.89970 - 0.691434i) q^{2} +(1.59869 + 1.34146i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-1.54609 + 2.67790i) q^{7} +(-0.0878797 - 0.152212i) q^{8} +O(q^{10})\) \(q+(-1.89970 - 0.691434i) q^{2} +(1.59869 + 1.34146i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-1.54609 + 2.67790i) q^{7} +(-0.0878797 - 0.152212i) q^{8} +(-1.89970 + 0.691434i) q^{10} +(0.481594 + 0.834145i) q^{11} +(-0.513859 + 2.91424i) q^{13} +(4.78870 - 4.01819i) q^{14} +(-0.663086 - 3.76055i) q^{16} +(0.0366124 + 0.0133258i) q^{17} +(-4.31788 - 0.596607i) q^{19} +2.08694 q^{20} +(-0.338127 - 1.91762i) q^{22} +(-2.97348 - 2.49504i) q^{23} +(0.173648 - 0.984808i) q^{25} +(2.99118 - 5.18088i) q^{26} +(-6.06401 + 2.20712i) q^{28} +(-8.76529 + 3.19030i) q^{29} +(4.68894 - 8.12148i) q^{31} +(-1.40155 + 7.94857i) q^{32} +(-0.0603386 - 0.0506301i) q^{34} +(0.536951 + 3.04520i) q^{35} -1.11739 q^{37} +(7.79016 + 4.11890i) q^{38} +(-0.165160 - 0.0601132i) q^{40} +(-2.09674 - 11.8912i) q^{41} +(-3.79459 + 3.18404i) q^{43} +(-0.349053 + 1.97958i) q^{44} +(3.92356 + 6.79580i) q^{46} +(7.53217 - 2.74148i) q^{47} +(-1.28078 - 2.21837i) q^{49} +(-1.01081 + 1.75077i) q^{50} +(-4.73083 + 3.96964i) q^{52} +(-4.64208 - 3.89517i) q^{53} +(0.905101 + 0.329430i) q^{55} +0.543479 q^{56} +18.8573 q^{58} +(2.60732 + 0.948987i) q^{59} +(-7.68360 - 6.44731i) q^{61} +(-14.5230 + 12.1863i) q^{62} +(4.33987 - 7.51688i) q^{64} +(1.47960 + 2.56274i) q^{65} +(-8.78501 + 3.19748i) q^{67} +(0.0406557 + 0.0704178i) q^{68} +(1.08551 - 6.15623i) q^{70} +(-9.64404 + 8.09231i) q^{71} +(0.155782 + 0.883486i) q^{73} +(2.12271 + 0.772603i) q^{74} +(-6.10262 - 6.74604i) q^{76} -2.97835 q^{77} +(1.54415 + 8.75731i) q^{79} +(-2.92519 - 2.45452i) q^{80} +(-4.23882 + 24.0395i) q^{82} +(-4.80224 + 8.31772i) q^{83} +(0.0366124 - 0.0133258i) q^{85} +(9.41012 - 3.42500i) q^{86} +(0.0846446 - 0.146609i) q^{88} +(1.51886 - 8.61386i) q^{89} +(-7.00958 - 5.88173i) q^{91} +(-1.40667 - 7.97760i) q^{92} -16.2044 q^{94} +(-3.69118 + 2.31845i) q^{95} +(-7.31855 - 2.66374i) q^{97} +(0.899233 + 5.09981i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{9}\right)\)

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 −0.432443 0.901661i \(-0.642348\pi\)
−0.910847 + 0.412743i \(0.864571\pi\)
\(3\) 0 0
\(4\) 1.59869 + 1.34146i 0.799344 + 0.670730i
\(5\) 0.766044 0.642788i 0.342585 0.287463i
\(6\) 0 0
\(7\) −1.54609 + 2.67790i −0.584366 + 1.01215i 0.410588 + 0.911821i \(0.365324\pi\)
−0.994954 + 0.100331i \(0.968010\pi\)
\(8\) −0.0878797 0.152212i −0.0310701 0.0538151i
\(9\) 0 0
\(10\) −1.89970 + 0.691434i −0.600738 + 0.218651i
\(11\) 0.481594 + 0.834145i 0.145206 + 0.251504i 0.929450 0.368949i \(-0.120282\pi\)
−0.784244 + 0.620453i \(0.786949\pi\)
\(12\) 0 0
\(13\) −0.513859 + 2.91424i −0.142519 + 0.808264i 0.826807 + 0.562486i \(0.190155\pi\)
−0.969326 + 0.245779i \(0.920956\pi\)
\(14\) 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 0.346456 0.938066i \(-0.387385\pi\)
−0.337576 + 0.941298i \(0.609607\pi\)
\(18\) 0 0
\(19\) −4.31788 0.596607i −0.990589 0.136871i
\(20\) 2.08694 0.466654
\(21\) 0 0
\(22\) −0.338127 1.91762i −0.0720890 0.408837i
\(23\) −2.97348 2.49504i −0.620013 0.520253i 0.277795 0.960641i \(-0.410397\pi\)
−0.897808 + 0.440388i \(0.854841\pi\)
\(24\) 0 0
\(25\) 0.173648 0.984808i 0.0347296 0.196962i
\(26\) 2.99118 5.18088i 0.586619 1.01605i
\(27\) 0 0
\(28\) −6.06401 + 2.20712i −1.14599 + 0.417106i
\(29\) −8.76529 + 3.19030i −1.62767 + 0.592425i −0.984822 0.173566i \(-0.944471\pi\)
−0.642851 + 0.765991i \(0.722249\pi\)
\(30\) 0 0
\(31\) 4.68894 8.12148i 0.842158 1.45866i −0.0459085 0.998946i \(-0.514618\pi\)
0.888067 0.459715i \(-0.152048\pi\)
\(32\) −1.40155 + 7.94857i −0.247761 + 1.40512i
\(33\) 0 0
\(34\) −0.0603386 0.0506301i −0.0103480 0.00868299i
\(35\) 0.536951 + 3.04520i 0.0907612 + 0.514733i
\(36\) 0 0
\(37\) −1.11739 −0.183698 −0.0918491 0.995773i \(-0.529278\pi\)
−0.0918491 + 0.995773i \(0.529278\pi\)
\(38\) 7.79016 + 4.11890i 1.26373 + 0.668174i
\(39\) 0 0
\(40\) −0.165160 0.0601132i −0.0261140 0.00950473i
\(41\) −2.09674 11.8912i −0.327456 1.85710i −0.491818 0.870698i \(-0.663668\pi\)
0.164362 0.986400i \(-0.447443\pi\)
\(42\) 0 0
\(43\) −3.79459 + 3.18404i −0.578669 + 0.485561i −0.884510 0.466522i \(-0.845507\pi\)
0.305841 + 0.952083i \(0.401062\pi\)
\(44\) −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 0.271850 0.962340i \(-0.412364\pi\)
0.826829 + 0.562453i \(0.190142\pi\)
\(48\) 0 0
\(49\) −1.28078 2.21837i −0.182968 0.316910i
\(50\) −1.01081 + 1.75077i −0.142950 + 0.247597i
\(51\) 0 0
\(52\) −4.73083 + 3.96964i −0.656048 + 0.550490i
\(53\) −4.64208 3.89517i −0.637639 0.535043i 0.265653 0.964069i \(-0.414412\pi\)
−0.903292 + 0.429026i \(0.858857\pi\)
\(54\) 0 0
\(55\) 0.905101 + 0.329430i 0.122044 + 0.0444203i
\(56\) 0.543479 0.0726254
\(57\) 0 0
\(58\) 18.8573 2.47609
\(59\) 2.60732 + 0.948987i 0.339444 + 0.123548i 0.506117 0.862465i \(-0.331080\pi\)
−0.166673 + 0.986012i \(0.553302\pi\)
\(60\) 0 0
\(61\) −7.68360 6.44731i −0.983784 0.825493i 0.000871917 1.00000i \(-0.499722\pi\)
−0.984656 + 0.174507i \(0.944167\pi\)
\(62\) −14.5230 + 12.1863i −1.84443 + 1.54766i
\(63\) 0 0
\(64\) 4.33987 7.51688i 0.542484 0.939610i
\(65\) 1.47960 + 2.56274i 0.183522 + 0.317869i
\(66\) 0 0
\(67\) −8.78501 + 3.19748i −1.07326 + 0.390635i −0.817395 0.576078i \(-0.804582\pi\)
−0.255865 + 0.966713i \(0.582360\pi\)
\(68\) 0.0406557 + 0.0704178i 0.00493023 + 0.00853941i
\(69\) 0 0
\(70\) 1.08551 6.15623i 0.129743 0.735810i
\(71\) −9.64404 + 8.09231i −1.14454 + 0.960381i −0.999578 0.0290571i \(-0.990750\pi\)
−0.144959 + 0.989438i \(0.546305\pi\)
\(72\) 0 0
\(73\) 0.155782 + 0.883486i 0.0182330 + 0.103404i 0.992566 0.121707i \(-0.0388367\pi\)
−0.974333 + 0.225111i \(0.927726\pi\)
\(74\) 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
\(78\) 0 0
\(79\) 1.54415 + 8.75731i 0.173731 + 0.985275i 0.939599 + 0.342277i \(0.111198\pi\)
−0.765868 + 0.642997i \(0.777691\pi\)
\(80\) −2.92519 2.45452i −0.327046 0.274424i
\(81\) 0 0
\(82\) −4.23882 + 24.0395i −0.468099 + 2.65472i
\(83\) −4.80224 + 8.31772i −0.527114 + 0.912988i 0.472387 + 0.881391i \(0.343393\pi\)
−0.999501 + 0.0315966i \(0.989941\pi\)
\(84\) 0 0
\(85\) 0.0366124 0.0133258i 0.00397117 0.00144539i
\(86\) 9.41012 3.42500i 1.01472 0.369328i
\(87\) 0 0
\(88\) 0.0846446 0.146609i 0.00902315 0.0156285i
\(89\) 1.51886 8.61386i 0.160998 0.913068i −0.792096 0.610396i \(-0.791010\pi\)
0.953095 0.302672i \(-0.0978786\pi\)
\(90\) 0 0
\(91\) −7.00958 5.88173i −0.734803 0.616573i
\(92\) −1.40667 7.97760i −0.146655 0.831722i
\(93\) 0 0
\(94\) −16.2044 −1.67136
\(95\) −3.69118 + 2.31845i −0.378707 + 0.237868i
\(96\) 0 0
\(97\) −7.31855 2.66374i −0.743087 0.270461i −0.0573929 0.998352i \(-0.518279\pi\)
−0.685694 + 0.727890i \(0.740501\pi\)
\(98\) 0.899233 + 5.09981i 0.0908363 + 0.515158i
\(99\) 0 0
\(100\) 1.59869 1.34146i 0.159869 0.134146i
\(101\) 0.528521 2.99739i 0.0525898 0.298251i −0.947157 0.320771i \(-0.896058\pi\)
0.999746 + 0.0225200i \(0.00716895\pi\)
\(102\) 0 0
\(103\) 0.164287 + 0.284553i 0.0161876 + 0.0280378i 0.874006 0.485916i \(-0.161514\pi\)
−0.857818 + 0.513953i \(0.828180\pi\)
\(104\) 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 0.371734 + 0.928339i \(0.378763\pi\)
−0.989832 + 0.142239i \(0.954570\pi\)
\(108\) 0 0
\(109\) −11.6754 + 9.79682i −1.11830 + 0.938366i −0.998517 0.0544346i \(-0.982664\pi\)
−0.119783 + 0.992800i \(0.538220\pi\)
\(110\) −1.49164 1.25163i −0.142222 0.119339i
\(111\) 0 0
\(112\) 11.0956 + 4.03846i 1.04843 + 0.381598i
\(113\) −2.56380 −0.241182 −0.120591 0.992702i \(-0.538479\pi\)
−0.120591 + 0.992702i \(0.538479\pi\)
\(114\) 0 0
\(115\) −3.88160 −0.361961
\(116\) −18.2926 6.65797i −1.69843 0.618177i
\(117\) 0 0
\(118\) −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
\(123\) 0 0
\(124\) 18.3908 6.69370i 1.65154 0.601112i
\(125\) −0.500000 0.866025i −0.0447214 0.0774597i
\(126\) 0 0
\(127\) −2.68740 + 15.2410i −0.238468 + 1.35242i 0.596718 + 0.802451i \(0.296471\pi\)
−0.835186 + 0.549968i \(0.814640\pi\)
\(128\) −1.07610 + 0.902953i −0.0951145 + 0.0798105i
\(129\) 0 0
\(130\) −1.03883 5.89148i −0.0911111 0.516717i
\(131\) 0.791413 + 0.288051i 0.0691461 + 0.0251671i 0.376362 0.926473i \(-0.377175\pi\)
−0.307216 + 0.951640i \(0.599397\pi\)
\(132\) 0 0
\(133\) 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 0.793542 0.608516i \(-0.208235\pi\)
−0.461474 + 0.887154i \(0.652679\pi\)
\(138\) 0 0
\(139\) 0.474127 2.68891i 0.0402150 0.228070i −0.958076 0.286515i \(-0.907503\pi\)
0.998291 + 0.0584449i \(0.0186142\pi\)
\(140\) −3.22659 + 5.58862i −0.272697 + 0.472325i
\(141\) 0 0
\(142\) 23.9161 8.70474i 2.00699 0.730486i
\(143\) −2.67837 + 0.974847i −0.223977 + 0.0815208i
\(144\) 0 0
\(145\) −4.66391 + 8.07814i −0.387317 + 0.670853i
\(146\) 0.314933 1.78607i 0.0260640 0.147816i
\(147\) 0 0
\(148\) −1.78636 1.49894i −0.146838 0.123212i
\(149\) 1.15401 + 6.54471i 0.0945401 + 0.536164i 0.994887 + 0.100991i \(0.0322014\pi\)
−0.900347 + 0.435172i \(0.856687\pi\)
\(150\) 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 0
\(154\) 5.65796 + 2.05933i 0.455932 + 0.165946i
\(155\) −1.62845 9.23540i −0.130800 0.741806i
\(156\) 0 0
\(157\) 8.92275 7.48708i 0.712113 0.597534i −0.213078 0.977035i \(-0.568349\pi\)
0.925191 + 0.379501i \(0.123904\pi\)
\(158\) 3.12168 17.7039i 0.248348 1.40845i
\(159\) 0 0
\(160\) 4.03560 + 6.98986i 0.319042 + 0.552597i
\(161\) 11.2787 4.10513i 0.888890 0.323529i
\(162\) 0 0
\(163\) 0.278398 + 0.482199i 0.0218058 + 0.0377688i 0.876722 0.480997i \(-0.159725\pi\)
−0.854917 + 0.518765i \(0.826392\pi\)
\(164\) 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 −0.987662 0.156600i \(-0.949947\pi\)
−0.325727 0.945464i \(-0.605609\pi\)
\(168\) 0 0
\(169\) 3.98727 + 1.45125i 0.306713 + 0.111634i
\(170\) −0.0787664 −0.00604111
\(171\) 0 0
\(172\) −10.3376 −0.788236
\(173\) −10.7653 3.91823i −0.818467 0.297898i −0.101350 0.994851i \(-0.532316\pi\)
−0.717117 + 0.696953i \(0.754539\pi\)
\(174\) 0 0
\(175\) 2.36874 + 1.98761i 0.179060 + 0.150249i
\(176\) 2.81751 2.36417i 0.212377 0.178206i
\(177\) 0 0
\(178\) −8.84129 + 15.3136i −0.662683 + 1.14780i
\(179\) 2.98306 + 5.16681i 0.222964 + 0.386185i 0.955707 0.294321i \(-0.0950934\pi\)
−0.732743 + 0.680506i \(0.761760\pi\)
\(180\) 0 0
\(181\) 5.80527 2.11294i 0.431502 0.157054i −0.117132 0.993116i \(-0.537370\pi\)
0.548634 + 0.836062i \(0.315148\pi\)
\(182\) 9.24926 + 16.0202i 0.685601 + 1.18750i
\(183\) 0 0
\(184\) −0.118468 + 0.671863i −0.00873354 + 0.0495304i
\(185\) −0.855972 + 0.718246i −0.0629323 + 0.0528065i
\(186\) 0 0
\(187\) 0.00651663 + 0.0369577i 0.000476543 + 0.00270261i
\(188\) 15.7192 + 5.72131i 1.14644 + 0.417270i
\(189\) 0 0
\(190\) 8.61518 1.85215i 0.625011 0.134369i
\(191\) 18.6639 1.35047 0.675235 0.737602i \(-0.264042\pi\)
0.675235 + 0.737602i \(0.264042\pi\)
\(192\) 0 0
\(193\) −4.15136 23.5435i −0.298821 1.69470i −0.651252 0.758861i \(-0.725756\pi\)
0.352431 0.935838i \(-0.385355\pi\)
\(194\) 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 −0.960351 0.278795i \(-0.910065\pi\)
0.721619 + 0.692290i \(0.243398\pi\)
\(198\) 0 0
\(199\) −2.96836 + 1.08040i −0.210422 + 0.0765872i −0.445080 0.895491i \(-0.646825\pi\)
0.234659 + 0.972078i \(0.424603\pi\)
\(200\) −0.165160 + 0.0601132i −0.0116786 + 0.00425065i
\(201\) 0 0
\(202\) −3.07653 + 5.32870i −0.216464 + 0.374926i
\(203\) 5.00858 28.4051i 0.351534 1.99365i
\(204\) 0 0
\(205\) −9.24973 7.76145i −0.646029 0.542083i
\(206\) −0.115346 0.654158i −0.00803652 0.0455774i
\(207\) 0 0
\(208\) 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 0.684911 0.728627i \(-0.259841\pi\)
0.0563198 + 0.998413i \(0.482063\pi\)
\(212\) −2.19603 12.4543i −0.150824 0.855367i
\(213\) 0 0
\(214\) 19.8031 16.6168i 1.35371 1.13590i
\(215\) −0.860163 + 4.87822i −0.0586626 + 0.332692i
\(216\) 0 0
\(217\) 14.4990 + 25.1130i 0.984258 + 1.70478i
\(218\) 28.9536 10.5383i 1.96099 0.713741i
\(219\) 0 0
\(220\) 1.00506 + 1.74081i 0.0677610 + 0.117365i
\(221\) −0.0576482 + 0.0998496i −0.00387784 + 0.00671661i
\(222\) 0 0
\(223\) −5.75623 + 4.83005i −0.385465 + 0.323444i −0.814844 0.579681i \(-0.803177\pi\)
0.429378 + 0.903125i \(0.358733\pi\)
\(224\) −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 \(0.455469\pi\)
\(228\) 0 0
\(229\) 22.5758 1.49185 0.745927 0.666028i \(-0.232007\pi\)
0.745927 + 0.666028i \(0.232007\pi\)
\(230\) 7.37388 + 2.68387i 0.486219 + 0.176969i
\(231\) 0 0
\(232\) 1.25589 + 1.05382i 0.0824534 + 0.0691867i
\(233\) 8.41032 7.05710i 0.550978 0.462326i −0.324294 0.945956i \(-0.605127\pi\)
0.875272 + 0.483631i \(0.160682\pi\)
\(234\) 0 0
\(235\) 4.00778 6.94168i 0.261439 0.452826i
\(236\) 2.89527 + 5.01475i 0.188466 + 0.326432i
\(237\) 0 0
\(238\) 0.228871 0.0833023i 0.0148355 0.00539969i
\(239\) −1.36280 2.36043i −0.0881520 0.152684i 0.818578 0.574395i \(-0.194763\pi\)
−0.906730 + 0.421712i \(0.861429\pi\)
\(240\) 0 0
\(241\) 1.93687 10.9846i 0.124765 0.707577i −0.856682 0.515845i \(-0.827478\pi\)
0.981447 0.191733i \(-0.0614107\pi\)
\(242\) −15.5984 + 13.0886i −1.00270 + 0.841369i
\(243\) 0 0
\(244\) −3.63489 20.6145i −0.232700 1.31971i
\(245\) −2.40707 0.876102i −0.153782 0.0559721i
\(246\) 0 0
\(247\) 3.95743 12.2768i 0.251805 0.781151i
\(248\) −1.64825 −0.104664
\(249\) 0 0
\(250\) 0.351050 + 1.99091i 0.0222024 + 0.125916i
\(251\) 20.9654 + 17.5920i 1.32332 + 1.11040i 0.985589 + 0.169156i \(0.0541042\pi\)
0.337732 + 0.941242i \(0.390340\pi\)
\(252\) 0 0
\(253\) 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 −0.858927 0.512098i \(-0.828869\pi\)
−0.328806 + 0.944397i \(0.606646\pi\)
\(258\) 0 0
\(259\) 1.72759 2.99227i 0.107347 0.185931i
\(260\) −1.07239 + 6.08184i −0.0665070 + 0.377180i
\(261\) 0 0
\(262\) −1.30428 1.09442i −0.0805786 0.0676135i
\(263\) −1.66049 9.41708i −0.102390 0.580682i −0.992231 0.124411i \(-0.960296\pi\)
0.889841 0.456271i \(-0.150815\pi\)
\(264\) 0 0
\(265\) −6.05981 −0.372251
\(266\) −23.0743 + 14.4931i −1.41477 + 0.888629i
\(267\) 0 0
\(268\) −18.3338 6.67295i −1.11991 0.407615i
\(269\) −0.794363 4.50506i −0.0484332 0.274678i 0.950968 0.309290i \(-0.100091\pi\)
−0.999401 + 0.0346123i \(0.988980\pi\)
\(270\) 0 0
\(271\) −16.9571 + 14.2287i −1.03007 + 0.864330i −0.990859 0.134901i \(-0.956928\pi\)
−0.0392098 + 0.999231i \(0.512484\pi\)
\(272\) 0.0258352 0.146519i 0.00156649 0.00888400i
\(273\) 0 0
\(274\) −5.12864 8.88306i −0.309832 0.536645i
\(275\) 0.905101 0.329430i 0.0545796 0.0198654i
\(276\) 0 0
\(277\) −11.7771 20.3985i −0.707617 1.22563i −0.965739 0.259516i \(-0.916437\pi\)
0.258122 0.966112i \(-0.416896\pi\)
\(278\) −2.75990 + 4.78029i −0.165528 + 0.286703i
\(279\) 0 0
\(280\) 0.416329 0.349341i 0.0248804 0.0208771i
\(281\) −7.90783 6.63545i −0.471741 0.395838i 0.375688 0.926746i \(-0.377406\pi\)
−0.847429 + 0.530908i \(0.821851\pi\)
\(282\) 0 0
\(283\) 29.0110 + 10.5592i 1.72453 + 0.627676i 0.998217 0.0596910i \(-0.0190115\pi\)
0.726310 + 0.687367i \(0.241234\pi\)
\(284\) −26.2733 −1.55903
\(285\) 0 0
\(286\) 5.76214 0.340722
\(287\) 35.0853 + 12.7700i 2.07102 + 0.753790i
\(288\) 0 0
\(289\) −13.0216 10.9264i −0.765976 0.642730i
\(290\) 14.4455 12.1212i 0.848271 0.711784i
\(291\) 0 0
\(292\) −0.936113 + 1.62140i −0.0547819 + 0.0948850i
\(293\) 3.18052 + 5.50882i 0.185808 + 0.321828i 0.943848 0.330379i \(-0.107176\pi\)
−0.758041 + 0.652207i \(0.773843\pi\)
\(294\) 0 0
\(295\) 2.60732 0.948987i 0.151804 0.0552522i
\(296\) 0.0981961 + 0.170081i 0.00570753 + 0.00988573i
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) 0.619557 + 16.6332i 0.0355340 + 0.953979i
\(305\) −10.0302 −0.574329
\(306\) 0 0
\(307\) −1.02217 5.79702i −0.0583384 0.330854i 0.941645 0.336608i \(-0.109280\pi\)
−0.999983 + 0.00575393i \(0.998168\pi\)
\(308\) −4.76145 3.99533i −0.271309 0.227655i
\(309\) 0 0
\(310\) −3.29211 + 18.6705i −0.186979 + 1.06041i
\(311\) −12.6942 + 21.9871i −0.719825 + 1.24677i 0.241245 + 0.970464i \(0.422444\pi\)
−0.961069 + 0.276308i \(0.910889\pi\)
\(312\) 0 0
\(313\) −5.67434 + 2.06529i −0.320733 + 0.116737i −0.497369 0.867539i \(-0.665701\pi\)
0.176637 + 0.984276i \(0.443478\pi\)
\(314\) −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 0.804098 + 0.594497i \(0.202649\pi\)
−0.958935 + 0.283627i \(0.908462\pi\)
\(318\) 0 0
\(319\) −6.88249 5.77509i −0.385345 0.323343i
\(320\) −1.50722 8.54788i −0.0842563 0.477841i
\(321\) 0 0
\(322\) −24.2647 −1.35222
\(323\) −0.150137 0.0793824i −0.00835387 0.00441695i
\(324\) 0 0
\(325\) 2.78073 + 1.01210i 0.154247 + 0.0561415i
\(326\) −0.195463 1.10853i −0.0108257 0.0613956i
\(327\) 0 0
\(328\) −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 0.992371 0.123288i \(-0.0393440\pi\)
−0.602956 + 0.797774i \(0.706011\pi\)
\(332\) −18.8352 + 6.85544i −1.03371 + 0.376241i
\(333\) 0 0
\(334\) 22.3958 + 38.7907i 1.22544 + 2.12253i
\(335\) −4.67441 + 8.09631i −0.255390 + 0.442349i
\(336\) 0 0
\(337\) −1.64694 + 1.38195i −0.0897147 + 0.0752796i −0.686542 0.727090i \(-0.740872\pi\)
0.596827 + 0.802370i \(0.296428\pi\)
\(338\) −6.57117 5.51387i −0.357425 0.299915i
\(339\) 0 0
\(340\) 0.0764078 + 0.0278102i 0.00414380 + 0.00150822i
\(341\) 9.03266 0.489146
\(342\) 0 0
\(343\) −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 −0.386592 0.922251i \(-0.626348\pi\)
0.841109 + 0.540866i \(0.181903\pi\)
\(348\) 0 0
\(349\) −17.6725 + 30.6097i −0.945989 + 1.63850i −0.192229 + 0.981350i \(0.561572\pi\)
−0.753759 + 0.657151i \(0.771762\pi\)
\(350\) −3.12560 5.41370i −0.167070 0.289374i
\(351\) 0 0
\(352\) −7.30524 + 2.65889i −0.389371 + 0.141719i
\(353\) 11.0952 + 19.2174i 0.590538 + 1.02284i 0.994160 + 0.107916i \(0.0344176\pi\)
−0.403622 + 0.914926i \(0.632249\pi\)
\(354\) 0 0
\(355\) −2.18613 + 12.3981i −0.116028 + 0.658025i
\(356\) 13.9833 11.7334i 0.741115 0.621869i
\(357\) 0 0
\(358\) −2.09441 11.8780i −0.110693 0.627770i
\(359\) −8.93517 3.25214i −0.471580 0.171641i 0.0952879 0.995450i \(-0.469623\pi\)
−0.566868 + 0.823809i \(0.691845\pi\)
\(360\) 0 0
\(361\) 18.2881 + 5.15215i 0.962533 + 0.271166i
\(362\) −12.4892 −0.656419
\(363\) 0 0
\(364\) −3.31603 18.8061i −0.173807 0.985709i
\(365\) 0.687230 + 0.576655i 0.0359713 + 0.0301835i
\(366\) 0 0
\(367\) −0.379110 + 2.15004i −0.0197894 + 0.112231i −0.993102 0.117250i \(-0.962592\pi\)
0.973313 + 0.229482i \(0.0737031\pi\)
\(368\) −7.41107 + 12.8363i −0.386328 + 0.669141i
\(369\) 0 0
\(370\) 2.12271 0.772603i 0.110354 0.0401657i
\(371\) 17.6079 6.40877i 0.914159 0.332727i
\(372\) 0 0
\(373\) 6.17035 10.6874i 0.319488 0.553370i −0.660893 0.750480i \(-0.729822\pi\)
0.980381 + 0.197110i \(0.0631556\pi\)
\(374\) 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
\(378\) 0 0
\(379\) −18.5014 −0.950352 −0.475176 0.879891i \(-0.657616\pi\)
−0.475176 + 0.879891i \(0.657616\pi\)
\(380\) −9.01115 1.24508i −0.462262 0.0638714i
\(381\) 0 0
\(382\) −35.4558 12.9048i −1.81407 0.660269i
\(383\) 1.98517 + 11.2585i 0.101438 + 0.575282i 0.992584 + 0.121565i \(0.0387912\pi\)
−0.891146 + 0.453717i \(0.850098\pi\)
\(384\) 0 0
\(385\) −2.28155 + 1.91444i −0.116278 + 0.0975691i
\(386\) −8.39246 + 47.5960i −0.427165 + 2.42257i
\(387\) 0 0
\(388\) −8.12680 14.0760i −0.412576 0.714602i
\(389\) 11.7685 4.28337i 0.596684 0.217175i −0.0259826 0.999662i \(-0.508271\pi\)
0.622667 + 0.782487i \(0.286049\pi\)
\(390\) 0 0
\(391\) −0.0756176 0.130974i −0.00382415 0.00662361i
\(392\) −0.225108 + 0.389899i −0.0113697 + 0.0196929i
\(393\) 0 0
\(394\) 10.3783 8.70843i 0.522851 0.438724i
\(395\) 6.81198 + 5.71593i 0.342748 + 0.287600i
\(396\) 0 0
\(397\) −11.0417 4.01886i −0.554168 0.201701i 0.0497292 0.998763i \(-0.484164\pi\)
−0.603898 + 0.797062i \(0.706386\pi\)
\(398\) 6.38602 0.320102
\(399\) 0 0
\(400\) −3.81856 −0.190928
\(401\) −13.7588 5.00780i −0.687083 0.250078i −0.0251970 0.999683i \(-0.508021\pi\)
−0.661886 + 0.749605i \(0.730244\pi\)
\(402\) 0 0
\(403\) 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 0
\(409\) −11.9790 + 4.36001i −0.592324 + 0.215588i −0.620751 0.784007i \(-0.713172\pi\)
0.0284271 + 0.999596i \(0.490950\pi\)
\(410\) 12.2052 + 21.1400i 0.602771 + 1.04403i
\(411\) 0 0
\(412\) −0.119073 + 0.675295i −0.00586630 + 0.0332694i
\(413\) −6.57244 + 5.51494i −0.323409 + 0.271372i
\(414\) 0 0
\(415\) 1.66780 + 9.45856i 0.0818690 + 0.464302i
\(416\) −22.4438 8.16889i −1.10040 0.400513i
\(417\) 0 0
\(418\) 0.315930 + 8.48176i 0.0154527 + 0.414856i
\(419\) −2.84601 −0.139037 −0.0695184 0.997581i \(-0.522146\pi\)
−0.0695184 + 0.997581i \(0.522146\pi\)
\(420\) 0 0
\(421\) 1.93626 + 10.9811i 0.0943677 + 0.535186i 0.994939 + 0.100478i \(0.0320372\pi\)
−0.900572 + 0.434708i \(0.856852\pi\)
\(422\) −17.7444 14.8893i −0.863785 0.724802i
\(423\) 0 0
\(424\) −0.184947 + 1.04889i −0.00898182 + 0.0509384i
\(425\) 0.0194810 0.0337421i 0.000944969 0.00163673i
\(426\) 0 0
\(427\) 29.1448 10.6078i 1.41041 0.513349i
\(428\) −25.0770 + 9.12728i −1.21214 + 0.441184i
\(429\) 0 0
\(430\) 5.00702 8.67242i 0.241460 0.418221i
\(431\) 2.59366 14.7094i 0.124932 0.708525i −0.856416 0.516286i \(-0.827314\pi\)
0.981348 0.192239i \(-0.0615747\pi\)
\(432\) 0 0
\(433\) −29.6894 24.9123i −1.42678 1.19721i −0.947585 0.319503i \(-0.896484\pi\)
−0.479195 0.877708i \(-0.659071\pi\)
\(434\) −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
\(438\) 0 0
\(439\) 29.5331 + 10.7492i 1.40954 + 0.513030i 0.930994 0.365034i \(-0.118943\pi\)
0.478544 + 0.878064i \(0.341165\pi\)
\(440\) −0.0293968 0.166717i −0.00140144 0.00794794i
\(441\) 0 0
\(442\) 0.178554 0.149824i 0.00849293 0.00712641i
\(443\) −1.84950 + 10.4890i −0.0878722 + 0.498348i 0.908828 + 0.417172i \(0.136979\pi\)
−0.996700 + 0.0811761i \(0.974132\pi\)
\(444\) 0 0
\(445\) −4.37337 7.57490i −0.207318 0.359085i
\(446\) 14.2748 5.19559i 0.675930 0.246018i
\(447\) 0 0
\(448\) 13.4196 + 23.2435i 0.634019 + 1.09815i
\(449\) 2.05200 3.55417i 0.0968399 0.167732i −0.813535 0.581516i \(-0.802460\pi\)
0.910375 + 0.413784i \(0.135793\pi\)
\(450\) 0 0
\(451\) 8.90923 7.47573i 0.419519 0.352019i
\(452\) −4.09871 3.43923i −0.192787 0.161768i
\(453\) 0 0
\(454\) −7.98224 2.90530i −0.374625 0.136352i
\(455\) −9.15035 −0.428975
\(456\) 0 0
\(457\) 9.25947 0.433140 0.216570 0.976267i \(-0.430513\pi\)
0.216570 + 0.976267i \(0.430513\pi\)
\(458\) −42.8873 15.6097i −2.00399 0.729394i
\(459\) 0 0
\(460\) −6.20547 5.20701i −0.289332 0.242778i
\(461\) −5.09121 + 4.27203i −0.237121 + 0.198968i −0.753603 0.657330i \(-0.771686\pi\)
0.516482 + 0.856298i \(0.327241\pi\)
\(462\) 0 0
\(463\) −11.1474 + 19.3079i −0.518064 + 0.897313i 0.481716 + 0.876327i \(0.340014\pi\)
−0.999780 + 0.0209853i \(0.993320\pi\)
\(464\) 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 0.629606 0.776914i \(-0.283216\pi\)
−0.987631 + 0.156798i \(0.949883\pi\)
\(468\) 0 0
\(469\) 5.01985 28.4690i 0.231795 1.31458i
\(470\) −12.4133 + 10.4160i −0.572583 + 0.480454i
\(471\) 0 0
\(472\) −0.0846832 0.480262i −0.00389786 0.0221059i
\(473\) −4.48340 1.63182i −0.206147 0.0750313i
\(474\) 0 0
\(475\) −1.33733 + 4.14868i −0.0613611 + 0.190354i
\(476\) −0.251429 −0.0115242
\(477\) 0 0
\(478\) 0.956820 + 5.42640i 0.0437639 + 0.248198i
\(479\) −24.6710 20.7014i −1.12725 0.945872i −0.128299 0.991736i \(-0.540952\pi\)
−0.998948 + 0.0458635i \(0.985396\pi\)
\(480\) 0 0
\(481\) 0.574182 3.25635i 0.0261805 0.148477i
\(482\) −11.2746 + 19.5281i −0.513543 + 0.889482i
\(483\) 0 0
\(484\) 19.7525 7.18934i 0.897843 0.326788i
\(485\) −7.31855 + 2.66374i −0.332318 + 0.120954i
\(486\) 0 0
\(487\) 1.82569 3.16219i 0.0827301 0.143293i −0.821692 0.569932i \(-0.806969\pi\)
0.904422 + 0.426640i \(0.140303\pi\)
\(488\) −0.306125 + 1.73612i −0.0138576 + 0.0785906i
\(489\) 0 0
\(490\) 3.96694 + 3.32866i 0.179208 + 0.150374i
\(491\) −0.789859 4.47952i −0.0356459 0.202158i 0.961784 0.273810i \(-0.0882839\pi\)
−0.997430 + 0.0716523i \(0.977173\pi\)
\(492\) 0 0
\(493\) −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
\(498\) 0 0
\(499\) −16.7177 + 14.0278i −0.748387 + 0.627972i −0.935076 0.354448i \(-0.884669\pi\)
0.186689 + 0.982419i \(0.440224\pi\)
\(500\) 0.362393 2.05523i 0.0162067 0.0919129i
\(501\) 0 0
\(502\) −27.6641 47.9157i −1.23471 2.13858i
\(503\) −23.2469 + 8.46117i −1.03653 + 0.377265i −0.803562 0.595221i \(-0.797065\pi\)
−0.232964 + 0.972485i \(0.574842\pi\)
\(504\) 0 0
\(505\) −1.52181 2.63586i −0.0677199 0.117294i
\(506\) −3.77912 + 6.54563i −0.168003 + 0.290989i
\(507\) 0 0
\(508\) −24.7415 + 20.7606i −1.09773 + 0.921101i
\(509\) 13.2902 + 11.1518i 0.589078 + 0.494295i 0.887914 0.460009i \(-0.152154\pi\)
−0.298836 + 0.954305i \(0.596598\pi\)
\(510\) 0 0
\(511\) −2.60674 0.948777i −0.115316 0.0419714i
\(512\) 32.1626 1.42140
\(513\) 0 0
\(514\) 40.9637 1.80683
\(515\) 0.308758 + 0.112379i 0.0136055 + 0.00495200i
\(516\) 0 0
\(517\) 5.91424 + 4.96264i 0.260108 + 0.218257i
\(518\) −5.35085 + 4.48990i −0.235103 + 0.197275i
\(519\) 0 0
\(520\) 0.260053 0.450425i 0.0114041 0.0197524i
\(521\) 0.228337 + 0.395492i 0.0100036 + 0.0173268i 0.870984 0.491312i \(-0.163482\pi\)
−0.860980 + 0.508638i \(0.830149\pi\)
\(522\) 0 0
\(523\) 35.5171 12.9272i 1.55305 0.565265i 0.583922 0.811810i \(-0.301517\pi\)
0.969132 + 0.246544i \(0.0792951\pi\)
\(524\) 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
\(528\) 0 0
\(529\) −1.37758 7.81265i −0.0598949 0.339681i
\(530\) 11.5118 + 4.18996i 0.500041 + 0.182000i
\(531\) 0 0
\(532\) 27.5004 5.91224i 1.19229 0.256328i
\(533\) 35.7313 1.54769
\(534\) 0 0
\(535\) 2.22050 + 12.5931i 0.0960004 + 0.544445i
\(536\) 1.25872 + 1.05619i 0.0543684 + 0.0456205i
\(537\) 0 0
\(538\) −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 0.122127 0.992514i \(-0.461028\pi\)
0.731531 + 0.681808i \(0.238806\pi\)
\(542\) 42.0515 15.3055i 1.80627 0.657428i
\(543\) 0 0
\(544\) −0.157235 + 0.272339i −0.00674140 + 0.0116765i
\(545\) −2.64660 + 15.0096i −0.113368 + 0.642941i
\(546\) 0 0
\(547\) −9.60806 8.06212i −0.410811 0.344711i 0.413843 0.910348i \(-0.364186\pi\)
−0.824655 + 0.565637i \(0.808631\pi\)
\(548\) 1.83871 + 10.4278i 0.0785458 + 0.445455i
\(549\) 0 0
\(550\) −1.94720 −0.0830288
\(551\) 39.7508 8.54591i 1.69344 0.364068i
\(552\) 0 0
\(553\) −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 −0.605647 0.795733i \(-0.707086\pi\)
0.841279 0.540601i \(-0.181803\pi\)
\(558\) 0 0
\(559\) −7.32916 12.6945i −0.309990 0.536919i
\(560\) 11.0956 4.03846i 0.468874 0.170656i
\(561\) 0 0
\(562\) 10.4345 + 18.0731i 0.440153 + 0.762368i
\(563\) 9.79034 16.9574i 0.412614 0.714668i −0.582561 0.812787i \(-0.697949\pi\)
0.995175 + 0.0981190i \(0.0312826\pi\)
\(564\) 0 0
\(565\) −1.96398 + 1.64798i −0.0826254 + 0.0693309i
\(566\) −47.8113 40.1184i −2.00966 1.68630i
\(567\) 0 0
\(568\) 2.07926 + 0.756789i 0.0872439 + 0.0317542i
\(569\) 18.6525 0.781953 0.390977 0.920401i \(-0.372137\pi\)
0.390977 + 0.920401i \(0.372137\pi\)
\(570\) 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
\(573\) 0 0
\(574\) −57.8219 48.5184i −2.41344 2.02512i
\(575\) −2.97348 + 2.49504i −0.124003 + 0.104051i
\(576\) 0 0
\(577\) −5.87392 + 10.1739i −0.244534 + 0.423546i −0.962001 0.273047i \(-0.911968\pi\)
0.717466 + 0.696593i \(0.245302\pi\)
\(578\) 17.1822 + 29.7605i 0.714686 + 1.23787i
\(579\) 0 0
\(580\) −18.2926 + 6.65797i −0.759560 + 0.276457i
\(581\) −14.8494 25.7198i −0.616055 1.06704i
\(582\) 0 0
\(583\) 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 0.245235 0.969464i \(-0.421135\pi\)
−0.435298 + 0.900286i \(0.643357\pi\)
\(588\) 0 0
\(589\) −25.0916 + 32.2701i −1.03388 + 1.32967i
\(590\) −5.60929 −0.230931
\(591\) 0 0
\(592\) 0.740928 + 4.20201i 0.0304519 + 0.172702i
\(593\) 14.1700 + 11.8900i 0.581892 + 0.488265i 0.885568 0.464510i \(-0.153770\pi\)
−0.303676 + 0.952775i \(0.598214\pi\)
\(594\) 0 0
\(595\) −0.0209207 + 0.118647i −0.000857665 + 0.00486406i
\(596\) −6.93456 + 12.0110i −0.284051 + 0.491990i
\(597\) 0 0
\(598\) −21.8207 + 7.94210i −0.892316 + 0.324777i
\(599\) −20.1336 + 7.32805i −0.822638 + 0.299416i −0.718834 0.695182i \(-0.755324\pi\)
−0.103804 + 0.994598i \(0.533102\pi\)
\(600\) 0 0
\(601\) −15.0195 + 26.0146i −0.612659 + 1.06116i 0.378132 + 0.925752i \(0.376567\pi\)
−0.990790 + 0.135404i \(0.956767\pi\)
\(602\) −5.37705 + 30.4948i −0.219152 + 1.24287i
\(603\) 0 0
\(604\) −8.29813 6.96296i −0.337646 0.283319i
\(605\) −1.74903 9.91925i −0.0711082 0.403275i
\(606\) 0 0
\(607\) 29.3882 1.19283 0.596415 0.802676i \(-0.296591\pi\)
0.596415 + 0.802676i \(0.296591\pi\)
\(608\) 10.7939 33.4848i 0.437750 1.35799i
\(609\) 0 0
\(610\) 19.0544 + 6.93524i 0.771491 + 0.280800i
\(611\) 4.11887 + 23.3593i 0.166632 + 0.945015i
\(612\) 0 0
\(613\) −4.22183 + 3.54254i −0.170518 + 0.143082i −0.724053 0.689744i \(-0.757723\pi\)
0.553535 + 0.832826i \(0.313279\pi\)
\(614\) −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 0.737606 0.675232i \(-0.235956\pi\)
0.999069 + 0.0431340i \(0.0137342\pi\)
\(618\) 0 0
\(619\) 0.239303 + 0.414484i 0.00961839 + 0.0166595i 0.870795 0.491647i \(-0.163605\pi\)
−0.861176 + 0.508307i \(0.830272\pi\)
\(620\) 9.78553 16.9490i 0.392996 0.680690i
\(621\) 0 0
\(622\) 39.3179 32.9916i 1.57650 1.32284i
\(623\) 20.7188 + 17.3851i 0.830081 + 0.696521i
\(624\) 0 0
\(625\) −0.939693 0.342020i −0.0375877 0.0136808i
\(626\) 12.2075 0.487912
\(627\) 0 0
\(628\) 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 0.862527 0.506011i \(-0.168880\pi\)
−0.348547 + 0.937291i \(0.613325\pi\)
\(632\) 1.19727 1.00463i 0.0476248 0.0399620i
\(633\) 0 0
\(634\) 16.0473 27.7948i 0.637321 1.10387i
\(635\) 7.73805 + 13.4027i 0.307075 + 0.531870i
\(636\) 0 0
\(637\) 7.12299 2.59256i 0.282223 0.102721i
\(638\) 9.08156 + 15.7297i 0.359543 + 0.622746i
\(639\) 0 0
\(640\) −0.243932 + 1.38340i −0.00964224 + 0.0546839i
\(641\) −17.5433 + 14.7206i −0.692920 + 0.581429i −0.919750 0.392506i \(-0.871608\pi\)
0.226830 + 0.973934i \(0.427164\pi\)
\(642\) 0 0
\(643\) −1.49019 8.45131i −0.0587675 0.333287i 0.941222 0.337788i \(-0.109679\pi\)
−0.999990 + 0.00450051i \(0.998567\pi\)
\(644\) 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 \(0.319957\pi\)
\(648\) 0 0
\(649\) 0.464077 + 2.63191i 0.0182166 + 0.103312i
\(650\) −4.58276 3.84539i −0.179750 0.150829i
\(651\) 0 0
\(652\) −0.201779 + 1.14435i −0.00790228 + 0.0448160i
\(653\) −13.1299 + 22.7417i −0.513813 + 0.889950i 0.486059 + 0.873926i \(0.338434\pi\)
−0.999872 + 0.0160238i \(0.994899\pi\)
\(654\) 0 0
\(655\) 0.791413 0.288051i 0.0309231 0.0112551i
\(656\) −43.3272 + 15.7698i −1.69164 + 0.615708i
\(657\) 0 0
\(658\) 25.0534 43.3938i 0.976685 1.69167i
\(659\) 3.99590 22.6619i 0.155658 0.882781i −0.802524 0.596620i \(-0.796510\pi\)
0.958182 0.286160i \(-0.0923790\pi\)
\(660\) 0 0
\(661\) 23.4408 + 19.6692i 0.911742 + 0.765042i 0.972450 0.233114i \(-0.0748914\pi\)
−0.0607080 + 0.998156i \(0.519336\pi\)
\(662\) −4.97423 28.2102i −0.193329 1.09642i
\(663\) 0 0
\(664\) 1.68807 0.0655100
\(665\) −0.501701 13.4691i −0.0194551 0.522311i
\(666\) 0 0
\(667\) 34.0234 + 12.3835i 1.31739 + 0.479491i
\(668\) −8.02930 45.5364i −0.310663 1.76186i
\(669\) 0 0
\(670\) 14.4780 12.1485i 0.559335 0.469338i
\(671\) 1.67761 9.51422i 0.0647636 0.367292i
\(672\) 0 0
\(673\) 18.9334 + 32.7936i 0.729828 + 1.26410i 0.956956 + 0.290234i \(0.0937331\pi\)
−0.227128 + 0.973865i \(0.572934\pi\)
\(674\) 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 0.0505308 + 0.998723i \(0.483909\pi\)
−0.890184 + 0.455600i \(0.849425\pi\)
\(678\) 0 0
\(679\) 18.4484 15.4800i 0.707983 0.594068i
\(680\) −0.00524583 0.00440177i −0.000201168 0.000168800i
\(681\) 0 0
\(682\) −17.1593 6.24549i −0.657065 0.239152i
\(683\) −15.0878 −0.577320 −0.288660 0.957432i \(-0.593210\pi\)
−0.288660 + 0.957432i \(0.593210\pi\)
\(684\) 0 0
\(685\) 5.07379 0.193860
\(686\) 26.0724 + 9.48956i 0.995447 + 0.362313i
\(687\) 0 0
\(688\) 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 −0.949787 0.312897i \(-0.898701\pi\)
0.745870 + 0.666091i \(0.232034\pi\)
\(692\) −11.9541 20.7052i −0.454428 0.787093i
\(693\) 0 0
\(694\) −20.9964 + 7.64207i −0.797013 + 0.290089i
\(695\) −1.36520 2.36459i −0.0517848 0.0896939i
\(696\) 0 0
\(697\) 0.0816935 0.463307i 0.00309436 0.0175490i
\(698\) 54.7371 45.9299i 2.07183 1.73847i
\(699\) 0 0
\(700\) 1.12058 + 6.35515i 0.0423541 + 0.240202i
\(701\) 23.0611 + 8.39354i 0.871005 + 0.317020i 0.738574 0.674172i \(-0.235500\pi\)
0.132431 + 0.991192i \(0.457722\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) −7.43295 + 42.1543i −0.279150 + 1.58314i 0.446312 + 0.894878i \(0.352737\pi\)
−0.725462 + 0.688262i \(0.758374\pi\)
\(710\) 12.7255 22.0412i 0.477579 0.827191i
\(711\) 0 0
\(712\) −1.44461 + 0.525795i −0.0541391 + 0.0197050i
\(713\) −34.2059 + 12.4499i −1.28102 + 0.466254i
\(714\) 0 0
\(715\) −1.42513 + 2.46840i −0.0532969 + 0.0923129i
\(716\) −2.16208 + 12.2618i −0.0808007 + 0.458244i
\(717\) 0 0
\(718\) 14.7255 + 12.3562i 0.549551 + 0.461128i
\(719\) −3.69371 20.9481i −0.137752 0.781231i −0.972904 0.231211i \(-0.925731\pi\)
0.835152 0.550020i \(-0.185380\pi\)
\(720\) 0 0
\(721\) −1.01601 −0.0378381
\(722\) −31.1796 22.4326i −1.16038 0.834854i
\(723\) 0 0
\(724\) 12.1152 + 4.40959i 0.450259 + 0.163881i
\(725\) 1.61976 + 9.18612i 0.0601564 + 0.341164i
\(726\) 0 0
\(727\) −8.06976 + 6.77133i −0.299291 + 0.251135i −0.780049 0.625718i \(-0.784806\pi\)
0.480758 + 0.876853i \(0.340361\pi\)
\(728\) −0.279271 + 1.58383i −0.0103505 + 0.0587005i
\(729\) 0 0
\(730\) −0.906813 1.57065i −0.0335626 0.0581322i
\(731\) −0.181359 + 0.0660091i −0.00670779 + 0.00244144i
\(732\) 0 0
\(733\) 12.5446 + 21.7279i 0.463346 + 0.802538i 0.999125 0.0418196i \(-0.0133155\pi\)
−0.535779 + 0.844358i \(0.679982\pi\)
\(734\) 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
\(738\) 0 0
\(739\) −26.7511 9.73660i −0.984054 0.358166i −0.200639 0.979665i \(-0.564302\pi\)
−0.783415 + 0.621499i \(0.786524\pi\)
\(740\) −2.33193 −0.0857235
\(741\) 0 0
\(742\) −37.8811 −1.39066
\(743\) −9.54830 3.47530i −0.350293 0.127496i 0.160880 0.986974i \(-0.448567\pi\)
−0.511173 + 0.859478i \(0.670789\pi\)
\(744\) 0 0
\(745\) 5.09088 + 4.27176i 0.186515 + 0.156505i
\(746\) −19.1114 + 16.0364i −0.699718 + 0.587133i
\(747\) 0 0
\(748\) −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 0.138330 0.990386i \(-0.455826\pi\)
0.742575 + 0.669763i \(0.233604\pi\)
\(752\) −15.3040 26.5072i −0.558078 0.966620i
\(753\) 0 0
\(754\) −9.68999 + 54.9547i −0.352889 + 2.00133i
\(755\) −3.97622 + 3.33644i −0.144709 + 0.121426i
\(756\) 0 0
\(757\) −5.48348 31.0983i −0.199300 1.13029i −0.906160 0.422935i \(-0.861000\pi\)
0.706860 0.707354i \(-0.250111\pi\)
\(758\) 35.1471 + 12.7925i 1.27660 + 0.464644i
\(759\) 0 0
\(760\) 0.677275 + 0.358097i 0.0245674 + 0.0129895i
\(761\) 3.42183 0.124041 0.0620207 0.998075i \(-0.480246\pi\)
0.0620207 + 0.998075i \(0.480246\pi\)
\(762\) 0 0
\(763\) −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
\(768\) 0 0
\(769\) 26.7893 9.75052i 0.966048 0.351613i 0.189648 0.981852i \(-0.439265\pi\)
0.776401 + 0.630239i \(0.217043\pi\)
\(770\) 5.65796 2.05933i 0.203899 0.0742131i
\(771\) 0 0
\(772\) 24.9459 43.2076i 0.897824 1.55508i
\(773\) −0.247597 + 1.40419i −0.00890545 + 0.0505053i −0.988937 0.148338i \(-0.952608\pi\)
0.980031 + 0.198844i \(0.0637186\pi\)
\(774\) 0 0
\(775\) −7.18387 6.02798i −0.258052 0.216532i
\(776\) 0.237699 + 1.34806i 0.00853291 + 0.0483925i
\(777\) 0 0
\(778\) −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
\(783\) 0 0
\(784\) −7.49302 + 6.28739i −0.267608 + 0.224550i
\(785\) 2.02262 11.4709i 0.0721906 0.409413i
\(786\) 0 0
\(787\) −12.1600 21.0617i −0.433456 0.750768i 0.563712 0.825971i \(-0.309373\pi\)
−0.997168 + 0.0752034i \(0.976039\pi\)
\(788\) −13.1422 + 4.78338i −0.468172 + 0.170401i
\(789\) 0 0
\(790\) −8.98853 15.5686i −0.319797 0.553905i
\(791\) 3.96386 6.86560i 0.140938 0.244113i
\(792\) 0 0
\(793\) 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 \(0.702681\pi\)
\(798\) 0 0
\(799\) 0.312303 0.0110485
\(800\) 7.58444 + 2.76051i 0.268150 + 0.0975988i
\(801\) 0 0
\(802\) 22.6751 + 19.0266i 0.800684 + 0.671854i
\(803\) −0.661932 + 0.555427i −0.0233591 + 0.0196006i
\(804\) 0 0
\(805\) 6.00130 10.3945i 0.211518 0.366360i
\(806\) −28.0509 48.5856i −0.988052 1.71136i
\(807\) 0 0
\(808\) −0.502685 + 0.182962i −0.0176844 + 0.00643659i
\(809\) 9.12037 + 15.7970i 0.320655 + 0.555391i 0.980623 0.195902i \(-0.0627636\pi\)
−0.659968 + 0.751294i \(0.729430\pi\)
\(810\) 0 0
\(811\) −6.34578 + 35.9887i −0.222830 + 1.26373i 0.643959 + 0.765060i \(0.277291\pi\)
−0.866790 + 0.498674i \(0.833820\pi\)
\(812\) 46.1114 38.6921i 1.61819 1.35783i
\(813\) 0 0
\(814\) 0.377821 + 2.14273i 0.0132426 + 0.0751026i
\(815\) 0.523217 + 0.190435i 0.0183275 + 0.00667066i
\(816\) 0 0
\(817\) 18.2842 11.4844i 0.639682 0.401788i
\(818\) 25.7712 0.901069
\(819\) 0 0
\(820\) −4.37578 24.8163i −0.152809 0.866622i
\(821\) −8.13847 6.82899i −0.284035 0.238333i 0.489628 0.871932i \(-0.337133\pi\)
−0.773662 + 0.633598i \(0.781577\pi\)
\(822\) 0 0
\(823\) −6.43574 + 36.4989i −0.224336 + 1.27227i 0.639615 + 0.768696i \(0.279094\pi\)
−0.863951 + 0.503577i \(0.832017\pi\)
\(824\) 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 0.155174 0.987887i \(-0.450406\pi\)
0.753871 + 0.657022i \(0.228184\pi\)
\(828\) 0 0
\(829\) 6.90991 11.9683i 0.239991 0.415677i −0.720720 0.693226i \(-0.756189\pi\)
0.960711 + 0.277549i \(0.0895221\pi\)
\(830\) 3.37165 19.1216i 0.117032 0.663720i
\(831\) 0 0
\(832\) 19.6759 + 16.5100i 0.682139 + 0.572383i
\(833\) −0.0173307 0.0982871i −0.000600472 0.00340545i
\(834\) 0 0
\(835\) −22.1563 −0.766751
\(836\) 2.68820 8.33932i 0.0929732 0.288422i
\(837\) 0 0
\(838\) 5.40657 + 1.96783i 0.186767 + 0.0679776i
\(839\) 1.11616 + 6.33006i 0.0385341 + 0.218538i 0.997994 0.0633071i \(-0.0201648\pi\)
−0.959460 + 0.281845i \(0.909054\pi\)
\(840\) 0 0
\(841\) 44.4370 37.2871i 1.53231 1.28576i
\(842\) 3.91439 22.1996i 0.134899 0.765048i
\(843\) 0 0
\(844\) 11.9561 + 20.7085i 0.411545 + 0.712817i
\(845\) 3.98727 1.45125i 0.137166 0.0499244i
\(846\) 0 0
\(847\) 15.5726 + 26.9726i 0.535081 + 0.926788i
\(848\) −11.5699 + 20.0396i −0.397311 + 0.688163i
\(849\) 0 0
\(850\) −0.0603386 + 0.0506301i −0.00206960 + 0.00173660i
\(851\) 3.32254 + 2.78794i 0.113895 + 0.0955695i
\(852\) 0 0
\(853\) −24.8033 9.02767i −0.849250 0.309102i −0.119515 0.992832i \(-0.538134\pi\)
−0.729734 + 0.683731i \(0.760356\pi\)
\(854\) −62.7009 −2.14558
\(855\) 0 0
\(856\) 2.24749 0.0768177
\(857\) 16.0036 + 5.82483i 0.546672 + 0.198973i 0.600567 0.799574i \(-0.294941\pi\)
−0.0538950 + 0.998547i \(0.517164\pi\)
\(858\) 0 0
\(859\) 18.9375 + 15.8905i 0.646140 + 0.542176i 0.905897 0.423498i \(-0.139198\pi\)
−0.259757 + 0.965674i \(0.583642\pi\)
\(860\) −7.91907 + 6.64489i −0.270038 + 0.226589i
\(861\) 0 0
\(862\) −15.0977 + 26.1500i −0.514230 + 0.890673i
\(863\) −0.519450 0.899714i −0.0176823 0.0306266i 0.857049 0.515235i \(-0.172295\pi\)
−0.874731 + 0.484609i \(0.838962\pi\)
\(864\) 0 0
\(865\) −10.7653 + 3.91823i −0.366030 + 0.133224i
\(866\) 39.1757 + 67.8542i 1.33124 + 2.30578i
\(867\) 0 0
\(868\) −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
\(873\) 0 0
\(874\) −12.8870 31.6842i −0.435910 1.07174i
\(875\) 3.09218 0.104535
\(876\) 0 0
\(877\) 3.68173 + 20.8801i 0.124323 + 0.705071i 0.981708 + 0.190395i \(0.0609768\pi\)
−0.857385 + 0.514676i \(0.827912\pi\)
\(878\) −48.6717 40.8404i −1.64259 1.37830i
\(879\) 0 0
\(880\) 0.638677 3.62212i 0.0215298 0.122101i
\(881\) 7.84097 13.5810i 0.264169 0.457554i −0.703176 0.711015i \(-0.748236\pi\)
0.967346 + 0.253461i \(0.0815690\pi\)
\(882\) 0 0
\(883\) −18.4562 + 6.71750i −0.621100 + 0.226062i −0.633353 0.773863i \(-0.718322\pi\)
0.0122532 + 0.999925i \(0.496100\pi\)
\(884\) −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 0.823296 + 0.567612i \(0.192133\pi\)
−0.967780 + 0.251797i \(0.918979\pi\)
\(888\) 0 0
\(889\) −36.6589 30.7605i −1.22950 1.03167i
\(890\) 3.07055 + 17.4139i 0.102925 + 0.583717i
\(891\) 0 0
\(892\) −15.6817 −0.525063
\(893\) −34.1586 + 7.34365i −1.14307 + 0.245746i
\(894\) 0 0
\(895\) 5.60632 + 2.04053i 0.187398 + 0.0682075i
\(896\) −0.754279 4.27773i −0.0251987 0.142909i
\(897\) 0 0
\(898\) −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
\(903\) 0 0
\(904\) 0.225306 + 0.390241i 0.00749355 + 0.0129792i
\(905\) 3.08892 5.35016i 0.102679 0.177845i
\(906\) 0 0
\(907\) −16.3342 + 13.7060i −0.542368 + 0.455100i −0.872347 0.488888i \(-0.837403\pi\)
0.329979 + 0.943988i \(0.392958\pi\)
\(908\) 6.71744 + 5.63660i 0.222926 + 0.187057i
\(909\) 0 0
\(910\) 17.3829 + 6.32687i 0.576238 + 0.209734i
\(911\) 34.0175 1.12705 0.563524 0.826100i \(-0.309445\pi\)
0.563524 + 0.826100i \(0.309445\pi\)
\(912\) 0 0
\(913\) −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 0
\(919\) 20.8710 36.1496i 0.688470 1.19246i −0.283863 0.958865i \(-0.591616\pi\)
0.972333 0.233600i \(-0.0750505\pi\)
\(920\) 0.341114 + 0.590826i 0.0112462 + 0.0194790i
\(921\) 0 0
\(922\) 12.6256 4.59534i 0.415802 0.151340i
\(923\) −18.6272 32.2633i −0.613123 1.06196i
\(924\) 0 0
\(925\) −0.194033 + 1.10042i −0.00637977 + 0.0361815i
\(926\) 34.5268 28.9715i 1.13462 0.952061i
\(927\) 0 0
\(928\) −13.0734 74.1429i −0.429155 2.43386i
\(929\) −21.5234 7.83389i −0.706161 0.257022i −0.0361220 0.999347i \(-0.511500\pi\)
−0.670039 + 0.742326i \(0.733723\pi\)
\(930\) 0 0
\(931\) 4.20674 + 10.3428i 0.137870 + 0.338970i
\(932\) 22.9123 0.750517
\(933\) 0 0
\(934\) 5.43213 + 30.8071i 0.177745 + 1.00804i
\(935\) 0.0287480 + 0.0241224i 0.000940159 + 0.000788887i
\(936\) 0 0
\(937\) 2.02604 11.4902i 0.0661877 0.375369i −0.933664 0.358150i \(-0.883408\pi\)
0.999852 0.0172191i \(-0.00548128\pi\)
\(938\) −29.2206 + 50.6116i −0.954088 + 1.65253i
\(939\) 0 0
\(940\) 15.7192 5.72131i 0.512703 0.186609i
\(941\) 52.0967 18.9616i 1.69830 0.618132i 0.702672 0.711514i \(-0.251990\pi\)
0.995630 + 0.0933820i \(0.0297678\pi\)
\(942\) 0 0
\(943\) −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 0.999741 0.0227671i \(-0.00724762\pi\)
−0.947236 + 0.320537i \(0.896137\pi\)
\(948\) 0 0
\(949\) −2.65474 −0.0861765
\(950\) 5.40907 6.95657i 0.175493 0.225701i
\(951\) 0 0
\(952\) 0.0198980 + 0.00724229i 0.000644899 + 0.000234724i
\(953\) 2.99473 + 16.9840i 0.0970090 + 0.550165i 0.994113 + 0.108346i \(0.0345555\pi\)
−0.897104 + 0.441819i \(0.854333\pi\)
\(954\) 0 0
\(955\) 14.2974 11.9969i 0.462652 0.388211i
\(956\) 0.987737 5.60173i 0.0319457 0.181173i
\(957\) 0 0
\(958\) 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
\(963\) 0 0
\(964\) 17.8318 14.9626i 0.574323 0.481914i
\(965\) −18.3136 15.3669i −0.589536 0.494679i
\(966\) 0 0
\(967\) −3.46405 1.26081i −0.111396 0.0405449i 0.285721 0.958313i \(-0.407767\pi\)
−0.397117 + 0.917768i \(0.629989\pi\)
\(968\) −1.77029 −0.0568994
\(969\) 0 0
\(970\) 15.7449 0.505537
\(971\) −21.3740 7.77948i −0.685923 0.249656i −0.0245344 0.999699i \(-0.507810\pi\)
−0.661389 + 0.750043i \(0.730033\pi\)
\(972\) 0 0
\(973\) 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 −0.960951 0.276720i \(-0.910753\pi\)
0.240829 0.970568i \(-0.422581\pi\)
\(978\) 0 0
\(979\) 7.91669 2.88144i 0.253018 0.0920911i
\(980\) −2.67290 4.62960i −0.0853827 0.147887i
\(981\) 0 0
\(982\) −1.59679 + 9.05587i −0.0509557 + 0.288984i
\(983\) −32.4157 + 27.2000i −1.03390 + 0.867544i −0.991310 0.131548i \(-0.958005\pi\)
−0.0425891 + 0.999093i \(0.513561\pi\)
\(984\) 0 0
\(985\) 1.16371 + 6.59971i 0.0370788 + 0.210284i
\(986\) 0.690411 + 0.251289i 0.0219872 + 0.00800267i
\(987\) 0 0
\(988\) 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 0.941688 + 0.336488i \(0.109239\pi\)
−0.769812 + 0.638271i \(0.779650\pi\)
\(992\) 57.9824 + 48.6530i 1.84094 + 1.54473i
\(993\) 0 0
\(994\) −13.6659 + 77.5032i −0.433456 + 2.45825i
\(995\) −1.57943 + 2.73566i −0.0500714 + 0.0867261i
\(996\) 0 0
\(997\) −36.5451 + 13.3013i −1.15740 + 0.421258i −0.848166 0.529730i \(-0.822293\pi\)
−0.309229 + 0.950987i \(0.600071\pi\)
\(998\) 41.4579 15.0895i 1.31233 0.477648i
\(999\) 0 0
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 855.2.bs.b.631.1 18
3.2 odd 2 95.2.k.b.61.3 18
15.2 even 4 475.2.u.c.99.1 36
15.8 even 4 475.2.u.c.99.6 36
15.14 odd 2 475.2.l.b.251.1 18
19.5 even 9 inner 855.2.bs.b.271.1 18
57.5 odd 18 95.2.k.b.81.3 yes 18
57.29 even 18 1805.2.a.u.1.9 9
57.47 odd 18 1805.2.a.t.1.1 9
285.29 even 18 9025.2.a.cd.1.1 9
285.62 even 36 475.2.u.c.24.6 36
285.104 odd 18 9025.2.a.ce.1.9 9
285.119 odd 18 475.2.l.b.176.1 18
285.233 even 36 475.2.u.c.24.1 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.b.61.3 18 3.2 odd 2
95.2.k.b.81.3 yes 18 57.5 odd 18
475.2.l.b.176.1 18 285.119 odd 18
475.2.l.b.251.1 18 15.14 odd 2
475.2.u.c.24.1 36 285.233 even 36
475.2.u.c.24.6 36 285.62 even 36
475.2.u.c.99.1 36 15.2 even 4
475.2.u.c.99.6 36 15.8 even 4
855.2.bs.b.271.1 18 19.5 even 9 inner
855.2.bs.b.631.1 18 1.1 even 1 trivial
1805.2.a.t.1.1 9 57.47 odd 18
1805.2.a.u.1.9 9 57.29 even 18
9025.2.a.cd.1.1 9 285.29 even 18
9025.2.a.ce.1.9 9 285.104 odd 18