Properties

Label 950.2.j.i.49.4
Level $950$
Weight $2$
Character 950.49
Analytic conductor $7.586$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(49,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 8 x^{14} - 36 x^{13} + 67 x^{12} + 34 x^{11} - 24 x^{10} + 182 x^{9} - 495 x^{8} - 166 x^{7} + 258 x^{6} - 1292 x^{5} + 2920 x^{4} + 1176 x^{3} + 200 x^{2} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.4
Root \(0.399276 + 1.49012i\) of defining polynomial
Character \(\chi\) \(=\) 950.49
Dual form 950.2.j.i.349.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(2.82754 + 1.63248i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.63248 - 2.82754i) q^{6} +2.62013i q^{7} -1.00000i q^{8} +(3.82998 + 6.63372i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(2.82754 + 1.63248i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.63248 - 2.82754i) q^{6} +2.62013i q^{7} -1.00000i q^{8} +(3.82998 + 6.63372i) q^{9} +5.03983 q^{11} +3.26496i q^{12} +(4.02254 - 2.32241i) q^{13} +(1.31007 - 2.26910i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.16962 - 1.82998i) q^{17} -7.65996i q^{18} +(-0.697500 - 4.30273i) q^{19} +(-4.27731 + 7.40852i) q^{21} +(-4.36462 - 2.51991i) q^{22} +(-4.05703 + 2.34233i) q^{23} +(1.63248 - 2.82754i) q^{24} -4.64483 q^{26} +15.2146i q^{27} +(-2.26910 + 1.31007i) q^{28} +(-4.01991 - 6.96270i) q^{29} -3.28009 q^{31} +(0.866025 - 0.500000i) q^{32} +(14.2503 + 8.22742i) q^{33} +(1.82998 + 3.16962i) q^{34} +(-3.82998 + 6.63372i) q^{36} +5.75505i q^{37} +(-1.54731 + 4.07502i) q^{38} +15.1652 q^{39} +(2.90735 - 5.03568i) q^{41} +(7.40852 - 4.27731i) q^{42} +(0.502555 + 0.290150i) q^{43} +(2.51991 + 4.36462i) q^{44} +4.68466 q^{46} +(-4.00115 + 2.31007i) q^{47} +(-2.82754 + 1.63248i) q^{48} +0.134919 q^{49} +(-5.97481 - 10.3487i) q^{51} +(4.02254 + 2.32241i) q^{52} +(-4.00115 + 2.31007i) q^{53} +(7.60729 - 13.1762i) q^{54} +2.62013 q^{56} +(5.05191 - 13.3048i) q^{57} +8.03983i q^{58} +(-1.88743 + 3.26913i) q^{59} +(-0.0650203 - 0.112618i) q^{61} +(2.84064 + 1.64004i) q^{62} +(-17.3812 + 10.0350i) q^{63} -1.00000 q^{64} +(-8.22742 - 14.2503i) q^{66} +(-0.328977 + 0.189935i) q^{67} -3.65996i q^{68} -15.2952 q^{69} +(4.56746 - 7.91107i) q^{71} +(6.63372 - 3.82998i) q^{72} +(7.36574 + 4.25261i) q^{73} +(2.87752 - 4.98402i) q^{74} +(3.37752 - 2.75542i) q^{76} +13.2050i q^{77} +(-13.1334 - 7.58259i) q^{78} +(-3.98237 + 6.89767i) q^{79} +(-13.3475 + 23.1186i) q^{81} +(-5.03568 + 2.90735i) q^{82} +7.86996i q^{83} -8.55462 q^{84} +(-0.290150 - 0.502555i) q^{86} -26.2497i q^{87} -5.03983i q^{88} +(-4.14483 - 7.17905i) q^{89} +(6.08503 + 10.5396i) q^{91} +(-4.05703 - 2.34233i) q^{92} +(-9.27458 - 5.35468i) q^{93} +4.62013 q^{94} +3.26496 q^{96} +(-14.0208 - 8.09494i) q^{97} +(-0.116843 - 0.0674593i) q^{98} +(19.3024 + 33.4328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9} + 20 q^{11} + 12 q^{14} - 8 q^{16} - 2 q^{21} - 2 q^{24} - 36 q^{26} - 34 q^{29} + 44 q^{31} - 10 q^{34} - 22 q^{36} + 72 q^{39} + 14 q^{41} + 10 q^{44} - 24 q^{46} - 88 q^{49} - 18 q^{51} + 16 q^{54} + 24 q^{56} - 28 q^{59} - 18 q^{61} - 16 q^{64} - 8 q^{66} - 108 q^{69} + 28 q^{71} - 8 q^{74} + 34 q^{79} - 72 q^{81} - 4 q^{84} - 26 q^{86} - 28 q^{89} - 50 q^{91} + 56 q^{94} - 4 q^{96} + 120 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 2.82754 + 1.63248i 1.63248 + 0.942513i 0.983325 + 0.181856i \(0.0582105\pi\)
0.649154 + 0.760657i \(0.275123\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −1.63248 2.82754i −0.666457 1.15434i
\(7\) 2.62013i 0.990316i 0.868803 + 0.495158i \(0.164890\pi\)
−0.868803 + 0.495158i \(0.835110\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 3.82998 + 6.63372i 1.27666 + 2.21124i
\(10\) 0 0
\(11\) 5.03983 1.51957 0.759783 0.650177i \(-0.225305\pi\)
0.759783 + 0.650177i \(0.225305\pi\)
\(12\) 3.26496i 0.942513i
\(13\) 4.02254 2.32241i 1.11565 0.644122i 0.175365 0.984504i \(-0.443890\pi\)
0.940287 + 0.340382i \(0.110556\pi\)
\(14\) 1.31007 2.26910i 0.350130 0.606442i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.16962 1.82998i −0.768745 0.443835i 0.0636816 0.997970i \(-0.479716\pi\)
−0.832427 + 0.554135i \(0.813049\pi\)
\(18\) 7.65996i 1.80547i
\(19\) −0.697500 4.30273i −0.160017 0.987114i
\(20\) 0 0
\(21\) −4.27731 + 7.40852i −0.933385 + 1.61667i
\(22\) −4.36462 2.51991i −0.930540 0.537248i
\(23\) −4.05703 + 2.34233i −0.845950 + 0.488409i −0.859282 0.511502i \(-0.829089\pi\)
0.0133324 + 0.999911i \(0.495756\pi\)
\(24\) 1.63248 2.82754i 0.333229 0.577169i
\(25\) 0 0
\(26\) −4.64483 −0.910926
\(27\) 15.2146i 2.92805i
\(28\) −2.26910 + 1.31007i −0.428819 + 0.247579i
\(29\) −4.01991 6.96270i −0.746479 1.29294i −0.949500 0.313766i \(-0.898409\pi\)
0.203021 0.979174i \(-0.434924\pi\)
\(30\) 0 0
\(31\) −3.28009 −0.589121 −0.294561 0.955633i \(-0.595173\pi\)
−0.294561 + 0.955633i \(0.595173\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 14.2503 + 8.22742i 2.48066 + 1.43221i
\(34\) 1.82998 + 3.16962i 0.313839 + 0.543585i
\(35\) 0 0
\(36\) −3.82998 + 6.63372i −0.638330 + 1.10562i
\(37\) 5.75505i 0.946124i 0.881029 + 0.473062i \(0.156851\pi\)
−0.881029 + 0.473062i \(0.843149\pi\)
\(38\) −1.54731 + 4.07502i −0.251007 + 0.661056i
\(39\) 15.1652 2.42837
\(40\) 0 0
\(41\) 2.90735 5.03568i 0.454052 0.786441i −0.544581 0.838708i \(-0.683311\pi\)
0.998633 + 0.0522673i \(0.0166448\pi\)
\(42\) 7.40852 4.27731i 1.14316 0.660003i
\(43\) 0.502555 + 0.290150i 0.0766390 + 0.0442475i 0.537830 0.843053i \(-0.319244\pi\)
−0.461191 + 0.887301i \(0.652578\pi\)
\(44\) 2.51991 + 4.36462i 0.379891 + 0.657991i
\(45\) 0 0
\(46\) 4.68466 0.690715
\(47\) −4.00115 + 2.31007i −0.583628 + 0.336958i −0.762574 0.646901i \(-0.776065\pi\)
0.178946 + 0.983859i \(0.442731\pi\)
\(48\) −2.82754 + 1.63248i −0.408120 + 0.235628i
\(49\) 0.134919 0.0192741
\(50\) 0 0
\(51\) −5.97481 10.3487i −0.836641 1.44910i
\(52\) 4.02254 + 2.32241i 0.557826 + 0.322061i
\(53\) −4.00115 + 2.31007i −0.549600 + 0.317312i −0.748961 0.662614i \(-0.769447\pi\)
0.199361 + 0.979926i \(0.436114\pi\)
\(54\) 7.60729 13.1762i 1.03522 1.79306i
\(55\) 0 0
\(56\) 2.62013 0.350130
\(57\) 5.05191 13.3048i 0.669142 1.76226i
\(58\) 8.03983i 1.05568i
\(59\) −1.88743 + 3.26913i −0.245723 + 0.425605i −0.962335 0.271868i \(-0.912359\pi\)
0.716612 + 0.697472i \(0.245692\pi\)
\(60\) 0 0
\(61\) −0.0650203 0.112618i −0.00832500 0.0144193i 0.861833 0.507192i \(-0.169317\pi\)
−0.870158 + 0.492773i \(0.835983\pi\)
\(62\) 2.84064 + 1.64004i 0.360762 + 0.208286i
\(63\) −17.3812 + 10.0350i −2.18983 + 1.26430i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −8.22742 14.2503i −1.01273 1.75409i
\(67\) −0.328977 + 0.189935i −0.0401909 + 0.0232043i −0.519961 0.854190i \(-0.674053\pi\)
0.479770 + 0.877394i \(0.340720\pi\)
\(68\) 3.65996i 0.443835i
\(69\) −15.2952 −1.84133
\(70\) 0 0
\(71\) 4.56746 7.91107i 0.542058 0.938871i −0.456728 0.889606i \(-0.650979\pi\)
0.998786 0.0492651i \(-0.0156879\pi\)
\(72\) 6.63372 3.82998i 0.781791 0.451367i
\(73\) 7.36574 + 4.25261i 0.862094 + 0.497730i 0.864713 0.502266i \(-0.167500\pi\)
−0.00261883 + 0.999997i \(0.500834\pi\)
\(74\) 2.87752 4.98402i 0.334505 0.579380i
\(75\) 0 0
\(76\) 3.37752 2.75542i 0.387429 0.316068i
\(77\) 13.2050i 1.50485i
\(78\) −13.1334 7.58259i −1.48707 0.858559i
\(79\) −3.98237 + 6.89767i −0.448052 + 0.776049i −0.998259 0.0589793i \(-0.981215\pi\)
0.550207 + 0.835028i \(0.314549\pi\)
\(80\) 0 0
\(81\) −13.3475 + 23.1186i −1.48306 + 2.56874i
\(82\) −5.03568 + 2.90735i −0.556098 + 0.321063i
\(83\) 7.86996i 0.863840i 0.901912 + 0.431920i \(0.142164\pi\)
−0.901912 + 0.431920i \(0.857836\pi\)
\(84\) −8.55462 −0.933385
\(85\) 0 0
\(86\) −0.290150 0.502555i −0.0312877 0.0541919i
\(87\) 26.2497i 2.81426i
\(88\) 5.03983i 0.537248i
\(89\) −4.14483 7.17905i −0.439351 0.760978i 0.558289 0.829647i \(-0.311458\pi\)
−0.997640 + 0.0686686i \(0.978125\pi\)
\(90\) 0 0
\(91\) 6.08503 + 10.5396i 0.637884 + 1.10485i
\(92\) −4.05703 2.34233i −0.422975 0.244205i
\(93\) −9.27458 5.35468i −0.961729 0.555254i
\(94\) 4.62013 0.476530
\(95\) 0 0
\(96\) 3.26496 0.333229
\(97\) −14.0208 8.09494i −1.42360 0.821917i −0.426997 0.904253i \(-0.640428\pi\)
−0.996605 + 0.0823367i \(0.973762\pi\)
\(98\) −0.116843 0.0674593i −0.0118029 0.00681442i
\(99\) 19.3024 + 33.4328i 1.93997 + 3.36012i
\(100\) 0 0
\(101\) −4.23270 7.33124i −0.421169 0.729486i 0.574885 0.818234i \(-0.305047\pi\)
−0.996054 + 0.0887481i \(0.971713\pi\)
\(102\) 11.9496i 1.18319i
\(103\) 11.8498i 1.16760i 0.811898 + 0.583800i \(0.198435\pi\)
−0.811898 + 0.583800i \(0.801565\pi\)
\(104\) −2.32241 4.02254i −0.227731 0.394443i
\(105\) 0 0
\(106\) 4.62013 0.448747
\(107\) 16.8100i 1.62508i −0.582902 0.812542i \(-0.698083\pi\)
0.582902 0.812542i \(-0.301917\pi\)
\(108\) −13.1762 + 7.60729i −1.26788 + 0.732012i
\(109\) 10.0023 17.3245i 0.958045 1.65938i 0.230806 0.973000i \(-0.425864\pi\)
0.727240 0.686384i \(-0.240803\pi\)
\(110\) 0 0
\(111\) −9.39500 + 16.2726i −0.891734 + 1.54453i
\(112\) −2.26910 1.31007i −0.214410 0.123790i
\(113\) 14.3505i 1.34998i −0.737827 0.674990i \(-0.764148\pi\)
0.737827 0.674990i \(-0.235852\pi\)
\(114\) −11.0275 + 8.99633i −1.03282 + 0.842583i
\(115\) 0 0
\(116\) 4.01991 6.96270i 0.373240 0.646470i
\(117\) 30.8125 + 17.7896i 2.84862 + 1.64465i
\(118\) 3.26913 1.88743i 0.300948 0.173752i
\(119\) 4.79478 8.30481i 0.439537 0.761301i
\(120\) 0 0
\(121\) 14.3999 1.30908
\(122\) 0.130041i 0.0117733i
\(123\) 16.4413 9.49238i 1.48246 0.855899i
\(124\) −1.64004 2.84064i −0.147280 0.255097i
\(125\) 0 0
\(126\) 20.0701 1.78799
\(127\) −6.82869 + 3.94254i −0.605948 + 0.349844i −0.771378 0.636377i \(-0.780432\pi\)
0.165430 + 0.986222i \(0.447099\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0.947329 + 1.64082i 0.0834077 + 0.144466i
\(130\) 0 0
\(131\) −1.20228 + 2.08242i −0.105044 + 0.181942i −0.913756 0.406263i \(-0.866832\pi\)
0.808712 + 0.588205i \(0.200165\pi\)
\(132\) 16.4548i 1.43221i
\(133\) 11.2737 1.82754i 0.977555 0.158468i
\(134\) 0.379870 0.0328158
\(135\) 0 0
\(136\) −1.82998 + 3.16962i −0.156919 + 0.271792i
\(137\) 15.0992 8.71751i 1.29001 0.744787i 0.311353 0.950294i \(-0.399218\pi\)
0.978656 + 0.205507i \(0.0658844\pi\)
\(138\) 13.2460 + 7.64761i 1.12758 + 0.651008i
\(139\) 4.78487 + 8.28764i 0.405848 + 0.702949i 0.994420 0.105496i \(-0.0336430\pi\)
−0.588572 + 0.808445i \(0.700310\pi\)
\(140\) 0 0
\(141\) −15.0845 −1.27035
\(142\) −7.91107 + 4.56746i −0.663882 + 0.383293i
\(143\) 20.2729 11.7046i 1.69531 0.978786i
\(144\) −7.65996 −0.638330
\(145\) 0 0
\(146\) −4.25261 7.36574i −0.351948 0.609593i
\(147\) 0.381488 + 0.220252i 0.0314646 + 0.0181661i
\(148\) −4.98402 + 2.87752i −0.409684 + 0.236531i
\(149\) −8.56218 + 14.8301i −0.701441 + 1.21493i 0.266519 + 0.963830i \(0.414126\pi\)
−0.967961 + 0.251102i \(0.919207\pi\)
\(150\) 0 0
\(151\) −5.44440 −0.443059 −0.221529 0.975154i \(-0.571105\pi\)
−0.221529 + 0.975154i \(0.571105\pi\)
\(152\) −4.30273 + 0.697500i −0.348998 + 0.0565747i
\(153\) 28.0351i 2.26651i
\(154\) 6.60250 11.4359i 0.532045 0.921529i
\(155\) 0 0
\(156\) 7.58259 + 13.1334i 0.607093 + 1.05152i
\(157\) 0.0213902 + 0.0123496i 0.00170712 + 0.000985608i 0.500853 0.865532i \(-0.333020\pi\)
−0.499146 + 0.866518i \(0.666353\pi\)
\(158\) 6.89767 3.98237i 0.548749 0.316821i
\(159\) −15.0845 −1.19628
\(160\) 0 0
\(161\) −6.13721 10.6300i −0.483680 0.837758i
\(162\) 23.1186 13.3475i 1.81637 1.04868i
\(163\) 10.8347i 0.848640i 0.905512 + 0.424320i \(0.139487\pi\)
−0.905512 + 0.424320i \(0.860513\pi\)
\(164\) 5.81470 0.454052
\(165\) 0 0
\(166\) 3.93498 6.81558i 0.305414 0.528992i
\(167\) −5.44278 + 3.14239i −0.421175 + 0.243165i −0.695580 0.718449i \(-0.744852\pi\)
0.274405 + 0.961614i \(0.411519\pi\)
\(168\) 7.40852 + 4.27731i 0.571579 + 0.330002i
\(169\) 4.28722 7.42568i 0.329786 0.571206i
\(170\) 0 0
\(171\) 25.8717 21.1064i 1.97846 1.61405i
\(172\) 0.580301i 0.0442475i
\(173\) −0.324914 0.187589i −0.0247028 0.0142622i 0.487598 0.873068i \(-0.337873\pi\)
−0.512301 + 0.858806i \(0.671207\pi\)
\(174\) −13.1249 + 22.7329i −0.994993 + 1.72338i
\(175\) 0 0
\(176\) −2.51991 + 4.36462i −0.189946 + 0.328996i
\(177\) −10.6736 + 6.16240i −0.802276 + 0.463194i
\(178\) 8.28966i 0.621336i
\(179\) 8.04940 0.601640 0.300820 0.953681i \(-0.402740\pi\)
0.300820 + 0.953681i \(0.402740\pi\)
\(180\) 0 0
\(181\) 10.5251 + 18.2301i 0.782327 + 1.35503i 0.930583 + 0.366081i \(0.119301\pi\)
−0.148256 + 0.988949i \(0.547366\pi\)
\(182\) 12.1701i 0.902105i
\(183\) 0.424577i 0.0313857i
\(184\) 2.34233 + 4.05703i 0.172679 + 0.299088i
\(185\) 0 0
\(186\) 5.35468 + 9.27458i 0.392624 + 0.680045i
\(187\) −15.9743 9.22278i −1.16816 0.674437i
\(188\) −4.00115 2.31007i −0.291814 0.168479i
\(189\) −39.8642 −2.89969
\(190\) 0 0
\(191\) 8.03983 0.581742 0.290871 0.956762i \(-0.406055\pi\)
0.290871 + 0.956762i \(0.406055\pi\)
\(192\) −2.82754 1.63248i −0.204060 0.117814i
\(193\) −17.5325 10.1224i −1.26202 0.728628i −0.288555 0.957463i \(-0.593175\pi\)
−0.973465 + 0.228836i \(0.926508\pi\)
\(194\) 8.09494 + 14.0208i 0.581183 + 1.00664i
\(195\) 0 0
\(196\) 0.0674593 + 0.116843i 0.00481852 + 0.00834593i
\(197\) 2.92004i 0.208044i −0.994575 0.104022i \(-0.966829\pi\)
0.994575 0.104022i \(-0.0331713\pi\)
\(198\) 38.6049i 2.74353i
\(199\) −7.80244 13.5142i −0.553101 0.957998i −0.998049 0.0624418i \(-0.980111\pi\)
0.444948 0.895556i \(-0.353222\pi\)
\(200\) 0 0
\(201\) −1.24026 −0.0874812
\(202\) 8.46539i 0.595623i
\(203\) 18.2432 10.5327i 1.28042 0.739251i
\(204\) 5.97481 10.3487i 0.418320 0.724552i
\(205\) 0 0
\(206\) 5.92492 10.2623i 0.412809 0.715006i
\(207\) −31.0767 17.9421i −2.15998 1.24707i
\(208\) 4.64483i 0.322061i
\(209\) −3.51528 21.6850i −0.243157 1.49998i
\(210\) 0 0
\(211\) −0.572585 + 0.991747i −0.0394184 + 0.0682747i −0.885062 0.465474i \(-0.845884\pi\)
0.845643 + 0.533749i \(0.179217\pi\)
\(212\) −4.00115 2.31007i −0.274800 0.158656i
\(213\) 25.8293 14.9126i 1.76980 1.02179i
\(214\) −8.40500 + 14.5579i −0.574554 + 0.995157i
\(215\) 0 0
\(216\) 15.2146 1.03522
\(217\) 8.59426i 0.583416i
\(218\) −17.3245 + 10.0023i −1.17336 + 0.677440i
\(219\) 13.8846 + 24.0488i 0.938234 + 1.62507i
\(220\) 0 0
\(221\) −16.9999 −1.14354
\(222\) 16.2726 9.39500i 1.09215 0.630551i
\(223\) −13.2757 7.66474i −0.889008 0.513269i −0.0153903 0.999882i \(-0.504899\pi\)
−0.873618 + 0.486612i \(0.838232\pi\)
\(224\) 1.31007 + 2.26910i 0.0875324 + 0.151611i
\(225\) 0 0
\(226\) −7.17524 + 12.4279i −0.477290 + 0.826690i
\(227\) 19.2850i 1.27999i 0.768380 + 0.639994i \(0.221063\pi\)
−0.768380 + 0.639994i \(0.778937\pi\)
\(228\) 14.0482 2.27731i 0.930368 0.150818i
\(229\) −14.3752 −0.949939 −0.474969 0.880002i \(-0.657541\pi\)
−0.474969 + 0.880002i \(0.657541\pi\)
\(230\) 0 0
\(231\) −21.5569 + 37.3377i −1.41834 + 2.45664i
\(232\) −6.96270 + 4.01991i −0.457123 + 0.263920i
\(233\) −11.9732 6.91272i −0.784389 0.452867i 0.0535944 0.998563i \(-0.482932\pi\)
−0.837984 + 0.545695i \(0.816266\pi\)
\(234\) −17.7896 30.8125i −1.16294 2.01428i
\(235\) 0 0
\(236\) −3.77487 −0.245723
\(237\) −22.5206 + 13.0023i −1.46287 + 0.844589i
\(238\) −8.30481 + 4.79478i −0.538321 + 0.310800i
\(239\) 14.9696 0.968305 0.484152 0.874984i \(-0.339128\pi\)
0.484152 + 0.874984i \(0.339128\pi\)
\(240\) 0 0
\(241\) 9.66469 + 16.7397i 0.622557 + 1.07830i 0.989008 + 0.147863i \(0.0472395\pi\)
−0.366451 + 0.930437i \(0.619427\pi\)
\(242\) −12.4707 7.19994i −0.801644 0.462830i
\(243\) −35.9528 + 20.7573i −2.30637 + 1.33158i
\(244\) 0.0650203 0.112618i 0.00416250 0.00720966i
\(245\) 0 0
\(246\) −18.9848 −1.21042
\(247\) −12.7984 15.6880i −0.814346 0.998205i
\(248\) 3.28009i 0.208286i
\(249\) −12.8475 + 22.2526i −0.814180 + 1.41020i
\(250\) 0 0
\(251\) −5.16246 8.94164i −0.325851 0.564391i 0.655833 0.754906i \(-0.272318\pi\)
−0.981684 + 0.190515i \(0.938984\pi\)
\(252\) −17.3812 10.0350i −1.09491 0.632148i
\(253\) −20.4468 + 11.8049i −1.28548 + 0.742170i
\(254\) 7.88509 0.494755
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 24.9149 14.3846i 1.55415 0.897287i 0.556349 0.830949i \(-0.312202\pi\)
0.997797 0.0663376i \(-0.0211314\pi\)
\(258\) 1.89466i 0.117956i
\(259\) −15.0790 −0.936962
\(260\) 0 0
\(261\) 30.7924 53.3340i 1.90600 3.30129i
\(262\) 2.08242 1.20228i 0.128652 0.0742774i
\(263\) −7.91107 4.56746i −0.487818 0.281642i 0.235851 0.971789i \(-0.424212\pi\)
−0.723669 + 0.690148i \(0.757546\pi\)
\(264\) 8.22742 14.2503i 0.506363 0.877046i
\(265\) 0 0
\(266\) −10.6771 4.05416i −0.654655 0.248577i
\(267\) 27.0654i 1.65638i
\(268\) −0.328977 0.189935i −0.0200955 0.0116021i
\(269\) 8.45474 14.6440i 0.515495 0.892863i −0.484343 0.874878i \(-0.660941\pi\)
0.999838 0.0179853i \(-0.00572519\pi\)
\(270\) 0 0
\(271\) 7.94483 13.7609i 0.482614 0.835912i −0.517187 0.855873i \(-0.673021\pi\)
0.999801 + 0.0199603i \(0.00635399\pi\)
\(272\) 3.16962 1.82998i 0.192186 0.110959i
\(273\) 39.7347i 2.40486i
\(274\) −17.4350 −1.05329
\(275\) 0 0
\(276\) −7.64761 13.2460i −0.460332 0.797318i
\(277\) 11.4852i 0.690079i 0.938588 + 0.345040i \(0.112135\pi\)
−0.938588 + 0.345040i \(0.887865\pi\)
\(278\) 9.56975i 0.573955i
\(279\) −12.5627 21.7592i −0.752108 1.30269i
\(280\) 0 0
\(281\) 7.14483 + 12.3752i 0.426225 + 0.738243i 0.996534 0.0831872i \(-0.0265099\pi\)
−0.570309 + 0.821430i \(0.693177\pi\)
\(282\) 13.0636 + 7.54227i 0.777926 + 0.449136i
\(283\) 2.74037 + 1.58215i 0.162898 + 0.0940493i 0.579233 0.815162i \(-0.303352\pi\)
−0.416335 + 0.909211i \(0.636686\pi\)
\(284\) 9.13492 0.542058
\(285\) 0 0
\(286\) −23.4091 −1.38421
\(287\) 13.1941 + 7.61763i 0.778825 + 0.449655i
\(288\) 6.63372 + 3.82998i 0.390896 + 0.225684i
\(289\) −1.80235 3.12176i −0.106021 0.183633i
\(290\) 0 0
\(291\) −26.4296 45.7775i −1.54933 2.68352i
\(292\) 8.50522i 0.497730i
\(293\) 14.7094i 0.859330i −0.902988 0.429665i \(-0.858632\pi\)
0.902988 0.429665i \(-0.141368\pi\)
\(294\) −0.220252 0.381488i −0.0128454 0.0222488i
\(295\) 0 0
\(296\) 5.75505 0.334505
\(297\) 76.6789i 4.44936i
\(298\) 14.8301 8.56218i 0.859087 0.495994i
\(299\) −10.8797 + 18.8442i −0.629190 + 1.08979i
\(300\) 0 0
\(301\) −0.760232 + 1.31676i −0.0438190 + 0.0758968i
\(302\) 4.71499 + 2.72220i 0.271317 + 0.156645i
\(303\) 27.6392i 1.58783i
\(304\) 4.07502 + 1.54731i 0.233719 + 0.0887445i
\(305\) 0 0
\(306\) −14.0176 + 24.2791i −0.801331 + 1.38795i
\(307\) 22.6425 + 13.0727i 1.29228 + 0.746097i 0.979058 0.203583i \(-0.0652587\pi\)
0.313221 + 0.949680i \(0.398592\pi\)
\(308\) −11.4359 + 6.60250i −0.651619 + 0.376213i
\(309\) −19.3446 + 33.5059i −1.10048 + 1.90608i
\(310\) 0 0
\(311\) 6.65039 0.377109 0.188555 0.982063i \(-0.439620\pi\)
0.188555 + 0.982063i \(0.439620\pi\)
\(312\) 15.1652i 0.858559i
\(313\) 15.0513 8.68988i 0.850750 0.491181i −0.0101536 0.999948i \(-0.503232\pi\)
0.860904 + 0.508768i \(0.169899\pi\)
\(314\) −0.0123496 0.0213902i −0.000696930 0.00120712i
\(315\) 0 0
\(316\) −7.96475 −0.448052
\(317\) 1.19104 0.687647i 0.0668954 0.0386221i −0.466179 0.884690i \(-0.654370\pi\)
0.533075 + 0.846068i \(0.321036\pi\)
\(318\) 13.0636 + 7.54227i 0.732570 + 0.422949i
\(319\) −20.2597 35.0908i −1.13432 1.96471i
\(320\) 0 0
\(321\) 27.4420 47.5309i 1.53166 2.65292i
\(322\) 12.2744i 0.684026i
\(323\) −5.66310 + 14.9144i −0.315103 + 0.829861i
\(324\) −26.6951 −1.48306
\(325\) 0 0
\(326\) 5.41735 9.38313i 0.300039 0.519684i
\(327\) 56.5637 32.6571i 3.12798 1.80594i
\(328\) −5.03568 2.90735i −0.278049 0.160532i
\(329\) −6.05267 10.4835i −0.333695 0.577976i
\(330\) 0 0
\(331\) 11.7399 0.645284 0.322642 0.946521i \(-0.395429\pi\)
0.322642 + 0.946521i \(0.395429\pi\)
\(332\) −6.81558 + 3.93498i −0.374054 + 0.215960i
\(333\) −38.1774 + 22.0417i −2.09211 + 1.20788i
\(334\) 6.28478 0.343888
\(335\) 0 0
\(336\) −4.27731 7.40852i −0.233346 0.404168i
\(337\) −11.1545 6.44005i −0.607624 0.350812i 0.164411 0.986392i \(-0.447428\pi\)
−0.772035 + 0.635580i \(0.780761\pi\)
\(338\) −7.42568 + 4.28722i −0.403904 + 0.233194i
\(339\) 23.4269 40.5765i 1.27237 2.20381i
\(340\) 0 0
\(341\) −16.5311 −0.895209
\(342\) −32.9587 + 5.34282i −1.78220 + 0.288907i
\(343\) 18.6944i 1.00940i
\(344\) 0.290150 0.502555i 0.0156439 0.0270960i
\(345\) 0 0
\(346\) 0.187589 + 0.324914i 0.0100849 + 0.0174675i
\(347\) 4.27339 + 2.46724i 0.229408 + 0.132449i 0.610299 0.792171i \(-0.291049\pi\)
−0.380891 + 0.924620i \(0.624383\pi\)
\(348\) 22.7329 13.1249i 1.21861 0.703566i
\(349\) −1.26594 −0.0677644 −0.0338822 0.999426i \(-0.510787\pi\)
−0.0338822 + 0.999426i \(0.510787\pi\)
\(350\) 0 0
\(351\) 35.3346 + 61.2012i 1.88602 + 3.26668i
\(352\) 4.36462 2.51991i 0.232635 0.134312i
\(353\) 2.16060i 0.114997i 0.998346 + 0.0574986i \(0.0183125\pi\)
−0.998346 + 0.0574986i \(0.981688\pi\)
\(354\) 12.3248 0.655056
\(355\) 0 0
\(356\) 4.14483 7.17905i 0.219676 0.380489i
\(357\) 27.1149 15.6548i 1.43507 0.828539i
\(358\) −6.97098 4.02470i −0.368428 0.212712i
\(359\) −2.36981 + 4.10463i −0.125074 + 0.216634i −0.921762 0.387757i \(-0.873250\pi\)
0.796688 + 0.604391i \(0.206583\pi\)
\(360\) 0 0
\(361\) −18.0270 + 6.00231i −0.948789 + 0.315911i
\(362\) 21.0503i 1.10638i
\(363\) 40.7162 + 23.5075i 2.13705 + 1.23382i
\(364\) −6.08503 + 10.5396i −0.318942 + 0.552424i
\(365\) 0 0
\(366\) −0.212289 + 0.367695i −0.0110965 + 0.0192197i
\(367\) 19.8271 11.4472i 1.03497 0.597538i 0.116563 0.993183i \(-0.462812\pi\)
0.918403 + 0.395645i \(0.129479\pi\)
\(368\) 4.68466i 0.244205i
\(369\) 44.5404 2.31868
\(370\) 0 0
\(371\) −6.05267 10.4835i −0.314239 0.544278i
\(372\) 10.7094i 0.555254i
\(373\) 19.2393i 0.996172i 0.867128 + 0.498086i \(0.165964\pi\)
−0.867128 + 0.498086i \(0.834036\pi\)
\(374\) 9.22278 + 15.9743i 0.476899 + 0.826013i
\(375\) 0 0
\(376\) 2.31007 + 4.00115i 0.119133 + 0.206344i
\(377\) −32.3405 18.6718i −1.66562 0.961647i
\(378\) 34.5234 + 19.9321i 1.77569 + 1.02520i
\(379\) 6.45953 0.331804 0.165902 0.986142i \(-0.446947\pi\)
0.165902 + 0.986142i \(0.446947\pi\)
\(380\) 0 0
\(381\) −25.7445 −1.31893
\(382\) −6.96270 4.01991i −0.356243 0.205677i
\(383\) −7.91107 4.56746i −0.404237 0.233386i 0.284074 0.958802i \(-0.408314\pi\)
−0.688310 + 0.725416i \(0.741647\pi\)
\(384\) 1.63248 + 2.82754i 0.0833071 + 0.144292i
\(385\) 0 0
\(386\) 10.1224 + 17.5325i 0.515218 + 0.892383i
\(387\) 4.44508i 0.225956i
\(388\) 16.1899i 0.821917i
\(389\) −13.3424 23.1098i −0.676488 1.17171i −0.976032 0.217629i \(-0.930168\pi\)
0.299544 0.954082i \(-0.403165\pi\)
\(390\) 0 0
\(391\) 17.1457 0.867093
\(392\) 0.134919i 0.00681442i
\(393\) −6.79901 + 3.92541i −0.342965 + 0.198011i
\(394\) −1.46002 + 2.52883i −0.0735548 + 0.127401i
\(395\) 0 0
\(396\) −19.3024 + 33.4328i −0.969984 + 1.68006i
\(397\) −12.7732 7.37459i −0.641067 0.370120i 0.143958 0.989584i \(-0.454017\pi\)
−0.785025 + 0.619464i \(0.787350\pi\)
\(398\) 15.6049i 0.782202i
\(399\) 34.8603 + 13.2367i 1.74520 + 0.662662i
\(400\) 0 0
\(401\) −5.82720 + 10.0930i −0.290996 + 0.504021i −0.974046 0.226352i \(-0.927320\pi\)
0.683049 + 0.730372i \(0.260653\pi\)
\(402\) 1.07410 + 0.620130i 0.0535711 + 0.0309293i
\(403\) −13.1943 + 7.61773i −0.657254 + 0.379466i
\(404\) 4.23270 7.33124i 0.210584 0.364743i
\(405\) 0 0
\(406\) −21.0654 −1.04546
\(407\) 29.0045i 1.43770i
\(408\) −10.3487 + 5.97481i −0.512336 + 0.295797i
\(409\) 19.7824 + 34.2641i 0.978176 + 1.69425i 0.669030 + 0.743235i \(0.266710\pi\)
0.309145 + 0.951015i \(0.399957\pi\)
\(410\) 0 0
\(411\) 56.9246 2.80788
\(412\) −10.2623 + 5.92492i −0.505585 + 0.291900i
\(413\) −8.56555 4.94532i −0.421483 0.243344i
\(414\) 17.9421 + 31.0767i 0.881808 + 1.52734i
\(415\) 0 0
\(416\) 2.32241 4.02254i 0.113866 0.197221i
\(417\) 31.2448i 1.53007i
\(418\) −7.79819 + 20.5374i −0.381422 + 1.00452i
\(419\) −17.3292 −0.846586 −0.423293 0.905993i \(-0.639126\pi\)
−0.423293 + 0.905993i \(0.639126\pi\)
\(420\) 0 0
\(421\) −12.1652 + 21.0707i −0.592895 + 1.02692i 0.400946 + 0.916102i \(0.368682\pi\)
−0.993840 + 0.110822i \(0.964652\pi\)
\(422\) 0.991747 0.572585i 0.0482775 0.0278730i
\(423\) −30.6486 17.6950i −1.49019 0.860361i
\(424\) 2.31007 + 4.00115i 0.112187 + 0.194313i
\(425\) 0 0
\(426\) −29.8251 −1.44503
\(427\) 0.295075 0.170362i 0.0142797 0.00824438i
\(428\) 14.5579 8.40500i 0.703682 0.406271i
\(429\) 76.4299 3.69007
\(430\) 0 0
\(431\) −14.1173 24.4519i −0.680006 1.17781i −0.974978 0.222299i \(-0.928644\pi\)
0.294972 0.955506i \(-0.404690\pi\)
\(432\) −13.1762 7.60729i −0.633941 0.366006i
\(433\) 20.2475 11.6899i 0.973031 0.561780i 0.0728720 0.997341i \(-0.476784\pi\)
0.900159 + 0.435562i \(0.143450\pi\)
\(434\) −4.29713 + 7.44285i −0.206269 + 0.357268i
\(435\) 0 0
\(436\) 20.0046 0.958045
\(437\) 12.9082 + 15.8225i 0.617483 + 0.756895i
\(438\) 27.7692i 1.32686i
\(439\) 13.3775 23.1705i 0.638472 1.10587i −0.347297 0.937755i \(-0.612900\pi\)
0.985768 0.168110i \(-0.0537664\pi\)
\(440\) 0 0
\(441\) 0.516736 + 0.895013i 0.0246065 + 0.0426197i
\(442\) 14.7223 + 8.49994i 0.700270 + 0.404301i
\(443\) 15.3285 8.84989i 0.728277 0.420471i −0.0895142 0.995986i \(-0.528531\pi\)
0.817792 + 0.575514i \(0.195198\pi\)
\(444\) −18.7900 −0.891734
\(445\) 0 0
\(446\) 7.66474 + 13.2757i 0.362936 + 0.628624i
\(447\) −48.4198 + 27.9552i −2.29018 + 1.32223i
\(448\) 2.62013i 0.123790i
\(449\) −28.3541 −1.33811 −0.669056 0.743212i \(-0.733301\pi\)
−0.669056 + 0.743212i \(0.733301\pi\)
\(450\) 0 0
\(451\) 14.6525 25.3790i 0.689961 1.19505i
\(452\) 12.4279 7.17524i 0.584558 0.337495i
\(453\) −15.3942 8.88787i −0.723285 0.417589i
\(454\) 9.64248 16.7013i 0.452544 0.783830i
\(455\) 0 0
\(456\) −13.3048 5.05191i −0.623054 0.236578i
\(457\) 11.5898i 0.542146i 0.962559 + 0.271073i \(0.0873785\pi\)
−0.962559 + 0.271073i \(0.912622\pi\)
\(458\) 12.4493 + 7.18759i 0.581716 + 0.335854i
\(459\) 27.8424 48.2244i 1.29957 2.25092i
\(460\) 0 0
\(461\) −17.8899 + 30.9862i −0.833214 + 1.44317i 0.0622614 + 0.998060i \(0.480169\pi\)
−0.895476 + 0.445110i \(0.853165\pi\)
\(462\) 37.3377 21.5569i 1.73711 1.00292i
\(463\) 23.5039i 1.09232i −0.837681 0.546160i \(-0.816089\pi\)
0.837681 0.546160i \(-0.183911\pi\)
\(464\) 8.03983 0.373240
\(465\) 0 0
\(466\) 6.91272 + 11.9732i 0.320226 + 0.554647i
\(467\) 1.12047i 0.0518492i −0.999664 0.0259246i \(-0.991747\pi\)
0.999664 0.0259246i \(-0.00825299\pi\)
\(468\) 35.5792i 1.64465i
\(469\) −0.497654 0.861963i −0.0229795 0.0398017i
\(470\) 0 0
\(471\) 0.0403210 + 0.0698381i 0.00185790 + 0.00321797i
\(472\) 3.26913 + 1.88743i 0.150474 + 0.0868762i
\(473\) 2.53279 + 1.46231i 0.116458 + 0.0672370i
\(474\) 26.0046 1.19443
\(475\) 0 0
\(476\) 9.58957 0.439537
\(477\) −30.6486 17.6950i −1.40331 0.810199i
\(478\) −12.9641 7.48481i −0.592963 0.342347i
\(479\) 13.6547 + 23.6506i 0.623898 + 1.08062i 0.988753 + 0.149559i \(0.0477854\pi\)
−0.364854 + 0.931065i \(0.618881\pi\)
\(480\) 0 0
\(481\) 13.3656 + 23.1499i 0.609419 + 1.05555i
\(482\) 19.3294i 0.880429i
\(483\) 40.0755i 1.82350i
\(484\) 7.19994 + 12.4707i 0.327270 + 0.566848i
\(485\) 0 0
\(486\) 41.5147 1.88314
\(487\) 6.32003i 0.286388i 0.989695 + 0.143194i \(0.0457373\pi\)
−0.989695 + 0.143194i \(0.954263\pi\)
\(488\) −0.112618 + 0.0650203i −0.00509800 + 0.00294333i
\(489\) −17.6874 + 30.6355i −0.799854 + 1.38539i
\(490\) 0 0
\(491\) 12.9025 22.3478i 0.582282 1.00854i −0.412926 0.910764i \(-0.635493\pi\)
0.995208 0.0977776i \(-0.0311734\pi\)
\(492\) 16.4413 + 9.49238i 0.741230 + 0.427949i
\(493\) 29.4254i 1.32526i
\(494\) 3.23977 + 19.9855i 0.145764 + 0.899188i
\(495\) 0 0
\(496\) 1.64004 2.84064i 0.0736402 0.127549i
\(497\) 20.7280 + 11.9673i 0.929779 + 0.536808i
\(498\) 22.2526 12.8475i 0.997163 0.575712i
\(499\) −14.4572 + 25.0406i −0.647192 + 1.12097i 0.336598 + 0.941648i \(0.390724\pi\)
−0.983790 + 0.179322i \(0.942610\pi\)
\(500\) 0 0
\(501\) −20.5196 −0.916746
\(502\) 10.3249i 0.460823i
\(503\) 0.995971 0.575024i 0.0444082 0.0256391i −0.477632 0.878560i \(-0.658505\pi\)
0.522040 + 0.852921i \(0.325171\pi\)
\(504\) 10.0350 + 17.3812i 0.446996 + 0.774220i
\(505\) 0 0
\(506\) 23.6099 1.04959
\(507\) 24.2445 13.9976i 1.07674 0.621655i
\(508\) −6.82869 3.94254i −0.302974 0.174922i
\(509\) 20.3673 + 35.2772i 0.902765 + 1.56364i 0.823889 + 0.566751i \(0.191800\pi\)
0.0788760 + 0.996884i \(0.474867\pi\)
\(510\) 0 0
\(511\) −11.1424 + 19.2992i −0.492910 + 0.853746i
\(512\) 1.00000i 0.0441942i
\(513\) 65.4642 10.6122i 2.89032 0.468539i
\(514\) −28.7692 −1.26895
\(515\) 0 0
\(516\) −0.947329 + 1.64082i −0.0417038 + 0.0722332i
\(517\) −20.1651 + 11.6423i −0.886861 + 0.512029i
\(518\) 13.0588 + 7.53949i 0.573770 + 0.331266i
\(519\) −0.612472 1.06083i −0.0268845 0.0465654i
\(520\) 0 0
\(521\) −11.4246 −0.500520 −0.250260 0.968179i \(-0.580516\pi\)
−0.250260 + 0.968179i \(0.580516\pi\)
\(522\) −53.3340 + 30.7924i −2.33436 + 1.34775i
\(523\) 11.3570 6.55696i 0.496607 0.286716i −0.230704 0.973024i \(-0.574103\pi\)
0.727311 + 0.686308i \(0.240770\pi\)
\(524\) −2.40457 −0.105044
\(525\) 0 0
\(526\) 4.56746 + 7.91107i 0.199151 + 0.344939i
\(527\) 10.3966 + 6.00250i 0.452884 + 0.261473i
\(528\) −14.2503 + 8.22742i −0.620165 + 0.358052i
\(529\) −0.526988 + 0.912769i −0.0229125 + 0.0396856i
\(530\) 0 0
\(531\) −28.9153 −1.25482
\(532\) 7.21955 + 8.84955i 0.313007 + 0.383677i
\(533\) 27.0083i 1.16986i
\(534\) −13.5327 + 23.4393i −0.585617 + 1.01432i
\(535\) 0 0
\(536\) 0.189935 + 0.328977i 0.00820394 + 0.0142096i
\(537\) 22.7600 + 13.1405i 0.982166 + 0.567054i
\(538\) −14.6440 + 8.45474i −0.631350 + 0.364510i
\(539\) 0.679967 0.0292883
\(540\) 0 0
\(541\) 14.4949 + 25.1059i 0.623183 + 1.07939i 0.988889 + 0.148655i \(0.0474943\pi\)
−0.365706 + 0.930730i \(0.619172\pi\)
\(542\) −13.7609 + 7.94483i −0.591079 + 0.341260i
\(543\) 68.7283i 2.94941i
\(544\) −3.65996 −0.156919
\(545\) 0 0
\(546\) 19.8674 34.4113i 0.850245 1.47267i
\(547\) 30.8724 17.8242i 1.32001 0.762108i 0.336280 0.941762i \(-0.390831\pi\)
0.983730 + 0.179654i \(0.0574977\pi\)
\(548\) 15.0992 + 8.71751i 0.645004 + 0.372393i
\(549\) 0.498053 0.862653i 0.0212564 0.0368171i
\(550\) 0 0
\(551\) −27.1547 + 22.1531i −1.15683 + 0.943753i
\(552\) 15.2952i 0.651008i
\(553\) −18.0728 10.4343i −0.768534 0.443713i
\(554\) 5.74261 9.94648i 0.243980 0.422586i
\(555\) 0 0
\(556\) −4.78487 + 8.28764i −0.202924 + 0.351474i
\(557\) −10.8726 + 6.27731i −0.460688 + 0.265978i −0.712333 0.701841i \(-0.752362\pi\)
0.251646 + 0.967819i \(0.419028\pi\)
\(558\) 25.1253i 1.06364i
\(559\) 2.69540 0.114003
\(560\) 0 0
\(561\) −30.1120 52.1555i −1.27133 2.20201i
\(562\) 14.2897i 0.602773i
\(563\) 2.88509i 0.121592i −0.998150 0.0607960i \(-0.980636\pi\)
0.998150 0.0607960i \(-0.0193639\pi\)
\(564\) −7.54227 13.0636i −0.317587 0.550076i
\(565\) 0 0
\(566\) −1.58215 2.74037i −0.0665029 0.115186i
\(567\) −60.5738 34.9723i −2.54386 1.46870i
\(568\) −7.91107 4.56746i −0.331941 0.191646i
\(569\) 10.9249 0.457996 0.228998 0.973427i \(-0.426455\pi\)
0.228998 + 0.973427i \(0.426455\pi\)
\(570\) 0 0
\(571\) 6.27911 0.262772 0.131386 0.991331i \(-0.458057\pi\)
0.131386 + 0.991331i \(0.458057\pi\)
\(572\) 20.2729 + 11.7046i 0.847653 + 0.489393i
\(573\) 22.7329 + 13.1249i 0.949681 + 0.548299i
\(574\) −7.61763 13.1941i −0.317954 0.550712i
\(575\) 0 0
\(576\) −3.82998 6.63372i −0.159582 0.276405i
\(577\) 25.9848i 1.08176i 0.841100 + 0.540880i \(0.181909\pi\)
−0.841100 + 0.540880i \(0.818091\pi\)
\(578\) 3.60470i 0.149936i
\(579\) −33.0493 57.2430i −1.37348 2.37894i
\(580\) 0 0
\(581\) −20.6203 −0.855475
\(582\) 52.8593i 2.19109i
\(583\) −20.1651 + 11.6423i −0.835154 + 0.482176i
\(584\) 4.25261 7.36574i 0.175974 0.304796i
\(585\) 0 0
\(586\) −7.35468 + 12.7387i −0.303819 + 0.526230i
\(587\) 31.4448 + 18.1547i 1.29787 + 0.749324i 0.980035 0.198823i \(-0.0637119\pi\)
0.317832 + 0.948147i \(0.397045\pi\)
\(588\) 0.440504i 0.0181661i
\(589\) 2.28786 + 14.1133i 0.0942697 + 0.581530i
\(590\) 0 0
\(591\) 4.76691 8.25652i 0.196084 0.339628i
\(592\) −4.98402 2.87752i −0.204842 0.118266i
\(593\) −27.4783 + 15.8646i −1.12840 + 0.651482i −0.943532 0.331281i \(-0.892519\pi\)
−0.184868 + 0.982763i \(0.559186\pi\)
\(594\) 38.3394 66.4058i 1.57309 2.72466i
\(595\) 0 0
\(596\) −17.1244 −0.701441
\(597\) 50.9493i 2.08522i
\(598\) 18.8442 10.8797i 0.770598 0.444905i
\(599\) −0.174654 0.302510i −0.00713619 0.0123602i 0.862435 0.506167i \(-0.168938\pi\)
−0.869571 + 0.493807i \(0.835605\pi\)
\(600\) 0 0
\(601\) 33.7305 1.37590 0.687949 0.725759i \(-0.258511\pi\)
0.687949 + 0.725759i \(0.258511\pi\)
\(602\) 1.31676 0.760232i 0.0536671 0.0309847i
\(603\) −2.51995 1.45489i −0.102620 0.0592479i
\(604\) −2.72220 4.71499i −0.110765 0.191850i
\(605\) 0 0
\(606\) −13.8196 + 23.9362i −0.561382 + 0.972342i
\(607\) 28.0561i 1.13876i −0.822073 0.569382i \(-0.807183\pi\)
0.822073 0.569382i \(-0.192817\pi\)
\(608\) −2.75542 3.37752i −0.111747 0.136977i
\(609\) 68.7777 2.78701
\(610\) 0 0
\(611\) −10.7299 + 18.5847i −0.434084 + 0.751855i
\(612\) 24.2791 14.0176i 0.981426 0.566627i
\(613\) −35.8969 20.7251i −1.44986 0.837078i −0.451389 0.892327i \(-0.649071\pi\)
−0.998473 + 0.0552496i \(0.982405\pi\)
\(614\) −13.0727 22.6425i −0.527570 0.913779i
\(615\) 0 0
\(616\) 13.2050 0.532045
\(617\) 5.09985 2.94440i 0.205312 0.118537i −0.393819 0.919188i \(-0.628846\pi\)
0.599131 + 0.800651i \(0.295513\pi\)
\(618\) 33.5059 19.3446i 1.34780 0.778155i
\(619\) −13.7152 −0.551261 −0.275631 0.961264i \(-0.588887\pi\)
−0.275631 + 0.961264i \(0.588887\pi\)
\(620\) 0 0
\(621\) −35.6375 61.7260i −1.43009 2.47698i
\(622\) −5.75941 3.32519i −0.230931 0.133328i
\(623\) 18.8101 10.8600i 0.753609 0.435096i
\(624\) −7.58259 + 13.1334i −0.303547 + 0.525758i
\(625\) 0 0
\(626\) −17.3798 −0.694635
\(627\) 25.4608 67.0539i 1.01681 2.67787i
\(628\) 0.0246993i 0.000985608i
\(629\) 10.5316 18.2413i 0.419923 0.727328i
\(630\) 0 0
\(631\) 8.14468 + 14.1070i 0.324235 + 0.561591i 0.981357 0.192193i \(-0.0615600\pi\)
−0.657123 + 0.753784i \(0.728227\pi\)
\(632\) 6.89767 + 3.98237i 0.274375 + 0.158410i
\(633\) −3.23801 + 1.86947i −0.128699 + 0.0743047i
\(634\) −1.37529 −0.0546199
\(635\) 0 0
\(636\) −7.54227 13.0636i −0.299070 0.518005i
\(637\) 0.542716 0.313337i 0.0215032 0.0124149i
\(638\) 40.5194i 1.60418i
\(639\) 69.9731 2.76809
\(640\) 0 0
\(641\) −14.8124 + 25.6559i −0.585056 + 1.01335i 0.409812 + 0.912170i \(0.365594\pi\)
−0.994868 + 0.101177i \(0.967739\pi\)
\(642\) −47.5309 + 27.4420i −1.87590 + 1.08305i
\(643\) −10.4105 6.01050i −0.410549 0.237031i 0.280476 0.959861i \(-0.409508\pi\)
−0.691026 + 0.722830i \(0.742841\pi\)
\(644\) 6.13721 10.6300i 0.241840 0.418879i
\(645\) 0 0
\(646\) 12.3616 10.0847i 0.486361 0.396778i
\(647\) 3.16079i 0.124263i 0.998068 + 0.0621317i \(0.0197899\pi\)
−0.998068 + 0.0621317i \(0.980210\pi\)
\(648\) 23.1186 + 13.3475i 0.908186 + 0.524341i
\(649\) −9.51235 + 16.4759i −0.373392 + 0.646735i
\(650\) 0 0
\(651\) 14.0300 24.3006i 0.549877 0.952415i
\(652\) −9.38313 + 5.41735i −0.367472 + 0.212160i
\(653\) 19.6097i 0.767387i 0.923461 + 0.383693i \(0.125348\pi\)
−0.923461 + 0.383693i \(0.874652\pi\)
\(654\) −65.3141 −2.55398
\(655\) 0 0
\(656\) 2.90735 + 5.03568i 0.113513 + 0.196610i
\(657\) 65.1496i 2.54173i
\(658\) 12.1053i 0.471915i
\(659\) −9.03748 15.6534i −0.352050 0.609769i 0.634558 0.772875i \(-0.281182\pi\)
−0.986609 + 0.163106i \(0.947849\pi\)
\(660\) 0 0
\(661\) 7.26715 + 12.5871i 0.282660 + 0.489581i 0.972039 0.234820i \(-0.0754500\pi\)
−0.689379 + 0.724400i \(0.742117\pi\)
\(662\) −10.1671 5.86996i −0.395154 0.228142i
\(663\) −48.0678 27.7520i −1.86680 1.07780i
\(664\) 7.86996 0.305414
\(665\) 0 0
\(666\) 44.0834 1.70820
\(667\) 32.6179 + 18.8319i 1.26297 + 0.729175i
\(668\) −5.44278 3.14239i −0.210587 0.121583i
\(669\) −25.0251 43.3447i −0.967525 1.67580i
\(670\) 0 0
\(671\) −0.327691 0.567578i −0.0126504 0.0219111i
\(672\) 8.55462i 0.330002i
\(673\) 6.13522i 0.236495i −0.992984 0.118248i \(-0.962272\pi\)
0.992984 0.118248i \(-0.0377277\pi\)
\(674\) 6.44005 + 11.1545i 0.248061 + 0.429655i
\(675\) 0 0
\(676\) 8.57444 0.329786
\(677\) 13.6380i 0.524150i −0.965047 0.262075i \(-0.915593\pi\)
0.965047 0.262075i \(-0.0844068\pi\)
\(678\) −40.5765 + 23.4269i −1.55833 + 0.899703i
\(679\) 21.2098 36.7364i 0.813957 1.40982i
\(680\) 0 0
\(681\) −31.4823 + 54.5290i −1.20640 + 2.08955i
\(682\) 14.3163 + 8.26554i 0.548201 + 0.316504i
\(683\) 16.7550i 0.641114i −0.947229 0.320557i \(-0.896130\pi\)
0.947229 0.320557i \(-0.103870\pi\)
\(684\) 31.2145 + 11.8524i 1.19352 + 0.453186i
\(685\) 0 0
\(686\) 9.34721 16.1898i 0.356878 0.618131i
\(687\) −40.6464 23.4672i −1.55076 0.895329i
\(688\) −0.502555 + 0.290150i −0.0191597 + 0.0110619i
\(689\) −10.7299 + 18.5847i −0.408775 + 0.708019i
\(690\) 0 0
\(691\) 21.5889 0.821280 0.410640 0.911798i \(-0.365305\pi\)
0.410640 + 0.911798i \(0.365305\pi\)
\(692\) 0.375179i 0.0142622i
\(693\) −87.5983 + 50.5749i −3.32758 + 1.92118i
\(694\) −2.46724 4.27339i −0.0936553 0.162216i
\(695\) 0 0
\(696\) −26.2497 −0.994993
\(697\) −18.4304 + 10.6408i −0.698100 + 0.403048i
\(698\) 1.09634 + 0.632972i 0.0414970 + 0.0239583i
\(699\) −22.5697 39.0919i −0.853666 1.47859i
\(700\) 0 0
\(701\) 18.8628 32.6713i 0.712437 1.23398i −0.251503 0.967857i \(-0.580925\pi\)
0.963940 0.266121i \(-0.0857419\pi\)
\(702\) 70.6691i 2.66723i
\(703\) 24.7624 4.01415i 0.933933 0.151396i
\(704\) −5.03983 −0.189946
\(705\) 0 0
\(706\) 1.08030 1.87114i 0.0406577 0.0704211i
\(707\) 19.2088 11.0902i 0.722422 0.417090i
\(708\) −10.6736 6.16240i −0.401138 0.231597i
\(709\) −10.4795 18.1511i −0.393567 0.681678i 0.599350 0.800487i \(-0.295426\pi\)
−0.992917 + 0.118809i \(0.962092\pi\)
\(710\) 0 0
\(711\) −61.0096 −2.28804
\(712\) −7.17905 + 4.14483i −0.269046 + 0.155334i
\(713\) 13.3074 7.68305i 0.498367 0.287732i
\(714\) −31.3096 −1.17173
\(715\) 0 0
\(716\) 4.02470 + 6.97098i 0.150410 + 0.260518i
\(717\) 42.3272 + 24.4376i 1.58074 + 0.912639i
\(718\) 4.10463 2.36981i 0.153183 0.0884405i
\(719\) −22.1401 + 38.3477i −0.825686 + 1.43013i 0.0757084 + 0.997130i \(0.475878\pi\)
−0.901394 + 0.433000i \(0.857455\pi\)
\(720\) 0 0
\(721\) −31.0481 −1.15629
\(722\) 18.6130 + 3.81534i 0.692704 + 0.141992i
\(723\) 63.1096i 2.34707i
\(724\) −10.5251 + 18.2301i −0.391164 + 0.677515i
\(725\) 0 0
\(726\) −23.5075 40.7162i −0.872445 1.51112i
\(727\) −41.9448 24.2169i −1.55565 0.898154i −0.997665 0.0683017i \(-0.978242\pi\)
−0.557983 0.829852i \(-0.688425\pi\)
\(728\) 10.5396 6.08503i 0.390623 0.225526i
\(729\) −55.4584 −2.05402
\(730\) 0 0
\(731\) −1.06194 1.83933i −0.0392772 0.0680301i
\(732\) 0.367695 0.212289i 0.0135904 0.00784641i
\(733\) 9.62940i 0.355670i −0.984060 0.177835i \(-0.943091\pi\)
0.984060 0.177835i \(-0.0569093\pi\)
\(734\) −22.8944 −0.845046
\(735\) 0 0
\(736\) −2.34233 + 4.05703i −0.0863394 + 0.149544i
\(737\) −1.65799 + 0.957240i −0.0610728 + 0.0352604i
\(738\) −38.5731 22.2702i −1.41989 0.819777i
\(739\) −20.3423 + 35.2338i −0.748303 + 1.29610i 0.200333 + 0.979728i \(0.435798\pi\)
−0.948636 + 0.316370i \(0.897536\pi\)
\(740\) 0 0
\(741\) −10.5777 65.2517i −0.388582 2.39708i
\(742\) 12.1053i 0.444401i
\(743\) −2.48123 1.43254i −0.0910276 0.0525548i 0.453795 0.891106i \(-0.350070\pi\)
−0.544823 + 0.838551i \(0.683403\pi\)
\(744\) −5.35468 + 9.27458i −0.196312 + 0.340022i
\(745\) 0 0
\(746\) 9.61964 16.6617i 0.352200 0.610028i
\(747\) −52.2071 + 30.1418i −1.91016 + 1.10283i
\(748\) 18.4456i 0.674437i
\(749\) 44.0444 1.60935
\(750\) 0 0
\(751\) 13.1148 + 22.7155i 0.478566 + 0.828900i 0.999698 0.0245758i \(-0.00782351\pi\)
−0.521132 + 0.853476i \(0.674490\pi\)
\(752\) 4.62013i 0.168479i
\(753\) 33.7104i 1.22848i
\(754\) 18.6718 + 32.3405i 0.679987 + 1.17777i
\(755\) 0 0
\(756\) −19.9321 34.5234i −0.724923 1.25560i
\(757\) 5.70182 + 3.29195i 0.207236 + 0.119648i 0.600026 0.799980i \(-0.295157\pi\)
−0.392790 + 0.919628i \(0.628490\pi\)
\(758\) −5.59412 3.22976i −0.203187 0.117310i
\(759\) −77.0853 −2.79802
\(760\) 0 0
\(761\) −27.7549 −1.00612 −0.503058 0.864253i \(-0.667792\pi\)
−0.503058 + 0.864253i \(0.667792\pi\)
\(762\) 22.2954 + 12.8722i 0.807677 + 0.466312i
\(763\) 45.3924 + 26.2073i 1.64331 + 0.948768i
\(764\) 4.01991 + 6.96270i 0.145435 + 0.251902i
\(765\) 0 0
\(766\) 4.56746 + 7.91107i 0.165029 + 0.285839i
\(767\) 17.5336i 0.633103i
\(768\) 3.26496i 0.117814i
\(769\) 8.32285 + 14.4156i 0.300130 + 0.519840i 0.976165 0.217029i \(-0.0696367\pi\)
−0.676035 + 0.736869i \(0.736303\pi\)
\(770\) 0 0
\(771\) 93.9303 3.38282
\(772\) 20.2448i 0.728628i
\(773\) −20.9664 + 12.1049i −0.754108 + 0.435385i −0.827176 0.561942i \(-0.810054\pi\)
0.0730682 + 0.997327i \(0.476721\pi\)
\(774\) 2.22254 3.84955i 0.0798876 0.138369i
\(775\) 0 0
\(776\) −8.09494 + 14.0208i −0.290591 + 0.503319i
\(777\) −42.6364 24.6161i −1.52957 0.883098i
\(778\) 26.6848i 0.956698i
\(779\) −23.6950 8.99716i −0.848963 0.322357i
\(780\) 0 0
\(781\) 23.0192 39.8704i 0.823692 1.42668i
\(782\) −14.8486 8.57283i −0.530984 0.306564i
\(783\) 105.934 61.1613i 3.78579 2.18573i
\(784\) −0.0674593 + 0.116843i −0.00240926 + 0.00417296i
\(785\) 0 0
\(786\) 7.85082 0.280030
\(787\) 1.63409i 0.0582490i 0.999576 + 0.0291245i \(0.00927193\pi\)
−0.999576 + 0.0291245i \(0.990728\pi\)
\(788\) 2.52883 1.46002i 0.0900858 0.0520111i
\(789\) −14.9126 25.8293i −0.530902 0.919548i
\(790\) 0 0
\(791\) 37.6001 1.33691
\(792\) 33.4328 19.3024i 1.18798 0.685882i
\(793\) −0.523094 0.302008i −0.0185756 0.0107246i
\(794\) 7.37459 + 12.7732i 0.261715 + 0.453303i
\(795\) 0 0
\(796\) 7.80244 13.5142i 0.276550 0.478999i
\(797\) 12.2802i 0.434987i 0.976062 + 0.217494i \(0.0697881\pi\)
−0.976062 + 0.217494i \(0.930212\pi\)
\(798\) −23.5715 28.8934i −0.834424 1.02282i
\(799\) 16.9095 0.598215
\(800\) 0 0
\(801\) 31.7492 54.9913i 1.12180 1.94302i
\(802\) 10.0930 5.82720i 0.356396 0.205766i
\(803\) 37.1221 + 21.4324i 1.31001 + 0.756334i
\(804\) −0.620130 1.07410i −0.0218703 0.0378805i
\(805\) 0 0
\(806\) 15.2355 0.536646
\(807\) 47.8122 27.6044i 1.68307 0.971721i
\(808\) −7.33124 + 4.23270i −0.257912 + 0.148906i
\(809\) −49.2846 −1.73275 −0.866376 0.499392i \(-0.833557\pi\)
−0.866376 + 0.499392i \(0.833557\pi\)
\(810\) 0 0
\(811\) −11.5927 20.0791i −0.407073 0.705071i 0.587487 0.809233i \(-0.300117\pi\)
−0.994560 + 0.104162i \(0.966784\pi\)
\(812\) 18.2432 + 10.5327i 0.640210 + 0.369625i
\(813\) 44.9286 25.9396i 1.57572 0.909740i
\(814\) 14.5022 25.1186i 0.508303 0.880407i
\(815\) 0 0
\(816\) 11.9496 0.418320
\(817\) 0.897907 2.36474i 0.0314138 0.0827318i
\(818\) 39.5648i 1.38335i
\(819\) −46.6111 + 80.7327i −1.62872 + 2.82103i
\(820\) 0 0
\(821\) −13.5793 23.5201i −0.473921 0.820856i 0.525633 0.850712i \(-0.323829\pi\)
−0.999554 + 0.0298556i \(0.990495\pi\)
\(822\) −49.2982 28.4623i −1.71947 0.992737i
\(823\) −7.77209 + 4.48722i −0.270918 + 0.156415i −0.629305 0.777159i \(-0.716660\pi\)
0.358387 + 0.933573i \(0.383327\pi\)
\(824\) 11.8498 0.412809
\(825\) 0 0
\(826\) 4.94532 + 8.56555i 0.172070 + 0.298034i
\(827\) −20.7890 + 12.0025i −0.722904 + 0.417369i −0.815821 0.578305i \(-0.803714\pi\)
0.0929165 + 0.995674i \(0.470381\pi\)
\(828\) 35.8843i 1.24707i
\(829\) −25.7361 −0.893852 −0.446926 0.894571i \(-0.647481\pi\)
−0.446926 + 0.894571i \(0.647481\pi\)
\(830\) 0 0
\(831\) −18.7494 + 32.4749i −0.650409 + 1.12654i
\(832\) −4.02254 + 2.32241i −0.139456 + 0.0805152i
\(833\) −0.427641 0.246898i −0.0148169 0.00855452i
\(834\) 15.6224 27.0588i 0.540960 0.936970i
\(835\) 0 0
\(836\) 17.0221 13.8868i 0.588723 0.480286i
\(837\) 49.9052i 1.72498i
\(838\) 15.0075 + 8.66459i 0.518426 + 0.299313i
\(839\) −16.3570 + 28.3311i −0.564705 + 0.978098i 0.432372 + 0.901695i \(0.357677\pi\)
−0.997077 + 0.0764027i \(0.975657\pi\)
\(840\) 0 0
\(841\) −17.8194 + 30.8642i −0.614463 + 1.06428i
\(842\) 21.0707 12.1652i 0.726145 0.419240i
\(843\) 46.6552i 1.60689i
\(844\) −1.14517 −0.0394184
\(845\) 0 0
\(846\) 17.6950 + 30.6486i 0.608367 + 1.05372i
\(847\) 37.7296i 1.29640i
\(848\) 4.62013i 0.158656i
\(849\) 5.16567 + 8.94720i 0.177285 + 0.307067i
\(850\) 0 0
\(851\) −13.4802 23.3484i −0.462096 0.800374i
\(852\) 25.8293 + 14.9126i 0.884898 + 0.510896i
\(853\) −26.8384 15.4952i −0.918929 0.530544i −0.0356360 0.999365i \(-0.511346\pi\)
−0.883293 + 0.468821i \(0.844679\pi\)
\(854\) −0.340723 −0.0116593
\(855\) 0 0
\(856\) −16.8100 −0.574554
\(857\) −18.1865 10.5000i −0.621240 0.358673i 0.156112 0.987739i \(-0.450104\pi\)
−0.777352 + 0.629066i \(0.783437\pi\)
\(858\) −66.1902 38.2150i −2.25970 1.30464i
\(859\) 14.1575 + 24.5215i 0.483048 + 0.836664i 0.999811 0.0194647i \(-0.00619620\pi\)
−0.516762 + 0.856129i \(0.672863\pi\)
\(860\) 0 0
\(861\) 24.8713 + 43.0783i 0.847610 + 1.46810i
\(862\) 28.2346i 0.961674i
\(863\) 10.9254i 0.371905i −0.982559 0.185953i \(-0.940463\pi\)
0.982559 0.185953i \(-0.0595371\pi\)
\(864\) 7.60729 + 13.1762i 0.258805 + 0.448264i
\(865\) 0 0
\(866\) −23.3798 −0.794476
\(867\) 11.7692i 0.399703i
\(868\) 7.44285 4.29713i 0.252627 0.145854i
\(869\) −20.0705 + 34.7631i −0.680845 + 1.17926i
\(870\) 0 0
\(871\) −0.882216 + 1.52804i −0.0298927 + 0.0517757i
\(872\) −17.3245 10.0023i −0.586681 0.338720i
\(873\) 124.014i 4.19723i
\(874\) −3.26755 20.1568i −0.110526 0.681815i
\(875\) 0 0
\(876\) −13.8846 + 24.0488i −0.469117 + 0.812535i
\(877\) 29.2972 + 16.9148i 0.989297 + 0.571171i 0.905064 0.425275i \(-0.139823\pi\)
0.0842330 + 0.996446i \(0.473156\pi\)
\(878\) −23.1705 + 13.3775i −0.781965 + 0.451468i
\(879\) 24.0127 41.5913i 0.809929 1.40284i
\(880\) 0 0
\(881\) 29.3696 0.989488 0.494744 0.869039i \(-0.335262\pi\)
0.494744 + 0.869039i \(0.335262\pi\)
\(882\) 1.03347i 0.0347988i
\(883\) −35.6803 + 20.6000i −1.20074 + 0.693245i −0.960719 0.277523i \(-0.910486\pi\)
−0.240017 + 0.970769i \(0.577153\pi\)
\(884\) −8.49994 14.7223i −0.285884 0.495166i
\(885\) 0 0
\(886\) −17.6998 −0.594636
\(887\) 22.4221 12.9454i 0.752861 0.434665i −0.0738656 0.997268i \(-0.523534\pi\)
0.826727 + 0.562604i \(0.190200\pi\)
\(888\) 16.2726 + 9.39500i 0.546073 + 0.315276i
\(889\) −10.3300 17.8920i −0.346456 0.600080i
\(890\) 0 0
\(891\) −67.2694 + 116.514i −2.25361 + 3.90336i
\(892\) 15.3295i 0.513269i
\(893\) 12.7304 + 15.6046i 0.426006 + 0.522188i
\(894\) 55.9104 1.86992
\(895\) 0 0
\(896\) −1.31007 + 2.26910i −0.0437662 + 0.0758053i
\(897\) −61.5256 + 35.5218i −2.05428 + 1.18604i
\(898\) 24.5553 + 14.1770i 0.819423 + 0.473094i
\(899\) 13.1857 + 22.8383i 0.439767 + 0.761699i
\(900\) 0 0
\(901\) 16.9095 0.563337
\(902\) −25.3790 + 14.6525i −0.845027 + 0.487876i
\(903\) −4.29917 + 2.48213i −0.143067 + 0.0826000i
\(904\) −14.3505 −0.477290
\(905\) 0 0
\(906\) 8.88787 + 15.3942i 0.295280 + 0.511439i
\(907\) 22.0706 + 12.7425i 0.732842 + 0.423106i 0.819461 0.573135i \(-0.194273\pi\)
−0.0866192 + 0.996241i \(0.527606\pi\)
\(908\) −16.7013 + 9.64248i −0.554251 + 0.319997i
\(909\) 32.4223 56.1570i 1.07538 1.86261i
\(910\) 0 0
\(911\) 10.1197 0.335280 0.167640 0.985848i \(-0.446385\pi\)
0.167640 + 0.985848i \(0.446385\pi\)
\(912\) 8.99633 + 11.0275i 0.297898 + 0.365156i
\(913\) 39.6633i 1.31266i
\(914\) 5.79488 10.0370i 0.191678 0.331995i
\(915\) 0 0
\(916\) −7.18759 12.4493i −0.237485 0.411335i
\(917\) −5.45621 3.15014i −0.180180 0.104027i
\(918\) −48.2244 + 27.8424i −1.59164 + 0.918935i
\(919\) 15.0939 0.497902 0.248951 0.968516i \(-0.419914\pi\)
0.248951 + 0.968516i \(0.419914\pi\)
\(920\) 0 0
\(921\) 42.6818 + 73.9270i 1.40641 + 2.43598i
\(922\) 30.9862 17.8899i 1.02048 0.589172i
\(923\) 42.4301i 1.39660i
\(924\) −43.1138 −1.41834
\(925\) 0 0
\(926\) −11.7520 + 20.3550i −0.386194 + 0.668907i
\(927\) −78.6085 + 45.3846i −2.58184 + 1.49063i
\(928\) −6.96270 4.01991i −0.228562 0.131960i
\(929\) −5.40003 + 9.35312i −0.177169 + 0.306866i −0.940910 0.338657i \(-0.890027\pi\)
0.763741 + 0.645523i \(0.223361\pi\)
\(930\) 0 0
\(931\) −0.0941058 0.580519i −0.00308419 0.0190257i
\(932\) 13.8254i 0.452867i
\(933\) 18.8042 + 10.8566i 0.615623 + 0.355430i
\(934\) −0.560236 + 0.970357i −0.0183315 + 0.0317510i
\(935\) 0 0
\(936\) 17.7896 30.8125i 0.581471 1.00714i
\(937\) −39.3163 + 22.6993i −1.28441 + 0.741554i −0.977651 0.210234i \(-0.932577\pi\)
−0.306758 + 0.951788i \(0.599244\pi\)
\(938\) 0.995309i 0.0324980i
\(939\) 56.7442 1.85178
\(940\) 0 0
\(941\) −0.155325 0.269031i −0.00506346 0.00877016i 0.863483 0.504379i \(-0.168278\pi\)
−0.868546 + 0.495609i \(0.834945\pi\)
\(942\) 0.0806421i 0.00262746i
\(943\) 27.2399i 0.887053i
\(944\) −1.88743 3.26913i −0.0614308 0.106401i
\(945\) 0 0
\(946\) −1.46231 2.53279i −0.0475438 0.0823482i
\(947\) 3.65897 + 2.11251i 0.118901 + 0.0686473i 0.558271 0.829659i \(-0.311465\pi\)
−0.439370 + 0.898306i \(0.644798\pi\)
\(948\) −22.5206 13.0023i −0.731436 0.422295i
\(949\) 39.5053 1.28240
\(950\) 0 0
\(951\) 4.49028 0.145607
\(952\) −8.30481 4.79478i −0.269160 0.155400i
\(953\) 29.3008 + 16.9168i 0.949145 + 0.547989i 0.892815 0.450423i \(-0.148727\pi\)
0.0563297 + 0.998412i \(0.482060\pi\)
\(954\) 17.6950 + 30.6486i 0.572897 + 0.992287i
\(955\) 0 0
\(956\) 7.48481 + 12.9641i 0.242076 + 0.419288i
\(957\) 132.294i 4.27646i
\(958\) 27.3094i 0.882326i
\(959\) 22.8410 + 39.5618i 0.737574 + 1.27752i
\(960\) 0 0
\(961\) −20.2410 −0.652936
\(962\) 26.7312i 0.861849i
\(963\) 111.513 64.3820i 3.59345 2.07468i
\(964\) −9.66469 + 16.7397i −0.311279 + 0.539150i
\(965\) 0 0
\(966\) −20.0377 + 34.7064i −0.644703 + 1.11666i
\(967\) 33.9875 + 19.6227i 1.09296 + 0.631024i 0.934364 0.356319i \(-0.115968\pi\)
0.158601 + 0.987343i \(0.449302\pi\)
\(968\) 14.3999i 0.462830i
\(969\) −40.3601 + 32.9262i −1.29655 + 1.05774i
\(970\) 0 0
\(971\) −20.3469 + 35.2419i −0.652963 + 1.13097i 0.329437 + 0.944178i \(0.393141\pi\)
−0.982400 + 0.186788i \(0.940192\pi\)
\(972\) −35.9528 20.7573i −1.15319 0.665792i
\(973\) −21.7147 + 12.5370i −0.696142 + 0.401918i
\(974\) 3.16002 5.47331i 0.101253 0.175376i
\(975\) 0 0
\(976\) 0.130041 0.00416250
\(977\) 26.7081i 0.854467i 0.904141 + 0.427233i \(0.140512\pi\)
−0.904141 + 0.427233i \(0.859488\pi\)
\(978\) 30.6355 17.6874i 0.979617 0.565582i
\(979\) −20.8892 36.1812i −0.667623 1.15636i
\(980\) 0 0
\(981\) 153.234 4.89239
\(982\) −22.3478 + 12.9025i −0.713147 + 0.411736i
\(983\) 21.6233 + 12.4842i 0.689677 + 0.398185i 0.803491 0.595317i \(-0.202974\pi\)
−0.113814 + 0.993502i \(0.536307\pi\)
\(984\) −9.49238 16.4413i −0.302606 0.524129i
\(985\) 0 0
\(986\) 14.7127 25.4832i 0.468549 0.811550i
\(987\) 39.5234i 1.25805i
\(988\) 7.18700 18.9278i 0.228649 0.602173i
\(989\) −2.71851 −0.0864436
\(990\) 0 0
\(991\) 7.53968 13.0591i 0.239506 0.414836i −0.721067 0.692866i \(-0.756348\pi\)
0.960573 + 0.278029i \(0.0896813\pi\)
\(992\) −2.84064 + 1.64004i −0.0901904 + 0.0520715i
\(993\) 33.1951 + 19.1652i 1.05341 + 0.608189i
\(994\) −11.9673 20.7280i −0.379581 0.657453i
\(995\) 0 0
\(996\) −25.6951 −0.814180
\(997\) 35.6158 20.5628i 1.12796 0.651229i 0.184541 0.982825i \(-0.440920\pi\)
0.943422 + 0.331595i \(0.107587\pi\)
\(998\) 25.0406 14.4572i 0.792646 0.457634i
\(999\) −87.5606 −2.77030
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 950.2.j.i.49.4 16
5.2 odd 4 950.2.e.m.201.4 yes 8
5.3 odd 4 950.2.e.l.201.1 8
5.4 even 2 inner 950.2.j.i.49.5 16
19.7 even 3 inner 950.2.j.i.349.5 16
95.7 odd 12 950.2.e.m.501.4 yes 8
95.64 even 6 inner 950.2.j.i.349.4 16
95.83 odd 12 950.2.e.l.501.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.e.l.201.1 8 5.3 odd 4
950.2.e.l.501.1 yes 8 95.83 odd 12
950.2.e.m.201.4 yes 8 5.2 odd 4
950.2.e.m.501.4 yes 8 95.7 odd 12
950.2.j.i.49.4 16 1.1 even 1 trivial
950.2.j.i.49.5 16 5.4 even 2 inner
950.2.j.i.349.4 16 95.64 even 6 inner
950.2.j.i.349.5 16 19.7 even 3 inner