Properties

Label 35.3.i.a.19.3
Level $35$
Weight $3$
Character 35.19
Analytic conductor $0.954$
Analytic rank $0$
Dimension $12$
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] = [35,3,Mod(19,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.i (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.953680925261\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 15x^{10} + 180x^{8} - 669x^{6} + 1980x^{4} - 135x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.3
Root \(-0.226181 - 0.130586i\) of defining polynomial
Character \(\chi\) \(=\) 35.19
Dual form 35.3.i.a.24.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.226181 - 0.130586i) q^{2} +(-1.88157 - 3.25898i) q^{3} +(-1.96589 - 3.40503i) q^{4} +(4.98089 - 0.436783i) q^{5} +0.982826i q^{6} +(1.66053 + 6.80019i) q^{7} +2.07156i q^{8} +(-2.58064 + 4.46979i) q^{9} +O(q^{10})\) \(q+(-0.226181 - 0.130586i) q^{2} +(-1.88157 - 3.25898i) q^{3} +(-1.96589 - 3.40503i) q^{4} +(4.98089 - 0.436783i) q^{5} +0.982826i q^{6} +(1.66053 + 6.80019i) q^{7} +2.07156i q^{8} +(-2.58064 + 4.46979i) q^{9} +(-1.18362 - 0.551640i) q^{10} +(-3.04653 - 5.27675i) q^{11} +(-7.39795 + 12.8136i) q^{12} +13.0886 q^{13} +(0.512426 - 1.75492i) q^{14} +(-10.7954 - 15.4108i) q^{15} +(-7.59306 + 13.1516i) q^{16} +(5.05373 + 8.75332i) q^{17} +(1.16738 - 0.673989i) q^{18} +(19.5373 + 11.2799i) q^{19} +(-11.2792 - 16.1014i) q^{20} +(19.0373 - 18.2067i) q^{21} +1.59133i q^{22} +(-30.2957 - 17.4912i) q^{23} +(6.75116 - 3.89779i) q^{24} +(24.6184 - 4.35113i) q^{25} +(-2.96039 - 1.70918i) q^{26} -14.4457 q^{27} +(19.8904 - 19.0226i) q^{28} -16.3474 q^{29} +(0.429282 + 4.89535i) q^{30} +(-23.4907 + 13.5624i) q^{31} +(10.6109 - 6.12620i) q^{32} +(-11.4645 + 19.8572i) q^{33} -2.63978i q^{34} +(11.2411 + 33.1457i) q^{35} +20.2930 q^{36} +(14.4349 + 8.33401i) q^{37} +(-2.94598 - 5.10258i) q^{38} +(-24.6272 - 42.6555i) q^{39} +(0.904820 + 10.3182i) q^{40} +19.7267i q^{41} +(-6.68341 + 1.63202i) q^{42} +53.4739i q^{43} +(-11.9783 + 20.7471i) q^{44} +(-10.9015 + 23.3907i) q^{45} +(4.56821 + 7.91237i) q^{46} +(18.3385 - 31.7632i) q^{47} +57.1476 q^{48} +(-43.4852 + 22.5839i) q^{49} +(-6.13642 - 2.23067i) q^{50} +(19.0179 - 32.9400i) q^{51} +(-25.7308 - 44.5671i) q^{52} +(-31.9730 + 18.4596i) q^{53} +(3.26734 + 1.88640i) q^{54} +(-17.4792 - 24.9522i) q^{55} +(-14.0870 + 3.43989i) q^{56} -84.8955i q^{57} +(3.69747 + 2.13474i) q^{58} +(92.4861 - 53.3969i) q^{59} +(-31.2516 + 67.0545i) q^{60} +(-18.4211 - 10.6354i) q^{61} +7.08422 q^{62} +(-34.6807 - 10.1266i) q^{63} +57.5445 q^{64} +(65.1928 - 5.71688i) q^{65} +(5.18613 - 2.99421i) q^{66} +(-5.33016 + 3.07737i) q^{67} +(19.8702 - 34.4162i) q^{68} +131.644i q^{69} +(1.78582 - 8.96486i) q^{70} -48.1133 q^{71} +(-9.25943 - 5.34594i) q^{72} +(2.82277 + 4.88919i) q^{73} +(-2.17660 - 3.76999i) q^{74} +(-60.5017 - 72.0441i) q^{75} -88.7000i q^{76} +(30.8240 - 29.4792i) q^{77} +12.8638i q^{78} +(19.1607 - 33.1873i) q^{79} +(-32.0758 + 68.8230i) q^{80} +(50.4064 + 87.3064i) q^{81} +(2.57602 - 4.46180i) q^{82} -102.359 q^{83} +(-99.4197 - 29.0300i) q^{84} +(28.9953 + 41.3919i) q^{85} +(6.98292 - 12.0948i) q^{86} +(30.7588 + 53.2759i) q^{87} +(10.9311 - 6.31106i) q^{88} +(-34.1003 - 19.6878i) q^{89} +(5.52021 - 3.86695i) q^{90} +(21.7341 + 89.0050i) q^{91} +137.544i q^{92} +(88.3991 + 51.0373i) q^{93} +(-8.29564 + 4.78949i) q^{94} +(102.240 + 47.6501i) q^{95} +(-39.9304 - 23.0538i) q^{96} -33.5609 q^{97} +(12.7847 + 0.570497i) q^{98} +31.4480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.226181 0.130586i −0.113091 0.0652929i 0.442388 0.896824i \(-0.354131\pi\)
−0.555478 + 0.831531i \(0.687465\pi\)
\(3\) −1.88157 3.25898i −0.627191 1.08633i −0.988113 0.153731i \(-0.950871\pi\)
0.360922 0.932596i \(-0.382462\pi\)
\(4\) −1.96589 3.40503i −0.491474 0.851257i
\(5\) 4.98089 0.436783i 0.996177 0.0873566i
\(6\) 0.982826i 0.163804i
\(7\) 1.66053 + 6.80019i 0.237219 + 0.971456i
\(8\) 2.07156i 0.258945i
\(9\) −2.58064 + 4.46979i −0.286737 + 0.496644i
\(10\) −1.18362 0.551640i −0.118362 0.0551640i
\(11\) −3.04653 5.27675i −0.276957 0.479704i 0.693670 0.720293i \(-0.255993\pi\)
−0.970627 + 0.240589i \(0.922659\pi\)
\(12\) −7.39795 + 12.8136i −0.616496 + 1.06780i
\(13\) 13.0886 1.00682 0.503408 0.864049i \(-0.332079\pi\)
0.503408 + 0.864049i \(0.332079\pi\)
\(14\) 0.512426 1.75492i 0.0366019 0.125351i
\(15\) −10.7954 15.4108i −0.719691 1.02738i
\(16\) −7.59306 + 13.1516i −0.474566 + 0.821973i
\(17\) 5.05373 + 8.75332i 0.297278 + 0.514901i 0.975512 0.219945i \(-0.0705878\pi\)
−0.678234 + 0.734846i \(0.737254\pi\)
\(18\) 1.16738 0.673989i 0.0648546 0.0374438i
\(19\) 19.5373 + 11.2799i 1.02828 + 0.593676i 0.916491 0.400056i \(-0.131009\pi\)
0.111787 + 0.993732i \(0.464343\pi\)
\(20\) −11.2792 16.1014i −0.563958 0.805070i
\(21\) 19.0373 18.2067i 0.906537 0.866986i
\(22\) 1.59133i 0.0723334i
\(23\) −30.2957 17.4912i −1.31720 0.760488i −0.333927 0.942599i \(-0.608374\pi\)
−0.983278 + 0.182111i \(0.941707\pi\)
\(24\) 6.75116 3.89779i 0.281298 0.162408i
\(25\) 24.6184 4.35113i 0.984738 0.174045i
\(26\) −2.96039 1.70918i −0.113861 0.0657379i
\(27\) −14.4457 −0.535026
\(28\) 19.8904 19.0226i 0.710372 0.679380i
\(29\) −16.3474 −0.563703 −0.281852 0.959458i \(-0.590949\pi\)
−0.281852 + 0.959458i \(0.590949\pi\)
\(30\) 0.429282 + 4.89535i 0.0143094 + 0.163178i
\(31\) −23.4907 + 13.5624i −0.757766 + 0.437496i −0.828493 0.559999i \(-0.810801\pi\)
0.0707270 + 0.997496i \(0.477468\pi\)
\(32\) 10.6109 6.12620i 0.331591 0.191444i
\(33\) −11.4645 + 19.8572i −0.347410 + 0.601733i
\(34\) 2.63978i 0.0776406i
\(35\) 11.2411 + 33.1457i 0.321175 + 0.947020i
\(36\) 20.2930 0.563696
\(37\) 14.4349 + 8.33401i 0.390133 + 0.225243i 0.682218 0.731149i \(-0.261016\pi\)
−0.292085 + 0.956392i \(0.594349\pi\)
\(38\) −2.94598 5.10258i −0.0775257 0.134278i
\(39\) −24.6272 42.6555i −0.631466 1.09373i
\(40\) 0.904820 + 10.3182i 0.0226205 + 0.257955i
\(41\) 19.7267i 0.481139i 0.970632 + 0.240569i \(0.0773341\pi\)
−0.970632 + 0.240569i \(0.922666\pi\)
\(42\) −6.68341 + 1.63202i −0.159129 + 0.0388576i
\(43\) 53.4739i 1.24358i 0.783185 + 0.621789i \(0.213594\pi\)
−0.783185 + 0.621789i \(0.786406\pi\)
\(44\) −11.9783 + 20.7471i −0.272235 + 0.471524i
\(45\) −10.9015 + 23.3907i −0.242256 + 0.519794i
\(46\) 4.56821 + 7.91237i 0.0993089 + 0.172008i
\(47\) 18.3385 31.7632i 0.390181 0.675813i −0.602293 0.798275i \(-0.705746\pi\)
0.992473 + 0.122463i \(0.0390792\pi\)
\(48\) 57.1476 1.19058
\(49\) −43.4852 + 22.5839i −0.887454 + 0.460896i
\(50\) −6.13642 2.23067i −0.122728 0.0446135i
\(51\) 19.0179 32.9400i 0.372901 0.645883i
\(52\) −25.7308 44.5671i −0.494823 0.857059i
\(53\) −31.9730 + 18.4596i −0.603264 + 0.348294i −0.770324 0.637652i \(-0.779906\pi\)
0.167061 + 0.985947i \(0.446572\pi\)
\(54\) 3.26734 + 1.88640i 0.0605063 + 0.0349333i
\(55\) −17.4792 24.9522i −0.317804 0.453676i
\(56\) −14.0870 + 3.43989i −0.251553 + 0.0614266i
\(57\) 84.8955i 1.48939i
\(58\) 3.69747 + 2.13474i 0.0637495 + 0.0368058i
\(59\) 92.4861 53.3969i 1.56756 0.905032i 0.571108 0.820875i \(-0.306514\pi\)
0.996452 0.0841571i \(-0.0268198\pi\)
\(60\) −31.2516 + 67.0545i −0.520860 + 1.11758i
\(61\) −18.4211 10.6354i −0.301985 0.174351i 0.341349 0.939937i \(-0.389116\pi\)
−0.643334 + 0.765585i \(0.722450\pi\)
\(62\) 7.08422 0.114262
\(63\) −34.6807 10.1266i −0.550487 0.160739i
\(64\) 57.5445 0.899133
\(65\) 65.1928 5.71688i 1.00297 0.0879520i
\(66\) 5.18613 2.99421i 0.0785777 0.0453668i
\(67\) −5.33016 + 3.07737i −0.0795546 + 0.0459309i −0.539250 0.842146i \(-0.681292\pi\)
0.459695 + 0.888077i \(0.347959\pi\)
\(68\) 19.8702 34.4162i 0.292209 0.506121i
\(69\) 131.644i 1.90789i
\(70\) 1.78582 8.96486i 0.0255117 0.128069i
\(71\) −48.1133 −0.677652 −0.338826 0.940849i \(-0.610030\pi\)
−0.338826 + 0.940849i \(0.610030\pi\)
\(72\) −9.25943 5.34594i −0.128603 0.0742491i
\(73\) 2.82277 + 4.88919i 0.0386681 + 0.0669752i 0.884712 0.466138i \(-0.154355\pi\)
−0.846044 + 0.533114i \(0.821022\pi\)
\(74\) −2.17660 3.76999i −0.0294136 0.0509458i
\(75\) −60.5017 72.0441i −0.806689 0.960587i
\(76\) 88.7000i 1.16711i
\(77\) 30.8240 29.4792i 0.400312 0.382847i
\(78\) 12.8638i 0.164921i
\(79\) 19.1607 33.1873i 0.242540 0.420092i −0.718897 0.695117i \(-0.755353\pi\)
0.961437 + 0.275024i \(0.0886860\pi\)
\(80\) −32.0758 + 68.8230i −0.400947 + 0.860287i
\(81\) 50.4064 + 87.3064i 0.622301 + 1.07786i
\(82\) 2.57602 4.46180i 0.0314149 0.0544122i
\(83\) −102.359 −1.23325 −0.616623 0.787259i \(-0.711500\pi\)
−0.616623 + 0.787259i \(0.711500\pi\)
\(84\) −99.4197 29.0300i −1.18357 0.345595i
\(85\) 28.9953 + 41.3919i 0.341122 + 0.486963i
\(86\) 6.98292 12.0948i 0.0811968 0.140637i
\(87\) 30.7588 + 53.2759i 0.353550 + 0.612366i
\(88\) 10.9311 6.31106i 0.124217 0.0717166i
\(89\) −34.1003 19.6878i −0.383149 0.221211i 0.296038 0.955176i \(-0.404334\pi\)
−0.679187 + 0.733965i \(0.737668\pi\)
\(90\) 5.52021 3.86695i 0.0613357 0.0429661i
\(91\) 21.7341 + 89.0050i 0.238836 + 0.978077i
\(92\) 137.544i 1.49504i
\(93\) 88.3991 + 51.0373i 0.950528 + 0.548788i
\(94\) −8.29564 + 4.78949i −0.0882515 + 0.0509520i
\(95\) 102.240 + 47.6501i 1.07621 + 0.501580i
\(96\) −39.9304 23.0538i −0.415941 0.240144i
\(97\) −33.5609 −0.345989 −0.172994 0.984923i \(-0.555344\pi\)
−0.172994 + 0.984923i \(0.555344\pi\)
\(98\) 12.7847 + 0.570497i 0.130456 + 0.00582140i
\(99\) 31.4480 0.317656
\(100\) −63.2130 75.2727i −0.632130 0.752727i
\(101\) −16.5905 + 9.57851i −0.164262 + 0.0948367i −0.579877 0.814704i \(-0.696900\pi\)
0.415615 + 0.909540i \(0.363566\pi\)
\(102\) −8.60299 + 4.96694i −0.0843430 + 0.0486955i
\(103\) 11.1967 19.3933i 0.108706 0.188285i −0.806540 0.591179i \(-0.798663\pi\)
0.915246 + 0.402895i \(0.131996\pi\)
\(104\) 27.1138i 0.260709i
\(105\) 86.8701 99.0007i 0.827335 0.942864i
\(106\) 9.64224 0.0909646
\(107\) 44.9916 + 25.9759i 0.420482 + 0.242766i 0.695284 0.718735i \(-0.255279\pi\)
−0.274801 + 0.961501i \(0.588612\pi\)
\(108\) 28.3987 + 49.1880i 0.262951 + 0.455444i
\(109\) −90.8644 157.382i −0.833619 1.44387i −0.895150 0.445765i \(-0.852932\pi\)
0.0615316 0.998105i \(-0.480401\pi\)
\(110\) 0.695067 + 7.92625i 0.00631879 + 0.0720568i
\(111\) 62.7242i 0.565083i
\(112\) −102.042 29.7957i −0.911087 0.266033i
\(113\) 195.000i 1.72566i −0.505492 0.862831i \(-0.668689\pi\)
0.505492 0.862831i \(-0.331311\pi\)
\(114\) −11.0861 + 19.2018i −0.0972468 + 0.168436i
\(115\) −158.539 73.8892i −1.37860 0.642515i
\(116\) 32.1373 + 55.6634i 0.277045 + 0.479857i
\(117\) −33.7769 + 58.5034i −0.288692 + 0.500029i
\(118\) −27.8915 −0.236368
\(119\) −51.1323 + 48.9015i −0.429684 + 0.410937i
\(120\) 31.9243 22.3632i 0.266036 0.186360i
\(121\) 41.9373 72.6375i 0.346589 0.600310i
\(122\) 2.77767 + 4.81107i 0.0227678 + 0.0394350i
\(123\) 64.2889 37.1172i 0.522674 0.301766i
\(124\) 92.3607 + 53.3245i 0.744844 + 0.430036i
\(125\) 120.721 32.4254i 0.965769 0.259403i
\(126\) 6.52173 + 6.81924i 0.0517598 + 0.0541210i
\(127\) 67.3739i 0.530503i 0.964179 + 0.265252i \(0.0854550\pi\)
−0.964179 + 0.265252i \(0.914545\pi\)
\(128\) −55.4591 32.0193i −0.433274 0.250151i
\(129\) 174.270 100.615i 1.35093 0.779961i
\(130\) −15.4919 7.22020i −0.119169 0.0555400i
\(131\) 82.1026 + 47.4019i 0.626737 + 0.361847i 0.779487 0.626418i \(-0.215480\pi\)
−0.152750 + 0.988265i \(0.548813\pi\)
\(132\) 90.1524 0.682972
\(133\) −44.2628 + 151.588i −0.332803 + 1.13976i
\(134\) 1.60744 0.0119958
\(135\) −71.9523 + 6.30963i −0.532980 + 0.0467380i
\(136\) −18.1330 + 10.4691i −0.133331 + 0.0769786i
\(137\) −141.017 + 81.4160i −1.02932 + 0.594278i −0.916789 0.399371i \(-0.869229\pi\)
−0.112529 + 0.993648i \(0.535895\pi\)
\(138\) 17.1908 29.7754i 0.124571 0.215764i
\(139\) 120.304i 0.865495i 0.901515 + 0.432747i \(0.142456\pi\)
−0.901515 + 0.432747i \(0.857544\pi\)
\(140\) 90.7632 103.437i 0.648308 0.738838i
\(141\) −138.021 −0.978871
\(142\) 10.8823 + 6.28290i 0.0766360 + 0.0442458i
\(143\) −39.8748 69.0653i −0.278845 0.482974i
\(144\) −39.1899 67.8789i −0.272152 0.471381i
\(145\) −81.4245 + 7.14026i −0.561548 + 0.0492432i
\(146\) 1.47446i 0.0100990i
\(147\) 155.421 + 99.2243i 1.05729 + 0.674995i
\(148\) 65.5351i 0.442805i
\(149\) −107.789 + 186.696i −0.723414 + 1.25299i 0.236209 + 0.971702i \(0.424095\pi\)
−0.959623 + 0.281288i \(0.909238\pi\)
\(150\) 4.27641 + 24.1957i 0.0285094 + 0.161304i
\(151\) −58.8121 101.866i −0.389484 0.674607i 0.602896 0.797820i \(-0.294013\pi\)
−0.992380 + 0.123213i \(0.960680\pi\)
\(152\) −23.3669 + 40.4726i −0.153729 + 0.266267i
\(153\) −52.1674 −0.340963
\(154\) −10.8214 + 2.64247i −0.0702687 + 0.0171589i
\(155\) −111.081 + 77.8131i −0.716651 + 0.502020i
\(156\) −96.8288 + 167.712i −0.620698 + 1.07508i
\(157\) 12.4693 + 21.5974i 0.0794222 + 0.137563i 0.903001 0.429639i \(-0.141359\pi\)
−0.823579 + 0.567202i \(0.808026\pi\)
\(158\) −8.66757 + 5.00423i −0.0548581 + 0.0316723i
\(159\) 120.319 + 69.4662i 0.756723 + 0.436894i
\(160\) 50.1758 35.1486i 0.313599 0.219679i
\(161\) 68.6367 235.061i 0.426315 1.46001i
\(162\) 26.3294i 0.162527i
\(163\) 112.324 + 64.8502i 0.689103 + 0.397854i 0.803276 0.595607i \(-0.203088\pi\)
−0.114173 + 0.993461i \(0.536422\pi\)
\(164\) 67.1699 38.7806i 0.409573 0.236467i
\(165\) −48.4303 + 103.914i −0.293517 + 0.629781i
\(166\) 23.1518 + 13.3667i 0.139468 + 0.0805222i
\(167\) 65.7030 0.393431 0.196716 0.980461i \(-0.436972\pi\)
0.196716 + 0.980461i \(0.436972\pi\)
\(168\) 37.7162 + 39.4368i 0.224501 + 0.234743i
\(169\) 2.31155 0.0136778
\(170\) −1.15301 13.1484i −0.00678241 0.0773438i
\(171\) −100.837 + 58.2184i −0.589692 + 0.340459i
\(172\) 182.080 105.124i 1.05860 0.611186i
\(173\) −49.9582 + 86.5301i −0.288775 + 0.500174i −0.973518 0.228612i \(-0.926581\pi\)
0.684742 + 0.728785i \(0.259915\pi\)
\(174\) 16.0667i 0.0923371i
\(175\) 70.4683 + 160.185i 0.402676 + 0.915343i
\(176\) 92.5300 0.525739
\(177\) −348.039 200.940i −1.96632 1.13526i
\(178\) 5.14189 + 8.90601i 0.0288870 + 0.0500338i
\(179\) −72.1529 124.972i −0.403089 0.698170i 0.591008 0.806665i \(-0.298730\pi\)
−0.994097 + 0.108495i \(0.965397\pi\)
\(180\) 101.077 8.86365i 0.561541 0.0492425i
\(181\) 62.7672i 0.346780i 0.984853 + 0.173390i \(0.0554722\pi\)
−0.984853 + 0.173390i \(0.944528\pi\)
\(182\) 6.70695 22.9694i 0.0368514 0.126206i
\(183\) 80.0454i 0.437407i
\(184\) 36.2341 62.7593i 0.196924 0.341083i
\(185\) 75.5389 + 35.2058i 0.408318 + 0.190302i
\(186\) −13.3295 23.0873i −0.0716638 0.124125i
\(187\) 30.7927 53.3345i 0.164667 0.285211i
\(188\) −144.206 −0.767054
\(189\) −23.9876 98.2335i −0.126918 0.519754i
\(190\) −16.9023 24.1286i −0.0889594 0.126993i
\(191\) 28.7734 49.8369i 0.150646 0.260926i −0.780819 0.624757i \(-0.785198\pi\)
0.931465 + 0.363831i \(0.118531\pi\)
\(192\) −108.274 187.537i −0.563928 0.976753i
\(193\) 213.940 123.518i 1.10850 0.639991i 0.170057 0.985434i \(-0.445605\pi\)
0.938440 + 0.345444i \(0.112272\pi\)
\(194\) 7.59084 + 4.38258i 0.0391281 + 0.0225906i
\(195\) −141.296 201.705i −0.724596 1.03439i
\(196\) 162.386 + 103.671i 0.828502 + 0.528933i
\(197\) 225.394i 1.14413i −0.820207 0.572067i \(-0.806142\pi\)
0.820207 0.572067i \(-0.193858\pi\)
\(198\) −7.11294 4.10666i −0.0359239 0.0207407i
\(199\) −159.406 + 92.0330i −0.801034 + 0.462477i −0.843833 0.536606i \(-0.819706\pi\)
0.0427985 + 0.999084i \(0.486373\pi\)
\(200\) 9.01361 + 50.9985i 0.0450681 + 0.254992i
\(201\) 20.0582 + 11.5806i 0.0997919 + 0.0576149i
\(202\) 5.00327 0.0247686
\(203\) −27.1454 111.165i −0.133721 0.547613i
\(204\) −149.549 −0.733083
\(205\) 8.61628 + 98.2564i 0.0420306 + 0.479299i
\(206\) −5.06498 + 2.92427i −0.0245873 + 0.0141955i
\(207\) 156.364 90.2771i 0.755384 0.436121i
\(208\) −99.3826 + 172.136i −0.477801 + 0.827576i
\(209\) 137.458i 0.657692i
\(210\) −32.5765 + 11.0481i −0.155126 + 0.0526100i
\(211\) 189.894 0.899972 0.449986 0.893036i \(-0.351429\pi\)
0.449986 + 0.893036i \(0.351429\pi\)
\(212\) 125.711 + 72.5793i 0.592977 + 0.342355i
\(213\) 90.5286 + 156.800i 0.425017 + 0.736151i
\(214\) −6.78416 11.7505i −0.0317017 0.0549090i
\(215\) 23.3565 + 266.347i 0.108635 + 1.23882i
\(216\) 29.9251i 0.138542i
\(217\) −131.234 137.221i −0.604765 0.632354i
\(218\) 47.4624i 0.217717i
\(219\) 10.6225 18.3987i 0.0485046 0.0840125i
\(220\) −50.6007 + 108.571i −0.230003 + 0.493503i
\(221\) 66.1463 + 114.569i 0.299304 + 0.518410i
\(222\) −8.19088 + 14.1870i −0.0368959 + 0.0639055i
\(223\) 310.730 1.39341 0.696703 0.717360i \(-0.254650\pi\)
0.696703 + 0.717360i \(0.254650\pi\)
\(224\) 59.2791 + 61.9834i 0.264639 + 0.276711i
\(225\) −44.0826 + 121.268i −0.195923 + 0.538969i
\(226\) −25.4642 + 44.1053i −0.112673 + 0.195156i
\(227\) 81.9716 + 141.979i 0.361108 + 0.625458i 0.988144 0.153533i \(-0.0490651\pi\)
−0.627035 + 0.778991i \(0.715732\pi\)
\(228\) −289.072 + 166.896i −1.26786 + 0.731998i
\(229\) −13.5862 7.84399i −0.0593283 0.0342532i 0.470042 0.882644i \(-0.344239\pi\)
−0.529371 + 0.848391i \(0.677572\pi\)
\(230\) 26.2097 + 37.4153i 0.113955 + 0.162675i
\(231\) −154.070 44.9876i −0.666969 0.194751i
\(232\) 33.8646i 0.145968i
\(233\) −236.940 136.798i −1.01691 0.587114i −0.103704 0.994608i \(-0.533069\pi\)
−0.913208 + 0.407494i \(0.866403\pi\)
\(234\) 15.2794 8.82157i 0.0652966 0.0376990i
\(235\) 77.4683 166.219i 0.329652 0.707314i
\(236\) −363.636 209.945i −1.54083 0.889599i
\(237\) −144.209 −0.608477
\(238\) 17.9510 4.38345i 0.0754244 0.0184178i
\(239\) 87.2116 0.364902 0.182451 0.983215i \(-0.441597\pi\)
0.182451 + 0.983215i \(0.441597\pi\)
\(240\) 284.646 24.9611i 1.18602 0.104005i
\(241\) −121.507 + 70.1522i −0.504179 + 0.291088i −0.730438 0.682979i \(-0.760684\pi\)
0.226259 + 0.974067i \(0.427351\pi\)
\(242\) −18.9708 + 10.9528i −0.0783919 + 0.0452596i
\(243\) 124.681 215.954i 0.513090 0.888698i
\(244\) 83.6326i 0.342756i
\(245\) −206.731 + 131.482i −0.843799 + 0.536659i
\(246\) −19.3879 −0.0788126
\(247\) 255.716 + 147.638i 1.03529 + 0.597723i
\(248\) −28.0953 48.6624i −0.113287 0.196219i
\(249\) 192.597 + 333.587i 0.773481 + 1.33971i
\(250\) −31.5391 8.43044i −0.126157 0.0337218i
\(251\) 252.962i 1.00782i 0.863757 + 0.503909i \(0.168105\pi\)
−0.863757 + 0.503909i \(0.831895\pi\)
\(252\) 33.6973 + 137.997i 0.133719 + 0.547606i
\(253\) 213.150i 0.842492i
\(254\) 8.79807 15.2387i 0.0346381 0.0599949i
\(255\) 80.3385 172.377i 0.315053 0.675989i
\(256\) −106.727 184.856i −0.416900 0.722093i
\(257\) 188.929 327.234i 0.735132 1.27329i −0.219534 0.975605i \(-0.570454\pi\)
0.954666 0.297680i \(-0.0962129\pi\)
\(258\) −52.5555 −0.203704
\(259\) −32.7032 + 111.999i −0.126267 + 0.432429i
\(260\) −147.628 210.745i −0.567802 0.810557i
\(261\) 42.1867 73.0695i 0.161635 0.279960i
\(262\) −12.3800 21.4428i −0.0472520 0.0818429i
\(263\) −194.747 + 112.437i −0.740484 + 0.427518i −0.822245 0.569133i \(-0.807279\pi\)
0.0817614 + 0.996652i \(0.473945\pi\)
\(264\) −41.1353 23.7495i −0.155815 0.0899601i
\(265\) −151.191 + 105.910i −0.570532 + 0.399662i
\(266\) 29.8066 28.5062i 0.112055 0.107166i
\(267\) 148.176i 0.554967i
\(268\) 20.9571 + 12.0996i 0.0781980 + 0.0451476i
\(269\) 224.966 129.884i 0.836305 0.482841i −0.0197015 0.999806i \(-0.506272\pi\)
0.856007 + 0.516965i \(0.172938\pi\)
\(270\) 17.0982 + 7.96883i 0.0633267 + 0.0295142i
\(271\) 142.862 + 82.4817i 0.527168 + 0.304360i 0.739862 0.672758i \(-0.234891\pi\)
−0.212695 + 0.977119i \(0.568224\pi\)
\(272\) −153.493 −0.564313
\(273\) 249.171 238.300i 0.912716 0.872895i
\(274\) 42.5271 0.155208
\(275\) −97.9607 116.649i −0.356221 0.424180i
\(276\) 448.252 258.799i 1.62410 0.937676i
\(277\) −437.005 + 252.305i −1.57764 + 0.910848i −0.582447 + 0.812869i \(0.697905\pi\)
−0.995188 + 0.0979797i \(0.968762\pi\)
\(278\) 15.7100 27.2104i 0.0565106 0.0978793i
\(279\) 139.998i 0.501786i
\(280\) −68.6632 + 23.2867i −0.245226 + 0.0831667i
\(281\) 119.284 0.424498 0.212249 0.977216i \(-0.431921\pi\)
0.212249 + 0.977216i \(0.431921\pi\)
\(282\) 31.2177 + 18.0235i 0.110701 + 0.0639133i
\(283\) −194.704 337.236i −0.687998 1.19165i −0.972484 0.232968i \(-0.925156\pi\)
0.284486 0.958680i \(-0.408177\pi\)
\(284\) 94.5856 + 163.827i 0.333048 + 0.576856i
\(285\) −37.0809 422.855i −0.130108 1.48370i
\(286\) 20.8283i 0.0728264i
\(287\) −134.145 + 32.7569i −0.467405 + 0.114135i
\(288\) 63.2380i 0.219577i
\(289\) 93.4196 161.808i 0.323251 0.559888i
\(290\) 19.3491 + 9.01789i 0.0667210 + 0.0310962i
\(291\) 63.1473 + 109.374i 0.217001 + 0.375857i
\(292\) 11.0986 19.2233i 0.0380088 0.0658331i
\(293\) 482.593 1.64708 0.823538 0.567261i \(-0.191997\pi\)
0.823538 + 0.567261i \(0.191997\pi\)
\(294\) −22.1961 42.7384i −0.0754968 0.145369i
\(295\) 437.340 306.360i 1.48251 1.03851i
\(296\) −17.2644 + 29.9028i −0.0583256 + 0.101023i
\(297\) 44.0093 + 76.2263i 0.148179 + 0.256654i
\(298\) 48.7595 28.1513i 0.163623 0.0944675i
\(299\) −396.529 228.936i −1.32618 0.765672i
\(300\) −126.372 + 347.641i −0.421241 + 1.15880i
\(301\) −363.633 + 88.7952i −1.20808 + 0.295001i
\(302\) 30.7201i 0.101722i
\(303\) 62.4324 + 36.0453i 0.206047 + 0.118962i
\(304\) −296.696 + 171.297i −0.975972 + 0.563478i
\(305\) −96.3988 44.9279i −0.316062 0.147304i
\(306\) 11.7993 + 6.81231i 0.0385597 + 0.0222625i
\(307\) 87.6642 0.285551 0.142776 0.989755i \(-0.454397\pi\)
0.142776 + 0.989755i \(0.454397\pi\)
\(308\) −160.974 47.0037i −0.522644 0.152609i
\(309\) −84.2700 −0.272718
\(310\) 35.2857 3.09426i 0.113825 0.00998150i
\(311\) −149.803 + 86.4888i −0.481681 + 0.278099i −0.721117 0.692813i \(-0.756371\pi\)
0.239435 + 0.970912i \(0.423038\pi\)
\(312\) 88.3633 51.0166i 0.283216 0.163515i
\(313\) −31.1714 + 53.9905i −0.0995891 + 0.172493i −0.911515 0.411268i \(-0.865086\pi\)
0.811926 + 0.583761i \(0.198420\pi\)
\(314\) 6.51324i 0.0207428i
\(315\) −177.164 35.2914i −0.562424 0.112036i
\(316\) −150.672 −0.476809
\(317\) 143.150 + 82.6479i 0.451578 + 0.260719i 0.708497 0.705714i \(-0.249374\pi\)
−0.256918 + 0.966433i \(0.582707\pi\)
\(318\) −18.1426 31.4239i −0.0570522 0.0988173i
\(319\) 49.8029 + 86.2611i 0.156122 + 0.270411i
\(320\) 286.623 25.1345i 0.895696 0.0785452i
\(321\) 195.502i 0.609041i
\(322\) −46.2200 + 44.2035i −0.143540 + 0.137278i
\(323\) 228.021i 0.705948i
\(324\) 198.187 343.270i 0.611689 1.05948i
\(325\) 322.221 56.9502i 0.991449 0.175231i
\(326\) −16.9370 29.3358i −0.0519541 0.0899871i
\(327\) −341.936 + 592.251i −1.04568 + 1.81116i
\(328\) −40.8649 −0.124588
\(329\) 246.448 + 71.9614i 0.749081 + 0.218728i
\(330\) 24.5237 17.1790i 0.0743142 0.0520577i
\(331\) 166.380 288.178i 0.502657 0.870628i −0.497338 0.867557i \(-0.665689\pi\)
0.999995 0.00307088i \(-0.000977494\pi\)
\(332\) 201.228 + 348.537i 0.606108 + 1.04981i
\(333\) −74.5026 + 43.0141i −0.223732 + 0.129171i
\(334\) −14.8608 8.57988i −0.0444934 0.0256882i
\(335\) −25.2048 + 17.6561i −0.0752381 + 0.0527049i
\(336\) 94.8956 + 388.615i 0.282427 + 1.15659i
\(337\) 313.978i 0.931685i 0.884868 + 0.465842i \(0.154249\pi\)
−0.884868 + 0.465842i \(0.845751\pi\)
\(338\) −0.522828 0.301855i −0.00154683 0.000893062i
\(339\) −635.501 + 366.907i −1.87463 + 1.08232i
\(340\) 83.9388 180.102i 0.246879 0.529712i
\(341\) 143.131 + 82.6365i 0.419738 + 0.242336i
\(342\) 30.4100 0.0889180
\(343\) −225.784 258.207i −0.658262 0.752789i
\(344\) −110.774 −0.322018
\(345\) 57.4999 + 655.705i 0.166666 + 1.90059i
\(346\) 22.5992 13.0476i 0.0653156 0.0377100i
\(347\) 188.880 109.050i 0.544322 0.314264i −0.202507 0.979281i \(-0.564909\pi\)
0.746829 + 0.665017i \(0.231576\pi\)
\(348\) 120.937 209.469i 0.347521 0.601924i
\(349\) 452.923i 1.29777i −0.760885 0.648886i \(-0.775235\pi\)
0.760885 0.648886i \(-0.224765\pi\)
\(350\) 4.97927 45.4330i 0.0142265 0.129808i
\(351\) −189.074 −0.538672
\(352\) −64.6529 37.3274i −0.183673 0.106044i
\(353\) 113.487 + 196.565i 0.321493 + 0.556842i 0.980796 0.195035i \(-0.0624821\pi\)
−0.659304 + 0.751877i \(0.729149\pi\)
\(354\) 52.4799 + 90.8978i 0.148248 + 0.256773i
\(355\) −239.647 + 21.0150i −0.675061 + 0.0591973i
\(356\) 154.817i 0.434878i
\(357\) 255.578 + 74.6275i 0.715906 + 0.209041i
\(358\) 37.6885i 0.105275i
\(359\) −124.724 + 216.028i −0.347420 + 0.601748i −0.985790 0.167981i \(-0.946275\pi\)
0.638371 + 0.769729i \(0.279609\pi\)
\(360\) −48.4552 22.5831i −0.134598 0.0627309i
\(361\) 73.9702 + 128.120i 0.204904 + 0.354903i
\(362\) 8.19650 14.1968i 0.0226423 0.0392176i
\(363\) −315.632 −0.869511
\(364\) 260.338 248.980i 0.715214 0.684010i
\(365\) 16.1954 + 23.1196i 0.0443710 + 0.0633412i
\(366\) 10.4528 18.1048i 0.0285595 0.0494665i
\(367\) −152.029 263.322i −0.414247 0.717497i 0.581102 0.813831i \(-0.302622\pi\)
−0.995349 + 0.0963334i \(0.969288\pi\)
\(368\) 460.074 265.624i 1.25020 0.721805i
\(369\) −88.1742 50.9074i −0.238955 0.137960i
\(370\) −12.4881 17.8272i −0.0337516 0.0481816i
\(371\) −178.621 186.770i −0.481459 0.503422i
\(372\) 401.336i 1.07886i
\(373\) −306.192 176.780i −0.820889 0.473940i 0.0298340 0.999555i \(-0.490502\pi\)
−0.850723 + 0.525614i \(0.823835\pi\)
\(374\) −13.9294 + 8.04217i −0.0372445 + 0.0215031i
\(375\) −332.819 332.417i −0.887518 0.886446i
\(376\) 65.7993 + 37.9892i 0.174998 + 0.101035i
\(377\) −213.965 −0.567545
\(378\) −7.40235 + 25.3510i −0.0195829 + 0.0670661i
\(379\) 435.916 1.15017 0.575087 0.818092i \(-0.304968\pi\)
0.575087 + 0.818092i \(0.304968\pi\)
\(380\) −38.7426 441.805i −0.101954 1.16264i
\(381\) 219.570 126.769i 0.576300 0.332727i
\(382\) −13.0160 + 7.51478i −0.0340733 + 0.0196722i
\(383\) −104.085 + 180.281i −0.271764 + 0.470708i −0.969314 0.245828i \(-0.920940\pi\)
0.697550 + 0.716536i \(0.254274\pi\)
\(384\) 240.987i 0.627570i
\(385\) 140.655 160.296i 0.365338 0.416353i
\(386\) −64.5188 −0.167147
\(387\) −239.017 137.997i −0.617615 0.356580i
\(388\) 65.9772 + 114.276i 0.170044 + 0.294525i
\(389\) 284.349 + 492.507i 0.730975 + 1.26609i 0.956467 + 0.291840i \(0.0942675\pi\)
−0.225493 + 0.974245i \(0.572399\pi\)
\(390\) 5.61870 + 64.0732i 0.0144069 + 0.164290i
\(391\) 353.584i 0.904307i
\(392\) −46.7839 90.0822i −0.119347 0.229801i
\(393\) 356.761i 0.907789i
\(394\) −29.4333 + 50.9799i −0.0747038 + 0.129391i
\(395\) 80.9416 173.671i 0.204915 0.439674i
\(396\) −61.8234 107.081i −0.156120 0.270407i
\(397\) 142.678 247.125i 0.359390 0.622482i −0.628469 0.777835i \(-0.716318\pi\)
0.987859 + 0.155353i \(0.0496515\pi\)
\(398\) 48.0728 0.120786
\(399\) 577.306 140.972i 1.44688 0.353313i
\(400\) −129.705 + 356.810i −0.324263 + 0.892024i
\(401\) −140.086 + 242.635i −0.349341 + 0.605076i −0.986132 0.165960i \(-0.946928\pi\)
0.636792 + 0.771036i \(0.280261\pi\)
\(402\) −3.02452 5.23862i −0.00752368 0.0130314i
\(403\) −307.461 + 177.513i −0.762931 + 0.440478i
\(404\) 65.2302 + 37.6607i 0.161461 + 0.0932195i
\(405\) 289.202 + 412.846i 0.714080 + 1.01937i
\(406\) −8.37684 + 28.6883i −0.0206326 + 0.0706609i
\(407\) 101.559i 0.249531i
\(408\) 68.2371 + 39.3967i 0.167248 + 0.0965606i
\(409\) −62.2921 + 35.9644i −0.152303 + 0.0879325i −0.574215 0.818705i \(-0.694693\pi\)
0.421911 + 0.906637i \(0.361359\pi\)
\(410\) 10.8820 23.3489i 0.0265416 0.0569485i
\(411\) 530.666 + 306.380i 1.29116 + 0.745451i
\(412\) −88.0465 −0.213705
\(413\) 516.685 + 540.256i 1.25105 + 1.30813i
\(414\) −47.1556 −0.113902
\(415\) −509.841 + 44.7088i −1.22853 + 0.107732i
\(416\) 138.882 80.1835i 0.333851 0.192749i
\(417\) 392.068 226.360i 0.940210 0.542831i
\(418\) −17.9500 + 31.0903i −0.0429426 + 0.0743788i
\(419\) 465.475i 1.11092i −0.831544 0.555459i \(-0.812542\pi\)
0.831544 0.555459i \(-0.187458\pi\)
\(420\) −507.878 101.170i −1.20923 0.240882i
\(421\) −368.126 −0.874410 −0.437205 0.899362i \(-0.644032\pi\)
−0.437205 + 0.899362i \(0.644032\pi\)
\(422\) −42.9505 24.7975i −0.101778 0.0587618i
\(423\) 94.6500 + 163.939i 0.223759 + 0.387562i
\(424\) −38.2401 66.2338i −0.0901890 0.156212i
\(425\) 162.502 + 193.504i 0.382357 + 0.455303i
\(426\) 47.2870i 0.111002i
\(427\) 41.7341 142.928i 0.0977379 0.334725i
\(428\) 204.264i 0.477251i
\(429\) −150.055 + 259.903i −0.349778 + 0.605834i
\(430\) 29.4983 63.2927i 0.0686008 0.147192i
\(431\) −379.314 656.992i −0.880080 1.52434i −0.851251 0.524758i \(-0.824156\pi\)
−0.0288283 0.999584i \(-0.509178\pi\)
\(432\) 109.687 189.984i 0.253905 0.439777i
\(433\) −423.683 −0.978482 −0.489241 0.872149i \(-0.662726\pi\)
−0.489241 + 0.872149i \(0.662726\pi\)
\(434\) 11.7636 + 48.1740i 0.0271050 + 0.111000i
\(435\) 176.476 + 251.926i 0.405692 + 0.579140i
\(436\) −357.260 + 618.792i −0.819403 + 1.41925i
\(437\) −394.597 683.462i −0.902968 1.56399i
\(438\) −4.80522 + 2.77430i −0.0109708 + 0.00633401i
\(439\) −63.4357 36.6246i −0.144500 0.0834273i 0.426007 0.904720i \(-0.359920\pi\)
−0.570507 + 0.821293i \(0.693253\pi\)
\(440\) 51.6899 36.2092i 0.117477 0.0822936i
\(441\) 11.2742 252.651i 0.0255650 0.572905i
\(442\) 34.5510i 0.0781697i
\(443\) 499.601 + 288.445i 1.12777 + 0.651117i 0.943372 0.331736i \(-0.107634\pi\)
0.184395 + 0.982852i \(0.440968\pi\)
\(444\) −213.578 + 123.309i −0.481031 + 0.277723i
\(445\) −178.449 83.1682i −0.401008 0.186895i
\(446\) −70.2811 40.5768i −0.157581 0.0909794i
\(447\) 811.249 1.81488
\(448\) 95.5547 + 391.314i 0.213292 + 0.873469i
\(449\) −652.932 −1.45419 −0.727095 0.686537i \(-0.759130\pi\)
−0.727095 + 0.686537i \(0.759130\pi\)
\(450\) 25.8065 21.6720i 0.0573478 0.0481600i
\(451\) 104.093 60.0980i 0.230804 0.133255i
\(452\) −663.980 + 383.349i −1.46898 + 0.848118i
\(453\) −221.319 + 383.335i −0.488562 + 0.846215i
\(454\) 42.8173i 0.0943112i
\(455\) 147.131 + 433.831i 0.323365 + 0.953474i
\(456\) 175.866 0.385671
\(457\) 108.778 + 62.8031i 0.238027 + 0.137425i 0.614269 0.789096i \(-0.289451\pi\)
−0.376243 + 0.926521i \(0.622784\pi\)
\(458\) 2.04863 + 3.54832i 0.00447298 + 0.00774743i
\(459\) −73.0046 126.448i −0.159051 0.275485i
\(460\) 60.0767 + 685.089i 0.130602 + 1.48932i
\(461\) 695.270i 1.50818i 0.656773 + 0.754089i \(0.271921\pi\)
−0.656773 + 0.754089i \(0.728079\pi\)
\(462\) 28.9730 + 30.2947i 0.0627120 + 0.0655729i
\(463\) 438.632i 0.947370i −0.880694 0.473685i \(-0.842924\pi\)
0.880694 0.473685i \(-0.157076\pi\)
\(464\) 124.127 214.994i 0.267515 0.463349i
\(465\) 462.598 + 215.600i 0.994835 + 0.463655i
\(466\) 35.7276 + 61.8821i 0.0766687 + 0.132794i
\(467\) −41.6921 + 72.2129i −0.0892765 + 0.154631i −0.907206 0.420688i \(-0.861789\pi\)
0.817929 + 0.575319i \(0.195122\pi\)
\(468\) 265.608 0.567538
\(469\) −29.7776 31.1360i −0.0634917 0.0663881i
\(470\) −39.2277 + 27.4793i −0.0834631 + 0.0584666i
\(471\) 46.9237 81.2743i 0.0996258 0.172557i
\(472\) 110.615 + 191.590i 0.234353 + 0.405911i
\(473\) 282.168 162.910i 0.596550 0.344418i
\(474\) 32.6174 + 18.8316i 0.0688130 + 0.0397292i
\(475\) 530.057 + 192.683i 1.11591 + 0.405649i
\(476\) 267.032 + 77.9719i 0.560991 + 0.163807i
\(477\) 190.550i 0.399476i
\(478\) −19.7256 11.3886i −0.0412670 0.0238255i
\(479\) −270.669 + 156.271i −0.565071 + 0.326244i −0.755178 0.655520i \(-0.772450\pi\)
0.190108 + 0.981763i \(0.439116\pi\)
\(480\) −208.958 97.3875i −0.435329 0.202891i
\(481\) 188.933 + 109.081i 0.392792 + 0.226779i
\(482\) 36.6435 0.0760239
\(483\) −895.206 + 218.600i −1.85343 + 0.452587i
\(484\) −329.777 −0.681358
\(485\) −167.163 + 14.6588i −0.344666 + 0.0302244i
\(486\) −56.4009 + 32.5631i −0.116051 + 0.0670022i
\(487\) 425.683 245.768i 0.874093 0.504658i 0.00538659 0.999985i \(-0.498285\pi\)
0.868706 + 0.495328i \(0.164952\pi\)
\(488\) 22.0319 38.1604i 0.0451473 0.0781975i
\(489\) 488.082i 0.998122i
\(490\) 63.9282 2.74255i 0.130466 0.00559703i
\(491\) 693.987 1.41342 0.706708 0.707506i \(-0.250180\pi\)
0.706708 + 0.707506i \(0.250180\pi\)
\(492\) −252.770 145.937i −0.513761 0.296620i
\(493\) −82.6153 143.094i −0.167577 0.290251i
\(494\) −38.5587 66.7856i −0.0780541 0.135194i
\(495\) 156.639 13.7359i 0.316442 0.0277494i
\(496\) 411.920i 0.830485i
\(497\) −79.8938 327.179i −0.160752 0.658309i
\(498\) 100.602i 0.202011i
\(499\) 35.7821 61.9763i 0.0717075 0.124201i −0.827942 0.560813i \(-0.810489\pi\)
0.899650 + 0.436612i \(0.143822\pi\)
\(500\) −347.734 347.314i −0.695469 0.694628i
\(501\) −123.625 214.125i −0.246757 0.427395i
\(502\) 33.0333 57.2153i 0.0658033 0.113975i
\(503\) −573.959 −1.14107 −0.570535 0.821273i \(-0.693264\pi\)
−0.570535 + 0.821273i \(0.693264\pi\)
\(504\) 20.9778 71.8430i 0.0416226 0.142546i
\(505\) −78.4515 + 54.9559i −0.155349 + 0.108824i
\(506\) 27.8344 48.2106i 0.0550087 0.0952778i
\(507\) −4.34935 7.53329i −0.00857859 0.0148586i
\(508\) 229.410 132.450i 0.451595 0.260728i
\(509\) 394.898 + 227.995i 0.775832 + 0.447927i 0.834951 0.550324i \(-0.185496\pi\)
−0.0591192 + 0.998251i \(0.518829\pi\)
\(510\) −40.6810 + 28.4974i −0.0797667 + 0.0558772i
\(511\) −28.5601 + 27.3141i −0.0558906 + 0.0534522i
\(512\) 311.902i 0.609184i
\(513\) −282.229 162.945i −0.550155 0.317632i
\(514\) −85.4642 + 49.3428i −0.166273 + 0.0959977i
\(515\) 47.2990 101.487i 0.0918428 0.197061i
\(516\) −685.194 395.597i −1.32790 0.766661i
\(517\) −223.475 −0.432254
\(518\) 22.0223 21.0615i 0.0425142 0.0406593i
\(519\) 376.000 0.724470
\(520\) 11.8428 + 135.051i 0.0227747 + 0.259713i
\(521\) −318.552 + 183.916i −0.611424 + 0.353006i −0.773523 0.633769i \(-0.781507\pi\)
0.162098 + 0.986775i \(0.448174\pi\)
\(522\) −19.0837 + 11.0180i −0.0365588 + 0.0211072i
\(523\) 329.927 571.450i 0.630835 1.09264i −0.356546 0.934278i \(-0.616046\pi\)
0.987381 0.158361i \(-0.0506210\pi\)
\(524\) 372.749i 0.711353i
\(525\) 389.448 531.055i 0.741806 1.01153i
\(526\) 58.7308 0.111656
\(527\) −237.432 137.081i −0.450535 0.260116i
\(528\) −174.102 301.554i −0.329739 0.571124i
\(529\) 347.387 + 601.691i 0.656685 + 1.13741i
\(530\) 48.0269 4.21157i 0.0906168 0.00794635i
\(531\) 551.192i 1.03803i
\(532\) 603.177 147.289i 1.13379 0.276860i
\(533\) 258.195i 0.484418i
\(534\) 19.3497 33.5146i 0.0362354 0.0627615i
\(535\) 235.444 + 109.731i 0.440082 + 0.205106i
\(536\) −6.37494 11.0417i −0.0118935 0.0206002i
\(537\) −271.522 + 470.290i −0.505627 + 0.875772i
\(538\) −67.8441 −0.126104
\(539\) 251.649 + 160.658i 0.466881 + 0.298067i
\(540\) 162.935 + 232.596i 0.301732 + 0.430733i
\(541\) 237.101 410.672i 0.438265 0.759098i −0.559291 0.828972i \(-0.688926\pi\)
0.997556 + 0.0698740i \(0.0222597\pi\)
\(542\) −21.5419 37.3116i −0.0397451 0.0688406i
\(543\) 204.557 118.101i 0.376717 0.217498i
\(544\) 107.249 + 61.9204i 0.197149 + 0.113824i
\(545\) −521.327 744.213i −0.956563 1.36553i
\(546\) −87.4765 + 21.3608i −0.160213 + 0.0391224i
\(547\) 401.484i 0.733975i 0.930226 + 0.366987i \(0.119611\pi\)
−0.930226 + 0.366987i \(0.880389\pi\)
\(548\) 554.448 + 320.111i 1.01177 + 0.584144i
\(549\) 95.0764 54.8924i 0.173181 0.0999861i
\(550\) 6.92410 + 39.1762i 0.0125893 + 0.0712294i
\(551\) −319.384 184.396i −0.579644 0.334657i
\(552\) −272.708 −0.494037
\(553\) 257.497 + 75.1878i 0.465637 + 0.135963i
\(554\) 131.790 0.237888
\(555\) −27.3969 312.422i −0.0493637 0.562923i
\(556\) 409.638 236.505i 0.736759 0.425368i
\(557\) 35.2935 20.3767i 0.0633636 0.0365830i −0.467984 0.883737i \(-0.655019\pi\)
0.531347 + 0.847154i \(0.321686\pi\)
\(558\) −18.2818 + 31.6650i −0.0327631 + 0.0567473i
\(559\) 699.898i 1.25205i
\(560\) −521.273 103.839i −0.930844 0.185426i
\(561\) −231.755 −0.413110
\(562\) −26.9797 15.5768i −0.0480067 0.0277167i
\(563\) 368.838 + 638.845i 0.655129 + 1.13472i 0.981861 + 0.189600i \(0.0607190\pi\)
−0.326733 + 0.945117i \(0.605948\pi\)
\(564\) 271.334 + 469.965i 0.481089 + 0.833271i
\(565\) −85.1726 971.272i −0.150748 1.71907i
\(566\) 101.702i 0.179685i
\(567\) −509.999 + 487.748i −0.899469 + 0.860226i
\(568\) 99.6694i 0.175474i
\(569\) 255.233 442.077i 0.448564 0.776936i −0.549729 0.835343i \(-0.685269\pi\)
0.998293 + 0.0584072i \(0.0186022\pi\)
\(570\) −46.8318 + 100.484i −0.0821610 + 0.176288i
\(571\) 328.855 + 569.594i 0.575928 + 0.997537i 0.995940 + 0.0900183i \(0.0286925\pi\)
−0.420012 + 0.907519i \(0.637974\pi\)
\(572\) −156.779 + 271.550i −0.274090 + 0.474738i
\(573\) −216.557 −0.377935
\(574\) 34.6187 + 10.1085i 0.0603113 + 0.0176106i
\(575\) −821.940 298.786i −1.42946 0.519628i
\(576\) −148.502 + 257.212i −0.257815 + 0.446549i
\(577\) 517.946 + 897.109i 0.897654 + 1.55478i 0.830485 + 0.557041i \(0.188063\pi\)
0.0671686 + 0.997742i \(0.478603\pi\)
\(578\) −42.2595 + 24.3985i −0.0731133 + 0.0422120i
\(579\) −805.087 464.817i −1.39048 0.802793i
\(580\) 184.385 + 263.216i 0.317905 + 0.453821i
\(581\) −169.971 696.064i −0.292550 1.19804i
\(582\) 32.9845i 0.0566745i
\(583\) 194.813 + 112.476i 0.334157 + 0.192925i
\(584\) −10.1282 + 5.84754i −0.0173429 + 0.0100129i
\(585\) −142.686 + 306.152i −0.243907 + 0.523336i
\(586\) −109.153 63.0198i −0.186269 0.107542i
\(587\) 18.0678 0.0307799 0.0153900 0.999882i \(-0.495101\pi\)
0.0153900 + 0.999882i \(0.495101\pi\)
\(588\) 32.3198 724.278i 0.0549657 1.23177i
\(589\) −611.927 −1.03893
\(590\) −138.924 + 12.1825i −0.235465 + 0.0206483i
\(591\) −734.556 + 424.096i −1.24290 + 0.717591i
\(592\) −219.211 + 126.561i −0.370288 + 0.213786i
\(593\) 1.41323 2.44778i 0.00238318 0.00412779i −0.864831 0.502062i \(-0.832575\pi\)
0.867215 + 0.497935i \(0.165908\pi\)
\(594\) 22.9879i 0.0387002i
\(595\) −233.325 + 265.907i −0.392143 + 0.446902i
\(596\) 847.605 1.42216
\(597\) 599.867 + 346.334i 1.00480 + 0.580123i
\(598\) 59.7915 + 103.562i 0.0999858 + 0.173180i
\(599\) −158.480 274.495i −0.264574 0.458256i 0.702878 0.711310i \(-0.251898\pi\)
−0.967452 + 0.253055i \(0.918565\pi\)
\(600\) 149.243 125.333i 0.248739 0.208888i
\(601\) 479.510i 0.797854i 0.916983 + 0.398927i \(0.130617\pi\)
−0.916983 + 0.398927i \(0.869383\pi\)
\(602\) 93.8422 + 27.4014i 0.155884 + 0.0455173i
\(603\) 31.7663i 0.0526804i
\(604\) −231.237 + 400.514i −0.382843 + 0.663103i
\(605\) 177.158 380.117i 0.292823 0.628292i
\(606\) −9.41401 16.3055i −0.0155347 0.0269068i
\(607\) 142.302 246.475i 0.234436 0.406054i −0.724673 0.689093i \(-0.758009\pi\)
0.959108 + 0.283039i \(0.0913425\pi\)
\(608\) 276.411 0.454623
\(609\) −311.210 + 297.632i −0.511018 + 0.488723i
\(610\) 15.9367 + 22.7501i 0.0261257 + 0.0372953i
\(611\) 240.025 415.736i 0.392840 0.680419i
\(612\) 102.556 + 177.631i 0.167574 + 0.290247i
\(613\) −820.234 + 473.562i −1.33807 + 0.772533i −0.986520 0.163638i \(-0.947677\pi\)
−0.351545 + 0.936171i \(0.614344\pi\)
\(614\) −19.8280 11.4477i −0.0322931 0.0186444i
\(615\) 304.003 212.957i 0.494315 0.346271i
\(616\) 61.0679 + 63.8537i 0.0991362 + 0.103659i
\(617\) 626.960i 1.01614i 0.861315 + 0.508071i \(0.169641\pi\)
−0.861315 + 0.508071i \(0.830359\pi\)
\(618\) 19.0603 + 11.0045i 0.0308419 + 0.0178066i
\(619\) 826.701 477.296i 1.33554 0.771076i 0.349399 0.936974i \(-0.386386\pi\)
0.986143 + 0.165898i \(0.0530523\pi\)
\(620\) 483.329 + 225.261i 0.779563 + 0.363325i
\(621\) 437.642 + 252.673i 0.704738 + 0.406881i
\(622\) 45.1768 0.0726315
\(623\) 77.2561 264.581i 0.124007 0.424688i
\(624\) 747.983 1.19869
\(625\) 587.135 214.236i 0.939417 0.342778i
\(626\) 14.1008 8.14108i 0.0225252 0.0130049i
\(627\) −447.972 + 258.637i −0.714469 + 0.412499i
\(628\) 49.0266 84.9166i 0.0780678 0.135217i
\(629\) 168.471i 0.267840i
\(630\) 35.4625 + 31.1173i 0.0562897 + 0.0493925i
\(631\) −773.291 −1.22550 −0.612751 0.790276i \(-0.709937\pi\)
−0.612751 + 0.790276i \(0.709937\pi\)
\(632\) 68.7494 + 39.6925i 0.108781 + 0.0628045i
\(633\) −357.300 618.861i −0.564455 0.977664i
\(634\) −21.5853 37.3868i −0.0340462 0.0589697i
\(635\) 29.4278 + 335.582i 0.0463429 + 0.528475i
\(636\) 546.253i 0.858888i
\(637\) −569.161 + 295.592i −0.893503 + 0.464038i
\(638\) 26.0142i 0.0407746i
\(639\) 124.163 215.056i 0.194308 0.336551i
\(640\) −290.221 135.261i −0.453470 0.211345i
\(641\) 85.9409 + 148.854i 0.134073 + 0.232222i 0.925243 0.379375i \(-0.123861\pi\)
−0.791170 + 0.611597i \(0.790528\pi\)
\(642\) −25.5298 + 44.2189i −0.0397661 + 0.0688768i
\(643\) 301.390 0.468725 0.234363 0.972149i \(-0.424700\pi\)
0.234363 + 0.972149i \(0.424700\pi\)
\(644\) −935.324 + 228.396i −1.45237 + 0.354652i
\(645\) 824.073 577.270i 1.27763 0.894992i
\(646\) 29.7763 51.5741i 0.0460934 0.0798361i
\(647\) −347.837 602.471i −0.537615 0.931177i −0.999032 0.0439931i \(-0.985992\pi\)
0.461417 0.887184i \(-0.347341\pi\)
\(648\) −180.860 + 104.420i −0.279105 + 0.161141i
\(649\) −563.524 325.351i −0.868295 0.501311i
\(650\) −80.3172 29.1964i −0.123565 0.0449175i
\(651\) −200.273 + 685.880i −0.307640 + 1.05358i
\(652\) 509.955i 0.782139i
\(653\) −522.355 301.582i −0.799930 0.461840i 0.0435164 0.999053i \(-0.486144\pi\)
−0.843447 + 0.537213i \(0.819477\pi\)
\(654\) 154.679 89.3040i 0.236512 0.136550i
\(655\) 429.648 + 200.243i 0.655951 + 0.305714i
\(656\) −259.437 149.786i −0.395483 0.228332i
\(657\) −29.1382 −0.0443504
\(658\) −46.3446 48.4588i −0.0704326 0.0736456i
\(659\) 403.838 0.612804 0.306402 0.951902i \(-0.400875\pi\)
0.306402 + 0.951902i \(0.400875\pi\)
\(660\) 449.039 39.3770i 0.680362 0.0596621i
\(661\) 680.021 392.610i 1.02878 0.593964i 0.112142 0.993692i \(-0.464229\pi\)
0.916634 + 0.399728i \(0.130896\pi\)
\(662\) −75.2638 + 43.4536i −0.113692 + 0.0656398i
\(663\) 248.918 431.139i 0.375442 0.650285i
\(664\) 212.043i 0.319342i
\(665\) −154.257 + 774.375i −0.231966 + 1.16447i
\(666\) 22.4681 0.0337359
\(667\) 495.256 + 285.936i 0.742513 + 0.428690i
\(668\) −129.165 223.721i −0.193361 0.334911i
\(669\) −584.660 1012.66i −0.873932 1.51369i
\(670\) 8.00648 0.702103i 0.0119500 0.00104791i
\(671\) 129.605i 0.193152i
\(672\) 90.4646 309.816i 0.134620 0.461035i
\(673\) 374.318i 0.556193i −0.960553 0.278096i \(-0.910297\pi\)
0.960553 0.278096i \(-0.0897035\pi\)
\(674\) 41.0010 71.0158i 0.0608324 0.105365i
\(675\) −355.630 + 62.8551i −0.526860 + 0.0931186i
\(676\) −4.54426 7.87089i −0.00672228 0.0116433i
\(677\) 470.298 814.579i 0.694679 1.20322i −0.275610 0.961270i \(-0.588880\pi\)
0.970289 0.241950i \(-0.0777869\pi\)
\(678\) 191.651 0.282671
\(679\) −55.7291 228.221i −0.0820752 0.336113i
\(680\) −85.7456 + 60.0655i −0.126097 + 0.0883316i
\(681\) 308.471 534.288i 0.452968 0.784563i
\(682\) −21.5823 37.3816i −0.0316456 0.0548118i
\(683\) −0.311813 + 0.180026i −0.000456535 + 0.000263581i −0.500228 0.865894i \(-0.666751\pi\)
0.499772 + 0.866157i \(0.333417\pi\)
\(684\) 396.471 + 228.903i 0.579636 + 0.334653i
\(685\) −666.827 + 467.118i −0.973470 + 0.681923i
\(686\) 17.3499 + 87.8856i 0.0252914 + 0.128113i
\(687\) 59.0362i 0.0859333i
\(688\) −703.265 406.030i −1.02219 0.590160i
\(689\) −418.482 + 241.610i −0.607375 + 0.350668i
\(690\) 72.6202 155.817i 0.105247 0.225821i
\(691\) −64.7660 37.3927i −0.0937280 0.0541139i 0.452403 0.891813i \(-0.350567\pi\)
−0.546131 + 0.837700i \(0.683900\pi\)
\(692\) 392.850 0.567702
\(693\) 52.2205 + 213.852i 0.0753542 + 0.308589i
\(694\) −56.9613 −0.0820768
\(695\) 52.5466 + 599.219i 0.0756066 + 0.862186i
\(696\) −110.364 + 63.7187i −0.158569 + 0.0915498i
\(697\) −172.674 + 99.6933i −0.247739 + 0.143032i
\(698\) −59.1452 + 102.443i −0.0847353 + 0.146766i
\(699\) 1029.58i 1.47293i
\(700\) 406.901 554.853i 0.581287 0.792648i
\(701\) 661.374 0.943472 0.471736 0.881740i \(-0.343628\pi\)
0.471736 + 0.881740i \(0.343628\pi\)
\(702\) 42.7649 + 24.6904i 0.0609187 + 0.0351714i
\(703\) 188.013 + 325.648i 0.267444 + 0.463226i
\(704\) −175.311 303.648i −0.249022 0.431318i
\(705\) −687.466 + 60.2851i −0.975129 + 0.0855108i
\(706\) 59.2791i 0.0839647i
\(707\) −92.6848 96.9129i −0.131096 0.137076i
\(708\) 1580.11i 2.23179i
\(709\) −33.3002 + 57.6776i −0.0469678 + 0.0813506i −0.888554 0.458773i \(-0.848289\pi\)
0.841586 + 0.540124i \(0.181622\pi\)
\(710\) 56.9478 + 26.5412i 0.0802082 + 0.0373820i
\(711\) 98.8936 + 171.289i 0.139091 + 0.240912i
\(712\) 40.7844 70.6406i 0.0572814 0.0992144i
\(713\) 948.892 1.33084
\(714\) −48.0617 50.2542i −0.0673133 0.0703841i
\(715\) −228.779 326.589i −0.319970 0.456769i
\(716\) −283.690 + 491.365i −0.396215 + 0.686264i
\(717\) −164.095 284.221i −0.228863 0.396403i
\(718\) 56.4202 32.5742i 0.0785797 0.0453680i
\(719\) 963.069 + 556.028i 1.33946 + 0.773336i 0.986727 0.162390i \(-0.0519201\pi\)
0.352730 + 0.935725i \(0.385253\pi\)
\(720\) −224.849 320.979i −0.312290 0.445805i
\(721\) 150.471 + 43.9367i 0.208698 + 0.0609386i
\(722\) 38.6378i 0.0535150i
\(723\) 457.249 + 263.993i 0.632433 + 0.365136i
\(724\) 213.724 123.394i 0.295199 0.170433i
\(725\) −402.448 + 71.1297i −0.555100 + 0.0981099i
\(726\) 71.3901 + 41.2171i 0.0983334 + 0.0567728i
\(727\) −1077.98 −1.48278 −0.741391 0.671073i \(-0.765834\pi\)
−0.741391 + 0.671073i \(0.765834\pi\)
\(728\) −184.379 + 45.0234i −0.253268 + 0.0618453i
\(729\) −31.0708 −0.0426211
\(730\) −0.644017 7.34410i −0.000882215 0.0100604i
\(731\) −468.074 + 270.242i −0.640320 + 0.369689i
\(732\) 272.557 157.361i 0.372346 0.214974i
\(733\) −414.302 + 717.592i −0.565214 + 0.978980i 0.431815 + 0.901962i \(0.357873\pi\)
−0.997030 + 0.0770179i \(0.975460\pi\)
\(734\) 79.4111i 0.108190i
\(735\) 817.475 + 426.339i 1.11221 + 0.580054i
\(736\) −428.620 −0.582363
\(737\) 32.4770 + 18.7506i 0.0440665 + 0.0254418i
\(738\) 13.2956 + 23.0286i 0.0180157 + 0.0312040i
\(739\) 22.9967 + 39.8315i 0.0311187 + 0.0538992i 0.881165 0.472808i \(-0.156760\pi\)
−0.850047 + 0.526707i \(0.823426\pi\)
\(740\) −28.6246 326.423i −0.0386819 0.441112i
\(741\) 1111.16i 1.49955i
\(742\) 16.0113 + 65.5691i 0.0215785 + 0.0883681i
\(743\) 1104.41i 1.48642i 0.669060 + 0.743209i \(0.266697\pi\)
−0.669060 + 0.743209i \(0.733303\pi\)
\(744\) −105.727 + 183.124i −0.142106 + 0.246134i
\(745\) −455.338 + 976.989i −0.611192 + 1.31140i
\(746\) 46.1698 + 79.9685i 0.0618899 + 0.107196i
\(747\) 264.153 457.526i 0.353618 0.612484i
\(748\) −242.141 −0.323718
\(749\) −101.931 + 349.085i −0.136090 + 0.466069i
\(750\) 31.8685 + 118.648i 0.0424914 + 0.158197i
\(751\) −78.7995 + 136.485i −0.104926 + 0.181737i −0.913708 0.406371i \(-0.866794\pi\)
0.808782 + 0.588109i \(0.200127\pi\)
\(752\) 278.491 + 482.360i 0.370333 + 0.641436i
\(753\) 824.400 475.967i 1.09482 0.632095i
\(754\) 48.3948 + 27.9407i 0.0641840 + 0.0370567i
\(755\) −337.430 481.693i −0.446927 0.638004i
\(756\) −287.331 + 274.795i −0.380067 + 0.363486i
\(757\) 1148.34i 1.51696i −0.651695 0.758481i \(-0.725942\pi\)
0.651695 0.758481i \(-0.274058\pi\)
\(758\) −98.5960 56.9244i −0.130074 0.0750982i
\(759\) 694.653 401.058i 0.915221 0.528403i
\(760\) −98.7099 + 211.796i −0.129881 + 0.278678i
\(761\) −761.832 439.844i −1.00109 0.577981i −0.0925215 0.995711i \(-0.529493\pi\)
−0.908571 + 0.417729i \(0.862826\pi\)
\(762\) −66.2169 −0.0868988
\(763\) 919.343 879.234i 1.20491 1.15234i
\(764\) −226.262 −0.296154
\(765\) −259.840 + 22.7858i −0.339660 + 0.0297854i
\(766\) 47.0843 27.1841i 0.0614678 0.0354884i
\(767\) 1210.51 698.890i 1.57824 0.911200i
\(768\) −401.628 + 695.639i −0.522953 + 0.905780i
\(769\) 725.749i 0.943757i 0.881664 + 0.471879i \(0.156424\pi\)
−0.881664 + 0.471879i \(0.843576\pi\)
\(770\) −52.7459 + 17.8884i −0.0685011 + 0.0232317i
\(771\) −1421.93 −1.84427
\(772\) −841.166 485.648i −1.08959 0.629077i
\(773\) −82.5496 142.980i −0.106791 0.184968i 0.807677 0.589625i \(-0.200724\pi\)
−0.914469 + 0.404657i \(0.867391\pi\)
\(774\) 36.0408 + 62.4244i 0.0465643 + 0.0806517i
\(775\) −519.294 + 436.096i −0.670057 + 0.562705i
\(776\) 69.5233i 0.0895919i
\(777\) 426.537 104.156i 0.548953 0.134049i
\(778\) 148.528i 0.190910i
\(779\) −222.514 + 385.406i −0.285641 + 0.494744i
\(780\) −409.039 + 877.650i −0.524410 + 1.12519i
\(781\) 146.579 + 253.882i 0.187681 + 0.325072i
\(782\) −46.1730 + 79.9740i −0.0590448 + 0.102269i
\(783\) 236.149 0.301596
\(784\) 33.1722 743.380i 0.0423115 0.948189i
\(785\) 71.5415 + 102.128i 0.0911356 + 0.130099i
\(786\) −46.5879 + 80.6926i −0.0592721 + 0.102662i
\(787\) −99.1839 171.792i −0.126028 0.218287i 0.796106 0.605157i \(-0.206890\pi\)
−0.922134 + 0.386870i \(0.873556\pi\)
\(788\) −767.474 + 443.102i −0.973952 + 0.562312i
\(789\) 732.862 + 423.118i 0.928850 + 0.536272i
\(790\) −40.9864 + 28.7113i −0.0518816 + 0.0363434i
\(791\) 1326.04 323.804i 1.67641 0.409360i
\(792\) 65.1462i 0.0822554i
\(793\) −241.107 139.203i −0.304044 0.175540i
\(794\) −64.5420 + 37.2634i −0.0812872 + 0.0469312i
\(795\) 629.637 + 293.450i 0.791996 + 0.369119i
\(796\) 626.750 + 361.854i 0.787374 + 0.454591i
\(797\) 266.357 0.334199 0.167100 0.985940i \(-0.446560\pi\)
0.167100 + 0.985940i \(0.446560\pi\)
\(798\) −148.985 43.5027i −0.186697 0.0545146i
\(799\) 370.711 0.463969
\(800\) 234.568 196.987i 0.293210 0.246234i
\(801\) 176.001 101.614i 0.219726 0.126859i
\(802\) 63.3694 36.5863i 0.0790142 0.0456189i
\(803\) 17.1993 29.7901i 0.0214189 0.0370986i
\(804\) 91.0649i 0.113265i
\(805\) 239.201 1200.79i 0.297144 1.49167i
\(806\) 92.7225 0.115040
\(807\) −846.580 488.773i −1.04905 0.605667i
\(808\) −19.8424 34.3681i −0.0245575 0.0425348i
\(809\) −472.741 818.812i −0.584352 1.01213i −0.994956 0.100314i \(-0.968015\pi\)
0.410603 0.911814i \(-0.365318\pi\)
\(810\) −11.5002 131.144i −0.0141978 0.161906i
\(811\) 1402.01i 1.72875i −0.502850 0.864374i \(-0.667715\pi\)
0.502850 0.864374i \(-0.332285\pi\)
\(812\) −325.157 + 310.971i −0.400439 + 0.382969i
\(813\) 620.781i 0.763569i
\(814\) −13.2622 + 22.9708i −0.0162926 + 0.0282196i
\(815\) 587.798 + 273.950i 0.721224 + 0.336135i
\(816\) 288.809 + 500.231i 0.353932 + 0.613028i
\(817\) −603.177 + 1044.73i −0.738283 + 1.27874i
\(818\) 18.7857 0.0229654
\(819\) −453.922 132.543i −0.554239 0.161835i
\(820\) 317.627 222.500i 0.387350 0.271342i
\(821\) −224.015 + 388.005i −0.272856 + 0.472601i −0.969592 0.244727i \(-0.921302\pi\)
0.696736 + 0.717328i \(0.254635\pi\)
\(822\) −80.0178 138.595i −0.0973453 0.168607i
\(823\) −325.923 + 188.172i −0.396018 + 0.228641i −0.684764 0.728765i \(-0.740095\pi\)
0.288746 + 0.957406i \(0.406762\pi\)
\(824\) 40.1744 + 23.1947i 0.0487553 + 0.0281489i
\(825\) −195.838 + 538.736i −0.237380 + 0.653014i
\(826\) −46.3148 189.667i −0.0560711 0.229622i
\(827\) 1506.52i 1.82166i −0.412778 0.910832i \(-0.635441\pi\)
0.412778 0.910832i \(-0.364559\pi\)
\(828\) −614.792 354.950i −0.742503 0.428684i
\(829\) 1072.01 618.925i 1.29313 0.746592i 0.313926 0.949447i \(-0.398356\pi\)
0.979209 + 0.202856i \(0.0650222\pi\)
\(830\) 121.155 + 56.4656i 0.145969 + 0.0680308i
\(831\) 1644.51 + 949.461i 1.97896 + 1.14255i
\(832\) 753.178 0.905261
\(833\) −417.447 266.507i −0.501137 0.319937i
\(834\) −118.238 −0.141772
\(835\) 327.259 28.6980i 0.391927 0.0343688i
\(836\) −468.048 + 270.227i −0.559866 + 0.323239i
\(837\) 339.340 195.918i 0.405424 0.234072i
\(838\) −60.7844 + 105.282i −0.0725350 + 0.125634i
\(839\) 158.707i 0.189162i 0.995517 + 0.0945808i \(0.0301511\pi\)
−0.995517 + 0.0945808i \(0.969849\pi\)
\(840\) 205.086 + 179.956i 0.244150 + 0.214234i
\(841\) −573.762 −0.682238
\(842\) 83.2632 + 48.0721i 0.0988875 + 0.0570927i
\(843\) −224.441 388.744i −0.266241 0.461143i
\(844\) −373.312 646.595i −0.442313 0.766108i
\(845\) 11.5136 1.00964i 0.0136255 0.00119484i
\(846\) 49.4397i 0.0584394i
\(847\) 563.587 + 164.565i 0.665393 + 0.194291i
\(848\) 560.660i 0.661156i
\(849\) −732.698 + 1269.07i −0.863013 + 1.49478i
\(850\) −11.4860 64.9873i −0.0135130 0.0764556i
\(851\) −291.544 504.969i −0.342590 0.593384i
\(852\) 355.940 616.505i 0.417769 0.723598i
\(853\) 329.313 0.386064 0.193032 0.981192i \(-0.438168\pi\)
0.193032 + 0.981192i \(0.438168\pi\)
\(854\) −28.1038 + 26.8776i −0.0329084 + 0.0314727i
\(855\) −476.830 + 334.023i −0.557696 + 0.390670i
\(856\) −53.8106 + 93.2026i −0.0628628 + 0.108882i
\(857\) 336.964 + 583.639i 0.393190 + 0.681025i 0.992868 0.119216i \(-0.0380381\pi\)
−0.599678 + 0.800241i \(0.704705\pi\)
\(858\) 67.8792 39.1900i 0.0791132 0.0456760i
\(859\) −717.735 414.384i −0.835547 0.482403i 0.0202012 0.999796i \(-0.493569\pi\)
−0.855748 + 0.517393i \(0.826903\pi\)
\(860\) 861.004 603.140i 1.00117 0.701325i
\(861\) 359.158 + 375.542i 0.417141 + 0.436170i
\(862\) 198.132i 0.229852i
\(863\) −89.2709 51.5406i −0.103443 0.0597226i 0.447386 0.894341i \(-0.352355\pi\)
−0.550829 + 0.834618i \(0.685688\pi\)
\(864\) −153.282 + 88.4972i −0.177409 + 0.102427i
\(865\) −211.041 + 452.817i −0.243978 + 0.523488i
\(866\) 95.8290 + 55.3269i 0.110657 + 0.0638879i
\(867\) −703.104 −0.810961
\(868\) −209.248 + 716.618i −0.241070 + 0.825596i
\(869\) −233.495 −0.268694
\(870\) −7.01764 80.0262i −0.00806625 0.0919841i
\(871\) −69.7643 + 40.2784i −0.0800968 + 0.0462439i
\(872\) 326.025 188.231i 0.373882 0.215861i
\(873\) 86.6085 150.010i 0.0992079 0.171833i
\(874\) 206.115i 0.235829i
\(875\) 420.961 + 767.084i 0.481098 + 0.876667i
\(876\) −83.5310 −0.0953550
\(877\) 46.5819 + 26.8941i 0.0531151 + 0.0306660i 0.526322 0.850285i \(-0.323571\pi\)
−0.473207 + 0.880951i \(0.656904\pi\)
\(878\) 9.56530 + 16.5676i 0.0108944 + 0.0188697i
\(879\) −908.035 1572.76i −1.03303 1.78926i
\(880\) 460.881 40.4155i 0.523729 0.0459267i
\(881\) 1300.77i 1.47647i 0.674545 + 0.738234i \(0.264340\pi\)
−0.674545 + 0.738234i \(0.735660\pi\)
\(882\) −35.5426 + 55.6726i −0.0402977 + 0.0631209i
\(883\) 525.467i 0.595093i 0.954707 + 0.297546i \(0.0961683\pi\)
−0.954707 + 0.297546i \(0.903832\pi\)
\(884\) 260.073 450.460i 0.294200 0.509570i
\(885\) −1821.31 848.843i −2.05798 0.959145i
\(886\) −75.3335 130.481i −0.0850265 0.147270i
\(887\) −698.419 + 1209.70i −0.787395 + 1.36381i 0.140164 + 0.990128i \(0.455237\pi\)
−0.927558 + 0.373679i \(0.878096\pi\)
\(888\) 129.937 0.146325
\(889\) −458.156 + 111.877i −0.515361 + 0.125846i
\(890\) 29.5012 + 42.1139i 0.0331474 + 0.0473190i
\(891\) 307.129 531.963i 0.344702 0.597041i
\(892\) −610.862 1058.04i −0.684822 1.18615i
\(893\) 716.568 413.711i 0.802428 0.463282i
\(894\) −183.489 105.938i −0.205245 0.118498i
\(895\) −413.971 590.958i −0.462537 0.660289i
\(896\) 125.646 430.302i 0.140230 0.480247i
\(897\) 1723.04i 1.92089i
\(898\) 147.681 + 85.2635i 0.164455 + 0.0949483i
\(899\) 384.013 221.710i 0.427155 0.246618i
\(900\) 499.583 88.2977i 0.555092 0.0981085i
\(901\) −323.166 186.580i −0.358674 0.207081i
\(902\) −31.3917 −0.0348024
\(903\) 973.583 + 1018.00i 1.07817 + 1.12735i
\(904\) 403.953 0.446851
\(905\) 27.4157 + 312.636i 0.0302935 + 0.345455i
\(906\) 100.116 57.8021i 0.110504 0.0637992i
\(907\) −1436.20 + 829.191i −1.58346 + 0.914213i −0.589114 + 0.808050i \(0.700523\pi\)
−0.994349 + 0.106162i \(0.966144\pi\)
\(908\) 322.295 558.231i 0.354950 0.614792i
\(909\) 98.8746i 0.108773i
\(910\) 23.3739 117.338i 0.0256856 0.128942i
\(911\) 891.683 0.978796 0.489398 0.872061i \(-0.337217\pi\)
0.489398 + 0.872061i \(0.337217\pi\)
\(912\) 1116.51 + 644.617i 1.22424 + 0.706817i
\(913\) 311.841 + 540.125i 0.341557 + 0.591593i
\(914\) −16.4024 28.4097i −0.0179457 0.0310829i
\(915\) 34.9625 + 398.697i 0.0382103 + 0.435734i
\(916\) 61.6818i 0.0673383i
\(917\) −186.008 + 637.026i −0.202844 + 0.694685i
\(918\) 38.1334i 0.0415397i
\(919\) −476.682 + 825.638i −0.518697 + 0.898409i 0.481067 + 0.876684i \(0.340249\pi\)
−0.999764 + 0.0217255i \(0.993084\pi\)
\(920\) 153.066 328.423i 0.166376 0.356982i
\(921\) −164.947 285.696i −0.179095 0.310202i
\(922\) 90.7923 157.257i 0.0984732 0.170561i
\(923\) −629.735 −0.682270
\(924\) 149.701 + 613.053i 0.162014 + 0.663478i
\(925\) 391.628 + 142.362i 0.423381 + 0.153905i
\(926\) −57.2791 + 99.2103i −0.0618565 + 0.107139i
\(927\) 57.7895 + 100.094i 0.0623403 + 0.107977i
\(928\) −173.461 + 100.148i −0.186919 + 0.107918i
\(929\) 1235.66 + 713.408i 1.33010 + 0.767931i 0.985314 0.170751i \(-0.0546195\pi\)
0.344782 + 0.938683i \(0.387953\pi\)
\(930\) −76.4767 109.173i −0.0822330 0.117391i
\(931\) −1104.33 49.2789i −1.18617 0.0529312i
\(932\) 1075.72i 1.15420i
\(933\) 563.730 + 325.470i 0.604213 + 0.348842i
\(934\) 18.8599 10.8888i 0.0201927 0.0116582i
\(935\) 130.079 279.103i 0.139122 0.298506i
\(936\) −121.193 69.9708i −0.129480 0.0747552i
\(937\) 1775.21 1.89456 0.947282 0.320400i \(-0.103817\pi\)
0.947282 + 0.320400i \(0.103817\pi\)
\(938\) 2.66921 + 10.9309i 0.00284564 + 0.0116534i
\(939\) 234.605 0.249846
\(940\) −718.274 + 62.9868i −0.764122 + 0.0670072i
\(941\) −1361.38 + 785.994i −1.44674 + 0.835275i −0.998286 0.0585313i \(-0.981358\pi\)
−0.448453 + 0.893806i \(0.648025\pi\)
\(942\) −21.2265 + 12.2551i −0.0225335 + 0.0130097i
\(943\) 345.044 597.634i 0.365900 0.633758i
\(944\) 1621.78i 1.71799i
\(945\) −162.386 478.812i −0.171837 0.506680i
\(946\) −85.0948 −0.0899522
\(947\) −477.980 275.962i −0.504731 0.291407i 0.225934 0.974143i \(-0.427457\pi\)
−0.730665 + 0.682736i \(0.760790\pi\)
\(948\) 283.500 + 491.036i 0.299050 + 0.517970i
\(949\) 36.9462 + 63.9927i 0.0389317 + 0.0674317i
\(950\) −94.7273 112.799i −0.0997130 0.118736i
\(951\) 622.032i 0.654082i
\(952\) −101.302 105.924i −0.106410 0.111264i
\(953\) 1328.92i 1.39446i −0.716846 0.697232i \(-0.754415\pi\)
0.716846 0.697232i \(-0.245585\pi\)
\(954\) −24.8831 + 43.0988i −0.0260829 + 0.0451770i
\(955\) 121.549 260.800i 0.127276 0.273089i
\(956\) −171.449 296.958i −0.179340 0.310626i
\(957\) 187.416 324.613i 0.195836 0.339199i
\(958\) 81.6269 0.0852055
\(959\) −787.808 823.747i −0.821489 0.858964i
\(960\) −621.214 886.806i −0.647098 0.923756i
\(961\) −112.623 + 195.069i −0.117194 + 0.202986i
\(962\) −28.4887 49.3439i −0.0296141 0.0512930i
\(963\) −232.214 + 134.069i −0.241136 + 0.139220i
\(964\) 477.741 + 275.824i 0.495582 + 0.286124i
\(965\) 1011.66 708.675i 1.04835 0.734378i
\(966\) 231.025 + 67.4579i 0.239156 + 0.0698322i
\(967\) 380.091i 0.393062i 0.980498 + 0.196531i \(0.0629676\pi\)
−0.980498 + 0.196531i \(0.937032\pi\)
\(968\) 150.473 + 86.8755i 0.155447 + 0.0897474i
\(969\) 743.117 429.039i 0.766891 0.442765i
\(970\) 39.7234 + 18.5136i 0.0409519 + 0.0190861i
\(971\) −1539.11 888.604i −1.58508 0.915144i −0.994102 0.108453i \(-0.965410\pi\)
−0.590974 0.806691i \(-0.701256\pi\)
\(972\) −980.438 −1.00868
\(973\) −818.089 + 199.769i −0.840790 + 0.205312i
\(974\) −128.375 −0.131802
\(975\) −791.882 942.956i −0.812187 0.967134i
\(976\) 279.745 161.511i 0.286624 0.165483i
\(977\) −842.114 + 486.195i −0.861939 + 0.497641i −0.864661 0.502356i \(-0.832467\pi\)
0.00272235 + 0.999996i \(0.499133\pi\)
\(978\) −63.7365 + 110.395i −0.0651702 + 0.112878i
\(979\) 239.918i 0.245064i
\(980\) 854.109 + 445.446i 0.871540 + 0.454536i
\(981\) 937.952 0.956119
\(982\) −156.967 90.6248i −0.159844 0.0922859i
\(983\) −693.763 1201.63i −0.705761 1.22241i −0.966416 0.256982i \(-0.917272\pi\)
0.260655 0.965432i \(-0.416061\pi\)
\(984\) 76.8904 + 133.178i 0.0781406 + 0.135344i
\(985\) −98.4484 1122.66i −0.0999476 1.13976i
\(986\) 43.1535i 0.0437663i
\(987\) −229.188 938.568i −0.232207 0.950930i
\(988\) 1160.96i 1.17506i
\(989\) 935.324 1620.03i 0.945727 1.63805i
\(990\) −37.2224 17.3480i −0.0375984 0.0175232i
\(991\) 963.975 + 1669.65i 0.972730 + 1.68482i 0.687231 + 0.726439i \(0.258826\pi\)
0.285499 + 0.958379i \(0.407841\pi\)
\(992\) −166.172 + 287.818i −0.167512 + 0.290139i
\(993\) −1252.22 −1.26105
\(994\) −24.6545 + 84.4348i −0.0248033 + 0.0849445i
\(995\) −753.784 + 528.031i −0.757571 + 0.530685i
\(996\) 757.250 1311.60i 0.760291 1.31686i
\(997\) 666.163 + 1153.83i 0.668167 + 1.15730i 0.978416 + 0.206644i \(0.0662543\pi\)
−0.310249 + 0.950655i \(0.600412\pi\)
\(998\) −16.1864 + 9.34525i −0.0162189 + 0.00936398i
\(999\) −208.522 120.391i −0.208731 0.120511i
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 35.3.i.a.19.3 12
3.2 odd 2 315.3.bi.c.19.4 12
4.3 odd 2 560.3.br.a.369.5 12
5.2 odd 4 175.3.i.c.26.4 12
5.3 odd 4 175.3.i.c.26.3 12
5.4 even 2 inner 35.3.i.a.19.4 yes 12
7.2 even 3 245.3.c.a.244.8 12
7.3 odd 6 inner 35.3.i.a.24.4 yes 12
7.4 even 3 245.3.i.d.129.4 12
7.5 odd 6 245.3.c.a.244.7 12
7.6 odd 2 245.3.i.d.19.3 12
15.14 odd 2 315.3.bi.c.19.3 12
20.19 odd 2 560.3.br.a.369.2 12
21.17 even 6 315.3.bi.c.199.3 12
28.3 even 6 560.3.br.a.129.2 12
35.3 even 12 175.3.i.c.101.3 12
35.4 even 6 245.3.i.d.129.3 12
35.9 even 6 245.3.c.a.244.5 12
35.17 even 12 175.3.i.c.101.4 12
35.19 odd 6 245.3.c.a.244.6 12
35.24 odd 6 inner 35.3.i.a.24.3 yes 12
35.34 odd 2 245.3.i.d.19.4 12
105.59 even 6 315.3.bi.c.199.4 12
140.59 even 6 560.3.br.a.129.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.3.i.a.19.3 12 1.1 even 1 trivial
35.3.i.a.19.4 yes 12 5.4 even 2 inner
35.3.i.a.24.3 yes 12 35.24 odd 6 inner
35.3.i.a.24.4 yes 12 7.3 odd 6 inner
175.3.i.c.26.3 12 5.3 odd 4
175.3.i.c.26.4 12 5.2 odd 4
175.3.i.c.101.3 12 35.3 even 12
175.3.i.c.101.4 12 35.17 even 12
245.3.c.a.244.5 12 35.9 even 6
245.3.c.a.244.6 12 35.19 odd 6
245.3.c.a.244.7 12 7.5 odd 6
245.3.c.a.244.8 12 7.2 even 3
245.3.i.d.19.3 12 7.6 odd 2
245.3.i.d.19.4 12 35.34 odd 2
245.3.i.d.129.3 12 35.4 even 6
245.3.i.d.129.4 12 7.4 even 3
315.3.bi.c.19.3 12 15.14 odd 2
315.3.bi.c.19.4 12 3.2 odd 2
315.3.bi.c.199.3 12 21.17 even 6
315.3.bi.c.199.4 12 105.59 even 6
560.3.br.a.129.2 12 28.3 even 6
560.3.br.a.129.5 12 140.59 even 6
560.3.br.a.369.2 12 20.19 odd 2
560.3.br.a.369.5 12 4.3 odd 2