Properties

Label 950.2.l.l.301.4
Level $950$
Weight $2$
Character 950.301
Analytic conductor $7.586$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 301.4
Character \(\chi\) \(=\) 950.301
Dual form 950.2.l.l.101.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 - 0.642788i) q^{2} +(0.845354 - 0.307684i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.845354 - 0.307684i) q^{6} +(1.06731 + 1.84863i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.67818 + 1.40816i) q^{9} +O(q^{10})\) \(q+(-0.766044 - 0.642788i) q^{2} +(0.845354 - 0.307684i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.845354 - 0.307684i) q^{6} +(1.06731 + 1.84863i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.67818 + 1.40816i) q^{9} +(-0.575411 + 0.996641i) q^{11} +(0.449804 + 0.779083i) q^{12} +(2.12509 + 0.773468i) q^{13} +(0.370673 - 2.10219i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(0.0280660 + 0.0235502i) q^{17} +2.19071 q^{18} +(-3.00691 - 3.15571i) q^{19} +(1.47105 + 1.23436i) q^{21} +(1.08142 - 0.393604i) q^{22} +(1.40659 + 7.97719i) q^{23} +(0.156215 - 0.885940i) q^{24} +(-1.13073 - 1.95849i) q^{26} +(-2.33480 + 4.04399i) q^{27} +(-1.63521 + 1.37211i) q^{28} +(-4.74371 + 3.98044i) q^{29} +(2.21180 + 3.83095i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.179776 + 1.01956i) q^{33} +(-0.00636204 - 0.0360809i) q^{34} +(-1.67818 - 1.40816i) q^{36} +5.64857 q^{37} +(0.274975 + 4.35022i) q^{38} +2.03443 q^{39} +(-7.81864 + 2.84575i) q^{41} +(-0.333460 - 1.89115i) q^{42} +(0.121234 - 0.687551i) q^{43} +(-1.08142 - 0.393604i) q^{44} +(4.05013 - 7.01502i) q^{46} +(5.57985 - 4.68205i) q^{47} +(-0.689139 + 0.578256i) q^{48} +(1.22170 - 2.11605i) q^{49} +(0.0309717 + 0.0112728i) q^{51} +(-0.392700 + 2.22711i) q^{52} +(2.05103 + 11.6320i) q^{53} +(4.38799 - 1.59710i) q^{54} +2.13462 q^{56} +(-3.51286 - 1.74252i) q^{57} +6.19247 q^{58} +(1.27093 + 1.06644i) q^{59} +(-1.03441 - 5.86645i) q^{61} +(0.768149 - 4.35639i) q^{62} +(-4.39431 - 1.59940i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.793077 - 0.665470i) q^{66} +(-7.48620 + 6.28167i) q^{67} +(-0.0183188 + 0.0317290i) q^{68} +(3.64352 + 6.31077i) q^{69} +(-1.70377 + 9.66255i) q^{71} +(0.380412 + 2.15742i) q^{72} +(5.53912 - 2.01607i) q^{73} +(-4.32706 - 3.63083i) q^{74} +(2.58562 - 3.50921i) q^{76} -2.45657 q^{77} +(-1.55847 - 1.30771i) q^{78} +(8.50752 - 3.09648i) q^{79} +(0.411775 - 2.33529i) q^{81} +(7.81864 + 2.84575i) q^{82} +(-2.73497 - 4.73712i) q^{83} +(-0.960160 + 1.66305i) q^{84} +(-0.534820 + 0.448767i) q^{86} +(-2.78540 + 4.82445i) q^{87} +(0.575411 + 0.996641i) q^{88} +(6.65071 + 2.42066i) q^{89} +(0.838265 + 4.75404i) q^{91} +(-7.61175 + 2.77045i) q^{92} +(3.04847 + 2.55797i) q^{93} -7.28398 q^{94} +0.899607 q^{96} +(6.34610 + 5.32501i) q^{97} +(-2.29604 + 0.835691i) q^{98} +(-0.437787 - 2.48281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766044 0.642788i −0.541675 0.454519i
\(3\) 0.845354 0.307684i 0.488066 0.177641i −0.0862529 0.996273i \(-0.527489\pi\)
0.574319 + 0.818632i \(0.305267\pi\)
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) 0 0
\(6\) −0.845354 0.307684i −0.345114 0.125611i
\(7\) 1.06731 + 1.84863i 0.403405 + 0.698718i 0.994134 0.108152i \(-0.0344932\pi\)
−0.590729 + 0.806870i \(0.701160\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) −1.67818 + 1.40816i −0.559393 + 0.469386i
\(10\) 0 0
\(11\) −0.575411 + 0.996641i −0.173493 + 0.300499i −0.939639 0.342168i \(-0.888839\pi\)
0.766146 + 0.642667i \(0.222172\pi\)
\(12\) 0.449804 + 0.779083i 0.129847 + 0.224902i
\(13\) 2.12509 + 0.773468i 0.589393 + 0.214521i 0.619462 0.785026i \(-0.287351\pi\)
−0.0300696 + 0.999548i \(0.509573\pi\)
\(14\) 0.370673 2.10219i 0.0990665 0.561834i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 0.0280660 + 0.0235502i 0.00680700 + 0.00571175i 0.646185 0.763181i \(-0.276364\pi\)
−0.639378 + 0.768893i \(0.720808\pi\)
\(18\) 2.19071 0.516354
\(19\) −3.00691 3.15571i −0.689832 0.723969i
\(20\) 0 0
\(21\) 1.47105 + 1.23436i 0.321009 + 0.269359i
\(22\) 1.08142 0.393604i 0.230559 0.0839167i
\(23\) 1.40659 + 7.97719i 0.293295 + 1.66336i 0.674052 + 0.738684i \(0.264552\pi\)
−0.380757 + 0.924675i \(0.624336\pi\)
\(24\) 0.156215 0.885940i 0.0318873 0.180842i
\(25\) 0 0
\(26\) −1.13073 1.95849i −0.221755 0.384091i
\(27\) −2.33480 + 4.04399i −0.449332 + 0.778266i
\(28\) −1.63521 + 1.37211i −0.309026 + 0.259304i
\(29\) −4.74371 + 3.98044i −0.880884 + 0.739150i −0.966361 0.257191i \(-0.917203\pi\)
0.0854764 + 0.996340i \(0.472759\pi\)
\(30\) 0 0
\(31\) 2.21180 + 3.83095i 0.397251 + 0.688058i 0.993386 0.114826i \(-0.0366311\pi\)
−0.596135 + 0.802884i \(0.703298\pi\)
\(32\) 0.939693 + 0.342020i 0.166116 + 0.0604612i
\(33\) −0.179776 + 1.01956i −0.0312950 + 0.177483i
\(34\) −0.00636204 0.0360809i −0.00109108 0.00618783i
\(35\) 0 0
\(36\) −1.67818 1.40816i −0.279696 0.234693i
\(37\) 5.64857 0.928619 0.464310 0.885673i \(-0.346302\pi\)
0.464310 + 0.885673i \(0.346302\pi\)
\(38\) 0.274975 + 4.35022i 0.0446068 + 0.705698i
\(39\) 2.03443 0.325770
\(40\) 0 0
\(41\) −7.81864 + 2.84575i −1.22107 + 0.444432i −0.870529 0.492117i \(-0.836223\pi\)
−0.350537 + 0.936549i \(0.614001\pi\)
\(42\) −0.333460 1.89115i −0.0514540 0.291810i
\(43\) 0.121234 0.687551i 0.0184880 0.104851i −0.974167 0.225827i \(-0.927492\pi\)
0.992655 + 0.120977i \(0.0386026\pi\)
\(44\) −1.08142 0.393604i −0.163030 0.0593381i
\(45\) 0 0
\(46\) 4.05013 7.01502i 0.597159 1.03431i
\(47\) 5.57985 4.68205i 0.813905 0.682947i −0.137632 0.990483i \(-0.543949\pi\)
0.951536 + 0.307536i \(0.0995045\pi\)
\(48\) −0.689139 + 0.578256i −0.0994687 + 0.0834641i
\(49\) 1.22170 2.11605i 0.174528 0.302292i
\(50\) 0 0
\(51\) 0.0309717 + 0.0112728i 0.00433691 + 0.00157850i
\(52\) −0.392700 + 2.22711i −0.0544577 + 0.308845i
\(53\) 2.05103 + 11.6320i 0.281730 + 1.59777i 0.716736 + 0.697344i \(0.245635\pi\)
−0.435006 + 0.900428i \(0.643254\pi\)
\(54\) 4.38799 1.59710i 0.597129 0.217337i
\(55\) 0 0
\(56\) 2.13462 0.285251
\(57\) −3.51286 1.74252i −0.465290 0.230802i
\(58\) 6.19247 0.813111
\(59\) 1.27093 + 1.06644i 0.165462 + 0.138839i 0.721759 0.692145i \(-0.243334\pi\)
−0.556297 + 0.830983i \(0.687778\pi\)
\(60\) 0 0
\(61\) −1.03441 5.86645i −0.132443 0.751122i −0.976606 0.215035i \(-0.931013\pi\)
0.844163 0.536086i \(-0.180098\pi\)
\(62\) 0.768149 4.35639i 0.0975550 0.553262i
\(63\) −4.39431 1.59940i −0.553631 0.201505i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 0 0
\(66\) 0.793077 0.665470i 0.0976210 0.0819137i
\(67\) −7.48620 + 6.28167i −0.914585 + 0.767428i −0.972986 0.230865i \(-0.925844\pi\)
0.0584009 + 0.998293i \(0.481400\pi\)
\(68\) −0.0183188 + 0.0317290i −0.00222148 + 0.00384771i
\(69\) 3.64352 + 6.31077i 0.438629 + 0.759727i
\(70\) 0 0
\(71\) −1.70377 + 9.66255i −0.202200 + 1.14673i 0.699585 + 0.714549i \(0.253368\pi\)
−0.901785 + 0.432184i \(0.857743\pi\)
\(72\) 0.380412 + 2.15742i 0.0448320 + 0.254255i
\(73\) 5.53912 2.01607i 0.648305 0.235964i 0.00312576 0.999995i \(-0.499005\pi\)
0.645179 + 0.764031i \(0.276783\pi\)
\(74\) −4.32706 3.63083i −0.503010 0.422076i
\(75\) 0 0
\(76\) 2.58562 3.50921i 0.296591 0.402534i
\(77\) −2.45657 −0.279952
\(78\) −1.55847 1.30771i −0.176462 0.148069i
\(79\) 8.50752 3.09648i 0.957170 0.348382i 0.184246 0.982880i \(-0.441016\pi\)
0.772924 + 0.634499i \(0.218793\pi\)
\(80\) 0 0
\(81\) 0.411775 2.33529i 0.0457527 0.259477i
\(82\) 7.81864 + 2.84575i 0.863424 + 0.314261i
\(83\) −2.73497 4.73712i −0.300203 0.519966i 0.675979 0.736921i \(-0.263721\pi\)
−0.976182 + 0.216955i \(0.930388\pi\)
\(84\) −0.960160 + 1.66305i −0.104762 + 0.181453i
\(85\) 0 0
\(86\) −0.534820 + 0.448767i −0.0576711 + 0.0483918i
\(87\) −2.78540 + 4.82445i −0.298626 + 0.517235i
\(88\) 0.575411 + 0.996641i 0.0613390 + 0.106242i
\(89\) 6.65071 + 2.42066i 0.704974 + 0.256589i 0.669533 0.742782i \(-0.266494\pi\)
0.0354408 + 0.999372i \(0.488716\pi\)
\(90\) 0 0
\(91\) 0.838265 + 4.75404i 0.0878740 + 0.498358i
\(92\) −7.61175 + 2.77045i −0.793580 + 0.288839i
\(93\) 3.04847 + 2.55797i 0.316112 + 0.265249i
\(94\) −7.28398 −0.751285
\(95\) 0 0
\(96\) 0.899607 0.0918158
\(97\) 6.34610 + 5.32501i 0.644349 + 0.540673i 0.905350 0.424666i \(-0.139608\pi\)
−0.261002 + 0.965338i \(0.584053\pi\)
\(98\) −2.29604 + 0.835691i −0.231935 + 0.0844176i
\(99\) −0.437787 2.48281i −0.0439992 0.249532i
\(100\) 0 0
\(101\) −0.354959 0.129194i −0.0353197 0.0128553i 0.324300 0.945954i \(-0.394871\pi\)
−0.359620 + 0.933099i \(0.617094\pi\)
\(102\) −0.0164797 0.0285437i −0.00163173 0.00282624i
\(103\) 6.90619 11.9619i 0.680487 1.17864i −0.294345 0.955699i \(-0.595102\pi\)
0.974832 0.222939i \(-0.0715652\pi\)
\(104\) 1.73239 1.45364i 0.169874 0.142542i
\(105\) 0 0
\(106\) 5.90570 10.2290i 0.573612 0.993525i
\(107\) −3.23875 5.60969i −0.313102 0.542309i 0.665930 0.746014i \(-0.268035\pi\)
−0.979032 + 0.203705i \(0.934702\pi\)
\(108\) −4.38799 1.59710i −0.422234 0.153681i
\(109\) −0.298211 + 1.69124i −0.0285634 + 0.161991i −0.995753 0.0920643i \(-0.970653\pi\)
0.967190 + 0.254056i \(0.0817646\pi\)
\(110\) 0 0
\(111\) 4.77504 1.73797i 0.453227 0.164961i
\(112\) −1.63521 1.37211i −0.154513 0.129652i
\(113\) 6.92537 0.651484 0.325742 0.945459i \(-0.394386\pi\)
0.325742 + 0.945459i \(0.394386\pi\)
\(114\) 1.57094 + 3.59287i 0.147132 + 0.336503i
\(115\) 0 0
\(116\) −4.74371 3.98044i −0.440442 0.369575i
\(117\) −4.65544 + 1.69444i −0.430395 + 0.156651i
\(118\) −0.288097 1.63388i −0.0265215 0.150411i
\(119\) −0.0135805 + 0.0770191i −0.00124493 + 0.00706033i
\(120\) 0 0
\(121\) 4.83780 + 8.37932i 0.439800 + 0.761757i
\(122\) −2.97847 + 5.15887i −0.269658 + 0.467062i
\(123\) −5.73393 + 4.81134i −0.517011 + 0.433824i
\(124\) −3.38867 + 2.84343i −0.304312 + 0.255348i
\(125\) 0 0
\(126\) 2.33816 + 4.04982i 0.208300 + 0.360786i
\(127\) 13.7727 + 5.01285i 1.22213 + 0.444818i 0.870895 0.491470i \(-0.163540\pi\)
0.351234 + 0.936288i \(0.385762\pi\)
\(128\) −0.173648 + 0.984808i −0.0153485 + 0.0870455i
\(129\) −0.109063 0.618526i −0.00960245 0.0544582i
\(130\) 0 0
\(131\) 3.95429 + 3.31804i 0.345488 + 0.289899i 0.798975 0.601364i \(-0.205376\pi\)
−0.453487 + 0.891263i \(0.649820\pi\)
\(132\) −1.03529 −0.0901103
\(133\) 2.62445 8.92680i 0.227569 0.774051i
\(134\) 9.77254 0.844219
\(135\) 0 0
\(136\) 0.0344280 0.0125308i 0.00295218 0.00107451i
\(137\) −2.64600 15.0062i −0.226063 1.28207i −0.860643 0.509209i \(-0.829938\pi\)
0.634580 0.772857i \(-0.281173\pi\)
\(138\) 1.26538 7.17634i 0.107717 0.610891i
\(139\) 9.21476 + 3.35390i 0.781586 + 0.284474i 0.701834 0.712341i \(-0.252365\pi\)
0.0797522 + 0.996815i \(0.474587\pi\)
\(140\) 0 0
\(141\) 3.27636 5.67482i 0.275919 0.477906i
\(142\) 7.51613 6.30678i 0.630740 0.529253i
\(143\) −1.99367 + 1.67289i −0.166719 + 0.139894i
\(144\) 1.09535 1.89721i 0.0912794 0.158101i
\(145\) 0 0
\(146\) −5.53912 2.01607i −0.458421 0.166851i
\(147\) 0.381696 2.16471i 0.0314817 0.178542i
\(148\) 0.980864 + 5.56276i 0.0806265 + 0.457256i
\(149\) −20.8349 + 7.58328i −1.70686 + 0.621246i −0.996577 0.0826704i \(-0.973655\pi\)
−0.710283 + 0.703917i \(0.751433\pi\)
\(150\) 0 0
\(151\) −17.5102 −1.42496 −0.712482 0.701691i \(-0.752429\pi\)
−0.712482 + 0.701691i \(0.752429\pi\)
\(152\) −4.23638 + 1.02620i −0.343616 + 0.0832362i
\(153\) −0.0802621 −0.00648881
\(154\) 1.88184 + 1.57905i 0.151643 + 0.127244i
\(155\) 0 0
\(156\) 0.353276 + 2.00353i 0.0282847 + 0.160410i
\(157\) 3.67952 20.8676i 0.293657 1.66541i −0.378952 0.925416i \(-0.623716\pi\)
0.672610 0.739997i \(-0.265173\pi\)
\(158\) −8.50752 3.09648i −0.676822 0.246343i
\(159\) 5.31281 + 9.20206i 0.421333 + 0.729771i
\(160\) 0 0
\(161\) −13.2456 + 11.1144i −1.04390 + 0.875939i
\(162\) −1.81653 + 1.52425i −0.142720 + 0.119757i
\(163\) −4.80181 + 8.31699i −0.376107 + 0.651437i −0.990492 0.137570i \(-0.956071\pi\)
0.614385 + 0.789006i \(0.289404\pi\)
\(164\) −4.16021 7.20569i −0.324858 0.562670i
\(165\) 0 0
\(166\) −0.949847 + 5.38685i −0.0737224 + 0.418101i
\(167\) −1.24764 7.07571i −0.0965451 0.547535i −0.994263 0.106964i \(-0.965887\pi\)
0.897718 0.440571i \(-0.145224\pi\)
\(168\) 1.80451 0.656788i 0.139221 0.0506723i
\(169\) −6.04084 5.06887i −0.464680 0.389913i
\(170\) 0 0
\(171\) 9.48987 + 1.06164i 0.725708 + 0.0811855i
\(172\) 0.698158 0.0532340
\(173\) −19.4568 16.3262i −1.47927 1.24126i −0.906957 0.421224i \(-0.861601\pi\)
−0.572316 0.820033i \(-0.693955\pi\)
\(174\) 5.23483 1.90532i 0.396852 0.144442i
\(175\) 0 0
\(176\) 0.199838 1.13334i 0.0150634 0.0854286i
\(177\) 1.40252 + 0.510474i 0.105420 + 0.0383696i
\(178\) −3.53877 6.12933i −0.265242 0.459412i
\(179\) 5.27690 9.13986i 0.394414 0.683145i −0.598612 0.801039i \(-0.704281\pi\)
0.993026 + 0.117894i \(0.0376143\pi\)
\(180\) 0 0
\(181\) −0.332674 + 0.279147i −0.0247275 + 0.0207488i −0.655068 0.755570i \(-0.727360\pi\)
0.630340 + 0.776319i \(0.282915\pi\)
\(182\) 2.41369 4.18063i 0.178914 0.309889i
\(183\) −2.67946 4.64096i −0.198071 0.343069i
\(184\) 7.61175 + 2.77045i 0.561145 + 0.204240i
\(185\) 0 0
\(186\) −0.691033 3.91904i −0.0506690 0.287358i
\(187\) −0.0396205 + 0.0144207i −0.00289734 + 0.00105455i
\(188\) 5.57985 + 4.68205i 0.406952 + 0.341474i
\(189\) −9.96782 −0.725052
\(190\) 0 0
\(191\) 26.4706 1.91534 0.957672 0.287861i \(-0.0929443\pi\)
0.957672 + 0.287861i \(0.0929443\pi\)
\(192\) −0.689139 0.578256i −0.0497343 0.0417321i
\(193\) −11.2801 + 4.10561i −0.811957 + 0.295528i −0.714432 0.699705i \(-0.753315\pi\)
−0.0975250 + 0.995233i \(0.531093\pi\)
\(194\) −1.43854 8.15839i −0.103281 0.585738i
\(195\) 0 0
\(196\) 2.29604 + 0.835691i 0.164003 + 0.0596922i
\(197\) 12.1859 + 21.1067i 0.868212 + 1.50379i 0.863822 + 0.503796i \(0.168064\pi\)
0.00438927 + 0.999990i \(0.498603\pi\)
\(198\) −1.26056 + 2.18335i −0.0895839 + 0.155164i
\(199\) 0.197234 0.165499i 0.0139815 0.0117319i −0.635770 0.771878i \(-0.719317\pi\)
0.649752 + 0.760147i \(0.274873\pi\)
\(200\) 0 0
\(201\) −4.39572 + 7.61362i −0.310050 + 0.537023i
\(202\) 0.188870 + 0.327132i 0.0132888 + 0.0230169i
\(203\) −12.4214 4.52102i −0.871811 0.317313i
\(204\) −0.00572334 + 0.0324587i −0.000400714 + 0.00227256i
\(205\) 0 0
\(206\) −12.9794 + 4.72411i −0.904317 + 0.329145i
\(207\) −13.5937 11.4064i −0.944825 0.792803i
\(208\) −2.26147 −0.156805
\(209\) 4.87532 1.18098i 0.337233 0.0816900i
\(210\) 0 0
\(211\) 2.05853 + 1.72731i 0.141715 + 0.118913i 0.710889 0.703304i \(-0.248293\pi\)
−0.569175 + 0.822217i \(0.692737\pi\)
\(212\) −11.0991 + 4.03974i −0.762288 + 0.277450i
\(213\) 1.53272 + 8.69250i 0.105020 + 0.595600i
\(214\) −1.12481 + 6.37910i −0.0768903 + 0.436066i
\(215\) 0 0
\(216\) 2.33480 + 4.04399i 0.158863 + 0.275159i
\(217\) −4.72135 + 8.17761i −0.320506 + 0.555132i
\(218\) 1.31555 1.10388i 0.0891003 0.0747640i
\(219\) 4.06220 3.40859i 0.274498 0.230331i
\(220\) 0 0
\(221\) 0.0414273 + 0.0717542i 0.00278670 + 0.00482671i
\(222\) −4.77504 1.73797i −0.320480 0.116645i
\(223\) 1.06235 6.02489i 0.0711403 0.403457i −0.928355 0.371694i \(-0.878777\pi\)
0.999495 0.0317623i \(-0.0101120\pi\)
\(224\) 0.370673 + 2.10219i 0.0247666 + 0.140458i
\(225\) 0 0
\(226\) −5.30514 4.45154i −0.352893 0.296112i
\(227\) −0.981843 −0.0651672 −0.0325836 0.999469i \(-0.510374\pi\)
−0.0325836 + 0.999469i \(0.510374\pi\)
\(228\) 1.10604 3.76208i 0.0732493 0.249150i
\(229\) −20.0859 −1.32731 −0.663657 0.748037i \(-0.730997\pi\)
−0.663657 + 0.748037i \(0.730997\pi\)
\(230\) 0 0
\(231\) −2.07667 + 0.755846i −0.136635 + 0.0497310i
\(232\) 1.07531 + 6.09839i 0.0705976 + 0.400379i
\(233\) 2.79441 15.8479i 0.183068 1.03823i −0.745345 0.666679i \(-0.767715\pi\)
0.928413 0.371550i \(-0.121174\pi\)
\(234\) 4.65544 + 1.69444i 0.304336 + 0.110769i
\(235\) 0 0
\(236\) −0.829543 + 1.43681i −0.0539987 + 0.0935284i
\(237\) 6.23913 5.23525i 0.405275 0.340066i
\(238\) 0.0599102 0.0502706i 0.00388340 0.00325856i
\(239\) 4.29381 7.43711i 0.277744 0.481066i −0.693080 0.720861i \(-0.743747\pi\)
0.970824 + 0.239794i \(0.0770800\pi\)
\(240\) 0 0
\(241\) −11.1897 4.07273i −0.720793 0.262347i −0.0445308 0.999008i \(-0.514179\pi\)
−0.676263 + 0.736661i \(0.736401\pi\)
\(242\) 1.68015 9.52861i 0.108004 0.612523i
\(243\) −2.80304 15.8968i −0.179815 1.01978i
\(244\) 5.59770 2.03740i 0.358356 0.130431i
\(245\) 0 0
\(246\) 7.48511 0.477233
\(247\) −3.94910 9.03190i −0.251275 0.574686i
\(248\) 4.42359 0.280899
\(249\) −3.76956 3.16303i −0.238886 0.200449i
\(250\) 0 0
\(251\) −3.11493 17.6657i −0.196613 1.11505i −0.910103 0.414382i \(-0.863998\pi\)
0.713490 0.700665i \(-0.247113\pi\)
\(252\) 0.812035 4.60528i 0.0511534 0.290105i
\(253\) −8.75977 3.18829i −0.550722 0.200446i
\(254\) −7.32829 12.6930i −0.459818 0.796428i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −20.8725 + 17.5141i −1.30199 + 1.09250i −0.312197 + 0.950018i \(0.601065\pi\)
−0.989797 + 0.142485i \(0.954491\pi\)
\(258\) −0.314034 + 0.543923i −0.0195509 + 0.0338632i
\(259\) 6.02878 + 10.4421i 0.374610 + 0.648843i
\(260\) 0 0
\(261\) 2.35569 13.3598i 0.145814 0.826950i
\(262\) −0.896365 5.08354i −0.0553776 0.314062i
\(263\) 0.470923 0.171402i 0.0290384 0.0105691i −0.327460 0.944865i \(-0.606193\pi\)
0.356498 + 0.934296i \(0.383970\pi\)
\(264\) 0.793077 + 0.665470i 0.0488105 + 0.0409569i
\(265\) 0 0
\(266\) −7.74848 + 5.15136i −0.475090 + 0.315850i
\(267\) 6.36700 0.389654
\(268\) −7.48620 6.28167i −0.457292 0.383714i
\(269\) −19.3314 + 7.03604i −1.17865 + 0.428995i −0.855726 0.517429i \(-0.826889\pi\)
−0.322928 + 0.946424i \(0.604667\pi\)
\(270\) 0 0
\(271\) 1.87357 10.6255i 0.113811 0.645456i −0.873521 0.486787i \(-0.838169\pi\)
0.987332 0.158669i \(-0.0507202\pi\)
\(272\) −0.0344280 0.0125308i −0.00208751 0.000759790i
\(273\) 2.17137 + 3.76093i 0.131417 + 0.227622i
\(274\) −7.61885 + 13.1962i −0.460272 + 0.797214i
\(275\) 0 0
\(276\) −5.58220 + 4.68402i −0.336009 + 0.281945i
\(277\) −10.0957 + 17.4863i −0.606594 + 1.05065i 0.385203 + 0.922832i \(0.374131\pi\)
−0.991797 + 0.127820i \(0.959202\pi\)
\(278\) −4.90307 8.49237i −0.294067 0.509339i
\(279\) −9.10637 3.31445i −0.545184 0.198431i
\(280\) 0 0
\(281\) −0.196386 1.11376i −0.0117154 0.0664415i 0.978390 0.206770i \(-0.0662952\pi\)
−0.990105 + 0.140329i \(0.955184\pi\)
\(282\) −6.15754 + 2.24116i −0.366676 + 0.133459i
\(283\) 5.78772 + 4.85647i 0.344044 + 0.288687i 0.798393 0.602136i \(-0.205684\pi\)
−0.454349 + 0.890824i \(0.650128\pi\)
\(284\) −9.81161 −0.582212
\(285\) 0 0
\(286\) 2.60255 0.153892
\(287\) −13.6057 11.4165i −0.803117 0.673895i
\(288\) −2.05859 + 0.749266i −0.121304 + 0.0441509i
\(289\) −2.95179 16.7404i −0.173634 0.984730i
\(290\) 0 0
\(291\) 7.00312 + 2.54893i 0.410530 + 0.149421i
\(292\) 2.94730 + 5.10488i 0.172478 + 0.298740i
\(293\) 8.42459 14.5918i 0.492170 0.852463i −0.507790 0.861481i \(-0.669537\pi\)
0.999959 + 0.00901811i \(0.00287059\pi\)
\(294\) −1.68384 + 1.41291i −0.0982036 + 0.0824026i
\(295\) 0 0
\(296\) 2.82429 4.89181i 0.164158 0.284330i
\(297\) −2.68694 4.65391i −0.155912 0.270047i
\(298\) 20.8349 + 7.58328i 1.20693 + 0.439287i
\(299\) −3.18097 + 18.0402i −0.183960 + 1.04329i
\(300\) 0 0
\(301\) 1.40043 0.509713i 0.0807192 0.0293794i
\(302\) 13.4136 + 11.2554i 0.771867 + 0.647674i
\(303\) −0.339817 −0.0195220
\(304\) 3.90489 + 1.93697i 0.223961 + 0.111093i
\(305\) 0 0
\(306\) 0.0614843 + 0.0515915i 0.00351483 + 0.00294929i
\(307\) 18.3440 6.67668i 1.04695 0.381058i 0.239439 0.970911i \(-0.423037\pi\)
0.807511 + 0.589853i \(0.200814\pi\)
\(308\) −0.426578 2.41925i −0.0243066 0.137849i
\(309\) 2.15770 12.2369i 0.122747 0.696136i
\(310\) 0 0
\(311\) −16.0432 27.7876i −0.909725 1.57569i −0.814446 0.580239i \(-0.802959\pi\)
−0.0952788 0.995451i \(-0.530374\pi\)
\(312\) 1.01722 1.76187i 0.0575886 0.0997463i
\(313\) 4.98909 4.18634i 0.282000 0.236626i −0.490805 0.871269i \(-0.663297\pi\)
0.772805 + 0.634643i \(0.218853\pi\)
\(314\) −16.2321 + 13.6203i −0.916030 + 0.768640i
\(315\) 0 0
\(316\) 4.52676 + 7.84057i 0.254650 + 0.441067i
\(317\) −7.23292 2.63257i −0.406241 0.147860i 0.130814 0.991407i \(-0.458241\pi\)
−0.537055 + 0.843547i \(0.680463\pi\)
\(318\) 1.84512 10.4642i 0.103469 0.586803i
\(319\) −1.23749 7.01816i −0.0692862 0.392942i
\(320\) 0 0
\(321\) −4.46391 3.74566i −0.249151 0.209062i
\(322\) 17.2910 0.963588
\(323\) −0.0100744 0.159381i −0.000560554 0.00886821i
\(324\) 2.37131 0.131740
\(325\) 0 0
\(326\) 9.02446 3.28463i 0.499819 0.181919i
\(327\) 0.268273 + 1.52145i 0.0148355 + 0.0841364i
\(328\) −1.44483 + 8.19401i −0.0797771 + 0.452439i
\(329\) 14.6108 + 5.31791i 0.805521 + 0.293186i
\(330\) 0 0
\(331\) 10.0884 17.4736i 0.554508 0.960436i −0.443433 0.896307i \(-0.646240\pi\)
0.997942 0.0641290i \(-0.0204269\pi\)
\(332\) 4.19022 3.51602i 0.229968 0.192966i
\(333\) −9.47931 + 7.95409i −0.519463 + 0.435881i
\(334\) −3.59243 + 6.22227i −0.196569 + 0.340468i
\(335\) 0 0
\(336\) −1.80451 0.656788i −0.0984441 0.0358307i
\(337\) 1.24455 7.05822i 0.0677952 0.384486i −0.931964 0.362550i \(-0.881906\pi\)
0.999759 0.0219353i \(-0.00698280\pi\)
\(338\) 1.36935 + 7.76596i 0.0744827 + 0.422412i
\(339\) 5.85439 2.13083i 0.317967 0.115731i
\(340\) 0 0
\(341\) −5.09077 −0.275681
\(342\) −6.58725 6.91323i −0.356198 0.373825i
\(343\) 20.1581 1.08843
\(344\) −0.534820 0.448767i −0.0288356 0.0241959i
\(345\) 0 0
\(346\) 4.41050 + 25.0132i 0.237110 + 1.34472i
\(347\) −1.29390 + 7.33806i −0.0694601 + 0.393928i 0.930180 + 0.367104i \(0.119651\pi\)
−0.999640 + 0.0268241i \(0.991461\pi\)
\(348\) −5.23483 1.90532i −0.280616 0.102136i
\(349\) −13.0654 22.6299i −0.699373 1.21135i −0.968684 0.248297i \(-0.920129\pi\)
0.269311 0.963053i \(-0.413204\pi\)
\(350\) 0 0
\(351\) −8.08954 + 6.78793i −0.431788 + 0.362313i
\(352\) −0.881581 + 0.739734i −0.0469884 + 0.0394280i
\(353\) −7.03480 + 12.1846i −0.374425 + 0.648523i −0.990241 0.139367i \(-0.955493\pi\)
0.615816 + 0.787890i \(0.288826\pi\)
\(354\) −0.746263 1.29257i −0.0396634 0.0686991i
\(355\) 0 0
\(356\) −1.22900 + 6.97001i −0.0651369 + 0.369410i
\(357\) 0.0122172 + 0.0692869i 0.000646600 + 0.00366705i
\(358\) −9.91733 + 3.60961i −0.524147 + 0.190774i
\(359\) 21.4311 + 17.9828i 1.13109 + 0.949097i 0.999111 0.0421551i \(-0.0134224\pi\)
0.131979 + 0.991252i \(0.457867\pi\)
\(360\) 0 0
\(361\) −0.917004 + 18.9779i −0.0482634 + 0.998835i
\(362\) 0.434275 0.0228250
\(363\) 6.66784 + 5.59498i 0.349971 + 0.293660i
\(364\) −4.53625 + 1.65106i −0.237764 + 0.0865390i
\(365\) 0 0
\(366\) −0.930566 + 5.27750i −0.0486414 + 0.275859i
\(367\) 23.8004 + 8.66262i 1.24237 + 0.452185i 0.877816 0.478998i \(-0.159000\pi\)
0.364552 + 0.931183i \(0.381222\pi\)
\(368\) −4.05013 7.01502i −0.211127 0.365683i
\(369\) 9.11380 15.7856i 0.474445 0.821763i
\(370\) 0 0
\(371\) −19.3142 + 16.2065i −1.00274 + 0.841400i
\(372\) −1.98975 + 3.44635i −0.103164 + 0.178685i
\(373\) 10.6981 + 18.5296i 0.553925 + 0.959427i 0.997986 + 0.0634302i \(0.0202040\pi\)
−0.444061 + 0.895997i \(0.646463\pi\)
\(374\) 0.0396205 + 0.0144207i 0.00204873 + 0.000745676i
\(375\) 0 0
\(376\) −1.26485 7.17332i −0.0652296 0.369936i
\(377\) −13.1595 + 4.78968i −0.677750 + 0.246681i
\(378\) 7.63579 + 6.40719i 0.392743 + 0.329550i
\(379\) 37.8831 1.94592 0.972961 0.230968i \(-0.0741894\pi\)
0.972961 + 0.230968i \(0.0741894\pi\)
\(380\) 0 0
\(381\) 13.1852 0.675497
\(382\) −20.2776 17.0150i −1.03749 0.870561i
\(383\) −3.09921 + 1.12802i −0.158362 + 0.0576391i −0.419985 0.907531i \(-0.637965\pi\)
0.261623 + 0.965170i \(0.415742\pi\)
\(384\) 0.156215 + 0.885940i 0.00797182 + 0.0452105i
\(385\) 0 0
\(386\) 11.2801 + 4.10561i 0.574140 + 0.208970i
\(387\) 0.764730 + 1.32455i 0.0388734 + 0.0673307i
\(388\) −4.14212 + 7.17436i −0.210284 + 0.364223i
\(389\) 3.32824 2.79272i 0.168748 0.141597i −0.554503 0.832182i \(-0.687091\pi\)
0.723251 + 0.690585i \(0.242647\pi\)
\(390\) 0 0
\(391\) −0.148387 + 0.257013i −0.00750424 + 0.0129977i
\(392\) −1.22170 2.11605i −0.0617051 0.106876i
\(393\) 4.36368 + 1.58825i 0.220119 + 0.0801167i
\(394\) 4.23213 24.0016i 0.213212 1.20918i
\(395\) 0 0
\(396\) 2.36907 0.862272i 0.119050 0.0433308i
\(397\) 19.8582 + 16.6630i 0.996654 + 0.836292i 0.986517 0.163656i \(-0.0523289\pi\)
0.0101368 + 0.999949i \(0.496773\pi\)
\(398\) −0.257470 −0.0129058
\(399\) −0.528039 8.35381i −0.0264350 0.418213i
\(400\) 0 0
\(401\) 2.96077 + 2.48438i 0.147854 + 0.124064i 0.713714 0.700437i \(-0.247011\pi\)
−0.565861 + 0.824501i \(0.691456\pi\)
\(402\) 8.26126 3.00685i 0.412034 0.149968i
\(403\) 1.73715 + 9.85184i 0.0865334 + 0.490755i
\(404\) 0.0655937 0.372001i 0.00326341 0.0185077i
\(405\) 0 0
\(406\) 6.60928 + 11.4476i 0.328013 + 0.568136i
\(407\) −3.25025 + 5.62960i −0.161109 + 0.279049i
\(408\) 0.0252484 0.0211859i 0.00124998 0.00104886i
\(409\) −6.68991 + 5.61350i −0.330795 + 0.277570i −0.793024 0.609191i \(-0.791494\pi\)
0.462229 + 0.886761i \(0.347050\pi\)
\(410\) 0 0
\(411\) −6.85398 11.8714i −0.338082 0.585575i
\(412\) 12.9794 + 4.72411i 0.639449 + 0.232740i
\(413\) −0.614978 + 3.48772i −0.0302611 + 0.171619i
\(414\) 3.08143 + 17.4757i 0.151444 + 0.858883i
\(415\) 0 0
\(416\) 1.73239 + 1.45364i 0.0849372 + 0.0712708i
\(417\) 8.82168 0.432000
\(418\) −4.49383 2.22911i −0.219800 0.109029i
\(419\) 1.35441 0.0661673 0.0330836 0.999453i \(-0.489467\pi\)
0.0330836 + 0.999453i \(0.489467\pi\)
\(420\) 0 0
\(421\) 2.38379 0.867629i 0.116179 0.0422856i −0.283277 0.959038i \(-0.591421\pi\)
0.399455 + 0.916753i \(0.369199\pi\)
\(422\) −0.466630 2.64639i −0.0227152 0.128824i
\(423\) −2.77091 + 15.7146i −0.134726 + 0.764072i
\(424\) 11.0991 + 4.03974i 0.539019 + 0.196187i
\(425\) 0 0
\(426\) 4.41330 7.64406i 0.213825 0.370356i
\(427\) 9.74088 8.17357i 0.471394 0.395547i
\(428\) 4.96206 4.16366i 0.239850 0.201258i
\(429\) −1.17064 + 2.02760i −0.0565188 + 0.0978935i
\(430\) 0 0
\(431\) 13.9605 + 5.08122i 0.672455 + 0.244754i 0.655605 0.755104i \(-0.272414\pi\)
0.0168504 + 0.999858i \(0.494636\pi\)
\(432\) 0.810867 4.59866i 0.0390129 0.221253i
\(433\) −0.474466 2.69083i −0.0228014 0.129313i 0.971282 0.237930i \(-0.0764689\pi\)
−0.994084 + 0.108617i \(0.965358\pi\)
\(434\) 8.87323 3.22959i 0.425929 0.155025i
\(435\) 0 0
\(436\) −1.71733 −0.0822451
\(437\) 20.9442 28.4255i 1.00190 1.35978i
\(438\) −5.30283 −0.253379
\(439\) 22.0695 + 18.5185i 1.05332 + 0.883839i 0.993439 0.114366i \(-0.0364837\pi\)
0.0598800 + 0.998206i \(0.480928\pi\)
\(440\) 0 0
\(441\) 0.929499 + 5.27145i 0.0442618 + 0.251021i
\(442\) 0.0143876 0.0815959i 0.000684346 0.00388112i
\(443\) 12.8763 + 4.68659i 0.611772 + 0.222667i 0.629278 0.777180i \(-0.283351\pi\)
−0.0175066 + 0.999847i \(0.505573\pi\)
\(444\) 2.54075 + 4.40070i 0.120579 + 0.208848i
\(445\) 0 0
\(446\) −4.68654 + 3.93247i −0.221914 + 0.186208i
\(447\) −15.2796 + 12.8211i −0.722700 + 0.606418i
\(448\) 1.06731 1.84863i 0.0504257 0.0873398i
\(449\) 10.4586 + 18.1148i 0.493572 + 0.854891i 0.999973 0.00740712i \(-0.00235778\pi\)
−0.506401 + 0.862298i \(0.669024\pi\)
\(450\) 0 0
\(451\) 1.66274 9.42985i 0.0782952 0.444034i
\(452\) 1.20258 + 6.82016i 0.0565645 + 0.320793i
\(453\) −14.8024 + 5.38762i −0.695476 + 0.253132i
\(454\) 0.752136 + 0.631117i 0.0352995 + 0.0296198i
\(455\) 0 0
\(456\) −3.26549 + 2.17097i −0.152921 + 0.101665i
\(457\) 40.8499 1.91088 0.955438 0.295190i \(-0.0953831\pi\)
0.955438 + 0.295190i \(0.0953831\pi\)
\(458\) 15.3867 + 12.9110i 0.718973 + 0.603290i
\(459\) −0.160765 + 0.0585137i −0.00750387 + 0.00273118i
\(460\) 0 0
\(461\) 5.01978 28.4686i 0.233794 1.32591i −0.611344 0.791365i \(-0.709371\pi\)
0.845138 0.534548i \(-0.179518\pi\)
\(462\) 2.07667 + 0.755846i 0.0966154 + 0.0351651i
\(463\) 16.0908 + 27.8701i 0.747803 + 1.29523i 0.948874 + 0.315656i \(0.102224\pi\)
−0.201071 + 0.979577i \(0.564442\pi\)
\(464\) 3.09623 5.36284i 0.143739 0.248963i
\(465\) 0 0
\(466\) −12.3275 + 10.3440i −0.571059 + 0.479175i
\(467\) −18.4169 + 31.8990i −0.852232 + 1.47611i 0.0269574 + 0.999637i \(0.491418\pi\)
−0.879189 + 0.476472i \(0.841915\pi\)
\(468\) −2.47711 4.29048i −0.114504 0.198327i
\(469\) −19.6026 7.13476i −0.905164 0.329453i
\(470\) 0 0
\(471\) −3.31012 18.7726i −0.152522 0.864997i
\(472\) 1.55903 0.567441i 0.0717602 0.0261186i
\(473\) 0.615483 + 0.516451i 0.0282999 + 0.0237465i
\(474\) −8.14460 −0.374094
\(475\) 0 0
\(476\) −0.0782072 −0.00358462
\(477\) −19.8216 16.6323i −0.907570 0.761542i
\(478\) −8.06973 + 2.93714i −0.369101 + 0.134342i
\(479\) −1.28216 7.27148i −0.0585833 0.332242i 0.941404 0.337281i \(-0.109507\pi\)
−0.999987 + 0.00503861i \(0.998396\pi\)
\(480\) 0 0
\(481\) 12.0037 + 4.36899i 0.547321 + 0.199209i
\(482\) 5.95393 + 10.3125i 0.271194 + 0.469722i
\(483\) −7.77754 + 13.4711i −0.353890 + 0.612956i
\(484\) −7.41195 + 6.21936i −0.336907 + 0.282698i
\(485\) 0 0
\(486\) −8.07102 + 13.9794i −0.366109 + 0.634119i
\(487\) −13.2286 22.9127i −0.599446 1.03827i −0.992903 0.118928i \(-0.962054\pi\)
0.393457 0.919343i \(-0.371279\pi\)
\(488\) −5.59770 2.03740i −0.253396 0.0922286i
\(489\) −1.50023 + 8.50824i −0.0678429 + 0.384756i
\(490\) 0 0
\(491\) 7.54434 2.74591i 0.340471 0.123921i −0.166125 0.986105i \(-0.553126\pi\)
0.506596 + 0.862183i \(0.330903\pi\)
\(492\) −5.73393 4.81134i −0.258505 0.216912i
\(493\) −0.226877 −0.0102180
\(494\) −2.78041 + 9.45727i −0.125096 + 0.425503i
\(495\) 0 0
\(496\) −3.38867 2.84343i −0.152156 0.127674i
\(497\) −19.6810 + 7.16329i −0.882812 + 0.321317i
\(498\) 0.854489 + 4.84605i 0.0382906 + 0.217157i
\(499\) 3.76753 21.3667i 0.168658 0.956506i −0.776555 0.630050i \(-0.783034\pi\)
0.945212 0.326456i \(-0.105854\pi\)
\(500\) 0 0
\(501\) −3.23178 5.59760i −0.144385 0.250082i
\(502\) −8.96909 + 15.5349i −0.400310 + 0.693358i
\(503\) 15.1058 12.6753i 0.673536 0.565164i −0.240574 0.970631i \(-0.577336\pi\)
0.914110 + 0.405467i \(0.132891\pi\)
\(504\) −3.58227 + 3.00588i −0.159567 + 0.133893i
\(505\) 0 0
\(506\) 4.66097 + 8.07304i 0.207206 + 0.358891i
\(507\) −6.66626 2.42632i −0.296059 0.107757i
\(508\) −2.54509 + 14.4339i −0.112920 + 0.640402i
\(509\) 0.901498 + 5.11265i 0.0399582 + 0.226614i 0.998247 0.0591880i \(-0.0188511\pi\)
−0.958289 + 0.285802i \(0.907740\pi\)
\(510\) 0 0
\(511\) 9.63894 + 8.08803i 0.426402 + 0.357793i
\(512\) −1.00000 −0.0441942
\(513\) 19.7822 4.79196i 0.873405 0.211570i
\(514\) 27.2472 1.20182
\(515\) 0 0
\(516\) 0.590191 0.214812i 0.0259817 0.00945657i
\(517\) 1.45562 + 8.25521i 0.0640179 + 0.363064i
\(518\) 2.09377 11.8744i 0.0919951 0.521730i
\(519\) −21.4712 7.81487i −0.942481 0.343035i
\(520\) 0 0
\(521\) −14.6395 + 25.3563i −0.641366 + 1.11088i 0.343762 + 0.939057i \(0.388299\pi\)
−0.985128 + 0.171822i \(0.945035\pi\)
\(522\) −10.3921 + 8.71998i −0.454849 + 0.381663i
\(523\) −1.39649 + 1.17180i −0.0610643 + 0.0512390i −0.672809 0.739816i \(-0.734912\pi\)
0.611745 + 0.791055i \(0.290468\pi\)
\(524\) −2.58098 + 4.47039i −0.112751 + 0.195290i
\(525\) 0 0
\(526\) −0.470923 0.171402i −0.0205332 0.00747348i
\(527\) −0.0281431 + 0.159607i −0.00122593 + 0.00695261i
\(528\) −0.179776 1.01956i −0.00782374 0.0443706i
\(529\) −40.0441 + 14.5749i −1.74105 + 0.633690i
\(530\) 0 0
\(531\) −3.63457 −0.157727
\(532\) 9.24691 + 1.03446i 0.400904 + 0.0448495i
\(533\) −18.8164 −0.815027
\(534\) −4.87741 4.09263i −0.211066 0.177106i
\(535\) 0 0
\(536\) 1.69698 + 9.62407i 0.0732985 + 0.415697i
\(537\) 1.64866 9.35004i 0.0711451 0.403484i
\(538\) 19.3314 + 7.03604i 0.833434 + 0.303345i
\(539\) 1.40596 + 2.43519i 0.0605589 + 0.104891i
\(540\) 0 0
\(541\) 9.50497 7.97562i 0.408651 0.342899i −0.415175 0.909741i \(-0.636280\pi\)
0.823826 + 0.566843i \(0.191835\pi\)
\(542\) −8.26521 + 6.93533i −0.355021 + 0.297898i
\(543\) −0.195339 + 0.338336i −0.00838278 + 0.0145194i
\(544\) 0.0183188 + 0.0317290i 0.000785411 + 0.00136037i
\(545\) 0 0
\(546\) 0.754109 4.27677i 0.0322729 0.183029i
\(547\) 6.88009 + 39.0189i 0.294171 + 1.66833i 0.670551 + 0.741863i \(0.266058\pi\)
−0.376380 + 0.926465i \(0.622831\pi\)
\(548\) 14.3188 5.21160i 0.611667 0.222629i
\(549\) 9.99682 + 8.38833i 0.426654 + 0.358005i
\(550\) 0 0
\(551\) 26.8250 + 3.00093i 1.14278 + 0.127844i
\(552\) 7.28705 0.310157
\(553\) 14.8044 + 12.4224i 0.629548 + 0.528254i
\(554\) 18.9738 6.90589i 0.806119 0.293403i
\(555\) 0 0
\(556\) −1.70282 + 9.65717i −0.0722156 + 0.409555i
\(557\) −37.8354 13.7710i −1.60314 0.583495i −0.623072 0.782165i \(-0.714116\pi\)
−0.980066 + 0.198670i \(0.936338\pi\)
\(558\) 4.84540 + 8.39248i 0.205122 + 0.355282i
\(559\) 0.789431 1.36733i 0.0333894 0.0578321i
\(560\) 0 0
\(561\) −0.0290564 + 0.0243812i −0.00122676 + 0.00102937i
\(562\) −0.565472 + 0.979426i −0.0238530 + 0.0413146i
\(563\) 4.61587 + 7.99492i 0.194536 + 0.336946i 0.946748 0.321975i \(-0.104347\pi\)
−0.752213 + 0.658921i \(0.771013\pi\)
\(564\) 6.15754 + 2.24116i 0.259279 + 0.0943699i
\(565\) 0 0
\(566\) −1.31197 7.44055i −0.0551462 0.312750i
\(567\) 4.75659 1.73126i 0.199758 0.0727059i
\(568\) 7.51613 + 6.30678i 0.315370 + 0.264627i
\(569\) 1.97117 0.0826355 0.0413178 0.999146i \(-0.486844\pi\)
0.0413178 + 0.999146i \(0.486844\pi\)
\(570\) 0 0
\(571\) −13.6836 −0.572642 −0.286321 0.958134i \(-0.592432\pi\)
−0.286321 + 0.958134i \(0.592432\pi\)
\(572\) −1.99367 1.67289i −0.0833594 0.0699469i
\(573\) 22.3770 8.14457i 0.934814 0.340244i
\(574\) 3.08415 + 17.4911i 0.128730 + 0.730064i
\(575\) 0 0
\(576\) 2.05859 + 0.749266i 0.0857746 + 0.0312194i
\(577\) 11.7284 + 20.3142i 0.488260 + 0.845692i 0.999909 0.0135033i \(-0.00429835\pi\)
−0.511649 + 0.859195i \(0.670965\pi\)
\(578\) −8.49933 + 14.7213i −0.353525 + 0.612324i
\(579\) −8.27243 + 6.94139i −0.343790 + 0.288474i
\(580\) 0 0
\(581\) 5.83813 10.1119i 0.242207 0.419514i
\(582\) −3.72628 6.45411i −0.154459 0.267532i
\(583\) −12.7731 4.64902i −0.529006 0.192543i
\(584\) 1.02359 5.80505i 0.0423564 0.240215i
\(585\) 0 0
\(586\) −15.8330 + 5.76276i −0.654057 + 0.238057i
\(587\) 13.5997 + 11.4115i 0.561320 + 0.471004i 0.878753 0.477277i \(-0.158376\pi\)
−0.317432 + 0.948281i \(0.602821\pi\)
\(588\) 2.19810 0.0906481
\(589\) 5.43868 18.4991i 0.224097 0.762242i
\(590\) 0 0
\(591\) 16.7956 + 14.0932i 0.690879 + 0.579716i
\(592\) −5.30792 + 1.93193i −0.218154 + 0.0794016i
\(593\) −7.21492 40.9178i −0.296281 1.68029i −0.661949 0.749549i \(-0.730270\pi\)
0.365668 0.930746i \(-0.380841\pi\)
\(594\) −0.933164 + 5.29223i −0.0382882 + 0.217143i
\(595\) 0 0
\(596\) −11.0860 19.2015i −0.454101 0.786525i
\(597\) 0.115811 0.200591i 0.00473983 0.00820963i
\(598\) 14.0328 11.7749i 0.573842 0.481511i
\(599\) 20.4270 17.1403i 0.834624 0.700333i −0.121724 0.992564i \(-0.538842\pi\)
0.956348 + 0.292231i \(0.0943978\pi\)
\(600\) 0 0
\(601\) 7.11077 + 12.3162i 0.290054 + 0.502389i 0.973822 0.227311i \(-0.0729933\pi\)
−0.683768 + 0.729699i \(0.739660\pi\)
\(602\) −1.40043 0.509713i −0.0570771 0.0207744i
\(603\) 3.71759 21.0835i 0.151392 0.858587i
\(604\) −3.04062 17.2442i −0.123721 0.701658i
\(605\) 0 0
\(606\) 0.260315 + 0.218430i 0.0105746 + 0.00887312i
\(607\) 14.9537 0.606953 0.303476 0.952839i \(-0.401853\pi\)
0.303476 + 0.952839i \(0.401853\pi\)
\(608\) −1.74625 3.99382i −0.0708199 0.161971i
\(609\) −11.8915 −0.481869
\(610\) 0 0
\(611\) 15.4791 5.63392i 0.626216 0.227924i
\(612\) −0.0139374 0.0790427i −0.000563385 0.00319511i
\(613\) 0.854395 4.84551i 0.0345087 0.195708i −0.962680 0.270643i \(-0.912764\pi\)
0.997188 + 0.0749346i \(0.0238748\pi\)
\(614\) −18.3440 6.67668i −0.740305 0.269449i
\(615\) 0 0
\(616\) −1.22828 + 2.12745i −0.0494890 + 0.0857174i
\(617\) 17.3980 14.5987i 0.700419 0.587721i −0.221474 0.975166i \(-0.571087\pi\)
0.921893 + 0.387445i \(0.126642\pi\)
\(618\) −9.51865 + 7.98710i −0.382896 + 0.321288i
\(619\) −6.64360 + 11.5071i −0.267029 + 0.462508i −0.968093 0.250590i \(-0.919375\pi\)
0.701064 + 0.713098i \(0.252709\pi\)
\(620\) 0 0
\(621\) −35.5438 12.9369i −1.42632 0.519139i
\(622\) −5.57174 + 31.5989i −0.223406 + 1.26700i
\(623\) 2.62345 + 14.8783i 0.105106 + 0.596088i
\(624\) −1.91174 + 0.695817i −0.0765309 + 0.0278550i
\(625\) 0 0
\(626\) −6.51280 −0.260304
\(627\) 3.75800 2.49840i 0.150080 0.0997766i
\(628\) 21.1895 0.845553
\(629\) 0.158533 + 0.133025i 0.00632111 + 0.00530404i
\(630\) 0 0
\(631\) −6.43164 36.4757i −0.256040 1.45207i −0.793390 0.608714i \(-0.791686\pi\)
0.537350 0.843359i \(-0.319425\pi\)
\(632\) 1.57213 8.91597i 0.0625358 0.354658i
\(633\) 2.27165 + 0.826812i 0.0902899 + 0.0328628i
\(634\) 3.84856 + 6.66590i 0.152846 + 0.264737i
\(635\) 0 0
\(636\) −8.13970 + 6.83002i −0.322760 + 0.270828i
\(637\) 4.23291 3.55183i 0.167714 0.140729i
\(638\) −3.56322 + 6.17167i −0.141069 + 0.244339i
\(639\) −10.7472 18.6147i −0.425152 0.736385i
\(640\) 0 0
\(641\) −5.38419 + 30.5353i −0.212663 + 1.20607i 0.672254 + 0.740321i \(0.265326\pi\)
−0.884917 + 0.465749i \(0.845785\pi\)
\(642\) 1.01189 + 5.73869i 0.0399359 + 0.226488i
\(643\) −15.2806 + 5.56168i −0.602608 + 0.219331i −0.625266 0.780412i \(-0.715009\pi\)
0.0226580 + 0.999743i \(0.492787\pi\)
\(644\) −13.2456 11.1144i −0.521951 0.437969i
\(645\) 0 0
\(646\) −0.0947309 + 0.128569i −0.00372714 + 0.00505847i
\(647\) 47.0983 1.85162 0.925812 0.377985i \(-0.123383\pi\)
0.925812 + 0.377985i \(0.123383\pi\)
\(648\) −1.81653 1.52425i −0.0713601 0.0598783i
\(649\) −1.79417 + 0.653024i −0.0704272 + 0.0256334i
\(650\) 0 0
\(651\) −1.47509 + 8.36566i −0.0578134 + 0.327876i
\(652\) −9.02446 3.28463i −0.353425 0.128636i
\(653\) 13.1067 + 22.7015i 0.512906 + 0.888380i 0.999888 + 0.0149675i \(0.00476448\pi\)
−0.486982 + 0.873412i \(0.661902\pi\)
\(654\) 0.772461 1.33794i 0.0302056 0.0523176i
\(655\) 0 0
\(656\) 6.37381 5.34826i 0.248855 0.208815i
\(657\) −6.45668 + 11.1833i −0.251899 + 0.436302i
\(658\) −7.77426 13.4654i −0.303072 0.524937i
\(659\) −7.18816 2.61628i −0.280011 0.101916i 0.198197 0.980162i \(-0.436491\pi\)
−0.478208 + 0.878246i \(0.658714\pi\)
\(660\) 0 0
\(661\) −8.35220 47.3677i −0.324863 1.84239i −0.510635 0.859797i \(-0.670590\pi\)
0.185772 0.982593i \(-0.440521\pi\)
\(662\) −18.9600 + 6.90087i −0.736900 + 0.268210i
\(663\) 0.0570984 + 0.0479112i 0.00221752 + 0.00186072i
\(664\) −5.46995 −0.212275
\(665\) 0 0
\(666\) 12.3744 0.479497
\(667\) −38.4252 32.2426i −1.48783 1.24844i
\(668\) 6.75156 2.45737i 0.261226 0.0950784i
\(669\) −0.955699 5.42004i −0.0369495 0.209551i
\(670\) 0 0
\(671\) 6.44196 + 2.34468i 0.248689 + 0.0905154i
\(672\) 0.960160 + 1.66305i 0.0370390 + 0.0641534i
\(673\) −22.2011 + 38.4534i −0.855789 + 1.48227i 0.0201219 + 0.999798i \(0.493595\pi\)
−0.875911 + 0.482473i \(0.839739\pi\)
\(674\) −5.49032 + 4.60693i −0.211479 + 0.177452i
\(675\) 0 0
\(676\) 3.94288 6.82927i 0.151649 0.262664i
\(677\) −1.53312 2.65544i −0.0589226 0.102057i 0.835059 0.550160i \(-0.185433\pi\)
−0.893982 + 0.448103i \(0.852100\pi\)
\(678\) −5.85439 2.13083i −0.224837 0.0818339i
\(679\) −3.07074 + 17.4151i −0.117844 + 0.668328i
\(680\) 0 0
\(681\) −0.830006 + 0.302097i −0.0318059 + 0.0115764i
\(682\) 3.89976 + 3.27228i 0.149329 + 0.125302i
\(683\) 31.7607 1.21529 0.607644 0.794210i \(-0.292115\pi\)
0.607644 + 0.794210i \(0.292115\pi\)
\(684\) 0.602389 + 9.53005i 0.0230329 + 0.364391i
\(685\) 0 0
\(686\) −15.4420 12.9574i −0.589577 0.494714i
\(687\) −16.9797 + 6.18011i −0.647816 + 0.235786i
\(688\) 0.121234 + 0.687551i 0.00462200 + 0.0262126i
\(689\) −4.63833 + 26.3053i −0.176706 + 1.00215i
\(690\) 0 0
\(691\) 6.89195 + 11.9372i 0.262182 + 0.454112i 0.966821 0.255453i \(-0.0822246\pi\)
−0.704640 + 0.709565i \(0.748891\pi\)
\(692\) 12.6995 21.9962i 0.482763 0.836171i
\(693\) 4.12256 3.45924i 0.156603 0.131406i
\(694\) 5.70800 4.78958i 0.216673 0.181810i
\(695\) 0 0
\(696\) 2.78540 + 4.82445i 0.105580 + 0.182870i
\(697\) −0.286456 0.104261i −0.0108503 0.00394918i
\(698\) −4.53756 + 25.7338i −0.171749 + 0.974037i
\(699\) −2.51387 14.2569i −0.0950833 0.539244i
\(700\) 0 0
\(701\) −22.8905 19.2074i −0.864562 0.725454i 0.0983834 0.995149i \(-0.468633\pi\)
−0.962946 + 0.269695i \(0.913077\pi\)
\(702\) 10.5601 0.398567
\(703\) −16.9847 17.8252i −0.640591 0.672292i
\(704\) 1.15082 0.0433732
\(705\) 0 0
\(706\) 13.2211 4.81209i 0.497583 0.181105i
\(707\) −0.140018 0.794080i −0.00526591 0.0298644i
\(708\) −0.259175 + 1.46985i −0.00974037 + 0.0552404i
\(709\) 24.2954 + 8.84281i 0.912433 + 0.332099i 0.755224 0.655467i \(-0.227528\pi\)
0.157209 + 0.987565i \(0.449750\pi\)
\(710\) 0 0
\(711\) −9.91679 + 17.1764i −0.371909 + 0.644165i
\(712\) 5.42171 4.54935i 0.203187 0.170494i
\(713\) −27.4491 + 23.0325i −1.02798 + 0.862574i
\(714\) 0.0351779 0.0609299i 0.00131650 0.00228024i
\(715\) 0 0
\(716\) 9.91733 + 3.60961i 0.370628 + 0.134898i
\(717\) 1.34152 7.60813i 0.0500999 0.284131i
\(718\) −4.85804 27.5513i −0.181300 1.02821i
\(719\) 17.7416 6.45741i 0.661650 0.240821i 0.0107012 0.999943i \(-0.496594\pi\)
0.650948 + 0.759122i \(0.274371\pi\)
\(720\) 0 0
\(721\) 29.4842 1.09805
\(722\) 12.9012 13.9484i 0.480133 0.519107i
\(723\) −10.7124 −0.398398
\(724\) −0.332674 0.279147i −0.0123637 0.0103744i
\(725\) 0 0
\(726\) −1.51148 8.57201i −0.0560962 0.318137i
\(727\) 5.17269 29.3358i 0.191845 1.08800i −0.724997 0.688752i \(-0.758159\pi\)
0.916841 0.399252i \(-0.130730\pi\)
\(728\) 4.53625 + 1.65106i 0.168125 + 0.0611923i
\(729\) −3.70378 6.41513i −0.137177 0.237598i
\(730\) 0 0
\(731\) 0.0195945 0.0164417i 0.000724728 0.000608119i
\(732\) 4.10517 3.44464i 0.151731 0.127318i
\(733\) 6.66338 11.5413i 0.246118 0.426288i −0.716328 0.697764i \(-0.754178\pi\)
0.962445 + 0.271476i \(0.0875117\pi\)
\(734\) −12.6639 21.9345i −0.467433 0.809618i
\(735\) 0 0
\(736\) −1.40659 + 7.97719i −0.0518477 + 0.294043i
\(737\) −1.95293 11.0756i −0.0719370 0.407975i
\(738\) −17.1283 + 6.23421i −0.630503 + 0.229484i
\(739\) −36.7309 30.8208i −1.35117 1.13376i −0.978603 0.205756i \(-0.934035\pi\)
−0.372563 0.928007i \(-0.621521\pi\)
\(740\) 0 0
\(741\) −6.11736 6.42008i −0.224727 0.235848i
\(742\) 25.2128 0.925592
\(743\) −26.6169 22.3342i −0.976478 0.819362i 0.00707666 0.999975i \(-0.497747\pi\)
−0.983554 + 0.180613i \(0.942192\pi\)
\(744\) 3.73951 1.36107i 0.137097 0.0498992i
\(745\) 0 0
\(746\) 3.71540 21.0711i 0.136031 0.771468i
\(747\) 11.2604 + 4.09845i 0.411996 + 0.149954i
\(748\) −0.0210816 0.0365145i −0.000770821 0.00133510i
\(749\) 6.91351 11.9745i 0.252614 0.437541i
\(750\) 0 0
\(751\) −16.8228 + 14.1160i −0.613873 + 0.515101i −0.895871 0.444314i \(-0.853447\pi\)
0.281998 + 0.959415i \(0.409003\pi\)
\(752\) −3.64199 + 6.30811i −0.132810 + 0.230033i
\(753\) −8.06866 13.9753i −0.294038 0.509290i
\(754\) 13.1595 + 4.78968i 0.479242 + 0.174430i
\(755\) 0 0
\(756\) −1.73089 9.81638i −0.0629520 0.357018i
\(757\) −8.72443 + 3.17543i −0.317095 + 0.115413i −0.495664 0.868514i \(-0.665075\pi\)
0.178569 + 0.983927i \(0.442853\pi\)
\(758\) −29.0201 24.3508i −1.05406 0.884460i
\(759\) −8.38609 −0.304396
\(760\) 0 0
\(761\) −13.5581 −0.491482 −0.245741 0.969336i \(-0.579031\pi\)
−0.245741 + 0.969336i \(0.579031\pi\)
\(762\) −10.1004 8.47527i −0.365900 0.307027i
\(763\) −3.44477 + 1.25379i −0.124709 + 0.0453903i
\(764\) 4.59657 + 26.0684i 0.166298 + 0.943123i
\(765\) 0 0
\(766\) 3.09921 + 1.12802i 0.111979 + 0.0407570i
\(767\) 1.87599 + 3.24930i 0.0677379 + 0.117326i
\(768\) 0.449804 0.779083i 0.0162309 0.0281127i
\(769\) −15.1389 + 12.7031i −0.545924 + 0.458085i −0.873558 0.486720i \(-0.838193\pi\)
0.327634 + 0.944805i \(0.393749\pi\)
\(770\) 0 0
\(771\) −12.2559 + 21.2278i −0.441385 + 0.764501i
\(772\) −6.00200 10.3958i −0.216017 0.374152i
\(773\) 16.0490 + 5.84138i 0.577244 + 0.210100i 0.614110 0.789221i \(-0.289515\pi\)
−0.0368657 + 0.999320i \(0.511737\pi\)
\(774\) 0.265588 1.50622i 0.00954636 0.0541401i
\(775\) 0 0
\(776\) 7.78464 2.83338i 0.279452 0.101712i
\(777\) 8.30933 + 6.97236i 0.298096 + 0.250132i
\(778\) −4.34471 −0.155765
\(779\) 32.4903 + 16.1164i 1.16409 + 0.577431i
\(780\) 0 0
\(781\) −8.64973 7.25798i −0.309512 0.259711i
\(782\) 0.278876 0.101502i 0.00997257 0.00362972i
\(783\) −5.02127 28.4770i −0.179446 1.01769i
\(784\) −0.424292 + 2.40628i −0.0151533 + 0.0859385i
\(785\) 0 0
\(786\) −2.32187 4.02159i −0.0828183 0.143445i
\(787\) 12.5839 21.7960i 0.448568 0.776942i −0.549725 0.835346i \(-0.685268\pi\)
0.998293 + 0.0584033i \(0.0186009\pi\)
\(788\) −18.6699 + 15.6659i −0.665089 + 0.558076i
\(789\) 0.345359 0.289791i 0.0122951 0.0103168i
\(790\) 0 0
\(791\) 7.39152 + 12.8025i 0.262812 + 0.455204i
\(792\) −2.36907 0.862272i −0.0841813 0.0306395i
\(793\) 2.33929 13.2668i 0.0830707 0.471117i
\(794\) −4.50149 25.5292i −0.159752 0.905997i
\(795\) 0 0
\(796\) 0.197234 + 0.165499i 0.00699076 + 0.00586594i
\(797\) 28.2917 1.00214 0.501071 0.865406i \(-0.332939\pi\)
0.501071 + 0.865406i \(0.332939\pi\)
\(798\) −4.96522 + 6.73880i −0.175767 + 0.238551i
\(799\) 0.266867 0.00944107
\(800\) 0 0
\(801\) −14.5698 + 5.30296i −0.514797 + 0.187371i
\(802\) −0.671152 3.80629i −0.0236992 0.134405i
\(803\) −1.17797 + 6.68058i −0.0415696 + 0.235753i
\(804\) −8.26126 3.00685i −0.291352 0.106044i
\(805\) 0 0
\(806\) 5.00191 8.66356i 0.176185 0.305161i
\(807\) −14.1770 + 11.8959i −0.499053 + 0.418755i
\(808\) −0.289365 + 0.242806i −0.0101798 + 0.00854189i
\(809\) −1.15497 + 2.00046i −0.0406064 + 0.0703324i −0.885614 0.464421i \(-0.846262\pi\)
0.845008 + 0.534754i \(0.179596\pi\)
\(810\) 0 0
\(811\) −12.1095 4.40751i −0.425223 0.154769i 0.120539 0.992709i \(-0.461538\pi\)
−0.545762 + 0.837940i \(0.683760\pi\)
\(812\) 2.29538 13.0177i 0.0805521 0.456833i
\(813\) −1.68548 9.55882i −0.0591123 0.335242i
\(814\) 6.10847 2.22330i 0.214102 0.0779267i
\(815\) 0 0
\(816\) −0.0329594 −0.00115381
\(817\) −2.53425 + 1.68482i −0.0886622 + 0.0589446i
\(818\) 8.73306 0.305344
\(819\) −8.10120 6.79771i −0.283079 0.237531i
\(820\) 0 0
\(821\) 2.54626 + 14.4405i 0.0888650 + 0.503978i 0.996455 + 0.0841217i \(0.0268085\pi\)
−0.907591 + 0.419856i \(0.862080\pi\)
\(822\) −2.38036 + 13.4997i −0.0830246 + 0.470856i
\(823\) 31.3707 + 11.4180i 1.09351 + 0.398006i 0.824921 0.565248i \(-0.191219\pi\)
0.268592 + 0.963254i \(0.413442\pi\)
\(824\) −6.90619 11.9619i −0.240589 0.416712i
\(825\) 0 0
\(826\) 2.71296 2.27644i 0.0943960 0.0792076i
\(827\) 5.64874 4.73986i 0.196426 0.164821i −0.539270 0.842133i \(-0.681300\pi\)
0.735696 + 0.677312i \(0.236855\pi\)
\(828\) 8.87264 15.3679i 0.308345 0.534070i
\(829\) −3.66811 6.35335i −0.127399 0.220661i 0.795269 0.606256i \(-0.207329\pi\)
−0.922668 + 0.385595i \(0.873996\pi\)
\(830\) 0 0
\(831\) −3.15421 + 17.8884i −0.109418 + 0.620543i
\(832\) −0.392700 2.22711i −0.0136144 0.0772112i
\(833\) 0.0841214 0.0306177i 0.00291463 0.00106084i
\(834\) −6.75780 5.67047i −0.234003 0.196352i
\(835\) 0 0
\(836\) 2.00963 + 4.59618i 0.0695044 + 0.158962i
\(837\) −20.6564 −0.713990
\(838\) −1.03754 0.870598i −0.0358412 0.0300743i
\(839\) −14.5357 + 5.29055i −0.501827 + 0.182650i −0.580516 0.814249i \(-0.697149\pi\)
0.0786886 + 0.996899i \(0.474927\pi\)
\(840\) 0 0
\(841\) 1.62303 9.20468i 0.0559667 0.317403i
\(842\) −2.38379 0.867629i −0.0821508 0.0299005i
\(843\) −0.508702 0.881099i −0.0175206 0.0303466i
\(844\) −1.34361 + 2.32720i −0.0462489 + 0.0801054i
\(845\) 0 0
\(846\) 12.2238 10.2570i 0.420263 0.352643i
\(847\) −10.3269 + 17.8867i −0.354836 + 0.614593i
\(848\) −5.90570 10.2290i −0.202802 0.351264i
\(849\) 6.38693 + 2.32465i 0.219199 + 0.0797819i
\(850\) 0 0
\(851\) 7.94525 + 45.0597i 0.272360 + 1.54463i
\(852\) −8.29429 + 3.01887i −0.284158 + 0.103425i
\(853\) −29.8285 25.0291i −1.02131 0.856980i −0.0315176 0.999503i \(-0.510034\pi\)
−0.989791 + 0.142523i \(0.954478\pi\)
\(854\) −12.7158 −0.435126
\(855\) 0 0
\(856\) −6.47751 −0.221397
\(857\) −40.6768 34.1319i −1.38949 1.16592i −0.965545 0.260236i \(-0.916200\pi\)
−0.423948 0.905687i \(-0.639356\pi\)
\(858\) 2.20008 0.800762i 0.0751093 0.0273376i
\(859\) 0.385392 + 2.18567i 0.0131494 + 0.0745740i 0.990676 0.136237i \(-0.0435008\pi\)
−0.977527 + 0.210811i \(0.932390\pi\)
\(860\) 0 0
\(861\) −15.0143 5.46475i −0.511685 0.186238i
\(862\) −7.42824 12.8661i −0.253007 0.438221i
\(863\) −4.65949 + 8.07047i −0.158611 + 0.274722i −0.934368 0.356310i \(-0.884035\pi\)
0.775757 + 0.631032i \(0.217368\pi\)
\(864\) −3.57712 + 3.00156i −0.121696 + 0.102115i
\(865\) 0 0
\(866\) −1.36617 + 2.36628i −0.0464244 + 0.0804094i
\(867\) −7.64606 13.2434i −0.259674 0.449768i
\(868\) −8.87323 3.22959i −0.301177 0.109619i
\(869\) −1.80924 + 10.2607i −0.0613741 + 0.348070i
\(870\) 0 0
\(871\) −20.7675 + 7.55874i −0.703679 + 0.256118i
\(872\) 1.31555 + 1.10388i 0.0445501 + 0.0373820i
\(873\) −18.1483 −0.614228
\(874\) −34.3157 + 8.31251i −1.16075 + 0.281175i
\(875\) 0 0
\(876\) 4.06220 + 3.40859i 0.137249 + 0.115166i
\(877\) 8.00218 2.91255i 0.270214 0.0983500i −0.203359 0.979104i \(-0.565186\pi\)
0.473574 + 0.880754i \(0.342964\pi\)
\(878\) −5.00274 28.3720i −0.168834 0.957508i
\(879\) 2.63210 14.9274i 0.0887784 0.503488i
\(880\) 0 0
\(881\) 18.8598 + 32.6661i 0.635402 + 1.10055i 0.986430 + 0.164184i \(0.0524991\pi\)
−0.351027 + 0.936365i \(0.614168\pi\)
\(882\) 2.67638 4.63563i 0.0901186 0.156090i
\(883\) 39.6674 33.2849i 1.33491 1.12012i 0.352011 0.935996i \(-0.385498\pi\)
0.982902 0.184129i \(-0.0589463\pi\)
\(884\) −0.0634703 + 0.0532579i −0.00213474 + 0.00179126i
\(885\) 0 0
\(886\) −6.85134 11.8669i −0.230175 0.398675i
\(887\) −25.3400 9.22299i −0.850833 0.309678i −0.120453 0.992719i \(-0.538435\pi\)
−0.730380 + 0.683041i \(0.760657\pi\)
\(888\) 0.882393 5.00430i 0.0296112 0.167933i
\(889\) 5.43280 + 30.8109i 0.182210 + 1.03337i
\(890\) 0 0
\(891\) 2.09051 + 1.75414i 0.0700346 + 0.0587660i
\(892\) 6.11784 0.204840
\(893\) −31.5533 3.52989i −1.05589 0.118123i
\(894\) 19.9461 0.667098
\(895\) 0 0
\(896\) −2.00589 + 0.730083i −0.0670120 + 0.0243904i
\(897\) 2.86162 + 16.2291i 0.0955468 + 0.541873i
\(898\) 3.63223 20.5994i 0.121209 0.687411i
\(899\) −25.7410 9.36895i −0.858510 0.312472i
\(900\) 0 0
\(901\) −0.216370 + 0.374764i −0.00720834 + 0.0124852i
\(902\) −7.33512 + 6.15490i −0.244233 + 0.204936i
\(903\) 1.02703 0.861777i 0.0341773 0.0286781i
\(904\) 3.46269 5.99755i 0.115167 0.199476i
\(905\) 0 0
\(906\) 14.8024 + 5.38762i 0.491776 + 0.178992i
\(907\) −5.76401 + 32.6893i −0.191391 + 1.08543i 0.726075 + 0.687616i \(0.241343\pi\)
−0.917465 + 0.397815i \(0.869768\pi\)
\(908\) −0.170495 0.966927i −0.00565809 0.0320886i
\(909\) 0.777610 0.283027i 0.0257917 0.00938741i
\(910\) 0 0
\(911\) 18.6372 0.617476 0.308738 0.951147i \(-0.400093\pi\)
0.308738 + 0.951147i \(0.400093\pi\)
\(912\) 3.89699 + 0.435959i 0.129042 + 0.0144360i
\(913\) 6.29494 0.208332
\(914\) −31.2928 26.2578i −1.03507 0.868531i
\(915\) 0 0
\(916\) −3.48788 19.7808i −0.115243 0.653575i
\(917\) −1.91340 + 10.8514i −0.0631860 + 0.358345i
\(918\) 0.160765 + 0.0585137i 0.00530604 + 0.00193124i
\(919\) 25.8149 + 44.7127i 0.851555 + 1.47494i 0.879805 + 0.475335i \(0.157673\pi\)
−0.0282498 + 0.999601i \(0.508993\pi\)
\(920\) 0 0
\(921\) 13.4529 11.2883i 0.443288 0.371963i
\(922\) −22.1446 + 18.5815i −0.729294 + 0.611950i
\(923\) −11.0943 + 19.2159i −0.365174 + 0.632500i
\(924\) −1.10497 1.91387i −0.0363509 0.0629617i
\(925\) 0 0
\(926\) 5.58828 31.6927i 0.183642 1.04149i
\(927\) 5.25440 + 29.7992i 0.172577 + 0.978733i
\(928\) −5.81902 + 2.11795i −0.191019 + 0.0695251i
\(929\) 39.5095 + 33.1524i 1.29626 + 1.08770i 0.990777 + 0.135499i \(0.0432637\pi\)
0.305487 + 0.952196i \(0.401181\pi\)
\(930\) 0 0
\(931\) −10.3512 + 2.50743i −0.339246 + 0.0821776i
\(932\) 16.0924 0.527123
\(933\) −22.1120 18.5541i −0.723913 0.607435i
\(934\) 34.6124 12.5979i 1.13255 0.412216i
\(935\) 0 0
\(936\) −0.860290 + 4.87895i −0.0281195 + 0.159473i
\(937\) −2.46321 0.896535i −0.0804696 0.0292885i 0.301472 0.953475i \(-0.402522\pi\)
−0.381941 + 0.924187i \(0.624744\pi\)
\(938\) 10.4303 + 18.0659i 0.340562 + 0.589871i
\(939\) 2.92948 5.07401i 0.0955999 0.165584i
\(940\) 0 0
\(941\) 24.2663 20.3619i 0.791060 0.663778i −0.154948 0.987923i \(-0.549521\pi\)
0.946008 + 0.324145i \(0.105076\pi\)
\(942\) −9.53111 + 16.5084i −0.310540 + 0.537872i
\(943\) −33.6987 58.3679i −1.09738 1.90072i
\(944\) −1.55903 0.567441i −0.0507421 0.0184686i
\(945\) 0 0
\(946\) −0.139519 0.791249i −0.00453614 0.0257257i
\(947\) −45.3917 + 16.5212i −1.47503 + 0.536868i −0.949462 0.313881i \(-0.898371\pi\)
−0.525571 + 0.850750i \(0.676148\pi\)
\(948\) 6.23913 + 5.23525i 0.202637 + 0.170033i
\(949\) 13.3305 0.432725
\(950\) 0 0
\(951\) −6.92438 −0.224538
\(952\) 0.0599102 + 0.0502706i 0.00194170 + 0.00162928i
\(953\) 32.4750 11.8199i 1.05197 0.382885i 0.242562 0.970136i \(-0.422012\pi\)
0.809405 + 0.587251i \(0.199790\pi\)
\(954\) 4.49320 + 25.4822i 0.145473 + 0.825017i
\(955\) 0 0
\(956\) 8.06973 + 2.93714i 0.260994 + 0.0949940i
\(957\) −3.20549 5.55208i −0.103619 0.179473i
\(958\) −3.69183 + 6.39443i −0.119278 + 0.206595i
\(959\) 24.9169 20.9078i 0.804609 0.675147i
\(960\) 0 0
\(961\) 5.71591 9.90024i 0.184384 0.319363i
\(962\) −6.38703 11.0627i −0.205926 0.356675i
\(963\) 13.3345 + 4.85338i 0.429700 + 0.156398i
\(964\) 2.06778 11.7269i 0.0665986 0.377699i
\(965\) 0 0
\(966\) 14.6170 5.32015i 0.470294 0.171173i
\(967\) 5.87837 + 4.93254i 0.189036 + 0.158620i 0.732394 0.680881i \(-0.238403\pi\)
−0.543358 + 0.839501i \(0.682847\pi\)
\(968\) 9.67561 0.310986
\(969\) −0.0575555 0.131634i −0.00184895 0.00422869i
\(970\) 0 0
\(971\) 38.0452 + 31.9237i 1.22093 + 1.02448i 0.998776 + 0.0494674i \(0.0157524\pi\)
0.222151 + 0.975012i \(0.428692\pi\)
\(972\) 15.1686 5.52090i 0.486532 0.177083i
\(973\) 3.63487 + 20.6144i 0.116529 + 0.660867i
\(974\) −4.59425 + 26.0553i −0.147209 + 0.834866i
\(975\) 0 0
\(976\) 2.97847 + 5.15887i 0.0953386 + 0.165131i
\(977\) −12.5824 + 21.7934i −0.402548 + 0.697233i −0.994033 0.109083i \(-0.965209\pi\)
0.591485 + 0.806316i \(0.298542\pi\)
\(978\) 6.61824 5.55336i 0.211628 0.177577i
\(979\) −6.23942 + 5.23550i −0.199413 + 0.167327i
\(980\) 0 0
\(981\) −1.88108 3.25813i −0.0600583 0.104024i
\(982\) −7.54434 2.74591i −0.240749 0.0876256i
\(983\) −2.23197 + 12.6581i −0.0711888 + 0.403732i 0.928302 + 0.371827i \(0.121268\pi\)
−0.999491 + 0.0319049i \(0.989843\pi\)
\(984\) 1.29978 + 7.37139i 0.0414353 + 0.234991i
\(985\) 0 0
\(986\) 0.173798 + 0.145834i 0.00553485 + 0.00464429i
\(987\) 13.9876 0.445229
\(988\) 8.20893 5.45747i 0.261161 0.173625i
\(989\) 5.65526 0.179827
\(990\) 0 0
\(991\) −20.4702 + 7.45056i −0.650259 + 0.236675i −0.646025 0.763316i \(-0.723570\pi\)
−0.00423369 + 0.999991i \(0.501348\pi\)
\(992\) 0.768149 + 4.35639i 0.0243888 + 0.138316i
\(993\) 3.15192 17.8754i 0.100023 0.567260i
\(994\) 19.6810 + 7.16329i 0.624243 + 0.227206i
\(995\) 0 0
\(996\) 2.46040 4.26154i 0.0779609 0.135032i
\(997\) −17.0267 + 14.2871i −0.539240 + 0.452477i −0.871278 0.490790i \(-0.836708\pi\)
0.332038 + 0.943266i \(0.392264\pi\)
\(998\) −16.6204 + 13.9461i −0.526108 + 0.441457i
\(999\) −13.1883 + 22.8428i −0.417259 + 0.722713i
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.l.l.301.4 30
5.2 odd 4 190.2.p.a.149.7 yes 60
5.3 odd 4 190.2.p.a.149.4 yes 60
5.4 even 2 950.2.l.m.301.2 30
19.6 even 9 inner 950.2.l.l.101.4 30
95.44 even 18 950.2.l.m.101.2 30
95.63 odd 36 190.2.p.a.139.7 yes 60
95.82 odd 36 190.2.p.a.139.4 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.p.a.139.4 60 95.82 odd 36
190.2.p.a.139.7 yes 60 95.63 odd 36
190.2.p.a.149.4 yes 60 5.3 odd 4
190.2.p.a.149.7 yes 60 5.2 odd 4
950.2.l.l.101.4 30 19.6 even 9 inner
950.2.l.l.301.4 30 1.1 even 1 trivial
950.2.l.m.101.2 30 95.44 even 18
950.2.l.m.301.2 30 5.4 even 2