Properties

Label 140.2.o.a.131.1
Level $140$
Weight $2$
Character 140.131
Analytic conductor $1.118$
Analytic rank $0$
Dimension $32$
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] = [140,2,Mod(31,140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(140, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("140.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.o (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: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.1
Character \(\chi\) \(=\) 140.131
Dual form 140.2.o.a.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39328 - 0.242400i) q^{2} +(-0.406021 - 0.703249i) q^{3} +(1.88248 + 0.675465i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.395235 + 1.07825i) q^{6} +(0.336411 + 2.62428i) q^{7} +(-2.45910 - 1.39743i) q^{8} +(1.17029 - 2.02701i) q^{9} +O(q^{10})\) \(q+(-1.39328 - 0.242400i) q^{2} +(-0.406021 - 0.703249i) q^{3} +(1.88248 + 0.675465i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.395235 + 1.07825i) q^{6} +(0.336411 + 2.62428i) q^{7} +(-2.45910 - 1.39743i) q^{8} +(1.17029 - 2.02701i) q^{9} +(-1.08542 - 0.906567i) q^{10} +(4.20925 - 2.43021i) q^{11} +(-0.289308 - 1.59811i) q^{12} +0.895933i q^{13} +(0.167409 - 3.73791i) q^{14} -0.812042i q^{15} +(3.08749 + 2.54310i) q^{16} +(5.10231 - 2.94582i) q^{17} +(-2.12190 + 2.54052i) q^{18} +(-1.45818 + 2.52565i) q^{19} +(1.29255 + 1.52621i) q^{20} +(1.70893 - 1.30209i) q^{21} +(-6.45377 + 2.36566i) q^{22} +(-1.35231 - 0.780755i) q^{23} +(0.0157066 + 2.29675i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.217174 - 1.24829i) q^{26} -4.33678 q^{27} +(-1.13932 + 5.16739i) q^{28} -9.73084 q^{29} +(-0.196839 + 1.13141i) q^{30} +(2.20757 + 3.82363i) q^{31} +(-3.68531 - 4.29168i) q^{32} +(-3.41809 - 1.97344i) q^{33} +(-7.82304 + 2.86757i) q^{34} +(-1.02080 + 2.44090i) q^{35} +(3.57223 - 3.02532i) q^{36} +(0.910682 - 1.57735i) q^{37} +(2.64388 - 3.16548i) q^{38} +(0.630064 - 0.363768i) q^{39} +(-1.43093 - 2.43976i) q^{40} +10.4920i q^{41} +(-2.69665 + 1.39994i) q^{42} -3.04581i q^{43} +(9.56538 - 1.73164i) q^{44} +(2.02701 - 1.17029i) q^{45} +(1.69489 + 1.41561i) q^{46} +(-2.60966 + 4.52006i) q^{47} +(0.534848 - 3.20383i) q^{48} +(-6.77366 + 1.76567i) q^{49} +(-0.486718 - 1.32782i) q^{50} +(-4.14329 - 2.39213i) q^{51} +(-0.605172 + 1.68658i) q^{52} +(-0.0898619 - 0.155645i) q^{53} +(6.04237 + 1.05124i) q^{54} +4.86043 q^{55} +(2.83997 - 6.92348i) q^{56} +2.36821 q^{57} +(13.5578 + 2.35876i) q^{58} +(-5.68287 - 9.84302i) q^{59} +(0.548506 - 1.52866i) q^{60} +(-5.33107 - 3.07789i) q^{61} +(-2.14893 - 5.86252i) q^{62} +(5.71313 + 2.38927i) q^{63} +(4.09438 + 6.87285i) q^{64} +(-0.447967 + 0.775901i) q^{65} +(4.28401 + 3.57810i) q^{66} +(6.75417 - 3.89952i) q^{67} +(11.5948 - 2.09903i) q^{68} +1.26801i q^{69} +(2.01394 - 3.15342i) q^{70} -8.38078i q^{71} +(-5.71048 + 3.34922i) q^{72} +(-7.60453 + 4.39048i) q^{73} +(-1.65119 + 1.97695i) q^{74} +(0.406021 - 0.703249i) q^{75} +(-4.45099 + 3.76954i) q^{76} +(7.79359 + 10.2287i) q^{77} +(-0.966036 + 0.354104i) q^{78} +(3.14686 + 1.81684i) q^{79} +(1.40230 + 3.74614i) q^{80} +(-1.75006 - 3.03119i) q^{81} +(2.54327 - 14.6184i) q^{82} -2.03796 q^{83} +(4.09655 - 1.29685i) q^{84} +5.89164 q^{85} +(-0.738304 + 4.24367i) q^{86} +(3.95092 + 6.84320i) q^{87} +(-13.7470 + 0.0940110i) q^{88} +(1.52812 + 0.882262i) q^{89} +(-3.10788 + 1.13921i) q^{90} +(-2.35118 + 0.301402i) q^{91} +(-2.01832 - 2.38320i) q^{92} +(1.79264 - 3.10495i) q^{93} +(4.73166 - 5.66515i) q^{94} +(-2.52565 + 1.45818i) q^{95} +(-1.52181 + 4.33420i) q^{96} -7.83641i q^{97} +(9.86563 - 0.818148i) q^{98} -11.3763i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39328 0.242400i −0.985201 0.171403i
\(3\) −0.406021 0.703249i −0.234416 0.406021i 0.724687 0.689079i \(-0.241985\pi\)
−0.959103 + 0.283058i \(0.908651\pi\)
\(4\) 1.88248 + 0.675465i 0.941242 + 0.337733i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 0.395235 + 1.07825i 0.161354 + 0.440192i
\(7\) 0.336411 + 2.62428i 0.127151 + 0.991883i
\(8\) −2.45910 1.39743i −0.869424 0.494066i
\(9\) 1.17029 2.02701i 0.390098 0.675670i
\(10\) −1.08542 0.906567i −0.343240 0.286682i
\(11\) 4.20925 2.43021i 1.26914 0.732737i 0.294313 0.955709i \(-0.404909\pi\)
0.974825 + 0.222972i \(0.0715759\pi\)
\(12\) −0.289308 1.59811i −0.0835160 0.461334i
\(13\) 0.895933i 0.248487i 0.992252 + 0.124244i \(0.0396504\pi\)
−0.992252 + 0.124244i \(0.960350\pi\)
\(14\) 0.167409 3.73791i 0.0447419 0.998999i
\(15\) 0.812042i 0.209668i
\(16\) 3.08749 + 2.54310i 0.771873 + 0.635776i
\(17\) 5.10231 2.94582i 1.23749 0.714467i 0.268911 0.963165i \(-0.413336\pi\)
0.968581 + 0.248698i \(0.0800028\pi\)
\(18\) −2.12190 + 2.54052i −0.500137 + 0.598806i
\(19\) −1.45818 + 2.52565i −0.334530 + 0.579423i −0.983394 0.181481i \(-0.941911\pi\)
0.648865 + 0.760904i \(0.275244\pi\)
\(20\) 1.29255 + 1.52621i 0.289022 + 0.341271i
\(21\) 1.70893 1.30209i 0.372919 0.284140i
\(22\) −6.45377 + 2.36566i −1.37595 + 0.504359i
\(23\) −1.35231 0.780755i −0.281976 0.162799i 0.352342 0.935871i \(-0.385385\pi\)
−0.634317 + 0.773073i \(0.718719\pi\)
\(24\) 0.0157066 + 2.29675i 0.00320610 + 0.468822i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0.217174 1.24829i 0.0425914 0.244810i
\(27\) −4.33678 −0.834614
\(28\) −1.13932 + 5.16739i −0.215311 + 0.976546i
\(29\) −9.73084 −1.80697 −0.903486 0.428618i \(-0.859001\pi\)
−0.903486 + 0.428618i \(0.859001\pi\)
\(30\) −0.196839 + 1.13141i −0.0359377 + 0.206565i
\(31\) 2.20757 + 3.82363i 0.396492 + 0.686744i 0.993290 0.115647i \(-0.0368941\pi\)
−0.596798 + 0.802391i \(0.703561\pi\)
\(32\) −3.68531 4.29168i −0.651477 0.758669i
\(33\) −3.41809 1.97344i −0.595013 0.343531i
\(34\) −7.82304 + 2.86757i −1.34164 + 0.491783i
\(35\) −1.02080 + 2.44090i −0.172546 + 0.412587i
\(36\) 3.57223 3.02532i 0.595372 0.504220i
\(37\) 0.910682 1.57735i 0.149715 0.259314i −0.781407 0.624022i \(-0.785498\pi\)
0.931122 + 0.364707i \(0.118831\pi\)
\(38\) 2.64388 3.16548i 0.428894 0.513509i
\(39\) 0.630064 0.363768i 0.100891 0.0582494i
\(40\) −1.43093 2.43976i −0.226250 0.385760i
\(41\) 10.4920i 1.63858i 0.573381 + 0.819289i \(0.305632\pi\)
−0.573381 + 0.819289i \(0.694368\pi\)
\(42\) −2.69665 + 1.39994i −0.416103 + 0.216015i
\(43\) 3.04581i 0.464481i −0.972658 0.232240i \(-0.925394\pi\)
0.972658 0.232240i \(-0.0746056\pi\)
\(44\) 9.56538 1.73164i 1.44204 0.261054i
\(45\) 2.02701 1.17029i 0.302169 0.174457i
\(46\) 1.69489 + 1.41561i 0.249898 + 0.208721i
\(47\) −2.60966 + 4.52006i −0.380658 + 0.659319i −0.991156 0.132698i \(-0.957636\pi\)
0.610498 + 0.792017i \(0.290969\pi\)
\(48\) 0.534848 3.20383i 0.0771987 0.462433i
\(49\) −6.77366 + 1.76567i −0.967665 + 0.252239i
\(50\) −0.486718 1.32782i −0.0688323 0.187782i
\(51\) −4.14329 2.39213i −0.580177 0.334965i
\(52\) −0.605172 + 1.68658i −0.0839222 + 0.233887i
\(53\) −0.0898619 0.155645i −0.0123435 0.0213795i 0.859788 0.510652i \(-0.170596\pi\)
−0.872131 + 0.489272i \(0.837262\pi\)
\(54\) 6.04237 + 1.05124i 0.822262 + 0.143055i
\(55\) 4.86043 0.655380
\(56\) 2.83997 6.92348i 0.379507 0.925189i
\(57\) 2.36821 0.313677
\(58\) 13.5578 + 2.35876i 1.78023 + 0.309720i
\(59\) −5.68287 9.84302i −0.739846 1.28145i −0.952564 0.304338i \(-0.901565\pi\)
0.212718 0.977114i \(-0.431768\pi\)
\(60\) 0.548506 1.52866i 0.0708118 0.197349i
\(61\) −5.33107 3.07789i −0.682573 0.394084i 0.118251 0.992984i \(-0.462271\pi\)
−0.800824 + 0.598900i \(0.795605\pi\)
\(62\) −2.14893 5.86252i −0.272914 0.744541i
\(63\) 5.71313 + 2.38927i 0.719787 + 0.301019i
\(64\) 4.09438 + 6.87285i 0.511798 + 0.859106i
\(65\) −0.447967 + 0.775901i −0.0555634 + 0.0962387i
\(66\) 4.28401 + 3.57810i 0.527325 + 0.440434i
\(67\) 6.75417 3.89952i 0.825154 0.476403i −0.0270367 0.999634i \(-0.508607\pi\)
0.852190 + 0.523232i \(0.175274\pi\)
\(68\) 11.5948 2.09903i 1.40608 0.254545i
\(69\) 1.26801i 0.152651i
\(70\) 2.01394 3.15342i 0.240711 0.376906i
\(71\) 8.38078i 0.994616i −0.867574 0.497308i \(-0.834322\pi\)
0.867574 0.497308i \(-0.165678\pi\)
\(72\) −5.71048 + 3.34922i −0.672986 + 0.394709i
\(73\) −7.60453 + 4.39048i −0.890043 + 0.513866i −0.873956 0.486004i \(-0.838454\pi\)
−0.0160862 + 0.999871i \(0.505121\pi\)
\(74\) −1.65119 + 1.97695i −0.191947 + 0.229815i
\(75\) 0.406021 0.703249i 0.0468833 0.0812042i
\(76\) −4.45099 + 3.76954i −0.510564 + 0.432396i
\(77\) 7.79359 + 10.2287i 0.888162 + 1.16567i
\(78\) −0.966036 + 0.354104i −0.109382 + 0.0400944i
\(79\) 3.14686 + 1.81684i 0.354049 + 0.204410i 0.666467 0.745534i \(-0.267806\pi\)
−0.312418 + 0.949945i \(0.601139\pi\)
\(80\) 1.40230 + 3.74614i 0.156781 + 0.418831i
\(81\) −1.75006 3.03119i −0.194451 0.336799i
\(82\) 2.54327 14.6184i 0.280857 1.61433i
\(83\) −2.03796 −0.223695 −0.111847 0.993725i \(-0.535677\pi\)
−0.111847 + 0.993725i \(0.535677\pi\)
\(84\) 4.09655 1.29685i 0.446970 0.141497i
\(85\) 5.89164 0.639038
\(86\) −0.738304 + 4.24367i −0.0796134 + 0.457607i
\(87\) 3.95092 + 6.84320i 0.423584 + 0.733668i
\(88\) −13.7470 + 0.0940110i −1.46544 + 0.0100216i
\(89\) 1.52812 + 0.882262i 0.161981 + 0.0935195i 0.578799 0.815470i \(-0.303522\pi\)
−0.416818 + 0.908990i \(0.636855\pi\)
\(90\) −3.10788 + 1.13921i −0.327599 + 0.120083i
\(91\) −2.35118 + 0.301402i −0.246470 + 0.0315955i
\(92\) −2.01832 2.38320i −0.210425 0.248465i
\(93\) 1.79264 3.10495i 0.185888 0.321968i
\(94\) 4.73166 5.66515i 0.488034 0.584316i
\(95\) −2.52565 + 1.45818i −0.259126 + 0.149606i
\(96\) −1.52181 + 4.33420i −0.155319 + 0.442357i
\(97\) 7.83641i 0.795667i −0.917458 0.397834i \(-0.869762\pi\)
0.917458 0.397834i \(-0.130238\pi\)
\(98\) 9.86563 0.818148i 0.996579 0.0826454i
\(99\) 11.3763i 1.14336i
\(100\) 0.356272 + 1.96801i 0.0356272 + 0.196801i
\(101\) −6.30931 + 3.64268i −0.627799 + 0.362460i −0.779899 0.625905i \(-0.784730\pi\)
0.152100 + 0.988365i \(0.451396\pi\)
\(102\) 5.19293 + 4.33725i 0.514177 + 0.429452i
\(103\) −4.60525 + 7.97652i −0.453768 + 0.785950i −0.998616 0.0525850i \(-0.983254\pi\)
0.544848 + 0.838535i \(0.316587\pi\)
\(104\) 1.25200 2.20319i 0.122769 0.216041i
\(105\) 2.13102 0.273180i 0.207966 0.0266596i
\(106\) 0.0874748 + 0.238641i 0.00849630 + 0.0231789i
\(107\) −12.9808 7.49445i −1.25490 0.724516i −0.282820 0.959173i \(-0.591270\pi\)
−0.972078 + 0.234657i \(0.924603\pi\)
\(108\) −8.16392 2.92934i −0.785574 0.281876i
\(109\) −0.795610 1.37804i −0.0762056 0.131992i 0.825404 0.564542i \(-0.190947\pi\)
−0.901610 + 0.432550i \(0.857614\pi\)
\(110\) −6.77196 1.17817i −0.645681 0.112334i
\(111\) −1.47902 −0.140383
\(112\) −5.63514 + 8.95797i −0.532471 + 0.846448i
\(113\) 3.57866 0.336652 0.168326 0.985731i \(-0.446164\pi\)
0.168326 + 0.985731i \(0.446164\pi\)
\(114\) −3.29959 0.574055i −0.309035 0.0537651i
\(115\) −0.780755 1.35231i −0.0728058 0.126103i
\(116\) −18.3182 6.57284i −1.70080 0.610273i
\(117\) 1.81606 + 1.04851i 0.167895 + 0.0969344i
\(118\) 5.53190 + 15.0917i 0.509253 + 1.38930i
\(119\) 9.44712 + 12.3989i 0.866016 + 1.13660i
\(120\) −1.13477 + 1.99689i −0.103590 + 0.182291i
\(121\) 6.31188 10.9325i 0.573807 0.993863i
\(122\) 6.68161 + 5.58063i 0.604925 + 0.505247i
\(123\) 7.37850 4.25998i 0.665297 0.384109i
\(124\) 1.57299 + 8.68906i 0.141259 + 0.780301i
\(125\) 1.00000i 0.0894427i
\(126\) −7.38086 4.71379i −0.657539 0.419938i
\(127\) 7.67404i 0.680961i 0.940252 + 0.340481i \(0.110590\pi\)
−0.940252 + 0.340481i \(0.889410\pi\)
\(128\) −4.03866 10.5683i −0.356970 0.934116i
\(129\) −2.14196 + 1.23666i −0.188589 + 0.108882i
\(130\) 0.812224 0.972464i 0.0712367 0.0852907i
\(131\) −9.95404 + 17.2409i −0.869689 + 1.50635i −0.00737416 + 0.999973i \(0.502347\pi\)
−0.862315 + 0.506373i \(0.830986\pi\)
\(132\) −5.10151 6.02376i −0.444030 0.524301i
\(133\) −7.11854 2.97702i −0.617256 0.258140i
\(134\) −10.3557 + 3.79593i −0.894599 + 0.327919i
\(135\) −3.75576 2.16839i −0.323245 0.186625i
\(136\) −16.6637 + 0.113957i −1.42890 + 0.00977172i
\(137\) 4.41809 + 7.65236i 0.377463 + 0.653785i 0.990692 0.136120i \(-0.0434632\pi\)
−0.613229 + 0.789905i \(0.710130\pi\)
\(138\) 0.307366 1.76670i 0.0261648 0.150392i
\(139\) 7.91285 0.671159 0.335580 0.942012i \(-0.391068\pi\)
0.335580 + 0.942012i \(0.391068\pi\)
\(140\) −3.57038 + 3.90543i −0.301752 + 0.330069i
\(141\) 4.23831 0.356930
\(142\) −2.03150 + 11.6768i −0.170480 + 0.979897i
\(143\) 2.17731 + 3.77121i 0.182076 + 0.315364i
\(144\) 8.76817 3.28220i 0.730681 0.273516i
\(145\) −8.42715 4.86542i −0.699837 0.404051i
\(146\) 11.6595 4.27384i 0.964949 0.353706i
\(147\) 3.99195 + 4.04667i 0.329251 + 0.333763i
\(148\) 2.77979 2.35420i 0.228497 0.193514i
\(149\) 0.861502 1.49217i 0.0705770 0.122243i −0.828577 0.559875i \(-0.810849\pi\)
0.899154 + 0.437632i \(0.144183\pi\)
\(150\) −0.736170 + 0.881406i −0.0601081 + 0.0719665i
\(151\) 0.705057 0.407065i 0.0573767 0.0331265i −0.471037 0.882113i \(-0.656120\pi\)
0.528414 + 0.848987i \(0.322787\pi\)
\(152\) 7.11523 4.17312i 0.577122 0.338484i
\(153\) 13.7899i 1.11485i
\(154\) −8.37926 16.1407i −0.675220 1.30065i
\(155\) 4.41515i 0.354633i
\(156\) 1.43180 0.259201i 0.114636 0.0207527i
\(157\) 11.5660 6.67764i 0.923068 0.532934i 0.0384557 0.999260i \(-0.487756\pi\)
0.884613 + 0.466327i \(0.154423\pi\)
\(158\) −3.94407 3.29417i −0.313773 0.262070i
\(159\) −0.0729717 + 0.126391i −0.00578703 + 0.0100234i
\(160\) −1.04573 5.55936i −0.0826724 0.439506i
\(161\) 1.59399 3.81148i 0.125624 0.300387i
\(162\) 1.70357 + 4.64753i 0.133845 + 0.365144i
\(163\) −7.77441 4.48856i −0.608939 0.351571i 0.163611 0.986525i \(-0.447686\pi\)
−0.772550 + 0.634954i \(0.781019\pi\)
\(164\) −7.08699 + 19.7511i −0.553401 + 1.54230i
\(165\) −1.97344 3.41809i −0.153632 0.266098i
\(166\) 2.83945 + 0.494001i 0.220384 + 0.0383419i
\(167\) 17.0324 1.31801 0.659003 0.752140i \(-0.270978\pi\)
0.659003 + 0.752140i \(0.270978\pi\)
\(168\) −6.02202 + 0.813870i −0.464609 + 0.0627914i
\(169\) 12.1973 0.938254
\(170\) −8.20873 1.42814i −0.629581 0.109533i
\(171\) 3.41300 + 5.91150i 0.260999 + 0.452063i
\(172\) 2.05734 5.73368i 0.156870 0.437189i
\(173\) 14.2599 + 8.23299i 1.08416 + 0.625942i 0.932017 0.362416i \(-0.118048\pi\)
0.152147 + 0.988358i \(0.451381\pi\)
\(174\) −3.84597 10.4922i −0.291562 0.795414i
\(175\) −2.10448 + 1.60348i −0.159084 + 0.121212i
\(176\) 19.1763 + 3.20130i 1.44547 + 0.241307i
\(177\) −4.61473 + 7.99294i −0.346864 + 0.600786i
\(178\) −1.91525 1.59966i −0.143554 0.119899i
\(179\) −9.26501 + 5.34916i −0.692499 + 0.399815i −0.804548 0.593888i \(-0.797592\pi\)
0.112048 + 0.993703i \(0.464259\pi\)
\(180\) 4.60630 0.833887i 0.343334 0.0621542i
\(181\) 10.8661i 0.807672i −0.914831 0.403836i \(-0.867677\pi\)
0.914831 0.403836i \(-0.132323\pi\)
\(182\) 3.34892 + 0.149987i 0.248238 + 0.0111178i
\(183\) 4.99875i 0.369519i
\(184\) 2.23441 + 3.80971i 0.164723 + 0.280856i
\(185\) 1.57735 0.910682i 0.115969 0.0669547i
\(186\) −3.25030 + 3.89154i −0.238324 + 0.285341i
\(187\) 14.3179 24.7994i 1.04703 1.81351i
\(188\) −7.96579 + 6.74622i −0.580965 + 0.492018i
\(189\) −1.45894 11.3809i −0.106122 0.827840i
\(190\) 3.87241 1.41945i 0.280934 0.102977i
\(191\) 0.439231 + 0.253590i 0.0317816 + 0.0183491i 0.515807 0.856705i \(-0.327492\pi\)
−0.484025 + 0.875054i \(0.660826\pi\)
\(192\) 3.17092 5.66989i 0.228841 0.409189i
\(193\) 10.4098 + 18.0302i 0.749311 + 1.29784i 0.948153 + 0.317813i \(0.102949\pi\)
−0.198842 + 0.980031i \(0.563718\pi\)
\(194\) −1.89955 + 10.9184i −0.136380 + 0.783892i
\(195\) 0.727535 0.0520999
\(196\) −13.9439 1.25152i −0.995996 0.0893941i
\(197\) −8.86095 −0.631317 −0.315658 0.948873i \(-0.602225\pi\)
−0.315658 + 0.948873i \(0.602225\pi\)
\(198\) −2.75761 + 15.8504i −0.195975 + 1.12644i
\(199\) −11.6081 20.1059i −0.822878 1.42527i −0.903530 0.428524i \(-0.859034\pi\)
0.0806522 0.996742i \(-0.474300\pi\)
\(200\) −0.0193421 2.82836i −0.00136769 0.199995i
\(201\) −5.48467 3.16658i −0.386859 0.223353i
\(202\) 9.67365 3.54591i 0.680635 0.249490i
\(203\) −3.27356 25.5364i −0.229759 1.79231i
\(204\) −6.18388 7.30179i −0.432958 0.511228i
\(205\) −5.24601 + 9.08636i −0.366397 + 0.634619i
\(206\) 8.34993 9.99725i 0.581767 0.696541i
\(207\) −3.16519 + 1.82743i −0.219996 + 0.127015i
\(208\) −2.27845 + 2.76619i −0.157982 + 0.191801i
\(209\) 14.1748i 0.980490i
\(210\) −3.03534 0.135943i −0.209458 0.00938095i
\(211\) 6.21092i 0.427578i 0.976880 + 0.213789i \(0.0685804\pi\)
−0.976880 + 0.213789i \(0.931420\pi\)
\(212\) −0.0640306 0.353699i −0.00439764 0.0242921i
\(213\) −5.89378 + 3.40277i −0.403835 + 0.233154i
\(214\) 16.2692 + 13.5884i 1.11214 + 0.928887i
\(215\) 1.52290 2.63774i 0.103861 0.179893i
\(216\) 10.6646 + 6.06035i 0.725634 + 0.412354i
\(217\) −9.29161 + 7.07960i −0.630756 + 0.480594i
\(218\) 0.774475 + 2.11285i 0.0524541 + 0.143101i
\(219\) 6.17519 + 3.56525i 0.417281 + 0.240917i
\(220\) 9.14968 + 3.28305i 0.616871 + 0.221343i
\(221\) 2.63926 + 4.57133i 0.177536 + 0.307501i
\(222\) 2.06070 + 0.358516i 0.138305 + 0.0240620i
\(223\) −12.8221 −0.858632 −0.429316 0.903154i \(-0.641245\pi\)
−0.429316 + 0.903154i \(0.641245\pi\)
\(224\) 10.0228 11.1150i 0.669675 0.742655i
\(225\) 2.34059 0.156039
\(226\) −4.98609 0.867468i −0.331670 0.0577031i
\(227\) −1.80332 3.12345i −0.119691 0.207310i 0.799954 0.600061i \(-0.204857\pi\)
−0.919645 + 0.392750i \(0.871524\pi\)
\(228\) 4.45812 + 1.59964i 0.295246 + 0.105939i
\(229\) 15.4049 + 8.89400i 1.01798 + 0.587732i 0.913519 0.406796i \(-0.133354\pi\)
0.104463 + 0.994529i \(0.466687\pi\)
\(230\) 0.760014 + 2.07340i 0.0501139 + 0.136716i
\(231\) 4.02896 9.63390i 0.265086 0.633864i
\(232\) 23.9291 + 13.5982i 1.57103 + 0.892763i
\(233\) −0.137037 + 0.237354i −0.00897756 + 0.0155496i −0.870479 0.492205i \(-0.836191\pi\)
0.861502 + 0.507755i \(0.169524\pi\)
\(234\) −2.27614 1.90108i −0.148796 0.124278i
\(235\) −4.52006 + 2.60966i −0.294856 + 0.170235i
\(236\) −4.04930 22.3679i −0.263587 1.45603i
\(237\) 2.95070i 0.191668i
\(238\) −10.1570 19.5651i −0.658383 1.26822i
\(239\) 23.0254i 1.48939i 0.667406 + 0.744694i \(0.267405\pi\)
−0.667406 + 0.744694i \(0.732595\pi\)
\(240\) 2.06511 2.50717i 0.133302 0.161837i
\(241\) 3.25210 1.87760i 0.209486 0.120947i −0.391587 0.920141i \(-0.628074\pi\)
0.601072 + 0.799195i \(0.294740\pi\)
\(242\) −11.4443 + 13.7021i −0.735666 + 0.880803i
\(243\) −7.92629 + 13.7287i −0.508472 + 0.880699i
\(244\) −7.95664 9.39503i −0.509372 0.601455i
\(245\) −6.74899 1.85771i −0.431177 0.118685i
\(246\) −11.3130 + 4.14681i −0.721289 + 0.264391i
\(247\) −2.26281 1.30643i −0.143979 0.0831264i
\(248\) −0.0853983 12.4876i −0.00542280 0.792965i
\(249\) 0.827453 + 1.43319i 0.0524377 + 0.0908248i
\(250\) 0.242400 1.39328i 0.0153307 0.0881191i
\(251\) 0.268218 0.0169298 0.00846489 0.999964i \(-0.497306\pi\)
0.00846489 + 0.999964i \(0.497306\pi\)
\(252\) 9.14101 + 8.35678i 0.575830 + 0.526428i
\(253\) −7.58961 −0.477155
\(254\) 1.86019 10.6921i 0.116719 0.670884i
\(255\) −2.39213 4.14329i −0.149801 0.259463i
\(256\) 3.06524 + 15.7036i 0.191577 + 0.981478i
\(257\) −26.9207 15.5426i −1.67926 0.969524i −0.962131 0.272588i \(-0.912120\pi\)
−0.717134 0.696936i \(-0.754546\pi\)
\(258\) 3.28413 1.20381i 0.204461 0.0749459i
\(259\) 4.44576 + 1.85924i 0.276246 + 0.115528i
\(260\) −1.36738 + 1.15804i −0.0848016 + 0.0718183i
\(261\) −11.3879 + 19.7245i −0.704896 + 1.22092i
\(262\) 18.0480 21.6086i 1.11501 1.33499i
\(263\) 24.1154 13.9230i 1.48702 0.858532i 0.487130 0.873329i \(-0.338044\pi\)
0.999891 + 0.0147973i \(0.00471030\pi\)
\(264\) 5.64770 + 9.62942i 0.347592 + 0.592650i
\(265\) 0.179724i 0.0110404i
\(266\) 9.19652 + 5.87337i 0.563875 + 0.360119i
\(267\) 1.43287i 0.0876900i
\(268\) 15.3486 2.77858i 0.937566 0.169729i
\(269\) −1.25127 + 0.722424i −0.0762916 + 0.0440470i −0.537661 0.843161i \(-0.680692\pi\)
0.461369 + 0.887208i \(0.347358\pi\)
\(270\) 4.70723 + 3.93158i 0.286473 + 0.239269i
\(271\) 6.99708 12.1193i 0.425042 0.736195i −0.571382 0.820684i \(-0.693593\pi\)
0.996424 + 0.0844893i \(0.0269259\pi\)
\(272\) 23.2449 + 3.88051i 1.40943 + 0.235290i
\(273\) 1.16659 + 1.53109i 0.0706051 + 0.0926656i
\(274\) −4.30072 11.7329i −0.259816 0.708808i
\(275\) 4.20925 + 2.43021i 0.253828 + 0.146547i
\(276\) −0.856497 + 2.38701i −0.0515551 + 0.143681i
\(277\) −9.25674 16.0332i −0.556184 0.963339i −0.997810 0.0661397i \(-0.978932\pi\)
0.441627 0.897199i \(-0.354402\pi\)
\(278\) −11.0249 1.91808i −0.661227 0.115039i
\(279\) 10.3340 0.618683
\(280\) 5.92123 4.57592i 0.353861 0.273464i
\(281\) −9.00853 −0.537404 −0.268702 0.963223i \(-0.586595\pi\)
−0.268702 + 0.963223i \(0.586595\pi\)
\(282\) −5.90517 1.02737i −0.351648 0.0611788i
\(283\) 13.6475 + 23.6382i 0.811261 + 1.40515i 0.911982 + 0.410231i \(0.134552\pi\)
−0.100720 + 0.994915i \(0.532115\pi\)
\(284\) 5.66093 15.7767i 0.335914 0.936174i
\(285\) 2.05093 + 1.18410i 0.121487 + 0.0701403i
\(286\) −2.11947 5.78215i −0.125327 0.341906i
\(287\) −27.5340 + 3.52963i −1.62528 + 0.208348i
\(288\) −13.0122 + 2.44763i −0.766749 + 0.144228i
\(289\) 8.85572 15.3386i 0.520925 0.902268i
\(290\) 10.5620 + 8.82166i 0.620225 + 0.518026i
\(291\) −5.51095 + 3.18175i −0.323058 + 0.186517i
\(292\) −17.2810 + 3.12841i −1.01129 + 0.183076i
\(293\) 10.6330i 0.621188i −0.950543 0.310594i \(-0.899472\pi\)
0.950543 0.310594i \(-0.100528\pi\)
\(294\) −4.58101 6.60581i −0.267170 0.385258i
\(295\) 11.3657i 0.661739i
\(296\) −4.44370 + 2.60625i −0.258285 + 0.151485i
\(297\) −18.2546 + 10.5393i −1.05924 + 0.611552i
\(298\) −1.56202 + 1.87018i −0.0904854 + 0.108337i
\(299\) 0.699505 1.21158i 0.0404534 0.0700673i
\(300\) 1.23935 1.04960i 0.0715538 0.0605988i
\(301\) 7.99304 1.02464i 0.460711 0.0590594i
\(302\) −1.08102 + 0.396251i −0.0622056 + 0.0228017i
\(303\) 5.12342 + 2.95801i 0.294333 + 0.169933i
\(304\) −10.9251 + 4.08961i −0.626598 + 0.234555i
\(305\) −3.07789 5.33107i −0.176240 0.305256i
\(306\) −3.34268 + 19.2133i −0.191088 + 1.09835i
\(307\) −17.9812 −1.02624 −0.513120 0.858317i \(-0.671510\pi\)
−0.513120 + 0.858317i \(0.671510\pi\)
\(308\) 7.76219 + 24.5197i 0.442292 + 1.39714i
\(309\) 7.47930 0.425483
\(310\) 1.07023 6.15156i 0.0607851 0.349385i
\(311\) −14.1579 24.5222i −0.802821 1.39053i −0.917752 0.397153i \(-0.869998\pi\)
0.114931 0.993373i \(-0.463335\pi\)
\(312\) −2.05773 + 0.0140721i −0.116496 + 0.000796674i
\(313\) −4.84537 2.79748i −0.273877 0.158123i 0.356771 0.934192i \(-0.383878\pi\)
−0.630648 + 0.776069i \(0.717211\pi\)
\(314\) −17.7334 + 6.50025i −1.00075 + 0.366830i
\(315\) 3.75308 + 4.92573i 0.211462 + 0.277534i
\(316\) 4.69670 + 5.54576i 0.264210 + 0.311974i
\(317\) −15.6736 + 27.1475i −0.880318 + 1.52476i −0.0293312 + 0.999570i \(0.509338\pi\)
−0.850987 + 0.525186i \(0.823996\pi\)
\(318\) 0.132307 0.158410i 0.00741943 0.00888318i
\(319\) −40.9596 + 23.6480i −2.29330 + 1.32404i
\(320\) 0.109413 + 7.99925i 0.00611637 + 0.447172i
\(321\) 12.1716i 0.679353i
\(322\) −3.14478 + 4.92410i −0.175252 + 0.274409i
\(323\) 17.1822i 0.956042i
\(324\) −1.24699 6.88827i −0.0692775 0.382682i
\(325\) −0.775901 + 0.447967i −0.0430392 + 0.0248487i
\(326\) 9.74394 + 8.13835i 0.539667 + 0.450742i
\(327\) −0.646069 + 1.11902i −0.0357277 + 0.0618822i
\(328\) 14.6619 25.8010i 0.809566 1.42462i
\(329\) −12.7398 5.32787i −0.702369 0.293735i
\(330\) 1.92101 + 5.24073i 0.105748 + 0.288493i
\(331\) 18.6312 + 10.7567i 1.02406 + 0.591244i 0.915279 0.402821i \(-0.131970\pi\)
0.108786 + 0.994065i \(0.465304\pi\)
\(332\) −3.83642 1.37657i −0.210551 0.0755490i
\(333\) −2.13153 3.69192i −0.116807 0.202316i
\(334\) −23.7310 4.12866i −1.29850 0.225910i
\(335\) 7.79905 0.426108
\(336\) 8.58767 + 0.325786i 0.468496 + 0.0177731i
\(337\) −0.0584151 −0.00318207 −0.00159104 0.999999i \(-0.500506\pi\)
−0.00159104 + 0.999999i \(0.500506\pi\)
\(338\) −16.9943 2.95663i −0.924369 0.160819i
\(339\) −1.45301 2.51669i −0.0789167 0.136688i
\(340\) 11.0909 + 3.97960i 0.601490 + 0.215824i
\(341\) 18.5845 + 10.7298i 1.00641 + 0.581049i
\(342\) −3.32234 9.06371i −0.179651 0.490109i
\(343\) −6.91235 17.1820i −0.373232 0.927738i
\(344\) −4.25630 + 7.48995i −0.229484 + 0.403831i
\(345\) −0.634006 + 1.09813i −0.0341337 + 0.0591213i
\(346\) −17.8725 14.9275i −0.960831 0.802508i
\(347\) 7.63282 4.40681i 0.409751 0.236570i −0.280932 0.959728i \(-0.590643\pi\)
0.690683 + 0.723158i \(0.257310\pi\)
\(348\) 2.81521 + 15.5509i 0.150911 + 0.833617i
\(349\) 1.78555i 0.0955784i 0.998857 + 0.0477892i \(0.0152176\pi\)
−0.998857 + 0.0477892i \(0.984782\pi\)
\(350\) 3.32083 1.72398i 0.177506 0.0921503i
\(351\) 3.88547i 0.207391i
\(352\) −25.9421 9.10867i −1.38272 0.485494i
\(353\) 23.8096 13.7465i 1.26726 0.731651i 0.292789 0.956177i \(-0.405417\pi\)
0.974468 + 0.224526i \(0.0720835\pi\)
\(354\) 8.36712 10.0178i 0.444707 0.532442i
\(355\) 4.19039 7.25797i 0.222403 0.385213i
\(356\) 2.28073 + 2.69304i 0.120878 + 0.142731i
\(357\) 4.88376 11.6779i 0.258476 0.618059i
\(358\) 14.2054 5.20706i 0.750780 0.275201i
\(359\) 16.1118 + 9.30213i 0.850346 + 0.490948i 0.860768 0.508998i \(-0.169984\pi\)
−0.0104213 + 0.999946i \(0.503317\pi\)
\(360\) −6.62003 + 0.0452719i −0.348906 + 0.00238604i
\(361\) 5.24741 + 9.08878i 0.276179 + 0.478357i
\(362\) −2.63395 + 15.1396i −0.138437 + 0.795720i
\(363\) −10.2510 −0.538039
\(364\) −4.62964 1.02075i −0.242659 0.0535020i
\(365\) −8.78095 −0.459616
\(366\) 1.21170 6.96469i 0.0633365 0.364050i
\(367\) 10.9922 + 19.0390i 0.573788 + 0.993829i 0.996172 + 0.0874124i \(0.0278598\pi\)
−0.422385 + 0.906417i \(0.638807\pi\)
\(368\) −2.18970 5.84964i −0.114146 0.304933i
\(369\) 21.2674 + 12.2787i 1.10714 + 0.639206i
\(370\) −2.41844 + 0.886490i −0.125729 + 0.0460864i
\(371\) 0.378226 0.288183i 0.0196365 0.0149617i
\(372\) 5.47190 4.63415i 0.283705 0.240269i
\(373\) −0.282808 + 0.489838i −0.0146433 + 0.0253629i −0.873254 0.487265i \(-0.837995\pi\)
0.858611 + 0.512628i \(0.171328\pi\)
\(374\) −25.9604 + 31.0820i −1.34238 + 1.60721i
\(375\) 0.703249 0.406021i 0.0363156 0.0209668i
\(376\) 12.7339 7.46849i 0.656701 0.385158i
\(377\) 8.71818i 0.449009i
\(378\) −0.726015 + 16.2105i −0.0373422 + 0.833778i
\(379\) 28.3294i 1.45518i −0.686010 0.727592i \(-0.740639\pi\)
0.686010 0.727592i \(-0.259361\pi\)
\(380\) −5.73944 + 1.03902i −0.294427 + 0.0533006i
\(381\) 5.39676 3.11582i 0.276484 0.159628i
\(382\) −0.550504 0.459793i −0.0281662 0.0235251i
\(383\) 1.54300 2.67256i 0.0788438 0.136561i −0.823908 0.566724i \(-0.808210\pi\)
0.902751 + 0.430163i \(0.141544\pi\)
\(384\) −5.79237 + 7.13114i −0.295591 + 0.363909i
\(385\) 1.63510 + 12.7551i 0.0833325 + 0.650060i
\(386\) −10.1332 27.6446i −0.515768 1.40707i
\(387\) −6.17387 3.56449i −0.313836 0.181193i
\(388\) 5.29322 14.7519i 0.268723 0.748916i
\(389\) −8.17685 14.1627i −0.414583 0.718078i 0.580802 0.814045i \(-0.302739\pi\)
−0.995385 + 0.0959669i \(0.969406\pi\)
\(390\) −1.01366 0.176355i −0.0513289 0.00893007i
\(391\) −9.19986 −0.465257
\(392\) 19.1245 + 5.12374i 0.965934 + 0.258788i
\(393\) 16.1662 0.815477
\(394\) 12.3458 + 2.14790i 0.621974 + 0.108210i
\(395\) 1.81684 + 3.14686i 0.0914151 + 0.158336i
\(396\) 7.68427 21.4156i 0.386149 1.07618i
\(397\) −6.77631 3.91230i −0.340093 0.196353i 0.320220 0.947343i \(-0.396243\pi\)
−0.660313 + 0.750990i \(0.729576\pi\)
\(398\) 11.2998 + 30.8270i 0.566406 + 1.54522i
\(399\) 0.796692 + 6.21484i 0.0398845 + 0.311131i
\(400\) −0.658646 + 3.94540i −0.0329323 + 0.197270i
\(401\) 9.89379 17.1366i 0.494072 0.855758i −0.505904 0.862590i \(-0.668841\pi\)
0.999977 + 0.00683114i \(0.00217444\pi\)
\(402\) 6.87413 + 5.74143i 0.342850 + 0.286356i
\(403\) −3.42572 + 1.97784i −0.170647 + 0.0985232i
\(404\) −14.3377 + 2.59557i −0.713326 + 0.129135i
\(405\) 3.50012i 0.173922i
\(406\) −1.62903 + 36.3730i −0.0808473 + 1.80516i
\(407\) 8.85261i 0.438808i
\(408\) 6.84595 + 11.6725i 0.338925 + 0.577872i
\(409\) 21.9116 12.6507i 1.08346 0.625536i 0.151633 0.988437i \(-0.451547\pi\)
0.931828 + 0.362900i \(0.118214\pi\)
\(410\) 9.51172 11.3882i 0.469750 0.562425i
\(411\) 3.58767 6.21403i 0.176967 0.306516i
\(412\) −14.0572 + 11.9050i −0.692547 + 0.586517i
\(413\) 23.9190 18.2247i 1.17698 0.896780i
\(414\) 4.85299 1.77888i 0.238511 0.0874272i
\(415\) −1.76492 1.01898i −0.0866366 0.0500197i
\(416\) 3.84506 3.30179i 0.188519 0.161884i
\(417\) −3.21278 5.56470i −0.157331 0.272505i
\(418\) 3.43597 19.7495i 0.168059 0.965980i
\(419\) 16.6804 0.814889 0.407445 0.913230i \(-0.366420\pi\)
0.407445 + 0.913230i \(0.366420\pi\)
\(420\) 4.19614 + 0.925174i 0.204751 + 0.0451439i
\(421\) 3.13305 0.152695 0.0763477 0.997081i \(-0.475674\pi\)
0.0763477 + 0.997081i \(0.475674\pi\)
\(422\) 1.50553 8.65358i 0.0732880 0.421250i
\(423\) 6.10814 + 10.5796i 0.296988 + 0.514398i
\(424\) 0.00347624 + 0.508324i 0.000168821 + 0.0246864i
\(425\) 5.10231 + 2.94582i 0.247498 + 0.142893i
\(426\) 9.03654 3.31238i 0.437822 0.160485i
\(427\) 6.28381 15.0256i 0.304095 0.727141i
\(428\) −19.3739 22.8762i −0.936470 1.10576i
\(429\) 1.76807 3.06238i 0.0853630 0.147853i
\(430\) −2.76123 + 3.30598i −0.133158 + 0.159428i
\(431\) 23.5490 13.5960i 1.13432 0.654898i 0.189300 0.981919i \(-0.439378\pi\)
0.945017 + 0.327021i \(0.106045\pi\)
\(432\) −13.3898 11.0289i −0.644216 0.530628i
\(433\) 32.0204i 1.53880i 0.638766 + 0.769401i \(0.279445\pi\)
−0.638766 + 0.769401i \(0.720555\pi\)
\(434\) 14.6620 7.61160i 0.703796 0.365369i
\(435\) 7.90185i 0.378865i
\(436\) −0.566908 3.13154i −0.0271500 0.149974i
\(437\) 3.94382 2.27697i 0.188659 0.108922i
\(438\) −7.73959 6.46428i −0.369812 0.308875i
\(439\) 10.0502 17.4074i 0.479668 0.830809i −0.520060 0.854130i \(-0.674091\pi\)
0.999728 + 0.0233207i \(0.00742388\pi\)
\(440\) −11.9523 6.79211i −0.569803 0.323801i
\(441\) −4.34814 + 15.7966i −0.207054 + 0.752220i
\(442\) −2.56915 7.00892i −0.122202 0.333380i
\(443\) 12.9010 + 7.44839i 0.612945 + 0.353884i 0.774117 0.633042i \(-0.218194\pi\)
−0.161172 + 0.986926i \(0.551527\pi\)
\(444\) −2.78424 0.999029i −0.132134 0.0474118i
\(445\) 0.882262 + 1.52812i 0.0418232 + 0.0724399i
\(446\) 17.8648 + 3.10808i 0.845925 + 0.147172i
\(447\) −1.39915 −0.0661776
\(448\) −16.6589 + 13.0569i −0.787057 + 0.616880i
\(449\) −6.18602 −0.291936 −0.145968 0.989289i \(-0.546630\pi\)
−0.145968 + 0.989289i \(0.546630\pi\)
\(450\) −3.26111 0.567359i −0.153730 0.0267456i
\(451\) 25.4979 + 44.1636i 1.20065 + 2.07958i
\(452\) 6.73677 + 2.41726i 0.316871 + 0.113698i
\(453\) −0.572536 0.330554i −0.0269001 0.0155308i
\(454\) 1.75542 + 4.78898i 0.0823858 + 0.224758i
\(455\) −2.18688 0.914567i −0.102523 0.0428755i
\(456\) −5.82367 3.30941i −0.272718 0.154977i
\(457\) 11.6751 20.2219i 0.546140 0.945943i −0.452394 0.891818i \(-0.649430\pi\)
0.998534 0.0541246i \(-0.0172368\pi\)
\(458\) −19.3075 16.1260i −0.902178 0.753520i
\(459\) −22.1276 + 12.7754i −1.03283 + 0.596304i
\(460\) −0.556323 3.07307i −0.0259387 0.143283i
\(461\) 17.4080i 0.810772i −0.914146 0.405386i \(-0.867137\pi\)
0.914146 0.405386i \(-0.132863\pi\)
\(462\) −7.94874 + 12.4461i −0.369809 + 0.579047i
\(463\) 0.962509i 0.0447316i −0.999750 0.0223658i \(-0.992880\pi\)
0.999750 0.0223658i \(-0.00711985\pi\)
\(464\) −30.0439 24.7465i −1.39475 1.14883i
\(465\) 3.10495 1.79264i 0.143988 0.0831318i
\(466\) 0.248466 0.297484i 0.0115099 0.0137807i
\(467\) 0.145490 0.251997i 0.00673249 0.0116610i −0.862640 0.505819i \(-0.831190\pi\)
0.869372 + 0.494158i \(0.164524\pi\)
\(468\) 2.71048 + 3.20048i 0.125292 + 0.147942i
\(469\) 12.5056 + 16.4130i 0.577455 + 0.757881i
\(470\) 6.93032 2.54034i 0.319672 0.117177i
\(471\) −9.39209 5.42252i −0.432764 0.249857i
\(472\) 0.219837 + 32.1464i 0.0101188 + 1.47966i
\(473\) −7.40196 12.8206i −0.340342 0.589490i
\(474\) −0.715250 + 4.11116i −0.0328525 + 0.188832i
\(475\) −2.91636 −0.133812
\(476\) 9.40906 + 29.7219i 0.431263 + 1.36230i
\(477\) −0.420660 −0.0192607
\(478\) 5.58136 32.0809i 0.255285 1.46735i
\(479\) −9.89481 17.1383i −0.452106 0.783070i 0.546411 0.837517i \(-0.315994\pi\)
−0.998517 + 0.0544474i \(0.982660\pi\)
\(480\) −3.48502 + 2.99262i −0.159069 + 0.136594i
\(481\) 1.41320 + 0.815911i 0.0644363 + 0.0372023i
\(482\) −4.98623 + 1.82772i −0.227116 + 0.0832504i
\(483\) −3.32761 + 0.426573i −0.151412 + 0.0194098i
\(484\) 19.2665 16.3168i 0.875751 0.741672i
\(485\) 3.91821 6.78653i 0.177917 0.308161i
\(486\) 14.3714 17.2067i 0.651901 0.780512i
\(487\) −19.5908 + 11.3108i −0.887745 + 0.512540i −0.873204 0.487355i \(-0.837962\pi\)
−0.0145405 + 0.999894i \(0.504629\pi\)
\(488\) 8.80851 + 15.0186i 0.398742 + 0.679862i
\(489\) 7.28979i 0.329656i
\(490\) 8.95296 + 4.22428i 0.404453 + 0.190833i
\(491\) 38.9565i 1.75808i 0.476745 + 0.879042i \(0.341816\pi\)
−0.476745 + 0.879042i \(0.658184\pi\)
\(492\) 16.7674 3.03542i 0.755932 0.136848i
\(493\) −49.6498 + 28.6653i −2.23611 + 1.29102i
\(494\) 2.83606 + 2.36874i 0.127600 + 0.106575i
\(495\) 5.68813 9.85213i 0.255662 0.442820i
\(496\) −2.90802 + 17.4195i −0.130574 + 0.782160i
\(497\) 21.9935 2.81939i 0.986543 0.126467i
\(498\) −0.805472 2.19742i −0.0360941 0.0984686i
\(499\) 32.6131 + 18.8292i 1.45996 + 0.842909i 0.999009 0.0445156i \(-0.0141744\pi\)
0.460953 + 0.887425i \(0.347508\pi\)
\(500\) −0.675465 + 1.88248i −0.0302077 + 0.0841873i
\(501\) −6.91551 11.9780i −0.308962 0.535138i
\(502\) −0.373704 0.0650161i −0.0166792 0.00290181i
\(503\) −42.9688 −1.91589 −0.957943 0.286959i \(-0.907356\pi\)
−0.957943 + 0.286959i \(0.907356\pi\)
\(504\) −10.7103 13.8592i −0.477077 0.617336i
\(505\) −7.28536 −0.324194
\(506\) 10.5745 + 1.83972i 0.470093 + 0.0817856i
\(507\) −4.95236 8.57774i −0.219942 0.380951i
\(508\) −5.18355 + 14.4463i −0.229983 + 0.640949i
\(509\) 4.13736 + 2.38870i 0.183385 + 0.105877i 0.588882 0.808219i \(-0.299568\pi\)
−0.405497 + 0.914096i \(0.632902\pi\)
\(510\) 2.32858 + 6.35264i 0.103111 + 0.281299i
\(511\) −14.0801 18.4794i −0.622866 0.817480i
\(512\) −0.464182 22.6227i −0.0205141 0.999790i
\(513\) 6.32382 10.9532i 0.279203 0.483594i
\(514\) 33.7406 + 28.1809i 1.48823 + 1.24301i
\(515\) −7.97652 + 4.60525i −0.351487 + 0.202931i
\(516\) −4.86753 + 0.881176i −0.214281 + 0.0387916i
\(517\) 25.3681i 1.11569i
\(518\) −5.74353 3.66811i −0.252356 0.161168i
\(519\) 13.3711i 0.586924i
\(520\) 2.18586 1.28202i 0.0958565 0.0562203i
\(521\) −15.8425 + 9.14670i −0.694075 + 0.400724i −0.805137 0.593089i \(-0.797908\pi\)
0.111062 + 0.993813i \(0.464575\pi\)
\(522\) 20.6479 24.7214i 0.903733 1.08203i
\(523\) 9.25624 16.0323i 0.404747 0.701043i −0.589545 0.807736i \(-0.700693\pi\)
0.994292 + 0.106693i \(0.0340262\pi\)
\(524\) −30.3840 + 25.7321i −1.32733 + 1.12411i
\(525\) 1.98211 + 0.828930i 0.0865063 + 0.0361775i
\(526\) −36.9746 + 13.5532i −1.61217 + 0.590947i
\(527\) 22.5275 + 13.0062i 0.981311 + 0.566560i
\(528\) −5.53468 14.7855i −0.240866 0.643458i
\(529\) −10.2808 17.8069i −0.446993 0.774215i
\(530\) −0.0435651 + 0.250407i −0.00189235 + 0.0108770i
\(531\) −26.6025 −1.15445
\(532\) −11.3897 10.4125i −0.493805 0.451440i
\(533\) −9.40015 −0.407166
\(534\) −0.347327 + 1.99639i −0.0150303 + 0.0863923i
\(535\) −7.49445 12.9808i −0.324013 0.561207i
\(536\) −22.0585 + 0.150850i −0.952783 + 0.00651573i
\(537\) 7.52358 + 4.34374i 0.324666 + 0.187446i
\(538\) 1.91850 0.703233i 0.0827123 0.0303185i
\(539\) −24.2211 + 23.8936i −1.04328 + 1.02917i
\(540\) −5.60549 6.61885i −0.241222 0.284830i
\(541\) 1.99811 3.46083i 0.0859055 0.148793i −0.819871 0.572548i \(-0.805955\pi\)
0.905777 + 0.423755i \(0.139288\pi\)
\(542\) −12.6866 + 15.1895i −0.544938 + 0.652446i
\(543\) −7.64159 + 4.41187i −0.327932 + 0.189332i
\(544\) −31.4461 11.0412i −1.34824 0.473388i
\(545\) 1.59122i 0.0681604i
\(546\) −1.25425 2.41602i −0.0536771 0.103396i
\(547\) 13.3961i 0.572774i 0.958114 + 0.286387i \(0.0924543\pi\)
−0.958114 + 0.286387i \(0.907546\pi\)
\(548\) 3.14809 + 17.3897i 0.134480 + 0.742851i
\(549\) −12.4778 + 7.20408i −0.532541 + 0.307463i
\(550\) −5.27560 4.40630i −0.224953 0.187885i
\(551\) 14.1893 24.5767i 0.604486 1.04700i
\(552\) 1.77196 3.11817i 0.0754195 0.132718i
\(553\) −3.70925 + 8.86943i −0.157733 + 0.377167i
\(554\) 9.01084 + 24.5826i 0.382834 + 1.04441i
\(555\) −1.28087 0.739512i −0.0543700 0.0313905i
\(556\) 14.8958 + 5.34486i 0.631723 + 0.226672i
\(557\) −7.20598 12.4811i −0.305327 0.528842i 0.672007 0.740545i \(-0.265432\pi\)
−0.977334 + 0.211703i \(0.932099\pi\)
\(558\) −14.3983 2.50497i −0.609527 0.106044i
\(559\) 2.72884 0.115418
\(560\) −9.35916 + 4.94026i −0.395497 + 0.208764i
\(561\) −23.2535 −0.981766
\(562\) 12.5515 + 2.18367i 0.529451 + 0.0921126i
\(563\) −3.33957 5.78430i −0.140746 0.243779i 0.787032 0.616912i \(-0.211617\pi\)
−0.927778 + 0.373133i \(0.878283\pi\)
\(564\) 7.97855 + 2.86283i 0.335957 + 0.120547i
\(565\) 3.09921 + 1.78933i 0.130385 + 0.0752777i
\(566\) −13.2850 36.2429i −0.558410 1.52340i
\(567\) 7.36594 5.61236i 0.309341 0.235697i
\(568\) −11.7116 + 20.6092i −0.491406 + 0.864743i
\(569\) −10.4511 + 18.1019i −0.438134 + 0.758871i −0.997546 0.0700192i \(-0.977694\pi\)
0.559411 + 0.828890i \(0.311027\pi\)
\(570\) −2.57050 2.14694i −0.107666 0.0899255i
\(571\) −4.83991 + 2.79432i −0.202544 + 0.116939i −0.597841 0.801614i \(-0.703975\pi\)
0.395298 + 0.918553i \(0.370641\pi\)
\(572\) 1.55143 + 8.56994i 0.0648685 + 0.358327i
\(573\) 0.411852i 0.0172053i
\(574\) 39.2182 + 1.75646i 1.63694 + 0.0733130i
\(575\) 1.56151i 0.0651195i
\(576\) 18.7230 0.256091i 0.780123 0.0106704i
\(577\) −1.57544 + 0.909582i −0.0655865 + 0.0378664i −0.532435 0.846471i \(-0.678723\pi\)
0.466848 + 0.884337i \(0.345389\pi\)
\(578\) −16.0566 + 19.2244i −0.667867 + 0.799628i
\(579\) 8.45316 14.6413i 0.351301 0.608472i
\(580\) −12.5776 14.8513i −0.522255 0.616668i
\(581\) −0.685592 5.34816i −0.0284431 0.221879i
\(582\) 8.44958 3.09723i 0.350246 0.128384i
\(583\) −0.756503 0.436767i −0.0313312 0.0180891i
\(584\) 24.8357 0.169842i 1.02771 0.00702812i
\(585\) 1.04851 + 1.81606i 0.0433504 + 0.0750850i
\(586\) −2.57745 + 14.8148i −0.106473 + 0.611996i
\(587\) 26.1792 1.08053 0.540265 0.841495i \(-0.318324\pi\)
0.540265 + 0.841495i \(0.318324\pi\)
\(588\) 4.78141 + 10.3142i 0.197182 + 0.425351i
\(589\) −12.8762 −0.530554
\(590\) −2.75506 + 15.8357i −0.113424 + 0.651946i
\(591\) 3.59773 + 6.23146i 0.147991 + 0.256328i
\(592\) 6.82309 2.55409i 0.280427 0.104973i
\(593\) −23.9296 13.8158i −0.982671 0.567345i −0.0795955 0.996827i \(-0.525363\pi\)
−0.903075 + 0.429482i \(0.858696\pi\)
\(594\) 27.9886 10.2593i 1.14839 0.420945i
\(595\) 1.98201 + 15.4613i 0.0812547 + 0.633851i
\(596\) 2.62967 2.22706i 0.107716 0.0912241i
\(597\) −9.42628 + 16.3268i −0.385792 + 0.668211i
\(598\) −1.26830 + 1.51851i −0.0518645 + 0.0620966i
\(599\) 4.82336 2.78477i 0.197077 0.113783i −0.398214 0.917292i \(-0.630370\pi\)
0.595291 + 0.803510i \(0.297037\pi\)
\(600\) −1.98119 + 1.16198i −0.0808817 + 0.0474375i
\(601\) 30.5902i 1.24780i −0.781504 0.623901i \(-0.785547\pi\)
0.781504 0.623901i \(-0.214453\pi\)
\(602\) −11.3849 0.509894i −0.464016 0.0207817i
\(603\) 18.2544i 0.743375i
\(604\) 1.60222 0.290052i 0.0651933 0.0118020i
\(605\) 10.9325 6.31188i 0.444469 0.256614i
\(606\) −6.42136 5.36327i −0.260850 0.217868i
\(607\) −10.1110 + 17.5127i −0.410391 + 0.710818i −0.994932 0.100546i \(-0.967941\pi\)
0.584541 + 0.811364i \(0.301275\pi\)
\(608\) 16.2131 3.04974i 0.657528 0.123683i
\(609\) −16.6293 + 12.6704i −0.673854 + 0.513432i
\(610\) 2.99613 + 8.17377i 0.121310 + 0.330946i
\(611\) −4.04968 2.33808i −0.163832 0.0945887i
\(612\) 9.31460 25.9593i 0.376520 1.04934i
\(613\) 11.2510 + 19.4874i 0.454425 + 0.787087i 0.998655 0.0518488i \(-0.0165114\pi\)
−0.544230 + 0.838936i \(0.683178\pi\)
\(614\) 25.0529 + 4.35864i 1.01105 + 0.175900i
\(615\) 8.51996 0.343558
\(616\) −4.87137 36.0444i −0.196273 1.45227i
\(617\) 22.5772 0.908922 0.454461 0.890767i \(-0.349832\pi\)
0.454461 + 0.890767i \(0.349832\pi\)
\(618\) −10.4208 1.81298i −0.419186 0.0729289i
\(619\) −6.15713 10.6645i −0.247476 0.428641i 0.715349 0.698768i \(-0.246268\pi\)
−0.962825 + 0.270126i \(0.912935\pi\)
\(620\) −2.98228 + 8.31145i −0.119771 + 0.333796i
\(621\) 5.86466 + 3.38596i 0.235341 + 0.135874i
\(622\) 13.7818 + 37.5983i 0.552600 + 1.50755i
\(623\) −1.80122 + 4.30702i −0.0721644 + 0.172557i
\(624\) 2.87042 + 0.479188i 0.114909 + 0.0191829i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 6.07287 + 5.07220i 0.242721 + 0.202726i
\(627\) 9.96839 5.75526i 0.398099 0.229843i
\(628\) 26.2834 4.75812i 1.04882 0.189869i
\(629\) 10.7308i 0.427866i
\(630\) −4.03512 7.77269i −0.160763 0.309672i
\(631\) 22.9961i 0.915459i −0.889091 0.457730i \(-0.848663\pi\)
0.889091 0.457730i \(-0.151337\pi\)
\(632\) −5.19954 8.86531i −0.206827 0.352643i
\(633\) 4.36782 2.52176i 0.173605 0.100231i
\(634\) 28.4184 34.0249i 1.12864 1.35130i
\(635\) −3.83702 + 6.64592i −0.152268 + 0.263735i
\(636\) −0.222740 + 0.188639i −0.00883223 + 0.00748000i
\(637\) −1.58192 6.06874i −0.0626781 0.240452i
\(638\) 62.8006 23.0198i 2.48630 0.911363i
\(639\) −16.9879 9.80798i −0.672032 0.387998i
\(640\) 1.78658 11.1718i 0.0706207 0.441602i
\(641\) 17.7377 + 30.7226i 0.700598 + 1.21347i 0.968257 + 0.249957i \(0.0804165\pi\)
−0.267659 + 0.963514i \(0.586250\pi\)
\(642\) 2.95040 16.9585i 0.116443 0.669299i
\(643\) 8.46366 0.333774 0.166887 0.985976i \(-0.446628\pi\)
0.166887 + 0.985976i \(0.446628\pi\)
\(644\) 5.57518 6.09838i 0.219693 0.240310i
\(645\) −2.47332 −0.0973869
\(646\) 4.16496 23.9397i 0.163868 0.941893i
\(647\) 2.47704 + 4.29036i 0.0973826 + 0.168672i 0.910600 0.413288i \(-0.135620\pi\)
−0.813218 + 0.581959i \(0.802286\pi\)
\(648\) 0.0676997 + 9.89959i 0.00265949 + 0.388893i
\(649\) −47.8413 27.6212i −1.87793 1.08423i
\(650\) 1.18964 0.436066i 0.0466615 0.0171039i
\(651\) 8.75130 + 3.65985i 0.342991 + 0.143441i
\(652\) −11.6033 13.7010i −0.454422 0.536572i
\(653\) 0.945688 1.63798i 0.0370076 0.0640991i −0.846928 0.531707i \(-0.821551\pi\)
0.883936 + 0.467608i \(0.154884\pi\)
\(654\) 1.17141 1.40251i 0.0458057 0.0548425i
\(655\) −17.2409 + 9.95404i −0.673658 + 0.388937i
\(656\) −26.6823 + 32.3940i −1.04177 + 1.26478i
\(657\) 20.5526i 0.801833i
\(658\) 16.4587 + 10.5114i 0.641628 + 0.409776i
\(659\) 4.20598i 0.163842i −0.996639 0.0819209i \(-0.973895\pi\)
0.996639 0.0819209i \(-0.0261055\pi\)
\(660\) −1.40616 7.76749i −0.0547347 0.302349i
\(661\) 9.78997 5.65224i 0.380786 0.219847i −0.297374 0.954761i \(-0.596111\pi\)
0.678160 + 0.734914i \(0.262778\pi\)
\(662\) −23.3512 19.5034i −0.907569 0.758022i
\(663\) 2.14319 3.71211i 0.0832346 0.144166i
\(664\) 5.01155 + 2.84790i 0.194486 + 0.110520i
\(665\) −4.67633 6.13744i −0.181340 0.238000i
\(666\) 2.07491 + 5.66058i 0.0804011 + 0.219343i
\(667\) 13.1591 + 7.59740i 0.509522 + 0.294173i
\(668\) 32.0632 + 11.5048i 1.24056 + 0.445134i
\(669\) 5.20604 + 9.01713i 0.201277 + 0.348622i
\(670\) −10.8663 1.89049i −0.419802 0.0730361i
\(671\) −29.9197 −1.15504
\(672\) −11.8861 2.53556i −0.458516 0.0978115i
\(673\) −36.8435 −1.42021 −0.710106 0.704095i \(-0.751353\pi\)
−0.710106 + 0.704095i \(0.751353\pi\)
\(674\) 0.0813888 + 0.0141598i 0.00313498 + 0.000545416i
\(675\) −2.16839 3.75576i −0.0834614 0.144559i
\(676\) 22.9612 + 8.23885i 0.883124 + 0.316879i
\(677\) 24.0708 + 13.8973i 0.925115 + 0.534115i 0.885263 0.465090i \(-0.153978\pi\)
0.0398518 + 0.999206i \(0.487311\pi\)
\(678\) 1.41441 + 3.85867i 0.0543202 + 0.148191i
\(679\) 20.5649 2.63626i 0.789209 0.101170i
\(680\) −14.4882 8.23316i −0.555595 0.315727i
\(681\) −1.46437 + 2.53637i −0.0561149 + 0.0971939i
\(682\) −23.2926 19.4545i −0.891919 0.744951i
\(683\) 40.9116 23.6203i 1.56544 0.903806i 0.568748 0.822512i \(-0.307428\pi\)
0.996690 0.0812945i \(-0.0259054\pi\)
\(684\) 2.43192 + 13.4337i 0.0929867 + 0.513649i
\(685\) 8.83618i 0.337613i
\(686\) 5.46595 + 25.6149i 0.208691 + 0.977982i
\(687\) 14.4446i 0.551096i
\(688\) 7.74580 9.40391i 0.295306 0.358521i
\(689\) 0.139448 0.0805103i 0.00531254 0.00306720i
\(690\) 1.14954 1.37632i 0.0437621 0.0523958i
\(691\) −17.2216 + 29.8286i −0.655139 + 1.13473i 0.326720 + 0.945121i \(0.394057\pi\)
−0.981859 + 0.189613i \(0.939277\pi\)
\(692\) 21.2830 + 25.1306i 0.809060 + 0.955321i
\(693\) 29.8544 3.82710i 1.13408 0.145380i
\(694\) −11.7029 + 4.28974i −0.444236 + 0.162836i
\(695\) 6.85273 + 3.95643i 0.259939 + 0.150076i
\(696\) −0.152838 22.3493i −0.00579333 0.847147i
\(697\) 30.9076 + 53.5336i 1.17071 + 2.02773i
\(698\) 0.432818 2.48778i 0.0163824 0.0941639i
\(699\) 0.222559 0.00841795
\(700\) −5.04475 + 1.59702i −0.190674 + 0.0603616i
\(701\) −28.7191 −1.08470 −0.542352 0.840151i \(-0.682466\pi\)
−0.542352 + 0.840151i \(0.682466\pi\)
\(702\) −0.941838 + 5.41356i −0.0355474 + 0.204322i
\(703\) 2.65588 + 4.60012i 0.100168 + 0.173497i
\(704\) 33.9368 + 18.9793i 1.27904 + 0.715311i
\(705\) 3.67048 + 2.11915i 0.138238 + 0.0798119i
\(706\) −36.5057 + 13.3813i −1.37391 + 0.503612i
\(707\) −11.6819 15.3319i −0.439344 0.576616i
\(708\) −14.0861 + 11.9295i −0.529388 + 0.448338i
\(709\) −24.7310 + 42.8354i −0.928794 + 1.60872i −0.143450 + 0.989658i \(0.545820\pi\)
−0.785344 + 0.619060i \(0.787514\pi\)
\(710\) −7.59774 + 9.09667i −0.285138 + 0.341392i
\(711\) 7.36550 4.25247i 0.276228 0.159480i
\(712\) −2.52491 4.30502i −0.0946251 0.161337i
\(713\) 6.89430i 0.258193i
\(714\) −9.63519 + 15.0868i −0.360588 + 0.564609i
\(715\) 4.35462i 0.162854i
\(716\) −21.0544 + 3.81151i −0.786840 + 0.142443i
\(717\) 16.1926 9.34879i 0.604723 0.349137i
\(718\) −20.1934 16.8660i −0.753612 0.629434i
\(719\) −2.38663 + 4.13376i −0.0890061 + 0.154163i −0.907091 0.420934i \(-0.861702\pi\)
0.818085 + 0.575097i \(0.195036\pi\)
\(720\) 9.23456 + 1.54162i 0.344152 + 0.0574528i
\(721\) −22.4818 9.40205i −0.837268 0.350151i
\(722\) −5.10801 13.9352i −0.190101 0.518616i
\(723\) −2.64084 1.52469i −0.0982138 0.0567038i
\(724\) 7.33968 20.4553i 0.272777 0.760215i
\(725\) −4.86542 8.42715i −0.180697 0.312977i
\(726\) 14.2826 + 2.48485i 0.530076 + 0.0922214i
\(727\) −20.9881 −0.778405 −0.389202 0.921152i \(-0.627249\pi\)
−0.389202 + 0.921152i \(0.627249\pi\)
\(728\) 6.20298 + 2.54443i 0.229898 + 0.0943027i
\(729\) 2.37261 0.0878744
\(730\) 12.2344 + 2.12850i 0.452814 + 0.0787795i
\(731\) −8.97240 15.5406i −0.331856 0.574792i
\(732\) −3.37648 + 9.41008i −0.124798 + 0.347806i
\(733\) 16.4524 + 9.49880i 0.607684 + 0.350846i 0.772058 0.635552i \(-0.219227\pi\)
−0.164375 + 0.986398i \(0.552561\pi\)
\(734\) −10.7002 29.1913i −0.394951 1.07747i
\(735\) 1.43380 + 5.50049i 0.0528865 + 0.202889i
\(736\) 1.63292 + 8.68099i 0.0601903 + 0.319986i
\(737\) 18.9534 32.8282i 0.698156 1.20924i
\(738\) −26.6552 22.2630i −0.981191 0.819513i
\(739\) 15.2226 8.78874i 0.559971 0.323299i −0.193163 0.981167i \(-0.561875\pi\)
0.753134 + 0.657867i \(0.228541\pi\)
\(740\) 3.58447 0.648902i 0.131768 0.0238541i
\(741\) 2.12176i 0.0779447i
\(742\) −0.596832 + 0.309839i −0.0219104 + 0.0113746i
\(743\) 0.624385i 0.0229065i 0.999934 + 0.0114532i \(0.00364575\pi\)
−0.999934 + 0.0114532i \(0.996354\pi\)
\(744\) −8.74724 + 5.13030i −0.320689 + 0.188086i
\(745\) 1.49217 0.861502i 0.0546687 0.0315630i
\(746\) 0.512769 0.613931i 0.0187738 0.0224776i
\(747\) −2.38501 + 4.13096i −0.0872629 + 0.151144i
\(748\) 43.7045 37.0132i 1.59799 1.35334i
\(749\) 15.3006 36.5863i 0.559073 1.33684i
\(750\) −1.07825 + 0.395235i −0.0393720 + 0.0144319i
\(751\) −28.7011 16.5706i −1.04732 0.604670i −0.125422 0.992103i \(-0.540028\pi\)
−0.921898 + 0.387433i \(0.873362\pi\)
\(752\) −19.5523 + 7.31903i −0.712999 + 0.266898i
\(753\) −0.108902 0.188624i −0.00396862 0.00687384i
\(754\) −2.11329 + 12.1469i −0.0769615 + 0.442364i
\(755\) 0.814130 0.0296292
\(756\) 4.94097 22.4099i 0.179701 0.815038i
\(757\) 43.9649 1.59793 0.798966 0.601376i \(-0.205380\pi\)
0.798966 + 0.601376i \(0.205380\pi\)
\(758\) −6.86705 + 39.4709i −0.249423 + 1.43365i
\(759\) 3.08154 + 5.33738i 0.111853 + 0.193735i
\(760\) 8.24853 0.0564087i 0.299206 0.00204616i
\(761\) −6.43253 3.71382i −0.233179 0.134626i 0.378859 0.925455i \(-0.376317\pi\)
−0.612038 + 0.790829i \(0.709650\pi\)
\(762\) −8.27450 + 3.03305i −0.299754 + 0.109876i
\(763\) 3.34870 2.55149i 0.121231 0.0923701i
\(764\) 0.655554 + 0.774065i 0.0237171 + 0.0280047i
\(765\) 6.89495 11.9424i 0.249288 0.431779i
\(766\) −2.79767 + 3.34961i −0.101084 + 0.121026i
\(767\) 8.81869 5.09147i 0.318424 0.183842i
\(768\) 9.79902 8.53163i 0.353592 0.307859i
\(769\) 17.2607i 0.622438i 0.950338 + 0.311219i \(0.100737\pi\)
−0.950338 + 0.311219i \(0.899263\pi\)
\(770\) 0.813678 18.1678i 0.0293229 0.654724i
\(771\) 25.2426i 0.909089i
\(772\) 7.41742 + 40.9731i 0.266959 + 1.47465i
\(773\) 30.6272 17.6826i 1.10158 0.636000i 0.164948 0.986302i \(-0.447254\pi\)
0.936637 + 0.350302i \(0.113921\pi\)
\(774\) 7.73793 + 6.46289i 0.278134 + 0.232304i
\(775\) −2.20757 + 3.82363i −0.0792984 + 0.137349i
\(776\) −10.9508 + 19.2706i −0.393112 + 0.691773i
\(777\) −0.497560 3.88137i −0.0178499 0.139243i
\(778\) 7.95963 + 21.7148i 0.285367 + 0.778512i
\(779\) −26.4991 15.2993i −0.949430 0.548153i
\(780\) 1.36957 + 0.491425i 0.0490386 + 0.0175958i
\(781\) −20.3671 35.2768i −0.728792 1.26230i
\(782\) 12.8180 + 2.23005i 0.458372 + 0.0797464i
\(783\) 42.2005 1.50812
\(784\) −25.4039 11.7746i −0.907282 0.420522i
\(785\) 13.3553 0.476670
\(786\) −22.5241 3.91869i −0.803409 0.139775i
\(787\) −5.59512 9.69103i −0.199444 0.345448i 0.748904 0.662678i \(-0.230580\pi\)
−0.948348 + 0.317231i \(0.897247\pi\)
\(788\) −16.6806 5.98527i −0.594222 0.213216i
\(789\) −19.5827 11.3061i −0.697164 0.402508i
\(790\) −1.76858 4.82487i −0.0629231 0.171661i
\(791\) 1.20390 + 9.39140i 0.0428058 + 0.333920i
\(792\) −15.8975 + 27.9754i −0.564894 + 0.994062i
\(793\) 2.75759 4.77628i 0.0979248 0.169611i
\(794\) 8.49298 + 7.09353i 0.301405 + 0.251740i
\(795\) −0.126391 + 0.0729717i −0.00448261 + 0.00258804i
\(796\) −8.27130 45.6898i −0.293169 1.61943i
\(797\) 9.18543i 0.325365i −0.986679 0.162682i \(-0.947985\pi\)
0.986679 0.162682i \(-0.0520146\pi\)
\(798\) 0.396459 8.85215i 0.0140345 0.313363i
\(799\) 30.7504i 1.08787i
\(800\) 1.87405 5.33741i 0.0662576 0.188706i
\(801\) 3.57670 2.06501i 0.126377 0.0729636i
\(802\) −17.9388 + 21.4778i −0.633440 + 0.758409i
\(803\) −21.3396 + 36.9613i −0.753058 + 1.30433i
\(804\) −8.18590 9.66574i −0.288694 0.340884i
\(805\) 3.28617 2.50385i 0.115822 0.0882491i
\(806\) 5.25243 1.92530i 0.185009 0.0678157i
\(807\) 1.01609 + 0.586638i 0.0357680 + 0.0206506i
\(808\) 20.6056 0.140914i 0.724903 0.00495735i
\(809\) 0.0848856 + 0.147026i 0.00298442 + 0.00516917i 0.867514 0.497413i \(-0.165717\pi\)
−0.864529 + 0.502582i \(0.832383\pi\)
\(810\) −0.848429 + 4.87666i −0.0298108 + 0.171348i
\(811\) 38.6906 1.35861 0.679306 0.733855i \(-0.262281\pi\)
0.679306 + 0.733855i \(0.262281\pi\)
\(812\) 11.0865 50.2831i 0.389061 1.76459i
\(813\) −11.3638 −0.398547
\(814\) −2.14588 + 12.3342i −0.0752129 + 0.432314i
\(815\) −4.48856 7.77441i −0.157227 0.272326i
\(816\) −6.70895 17.9225i −0.234860 0.627413i
\(817\) 7.69262 + 4.44134i 0.269131 + 0.155383i
\(818\) −33.5957 + 12.3146i −1.17465 + 0.430571i
\(819\) −2.14062 + 5.11859i −0.0747995 + 0.178858i
\(820\) −16.0130 + 13.5614i −0.559200 + 0.473585i
\(821\) −16.9114 + 29.2914i −0.590213 + 1.02228i 0.403991 + 0.914763i \(0.367623\pi\)
−0.994203 + 0.107515i \(0.965710\pi\)
\(822\) −6.50493 + 7.78826i −0.226886 + 0.271647i
\(823\) −9.03275 + 5.21506i −0.314862 + 0.181786i −0.649100 0.760703i \(-0.724854\pi\)
0.334238 + 0.942489i \(0.391521\pi\)
\(824\) 22.4714 13.1796i 0.782828 0.459132i
\(825\) 3.94687i 0.137412i
\(826\) −37.7437 + 19.5942i −1.31327 + 0.681771i
\(827\) 10.1110i 0.351594i −0.984426 0.175797i \(-0.943750\pi\)
0.984426 0.175797i \(-0.0562502\pi\)
\(828\) −7.19279 + 1.30212i −0.249967 + 0.0452519i
\(829\) 6.66205 3.84634i 0.231383 0.133589i −0.379827 0.925058i \(-0.624017\pi\)
0.611210 + 0.791469i \(0.290683\pi\)
\(830\) 2.21204 + 1.84754i 0.0767810 + 0.0641292i
\(831\) −7.51686 + 13.0196i −0.260757 + 0.451645i
\(832\) −6.15761 + 3.66829i −0.213477 + 0.127175i
\(833\) −29.3599 + 28.9630i −1.01726 + 1.00351i
\(834\) 3.12744 + 8.53200i 0.108294 + 0.295439i
\(835\) 14.7505 + 8.51620i 0.510462 + 0.294715i
\(836\) −9.57457 + 26.6838i −0.331143 + 0.922878i
\(837\) −9.57376 16.5822i −0.330918 0.573166i
\(838\) −23.2405 4.04332i −0.802830 0.139674i
\(839\) 46.1347 1.59275 0.796373 0.604806i \(-0.206749\pi\)
0.796373 + 0.604806i \(0.206749\pi\)
\(840\) −5.62215 2.30618i −0.193983 0.0795706i
\(841\) 65.6893 2.26515
\(842\) −4.36522 0.759451i −0.150436 0.0261724i
\(843\) 3.65765 + 6.33524i 0.125976 + 0.218197i
\(844\) −4.19526 + 11.6920i −0.144407 + 0.402454i
\(845\) 10.5632 + 6.09865i 0.363384 + 0.209800i
\(846\) −5.94588 16.2210i −0.204423 0.557690i
\(847\) 30.8133 + 12.8863i 1.05876 + 0.442778i
\(848\) 0.118374 0.709083i 0.00406500 0.0243500i
\(849\) 11.0824 19.1952i 0.380346 0.658778i
\(850\) −6.39490 5.34117i −0.219343 0.183201i
\(851\) −2.46305 + 1.42204i −0.0844321 + 0.0487469i
\(852\) −13.3934 + 2.42463i −0.458850 + 0.0830663i
\(853\) 29.1420i 0.997804i −0.866658 0.498902i \(-0.833737\pi\)
0.866658 0.498902i \(-0.166263\pi\)
\(854\) −12.3974 + 19.4118i −0.424229 + 0.664258i
\(855\) 6.82601i 0.233445i
\(856\) 21.4481 + 36.5693i 0.733080 + 1.24991i
\(857\) −10.5403 + 6.08543i −0.360049 + 0.207874i −0.669102 0.743170i \(-0.733321\pi\)
0.309053 + 0.951045i \(0.399988\pi\)
\(858\) −3.20574 + 3.83819i −0.109442 + 0.131034i
\(859\) 2.45770 4.25686i 0.0838555 0.145242i −0.821047 0.570860i \(-0.806610\pi\)
0.904903 + 0.425618i \(0.139943\pi\)
\(860\) 4.64854 3.93685i 0.158514 0.134245i
\(861\) 13.6616 + 17.9301i 0.465585 + 0.611057i
\(862\) −36.1062 + 13.2349i −1.22978 + 0.450781i
\(863\) −18.5564 10.7135i −0.631666 0.364692i 0.149731 0.988727i \(-0.452159\pi\)
−0.781397 + 0.624034i \(0.785493\pi\)
\(864\) 15.9824 + 18.6121i 0.543731 + 0.633195i
\(865\) 8.23299 + 14.2599i 0.279930 + 0.484853i
\(866\) 7.76175 44.6135i 0.263755 1.51603i
\(867\) −14.3824 −0.488453
\(868\) −22.2733 + 7.05107i −0.756006 + 0.239329i
\(869\) 17.6612 0.599116
\(870\) 1.91541 11.0095i 0.0649385 0.373258i
\(871\) 3.49371 + 6.05129i 0.118380 + 0.205040i
\(872\) 0.0307776 + 4.50055i 0.00104226 + 0.152408i
\(873\) −15.8845 9.17091i −0.537608 0.310388i
\(874\) −6.04680 + 2.21648i −0.204536 + 0.0749735i
\(875\) −2.62428 + 0.336411i −0.0887167 + 0.0113728i
\(876\) 9.21650 + 10.8827i 0.311397 + 0.367691i
\(877\) 12.1125 20.9794i 0.409009 0.708424i −0.585770 0.810477i \(-0.699208\pi\)
0.994779 + 0.102053i \(0.0325412\pi\)
\(878\) −18.2223 + 21.8173i −0.614972 + 0.736297i
\(879\) −7.47767 + 4.31723i −0.252216 + 0.145617i
\(880\) 15.0065 + 12.3606i 0.505870 + 0.416675i
\(881\) 30.4932i 1.02734i −0.857987 0.513671i \(-0.828285\pi\)
0.857987 0.513671i \(-0.171715\pi\)
\(882\) 9.88729 20.9552i 0.332922 0.705598i
\(883\) 0.362622i 0.0122032i 0.999981 + 0.00610160i \(0.00194221\pi\)
−0.999981 + 0.00610160i \(0.998058\pi\)
\(884\) 1.88059 + 10.3882i 0.0632511 + 0.349393i
\(885\) −7.99294 + 4.61473i −0.268680 + 0.155122i
\(886\) −16.1693 13.5049i −0.543217 0.453707i
\(887\) −18.8687 + 32.6816i −0.633550 + 1.09734i 0.353270 + 0.935521i \(0.385070\pi\)
−0.986820 + 0.161820i \(0.948264\pi\)
\(888\) 3.63707 + 2.06683i 0.122052 + 0.0693584i
\(889\) −20.1388 + 2.58163i −0.675434 + 0.0865852i
\(890\) −0.858824 2.34297i −0.0287879 0.0785365i
\(891\) −14.7329 8.50603i −0.493570 0.284963i
\(892\) −24.1374 8.66089i −0.808180 0.289988i
\(893\) −7.61072 13.1822i −0.254683 0.441124i
\(894\) 1.94942 + 0.339155i 0.0651983 + 0.0113430i
\(895\) −10.6983 −0.357605
\(896\) 26.3755 14.1539i 0.881145 0.472847i
\(897\) −1.13605 −0.0379317
\(898\) 8.61888 + 1.49949i 0.287616 + 0.0500387i
\(899\) −21.4815 37.2071i −0.716450 1.24093i
\(900\) 4.40612 + 1.58099i 0.146871 + 0.0526995i
\(901\) −0.917007 0.529434i −0.0305499 0.0176380i
\(902\) −24.8205 67.7131i −0.826432 2.25460i
\(903\) −3.96592 5.20507i −0.131978 0.173214i
\(904\) −8.80030 5.00093i −0.292694 0.166328i
\(905\) 5.43306 9.41034i 0.180601 0.312810i
\(906\) 0.717579 + 0.599338i 0.0238400 + 0.0199117i
\(907\) −4.41171 + 2.54710i −0.146489 + 0.0845752i −0.571453 0.820635i \(-0.693620\pi\)
0.424964 + 0.905210i \(0.360287\pi\)
\(908\) −1.28495 7.09792i −0.0426425 0.235553i
\(909\) 17.0520i 0.565580i
\(910\) 2.82526 + 1.80435i 0.0936563 + 0.0598137i
\(911\) 4.73127i 0.156754i −0.996924 0.0783769i \(-0.975026\pi\)
0.996924 0.0783769i \(-0.0249738\pi\)
\(912\) 7.31183 + 6.02260i 0.242119 + 0.199428i
\(913\) −8.57828 + 4.95267i −0.283900 + 0.163910i
\(914\) −21.1686 + 25.3449i −0.700195 + 0.838334i
\(915\) −2.49938 + 4.32905i −0.0826269 + 0.143114i
\(916\) 22.9918 + 27.1483i 0.759671 + 0.897004i
\(917\) −48.5936 20.3221i −1.60470 0.671096i
\(918\) 33.9268 12.4360i 1.11975 0.410449i
\(919\) −25.6239 14.7939i −0.845254 0.488007i 0.0137930 0.999905i \(-0.495609\pi\)
−0.859047 + 0.511898i \(0.828943\pi\)
\(920\) 0.0302029 + 4.41651i 0.000995760 + 0.145608i
\(921\) 7.30073 + 12.6452i 0.240567 + 0.416675i
\(922\) −4.21970 + 24.2543i −0.138969 + 0.798773i
\(923\) 7.50862 0.247149
\(924\) 14.0918 15.4142i 0.463586 0.507091i
\(925\) 1.82136 0.0598861
\(926\) −0.233312 + 1.34105i −0.00766712 + 0.0440696i
\(927\) 10.7790 + 18.6697i 0.354028 + 0.613195i
\(928\) 35.8612 + 41.7616i 1.17720 + 1.37089i
\(929\) 0.232942 + 0.134489i 0.00764257 + 0.00441244i 0.503816 0.863811i \(-0.331929\pi\)
−0.496174 + 0.868223i \(0.665262\pi\)
\(930\) −4.76061 + 1.74502i −0.156107 + 0.0572215i
\(931\) 5.41776 19.6825i 0.177560 0.645069i
\(932\) −0.418294 + 0.354252i −0.0137017 + 0.0116039i
\(933\) −11.4968 + 19.9131i −0.376389 + 0.651924i
\(934\) −0.263793 + 0.315836i −0.00863158 + 0.0103345i
\(935\) 24.7994 14.3179i 0.811028 0.468247i
\(936\) −3.00068 5.11621i −0.0980802 0.167228i
\(937\) 32.3858i 1.05800i −0.848623 0.528999i \(-0.822568\pi\)
0.848623 0.528999i \(-0.177432\pi\)
\(938\) −13.4454 25.8993i −0.439007 0.845643i
\(939\) 4.54334i 0.148266i
\(940\) −10.2717 + 1.85950i −0.335025 + 0.0606502i
\(941\) −14.7440 + 8.51248i −0.480642 + 0.277499i −0.720684 0.693264i \(-0.756172\pi\)
0.240042 + 0.970763i \(0.422839\pi\)
\(942\) 11.7714 + 9.83176i 0.383534 + 0.320336i
\(943\) 8.19170 14.1884i 0.266758 0.462039i
\(944\) 7.48600 44.8424i 0.243649 1.45950i
\(945\) 4.42698 10.5856i 0.144010 0.344351i
\(946\) 7.20533 + 19.6569i 0.234265 + 0.639102i
\(947\) 0.317117 + 0.183088i 0.0103049 + 0.00594955i 0.505144 0.863035i \(-0.331440\pi\)
−0.494839 + 0.868985i \(0.664773\pi\)
\(948\) 1.99309 5.55464i 0.0647327 0.180406i
\(949\) −3.93357 6.81315i −0.127689 0.221164i
\(950\) 4.06333 + 0.706927i 0.131832 + 0.0229358i
\(951\) 25.4553 0.825444
\(952\) −5.90491 43.6918i −0.191379 1.41606i
\(953\) 28.7452 0.931148 0.465574 0.885009i \(-0.345848\pi\)
0.465574 + 0.885009i \(0.345848\pi\)
\(954\) 0.586099 + 0.101968i 0.0189756 + 0.00330134i
\(955\) 0.253590 + 0.439231i 0.00820599 + 0.0142132i
\(956\) −15.5528 + 43.3449i −0.503015 + 1.40187i
\(957\) 33.2609 + 19.2032i 1.07517 + 0.620751i
\(958\) 9.63196 + 26.2771i 0.311194 + 0.848973i
\(959\) −18.5956 + 14.1686i −0.600483 + 0.457529i
\(960\) 5.58104 3.32481i 0.180127 0.107308i
\(961\) 5.75324 9.96490i 0.185588 0.321448i
\(962\) −1.77121 1.47936i −0.0571061 0.0476963i
\(963\) −30.3826 + 17.5414i −0.979067 + 0.565264i
\(964\) 7.39027 1.33787i 0.238025 0.0430900i
\(965\) 20.8195i 0.670204i
\(966\) 4.73971 + 0.212276i 0.152498 + 0.00682987i
\(967\) 38.1396i 1.22649i 0.789895 + 0.613243i \(0.210135\pi\)
−0.789895 + 0.613243i \(0.789865\pi\)
\(968\) −30.7990 + 18.0637i −0.989916 + 0.580590i
\(969\) 12.0833 6.97632i 0.388173 0.224112i
\(970\) −7.10424 + 8.50580i −0.228103 + 0.273105i
\(971\) 2.80103 4.85153i 0.0898895 0.155693i −0.817575 0.575822i \(-0.804682\pi\)
0.907464 + 0.420129i \(0.138015\pi\)
\(972\) −24.1944 + 20.4902i −0.776036 + 0.657224i
\(973\) 2.66197 + 20.7655i 0.0853389 + 0.665712i
\(974\) 30.0373 11.0103i 0.962458 0.352793i
\(975\) 0.630064 + 0.363768i 0.0201782 + 0.0116499i
\(976\) −8.63223 23.0604i −0.276311 0.738146i
\(977\) 20.7850 + 36.0007i 0.664972 + 1.15176i 0.979293 + 0.202448i \(0.0648898\pi\)
−0.314321 + 0.949317i \(0.601777\pi\)
\(978\) 1.76705 10.1568i 0.0565039 0.324777i
\(979\) 8.57634 0.274101
\(980\) −11.4501 8.05582i −0.365759 0.257334i
\(981\) −3.72439 −0.118911
\(982\) 9.44307 54.2775i 0.301340 1.73207i
\(983\) 22.5595 + 39.0742i 0.719536 + 1.24627i 0.961184 + 0.275909i \(0.0889789\pi\)
−0.241647 + 0.970364i \(0.577688\pi\)
\(984\) −24.0975 + 0.164794i −0.768201 + 0.00525344i
\(985\) −7.67381 4.43048i −0.244508 0.141167i
\(986\) 76.1248 27.9038i 2.42431 0.888639i
\(987\) 1.42581 + 11.1225i 0.0453842 + 0.354033i
\(988\) −3.37725 3.98779i −0.107445 0.126869i
\(989\) −2.37803 + 4.11887i −0.0756169 + 0.130972i
\(990\) −10.3133 + 12.3480i −0.327780 + 0.392446i
\(991\) 22.2587 12.8510i 0.707069 0.408227i −0.102906 0.994691i \(-0.532814\pi\)
0.809975 + 0.586464i \(0.199481\pi\)
\(992\) 8.27420 23.5655i 0.262706 0.748204i
\(993\) 17.4699i 0.554389i
\(994\) −31.3266 1.40302i −0.993620 0.0445010i
\(995\) 23.2162i 0.736005i
\(996\) 0.589597 + 3.25688i 0.0186821 + 0.103198i
\(997\) −25.9069 + 14.9574i −0.820481 + 0.473705i −0.850582 0.525842i \(-0.823750\pi\)
0.0301015 + 0.999547i \(0.490417\pi\)
\(998\) −40.8751 34.1398i −1.29388 1.08068i
\(999\) −3.94943 + 6.84061i −0.124954 + 0.216427i
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 140.2.o.a.131.1 yes 32
4.3 odd 2 inner 140.2.o.a.131.12 yes 32
5.2 odd 4 700.2.t.c.299.8 32
5.3 odd 4 700.2.t.d.299.9 32
5.4 even 2 700.2.p.c.551.16 32
7.2 even 3 980.2.g.a.391.24 32
7.3 odd 6 inner 140.2.o.a.31.12 yes 32
7.4 even 3 980.2.o.f.31.12 32
7.5 odd 6 980.2.g.a.391.23 32
7.6 odd 2 980.2.o.f.411.1 32
20.3 even 4 700.2.t.d.299.13 32
20.7 even 4 700.2.t.c.299.4 32
20.19 odd 2 700.2.p.c.551.5 32
28.3 even 6 inner 140.2.o.a.31.1 32
28.11 odd 6 980.2.o.f.31.1 32
28.19 even 6 980.2.g.a.391.22 32
28.23 odd 6 980.2.g.a.391.21 32
28.27 even 2 980.2.o.f.411.12 32
35.3 even 12 700.2.t.c.199.4 32
35.17 even 12 700.2.t.d.199.13 32
35.24 odd 6 700.2.p.c.451.5 32
140.3 odd 12 700.2.t.c.199.8 32
140.59 even 6 700.2.p.c.451.16 32
140.87 odd 12 700.2.t.d.199.9 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.1 32 28.3 even 6 inner
140.2.o.a.31.12 yes 32 7.3 odd 6 inner
140.2.o.a.131.1 yes 32 1.1 even 1 trivial
140.2.o.a.131.12 yes 32 4.3 odd 2 inner
700.2.p.c.451.5 32 35.24 odd 6
700.2.p.c.451.16 32 140.59 even 6
700.2.p.c.551.5 32 20.19 odd 2
700.2.p.c.551.16 32 5.4 even 2
700.2.t.c.199.4 32 35.3 even 12
700.2.t.c.199.8 32 140.3 odd 12
700.2.t.c.299.4 32 20.7 even 4
700.2.t.c.299.8 32 5.2 odd 4
700.2.t.d.199.9 32 140.87 odd 12
700.2.t.d.199.13 32 35.17 even 12
700.2.t.d.299.9 32 5.3 odd 4
700.2.t.d.299.13 32 20.3 even 4
980.2.g.a.391.21 32 28.23 odd 6
980.2.g.a.391.22 32 28.19 even 6
980.2.g.a.391.23 32 7.5 odd 6
980.2.g.a.391.24 32 7.2 even 3
980.2.o.f.31.1 32 28.11 odd 6
980.2.o.f.31.12 32 7.4 even 3
980.2.o.f.411.1 32 7.6 odd 2
980.2.o.f.411.12 32 28.27 even 2