Properties

Label 841.2.d.f.605.1
Level $841$
Weight $2$
Character 841.605
Analytic conductor $6.715$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $6$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(190,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.190");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.d (of order \(7\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.71541880999\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{7})\)
Coefficient field: 12.0.74049191673856.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 2x^{10} + 4x^{8} + 8x^{6} + 16x^{4} + 32x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 605.1
Root \(-0.314692 + 1.37876i\) of defining polynomial
Character \(\chi\) \(=\) 841.605
Dual form 841.2.d.f.645.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.537213 + 2.35368i) q^{2} +(2.17513 - 1.04749i) q^{3} +(-3.44929 - 1.66109i) q^{4} +(0.222521 - 0.974928i) q^{5} +(1.29695 + 5.68230i) q^{6} +(2.54832 - 1.22721i) q^{7} +(2.75222 - 3.45117i) q^{8} +(1.76350 - 2.21135i) q^{9} +O(q^{10})\) \(q+(-0.537213 + 2.35368i) q^{2} +(2.17513 - 1.04749i) q^{3} +(-3.44929 - 1.66109i) q^{4} +(0.222521 - 0.974928i) q^{5} +(1.29695 + 5.68230i) q^{6} +(2.54832 - 1.22721i) q^{7} +(2.75222 - 3.45117i) q^{8} +(1.76350 - 2.21135i) q^{9} +(2.17513 + 1.04749i) q^{10} +(0.258258 + 0.323845i) q^{11} -9.24264 q^{12} +(-2.38699 - 2.99318i) q^{13} +(1.51947 + 6.65722i) q^{14} +(-0.537213 - 2.35368i) q^{15} +(1.87047 + 2.34549i) q^{16} -0.828427 q^{17} +(4.25745 + 5.33868i) q^{18} +(5.40581 + 2.60330i) q^{19} +(-2.38699 + 2.99318i) q^{20} +(4.25745 - 5.33868i) q^{21} +(-0.900969 + 0.433884i) q^{22} +(-0.813727 - 3.56517i) q^{23} +(2.37137 - 10.3897i) q^{24} +(3.60388 + 1.73553i) q^{25} +(8.32733 - 4.01023i) q^{26} +(-0.0921712 + 0.403828i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(2.24102 - 9.81857i) q^{31} +(1.42874 - 0.688047i) q^{32} +(0.900969 + 0.433884i) q^{33} +(0.445042 - 1.94986i) q^{34} +(-0.629384 - 2.75751i) q^{35} +(-9.75608 + 4.69828i) q^{36} +(2.49396 - 3.12733i) q^{37} +(-9.03143 + 11.3250i) q^{38} +(-8.32733 - 4.01023i) q^{39} +(-2.75222 - 3.45117i) q^{40} +4.48528 q^{41} +(10.2784 + 12.8887i) q^{42} +(0.797913 + 3.49588i) q^{43} +(-0.352871 - 1.54603i) q^{44} +(-1.76350 - 2.21135i) q^{45} +8.82843 q^{46} +(2.02175 + 2.53520i) q^{47} +(6.52539 + 3.14246i) q^{48} +(0.623490 - 0.781831i) q^{49} +(-6.02095 + 7.55003i) q^{50} +(-1.80194 + 0.867767i) q^{51} +(3.26146 + 14.2894i) q^{52} +(-2.11067 + 9.24747i) q^{53} +(-0.900969 - 0.433884i) q^{54} +(0.373194 - 0.179721i) q^{55} +(2.77824 - 12.1722i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(-2.05668 + 9.01091i) q^{60} +(-4.35026 + 2.09498i) q^{61} +(21.9059 + 10.5493i) q^{62} +(1.78017 - 7.79942i) q^{63} +(2.18703 + 9.58201i) q^{64} +(-3.44929 + 1.66109i) q^{65} +(-1.50524 + 1.88751i) q^{66} +(3.52699 - 4.42271i) q^{67} +(2.85749 + 1.37609i) q^{68} +(-5.50443 - 6.90234i) q^{69} +6.82843 q^{70} +(-5.50443 - 6.90234i) q^{71} +(-2.77824 - 12.1722i) q^{72} +(0.890084 + 3.89971i) q^{73} +(6.02095 + 7.55003i) q^{74} +9.65685 q^{75} +(-14.3219 - 17.9591i) q^{76} +(1.05555 + 0.508326i) q^{77} +(13.9124 - 17.4456i) q^{78} +(1.50524 - 1.88751i) q^{79} +(2.70291 - 1.30165i) q^{80} +(2.11067 + 9.24747i) q^{81} +(-2.40955 + 10.5569i) q^{82} +(-6.89859 - 3.32218i) q^{83} +(-23.5533 + 11.3426i) q^{84} +(-0.184342 + 0.807657i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(-2.77824 + 12.1722i) q^{89} +(6.15220 - 2.96274i) q^{90} +(-9.75608 - 4.69828i) q^{91} +(-3.11529 + 13.6490i) q^{92} +(-5.41031 - 23.7041i) q^{93} +(-7.05317 + 3.39663i) q^{94} +(3.74094 - 4.69099i) q^{95} +(2.38699 - 2.99318i) q^{96} +(4.04110 + 1.94609i) q^{97} +(1.50524 + 1.88751i) q^{98} +1.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8} + 2 q^{10} + 2 q^{11} - 60 q^{12} + 2 q^{13} + 8 q^{14} - 2 q^{15} - 6 q^{16} + 24 q^{17} - 8 q^{18} + 12 q^{19} + 2 q^{20} - 8 q^{21} - 2 q^{22} + 4 q^{23} + 10 q^{24} + 8 q^{25} + 10 q^{26} + 2 q^{27} - 96 q^{28} + 36 q^{30} + 6 q^{31} + 6 q^{32} + 2 q^{33} + 4 q^{34} - 16 q^{36} - 8 q^{37} + 12 q^{38} - 10 q^{39} + 6 q^{40} - 48 q^{41} - 16 q^{42} + 10 q^{43} - 6 q^{44} + 72 q^{46} + 2 q^{47} + 6 q^{48} - 2 q^{49} + 8 q^{50} - 4 q^{51} + 18 q^{52} - 2 q^{53} - 2 q^{54} - 2 q^{55} + 8 q^{56} + 72 q^{57} + 24 q^{59} - 10 q^{60} - 4 q^{61} + 26 q^{62} + 16 q^{63} + 14 q^{64} - 2 q^{65} + 2 q^{66} + 12 q^{68} + 12 q^{69} + 48 q^{70} + 12 q^{71} - 8 q^{72} + 8 q^{73} - 8 q^{74} + 48 q^{75} + 12 q^{76} + 8 q^{77} - 22 q^{78} - 2 q^{79} + 6 q^{80} + 2 q^{81} - 16 q^{82} - 4 q^{83} - 24 q^{84} + 4 q^{85} - 36 q^{86} - 12 q^{88} - 8 q^{89} + 8 q^{90} - 16 q^{91} - 28 q^{92} - 26 q^{93} - 10 q^{94} - 12 q^{95} - 2 q^{96} - 8 q^{97} - 2 q^{98} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/841\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.537213 + 2.35368i −0.379867 + 1.66431i 0.318009 + 0.948088i \(0.396986\pi\)
−0.697876 + 0.716218i \(0.745871\pi\)
\(3\) 2.17513 1.04749i 1.25581 0.604767i 0.316749 0.948510i \(-0.397409\pi\)
0.939064 + 0.343742i \(0.111695\pi\)
\(4\) −3.44929 1.66109i −1.72465 0.830546i
\(5\) 0.222521 0.974928i 0.0995144 0.436001i −0.900485 0.434887i \(-0.856788\pi\)
0.999999 0.00111393i \(-0.000354575\pi\)
\(6\) 1.29695 + 5.68230i 0.529476 + 2.31979i
\(7\) 2.54832 1.22721i 0.963176 0.463841i 0.114889 0.993378i \(-0.463349\pi\)
0.848287 + 0.529537i \(0.177634\pi\)
\(8\) 2.75222 3.45117i 0.973056 1.22017i
\(9\) 1.76350 2.21135i 0.587832 0.737118i
\(10\) 2.17513 + 1.04749i 0.687837 + 0.331245i
\(11\) 0.258258 + 0.323845i 0.0778677 + 0.0976430i 0.819240 0.573452i \(-0.194396\pi\)
−0.741372 + 0.671095i \(0.765824\pi\)
\(12\) −9.24264 −2.66812
\(13\) −2.38699 2.99318i −0.662031 0.830160i 0.331532 0.943444i \(-0.392434\pi\)
−0.993563 + 0.113284i \(0.963863\pi\)
\(14\) 1.51947 + 6.65722i 0.406095 + 1.77922i
\(15\) −0.537213 2.35368i −0.138708 0.607719i
\(16\) 1.87047 + 2.34549i 0.467617 + 0.586374i
\(17\) −0.828427 −0.200923 −0.100462 0.994941i \(-0.532032\pi\)
−0.100462 + 0.994941i \(0.532032\pi\)
\(18\) 4.25745 + 5.33868i 1.00349 + 1.25834i
\(19\) 5.40581 + 2.60330i 1.24018 + 0.597239i 0.934862 0.355012i \(-0.115523\pi\)
0.305317 + 0.952251i \(0.401238\pi\)
\(20\) −2.38699 + 2.99318i −0.533746 + 0.669296i
\(21\) 4.25745 5.33868i 0.929053 1.16500i
\(22\) −0.900969 + 0.433884i −0.192087 + 0.0925043i
\(23\) −0.813727 3.56517i −0.169674 0.743389i −0.986129 0.165981i \(-0.946921\pi\)
0.816455 0.577409i \(-0.195936\pi\)
\(24\) 2.37137 10.3897i 0.484055 2.12078i
\(25\) 3.60388 + 1.73553i 0.720775 + 0.347107i
\(26\) 8.32733 4.01023i 1.63312 0.786471i
\(27\) −0.0921712 + 0.403828i −0.0177384 + 0.0777168i
\(28\) −10.8284 −2.04638
\(29\) 0 0
\(30\) 5.82843 1.06412
\(31\) 2.24102 9.81857i 0.402500 1.76347i −0.214720 0.976676i \(-0.568884\pi\)
0.617220 0.786791i \(-0.288259\pi\)
\(32\) 1.42874 0.688047i 0.252569 0.121631i
\(33\) 0.900969 + 0.433884i 0.156839 + 0.0755295i
\(34\) 0.445042 1.94986i 0.0763241 0.334398i
\(35\) −0.629384 2.75751i −0.106385 0.466105i
\(36\) −9.75608 + 4.69828i −1.62601 + 0.783046i
\(37\) 2.49396 3.12733i 0.410004 0.514129i −0.533360 0.845889i \(-0.679071\pi\)
0.943364 + 0.331759i \(0.107642\pi\)
\(38\) −9.03143 + 11.3250i −1.46509 + 1.83717i
\(39\) −8.32733 4.01023i −1.33344 0.642151i
\(40\) −2.75222 3.45117i −0.435164 0.545678i
\(41\) 4.48528 0.700483 0.350242 0.936659i \(-0.386099\pi\)
0.350242 + 0.936659i \(0.386099\pi\)
\(42\) 10.2784 + 12.8887i 1.58599 + 1.98877i
\(43\) 0.797913 + 3.49588i 0.121681 + 0.533117i 0.998620 + 0.0525165i \(0.0167242\pi\)
−0.876940 + 0.480601i \(0.840419\pi\)
\(44\) −0.352871 1.54603i −0.0531973 0.233072i
\(45\) −1.76350 2.21135i −0.262886 0.329649i
\(46\) 8.82843 1.30168
\(47\) 2.02175 + 2.53520i 0.294903 + 0.369797i 0.907105 0.420905i \(-0.138287\pi\)
−0.612202 + 0.790702i \(0.709716\pi\)
\(48\) 6.52539 + 3.14246i 0.941859 + 0.453576i
\(49\) 0.623490 0.781831i 0.0890700 0.111690i
\(50\) −6.02095 + 7.55003i −0.851491 + 1.06774i
\(51\) −1.80194 + 0.867767i −0.252322 + 0.121512i
\(52\) 3.26146 + 14.2894i 0.452283 + 1.98158i
\(53\) −2.11067 + 9.24747i −0.289923 + 1.27024i 0.594706 + 0.803943i \(0.297268\pi\)
−0.884630 + 0.466294i \(0.845589\pi\)
\(54\) −0.900969 0.433884i −0.122606 0.0590441i
\(55\) 0.373194 0.179721i 0.0503214 0.0242335i
\(56\) 2.77824 12.1722i 0.371257 1.62659i
\(57\) 14.4853 1.91862
\(58\) 0 0
\(59\) −3.65685 −0.476082 −0.238041 0.971255i \(-0.576505\pi\)
−0.238041 + 0.971255i \(0.576505\pi\)
\(60\) −2.05668 + 9.01091i −0.265516 + 1.16330i
\(61\) −4.35026 + 2.09498i −0.556994 + 0.268234i −0.691132 0.722728i \(-0.742888\pi\)
0.134138 + 0.990963i \(0.457173\pi\)
\(62\) 21.9059 + 10.5493i 2.78205 + 1.33977i
\(63\) 1.78017 7.79942i 0.224280 0.982635i
\(64\) 2.18703 + 9.58201i 0.273379 + 1.19775i
\(65\) −3.44929 + 1.66109i −0.427832 + 0.206033i
\(66\) −1.50524 + 1.88751i −0.185282 + 0.232336i
\(67\) 3.52699 4.42271i 0.430891 0.540320i −0.518226 0.855243i \(-0.673408\pi\)
0.949117 + 0.314924i \(0.101979\pi\)
\(68\) 2.85749 + 1.37609i 0.346521 + 0.166876i
\(69\) −5.50443 6.90234i −0.662656 0.830944i
\(70\) 6.82843 0.816153
\(71\) −5.50443 6.90234i −0.653256 0.819157i 0.339334 0.940666i \(-0.389798\pi\)
−0.992590 + 0.121509i \(0.961227\pi\)
\(72\) −2.77824 12.1722i −0.327418 1.43451i
\(73\) 0.890084 + 3.89971i 0.104176 + 0.456427i 0.999929 + 0.0118748i \(0.00377995\pi\)
−0.895753 + 0.444552i \(0.853363\pi\)
\(74\) 6.02095 + 7.55003i 0.699921 + 0.877673i
\(75\) 9.65685 1.11508
\(76\) −14.3219 17.9591i −1.64284 2.06005i
\(77\) 1.05555 + 0.508326i 0.120291 + 0.0579292i
\(78\) 13.9124 17.4456i 1.57527 1.97532i
\(79\) 1.50524 1.88751i 0.169352 0.212361i −0.689911 0.723894i \(-0.742351\pi\)
0.859264 + 0.511532i \(0.170922\pi\)
\(80\) 2.70291 1.30165i 0.302194 0.145529i
\(81\) 2.11067 + 9.24747i 0.234519 + 1.02750i
\(82\) −2.40955 + 10.5569i −0.266090 + 1.16582i
\(83\) −6.89859 3.32218i −0.757218 0.364657i 0.0151057 0.999886i \(-0.495192\pi\)
−0.772324 + 0.635229i \(0.780906\pi\)
\(84\) −23.5533 + 11.3426i −2.56987 + 1.23758i
\(85\) −0.184342 + 0.807657i −0.0199947 + 0.0876027i
\(86\) −8.65685 −0.933493
\(87\) 0 0
\(88\) 1.82843 0.194911
\(89\) −2.77824 + 12.1722i −0.294492 + 1.29026i 0.583708 + 0.811964i \(0.301601\pi\)
−0.878201 + 0.478292i \(0.841256\pi\)
\(90\) 6.15220 2.96274i 0.648499 0.312301i
\(91\) −9.75608 4.69828i −1.02271 0.492513i
\(92\) −3.11529 + 13.6490i −0.324792 + 1.42301i
\(93\) −5.41031 23.7041i −0.561023 2.45800i
\(94\) −7.05317 + 3.39663i −0.727479 + 0.350335i
\(95\) 3.74094 4.69099i 0.383812 0.481285i
\(96\) 2.38699 2.99318i 0.243621 0.305491i
\(97\) 4.04110 + 1.94609i 0.410311 + 0.197596i 0.627641 0.778503i \(-0.284020\pi\)
−0.217330 + 0.976098i \(0.569735\pi\)
\(98\) 1.50524 + 1.88751i 0.152052 + 0.190667i
\(99\) 1.17157 0.117748
\(100\) −9.54794 11.9727i −0.954794 1.19727i
\(101\) −0.521399 2.28440i −0.0518811 0.227306i 0.942340 0.334657i \(-0.108620\pi\)
−0.994221 + 0.107351i \(0.965763\pi\)
\(102\) −1.07443 4.70737i −0.106384 0.466099i
\(103\) −3.01048 3.77502i −0.296631 0.371963i 0.611073 0.791574i \(-0.290738\pi\)
−0.907704 + 0.419611i \(0.862167\pi\)
\(104\) −16.8995 −1.65713
\(105\) −4.25745 5.33868i −0.415485 0.521002i
\(106\) −20.6317 9.93572i −2.00393 0.965042i
\(107\) −9.24537 + 11.5933i −0.893784 + 1.12077i 0.0982954 + 0.995157i \(0.468661\pi\)
−0.992079 + 0.125612i \(0.959910\pi\)
\(108\) 0.988722 1.23982i 0.0951398 0.119302i
\(109\) −11.4034 + 5.49160i −1.09225 + 0.526000i −0.891214 0.453583i \(-0.850145\pi\)
−0.201037 + 0.979584i \(0.564431\pi\)
\(110\) 0.222521 + 0.974928i 0.0212165 + 0.0929557i
\(111\) 2.14885 9.41474i 0.203960 0.893607i
\(112\) 7.64497 + 3.68163i 0.722382 + 0.347881i
\(113\) −11.9952 + 5.77660i −1.12842 + 0.543417i −0.902483 0.430726i \(-0.858258\pi\)
−0.225934 + 0.974143i \(0.572543\pi\)
\(114\) −7.78168 + 34.0938i −0.728821 + 3.19317i
\(115\) −3.65685 −0.341003
\(116\) 0 0
\(117\) −10.8284 −1.00109
\(118\) 1.96451 8.60708i 0.180848 0.792346i
\(119\) −2.11110 + 1.01665i −0.193524 + 0.0931964i
\(120\) −9.60149 4.62384i −0.876492 0.422097i
\(121\) 2.40955 10.5569i 0.219050 0.959721i
\(122\) −2.59389 11.3646i −0.234840 1.02890i
\(123\) 9.75608 4.69828i 0.879676 0.423630i
\(124\) −24.0395 + 30.1446i −2.15881 + 2.70706i
\(125\) 5.61141 7.03648i 0.501900 0.629362i
\(126\) 17.4011 + 8.37990i 1.55021 + 0.746541i
\(127\) 2.70791 + 3.39561i 0.240288 + 0.301311i 0.887323 0.461149i \(-0.152563\pi\)
−0.647035 + 0.762460i \(0.723991\pi\)
\(128\) −20.5563 −1.81694
\(129\) 5.39746 + 6.76820i 0.475220 + 0.595907i
\(130\) −2.05668 9.01091i −0.180383 0.790309i
\(131\) 4.74275 + 20.7793i 0.414376 + 1.81550i 0.562822 + 0.826578i \(0.309716\pi\)
−0.148447 + 0.988920i \(0.547427\pi\)
\(132\) −2.38699 2.99318i −0.207760 0.260523i
\(133\) 16.9706 1.47153
\(134\) 8.51491 + 10.6774i 0.735576 + 0.922383i
\(135\) 0.373194 + 0.179721i 0.0321194 + 0.0154679i
\(136\) −2.28001 + 2.85904i −0.195509 + 0.245161i
\(137\) −7.48188 + 9.38198i −0.639220 + 0.801556i −0.990905 0.134562i \(-0.957037\pi\)
0.351685 + 0.936118i \(0.385609\pi\)
\(138\) 19.2030 9.24767i 1.63467 0.787214i
\(139\) −3.11529 13.6490i −0.264236 1.15769i −0.916606 0.399792i \(-0.869082\pi\)
0.652370 0.757900i \(-0.273775\pi\)
\(140\) −2.40955 + 10.5569i −0.203644 + 0.892224i
\(141\) 7.05317 + 3.39663i 0.593984 + 0.286048i
\(142\) 19.2030 9.24767i 1.61148 0.776047i
\(143\) 0.352871 1.54603i 0.0295085 0.129285i
\(144\) 8.48528 0.707107
\(145\) 0 0
\(146\) −9.65685 −0.799207
\(147\) 0.537213 2.35368i 0.0443086 0.194129i
\(148\) −13.7972 + 6.64437i −1.13412 + 0.546164i
\(149\) 7.05317 + 3.39663i 0.577818 + 0.278263i 0.699881 0.714260i \(-0.253237\pi\)
−0.122062 + 0.992522i \(0.538951\pi\)
\(150\) −5.18779 + 22.7292i −0.423581 + 1.85583i
\(151\) 3.14692 + 13.7876i 0.256093 + 1.12202i 0.925389 + 0.379020i \(0.123739\pi\)
−0.669296 + 0.742996i \(0.733404\pi\)
\(152\) 23.8624 11.4915i 1.93550 0.932086i
\(153\) −1.46093 + 1.83195i −0.118109 + 0.148104i
\(154\) −1.76350 + 2.21135i −0.142107 + 0.178196i
\(155\) −9.07372 4.36967i −0.728819 0.350981i
\(156\) 22.0620 + 27.6649i 1.76638 + 2.21497i
\(157\) −8.48528 −0.677199 −0.338600 0.940931i \(-0.609953\pi\)
−0.338600 + 0.940931i \(0.609953\pi\)
\(158\) 3.63396 + 4.55685i 0.289103 + 0.362523i
\(159\) 5.09562 + 22.3254i 0.404109 + 1.77052i
\(160\) −0.352871 1.54603i −0.0278969 0.122224i
\(161\) −6.44885 8.08660i −0.508240 0.637313i
\(162\) −22.8995 −1.79915
\(163\) −2.44965 3.07176i −0.191871 0.240599i 0.676585 0.736364i \(-0.263459\pi\)
−0.868457 + 0.495765i \(0.834888\pi\)
\(164\) −15.4711 7.45047i −1.20809 0.581784i
\(165\) 0.623490 0.781831i 0.0485386 0.0608655i
\(166\) 11.5254 14.4524i 0.894543 1.12172i
\(167\) 2.85749 1.37609i 0.221119 0.106485i −0.320045 0.947402i \(-0.603698\pi\)
0.541164 + 0.840917i \(0.317984\pi\)
\(168\) −6.70726 29.3864i −0.517476 2.26721i
\(169\) −0.368685 + 1.61531i −0.0283604 + 0.124255i
\(170\) −1.80194 0.867767i −0.138202 0.0665547i
\(171\) 15.2899 7.36325i 1.16925 0.563082i
\(172\) 3.05475 13.3837i 0.232923 1.02050i
\(173\) 12.3431 0.938432 0.469216 0.883083i \(-0.344537\pi\)
0.469216 + 0.883083i \(0.344537\pi\)
\(174\) 0 0
\(175\) 11.3137 0.855236
\(176\) −0.276514 + 1.21149i −0.0208430 + 0.0913191i
\(177\) −7.95414 + 3.83051i −0.597870 + 0.287919i
\(178\) −27.1571 13.0782i −2.03551 0.980251i
\(179\) 1.44311 6.32268i 0.107863 0.472579i −0.891929 0.452176i \(-0.850648\pi\)
0.999792 0.0204033i \(-0.00649502\pi\)
\(180\) 2.40955 + 10.5569i 0.179597 + 0.786868i
\(181\) −7.49039 + 3.60718i −0.556756 + 0.268120i −0.691032 0.722824i \(-0.742844\pi\)
0.134275 + 0.990944i \(0.457129\pi\)
\(182\) 16.2994 20.4387i 1.20819 1.51502i
\(183\) −7.26793 + 9.11370i −0.537261 + 0.673704i
\(184\) −14.5436 7.00381i −1.07217 0.516328i
\(185\) −2.49396 3.12733i −0.183360 0.229926i
\(186\) 58.6985 4.30398
\(187\) −0.213948 0.268282i −0.0156454 0.0196187i
\(188\) −2.76242 12.1030i −0.201470 0.882699i
\(189\) 0.260699 + 1.14220i 0.0189631 + 0.0830828i
\(190\) 9.03143 + 11.3250i 0.655208 + 0.821605i
\(191\) −25.3137 −1.83164 −0.915818 0.401594i \(-0.868456\pi\)
−0.915818 + 0.401594i \(0.868456\pi\)
\(192\) 14.7941 + 18.5512i 1.06767 + 1.33882i
\(193\) −4.65943 2.24386i −0.335393 0.161517i 0.258605 0.965983i \(-0.416737\pi\)
−0.593998 + 0.804466i \(0.702451\pi\)
\(194\) −6.75141 + 8.46601i −0.484723 + 0.607824i
\(195\) −5.76269 + 7.22619i −0.412675 + 0.517478i
\(196\) −3.44929 + 1.66109i −0.246378 + 0.118649i
\(197\) −0.445042 1.94986i −0.0317079 0.138921i 0.956596 0.291416i \(-0.0941264\pi\)
−0.988304 + 0.152495i \(0.951269\pi\)
\(198\) −0.629384 + 2.75751i −0.0447284 + 0.195968i
\(199\) 0.437223 + 0.210556i 0.0309939 + 0.0149259i 0.449317 0.893373i \(-0.351668\pi\)
−0.418323 + 0.908299i \(0.637382\pi\)
\(200\) 15.9083 7.66102i 1.12488 0.541716i
\(201\) 3.03894 13.3144i 0.214350 0.939129i
\(202\) 5.65685 0.398015
\(203\) 0 0
\(204\) 7.65685 0.536087
\(205\) 0.998069 4.37283i 0.0697082 0.305411i
\(206\) 10.5025 5.05772i 0.731741 0.352388i
\(207\) −9.31885 4.48772i −0.647705 0.311918i
\(208\) 2.55572 11.1973i 0.177207 0.776395i
\(209\) 0.553027 + 2.42297i 0.0382537 + 0.167600i
\(210\) 14.8527 7.15270i 1.02494 0.493583i
\(211\) 12.0862 15.1556i 0.832049 1.04336i −0.166309 0.986074i \(-0.553185\pi\)
0.998358 0.0572828i \(-0.0182437\pi\)
\(212\) 22.6412 28.3912i 1.55501 1.94992i
\(213\) −19.2030 9.24767i −1.31577 0.633640i
\(214\) −22.3203 27.9888i −1.52578 1.91327i
\(215\) 3.58579 0.244549
\(216\) 1.14001 + 1.42952i 0.0775676 + 0.0972666i
\(217\) −6.33857 27.7711i −0.430290 1.88522i
\(218\) −6.79943 29.7902i −0.460515 2.01765i
\(219\) 6.02095 + 7.55003i 0.406858 + 0.510184i
\(220\) −1.58579 −0.106914
\(221\) 1.97744 + 2.47964i 0.133017 + 0.166798i
\(222\) 21.0049 + 10.1154i 1.40976 + 0.678904i
\(223\) −1.97744 + 2.47964i −0.132419 + 0.166049i −0.843620 0.536940i \(-0.819580\pi\)
0.711201 + 0.702989i \(0.248152\pi\)
\(224\) 2.79653 3.50673i 0.186851 0.234304i
\(225\) 10.1933 4.90883i 0.679553 0.327256i
\(226\) −7.15230 31.3363i −0.475764 2.08446i
\(227\) 1.81180 7.93800i 0.120253 0.526863i −0.878536 0.477675i \(-0.841480\pi\)
0.998790 0.0491879i \(-0.0156633\pi\)
\(228\) −49.9640 24.0614i −3.30895 1.59350i
\(229\) −3.16665 + 1.52498i −0.209258 + 0.100773i −0.535577 0.844486i \(-0.679906\pi\)
0.326319 + 0.945260i \(0.394192\pi\)
\(230\) 1.96451 8.60708i 0.129536 0.567534i
\(231\) 2.82843 0.186097
\(232\) 0 0
\(233\) 18.3137 1.19977 0.599885 0.800086i \(-0.295213\pi\)
0.599885 + 0.800086i \(0.295213\pi\)
\(234\) 5.81717 25.4867i 0.380280 1.66612i
\(235\) 2.92152 1.40693i 0.190579 0.0917779i
\(236\) 12.6136 + 6.07437i 0.821073 + 0.395408i
\(237\) 1.29695 5.68230i 0.0842458 0.369105i
\(238\) −1.25877 5.51503i −0.0815938 0.357486i
\(239\) 17.7102 8.52879i 1.14558 0.551682i 0.237876 0.971296i \(-0.423549\pi\)
0.907703 + 0.419614i \(0.137835\pi\)
\(240\) 4.51571 5.66252i 0.291488 0.365514i
\(241\) −11.4184 + 14.3182i −0.735524 + 0.922319i −0.999104 0.0423191i \(-0.986525\pi\)
0.263580 + 0.964638i \(0.415097\pi\)
\(242\) 23.5533 + 11.3426i 1.51406 + 0.729133i
\(243\) 13.5028 + 16.9320i 0.866207 + 1.08619i
\(244\) 18.4853 1.18340
\(245\) −0.623490 0.781831i −0.0398333 0.0499494i
\(246\) 5.81717 + 25.4867i 0.370889 + 1.62497i
\(247\) −5.11143 22.3946i −0.325233 1.42494i
\(248\) −27.7178 34.7570i −1.76008 2.20707i
\(249\) −18.4853 −1.17146
\(250\) 13.5471 + 16.9876i 0.856796 + 1.07439i
\(251\) 18.0834 + 8.70851i 1.14141 + 0.549676i 0.906444 0.422326i \(-0.138786\pi\)
0.234971 + 0.972002i \(0.424501\pi\)
\(252\) −19.0959 + 23.9455i −1.20293 + 1.50842i
\(253\) 0.944412 1.18425i 0.0593746 0.0744535i
\(254\) −9.44691 + 4.54939i −0.592752 + 0.285454i
\(255\) 0.445042 + 1.94986i 0.0278696 + 0.122105i
\(256\) 6.66908 29.2191i 0.416817 1.82620i
\(257\) 16.3720 + 7.88435i 1.02126 + 0.491812i 0.868100 0.496389i \(-0.165341\pi\)
0.153159 + 0.988202i \(0.451055\pi\)
\(258\) −18.8298 + 9.06795i −1.17229 + 0.564546i
\(259\) 2.51754 11.0301i 0.156432 0.685374i
\(260\) 14.6569 0.908980
\(261\) 0 0
\(262\) −51.4558 −3.17895
\(263\) 0.613570 2.68823i 0.0378344 0.165763i −0.952481 0.304597i \(-0.901478\pi\)
0.990316 + 0.138834i \(0.0443354\pi\)
\(264\) 3.97707 1.91526i 0.244772 0.117876i
\(265\) 8.54594 + 4.11551i 0.524973 + 0.252814i
\(266\) −9.11681 + 39.9433i −0.558987 + 2.44908i
\(267\) 6.70726 + 29.3864i 0.410477 + 1.79842i
\(268\) −19.5122 + 9.39656i −1.19189 + 0.573986i
\(269\) −19.6124 + 24.5932i −1.19579 + 1.49947i −0.376182 + 0.926546i \(0.622763\pi\)
−0.819607 + 0.572926i \(0.805808\pi\)
\(270\) −0.623490 + 0.781831i −0.0379444 + 0.0475807i
\(271\) 14.9168 + 7.18353i 0.906128 + 0.436368i 0.828099 0.560583i \(-0.189423\pi\)
0.0780298 + 0.996951i \(0.475137\pi\)
\(272\) −1.54955 1.94307i −0.0939551 0.117816i
\(273\) −26.1421 −1.58219
\(274\) −18.0629 22.6501i −1.09122 1.36834i
\(275\) 0.368685 + 1.61531i 0.0222325 + 0.0974071i
\(276\) 7.52098 + 32.9516i 0.452710 + 1.98345i
\(277\) −10.7949 13.5364i −0.648604 0.813324i 0.343445 0.939173i \(-0.388406\pi\)
−0.992049 + 0.125849i \(0.959835\pi\)
\(278\) 33.7990 2.02713
\(279\) −17.7603 22.2707i −1.06328 1.33331i
\(280\) −11.2488 5.41716i −0.672247 0.323737i
\(281\) 19.9333 24.9956i 1.18912 1.49111i 0.359175 0.933270i \(-0.383058\pi\)
0.829947 0.557842i \(-0.188370\pi\)
\(282\) −11.7836 + 14.7762i −0.701706 + 0.879911i
\(283\) −10.5025 + 5.05772i −0.624307 + 0.300650i −0.719164 0.694841i \(-0.755475\pi\)
0.0948571 + 0.995491i \(0.469761\pi\)
\(284\) 7.52098 + 32.9516i 0.446288 + 1.95532i
\(285\) 3.22328 14.1221i 0.190931 0.836521i
\(286\) 3.44929 + 1.66109i 0.203961 + 0.0982224i
\(287\) 11.4300 5.50438i 0.674689 0.324913i
\(288\) 0.998069 4.37283i 0.0588118 0.257671i
\(289\) −16.3137 −0.959630
\(290\) 0 0
\(291\) 10.8284 0.634774
\(292\) 3.40762 14.9298i 0.199416 0.873698i
\(293\) 6.89859 3.32218i 0.403020 0.194084i −0.221382 0.975187i \(-0.571057\pi\)
0.624402 + 0.781103i \(0.285343\pi\)
\(294\) 5.25123 + 2.52886i 0.306258 + 0.147486i
\(295\) −0.813727 + 3.56517i −0.0473770 + 0.207572i
\(296\) −3.92902 17.2142i −0.228370 1.00055i
\(297\) −0.154582 + 0.0744427i −0.00896975 + 0.00431960i
\(298\) −11.7836 + 14.7762i −0.682608 + 0.855963i
\(299\) −8.72886 + 10.9456i −0.504803 + 0.633003i
\(300\) −33.3093 16.0409i −1.92311 0.926123i
\(301\) 6.32352 + 7.92944i 0.364482 + 0.457045i
\(302\) −34.1421 −1.96466
\(303\) −3.52699 4.42271i −0.202620 0.254078i
\(304\) 4.00538 + 17.5487i 0.229724 + 1.00649i
\(305\) 1.07443 + 4.70737i 0.0615215 + 0.269543i
\(306\) −3.52699 4.42271i −0.201625 0.252829i
\(307\) −2.89949 −0.165483 −0.0827415 0.996571i \(-0.526368\pi\)
−0.0827415 + 0.996571i \(0.526368\pi\)
\(308\) −2.79653 3.50673i −0.159347 0.199815i
\(309\) −10.5025 5.05772i −0.597464 0.287724i
\(310\) 15.1593 19.0092i 0.860993 1.07965i
\(311\) −1.67488 + 2.10023i −0.0949735 + 0.119093i −0.827047 0.562132i \(-0.809981\pi\)
0.732074 + 0.681225i \(0.238553\pi\)
\(312\) −36.7586 + 17.7020i −2.08105 + 1.00218i
\(313\) −2.18703 9.58201i −0.123618 0.541607i −0.998372 0.0570392i \(-0.981834\pi\)
0.874754 0.484568i \(-0.161023\pi\)
\(314\) 4.55840 19.9717i 0.257246 1.12707i
\(315\) −7.20775 3.47107i −0.406111 0.195573i
\(316\) −8.32733 + 4.01023i −0.468449 + 0.225593i
\(317\) −6.99958 + 30.6672i −0.393136 + 1.72244i 0.260361 + 0.965511i \(0.416158\pi\)
−0.653497 + 0.756929i \(0.726699\pi\)
\(318\) −55.2843 −3.10019
\(319\) 0 0
\(320\) 9.82843 0.549426
\(321\) −7.96602 + 34.9014i −0.444620 + 1.94801i
\(322\) 22.4977 10.8343i 1.25375 0.603773i
\(323\) −4.47832 2.15665i −0.249181 0.119999i
\(324\) 8.08056 35.4032i 0.448920 1.96685i
\(325\) −3.40762 14.9298i −0.189021 0.828154i
\(326\) 8.54594 4.11551i 0.473316 0.227937i
\(327\) −19.0516 + 23.8899i −1.05355 + 1.32112i
\(328\) 12.3445 15.4795i 0.681609 0.854711i
\(329\) 8.26330 + 3.97940i 0.455571 + 0.219391i
\(330\) 1.50524 + 1.88751i 0.0828606 + 0.103904i
\(331\) 2.41421 0.132697 0.0663486 0.997797i \(-0.478865\pi\)
0.0663486 + 0.997797i \(0.478865\pi\)
\(332\) 18.2768 + 22.9184i 1.00307 + 1.25781i
\(333\) −2.51754 11.0301i −0.137960 0.604443i
\(334\) 1.70381 + 7.46488i 0.0932284 + 0.408460i
\(335\) −3.52699 4.42271i −0.192700 0.241638i
\(336\) 20.4853 1.11756
\(337\) −13.5914 17.0431i −0.740373 0.928399i 0.258923 0.965898i \(-0.416632\pi\)
−0.999297 + 0.0374991i \(0.988061\pi\)
\(338\) −3.60388 1.73553i −0.196025 0.0944007i
\(339\) −20.0403 + 25.1297i −1.08844 + 1.36486i
\(340\) 1.97744 2.47964i 0.107242 0.134477i
\(341\) 3.75846 1.80998i 0.203532 0.0980158i
\(342\) 9.11681 + 39.9433i 0.492981 + 2.15989i
\(343\) −3.77631 + 16.5451i −0.203901 + 0.893350i
\(344\) 14.2609 + 6.86770i 0.768897 + 0.370281i
\(345\) −7.95414 + 3.83051i −0.428236 + 0.206228i
\(346\) −6.63090 + 29.0519i −0.356479 + 1.56184i
\(347\) 2.48528 0.133417 0.0667084 0.997773i \(-0.478750\pi\)
0.0667084 + 0.997773i \(0.478750\pi\)
\(348\) 0 0
\(349\) −5.14214 −0.275252 −0.137626 0.990484i \(-0.543947\pi\)
−0.137626 + 0.990484i \(0.543947\pi\)
\(350\) −6.07787 + 26.6289i −0.324876 + 1.42337i
\(351\) 1.42874 0.688047i 0.0762607 0.0367252i
\(352\) 0.591805 + 0.284998i 0.0315433 + 0.0151905i
\(353\) −6.00151 + 26.2944i −0.319428 + 1.39951i 0.519130 + 0.854695i \(0.326256\pi\)
−0.838558 + 0.544812i \(0.816601\pi\)
\(354\) −4.74275 20.7793i −0.252074 1.10441i
\(355\) −7.95414 + 3.83051i −0.422162 + 0.203302i
\(356\) 29.8022 37.3708i 1.57951 1.98065i
\(357\) −3.52699 + 4.42271i −0.186668 + 0.234074i
\(358\) 14.1063 + 6.79325i 0.745543 + 0.359035i
\(359\) −2.44965 3.07176i −0.129288 0.162121i 0.712974 0.701190i \(-0.247348\pi\)
−0.842262 + 0.539069i \(0.818776\pi\)
\(360\) −12.4853 −0.658032
\(361\) 10.5993 + 13.2911i 0.557859 + 0.699533i
\(362\) −4.46623 19.5678i −0.234740 1.02846i
\(363\) −5.81717 25.4867i −0.305322 1.33770i
\(364\) 25.8473 + 32.4115i 1.35477 + 1.69882i
\(365\) 4.00000 0.209370
\(366\) −17.5463 22.0024i −0.917162 1.15008i
\(367\) 16.2174 + 7.80991i 0.846543 + 0.407674i 0.806293 0.591516i \(-0.201470\pi\)
0.0402500 + 0.999190i \(0.487185\pi\)
\(368\) 6.84003 8.57713i 0.356561 0.447114i
\(369\) 7.90977 9.91854i 0.411766 0.516339i
\(370\) 8.70053 4.18995i 0.452319 0.217825i
\(371\) 5.96989 + 26.1558i 0.309941 + 1.35794i
\(372\) −20.7130 + 90.7495i −1.07392 + 4.70514i
\(373\) 23.7078 + 11.4171i 1.22755 + 0.591155i 0.931403 0.363989i \(-0.118586\pi\)
0.296142 + 0.955144i \(0.404300\pi\)
\(374\) 0.746387 0.359441i 0.0385948 0.0185863i
\(375\) 4.83492 21.1832i 0.249674 1.09389i
\(376\) 14.3137 0.738173
\(377\) 0 0
\(378\) −2.82843 −0.145479
\(379\) −1.55110 + 6.79580i −0.0796745 + 0.349077i −0.999014 0.0443876i \(-0.985866\pi\)
0.919340 + 0.393464i \(0.128723\pi\)
\(380\) −20.6958 + 9.96655i −1.06167 + 0.511273i
\(381\) 9.44691 + 4.54939i 0.483980 + 0.233072i
\(382\) 13.5989 59.5805i 0.695778 3.04840i
\(383\) 0.782098 + 3.42660i 0.0399634 + 0.175091i 0.990971 0.134077i \(-0.0428068\pi\)
−0.951008 + 0.309167i \(0.899950\pi\)
\(384\) −44.7128 + 21.5325i −2.28174 + 1.09883i
\(385\) 0.730464 0.915973i 0.0372279 0.0466823i
\(386\) 7.78445 9.76139i 0.396218 0.496841i
\(387\) 9.13775 + 4.40051i 0.464498 + 0.223690i
\(388\) −10.7063 13.4253i −0.543530 0.681565i
\(389\) −3.02944 −0.153599 −0.0767993 0.997047i \(-0.524470\pi\)
−0.0767993 + 0.997047i \(0.524470\pi\)
\(390\) −13.9124 17.4456i −0.704480 0.883390i
\(391\) 0.674113 + 2.95348i 0.0340914 + 0.149364i
\(392\) −0.982255 4.30354i −0.0496114 0.217362i
\(393\) 32.0822 + 40.2298i 1.61833 + 2.02932i
\(394\) 4.82843 0.243253
\(395\) −1.50524 1.88751i −0.0757367 0.0949708i
\(396\) −4.04110 1.94609i −0.203073 0.0977947i
\(397\) 12.0603 15.1231i 0.605287 0.759006i −0.380905 0.924614i \(-0.624387\pi\)
0.986192 + 0.165609i \(0.0529589\pi\)
\(398\) −0.730464 + 0.915973i −0.0366148 + 0.0459136i
\(399\) 36.9132 17.7765i 1.84797 0.889936i
\(400\) 2.67025 + 11.6991i 0.133513 + 0.584957i
\(401\) 4.15154 18.1891i 0.207318 0.908320i −0.759025 0.651062i \(-0.774324\pi\)
0.966343 0.257258i \(-0.0828190\pi\)
\(402\) 29.7055 + 14.3054i 1.48157 + 0.713488i
\(403\) −34.7381 + 16.7290i −1.73043 + 0.833329i
\(404\) −1.99614 + 8.74565i −0.0993116 + 0.435112i
\(405\) 9.48528 0.471327
\(406\) 0 0
\(407\) 1.65685 0.0821272
\(408\) −1.96451 + 8.60708i −0.0972577 + 0.426114i
\(409\) −17.0919 + 8.23102i −0.845139 + 0.406998i −0.805771 0.592227i \(-0.798249\pi\)
−0.0393683 + 0.999225i \(0.512535\pi\)
\(410\) 9.75608 + 4.69828i 0.481818 + 0.232031i
\(411\) −6.44656 + 28.2442i −0.317985 + 1.39318i
\(412\) 4.11336 + 18.0218i 0.202651 + 0.887871i
\(413\) −9.31885 + 4.48772i −0.458551 + 0.220826i
\(414\) 15.5689 19.5228i 0.765169 0.959492i
\(415\) −4.77397 + 5.98637i −0.234345 + 0.293859i
\(416\) −5.46984 2.63414i −0.268181 0.129149i
\(417\) −21.0733 26.4251i −1.03197 1.29404i
\(418\) −6.00000 −0.293470
\(419\) −5.93233 7.43891i −0.289813 0.363414i 0.615516 0.788124i \(-0.288948\pi\)
−0.905330 + 0.424710i \(0.860376\pi\)
\(420\) 5.81717 + 25.4867i 0.283849 + 1.24362i
\(421\) 8.25835 + 36.1822i 0.402487 + 1.76341i 0.617270 + 0.786751i \(0.288238\pi\)
−0.214783 + 0.976662i \(0.568904\pi\)
\(422\) 29.1787 + 36.5889i 1.42040 + 1.78112i
\(423\) 9.17157 0.445937
\(424\) 26.1056 + 32.7353i 1.26780 + 1.58977i
\(425\) −2.98555 1.43776i −0.144820 0.0697418i
\(426\) 32.0822 40.2298i 1.55439 1.94914i
\(427\) −8.51491 + 10.6774i −0.412065 + 0.516714i
\(428\) 51.1476 24.6314i 2.47231 1.19060i
\(429\) −0.851905 3.73244i −0.0411304 0.180204i
\(430\) −1.92633 + 8.43981i −0.0928959 + 0.407004i
\(431\) −17.7102 8.52879i −0.853071 0.410817i −0.0443544 0.999016i \(-0.514123\pi\)
−0.808717 + 0.588199i \(0.799837\pi\)
\(432\) −1.11958 + 0.539162i −0.0538658 + 0.0259404i
\(433\) 6.81524 29.8595i 0.327520 1.43496i −0.496323 0.868138i \(-0.665317\pi\)
0.823842 0.566819i \(-0.191826\pi\)
\(434\) 68.7696 3.30104
\(435\) 0 0
\(436\) 48.4558 2.32061
\(437\) 4.88236 21.3910i 0.233555 1.02327i
\(438\) −21.0049 + 10.1154i −1.00365 + 0.483334i
\(439\) 0.309164 + 0.148885i 0.0147556 + 0.00710591i 0.441247 0.897386i \(-0.354536\pi\)
−0.426491 + 0.904492i \(0.640251\pi\)
\(440\) 0.406863 1.78258i 0.0193964 0.0849814i
\(441\) −0.629384 2.75751i −0.0299707 0.131310i
\(442\) −6.89859 + 3.32218i −0.328132 + 0.158020i
\(443\) 15.1777 19.0322i 0.721114 0.904249i −0.277286 0.960787i \(-0.589435\pi\)
0.998400 + 0.0565385i \(0.0180064\pi\)
\(444\) −23.0508 + 28.9047i −1.09394 + 1.37176i
\(445\) 11.2488 + 5.41716i 0.533247 + 0.256798i
\(446\) −4.77397 5.98637i −0.226054 0.283463i
\(447\) 18.8995 0.893915
\(448\) 17.3324 + 21.7341i 0.818878 + 1.02684i
\(449\) −7.78168 34.0938i −0.367240 1.60898i −0.734325 0.678798i \(-0.762501\pi\)
0.367085 0.930187i \(-0.380356\pi\)
\(450\) 6.07787 + 26.6289i 0.286514 + 1.25530i
\(451\) 1.15836 + 1.45254i 0.0545450 + 0.0683973i
\(452\) 50.9706 2.39745
\(453\) 21.2873 + 26.6934i 1.00016 + 1.25417i
\(454\) 17.7102 + 8.52879i 0.831182 + 0.400276i
\(455\) −6.75141 + 8.46601i −0.316511 + 0.396892i
\(456\) 39.8666 49.9912i 1.86693 2.34105i
\(457\) −0.927491 + 0.446656i −0.0433862 + 0.0208937i −0.455451 0.890261i \(-0.650522\pi\)
0.412065 + 0.911155i \(0.364808\pi\)
\(458\) −1.88815 8.27254i −0.0882276 0.386550i
\(459\) 0.0763571 0.334542i 0.00356404 0.0156151i
\(460\) 12.6136 + 6.07437i 0.588110 + 0.283219i
\(461\) 12.6136 6.07437i 0.587472 0.282912i −0.116441 0.993198i \(-0.537149\pi\)
0.703913 + 0.710286i \(0.251434\pi\)
\(462\) −1.51947 + 6.65722i −0.0706920 + 0.309722i
\(463\) −26.0000 −1.20832 −0.604161 0.796862i \(-0.706492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) 0 0
\(465\) −24.3137 −1.12752
\(466\) −9.83836 + 43.1047i −0.455753 + 1.99679i
\(467\) −34.5570 + 16.6418i −1.59911 + 0.770089i −0.999543 0.0302389i \(-0.990373\pi\)
−0.599563 + 0.800328i \(0.704659\pi\)
\(468\) 37.3504 + 17.9870i 1.72652 + 0.831450i
\(469\) 3.56033 15.5988i 0.164401 0.720288i
\(470\) 1.74199 + 7.63215i 0.0803520 + 0.352045i
\(471\) −18.4566 + 8.88823i −0.850435 + 0.409548i
\(472\) −10.0645 + 12.6204i −0.463254 + 0.580902i
\(473\) −0.926058 + 1.16124i −0.0425802 + 0.0533939i
\(474\) 12.6776 + 6.10521i 0.582301 + 0.280421i
\(475\) 14.9638 + 18.7640i 0.686584 + 0.860949i
\(476\) 8.97056 0.411165
\(477\) 16.7273 + 20.9753i 0.765888 + 0.960393i
\(478\) 10.5599 + 46.2660i 0.482999 + 2.11616i
\(479\) 1.53528 + 6.72651i 0.0701488 + 0.307342i 0.997815 0.0660682i \(-0.0210455\pi\)
−0.927666 + 0.373410i \(0.878188\pi\)
\(480\) −2.38699 2.99318i −0.108950 0.136620i
\(481\) −15.3137 −0.698245
\(482\) −27.5665 34.5673i −1.25562 1.57450i
\(483\) −22.4977 10.8343i −1.02368 0.492979i
\(484\) −25.8473 + 32.4115i −1.17488 + 1.47325i
\(485\) 2.79653 3.50673i 0.126984 0.159233i
\(486\) −47.1065 + 22.6853i −2.13679 + 1.02903i
\(487\) 2.56227 + 11.2260i 0.116107 + 0.508700i 0.999218 + 0.0395351i \(0.0125877\pi\)
−0.883111 + 0.469164i \(0.844555\pi\)
\(488\) −4.74275 + 20.7793i −0.214694 + 0.940636i
\(489\) −8.54594 4.11551i −0.386461 0.186110i
\(490\) 2.17513 1.04749i 0.0982624 0.0473207i
\(491\) −4.72693 + 20.7100i −0.213323 + 0.934631i 0.748967 + 0.662607i \(0.230550\pi\)
−0.962290 + 0.272024i \(0.912307\pi\)
\(492\) −41.4558 −1.86897
\(493\) 0 0
\(494\) 55.4558 2.49508
\(495\) 0.260699 1.14220i 0.0117176 0.0513380i
\(496\) 27.2212 13.1090i 1.22227 0.588612i
\(497\) −22.4977 10.8343i −1.00916 0.485986i
\(498\) 9.93053 43.5085i 0.444998 1.94966i
\(499\) −4.22135 18.4949i −0.188973 0.827947i −0.977159 0.212509i \(-0.931836\pi\)
0.788186 0.615438i \(-0.211021\pi\)
\(500\) −31.0436 + 14.9498i −1.38831 + 0.668577i
\(501\) 4.77397 5.98637i 0.213285 0.267451i
\(502\) −30.2117 + 37.8843i −1.34842 + 1.69086i
\(503\) 0.245134 + 0.118050i 0.0109300 + 0.00526360i 0.439341 0.898320i \(-0.355212\pi\)
−0.428411 + 0.903584i \(0.640926\pi\)
\(504\) −22.0177 27.6094i −0.980748 1.22982i
\(505\) −2.34315 −0.104269
\(506\) 2.28001 + 2.85904i 0.101359 + 0.127100i
\(507\) 0.890084 + 3.89971i 0.0395300 + 0.173192i
\(508\) −3.69995 16.2105i −0.164159 0.719226i
\(509\) −6.55582 8.22074i −0.290582 0.364378i 0.615017 0.788514i \(-0.289149\pi\)
−0.905598 + 0.424136i \(0.860578\pi\)
\(510\) −4.82843 −0.213806
\(511\) 7.05398 + 8.84541i 0.312050 + 0.391298i
\(512\) 28.1486 + 13.5557i 1.24401 + 0.599082i
\(513\) −1.54955 + 1.94307i −0.0684142 + 0.0857887i
\(514\) −27.3525 + 34.2990i −1.20647 + 1.51286i
\(515\) −4.35026 + 2.09498i −0.191695 + 0.0923157i
\(516\) −7.37482 32.3112i −0.324658 1.42242i
\(517\) −0.298878 + 1.30947i −0.0131446 + 0.0575904i
\(518\) 24.6088 + 11.8510i 1.08125 + 0.520702i
\(519\) 26.8480 12.9293i 1.17849 0.567533i
\(520\) −3.76049 + 16.4758i −0.164908 + 0.722511i
\(521\) −29.1421 −1.27674 −0.638370 0.769730i \(-0.720391\pi\)
−0.638370 + 0.769730i \(0.720391\pi\)
\(522\) 0 0
\(523\) 4.68629 0.204917 0.102459 0.994737i \(-0.467329\pi\)
0.102459 + 0.994737i \(0.467329\pi\)
\(524\) 18.1573 79.5521i 0.793204 3.47525i
\(525\) 24.6088 11.8510i 1.07402 0.517219i
\(526\) 5.99762 + 2.88830i 0.261509 + 0.125936i
\(527\) −1.85652 + 8.13397i −0.0808715 + 0.354321i
\(528\) 0.667563 + 2.92478i 0.0290519 + 0.127285i
\(529\) 8.67400 4.17718i 0.377131 0.181617i
\(530\) −14.2776 + 17.9035i −0.620179 + 0.777680i
\(531\) −6.44885 + 8.08660i −0.279856 + 0.350928i
\(532\) −58.5365 28.1897i −2.53788 1.22218i
\(533\) −10.7063 13.4253i −0.463741 0.581513i
\(534\) −72.7696 −3.14905
\(535\) 9.24537 + 11.5933i 0.399712 + 0.501223i
\(536\) −5.55647 24.3445i −0.240003 1.05152i
\(537\) −3.48398 15.2643i −0.150345 0.658703i
\(538\) −47.3485 59.3732i −2.04134 2.55976i
\(539\) 0.414214 0.0178414
\(540\) −0.988722 1.23982i −0.0425478 0.0533533i
\(541\) −9.31885 4.48772i −0.400649 0.192942i 0.222699 0.974887i \(-0.428513\pi\)
−0.623347 + 0.781945i \(0.714228\pi\)
\(542\) −24.9212 + 31.2502i −1.07046 + 1.34231i
\(543\) −12.5141 + 15.6922i −0.537032 + 0.673416i
\(544\) −1.18361 + 0.569997i −0.0507469 + 0.0244384i
\(545\) 2.81642 + 12.3395i 0.120642 + 0.528567i
\(546\) 14.0439 61.5303i 0.601023 2.63326i
\(547\) −32.2538 15.5326i −1.37907 0.664126i −0.410270 0.911964i \(-0.634566\pi\)
−0.968802 + 0.247838i \(0.920280\pi\)
\(548\) 41.3915 19.9331i 1.76816 0.851500i
\(549\) −3.03894 + 13.3144i −0.129699 + 0.568247i
\(550\) −4.00000 −0.170561
\(551\) 0 0
\(552\) −38.9706 −1.65870
\(553\) 1.51947 6.65722i 0.0646144 0.283094i
\(554\) 37.6596 18.1359i 1.60000 0.770521i
\(555\) −8.70053 4.18995i −0.369317 0.177854i
\(556\) −11.9267 + 52.2542i −0.505804 + 2.21607i
\(557\) 3.85266 + 16.8796i 0.163243 + 0.715212i 0.988596 + 0.150595i \(0.0481190\pi\)
−0.825353 + 0.564617i \(0.809024\pi\)
\(558\) 61.9592 29.8380i 2.62294 1.26314i
\(559\) 8.55922 10.7329i 0.362016 0.453954i
\(560\) 5.29049 6.63406i 0.223564 0.280340i
\(561\) −0.746387 0.359441i −0.0315125 0.0151756i
\(562\) 48.1233 + 60.3447i 2.02996 + 2.54549i
\(563\) 0.757359 0.0319189 0.0159594 0.999873i \(-0.494920\pi\)
0.0159594 + 0.999873i \(0.494920\pi\)
\(564\) −18.6863 23.4319i −0.786837 0.986662i
\(565\) 2.96258 + 12.9799i 0.124637 + 0.546069i
\(566\) −6.26221 27.4366i −0.263221 1.15324i
\(567\) 16.7273 + 20.9753i 0.702479 + 0.880880i
\(568\) −38.9706 −1.63517
\(569\) 24.7256 + 31.0050i 1.03655 + 1.29980i 0.952895 + 0.303302i \(0.0980890\pi\)
0.0836584 + 0.996494i \(0.473340\pi\)
\(570\) 31.5074 + 15.1732i 1.31970 + 0.635534i
\(571\) 9.12005 11.4362i 0.381662 0.478589i −0.553480 0.832863i \(-0.686700\pi\)
0.935142 + 0.354274i \(0.115272\pi\)
\(572\) −3.78525 + 4.74655i −0.158269 + 0.198463i
\(573\) −55.0606 + 26.5158i −2.30019 + 1.10771i
\(574\) 6.81524 + 29.8595i 0.284463 + 1.24631i
\(575\) 3.25491 14.2607i 0.135739 0.594711i
\(576\) 25.0460 + 12.0615i 1.04358 + 0.502564i
\(577\) −26.8480 + 12.9293i −1.11770 + 0.538254i −0.899180 0.437580i \(-0.855836\pi\)
−0.218516 + 0.975833i \(0.570121\pi\)
\(578\) 8.76394 38.3973i 0.364532 1.59712i
\(579\) −12.4853 −0.518871
\(580\) 0 0
\(581\) −21.6569 −0.898478
\(582\) −5.81717 + 25.4867i −0.241130 + 1.05646i
\(583\) −3.53985 + 1.70470i −0.146605 + 0.0706015i
\(584\) 15.9083 + 7.66102i 0.658289 + 0.317015i
\(585\) −2.40955 + 10.5569i −0.0996227 + 0.436476i
\(586\) 4.11336 + 18.0218i 0.169921 + 0.744474i
\(587\) −6.89859 + 3.32218i −0.284735 + 0.137121i −0.570800 0.821089i \(-0.693367\pi\)
0.286065 + 0.958210i \(0.407653\pi\)
\(588\) −5.76269 + 7.22619i −0.237649 + 0.298003i
\(589\) 37.6752 47.2433i 1.55238 1.94662i
\(590\) −7.95414 3.83051i −0.327467 0.157700i
\(591\) −3.01048 3.77502i −0.123834 0.155283i
\(592\) 12.0000 0.493197
\(593\) −12.1489 15.2342i −0.498894 0.625594i 0.467085 0.884212i \(-0.345304\pi\)
−0.965980 + 0.258619i \(0.916733\pi\)
\(594\) −0.0921712 0.403828i −0.00378183 0.0165693i
\(595\) 0.521399 + 2.28440i 0.0213753 + 0.0936512i
\(596\) −18.6863 23.4319i −0.765422 0.959809i
\(597\) 1.17157 0.0479493
\(598\) −21.0733 26.4251i −0.861752 1.08060i
\(599\) 8.89261 + 4.28246i 0.363342 + 0.174976i 0.606643 0.794974i \(-0.292516\pi\)
−0.243300 + 0.969951i \(0.578230\pi\)
\(600\) 26.5778 33.3275i 1.08503 1.36059i
\(601\) 10.7063 13.4253i 0.436719 0.547628i −0.513956 0.857816i \(-0.671821\pi\)
0.950675 + 0.310188i \(0.100392\pi\)
\(602\) −22.0605 + 10.6238i −0.899118 + 0.432992i
\(603\) −3.56033 15.5988i −0.144988 0.635234i
\(604\) 12.0478 52.7847i 0.490216 2.14778i
\(605\) −9.75608 4.69828i −0.396641 0.191012i
\(606\) 12.3044 5.92549i 0.499832 0.240706i
\(607\) −1.71962 + 7.53417i −0.0697974 + 0.305802i −0.997762 0.0668661i \(-0.978700\pi\)
0.927965 + 0.372668i \(0.121557\pi\)
\(608\) 9.51472 0.385873
\(609\) 0 0
\(610\) −11.6569 −0.471972
\(611\) 2.76242 12.1030i 0.111756 0.489633i
\(612\) 8.08220 3.89218i 0.326703 0.157332i
\(613\) 8.10872 + 3.90495i 0.327508 + 0.157720i 0.590411 0.807103i \(-0.298966\pi\)
−0.262903 + 0.964822i \(0.584680\pi\)
\(614\) 1.55765 6.82450i 0.0628615 0.275414i
\(615\) −2.40955 10.5569i −0.0971625 0.425697i
\(616\) 4.65943 2.24386i 0.187734 0.0904078i
\(617\) −0.427896 + 0.536564i −0.0172264 + 0.0216013i −0.790370 0.612630i \(-0.790112\pi\)
0.773144 + 0.634231i \(0.218683\pi\)
\(618\) 17.5463 22.0024i 0.705817 0.885067i
\(619\) 30.2597 + 14.5723i 1.21624 + 0.585711i 0.928263 0.371925i \(-0.121302\pi\)
0.287979 + 0.957637i \(0.407017\pi\)
\(620\) 24.0395 + 30.1446i 0.965449 + 1.21063i
\(621\) 1.51472 0.0607836
\(622\) −4.04351 5.07040i −0.162130 0.203304i
\(623\) 7.85804 + 34.4283i 0.314826 + 1.37934i
\(624\) −6.17004 27.0327i −0.246999 1.08218i
\(625\) 6.85839 + 8.60015i 0.274336 + 0.344006i
\(626\) 23.7279 0.948358
\(627\) 3.74094 + 4.69099i 0.149399 + 0.187340i
\(628\) 29.2682 + 14.0948i 1.16793 + 0.562445i
\(629\) −2.06606 + 2.59076i −0.0823793 + 0.103300i
\(630\) 12.0419 15.1001i 0.479761 0.601601i
\(631\) 33.1813 15.9793i 1.32093 0.636124i 0.365350 0.930870i \(-0.380949\pi\)
0.955576 + 0.294746i \(0.0952351\pi\)
\(632\) −2.37137 10.3897i −0.0943282 0.413279i
\(633\) 10.4138 45.6256i 0.413910 1.81346i
\(634\) −68.4206 32.9496i −2.71733 1.30860i
\(635\) 3.91304 1.88442i 0.155284 0.0747809i
\(636\) 19.5082 85.4710i 0.773550 3.38915i
\(637\) −3.82843 −0.151688
\(638\) 0 0
\(639\) −24.9706 −0.987820
\(640\) −4.57422 + 20.0410i −0.180812 + 0.792188i
\(641\) 16.0363 7.72269i 0.633397 0.305028i −0.0894967 0.995987i \(-0.528526\pi\)
0.722894 + 0.690959i \(0.242812\pi\)
\(642\) −77.8675 37.4990i −3.07319 1.47997i
\(643\) −7.22866 + 31.6708i −0.285070 + 1.24897i 0.606130 + 0.795365i \(0.292721\pi\)
−0.891201 + 0.453609i \(0.850136\pi\)
\(644\) 8.81138 + 38.6052i 0.347217 + 1.52126i
\(645\) 7.79956 3.75607i 0.307107 0.147895i
\(646\) 7.48188 9.38198i 0.294371 0.369129i
\(647\) 24.7256 31.0050i 0.972065 1.21893i −0.00367336 0.999993i \(-0.501169\pi\)
0.975739 0.218938i \(-0.0702593\pi\)
\(648\) 37.7236 + 18.1667i 1.48192 + 0.713657i
\(649\) −0.944412 1.18425i −0.0370714 0.0464861i
\(650\) 36.9706 1.45010
\(651\) −42.8771 53.7662i −1.68049 2.10726i
\(652\) 3.34708 + 14.6645i 0.131082 + 0.574306i
\(653\) −6.70726 29.3864i −0.262475 1.14998i −0.918557 0.395289i \(-0.870644\pi\)
0.656082 0.754690i \(-0.272213\pi\)
\(654\) −45.9946 57.6754i −1.79853 2.25528i
\(655\) 21.3137 0.832796
\(656\) 8.38958 + 10.5202i 0.327558 + 0.410745i
\(657\) 10.1933 + 4.90883i 0.397678 + 0.191512i
\(658\) −13.8054 + 17.3114i −0.538190 + 0.674869i
\(659\) −8.98712 + 11.2695i −0.350088 + 0.438997i −0.925431 0.378915i \(-0.876297\pi\)
0.575343 + 0.817912i \(0.304869\pi\)
\(660\) −3.44929 + 1.66109i −0.134264 + 0.0646579i
\(661\) −7.41300 32.4785i −0.288332 1.26327i −0.886813 0.462129i \(-0.847086\pi\)
0.598481 0.801137i \(-0.295771\pi\)
\(662\) −1.29695 + 5.68230i −0.0504073 + 0.220849i
\(663\) 6.89859 + 3.32218i 0.267919 + 0.129023i
\(664\) −30.4518 + 14.6648i −1.18176 + 0.569106i
\(665\) 3.77631 16.5451i 0.146439 0.641591i
\(666\) 27.3137 1.05838
\(667\) 0 0
\(668\) −12.1421 −0.469793
\(669\) −1.70381 + 7.46488i −0.0658731 + 0.288609i
\(670\) 12.3044 5.92549i 0.475360 0.228922i
\(671\) −1.80194 0.867767i −0.0695630 0.0334998i
\(672\) 2.40955 10.5569i 0.0929505 0.407243i
\(673\) 4.81255 + 21.0852i 0.185510 + 0.812774i 0.978946 + 0.204120i \(0.0654331\pi\)
−0.793436 + 0.608654i \(0.791710\pi\)
\(674\) 47.4157 22.8342i 1.82638 0.879540i
\(675\) −1.03303 + 1.29538i −0.0397614 + 0.0498592i
\(676\) 3.95489 4.95927i 0.152111 0.190741i
\(677\) −19.8213 9.54544i −0.761795 0.366861i 0.0123051 0.999924i \(-0.496083\pi\)
−0.774100 + 0.633063i \(0.781797\pi\)
\(678\) −48.3815 60.6685i −1.85808 2.32996i
\(679\) 12.6863 0.486855
\(680\) 2.28001 + 2.85904i 0.0874344 + 0.109639i
\(681\) −4.37406 19.1640i −0.167614 0.734367i
\(682\) 2.24102 + 9.81857i 0.0858132 + 0.375972i
\(683\) 13.0749 + 16.3954i 0.500298 + 0.627354i 0.966297 0.257431i \(-0.0828761\pi\)
−0.465998 + 0.884786i \(0.654305\pi\)
\(684\) −64.9706 −2.48421
\(685\) 7.48188 + 9.38198i 0.285868 + 0.358467i
\(686\) −36.9132 17.7765i −1.40935 0.678708i
\(687\) −5.29049 + 6.63406i −0.201845 + 0.253105i
\(688\) −6.70710 + 8.41044i −0.255706 + 0.320645i
\(689\) 32.7175 15.7559i 1.24644 0.600253i
\(690\) −4.74275 20.7793i −0.180553 0.791056i
\(691\) −10.6810 + 46.7965i −0.406325 + 1.78022i 0.194562 + 0.980890i \(0.437671\pi\)
−0.600887 + 0.799334i \(0.705186\pi\)
\(692\) −42.5751 20.5031i −1.61846 0.779411i
\(693\) 2.98555 1.43776i 0.113412 0.0546161i
\(694\) −1.33513 + 5.84957i −0.0506807 + 0.222047i
\(695\) −14.0000 −0.531050
\(696\) 0 0
\(697\) −3.71573 −0.140743
\(698\) 2.76242 12.1030i 0.104559 0.458104i
\(699\) 39.8347 19.1834i 1.50669 0.725582i
\(700\) −39.0243 18.7931i −1.47498 0.710313i
\(701\) 8.92592 39.1070i 0.337127 1.47705i −0.467883 0.883790i \(-0.654983\pi\)
0.805011 0.593260i \(-0.202160\pi\)
\(702\) 0.851905 + 3.73244i 0.0321531 + 0.140872i
\(703\) 21.6233 10.4132i 0.815536 0.392742i
\(704\) −2.53827 + 3.18289i −0.0956646 + 0.119960i
\(705\) 4.88094 6.12051i 0.183827 0.230512i
\(706\) −58.6645 28.2513i −2.20787 1.06325i
\(707\) −4.13213 5.18152i −0.155405 0.194871i
\(708\) 33.7990 1.27024
\(709\) 18.1698 + 22.7842i 0.682382 + 0.855680i 0.995571 0.0940107i \(-0.0299688\pi\)
−0.313189 + 0.949691i \(0.601397\pi\)
\(710\) −4.74275 20.7793i −0.177992 0.779834i
\(711\) −1.51947 6.65722i −0.0569845 0.249665i
\(712\) 34.3622 + 43.0888i 1.28778 + 1.61482i
\(713\) −36.8284 −1.37924
\(714\) −8.51491 10.6774i −0.318662 0.399590i
\(715\) −1.42874 0.688047i −0.0534320 0.0257315i
\(716\) −15.4803 + 19.4116i −0.578525 + 0.725447i
\(717\) 29.5882 37.1025i 1.10499 1.38562i
\(718\) 8.54594 4.11551i 0.318932 0.153589i
\(719\) 4.48205 + 19.6371i 0.167152 + 0.732341i 0.987127 + 0.159941i \(0.0511305\pi\)
−0.819974 + 0.572400i \(0.806012\pi\)
\(720\) 1.88815 8.27254i 0.0703673 0.308299i
\(721\) −12.3044 5.92549i −0.458240 0.220677i
\(722\) −36.9772 + 17.8073i −1.37615 + 0.662719i
\(723\) −9.83836 + 43.1047i −0.365893 + 1.60308i
\(724\) 31.8284 1.18289
\(725\) 0 0
\(726\) 63.1127 2.34233
\(727\) 0.292328 1.28077i 0.0108418 0.0475012i −0.969218 0.246205i \(-0.920816\pi\)
0.980059 + 0.198704i \(0.0636733\pi\)
\(728\) −43.0654 + 20.7392i −1.59611 + 0.768646i
\(729\) 21.4687 + 10.3388i 0.795136 + 0.382917i
\(730\) −2.14885 + 9.41474i −0.0795326 + 0.348455i
\(731\) −0.661012 2.89608i −0.0244484 0.107116i
\(732\) 40.2079 19.3631i 1.48613 0.715681i
\(733\) 25.7220 32.2543i 0.950063 1.19134i −0.0313650 0.999508i \(-0.509985\pi\)
0.981428 0.191833i \(-0.0614431\pi\)
\(734\) −27.0943 + 33.9751i −1.00007 + 1.25405i
\(735\) −2.17513 1.04749i −0.0802309 0.0386372i
\(736\) −3.61561 4.53383i −0.133273 0.167119i
\(737\) 2.34315 0.0863109
\(738\) 19.0959 + 23.9455i 0.702929 + 0.881445i
\(739\) 0.905898 + 3.96900i 0.0333240 + 0.146002i 0.988853 0.148895i \(-0.0475717\pi\)
−0.955529 + 0.294897i \(0.904715\pi\)
\(740\) 3.40762 + 14.9298i 0.125267 + 0.548829i
\(741\) −34.5762 43.3571i −1.27019 1.59276i
\(742\) −64.7696 −2.37777
\(743\) −14.7498 18.4957i −0.541118 0.678540i 0.433825 0.900997i \(-0.357164\pi\)
−0.974943 + 0.222457i \(0.928592\pi\)
\(744\) −96.6973 46.5670i −3.54509 1.70723i
\(745\) 4.88094 6.12051i 0.178824 0.224238i
\(746\) −39.6084 + 49.6673i −1.45017 + 1.81845i
\(747\) −19.5122 + 9.39656i −0.713912 + 0.343802i
\(748\) 0.292328 + 1.28077i 0.0106886 + 0.0468296i
\(749\) −9.33278 + 40.8896i −0.341012 + 1.49407i
\(750\) 47.2611 + 22.7597i 1.72573 + 0.831068i
\(751\) 22.8069 10.9832i 0.832234 0.400783i 0.0312816 0.999511i \(-0.490041\pi\)
0.800953 + 0.598728i \(0.204327\pi\)
\(752\) −2.16467 + 9.48402i −0.0789373 + 0.345847i
\(753\) 48.4558 1.76583
\(754\) 0 0
\(755\) 14.1421 0.514685
\(756\) 0.998069 4.37283i 0.0362994 0.159038i
\(757\) 22.9880 11.0704i 0.835512 0.402361i 0.0333324 0.999444i \(-0.489388\pi\)
0.802179 + 0.597083i \(0.203674\pi\)
\(758\) −15.1619 7.30158i −0.550705 0.265205i
\(759\) 0.813727 3.56517i 0.0295364 0.129407i
\(760\) −5.89353 25.8212i −0.213781 0.936635i
\(761\) −41.0824 + 19.7842i −1.48923 + 0.717177i −0.988890 0.148649i \(-0.952508\pi\)
−0.500344 + 0.865826i \(0.666793\pi\)
\(762\) −15.7828 + 19.7911i −0.571752 + 0.716954i
\(763\) −22.3203 + 27.9888i −0.808049 + 1.01326i
\(764\) 87.3144 + 42.0484i 3.15892 + 1.52126i
\(765\) 1.46093 + 1.83195i 0.0528199 + 0.0662341i
\(766\) −8.48528 −0.306586
\(767\) 8.72886 + 10.9456i 0.315181 + 0.395224i
\(768\) −16.1006 70.5412i −0.580980 2.54544i
\(769\) −10.9286 47.8813i −0.394096 1.72665i −0.649992 0.759941i \(-0.725228\pi\)
0.255896 0.966704i \(-0.417629\pi\)
\(770\) 1.76350 + 2.21135i 0.0635520 + 0.0796916i
\(771\) 43.8701 1.57994
\(772\) 12.3445 + 15.4795i 0.444287 + 0.557118i
\(773\) −17.5822 8.46712i −0.632386 0.304541i 0.0900935 0.995933i \(-0.471283\pi\)
−0.722480 + 0.691392i \(0.756998\pi\)
\(774\) −15.2663 + 19.1434i −0.548737 + 0.688094i
\(775\) 25.1168 31.4955i 0.902223 1.13135i
\(776\) 17.8383 8.59046i 0.640357 0.308380i
\(777\) −6.07787 26.6289i −0.218042 0.955306i
\(778\) 1.62745 7.13034i 0.0583470 0.255635i
\(779\) 24.2466 + 11.6765i 0.868724 + 0.418356i
\(780\) 31.8806 15.3529i 1.14151 0.549721i
\(781\) 0.813727 3.56517i 0.0291174 0.127572i
\(782\) −7.31371 −0.261538
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −1.88815 + 8.27254i −0.0673911 + 0.295260i
\(786\) −111.923 + 53.8994i −3.99217 + 1.92253i
\(787\) 48.7273 + 23.4658i 1.73694 + 0.836467i 0.983952 + 0.178435i \(0.0571036\pi\)
0.752990 + 0.658032i \(0.228611\pi\)
\(788\) −1.70381 + 7.46488i −0.0606957 + 0.265925i
\(789\) −1.48129 6.48995i −0.0527353 0.231048i
\(790\) 5.25123 2.52886i 0.186830 0.0899728i
\(791\) −23.4787 + 29.4413i −0.834805 + 1.04681i
\(792\) 3.22442 4.04330i 0.114575 0.143672i
\(793\) 16.6547 + 8.02046i 0.591424 + 0.284815i
\(794\) 29.1160 + 36.5103i 1.03329 + 1.29570i
\(795\) 22.8995 0.812161
\(796\) −1.15836 1.45254i −0.0410570 0.0514838i
\(797\) 11.5133 + 50.4429i 0.407821 + 1.78678i 0.594218 + 0.804304i \(0.297462\pi\)
−0.186397 + 0.982474i \(0.559681\pi\)
\(798\) 22.0099 + 96.4318i 0.779143 + 3.41365i
\(799\) −1.67488 2.10023i −0.0592528 0.0743007i
\(800\) 6.34315 0.224264
\(801\) 22.0177 + 27.6094i 0.777958 + 0.975529i
\(802\) 40.5811 + 19.5428i 1.43297 + 0.690081i
\(803\) −1.03303 + 1.29538i −0.0364549 + 0.0457130i
\(804\) −32.5987 + 40.8775i −1.14967 + 1.44164i
\(805\) −9.31885 + 4.48772i −0.328446 + 0.158171i
\(806\) −20.7130 90.7495i −0.729583 3.19651i
\(807\) −16.8985 + 74.0371i −0.594855 + 2.60623i
\(808\) −9.31885 4.48772i −0.327836 0.157878i
\(809\) 32.6910 15.7432i 1.14935 0.553500i 0.240515 0.970646i \(-0.422684\pi\)
0.908840 + 0.417146i \(0.136970\pi\)
\(810\) −5.09562 + 22.3254i −0.179042 + 0.784433i
\(811\) 10.8284 0.380238 0.190119 0.981761i \(-0.439113\pi\)
0.190119 + 0.981761i \(0.439113\pi\)
\(812\) 0 0
\(813\) 39.9706 1.40183
\(814\) −0.890084 + 3.89971i −0.0311974 + 0.136685i
\(815\) −3.53985 + 1.70470i −0.123995 + 0.0597130i
\(816\) −5.40581 2.60330i −0.189241 0.0911338i
\(817\) −4.78748 + 20.9753i −0.167493 + 0.733833i
\(818\) −10.1912 44.6507i −0.356328 1.56118i
\(819\) −27.5943 + 13.2887i −0.964225 + 0.464346i
\(820\) −10.7063 + 13.4253i −0.373880 + 0.468831i
\(821\) −0.926058 + 1.16124i −0.0323196 + 0.0405275i −0.797729 0.603017i \(-0.793965\pi\)
0.765409 + 0.643544i \(0.222537\pi\)
\(822\) −63.0148 30.3463i −2.19789 1.05845i
\(823\) 33.8457 + 42.4412i 1.17979 + 1.47941i 0.843074 + 0.537798i \(0.180744\pi\)
0.336713 + 0.941607i \(0.390685\pi\)
\(824\) −21.3137 −0.742498
\(825\) 2.49396 + 3.12733i 0.0868285 + 0.108880i
\(826\) −5.55647 24.3445i −0.193334 0.847053i
\(827\) 7.32083 + 32.0746i 0.254570 + 1.11534i 0.926964 + 0.375151i \(0.122409\pi\)
−0.672394 + 0.740194i \(0.734734\pi\)
\(828\) 24.6889 + 30.9589i 0.858000 + 1.07590i
\(829\) 29.7990 1.03496 0.517481 0.855695i \(-0.326870\pi\)
0.517481 + 0.855695i \(0.326870\pi\)
\(830\) −11.5254 14.4524i −0.400052 0.501649i
\(831\) −37.6596 18.1359i −1.30640 0.629127i
\(832\) 23.4603 29.4183i 0.813340 1.01990i
\(833\) −0.516516 + 0.647690i −0.0178962 + 0.0224411i
\(834\) 73.5172 35.4040i 2.54569 1.22594i
\(835\) −0.705741 3.09205i −0.0244232 0.107005i
\(836\) 2.11722 9.27616i 0.0732257 0.320823i
\(837\) 3.75846 + 1.80998i 0.129911 + 0.0625620i
\(838\) 20.6958 9.96655i 0.714923 0.344289i
\(839\) −1.76435 + 7.73014i −0.0609122 + 0.266874i −0.996209 0.0869898i \(-0.972275\pi\)
0.935297 + 0.353864i \(0.115132\pi\)
\(840\) −30.1421 −1.04000
\(841\) 0 0
\(842\) −89.5980 −3.08775
\(843\) 17.1750 75.2486i 0.591539 2.59170i
\(844\) −66.8638 + 32.1999i −2.30155 + 1.10837i
\(845\) 1.49277 + 0.718882i 0.0513530 + 0.0247303i
\(846\) −4.92709 + 21.5870i −0.169397 + 0.742176i
\(847\) −6.81524 29.8595i −0.234174 1.02599i
\(848\) −25.6378 + 12.3465i −0.880407 + 0.423982i
\(849\) −17.5463 + 22.0024i −0.602189 + 0.755121i
\(850\) 4.98792 6.25465i 0.171084 0.214533i
\(851\) −13.1788 6.34660i −0.451765 0.217559i
\(852\) 50.8755 + 63.7959i 1.74297 + 2.18561i
\(853\) 22.9706 0.786497 0.393249 0.919432i \(-0.371351\pi\)
0.393249 + 0.919432i \(0.371351\pi\)
\(854\) −20.5568 25.7774i −0.703440 0.882085i
\(855\) −3.77631 16.5451i −0.129147 0.565830i
\(856\) 14.5653 + 63.8147i 0.497832 + 2.18114i
\(857\) −3.84791 4.82513i −0.131442 0.164823i 0.711755 0.702428i \(-0.247901\pi\)
−0.843197 + 0.537605i \(0.819329\pi\)
\(858\) 9.24264 0.315539
\(859\) −12.3002 15.4239i −0.419676 0.526257i 0.526385 0.850247i \(-0.323547\pi\)
−0.946061 + 0.323989i \(0.894976\pi\)
\(860\) −12.3684 5.95632i −0.421760 0.203109i
\(861\) 19.0959 23.9455i 0.650786 0.816060i
\(862\) 29.5882 37.1025i 1.00778 1.26372i
\(863\) −15.4180 + 7.42492i −0.524835 + 0.252747i −0.677490 0.735532i \(-0.736932\pi\)
0.152654 + 0.988280i \(0.451218\pi\)
\(864\) 0.146164 + 0.640386i 0.00497259 + 0.0217864i
\(865\) 2.74661 12.0337i 0.0933875 0.409157i
\(866\) 66.6187 + 32.0819i 2.26379 + 1.09019i
\(867\) −35.4845 + 17.0884i −1.20512 + 0.580353i
\(868\) −24.2668 + 106.320i −0.823667 + 3.60872i
\(869\) 1.00000 0.0339227
\(870\) 0 0
\(871\) −21.6569 −0.733815
\(872\) −12.4323 + 54.4693i −0.421009 + 1.84456i
\(873\) 11.4300 5.50438i 0.386845 0.186295i
\(874\) 47.7248 + 22.9831i 1.61432 + 0.777414i
\(875\) 5.66446 24.8176i 0.191494 0.838988i
\(876\) −8.22672 36.0436i −0.277955 1.21780i
\(877\) 33.4639 16.1154i 1.13000 0.544177i 0.227029 0.973888i \(-0.427099\pi\)
0.902967 + 0.429711i \(0.141384\pi\)
\(878\) −0.516516 + 0.647690i −0.0174316 + 0.0218585i
\(879\) 11.5254 14.4524i 0.388742 0.487467i
\(880\) 1.11958 + 0.539162i 0.0377411 + 0.0181751i
\(881\) −8.72886 10.9456i −0.294083 0.368768i 0.612737 0.790287i \(-0.290069\pi\)
−0.906820 + 0.421519i \(0.861497\pi\)
\(882\) 6.82843 0.229925
\(883\) 23.9585 + 30.0430i 0.806267 + 1.01103i 0.999553 + 0.0298842i \(0.00951387\pi\)
−0.193287 + 0.981142i \(0.561915\pi\)
\(884\) −2.70188 11.8377i −0.0908740 0.398145i
\(885\) 1.96451 + 8.60708i 0.0660363 + 0.289324i
\(886\) 36.6422 + 45.9479i 1.23102 + 1.54365i
\(887\) −17.1005 −0.574179 −0.287089 0.957904i \(-0.592688\pi\)
−0.287089 + 0.957904i \(0.592688\pi\)
\(888\) −26.5778 33.3275i −0.891891 1.11840i
\(889\) 11.0677 + 5.32995i 0.371200 + 0.178761i
\(890\) −18.7933 + 23.5661i −0.629953 + 0.789936i
\(891\) −2.44965 + 3.07176i −0.0820663 + 0.102908i
\(892\) 10.9397 5.26828i 0.366288 0.176395i
\(893\) 4.32933 + 18.9680i 0.144876 + 0.634741i
\(894\) −10.1531 + 44.4834i −0.339569 + 1.48775i
\(895\) −5.84304 2.81386i −0.195311 0.0940569i
\(896\) −52.3843 + 25.2269i −1.75004 + 0.842772i
\(897\) −7.52098 + 32.9516i −0.251118 + 1.10022i
\(898\) 84.4264 2.81735
\(899\) 0 0
\(900\) −43.3137 −1.44379
\(901\) 1.74854 7.66085i 0.0582523 0.255220i
\(902\) −4.04110 + 1.94609i −0.134554 + 0.0647977i
\(903\) 22.0605 + 10.6238i 0.734127 + 0.353537i
\(904\) −13.0775 + 57.2961i −0.434950 + 1.90564i
\(905\) 1.84997 + 8.10527i 0.0614952 + 0.269428i
\(906\) −74.2636 + 35.7635i −2.46724 + 1.18816i
\(907\) −13.8940 + 17.4225i −0.461343 + 0.578506i −0.957028 0.289997i \(-0.906346\pi\)
0.495684 + 0.868503i \(0.334917\pi\)
\(908\) −19.4352 + 24.3709i −0.644978 + 0.808777i
\(909\) −5.97110 2.87553i −0.198049 0.0953753i
\(910\) −16.2994 20.4387i −0.540318 0.677538i
\(911\) 15.4437 0.511671 0.255835 0.966720i \(-0.417649\pi\)
0.255835 + 0.966720i \(0.417649\pi\)
\(912\) 27.0943 + 33.9751i 0.897181 + 1.12503i
\(913\) −0.705741 3.09205i −0.0233566 0.102332i
\(914\) −0.553027 2.42297i −0.0182925 0.0801447i
\(915\) 7.26793 + 9.11370i 0.240270 + 0.301289i
\(916\) 13.4558 0.444594
\(917\) 37.5866 + 47.1321i 1.24122 + 1.55644i
\(918\) 0.746387 + 0.359441i 0.0246344 + 0.0118633i
\(919\) 5.07654 6.36578i 0.167460 0.209988i −0.691020 0.722836i \(-0.742838\pi\)
0.858479 + 0.512848i \(0.171410\pi\)
\(920\) −10.0645 + 12.6204i −0.331815 + 0.416083i
\(921\) −6.30678 + 3.03719i −0.207816 + 0.100079i
\(922\) 7.52098 + 32.9516i 0.247690 + 1.08520i
\(923\) −7.52098 + 32.9516i −0.247556 + 1.08461i
\(924\) −9.75608 4.69828i −0.320951 0.154562i
\(925\) 14.4155 6.94214i 0.473979 0.228256i
\(926\) 13.9675 61.1958i 0.459002 2.01102i
\(927\) −13.6569 −0.448550
\(928\) 0 0
\(929\) 18.6863 0.613077 0.306539 0.951858i \(-0.400829\pi\)
0.306539 + 0.951858i \(0.400829\pi\)
\(930\) 13.0616 57.2268i 0.428308 1.87654i
\(931\) 5.40581 2.60330i 0.177168 0.0853198i
\(932\) −63.1694 30.4208i −2.06918 0.996465i
\(933\) −1.44311 + 6.32268i −0.0472453 + 0.206995i
\(934\) −20.6050 90.2764i −0.674216 2.95393i
\(935\) −0.309164 + 0.148885i −0.0101107 + 0.00486907i
\(936\) −29.8022 + 37.3708i −0.974115 + 1.22150i
\(937\) −10.3670 + 12.9998i −0.338676 + 0.424686i −0.921781 0.387710i \(-0.873266\pi\)
0.583105 + 0.812397i \(0.301837\pi\)
\(938\) 34.8021 + 16.7598i 1.13633 + 0.547227i
\(939\) −14.7941 18.5512i −0.482788 0.605397i
\(940\) −12.4142 −0.404907
\(941\) −35.2883 44.2501i −1.15036 1.44251i −0.876928 0.480621i \(-0.840411\pi\)
−0.273436 0.961890i \(-0.588160\pi\)
\(942\) −11.0050 48.2159i −0.358561 1.57096i
\(943\) −3.64979 15.9908i −0.118854 0.520732i
\(944\) −6.84003 8.57713i −0.222624 0.279162i
\(945\) 1.17157 0.0381113
\(946\) −2.23570 2.80348i −0.0726889 0.0911490i
\(947\) 2.35624 + 1.13470i 0.0765674 + 0.0368729i 0.471776 0.881719i \(-0.343613\pi\)
−0.395208 + 0.918592i \(0.629328\pi\)
\(948\) −13.9124 + 17.4456i −0.451853 + 0.566605i
\(949\) 9.54794 11.9727i 0.309939 0.388652i
\(950\) −52.2032 + 25.1397i −1.69369 + 0.815640i
\(951\) 16.8985 + 74.0371i 0.547971 + 2.40082i
\(952\) −2.30157 + 10.0838i −0.0745942 + 0.326819i
\(953\) 32.0992 + 15.4582i 1.03979 + 0.500739i 0.874256 0.485465i \(-0.161350\pi\)
0.165538 + 0.986203i \(0.447064\pi\)
\(954\) −58.3554 + 28.1025i −1.88932 + 0.909851i
\(955\) −5.63283 + 24.6790i −0.182274 + 0.798595i
\(956\) −75.2548 −2.43392
\(957\) 0 0
\(958\) −16.6569 −0.538159
\(959\) −7.55261 + 33.0902i −0.243887 + 1.06854i
\(960\) 21.3781 10.2952i 0.689976 0.332275i
\(961\) −63.4520 30.5569i −2.04684 0.985706i
\(962\) 8.22672 36.0436i 0.265240 1.16209i
\(963\) 9.33278 + 40.8896i 0.300745 + 1.31765i
\(964\) 63.1694 30.4208i 2.03455 0.979787i
\(965\) −3.22442 + 4.04330i −0.103798 + 0.130158i
\(966\) 37.5866 47.1321i 1.20933 1.51645i
\(967\) −31.7525 15.2912i −1.02109 0.491732i −0.153048 0.988219i \(-0.548909\pi\)
−0.868044 + 0.496487i \(0.834623\pi\)
\(968\) −29.8022 37.3708i −0.957878 1.20114i
\(969\) −12.0000 −0.385496
\(970\) 6.75141 + 8.46601i 0.216775 + 0.271827i
\(971\) −3.48398 15.2643i −0.111806 0.489855i −0.999564 0.0295431i \(-0.990595\pi\)
0.887757 0.460312i \(-0.152262\pi\)
\(972\) −18.4496 80.8329i −0.591771 2.59272i
\(973\) −24.6889 30.9589i −0.791491 0.992498i
\(974\) −27.7990 −0.890737
\(975\) −23.0508 28.9047i −0.738215 0.925693i
\(976\) −13.0508 6.28493i −0.417746 0.201176i
\(977\) 22.5526 28.2801i 0.721522 0.904760i −0.276901 0.960898i \(-0.589307\pi\)
0.998423 + 0.0561387i \(0.0178789\pi\)
\(978\) 14.2776 17.9035i 0.456547 0.572492i
\(979\) −4.65943 + 2.24386i −0.148916 + 0.0717141i
\(980\) 0.851905 + 3.73244i 0.0272131 + 0.119228i
\(981\) −7.96602 + 34.9014i −0.254336 + 1.11432i
\(982\) −46.2055 22.2514i −1.47448 0.710071i
\(983\) −19.7042 + 9.48906i −0.628468 + 0.302654i −0.720873 0.693067i \(-0.756259\pi\)
0.0924051 + 0.995721i \(0.470545\pi\)
\(984\) 10.6363 46.6006i 0.339072 1.48557i
\(985\) −2.00000 −0.0637253
\(986\) 0 0
\(987\) 22.1421 0.704792
\(988\) −19.5687 + 85.7363i −0.622565 + 2.72763i
\(989\) 11.8141 5.68939i 0.375668 0.180912i
\(990\) 2.54832 + 1.22721i 0.0809911 + 0.0390032i
\(991\) 2.85459 12.5068i 0.0906792 0.397291i −0.909136 0.416499i \(-0.863257\pi\)
0.999816 + 0.0192072i \(0.00611423\pi\)
\(992\) −3.55378 15.5701i −0.112833 0.494353i
\(993\) 5.25123 2.52886i 0.166643 0.0802509i
\(994\) 37.5866 47.1321i 1.19218 1.49494i
\(995\) 0.302568 0.379408i 0.00959205 0.0120281i
\(996\) 63.7612 + 30.7058i 2.02035 + 0.972949i
\(997\) −17.6350 22.1135i −0.558505 0.700343i 0.419776 0.907628i \(-0.362109\pi\)
−0.978281 + 0.207285i \(0.933537\pi\)
\(998\) 45.7990 1.44974
\(999\) 1.03303 + 1.29538i 0.0326837 + 0.0409840i
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 841.2.d.f.605.1 12
29.2 odd 28 841.2.e.k.651.1 24
29.3 odd 28 841.2.e.k.196.1 24
29.4 even 14 841.2.d.j.574.1 12
29.5 even 14 841.2.d.j.190.2 12
29.6 even 14 29.2.a.a.1.1 2
29.7 even 7 inner 841.2.d.f.645.1 12
29.8 odd 28 841.2.e.k.63.1 24
29.9 even 14 841.2.d.j.778.1 12
29.10 odd 28 841.2.e.k.267.4 24
29.11 odd 28 841.2.e.k.270.4 24
29.12 odd 4 841.2.e.k.236.1 24
29.13 even 14 841.2.d.j.571.2 12
29.14 odd 28 841.2.b.a.840.1 4
29.15 odd 28 841.2.b.a.840.4 4
29.16 even 7 inner 841.2.d.f.571.1 12
29.17 odd 4 841.2.e.k.236.4 24
29.18 odd 28 841.2.e.k.270.1 24
29.19 odd 28 841.2.e.k.267.1 24
29.20 even 7 inner 841.2.d.f.778.2 12
29.21 odd 28 841.2.e.k.63.4 24
29.22 even 14 841.2.d.j.645.2 12
29.23 even 7 841.2.a.d.1.2 2
29.24 even 7 inner 841.2.d.f.190.1 12
29.25 even 7 inner 841.2.d.f.574.2 12
29.26 odd 28 841.2.e.k.196.4 24
29.27 odd 28 841.2.e.k.651.4 24
29.28 even 2 841.2.d.j.605.2 12
87.23 odd 14 7569.2.a.c.1.1 2
87.35 odd 14 261.2.a.d.1.2 2
116.35 odd 14 464.2.a.h.1.1 2
145.64 even 14 725.2.a.b.1.2 2
145.93 odd 28 725.2.b.b.349.4 4
145.122 odd 28 725.2.b.b.349.1 4
203.6 odd 14 1421.2.a.j.1.1 2
232.35 odd 14 1856.2.a.w.1.2 2
232.93 even 14 1856.2.a.r.1.1 2
319.296 odd 14 3509.2.a.j.1.2 2
348.35 even 14 4176.2.a.bq.1.2 2
377.64 even 14 4901.2.a.g.1.2 2
435.209 odd 14 6525.2.a.o.1.1 2
493.441 even 14 8381.2.a.e.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.a.a.1.1 2 29.6 even 14
261.2.a.d.1.2 2 87.35 odd 14
464.2.a.h.1.1 2 116.35 odd 14
725.2.a.b.1.2 2 145.64 even 14
725.2.b.b.349.1 4 145.122 odd 28
725.2.b.b.349.4 4 145.93 odd 28
841.2.a.d.1.2 2 29.23 even 7
841.2.b.a.840.1 4 29.14 odd 28
841.2.b.a.840.4 4 29.15 odd 28
841.2.d.f.190.1 12 29.24 even 7 inner
841.2.d.f.571.1 12 29.16 even 7 inner
841.2.d.f.574.2 12 29.25 even 7 inner
841.2.d.f.605.1 12 1.1 even 1 trivial
841.2.d.f.645.1 12 29.7 even 7 inner
841.2.d.f.778.2 12 29.20 even 7 inner
841.2.d.j.190.2 12 29.5 even 14
841.2.d.j.571.2 12 29.13 even 14
841.2.d.j.574.1 12 29.4 even 14
841.2.d.j.605.2 12 29.28 even 2
841.2.d.j.645.2 12 29.22 even 14
841.2.d.j.778.1 12 29.9 even 14
841.2.e.k.63.1 24 29.8 odd 28
841.2.e.k.63.4 24 29.21 odd 28
841.2.e.k.196.1 24 29.3 odd 28
841.2.e.k.196.4 24 29.26 odd 28
841.2.e.k.236.1 24 29.12 odd 4
841.2.e.k.236.4 24 29.17 odd 4
841.2.e.k.267.1 24 29.19 odd 28
841.2.e.k.267.4 24 29.10 odd 28
841.2.e.k.270.1 24 29.18 odd 28
841.2.e.k.270.4 24 29.11 odd 28
841.2.e.k.651.1 24 29.2 odd 28
841.2.e.k.651.4 24 29.27 odd 28
1421.2.a.j.1.1 2 203.6 odd 14
1856.2.a.r.1.1 2 232.93 even 14
1856.2.a.w.1.2 2 232.35 odd 14
3509.2.a.j.1.2 2 319.296 odd 14
4176.2.a.bq.1.2 2 348.35 even 14
4901.2.a.g.1.2 2 377.64 even 14
6525.2.a.o.1.1 2 435.209 odd 14
7569.2.a.c.1.1 2 87.23 odd 14
8381.2.a.e.1.1 2 493.441 even 14