Properties

Label 140.2.o.a.31.10
Level $140$
Weight $2$
Character 140.31
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 31.10
Character \(\chi\) \(=\) 140.31
Dual form 140.2.o.a.131.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.569639 + 1.29442i) q^{2} +(-1.51353 + 2.62152i) q^{3} +(-1.35102 + 1.47470i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-4.25550 - 0.465823i) q^{6} +(2.57616 - 0.602834i) q^{7} +(-2.67847 - 0.908739i) q^{8} +(-3.08156 - 5.33743i) q^{9} +O(q^{10})\) \(q+(0.569639 + 1.29442i) q^{2} +(-1.51353 + 2.62152i) q^{3} +(-1.35102 + 1.47470i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-4.25550 - 0.465823i) q^{6} +(2.57616 - 0.602834i) q^{7} +(-2.67847 - 0.908739i) q^{8} +(-3.08156 - 5.33743i) q^{9} +(1.14053 + 0.836177i) q^{10} +(-1.03659 - 0.598478i) q^{11} +(-1.82113 - 5.77373i) q^{12} +4.83692i q^{13} +(2.24780 + 2.99122i) q^{14} +3.02707i q^{15} +(-0.349474 - 3.98470i) q^{16} +(2.20430 + 1.27265i) q^{17} +(5.15347 - 7.02923i) q^{18} +(0.711130 + 1.23171i) q^{19} +(-0.432671 + 1.95264i) q^{20} +(-2.31876 + 7.66585i) q^{21} +(0.184195 - 1.68270i) q^{22} +(5.02859 - 2.90326i) q^{23} +(6.43623 - 5.64624i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-6.26099 + 2.75530i) q^{26} +9.57500 q^{27} +(-2.59145 + 4.61350i) q^{28} +0.774233 q^{29} +(-3.91828 + 1.72433i) q^{30} +(-3.31933 + 5.74924i) q^{31} +(4.95879 - 2.72221i) q^{32} +(3.13784 - 1.81163i) q^{33} +(-0.391687 + 3.57823i) q^{34} +(1.92960 - 1.81015i) q^{35} +(12.0344 + 2.66661i) q^{36} +(-2.55465 - 4.42479i) q^{37} +(-1.18926 + 1.62213i) q^{38} +(-12.6801 - 7.32084i) q^{39} +(-2.77399 + 0.552243i) q^{40} -7.46685i q^{41} +(-11.2437 + 1.36532i) q^{42} +1.38202i q^{43} +(2.28304 - 0.720107i) q^{44} +(-5.33743 - 3.08156i) q^{45} +(6.62250 + 4.85528i) q^{46} +(-0.535428 - 0.927389i) q^{47} +(10.9749 + 5.11483i) q^{48} +(6.27318 - 3.10599i) q^{49} +(1.40582 + 0.153886i) q^{50} +(-6.67256 + 3.85240i) q^{51} +(-7.13300 - 6.53479i) q^{52} +(-1.68099 + 2.91156i) q^{53} +(5.45429 + 12.3940i) q^{54} -1.19696 q^{55} +(-7.44798 - 0.726385i) q^{56} -4.30528 q^{57} +(0.441033 + 1.00218i) q^{58} +(4.94206 - 8.55990i) q^{59} +(-4.46401 - 4.08964i) q^{60} +(8.31115 - 4.79845i) q^{61} +(-9.33272 - 1.02160i) q^{62} +(-11.1562 - 11.8924i) q^{63} +(6.34839 + 4.86806i) q^{64} +(2.41846 + 4.18890i) q^{65} +(4.13244 + 3.02969i) q^{66} +(9.14135 + 5.27776i) q^{67} +(-4.85484 + 1.53129i) q^{68} +17.5767i q^{69} +(3.44226 + 1.46658i) q^{70} -16.3277i q^{71} +(3.40354 + 17.0965i) q^{72} +(0.0927594 + 0.0535547i) q^{73} +(4.27228 - 5.82731i) q^{74} +(1.51353 + 2.62152i) q^{75} +(-2.77716 - 0.615371i) q^{76} +(-3.03121 - 0.916880i) q^{77} +(2.25315 - 20.5835i) q^{78} +(-9.32609 + 5.38442i) q^{79} +(-2.29501 - 3.27612i) q^{80} +(-5.24739 + 9.08874i) q^{81} +(9.66521 - 4.25341i) q^{82} -15.8027 q^{83} +(-8.17212 - 13.7762i) q^{84} +2.54530 q^{85} +(-1.78890 + 0.787251i) q^{86} +(-1.17183 + 2.02967i) q^{87} +(2.23262 + 2.54500i) q^{88} +(-3.41325 + 1.97064i) q^{89} +(0.948419 - 8.66423i) q^{90} +(2.91586 + 12.4607i) q^{91} +(-2.51231 + 11.3380i) q^{92} +(-10.0478 - 17.4033i) q^{93} +(0.895426 - 1.22134i) q^{94} +(1.23171 + 0.711130i) q^{95} +(-0.368983 + 17.1197i) q^{96} +8.71387i q^{97} +(7.59389 + 6.35081i) q^{98} +7.37699i 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 \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.569639 + 1.29442i 0.402796 + 0.915290i
\(3\) −1.51353 + 2.62152i −0.873839 + 1.51353i −0.0158441 + 0.999874i \(0.505044\pi\)
−0.857995 + 0.513659i \(0.828290\pi\)
\(4\) −1.35102 + 1.47470i −0.675512 + 0.737349i
\(5\) 0.866025 0.500000i 0.387298 0.223607i
\(6\) −4.25550 0.465823i −1.73730 0.190171i
\(7\) 2.57616 0.602834i 0.973696 0.227850i
\(8\) −2.67847 0.908739i −0.946982 0.321288i
\(9\) −3.08156 5.33743i −1.02719 1.77914i
\(10\) 1.14053 + 0.836177i 0.360667 + 0.264422i
\(11\) −1.03659 0.598478i −0.312545 0.180448i 0.335520 0.942033i \(-0.391088\pi\)
−0.648065 + 0.761585i \(0.724421\pi\)
\(12\) −1.82113 5.77373i −0.525715 1.66673i
\(13\) 4.83692i 1.34152i 0.741674 + 0.670760i \(0.234032\pi\)
−0.741674 + 0.670760i \(0.765968\pi\)
\(14\) 2.24780 + 2.99122i 0.600749 + 0.799438i
\(15\) 3.02707i 0.781585i
\(16\) −0.349474 3.98470i −0.0873684 0.996176i
\(17\) 2.20430 + 1.27265i 0.534621 + 0.308664i 0.742896 0.669407i \(-0.233452\pi\)
−0.208275 + 0.978070i \(0.566785\pi\)
\(18\) 5.15347 7.02923i 1.21468 1.65681i
\(19\) 0.711130 + 1.23171i 0.163144 + 0.282575i 0.935995 0.352014i \(-0.114503\pi\)
−0.772850 + 0.634588i \(0.781170\pi\)
\(20\) −0.432671 + 1.95264i −0.0967481 + 0.436623i
\(21\) −2.31876 + 7.66585i −0.505996 + 1.67283i
\(22\) 0.184195 1.68270i 0.0392704 0.358753i
\(23\) 5.02859 2.90326i 1.04853 0.605371i 0.126295 0.991993i \(-0.459691\pi\)
0.922238 + 0.386622i \(0.126358\pi\)
\(24\) 6.43623 5.64624i 1.31379 1.15253i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −6.26099 + 2.75530i −1.22788 + 0.540359i
\(27\) 9.57500 1.84271
\(28\) −2.59145 + 4.61350i −0.489738 + 0.871870i
\(29\) 0.774233 0.143772 0.0718858 0.997413i \(-0.477098\pi\)
0.0718858 + 0.997413i \(0.477098\pi\)
\(30\) −3.91828 + 1.72433i −0.715377 + 0.314819i
\(31\) −3.31933 + 5.74924i −0.596169 + 1.03259i 0.397212 + 0.917727i \(0.369978\pi\)
−0.993381 + 0.114867i \(0.963356\pi\)
\(32\) 4.95879 2.72221i 0.876598 0.481223i
\(33\) 3.13784 1.81163i 0.546228 0.315365i
\(34\) −0.391687 + 3.57823i −0.0671737 + 0.613661i
\(35\) 1.92960 1.81015i 0.326162 0.305971i
\(36\) 12.0344 + 2.66661i 2.00573 + 0.444434i
\(37\) −2.55465 4.42479i −0.419982 0.727431i 0.575955 0.817481i \(-0.304630\pi\)
−0.995937 + 0.0900509i \(0.971297\pi\)
\(38\) −1.18926 + 1.62213i −0.192924 + 0.263144i
\(39\) −12.6801 7.32084i −2.03044 1.17227i
\(40\) −2.77399 + 0.552243i −0.438607 + 0.0873173i
\(41\) 7.46685i 1.16613i −0.812427 0.583063i \(-0.801854\pi\)
0.812427 0.583063i \(-0.198146\pi\)
\(42\) −11.2437 + 1.36532i −1.73493 + 0.210674i
\(43\) 1.38202i 0.210756i 0.994432 + 0.105378i \(0.0336052\pi\)
−0.994432 + 0.105378i \(0.966395\pi\)
\(44\) 2.28304 0.720107i 0.344181 0.108560i
\(45\) −5.33743 3.08156i −0.795657 0.459373i
\(46\) 6.62250 + 4.85528i 0.976434 + 0.715871i
\(47\) −0.535428 0.927389i −0.0781002 0.135274i 0.824330 0.566110i \(-0.191552\pi\)
−0.902430 + 0.430836i \(0.858219\pi\)
\(48\) 10.9749 + 5.11483i 1.58409 + 0.738262i
\(49\) 6.27318 3.10599i 0.896169 0.443713i
\(50\) 1.40582 + 0.153886i 0.198812 + 0.0217628i
\(51\) −6.67256 + 3.85240i −0.934345 + 0.539444i
\(52\) −7.13300 6.53479i −0.989170 0.906213i
\(53\) −1.68099 + 2.91156i −0.230902 + 0.399934i −0.958074 0.286521i \(-0.907501\pi\)
0.727172 + 0.686456i \(0.240834\pi\)
\(54\) 5.45429 + 12.3940i 0.742235 + 1.68661i
\(55\) −1.19696 −0.161398
\(56\) −7.44798 0.726385i −0.995278 0.0970673i
\(57\) −4.30528 −0.570248
\(58\) 0.441033 + 1.00218i 0.0579105 + 0.131593i
\(59\) 4.94206 8.55990i 0.643402 1.11440i −0.341267 0.939967i \(-0.610856\pi\)
0.984668 0.174438i \(-0.0558108\pi\)
\(60\) −4.46401 4.08964i −0.576301 0.527970i
\(61\) 8.31115 4.79845i 1.06413 0.614378i 0.137561 0.990493i \(-0.456074\pi\)
0.926573 + 0.376115i \(0.122740\pi\)
\(62\) −9.33272 1.02160i −1.18526 0.129743i
\(63\) −11.1562 11.8924i −1.40555 1.49830i
\(64\) 6.34839 + 4.86806i 0.793548 + 0.608507i
\(65\) 2.41846 + 4.18890i 0.299973 + 0.519569i
\(66\) 4.13244 + 3.02969i 0.508668 + 0.372929i
\(67\) 9.14135 + 5.27776i 1.11679 + 0.644781i 0.940580 0.339571i \(-0.110282\pi\)
0.176213 + 0.984352i \(0.443615\pi\)
\(68\) −4.85484 + 1.53129i −0.588735 + 0.185697i
\(69\) 17.5767i 2.11599i
\(70\) 3.44226 + 1.46658i 0.411429 + 0.175289i
\(71\) 16.3277i 1.93775i −0.247558 0.968873i \(-0.579628\pi\)
0.247558 0.968873i \(-0.420372\pi\)
\(72\) 3.40354 + 17.0965i 0.401112 + 2.01484i
\(73\) 0.0927594 + 0.0535547i 0.0108567 + 0.00626810i 0.505419 0.862874i \(-0.331338\pi\)
−0.494562 + 0.869142i \(0.664671\pi\)
\(74\) 4.27228 5.82731i 0.496643 0.677411i
\(75\) 1.51353 + 2.62152i 0.174768 + 0.302707i
\(76\) −2.77716 0.615371i −0.318562 0.0705879i
\(77\) −3.03121 0.916880i −0.345439 0.104488i
\(78\) 2.25315 20.5835i 0.255119 2.33062i
\(79\) −9.32609 + 5.38442i −1.04927 + 0.605795i −0.922444 0.386130i \(-0.873811\pi\)
−0.126823 + 0.991925i \(0.540478\pi\)
\(80\) −2.29501 3.27612i −0.256589 0.366281i
\(81\) −5.24739 + 9.08874i −0.583043 + 1.00986i
\(82\) 9.66521 4.25341i 1.06734 0.469711i
\(83\) −15.8027 −1.73457 −0.867287 0.497808i \(-0.834138\pi\)
−0.867287 + 0.497808i \(0.834138\pi\)
\(84\) −8.17212 13.7762i −0.891651 1.50311i
\(85\) 2.54530 0.276077
\(86\) −1.78890 + 0.787251i −0.192903 + 0.0848914i
\(87\) −1.17183 + 2.02967i −0.125633 + 0.217603i
\(88\) 2.23262 + 2.54500i 0.237999 + 0.271298i
\(89\) −3.41325 + 1.97064i −0.361803 + 0.208887i −0.669872 0.742477i \(-0.733651\pi\)
0.308068 + 0.951364i \(0.400318\pi\)
\(90\) 0.948419 8.66423i 0.0999722 0.913290i
\(91\) 2.91586 + 12.4607i 0.305665 + 1.30623i
\(92\) −2.51231 + 11.3380i −0.261926 + 1.18207i
\(93\) −10.0478 17.4033i −1.04191 1.80464i
\(94\) 0.895426 1.22134i 0.0923561 0.125972i
\(95\) 1.23171 + 0.711130i 0.126371 + 0.0729604i
\(96\) −0.368983 + 17.1197i −0.0376591 + 1.74727i
\(97\) 8.71387i 0.884760i 0.896828 + 0.442380i \(0.145866\pi\)
−0.896828 + 0.442380i \(0.854134\pi\)
\(98\) 7.59389 + 6.35081i 0.767099 + 0.641529i
\(99\) 7.37699i 0.741416i
\(100\) 0.601615 + 1.90737i 0.0601615 + 0.190737i
\(101\) −2.60279 1.50272i −0.258987 0.149526i 0.364885 0.931052i \(-0.381108\pi\)
−0.623872 + 0.781526i \(0.714442\pi\)
\(102\) −8.78756 6.44258i −0.870098 0.637911i
\(103\) 0.191374 + 0.331470i 0.0188567 + 0.0326607i 0.875300 0.483581i \(-0.160664\pi\)
−0.856443 + 0.516241i \(0.827331\pi\)
\(104\) 4.39550 12.9555i 0.431014 1.27040i
\(105\) 1.82482 + 7.79820i 0.178084 + 0.761027i
\(106\) −4.72633 0.517362i −0.459062 0.0502507i
\(107\) 0.729600 0.421235i 0.0705331 0.0407223i −0.464319 0.885668i \(-0.653701\pi\)
0.534852 + 0.844946i \(0.320367\pi\)
\(108\) −12.9360 + 14.1202i −1.24477 + 1.35872i
\(109\) −1.97534 + 3.42139i −0.189203 + 0.327710i −0.944985 0.327114i \(-0.893924\pi\)
0.755781 + 0.654824i \(0.227257\pi\)
\(110\) −0.681833 1.54936i −0.0650102 0.147726i
\(111\) 15.4662 1.46799
\(112\) −3.30241 10.0546i −0.312049 0.950066i
\(113\) 2.68201 0.252302 0.126151 0.992011i \(-0.459738\pi\)
0.126151 + 0.992011i \(0.459738\pi\)
\(114\) −2.45245 5.57282i −0.229693 0.521942i
\(115\) 2.90326 5.02859i 0.270730 0.468918i
\(116\) −1.04601 + 1.14176i −0.0971193 + 0.106010i
\(117\) 25.8167 14.9053i 2.38676 1.37799i
\(118\) 13.8953 + 1.52103i 1.27916 + 0.140022i
\(119\) 6.44582 + 1.94973i 0.590887 + 0.178731i
\(120\) 2.75081 8.10790i 0.251114 0.740147i
\(121\) −4.78365 8.28552i −0.434877 0.753229i
\(122\) 10.9455 + 8.02471i 0.990963 + 0.726523i
\(123\) 19.5745 + 11.3013i 1.76497 + 1.01901i
\(124\) −3.99391 12.6624i −0.358664 1.13711i
\(125\) 1.00000i 0.0894427i
\(126\) 9.03869 21.2151i 0.805231 1.88999i
\(127\) 2.14034i 0.189925i −0.995481 0.0949624i \(-0.969727\pi\)
0.995481 0.0949624i \(-0.0302731\pi\)
\(128\) −2.68500 + 10.9905i −0.237323 + 0.971431i
\(129\) −3.62298 2.09173i −0.318986 0.184166i
\(130\) −4.04452 + 5.51665i −0.354728 + 0.483842i
\(131\) −4.83287 8.37078i −0.422250 0.731359i 0.573909 0.818919i \(-0.305426\pi\)
−0.996159 + 0.0875604i \(0.972093\pi\)
\(132\) −1.56768 + 7.07493i −0.136449 + 0.615793i
\(133\) 2.57450 + 2.74440i 0.223238 + 0.237969i
\(134\) −1.62435 + 14.8391i −0.140322 + 1.28190i
\(135\) 8.29219 4.78750i 0.713679 0.412042i
\(136\) −4.74763 5.41189i −0.407106 0.464066i
\(137\) −2.13784 + 3.70285i −0.182648 + 0.316356i −0.942781 0.333411i \(-0.891800\pi\)
0.760133 + 0.649767i \(0.225134\pi\)
\(138\) −22.7516 + 10.0124i −1.93674 + 0.852310i
\(139\) −7.53742 −0.639316 −0.319658 0.947533i \(-0.603568\pi\)
−0.319658 + 0.947533i \(0.603568\pi\)
\(140\) 0.0624874 + 5.29113i 0.00528115 + 0.447182i
\(141\) 3.24155 0.272988
\(142\) 21.1349 9.30092i 1.77360 0.780516i
\(143\) 2.89479 5.01393i 0.242075 0.419286i
\(144\) −20.1911 + 14.1444i −1.68260 + 1.17870i
\(145\) 0.670506 0.387117i 0.0556825 0.0321483i
\(146\) −0.0164826 + 0.150576i −0.00136411 + 0.0124618i
\(147\) −1.35227 + 21.1463i −0.111533 + 1.74411i
\(148\) 9.97662 + 2.21065i 0.820073 + 0.181714i
\(149\) 1.42882 + 2.47480i 0.117054 + 0.202743i 0.918599 0.395191i \(-0.129322\pi\)
−0.801545 + 0.597934i \(0.795988\pi\)
\(150\) −2.53116 + 3.45246i −0.206669 + 0.281892i
\(151\) 5.72359 + 3.30451i 0.465779 + 0.268918i 0.714471 0.699665i \(-0.246667\pi\)
−0.248692 + 0.968583i \(0.580001\pi\)
\(152\) −0.785433 3.94534i −0.0637071 0.320009i
\(153\) 15.6870i 1.26822i
\(154\) −0.539873 4.44594i −0.0435042 0.358264i
\(155\) 6.63865i 0.533229i
\(156\) 27.9271 8.80866i 2.23596 0.705257i
\(157\) −13.4954 7.79155i −1.07705 0.621834i −0.146949 0.989144i \(-0.546945\pi\)
−0.930098 + 0.367310i \(0.880279\pi\)
\(158\) −12.2822 9.00466i −0.977118 0.716373i
\(159\) −5.08847 8.81350i −0.403542 0.698956i
\(160\) 2.93333 4.83689i 0.231900 0.382390i
\(161\) 11.2043 10.5107i 0.883019 0.828355i
\(162\) −14.7537 1.61500i −1.15916 0.126886i
\(163\) 8.34874 4.82015i 0.653924 0.377543i −0.136034 0.990704i \(-0.543436\pi\)
0.789958 + 0.613161i \(0.210102\pi\)
\(164\) 11.0114 + 10.0879i 0.859843 + 0.787732i
\(165\) 1.81163 3.13784i 0.141035 0.244280i
\(166\) −9.00185 20.4553i −0.698679 1.58764i
\(167\) −4.94876 −0.382947 −0.191473 0.981498i \(-0.561327\pi\)
−0.191473 + 0.981498i \(0.561327\pi\)
\(168\) 13.1770 18.4256i 1.01663 1.42156i
\(169\) −10.3958 −0.799678
\(170\) 1.44990 + 3.29468i 0.111203 + 0.252691i
\(171\) 4.38279 7.59121i 0.335160 0.580514i
\(172\) −2.03806 1.86714i −0.155401 0.142368i
\(173\) −6.00216 + 3.46535i −0.456336 + 0.263465i −0.710502 0.703695i \(-0.751532\pi\)
0.254167 + 0.967160i \(0.418199\pi\)
\(174\) −3.29475 0.360656i −0.249774 0.0273412i
\(175\) 0.766010 2.53244i 0.0579049 0.191434i
\(176\) −2.02250 + 4.33967i −0.152451 + 0.327115i
\(177\) 14.9599 + 25.9114i 1.12446 + 1.94762i
\(178\) −4.49514 3.29561i −0.336925 0.247016i
\(179\) 18.2838 + 10.5561i 1.36659 + 0.789003i 0.990491 0.137575i \(-0.0439307\pi\)
0.376103 + 0.926578i \(0.377264\pi\)
\(180\) 11.7554 3.70783i 0.876193 0.276366i
\(181\) 6.10438i 0.453735i −0.973926 0.226868i \(-0.927152\pi\)
0.973926 0.226868i \(-0.0728485\pi\)
\(182\) −14.4683 + 10.8724i −1.07246 + 0.805917i
\(183\) 29.0504i 2.14747i
\(184\) −16.1072 + 3.20661i −1.18744 + 0.236394i
\(185\) −4.42479 2.55465i −0.325317 0.187822i
\(186\) 16.8035 22.9197i 1.23209 1.68055i
\(187\) −1.52331 2.63845i −0.111395 0.192942i
\(188\) 2.09099 + 0.463328i 0.152501 + 0.0337917i
\(189\) 24.6667 5.77213i 1.79424 0.419861i
\(190\) −0.218866 + 1.99944i −0.0158782 + 0.145054i
\(191\) −3.21572 + 1.85660i −0.232681 + 0.134339i −0.611808 0.791006i \(-0.709558\pi\)
0.379127 + 0.925345i \(0.376224\pi\)
\(192\) −22.3702 + 9.27443i −1.61443 + 0.669324i
\(193\) −7.66545 + 13.2769i −0.551771 + 0.955695i 0.446376 + 0.894846i \(0.352714\pi\)
−0.998147 + 0.0608498i \(0.980619\pi\)
\(194\) −11.2794 + 4.96376i −0.809812 + 0.356377i
\(195\) −14.6417 −1.04851
\(196\) −3.89482 + 13.4473i −0.278201 + 0.960523i
\(197\) −24.4602 −1.74272 −0.871360 0.490644i \(-0.836761\pi\)
−0.871360 + 0.490644i \(0.836761\pi\)
\(198\) −9.54890 + 4.20222i −0.678610 + 0.298639i
\(199\) −6.43311 + 11.1425i −0.456031 + 0.789868i −0.998747 0.0500478i \(-0.984063\pi\)
0.542716 + 0.839916i \(0.317396\pi\)
\(200\) −2.12623 + 1.86525i −0.150347 + 0.131893i
\(201\) −27.6715 + 15.9761i −1.95179 + 1.12687i
\(202\) 0.462495 4.22510i 0.0325410 0.297277i
\(203\) 1.99455 0.466734i 0.139990 0.0327583i
\(204\) 3.33364 15.0447i 0.233402 1.05334i
\(205\) −3.73343 6.46649i −0.260754 0.451639i
\(206\) −0.320046 + 0.436536i −0.0222986 + 0.0304149i
\(207\) −30.9918 17.8931i −2.15408 1.24366i
\(208\) 19.2737 1.69038i 1.33639 0.117207i
\(209\) 1.70238i 0.117756i
\(210\) −9.05463 + 6.80423i −0.624829 + 0.469537i
\(211\) 16.9384i 1.16609i −0.812441 0.583044i \(-0.801862\pi\)
0.812441 0.583044i \(-0.198138\pi\)
\(212\) −2.02262 6.41255i −0.138914 0.440416i
\(213\) 42.8034 + 24.7126i 2.93284 + 1.69328i
\(214\) 0.960861 + 0.704454i 0.0656831 + 0.0481555i
\(215\) 0.691009 + 1.19686i 0.0471264 + 0.0816253i
\(216\) −25.6463 8.70118i −1.74501 0.592040i
\(217\) −5.08527 + 16.8120i −0.345211 + 1.14127i
\(218\) −5.55393 0.607955i −0.376160 0.0411759i
\(219\) −0.280789 + 0.162114i −0.0189740 + 0.0109546i
\(220\) 1.61711 1.76515i 0.109026 0.119006i
\(221\) −6.15572 + 10.6620i −0.414079 + 0.717205i
\(222\) 8.81015 + 20.0197i 0.591299 + 1.34363i
\(223\) −18.9687 −1.27024 −0.635119 0.772414i \(-0.719049\pi\)
−0.635119 + 0.772414i \(0.719049\pi\)
\(224\) 11.1336 10.0022i 0.743894 0.668297i
\(225\) −6.16313 −0.410875
\(226\) 1.52778 + 3.47164i 0.101626 + 0.230930i
\(227\) −0.467228 + 0.809262i −0.0310110 + 0.0537126i −0.881114 0.472903i \(-0.843206\pi\)
0.850103 + 0.526616i \(0.176539\pi\)
\(228\) 5.81653 6.34899i 0.385209 0.420472i
\(229\) −11.3283 + 6.54038i −0.748594 + 0.432201i −0.825185 0.564862i \(-0.808929\pi\)
0.0765920 + 0.997063i \(0.475596\pi\)
\(230\) 8.16289 + 0.893541i 0.538245 + 0.0589184i
\(231\) 6.99146 6.55865i 0.460004 0.431527i
\(232\) −2.07376 0.703576i −0.136149 0.0461920i
\(233\) 7.80080 + 13.5114i 0.511047 + 0.885160i 0.999918 + 0.0128037i \(0.00407566\pi\)
−0.488871 + 0.872356i \(0.662591\pi\)
\(234\) 33.9998 + 24.9269i 2.22264 + 1.62952i
\(235\) −0.927389 0.535428i −0.0604962 0.0349275i
\(236\) 5.94644 + 18.8527i 0.387080 + 1.22720i
\(237\) 32.5980i 2.11747i
\(238\) 1.14803 + 9.45421i 0.0744158 + 0.612825i
\(239\) 14.1327i 0.914167i −0.889424 0.457084i \(-0.848894\pi\)
0.889424 0.457084i \(-0.151106\pi\)
\(240\) 12.0620 1.05788i 0.778596 0.0682858i
\(241\) 18.6916 + 10.7916i 1.20403 + 0.695146i 0.961449 0.274985i \(-0.0886728\pi\)
0.242580 + 0.970131i \(0.422006\pi\)
\(242\) 7.99996 10.9118i 0.514257 0.701436i
\(243\) −1.52169 2.63564i −0.0976163 0.169076i
\(244\) −4.15230 + 18.7393i −0.265824 + 1.19966i
\(245\) 3.87974 5.82646i 0.247868 0.372239i
\(246\) −3.47823 + 31.7752i −0.221764 + 2.02591i
\(247\) −5.95770 + 3.43968i −0.379080 + 0.218862i
\(248\) 14.1153 12.3828i 0.896321 0.786306i
\(249\) 23.9179 41.4271i 1.51574 2.62534i
\(250\) 1.29442 0.569639i 0.0818660 0.0360271i
\(251\) 1.04460 0.0659345 0.0329673 0.999456i \(-0.489504\pi\)
0.0329673 + 0.999456i \(0.489504\pi\)
\(252\) 32.6099 0.385118i 2.05423 0.0242602i
\(253\) −6.95014 −0.436952
\(254\) 2.77050 1.21922i 0.173836 0.0765009i
\(255\) −3.85240 + 6.67256i −0.241247 + 0.417852i
\(256\) −15.7557 + 2.78510i −0.984734 + 0.174069i
\(257\) 4.24688 2.45194i 0.264913 0.152948i −0.361661 0.932310i \(-0.617790\pi\)
0.626574 + 0.779362i \(0.284457\pi\)
\(258\) 0.643775 5.88117i 0.0400797 0.366146i
\(259\) −9.24860 9.85892i −0.574680 0.612604i
\(260\) −9.44476 2.09280i −0.585739 0.129790i
\(261\) −2.38585 4.13241i −0.147680 0.255790i
\(262\) 8.08228 11.0241i 0.499325 0.681069i
\(263\) −6.75186 3.89819i −0.416337 0.240373i 0.277172 0.960820i \(-0.410603\pi\)
−0.693509 + 0.720448i \(0.743936\pi\)
\(264\) −10.0509 + 2.00092i −0.618590 + 0.123148i
\(265\) 3.36198i 0.206525i
\(266\) −2.08585 + 4.89579i −0.127892 + 0.300180i
\(267\) 11.9305i 0.730135i
\(268\) −20.1333 + 6.35036i −1.22984 + 0.387910i
\(269\) −18.2838 10.5562i −1.11479 0.643622i −0.174721 0.984618i \(-0.555902\pi\)
−0.940065 + 0.340996i \(0.889236\pi\)
\(270\) 10.9206 + 8.00640i 0.664605 + 0.487254i
\(271\) 10.7604 + 18.6375i 0.653647 + 1.13215i 0.982231 + 0.187676i \(0.0600954\pi\)
−0.328584 + 0.944475i \(0.606571\pi\)
\(272\) 4.30080 9.22824i 0.260774 0.559544i
\(273\) −37.0791 11.2157i −2.24413 0.678804i
\(274\) −6.01082 0.657967i −0.363127 0.0397492i
\(275\) −1.03659 + 0.598478i −0.0625090 + 0.0360896i
\(276\) −25.9203 23.7465i −1.56022 1.42937i
\(277\) 2.58372 4.47513i 0.155241 0.268884i −0.777906 0.628381i \(-0.783718\pi\)
0.933147 + 0.359496i \(0.117051\pi\)
\(278\) −4.29361 9.75655i −0.257513 0.585159i
\(279\) 40.9149 2.44951
\(280\) −6.81333 + 3.09492i −0.407174 + 0.184957i
\(281\) 15.6322 0.932539 0.466270 0.884643i \(-0.345598\pi\)
0.466270 + 0.884643i \(0.345598\pi\)
\(282\) 1.84651 + 4.19592i 0.109958 + 0.249863i
\(283\) 14.2850 24.7424i 0.849156 1.47078i −0.0328062 0.999462i \(-0.510444\pi\)
0.881962 0.471320i \(-0.156222\pi\)
\(284\) 24.0785 + 22.0592i 1.42880 + 1.30897i
\(285\) −3.72848 + 2.15264i −0.220856 + 0.127511i
\(286\) 8.13909 + 0.890936i 0.481274 + 0.0526821i
\(287\) −4.50127 19.2358i −0.265702 1.13545i
\(288\) −29.8104 18.0785i −1.75660 1.06529i
\(289\) −5.26071 9.11182i −0.309454 0.535990i
\(290\) 0.883036 + 0.647396i 0.0518537 + 0.0380164i
\(291\) −22.8436 13.1887i −1.33911 0.773137i
\(292\) −0.204297 + 0.0644386i −0.0119556 + 0.00377099i
\(293\) 0.657174i 0.0383925i 0.999816 + 0.0191963i \(0.00611074\pi\)
−0.999816 + 0.0191963i \(0.993889\pi\)
\(294\) −28.1424 + 10.2953i −1.64130 + 0.600436i
\(295\) 9.88412i 0.575476i
\(296\) 2.82158 + 14.1732i 0.164001 + 0.823799i
\(297\) −9.92539 5.73043i −0.575930 0.332513i
\(298\) −2.38950 + 3.25923i −0.138420 + 0.188802i
\(299\) 14.0428 + 24.3229i 0.812118 + 1.40663i
\(300\) −5.91077 1.30972i −0.341258 0.0756169i
\(301\) 0.833126 + 3.56030i 0.0480206 + 0.205212i
\(302\) −1.01704 + 9.29108i −0.0585239 + 0.534642i
\(303\) 7.87881 4.54883i 0.452626 0.261324i
\(304\) 4.65949 3.26410i 0.267240 0.187209i
\(305\) 4.79845 8.31115i 0.274758 0.475895i
\(306\) 20.3055 8.93595i 1.16079 0.510834i
\(307\) −4.88042 −0.278540 −0.139270 0.990254i \(-0.544476\pi\)
−0.139270 + 0.990254i \(0.544476\pi\)
\(308\) 5.44736 3.23140i 0.310392 0.184126i
\(309\) −1.15861 −0.0659108
\(310\) −8.59317 + 3.78163i −0.488059 + 0.214782i
\(311\) −5.94840 + 10.3029i −0.337303 + 0.584226i −0.983924 0.178585i \(-0.942848\pi\)
0.646621 + 0.762811i \(0.276181\pi\)
\(312\) 27.3104 + 31.1315i 1.54615 + 1.76248i
\(313\) 23.0427 13.3037i 1.30245 0.751970i 0.321626 0.946867i \(-0.395771\pi\)
0.980824 + 0.194897i \(0.0624372\pi\)
\(314\) 2.39802 21.9070i 0.135328 1.23628i
\(315\) −15.6077 4.72102i −0.879396 0.265999i
\(316\) 4.65936 21.0277i 0.262110 1.18290i
\(317\) 13.2278 + 22.9113i 0.742950 + 1.28683i 0.951147 + 0.308739i \(0.0999071\pi\)
−0.208197 + 0.978087i \(0.566760\pi\)
\(318\) 8.50973 11.6071i 0.477202 0.650895i
\(319\) −0.802566 0.463362i −0.0449351 0.0259433i
\(320\) 7.93189 + 1.04167i 0.443406 + 0.0582311i
\(321\) 2.55021i 0.142339i
\(322\) 19.9875 + 8.51569i 1.11386 + 0.474561i
\(323\) 3.62009i 0.201427i
\(324\) −6.31382 20.0174i −0.350768 1.11208i
\(325\) 4.18890 + 2.41846i 0.232358 + 0.134152i
\(326\) 10.9950 + 8.06100i 0.608959 + 0.446457i
\(327\) −5.97949 10.3568i −0.330667 0.572731i
\(328\) −6.78542 + 19.9997i −0.374662 + 1.10430i
\(329\) −1.93841 2.06633i −0.106868 0.113920i
\(330\) 5.09364 + 0.557570i 0.280396 + 0.0306932i
\(331\) −21.0294 + 12.1414i −1.15588 + 0.667349i −0.950314 0.311294i \(-0.899238\pi\)
−0.205569 + 0.978643i \(0.565904\pi\)
\(332\) 21.3498 23.3043i 1.17172 1.27899i
\(333\) −15.7447 + 27.2705i −0.862802 + 1.49442i
\(334\) −2.81901 6.40575i −0.154249 0.350507i
\(335\) 10.5555 0.576710
\(336\) 31.3565 + 6.56057i 1.71064 + 0.357909i
\(337\) 19.7077 1.07355 0.536774 0.843726i \(-0.319643\pi\)
0.536774 + 0.843726i \(0.319643\pi\)
\(338\) −5.92186 13.4565i −0.322107 0.731938i
\(339\) −4.05931 + 7.03094i −0.220472 + 0.381868i
\(340\) −3.43876 + 3.75356i −0.186493 + 0.203565i
\(341\) 6.88159 3.97309i 0.372659 0.215155i
\(342\) 12.3228 + 1.34890i 0.666340 + 0.0729401i
\(343\) 14.2883 11.7832i 0.771497 0.636233i
\(344\) 1.25589 3.70169i 0.0677132 0.199582i
\(345\) 8.78835 + 15.2219i 0.473149 + 0.819518i
\(346\) −7.90466 5.79529i −0.424957 0.311557i
\(347\) 7.30667 + 4.21851i 0.392242 + 0.226461i 0.683131 0.730296i \(-0.260618\pi\)
−0.290889 + 0.956757i \(0.593951\pi\)
\(348\) −1.40998 4.47022i −0.0755828 0.239629i
\(349\) 23.5784i 1.26212i 0.775732 + 0.631062i \(0.217381\pi\)
−0.775732 + 0.631062i \(0.782619\pi\)
\(350\) 3.71437 0.451039i 0.198542 0.0241090i
\(351\) 46.3135i 2.47203i
\(352\) −6.76943 0.145902i −0.360812 0.00777662i
\(353\) −17.9028 10.3362i −0.952872 0.550141i −0.0589002 0.998264i \(-0.518759\pi\)
−0.893972 + 0.448123i \(0.852093\pi\)
\(354\) −25.0183 + 34.1245i −1.32971 + 1.81370i
\(355\) −8.16387 14.1402i −0.433293 0.750486i
\(356\) 1.70528 7.69589i 0.0903794 0.407881i
\(357\) −14.8672 + 13.9468i −0.786856 + 0.738145i
\(358\) −3.24889 + 29.6800i −0.171709 + 1.56864i
\(359\) 23.7741 13.7260i 1.25475 0.724429i 0.282699 0.959209i \(-0.408770\pi\)
0.972049 + 0.234780i \(0.0754369\pi\)
\(360\) 11.4958 + 13.1042i 0.605881 + 0.690652i
\(361\) 8.48859 14.7027i 0.446768 0.773824i
\(362\) 7.90161 3.47729i 0.415299 0.182762i
\(363\) 28.9608 1.52005
\(364\) −22.3151 12.5346i −1.16963 0.656994i
\(365\) 0.107109 0.00560636
\(366\) −37.6033 + 16.5483i −1.96556 + 0.864991i
\(367\) −10.0213 + 17.3574i −0.523109 + 0.906051i 0.476529 + 0.879159i \(0.341895\pi\)
−0.999638 + 0.0268927i \(0.991439\pi\)
\(368\) −13.3260 19.0228i −0.694665 0.991633i
\(369\) −39.8538 + 23.0096i −2.07471 + 1.19783i
\(370\) 0.786250 7.18274i 0.0408752 0.373413i
\(371\) −2.57531 + 8.51401i −0.133704 + 0.442025i
\(372\) 39.2395 + 8.69480i 2.03447 + 0.450804i
\(373\) −10.2956 17.8325i −0.533085 0.923331i −0.999253 0.0386345i \(-0.987699\pi\)
0.466168 0.884696i \(-0.345634\pi\)
\(374\) 2.54751 3.47476i 0.131729 0.179675i
\(375\) 2.62152 + 1.51353i 0.135375 + 0.0781585i
\(376\) 0.591373 + 2.97055i 0.0304977 + 0.153194i
\(377\) 3.74491i 0.192873i
\(378\) 21.5227 + 28.6410i 1.10701 + 1.47313i
\(379\) 3.26339i 0.167629i −0.996481 0.0838145i \(-0.973290\pi\)
0.996481 0.0838145i \(-0.0267103\pi\)
\(380\) −2.71278 + 0.855654i −0.139163 + 0.0438941i
\(381\) 5.61095 + 3.23948i 0.287458 + 0.165964i
\(382\) −4.23500 3.10489i −0.216682 0.158860i
\(383\) 16.8755 + 29.2293i 0.862300 + 1.49355i 0.869704 + 0.493574i \(0.164310\pi\)
−0.00740376 + 0.999973i \(0.502357\pi\)
\(384\) −24.7479 23.6732i −1.26291 1.20807i
\(385\) −3.08355 + 0.721565i −0.157152 + 0.0367744i
\(386\) −21.5524 2.35921i −1.09699 0.120081i
\(387\) 7.37642 4.25878i 0.374964 0.216486i
\(388\) −12.8503 11.7726i −0.652377 0.597665i
\(389\) 1.80604 3.12816i 0.0915701 0.158604i −0.816602 0.577201i \(-0.804145\pi\)
0.908172 + 0.418597i \(0.137478\pi\)
\(390\) −8.34047 18.9524i −0.422336 0.959693i
\(391\) 14.7793 0.747424
\(392\) −19.6251 + 2.61861i −0.991215 + 0.132260i
\(393\) 29.2589 1.47591
\(394\) −13.9335 31.6617i −0.701960 1.59509i
\(395\) −5.38442 + 9.32609i −0.270920 + 0.469247i
\(396\) −10.8788 9.96649i −0.546683 0.500835i
\(397\) −6.47548 + 3.73862i −0.324995 + 0.187636i −0.653617 0.756826i \(-0.726749\pi\)
0.328622 + 0.944462i \(0.393416\pi\)
\(398\) −18.0875 1.97993i −0.906646 0.0992449i
\(399\) −11.0911 + 2.59537i −0.555248 + 0.129931i
\(400\) −3.62559 1.68970i −0.181280 0.0844850i
\(401\) 4.77337 + 8.26772i 0.238371 + 0.412870i 0.960247 0.279152i \(-0.0900533\pi\)
−0.721876 + 0.692022i \(0.756720\pi\)
\(402\) −36.4425 26.7178i −1.81759 1.33256i
\(403\) −27.8086 16.0553i −1.38525 0.799773i
\(404\) 5.73248 1.80812i 0.285202 0.0899572i
\(405\) 10.4948i 0.521490i
\(406\) 1.74032 + 2.31590i 0.0863706 + 0.114936i
\(407\) 6.11561i 0.303140i
\(408\) 21.3731 4.25492i 1.05812 0.210650i
\(409\) 18.7682 + 10.8358i 0.928026 + 0.535796i 0.886187 0.463328i \(-0.153345\pi\)
0.0418392 + 0.999124i \(0.486678\pi\)
\(410\) 6.24361 8.51617i 0.308350 0.420584i
\(411\) −6.47138 11.2088i −0.319210 0.552887i
\(412\) −0.747370 0.165604i −0.0368203 0.00815873i
\(413\) 7.57134 25.0309i 0.372561 1.23169i
\(414\) 5.50701 50.3090i 0.270655 2.47255i
\(415\) −13.6856 + 7.90136i −0.671798 + 0.387863i
\(416\) 13.1671 + 23.9853i 0.645570 + 1.17598i
\(417\) 11.4081 19.7595i 0.558659 0.967625i
\(418\) 2.20359 0.969744i 0.107781 0.0474317i
\(419\) −13.0327 −0.636690 −0.318345 0.947975i \(-0.603127\pi\)
−0.318345 + 0.947975i \(0.603127\pi\)
\(420\) −13.9654 7.84449i −0.681440 0.382772i
\(421\) −34.2800 −1.67070 −0.835352 0.549715i \(-0.814736\pi\)
−0.835352 + 0.549715i \(0.814736\pi\)
\(422\) 21.9253 9.64877i 1.06731 0.469695i
\(423\) −3.29991 + 5.71562i −0.160447 + 0.277903i
\(424\) 7.14834 6.27095i 0.347154 0.304544i
\(425\) 2.20430 1.27265i 0.106924 0.0617327i
\(426\) −7.60584 + 69.4827i −0.368504 + 3.36645i
\(427\) 18.5182 17.3718i 0.896158 0.840681i
\(428\) −0.364512 + 1.64504i −0.0176194 + 0.0795159i
\(429\) 8.76273 + 15.1775i 0.423068 + 0.732776i
\(430\) −1.15561 + 1.57623i −0.0557285 + 0.0760126i
\(431\) −2.47034 1.42625i −0.118992 0.0687001i 0.439323 0.898329i \(-0.355219\pi\)
−0.558315 + 0.829629i \(0.688552\pi\)
\(432\) −3.34621 38.1536i −0.160995 1.83566i
\(433\) 34.6179i 1.66363i −0.555053 0.831815i \(-0.687302\pi\)
0.555053 0.831815i \(-0.312698\pi\)
\(434\) −24.6584 + 2.99429i −1.18364 + 0.143730i
\(435\) 2.34366i 0.112370i
\(436\) −2.37679 7.53541i −0.113828 0.360881i
\(437\) 7.15196 + 4.12919i 0.342125 + 0.197526i
\(438\) −0.369791 0.271111i −0.0176693 0.0129542i
\(439\) 5.46905 + 9.47267i 0.261023 + 0.452106i 0.966514 0.256613i \(-0.0826067\pi\)
−0.705491 + 0.708719i \(0.749273\pi\)
\(440\) 3.20601 + 1.08772i 0.152840 + 0.0518551i
\(441\) −35.9092 23.9113i −1.70996 1.13864i
\(442\) −17.3076 1.89456i −0.823240 0.0901149i
\(443\) −30.6522 + 17.6971i −1.45633 + 0.840813i −0.998828 0.0483948i \(-0.984589\pi\)
−0.457503 + 0.889208i \(0.651256\pi\)
\(444\) −20.8952 + 22.8080i −0.991642 + 1.08242i
\(445\) −1.97064 + 3.41325i −0.0934172 + 0.161803i
\(446\) −10.8053 24.5534i −0.511646 1.16264i
\(447\) −8.65029 −0.409145
\(448\) 19.2891 + 8.71387i 0.911323 + 0.411692i
\(449\) 28.0029 1.32154 0.660768 0.750590i \(-0.270231\pi\)
0.660768 + 0.750590i \(0.270231\pi\)
\(450\) −3.51076 7.97765i −0.165499 0.376070i
\(451\) −4.46875 + 7.74010i −0.210425 + 0.364467i
\(452\) −3.62346 + 3.95516i −0.170433 + 0.186035i
\(453\) −17.3257 + 10.0030i −0.814031 + 0.469981i
\(454\) −1.31367 0.143800i −0.0616537 0.00674885i
\(455\) 8.75555 + 9.33333i 0.410466 + 0.437553i
\(456\) 11.5315 + 3.91237i 0.540014 + 0.183214i
\(457\) −10.0949 17.4849i −0.472220 0.817908i 0.527275 0.849695i \(-0.323214\pi\)
−0.999495 + 0.0317863i \(0.989880\pi\)
\(458\) −14.9190 10.9378i −0.697119 0.511092i
\(459\) 21.1062 + 12.1856i 0.985151 + 0.568777i
\(460\) 3.49329 + 11.0752i 0.162875 + 0.516382i
\(461\) 0.127845i 0.00595433i −0.999996 0.00297717i \(-0.999052\pi\)
0.999996 0.00297717i \(-0.000947663\pi\)
\(462\) 12.4722 + 5.31379i 0.580260 + 0.247220i
\(463\) 17.8655i 0.830282i −0.909757 0.415141i \(-0.863732\pi\)
0.909757 0.415141i \(-0.136268\pi\)
\(464\) −0.270574 3.08509i −0.0125611 0.143222i
\(465\) −17.4033 10.0478i −0.807060 0.465956i
\(466\) −13.0457 + 17.7941i −0.604330 + 0.824295i
\(467\) −7.33477 12.7042i −0.339413 0.587880i 0.644910 0.764259i \(-0.276895\pi\)
−0.984322 + 0.176379i \(0.943562\pi\)
\(468\) −12.8982 + 58.2093i −0.596218 + 2.69072i
\(469\) 26.7312 + 8.08563i 1.23433 + 0.373360i
\(470\) 0.164790 1.50543i 0.00760119 0.0694402i
\(471\) 40.8514 23.5855i 1.88233 1.08676i
\(472\) −21.0159 + 18.4364i −0.967334 + 0.848603i
\(473\) 0.827107 1.43259i 0.0380304 0.0658706i
\(474\) 42.1954 18.5691i 1.93810 0.852907i
\(475\) 1.42226 0.0652578
\(476\) −11.5837 + 6.87151i −0.530939 + 0.314955i
\(477\) 20.7203 0.948719
\(478\) 18.2936 8.05053i 0.836728 0.368223i
\(479\) −13.0757 + 22.6478i −0.597444 + 1.03480i 0.395753 + 0.918357i \(0.370483\pi\)
−0.993197 + 0.116446i \(0.962850\pi\)
\(480\) 8.24030 + 15.0106i 0.376117 + 0.685136i
\(481\) 21.4024 12.3567i 0.975863 0.563415i
\(482\) −3.32134 + 30.3419i −0.151283 + 1.38204i
\(483\) 10.5958 + 45.2804i 0.482127 + 2.06033i
\(484\) 18.6815 + 4.13949i 0.849158 + 0.188159i
\(485\) 4.35694 + 7.54644i 0.197838 + 0.342666i
\(486\) 2.54480 3.47106i 0.115435 0.157450i
\(487\) 14.3973 + 8.31227i 0.652403 + 0.376665i 0.789376 0.613910i \(-0.210404\pi\)
−0.136974 + 0.990575i \(0.543738\pi\)
\(488\) −26.6217 + 5.29982i −1.20511 + 0.239911i
\(489\) 29.1818i 1.31965i
\(490\) 9.75191 + 1.70302i 0.440546 + 0.0769346i
\(491\) 21.9094i 0.988758i −0.869246 0.494379i \(-0.835395\pi\)
0.869246 0.494379i \(-0.164605\pi\)
\(492\) −43.1116 + 13.5981i −1.94362 + 0.613050i
\(493\) 1.70664 + 0.985330i 0.0768633 + 0.0443770i
\(494\) −7.84612 5.75237i −0.353014 0.258811i
\(495\) 3.68850 + 6.38866i 0.165786 + 0.287149i
\(496\) 24.0690 + 11.2173i 1.08073 + 0.503673i
\(497\) −9.84291 42.0628i −0.441515 1.88678i
\(498\) 67.2485 + 7.36127i 3.01348 + 0.329867i
\(499\) 35.2377 20.3445i 1.57746 0.910745i 0.582243 0.813015i \(-0.302175\pi\)
0.995213 0.0977301i \(-0.0311582\pi\)
\(500\) 1.47470 + 1.35102i 0.0659505 + 0.0604196i
\(501\) 7.49011 12.9733i 0.334633 0.579602i
\(502\) 0.595044 + 1.35215i 0.0265581 + 0.0603492i
\(503\) −7.19624 −0.320864 −0.160432 0.987047i \(-0.551289\pi\)
−0.160432 + 0.987047i \(0.551289\pi\)
\(504\) 19.0744 + 41.9914i 0.849641 + 1.87045i
\(505\) −3.00544 −0.133740
\(506\) −3.95907 8.99637i −0.176002 0.399937i
\(507\) 15.7344 27.2528i 0.698790 1.21034i
\(508\) 3.15636 + 2.89166i 0.140041 + 0.128296i
\(509\) 4.45357 2.57127i 0.197401 0.113970i −0.398042 0.917367i \(-0.630310\pi\)
0.595443 + 0.803398i \(0.296977\pi\)
\(510\) −10.8315 1.18566i −0.479629 0.0525020i
\(511\) 0.271248 + 0.0820469i 0.0119993 + 0.00362954i
\(512\) −12.5802 18.8080i −0.555970 0.831203i
\(513\) 6.80907 + 11.7937i 0.300628 + 0.520703i
\(514\) 5.59301 + 4.10051i 0.246697 + 0.180866i
\(515\) 0.331470 + 0.191374i 0.0146063 + 0.00843296i
\(516\) 7.97940 2.51683i 0.351273 0.110797i
\(517\) 1.28177i 0.0563721i
\(518\) 7.49318 17.5876i 0.329231 0.772753i
\(519\) 20.9797i 0.920905i
\(520\) −2.67116 13.4176i −0.117138 0.588400i
\(521\) 7.85043 + 4.53245i 0.343934 + 0.198570i 0.662010 0.749495i \(-0.269704\pi\)
−0.318077 + 0.948065i \(0.603037\pi\)
\(522\) 3.98999 5.44227i 0.174637 0.238201i
\(523\) −8.80370 15.2485i −0.384959 0.666768i 0.606805 0.794851i \(-0.292451\pi\)
−0.991764 + 0.128083i \(0.959118\pi\)
\(524\) 18.8737 + 4.18209i 0.824502 + 0.182695i
\(525\) 5.47944 + 5.84103i 0.239142 + 0.254924i
\(526\) 1.19975 10.9603i 0.0523117 0.477890i
\(527\) −14.6336 + 8.44869i −0.637448 + 0.368031i
\(528\) −8.31541 11.8702i −0.361882 0.516586i
\(529\) 5.35780 9.27999i 0.232948 0.403478i
\(530\) −4.35180 + 1.91512i −0.189030 + 0.0831874i
\(531\) −60.9171 −2.64358
\(532\) −7.52537 + 0.0888734i −0.326266 + 0.00385315i
\(533\) 36.1166 1.56438
\(534\) 15.4430 6.79608i 0.668285 0.294095i
\(535\) 0.421235 0.729600i 0.0182116 0.0315434i
\(536\) −19.6887 22.4434i −0.850423 0.969408i
\(537\) −55.3462 + 31.9542i −2.38837 + 1.37892i
\(538\) 3.24890 29.6801i 0.140070 1.27960i
\(539\) −8.36161 0.534711i −0.360160 0.0230316i
\(540\) −4.14282 + 18.6965i −0.178279 + 0.804570i
\(541\) 13.9811 + 24.2160i 0.601094 + 1.04113i 0.992656 + 0.120974i \(0.0386018\pi\)
−0.391561 + 0.920152i \(0.628065\pi\)
\(542\) −17.9952 + 24.5451i −0.772960 + 1.05430i
\(543\) 16.0027 + 9.23918i 0.686743 + 0.396491i
\(544\) 14.3951 + 0.310258i 0.617184 + 0.0133022i
\(545\) 3.95068i 0.169229i
\(546\) −6.60396 54.3847i −0.282624 2.32745i
\(547\) 29.6385i 1.26725i 0.773640 + 0.633626i \(0.218434\pi\)
−0.773640 + 0.633626i \(0.781566\pi\)
\(548\) −2.57231 8.15530i −0.109884 0.348377i
\(549\) −51.2227 29.5735i −2.18613 1.26216i
\(550\) −1.36516 1.00087i −0.0582108 0.0426771i
\(551\) 0.550581 + 0.953634i 0.0234555 + 0.0406262i
\(552\) 15.9726 47.0786i 0.679841 2.00380i
\(553\) −20.7796 + 19.4932i −0.883638 + 0.828935i
\(554\) 7.26446 + 0.795196i 0.308637 + 0.0337846i
\(555\) 13.3941 7.73310i 0.568549 0.328252i
\(556\) 10.1832 11.1154i 0.431865 0.471399i
\(557\) −17.8667 + 30.9460i −0.757037 + 1.31123i 0.187319 + 0.982299i \(0.440020\pi\)
−0.944355 + 0.328927i \(0.893313\pi\)
\(558\) 23.3067 + 52.9608i 0.986651 + 2.24201i
\(559\) −6.68471 −0.282733
\(560\) −7.88725 7.05629i −0.333297 0.298183i
\(561\) 9.22231 0.389366
\(562\) 8.90471 + 20.2346i 0.375623 + 0.853544i
\(563\) −11.5023 + 19.9226i −0.484766 + 0.839639i −0.999847 0.0175025i \(-0.994429\pi\)
0.515081 + 0.857142i \(0.327762\pi\)
\(564\) −4.37941 + 4.78031i −0.184407 + 0.201288i
\(565\) 2.32269 1.34101i 0.0977163 0.0564166i
\(566\) 40.1642 + 4.39653i 1.68823 + 0.184800i
\(567\) −8.03910 + 26.5773i −0.337611 + 1.11614i
\(568\) −14.8377 + 43.7333i −0.622574 + 1.83501i
\(569\) 9.43937 + 16.3495i 0.395719 + 0.685405i 0.993193 0.116483i \(-0.0371621\pi\)
−0.597474 + 0.801888i \(0.703829\pi\)
\(570\) −4.91030 3.59997i −0.205670 0.150786i
\(571\) 20.7520 + 11.9812i 0.868446 + 0.501397i 0.866831 0.498601i \(-0.166153\pi\)
0.00161422 + 0.999999i \(0.499486\pi\)
\(572\) 3.48310 + 11.0429i 0.145636 + 0.461726i
\(573\) 11.2401i 0.469561i
\(574\) 22.3350 16.7840i 0.932246 0.700550i
\(575\) 5.80651i 0.242148i
\(576\) 6.41994 48.8853i 0.267498 2.03689i
\(577\) 9.20684 + 5.31557i 0.383286 + 0.221290i 0.679247 0.733910i \(-0.262307\pi\)
−0.295961 + 0.955200i \(0.595640\pi\)
\(578\) 8.79778 12.0000i 0.365939 0.499134i
\(579\) −23.2038 40.1902i −0.964318 1.67025i
\(580\) −0.334988 + 1.51180i −0.0139096 + 0.0627740i
\(581\) −40.7103 + 9.52641i −1.68895 + 0.395222i
\(582\) 4.05912 37.0819i 0.168256 1.53709i
\(583\) 3.48501 2.01207i 0.144335 0.0833316i
\(584\) −0.199786 0.227739i −0.00826720 0.00942389i
\(585\) 14.9053 25.8167i 0.616258 1.06739i
\(586\) −0.850656 + 0.374352i −0.0351403 + 0.0154643i
\(587\) −0.240690 −0.00993436 −0.00496718 0.999988i \(-0.501581\pi\)
−0.00496718 + 0.999988i \(0.501581\pi\)
\(588\) −29.3574 30.5633i −1.21068 1.26041i
\(589\) −9.44189 −0.389046
\(590\) 12.7942 5.63038i 0.526727 0.231799i
\(591\) 37.0214 64.1229i 1.52286 2.63766i
\(592\) −16.7387 + 11.7259i −0.687956 + 0.481931i
\(593\) −26.7822 + 15.4627i −1.09981 + 0.634977i −0.936172 0.351543i \(-0.885657\pi\)
−0.163640 + 0.986520i \(0.552324\pi\)
\(594\) 1.76366 16.1119i 0.0723640 0.661077i
\(595\) 6.55711 1.53440i 0.268815 0.0629041i
\(596\) −5.57995 1.23642i −0.228564 0.0506458i
\(597\) −19.4734 33.7290i −0.796995 1.38044i
\(598\) −23.4846 + 32.0325i −0.960356 + 1.30991i
\(599\) −25.9364 14.9744i −1.05973 0.611838i −0.134376 0.990930i \(-0.542903\pi\)
−0.925359 + 0.379092i \(0.876236\pi\)
\(600\) −1.67168 8.39706i −0.0682459 0.342808i
\(601\) 23.0748i 0.941241i 0.882336 + 0.470621i \(0.155970\pi\)
−0.882336 + 0.470621i \(0.844030\pi\)
\(602\) −4.13392 + 3.10649i −0.168486 + 0.126611i
\(603\) 65.0550i 2.64925i
\(604\) −12.6059 + 3.97609i −0.512925 + 0.161785i
\(605\) −8.28552 4.78365i −0.336854 0.194483i
\(606\) 10.3762 + 7.60726i 0.421502 + 0.309024i
\(607\) 8.94004 + 15.4846i 0.362865 + 0.628501i 0.988431 0.151670i \(-0.0484652\pi\)
−0.625566 + 0.780171i \(0.715132\pi\)
\(608\) 6.87932 + 4.17197i 0.278993 + 0.169196i
\(609\) −1.79526 + 5.93516i −0.0727477 + 0.240505i
\(610\) 13.4915 + 1.47683i 0.546254 + 0.0597950i
\(611\) 4.48571 2.58982i 0.181472 0.104773i
\(612\) 23.1337 + 21.1936i 0.935123 + 0.856699i
\(613\) 4.18505 7.24872i 0.169033 0.292773i −0.769047 0.639192i \(-0.779269\pi\)
0.938080 + 0.346419i \(0.112602\pi\)
\(614\) −2.78008 6.31729i −0.112195 0.254945i
\(615\) 22.6027 0.911427
\(616\) 7.28580 + 5.21042i 0.293553 + 0.209934i
\(617\) 33.7886 1.36028 0.680139 0.733084i \(-0.261920\pi\)
0.680139 + 0.733084i \(0.261920\pi\)
\(618\) −0.659987 1.49972i −0.0265486 0.0603275i
\(619\) 16.6442 28.8285i 0.668986 1.15872i −0.309203 0.950996i \(-0.600062\pi\)
0.978188 0.207721i \(-0.0666046\pi\)
\(620\) −9.79001 8.96897i −0.393176 0.360203i
\(621\) 48.1487 27.7987i 1.93214 1.11552i
\(622\) −16.7247 1.83075i −0.670600 0.0734065i
\(623\) −7.60510 + 7.13430i −0.304692 + 0.285830i
\(624\) −24.7400 + 53.0848i −0.990394 + 2.12509i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 30.3465 + 22.2485i 1.21289 + 0.889229i
\(627\) 4.46283 + 2.57661i 0.178228 + 0.102900i
\(628\) 29.7227 9.37503i 1.18607 0.374105i
\(629\) 13.0047i 0.518533i
\(630\) −2.77981 22.8922i −0.110750 0.912045i
\(631\) 43.1690i 1.71853i 0.511528 + 0.859266i \(0.329079\pi\)
−0.511528 + 0.859266i \(0.670921\pi\)
\(632\) 29.8727 5.94702i 1.18827 0.236560i
\(633\) 44.4043 + 25.6368i 1.76491 + 1.01897i
\(634\) −22.1216 + 30.1735i −0.878563 + 1.19834i
\(635\) −1.07017 1.85359i −0.0424685 0.0735576i
\(636\) 19.8719 + 4.40327i 0.787972 + 0.174601i
\(637\) 15.0234 + 30.3429i 0.595250 + 1.20223i
\(638\) 0.142610 1.30280i 0.00564597 0.0515784i
\(639\) −87.1481 + 50.3150i −3.44753 + 1.99043i
\(640\) 3.16996 + 10.8605i 0.125304 + 0.429301i
\(641\) −16.0131 + 27.7355i −0.632479 + 1.09548i 0.354565 + 0.935031i \(0.384629\pi\)
−0.987043 + 0.160454i \(0.948704\pi\)
\(642\) −3.30103 + 1.45270i −0.130281 + 0.0573335i
\(643\) 37.9515 1.49666 0.748331 0.663326i \(-0.230856\pi\)
0.748331 + 0.663326i \(0.230856\pi\)
\(644\) 0.362834 + 30.7230i 0.0142977 + 1.21066i
\(645\) −4.18346 −0.164723
\(646\) −4.68590 + 2.06214i −0.184364 + 0.0811339i
\(647\) 4.49386 7.78359i 0.176672 0.306004i −0.764067 0.645137i \(-0.776800\pi\)
0.940739 + 0.339133i \(0.110134\pi\)
\(648\) 22.3143 19.5754i 0.876587 0.768994i
\(649\) −10.2458 + 5.91543i −0.402184 + 0.232201i
\(650\) −0.744335 + 6.79982i −0.0291952 + 0.266711i
\(651\) −36.3761 38.7766i −1.42569 1.51977i
\(652\) −4.17108 + 18.8240i −0.163352 + 0.737205i
\(653\) −9.13956 15.8302i −0.357658 0.619483i 0.629911 0.776668i \(-0.283091\pi\)
−0.987569 + 0.157185i \(0.949758\pi\)
\(654\) 9.99983 13.6396i 0.391024 0.533349i
\(655\) −8.37078 4.83287i −0.327074 0.188836i
\(656\) −29.7532 + 2.60947i −1.16167 + 0.101883i
\(657\) 0.660129i 0.0257541i
\(658\) 1.57049 3.68617i 0.0612241 0.143702i
\(659\) 36.9643i 1.43992i 0.694014 + 0.719962i \(0.255841\pi\)
−0.694014 + 0.719962i \(0.744159\pi\)
\(660\) 2.17981 + 6.91091i 0.0848490 + 0.269007i
\(661\) −19.9261 11.5043i −0.775035 0.447466i 0.0596330 0.998220i \(-0.481007\pi\)
−0.834668 + 0.550754i \(0.814340\pi\)
\(662\) −27.6951 20.3046i −1.07640 0.789162i
\(663\) −18.6338 32.2746i −0.723676 1.25344i
\(664\) 42.3271 + 14.3606i 1.64261 + 0.557298i
\(665\) 3.60178 + 1.08947i 0.139671 + 0.0422477i
\(666\) −44.2682 4.84576i −1.71536 0.187769i
\(667\) 3.89330 2.24780i 0.150749 0.0870351i
\(668\) 6.68589 7.29793i 0.258685 0.282365i
\(669\) 28.7098 49.7268i 1.10998 1.92255i
\(670\) 6.01284 + 13.6632i 0.232296 + 0.527857i
\(671\) −11.4871 −0.443453
\(672\) 9.36977 + 44.3255i 0.361447 + 1.70989i
\(673\) −42.0925 −1.62255 −0.811273 0.584668i \(-0.801225\pi\)
−0.811273 + 0.584668i \(0.801225\pi\)
\(674\) 11.2263 + 25.5100i 0.432420 + 0.982608i
\(675\) 4.78750 8.29219i 0.184271 0.319167i
\(676\) 14.0450 15.3307i 0.540192 0.589642i
\(677\) 21.0662 12.1626i 0.809642 0.467447i −0.0371897 0.999308i \(-0.511841\pi\)
0.846831 + 0.531861i \(0.178507\pi\)
\(678\) −11.4133 1.24934i −0.438325 0.0479807i
\(679\) 5.25302 + 22.4483i 0.201592 + 0.861487i
\(680\) −6.81752 2.31302i −0.261440 0.0887002i
\(681\) −1.41433 2.44969i −0.0541972 0.0938723i
\(682\) 9.06285 + 6.64441i 0.347034 + 0.254428i
\(683\) −16.6251 9.59853i −0.636144 0.367278i 0.146984 0.989139i \(-0.453043\pi\)
−0.783127 + 0.621861i \(0.786377\pi\)
\(684\) 5.27350 + 16.7192i 0.201637 + 0.639274i
\(685\) 4.27568i 0.163365i
\(686\) 23.3915 + 11.7828i 0.893093 + 0.449871i
\(687\) 39.5963i 1.51069i
\(688\) 5.50693 0.482979i 0.209950 0.0184134i
\(689\) −14.0830 8.13083i −0.536520 0.309760i
\(690\) −14.6972 + 20.0467i −0.559514 + 0.763167i
\(691\) −7.00274 12.1291i −0.266397 0.461413i 0.701532 0.712638i \(-0.252500\pi\)
−0.967929 + 0.251225i \(0.919167\pi\)
\(692\) 2.99871 13.5331i 0.113994 0.514453i
\(693\) 4.44710 + 19.0043i 0.168931 + 0.721914i
\(694\) −1.29834 + 11.8609i −0.0492842 + 0.450233i
\(695\) −6.52760 + 3.76871i −0.247606 + 0.142955i
\(696\) 4.98314 4.37151i 0.188885 0.165702i
\(697\) 9.50271 16.4592i 0.359941 0.623436i
\(698\) −30.5203 + 13.4312i −1.15521 + 0.508378i
\(699\) −47.2271 −1.78629
\(700\) 2.69968 + 4.55101i 0.102038 + 0.172012i
\(701\) 11.9124 0.449923 0.224962 0.974368i \(-0.427774\pi\)
0.224962 + 0.974368i \(0.427774\pi\)
\(702\) −59.9490 + 26.3820i −2.26263 + 0.995724i
\(703\) 3.63338 6.29320i 0.137036 0.237353i
\(704\) −3.66727 8.84557i −0.138216 0.333380i
\(705\) 2.80727 1.62078i 0.105728 0.0610420i
\(706\) 3.18120 29.0616i 0.119726 1.09375i
\(707\) −7.61108 2.30220i −0.286244 0.0865830i
\(708\) −58.4227 12.9455i −2.19566 0.486520i
\(709\) −23.6490 40.9613i −0.888158 1.53833i −0.842051 0.539398i \(-0.818652\pi\)
−0.0461071 0.998937i \(-0.514682\pi\)
\(710\) 13.6529 18.6223i 0.512384 0.698881i
\(711\) 57.4779 + 33.1849i 2.15559 + 1.24453i
\(712\) 10.9331 2.17654i 0.409734 0.0815694i
\(713\) 38.5474i 1.44361i
\(714\) −26.5219 11.2997i −0.992559 0.422880i
\(715\) 5.78958i 0.216518i
\(716\) −40.2689 + 12.7015i −1.50492 + 0.474676i
\(717\) 37.0491 + 21.3903i 1.38362 + 0.798835i
\(718\) 31.3097 + 22.9547i 1.16847 + 0.856661i
\(719\) −0.888951 1.53971i −0.0331523 0.0574214i 0.848973 0.528436i \(-0.177221\pi\)
−0.882125 + 0.471014i \(0.843888\pi\)
\(720\) −10.4138 + 22.3450i −0.388101 + 0.832749i
\(721\) 0.692832 + 0.738552i 0.0258024 + 0.0275051i
\(722\) 23.8668 + 2.61255i 0.888230 + 0.0972290i
\(723\) −56.5806 + 32.6668i −2.10425 + 1.21489i
\(724\) 9.00213 + 8.24716i 0.334561 + 0.306503i
\(725\) 0.387117 0.670506i 0.0143772 0.0249020i
\(726\) 16.4972 + 37.4874i 0.612269 + 1.39129i
\(727\) −27.1619 −1.00738 −0.503689 0.863885i \(-0.668024\pi\)
−0.503689 + 0.863885i \(0.668024\pi\)
\(728\) 3.51347 36.0253i 0.130218 1.33519i
\(729\) −22.2718 −0.824883
\(730\) 0.0610137 + 0.138644i 0.00225822 + 0.00513145i
\(731\) −1.75883 + 3.04638i −0.0650526 + 0.112674i
\(732\) −42.8406 39.2478i −1.58344 1.45064i
\(733\) 19.7246 11.3880i 0.728543 0.420625i −0.0893459 0.996001i \(-0.528478\pi\)
0.817889 + 0.575376i \(0.195144\pi\)
\(734\) −28.1763 3.08428i −1.04001 0.113843i
\(735\) 9.40204 + 18.9893i 0.346799 + 0.700432i
\(736\) 17.0324 28.0855i 0.627824 1.03525i
\(737\) −6.31725 10.9418i −0.232699 0.403046i
\(738\) −52.4862 38.4802i −1.93205 1.41648i
\(739\) −28.1611 16.2588i −1.03592 0.598091i −0.117247 0.993103i \(-0.537407\pi\)
−0.918676 + 0.395012i \(0.870740\pi\)
\(740\) 9.74533 3.07384i 0.358246 0.112996i
\(741\) 20.8243i 0.764999i
\(742\) −12.4877 + 1.51638i −0.458437 + 0.0556682i
\(743\) 9.19402i 0.337296i 0.985676 + 0.168648i \(0.0539401\pi\)
−0.985676 + 0.168648i \(0.946060\pi\)
\(744\) 11.0977 + 55.7451i 0.406860 + 2.04372i
\(745\) 2.47480 + 1.42882i 0.0906695 + 0.0523480i
\(746\) 17.2179 23.4848i 0.630391 0.859841i
\(747\) 48.6971 + 84.3459i 1.78173 + 3.08605i
\(748\) 5.94894 + 1.31818i 0.217515 + 0.0481975i
\(749\) 1.62563 1.52499i 0.0593993 0.0557221i
\(750\) −0.465823 + 4.25550i −0.0170095 + 0.155389i
\(751\) 17.5852 10.1528i 0.641692 0.370481i −0.143574 0.989640i \(-0.545860\pi\)
0.785266 + 0.619159i \(0.212526\pi\)
\(752\) −3.50825 + 2.45762i −0.127933 + 0.0896202i
\(753\) −1.58104 + 2.73843i −0.0576161 + 0.0997941i
\(754\) −4.84747 + 2.13324i −0.176534 + 0.0776882i
\(755\) 6.60903 0.240527
\(756\) −24.8131 + 44.1743i −0.902446 + 1.60660i
\(757\) 10.9555 0.398184 0.199092 0.979981i \(-0.436201\pi\)
0.199092 + 0.979981i \(0.436201\pi\)
\(758\) 4.22418 1.85895i 0.153429 0.0675202i
\(759\) 10.5193 18.2199i 0.381825 0.661341i
\(760\) −2.65287 3.02405i −0.0962299 0.109694i
\(761\) −27.2104 + 15.7099i −0.986375 + 0.569484i −0.904189 0.427133i \(-0.859523\pi\)
−0.0821860 + 0.996617i \(0.526190\pi\)
\(762\) −0.997022 + 9.10823i −0.0361183 + 0.329957i
\(763\) −3.02626 + 10.0048i −0.109558 + 0.362200i
\(764\) 1.60659 7.25052i 0.0581243 0.262314i
\(765\) −7.84352 13.5854i −0.283583 0.491180i
\(766\) −28.2219 + 38.4941i −1.01970 + 1.39085i
\(767\) 41.4036 + 23.9044i 1.49500 + 0.863137i
\(768\) 16.5456 45.5193i 0.597040 1.64253i
\(769\) 23.9511i 0.863700i −0.901945 0.431850i \(-0.857861\pi\)
0.901945 0.431850i \(-0.142139\pi\)
\(770\) −2.69051 3.58036i −0.0969594 0.129027i
\(771\) 14.8444i 0.534606i
\(772\) −9.22330 29.2417i −0.331954 1.05243i
\(773\) −13.1506 7.59249i −0.472993 0.273083i 0.244499 0.969650i \(-0.421377\pi\)
−0.717492 + 0.696567i \(0.754710\pi\)
\(774\) 9.71452 + 7.12218i 0.349181 + 0.256002i
\(775\) 3.31933 + 5.74924i 0.119234 + 0.206519i
\(776\) 7.91864 23.3398i 0.284263 0.837851i
\(777\) 39.8434 9.32355i 1.42937 0.334480i
\(778\) 5.07793 + 0.555850i 0.182053 + 0.0199282i
\(779\) 9.19703 5.30991i 0.329518 0.190247i
\(780\) 19.7813 21.5921i 0.708282 0.773120i
\(781\) −9.77179 + 16.9252i −0.349662 + 0.605633i
\(782\) 8.41889 + 19.1306i 0.301059 + 0.684109i
\(783\) 7.41329 0.264929
\(784\) −14.5688 23.9113i −0.520313 0.853976i
\(785\) −15.5831 −0.556185
\(786\) 16.6670 + 37.8731i 0.594492 + 1.35089i
\(787\) −9.14982 + 15.8480i −0.326156 + 0.564919i −0.981746 0.190199i \(-0.939087\pi\)
0.655590 + 0.755117i \(0.272420\pi\)
\(788\) 33.0463 36.0715i 1.17723 1.28499i
\(789\) 20.4383 11.8001i 0.727624 0.420094i
\(790\) −15.1390 1.65717i −0.538622 0.0589596i
\(791\) 6.90929 1.61681i 0.245666 0.0574870i
\(792\) 6.70376 19.7590i 0.238208 0.702107i
\(793\) 23.2097 + 40.2004i 0.824201 + 1.42756i
\(794\) −8.52802 6.25230i −0.302648 0.221886i
\(795\) −8.81350 5.08847i −0.312583 0.180470i
\(796\) −7.74051 24.5406i −0.274355 0.869819i
\(797\) 15.0960i 0.534728i 0.963596 + 0.267364i \(0.0861526\pi\)
−0.963596 + 0.267364i \(0.913847\pi\)
\(798\) −9.67739 12.8780i −0.342576 0.455878i
\(799\) 2.72566i 0.0964268i
\(800\) 0.121894 5.65554i 0.00430962 0.199954i
\(801\) 21.0363 + 12.1453i 0.743280 + 0.429133i
\(802\) −7.98277 + 10.8883i −0.281881 + 0.384481i
\(803\) −0.0641026 0.111029i −0.00226213 0.00391813i
\(804\) 13.8248 62.3912i 0.487563 2.20037i
\(805\) 4.44785 14.7046i 0.156766 0.518270i
\(806\) 4.94138 45.1417i 0.174053 1.59005i
\(807\) 55.3464 31.9543i 1.94829 1.12484i
\(808\) 5.60590 + 6.39024i 0.197215 + 0.224808i
\(809\) −22.2240 + 38.4931i −0.781355 + 1.35335i 0.149797 + 0.988717i \(0.452138\pi\)
−0.931153 + 0.364630i \(0.881196\pi\)
\(810\) −13.5846 + 5.97823i −0.477314 + 0.210054i
\(811\) 34.6449 1.21655 0.608274 0.793727i \(-0.291862\pi\)
0.608274 + 0.793727i \(0.291862\pi\)
\(812\) −2.00639 + 3.57193i −0.0704104 + 0.125350i
\(813\) −65.1449 −2.28473
\(814\) −7.91614 + 3.48369i −0.277461 + 0.122103i
\(815\) 4.82015 8.34874i 0.168842 0.292444i
\(816\) 17.6826 + 25.2419i 0.619014 + 0.883642i
\(817\) −1.70225 + 0.982794i −0.0595542 + 0.0343836i
\(818\) −3.33496 + 30.4663i −0.116604 + 1.06523i
\(819\) 57.5225 53.9616i 2.01000 1.88557i
\(820\) 14.5801 + 3.23069i 0.509158 + 0.112821i
\(821\) −11.8550 20.5335i −0.413742 0.716622i 0.581553 0.813508i \(-0.302445\pi\)
−0.995296 + 0.0968858i \(0.969112\pi\)
\(822\) 10.8224 14.7616i 0.377476 0.514870i
\(823\) 5.62203 + 3.24588i 0.195972 + 0.113144i 0.594775 0.803892i \(-0.297241\pi\)
−0.398803 + 0.917036i \(0.630574\pi\)
\(824\) −0.211370 1.06174i −0.00736343 0.0369875i
\(825\) 3.62326i 0.126146i
\(826\) 36.7133 4.45812i 1.27742 0.155118i
\(827\) 39.4872i 1.37310i 0.727081 + 0.686552i \(0.240877\pi\)
−0.727081 + 0.686552i \(0.759123\pi\)
\(828\) 68.2577 21.5296i 2.37212 0.748205i
\(829\) −2.82562 1.63137i −0.0981377 0.0566598i 0.450128 0.892964i \(-0.351378\pi\)
−0.548266 + 0.836304i \(0.684712\pi\)
\(830\) −18.0235 13.2139i −0.625604 0.458660i
\(831\) 7.82108 + 13.5465i 0.271310 + 0.469923i
\(832\) −23.5464 + 30.7067i −0.816325 + 1.06456i
\(833\) 17.7808 + 1.13705i 0.616069 + 0.0393966i
\(834\) 32.0755 + 3.51110i 1.11068 + 0.121580i
\(835\) −4.28575 + 2.47438i −0.148315 + 0.0856294i
\(836\) 2.51050 + 2.29996i 0.0868276 + 0.0795457i
\(837\) −31.7826 + 55.0490i −1.09857 + 1.90277i
\(838\) −7.42394 16.8698i −0.256456 0.582756i
\(839\) −5.39522 −0.186264 −0.0931318 0.995654i \(-0.529688\pi\)
−0.0931318 + 0.995654i \(0.529688\pi\)
\(840\) 2.19882 22.5455i 0.0758664 0.777894i
\(841\) −28.4006 −0.979330
\(842\) −19.5272 44.3726i −0.672952 1.52918i
\(843\) −23.6599 + 40.9801i −0.814889 + 1.41143i
\(844\) 24.9790 + 22.8842i 0.859814 + 0.787706i
\(845\) −9.00304 + 5.19791i −0.309714 + 0.178814i
\(846\) −9.27814 1.01562i −0.318989 0.0349178i
\(847\) −17.3182 18.4611i −0.595061 0.634330i
\(848\) 12.1892 + 5.68074i 0.418578 + 0.195077i
\(849\) 43.2417 + 74.8968i 1.48405 + 2.57045i
\(850\) 2.90299 + 2.12833i 0.0995719 + 0.0730010i
\(851\) −25.6926 14.8336i −0.880731 0.508490i
\(852\) −94.2720 + 29.7349i −3.22971 + 1.01870i
\(853\) 10.7675i 0.368672i −0.982863 0.184336i \(-0.940987\pi\)
0.982863 0.184336i \(-0.0590134\pi\)
\(854\) 33.0350 + 14.0746i 1.13043 + 0.481622i
\(855\) 8.76558i 0.299776i
\(856\) −2.33700 + 0.465248i −0.0798771 + 0.0159018i
\(857\) −30.4752 17.5949i −1.04101 0.601029i −0.120892 0.992666i \(-0.538576\pi\)
−0.920120 + 0.391637i \(0.871909\pi\)
\(858\) −14.6544 + 19.9883i −0.500292 + 0.682389i
\(859\) 20.6193 + 35.7136i 0.703520 + 1.21853i 0.967223 + 0.253929i \(0.0817228\pi\)
−0.263703 + 0.964604i \(0.584944\pi\)
\(860\) −2.69858 0.597958i −0.0920208 0.0203902i
\(861\) 57.2398 + 17.3139i 1.95073 + 0.590055i
\(862\) 0.438960 4.01010i 0.0149510 0.136584i
\(863\) 19.9441 11.5147i 0.678906 0.391966i −0.120537 0.992709i \(-0.538462\pi\)
0.799443 + 0.600742i \(0.205128\pi\)
\(864\) 47.4804 26.0651i 1.61532 0.886754i
\(865\) −3.46535 + 6.00216i −0.117825 + 0.204079i
\(866\) 44.8099 19.7197i 1.52270 0.670103i
\(867\) 31.8491 1.08165
\(868\) −17.9223 30.2126i −0.608321 1.02548i
\(869\) 12.8898 0.437258
\(870\) −3.03366 + 1.33504i −0.102851 + 0.0452620i
\(871\) −25.5281 + 44.2160i −0.864987 + 1.49820i
\(872\) 8.40004 7.36902i 0.284461 0.249547i
\(873\) 46.5097 26.8524i 1.57411 0.908815i
\(874\) −1.27085 + 11.6098i −0.0429871 + 0.392706i
\(875\) −0.602834 2.57616i −0.0203795 0.0870900i
\(876\) 0.140284 0.633098i 0.00473974 0.0213904i
\(877\) −2.03136 3.51842i −0.0685941 0.118809i 0.829689 0.558227i \(-0.188518\pi\)
−0.898283 + 0.439418i \(0.855185\pi\)
\(878\) −9.14619 + 12.4752i −0.308669 + 0.421018i
\(879\) −1.72279 0.994655i −0.0581084 0.0335489i
\(880\) 0.418305 + 4.76952i 0.0141010 + 0.160780i
\(881\) 42.0606i 1.41706i −0.705682 0.708529i \(-0.749359\pi\)
0.705682 0.708529i \(-0.250641\pi\)
\(882\) 10.4959 60.1023i 0.353417 2.02375i
\(883\) 54.8918i 1.84725i −0.383291 0.923627i \(-0.625210\pi\)
0.383291 0.923627i \(-0.374790\pi\)
\(884\) −7.40675 23.4825i −0.249116 0.789801i
\(885\) 25.9114 + 14.9599i 0.871002 + 0.502873i
\(886\) −40.3681 29.5958i −1.35619 0.994290i
\(887\) −19.0622 33.0168i −0.640047 1.10859i −0.985422 0.170129i \(-0.945581\pi\)
0.345375 0.938465i \(-0.387752\pi\)
\(888\) −41.4257 14.0547i −1.39016 0.471646i
\(889\) −1.29027 5.51387i −0.0432743 0.184929i
\(890\) −5.54071 0.606507i −0.185725 0.0203302i
\(891\) 10.8788 6.28089i 0.364454 0.210418i
\(892\) 25.6272 27.9731i 0.858061 0.936610i
\(893\) 0.761518 1.31899i 0.0254832 0.0441383i
\(894\) −4.92754 11.1971i −0.164802 0.374486i
\(895\) 21.1123 0.705706
\(896\) −0.291560 + 29.9318i −0.00974032 + 0.999953i
\(897\) −85.0171 −2.83864
\(898\) 15.9515 + 36.2473i 0.532309 + 1.20959i
\(899\) −2.56993 + 4.45125i −0.0857121 + 0.148458i
\(900\) 8.32653 9.08876i 0.277551 0.302959i
\(901\) −7.41082 + 4.27864i −0.246890 + 0.142542i
\(902\) −12.5645 1.37536i −0.418351 0.0457943i
\(903\) −10.5943 3.20457i −0.352557 0.106641i
\(904\) −7.18369 2.43725i −0.238926 0.0810617i
\(905\) −3.05219 5.28655i −0.101458 0.175731i
\(906\) −22.8174 16.7285i −0.758057 0.555768i
\(907\) −0.307186 0.177354i −0.0101999 0.00588894i 0.494891 0.868955i \(-0.335208\pi\)
−0.505091 + 0.863066i \(0.668541\pi\)
\(908\) −0.562183 1.78235i −0.0186567 0.0591494i
\(909\) 18.5229i 0.614366i
\(910\) −7.09371 + 16.6499i −0.235154 + 0.551940i
\(911\) 12.2958i 0.407379i −0.979036 0.203690i \(-0.934707\pi\)
0.979036 0.203690i \(-0.0652934\pi\)
\(912\) 1.50458 + 17.1553i 0.0498216 + 0.568067i
\(913\) 16.3810 + 9.45758i 0.542132 + 0.313000i
\(914\) 16.8823 23.0271i 0.558415 0.761668i
\(915\) 14.5252 + 25.1584i 0.480189 + 0.831712i
\(916\) 5.65967 25.5420i 0.187001 0.843932i
\(917\) −17.4964 18.6510i −0.577783 0.615912i
\(918\) −3.75040 + 34.2616i −0.123782 + 1.13080i
\(919\) −0.243118 + 0.140364i −0.00801973 + 0.00463019i −0.504005 0.863701i \(-0.668141\pi\)
0.495985 + 0.868331i \(0.334807\pi\)
\(920\) −12.3460 + 10.8306i −0.407034 + 0.357075i
\(921\) 7.38668 12.7941i 0.243399 0.421580i
\(922\) 0.165485 0.0728255i 0.00544994 0.00239838i
\(923\) 78.9760 2.59953
\(924\) 0.226409 + 19.1712i 0.00744829 + 0.630685i
\(925\) −5.10930 −0.167993
\(926\) 23.1254 10.1769i 0.759949 0.334434i
\(927\) 1.17946 2.04289i 0.0387387 0.0670974i
\(928\) 3.83926 2.10762i 0.126030 0.0691861i
\(929\) 28.1316 16.2418i 0.922967 0.532875i 0.0383868 0.999263i \(-0.487778\pi\)
0.884580 + 0.466388i \(0.154445\pi\)
\(930\) 3.09244 28.2508i 0.101405 0.926379i
\(931\) 8.28674 + 5.51800i 0.271587 + 0.180845i
\(932\) −30.4643 6.75036i −0.997891 0.221115i
\(933\) −18.0062 31.1877i −0.589497 1.02104i
\(934\) 12.2663 16.7311i 0.401367 0.547457i
\(935\) −2.63845 1.52331i −0.0862865 0.0498175i
\(936\) −82.6943 + 16.4627i −2.70295 + 0.538100i
\(937\) 59.7020i 1.95038i −0.221368 0.975190i \(-0.571052\pi\)
0.221368 0.975190i \(-0.428948\pi\)
\(938\) 4.76095 + 39.2071i 0.155450 + 1.28016i
\(939\) 80.5424i 2.62840i
\(940\) 2.04252 0.644243i 0.0666196 0.0210129i
\(941\) 12.3373 + 7.12292i 0.402183 + 0.232201i 0.687426 0.726255i \(-0.258741\pi\)
−0.285242 + 0.958455i \(0.592074\pi\)
\(942\) 53.8000 + 39.4434i 1.75290 + 1.28514i
\(943\) −21.6782 37.5477i −0.705939 1.22272i
\(944\) −35.8358 16.7012i −1.16636 0.543578i
\(945\) 18.4759 17.3322i 0.601022 0.563816i
\(946\) 2.32552 + 0.254560i 0.0756092 + 0.00827647i
\(947\) 26.0696 15.0513i 0.847148 0.489101i −0.0125394 0.999921i \(-0.503992\pi\)
0.859688 + 0.510820i \(0.170658\pi\)
\(948\) 48.0722 + 44.0407i 1.56131 + 1.43037i
\(949\) −0.259040 + 0.448670i −0.00840879 + 0.0145645i
\(950\) 0.810175 + 1.84100i 0.0262855 + 0.0597298i
\(951\) −80.0831 −2.59687
\(952\) −15.4931 11.0799i −0.502135 0.359100i
\(953\) 3.58515 0.116134 0.0580672 0.998313i \(-0.481506\pi\)
0.0580672 + 0.998313i \(0.481506\pi\)
\(954\) 11.8031 + 26.8207i 0.382140 + 0.868353i
\(955\) −1.85660 + 3.21572i −0.0600780 + 0.104058i
\(956\) 20.8415 + 19.0936i 0.674061 + 0.617531i
\(957\) 2.42942 1.40263i 0.0785320 0.0453405i
\(958\) −36.7640 4.02433i −1.18779 0.130020i
\(959\) −3.27521 + 10.8279i −0.105762 + 0.349650i
\(960\) −14.7359 + 19.2170i −0.475600 + 0.620225i
\(961\) −6.53585 11.3204i −0.210834 0.365175i
\(962\) 28.1863 + 20.6647i 0.908761 + 0.666257i
\(963\) −4.49662 2.59612i −0.144902 0.0836589i
\(964\) −41.1670 + 12.9848i −1.32590 + 0.418211i
\(965\) 15.3309i 0.493519i
\(966\) −52.5758 + 39.5089i −1.69160 + 1.27118i
\(967\) 46.1614i 1.48445i 0.670150 + 0.742226i \(0.266230\pi\)
−0.670150 + 0.742226i \(0.733770\pi\)
\(968\) 5.28347 + 26.5396i 0.169817 + 0.853015i
\(969\) −9.49011 5.47912i −0.304866 0.176015i
\(970\) −7.28634 + 9.93843i −0.233950 + 0.319104i
\(971\) −5.83113 10.0998i −0.187130 0.324118i 0.757162 0.653227i \(-0.226585\pi\)
−0.944292 + 0.329108i \(0.893252\pi\)
\(972\) 5.94261 + 1.31678i 0.190609 + 0.0422357i
\(973\) −19.4176 + 4.54381i −0.622499 + 0.145668i
\(974\) −2.55828 + 23.3710i −0.0819727 + 0.748856i
\(975\) −12.6801 + 7.32084i −0.406087 + 0.234455i
\(976\) −22.0249 31.4406i −0.705001 1.00639i
\(977\) 21.2415 36.7913i 0.679575 1.17706i −0.295534 0.955332i \(-0.595497\pi\)
0.975109 0.221726i \(-0.0711692\pi\)
\(978\) −37.7734 + 16.6231i −1.20786 + 0.531548i
\(979\) 4.71754 0.150773
\(980\) 3.35065 + 13.5931i 0.107033 + 0.434217i
\(981\) 24.3486 0.777390
\(982\) 28.3599 12.4805i 0.905001 0.398267i
\(983\) −15.8715 + 27.4903i −0.506223 + 0.876804i 0.493751 + 0.869603i \(0.335625\pi\)
−0.999974 + 0.00720094i \(0.997708\pi\)
\(984\) −42.1597 48.0584i −1.34400 1.53204i
\(985\) −21.1832 + 12.2301i −0.674952 + 0.389684i
\(986\) −0.303257 + 2.77039i −0.00965767 + 0.0882270i
\(987\) 8.35075 1.95412i 0.265807 0.0622002i
\(988\) 2.97650 13.4329i 0.0946951 0.427358i
\(989\) 4.01235 + 6.94960i 0.127585 + 0.220984i
\(990\) −6.16847 + 8.41368i −0.196047 + 0.267404i
\(991\) −25.4182 14.6752i −0.807436 0.466173i 0.0386286 0.999254i \(-0.487701\pi\)
−0.846065 + 0.533080i \(0.821034\pi\)
\(992\) −0.809215 + 37.5452i −0.0256926 + 1.19206i
\(993\) 73.5053i 2.33262i
\(994\) 48.8399 36.7015i 1.54911 1.16410i
\(995\) 12.8662i 0.407886i
\(996\) 28.7788 + 91.2407i 0.911891 + 2.89107i
\(997\) 9.35899 + 5.40341i 0.296402 + 0.171128i 0.640825 0.767687i \(-0.278592\pi\)
−0.344423 + 0.938814i \(0.611926\pi\)
\(998\) 46.4070 + 34.0232i 1.46899 + 1.07699i
\(999\) −24.4608 42.3673i −0.773905 1.34044i
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.31.10 32
4.3 odd 2 inner 140.2.o.a.31.11 yes 32
5.2 odd 4 700.2.t.d.199.3 32
5.3 odd 4 700.2.t.c.199.14 32
5.4 even 2 700.2.p.c.451.7 32
7.2 even 3 980.2.o.f.411.11 32
7.3 odd 6 980.2.g.a.391.1 32
7.4 even 3 980.2.g.a.391.2 32
7.5 odd 6 inner 140.2.o.a.131.11 yes 32
7.6 odd 2 980.2.o.f.31.10 32
20.3 even 4 700.2.t.c.199.13 32
20.7 even 4 700.2.t.d.199.4 32
20.19 odd 2 700.2.p.c.451.6 32
28.3 even 6 980.2.g.a.391.4 32
28.11 odd 6 980.2.g.a.391.3 32
28.19 even 6 inner 140.2.o.a.131.10 yes 32
28.23 odd 6 980.2.o.f.411.10 32
28.27 even 2 980.2.o.f.31.11 32
35.12 even 12 700.2.t.c.299.13 32
35.19 odd 6 700.2.p.c.551.6 32
35.33 even 12 700.2.t.d.299.4 32
140.19 even 6 700.2.p.c.551.7 32
140.47 odd 12 700.2.t.c.299.14 32
140.103 odd 12 700.2.t.d.299.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.10 32 1.1 even 1 trivial
140.2.o.a.31.11 yes 32 4.3 odd 2 inner
140.2.o.a.131.10 yes 32 28.19 even 6 inner
140.2.o.a.131.11 yes 32 7.5 odd 6 inner
700.2.p.c.451.6 32 20.19 odd 2
700.2.p.c.451.7 32 5.4 even 2
700.2.p.c.551.6 32 35.19 odd 6
700.2.p.c.551.7 32 140.19 even 6
700.2.t.c.199.13 32 20.3 even 4
700.2.t.c.199.14 32 5.3 odd 4
700.2.t.c.299.13 32 35.12 even 12
700.2.t.c.299.14 32 140.47 odd 12
700.2.t.d.199.3 32 5.2 odd 4
700.2.t.d.199.4 32 20.7 even 4
700.2.t.d.299.3 32 140.103 odd 12
700.2.t.d.299.4 32 35.33 even 12
980.2.g.a.391.1 32 7.3 odd 6
980.2.g.a.391.2 32 7.4 even 3
980.2.g.a.391.3 32 28.11 odd 6
980.2.g.a.391.4 32 28.3 even 6
980.2.o.f.31.10 32 7.6 odd 2
980.2.o.f.31.11 32 28.27 even 2
980.2.o.f.411.10 32 28.23 odd 6
980.2.o.f.411.11 32 7.2 even 3