Properties

Label 825.2.s.a.479.98
Level $825$
Weight $2$
Character 825.479
Analytic conductor $6.588$
Analytic rank $0$
Dimension $464$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(479,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 1, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.479");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.s (of order \(10\), degree \(4\), 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: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(464\)
Relative dimension: \(116\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 479.98
Character \(\chi\) \(=\) 825.479
Dual form 825.2.s.a.794.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.11925i q^{2} +(1.69678 + 0.347748i) q^{3} -2.49121 q^{4} +(-0.713406 + 2.11921i) q^{5} +(-0.736965 + 3.59590i) q^{6} +(-4.07113 + 2.95785i) q^{7} -1.04100i q^{8} +(2.75814 + 1.18011i) q^{9} +O(q^{10})\) \(q+2.11925i q^{2} +(1.69678 + 0.347748i) q^{3} -2.49121 q^{4} +(-0.713406 + 2.11921i) q^{5} +(-0.736965 + 3.59590i) q^{6} +(-4.07113 + 2.95785i) q^{7} -1.04100i q^{8} +(2.75814 + 1.18011i) q^{9} +(-4.49113 - 1.51189i) q^{10} +(3.05198 - 1.29825i) q^{11} +(-4.22705 - 0.866316i) q^{12} +(1.02337 - 0.743519i) q^{13} +(-6.26841 - 8.62773i) q^{14} +(-1.94745 + 3.34775i) q^{15} -2.77628 q^{16} +(-1.21991 + 0.396374i) q^{17} +(-2.50094 + 5.84519i) q^{18} -3.25014i q^{19} +(1.77725 - 5.27940i) q^{20} +(-7.93640 + 3.60309i) q^{21} +(2.75131 + 6.46789i) q^{22} +(0.243965 - 0.750847i) q^{23} +(0.362007 - 1.76636i) q^{24} +(-3.98210 - 3.02372i) q^{25} +(1.57570 + 2.16877i) q^{26} +(4.26959 + 2.96152i) q^{27} +(10.1420 - 7.36862i) q^{28} +0.339242 q^{29} +(-7.09472 - 4.12712i) q^{30} +(7.05670 + 5.12699i) q^{31} -7.96564i q^{32} +(5.63000 - 1.14152i) q^{33} +(-0.840015 - 2.58530i) q^{34} +(-3.36393 - 10.7377i) q^{35} +(-6.87112 - 2.93990i) q^{36} +(2.14684 - 2.95488i) q^{37} +6.88785 q^{38} +(1.99499 - 0.905716i) q^{39} +(2.20610 + 0.742658i) q^{40} +(-0.721915 + 2.22182i) q^{41} +(-7.63585 - 16.8192i) q^{42} -7.35902 q^{43} +(-7.60312 + 3.23421i) q^{44} +(-4.46857 + 5.00319i) q^{45} +(1.59123 + 0.517022i) q^{46} +(3.64021 + 11.2034i) q^{47} +(-4.71075 - 0.965448i) q^{48} +(5.66209 - 17.4261i) q^{49} +(6.40800 - 8.43906i) q^{50} +(-2.20777 + 0.248337i) q^{51} +(-2.54942 + 1.85226i) q^{52} +(-3.16468 + 9.73989i) q^{53} +(-6.27621 + 9.04831i) q^{54} +(0.573957 + 7.39396i) q^{55} +(3.07913 + 4.23805i) q^{56} +(1.13023 - 5.51478i) q^{57} +0.718938i q^{58} +(2.29302 - 3.15606i) q^{59} +(4.85151 - 8.33997i) q^{60} +(-4.00161 + 5.50775i) q^{61} +(-10.8654 + 14.9549i) q^{62} +(-14.7193 + 3.35380i) q^{63} +11.3286 q^{64} +(0.845597 + 2.69916i) q^{65} +(2.41917 + 11.9314i) q^{66} +(-4.52611 - 6.22966i) q^{67} +(3.03907 - 0.987452i) q^{68} +(0.675061 - 1.18919i) q^{69} +(22.7559 - 7.12900i) q^{70} +(-1.26036 - 1.73473i) q^{71} +(1.22849 - 2.87123i) q^{72} +(1.21526 + 3.74019i) q^{73} +(6.26212 + 4.54970i) q^{74} +(-5.70527 - 6.51536i) q^{75} +8.09679i q^{76} +(-8.58497 + 14.3126i) q^{77} +(1.91944 + 4.22787i) q^{78} +(-2.82110 - 0.916631i) q^{79} +(1.98062 - 5.88353i) q^{80} +(6.21470 + 6.50981i) q^{81} +(-4.70860 - 1.52992i) q^{82} +(-1.45544 + 0.472902i) q^{83} +(19.7713 - 8.97607i) q^{84} +(0.0302944 - 2.86803i) q^{85} -15.5956i q^{86} +(0.575620 + 0.117971i) q^{87} +(-1.35148 - 3.17712i) q^{88} +(-2.78752 - 0.905721i) q^{89} +(-10.6030 - 9.47001i) q^{90} +(-1.96704 + 6.05392i) q^{91} +(-0.607769 + 1.87052i) q^{92} +(10.1908 + 11.1533i) q^{93} +(-23.7428 + 7.71450i) q^{94} +(6.88773 + 2.31867i) q^{95} +(2.77004 - 13.5160i) q^{96} +(15.6153 + 5.07373i) q^{97} +(36.9303 + 11.9994i) q^{98} +(9.94985 + 0.0209113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 464 q - 460 q^{4} + 5 q^{6} + 10 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 464 q - 460 q^{4} + 5 q^{6} + 10 q^{7} - 4 q^{9} + 30 q^{10} - 20 q^{12} - 10 q^{13} - 2 q^{15} + 404 q^{16} - 15 q^{21} - 20 q^{22} - 20 q^{24} + 16 q^{25} + 15 q^{27} - 40 q^{28} + 5 q^{30} + 8 q^{31} + 20 q^{33} - 8 q^{34} + 9 q^{36} - 30 q^{37} - 5 q^{39} - 30 q^{40} - 35 q^{42} + 3 q^{45} + 10 q^{46} + 30 q^{48} - 102 q^{49} - 25 q^{51} - 30 q^{52} - 10 q^{54} - 26 q^{55} - 6 q^{60} - 30 q^{61} - 5 q^{63} - 364 q^{64} - 20 q^{66} - 30 q^{67} + 36 q^{69} - 26 q^{70} - 40 q^{72} - 10 q^{73} - 28 q^{75} - 105 q^{78} - 80 q^{79} - 24 q^{81} + 20 q^{82} + 20 q^{84} + 30 q^{85} + 120 q^{88} + 5 q^{90} + 70 q^{91} - 55 q^{93} - 130 q^{94} + 50 q^{96} - 50 q^{97} + 23 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11925i 1.49853i 0.662268 + 0.749267i \(0.269594\pi\)
−0.662268 + 0.749267i \(0.730406\pi\)
\(3\) 1.69678 + 0.347748i 0.979638 + 0.200773i
\(4\) −2.49121 −1.24561
\(5\) −0.713406 + 2.11921i −0.319045 + 0.947740i
\(6\) −0.736965 + 3.59590i −0.300865 + 1.46802i
\(7\) −4.07113 + 2.95785i −1.53874 + 1.11796i −0.587622 + 0.809136i \(0.699936\pi\)
−0.951119 + 0.308825i \(0.900064\pi\)
\(8\) 1.04100i 0.368050i
\(9\) 2.75814 + 1.18011i 0.919381 + 0.393369i
\(10\) −4.49113 1.51189i −1.42022 0.478100i
\(11\) 3.05198 1.29825i 0.920205 0.391436i
\(12\) −4.22705 0.866316i −1.22024 0.250084i
\(13\) 1.02337 0.743519i 0.283831 0.206215i −0.436756 0.899580i \(-0.643873\pi\)
0.720587 + 0.693365i \(0.243873\pi\)
\(14\) −6.26841 8.62773i −1.67530 2.30586i
\(15\) −1.94745 + 3.34775i −0.502829 + 0.864386i
\(16\) −2.77628 −0.694071
\(17\) −1.21991 + 0.396374i −0.295873 + 0.0961348i −0.453192 0.891413i \(-0.649715\pi\)
0.157319 + 0.987548i \(0.449715\pi\)
\(18\) −2.50094 + 5.84519i −0.589477 + 1.37772i
\(19\) 3.25014i 0.745633i −0.927905 0.372817i \(-0.878392\pi\)
0.927905 0.372817i \(-0.121608\pi\)
\(20\) 1.77725 5.27940i 0.397405 1.18051i
\(21\) −7.93640 + 3.60309i −1.73186 + 0.786259i
\(22\) 2.75131 + 6.46789i 0.586580 + 1.37896i
\(23\) 0.243965 0.750847i 0.0508702 0.156562i −0.922394 0.386250i \(-0.873770\pi\)
0.973264 + 0.229687i \(0.0737703\pi\)
\(24\) 0.362007 1.76636i 0.0738944 0.360556i
\(25\) −3.98210 3.02372i −0.796421 0.604743i
\(26\) 1.57570 + 2.16877i 0.309021 + 0.425330i
\(27\) 4.26959 + 2.96152i 0.821682 + 0.569946i
\(28\) 10.1420 7.36862i 1.91667 1.39254i
\(29\) 0.339242 0.0629956 0.0314978 0.999504i \(-0.489972\pi\)
0.0314978 + 0.999504i \(0.489972\pi\)
\(30\) −7.09472 4.12712i −1.29531 0.753506i
\(31\) 7.05670 + 5.12699i 1.26742 + 0.920835i 0.999097 0.0424944i \(-0.0135305\pi\)
0.268323 + 0.963329i \(0.413530\pi\)
\(32\) 7.96564i 1.40814i
\(33\) 5.63000 1.14152i 0.980058 0.198713i
\(34\) −0.840015 2.58530i −0.144061 0.443375i
\(35\) −3.36393 10.7377i −0.568608 1.81501i
\(36\) −6.87112 2.93990i −1.14519 0.489983i
\(37\) 2.14684 2.95488i 0.352939 0.485779i −0.595225 0.803559i \(-0.702937\pi\)
0.948165 + 0.317780i \(0.102937\pi\)
\(38\) 6.88785 1.11736
\(39\) 1.99499 0.905716i 0.319454 0.145031i
\(40\) 2.20610 + 0.742658i 0.348816 + 0.117425i
\(41\) −0.721915 + 2.22182i −0.112744 + 0.346991i −0.991470 0.130336i \(-0.958394\pi\)
0.878726 + 0.477327i \(0.158394\pi\)
\(42\) −7.63585 16.8192i −1.17824 2.59526i
\(43\) −7.35902 −1.12224 −0.561120 0.827734i \(-0.689629\pi\)
−0.561120 + 0.827734i \(0.689629\pi\)
\(44\) −7.60312 + 3.23421i −1.14621 + 0.487575i
\(45\) −4.46857 + 5.00319i −0.666135 + 0.745831i
\(46\) 1.59123 + 0.517022i 0.234614 + 0.0762308i
\(47\) 3.64021 + 11.2034i 0.530979 + 1.63418i 0.752181 + 0.658956i \(0.229002\pi\)
−0.221203 + 0.975228i \(0.570998\pi\)
\(48\) −4.71075 0.965448i −0.679938 0.139350i
\(49\) 5.66209 17.4261i 0.808870 2.48945i
\(50\) 6.40800 8.43906i 0.906229 1.19346i
\(51\) −2.20777 + 0.248337i −0.309149 + 0.0347742i
\(52\) −2.54942 + 1.85226i −0.353541 + 0.256863i
\(53\) −3.16468 + 9.73989i −0.434702 + 1.33788i 0.458689 + 0.888597i \(0.348319\pi\)
−0.893391 + 0.449279i \(0.851681\pi\)
\(54\) −6.27621 + 9.04831i −0.854083 + 1.23132i
\(55\) 0.573957 + 7.39396i 0.0773924 + 0.997001i
\(56\) 3.07913 + 4.23805i 0.411466 + 0.566334i
\(57\) 1.13023 5.51478i 0.149703 0.730450i
\(58\) 0.718938i 0.0944012i
\(59\) 2.29302 3.15606i 0.298525 0.410885i −0.633235 0.773960i \(-0.718273\pi\)
0.931760 + 0.363075i \(0.118273\pi\)
\(60\) 4.85151 8.33997i 0.626327 1.07669i
\(61\) −4.00161 + 5.50775i −0.512354 + 0.705195i −0.984314 0.176425i \(-0.943547\pi\)
0.471960 + 0.881620i \(0.343547\pi\)
\(62\) −10.8654 + 14.9549i −1.37990 + 1.89927i
\(63\) −14.7193 + 3.35380i −1.85446 + 0.422538i
\(64\) 11.3286 1.41608
\(65\) 0.845597 + 2.69916i 0.104883 + 0.334790i
\(66\) 2.41917 + 11.9314i 0.297779 + 1.46865i
\(67\) −4.52611 6.22966i −0.552953 0.761074i 0.437457 0.899240i \(-0.355879\pi\)
−0.990409 + 0.138166i \(0.955879\pi\)
\(68\) 3.03907 0.987452i 0.368541 0.119746i
\(69\) 0.675061 1.18919i 0.0812678 0.143161i
\(70\) 22.7559 7.12900i 2.71985 0.852079i
\(71\) −1.26036 1.73473i −0.149577 0.205875i 0.727653 0.685945i \(-0.240611\pi\)
−0.877230 + 0.480071i \(0.840611\pi\)
\(72\) 1.22849 2.87123i 0.144780 0.338378i
\(73\) 1.21526 + 3.74019i 0.142236 + 0.437756i 0.996645 0.0818438i \(-0.0260809\pi\)
−0.854409 + 0.519600i \(0.826081\pi\)
\(74\) 6.26212 + 4.54970i 0.727957 + 0.528891i
\(75\) −5.70527 6.51536i −0.658788 0.752329i
\(76\) 8.09679i 0.928766i
\(77\) −8.58497 + 14.3126i −0.978348 + 1.63107i
\(78\) 1.91944 + 4.22787i 0.217334 + 0.478713i
\(79\) −2.82110 0.916631i −0.317399 0.103129i 0.145985 0.989287i \(-0.453365\pi\)
−0.463384 + 0.886158i \(0.653365\pi\)
\(80\) 1.98062 5.88353i 0.221440 0.657798i
\(81\) 6.21470 + 6.50981i 0.690522 + 0.723312i
\(82\) −4.70860 1.52992i −0.519978 0.168951i
\(83\) −1.45544 + 0.472902i −0.159756 + 0.0519077i −0.387803 0.921742i \(-0.626766\pi\)
0.228047 + 0.973650i \(0.426766\pi\)
\(84\) 19.7713 8.97607i 2.15722 0.979370i
\(85\) 0.0302944 2.86803i 0.00328588 0.311081i
\(86\) 15.5956i 1.68172i
\(87\) 0.575620 + 0.117971i 0.0617129 + 0.0126478i
\(88\) −1.35148 3.17712i −0.144068 0.338682i
\(89\) −2.78752 0.905721i −0.295477 0.0960062i 0.157527 0.987515i \(-0.449648\pi\)
−0.453004 + 0.891508i \(0.649648\pi\)
\(90\) −10.6030 9.47001i −1.11765 0.998227i
\(91\) −1.96704 + 6.05392i −0.206202 + 0.634623i
\(92\) −0.607769 + 1.87052i −0.0633643 + 0.195015i
\(93\) 10.1908 + 11.1533i 1.05673 + 1.15655i
\(94\) −23.7428 + 7.71450i −2.44888 + 0.795690i
\(95\) 6.88773 + 2.31867i 0.706666 + 0.237891i
\(96\) 2.77004 13.5160i 0.282716 1.37947i
\(97\) 15.6153 + 5.07373i 1.58550 + 0.515159i 0.963465 0.267834i \(-0.0863078\pi\)
0.622031 + 0.782993i \(0.286308\pi\)
\(98\) 36.9303 + 11.9994i 3.73052 + 1.21212i
\(99\) 9.94985 + 0.0209113i 0.999998 + 0.00210166i
\(100\) 9.92027 + 7.53272i 0.992027 + 0.753272i
\(101\) −0.0462410 0.142315i −0.00460115 0.0141609i 0.948730 0.316089i \(-0.102370\pi\)
−0.953331 + 0.301928i \(0.902370\pi\)
\(102\) −0.526289 4.67881i −0.0521103 0.463271i
\(103\) 7.69851i 0.758557i −0.925283 0.379279i \(-0.876172\pi\)
0.925283 0.379279i \(-0.123828\pi\)
\(104\) −0.774006 1.06533i −0.0758975 0.104464i
\(105\) −1.97383 19.3894i −0.192626 1.89221i
\(106\) −20.6412 6.70675i −2.00485 0.651417i
\(107\) −9.18947 + 12.6482i −0.888380 + 1.22275i 0.0856491 + 0.996325i \(0.472704\pi\)
−0.974029 + 0.226424i \(0.927296\pi\)
\(108\) −10.6365 7.37779i −1.02349 0.709928i
\(109\) 15.0703 4.89665i 1.44348 0.469014i 0.520498 0.853863i \(-0.325746\pi\)
0.922980 + 0.384849i \(0.125746\pi\)
\(110\) −15.6696 + 1.21636i −1.49404 + 0.115975i
\(111\) 4.67028 4.26722i 0.443284 0.405027i
\(112\) 11.3026 8.21182i 1.06799 0.775944i
\(113\) −4.71855 + 14.5222i −0.443884 + 1.36613i 0.439820 + 0.898086i \(0.355042\pi\)
−0.883703 + 0.468047i \(0.844958\pi\)
\(114\) 11.6872 + 2.39524i 1.09461 + 0.224335i
\(115\) 1.41716 + 1.05267i 0.132150 + 0.0981621i
\(116\) −0.845124 −0.0784678
\(117\) 3.70002 0.843050i 0.342067 0.0779400i
\(118\) 6.68849 + 4.85947i 0.615725 + 0.447350i
\(119\) 3.79401 5.22200i 0.347796 0.478700i
\(120\) 3.48502 + 2.02730i 0.318137 + 0.185066i
\(121\) 7.62911 7.92443i 0.693556 0.720403i
\(122\) −11.6723 8.48041i −1.05676 0.767780i
\(123\) −1.99757 + 3.51891i −0.180115 + 0.317289i
\(124\) −17.5797 12.7724i −1.57871 1.14700i
\(125\) 9.24875 6.28177i 0.827233 0.561859i
\(126\) −7.10752 31.1939i −0.633189 2.77897i
\(127\) 7.97888 + 5.79700i 0.708011 + 0.514400i 0.882531 0.470253i \(-0.155837\pi\)
−0.174520 + 0.984654i \(0.555837\pi\)
\(128\) 8.07684i 0.713899i
\(129\) −12.4867 2.55909i −1.09939 0.225315i
\(130\) −5.72019 + 1.79203i −0.501694 + 0.157171i
\(131\) 12.6981 9.22574i 1.10944 0.806057i 0.126866 0.991920i \(-0.459508\pi\)
0.982576 + 0.185863i \(0.0595082\pi\)
\(132\) −14.0255 + 2.84377i −1.22077 + 0.247519i
\(133\) 9.61341 + 13.2317i 0.833588 + 1.14734i
\(134\) 13.2022 9.59196i 1.14050 0.828619i
\(135\) −9.32204 + 6.93538i −0.802314 + 0.596903i
\(136\) 0.412627 + 1.26993i 0.0353824 + 0.108896i
\(137\) 6.22548 0.531879 0.265939 0.963990i \(-0.414318\pi\)
0.265939 + 0.963990i \(0.414318\pi\)
\(138\) 2.52018 + 1.43062i 0.214532 + 0.121783i
\(139\) −7.55529 + 2.45486i −0.640831 + 0.208219i −0.611367 0.791347i \(-0.709380\pi\)
−0.0294642 + 0.999566i \(0.509380\pi\)
\(140\) 8.38027 + 26.7499i 0.708262 + 2.26078i
\(141\) 2.28067 + 20.2756i 0.192067 + 1.70751i
\(142\) 3.67633 2.67101i 0.308511 0.224146i
\(143\) 2.15802 3.59778i 0.180463 0.300862i
\(144\) −7.65738 3.27631i −0.638115 0.273026i
\(145\) −0.242017 + 0.718925i −0.0200984 + 0.0597035i
\(146\) −7.92640 + 2.57544i −0.655993 + 0.213145i
\(147\) 15.6672 27.5994i 1.29221 2.27636i
\(148\) −5.34825 + 7.36123i −0.439623 + 0.605089i
\(149\) −1.32304 + 4.07190i −0.108388 + 0.333583i −0.990511 0.137436i \(-0.956114\pi\)
0.882123 + 0.471019i \(0.156114\pi\)
\(150\) 13.8077 12.0909i 1.12739 0.987217i
\(151\) −2.49628 + 3.43584i −0.203145 + 0.279604i −0.898418 0.439140i \(-0.855283\pi\)
0.695274 + 0.718745i \(0.255283\pi\)
\(152\) −3.38341 −0.274430
\(153\) −3.83246 0.346373i −0.309836 0.0280026i
\(154\) −30.3319 18.1937i −2.44422 1.46609i
\(155\) −15.8995 + 11.2970i −1.27708 + 0.907396i
\(156\) −4.96994 + 2.25633i −0.397914 + 0.180651i
\(157\) 1.78230 2.45313i 0.142243 0.195781i −0.731951 0.681357i \(-0.761390\pi\)
0.874194 + 0.485576i \(0.161390\pi\)
\(158\) 1.94257 5.97861i 0.154542 0.475633i
\(159\) −8.75681 + 15.4260i −0.694460 + 1.22336i
\(160\) 16.8809 + 5.68274i 1.33455 + 0.449260i
\(161\) 1.22768 + 3.77840i 0.0967545 + 0.297780i
\(162\) −13.7959 + 13.1705i −1.08391 + 1.03477i
\(163\) −4.16642 5.73459i −0.326339 0.449168i 0.614050 0.789267i \(-0.289539\pi\)
−0.940389 + 0.340099i \(0.889539\pi\)
\(164\) 1.79844 5.53504i 0.140435 0.432214i
\(165\) −1.59736 + 12.7455i −0.124354 + 0.992238i
\(166\) −1.00220 3.08444i −0.0777855 0.239399i
\(167\) 7.71008 10.6120i 0.596624 0.821182i −0.398770 0.917051i \(-0.630563\pi\)
0.995394 + 0.0958687i \(0.0305629\pi\)
\(168\) 3.75083 + 8.26182i 0.289383 + 0.637413i
\(169\) −3.52276 + 10.8419i −0.270982 + 0.833996i
\(170\) 6.07807 + 0.0642013i 0.466166 + 0.00492401i
\(171\) 3.83551 8.96435i 0.293309 0.685521i
\(172\) 18.3329 1.39787
\(173\) 6.98951 + 9.62024i 0.531403 + 0.731413i 0.987343 0.158597i \(-0.0506970\pi\)
−0.455940 + 0.890010i \(0.650697\pi\)
\(174\) −0.250009 + 1.21988i −0.0189532 + 0.0924789i
\(175\) 25.1553 + 0.531480i 1.90156 + 0.0401761i
\(176\) −8.47315 + 3.60430i −0.638688 + 0.271684i
\(177\) 4.98827 4.55776i 0.374941 0.342582i
\(178\) 1.91945 5.90745i 0.143869 0.442782i
\(179\) 16.2782 5.28910i 1.21669 0.395326i 0.370813 0.928708i \(-0.379079\pi\)
0.845875 + 0.533382i \(0.179079\pi\)
\(180\) 11.1322 12.4640i 0.829742 0.929012i
\(181\) 4.61454 + 14.2021i 0.342996 + 1.05563i 0.962648 + 0.270757i \(0.0872739\pi\)
−0.619652 + 0.784877i \(0.712726\pi\)
\(182\) −12.8298 4.16864i −0.951005 0.309000i
\(183\) −8.70517 + 7.95389i −0.643505 + 0.587969i
\(184\) −0.781634 0.253968i −0.0576228 0.0187228i
\(185\) 4.73043 + 6.65764i 0.347788 + 0.489480i
\(186\) −23.6367 + 21.5968i −1.73313 + 1.58355i
\(187\) −3.20856 + 2.79347i −0.234633 + 0.204279i
\(188\) −9.06853 27.9101i −0.661391 2.03555i
\(189\) −26.1418 + 0.572042i −1.90153 + 0.0416099i
\(190\) −4.91384 + 14.5968i −0.356487 + 1.05896i
\(191\) −2.38593 + 3.28396i −0.172640 + 0.237619i −0.886566 0.462603i \(-0.846916\pi\)
0.713925 + 0.700222i \(0.246916\pi\)
\(192\) 19.2222 + 3.93950i 1.38724 + 0.284309i
\(193\) 4.71497 14.5112i 0.339391 1.04454i −0.625128 0.780522i \(-0.714953\pi\)
0.964519 0.264015i \(-0.0850468\pi\)
\(194\) −10.7525 + 33.0928i −0.771984 + 2.37592i
\(195\) 0.496166 + 4.87394i 0.0355312 + 0.349030i
\(196\) −14.1055 + 43.4122i −1.00753 + 3.10087i
\(197\) −4.22156 + 5.81048i −0.300774 + 0.413979i −0.932476 0.361231i \(-0.882356\pi\)
0.631703 + 0.775211i \(0.282356\pi\)
\(198\) −0.0443162 + 21.0862i −0.00314942 + 1.49853i
\(199\) 13.0530 0.925303 0.462651 0.886540i \(-0.346898\pi\)
0.462651 + 0.886540i \(0.346898\pi\)
\(200\) −3.14770 + 4.14538i −0.222576 + 0.293123i
\(201\) −5.51347 12.1443i −0.388890 0.856595i
\(202\) 0.301601 0.0979962i 0.0212206 0.00689499i
\(203\) −1.38110 + 1.00343i −0.0969340 + 0.0704266i
\(204\) 5.50002 0.618661i 0.385078 0.0433150i
\(205\) −4.19349 3.11495i −0.292886 0.217558i
\(206\) 16.3151 1.13672
\(207\) 1.55897 1.78304i 0.108356 0.123930i
\(208\) −2.84115 + 2.06422i −0.196999 + 0.143128i
\(209\) −4.21948 9.91935i −0.291868 0.686136i
\(210\) 41.0909 4.18304i 2.83554 0.288657i
\(211\) 23.0370i 1.58593i 0.609267 + 0.792965i \(0.291464\pi\)
−0.609267 + 0.792965i \(0.708536\pi\)
\(212\) 7.88390 24.2641i 0.541468 1.66647i
\(213\) −1.53530 3.38175i −0.105197 0.231714i
\(214\) −26.8047 19.4748i −1.83233 1.33127i
\(215\) 5.24997 15.5953i 0.358045 1.06359i
\(216\) 3.08296 4.44465i 0.209769 0.302420i
\(217\) −43.8935 −2.97969
\(218\) 10.3772 + 31.9378i 0.702834 + 2.16310i
\(219\) 0.761390 + 6.76890i 0.0514499 + 0.457400i
\(220\) −1.42985 18.4199i −0.0964004 1.24187i
\(221\) −0.953707 + 1.31266i −0.0641533 + 0.0882994i
\(222\) 9.04331 + 9.89749i 0.606947 + 0.664276i
\(223\) −15.8111 21.7621i −1.05879 1.45730i −0.880934 0.473240i \(-0.843084\pi\)
−0.177854 0.984057i \(-0.556916\pi\)
\(224\) 23.5611 + 32.4291i 1.57424 + 2.16676i
\(225\) −7.41490 13.0391i −0.494327 0.869276i
\(226\) −30.7761 9.99977i −2.04720 0.665175i
\(227\) −23.5648 + 7.65668i −1.56405 + 0.508192i −0.957887 0.287146i \(-0.907293\pi\)
−0.606166 + 0.795338i \(0.707293\pi\)
\(228\) −2.81565 + 13.7385i −0.186471 + 0.909854i
\(229\) 7.91387 24.3564i 0.522963 1.60952i −0.245345 0.969436i \(-0.578901\pi\)
0.768308 0.640080i \(-0.221099\pi\)
\(230\) −2.23087 + 3.00331i −0.147099 + 0.198032i
\(231\) −19.5440 + 21.3000i −1.28590 + 1.40143i
\(232\) 0.353152i 0.0231856i
\(233\) 7.82006 10.7634i 0.512309 0.705133i −0.471998 0.881600i \(-0.656467\pi\)
0.984307 + 0.176467i \(0.0564669\pi\)
\(234\) 1.78663 + 7.84127i 0.116796 + 0.512600i
\(235\) −26.3393 0.278216i −1.71819 0.0181488i
\(236\) −5.71239 + 7.86243i −0.371845 + 0.511801i
\(237\) −4.46804 2.53636i −0.290230 0.164754i
\(238\) 11.0667 + 8.04045i 0.717349 + 0.521185i
\(239\) −19.6089 + 14.2467i −1.26840 + 0.921543i −0.999137 0.0415245i \(-0.986779\pi\)
−0.269258 + 0.963068i \(0.586779\pi\)
\(240\) 5.40666 9.29431i 0.348999 0.599945i
\(241\) −15.8560 + 5.15193i −1.02138 + 0.331865i −0.771375 0.636381i \(-0.780431\pi\)
−0.250000 + 0.968246i \(0.580431\pi\)
\(242\) 16.7938 + 16.1680i 1.07955 + 1.03932i
\(243\) 8.28121 + 13.2069i 0.531240 + 0.847221i
\(244\) 9.96887 13.7210i 0.638191 0.878395i
\(245\) 32.8902 + 24.4311i 2.10128 + 1.56084i
\(246\) −7.45744 4.23334i −0.475469 0.269908i
\(247\) −2.41654 3.32608i −0.153761 0.211634i
\(248\) 5.33721 7.34604i 0.338913 0.466474i
\(249\) −2.63402 + 0.296284i −0.166924 + 0.0187762i
\(250\) 13.3126 + 19.6004i 0.841965 + 1.23964i
\(251\) −10.8130 + 3.51335i −0.682510 + 0.221761i −0.629694 0.776843i \(-0.716820\pi\)
−0.0528160 + 0.998604i \(0.516820\pi\)
\(252\) 36.6690 8.35502i 2.30993 0.526317i
\(253\) −0.230209 2.60829i −0.0144731 0.163982i
\(254\) −12.2853 + 16.9092i −0.770847 + 1.06098i
\(255\) 1.04876 4.85589i 0.0656756 0.304087i
\(256\) 5.54037 0.346273
\(257\) 21.6018 15.6947i 1.34749 0.979006i 0.348353 0.937363i \(-0.386741\pi\)
0.999133 0.0416423i \(-0.0132590\pi\)
\(258\) 5.42334 26.4623i 0.337643 1.64747i
\(259\) 18.3797i 1.14206i
\(260\) −2.10656 6.72418i −0.130644 0.417016i
\(261\) 0.935677 + 0.400342i 0.0579170 + 0.0247805i
\(262\) 19.5516 + 26.9105i 1.20790 + 1.66254i
\(263\) 22.3677 7.26771i 1.37925 0.448146i 0.476828 0.878997i \(-0.341786\pi\)
0.902423 + 0.430851i \(0.141786\pi\)
\(264\) −1.18833 5.86085i −0.0731365 0.360710i
\(265\) −18.3832 13.6551i −1.12927 0.838827i
\(266\) −28.0413 + 20.3732i −1.71932 + 1.24916i
\(267\) −4.41486 2.50617i −0.270185 0.153375i
\(268\) 11.2755 + 15.5194i 0.688761 + 0.947999i
\(269\) 2.68761 0.873258i 0.163867 0.0532435i −0.225935 0.974142i \(-0.572544\pi\)
0.389801 + 0.920899i \(0.372544\pi\)
\(270\) −14.6978 19.7557i −0.894479 1.20230i
\(271\) 25.1337i 1.52676i −0.645948 0.763382i \(-0.723538\pi\)
0.645948 0.763382i \(-0.276462\pi\)
\(272\) 3.38683 1.10045i 0.205356 0.0667243i
\(273\) −5.44288 + 9.58815i −0.329418 + 0.580301i
\(274\) 13.1933i 0.797039i
\(275\) −16.0788 4.05856i −0.969589 0.244740i
\(276\) −1.68172 + 2.96251i −0.101228 + 0.178322i
\(277\) 9.55216 0.573934 0.286967 0.957941i \(-0.407353\pi\)
0.286967 + 0.957941i \(0.407353\pi\)
\(278\) −5.20246 16.0115i −0.312023 0.960308i
\(279\) 13.4130 + 22.4686i 0.803014 + 1.34516i
\(280\) −11.1780 + 3.50186i −0.668013 + 0.209276i
\(281\) −4.53614 13.9608i −0.270604 0.832832i −0.990349 0.138594i \(-0.955742\pi\)
0.719746 0.694238i \(-0.244258\pi\)
\(282\) −42.9691 + 4.83331i −2.55877 + 0.287820i
\(283\) 6.95639 0.413515 0.206757 0.978392i \(-0.433709\pi\)
0.206757 + 0.978392i \(0.433709\pi\)
\(284\) 3.13982 + 4.32159i 0.186314 + 0.256439i
\(285\) 10.8807 + 6.32948i 0.644515 + 0.374926i
\(286\) 7.62460 + 4.57338i 0.450852 + 0.270429i
\(287\) −3.63281 11.1806i −0.214438 0.659972i
\(288\) 9.40031 21.9704i 0.553918 1.29462i
\(289\) −12.4222 + 9.02527i −0.730718 + 0.530898i
\(290\) −1.52358 0.512895i −0.0894677 0.0301182i
\(291\) 24.7314 + 14.0392i 1.44978 + 0.822993i
\(292\) −3.02748 9.31762i −0.177170 0.545272i
\(293\) −7.81485 10.7562i −0.456549 0.628385i 0.517240 0.855840i \(-0.326959\pi\)
−0.973789 + 0.227455i \(0.926959\pi\)
\(294\) 58.4899 + 33.2028i 3.41120 + 1.93643i
\(295\) 5.05251 + 7.11094i 0.294169 + 0.414015i
\(296\) −3.07604 2.23487i −0.178791 0.129899i
\(297\) 16.8755 + 3.49553i 0.979214 + 0.202831i
\(298\) −8.62938 2.80385i −0.499886 0.162423i
\(299\) −0.308603 0.949784i −0.0178470 0.0549274i
\(300\) 14.2130 + 16.2311i 0.820591 + 0.937106i
\(301\) 29.9595 21.7669i 1.72684 1.25462i
\(302\) −7.28139 5.29024i −0.418997 0.304419i
\(303\) −0.0289711 0.257558i −0.00166434 0.0147963i
\(304\) 9.02331i 0.517522i
\(305\) −8.81730 12.4095i −0.504877 0.710567i
\(306\) 0.734050 8.12193i 0.0419629 0.464300i
\(307\) 32.5707 1.85891 0.929454 0.368937i \(-0.120278\pi\)
0.929454 + 0.368937i \(0.120278\pi\)
\(308\) 21.3870 35.6557i 1.21864 2.03167i
\(309\) 2.67715 13.0627i 0.152298 0.743111i
\(310\) −23.9411 33.6949i −1.35977 1.91374i
\(311\) −10.0235 13.7962i −0.568382 0.782310i 0.423980 0.905671i \(-0.360633\pi\)
−0.992362 + 0.123361i \(0.960633\pi\)
\(312\) −0.942853 2.07679i −0.0533786 0.117575i
\(313\) 0.905791i 0.0511983i −0.999672 0.0255992i \(-0.991851\pi\)
0.999672 0.0255992i \(-0.00814936\pi\)
\(314\) 5.19878 + 3.77714i 0.293384 + 0.213156i
\(315\) 3.39346 33.5859i 0.191200 1.89235i
\(316\) 7.02796 + 2.28352i 0.395354 + 0.128458i
\(317\) 8.84756 + 6.42813i 0.496928 + 0.361039i 0.807842 0.589398i \(-0.200635\pi\)
−0.310914 + 0.950438i \(0.600635\pi\)
\(318\) −32.6914 18.5578i −1.83324 1.04067i
\(319\) 1.03536 0.440419i 0.0579689 0.0246588i
\(320\) −8.08190 + 24.0077i −0.451792 + 1.34207i
\(321\) −19.9909 + 18.2657i −1.11579 + 1.01949i
\(322\) −8.00737 + 2.60175i −0.446233 + 0.144990i
\(323\) 1.28827 + 3.96489i 0.0716813 + 0.220612i
\(324\) −15.4821 16.2173i −0.860118 0.900962i
\(325\) −6.32334 0.133599i −0.350756 0.00741074i
\(326\) 12.1530 8.82968i 0.673093 0.489031i
\(327\) 27.2739 3.06786i 1.50825 0.169653i
\(328\) 2.31293 + 0.751515i 0.127710 + 0.0414955i
\(329\) −47.9577 34.8433i −2.64399 1.92097i
\(330\) −27.0109 3.38519i −1.48690 0.186349i
\(331\) 21.5459 15.6540i 1.18427 0.860421i 0.191621 0.981469i \(-0.438625\pi\)
0.992647 + 0.121048i \(0.0386255\pi\)
\(332\) 3.62582 1.17810i 0.198993 0.0646566i
\(333\) 9.40837 5.61647i 0.515576 0.307780i
\(334\) 22.4895 + 16.3396i 1.23057 + 0.894062i
\(335\) 16.4309 5.14750i 0.897717 0.281238i
\(336\) 22.0337 10.0032i 1.20204 0.545720i
\(337\) 6.83356 + 4.96487i 0.372248 + 0.270454i 0.758142 0.652089i \(-0.226107\pi\)
−0.385895 + 0.922543i \(0.626107\pi\)
\(338\) −22.9768 7.46561i −1.24977 0.406076i
\(339\) −13.0564 + 23.0001i −0.709127 + 1.24920i
\(340\) −0.0754697 + 7.14487i −0.00409292 + 0.387485i
\(341\) 28.1930 + 6.48612i 1.52673 + 0.351243i
\(342\) 18.9977 + 8.12840i 1.02728 + 0.439534i
\(343\) 17.6075 + 54.1903i 0.950715 + 2.92600i
\(344\) 7.66077i 0.413041i
\(345\) 2.03854 + 2.27897i 0.109751 + 0.122696i
\(346\) −20.3877 + 14.8125i −1.09605 + 0.796326i
\(347\) −5.58715 7.69006i −0.299934 0.412824i 0.632275 0.774744i \(-0.282121\pi\)
−0.932209 + 0.361920i \(0.882121\pi\)
\(348\) −1.43399 0.293891i −0.0768700 0.0157542i
\(349\) 1.86993 2.57374i 0.100095 0.137769i −0.756031 0.654535i \(-0.772864\pi\)
0.856127 + 0.516766i \(0.172864\pi\)
\(350\) −1.12634 + 53.3104i −0.0602053 + 2.84956i
\(351\) 6.57130 0.143795i 0.350750 0.00767522i
\(352\) −10.3414 24.3109i −0.551196 1.29578i
\(353\) 0.0352068 + 0.0255793i 0.00187387 + 0.00136145i 0.588722 0.808336i \(-0.299631\pi\)
−0.586848 + 0.809697i \(0.699631\pi\)
\(354\) 9.65903 + 10.5714i 0.513372 + 0.561862i
\(355\) 4.57541 1.43339i 0.242837 0.0760765i
\(356\) 6.94431 + 2.25634i 0.368048 + 0.119586i
\(357\) 8.25355 7.54125i 0.436824 0.399125i
\(358\) 11.2089 + 34.4975i 0.592409 + 1.82325i
\(359\) −13.2361 9.61660i −0.698576 0.507545i 0.180892 0.983503i \(-0.442101\pi\)
−0.879468 + 0.475958i \(0.842101\pi\)
\(360\) 5.20833 + 4.65180i 0.274503 + 0.245171i
\(361\) 8.43659 0.444031
\(362\) −30.0978 + 9.77936i −1.58190 + 0.513992i
\(363\) 15.7007 10.7930i 0.824071 0.566487i
\(364\) 4.90031 15.0816i 0.256846 0.790491i
\(365\) −8.79323 0.0928810i −0.460259 0.00486161i
\(366\) −16.8563 18.4484i −0.881092 0.964315i
\(367\) 9.28098 + 3.01557i 0.484463 + 0.157412i 0.541057 0.840986i \(-0.318024\pi\)
−0.0565942 + 0.998397i \(0.518024\pi\)
\(368\) −0.677316 + 2.08456i −0.0353075 + 0.108665i
\(369\) −4.61313 + 5.27617i −0.240150 + 0.274667i
\(370\) −14.1092 + 10.0250i −0.733502 + 0.521173i
\(371\) −15.9253 49.0129i −0.826799 2.54463i
\(372\) −25.3874 27.7854i −1.31628 1.44060i
\(373\) 4.88230 15.0262i 0.252796 0.778026i −0.741460 0.670997i \(-0.765866\pi\)
0.994256 0.107029i \(-0.0341337\pi\)
\(374\) −5.92006 6.79973i −0.306119 0.351606i
\(375\) 17.8776 7.44257i 0.923195 0.384333i
\(376\) 11.6628 3.78947i 0.601462 0.195427i
\(377\) 0.347169 0.252233i 0.0178801 0.0129907i
\(378\) −1.21230 55.4009i −0.0623539 2.84951i
\(379\) −4.64733 + 3.37648i −0.238717 + 0.173438i −0.700712 0.713445i \(-0.747134\pi\)
0.461994 + 0.886883i \(0.347134\pi\)
\(380\) −17.1588 5.77630i −0.880228 0.296318i
\(381\) 11.5225 + 12.6109i 0.590317 + 0.646075i
\(382\) −6.95952 5.05639i −0.356080 0.258707i
\(383\) −15.9965 11.6221i −0.817383 0.593863i 0.0985789 0.995129i \(-0.468570\pi\)
−0.915962 + 0.401266i \(0.868570\pi\)
\(384\) −2.80871 + 13.7046i −0.143331 + 0.699362i
\(385\) −24.2068 28.4040i −1.23369 1.44760i
\(386\) 30.7528 + 9.99218i 1.56528 + 0.508589i
\(387\) −20.2972 8.68443i −1.03177 0.441455i
\(388\) −38.9011 12.6397i −1.97490 0.641685i
\(389\) −27.4920 + 8.93268i −1.39390 + 0.452905i −0.907213 0.420672i \(-0.861794\pi\)
−0.486685 + 0.873577i \(0.661794\pi\)
\(390\) −10.3291 + 1.05150i −0.523034 + 0.0532447i
\(391\) 1.01267i 0.0512129i
\(392\) −18.1406 5.89425i −0.916241 0.297705i
\(393\) 24.7542 11.2383i 1.24869 0.566898i
\(394\) −12.3138 8.94653i −0.620363 0.450720i
\(395\) 3.95512 5.32457i 0.199004 0.267908i
\(396\) −24.7872 0.0520945i −1.24560 0.00261785i
\(397\) −15.2683 + 21.0150i −0.766292 + 1.05471i 0.230372 + 0.973103i \(0.426006\pi\)
−0.996664 + 0.0816082i \(0.973994\pi\)
\(398\) 27.6625i 1.38660i
\(399\) 11.7106 + 25.7944i 0.586261 + 1.29134i
\(400\) 11.0554 + 8.39469i 0.552772 + 0.419734i
\(401\) 33.1794 + 10.7807i 1.65690 + 0.538360i 0.980219 0.197915i \(-0.0634169\pi\)
0.676683 + 0.736275i \(0.263417\pi\)
\(402\) 25.7368 11.6844i 1.28364 0.582766i
\(403\) 11.0336 0.549623
\(404\) 0.115196 + 0.354538i 0.00573123 + 0.0176389i
\(405\) −18.2292 + 8.52611i −0.905819 + 0.423666i
\(406\) −2.12651 2.92689i −0.105537 0.145259i
\(407\) 2.71596 11.8053i 0.134625 0.585169i
\(408\) 0.258520 + 2.29829i 0.0127986 + 0.113782i
\(409\) 0.171494 + 0.236041i 0.00847984 + 0.0116715i 0.813236 0.581934i \(-0.197704\pi\)
−0.804756 + 0.593606i \(0.797704\pi\)
\(410\) 6.60136 8.88706i 0.326018 0.438900i
\(411\) 10.5633 + 2.16490i 0.521049 + 0.106787i
\(412\) 19.1786i 0.944864i
\(413\) 19.6311i 0.965984i
\(414\) 3.77870 + 3.30384i 0.185713 + 0.162375i
\(415\) 0.0361433 3.42176i 0.00177420 0.167968i
\(416\) −5.92260 8.15177i −0.290380 0.399673i
\(417\) −13.6734 + 1.53803i −0.669587 + 0.0753175i
\(418\) 21.0216 8.94213i 1.02820 0.437374i
\(419\) −21.0112 28.9194i −1.02646 1.41280i −0.907572 0.419897i \(-0.862066\pi\)
−0.118891 0.992907i \(-0.537934\pi\)
\(420\) 4.91724 + 48.3031i 0.239937 + 2.35695i
\(421\) 4.20310 + 12.9358i 0.204847 + 0.630453i 0.999720 + 0.0236773i \(0.00753743\pi\)
−0.794873 + 0.606776i \(0.792463\pi\)
\(422\) −48.8211 −2.37657
\(423\) −3.18101 + 35.1964i −0.154666 + 1.71131i
\(424\) 10.1393 + 3.29444i 0.492406 + 0.159992i
\(425\) 6.05634 + 2.11027i 0.293776 + 0.102363i
\(426\) 7.16677 3.25368i 0.347231 0.157641i
\(427\) 34.2589i 1.65790i
\(428\) 22.8929 31.5094i 1.10657 1.52307i
\(429\) 4.91281 5.35421i 0.237193 0.258504i
\(430\) 33.0503 + 11.1260i 1.59383 + 0.536543i
\(431\) 7.07319 + 5.13897i 0.340703 + 0.247536i 0.744959 0.667111i \(-0.232469\pi\)
−0.404255 + 0.914646i \(0.632469\pi\)
\(432\) −11.8536 8.22203i −0.570306 0.395583i
\(433\) −11.3903 3.70094i −0.547384 0.177856i 0.0222529 0.999752i \(-0.492916\pi\)
−0.569637 + 0.821897i \(0.692916\pi\)
\(434\) 93.0213i 4.46517i
\(435\) −0.660656 + 1.13570i −0.0316760 + 0.0544526i
\(436\) −37.5434 + 12.1986i −1.79801 + 0.584207i
\(437\) −2.44036 0.792920i −0.116738 0.0379305i
\(438\) −14.3450 + 1.61357i −0.685430 + 0.0770995i
\(439\) −15.1361 4.91802i −0.722407 0.234724i −0.0753404 0.997158i \(-0.524004\pi\)
−0.647066 + 0.762434i \(0.724004\pi\)
\(440\) 7.69713 0.597491i 0.366946 0.0284843i
\(441\) 36.1815 41.3819i 1.72293 1.97056i
\(442\) −2.78186 2.02114i −0.132320 0.0961359i
\(443\) −29.6541 21.5450i −1.40891 1.02363i −0.993480 0.114006i \(-0.963632\pi\)
−0.415428 0.909626i \(-0.636368\pi\)
\(444\) −11.6347 + 10.6306i −0.552157 + 0.504504i
\(445\) 3.90805 5.26120i 0.185259 0.249405i
\(446\) 46.1192 33.5076i 2.18381 1.58663i
\(447\) −3.66091 + 6.44905i −0.173155 + 0.305030i
\(448\) −46.1202 + 33.5083i −2.17897 + 1.58312i
\(449\) 1.09839 0.356888i 0.0518362 0.0168426i −0.282984 0.959125i \(-0.591324\pi\)
0.334820 + 0.942282i \(0.391324\pi\)
\(450\) 27.6332 15.7140i 1.30264 0.740765i
\(451\) 0.681209 + 7.71818i 0.0320769 + 0.363435i
\(452\) 11.7549 36.1779i 0.552904 1.70166i
\(453\) −5.43045 + 4.96179i −0.255145 + 0.233125i
\(454\) −16.2264 49.9397i −0.761543 2.34379i
\(455\) −11.4262 8.48747i −0.535670 0.397899i
\(456\) −5.74090 1.17657i −0.268842 0.0550981i
\(457\) 11.0596 34.0380i 0.517347 1.59223i −0.261624 0.965170i \(-0.584258\pi\)
0.778971 0.627060i \(-0.215742\pi\)
\(458\) 51.6172 + 16.7715i 2.41192 + 0.783679i
\(459\) −6.38240 1.92045i −0.297905 0.0896390i
\(460\) −3.53044 2.62243i −0.164608 0.122271i
\(461\) −0.349247 + 1.07487i −0.0162660 + 0.0500617i −0.958860 0.283879i \(-0.908379\pi\)
0.942594 + 0.333941i \(0.108379\pi\)
\(462\) −45.1399 41.4186i −2.10010 1.92697i
\(463\) 25.1012 8.15588i 1.16655 0.379036i 0.339198 0.940715i \(-0.389844\pi\)
0.827355 + 0.561679i \(0.189844\pi\)
\(464\) −0.941831 −0.0437234
\(465\) −30.9064 + 13.6395i −1.43325 + 0.632518i
\(466\) 22.8103 + 16.5726i 1.05667 + 0.767713i
\(467\) 0.0210667 + 0.0648368i 0.000974853 + 0.00300029i 0.951543 0.307516i \(-0.0994979\pi\)
−0.950568 + 0.310517i \(0.899498\pi\)
\(468\) −9.21754 + 2.10022i −0.426081 + 0.0970826i
\(469\) 36.8527 + 11.9742i 1.70170 + 0.552916i
\(470\) 0.589610 55.8195i 0.0271967 2.57476i
\(471\) 3.87725 3.54263i 0.178654 0.163236i
\(472\) −3.28547 2.38704i −0.151226 0.109872i
\(473\) −22.4596 + 9.55382i −1.03269 + 0.439285i
\(474\) 5.37517 9.46888i 0.246890 0.434920i
\(475\) −9.82750 + 12.9424i −0.450917 + 0.593838i
\(476\) −9.45168 + 13.0091i −0.433217 + 0.596272i
\(477\) −20.2227 + 23.1293i −0.925936 + 1.05902i
\(478\) −30.1923 41.5562i −1.38097 1.90074i
\(479\) −15.1456 + 11.0039i −0.692020 + 0.502782i −0.877323 0.479900i \(-0.840673\pi\)
0.185304 + 0.982681i \(0.440673\pi\)
\(480\) 26.6670 + 15.5127i 1.21718 + 0.708053i
\(481\) 4.62014i 0.210660i
\(482\) −10.9182 33.6028i −0.497311 1.53057i
\(483\) 0.769168 + 6.83805i 0.0349984 + 0.311142i
\(484\) −19.0058 + 19.7414i −0.863898 + 0.897339i
\(485\) −21.8924 + 29.4725i −0.994081 + 1.33828i
\(486\) −27.9886 + 17.5499i −1.26959 + 0.796082i
\(487\) −7.87384 2.55837i −0.356798 0.115931i 0.125133 0.992140i \(-0.460064\pi\)
−0.481931 + 0.876209i \(0.660064\pi\)
\(488\) 5.73358 + 4.16569i 0.259547 + 0.188572i
\(489\) −5.07532 11.1792i −0.229514 0.505542i
\(490\) −51.7755 + 69.7026i −2.33898 + 3.14884i
\(491\) 5.38185 + 3.91014i 0.242879 + 0.176462i 0.702565 0.711619i \(-0.252038\pi\)
−0.459686 + 0.888082i \(0.652038\pi\)
\(492\) 4.97637 8.76635i 0.224352 0.395218i
\(493\) −0.413846 + 0.134467i −0.0186387 + 0.00605607i
\(494\) 7.04880 5.12125i 0.317140 0.230416i
\(495\) −7.14260 + 21.0709i −0.321036 + 0.947067i
\(496\) −19.5914 14.2340i −0.879679 0.639124i
\(497\) 10.2621 + 3.33437i 0.460320 + 0.149567i
\(498\) −0.627899 5.58214i −0.0281368 0.250142i
\(499\) −12.8170 + 9.31210i −0.573768 + 0.416867i −0.836472 0.548010i \(-0.815386\pi\)
0.262704 + 0.964876i \(0.415386\pi\)
\(500\) −23.0406 + 15.6492i −1.03041 + 0.699855i
\(501\) 16.7726 15.3251i 0.749346 0.684675i
\(502\) −7.44567 22.9154i −0.332316 1.02276i
\(503\) 13.1023 4.25719i 0.584202 0.189819i −0.00198025 0.999998i \(-0.500630\pi\)
0.586182 + 0.810179i \(0.300630\pi\)
\(504\) 3.49131 + 15.3229i 0.155515 + 0.682534i
\(505\) 0.334585 + 0.00353414i 0.0148888 + 0.000157267i
\(506\) 5.52762 0.487870i 0.245733 0.0216884i
\(507\) −9.74763 + 17.1714i −0.432908 + 0.762608i
\(508\) −19.8771 14.4416i −0.881903 0.640740i
\(509\) −14.9002 4.84138i −0.660441 0.214590i −0.0404288 0.999182i \(-0.512872\pi\)
−0.620012 + 0.784592i \(0.712872\pi\)
\(510\) 10.2908 + 2.22257i 0.455686 + 0.0984172i
\(511\) −16.0104 11.6322i −0.708258 0.514580i
\(512\) 27.8951i 1.23280i
\(513\) 9.62537 13.8768i 0.424970 0.612674i
\(514\) 33.2609 + 45.7797i 1.46707 + 2.01925i
\(515\) 16.3148 + 5.49217i 0.718914 + 0.242014i
\(516\) 31.1069 + 6.37524i 1.36941 + 0.280654i
\(517\) 25.6546 + 29.4666i 1.12829 + 1.29594i
\(518\) −38.9512 −1.71142
\(519\) 8.51426 + 18.7541i 0.373735 + 0.823211i
\(520\) 2.80983 0.880269i 0.123219 0.0386024i
\(521\) 36.7712i 1.61098i −0.592612 0.805488i \(-0.701903\pi\)
0.592612 0.805488i \(-0.298097\pi\)
\(522\) −0.848424 + 1.98293i −0.0371345 + 0.0867906i
\(523\) 1.31491 + 0.955335i 0.0574968 + 0.0417739i 0.616162 0.787619i \(-0.288686\pi\)
−0.558666 + 0.829393i \(0.688686\pi\)
\(524\) −31.6338 + 22.9833i −1.38193 + 1.00403i
\(525\) 42.4983 + 9.64953i 1.85478 + 0.421140i
\(526\) 15.4021 + 47.4027i 0.671562 + 2.06686i
\(527\) −10.6408 3.45739i −0.463519 0.150606i
\(528\) −15.6305 + 3.16919i −0.680229 + 0.137921i
\(529\) 18.1031 + 13.1527i 0.787093 + 0.571857i
\(530\) 28.9386 38.9585i 1.25701 1.69225i
\(531\) 10.0490 5.99887i 0.436088 0.260329i
\(532\) −23.9491 32.9631i −1.03832 1.42913i
\(533\) 0.913186 + 2.81050i 0.0395545 + 0.121736i
\(534\) 5.31119 9.35617i 0.229838 0.404881i
\(535\) −20.2484 28.4977i −0.875415 1.23206i
\(536\) −6.48509 + 4.71170i −0.280113 + 0.203514i
\(537\) 29.4598 3.31374i 1.27128 0.142999i
\(538\) 1.85065 + 5.69572i 0.0797872 + 0.245560i
\(539\) −5.34283 60.5349i −0.230132 2.60742i
\(540\) 23.2232 17.2775i 0.999367 0.743506i
\(541\) −5.63811 7.76019i −0.242401 0.333636i 0.670431 0.741972i \(-0.266109\pi\)
−0.912832 + 0.408336i \(0.866109\pi\)
\(542\) 53.2646 2.28791
\(543\) 2.89112 + 25.7026i 0.124070 + 1.10300i
\(544\) 3.15737 + 9.71739i 0.135371 + 0.416630i
\(545\) −0.374245 + 35.4305i −0.0160309 + 1.51768i
\(546\) −20.3197 11.5348i −0.869602 0.493644i
\(547\) −4.56583 14.0522i −0.195221 0.600828i −0.999974 0.00721810i \(-0.997702\pi\)
0.804753 0.593610i \(-0.202298\pi\)
\(548\) −15.5090 −0.662512
\(549\) −17.5367 + 10.4688i −0.748450 + 0.446798i
\(550\) 8.60109 34.0750i 0.366752 1.45296i
\(551\) 1.10258i 0.0469716i
\(552\) −1.23795 0.702741i −0.0526905 0.0299106i
\(553\) 14.1963 4.61266i 0.603688 0.196150i
\(554\) 20.2434i 0.860059i
\(555\) 5.71133 + 12.9416i 0.242433 + 0.549339i
\(556\) 18.8218 6.11559i 0.798224 0.259359i
\(557\) 22.0234 + 30.3126i 0.933161 + 1.28439i 0.958614 + 0.284710i \(0.0918972\pi\)
−0.0254530 + 0.999676i \(0.508103\pi\)
\(558\) −47.6166 + 28.4254i −2.01577 + 1.20334i
\(559\) −7.53098 + 5.47157i −0.318526 + 0.231423i
\(560\) 9.33922 + 29.8109i 0.394654 + 1.25974i
\(561\) −6.41565 + 3.62414i −0.270869 + 0.153011i
\(562\) 29.5864 9.61321i 1.24803 0.405509i
\(563\) −2.21411 3.04747i −0.0933138 0.128435i 0.759807 0.650148i \(-0.225293\pi\)
−0.853121 + 0.521713i \(0.825293\pi\)
\(564\) −5.68164 50.5109i −0.239240 2.12689i
\(565\) −27.4093 20.3598i −1.15312 0.856544i
\(566\) 14.7423i 0.619666i
\(567\) −44.5558 8.12012i −1.87117 0.341013i
\(568\) −1.80586 + 1.31203i −0.0757722 + 0.0550518i
\(569\) 38.0237 1.59404 0.797019 0.603954i \(-0.206409\pi\)
0.797019 + 0.603954i \(0.206409\pi\)
\(570\) −13.4137 + 23.0588i −0.561839 + 0.965828i
\(571\) 1.70531 2.34715i 0.0713649 0.0982253i −0.771842 0.635814i \(-0.780665\pi\)
0.843207 + 0.537589i \(0.180665\pi\)
\(572\) −5.37609 + 8.96285i −0.224785 + 0.374755i
\(573\) −5.19040 + 4.74246i −0.216832 + 0.198119i
\(574\) 23.6945 7.69883i 0.988991 0.321343i
\(575\) −3.24184 + 2.25227i −0.135194 + 0.0939261i
\(576\) 31.2459 + 13.3690i 1.30191 + 0.557040i
\(577\) 0.119441 0.164397i 0.00497241 0.00684393i −0.806524 0.591202i \(-0.798654\pi\)
0.811496 + 0.584358i \(0.198654\pi\)
\(578\) −19.1268 26.3258i −0.795569 1.09501i
\(579\) 13.0465 22.9827i 0.542195 0.955128i
\(580\) 0.602917 1.79100i 0.0250348 0.0743670i
\(581\) 4.52652 6.23022i 0.187792 0.258473i
\(582\) −29.7526 + 52.4120i −1.23328 + 2.17255i
\(583\) 2.98624 + 33.8344i 0.123677 + 1.40128i
\(584\) 3.89355 1.26509i 0.161116 0.0523499i
\(585\) −0.853019 + 8.44256i −0.0352680 + 0.349057i
\(586\) 22.7951 16.5616i 0.941657 0.684154i
\(587\) 12.1636 + 8.83736i 0.502045 + 0.364757i 0.809797 0.586710i \(-0.199577\pi\)
−0.307753 + 0.951466i \(0.599577\pi\)
\(588\) −39.0305 + 68.7559i −1.60959 + 2.83545i
\(589\) 16.6634 22.9352i 0.686605 0.945030i
\(590\) −15.0698 + 10.7075i −0.620416 + 0.440822i
\(591\) −9.18365 + 8.39108i −0.377765 + 0.345163i
\(592\) −5.96025 + 8.20358i −0.244965 + 0.337165i
\(593\) 6.97966i 0.286620i 0.989678 + 0.143310i \(0.0457746\pi\)
−0.989678 + 0.143310i \(0.954225\pi\)
\(594\) −7.40789 + 35.7633i −0.303949 + 1.46739i
\(595\) 8.35985 + 11.7657i 0.342721 + 0.482347i
\(596\) 3.29598 10.1440i 0.135009 0.415514i
\(597\) 22.1481 + 4.53916i 0.906462 + 0.185775i
\(598\) 2.01283 0.654007i 0.0823107 0.0267444i
\(599\) 11.2452 + 3.65377i 0.459465 + 0.149289i 0.529598 0.848249i \(-0.322343\pi\)
−0.0701338 + 0.997538i \(0.522343\pi\)
\(600\) −6.78251 + 5.93920i −0.276895 + 0.242467i
\(601\) 20.0070 + 27.5372i 0.816101 + 1.12327i 0.990353 + 0.138566i \(0.0442492\pi\)
−0.174252 + 0.984701i \(0.555751\pi\)
\(602\) 46.1294 + 63.4916i 1.88009 + 2.58773i
\(603\) −5.13200 22.5236i −0.208991 0.917231i
\(604\) 6.21877 8.55940i 0.253038 0.348277i
\(605\) 11.3509 + 21.8210i 0.461479 + 0.887151i
\(606\) 0.545830 0.0613969i 0.0221728 0.00249408i
\(607\) −5.33284 16.4128i −0.216453 0.666175i −0.999047 0.0436423i \(-0.986104\pi\)
0.782594 0.622533i \(-0.213896\pi\)
\(608\) −25.8894 −1.04996
\(609\) −2.69236 + 1.22232i −0.109100 + 0.0495309i
\(610\) 26.2988 18.6860i 1.06481 0.756576i
\(611\) 12.0552 + 8.75862i 0.487702 + 0.354336i
\(612\) 9.54747 + 0.862889i 0.385934 + 0.0348802i
\(613\) −10.6407 + 32.7488i −0.429774 + 1.32271i 0.468573 + 0.883425i \(0.344768\pi\)
−0.898348 + 0.439285i \(0.855232\pi\)
\(614\) 69.0254i 2.78564i
\(615\) −6.03223 6.74368i −0.243243 0.271931i
\(616\) 14.8995 + 8.93698i 0.600316 + 0.360081i
\(617\) 4.85188 3.52510i 0.195329 0.141915i −0.485822 0.874058i \(-0.661480\pi\)
0.681151 + 0.732143i \(0.261480\pi\)
\(618\) 27.6831 + 5.67354i 1.11358 + 0.228223i
\(619\) 13.0102 0.522924 0.261462 0.965214i \(-0.415795\pi\)
0.261462 + 0.965214i \(0.415795\pi\)
\(620\) 39.6089 28.1432i 1.59073 1.13026i
\(621\) 3.26528 2.48330i 0.131031 0.0996513i
\(622\) 29.2376 21.2423i 1.17232 0.851740i
\(623\) 14.0273 4.55776i 0.561993 0.182603i
\(624\) −5.53865 + 2.51452i −0.221723 + 0.100662i
\(625\) 6.71429 + 24.0815i 0.268571 + 0.963260i
\(626\) 1.91960 0.0767225
\(627\) −3.71010 18.2983i −0.148167 0.730763i
\(628\) −4.44009 + 6.11126i −0.177179 + 0.243866i
\(629\) −1.44773 + 4.45565i −0.0577247 + 0.177658i
\(630\) 71.1770 + 7.19158i 2.83576 + 0.286519i
\(631\) 11.1213 34.2279i 0.442733 1.36259i −0.442218 0.896908i \(-0.645808\pi\)
0.884951 0.465684i \(-0.154192\pi\)
\(632\) −0.954216 + 2.93677i −0.0379567 + 0.116819i
\(633\) −8.01107 + 39.0887i −0.318411 + 1.55364i
\(634\) −13.6228 + 18.7502i −0.541030 + 0.744664i
\(635\) −17.9772 + 12.7733i −0.713405 + 0.506893i
\(636\) 21.8151 38.4294i 0.865024 1.52382i
\(637\) −7.16226 22.0432i −0.283779 0.873383i
\(638\) 0.933358 + 2.19418i 0.0369520 + 0.0868685i
\(639\) −1.42907 6.27199i −0.0565332 0.248116i
\(640\) −17.1165 5.76207i −0.676590 0.227766i
\(641\) −0.870660 0.282895i −0.0343890 0.0111737i 0.291772 0.956488i \(-0.405755\pi\)
−0.326161 + 0.945314i \(0.605755\pi\)
\(642\) −38.7095 42.3657i −1.52774 1.67204i
\(643\) −9.93447 3.22790i −0.391777 0.127296i 0.106503 0.994312i \(-0.466035\pi\)
−0.498280 + 0.867016i \(0.666035\pi\)
\(644\) −3.05841 9.41281i −0.120518 0.370916i
\(645\) 14.3313 24.6362i 0.564295 0.970049i
\(646\) −8.40259 + 2.73017i −0.330595 + 0.107417i
\(647\) 9.52277 29.3081i 0.374379 1.15222i −0.569518 0.821979i \(-0.692870\pi\)
0.943897 0.330240i \(-0.107130\pi\)
\(648\) 6.77673 6.46952i 0.266215 0.254147i
\(649\) 2.90088 12.6091i 0.113869 0.494952i
\(650\) 0.283129 13.4007i 0.0111053 0.525620i
\(651\) −74.4778 15.2639i −2.91901 0.598240i
\(652\) 10.3794 + 14.2861i 0.406490 + 0.559486i
\(653\) −19.7713 −0.773712 −0.386856 0.922140i \(-0.626439\pi\)
−0.386856 + 0.922140i \(0.626439\pi\)
\(654\) 6.50157 + 57.8002i 0.254231 + 2.26017i
\(655\) 10.4923 + 33.4917i 0.409970 + 1.30863i
\(656\) 2.00424 6.16841i 0.0782524 0.240836i
\(657\) −1.06196 + 11.7501i −0.0414311 + 0.458416i
\(658\) 73.8416 101.634i 2.87864 3.96211i
\(659\) 10.2129 + 31.4319i 0.397837 + 1.22441i 0.926730 + 0.375727i \(0.122607\pi\)
−0.528894 + 0.848688i \(0.677393\pi\)
\(660\) 3.97935 31.7518i 0.154896 1.23594i
\(661\) −8.95450 + 27.5591i −0.348290 + 1.07193i 0.611509 + 0.791237i \(0.290563\pi\)
−0.959799 + 0.280688i \(0.909437\pi\)
\(662\) 33.1747 + 45.6610i 1.28937 + 1.77467i
\(663\) −2.07471 + 1.89566i −0.0805751 + 0.0736212i
\(664\) 0.492292 + 1.51512i 0.0191046 + 0.0587981i
\(665\) −34.8991 + 10.9332i −1.35333 + 0.423973i
\(666\) 11.9027 + 19.9387i 0.461220 + 0.772608i
\(667\) 0.0827631 0.254719i 0.00320460 0.00986275i
\(668\) −19.2075 + 26.4368i −0.743159 + 1.02287i
\(669\) −19.2602 42.4238i −0.744643 1.64020i
\(670\) 10.9088 + 34.8212i 0.421445 + 1.34526i
\(671\) −5.06241 + 22.0046i −0.195432 + 0.849478i
\(672\) 28.7009 + 63.2185i 1.10716 + 2.43871i
\(673\) −3.42849 −0.132158 −0.0660792 0.997814i \(-0.521049\pi\)
−0.0660792 + 0.997814i \(0.521049\pi\)
\(674\) −10.5218 + 14.4820i −0.405284 + 0.557826i
\(675\) −8.04713 24.7031i −0.309734 0.950823i
\(676\) 8.77595 27.0096i 0.337537 1.03883i
\(677\) −2.61033 + 3.59282i −0.100323 + 0.138083i −0.856227 0.516599i \(-0.827198\pi\)
0.755904 + 0.654683i \(0.227198\pi\)
\(678\) −48.7430 27.6698i −1.87196 1.06265i
\(679\) −78.5792 + 25.5319i −3.01559 + 0.979826i
\(680\) −2.98563 0.0315365i −0.114494 0.00120937i
\(681\) −42.6470 + 4.79708i −1.63424 + 0.183825i
\(682\) −13.7457 + 59.7479i −0.526350 + 2.28786i
\(683\) −1.09099 + 0.792649i −0.0417455 + 0.0303299i −0.608462 0.793583i \(-0.708213\pi\)
0.566717 + 0.823913i \(0.308213\pi\)
\(684\) −9.55508 + 22.3321i −0.365348 + 0.853889i
\(685\) −4.44130 + 13.1931i −0.169693 + 0.504083i
\(686\) −114.843 + 37.3146i −4.38471 + 1.42468i
\(687\) 21.8980 38.5755i 0.835461 1.47175i
\(688\) 20.4307 0.778914
\(689\) 4.00316 + 12.3205i 0.152508 + 0.469373i
\(690\) −4.82970 + 4.32017i −0.183864 + 0.164466i
\(691\) 25.1249 18.2543i 0.955798 0.694428i 0.00362661 0.999993i \(-0.498846\pi\)
0.952171 + 0.305566i \(0.0988456\pi\)
\(692\) −17.4124 23.9661i −0.661919 0.911053i
\(693\) −40.5689 + 29.3450i −1.54109 + 1.11472i
\(694\) 16.2971 11.8406i 0.618631 0.449462i
\(695\) 0.187622 17.7626i 0.00711691 0.673772i
\(696\) 0.122808 0.599222i 0.00465503 0.0227134i
\(697\) 2.99658i 0.113504i
\(698\) 5.45440 + 3.96286i 0.206452 + 0.149996i
\(699\) 17.0119 15.5437i 0.643449 0.587917i
\(700\) −62.6673 1.32403i −2.36860 0.0500436i
\(701\) 5.71829 + 4.15458i 0.215977 + 0.156916i 0.690514 0.723319i \(-0.257385\pi\)
−0.474537 + 0.880236i \(0.657385\pi\)
\(702\) 0.304738 + 13.9262i 0.0115016 + 0.525611i
\(703\) −9.60377 6.97754i −0.362213 0.263163i
\(704\) 34.5746 14.7073i 1.30308 0.554303i
\(705\) −44.5953 9.63153i −1.67956 0.362744i
\(706\) −0.0542088 + 0.0746120i −0.00204018 + 0.00280806i
\(707\) 0.609200 + 0.442609i 0.0229113 + 0.0166460i
\(708\) −12.4268 + 11.3544i −0.467029 + 0.426723i
\(709\) 43.7522 1.64315 0.821573 0.570103i \(-0.193097\pi\)
0.821573 + 0.570103i \(0.193097\pi\)
\(710\) 3.03771 + 9.69642i 0.114003 + 0.363900i
\(711\) −6.69927 5.85740i −0.251242 0.219670i
\(712\) −0.942858 + 2.90182i −0.0353351 + 0.108750i
\(713\) 5.57117 4.04769i 0.208642 0.151587i
\(714\) 15.9818 + 17.4913i 0.598103 + 0.654596i
\(715\) 6.08492 + 7.13998i 0.227563 + 0.267020i
\(716\) −40.5524 + 13.1763i −1.51551 + 0.492420i
\(717\) −38.2264 + 17.3546i −1.42759 + 0.648120i
\(718\) 20.3800 28.0506i 0.760574 1.04684i
\(719\) −23.4473 7.61849i −0.874437 0.284122i −0.162791 0.986661i \(-0.552050\pi\)
−0.711646 + 0.702539i \(0.752050\pi\)
\(720\) 12.4060 13.8903i 0.462345 0.517659i
\(721\) 22.7710 + 31.3416i 0.848037 + 1.16722i
\(722\) 17.8792i 0.665396i
\(723\) −28.6958 + 3.22780i −1.06721 + 0.120043i
\(724\) −11.4958 35.3805i −0.427238 1.31490i
\(725\) −1.35090 1.02577i −0.0501710 0.0380962i
\(726\) 22.8731 + 33.2736i 0.848900 + 1.23490i
\(727\) −14.1608 4.60114i −0.525196 0.170647i 0.0344059 0.999408i \(-0.489046\pi\)
−0.559602 + 0.828761i \(0.689046\pi\)
\(728\) 6.30215 + 2.04769i 0.233573 + 0.0758925i
\(729\) 9.45875 + 25.2890i 0.350324 + 0.936629i
\(730\) 0.196838 18.6350i 0.00728529 0.689714i
\(731\) 8.97737 2.91692i 0.332040 0.107886i
\(732\) 21.6864 19.8148i 0.801554 0.732378i
\(733\) 11.1904 34.4404i 0.413326 1.27209i −0.500414 0.865786i \(-0.666819\pi\)
0.913740 0.406300i \(-0.133181\pi\)
\(734\) −6.39075 + 19.6687i −0.235887 + 0.725985i
\(735\) 47.3117 + 52.8917i 1.74512 + 1.95094i
\(736\) −5.98097 1.94334i −0.220462 0.0716323i
\(737\) −21.9012 13.1368i −0.806742 0.483899i
\(738\) −11.1815 9.77638i −0.411597 0.359873i
\(739\) 42.1967i 1.55223i −0.630592 0.776115i \(-0.717188\pi\)
0.630592 0.776115i \(-0.282812\pi\)
\(740\) −11.7845 16.5856i −0.433208 0.609699i
\(741\) −2.94370 6.48399i −0.108140 0.238195i
\(742\) 103.871 33.7496i 3.81321 1.23899i
\(743\) 38.4993 + 12.5092i 1.41240 + 0.458917i 0.913180 0.407557i \(-0.133619\pi\)
0.499222 + 0.866474i \(0.333619\pi\)
\(744\) 11.6107 10.6086i 0.425668 0.388931i
\(745\) −7.68535 5.70873i −0.281570 0.209152i
\(746\) 31.8442 + 10.3468i 1.16590 + 0.378823i
\(747\) −4.57239 0.413247i −0.167295 0.0151199i
\(748\) 7.99320 6.95913i 0.292260 0.254451i
\(749\) 78.6735i 2.87467i
\(750\) 15.7727 + 37.8870i 0.575936 + 1.38344i
\(751\) −14.9482 10.8605i −0.545466 0.396304i 0.280645 0.959812i \(-0.409452\pi\)
−0.826111 + 0.563507i \(0.809452\pi\)
\(752\) −10.1062 31.1038i −0.368537 1.13424i
\(753\) −19.5691 + 2.20120i −0.713136 + 0.0802161i
\(754\) 0.534544 + 0.735737i 0.0194669 + 0.0267940i
\(755\) −5.50040 7.74129i −0.200180 0.281735i
\(756\) 65.1247 1.42508i 2.36856 0.0518296i
\(757\) 11.7963 3.83286i 0.428745 0.139308i −0.0866921 0.996235i \(-0.527630\pi\)
0.515437 + 0.856928i \(0.327630\pi\)
\(758\) −7.15561 9.84885i −0.259903 0.357726i
\(759\) 0.516416 4.50576i 0.0187447 0.163549i
\(760\) 2.41374 7.17015i 0.0875557 0.260089i
\(761\) 26.8546 0.973479 0.486739 0.873547i \(-0.338186\pi\)
0.486739 + 0.873547i \(0.338186\pi\)
\(762\) −26.7256 + 24.4191i −0.968166 + 0.884611i
\(763\) −46.8697 + 64.5106i −1.69680 + 2.33544i
\(764\) 5.94387 8.18104i 0.215042 0.295980i
\(765\) 3.46814 7.87468i 0.125391 0.284710i
\(766\) 24.6302 33.9005i 0.889925 1.22488i
\(767\) 4.93471i 0.178182i
\(768\) 9.40080 + 1.92666i 0.339222 + 0.0695222i
\(769\) 6.04642 + 8.32218i 0.218040 + 0.300106i 0.903999 0.427534i \(-0.140617\pi\)
−0.685960 + 0.727639i \(0.740617\pi\)
\(770\) 60.1952 51.3003i 2.16929 1.84873i
\(771\) 42.1114 19.1184i 1.51661 0.688533i
\(772\) −11.7460 + 36.1504i −0.422747 + 1.30108i
\(773\) −43.2805 + 31.4451i −1.55669 + 1.13100i −0.618032 + 0.786153i \(0.712070\pi\)
−0.938658 + 0.344848i \(0.887930\pi\)
\(774\) 18.4045 43.0149i 0.661535 1.54614i
\(775\) −12.5979 41.7536i −0.452531 1.49984i
\(776\) 5.28177 16.2556i 0.189604 0.583542i
\(777\) −6.39152 + 31.1864i −0.229294 + 1.11880i
\(778\) −18.9306 58.2623i −0.678694 2.08880i
\(779\) 7.22124 + 2.34632i 0.258728 + 0.0840658i
\(780\) −1.23606 12.1420i −0.0442579 0.434754i
\(781\) −6.09869 3.65811i −0.218228 0.130897i
\(782\) −2.14610 −0.0767443
\(783\) 1.44842 + 1.00467i 0.0517624 + 0.0359041i
\(784\) −15.7196 + 48.3798i −0.561413 + 1.72785i
\(785\) 3.92718 + 5.52714i 0.140167 + 0.197272i
\(786\) 23.8168 + 52.4603i 0.849516 + 1.87120i
\(787\) 8.21858 0.292961 0.146480 0.989214i \(-0.453205\pi\)
0.146480 + 0.989214i \(0.453205\pi\)
\(788\) 10.5168 14.4751i 0.374646 0.515656i
\(789\) 40.4805 4.55338i 1.44114 0.162105i
\(790\) 11.2841 + 8.38189i 0.401470 + 0.298214i
\(791\) −23.7446 73.0784i −0.844261 2.59837i
\(792\) 0.0217687 10.3578i 0.000773518 0.368049i
\(793\) 8.61172i 0.305811i
\(794\) −44.5359 32.3572i −1.58052 1.14832i
\(795\) −26.4437 29.5625i −0.937861 1.04847i
\(796\) −32.5178 −1.15256
\(797\) −1.44091 + 1.04688i −0.0510397 + 0.0370825i −0.613013 0.790073i \(-0.710043\pi\)
0.561973 + 0.827156i \(0.310043\pi\)
\(798\) −54.6648 + 24.8176i −1.93511 + 0.878533i
\(799\) −8.88147 12.2243i −0.314204 0.432465i
\(800\) −24.0858 + 31.7200i −0.851563 + 1.12147i
\(801\) −6.61953 5.78768i −0.233890 0.204498i
\(802\) −22.8469 + 70.3155i −0.806751 + 2.48293i
\(803\) 8.56464 + 9.83727i 0.302240 + 0.347150i
\(804\) 13.7352 + 30.2541i 0.484405 + 1.06698i
\(805\) −8.88306 0.0938298i −0.313087 0.00330707i
\(806\) 23.3829i 0.823629i
\(807\) 4.86397 0.547116i 0.171220 0.0192594i
\(808\) −0.148151 + 0.0481371i −0.00521192 + 0.00169346i
\(809\) 40.6477 1.42910 0.714549 0.699585i \(-0.246632\pi\)
0.714549 + 0.699585i \(0.246632\pi\)
\(810\) −18.0689 38.6323i −0.634878 1.35740i
\(811\) −16.6144 22.8678i −0.583411 0.802997i 0.410653 0.911792i \(-0.365301\pi\)
−0.994064 + 0.108795i \(0.965301\pi\)
\(812\) 3.44061 2.49975i 0.120742 0.0877239i
\(813\) 8.74021 42.6464i 0.306532 1.49568i
\(814\) 25.0185 + 5.75579i 0.876897 + 0.201740i
\(815\) 15.1251 4.73843i 0.529811 0.165980i
\(816\) 6.12938 0.689455i 0.214571 0.0241357i
\(817\) 23.9179i 0.836780i
\(818\) −0.500230 + 0.363438i −0.0174901 + 0.0127073i
\(819\) −12.5696 + 14.3763i −0.439219 + 0.502347i
\(820\) 10.4469 + 7.76001i 0.364821 + 0.270991i
\(821\) 2.38128 0.0831073 0.0415536 0.999136i \(-0.486769\pi\)
0.0415536 + 0.999136i \(0.486769\pi\)
\(822\) −4.58796 + 22.3862i −0.160024 + 0.780810i
\(823\) 25.3819i 0.884756i −0.896829 0.442378i \(-0.854135\pi\)
0.896829 0.442378i \(-0.145865\pi\)
\(824\) −8.01418 −0.279187
\(825\) −25.8709 12.4779i −0.900709 0.434424i
\(826\) −41.6032 −1.44756
\(827\) 38.8467i 1.35083i −0.737438 0.675415i \(-0.763964\pi\)
0.737438 0.675415i \(-0.236036\pi\)
\(828\) −3.88373 + 4.44193i −0.134969 + 0.154368i
\(829\) 10.3589 0.359780 0.179890 0.983687i \(-0.442426\pi\)
0.179890 + 0.983687i \(0.442426\pi\)
\(830\) 7.25156 + 0.0765966i 0.251705 + 0.00265871i
\(831\) 16.2079 + 3.32175i 0.562247 + 0.115230i
\(832\) 11.5933 8.42303i 0.401926 0.292016i
\(833\) 23.5027i 0.814319i
\(834\) −3.25946 28.9772i −0.112866 1.00340i
\(835\) 16.9887 + 23.9100i 0.587917 + 0.827438i
\(836\) 10.5116 + 24.7112i 0.363552 + 0.854655i
\(837\) 14.9455 + 42.7887i 0.516591 + 1.47899i
\(838\) 61.2874 44.5279i 2.11714 1.53819i
\(839\) 15.4933 + 21.3247i 0.534888 + 0.736210i 0.987866 0.155312i \(-0.0496381\pi\)
−0.452977 + 0.891522i \(0.649638\pi\)
\(840\) −20.1844 + 2.05477i −0.696428 + 0.0708962i
\(841\) −28.8849 −0.996032
\(842\) −27.4142 + 8.90742i −0.944756 + 0.306970i
\(843\) −2.84200 25.2659i −0.0978836 0.870204i
\(844\) 57.3900i 1.97545i
\(845\) −20.4632 15.2002i −0.703956 0.522902i
\(846\) −74.5899 6.74135i −2.56445 0.231772i
\(847\) −7.61984 + 54.8271i −0.261821 + 1.88388i
\(848\) 8.78605 27.0407i 0.301714 0.928581i
\(849\) 11.8035 + 2.41907i 0.405095 + 0.0830224i
\(850\) −4.47219 + 12.8349i −0.153395 + 0.440233i
\(851\) −1.69491 2.33284i −0.0581006 0.0799686i
\(852\) 3.82476 + 8.42466i 0.131034 + 0.288624i
\(853\) 24.9947 18.1597i 0.855803 0.621777i −0.0709372 0.997481i \(-0.522599\pi\)
0.926740 + 0.375704i \(0.122599\pi\)
\(854\) 72.6031 2.48443
\(855\) 16.2611 + 14.5235i 0.556116 + 0.496692i
\(856\) 13.1668 + 9.56627i 0.450033 + 0.326968i
\(857\) 4.54844i 0.155372i 0.996978 + 0.0776859i \(0.0247531\pi\)
−0.996978 + 0.0776859i \(0.975247\pi\)
\(858\) 11.3469 + 10.4115i 0.387377 + 0.355442i
\(859\) −1.25755 3.87035i −0.0429072 0.132055i 0.927308 0.374299i \(-0.122117\pi\)
−0.970215 + 0.242244i \(0.922117\pi\)
\(860\) −13.0788 + 38.8513i −0.445983 + 1.32482i
\(861\) −2.27604 20.2344i −0.0775672 0.689587i
\(862\) −10.8908 + 14.9898i −0.370941 + 0.510556i
\(863\) −35.5231 −1.20922 −0.604610 0.796521i \(-0.706671\pi\)
−0.604610 + 0.796521i \(0.706671\pi\)
\(864\) 23.5904 34.0100i 0.802563 1.15704i
\(865\) −25.3737 + 7.94911i −0.862731 + 0.270278i
\(866\) 7.84321 24.1389i 0.266523 0.820274i
\(867\) −24.2163 + 10.9941i −0.822429 + 0.373379i
\(868\) 109.348 3.71152
\(869\) −9.79994 + 0.864946i −0.332440 + 0.0293413i
\(870\) −2.40683 1.40009i −0.0815990 0.0474676i
\(871\) −9.26374 3.00997i −0.313890 0.101989i
\(872\) −5.09743 15.6883i −0.172621 0.531272i
\(873\) 37.0817 + 32.4218i 1.25503 + 1.09731i
\(874\) 1.68039 5.17172i 0.0568402 0.174936i
\(875\) −19.0723 + 52.9303i −0.644761 + 1.78937i
\(876\) −1.89678 16.8628i −0.0640864 0.569740i
\(877\) −8.83152 + 6.41648i −0.298219 + 0.216669i −0.726825 0.686823i \(-0.759005\pi\)
0.428606 + 0.903492i \(0.359005\pi\)
\(878\) 10.4225 32.0772i 0.351742 1.08255i
\(879\) −9.51965 20.9686i −0.321090 0.707252i
\(880\) −1.59347 20.5277i −0.0537158 0.691989i
\(881\) −3.14050 4.32253i −0.105806 0.145630i 0.752830 0.658215i \(-0.228688\pi\)
−0.858637 + 0.512585i \(0.828688\pi\)
\(882\) 87.6984 + 76.6777i 2.95296 + 2.58187i
\(883\) 20.5036i 0.690001i 0.938603 + 0.345000i \(0.112121\pi\)
−0.938603 + 0.345000i \(0.887879\pi\)
\(884\) 2.37589 3.27013i 0.0799097 0.109986i
\(885\) 6.10020 + 13.8227i 0.205056 + 0.464646i
\(886\) 45.6591 62.8444i 1.53395 2.11130i
\(887\) −3.63727 + 5.00627i −0.122128 + 0.168094i −0.865703 0.500558i \(-0.833128\pi\)
0.743576 + 0.668652i \(0.233128\pi\)
\(888\) −4.44219 4.86178i −0.149070 0.163151i
\(889\) −49.6296 −1.66452
\(890\) 11.1498 + 8.28212i 0.373742 + 0.277617i
\(891\) 27.4184 + 11.7996i 0.918552 + 0.395300i
\(892\) 39.3888 + 54.2140i 1.31883 + 1.81522i
\(893\) 36.4126 11.8312i 1.21850 0.395915i
\(894\) −13.6671 7.75838i −0.457097 0.259479i
\(895\) −0.404239 + 38.2701i −0.0135122 + 1.27923i
\(896\) −23.8900 32.8818i −0.798110 1.09850i
\(897\) −0.193347 1.71889i −0.00645567 0.0573922i
\(898\) 0.756335 + 2.32776i 0.0252392 + 0.0776783i
\(899\) 2.39393 + 1.73929i 0.0798419 + 0.0580086i
\(900\) 18.4721 + 32.4833i 0.615736 + 1.08278i
\(901\) 13.1362i 0.437631i
\(902\) −16.3567 + 1.44365i −0.544620 + 0.0480683i
\(903\) 58.4042 26.5152i 1.94357 0.882372i
\(904\) 15.1176 + 4.91202i 0.502806 + 0.163371i
\(905\) −33.3893 0.352684i −1.10990 0.0117236i
\(906\) −10.5153 11.5085i −0.349346 0.382344i
\(907\) −20.0135 6.50277i −0.664537 0.215921i −0.0427238 0.999087i \(-0.513604\pi\)
−0.621813 + 0.783166i \(0.713604\pi\)
\(908\) 58.7050 19.0744i 1.94819 0.633007i
\(909\) 0.0404079 0.447095i 0.00134025 0.0148292i
\(910\) 17.9871 24.2150i 0.596265 0.802720i
\(911\) 27.2463i 0.902709i 0.892345 + 0.451354i \(0.149059\pi\)
−0.892345 + 0.451354i \(0.850941\pi\)
\(912\) −3.13784 + 15.3106i −0.103904 + 0.506984i
\(913\) −3.82803 + 3.33281i −0.126689 + 0.110300i
\(914\) 72.1350 + 23.4381i 2.38601 + 0.775263i
\(915\) −10.6456 24.1225i −0.351934 0.797464i
\(916\) −19.7151 + 60.6770i −0.651407 + 2.00482i
\(917\) −24.4074 + 75.1183i −0.806004 + 2.48062i
\(918\) 4.06991 13.5259i 0.134327 0.446421i
\(919\) −34.9657 + 11.3610i −1.15341 + 0.374766i −0.822427 0.568871i \(-0.807381\pi\)
−0.330984 + 0.943636i \(0.607381\pi\)
\(920\) 1.09583 1.47526i 0.0361286 0.0486380i
\(921\) 55.2654 + 11.3264i 1.82106 + 0.373218i
\(922\) −2.27792 0.740141i −0.0750193 0.0243752i
\(923\) −2.57961 0.838167i −0.0849090 0.0275886i
\(924\) 48.6883 53.0627i 1.60173 1.74564i
\(925\) −17.4837 + 5.27518i −0.574859 + 0.173447i
\(926\) 17.2843 + 53.1957i 0.567999 + 1.74812i
\(927\) 9.08507 21.2336i 0.298393 0.697403i
\(928\) 2.70228i 0.0887066i
\(929\) 19.5688 + 26.9342i 0.642032 + 0.883681i 0.998722 0.0505418i \(-0.0160948\pi\)
−0.356690 + 0.934223i \(0.616095\pi\)
\(930\) −28.9056 65.4984i −0.947850 2.14778i
\(931\) −56.6373 18.4026i −1.85621 0.603120i
\(932\) −19.4814 + 26.8139i −0.638135 + 0.878318i
\(933\) −12.2101 26.8948i −0.399742 0.880496i
\(934\) −0.137405 + 0.0446457i −0.00449604 + 0.00146085i
\(935\) −3.63095 8.79248i −0.118745 0.287545i
\(936\) −0.877617 3.85173i −0.0286858 0.125898i
\(937\) 0.881543 0.640478i 0.0287987 0.0209235i −0.573293 0.819351i \(-0.694334\pi\)
0.602092 + 0.798427i \(0.294334\pi\)
\(938\) −25.3763 + 78.1001i −0.828564 + 2.55006i
\(939\) 0.314987 1.53693i 0.0102792 0.0501558i
\(940\) 65.6168 + 0.693096i 2.14019 + 0.0226063i
\(941\) −19.3512 −0.630833 −0.315416 0.948953i \(-0.602144\pi\)
−0.315416 + 0.948953i \(0.602144\pi\)
\(942\) 7.50771 + 8.21685i 0.244614 + 0.267719i
\(943\) 1.49213 + 1.08409i 0.0485904 + 0.0353030i
\(944\) −6.36606 + 8.76213i −0.207198 + 0.285183i
\(945\) 17.4374 55.8080i 0.567239 1.81543i
\(946\) −20.2469 47.5974i −0.658284 1.54752i
\(947\) −30.2795 21.9994i −0.983953 0.714884i −0.0253643 0.999678i \(-0.508075\pi\)
−0.958589 + 0.284795i \(0.908075\pi\)
\(948\) 11.1308 + 6.31861i 0.361513 + 0.205219i
\(949\) 4.02456 + 2.92402i 0.130643 + 0.0949176i
\(950\) −27.4281 20.8269i −0.889886 0.675714i
\(951\) 12.7770 + 13.9839i 0.414323 + 0.453458i
\(952\) −5.43612 3.94957i −0.176186 0.128006i
\(953\) 15.7481i 0.510132i −0.966924 0.255066i \(-0.917903\pi\)
0.966924 0.255066i \(-0.0820973\pi\)
\(954\) −49.0168 42.8570i −1.58698 1.38755i
\(955\) −5.25725 7.39909i −0.170121 0.239429i
\(956\) 48.8500 35.4916i 1.57992 1.14788i
\(957\) 1.90993 0.387252i 0.0617394 0.0125181i
\(958\) −23.3200 32.0973i −0.753436 1.03702i
\(959\) −25.3447 + 18.4140i −0.818424 + 0.594620i
\(960\) −22.0619 + 37.9254i −0.712043 + 1.22404i
\(961\) 13.9314 + 42.8765i 0.449400 + 1.38311i
\(962\) 9.79123 0.315682
\(963\) −40.2721 + 24.0410i −1.29775 + 0.774711i
\(964\) 39.5007 12.8346i 1.27223 0.413373i
\(965\) 27.3885 + 20.3444i 0.881668 + 0.654908i
\(966\) −14.4915 + 1.63006i −0.466257 + 0.0524462i
\(967\) −39.7903 + 28.9093i −1.27957 + 0.929661i −0.999540 0.0303303i \(-0.990344\pi\)
−0.280029 + 0.959992i \(0.590344\pi\)
\(968\) −8.24936 7.94193i −0.265144 0.255263i
\(969\) 0.807131 + 7.17555i 0.0259288 + 0.230512i
\(970\) −62.4596 46.3954i −2.00546 1.48967i
\(971\) −36.9053 + 11.9912i −1.18435 + 0.384817i −0.833980 0.551795i \(-0.813943\pi\)
−0.350366 + 0.936613i \(0.613943\pi\)
\(972\) −20.6303 32.9011i −0.661716 1.05530i
\(973\) 23.4974 32.3414i 0.753293 1.03682i
\(974\) 5.42181 16.6866i 0.173726 0.534674i
\(975\) −10.6829 2.42562i −0.342126 0.0776820i
\(976\) 11.1096 15.2911i 0.355610 0.489455i
\(977\) 50.0818 1.60226 0.801129 0.598492i \(-0.204233\pi\)
0.801129 + 0.598492i \(0.204233\pi\)
\(978\) 23.6915 10.7559i 0.757572 0.343934i
\(979\) −9.68330 + 0.854651i −0.309480 + 0.0273148i
\(980\) −81.9366 60.8630i −2.61737 1.94420i
\(981\) 47.3447 + 4.27896i 1.51160 + 0.136617i
\(982\) −8.28656 + 11.4055i −0.264435 + 0.363963i
\(983\) 3.62985 11.1715i 0.115774 0.356317i −0.876333 0.481705i \(-0.840018\pi\)
0.992108 + 0.125388i \(0.0400177\pi\)
\(984\) 3.66319 + 2.07947i 0.116778 + 0.0662912i
\(985\) −9.30194 13.0916i −0.296384 0.417133i
\(986\) −0.284968 0.877042i −0.00907524 0.0279307i
\(987\) −69.2570 75.7987i −2.20448 2.41270i
\(988\) 6.02012 + 8.28598i 0.191526 + 0.263612i
\(989\) −1.79534 + 5.52550i −0.0570886 + 0.175701i
\(990\) −44.6545 15.1369i −1.41921 0.481084i
\(991\) 11.6938 + 35.9899i 0.371466 + 1.14326i 0.945832 + 0.324657i \(0.105249\pi\)
−0.574365 + 0.818599i \(0.694751\pi\)
\(992\) 40.8397 56.2111i 1.29666 1.78470i
\(993\) 42.0023 19.0689i 1.33290 0.605132i
\(994\) −7.06636 + 21.7480i −0.224131 + 0.689805i
\(995\) −9.31209 + 27.6621i −0.295213 + 0.876946i
\(996\) 6.56191 0.738106i 0.207922 0.0233878i
\(997\) −33.2016 −1.05151 −0.525753 0.850637i \(-0.676216\pi\)
−0.525753 + 0.850637i \(0.676216\pi\)
\(998\) −19.7347 27.1624i −0.624690 0.859812i
\(999\) 17.9171 6.25818i 0.566871 0.198000i
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 825.2.s.a.479.98 yes 464
3.2 odd 2 inner 825.2.s.a.479.19 464
11.2 odd 10 825.2.bu.a.629.19 yes 464
25.19 even 10 825.2.bu.a.644.98 yes 464
33.2 even 10 825.2.bu.a.629.98 yes 464
75.44 odd 10 825.2.bu.a.644.19 yes 464
275.244 odd 10 inner 825.2.s.a.794.98 yes 464
825.794 even 10 inner 825.2.s.a.794.19 yes 464
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
825.2.s.a.479.19 464 3.2 odd 2 inner
825.2.s.a.479.98 yes 464 1.1 even 1 trivial
825.2.s.a.794.19 yes 464 825.794 even 10 inner
825.2.s.a.794.98 yes 464 275.244 odd 10 inner
825.2.bu.a.629.19 yes 464 11.2 odd 10
825.2.bu.a.629.98 yes 464 33.2 even 10
825.2.bu.a.644.19 yes 464 75.44 odd 10
825.2.bu.a.644.98 yes 464 25.19 even 10