Properties

Label 525.2.t.i.26.9
Level $525$
Weight $2$
Character 525.26
Analytic conductor $4.192$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(26,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.t (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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} - 330 x^{11} + 879 x^{10} - 990 x^{9} + 2439 x^{8} - 3969 x^{7} + 4779 x^{6} + \cdots + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.9
Root \(-0.983931 - 1.42544i\) of defining polynomial
Character \(\chi\) \(=\) 525.26
Dual form 525.2.t.i.101.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.94891 + 1.12521i) q^{2} +(0.742502 + 1.56483i) q^{3} +(1.53217 + 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(1.42897 - 2.22667i) q^{7} +2.39522i q^{8} +(-1.89738 + 2.32378i) q^{9} +O(q^{10})\) \(q+(1.94891 + 1.12521i) q^{2} +(0.742502 + 1.56483i) q^{3} +(1.53217 + 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(1.42897 - 2.22667i) q^{7} +2.39522i q^{8} +(-1.89738 + 2.32378i) q^{9} +(-1.64925 + 0.952197i) q^{11} +(-3.01511 + 4.36805i) q^{12} +5.07948i q^{13} +(5.29039 - 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(-2.22839 - 3.85968i) q^{17} +(-6.31256 + 2.39390i) q^{18} +(3.85670 + 2.22667i) q^{19} +(4.54537 + 0.582783i) q^{21} -4.28567 q^{22} +(-2.46489 - 1.42310i) q^{23} +(-3.74811 + 1.77846i) q^{24} +(-5.71546 + 9.89947i) q^{26} +(-5.04513 - 1.24366i) q^{27} +(8.09857 + 0.380555i) q^{28} -8.82675i q^{29} +(4.81162 - 2.77799i) q^{31} +(5.58785 - 3.22615i) q^{32} +(-2.71460 - 1.87379i) q^{33} -10.0296i q^{34} +(-9.07397 - 1.47484i) q^{36} +(2.32292 - 4.02342i) q^{37} +(5.01092 + 8.67917i) q^{38} +(-7.94852 + 3.77153i) q^{39} +0.250819 q^{41} +(8.20277 + 6.25027i) q^{42} -9.23735 q^{43} +(-5.05389 - 2.91786i) q^{44} +(-3.20257 - 5.54701i) q^{46} +(-1.53816 + 2.66417i) q^{47} +(1.27491 + 0.102934i) q^{48} +(-2.91610 - 6.36367i) q^{49} +(4.38516 - 6.35287i) q^{51} +(-13.4799 + 7.78265i) q^{52} +(-2.09711 + 1.21077i) q^{53} +(-8.43313 - 8.10060i) q^{54} +(5.33336 + 3.42269i) q^{56} +(-0.620744 + 7.68839i) q^{57} +(9.93190 - 17.2026i) q^{58} +(6.95983 + 12.0548i) q^{59} +(-1.51554 - 0.874995i) q^{61} +12.5032 q^{62} +(2.46299 + 7.54544i) q^{63} +13.0434 q^{64} +(-3.18212 - 6.70634i) q^{66} +(4.14868 + 7.18573i) q^{67} +(6.82855 - 11.8274i) q^{68} +(0.396729 - 4.91379i) q^{69} -9.68436i q^{71} +(-5.56596 - 4.54465i) q^{72} +(5.47076 - 3.15855i) q^{73} +(9.05434 - 5.22752i) q^{74} +13.6466i q^{76} +(-0.236503 + 5.03300i) q^{77} +(-19.7347 - 1.59334i) q^{78} +(1.59436 - 2.76150i) q^{79} +(-1.79990 - 8.81818i) q^{81} +(0.488824 + 0.282223i) q^{82} -8.98988 q^{83} +(5.41770 + 12.9554i) q^{84} +(-18.0028 - 10.3939i) q^{86} +(13.8124 - 6.55388i) q^{87} +(-2.28072 - 3.95033i) q^{88} +(-5.43599 + 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} -8.72178i q^{92} +(7.91972 + 5.46670i) q^{93} +(-5.99548 + 3.46149i) q^{94} +(9.19736 + 6.34861i) q^{96} +8.94486i q^{97} +(1.47721 - 15.6835i) q^{98} +(0.916566 - 5.63918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.94891 + 1.12521i 1.37809 + 0.795640i 0.991929 0.126791i \(-0.0404679\pi\)
0.386160 + 0.922432i \(0.373801\pi\)
\(3\) 0.742502 + 1.56483i 0.428684 + 0.903455i
\(4\) 1.53217 + 2.65380i 0.766087 + 1.32690i
\(5\) 0 0
\(6\) −0.313682 + 3.88518i −0.128060 + 1.58612i
\(7\) 1.42897 2.22667i 0.540099 0.841602i
\(8\) 2.39522i 0.846839i
\(9\) −1.89738 + 2.32378i −0.632460 + 0.774593i
\(10\) 0 0
\(11\) −1.64925 + 0.952197i −0.497269 + 0.287098i −0.727585 0.686018i \(-0.759357\pi\)
0.230316 + 0.973116i \(0.426024\pi\)
\(12\) −3.01511 + 4.36805i −0.870386 + 1.26095i
\(13\) 5.07948i 1.40879i 0.709806 + 0.704397i \(0.248783\pi\)
−0.709806 + 0.704397i \(0.751217\pi\)
\(14\) 5.29039 2.73170i 1.41392 0.730078i
\(15\) 0 0
\(16\) 0.369233 0.639530i 0.0923082 0.159882i
\(17\) −2.22839 3.85968i −0.540463 0.936110i −0.998877 0.0473710i \(-0.984916\pi\)
0.458414 0.888739i \(-0.348418\pi\)
\(18\) −6.31256 + 2.39390i −1.48788 + 0.564248i
\(19\) 3.85670 + 2.22667i 0.884788 + 0.510833i 0.872234 0.489088i \(-0.162670\pi\)
0.0125541 + 0.999921i \(0.496004\pi\)
\(20\) 0 0
\(21\) 4.54537 + 0.582783i 0.991880 + 0.127174i
\(22\) −4.28567 −0.913708
\(23\) −2.46489 1.42310i −0.513965 0.296738i 0.220497 0.975388i \(-0.429232\pi\)
−0.734462 + 0.678650i \(0.762565\pi\)
\(24\) −3.74811 + 1.77846i −0.765080 + 0.363026i
\(25\) 0 0
\(26\) −5.71546 + 9.89947i −1.12089 + 1.94145i
\(27\) −5.04513 1.24366i −0.970935 0.239343i
\(28\) 8.09857 + 0.380555i 1.53049 + 0.0719181i
\(29\) 8.82675i 1.63909i −0.573018 0.819543i \(-0.694227\pi\)
0.573018 0.819543i \(-0.305773\pi\)
\(30\) 0 0
\(31\) 4.81162 2.77799i 0.864193 0.498942i −0.00122124 0.999999i \(-0.500389\pi\)
0.865414 + 0.501057i \(0.167055\pi\)
\(32\) 5.58785 3.22615i 0.987802 0.570308i
\(33\) −2.71460 1.87379i −0.472551 0.326185i
\(34\) 10.0296i 1.72006i
\(35\) 0 0
\(36\) −9.07397 1.47484i −1.51233 0.245807i
\(37\) 2.32292 4.02342i 0.381886 0.661446i −0.609446 0.792828i \(-0.708608\pi\)
0.991332 + 0.131382i \(0.0419414\pi\)
\(38\) 5.01092 + 8.67917i 0.812878 + 1.40795i
\(39\) −7.94852 + 3.77153i −1.27278 + 0.603928i
\(40\) 0 0
\(41\) 0.250819 0.0391713 0.0195857 0.999808i \(-0.493765\pi\)
0.0195857 + 0.999808i \(0.493765\pi\)
\(42\) 8.20277 + 6.25027i 1.26572 + 0.964437i
\(43\) −9.23735 −1.40868 −0.704341 0.709862i \(-0.748757\pi\)
−0.704341 + 0.709862i \(0.748757\pi\)
\(44\) −5.05389 2.91786i −0.761902 0.439885i
\(45\) 0 0
\(46\) −3.20257 5.54701i −0.472193 0.817863i
\(47\) −1.53816 + 2.66417i −0.224364 + 0.388610i −0.956128 0.292948i \(-0.905364\pi\)
0.731765 + 0.681557i \(0.238697\pi\)
\(48\) 1.27491 + 0.102934i 0.184018 + 0.0148572i
\(49\) −2.91610 6.36367i −0.416586 0.909096i
\(50\) 0 0
\(51\) 4.38516 6.35287i 0.614045 0.889579i
\(52\) −13.4799 + 7.78265i −1.86933 + 1.07926i
\(53\) −2.09711 + 1.21077i −0.288060 + 0.166312i −0.637067 0.770809i \(-0.719852\pi\)
0.349007 + 0.937120i \(0.386519\pi\)
\(54\) −8.43313 8.10060i −1.14760 1.10235i
\(55\) 0 0
\(56\) 5.33336 + 3.42269i 0.712701 + 0.457377i
\(57\) −0.620744 + 7.68839i −0.0822196 + 1.01835i
\(58\) 9.93190 17.2026i 1.30412 2.25881i
\(59\) 6.95983 + 12.0548i 0.906093 + 1.56940i 0.819443 + 0.573160i \(0.194283\pi\)
0.0866494 + 0.996239i \(0.472384\pi\)
\(60\) 0 0
\(61\) −1.51554 0.874995i −0.194044 0.112032i 0.399830 0.916589i \(-0.369069\pi\)
−0.593875 + 0.804558i \(0.702402\pi\)
\(62\) 12.5032 1.58791
\(63\) 2.46299 + 7.54544i 0.310308 + 0.950636i
\(64\) 13.0434 1.63042
\(65\) 0 0
\(66\) −3.18212 6.70634i −0.391692 0.825494i
\(67\) 4.14868 + 7.18573i 0.506842 + 0.877876i 0.999969 + 0.00791862i \(0.00252060\pi\)
−0.493127 + 0.869958i \(0.664146\pi\)
\(68\) 6.82855 11.8274i 0.828084 1.43428i
\(69\) 0.396729 4.91379i 0.0477606 0.591551i
\(70\) 0 0
\(71\) 9.68436i 1.14932i −0.818392 0.574661i \(-0.805134\pi\)
0.818392 0.574661i \(-0.194866\pi\)
\(72\) −5.56596 4.54465i −0.655955 0.535592i
\(73\) 5.47076 3.15855i 0.640304 0.369680i −0.144427 0.989515i \(-0.546134\pi\)
0.784732 + 0.619835i \(0.212801\pi\)
\(74\) 9.05434 5.22752i 1.05255 0.607687i
\(75\) 0 0
\(76\) 13.6466i 1.56537i
\(77\) −0.236503 + 5.03300i −0.0269520 + 0.573564i
\(78\) −19.7347 1.59334i −2.23452 0.180410i
\(79\) 1.59436 2.76150i 0.179379 0.310694i −0.762289 0.647237i \(-0.775924\pi\)
0.941668 + 0.336543i \(0.109258\pi\)
\(80\) 0 0
\(81\) −1.79990 8.81818i −0.199988 0.979798i
\(82\) 0.488824 + 0.282223i 0.0539816 + 0.0311663i
\(83\) −8.98988 −0.986768 −0.493384 0.869812i \(-0.664240\pi\)
−0.493384 + 0.869812i \(0.664240\pi\)
\(84\) 5.41770 + 12.9554i 0.591120 + 1.41355i
\(85\) 0 0
\(86\) −18.0028 10.3939i −1.94129 1.12080i
\(87\) 13.8124 6.55388i 1.48084 0.702650i
\(88\) −2.28072 3.95033i −0.243126 0.421106i
\(89\) −5.43599 + 9.41541i −0.576213 + 0.998031i 0.419695 + 0.907665i \(0.362137\pi\)
−0.995909 + 0.0903658i \(0.971196\pi\)
\(90\) 0 0
\(91\) 11.3103 + 7.25841i 1.18564 + 0.760889i
\(92\) 8.72178i 0.909308i
\(93\) 7.91972 + 5.46670i 0.821237 + 0.566871i
\(94\) −5.99548 + 3.46149i −0.618387 + 0.357026i
\(95\) 0 0
\(96\) 9.19736 + 6.34861i 0.938702 + 0.647952i
\(97\) 8.94486i 0.908213i 0.890947 + 0.454107i \(0.150041\pi\)
−0.890947 + 0.454107i \(0.849959\pi\)
\(98\) 1.47721 15.6835i 0.149220 1.58427i
\(99\) 0.916566 5.63918i 0.0921184 0.566759i
\(100\) 0 0
\(101\) 4.71346 + 8.16395i 0.469007 + 0.812344i 0.999372 0.0354254i \(-0.0112786\pi\)
−0.530365 + 0.847769i \(0.677945\pi\)
\(102\) 15.6946 7.44698i 1.55399 0.737361i
\(103\) −5.45692 3.15056i −0.537686 0.310433i 0.206454 0.978456i \(-0.433808\pi\)
−0.744141 + 0.668023i \(0.767141\pi\)
\(104\) −12.1665 −1.19302
\(105\) 0 0
\(106\) −5.44944 −0.529297
\(107\) −14.3818 8.30336i −1.39034 0.802716i −0.396991 0.917822i \(-0.629946\pi\)
−0.993353 + 0.115107i \(0.963279\pi\)
\(108\) −4.42957 15.2943i −0.426236 1.47169i
\(109\) 9.20177 + 15.9379i 0.881370 + 1.52658i 0.849818 + 0.527076i \(0.176712\pi\)
0.0315518 + 0.999502i \(0.489955\pi\)
\(110\) 0 0
\(111\) 8.02073 + 0.647577i 0.761294 + 0.0614653i
\(112\) −0.896399 1.73603i −0.0847018 0.164039i
\(113\) 4.37678i 0.411733i −0.978580 0.205866i \(-0.933999\pi\)
0.978580 0.205866i \(-0.0660012\pi\)
\(114\) −9.86079 + 14.2855i −0.923548 + 1.33796i
\(115\) 0 0
\(116\) 23.4245 13.5241i 2.17491 1.25568i
\(117\) −11.8036 9.63771i −1.09124 0.891007i
\(118\) 31.3250i 2.88370i
\(119\) −11.7785 0.553477i −1.07973 0.0507372i
\(120\) 0 0
\(121\) −3.68664 + 6.38545i −0.335149 + 0.580495i
\(122\) −1.96910 3.41058i −0.178274 0.308779i
\(123\) 0.186234 + 0.392489i 0.0167921 + 0.0353895i
\(124\) 14.7445 + 8.51273i 1.32409 + 0.764466i
\(125\) 0 0
\(126\) −3.69002 + 17.4768i −0.328733 + 1.55696i
\(127\) −12.7846 −1.13445 −0.567223 0.823564i \(-0.691982\pi\)
−0.567223 + 0.823564i \(0.691982\pi\)
\(128\) 14.2447 + 8.22419i 1.25907 + 0.726922i
\(129\) −6.85875 14.4549i −0.603880 1.27268i
\(130\) 0 0
\(131\) 2.59617 4.49669i 0.226828 0.392878i −0.730038 0.683406i \(-0.760498\pi\)
0.956866 + 0.290528i \(0.0938311\pi\)
\(132\) 0.813434 10.0750i 0.0708003 0.876916i
\(133\) 10.4692 5.40576i 0.907791 0.468739i
\(134\) 18.6725i 1.61306i
\(135\) 0 0
\(136\) 9.24478 5.33748i 0.792734 0.457685i
\(137\) −11.6770 + 6.74170i −0.997630 + 0.575982i −0.907546 0.419952i \(-0.862047\pi\)
−0.0900838 + 0.995934i \(0.528713\pi\)
\(138\) 6.30221 9.13015i 0.536480 0.777210i
\(139\) 2.02188i 0.171493i −0.996317 0.0857466i \(-0.972672\pi\)
0.996317 0.0857466i \(-0.0273276\pi\)
\(140\) 0 0
\(141\) −5.31106 0.428804i −0.447272 0.0361118i
\(142\) 10.8969 18.8740i 0.914447 1.58387i
\(143\) −4.83667 8.37736i −0.404463 0.700550i
\(144\) 0.785551 + 2.07145i 0.0654626 + 0.172621i
\(145\) 0 0
\(146\) 14.2161 1.17653
\(147\) 7.79285 9.28825i 0.642743 0.766082i
\(148\) 14.2365 1.17023
\(149\) −1.11049 0.641143i −0.0909750 0.0525244i 0.453822 0.891092i \(-0.350060\pi\)
−0.544797 + 0.838568i \(0.683393\pi\)
\(150\) 0 0
\(151\) −3.50501 6.07085i −0.285233 0.494039i 0.687432 0.726248i \(-0.258738\pi\)
−0.972666 + 0.232210i \(0.925404\pi\)
\(152\) −5.33336 + 9.23766i −0.432593 + 0.749273i
\(153\) 13.1971 + 2.14500i 1.06693 + 0.173413i
\(154\) −6.12408 + 9.54277i −0.493493 + 0.768978i
\(155\) 0 0
\(156\) −22.1874 15.3152i −1.77641 1.22620i
\(157\) 2.17668 1.25671i 0.173718 0.100296i −0.410620 0.911807i \(-0.634688\pi\)
0.584338 + 0.811511i \(0.301354\pi\)
\(158\) 6.21452 3.58795i 0.494401 0.285442i
\(159\) −3.45175 2.38262i −0.273742 0.188954i
\(160\) 0 0
\(161\) −6.69103 + 3.45492i −0.527327 + 0.272286i
\(162\) 6.41443 19.2111i 0.503965 1.50937i
\(163\) −1.73224 + 3.00033i −0.135680 + 0.235004i −0.925857 0.377874i \(-0.876655\pi\)
0.790177 + 0.612879i \(0.209989\pi\)
\(164\) 0.384298 + 0.665624i 0.0300087 + 0.0519765i
\(165\) 0 0
\(166\) −17.5205 10.1155i −1.35985 0.785112i
\(167\) −3.29851 −0.255246 −0.127623 0.991823i \(-0.540735\pi\)
−0.127623 + 0.991823i \(0.540735\pi\)
\(168\) −1.39589 + 10.8872i −0.107696 + 0.839963i
\(169\) −12.8011 −0.984703
\(170\) 0 0
\(171\) −12.4919 + 4.73729i −0.955281 + 0.362269i
\(172\) −14.1532 24.5141i −1.07917 1.86918i
\(173\) −8.72018 + 15.1038i −0.662983 + 1.14832i 0.316845 + 0.948477i \(0.397376\pi\)
−0.979828 + 0.199843i \(0.935957\pi\)
\(174\) 34.2935 + 2.76879i 2.59979 + 0.209901i
\(175\) 0 0
\(176\) 1.40633i 0.106006i
\(177\) −13.6960 + 19.8417i −1.02945 + 1.49139i
\(178\) −21.1885 + 12.2332i −1.58815 + 0.916917i
\(179\) 19.5347 11.2784i 1.46009 0.842985i 0.461077 0.887360i \(-0.347463\pi\)
0.999015 + 0.0443755i \(0.0141298\pi\)
\(180\) 0 0
\(181\) 3.48204i 0.258818i 0.991591 + 0.129409i \(0.0413080\pi\)
−0.991591 + 0.129409i \(0.958692\pi\)
\(182\) 13.8756 + 26.8725i 1.02853 + 1.99192i
\(183\) 0.243929 3.02124i 0.0180317 0.223336i
\(184\) 3.40865 5.90396i 0.251289 0.435245i
\(185\) 0 0
\(186\) 9.28369 + 19.5654i 0.680713 + 1.43461i
\(187\) 7.35035 + 4.24373i 0.537511 + 0.310332i
\(188\) −9.42692 −0.687529
\(189\) −9.97855 + 9.45667i −0.725833 + 0.687871i
\(190\) 0 0
\(191\) −8.27801 4.77931i −0.598976 0.345819i 0.169663 0.985502i \(-0.445732\pi\)
−0.768638 + 0.639683i \(0.779065\pi\)
\(192\) 9.68474 + 20.4107i 0.698936 + 1.47301i
\(193\) −2.88510 4.99714i −0.207674 0.359702i 0.743307 0.668950i \(-0.233256\pi\)
−0.950981 + 0.309248i \(0.899923\pi\)
\(194\) −10.0648 + 17.4328i −0.722611 + 1.25160i
\(195\) 0 0
\(196\) 12.4200 17.4890i 0.887140 1.24922i
\(197\) 4.34500i 0.309568i 0.987948 + 0.154784i \(0.0494682\pi\)
−0.987948 + 0.154784i \(0.950532\pi\)
\(198\) 8.13155 9.95895i 0.577884 0.707752i
\(199\) 7.53338 4.34940i 0.534027 0.308321i −0.208628 0.977995i \(-0.566900\pi\)
0.742655 + 0.669674i \(0.233566\pi\)
\(200\) 0 0
\(201\) −8.16403 + 11.8274i −0.575846 + 0.834240i
\(202\) 21.2144i 1.49264i
\(203\) −19.6542 12.6131i −1.37946 0.885269i
\(204\) 23.5781 + 1.90364i 1.65080 + 0.133282i
\(205\) 0 0
\(206\) −7.09004 12.2803i −0.493987 0.855610i
\(207\) 7.98381 3.02769i 0.554913 0.210439i
\(208\) 3.24848 + 1.87551i 0.225242 + 0.130043i
\(209\) −8.48091 −0.586637
\(210\) 0 0
\(211\) 10.6975 0.736446 0.368223 0.929737i \(-0.379966\pi\)
0.368223 + 0.929737i \(0.379966\pi\)
\(212\) −6.42627 3.71021i −0.441358 0.254818i
\(213\) 15.1544 7.19066i 1.03836 0.492696i
\(214\) −18.6860 32.3650i −1.27735 2.21243i
\(215\) 0 0
\(216\) 2.97885 12.0842i 0.202685 0.822225i
\(217\) 0.689986 14.6835i 0.0468393 0.996784i
\(218\) 41.4155i 2.80501i
\(219\) 9.00464 + 6.21558i 0.608477 + 0.420010i
\(220\) 0 0
\(221\) 19.6052 11.3190i 1.31879 0.761402i
\(222\) 14.9031 + 10.2870i 1.00023 + 0.690421i
\(223\) 16.9483i 1.13494i −0.823394 0.567471i \(-0.807922\pi\)
0.823394 0.567471i \(-0.192078\pi\)
\(224\) 0.801297 17.0523i 0.0535389 1.13936i
\(225\) 0 0
\(226\) 4.92477 8.52996i 0.327591 0.567404i
\(227\) −1.21572 2.10568i −0.0806899 0.139759i 0.822857 0.568249i \(-0.192379\pi\)
−0.903546 + 0.428490i \(0.859046\pi\)
\(228\) −21.3546 + 10.1326i −1.41424 + 0.671049i
\(229\) 0.204081 + 0.117826i 0.0134861 + 0.00778618i 0.506728 0.862106i \(-0.330855\pi\)
−0.493242 + 0.869892i \(0.664188\pi\)
\(230\) 0 0
\(231\) −8.05139 + 3.36693i −0.529743 + 0.221528i
\(232\) 21.1420 1.38804
\(233\) 9.59675 + 5.54068i 0.628704 + 0.362982i 0.780250 0.625468i \(-0.215092\pi\)
−0.151546 + 0.988450i \(0.548425\pi\)
\(234\) −12.1598 32.0645i −0.794909 2.09612i
\(235\) 0 0
\(236\) −21.3273 + 36.9401i −1.38829 + 2.40459i
\(237\) 5.50510 + 0.444470i 0.357594 + 0.0288714i
\(238\) −22.3325 14.3319i −1.44760 0.929001i
\(239\) 9.67610i 0.625895i 0.949770 + 0.312948i \(0.101316\pi\)
−0.949770 + 0.312948i \(0.898684\pi\)
\(240\) 0 0
\(241\) −13.9240 + 8.03902i −0.896923 + 0.517839i −0.876201 0.481947i \(-0.839930\pi\)
−0.0207223 + 0.999785i \(0.506597\pi\)
\(242\) −14.3699 + 8.29646i −0.923731 + 0.533316i
\(243\) 12.4625 9.36405i 0.799471 0.600704i
\(244\) 5.36258i 0.343304i
\(245\) 0 0
\(246\) −0.0786773 + 0.974478i −0.00501628 + 0.0621304i
\(247\) −11.3103 + 19.5901i −0.719659 + 1.24649i
\(248\) 6.65390 + 11.5249i 0.422523 + 0.731832i
\(249\) −6.67501 14.0676i −0.423012 0.891500i
\(250\) 0 0
\(251\) −14.3809 −0.907716 −0.453858 0.891074i \(-0.649953\pi\)
−0.453858 + 0.891074i \(0.649953\pi\)
\(252\) −16.2504 + 18.0972i −1.02368 + 1.14002i
\(253\) 5.42031 0.340772
\(254\) −24.9160 14.3852i −1.56337 0.902611i
\(255\) 0 0
\(256\) 5.46442 + 9.46465i 0.341526 + 0.591541i
\(257\) 2.37985 4.12202i 0.148451 0.257125i −0.782204 0.623022i \(-0.785905\pi\)
0.930655 + 0.365898i \(0.119238\pi\)
\(258\) 2.89759 35.8888i 0.180396 2.23434i
\(259\) −5.63944 10.9217i −0.350417 0.678642i
\(260\) 0 0
\(261\) 20.5114 + 16.7477i 1.26962 + 1.03666i
\(262\) 10.1194 5.84244i 0.625179 0.360947i
\(263\) 4.89251 2.82469i 0.301685 0.174178i −0.341514 0.939877i \(-0.610940\pi\)
0.643200 + 0.765698i \(0.277607\pi\)
\(264\) 4.48815 6.50207i 0.276226 0.400175i
\(265\) 0 0
\(266\) 26.4861 + 1.24459i 1.62396 + 0.0763108i
\(267\) −18.7697 1.51543i −1.14869 0.0927427i
\(268\) −12.7130 + 22.0196i −0.776570 + 1.34506i
\(269\) −0.356044 0.616686i −0.0217084 0.0376000i 0.854967 0.518682i \(-0.173577\pi\)
−0.876676 + 0.481082i \(0.840244\pi\)
\(270\) 0 0
\(271\) 2.80074 + 1.61701i 0.170133 + 0.0982264i 0.582649 0.812724i \(-0.302016\pi\)
−0.412516 + 0.910951i \(0.635350\pi\)
\(272\) −3.29117 −0.199557
\(273\) −2.96024 + 23.0881i −0.179162 + 1.39736i
\(274\) −30.3432 −1.83310
\(275\) 0 0
\(276\) 13.6481 6.47594i 0.821518 0.389806i
\(277\) 11.4567 + 19.8435i 0.688364 + 1.19228i 0.972367 + 0.233459i \(0.0750043\pi\)
−0.284002 + 0.958824i \(0.591662\pi\)
\(278\) 2.27503 3.94046i 0.136447 0.236333i
\(279\) −2.67404 + 16.4521i −0.160091 + 0.984959i
\(280\) 0 0
\(281\) 12.0342i 0.717900i 0.933357 + 0.358950i \(0.116865\pi\)
−0.933357 + 0.358950i \(0.883135\pi\)
\(282\) −9.86831 6.81174i −0.587649 0.405633i
\(283\) 15.5030 8.95065i 0.921556 0.532061i 0.0374249 0.999299i \(-0.488084\pi\)
0.884131 + 0.467239i \(0.154751\pi\)
\(284\) 25.7004 14.8381i 1.52504 0.880481i
\(285\) 0 0
\(286\) 21.7690i 1.28723i
\(287\) 0.358412 0.558491i 0.0211564 0.0329667i
\(288\) −3.10542 + 19.1062i −0.182989 + 1.12584i
\(289\) −1.43141 + 2.47928i −0.0842008 + 0.145840i
\(290\) 0 0
\(291\) −13.9972 + 6.64158i −0.820529 + 0.389336i
\(292\) 16.7643 + 9.67889i 0.981058 + 0.566414i
\(293\) −8.87318 −0.518377 −0.259188 0.965827i \(-0.583455\pi\)
−0.259188 + 0.965827i \(0.583455\pi\)
\(294\) 25.6388 9.33343i 1.49528 0.544337i
\(295\) 0 0
\(296\) 9.63697 + 5.56391i 0.560138 + 0.323396i
\(297\) 9.50491 2.75284i 0.551531 0.159736i
\(298\) −1.44283 2.49906i −0.0835811 0.144767i
\(299\) 7.22863 12.5204i 0.418043 0.724071i
\(300\) 0 0
\(301\) −13.1999 + 20.5685i −0.760828 + 1.18555i
\(302\) 15.7754i 0.907773i
\(303\) −9.27544 + 13.4375i −0.532860 + 0.771965i
\(304\) 2.84804 1.64432i 0.163346 0.0943081i
\(305\) 0 0
\(306\) 23.3065 + 19.0299i 1.33234 + 1.08787i
\(307\) 8.99889i 0.513594i −0.966465 0.256797i \(-0.917333\pi\)
0.966465 0.256797i \(-0.0826671\pi\)
\(308\) −13.7190 + 7.08380i −0.781710 + 0.403637i
\(309\) 0.878303 10.8784i 0.0499649 0.618853i
\(310\) 0 0
\(311\) −3.29851 5.71318i −0.187041 0.323965i 0.757221 0.653159i \(-0.226556\pi\)
−0.944262 + 0.329194i \(0.893223\pi\)
\(312\) −9.03364 19.0385i −0.511429 1.07784i
\(313\) −16.7007 9.64215i −0.943979 0.545007i −0.0527736 0.998607i \(-0.516806\pi\)
−0.891205 + 0.453600i \(0.850139\pi\)
\(314\) 5.65621 0.319198
\(315\) 0 0
\(316\) 9.77132 0.549680
\(317\) 16.6152 + 9.59278i 0.933202 + 0.538784i 0.887823 0.460186i \(-0.152217\pi\)
0.0453790 + 0.998970i \(0.485550\pi\)
\(318\) −4.04622 8.52745i −0.226901 0.478195i
\(319\) 8.40481 + 14.5576i 0.470579 + 0.815066i
\(320\) 0 0
\(321\) 2.31479 28.6704i 0.129199 1.60022i
\(322\) −16.9277 0.795441i −0.943345 0.0443282i
\(323\) 19.8475i 1.10435i
\(324\) 20.6440 18.2876i 1.14689 1.01598i
\(325\) 0 0
\(326\) −6.75198 + 3.89826i −0.373958 + 0.215905i
\(327\) −18.1078 + 26.2332i −1.00136 + 1.45070i
\(328\) 0.600767i 0.0331718i
\(329\) 3.73425 + 7.23199i 0.205876 + 0.398713i
\(330\) 0 0
\(331\) −5.98753 + 10.3707i −0.329104 + 0.570026i −0.982334 0.187134i \(-0.940080\pi\)
0.653230 + 0.757160i \(0.273413\pi\)
\(332\) −13.7741 23.8574i −0.755950 1.30934i
\(333\) 4.94207 + 13.0319i 0.270824 + 0.714144i
\(334\) −6.42851 3.71150i −0.351752 0.203084i
\(335\) 0 0
\(336\) 2.05101 2.69172i 0.111892 0.146845i
\(337\) 12.6992 0.691769 0.345885 0.938277i \(-0.387579\pi\)
0.345885 + 0.938277i \(0.387579\pi\)
\(338\) −24.9483 14.4039i −1.35701 0.783469i
\(339\) 6.84891 3.24977i 0.371982 0.176503i
\(340\) 0 0
\(341\) −5.29039 + 9.16323i −0.286491 + 0.496217i
\(342\) −29.6761 4.82341i −1.60470 0.260820i
\(343\) −18.3368 2.60028i −0.990095 0.140402i
\(344\) 22.1255i 1.19293i
\(345\) 0 0
\(346\) −33.9897 + 19.6240i −1.82730 + 1.05499i
\(347\) 4.85815 2.80486i 0.260799 0.150573i −0.363900 0.931438i \(-0.618555\pi\)
0.624699 + 0.780866i \(0.285222\pi\)
\(348\) 38.5556 + 26.6136i 2.06680 + 1.42664i
\(349\) 33.8725i 1.81315i 0.422041 + 0.906577i \(0.361314\pi\)
−0.422041 + 0.906577i \(0.638686\pi\)
\(350\) 0 0
\(351\) 6.31717 25.6266i 0.337186 1.36785i
\(352\) −6.14386 + 10.6415i −0.327469 + 0.567192i
\(353\) 18.3706 + 31.8188i 0.977767 + 1.69354i 0.670485 + 0.741923i \(0.266086\pi\)
0.307281 + 0.951619i \(0.400581\pi\)
\(354\) −49.0182 + 23.2589i −2.60529 + 1.23619i
\(355\) 0 0
\(356\) −33.3155 −1.76572
\(357\) −7.87948 18.8423i −0.417026 0.997242i
\(358\) 50.7619 2.68285
\(359\) 21.1388 + 12.2045i 1.11566 + 0.644127i 0.940290 0.340375i \(-0.110554\pi\)
0.175371 + 0.984502i \(0.443887\pi\)
\(360\) 0 0
\(361\) 0.416104 + 0.720714i 0.0219002 + 0.0379323i
\(362\) −3.91801 + 6.78619i −0.205926 + 0.356674i
\(363\) −12.7295 1.02775i −0.668124 0.0539429i
\(364\) −1.93302 + 41.1365i −0.101318 + 2.15614i
\(365\) 0 0
\(366\) 3.87491 5.61366i 0.202545 0.293431i
\(367\) 17.8968 10.3327i 0.934203 0.539362i 0.0460646 0.998938i \(-0.485332\pi\)
0.888138 + 0.459576i \(0.151999\pi\)
\(368\) −1.82024 + 1.05091i −0.0948864 + 0.0547827i
\(369\) −0.475899 + 0.582848i −0.0247743 + 0.0303418i
\(370\) 0 0
\(371\) −0.300725 + 6.39971i −0.0156129 + 0.332256i
\(372\) −2.37316 + 29.3933i −0.123042 + 1.52397i
\(373\) −10.4361 + 18.0759i −0.540363 + 0.935936i 0.458520 + 0.888684i \(0.348380\pi\)
−0.998883 + 0.0472520i \(0.984954\pi\)
\(374\) 9.55013 + 16.5413i 0.493825 + 0.855331i
\(375\) 0 0
\(376\) −6.38128 3.68424i −0.329090 0.190000i
\(377\) 44.8353 2.30914
\(378\) −30.0880 + 7.20230i −1.54756 + 0.370446i
\(379\) −27.0384 −1.38887 −0.694435 0.719556i \(-0.744345\pi\)
−0.694435 + 0.719556i \(0.744345\pi\)
\(380\) 0 0
\(381\) −9.49256 20.0056i −0.486319 1.02492i
\(382\) −10.7554 18.6289i −0.550295 0.953138i
\(383\) 3.16723 5.48580i 0.161838 0.280311i −0.773690 0.633564i \(-0.781591\pi\)
0.935528 + 0.353253i \(0.114924\pi\)
\(384\) −2.29272 + 28.3970i −0.117000 + 1.44913i
\(385\) 0 0
\(386\) 12.9853i 0.660936i
\(387\) 17.5268 21.4656i 0.890935 1.09116i
\(388\) −23.7379 + 13.7051i −1.20511 + 0.695770i
\(389\) 10.7869 6.22784i 0.546919 0.315764i −0.200959 0.979600i \(-0.564406\pi\)
0.747879 + 0.663836i \(0.231073\pi\)
\(390\) 0 0
\(391\) 12.6849i 0.641503i
\(392\) 15.2424 6.98471i 0.769858 0.352781i
\(393\) 8.96422 + 0.723752i 0.452185 + 0.0365085i
\(394\) −4.88902 + 8.46803i −0.246305 + 0.426613i
\(395\) 0 0
\(396\) 16.3696 6.20782i 0.822604 0.311955i
\(397\) −24.6611 14.2381i −1.23771 0.714591i −0.269082 0.963117i \(-0.586720\pi\)
−0.968625 + 0.248527i \(0.920054\pi\)
\(398\) 19.5759 0.981250
\(399\) 16.2325 + 12.3686i 0.812640 + 0.619207i
\(400\) 0 0
\(401\) −12.7515 7.36207i −0.636779 0.367644i 0.146594 0.989197i \(-0.453169\pi\)
−0.783373 + 0.621552i \(0.786502\pi\)
\(402\) −29.2192 + 13.8644i −1.45732 + 0.691491i
\(403\) 14.1108 + 24.4405i 0.702907 + 1.21747i
\(404\) −14.4437 + 25.0172i −0.718600 + 1.24465i
\(405\) 0 0
\(406\) −24.1120 46.6970i −1.19666 2.31753i
\(407\) 8.84751i 0.438555i
\(408\) 15.2165 + 10.5034i 0.753330 + 0.519997i
\(409\) −0.810609 + 0.468005i −0.0400820 + 0.0231414i −0.519907 0.854223i \(-0.674033\pi\)
0.479825 + 0.877364i \(0.340700\pi\)
\(410\) 0 0
\(411\) −19.2198 13.2667i −0.948041 0.654399i
\(412\) 19.3088i 0.951276i
\(413\) 36.7874 + 1.72865i 1.81019 + 0.0850615i
\(414\) 18.9665 + 3.08273i 0.932154 + 0.151508i
\(415\) 0 0
\(416\) 16.3872 + 28.3834i 0.803446 + 1.39161i
\(417\) 3.16389 1.50125i 0.154936 0.0735164i
\(418\) −16.5286 9.54277i −0.808438 0.466752i
\(419\) −30.1515 −1.47299 −0.736497 0.676440i \(-0.763522\pi\)
−0.736497 + 0.676440i \(0.763522\pi\)
\(420\) 0 0
\(421\) 36.3685 1.77249 0.886245 0.463217i \(-0.153305\pi\)
0.886245 + 0.463217i \(0.153305\pi\)
\(422\) 20.8485 + 12.0369i 1.01489 + 0.585946i
\(423\) −3.27247 8.62929i −0.159113 0.419571i
\(424\) −2.90005 5.02304i −0.140839 0.243940i
\(425\) 0 0
\(426\) 37.6255 + 3.03780i 1.82296 + 0.147182i
\(427\) −4.11397 + 2.12426i −0.199089 + 0.102800i
\(428\) 50.8887i 2.45980i
\(429\) 9.51789 13.7888i 0.459528 0.665728i
\(430\) 0 0
\(431\) −11.9349 + 6.89063i −0.574885 + 0.331910i −0.759098 0.650976i \(-0.774360\pi\)
0.184213 + 0.982886i \(0.441026\pi\)
\(432\) −2.65819 + 2.76731i −0.127892 + 0.133142i
\(433\) 1.16840i 0.0561499i 0.999606 + 0.0280750i \(0.00893771\pi\)
−0.999606 + 0.0280750i \(0.991062\pi\)
\(434\) 17.8667 27.8406i 0.857630 1.33639i
\(435\) 0 0
\(436\) −28.1974 + 48.8394i −1.35041 + 2.33898i
\(437\) −6.33756 10.9770i −0.303167 0.525100i
\(438\) 10.5555 + 22.2457i 0.504359 + 1.06294i
\(439\) 2.50353 + 1.44541i 0.119487 + 0.0689858i 0.558552 0.829469i \(-0.311357\pi\)
−0.439065 + 0.898455i \(0.644690\pi\)
\(440\) 0 0
\(441\) 20.3207 + 5.29793i 0.967654 + 0.252282i
\(442\) 50.9450 2.42321
\(443\) 14.2948 + 8.25313i 0.679169 + 0.392118i 0.799542 0.600611i \(-0.205076\pi\)
−0.120373 + 0.992729i \(0.538409\pi\)
\(444\) 10.5706 + 22.2776i 0.501659 + 1.05725i
\(445\) 0 0
\(446\) 19.0703 33.0307i 0.903005 1.56405i
\(447\) 0.178736 2.21378i 0.00845392 0.104708i
\(448\) 18.6386 29.0433i 0.880589 1.37217i
\(449\) 25.9824i 1.22618i −0.790012 0.613092i \(-0.789925\pi\)
0.790012 0.613092i \(-0.210075\pi\)
\(450\) 0 0
\(451\) −0.413664 + 0.238829i −0.0194787 + 0.0112460i
\(452\) 11.6151 6.70598i 0.546329 0.315423i
\(453\) 6.89737 9.99236i 0.324067 0.469482i
\(454\) 5.47172i 0.256801i
\(455\) 0 0
\(456\) −18.4154 1.48682i −0.862380 0.0696267i
\(457\) 0.750953 1.30069i 0.0351281 0.0608436i −0.847927 0.530113i \(-0.822149\pi\)
0.883055 + 0.469270i \(0.155483\pi\)
\(458\) 0.265158 + 0.459266i 0.0123900 + 0.0214601i
\(459\) 6.44235 + 22.2439i 0.300703 + 1.03826i
\(460\) 0 0
\(461\) −1.40468 −0.0654225 −0.0327113 0.999465i \(-0.510414\pi\)
−0.0327113 + 0.999465i \(0.510414\pi\)
\(462\) −19.4799 2.49762i −0.906289 0.116200i
\(463\) 20.2056 0.939033 0.469516 0.882924i \(-0.344428\pi\)
0.469516 + 0.882924i \(0.344428\pi\)
\(464\) −5.64497 3.25912i −0.262061 0.151301i
\(465\) 0 0
\(466\) 12.4688 + 21.5966i 0.577607 + 1.00044i
\(467\) 19.3296 33.4798i 0.894467 1.54926i 0.0600041 0.998198i \(-0.480889\pi\)
0.834463 0.551064i \(-0.185778\pi\)
\(468\) 7.49143 46.0911i 0.346291 2.13056i
\(469\) 21.9286 + 1.03043i 1.01257 + 0.0475809i
\(470\) 0 0
\(471\) 3.58272 + 2.47302i 0.165083 + 0.113951i
\(472\) −28.8739 + 16.6703i −1.32903 + 0.767314i
\(473\) 15.2347 8.79578i 0.700494 0.404430i
\(474\) 10.2288 + 7.06060i 0.469826 + 0.324304i
\(475\) 0 0
\(476\) −16.5779 32.1059i −0.759848 1.47157i
\(477\) 1.16546 7.17050i 0.0533627 0.328315i
\(478\) −10.8876 + 18.8579i −0.497987 + 0.862539i
\(479\) 15.3467 + 26.5813i 0.701210 + 1.21453i 0.968042 + 0.250788i \(0.0806898\pi\)
−0.266832 + 0.963743i \(0.585977\pi\)
\(480\) 0 0
\(481\) 20.4369 + 11.7992i 0.931841 + 0.537999i
\(482\) −36.1822 −1.64805
\(483\) −10.3745 7.90503i −0.472055 0.359691i
\(484\) −22.5943 −1.02701
\(485\) 0 0
\(486\) 34.8249 4.22682i 1.57969 0.191733i
\(487\) 14.8500 + 25.7209i 0.672915 + 1.16552i 0.977074 + 0.212902i \(0.0682916\pi\)
−0.304158 + 0.952622i \(0.598375\pi\)
\(488\) 2.09581 3.63004i 0.0948727 0.164324i
\(489\) −5.98120 0.482910i −0.270479 0.0218379i
\(490\) 0 0
\(491\) 7.13665i 0.322073i 0.986948 + 0.161036i \(0.0514836\pi\)
−0.986948 + 0.161036i \(0.948516\pi\)
\(492\) −0.756246 + 1.09559i −0.0340942 + 0.0493930i
\(493\) −34.0684 + 19.6694i −1.53436 + 0.885866i
\(494\) −44.0857 + 25.4529i −1.98351 + 1.14518i
\(495\) 0 0
\(496\) 4.10290i 0.184226i
\(497\) −21.5639 13.8386i −0.967271 0.620747i
\(498\) 2.81996 34.9273i 0.126365 1.56513i
\(499\) 6.67079 11.5541i 0.298626 0.517235i −0.677196 0.735802i \(-0.736805\pi\)
0.975822 + 0.218568i \(0.0701385\pi\)
\(500\) 0 0
\(501\) −2.44915 5.16160i −0.109420 0.230603i
\(502\) −28.0272 16.1815i −1.25091 0.722216i
\(503\) −30.4353 −1.35704 −0.678522 0.734580i \(-0.737379\pi\)
−0.678522 + 0.734580i \(0.737379\pi\)
\(504\) −18.0730 + 5.89941i −0.805035 + 0.262780i
\(505\) 0 0
\(506\) 10.5637 + 6.09896i 0.469614 + 0.271132i
\(507\) −9.50488 20.0316i −0.422126 0.889634i
\(508\) −19.5882 33.9277i −0.869084 1.50530i
\(509\) 16.4870 28.5563i 0.730774 1.26574i −0.225779 0.974179i \(-0.572493\pi\)
0.956553 0.291559i \(-0.0941740\pi\)
\(510\) 0 0
\(511\) 0.784506 16.6950i 0.0347045 0.738545i
\(512\) 8.30237i 0.366916i
\(513\) −16.6883 16.0303i −0.736808 0.707754i
\(514\) 9.27624 5.35564i 0.409157 0.236227i
\(515\) 0 0
\(516\) 27.8516 40.3492i 1.22610 1.77627i
\(517\) 5.85853i 0.257658i
\(518\) 1.29839 27.6310i 0.0570480 1.21404i
\(519\) −30.1096 2.43099i −1.32167 0.106708i
\(520\) 0 0
\(521\) 12.7254 + 22.0411i 0.557511 + 0.965638i 0.997703 + 0.0677342i \(0.0215770\pi\)
−0.440192 + 0.897904i \(0.645090\pi\)
\(522\) 21.1304 + 55.7194i 0.924850 + 2.43877i
\(523\) −20.9524 12.0969i −0.916184 0.528959i −0.0337685 0.999430i \(-0.510751\pi\)
−0.882416 + 0.470470i \(0.844084\pi\)
\(524\) 15.9111 0.695081
\(525\) 0 0
\(526\) 12.7134 0.554332
\(527\) −21.4443 12.3809i −0.934129 0.539320i
\(528\) −2.20067 + 1.04420i −0.0957717 + 0.0454431i
\(529\) −7.44955 12.9030i −0.323893 0.561000i
\(530\) 0 0
\(531\) −41.2181 6.69940i −1.78871 0.290729i
\(532\) 30.3864 + 19.5005i 1.31742 + 0.845454i
\(533\) 1.27403i 0.0551844i
\(534\) −34.8754 24.0732i −1.50921 1.04175i
\(535\) 0 0
\(536\) −17.2114 + 9.93701i −0.743419 + 0.429213i
\(537\) 32.1533 + 22.1943i 1.38752 + 0.957753i
\(538\) 1.60249i 0.0690882i
\(539\) 10.8689 + 7.71861i 0.468155 + 0.332464i
\(540\) 0 0
\(541\) 17.8529 30.9222i 0.767557 1.32945i −0.171328 0.985214i \(-0.554806\pi\)
0.938884 0.344233i \(-0.111861\pi\)
\(542\) 3.63894 + 6.30282i 0.156306 + 0.270729i
\(543\) −5.44880 + 2.58542i −0.233830 + 0.110951i
\(544\) −24.9038 14.3782i −1.06774 0.616460i
\(545\) 0 0
\(546\) −31.7481 + 41.6658i −1.35869 + 1.78313i
\(547\) −14.1119 −0.603380 −0.301690 0.953406i \(-0.597551\pi\)
−0.301690 + 0.953406i \(0.597551\pi\)
\(548\) −35.7823 20.6589i −1.52854 0.882505i
\(549\) 4.90884 1.86157i 0.209504 0.0794499i
\(550\) 0 0
\(551\) 19.6542 34.0421i 0.837299 1.45024i
\(552\) 11.7696 + 0.950254i 0.500948 + 0.0404455i
\(553\) −3.87067 7.49620i −0.164598 0.318771i
\(554\) 51.5644i 2.19076i
\(555\) 0 0
\(556\) 5.36566 3.09787i 0.227555 0.131379i
\(557\) 27.2162 15.7133i 1.15319 0.665792i 0.203524 0.979070i \(-0.434760\pi\)
0.949661 + 0.313278i \(0.101427\pi\)
\(558\) −23.7234 + 29.0548i −1.00429 + 1.22999i
\(559\) 46.9209i 1.98454i
\(560\) 0 0
\(561\) −1.18305 + 14.6530i −0.0499486 + 0.618651i
\(562\) −13.5409 + 23.4536i −0.571190 + 0.989330i
\(563\) −16.0333 27.7705i −0.675723 1.17039i −0.976257 0.216615i \(-0.930498\pi\)
0.300535 0.953771i \(-0.402835\pi\)
\(564\) −6.99951 14.7515i −0.294733 0.621151i
\(565\) 0 0
\(566\) 40.2853 1.69332
\(567\) −22.2072 8.59313i −0.932613 0.360877i
\(568\) 23.1962 0.973290
\(569\) −17.1344 9.89257i −0.718313 0.414718i 0.0958187 0.995399i \(-0.469453\pi\)
−0.814131 + 0.580681i \(0.802786\pi\)
\(570\) 0 0
\(571\) −12.9459 22.4229i −0.541768 0.938370i −0.998803 0.0489208i \(-0.984422\pi\)
0.457035 0.889449i \(-0.348912\pi\)
\(572\) 14.8212 25.6711i 0.619707 1.07336i
\(573\) 1.33236 16.5023i 0.0556602 0.689394i
\(574\) 1.32693 0.685162i 0.0553850 0.0285981i
\(575\) 0 0
\(576\) −24.7482 + 30.3099i −1.03118 + 1.26291i
\(577\) 20.3323 11.7388i 0.846443 0.488694i −0.0130060 0.999915i \(-0.504140\pi\)
0.859449 + 0.511221i \(0.170807\pi\)
\(578\) −5.57940 + 3.22127i −0.232073 + 0.133987i
\(579\) 5.67748 8.22508i 0.235948 0.341823i
\(580\) 0 0
\(581\) −12.8463 + 20.0175i −0.532952 + 0.830465i
\(582\) −34.7524 2.80584i −1.44053 0.116306i
\(583\) 2.30578 3.99372i 0.0954955 0.165403i
\(584\) 7.56542 + 13.1037i 0.313059 + 0.542234i
\(585\) 0 0
\(586\) −17.2930 9.98415i −0.714369 0.412441i
\(587\) 36.1962 1.49398 0.746988 0.664837i \(-0.231499\pi\)
0.746988 + 0.664837i \(0.231499\pi\)
\(588\) 36.5892 + 6.44947i 1.50891 + 0.265972i
\(589\) 24.7427 1.01950
\(590\) 0 0
\(591\) −6.79918 + 3.22617i −0.279681 + 0.132707i
\(592\) −1.71540 2.97115i −0.0705024 0.122114i
\(593\) 7.50446 12.9981i 0.308171 0.533768i −0.669791 0.742550i \(-0.733616\pi\)
0.977962 + 0.208781i \(0.0669497\pi\)
\(594\) 21.6217 + 5.32994i 0.887151 + 0.218690i
\(595\) 0 0
\(596\) 3.92937i 0.160953i
\(597\) 12.3996 + 8.55901i 0.507483 + 0.350297i
\(598\) 28.1760 16.2674i 1.15220 0.665223i
\(599\) −11.3793 + 6.56986i −0.464947 + 0.268437i −0.714122 0.700021i \(-0.753174\pi\)
0.249175 + 0.968458i \(0.419841\pi\)
\(600\) 0 0
\(601\) 17.2898i 0.705267i −0.935762 0.352633i \(-0.885286\pi\)
0.935762 0.352633i \(-0.114714\pi\)
\(602\) −48.8692 + 25.2337i −1.99176 + 1.02845i
\(603\) −24.5697 3.99344i −1.00055 0.162625i
\(604\) 10.7406 18.6032i 0.437027 0.756954i
\(605\) 0 0
\(606\) −33.1970 + 15.7518i −1.34854 + 0.639872i
\(607\) −0.391428 0.225991i −0.0158876 0.00917270i 0.492035 0.870575i \(-0.336253\pi\)
−0.507923 + 0.861403i \(0.669586\pi\)
\(608\) 28.7342 1.16533
\(609\) 5.14408 40.1208i 0.208449 1.62578i
\(610\) 0 0
\(611\) −13.5326 7.81306i −0.547471 0.316083i
\(612\) 14.5279 + 38.3091i 0.587256 + 1.54855i
\(613\) 0.774834 + 1.34205i 0.0312953 + 0.0542050i 0.881249 0.472653i \(-0.156703\pi\)
−0.849954 + 0.526858i \(0.823370\pi\)
\(614\) 10.1256 17.5380i 0.408636 0.707778i
\(615\) 0 0
\(616\) −12.0552 0.566476i −0.485716 0.0228240i
\(617\) 42.6618i 1.71750i 0.512394 + 0.858751i \(0.328759\pi\)
−0.512394 + 0.858751i \(0.671241\pi\)
\(618\) 13.9522 20.2129i 0.561241 0.813081i
\(619\) 21.8956 12.6414i 0.880058 0.508102i 0.00938032 0.999956i \(-0.497014\pi\)
0.870677 + 0.491854i \(0.163681\pi\)
\(620\) 0 0
\(621\) 10.6658 + 10.2452i 0.428004 + 0.411127i
\(622\) 14.8460i 0.595270i
\(623\) 13.1971 + 25.5584i 0.528732 + 1.02398i
\(624\) −0.522850 + 6.47589i −0.0209307 + 0.259243i
\(625\) 0 0
\(626\) −21.6988 37.5834i −0.867258 1.50214i
\(627\) −6.29710 13.2712i −0.251482 0.530000i
\(628\) 6.67010 + 3.85098i 0.266166 + 0.153671i
\(629\) −20.7055 −0.825581
\(630\) 0 0
\(631\) 4.91791 0.195779 0.0978895 0.995197i \(-0.468791\pi\)
0.0978895 + 0.995197i \(0.468791\pi\)
\(632\) 6.61441 + 3.81883i 0.263107 + 0.151905i
\(633\) 7.94292 + 16.7398i 0.315703 + 0.665346i
\(634\) 21.5877 + 37.3910i 0.857357 + 1.48499i
\(635\) 0 0
\(636\) 1.03432 12.8109i 0.0410135 0.507983i
\(637\) 32.3242 14.8123i 1.28073 0.586885i
\(638\) 37.8285i 1.49765i
\(639\) 22.5043 + 18.3749i 0.890256 + 0.726900i
\(640\) 0 0
\(641\) 11.0323 6.36950i 0.435750 0.251580i −0.266043 0.963961i \(-0.585716\pi\)
0.701793 + 0.712381i \(0.252383\pi\)
\(642\) 36.7714 53.2714i 1.45125 2.10246i
\(643\) 2.51652i 0.0992419i −0.998768 0.0496210i \(-0.984199\pi\)
0.998768 0.0496210i \(-0.0158013\pi\)
\(644\) −19.4205 12.4631i −0.765275 0.491116i
\(645\) 0 0
\(646\) 22.3325 38.6811i 0.878662 1.52189i
\(647\) 20.2058 + 34.9974i 0.794371 + 1.37589i 0.923238 + 0.384230i \(0.125533\pi\)
−0.128866 + 0.991662i \(0.541134\pi\)
\(648\) 21.1215 4.31115i 0.829731 0.169358i
\(649\) −22.9571 13.2543i −0.901143 0.520275i
\(650\) 0 0
\(651\) 23.4896 9.82286i 0.920628 0.384988i
\(652\) −10.6164 −0.415770
\(653\) 36.9723 + 21.3460i 1.44684 + 0.835332i 0.998292 0.0584277i \(-0.0186087\pi\)
0.448546 + 0.893760i \(0.351942\pi\)
\(654\) −64.8082 + 30.7511i −2.53420 + 1.20246i
\(655\) 0 0
\(656\) 0.0926106 0.160406i 0.00361584 0.00626281i
\(657\) −3.04035 + 18.7058i −0.118616 + 0.729783i
\(658\) −0.859751 + 18.2963i −0.0335166 + 0.713265i
\(659\) 2.08754i 0.0813192i −0.999173 0.0406596i \(-0.987054\pi\)
0.999173 0.0406596i \(-0.0129459\pi\)
\(660\) 0 0
\(661\) 20.5058 11.8391i 0.797585 0.460486i −0.0450412 0.998985i \(-0.514342\pi\)
0.842626 + 0.538499i \(0.181009\pi\)
\(662\) −23.3384 + 13.4744i −0.907071 + 0.523698i
\(663\) 32.2693 + 22.2743i 1.25323 + 0.865063i
\(664\) 21.5328i 0.835633i
\(665\) 0 0
\(666\) −5.03191 + 30.9589i −0.194983 + 1.19963i
\(667\) −12.5614 + 21.7570i −0.486379 + 0.842433i
\(668\) −5.05389 8.75359i −0.195541 0.338687i
\(669\) 26.5212 12.5841i 1.02537 0.486531i
\(670\) 0 0
\(671\) 3.33267 0.128656
\(672\) 27.2790 11.4075i 1.05231 0.440054i
\(673\) −29.6317 −1.14222 −0.571108 0.820875i \(-0.693486\pi\)
−0.571108 + 0.820875i \(0.693486\pi\)
\(674\) 24.7496 + 14.2892i 0.953320 + 0.550400i
\(675\) 0 0
\(676\) −19.6136 33.9717i −0.754368 1.30660i
\(677\) −17.0667 + 29.5604i −0.655927 + 1.13610i 0.325734 + 0.945462i \(0.394389\pi\)
−0.981661 + 0.190637i \(0.938945\pi\)
\(678\) 17.0046 + 1.37291i 0.653057 + 0.0527265i
\(679\) 19.9172 + 12.7819i 0.764354 + 0.490525i
\(680\) 0 0
\(681\) 2.39236 3.46586i 0.0916755 0.132812i
\(682\) −20.6210 + 11.9056i −0.789620 + 0.455887i
\(683\) 17.0344 9.83481i 0.651803 0.376319i −0.137344 0.990523i \(-0.543857\pi\)
0.789147 + 0.614205i \(0.210523\pi\)
\(684\) −31.7116 25.8927i −1.21252 0.990034i
\(685\) 0 0
\(686\) −32.8110 25.7004i −1.25273 0.981246i
\(687\) −0.0328473 + 0.406838i −0.00125320 + 0.0155219i
\(688\) −3.41073 + 5.90756i −0.130033 + 0.225224i
\(689\) −6.15006 10.6522i −0.234299 0.405817i
\(690\) 0 0
\(691\) −0.800772 0.462326i −0.0304628 0.0175877i 0.484691 0.874685i \(-0.338932\pi\)
−0.515154 + 0.857098i \(0.672265\pi\)
\(692\) −53.4433 −2.03161
\(693\) −11.2468 10.0991i −0.427232 0.383633i
\(694\) 12.6242 0.479206
\(695\) 0 0
\(696\) 15.6980 + 33.0836i 0.595031 + 1.25403i
\(697\) −0.558922 0.968081i −0.0211707 0.0366687i
\(698\) −38.1135 + 66.0145i −1.44262 + 2.49869i
\(699\) −1.54462 + 19.1312i −0.0584228 + 0.723610i
\(700\) 0 0
\(701\) 0.206478i 0.00779858i −0.999992 0.00389929i \(-0.998759\pi\)
0.999992 0.00389929i \(-0.00124119\pi\)
\(702\) 41.1468 42.8359i 1.55299 1.61674i
\(703\) 17.9176 10.3447i 0.675776 0.390160i
\(704\) −21.5118 + 12.4199i −0.810758 + 0.468091i
\(705\) 0 0
\(706\) 82.6826i 3.11180i
\(707\) 24.9138 + 1.17071i 0.936980 + 0.0440291i
\(708\) −73.6405 5.94558i −2.76758 0.223449i
\(709\) −20.5452 + 35.5852i −0.771589 + 1.33643i 0.165102 + 0.986276i \(0.447205\pi\)
−0.936692 + 0.350156i \(0.886129\pi\)
\(710\) 0 0
\(711\) 3.39203 + 8.94455i 0.127211 + 0.335447i
\(712\) −22.5520 13.0204i −0.845171 0.487960i
\(713\) −15.8135 −0.592220
\(714\) 5.84506 45.5881i 0.218746 1.70609i
\(715\) 0 0
\(716\) 59.8611 + 34.5608i 2.23712 + 1.29160i
\(717\) −15.1414 + 7.18453i −0.565468 + 0.268311i
\(718\) 27.4651 + 47.5709i 1.02499 + 1.77533i
\(719\) −4.36496 + 7.56034i −0.162786 + 0.281953i −0.935867 0.352354i \(-0.885381\pi\)
0.773081 + 0.634307i \(0.218715\pi\)
\(720\) 0 0
\(721\) −14.8130 + 7.64871i −0.551665 + 0.284853i
\(722\) 1.87281i 0.0696988i
\(723\) −22.9183 15.8197i −0.852340 0.588340i
\(724\) −9.24065 + 5.33509i −0.343426 + 0.198277i
\(725\) 0 0
\(726\) −23.6522 16.3263i −0.877816 0.605925i
\(727\) 26.6400i 0.988024i −0.869455 0.494012i \(-0.835530\pi\)
0.869455 0.494012i \(-0.164470\pi\)
\(728\) −17.3855 + 27.0907i −0.644350 + 1.00405i
\(729\) 23.9066 + 12.5489i 0.885430 + 0.464774i
\(730\) 0 0
\(731\) 20.5844 + 35.6532i 0.761341 + 1.31868i
\(732\) 8.39152 3.98173i 0.310159 0.147169i
\(733\) 27.1888 + 15.6975i 1.00424 + 0.579800i 0.909501 0.415702i \(-0.136464\pi\)
0.0947418 + 0.995502i \(0.469797\pi\)
\(734\) 46.5056 1.71655
\(735\) 0 0
\(736\) −18.3646 −0.676927
\(737\) −13.6845 7.90073i −0.504074 0.291027i
\(738\) −1.58331 + 0.600436i −0.0582824 + 0.0221023i
\(739\) −6.49377 11.2475i −0.238877 0.413747i 0.721515 0.692399i \(-0.243446\pi\)
−0.960392 + 0.278651i \(0.910113\pi\)
\(740\) 0 0
\(741\) −39.0530 3.15306i −1.43465 0.115831i
\(742\) −7.78708 + 12.1341i −0.285873 + 0.445457i
\(743\) 20.9456i 0.768419i 0.923246 + 0.384209i \(0.125526\pi\)
−0.923246 + 0.384209i \(0.874474\pi\)
\(744\) −13.0940 + 18.9695i −0.480048 + 0.695455i
\(745\) 0 0
\(746\) −40.6783 + 23.4856i −1.48934 + 0.859869i
\(747\) 17.0572 20.8905i 0.624091 0.764343i
\(748\) 26.0085i 0.950966i
\(749\) −39.0400 + 20.1583i −1.42649 + 0.736570i
\(750\) 0 0
\(751\) −2.17046 + 3.75935i −0.0792014 + 0.137181i −0.902906 0.429839i \(-0.858570\pi\)
0.823704 + 0.567020i \(0.191904\pi\)
\(752\) 1.13588 + 1.96740i 0.0414212 + 0.0717437i
\(753\) −10.6779 22.5037i −0.389123 0.820080i
\(754\) 87.3801 + 50.4489i 3.18220 + 1.83724i
\(755\) 0 0
\(756\) −40.3850 11.9918i −1.46879 0.436139i
\(757\) −0.401257 −0.0145839 −0.00729196 0.999973i \(-0.502321\pi\)
−0.00729196 + 0.999973i \(0.502321\pi\)
\(758\) −52.6955 30.4238i −1.91399 1.10504i
\(759\) 4.02459 + 8.48185i 0.146083 + 0.307872i
\(760\) 0 0
\(761\) 21.1371 36.6105i 0.766219 1.32713i −0.173381 0.984855i \(-0.555469\pi\)
0.939600 0.342275i \(-0.111197\pi\)
\(762\) 4.01028 49.6703i 0.145277 1.79937i
\(763\) 48.6375 + 2.28550i 1.76080 + 0.0827406i
\(764\) 29.2909i 1.05971i
\(765\) 0 0
\(766\) 12.3453 7.12757i 0.446054 0.257530i
\(767\) −61.2320 + 35.3523i −2.21096 + 1.27650i
\(768\) −10.7532 + 15.5784i −0.388023 + 0.562137i
\(769\) 0.306962i 0.0110693i 0.999985 + 0.00553466i \(0.00176175\pi\)
−0.999985 + 0.00553466i \(0.998238\pi\)
\(770\) 0 0
\(771\) 8.21730 + 0.663448i 0.295939 + 0.0238935i
\(772\) 8.84096 15.3130i 0.318193 0.551126i
\(773\) −1.06021 1.83633i −0.0381330 0.0660483i 0.846329 0.532661i \(-0.178808\pi\)
−0.884462 + 0.466612i \(0.845474\pi\)
\(774\) 58.3113 22.1133i 2.09596 0.794846i
\(775\) 0 0
\(776\) −21.4249 −0.769110
\(777\) 12.9033 16.9341i 0.462903 0.607509i
\(778\) 28.0304 1.00494
\(779\) 0.967334 + 0.558491i 0.0346583 + 0.0200100i
\(780\) 0 0
\(781\) 9.22142 + 15.9720i 0.329968 + 0.571522i
\(782\) −14.2731 + 24.7218i −0.510406 + 0.884049i
\(783\) −10.9775 + 44.5321i −0.392304 + 1.59145i
\(784\) −5.14648 0.484741i −0.183803 0.0173122i
\(785\) 0 0
\(786\) 16.6561 + 11.4971i 0.594104 + 0.410089i
\(787\) −17.7119 + 10.2260i −0.631360 + 0.364516i −0.781279 0.624183i \(-0.785432\pi\)
0.149919 + 0.988698i \(0.452099\pi\)
\(788\) −11.5308 + 6.65730i −0.410767 + 0.237156i
\(789\) 8.05286 + 5.55860i 0.286690 + 0.197892i
\(790\) 0 0
\(791\) −9.74563 6.25427i −0.346515 0.222376i
\(792\) 13.5071 + 2.19538i 0.479954 + 0.0780094i
\(793\) 4.44452 7.69814i 0.157830 0.273369i
\(794\) −32.0416 55.4977i −1.13711 1.96954i
\(795\) 0 0
\(796\) 23.0849 + 13.3281i 0.818223 + 0.472401i
\(797\) −21.2684 −0.753365 −0.376682 0.926342i \(-0.622935\pi\)
−0.376682 + 0.926342i \(0.622935\pi\)
\(798\) 17.7184 + 42.3703i 0.627224 + 1.49989i
\(799\) 13.7105 0.485042
\(800\) 0 0
\(801\) −11.5652 30.4966i −0.408636 1.07755i
\(802\) −16.5677 28.6961i −0.585025 1.01329i
\(803\) −6.01512 + 10.4185i −0.212269 + 0.367661i
\(804\) −43.8963 3.54410i −1.54810 0.124991i
\(805\) 0 0
\(806\) 63.5100i 2.23704i
\(807\) 0.700644 1.01504i 0.0246638 0.0357310i
\(808\) −19.5545 + 11.2898i −0.687924 + 0.397173i
\(809\) 19.3311 11.1608i 0.679646 0.392394i −0.120075 0.992765i \(-0.538314\pi\)
0.799722 + 0.600371i \(0.204980\pi\)
\(810\) 0 0
\(811\) 39.7633i 1.39628i 0.715962 + 0.698139i \(0.245988\pi\)
−0.715962 + 0.698139i \(0.754012\pi\)
\(812\) 3.35906 71.4840i 0.117880 2.50860i
\(813\) −0.450786 + 5.58332i −0.0158097 + 0.195816i
\(814\) −9.95527 + 17.2430i −0.348932 + 0.604368i
\(815\) 0 0
\(816\) −2.44370 5.15012i −0.0855468 0.180290i
\(817\) −35.6257 20.5685i −1.24639 0.719601i
\(818\) −2.10641 −0.0736488
\(819\) −38.3269 + 12.5107i −1.33925 + 0.437160i
\(820\) 0 0
\(821\) 34.1580 + 19.7211i 1.19212 + 0.688272i 0.958787 0.284125i \(-0.0917030\pi\)
0.233335 + 0.972397i \(0.425036\pi\)
\(822\) −22.5299 47.4819i −0.785820 1.65612i
\(823\) −23.8993 41.3948i −0.833077 1.44293i −0.895587 0.444887i \(-0.853244\pi\)
0.0625104 0.998044i \(-0.480089\pi\)
\(824\) 7.54628 13.0705i 0.262887 0.455334i
\(825\) 0 0
\(826\) 69.7503 + 44.7623i 2.42692 + 1.55748i
\(827\) 40.7367i 1.41655i −0.705935 0.708277i \(-0.749473\pi\)
0.705935 0.708277i \(-0.250527\pi\)
\(828\) 20.2675 + 16.5485i 0.704344 + 0.575101i
\(829\) −18.8083 + 10.8590i −0.653238 + 0.377147i −0.789696 0.613499i \(-0.789762\pi\)
0.136458 + 0.990646i \(0.456428\pi\)
\(830\) 0 0
\(831\) −22.5451 + 32.6616i −0.782082 + 1.13302i
\(832\) 66.2536i 2.29693i
\(833\) −18.0635 + 25.4360i −0.625864 + 0.881303i
\(834\) 7.85536 + 0.634225i 0.272009 + 0.0219614i
\(835\) 0 0
\(836\) −12.9942 22.5067i −0.449415 0.778410i
\(837\) −27.7301 + 8.03127i −0.958494 + 0.277601i
\(838\) −58.7626 33.9266i −2.02992 1.17197i
\(839\) −9.40638 −0.324744 −0.162372 0.986730i \(-0.551915\pi\)
−0.162372 + 0.986730i \(0.551915\pi\)
\(840\) 0 0
\(841\) −48.9115 −1.68660
\(842\) 70.8790 + 40.9220i 2.44265 + 1.41026i
\(843\) −18.8315 + 8.93542i −0.648590 + 0.307752i
\(844\) 16.3904 + 28.3891i 0.564182 + 0.977192i
\(845\) 0 0
\(846\) 3.33197 20.4999i 0.114555 0.704803i
\(847\) 8.95019 + 17.3335i 0.307532 + 0.595587i
\(848\) 1.78822i 0.0614077i
\(849\) 25.5172 + 17.6136i 0.875749 + 0.604498i
\(850\) 0 0
\(851\) −11.4515 + 6.61152i −0.392552 + 0.226640i
\(852\) 42.3017 + 29.1994i 1.44923 + 1.00035i
\(853\) 28.2296i 0.966562i 0.875465 + 0.483281i \(0.160555\pi\)
−0.875465 + 0.483281i \(0.839445\pi\)
\(854\) −10.4080 0.489076i −0.356154 0.0167358i
\(855\) 0 0
\(856\) 19.8884 34.4477i 0.679771 1.17740i
\(857\) 8.37845 + 14.5119i 0.286202 + 0.495717i 0.972900 0.231226i \(-0.0742737\pi\)
−0.686698 + 0.726943i \(0.740940\pi\)
\(858\) 34.0647 16.1635i 1.16295 0.551814i
\(859\) 8.38608 + 4.84171i 0.286129 + 0.165197i 0.636195 0.771528i \(-0.280507\pi\)
−0.350066 + 0.936725i \(0.613841\pi\)
\(860\) 0 0
\(861\) 1.14006 + 0.146173i 0.0388533 + 0.00498157i
\(862\) −31.0135 −1.05632
\(863\) 19.0593 + 11.0039i 0.648785 + 0.374576i 0.787990 0.615687i \(-0.211122\pi\)
−0.139206 + 0.990263i \(0.544455\pi\)
\(864\) −32.2037 + 9.32691i −1.09559 + 0.317308i
\(865\) 0 0
\(866\) −1.31469 + 2.27712i −0.0446751 + 0.0773796i
\(867\) −4.94248 0.399046i −0.167855 0.0135523i
\(868\) 40.0244 20.6667i 1.35852 0.701472i
\(869\) 6.07256i 0.205998i
\(870\) 0 0
\(871\) −36.4998 + 21.0732i −1.23675 + 0.714036i
\(872\) −38.1749 + 22.0403i −1.29276 + 0.746378i
\(873\) −20.7859 16.9718i −0.703496 0.574409i
\(874\) 28.5242i 0.964847i
\(875\) 0 0
\(876\) −2.69825 + 33.4199i −0.0911655 + 1.12915i
\(877\) 10.5609 18.2921i 0.356617 0.617679i −0.630776 0.775965i \(-0.717263\pi\)
0.987393 + 0.158286i \(0.0505968\pi\)
\(878\) 3.25277 + 5.63397i 0.109776 + 0.190137i
\(879\) −6.58836 13.8850i −0.222220 0.468330i
\(880\) 0 0
\(881\) 44.3021 1.49258 0.746288 0.665623i \(-0.231834\pi\)
0.746288 + 0.665623i \(0.231834\pi\)
\(882\) 33.6421 + 33.1902i 1.13279 + 1.11757i
\(883\) 5.12282 0.172397 0.0861984 0.996278i \(-0.472528\pi\)
0.0861984 + 0.996278i \(0.472528\pi\)
\(884\) 60.0771 + 34.6855i 2.02061 + 1.16660i
\(885\) 0 0
\(886\) 18.5729 + 32.1693i 0.623970 + 1.08075i
\(887\) −3.87397 + 6.70992i −0.130075 + 0.225297i −0.923705 0.383104i \(-0.874855\pi\)
0.793630 + 0.608401i \(0.208189\pi\)
\(888\) −1.55109 + 19.2114i −0.0520512 + 0.644693i
\(889\) −18.2687 + 28.4670i −0.612713 + 0.954751i
\(890\) 0 0
\(891\) 11.3651 + 12.8296i 0.380746 + 0.429807i
\(892\) 44.9774 25.9677i 1.50596 0.869464i
\(893\) −11.8645 + 6.84995i −0.397029 + 0.229225i
\(894\) 2.83930 4.11335i 0.0949603 0.137571i
\(895\) 0 0
\(896\) 38.6678 19.9661i 1.29180 0.667022i
\(897\) 24.9595 + 2.01518i 0.833374 + 0.0672848i
\(898\) 29.2355 50.6374i 0.975601 1.68979i
\(899\) −24.5206 42.4710i −0.817809 1.41649i
\(900\) 0 0
\(901\) 9.34634 + 5.39611i 0.311372 + 0.179770i
\(902\) −1.07493 −0.0357912
\(903\) −41.9871 5.38337i −1.39724 0.179147i
\(904\) 10.4833 0.348671
\(905\) 0 0
\(906\) 24.6858 11.7133i 0.820132 0.389148i
\(907\) 12.2639 + 21.2416i 0.407215 + 0.705316i 0.994576 0.104008i \(-0.0331668\pi\)
−0.587362 + 0.809324i \(0.699833\pi\)
\(908\) 3.72538 6.45254i 0.123631 0.214135i
\(909\) −27.9145 4.53708i −0.925864 0.150486i
\(910\) 0 0
\(911\) 43.8824i 1.45389i −0.686697 0.726944i \(-0.740940\pi\)
0.686697 0.726944i \(-0.259060\pi\)
\(912\) 4.68775 + 3.23579i 0.155227 + 0.107148i
\(913\) 14.8266 8.56014i 0.490689 0.283299i
\(914\) 2.92708 1.68995i 0.0968193 0.0558986i
\(915\) 0 0
\(916\) 0.722122i 0.0238596i
\(917\) −6.30281 12.2064i −0.208137 0.403092i
\(918\) −12.4734 + 50.6004i −0.411684 + 1.67006i
\(919\) 7.85902 13.6122i 0.259245 0.449026i −0.706795 0.707419i \(-0.749860\pi\)
0.966040 + 0.258393i \(0.0831929\pi\)
\(920\) 0 0
\(921\) 14.0817 6.68169i 0.464008 0.220169i
\(922\) −2.73760 1.58056i −0.0901581 0.0520528i
\(923\) 49.1915 1.61916
\(924\) −21.2713 16.2081i −0.699774 0.533207i
\(925\) 0 0
\(926\) 39.3789 + 22.7354i 1.29407 + 0.747132i
\(927\) 17.6750 6.70288i 0.580525 0.220151i
\(928\) −28.4764 49.3225i −0.934783 1.61909i
\(929\) −9.87128 + 17.0976i −0.323866 + 0.560952i −0.981282 0.192575i \(-0.938316\pi\)
0.657416 + 0.753528i \(0.271649\pi\)
\(930\) 0 0
\(931\) 2.92324 31.0360i 0.0958054 1.01716i
\(932\) 33.9572i 1.11230i
\(933\) 6.49101 9.40365i 0.212506 0.307862i
\(934\) 75.3434 43.4995i 2.46531 1.42335i
\(935\) 0 0
\(936\) 23.0844 28.2722i 0.754539 0.924106i
\(937\) 37.1538i 1.21376i 0.794793 + 0.606881i \(0.207580\pi\)
−0.794793 + 0.606881i \(0.792420\pi\)
\(938\) 41.5774 + 26.6824i 1.35755 + 0.871210i
\(939\) 2.68801 33.2930i 0.0877199 1.08648i
\(940\) 0 0
\(941\) −16.1049 27.8945i −0.525005 0.909336i −0.999576 0.0291183i \(-0.990730\pi\)
0.474571 0.880217i \(-0.342603\pi\)
\(942\) 4.19975 + 8.85100i 0.136835 + 0.288381i
\(943\) −0.618241 0.356942i −0.0201327 0.0116236i
\(944\) 10.2792 0.334559
\(945\) 0 0
\(946\) 39.5882 1.28712
\(947\) −24.5694 14.1852i −0.798400 0.460956i 0.0445115 0.999009i \(-0.485827\pi\)
−0.842911 + 0.538053i \(0.819160\pi\)
\(948\) 7.25523 + 15.2904i 0.235639 + 0.496611i
\(949\) 16.0438 + 27.7886i 0.520803 + 0.902057i
\(950\) 0 0
\(951\) −2.67425 + 33.1226i −0.0867185 + 1.07407i
\(952\) 1.32570 28.2122i 0.0429662 0.914361i
\(953\) 28.4105i 0.920305i −0.887840 0.460153i \(-0.847795\pi\)
0.887840 0.460153i \(-0.152205\pi\)
\(954\) 10.3397 12.6633i 0.334759 0.409989i
\(955\) 0 0
\(956\) −25.6785 + 14.8255i −0.830501 + 0.479490i
\(957\) −16.5395 + 23.9611i −0.534646 + 0.774552i
\(958\) 69.0729i 2.23164i
\(959\) −1.67447 + 35.6344i −0.0540716 + 1.15069i
\(960\) 0 0
\(961\) −0.0655266 + 0.113495i −0.00211376 + 0.00366114i
\(962\) 26.5531 + 45.9913i 0.856107 + 1.48282i
\(963\) 46.5830 17.6656i 1.50112 0.569265i
\(964\) −42.6680 24.6344i −1.37424 0.793419i
\(965\) 0 0
\(966\) −11.3241 27.0796i −0.364349 0.871272i
\(967\) −42.3117 −1.36065 −0.680326 0.732909i \(-0.738162\pi\)
−0.680326 + 0.732909i \(0.738162\pi\)
\(968\) −15.2946 8.83032i −0.491586 0.283817i
\(969\) 31.0580 14.7368i 0.997726 0.473415i
\(970\) 0 0
\(971\) −11.7297 + 20.3164i −0.376424 + 0.651985i −0.990539 0.137231i \(-0.956180\pi\)
0.614115 + 0.789216i \(0.289513\pi\)
\(972\) 43.9451 + 18.7257i 1.40954 + 0.600628i
\(973\) −4.50205 2.88919i −0.144329 0.0926233i
\(974\) 66.8370i 2.14159i
\(975\) 0 0
\(976\) −1.11917 + 0.646154i −0.0358238 + 0.0206829i
\(977\) 30.4577 17.5848i 0.974429 0.562587i 0.0738456 0.997270i \(-0.476473\pi\)
0.900584 + 0.434683i \(0.143139\pi\)
\(978\) −11.1135 7.67123i −0.355370 0.245299i
\(979\) 20.7045i 0.661720i
\(980\) 0 0
\(981\) −54.4955 8.85745i −1.73991 0.282796i
\(982\) −8.03020 + 13.9087i −0.256254 + 0.443845i
\(983\) −20.8391 36.0944i −0.664665 1.15123i −0.979376 0.202046i \(-0.935241\pi\)
0.314711 0.949187i \(-0.398092\pi\)
\(984\) −0.940098 + 0.446071i −0.0299692 + 0.0142202i
\(985\) 0 0
\(986\) −88.5285 −2.81932
\(987\) −8.54414 + 11.2132i −0.271963 + 0.356921i
\(988\) −69.3175 −2.20528
\(989\) 22.7690 + 13.1457i 0.724013 + 0.418009i
\(990\) 0 0
\(991\) −22.1571 38.3773i −0.703844 1.21909i −0.967107 0.254370i \(-0.918132\pi\)
0.263262 0.964724i \(-0.415201\pi\)
\(992\) 17.9244 31.0460i 0.569101 0.985711i
\(993\) −20.6741 1.66919i −0.656074 0.0529700i
\(994\) −26.4548 51.2340i −0.839094 1.62505i
\(995\) 0 0
\(996\) 27.1055 39.2682i 0.858869 1.24426i
\(997\) −38.6961 + 22.3412i −1.22552 + 0.707552i −0.966089 0.258210i \(-0.916867\pi\)
−0.259428 + 0.965763i \(0.583534\pi\)
\(998\) 26.0016 15.0120i 0.823065 0.475197i
\(999\) −16.7232 + 17.4097i −0.529099 + 0.550819i
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 525.2.t.i.26.9 yes 20
3.2 odd 2 inner 525.2.t.i.26.2 yes 20
5.2 odd 4 525.2.q.g.299.4 40
5.3 odd 4 525.2.q.g.299.17 40
5.4 even 2 525.2.t.h.26.2 20
7.3 odd 6 inner 525.2.t.i.101.2 yes 20
15.2 even 4 525.2.q.g.299.18 40
15.8 even 4 525.2.q.g.299.3 40
15.14 odd 2 525.2.t.h.26.9 yes 20
21.17 even 6 inner 525.2.t.i.101.9 yes 20
35.3 even 12 525.2.q.g.374.18 40
35.17 even 12 525.2.q.g.374.3 40
35.24 odd 6 525.2.t.h.101.9 yes 20
105.17 odd 12 525.2.q.g.374.17 40
105.38 odd 12 525.2.q.g.374.4 40
105.59 even 6 525.2.t.h.101.2 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.q.g.299.3 40 15.8 even 4
525.2.q.g.299.4 40 5.2 odd 4
525.2.q.g.299.17 40 5.3 odd 4
525.2.q.g.299.18 40 15.2 even 4
525.2.q.g.374.3 40 35.17 even 12
525.2.q.g.374.4 40 105.38 odd 12
525.2.q.g.374.17 40 105.17 odd 12
525.2.q.g.374.18 40 35.3 even 12
525.2.t.h.26.2 20 5.4 even 2
525.2.t.h.26.9 yes 20 15.14 odd 2
525.2.t.h.101.2 yes 20 105.59 even 6
525.2.t.h.101.9 yes 20 35.24 odd 6
525.2.t.i.26.2 yes 20 3.2 odd 2 inner
525.2.t.i.26.9 yes 20 1.1 even 1 trivial
525.2.t.i.101.2 yes 20 7.3 odd 6 inner
525.2.t.i.101.9 yes 20 21.17 even 6 inner