Properties

Label 475.2.e.f.26.3
Level $475$
Weight $2$
Character 475.26
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 26.3
Root \(-0.0149173 + 0.0258375i\) of defining polynomial
Character \(\chi\) \(=\) 475.26
Dual form 475.2.e.f.201.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.155554 - 0.269427i) q^{2} +(-0.514917 - 0.891863i) q^{3} +(0.951606 - 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038 q^{7} -1.21432 q^{8} +(0.969720 - 1.67960i) q^{9} +O(q^{10})\) \(q+(-0.155554 - 0.269427i) q^{2} +(-0.514917 - 0.891863i) q^{3} +(0.951606 - 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038 q^{7} -1.21432 q^{8} +(0.969720 - 1.67960i) q^{9} -5.16792 q^{11} -1.95999 q^{12} +(-1.76735 + 3.06115i) q^{13} +(0.510276 + 0.883825i) q^{14} +(-1.71432 - 2.96929i) q^{16} +(0.504641 + 0.874064i) q^{17} -0.603375 q^{18} +(2.42346 + 3.62310i) q^{19} +(1.68913 + 2.92565i) q^{21} +(0.803890 + 1.39238i) q^{22} +(3.83176 - 6.63680i) q^{23} +(0.625274 + 1.08301i) q^{24} +1.09968 q^{26} -5.08681 q^{27} +(-3.12163 + 5.40683i) q^{28} +(2.01303 - 3.48667i) q^{29} -4.60077 q^{31} +(-1.74766 + 3.02703i) q^{32} +(2.66105 + 4.60908i) q^{33} +(0.156998 - 0.271928i) q^{34} +(-1.84558 - 3.19664i) q^{36} -6.48831 q^{37} +(0.599183 - 1.21653i) q^{38} +3.64017 q^{39} +(3.40277 + 5.89377i) q^{41} +(0.525500 - 0.910193i) q^{42} +(-3.15511 - 5.46481i) q^{43} +(-4.91782 + 8.51792i) q^{44} -2.38418 q^{46} +(1.92079 - 3.32690i) q^{47} +(-1.76547 + 3.05788i) q^{48} +3.76091 q^{49} +(0.519697 - 0.900141i) q^{51} +(3.36365 + 5.82601i) q^{52} +(3.55946 - 6.16516i) q^{53} +(0.791273 + 1.37052i) q^{54} +3.98343 q^{56} +(1.98343 - 4.02699i) q^{57} -1.25254 q^{58} +(-6.73649 - 11.6679i) q^{59} +(-3.06850 + 5.31480i) q^{61} +(0.715668 + 1.23957i) q^{62} +(-3.18105 + 5.50975i) q^{63} -5.76986 q^{64} +(0.827874 - 1.43392i) q^{66} +(5.59897 - 9.69770i) q^{67} +1.92088 q^{68} -7.89215 q^{69} +(0.227702 + 0.394391i) q^{71} +(-1.17755 + 2.03958i) q^{72} +(-2.06691 - 3.57999i) q^{73} +(1.00928 + 1.74813i) q^{74} +(8.27788 - 0.546653i) q^{76} +16.9528 q^{77} +(-0.566242 - 0.980760i) q^{78} +(-1.44414 - 2.50132i) q^{79} +(-0.289876 - 0.502080i) q^{81} +(1.05863 - 1.83360i) q^{82} -5.50061 q^{83} +6.42953 q^{84} +(-0.981579 + 1.70014i) q^{86} -4.14617 q^{87} +6.27551 q^{88} +(3.56433 - 6.17360i) q^{89} +(5.79760 - 10.0417i) q^{91} +(-7.29264 - 12.6312i) q^{92} +(2.36902 + 4.10326i) q^{93} -1.19514 q^{94} +3.59960 q^{96} +(5.41252 + 9.37476i) q^{97} +(-0.585025 - 1.01329i) q^{98} +(-5.01144 + 8.68006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.155554 0.269427i −0.109993 0.190514i 0.805774 0.592223i \(-0.201750\pi\)
−0.915767 + 0.401709i \(0.868416\pi\)
\(3\) −0.514917 0.891863i −0.297288 0.514917i 0.678227 0.734853i \(-0.262749\pi\)
−0.975514 + 0.219935i \(0.929415\pi\)
\(4\) 0.951606 1.64823i 0.475803 0.824115i
\(5\) 0 0
\(6\) −0.160195 + 0.277466i −0.0653993 + 0.113275i
\(7\) −3.28038 −1.23987 −0.619934 0.784654i \(-0.712841\pi\)
−0.619934 + 0.784654i \(0.712841\pi\)
\(8\) −1.21432 −0.429327
\(9\) 0.969720 1.67960i 0.323240 0.559868i
\(10\) 0 0
\(11\) −5.16792 −1.55819 −0.779093 0.626908i \(-0.784320\pi\)
−0.779093 + 0.626908i \(0.784320\pi\)
\(12\) −1.95999 −0.565801
\(13\) −1.76735 + 3.06115i −0.490176 + 0.849010i −0.999936 0.0113069i \(-0.996401\pi\)
0.509760 + 0.860317i \(0.329734\pi\)
\(14\) 0.510276 + 0.883825i 0.136377 + 0.236212i
\(15\) 0 0
\(16\) −1.71432 2.96929i −0.428580 0.742322i
\(17\) 0.504641 + 0.874064i 0.122393 + 0.211992i 0.920711 0.390245i \(-0.127610\pi\)
−0.798318 + 0.602237i \(0.794276\pi\)
\(18\) −0.603375 −0.142217
\(19\) 2.42346 + 3.62310i 0.555979 + 0.831196i
\(20\) 0 0
\(21\) 1.68913 + 2.92565i 0.368598 + 0.638430i
\(22\) 0.803890 + 1.39238i 0.171390 + 0.296856i
\(23\) 3.83176 6.63680i 0.798976 1.38387i −0.121307 0.992615i \(-0.538709\pi\)
0.920283 0.391253i \(-0.127958\pi\)
\(24\) 0.625274 + 1.08301i 0.127634 + 0.221068i
\(25\) 0 0
\(26\) 1.09968 0.215664
\(27\) −5.08681 −0.978956
\(28\) −3.12163 + 5.40683i −0.589933 + 1.02179i
\(29\) 2.01303 3.48667i 0.373810 0.647458i −0.616338 0.787482i \(-0.711385\pi\)
0.990148 + 0.140024i \(0.0447179\pi\)
\(30\) 0 0
\(31\) −4.60077 −0.826323 −0.413162 0.910658i \(-0.635576\pi\)
−0.413162 + 0.910658i \(0.635576\pi\)
\(32\) −1.74766 + 3.02703i −0.308945 + 0.535109i
\(33\) 2.66105 + 4.60908i 0.463230 + 0.802337i
\(34\) 0.156998 0.271928i 0.0269249 0.0466353i
\(35\) 0 0
\(36\) −1.84558 3.19664i −0.307597 0.532774i
\(37\) −6.48831 −1.06667 −0.533336 0.845904i \(-0.679062\pi\)
−0.533336 + 0.845904i \(0.679062\pi\)
\(38\) 0.599183 1.21653i 0.0972004 0.197348i
\(39\) 3.64017 0.582893
\(40\) 0 0
\(41\) 3.40277 + 5.89377i 0.531423 + 0.920451i 0.999327 + 0.0366724i \(0.0116758\pi\)
−0.467904 + 0.883779i \(0.654991\pi\)
\(42\) 0.525500 0.910193i 0.0810865 0.140446i
\(43\) −3.15511 5.46481i −0.481150 0.833376i 0.518616 0.855007i \(-0.326447\pi\)
−0.999766 + 0.0216315i \(0.993114\pi\)
\(44\) −4.91782 + 8.51792i −0.741390 + 1.28412i
\(45\) 0 0
\(46\) −2.38418 −0.351528
\(47\) 1.92079 3.32690i 0.280175 0.485278i −0.691252 0.722613i \(-0.742941\pi\)
0.971428 + 0.237335i \(0.0762740\pi\)
\(48\) −1.76547 + 3.05788i −0.254823 + 0.441366i
\(49\) 3.76091 0.537273
\(50\) 0 0
\(51\) 0.519697 0.900141i 0.0727721 0.126045i
\(52\) 3.36365 + 5.82601i 0.466454 + 0.807923i
\(53\) 3.55946 6.16516i 0.488929 0.846850i −0.510990 0.859587i \(-0.670721\pi\)
0.999919 + 0.0127367i \(0.00405432\pi\)
\(54\) 0.791273 + 1.37052i 0.107679 + 0.186505i
\(55\) 0 0
\(56\) 3.98343 0.532309
\(57\) 1.98343 4.02699i 0.262711 0.533388i
\(58\) −1.25254 −0.164466
\(59\) −6.73649 11.6679i −0.877016 1.51904i −0.854599 0.519288i \(-0.826197\pi\)
−0.0224174 0.999749i \(-0.507136\pi\)
\(60\) 0 0
\(61\) −3.06850 + 5.31480i −0.392881 + 0.680491i −0.992828 0.119549i \(-0.961855\pi\)
0.599947 + 0.800040i \(0.295188\pi\)
\(62\) 0.715668 + 1.23957i 0.0908899 + 0.157426i
\(63\) −3.18105 + 5.50975i −0.400775 + 0.694163i
\(64\) −5.76986 −0.721232
\(65\) 0 0
\(66\) 0.827874 1.43392i 0.101904 0.176503i
\(67\) 5.59897 9.69770i 0.684023 1.18476i −0.289719 0.957112i \(-0.593562\pi\)
0.973743 0.227652i \(-0.0731047\pi\)
\(68\) 1.92088 0.232941
\(69\) −7.89215 −0.950103
\(70\) 0 0
\(71\) 0.227702 + 0.394391i 0.0270233 + 0.0468056i 0.879221 0.476415i \(-0.158064\pi\)
−0.852198 + 0.523220i \(0.824731\pi\)
\(72\) −1.17755 + 2.03958i −0.138776 + 0.240367i
\(73\) −2.06691 3.57999i −0.241914 0.419007i 0.719346 0.694652i \(-0.244442\pi\)
−0.961259 + 0.275646i \(0.911108\pi\)
\(74\) 1.00928 + 1.74813i 0.117327 + 0.203216i
\(75\) 0 0
\(76\) 8.27788 0.546653i 0.949538 0.0627054i
\(77\) 16.9528 1.93195
\(78\) −0.566242 0.980760i −0.0641143 0.111049i
\(79\) −1.44414 2.50132i −0.162478 0.281421i 0.773278 0.634067i \(-0.218615\pi\)
−0.935757 + 0.352646i \(0.885282\pi\)
\(80\) 0 0
\(81\) −0.289876 0.502080i −0.0322085 0.0557867i
\(82\) 1.05863 1.83360i 0.116906 0.202487i
\(83\) −5.50061 −0.603770 −0.301885 0.953344i \(-0.597616\pi\)
−0.301885 + 0.953344i \(0.597616\pi\)
\(84\) 6.42953 0.701519
\(85\) 0 0
\(86\) −0.981579 + 1.70014i −0.105846 + 0.183331i
\(87\) −4.14617 −0.444516
\(88\) 6.27551 0.668971
\(89\) 3.56433 6.17360i 0.377818 0.654400i −0.612926 0.790140i \(-0.710008\pi\)
0.990745 + 0.135740i \(0.0433411\pi\)
\(90\) 0 0
\(91\) 5.79760 10.0417i 0.607754 1.05266i
\(92\) −7.29264 12.6312i −0.760311 1.31690i
\(93\) 2.36902 + 4.10326i 0.245656 + 0.425488i
\(94\) −1.19514 −0.123270
\(95\) 0 0
\(96\) 3.59960 0.367382
\(97\) 5.41252 + 9.37476i 0.549558 + 0.951862i 0.998305 + 0.0582034i \(0.0185372\pi\)
−0.448747 + 0.893659i \(0.648129\pi\)
\(98\) −0.585025 1.01329i −0.0590964 0.102358i
\(99\) −5.01144 + 8.68006i −0.503668 + 0.872379i
\(100\) 0 0
\(101\) 3.09011 5.35223i 0.307478 0.532567i −0.670332 0.742061i \(-0.733848\pi\)
0.977810 + 0.209494i \(0.0671818\pi\)
\(102\) −0.323363 −0.0320177
\(103\) 18.3217 1.80529 0.902644 0.430387i \(-0.141623\pi\)
0.902644 + 0.430387i \(0.141623\pi\)
\(104\) 2.14613 3.71721i 0.210446 0.364503i
\(105\) 0 0
\(106\) −2.21475 −0.215116
\(107\) 8.73445 0.844391 0.422196 0.906505i \(-0.361260\pi\)
0.422196 + 0.906505i \(0.361260\pi\)
\(108\) −4.84064 + 8.38423i −0.465790 + 0.806773i
\(109\) 3.04839 + 5.27997i 0.291983 + 0.505730i 0.974279 0.225347i \(-0.0723515\pi\)
−0.682295 + 0.731077i \(0.739018\pi\)
\(110\) 0 0
\(111\) 3.34094 + 5.78668i 0.317108 + 0.549248i
\(112\) 5.62363 + 9.74041i 0.531383 + 0.920382i
\(113\) 10.3443 0.973111 0.486556 0.873650i \(-0.338253\pi\)
0.486556 + 0.873650i \(0.338253\pi\)
\(114\) −1.39351 + 0.0920244i −0.130514 + 0.00861887i
\(115\) 0 0
\(116\) −3.83122 6.63587i −0.355720 0.616125i
\(117\) 3.42768 + 5.93692i 0.316889 + 0.548868i
\(118\) −2.09578 + 3.62999i −0.192932 + 0.334168i
\(119\) −1.65542 2.86726i −0.151752 0.262842i
\(120\) 0 0
\(121\) 15.7074 1.42794
\(122\) 1.90927 0.172857
\(123\) 3.50429 6.06960i 0.315971 0.547278i
\(124\) −4.37812 + 7.58313i −0.393167 + 0.680985i
\(125\) 0 0
\(126\) 1.97930 0.176330
\(127\) −1.68356 + 2.91602i −0.149392 + 0.258755i −0.931003 0.365012i \(-0.881065\pi\)
0.781611 + 0.623766i \(0.214398\pi\)
\(128\) 4.39284 + 7.60862i 0.388276 + 0.672514i
\(129\) −3.24924 + 5.62785i −0.286080 + 0.495504i
\(130\) 0 0
\(131\) −1.21089 2.09732i −0.105796 0.183244i 0.808267 0.588816i \(-0.200406\pi\)
−0.914063 + 0.405572i \(0.867072\pi\)
\(132\) 10.1291 0.881624
\(133\) −7.94987 11.8852i −0.689341 1.03057i
\(134\) −3.48377 −0.300952
\(135\) 0 0
\(136\) −0.612795 1.06139i −0.0525468 0.0910137i
\(137\) 5.75955 9.97584i 0.492072 0.852293i −0.507886 0.861424i \(-0.669573\pi\)
0.999958 + 0.00913057i \(0.00290639\pi\)
\(138\) 1.22765 + 2.12636i 0.104505 + 0.181008i
\(139\) −3.53776 + 6.12759i −0.300069 + 0.519735i −0.976151 0.217091i \(-0.930343\pi\)
0.676082 + 0.736826i \(0.263676\pi\)
\(140\) 0 0
\(141\) −3.95618 −0.333171
\(142\) 0.0708399 0.122698i 0.00594475 0.0102966i
\(143\) 9.13355 15.8198i 0.763785 1.32292i
\(144\) −6.64964 −0.554137
\(145\) 0 0
\(146\) −0.643032 + 1.11376i −0.0532177 + 0.0921758i
\(147\) −1.93656 3.35422i −0.159725 0.276651i
\(148\) −6.17431 + 10.6942i −0.507525 + 0.879060i
\(149\) −6.37476 11.0414i −0.522240 0.904547i −0.999665 0.0258744i \(-0.991763\pi\)
0.477425 0.878673i \(-0.341570\pi\)
\(150\) 0 0
\(151\) −19.6361 −1.59797 −0.798983 0.601353i \(-0.794628\pi\)
−0.798983 + 0.601353i \(0.794628\pi\)
\(152\) −2.94285 4.39960i −0.238697 0.356855i
\(153\) 1.95744 0.158250
\(154\) −2.63707 4.56753i −0.212501 0.368062i
\(155\) 0 0
\(156\) 3.46400 5.99983i 0.277342 0.480371i
\(157\) −1.54244 2.67159i −0.123101 0.213216i 0.797888 0.602805i \(-0.205950\pi\)
−0.920989 + 0.389589i \(0.872617\pi\)
\(158\) −0.449283 + 0.778182i −0.0357431 + 0.0619088i
\(159\) −7.33131 −0.581410
\(160\) 0 0
\(161\) −12.5696 + 21.7712i −0.990625 + 1.71581i
\(162\) −0.0901827 + 0.156201i −0.00708542 + 0.0122723i
\(163\) −22.4721 −1.76015 −0.880077 0.474831i \(-0.842509\pi\)
−0.880077 + 0.474831i \(0.842509\pi\)
\(164\) 12.9524 1.01141
\(165\) 0 0
\(166\) 0.855642 + 1.48201i 0.0664107 + 0.115027i
\(167\) −5.26987 + 9.12769i −0.407795 + 0.706322i −0.994642 0.103376i \(-0.967036\pi\)
0.586847 + 0.809698i \(0.300369\pi\)
\(168\) −2.05114 3.55268i −0.158249 0.274095i
\(169\) 0.252915 + 0.438062i 0.0194550 + 0.0336970i
\(170\) 0 0
\(171\) 8.43545 0.557059i 0.645075 0.0425994i
\(172\) −12.0097 −0.915730
\(173\) −11.4691 19.8650i −0.871977 1.51031i −0.859949 0.510380i \(-0.829505\pi\)
−0.0120281 0.999928i \(-0.503829\pi\)
\(174\) 0.644953 + 1.11709i 0.0488938 + 0.0846865i
\(175\) 0 0
\(176\) 8.85947 + 15.3450i 0.667807 + 1.15668i
\(177\) −6.93747 + 12.0161i −0.521452 + 0.903182i
\(178\) −2.21778 −0.166230
\(179\) 23.2705 1.73932 0.869661 0.493649i \(-0.164337\pi\)
0.869661 + 0.493649i \(0.164337\pi\)
\(180\) 0 0
\(181\) 7.98346 13.8278i 0.593406 1.02781i −0.400364 0.916356i \(-0.631116\pi\)
0.993770 0.111453i \(-0.0355503\pi\)
\(182\) −3.60736 −0.267395
\(183\) 6.32010 0.467195
\(184\) −4.65298 + 8.05919i −0.343022 + 0.594132i
\(185\) 0 0
\(186\) 0.737020 1.27656i 0.0540409 0.0936016i
\(187\) −2.60794 4.51709i −0.190712 0.330322i
\(188\) −3.65566 6.33179i −0.266617 0.461793i
\(189\) 16.6867 1.21378
\(190\) 0 0
\(191\) −2.44600 −0.176986 −0.0884930 0.996077i \(-0.528205\pi\)
−0.0884930 + 0.996077i \(0.528205\pi\)
\(192\) 2.97100 + 5.14592i 0.214413 + 0.371375i
\(193\) 9.52280 + 16.4940i 0.685466 + 1.18726i 0.973290 + 0.229579i \(0.0737350\pi\)
−0.287824 + 0.957683i \(0.592932\pi\)
\(194\) 1.68388 2.91656i 0.120895 0.209397i
\(195\) 0 0
\(196\) 3.57891 6.19885i 0.255636 0.442775i
\(197\) −6.18524 −0.440680 −0.220340 0.975423i \(-0.570717\pi\)
−0.220340 + 0.975423i \(0.570717\pi\)
\(198\) 3.11819 0.221600
\(199\) −3.60525 + 6.24447i −0.255569 + 0.442659i −0.965050 0.262066i \(-0.915596\pi\)
0.709481 + 0.704725i \(0.248930\pi\)
\(200\) 0 0
\(201\) −11.5320 −0.813407
\(202\) −1.92272 −0.135282
\(203\) −6.60350 + 11.4376i −0.463475 + 0.802763i
\(204\) −0.989093 1.71316i −0.0692504 0.119945i
\(205\) 0 0
\(206\) −2.85001 4.93636i −0.198570 0.343933i
\(207\) −7.43146 12.8717i −0.516522 0.894643i
\(208\) 12.1192 0.840318
\(209\) −12.5242 18.7239i −0.866320 1.29516i
\(210\) 0 0
\(211\) 9.82333 + 17.0145i 0.676266 + 1.17133i 0.976097 + 0.217335i \(0.0697362\pi\)
−0.299831 + 0.953992i \(0.596930\pi\)
\(212\) −6.77440 11.7336i −0.465268 0.805868i
\(213\) 0.234495 0.406158i 0.0160674 0.0278295i
\(214\) −1.35868 2.35330i −0.0928773 0.160868i
\(215\) 0 0
\(216\) 6.17701 0.420292
\(217\) 15.0923 1.02453
\(218\) 0.948379 1.64264i 0.0642323 0.111254i
\(219\) −2.12858 + 3.68680i −0.143836 + 0.249131i
\(220\) 0 0
\(221\) −3.56752 −0.239977
\(222\) 1.03939 1.80028i 0.0697595 0.120827i
\(223\) 5.66690 + 9.81536i 0.379484 + 0.657285i 0.990987 0.133957i \(-0.0427683\pi\)
−0.611504 + 0.791242i \(0.709435\pi\)
\(224\) 5.73299 9.92983i 0.383051 0.663464i
\(225\) 0 0
\(226\) −1.60910 2.78704i −0.107036 0.185391i
\(227\) −11.1369 −0.739180 −0.369590 0.929195i \(-0.620502\pi\)
−0.369590 + 0.929195i \(0.620502\pi\)
\(228\) −4.74996 7.10125i −0.314574 0.470292i
\(229\) 3.51221 0.232093 0.116047 0.993244i \(-0.462978\pi\)
0.116047 + 0.993244i \(0.462978\pi\)
\(230\) 0 0
\(231\) −8.72927 15.1195i −0.574344 0.994792i
\(232\) −2.44446 + 4.23393i −0.160487 + 0.277971i
\(233\) −3.09499 5.36068i −0.202759 0.351190i 0.746657 0.665209i \(-0.231658\pi\)
−0.949417 + 0.314020i \(0.898324\pi\)
\(234\) 1.06638 1.84702i 0.0697113 0.120744i
\(235\) 0 0
\(236\) −25.6419 −1.66915
\(237\) −1.48723 + 2.57595i −0.0966057 + 0.167326i
\(238\) −0.515013 + 0.892028i −0.0333833 + 0.0578216i
\(239\) 12.1221 0.784116 0.392058 0.919940i \(-0.371763\pi\)
0.392058 + 0.919940i \(0.371763\pi\)
\(240\) 0 0
\(241\) 2.55102 4.41849i 0.164326 0.284620i −0.772090 0.635513i \(-0.780789\pi\)
0.936416 + 0.350893i \(0.114122\pi\)
\(242\) −2.44335 4.23200i −0.157064 0.272043i
\(243\) −7.92873 + 13.7330i −0.508629 + 0.880971i
\(244\) 5.84001 + 10.1152i 0.373868 + 0.647559i
\(245\) 0 0
\(246\) −2.18042 −0.139019
\(247\) −15.3740 + 1.01526i −0.978221 + 0.0645996i
\(248\) 5.58681 0.354763
\(249\) 2.83236 + 4.90579i 0.179494 + 0.310892i
\(250\) 0 0
\(251\) −12.7122 + 22.0181i −0.802385 + 1.38977i 0.115657 + 0.993289i \(0.463103\pi\)
−0.918042 + 0.396483i \(0.870231\pi\)
\(252\) 6.05422 + 10.4862i 0.381380 + 0.660570i
\(253\) −19.8022 + 34.2984i −1.24495 + 2.15632i
\(254\) 1.04754 0.0657285
\(255\) 0 0
\(256\) −4.40321 + 7.62659i −0.275201 + 0.476662i
\(257\) −9.22493 + 15.9781i −0.575436 + 0.996684i 0.420559 + 0.907265i \(0.361834\pi\)
−0.995994 + 0.0894183i \(0.971499\pi\)
\(258\) 2.02173 0.125867
\(259\) 21.2841 1.32253
\(260\) 0 0
\(261\) −3.90415 6.76218i −0.241661 0.418569i
\(262\) −0.376717 + 0.652493i −0.0232737 + 0.0403111i
\(263\) −6.47530 11.2155i −0.399284 0.691580i 0.594354 0.804204i \(-0.297408\pi\)
−0.993638 + 0.112624i \(0.964075\pi\)
\(264\) −3.23137 5.59689i −0.198877 0.344465i
\(265\) 0 0
\(266\) −1.96555 + 3.99069i −0.120516 + 0.244685i
\(267\) −7.34134 −0.449283
\(268\) −10.6560 18.4568i −0.650921 1.12743i
\(269\) −0.0782471 0.135528i −0.00477081 0.00826329i 0.863630 0.504126i \(-0.168185\pi\)
−0.868401 + 0.495863i \(0.834852\pi\)
\(270\) 0 0
\(271\) −13.9095 24.0920i −0.844944 1.46349i −0.885670 0.464315i \(-0.846301\pi\)
0.0407264 0.999170i \(-0.487033\pi\)
\(272\) 1.73023 2.99685i 0.104911 0.181711i
\(273\) −11.9411 −0.722711
\(274\) −3.58368 −0.216498
\(275\) 0 0
\(276\) −7.51022 + 13.0081i −0.452062 + 0.782994i
\(277\) −0.524062 −0.0314878 −0.0157439 0.999876i \(-0.505012\pi\)
−0.0157439 + 0.999876i \(0.505012\pi\)
\(278\) 2.20125 0.132022
\(279\) −4.46146 + 7.72748i −0.267101 + 0.462632i
\(280\) 0 0
\(281\) 2.44413 4.23336i 0.145804 0.252541i −0.783868 0.620927i \(-0.786756\pi\)
0.929673 + 0.368386i \(0.120090\pi\)
\(282\) 0.615400 + 1.06590i 0.0366465 + 0.0634736i
\(283\) 8.93931 + 15.4833i 0.531387 + 0.920389i 0.999329 + 0.0366299i \(0.0116623\pi\)
−0.467942 + 0.883759i \(0.655004\pi\)
\(284\) 0.866730 0.0514310
\(285\) 0 0
\(286\) −5.68304 −0.336045
\(287\) −11.1624 19.3338i −0.658894 1.14124i
\(288\) 3.38948 + 5.87075i 0.199727 + 0.345937i
\(289\) 7.99068 13.8403i 0.470040 0.814133i
\(290\) 0 0
\(291\) 5.57400 9.65445i 0.326754 0.565954i
\(292\) −7.86754 −0.460413
\(293\) 7.25399 0.423783 0.211891 0.977293i \(-0.432038\pi\)
0.211891 + 0.977293i \(0.432038\pi\)
\(294\) −0.602479 + 1.04352i −0.0351373 + 0.0608595i
\(295\) 0 0
\(296\) 7.87888 0.457951
\(297\) 26.2882 1.52540
\(298\) −1.98324 + 3.43507i −0.114886 + 0.198988i
\(299\) 13.5441 + 23.4591i 0.783278 + 1.35668i
\(300\) 0 0
\(301\) 10.3500 + 17.9267i 0.596562 + 1.03328i
\(302\) 3.05448 + 5.29051i 0.175766 + 0.304435i
\(303\) −6.36461 −0.365637
\(304\) 6.60345 13.4071i 0.378734 0.768950i
\(305\) 0 0
\(306\) −0.304488 0.527388i −0.0174064 0.0301488i
\(307\) −7.19015 12.4537i −0.410364 0.710771i 0.584566 0.811346i \(-0.301265\pi\)
−0.994929 + 0.100576i \(0.967932\pi\)
\(308\) 16.1323 27.9420i 0.919226 1.59215i
\(309\) −9.43415 16.3404i −0.536690 0.929574i
\(310\) 0 0
\(311\) 8.52590 0.483459 0.241730 0.970344i \(-0.422285\pi\)
0.241730 + 0.970344i \(0.422285\pi\)
\(312\) −4.42033 −0.250252
\(313\) 10.6809 18.4999i 0.603722 1.04568i −0.388530 0.921436i \(-0.627017\pi\)
0.992252 0.124241i \(-0.0396495\pi\)
\(314\) −0.479867 + 0.831153i −0.0270804 + 0.0469047i
\(315\) 0 0
\(316\) −5.49701 −0.309231
\(317\) −14.0464 + 24.3291i −0.788924 + 1.36646i 0.137702 + 0.990474i \(0.456028\pi\)
−0.926626 + 0.375983i \(0.877305\pi\)
\(318\) 1.14041 + 1.97525i 0.0639512 + 0.110767i
\(319\) −10.4032 + 18.0188i −0.582466 + 1.00886i
\(320\) 0 0
\(321\) −4.49752 7.78993i −0.251027 0.434792i
\(322\) 7.82102 0.435848
\(323\) −1.94384 + 3.94662i −0.108158 + 0.219596i
\(324\) −1.10339 −0.0612995
\(325\) 0 0
\(326\) 3.49563 + 6.05461i 0.193605 + 0.335334i
\(327\) 3.13934 5.43750i 0.173606 0.300694i
\(328\) −4.13205 7.15692i −0.228154 0.395175i
\(329\) −6.30091 + 10.9135i −0.347381 + 0.601681i
\(330\) 0 0
\(331\) 15.1725 0.833957 0.416979 0.908916i \(-0.363089\pi\)
0.416979 + 0.908916i \(0.363089\pi\)
\(332\) −5.23441 + 9.06627i −0.287276 + 0.497576i
\(333\) −6.29184 + 10.8978i −0.344791 + 0.597195i
\(334\) 3.27900 0.179419
\(335\) 0 0
\(336\) 5.79140 10.0310i 0.315947 0.547236i
\(337\) 8.75041 + 15.1562i 0.476665 + 0.825608i 0.999642 0.0267383i \(-0.00851209\pi\)
−0.522977 + 0.852347i \(0.675179\pi\)
\(338\) 0.0786838 0.136284i 0.00427984 0.00741289i
\(339\) −5.32647 9.22571i −0.289294 0.501072i
\(340\) 0 0
\(341\) 23.7764 1.28757
\(342\) −1.46225 2.18609i −0.0790697 0.118210i
\(343\) 10.6254 0.573720
\(344\) 3.83131 + 6.63603i 0.206570 + 0.357791i
\(345\) 0 0
\(346\) −3.56812 + 6.18016i −0.191823 + 0.332247i
\(347\) −8.68435 15.0417i −0.466201 0.807483i 0.533054 0.846081i \(-0.321044\pi\)
−0.999255 + 0.0385980i \(0.987711\pi\)
\(348\) −3.94552 + 6.83385i −0.211502 + 0.366333i
\(349\) −34.2563 −1.83370 −0.916850 0.399232i \(-0.869277\pi\)
−0.916850 + 0.399232i \(0.869277\pi\)
\(350\) 0 0
\(351\) 8.99019 15.5715i 0.479861 0.831144i
\(352\) 9.03176 15.6435i 0.481394 0.833799i
\(353\) 34.9287 1.85907 0.929534 0.368736i \(-0.120209\pi\)
0.929534 + 0.368736i \(0.120209\pi\)
\(354\) 4.31660 0.229425
\(355\) 0 0
\(356\) −6.78367 11.7497i −0.359534 0.622731i
\(357\) −1.70480 + 2.95281i −0.0902278 + 0.156279i
\(358\) −3.61982 6.26972i −0.191314 0.331365i
\(359\) 0.488273 + 0.845713i 0.0257701 + 0.0446350i 0.878623 0.477516i \(-0.158463\pi\)
−0.852853 + 0.522151i \(0.825130\pi\)
\(360\) 0 0
\(361\) −7.25370 + 17.5609i −0.381774 + 0.924256i
\(362\) −4.96743 −0.261082
\(363\) −8.08801 14.0088i −0.424510 0.735273i
\(364\) −11.0341 19.1116i −0.578342 1.00172i
\(365\) 0 0
\(366\) −0.983116 1.70281i −0.0513883 0.0890071i
\(367\) −4.93318 + 8.54451i −0.257510 + 0.446020i −0.965574 0.260128i \(-0.916235\pi\)
0.708064 + 0.706148i \(0.249569\pi\)
\(368\) −26.2754 −1.36970
\(369\) 13.1989 0.687109
\(370\) 0 0
\(371\) −11.6764 + 20.2241i −0.606208 + 1.04998i
\(372\) 9.01748 0.467535
\(373\) −12.9521 −0.670634 −0.335317 0.942105i \(-0.608843\pi\)
−0.335317 + 0.942105i \(0.608843\pi\)
\(374\) −0.811352 + 1.40530i −0.0419540 + 0.0726664i
\(375\) 0 0
\(376\) −2.33245 + 4.03992i −0.120287 + 0.208343i
\(377\) 7.11547 + 12.3244i 0.366465 + 0.634737i
\(378\) −2.59568 4.49585i −0.133507 0.231241i
\(379\) 5.21597 0.267926 0.133963 0.990986i \(-0.457230\pi\)
0.133963 + 0.990986i \(0.457230\pi\)
\(380\) 0 0
\(381\) 3.46758 0.177650
\(382\) 0.380484 + 0.659018i 0.0194673 + 0.0337183i
\(383\) −16.7657 29.0390i −0.856686 1.48382i −0.875072 0.483993i \(-0.839186\pi\)
0.0183857 0.999831i \(-0.494147\pi\)
\(384\) 4.52390 7.83562i 0.230859 0.399860i
\(385\) 0 0
\(386\) 2.96262 5.13141i 0.150793 0.261182i
\(387\) −12.2383 −0.622107
\(388\) 20.6023 1.04593
\(389\) −13.8703 + 24.0241i −0.703253 + 1.21807i 0.264066 + 0.964505i \(0.414936\pi\)
−0.967318 + 0.253565i \(0.918397\pi\)
\(390\) 0 0
\(391\) 7.73464 0.391158
\(392\) −4.56695 −0.230666
\(393\) −1.24702 + 2.15989i −0.0629036 + 0.108952i
\(394\) 0.962139 + 1.66647i 0.0484718 + 0.0839557i
\(395\) 0 0
\(396\) 9.53783 + 16.5200i 0.479294 + 0.830161i
\(397\) 2.74971 + 4.76264i 0.138004 + 0.239030i 0.926741 0.375701i \(-0.122598\pi\)
−0.788737 + 0.614731i \(0.789265\pi\)
\(398\) 2.24324 0.112444
\(399\) −6.50640 + 13.2101i −0.325728 + 0.661331i
\(400\) 0 0
\(401\) 4.25655 + 7.37256i 0.212562 + 0.368168i 0.952516 0.304490i \(-0.0984860\pi\)
−0.739954 + 0.672658i \(0.765153\pi\)
\(402\) 1.79385 + 3.10704i 0.0894692 + 0.154965i
\(403\) 8.13120 14.0836i 0.405044 0.701556i
\(404\) −5.88114 10.1864i −0.292597 0.506794i
\(405\) 0 0
\(406\) 4.10880 0.203917
\(407\) 33.5311 1.66207
\(408\) −0.631078 + 1.09306i −0.0312430 + 0.0541145i
\(409\) 10.7353 18.5941i 0.530826 0.919418i −0.468527 0.883449i \(-0.655215\pi\)
0.999353 0.0359683i \(-0.0114515\pi\)
\(410\) 0 0
\(411\) −11.8628 −0.585148
\(412\) 17.4350 30.1983i 0.858962 1.48777i
\(413\) 22.0983 + 38.2753i 1.08738 + 1.88341i
\(414\) −2.31199 + 4.00448i −0.113628 + 0.196809i
\(415\) 0 0
\(416\) −6.17746 10.6997i −0.302875 0.524595i
\(417\) 7.28662 0.356827
\(418\) −3.09653 + 6.28694i −0.151456 + 0.307504i
\(419\) −5.09378 −0.248848 −0.124424 0.992229i \(-0.539708\pi\)
−0.124424 + 0.992229i \(0.539708\pi\)
\(420\) 0 0
\(421\) −2.82911 4.90017i −0.137883 0.238820i 0.788812 0.614634i \(-0.210696\pi\)
−0.926695 + 0.375815i \(0.877363\pi\)
\(422\) 3.05611 5.29335i 0.148769 0.257676i
\(423\) −3.72525 6.45232i −0.181128 0.313723i
\(424\) −4.32232 + 7.48648i −0.209910 + 0.363576i
\(425\) 0 0
\(426\) −0.145907 −0.00706920
\(427\) 10.0659 17.4346i 0.487121 0.843719i
\(428\) 8.31176 14.3964i 0.401764 0.695876i
\(429\) −18.8121 −0.908256
\(430\) 0 0
\(431\) 19.1834 33.2267i 0.924033 1.60047i 0.130923 0.991392i \(-0.458206\pi\)
0.793109 0.609079i \(-0.208461\pi\)
\(432\) 8.72041 + 15.1042i 0.419561 + 0.726701i
\(433\) −3.48125 + 6.02970i −0.167298 + 0.289769i −0.937469 0.348069i \(-0.886838\pi\)
0.770171 + 0.637838i \(0.220171\pi\)
\(434\) −2.34767 4.06628i −0.112692 0.195188i
\(435\) 0 0
\(436\) 11.6035 0.555706
\(437\) 33.3319 2.20116i 1.59448 0.105296i
\(438\) 1.32443 0.0632839
\(439\) −4.76346 8.25055i −0.227347 0.393777i 0.729674 0.683796i \(-0.239672\pi\)
−0.957021 + 0.290018i \(0.906339\pi\)
\(440\) 0 0
\(441\) 3.64703 6.31685i 0.173668 0.300802i
\(442\) 0.554941 + 0.961187i 0.0263959 + 0.0457190i
\(443\) −17.3519 + 30.0544i −0.824414 + 1.42793i 0.0779516 + 0.996957i \(0.475162\pi\)
−0.902366 + 0.430971i \(0.858171\pi\)
\(444\) 12.7170 0.603524
\(445\) 0 0
\(446\) 1.76302 3.05363i 0.0834813 0.144594i
\(447\) −6.56495 + 11.3708i −0.310511 + 0.537821i
\(448\) 18.9273 0.894233
\(449\) −8.84228 −0.417293 −0.208646 0.977991i \(-0.566906\pi\)
−0.208646 + 0.977991i \(0.566906\pi\)
\(450\) 0 0
\(451\) −17.5852 30.4585i −0.828056 1.43423i
\(452\) 9.84371 17.0498i 0.463009 0.801956i
\(453\) 10.1110 + 17.5127i 0.475056 + 0.822821i
\(454\) 1.73238 + 3.00058i 0.0813048 + 0.140824i
\(455\) 0 0
\(456\) −2.40852 + 4.89005i −0.112789 + 0.228998i
\(457\) 0.664998 0.0311073 0.0155536 0.999879i \(-0.495049\pi\)
0.0155536 + 0.999879i \(0.495049\pi\)
\(458\) −0.546338 0.946285i −0.0255287 0.0442170i
\(459\) −2.56701 4.44619i −0.119818 0.207531i
\(460\) 0 0
\(461\) 19.7696 + 34.2420i 0.920762 + 1.59481i 0.798238 + 0.602342i \(0.205766\pi\)
0.122524 + 0.992466i \(0.460901\pi\)
\(462\) −2.71574 + 4.70381i −0.126348 + 0.218841i
\(463\) −15.5782 −0.723981 −0.361991 0.932182i \(-0.617903\pi\)
−0.361991 + 0.932182i \(0.617903\pi\)
\(464\) −13.8039 −0.640830
\(465\) 0 0
\(466\) −0.962875 + 1.66775i −0.0446043 + 0.0772569i
\(467\) 41.0358 1.89891 0.949456 0.313901i \(-0.101636\pi\)
0.949456 + 0.313901i \(0.101636\pi\)
\(468\) 13.0472 0.603107
\(469\) −18.3668 + 31.8122i −0.848099 + 1.46895i
\(470\) 0 0
\(471\) −1.58846 + 2.75130i −0.0731925 + 0.126773i
\(472\) 8.18025 + 14.1686i 0.376527 + 0.652163i
\(473\) 16.3053 + 28.2417i 0.749721 + 1.29855i
\(474\) 0.925375 0.0425039
\(475\) 0 0
\(476\) −6.30121 −0.288816
\(477\) −6.90336 11.9570i −0.316083 0.547472i
\(478\) −1.88565 3.26604i −0.0862475 0.149385i
\(479\) 11.7794 20.4024i 0.538213 0.932211i −0.460788 0.887510i \(-0.652433\pi\)
0.999000 0.0447012i \(-0.0142336\pi\)
\(480\) 0 0
\(481\) 11.4671 19.8617i 0.522857 0.905614i
\(482\) −1.58728 −0.0722988
\(483\) 25.8893 1.17800
\(484\) 14.9472 25.8894i 0.679420 1.17679i
\(485\) 0 0
\(486\) 4.93338 0.223783
\(487\) −23.9166 −1.08377 −0.541883 0.840454i \(-0.682288\pi\)
−0.541883 + 0.840454i \(0.682288\pi\)
\(488\) 3.72614 6.45387i 0.168675 0.292153i
\(489\) 11.5713 + 20.0421i 0.523272 + 0.906334i
\(490\) 0 0
\(491\) −8.17373 14.1573i −0.368875 0.638911i 0.620515 0.784195i \(-0.286924\pi\)
−0.989390 + 0.145284i \(0.953590\pi\)
\(492\) −6.66940 11.5517i −0.300680 0.520793i
\(493\) 4.06343 0.183007
\(494\) 2.66502 + 3.98423i 0.119905 + 0.179259i
\(495\) 0 0
\(496\) 7.88720 + 13.6610i 0.354146 + 0.613398i
\(497\) −0.746950 1.29375i −0.0335053 0.0580328i
\(498\) 0.881169 1.52623i 0.0394861 0.0683920i
\(499\) 16.0354 + 27.7742i 0.717844 + 1.24334i 0.961852 + 0.273569i \(0.0882041\pi\)
−0.244009 + 0.969773i \(0.578463\pi\)
\(500\) 0 0
\(501\) 10.8542 0.484930
\(502\) 7.90972 0.353028
\(503\) −7.36269 + 12.7525i −0.328286 + 0.568608i −0.982172 0.187985i \(-0.939804\pi\)
0.653886 + 0.756593i \(0.273138\pi\)
\(504\) 3.86282 6.69060i 0.172064 0.298023i
\(505\) 0 0
\(506\) 12.3212 0.547746
\(507\) 0.260461 0.451131i 0.0115675 0.0200354i
\(508\) 3.20418 + 5.54980i 0.142162 + 0.246232i
\(509\) 11.0332 19.1100i 0.489037 0.847036i −0.510884 0.859650i \(-0.670682\pi\)
0.999920 + 0.0126136i \(0.00401513\pi\)
\(510\) 0 0
\(511\) 6.78026 + 11.7438i 0.299941 + 0.519513i
\(512\) 20.3111 0.897633
\(513\) −12.3277 18.4300i −0.544280 0.813705i
\(514\) 5.73990 0.253176
\(515\) 0 0
\(516\) 6.18399 + 10.7110i 0.272235 + 0.471525i
\(517\) −9.92647 + 17.1931i −0.436565 + 0.756154i
\(518\) −3.31083 5.73453i −0.145470 0.251961i
\(519\) −11.8112 + 20.4577i −0.518456 + 0.897992i
\(520\) 0 0
\(521\) −14.7781 −0.647442 −0.323721 0.946153i \(-0.604934\pi\)
−0.323721 + 0.946153i \(0.604934\pi\)
\(522\) −1.21461 + 2.10377i −0.0531621 + 0.0920794i
\(523\) 6.35498 11.0072i 0.277884 0.481309i −0.692975 0.720962i \(-0.743700\pi\)
0.970859 + 0.239653i \(0.0770336\pi\)
\(524\) −4.60916 −0.201352
\(525\) 0 0
\(526\) −2.01452 + 3.48924i −0.0878371 + 0.152138i
\(527\) −2.32174 4.02137i −0.101136 0.175174i
\(528\) 9.12378 15.8029i 0.397062 0.687731i
\(529\) −17.8647 30.9426i −0.776726 1.34533i
\(530\) 0 0
\(531\) −26.1301 −1.13395
\(532\) −27.1546 + 1.79323i −1.17730 + 0.0777464i
\(533\) −24.0556 −1.04196
\(534\) 1.14197 + 1.97796i 0.0494180 + 0.0855946i
\(535\) 0 0
\(536\) −6.79894 + 11.7761i −0.293670 + 0.508651i
\(537\) −11.9824 20.7541i −0.517079 0.895607i
\(538\) −0.0243433 + 0.0421638i −0.00104951 + 0.00181781i
\(539\) −19.4361 −0.837172
\(540\) 0 0
\(541\) 15.1172 26.1838i 0.649941 1.12573i −0.333196 0.942858i \(-0.608127\pi\)
0.983137 0.182873i \(-0.0585396\pi\)
\(542\) −4.32736 + 7.49521i −0.185876 + 0.321947i
\(543\) −16.4433 −0.705649
\(544\) −3.52776 −0.151251
\(545\) 0 0
\(546\) 1.85749 + 3.21727i 0.0794933 + 0.137686i
\(547\) 3.90372 6.76144i 0.166911 0.289098i −0.770421 0.637535i \(-0.779954\pi\)
0.937332 + 0.348437i \(0.113287\pi\)
\(548\) −10.9617 18.9861i −0.468259 0.811048i
\(549\) 5.95118 + 10.3077i 0.253990 + 0.439924i
\(550\) 0 0
\(551\) 17.5110 1.15639i 0.745995 0.0492639i
\(552\) 9.58359 0.407905
\(553\) 4.73733 + 8.20530i 0.201452 + 0.348925i
\(554\) 0.0815198 + 0.141196i 0.00346345 + 0.00599886i
\(555\) 0 0
\(556\) 6.73311 + 11.6621i 0.285548 + 0.494583i
\(557\) −1.20747 + 2.09141i −0.0511623 + 0.0886157i −0.890472 0.455037i \(-0.849626\pi\)
0.839310 + 0.543653i \(0.182959\pi\)
\(558\) 2.77599 0.117517
\(559\) 22.3048 0.943392
\(560\) 0 0
\(561\) −2.68575 + 4.65186i −0.113392 + 0.196402i
\(562\) −1.52078 −0.0641500
\(563\) 25.3392 1.06792 0.533960 0.845510i \(-0.320703\pi\)
0.533960 + 0.845510i \(0.320703\pi\)
\(564\) −3.76473 + 6.52070i −0.158524 + 0.274571i
\(565\) 0 0
\(566\) 2.78109 4.81699i 0.116898 0.202473i
\(567\) 0.950905 + 1.64702i 0.0399342 + 0.0691681i
\(568\) −0.276503 0.478917i −0.0116018 0.0200949i
\(569\) −45.1046 −1.89088 −0.945441 0.325793i \(-0.894369\pi\)
−0.945441 + 0.325793i \(0.894369\pi\)
\(570\) 0 0
\(571\) −9.73299 −0.407313 −0.203656 0.979042i \(-0.565283\pi\)
−0.203656 + 0.979042i \(0.565283\pi\)
\(572\) −17.3831 30.1084i −0.726823 1.25889i
\(573\) 1.25949 + 2.18149i 0.0526158 + 0.0911332i
\(574\) −3.47270 + 6.01490i −0.144948 + 0.251057i
\(575\) 0 0
\(576\) −5.59515 + 9.69108i −0.233131 + 0.403795i
\(577\) −8.83145 −0.367658 −0.183829 0.982958i \(-0.558849\pi\)
−0.183829 + 0.982958i \(0.558849\pi\)
\(578\) −4.97192 −0.206805
\(579\) 9.80691 16.9861i 0.407561 0.705917i
\(580\) 0 0
\(581\) 18.0441 0.748596
\(582\) −3.46823 −0.143763
\(583\) −18.3950 + 31.8611i −0.761843 + 1.31955i
\(584\) 2.50989 + 4.34726i 0.103860 + 0.179891i
\(585\) 0 0
\(586\) −1.12839 1.95442i −0.0466132 0.0807365i
\(587\) 13.4966 + 23.3768i 0.557065 + 0.964865i 0.997740 + 0.0671982i \(0.0214060\pi\)
−0.440674 + 0.897667i \(0.645261\pi\)
\(588\) −7.37137 −0.303990
\(589\) −11.1498 16.6691i −0.459419 0.686837i
\(590\) 0 0
\(591\) 3.18489 + 5.51639i 0.131009 + 0.226914i
\(592\) 11.1230 + 19.2657i 0.457154 + 0.791814i
\(593\) 10.6170 18.3891i 0.435987 0.755151i −0.561389 0.827552i \(-0.689733\pi\)
0.997376 + 0.0724009i \(0.0230661\pi\)
\(594\) −4.08923 7.08276i −0.167783 0.290609i
\(595\) 0 0
\(596\) −24.2650 −0.993934
\(597\) 7.42562 0.303910
\(598\) 4.21369 7.29832i 0.172311 0.298451i
\(599\) 15.1647 26.2660i 0.619612 1.07320i −0.369945 0.929054i \(-0.620623\pi\)
0.989556 0.144146i \(-0.0460434\pi\)
\(600\) 0 0
\(601\) −10.7285 −0.437624 −0.218812 0.975767i \(-0.570218\pi\)
−0.218812 + 0.975767i \(0.570218\pi\)
\(602\) 3.21996 5.57713i 0.131236 0.227307i
\(603\) −10.8589 18.8081i −0.442208 0.765926i
\(604\) −18.6859 + 32.3649i −0.760317 + 1.31691i
\(605\) 0 0
\(606\) 0.990039 + 1.71480i 0.0402176 + 0.0696589i
\(607\) 8.81498 0.357789 0.178894 0.983868i \(-0.442748\pi\)
0.178894 + 0.983868i \(0.442748\pi\)
\(608\) −15.2026 + 1.00395i −0.616548 + 0.0407154i
\(609\) 13.6010 0.551142
\(610\) 0 0
\(611\) 6.78942 + 11.7596i 0.274671 + 0.475743i
\(612\) 1.86271 3.22631i 0.0752957 0.130416i
\(613\) −12.0654 20.8978i −0.487315 0.844055i 0.512578 0.858640i \(-0.328690\pi\)
−0.999894 + 0.0145856i \(0.995357\pi\)
\(614\) −2.23691 + 3.87445i −0.0902744 + 0.156360i
\(615\) 0 0
\(616\) −20.5861 −0.829436
\(617\) 7.73248 13.3930i 0.311298 0.539183i −0.667346 0.744748i \(-0.732570\pi\)
0.978644 + 0.205564i \(0.0659030\pi\)
\(618\) −2.93504 + 5.08363i −0.118065 + 0.204494i
\(619\) 0.0390990 0.00157152 0.000785761 1.00000i \(-0.499750\pi\)
0.000785761 1.00000i \(0.499750\pi\)
\(620\) 0 0
\(621\) −19.4914 + 33.7601i −0.782163 + 1.35475i
\(622\) −1.32624 2.29711i −0.0531772 0.0921057i
\(623\) −11.6924 + 20.2518i −0.468445 + 0.811370i
\(624\) −6.24041 10.8087i −0.249816 0.432694i
\(625\) 0 0
\(626\) −6.64584 −0.265621
\(627\) −10.2502 + 20.8112i −0.409353 + 0.831117i
\(628\) −5.87120 −0.234286
\(629\) −3.27427 5.67119i −0.130554 0.226125i
\(630\) 0 0
\(631\) −3.36758 + 5.83282i −0.134061 + 0.232201i −0.925238 0.379386i \(-0.876135\pi\)
0.791177 + 0.611587i \(0.209469\pi\)
\(632\) 1.75365 + 3.03741i 0.0697564 + 0.120822i
\(633\) 10.1164 17.5221i 0.402091 0.696442i
\(634\) 8.73989 0.347105
\(635\) 0 0
\(636\) −6.97651 + 12.0837i −0.276637 + 0.479149i
\(637\) −6.64687 + 11.5127i −0.263358 + 0.456150i
\(638\) 6.47301 0.256269
\(639\) 0.883229 0.0349400
\(640\) 0 0
\(641\) −13.7894 23.8840i −0.544649 0.943360i −0.998629 0.0523477i \(-0.983330\pi\)
0.453980 0.891012i \(-0.350004\pi\)
\(642\) −1.39921 + 2.42351i −0.0552226 + 0.0956483i
\(643\) −5.95407 10.3128i −0.234806 0.406695i 0.724410 0.689369i \(-0.242112\pi\)
−0.959216 + 0.282673i \(0.908779\pi\)
\(644\) 23.9227 + 41.4353i 0.942685 + 1.63278i
\(645\) 0 0
\(646\) 1.36570 0.0901878i 0.0537327 0.00354839i
\(647\) −11.6648 −0.458590 −0.229295 0.973357i \(-0.573642\pi\)
−0.229295 + 0.973357i \(0.573642\pi\)
\(648\) 0.352002 + 0.609686i 0.0138280 + 0.0239507i
\(649\) 34.8136 + 60.2990i 1.36656 + 2.36694i
\(650\) 0 0
\(651\) −7.77128 13.4603i −0.304581 0.527549i
\(652\) −21.3846 + 37.0393i −0.837487 + 1.45057i
\(653\) −40.7527 −1.59477 −0.797387 0.603468i \(-0.793785\pi\)
−0.797387 + 0.603468i \(0.793785\pi\)
\(654\) −1.95335 −0.0763819
\(655\) 0 0
\(656\) 11.6669 20.2076i 0.455514 0.788974i
\(657\) −8.01730 −0.312785
\(658\) 3.92053 0.152838
\(659\) 11.5723 20.0438i 0.450793 0.780796i −0.547643 0.836712i \(-0.684475\pi\)
0.998435 + 0.0559165i \(0.0178081\pi\)
\(660\) 0 0
\(661\) −2.44485 + 4.23460i −0.0950936 + 0.164707i −0.909648 0.415381i \(-0.863648\pi\)
0.814554 + 0.580088i \(0.196982\pi\)
\(662\) −2.36015 4.08789i −0.0917297 0.158880i
\(663\) 1.83698 + 3.18174i 0.0713423 + 0.123568i
\(664\) 6.67950 0.259215
\(665\) 0 0
\(666\) 3.91488 0.151699
\(667\) −15.4269 26.7201i −0.597331 1.03461i
\(668\) 10.0297 + 17.3719i 0.388060 + 0.672140i
\(669\) 5.83597 10.1082i 0.225632 0.390805i
\(670\) 0 0
\(671\) 15.8578 27.4665i 0.612182 1.06033i
\(672\) −11.8081 −0.455506
\(673\) 29.5149 1.13771 0.568857 0.822436i \(-0.307386\pi\)
0.568857 + 0.822436i \(0.307386\pi\)
\(674\) 2.72232 4.71520i 0.104860 0.181623i
\(675\) 0 0
\(676\) 0.962701 0.0370270
\(677\) −29.4248 −1.13089 −0.565443 0.824788i \(-0.691295\pi\)
−0.565443 + 0.824788i \(0.691295\pi\)
\(678\) −1.65711 + 2.87019i −0.0636408 + 0.110229i
\(679\) −17.7551 30.7528i −0.681380 1.18018i
\(680\) 0 0
\(681\) 5.73457 + 9.93256i 0.219749 + 0.380616i
\(682\) −3.69852 6.40602i −0.141623 0.245299i
\(683\) 29.9433 1.14575 0.572875 0.819643i \(-0.305828\pi\)
0.572875 + 0.819643i \(0.305828\pi\)
\(684\) 7.10907 14.4337i 0.271822 0.551885i
\(685\) 0 0
\(686\) −1.65283 2.86278i −0.0631053 0.109302i
\(687\) −1.80850 3.13241i −0.0689985 0.119509i
\(688\) −10.8177 + 18.7369i −0.412422 + 0.714336i
\(689\) 12.5816 + 21.7921i 0.479323 + 0.830211i
\(690\) 0 0
\(691\) −24.2225 −0.921467 −0.460733 0.887539i \(-0.652414\pi\)
−0.460733 + 0.887539i \(0.652414\pi\)
\(692\) −43.6561 −1.65956
\(693\) 16.4394 28.4739i 0.624482 1.08164i
\(694\) −2.70177 + 4.67960i −0.102558 + 0.177635i
\(695\) 0 0
\(696\) 5.03478 0.190843
\(697\) −3.43435 + 5.94847i −0.130085 + 0.225314i
\(698\) 5.32871 + 9.22959i 0.201695 + 0.349345i
\(699\) −3.18733 + 5.52061i −0.120556 + 0.208809i
\(700\) 0 0
\(701\) 7.42695 + 12.8639i 0.280512 + 0.485861i 0.971511 0.236995i \(-0.0761624\pi\)
−0.690999 + 0.722856i \(0.742829\pi\)
\(702\) −5.59384 −0.211126
\(703\) −15.7241 23.5078i −0.593047 0.886613i
\(704\) 29.8182 1.12381
\(705\) 0 0
\(706\) −5.43330 9.41075i −0.204485 0.354178i
\(707\) −10.1367 + 17.5574i −0.381232 + 0.660313i
\(708\) 13.2035 + 22.8691i 0.496217 + 0.859473i
\(709\) 14.9004 25.8083i 0.559598 0.969252i −0.437932 0.899008i \(-0.644289\pi\)
0.997530 0.0702441i \(-0.0223778\pi\)
\(710\) 0 0
\(711\) −5.60165 −0.210078
\(712\) −4.32823 + 7.49672i −0.162207 + 0.280952i
\(713\) −17.6290 + 30.5344i −0.660213 + 1.14352i
\(714\) 1.06076 0.0396978
\(715\) 0 0
\(716\) 22.1444 38.3552i 0.827575 1.43340i
\(717\) −6.24190 10.8113i −0.233108 0.403755i
\(718\) 0.151905 0.263108i 0.00566906 0.00981910i
\(719\) 12.9463 + 22.4236i 0.482814 + 0.836258i 0.999805 0.0197322i \(-0.00628136\pi\)
−0.516991 + 0.855991i \(0.672948\pi\)
\(720\) 0 0
\(721\) −60.1021 −2.23832
\(722\) 5.85972 0.777316i 0.218076 0.0289287i
\(723\) −5.25426 −0.195408
\(724\) −15.1942 26.3171i −0.564688 0.978069i
\(725\) 0 0
\(726\) −2.51624 + 4.35826i −0.0933865 + 0.161750i
\(727\) −4.67442 8.09634i −0.173365 0.300277i 0.766229 0.642567i \(-0.222131\pi\)
−0.939594 + 0.342291i \(0.888797\pi\)
\(728\) −7.04014 + 12.1939i −0.260925 + 0.451935i
\(729\) 14.5913 0.540419
\(730\) 0 0
\(731\) 3.18439 5.51553i 0.117779 0.203999i
\(732\) 6.01424 10.4170i 0.222293 0.385022i
\(733\) 7.20434 0.266098 0.133049 0.991109i \(-0.457523\pi\)
0.133049 + 0.991109i \(0.457523\pi\)
\(734\) 3.06950 0.113297
\(735\) 0 0
\(736\) 13.3932 + 23.1977i 0.493680 + 0.855079i
\(737\) −28.9350 + 50.1170i −1.06584 + 1.84608i
\(738\) −2.05314 3.55615i −0.0755773 0.130904i
\(739\) −6.48702 11.2359i −0.238629 0.413318i 0.721692 0.692214i \(-0.243365\pi\)
−0.960321 + 0.278897i \(0.910031\pi\)
\(740\) 0 0
\(741\) 8.82179 + 13.1887i 0.324077 + 0.484498i
\(742\) 7.26523 0.266715
\(743\) −4.61550 7.99428i −0.169326 0.293282i 0.768857 0.639421i \(-0.220826\pi\)
−0.938183 + 0.346139i \(0.887492\pi\)
\(744\) −2.87674 4.98267i −0.105467 0.182673i
\(745\) 0 0
\(746\) 2.01475 + 3.48965i 0.0737652 + 0.127765i
\(747\) −5.33405 + 9.23885i −0.195163 + 0.338032i
\(748\) −9.92694 −0.362965
\(749\) −28.6523 −1.04693
\(750\) 0 0
\(751\) −7.46131 + 12.9234i −0.272267 + 0.471580i −0.969442 0.245321i \(-0.921107\pi\)
0.697175 + 0.716901i \(0.254440\pi\)
\(752\) −13.1714 −0.480310
\(753\) 26.1829 0.954157
\(754\) 2.21368 3.83420i 0.0806174 0.139633i
\(755\) 0 0
\(756\) 15.8791 27.5035i 0.577519 1.00029i
\(757\) −12.2488 21.2156i −0.445191 0.771093i 0.552874 0.833265i \(-0.313531\pi\)
−0.998066 + 0.0621711i \(0.980198\pi\)
\(758\) −0.811365 1.40532i −0.0294701 0.0510437i
\(759\) 40.7860 1.48044
\(760\) 0 0
\(761\) −15.8968 −0.576260 −0.288130 0.957591i \(-0.593034\pi\)
−0.288130 + 0.957591i \(0.593034\pi\)
\(762\) −0.539396 0.934262i −0.0195403 0.0338447i
\(763\) −9.99990 17.3203i −0.362021 0.627038i
\(764\) −2.32762 + 4.03156i −0.0842105 + 0.145857i
\(765\) 0 0
\(766\) −5.21593 + 9.03426i −0.188459 + 0.326421i
\(767\) 47.6231 1.71957
\(768\) 9.06916 0.327255
\(769\) 14.7925 25.6214i 0.533432 0.923931i −0.465806 0.884887i \(-0.654235\pi\)
0.999238 0.0390437i \(-0.0124312\pi\)
\(770\) 0 0
\(771\) 19.0003 0.684280
\(772\) 36.2478 1.30459
\(773\) −7.06551 + 12.2378i −0.254129 + 0.440164i −0.964658 0.263503i \(-0.915122\pi\)
0.710530 + 0.703667i \(0.248455\pi\)
\(774\) 1.90371 + 3.29733i 0.0684276 + 0.118520i
\(775\) 0 0
\(776\) −6.57253 11.3840i −0.235940 0.408660i
\(777\) −10.9596 18.9825i −0.393172 0.680995i
\(778\) 8.63032 0.309412
\(779\) −13.1072 + 26.6119i −0.469615 + 0.953469i
\(780\) 0 0
\(781\) −1.17675 2.03818i −0.0421073 0.0729319i
\(782\) −1.20315 2.08392i −0.0430247 0.0745210i
\(783\) −10.2399 + 17.7360i −0.365944 + 0.633833i
\(784\) −6.44741 11.1672i −0.230265 0.398830i
\(785\) 0 0
\(786\) 0.775912 0.0276759
\(787\) 24.2465 0.864293 0.432146 0.901803i \(-0.357756\pi\)
0.432146 + 0.901803i \(0.357756\pi\)
\(788\) −5.88591 + 10.1947i −0.209677 + 0.363171i
\(789\) −6.66849 + 11.5502i −0.237404 + 0.411196i
\(790\) 0 0
\(791\) −33.9333 −1.20653
\(792\) 6.08549 10.5404i 0.216238 0.374536i
\(793\) −10.8463 18.7863i −0.385162 0.667120i
\(794\) 0.855456 1.48169i 0.0303590 0.0525833i
\(795\) 0 0
\(796\) 6.86155 + 11.8846i 0.243201 + 0.421237i
\(797\) −27.9258 −0.989184 −0.494592 0.869125i \(-0.664682\pi\)
−0.494592 + 0.869125i \(0.664682\pi\)
\(798\) 4.57125 0.301875i 0.161820 0.0106863i
\(799\) 3.87723 0.137166
\(800\) 0 0
\(801\) −6.91280 11.9733i −0.244252 0.423057i
\(802\) 1.32425 2.29366i 0.0467607 0.0809919i
\(803\) 10.6816 + 18.5011i 0.376946 + 0.652890i
\(804\) −10.9739 + 19.0074i −0.387021 + 0.670341i
\(805\) 0 0
\(806\) −5.05936 −0.178208
\(807\) −0.0805816 + 0.139571i −0.00283661 + 0.00491315i
\(808\) −3.75238 + 6.49932i −0.132008 + 0.228645i
\(809\) 8.78914 0.309010 0.154505 0.987992i \(-0.450622\pi\)
0.154505 + 0.987992i \(0.450622\pi\)
\(810\) 0 0
\(811\) 7.04963 12.2103i 0.247546 0.428762i −0.715298 0.698819i \(-0.753709\pi\)
0.962844 + 0.270057i \(0.0870425\pi\)
\(812\) 12.5679 + 21.7682i 0.441046 + 0.763914i
\(813\) −14.3245 + 24.8108i −0.502383 + 0.870152i
\(814\) −5.21589 9.03418i −0.182817 0.316648i
\(815\) 0 0
\(816\) −3.56370 −0.124755
\(817\) 12.1533 24.6750i 0.425189 0.863269i
\(818\) −6.67967 −0.233549
\(819\) −11.2441 19.4754i −0.392901 0.680524i
\(820\) 0 0
\(821\) 15.2663 26.4420i 0.532797 0.922832i −0.466469 0.884537i \(-0.654474\pi\)
0.999267 0.0382943i \(-0.0121924\pi\)
\(822\) 1.84530 + 3.19616i 0.0643623 + 0.111479i
\(823\) 7.17914 12.4346i 0.250249 0.433444i −0.713345 0.700813i \(-0.752821\pi\)
0.963594 + 0.267369i \(0.0861542\pi\)
\(824\) −22.2484 −0.775059
\(825\) 0 0
\(826\) 6.87495 11.9078i 0.239210 0.414324i
\(827\) 4.13682 7.16518i 0.143851 0.249158i −0.785092 0.619379i \(-0.787385\pi\)
0.928944 + 0.370221i \(0.120718\pi\)
\(828\) −28.2873 −0.983052
\(829\) 13.1498 0.456710 0.228355 0.973578i \(-0.426665\pi\)
0.228355 + 0.973578i \(0.426665\pi\)
\(830\) 0 0
\(831\) 0.269848 + 0.467391i 0.00936094 + 0.0162136i
\(832\) 10.1974 17.6624i 0.353531 0.612333i
\(833\) 1.89791 + 3.28728i 0.0657587 + 0.113897i
\(834\) −1.13346 1.96322i −0.0392486 0.0679806i
\(835\) 0 0
\(836\) −42.7794 + 2.82506i −1.47956 + 0.0977067i
\(837\) 23.4032 0.808934
\(838\) 0.792358 + 1.37240i 0.0273715 + 0.0474089i
\(839\) 4.20767 + 7.28790i 0.145265 + 0.251606i 0.929472 0.368893i \(-0.120263\pi\)
−0.784207 + 0.620500i \(0.786930\pi\)
\(840\) 0 0
\(841\) 6.39543 + 11.0772i 0.220532 + 0.381973i
\(842\) −0.880159 + 1.52448i −0.0303323 + 0.0525371i
\(843\) −5.03410 −0.173384
\(844\) 37.3918 1.28708
\(845\) 0 0
\(846\) −1.15895 + 2.00737i −0.0398457 + 0.0690147i
\(847\) −51.5262 −1.77046
\(848\) −24.4082 −0.838181
\(849\) 9.20601 15.9453i 0.315950 0.547241i
\(850\) 0 0
\(851\) −24.8616 + 43.0616i −0.852245 + 1.47613i
\(852\) −0.446294 0.773005i −0.0152898 0.0264827i
\(853\) −26.0182 45.0648i −0.890845 1.54299i −0.838865 0.544340i \(-0.816780\pi\)
−0.0519802 0.998648i \(-0.516553\pi\)
\(854\) −6.26314 −0.214320
\(855\) 0 0
\(856\) −10.6064 −0.362520
\(857\) 10.7298 + 18.5845i 0.366522 + 0.634834i 0.989019 0.147788i \(-0.0472152\pi\)
−0.622497 + 0.782622i \(0.713882\pi\)
\(858\) 2.92629 + 5.06849i 0.0999020 + 0.173035i
\(859\) −9.07396 + 15.7166i −0.309599 + 0.536242i −0.978275 0.207313i \(-0.933528\pi\)
0.668675 + 0.743554i \(0.266862\pi\)
\(860\) 0 0
\(861\) −11.4954 + 19.9106i −0.391762 + 0.678552i
\(862\) −11.9362 −0.406549
\(863\) −13.7867 −0.469303 −0.234652 0.972080i \(-0.575395\pi\)
−0.234652 + 0.972080i \(0.575395\pi\)
\(864\) 8.89000 15.3979i 0.302444 0.523848i
\(865\) 0 0
\(866\) 2.16609 0.0736066
\(867\) −16.4581 −0.558948
\(868\) 14.3619 24.8756i 0.487475 0.844332i
\(869\) 7.46320 + 12.9266i 0.253172 + 0.438506i
\(870\) 0 0
\(871\) 19.7907 + 34.2786i 0.670584 + 1.16148i
\(872\) −3.70173 6.41158i −0.125356 0.217123i
\(873\) 20.9945 0.710557
\(874\) −5.77796 8.63812i −0.195442 0.292189i
\(875\) 0 0
\(876\) 4.05113 + 7.01676i 0.136875 + 0.237075i
\(877\) 10.5968 + 18.3543i 0.357830 + 0.619780i 0.987598 0.157003i \(-0.0501834\pi\)
−0.629768 + 0.776783i \(0.716850\pi\)
\(878\) −1.48195 + 2.56681i −0.0500134 + 0.0866257i
\(879\) −3.73521 6.46957i −0.125985 0.218213i
\(880\) 0 0
\(881\) 44.5944 1.50242 0.751212 0.660061i \(-0.229469\pi\)
0.751212 + 0.660061i \(0.229469\pi\)
\(882\) −2.26924 −0.0764093
\(883\) −0.846773 + 1.46665i −0.0284962 + 0.0493568i −0.879922 0.475119i \(-0.842405\pi\)
0.851426 + 0.524475i \(0.175739\pi\)
\(884\) −3.39487 + 5.88009i −0.114182 + 0.197769i
\(885\) 0 0
\(886\) 10.7966 0.362720
\(887\) −24.2177 + 41.9463i −0.813151 + 1.40842i 0.0974969 + 0.995236i \(0.468916\pi\)
−0.910648 + 0.413183i \(0.864417\pi\)
\(888\) −4.05697 7.02688i −0.136143 0.235807i
\(889\) 5.52273 9.56565i 0.185227 0.320822i
\(890\) 0 0
\(891\) 1.49806 + 2.59471i 0.0501868 + 0.0869260i
\(892\) 21.5706 0.722238
\(893\) 16.7086 1.10340i 0.559133 0.0369239i
\(894\) 4.08481 0.136617
\(895\) 0 0
\(896\) −14.4102 24.9592i −0.481411 0.833828i
\(897\) 13.9482 24.1590i 0.465718 0.806647i
\(898\) 1.37545 + 2.38235i 0.0458994 + 0.0795001i
\(899\) −9.26149 + 16.0414i −0.308888 + 0.535009i
\(900\) 0 0
\(901\) 7.18499 0.239367
\(902\) −5.47090 + 9.47588i −0.182161 + 0.315512i
\(903\) 10.6588 18.4615i 0.354701 0.614360i
\(904\) −12.5613 −0.417783
\(905\) 0 0
\(906\) 3.14561 5.44835i 0.104506 0.181009i
\(907\) −13.9694 24.1957i −0.463846 0.803404i 0.535303 0.844660i \(-0.320197\pi\)
−0.999149 + 0.0412557i \(0.986864\pi\)
\(908\) −10.5979 + 18.3561i −0.351704 + 0.609169i
\(909\) −5.99309 10.3803i −0.198778 0.344294i
\(910\) 0 0
\(911\) 45.0862 1.49377 0.746887 0.664951i \(-0.231548\pi\)
0.746887 + 0.664951i \(0.231548\pi\)
\(912\) −15.3575 + 1.01418i −0.508538 + 0.0335828i
\(913\) 28.4267 0.940787
\(914\) −0.103443 0.179169i −0.00342159 0.00592637i
\(915\) 0 0
\(916\) 3.34224 5.78893i 0.110431 0.191272i
\(917\) 3.97218 + 6.88002i 0.131173 + 0.227198i
\(918\) −0.798617 + 1.38325i −0.0263583 + 0.0456539i
\(919\) −5.86849 −0.193584 −0.0967918 0.995305i \(-0.530858\pi\)
−0.0967918 + 0.995305i \(0.530858\pi\)
\(920\) 0 0
\(921\) −7.40467 + 12.8253i −0.243992 + 0.422607i
\(922\) 6.15048 10.6529i 0.202555 0.350836i
\(923\) −1.60972 −0.0529846
\(924\) −33.2273 −1.09310
\(925\) 0 0
\(926\) 2.42325 + 4.19720i 0.0796330 + 0.137928i
\(927\) 17.7669 30.7732i 0.583542 1.01072i
\(928\) 7.03617 + 12.1870i 0.230974 + 0.400058i
\(929\) −23.3157 40.3839i −0.764963 1.32495i −0.940266 0.340440i \(-0.889424\pi\)
0.175304 0.984514i \(-0.443909\pi\)
\(930\) 0 0
\(931\) 9.11442 + 13.6262i 0.298713 + 0.446579i
\(932\) −11.7808 −0.385894
\(933\) −4.39013 7.60393i −0.143726 0.248942i
\(934\) −6.38328 11.0562i −0.208867 0.361769i
\(935\) 0 0
\(936\) −4.16230 7.20931i −0.136049 0.235644i
\(937\) 25.6470 44.4219i 0.837850 1.45120i −0.0538383 0.998550i \(-0.517146\pi\)
0.891689 0.452649i \(-0.149521\pi\)
\(938\) 11.4281 0.373140
\(939\) −21.9992 −0.717916
\(940\) 0 0
\(941\) 5.67430 9.82817i 0.184977 0.320389i −0.758592 0.651566i \(-0.774112\pi\)
0.943569 + 0.331177i \(0.107446\pi\)
\(942\) 0.988367 0.0322027
\(943\) 52.1543 1.69838
\(944\) −23.0970 + 40.0052i −0.751743 + 1.30206i
\(945\) 0 0
\(946\) 5.07272 8.78621i 0.164928 0.285664i
\(947\) 3.60467 + 6.24348i 0.117136 + 0.202886i 0.918632 0.395115i \(-0.129295\pi\)
−0.801495 + 0.598001i \(0.795962\pi\)
\(948\) 2.83051 + 4.90258i 0.0919305 + 0.159228i
\(949\) 14.6119 0.474321
\(950\) 0 0
\(951\) 28.9309 0.938150
\(952\) 2.01020 + 3.48177i 0.0651511 + 0.112845i
\(953\) −10.2697 17.7877i −0.332669 0.576199i 0.650365 0.759622i \(-0.274616\pi\)
−0.983034 + 0.183422i \(0.941282\pi\)
\(954\) −2.14769 + 3.71991i −0.0695340 + 0.120436i
\(955\) 0 0
\(956\) 11.5355 19.9801i 0.373085 0.646202i
\(957\) 21.4271 0.692639
\(958\) −7.32930 −0.236799
\(959\) −18.8935 + 32.7246i −0.610104 + 1.05673i
\(960\) 0 0
\(961\) −9.83289 −0.317190
\(962\) −7.13504 −0.230043
\(963\) 8.46998 14.6704i 0.272941 0.472748i
\(964\) −4.85513 8.40933i −0.156373 0.270846i
\(965\) 0 0
\(966\) −4.02718 6.97528i −0.129572 0.224426i
\(967\) 8.53345 + 14.7804i 0.274417 + 0.475305i 0.969988 0.243153i \(-0.0781817\pi\)
−0.695571 + 0.718458i \(0.744848\pi\)
\(968\) −19.0738 −0.613055
\(969\) 4.52076 0.298541i 0.145228 0.00959053i
\(970\) 0 0
\(971\) 1.74085 + 3.01525i 0.0558667 + 0.0967639i 0.892606 0.450837i \(-0.148874\pi\)
−0.836740 + 0.547601i \(0.815541\pi\)
\(972\) 15.0901 + 26.1368i 0.484014 + 0.838337i
\(973\) 11.6052 20.1008i 0.372046 0.644403i
\(974\) 3.72032 + 6.44379i 0.119207 + 0.206472i
\(975\) 0 0
\(976\) 21.0416 0.673524
\(977\) 21.9600 0.702562 0.351281 0.936270i \(-0.385746\pi\)
0.351281 + 0.936270i \(0.385746\pi\)
\(978\) 3.59992 6.23524i 0.115113 0.199381i
\(979\) −18.4202 + 31.9047i −0.588711 + 1.01968i
\(980\) 0 0
\(981\) 11.8244 0.377523
\(982\) −2.54291 + 4.40445i −0.0811476 + 0.140552i
\(983\) 2.74852 + 4.76057i 0.0876641 + 0.151839i 0.906523 0.422156i \(-0.138726\pi\)
−0.818859 + 0.573994i \(0.805393\pi\)
\(984\) −4.25533 + 7.37044i −0.135655 + 0.234961i
\(985\) 0 0
\(986\) −0.632082 1.09480i −0.0201296 0.0348655i
\(987\) 12.9778 0.413088
\(988\) −12.9566 + 26.3059i −0.412203 + 0.836903i
\(989\) −48.3584 −1.53771
\(990\) 0 0
\(991\) 14.7485 + 25.5452i 0.468502 + 0.811469i 0.999352 0.0359970i \(-0.0114607\pi\)
−0.530850 + 0.847466i \(0.678127\pi\)
\(992\) 8.04058 13.9267i 0.255289 0.442173i
\(993\) −7.81259 13.5318i −0.247925 0.429419i
\(994\) −0.232382 + 0.402497i −0.00737071 + 0.0127664i
\(995\) 0 0
\(996\) 10.7812 0.341614
\(997\) 3.63224 6.29123i 0.115034 0.199245i −0.802759 0.596303i \(-0.796636\pi\)
0.917793 + 0.397058i \(0.129969\pi\)
\(998\) 4.98874 8.64076i 0.157916 0.273518i
\(999\) 33.0048 1.04422
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 475.2.e.f.26.3 12
5.2 odd 4 475.2.j.d.349.7 24
5.3 odd 4 475.2.j.d.349.6 24
5.4 even 2 475.2.e.h.26.4 yes 12
19.7 even 3 9025.2.a.bz.1.4 6
19.11 even 3 inner 475.2.e.f.201.3 yes 12
19.12 odd 6 9025.2.a.bs.1.3 6
95.49 even 6 475.2.e.h.201.4 yes 12
95.64 even 6 9025.2.a.br.1.3 6
95.68 odd 12 475.2.j.d.49.7 24
95.69 odd 6 9025.2.a.by.1.4 6
95.87 odd 12 475.2.j.d.49.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.3 12 1.1 even 1 trivial
475.2.e.f.201.3 yes 12 19.11 even 3 inner
475.2.e.h.26.4 yes 12 5.4 even 2
475.2.e.h.201.4 yes 12 95.49 even 6
475.2.j.d.49.6 24 95.87 odd 12
475.2.j.d.49.7 24 95.68 odd 12
475.2.j.d.349.6 24 5.3 odd 4
475.2.j.d.349.7 24 5.2 odd 4
9025.2.a.br.1.3 6 95.64 even 6
9025.2.a.bs.1.3 6 19.12 odd 6
9025.2.a.by.1.4 6 95.69 odd 6
9025.2.a.bz.1.4 6 19.7 even 3