Properties

Label 625.2.h.b.274.21
Level $625$
Weight $2$
Character 625.274
Analytic conductor $4.991$
Analytic rank $0$
Dimension $440$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [625,2,Mod(24,625)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(625, base_ring=CyclotomicField(50))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("625.24");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.h (of order \(50\), degree \(20\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{50})\)
Twist minimal: no (minimal twist has level 125)
Sato-Tate group: $\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label 274.21
Character \(\chi\) \(=\) 625.274
Dual form 625.2.h.b.349.21

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.618528 + 2.40901i) q^{2} +(3.26064 - 0.622000i) q^{3} +(-3.66812 + 2.01657i) q^{4} +(3.51519 + 7.47017i) q^{6} +(0.463359 - 0.637759i) q^{7} +(-3.72162 - 3.96312i) q^{8} +(7.45553 - 2.95185i) q^{9} +O(q^{10})\) \(q+(0.618528 + 2.40901i) q^{2} +(3.26064 - 0.622000i) q^{3} +(-3.66812 + 2.01657i) q^{4} +(3.51519 + 7.47017i) q^{6} +(0.463359 - 0.637759i) q^{7} +(-3.72162 - 3.96312i) q^{8} +(7.45553 - 2.95185i) q^{9} +(1.00576 - 0.258235i) q^{11} +(-10.7061 + 8.85686i) q^{12} +(-0.207600 - 0.524337i) q^{13} +(1.82297 + 0.721763i) q^{14} +(2.75944 - 4.34818i) q^{16} +(-1.66584 + 3.03015i) q^{17} +(11.7225 + 16.1346i) q^{18} +(-0.598583 + 3.13788i) q^{19} +(1.11416 - 2.36771i) q^{21} +(1.24418 + 2.26315i) q^{22} +(-3.37563 - 0.212377i) q^{23} +(-14.5999 - 10.6075i) q^{24} +(1.13473 - 0.824427i) q^{26} +(14.0657 - 8.92634i) q^{27} +(-0.413573 + 3.27377i) q^{28} +(-2.01748 - 0.254867i) q^{29} +(-5.56625 - 3.06007i) q^{31} +(1.84053 + 0.598023i) q^{32} +(3.11879 - 1.46759i) q^{33} +(-8.33001 - 2.13878i) q^{34} +(-21.3952 + 25.8623i) q^{36} +(-4.67893 - 2.96934i) q^{37} +(-7.92942 + 0.498877i) q^{38} +(-1.00305 - 1.58055i) q^{39} +(-0.714850 - 11.3622i) q^{41} +(6.39296 + 1.21952i) q^{42} +(2.69982 - 0.877225i) q^{43} +(-3.16849 + 2.97541i) q^{44} +(-1.57631 - 8.26328i) q^{46} +(1.00997 - 1.07551i) q^{47} +(6.29296 - 15.8942i) q^{48} +(1.97108 + 6.06637i) q^{49} +(-3.54694 + 10.9164i) q^{51} +(1.81886 + 1.50469i) q^{52} +(2.80343 + 1.31919i) q^{53} +(30.2036 + 28.3631i) q^{54} +(-4.25196 + 0.537148i) q^{56} +10.6038i q^{57} +(-0.633891 - 5.01776i) q^{58} +(-2.27401 - 2.74880i) q^{59} +(0.470039 - 7.47105i) q^{61} +(3.92885 - 15.3019i) q^{62} +(1.57202 - 6.12260i) q^{63} +(0.344501 - 5.47569i) q^{64} +(5.46449 + 6.60544i) q^{66} +(1.70582 + 13.5029i) q^{67} -14.4742i q^{68} +(-11.1388 + 1.40716i) q^{69} +(3.81072 + 3.57851i) q^{71} +(-39.4452 - 18.5615i) q^{72} +(4.81135 + 3.98029i) q^{73} +(4.25911 - 13.1082i) q^{74} +(-4.13207 - 12.7172i) q^{76} +(0.301335 - 0.761087i) q^{77} +(3.18714 - 3.39395i) q^{78} +(-1.73061 - 9.07217i) q^{79} +(22.7748 - 21.3870i) q^{81} +(26.9295 - 8.74992i) q^{82} +(-0.187696 - 0.0358049i) q^{83} +(0.687772 + 10.9318i) q^{84} +(3.78315 + 5.96130i) q^{86} +(-6.73680 + 0.423843i) q^{87} +(-4.76646 - 3.02489i) q^{88} +(1.42021 - 1.71673i) q^{89} +(-0.430594 - 0.110558i) q^{91} +(12.8105 - 6.02816i) q^{92} +(-20.0529 - 6.51558i) q^{93} +(3.21559 + 1.76779i) q^{94} +(6.37326 + 0.805130i) q^{96} +(-1.51887 + 12.0231i) q^{97} +(-13.3948 + 8.50057i) q^{98} +(6.73619 - 4.89413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{21}{50}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618528 + 2.40901i 0.437365 + 1.70342i 0.679920 + 0.733287i \(0.262015\pi\)
−0.242555 + 0.970138i \(0.577985\pi\)
\(3\) 3.26064 0.622000i 1.88253 0.359112i 0.887678 0.460464i \(-0.152317\pi\)
0.994851 + 0.101352i \(0.0323169\pi\)
\(4\) −3.66812 + 2.01657i −1.83406 + 1.00828i
\(5\) 0 0
\(6\) 3.51519 + 7.47017i 1.43507 + 3.04968i
\(7\) 0.463359 0.637759i 0.175133 0.241050i −0.712422 0.701751i \(-0.752402\pi\)
0.887555 + 0.460701i \(0.152402\pi\)
\(8\) −3.72162 3.96312i −1.31579 1.40117i
\(9\) 7.45553 2.95185i 2.48518 0.983952i
\(10\) 0 0
\(11\) 1.00576 0.258235i 0.303247 0.0778607i −0.0940002 0.995572i \(-0.529965\pi\)
0.397248 + 0.917711i \(0.369965\pi\)
\(12\) −10.7061 + 8.85686i −3.09059 + 2.55675i
\(13\) −0.207600 0.524337i −0.0575779 0.145425i 0.898140 0.439710i \(-0.144919\pi\)
−0.955718 + 0.294285i \(0.904919\pi\)
\(14\) 1.82297 + 0.721763i 0.487208 + 0.192899i
\(15\) 0 0
\(16\) 2.75944 4.34818i 0.689860 1.08705i
\(17\) −1.66584 + 3.03015i −0.404025 + 0.734919i −0.997554 0.0698933i \(-0.977734\pi\)
0.593529 + 0.804812i \(0.297734\pi\)
\(18\) 11.7225 + 16.1346i 2.76302 + 3.80297i
\(19\) −0.598583 + 3.13788i −0.137324 + 0.719880i 0.845303 + 0.534288i \(0.179420\pi\)
−0.982627 + 0.185592i \(0.940580\pi\)
\(20\) 0 0
\(21\) 1.11416 2.36771i 0.243129 0.516676i
\(22\) 1.24418 + 2.26315i 0.265260 + 0.482506i
\(23\) −3.37563 0.212377i −0.703868 0.0442836i −0.293177 0.956058i \(-0.594713\pi\)
−0.410691 + 0.911775i \(0.634713\pi\)
\(24\) −14.5999 10.6075i −2.98019 2.16524i
\(25\) 0 0
\(26\) 1.13473 0.824427i 0.222538 0.161683i
\(27\) 14.0657 8.92634i 2.70694 1.71788i
\(28\) −0.413573 + 3.27377i −0.0781580 + 0.618684i
\(29\) −2.01748 0.254867i −0.374637 0.0473276i −0.0642393 0.997935i \(-0.520462\pi\)
−0.310397 + 0.950607i \(0.600462\pi\)
\(30\) 0 0
\(31\) −5.56625 3.06007i −0.999729 0.549605i −0.104175 0.994559i \(-0.533220\pi\)
−0.895554 + 0.444954i \(0.853220\pi\)
\(32\) 1.84053 + 0.598023i 0.325362 + 0.105717i
\(33\) 3.11879 1.46759i 0.542911 0.255475i
\(34\) −8.33001 2.13878i −1.42859 0.366798i
\(35\) 0 0
\(36\) −21.3952 + 25.8623i −3.56586 + 4.31039i
\(37\) −4.67893 2.96934i −0.769212 0.488157i 0.0924015 0.995722i \(-0.470546\pi\)
−0.861613 + 0.507565i \(0.830546\pi\)
\(38\) −7.92942 + 0.498877i −1.28632 + 0.0809285i
\(39\) −1.00305 1.58055i −0.160616 0.253090i
\(40\) 0 0
\(41\) −0.714850 11.3622i −0.111641 1.77448i −0.512835 0.858487i \(-0.671405\pi\)
0.401195 0.915993i \(-0.368595\pi\)
\(42\) 6.39296 + 1.21952i 0.986456 + 0.188176i
\(43\) 2.69982 0.877225i 0.411719 0.133776i −0.0958317 0.995398i \(-0.530551\pi\)
0.507551 + 0.861622i \(0.330551\pi\)
\(44\) −3.16849 + 2.97541i −0.477668 + 0.448560i
\(45\) 0 0
\(46\) −1.57631 8.26328i −0.232414 1.21835i
\(47\) 1.00997 1.07551i 0.147319 0.156879i −0.651077 0.759012i \(-0.725682\pi\)
0.798396 + 0.602133i \(0.205682\pi\)
\(48\) 6.29296 15.8942i 0.908311 2.29413i
\(49\) 1.97108 + 6.06637i 0.281583 + 0.866625i
\(50\) 0 0
\(51\) −3.54694 + 10.9164i −0.496671 + 1.52860i
\(52\) 1.81886 + 1.50469i 0.252231 + 0.208664i
\(53\) 2.80343 + 1.31919i 0.385081 + 0.181205i 0.608568 0.793502i \(-0.291744\pi\)
−0.223487 + 0.974707i \(0.571744\pi\)
\(54\) 30.2036 + 28.3631i 4.11019 + 3.85973i
\(55\) 0 0
\(56\) −4.25196 + 0.537148i −0.568192 + 0.0717794i
\(57\) 10.6038i 1.40451i
\(58\) −0.633891 5.01776i −0.0832340 0.658865i
\(59\) −2.27401 2.74880i −0.296051 0.357864i 0.601424 0.798930i \(-0.294600\pi\)
−0.897474 + 0.441066i \(0.854600\pi\)
\(60\) 0 0
\(61\) 0.470039 7.47105i 0.0601823 0.956570i −0.845866 0.533396i \(-0.820916\pi\)
0.906048 0.423174i \(-0.139084\pi\)
\(62\) 3.92885 15.3019i 0.498965 1.94334i
\(63\) 1.57202 6.12260i 0.198056 0.771375i
\(64\) 0.344501 5.47569i 0.0430626 0.684461i
\(65\) 0 0
\(66\) 5.46449 + 6.60544i 0.672632 + 0.813073i
\(67\) 1.70582 + 13.5029i 0.208398 + 1.64964i 0.655525 + 0.755173i \(0.272447\pi\)
−0.447127 + 0.894471i \(0.647553\pi\)
\(68\) 14.4742i 1.75526i
\(69\) −11.1388 + 1.40716i −1.34096 + 0.169402i
\(70\) 0 0
\(71\) 3.81072 + 3.57851i 0.452249 + 0.424690i 0.876904 0.480665i \(-0.159605\pi\)
−0.424655 + 0.905355i \(0.639605\pi\)
\(72\) −39.4452 18.5615i −4.64866 2.18749i
\(73\) 4.81135 + 3.98029i 0.563126 + 0.465858i 0.874904 0.484297i \(-0.160924\pi\)
−0.311778 + 0.950155i \(0.600924\pi\)
\(74\) 4.25911 13.1082i 0.495112 1.52380i
\(75\) 0 0
\(76\) −4.13207 12.7172i −0.473981 1.45876i
\(77\) 0.301335 0.761087i 0.0343404 0.0867339i
\(78\) 3.18714 3.39395i 0.360872 0.384290i
\(79\) −1.73061 9.07217i −0.194709 1.02070i −0.936659 0.350243i \(-0.886099\pi\)
0.741950 0.670455i \(-0.233901\pi\)
\(80\) 0 0
\(81\) 22.7748 21.3870i 2.53054 2.37633i
\(82\) 26.9295 8.74992i 2.97386 0.966267i
\(83\) −0.187696 0.0358049i −0.0206023 0.00393010i 0.177070 0.984198i \(-0.443338\pi\)
−0.197672 + 0.980268i \(0.563338\pi\)
\(84\) 0.687772 + 10.9318i 0.0750420 + 1.19276i
\(85\) 0 0
\(86\) 3.78315 + 5.96130i 0.407948 + 0.642823i
\(87\) −6.73680 + 0.423843i −0.722260 + 0.0454408i
\(88\) −4.76646 3.02489i −0.508107 0.322454i
\(89\) 1.42021 1.71673i 0.150542 0.181973i −0.689851 0.723951i \(-0.742324\pi\)
0.840393 + 0.541977i \(0.182324\pi\)
\(90\) 0 0
\(91\) −0.430594 0.110558i −0.0451385 0.0115896i
\(92\) 12.8105 6.02816i 1.33559 0.628480i
\(93\) −20.0529 6.51558i −2.07939 0.675634i
\(94\) 3.21559 + 1.76779i 0.331663 + 0.182333i
\(95\) 0 0
\(96\) 6.37326 + 0.805130i 0.650468 + 0.0821732i
\(97\) −1.51887 + 12.0231i −0.154218 + 1.22076i 0.705020 + 0.709187i \(0.250938\pi\)
−0.859238 + 0.511576i \(0.829062\pi\)
\(98\) −13.3948 + 8.50057i −1.35307 + 0.858687i
\(99\) 6.73619 4.89413i 0.677013 0.491879i
\(100\) 0 0
\(101\) −8.25784 5.99967i −0.821686 0.596990i 0.0955088 0.995429i \(-0.469552\pi\)
−0.917195 + 0.398439i \(0.869552\pi\)
\(102\) −28.4915 1.79253i −2.82108 0.177487i
\(103\) 8.16330 + 14.8490i 0.804353 + 1.46311i 0.884606 + 0.466339i \(0.154427\pi\)
−0.0802527 + 0.996775i \(0.525573\pi\)
\(104\) −1.30541 + 2.77413i −0.128006 + 0.272026i
\(105\) 0 0
\(106\) −1.44395 + 7.56944i −0.140249 + 0.735209i
\(107\) −8.29283 11.4141i −0.801698 1.10344i −0.992552 0.121824i \(-0.961126\pi\)
0.190854 0.981618i \(-0.438874\pi\)
\(108\) −33.5940 + 61.1072i −3.23258 + 5.88005i
\(109\) 0.443460 0.698780i 0.0424757 0.0669310i −0.822427 0.568871i \(-0.807380\pi\)
0.864902 + 0.501940i \(0.167380\pi\)
\(110\) 0 0
\(111\) −17.1032 6.77165i −1.62337 0.642736i
\(112\) −1.49448 3.77463i −0.141215 0.356669i
\(113\) −5.01705 + 4.15047i −0.471965 + 0.390443i −0.842775 0.538265i \(-0.819080\pi\)
0.370811 + 0.928708i \(0.379080\pi\)
\(114\) −25.5446 + 6.55875i −2.39248 + 0.614283i
\(115\) 0 0
\(116\) 7.91432 3.13350i 0.734826 0.290938i
\(117\) −3.09554 3.29641i −0.286182 0.304753i
\(118\) 5.21535 7.17831i 0.480111 0.660817i
\(119\) 1.16062 + 2.46645i 0.106394 + 0.226099i
\(120\) 0 0
\(121\) −8.69451 + 4.77985i −0.790410 + 0.434532i
\(122\) 18.2885 3.48872i 1.65577 0.315854i
\(123\) −9.39816 36.6034i −0.847403 3.30042i
\(124\) 26.5885 2.38772
\(125\) 0 0
\(126\) 15.7217 1.40060
\(127\) −2.07182 8.06920i −0.183844 0.716026i −0.991911 0.126935i \(-0.959486\pi\)
0.808067 0.589091i \(-0.200514\pi\)
\(128\) 17.2060 3.28221i 1.52081 0.290110i
\(129\) 8.25750 4.53960i 0.727032 0.399689i
\(130\) 0 0
\(131\) 4.08655 + 8.68436i 0.357043 + 0.758756i 0.999974 0.00716837i \(-0.00228178\pi\)
−0.642931 + 0.765924i \(0.722282\pi\)
\(132\) −8.48060 + 11.6725i −0.738141 + 1.01596i
\(133\) 1.72385 + 1.83572i 0.149477 + 0.159177i
\(134\) −31.4735 + 12.4612i −2.71890 + 1.07649i
\(135\) 0 0
\(136\) 18.2085 4.67514i 1.56136 0.400890i
\(137\) 1.38806 1.14830i 0.118590 0.0981061i −0.576239 0.817281i \(-0.695480\pi\)
0.694829 + 0.719175i \(0.255480\pi\)
\(138\) −10.2795 25.9631i −0.875051 2.21013i
\(139\) −8.38439 3.31961i −0.711154 0.281566i −0.0154363 0.999881i \(-0.504914\pi\)
−0.695718 + 0.718315i \(0.744914\pi\)
\(140\) 0 0
\(141\) 2.62417 4.13503i 0.220995 0.348232i
\(142\) −6.26361 + 11.3935i −0.525630 + 0.956118i
\(143\) −0.344197 0.473747i −0.0287832 0.0396167i
\(144\) 7.73790 40.5635i 0.644825 3.38029i
\(145\) 0 0
\(146\) −6.61260 + 14.0525i −0.547263 + 1.16299i
\(147\) 10.2003 + 18.5542i 0.841304 + 1.53033i
\(148\) 23.1508 + 1.45652i 1.90298 + 0.119725i
\(149\) 4.91478 + 3.57079i 0.402634 + 0.292531i 0.770613 0.637303i \(-0.219950\pi\)
−0.367979 + 0.929834i \(0.619950\pi\)
\(150\) 0 0
\(151\) 8.84022 6.42279i 0.719407 0.522680i −0.166788 0.985993i \(-0.553340\pi\)
0.886195 + 0.463313i \(0.153340\pi\)
\(152\) 14.6635 9.30575i 1.18937 0.754796i
\(153\) −3.47516 + 27.5087i −0.280950 + 2.22395i
\(154\) 2.01985 + 0.255166i 0.162764 + 0.0205619i
\(155\) 0 0
\(156\) 6.86657 + 3.77493i 0.549765 + 0.302236i
\(157\) 14.1931 + 4.61162i 1.13273 + 0.368048i 0.814614 0.580003i \(-0.196949\pi\)
0.318120 + 0.948051i \(0.396949\pi\)
\(158\) 20.7845 9.78043i 1.65352 0.778089i
\(159\) 9.96151 + 2.55768i 0.789999 + 0.202837i
\(160\) 0 0
\(161\) −1.69958 + 2.05443i −0.133945 + 0.161912i
\(162\) 65.6083 + 41.6363i 5.15467 + 3.27125i
\(163\) 7.83419 0.492885i 0.613621 0.0386057i 0.247060 0.969000i \(-0.420535\pi\)
0.366560 + 0.930394i \(0.380535\pi\)
\(164\) 25.5348 + 40.2364i 1.99393 + 3.14194i
\(165\) 0 0
\(166\) −0.0298409 0.474307i −0.00231610 0.0368134i
\(167\) −9.20316 1.75560i −0.712162 0.135852i −0.181445 0.983401i \(-0.558077\pi\)
−0.530717 + 0.847549i \(0.678077\pi\)
\(168\) −13.5300 + 4.39616i −1.04386 + 0.339171i
\(169\) 9.24476 8.68141i 0.711135 0.667801i
\(170\) 0 0
\(171\) 4.79982 + 25.1615i 0.367051 + 1.92415i
\(172\) −8.13428 + 8.66213i −0.620233 + 0.660481i
\(173\) −8.18603 + 20.6756i −0.622372 + 1.57193i 0.185544 + 0.982636i \(0.440595\pi\)
−0.807916 + 0.589297i \(0.799405\pi\)
\(174\) −5.18794 15.9668i −0.393296 1.21044i
\(175\) 0 0
\(176\) 1.65248 5.08580i 0.124560 0.383357i
\(177\) −9.12446 7.54841i −0.685837 0.567373i
\(178\) 5.01406 + 2.35944i 0.375820 + 0.176847i
\(179\) −4.89894 4.60041i −0.366164 0.343851i 0.479524 0.877529i \(-0.340809\pi\)
−0.845688 + 0.533678i \(0.820809\pi\)
\(180\) 0 0
\(181\) 21.3240 2.69385i 1.58500 0.200232i 0.717100 0.696970i \(-0.245469\pi\)
0.867900 + 0.496738i \(0.165469\pi\)
\(182\) 1.10569i 0.0819590i
\(183\) −3.11437 24.6527i −0.230220 1.82238i
\(184\) 11.7211 + 14.1684i 0.864094 + 1.04451i
\(185\) 0 0
\(186\) 3.29280 52.3376i 0.241440 3.83758i
\(187\) −0.892941 + 3.47777i −0.0652983 + 0.254320i
\(188\) −1.53585 + 5.98175i −0.112013 + 0.436264i
\(189\) 0.824598 13.1066i 0.0599807 0.953365i
\(190\) 0 0
\(191\) −6.43755 7.78166i −0.465805 0.563061i 0.484336 0.874882i \(-0.339061\pi\)
−0.950141 + 0.311821i \(0.899061\pi\)
\(192\) −2.28258 18.0685i −0.164731 1.30398i
\(193\) 15.7585i 1.13433i 0.823606 + 0.567163i \(0.191959\pi\)
−0.823606 + 0.567163i \(0.808041\pi\)
\(194\) −29.9032 + 3.77766i −2.14693 + 0.271220i
\(195\) 0 0
\(196\) −19.4634 18.2774i −1.39024 1.30553i
\(197\) −14.1591 6.66276i −1.00879 0.474702i −0.150910 0.988547i \(-0.548220\pi\)
−0.857883 + 0.513846i \(0.828220\pi\)
\(198\) 15.9565 + 13.2004i 1.13398 + 0.938110i
\(199\) 4.36121 13.4224i 0.309158 0.951490i −0.668935 0.743321i \(-0.733250\pi\)
0.978093 0.208169i \(-0.0667505\pi\)
\(200\) 0 0
\(201\) 13.9609 + 42.9671i 0.984723 + 3.03066i
\(202\) 9.34555 23.6042i 0.657550 1.66078i
\(203\) −1.09736 + 1.16857i −0.0770197 + 0.0820176i
\(204\) −9.00296 47.1952i −0.630333 3.30432i
\(205\) 0 0
\(206\) −30.7221 + 28.8499i −2.14051 + 2.01007i
\(207\) −25.7941 + 8.38100i −1.79281 + 0.582520i
\(208\) −2.85277 0.544196i −0.197804 0.0377332i
\(209\) 0.208281 + 3.31053i 0.0144071 + 0.228994i
\(210\) 0 0
\(211\) 10.2934 + 16.2198i 0.708625 + 1.11661i 0.987702 + 0.156346i \(0.0499714\pi\)
−0.279077 + 0.960269i \(0.590029\pi\)
\(212\) −12.9436 + 0.814340i −0.888968 + 0.0559291i
\(213\) 14.6512 + 9.29794i 1.00388 + 0.637084i
\(214\) 22.3673 27.0374i 1.52900 1.84824i
\(215\) 0 0
\(216\) −87.7232 22.5235i −5.96881 1.53253i
\(217\) −4.53076 + 2.13202i −0.307568 + 0.144731i
\(218\) 1.95766 + 0.636082i 0.132589 + 0.0430809i
\(219\) 18.1638 + 9.98563i 1.22740 + 0.674767i
\(220\) 0 0
\(221\) 1.93465 + 0.244403i 0.130139 + 0.0164403i
\(222\) 5.73412 45.3902i 0.384849 3.04639i
\(223\) −3.95744 + 2.51147i −0.265010 + 0.168180i −0.661692 0.749776i \(-0.730161\pi\)
0.396682 + 0.917956i \(0.370161\pi\)
\(224\) 1.23422 0.896713i 0.0824647 0.0599141i
\(225\) 0 0
\(226\) −13.1017 9.51893i −0.871511 0.633190i
\(227\) 7.25785 + 0.456625i 0.481721 + 0.0303073i 0.301795 0.953373i \(-0.402414\pi\)
0.179926 + 0.983680i \(0.442414\pi\)
\(228\) −21.3833 38.8961i −1.41614 2.57595i
\(229\) −6.50796 + 13.8301i −0.430058 + 0.913920i 0.565932 + 0.824452i \(0.308517\pi\)
−0.995990 + 0.0894676i \(0.971483\pi\)
\(230\) 0 0
\(231\) 0.509150 2.66906i 0.0334996 0.175611i
\(232\) 6.49822 + 8.94404i 0.426629 + 0.587205i
\(233\) 7.63001 13.8789i 0.499858 0.909239i −0.499227 0.866471i \(-0.666383\pi\)
0.999085 0.0427674i \(-0.0136175\pi\)
\(234\) 6.02640 9.49609i 0.393958 0.620779i
\(235\) 0 0
\(236\) 13.8845 + 5.49725i 0.903802 + 0.357841i
\(237\) −11.2858 28.5046i −0.733089 1.85157i
\(238\) −5.22382 + 4.32152i −0.338610 + 0.280122i
\(239\) −7.69706 + 1.97627i −0.497882 + 0.127834i −0.489277 0.872129i \(-0.662739\pi\)
−0.00860512 + 0.999963i \(0.502739\pi\)
\(240\) 0 0
\(241\) −11.3987 + 4.51307i −0.734256 + 0.290712i −0.705340 0.708869i \(-0.749206\pi\)
−0.0289160 + 0.999582i \(0.509206\pi\)
\(242\) −16.8925 17.9887i −1.08589 1.15635i
\(243\) 31.5820 43.4689i 2.02599 2.78853i
\(244\) 13.3417 + 28.3526i 0.854115 + 1.81509i
\(245\) 0 0
\(246\) 82.3648 45.2804i 5.25139 2.88698i
\(247\) 1.76958 0.337565i 0.112595 0.0214787i
\(248\) 8.58803 + 33.4482i 0.545340 + 2.12396i
\(249\) −0.634279 −0.0401958
\(250\) 0 0
\(251\) −6.12354 −0.386514 −0.193257 0.981148i \(-0.561905\pi\)
−0.193257 + 0.981148i \(0.561905\pi\)
\(252\) 6.58029 + 25.6285i 0.414519 + 1.61444i
\(253\) −3.44991 + 0.658106i −0.216894 + 0.0413748i
\(254\) 18.1573 9.98204i 1.13929 0.626329i
\(255\) 0 0
\(256\) 13.8772 + 29.4905i 0.867322 + 1.84315i
\(257\) −10.4816 + 14.4267i −0.653823 + 0.899910i −0.999257 0.0385326i \(-0.987732\pi\)
0.345434 + 0.938443i \(0.387732\pi\)
\(258\) 16.0434 + 17.0845i 0.998819 + 1.06363i
\(259\) −4.06175 + 1.60816i −0.252385 + 0.0999262i
\(260\) 0 0
\(261\) −15.7937 + 4.05514i −0.977607 + 0.251007i
\(262\) −18.3930 + 15.2160i −1.13632 + 0.940050i
\(263\) 9.06757 + 22.9021i 0.559131 + 1.41220i 0.884466 + 0.466604i \(0.154523\pi\)
−0.325336 + 0.945599i \(0.605477\pi\)
\(264\) −17.4232 6.89833i −1.07232 0.424563i
\(265\) 0 0
\(266\) −3.35600 + 5.28822i −0.205770 + 0.324241i
\(267\) 3.56297 6.48101i 0.218050 0.396632i
\(268\) −33.4867 46.0904i −2.04552 2.81542i
\(269\) −1.33637 + 7.00550i −0.0814799 + 0.427133i 0.918050 + 0.396465i \(0.129763\pi\)
−0.999530 + 0.0306674i \(0.990237\pi\)
\(270\) 0 0
\(271\) 10.9628 23.2971i 0.665942 1.41520i −0.230958 0.972964i \(-0.574186\pi\)
0.896900 0.442234i \(-0.145814\pi\)
\(272\) 8.57885 + 15.6049i 0.520169 + 0.946185i
\(273\) −1.47278 0.0926593i −0.0891366 0.00560800i
\(274\) 3.62482 + 2.63359i 0.218983 + 0.159101i
\(275\) 0 0
\(276\) 38.0209 27.6238i 2.28859 1.66276i
\(277\) −3.21964 + 2.04324i −0.193449 + 0.122767i −0.629024 0.777386i \(-0.716545\pi\)
0.435575 + 0.900153i \(0.356545\pi\)
\(278\) 2.81099 22.2513i 0.168592 1.33455i
\(279\) −50.5323 6.38371i −3.02529 0.382183i
\(280\) 0 0
\(281\) −6.82242 3.75065i −0.406991 0.223745i 0.265089 0.964224i \(-0.414599\pi\)
−0.672080 + 0.740479i \(0.734599\pi\)
\(282\) 11.5844 + 3.76401i 0.689843 + 0.224144i
\(283\) 2.16893 1.02062i 0.128930 0.0606697i −0.360232 0.932863i \(-0.617303\pi\)
0.489162 + 0.872193i \(0.337303\pi\)
\(284\) −21.1945 5.44182i −1.25766 0.322912i
\(285\) 0 0
\(286\) 0.928364 1.12220i 0.0548953 0.0663570i
\(287\) −7.57759 4.80888i −0.447291 0.283859i
\(288\) 15.4874 0.974384i 0.912603 0.0574161i
\(289\) 2.70227 + 4.25810i 0.158957 + 0.250476i
\(290\) 0 0
\(291\) 2.52588 + 40.1478i 0.148070 + 2.35350i
\(292\) −25.6751 4.89779i −1.50252 0.286622i
\(293\) −10.5387 + 3.42423i −0.615677 + 0.200046i −0.600220 0.799835i \(-0.704920\pi\)
−0.0154571 + 0.999881i \(0.504920\pi\)
\(294\) −38.3881 + 36.0488i −2.23884 + 2.10241i
\(295\) 0 0
\(296\) 5.64535 + 29.5939i 0.328129 + 1.72011i
\(297\) 11.8416 12.6100i 0.687117 0.731705i
\(298\) −5.56214 + 14.0484i −0.322206 + 0.813800i
\(299\) 0.589424 + 1.81406i 0.0340873 + 0.104910i
\(300\) 0 0
\(301\) 0.691528 2.12830i 0.0398590 0.122673i
\(302\) 20.9405 + 17.3235i 1.20499 + 0.996853i
\(303\) −30.6576 14.4264i −1.76123 0.828774i
\(304\) 11.9923 + 11.2615i 0.687807 + 0.645894i
\(305\) 0 0
\(306\) −68.4181 + 8.64321i −3.91120 + 0.494100i
\(307\) 9.15311i 0.522396i −0.965285 0.261198i \(-0.915882\pi\)
0.965285 0.261198i \(-0.0841175\pi\)
\(308\) 0.429447 + 3.39942i 0.0244700 + 0.193700i
\(309\) 35.8536 + 43.3396i 2.03964 + 2.46550i
\(310\) 0 0
\(311\) −1.68332 + 26.7556i −0.0954523 + 1.51717i 0.600815 + 0.799388i \(0.294843\pi\)
−0.696267 + 0.717782i \(0.745157\pi\)
\(312\) −2.53095 + 9.85738i −0.143287 + 0.558064i
\(313\) 6.52893 25.4285i 0.369037 1.43730i −0.464860 0.885384i \(-0.653895\pi\)
0.833897 0.551920i \(-0.186105\pi\)
\(314\) −2.33059 + 37.0437i −0.131523 + 2.09050i
\(315\) 0 0
\(316\) 24.6427 + 29.7879i 1.38626 + 1.67570i
\(317\) 1.58301 + 12.5308i 0.0889106 + 0.703800i 0.972064 + 0.234716i \(0.0754160\pi\)
−0.883153 + 0.469084i \(0.844584\pi\)
\(318\) 25.5793i 1.43442i
\(319\) −2.09491 + 0.264649i −0.117293 + 0.0148175i
\(320\) 0 0
\(321\) −34.1395 32.0591i −1.90548 1.78936i
\(322\) −6.00038 2.82356i −0.334388 0.157351i
\(323\) −8.51111 7.04100i −0.473571 0.391772i
\(324\) −40.4126 + 124.377i −2.24514 + 6.90984i
\(325\) 0 0
\(326\) 6.03302 + 18.5677i 0.334138 + 1.02837i
\(327\) 1.01132 2.55430i 0.0559261 0.141253i
\(328\) −42.3694 + 45.1189i −2.33946 + 2.49127i
\(329\) −0.217936 1.14246i −0.0120152 0.0629859i
\(330\) 0 0
\(331\) 7.72986 7.25882i 0.424871 0.398981i −0.442399 0.896818i \(-0.645872\pi\)
0.867270 + 0.497838i \(0.165872\pi\)
\(332\) 0.760695 0.247165i 0.0417486 0.0135649i
\(333\) −43.6490 8.32650i −2.39195 0.456289i
\(334\) −1.46317 23.2564i −0.0800609 1.27253i
\(335\) 0 0
\(336\) −7.22077 11.3781i −0.393925 0.620727i
\(337\) 35.3624 2.22481i 1.92631 0.121193i 0.946703 0.322108i \(-0.104392\pi\)
0.979609 + 0.200915i \(0.0643915\pi\)
\(338\) 26.6317 + 16.9010i 1.44857 + 0.919293i
\(339\) −13.7772 + 16.6538i −0.748275 + 0.904509i
\(340\) 0 0
\(341\) −6.38852 1.64029i −0.345958 0.0888269i
\(342\) −57.6454 + 27.1259i −3.11711 + 1.46680i
\(343\) 10.0303 + 3.25905i 0.541586 + 0.175972i
\(344\) −13.5243 7.43502i −0.729179 0.400869i
\(345\) 0 0
\(346\) −54.8708 6.93180i −2.94987 0.372656i
\(347\) −3.75356 + 29.7125i −0.201502 + 1.59505i 0.489372 + 0.872075i \(0.337226\pi\)
−0.690874 + 0.722975i \(0.742774\pi\)
\(348\) 23.8567 15.1399i 1.27885 0.811584i
\(349\) −10.9765 + 7.97493i −0.587561 + 0.426888i −0.841442 0.540347i \(-0.818293\pi\)
0.253881 + 0.967235i \(0.418293\pi\)
\(350\) 0 0
\(351\) −7.60045 5.52205i −0.405682 0.294745i
\(352\) 2.00555 + 0.126179i 0.106896 + 0.00672535i
\(353\) −11.0371 20.0764i −0.587445 1.06856i −0.988315 0.152424i \(-0.951292\pi\)
0.400870 0.916135i \(-0.368708\pi\)
\(354\) 12.5404 26.6498i 0.666517 1.41642i
\(355\) 0 0
\(356\) −1.74758 + 9.16113i −0.0926215 + 0.485539i
\(357\) 5.31850 + 7.32029i 0.281485 + 0.387431i
\(358\) 8.05229 14.6471i 0.425577 0.774122i
\(359\) 10.3356 16.2863i 0.545493 0.859559i −0.454013 0.890995i \(-0.650008\pi\)
0.999506 + 0.0314359i \(0.0100080\pi\)
\(360\) 0 0
\(361\) 8.17775 + 3.23780i 0.430408 + 0.170410i
\(362\) 19.6790 + 49.7034i 1.03430 + 2.61235i
\(363\) −25.3766 + 20.9933i −1.33192 + 1.10186i
\(364\) 1.80242 0.462782i 0.0944724 0.0242564i
\(365\) 0 0
\(366\) 57.4623 22.7509i 3.00360 1.18921i
\(367\) 4.39423 + 4.67937i 0.229377 + 0.244261i 0.833353 0.552741i \(-0.186418\pi\)
−0.603977 + 0.797002i \(0.706418\pi\)
\(368\) −10.2383 + 14.0918i −0.533709 + 0.734587i
\(369\) −38.8692 82.6012i −2.02345 4.30005i
\(370\) 0 0
\(371\) 2.14032 1.17665i 0.111120 0.0610888i
\(372\) 86.6955 16.5381i 4.49495 0.857458i
\(373\) −1.32347 5.15457i −0.0685267 0.266894i 0.925083 0.379765i \(-0.123995\pi\)
−0.993610 + 0.112871i \(0.963995\pi\)
\(374\) −8.93029 −0.461774
\(375\) 0 0
\(376\) −8.02107 −0.413655
\(377\) 0.285192 + 1.11075i 0.0146882 + 0.0572066i
\(378\) 32.0839 6.12034i 1.65022 0.314796i
\(379\) −29.2409 + 16.0753i −1.50201 + 0.825735i −0.999251 0.0386947i \(-0.987680\pi\)
−0.502755 + 0.864429i \(0.667680\pi\)
\(380\) 0 0
\(381\) −11.7745 25.0221i −0.603225 1.28192i
\(382\) 14.7643 20.3213i 0.755405 1.03973i
\(383\) 10.6083 + 11.2967i 0.542061 + 0.577236i 0.940429 0.339990i \(-0.110424\pi\)
−0.398369 + 0.917225i \(0.630424\pi\)
\(384\) 54.0609 21.4042i 2.75878 1.09228i
\(385\) 0 0
\(386\) −37.9624 + 9.74710i −1.93224 + 0.496114i
\(387\) 17.5392 14.5097i 0.891566 0.737567i
\(388\) −18.6740 47.1652i −0.948029 2.39445i
\(389\) 8.97238 + 3.55241i 0.454917 + 0.180115i 0.584398 0.811467i \(-0.301331\pi\)
−0.129480 + 0.991582i \(0.541331\pi\)
\(390\) 0 0
\(391\) 6.26679 9.87489i 0.316925 0.499395i
\(392\) 16.7061 30.3884i 0.843788 1.53484i
\(393\) 18.7264 + 25.7747i 0.944623 + 1.30016i
\(394\) 7.29284 38.2304i 0.367408 1.92602i
\(395\) 0 0
\(396\) −14.8398 + 31.5362i −0.745729 + 1.58476i
\(397\) −4.88630 8.88815i −0.245236 0.446083i 0.724828 0.688929i \(-0.241919\pi\)
−0.970065 + 0.242846i \(0.921919\pi\)
\(398\) 35.0322 + 2.20404i 1.75601 + 0.110479i
\(399\) 6.76268 + 4.91337i 0.338557 + 0.245976i
\(400\) 0 0
\(401\) 15.5702 11.3124i 0.777537 0.564914i −0.126702 0.991941i \(-0.540439\pi\)
0.904239 + 0.427027i \(0.140439\pi\)
\(402\) −94.8728 + 60.2081i −4.73182 + 3.00291i
\(403\) −0.448958 + 3.55387i −0.0223642 + 0.177031i
\(404\) 42.3895 + 5.35504i 2.10896 + 0.266423i
\(405\) 0 0
\(406\) −3.49384 1.92076i −0.173397 0.0953255i
\(407\) −5.47266 1.77818i −0.271270 0.0881409i
\(408\) 56.4632 26.5696i 2.79535 1.31539i
\(409\) −24.7135 6.34535i −1.22201 0.313758i −0.418037 0.908430i \(-0.637282\pi\)
−0.803968 + 0.594672i \(0.797282\pi\)
\(410\) 0 0
\(411\) 3.81171 4.60757i 0.188018 0.227275i
\(412\) −59.8879 38.0060i −2.95047 1.87242i
\(413\) −2.80676 + 0.176586i −0.138111 + 0.00868923i
\(414\) −36.1442 56.9542i −1.77639 2.79914i
\(415\) 0 0
\(416\) −0.0685271 1.08921i −0.00335982 0.0534027i
\(417\) −29.4032 5.60897i −1.43988 0.274672i
\(418\) −7.84625 + 2.54940i −0.383773 + 0.124695i
\(419\) 26.8086 25.1749i 1.30969 1.22988i 0.354084 0.935213i \(-0.384793\pi\)
0.955601 0.294663i \(-0.0952074\pi\)
\(420\) 0 0
\(421\) −4.27563 22.4137i −0.208382 1.09237i −0.920627 0.390444i \(-0.872322\pi\)
0.712245 0.701931i \(-0.247678\pi\)
\(422\) −32.7068 + 34.8292i −1.59214 + 1.69546i
\(423\) 4.35511 10.9997i 0.211752 0.534826i
\(424\) −5.20517 16.0199i −0.252786 0.777994i
\(425\) 0 0
\(426\) −13.3366 + 41.0459i −0.646161 + 1.98868i
\(427\) −4.54693 3.76155i −0.220041 0.182034i
\(428\) 53.4364 + 25.1452i 2.58294 + 1.21544i
\(429\) −1.41697 1.33063i −0.0684121 0.0642432i
\(430\) 0 0
\(431\) −20.7583 + 2.62238i −0.999891 + 0.126316i −0.608202 0.793782i \(-0.708109\pi\)
−0.391689 + 0.920098i \(0.628109\pi\)
\(432\) 85.7917i 4.12766i
\(433\) 1.84693 + 14.6200i 0.0887578 + 0.702590i 0.972217 + 0.234082i \(0.0752084\pi\)
−0.883459 + 0.468508i \(0.844792\pi\)
\(434\) −7.93844 9.59592i −0.381057 0.460619i
\(435\) 0 0
\(436\) −0.217526 + 3.45748i −0.0104176 + 0.165583i
\(437\) 2.68701 10.4652i 0.128537 0.500619i
\(438\) −12.8206 + 49.9331i −0.612594 + 2.38590i
\(439\) 0.861319 13.6903i 0.0411085 0.653401i −0.922485 0.386032i \(-0.873846\pi\)
0.963594 0.267370i \(-0.0861545\pi\)
\(440\) 0 0
\(441\) 32.6025 + 39.4097i 1.55250 + 1.87665i
\(442\) 0.607865 + 4.81175i 0.0289132 + 0.228872i
\(443\) 5.72633i 0.272066i 0.990704 + 0.136033i \(0.0434354\pi\)
−0.990704 + 0.136033i \(0.956565\pi\)
\(444\) 76.3922 9.65058i 3.62541 0.457996i
\(445\) 0 0
\(446\) −8.49792 7.98008i −0.402388 0.377868i
\(447\) 18.2463 + 8.58607i 0.863022 + 0.406107i
\(448\) −3.33254 2.75692i −0.157448 0.130252i
\(449\) 0.254531 0.783366i 0.0120121 0.0369693i −0.944871 0.327443i \(-0.893813\pi\)
0.956883 + 0.290474i \(0.0938130\pi\)
\(450\) 0 0
\(451\) −3.65308 11.2430i −0.172017 0.529414i
\(452\) 10.0335 25.3416i 0.471934 1.19197i
\(453\) 24.8298 26.4410i 1.16660 1.24231i
\(454\) 3.38917 + 17.7666i 0.159062 + 0.833830i
\(455\) 0 0
\(456\) 42.0242 39.4633i 1.96796 1.84804i
\(457\) −8.06467 + 2.62037i −0.377250 + 0.122576i −0.491503 0.870876i \(-0.663552\pi\)
0.114254 + 0.993452i \(0.463552\pi\)
\(458\) −37.3422 7.12340i −1.74489 0.332855i
\(459\) 3.61702 + 57.4909i 0.168828 + 2.68345i
\(460\) 0 0
\(461\) −18.7334 29.5191i −0.872502 1.37484i −0.926497 0.376303i \(-0.877195\pi\)
0.0539945 0.998541i \(-0.482805\pi\)
\(462\) 6.74470 0.424340i 0.313792 0.0197421i
\(463\) −5.58091 3.54176i −0.259367 0.164599i 0.399785 0.916609i \(-0.369085\pi\)
−0.659152 + 0.752010i \(0.729085\pi\)
\(464\) −6.67532 + 8.06908i −0.309894 + 0.374598i
\(465\) 0 0
\(466\) 38.1538 + 9.79623i 1.76744 + 0.453801i
\(467\) 13.3371 6.27598i 0.617170 0.290418i −0.0916681 0.995790i \(-0.529220\pi\)
0.708838 + 0.705372i \(0.249220\pi\)
\(468\) 18.0022 + 5.84928i 0.832153 + 0.270383i
\(469\) 9.40201 + 5.16880i 0.434145 + 0.238673i
\(470\) 0 0
\(471\) 49.1470 + 6.20871i 2.26457 + 0.286082i
\(472\) −2.43085 + 19.2422i −0.111889 + 0.885692i
\(473\) 2.48884 1.57946i 0.114437 0.0726238i
\(474\) 61.6872 44.8184i 2.83339 2.05858i
\(475\) 0 0
\(476\) −9.23107 6.70676i −0.423105 0.307404i
\(477\) 24.7951 + 1.55998i 1.13529 + 0.0714265i
\(478\) −9.52169 17.3199i −0.435512 0.792194i
\(479\) −3.28956 + 6.99068i −0.150304 + 0.319412i −0.965773 0.259388i \(-0.916479\pi\)
0.815469 + 0.578801i \(0.196479\pi\)
\(480\) 0 0
\(481\) −0.585591 + 3.06978i −0.0267006 + 0.139970i
\(482\) −17.9224 24.6681i −0.816344 1.12360i
\(483\) −4.26384 + 7.75590i −0.194011 + 0.352906i
\(484\) 22.2536 35.0661i 1.01153 1.59391i
\(485\) 0 0
\(486\) 124.251 + 49.1945i 5.63615 + 2.23151i
\(487\) 10.2387 + 25.8600i 0.463959 + 1.17183i 0.953914 + 0.300079i \(0.0970131\pi\)
−0.489955 + 0.871748i \(0.662987\pi\)
\(488\) −31.3580 + 25.9416i −1.41951 + 1.17432i
\(489\) 25.2379 6.47998i 1.14130 0.293035i
\(490\) 0 0
\(491\) 15.9298 6.30707i 0.718904 0.284634i 0.0199499 0.999801i \(-0.493649\pi\)
0.698954 + 0.715167i \(0.253649\pi\)
\(492\) 108.287 + 115.314i 4.88194 + 5.19874i
\(493\) 4.13308 5.68870i 0.186145 0.256206i
\(494\) 1.90773 + 4.05412i 0.0858327 + 0.182404i
\(495\) 0 0
\(496\) −28.6655 + 15.7590i −1.28712 + 0.707599i
\(497\) 4.04796 0.772189i 0.181576 0.0346374i
\(498\) −0.392319 1.52798i −0.0175802 0.0684705i
\(499\) 7.49374 0.335466 0.167733 0.985832i \(-0.446355\pi\)
0.167733 + 0.985832i \(0.446355\pi\)
\(500\) 0 0
\(501\) −31.1001 −1.38945
\(502\) −3.78758 14.7516i −0.169048 0.658398i
\(503\) −31.6850 + 6.04424i −1.41276 + 0.269499i −0.836591 0.547828i \(-0.815455\pi\)
−0.576174 + 0.817327i \(0.695455\pi\)
\(504\) −30.1151 + 16.5559i −1.34143 + 0.737458i
\(505\) 0 0
\(506\) −3.71925 7.90381i −0.165341 0.351367i
\(507\) 24.7440 34.0571i 1.09892 1.51253i
\(508\) 23.8718 + 25.4208i 1.05914 + 1.12787i
\(509\) −21.8917 + 8.66755i −0.970335 + 0.384183i −0.799200 0.601065i \(-0.794743\pi\)
−0.171134 + 0.985248i \(0.554743\pi\)
\(510\) 0 0
\(511\) 4.76785 1.22418i 0.210917 0.0541544i
\(512\) −35.4663 + 29.3403i −1.56740 + 1.29667i
\(513\) 19.5903 + 49.4796i 0.864935 + 2.18458i
\(514\) −41.2371 16.3269i −1.81889 0.720149i
\(515\) 0 0
\(516\) −21.1351 + 33.3036i −0.930421 + 1.46611i
\(517\) 0.738049 1.34251i 0.0324594 0.0590434i
\(518\) −6.38637 8.79009i −0.280601 0.386214i
\(519\) −13.8315 + 72.5072i −0.607135 + 3.18271i
\(520\) 0 0
\(521\) −6.43758 + 13.6806i −0.282036 + 0.599356i −0.994777 0.102071i \(-0.967453\pi\)
0.712742 + 0.701427i \(0.247453\pi\)
\(522\) −19.5377 35.5390i −0.855142 1.55550i
\(523\) 38.1685 + 2.40136i 1.66899 + 0.105004i 0.868937 0.494922i \(-0.164803\pi\)
0.800055 + 0.599926i \(0.204803\pi\)
\(524\) −32.5025 23.6145i −1.41988 1.03160i
\(525\) 0 0
\(526\) −49.5627 + 36.0094i −2.16104 + 1.57008i
\(527\) 18.5450 11.7690i 0.807831 0.512665i
\(528\) 2.22476 17.6108i 0.0968202 0.766411i
\(529\) −11.4688 1.44885i −0.498645 0.0629935i
\(530\) 0 0
\(531\) −25.0680 13.7813i −1.08786 0.598055i
\(532\) −10.0251 3.25737i −0.434645 0.141225i
\(533\) −5.80923 + 2.73362i −0.251626 + 0.118406i
\(534\) 17.8166 + 4.57452i 0.771000 + 0.197959i
\(535\) 0 0
\(536\) 47.1653 57.0131i 2.03723 2.46259i
\(537\) −18.8351 11.9531i −0.812796 0.515816i
\(538\) −17.7029 + 1.11377i −0.763225 + 0.0480180i
\(539\) 3.54898 + 5.59230i 0.152865 + 0.240877i
\(540\) 0 0
\(541\) −0.275102 4.37262i −0.0118276 0.187994i −0.999504 0.0314854i \(-0.989976\pi\)
0.987677 0.156508i \(-0.0500238\pi\)
\(542\) 62.9036 + 11.9995i 2.70194 + 0.515423i
\(543\) 67.8542 22.0472i 2.91190 0.946135i
\(544\) −4.87812 + 4.58086i −0.209148 + 0.196403i
\(545\) 0 0
\(546\) −0.687737 3.60524i −0.0294324 0.154290i
\(547\) −18.4117 + 19.6064i −0.787226 + 0.838311i −0.990022 0.140910i \(-0.954997\pi\)
0.202796 + 0.979221i \(0.434997\pi\)
\(548\) −2.77594 + 7.01122i −0.118582 + 0.299505i
\(549\) −18.5491 57.0882i −0.791655 2.43646i
\(550\) 0 0
\(551\) 2.00737 6.17806i 0.0855169 0.263194i
\(552\) 47.0312 + 38.9076i 2.00178 + 1.65602i
\(553\) −6.58775 3.09996i −0.280140 0.131824i
\(554\) −6.91362 6.49232i −0.293731 0.275832i
\(555\) 0 0
\(556\) 37.4492 4.73093i 1.58820 0.200636i
\(557\) 9.84523i 0.417156i −0.978006 0.208578i \(-0.933117\pi\)
0.978006 0.208578i \(-0.0668835\pi\)
\(558\) −15.8772 125.681i −0.672136 5.32050i
\(559\) −1.02044 1.23351i −0.0431602 0.0521717i
\(560\) 0 0
\(561\) −0.748380 + 11.8952i −0.0315966 + 0.502214i
\(562\) 4.81550 18.7551i 0.203129 0.791137i
\(563\) −3.54726 + 13.8157i −0.149499 + 0.582260i 0.849045 + 0.528320i \(0.177178\pi\)
−0.998544 + 0.0539400i \(0.982822\pi\)
\(564\) −1.28721 + 20.4596i −0.0542013 + 0.861505i
\(565\) 0 0
\(566\) 3.80023 + 4.59369i 0.159736 + 0.193087i
\(567\) −3.08682 24.4347i −0.129634 1.02616i
\(568\) 28.4202i 1.19248i
\(569\) 26.4864 3.34601i 1.11037 0.140272i 0.451311 0.892367i \(-0.350956\pi\)
0.659055 + 0.752095i \(0.270956\pi\)
\(570\) 0 0
\(571\) 16.4283 + 15.4272i 0.687503 + 0.645609i 0.947409 0.320025i \(-0.103691\pi\)
−0.259906 + 0.965634i \(0.583691\pi\)
\(572\) 2.21790 + 1.04366i 0.0927350 + 0.0436378i
\(573\) −25.8307 21.3690i −1.07909 0.892703i
\(574\) 6.89768 21.2289i 0.287904 0.886076i
\(575\) 0 0
\(576\) −13.5950 41.8411i −0.566458 1.74338i
\(577\) −6.80093 + 17.1772i −0.283126 + 0.715095i 0.716716 + 0.697365i \(0.245644\pi\)
−0.999843 + 0.0177308i \(0.994356\pi\)
\(578\) −8.58635 + 9.14354i −0.357145 + 0.380321i
\(579\) 9.80181 + 51.3829i 0.407349 + 2.13540i
\(580\) 0 0
\(581\) −0.109806 + 0.103114i −0.00455550 + 0.00427790i
\(582\) −95.1539 + 30.9174i −3.94426 + 1.28157i
\(583\) 3.16023 + 0.602847i 0.130884 + 0.0249674i
\(584\) −2.13162 33.8811i −0.0882070 1.40201i
\(585\) 0 0
\(586\) −14.7675 23.2698i −0.610038 0.961267i
\(587\) 28.2931 1.78005i 1.16778 0.0734705i 0.532966 0.846136i \(-0.321077\pi\)
0.634813 + 0.772666i \(0.281077\pi\)
\(588\) −74.8316 47.4896i −3.08600 1.95844i
\(589\) 12.9340 15.6345i 0.532937 0.644210i
\(590\) 0 0
\(591\) −50.3119 12.9179i −2.06955 0.531371i
\(592\) −25.8225 + 12.1511i −1.06130 + 0.499408i
\(593\) −39.4502 12.8181i −1.62003 0.526378i −0.648078 0.761574i \(-0.724427\pi\)
−0.971948 + 0.235196i \(0.924427\pi\)
\(594\) 37.7019 + 20.7268i 1.54693 + 0.850430i
\(595\) 0 0
\(596\) −25.2287 3.18713i −1.03341 0.130550i
\(597\) 5.87157 46.4783i 0.240308 1.90223i
\(598\) −4.00551 + 2.54197i −0.163797 + 0.103949i
\(599\) −27.7097 + 20.1323i −1.13219 + 0.822583i −0.986012 0.166675i \(-0.946697\pi\)
−0.146177 + 0.989258i \(0.546697\pi\)
\(600\) 0 0
\(601\) 27.0658 + 19.6644i 1.10404 + 0.802130i 0.981714 0.190361i \(-0.0609658\pi\)
0.122322 + 0.992490i \(0.460966\pi\)
\(602\) 5.55483 + 0.349480i 0.226398 + 0.0142437i
\(603\) 52.5764 + 95.6362i 2.14108 + 3.89461i
\(604\) −19.4750 + 41.3865i −0.792426 + 1.68399i
\(605\) 0 0
\(606\) 15.7907 82.7775i 0.641451 3.36261i
\(607\) 16.7437 + 23.0458i 0.679607 + 0.935399i 0.999929 0.0119096i \(-0.00379104\pi\)
−0.320322 + 0.947309i \(0.603791\pi\)
\(608\) −2.97823 + 5.41739i −0.120783 + 0.219704i
\(609\) −2.85125 + 4.49284i −0.115538 + 0.182059i
\(610\) 0 0
\(611\) −0.773597 0.306289i −0.0312964 0.0123911i
\(612\) −42.7258 107.913i −1.72709 4.36213i
\(613\) −3.71313 + 3.07177i −0.149972 + 0.124068i −0.709384 0.704822i \(-0.751027\pi\)
0.559412 + 0.828890i \(0.311027\pi\)
\(614\) 22.0499 5.66145i 0.889862 0.228478i
\(615\) 0 0
\(616\) −4.13773 + 1.63824i −0.166714 + 0.0660068i
\(617\) −15.2887 16.2808i −0.615498 0.655439i 0.343400 0.939189i \(-0.388421\pi\)
−0.958898 + 0.283750i \(0.908421\pi\)
\(618\) −82.2288 + 113.178i −3.30773 + 4.55270i
\(619\) 8.92369 + 18.9638i 0.358673 + 0.762220i 0.999987 0.00505895i \(-0.00161032\pi\)
−0.641314 + 0.767279i \(0.721610\pi\)
\(620\) 0 0
\(621\) −49.3763 + 27.1448i −1.98140 + 1.08928i
\(622\) −65.4956 + 12.4939i −2.62613 + 0.500962i
\(623\) −0.436797 1.70121i −0.0174999 0.0681577i
\(624\) −9.64034 −0.385923
\(625\) 0 0
\(626\) 65.2957 2.60974
\(627\) 2.73827 + 10.6649i 0.109356 + 0.425914i
\(628\) −61.3617 + 11.7054i −2.44860 + 0.467095i
\(629\) 16.7919 9.23142i 0.669537 0.368081i
\(630\) 0 0
\(631\) 18.6737 + 39.6835i 0.743386 + 1.57978i 0.813042 + 0.582205i \(0.197810\pi\)
−0.0696553 + 0.997571i \(0.522190\pi\)
\(632\) −29.5134 + 40.6218i −1.17398 + 1.61585i
\(633\) 43.6516 + 46.4843i 1.73500 + 1.84758i
\(634\) −29.2077 + 11.5641i −1.15998 + 0.459270i
\(635\) 0 0
\(636\) −41.6977 + 10.7062i −1.65342 + 0.424527i
\(637\) 2.77163 2.29289i 0.109816 0.0908477i
\(638\) −1.93330 4.88296i −0.0765402 0.193318i
\(639\) 38.9742 + 15.4310i 1.54180 + 0.610440i
\(640\) 0 0
\(641\) 13.4110 21.1323i 0.529701 0.834675i −0.469124 0.883132i \(-0.655430\pi\)
0.998825 + 0.0484569i \(0.0154304\pi\)
\(642\) 56.1143 102.072i 2.21466 4.02844i
\(643\) −4.15494 5.71879i −0.163855 0.225527i 0.719192 0.694811i \(-0.244512\pi\)
−0.883047 + 0.469284i \(0.844512\pi\)
\(644\) 2.09135 10.9632i 0.0824106 0.432011i
\(645\) 0 0
\(646\) 11.6975 24.8584i 0.460230 0.978039i
\(647\) 4.89054 + 8.89586i 0.192267 + 0.349732i 0.954816 0.297198i \(-0.0960523\pi\)
−0.762549 + 0.646931i \(0.776052\pi\)
\(648\) −169.519 10.6652i −6.65932 0.418969i
\(649\) −2.99694 2.17740i −0.117640 0.0854705i
\(650\) 0 0
\(651\) −13.4471 + 9.76986i −0.527032 + 0.382911i
\(652\) −27.7428 + 17.6061i −1.08649 + 0.689509i
\(653\) 1.92930 15.2720i 0.0754993 0.597639i −0.908294 0.418332i \(-0.862615\pi\)
0.983793 0.179306i \(-0.0573853\pi\)
\(654\) 6.77885 + 0.856368i 0.265074 + 0.0334867i
\(655\) 0 0
\(656\) −51.3775 28.2450i −2.00596 1.10278i
\(657\) 47.6204 + 15.4728i 1.85785 + 0.603652i
\(658\) 2.61739 1.23165i 0.102037 0.0480148i
\(659\) 25.0852 + 6.44078i 0.977180 + 0.250897i 0.703321 0.710873i \(-0.251700\pi\)
0.273859 + 0.961770i \(0.411700\pi\)
\(660\) 0 0
\(661\) −28.1644 + 34.0449i −1.09547 + 1.32419i −0.153628 + 0.988129i \(0.549096\pi\)
−0.941839 + 0.336064i \(0.890904\pi\)
\(662\) 22.2677 + 14.1315i 0.865457 + 0.549236i
\(663\) 6.46020 0.406442i 0.250893 0.0157849i
\(664\) 0.556634 + 0.877115i 0.0216016 + 0.0340387i
\(665\) 0 0
\(666\) −6.93955 110.301i −0.268902 4.27407i
\(667\) 6.75615 + 1.28880i 0.261599 + 0.0499027i
\(668\) 37.2986 12.1190i 1.44313 0.468900i
\(669\) −11.3416 + 10.6505i −0.438493 + 0.411772i
\(670\) 0 0
\(671\) −1.45654 7.63545i −0.0562291 0.294763i
\(672\) 3.46658 3.69154i 0.133726 0.142404i
\(673\) 6.95425 17.5644i 0.268067 0.677059i −0.731924 0.681386i \(-0.761377\pi\)
0.999991 + 0.00432713i \(0.00137737\pi\)
\(674\) 27.2322 + 83.8121i 1.04894 + 3.22832i
\(675\) 0 0
\(676\) −16.4043 + 50.4871i −0.630933 + 1.94181i
\(677\) −34.8177 28.8037i −1.33815 1.10702i −0.985206 0.171371i \(-0.945180\pi\)
−0.352945 0.935644i \(-0.614820\pi\)
\(678\) −48.6406 22.8885i −1.86803 0.879029i
\(679\) 6.96407 + 6.53970i 0.267257 + 0.250971i
\(680\) 0 0
\(681\) 23.9492 3.02549i 0.917737 0.115937i
\(682\) 16.4045i 0.628163i
\(683\) 1.23898 + 9.80757i 0.0474084 + 0.375276i 0.997913 + 0.0645669i \(0.0205666\pi\)
−0.950505 + 0.310709i \(0.899433\pi\)
\(684\) −68.3462 82.6163i −2.61328 3.15891i
\(685\) 0 0
\(686\) −1.64704 + 26.1789i −0.0628842 + 0.999515i
\(687\) −12.6178 + 49.1429i −0.481397 + 1.87492i
\(688\) 3.63566 14.1600i 0.138608 0.539843i
\(689\) 0.109711 1.74381i 0.00417966 0.0664338i
\(690\) 0 0
\(691\) 12.3817 + 14.9669i 0.471023 + 0.569369i 0.951504 0.307636i \(-0.0995378\pi\)
−0.480481 + 0.877005i \(0.659538\pi\)
\(692\) −11.6663 92.3481i −0.443485 3.51055i
\(693\) 6.56381i 0.249338i
\(694\) −73.8993 + 9.33565i −2.80518 + 0.354376i
\(695\) 0 0
\(696\) 26.7515 + 25.1214i 1.01401 + 0.952223i
\(697\) 35.6200 + 16.7615i 1.34920 + 0.634888i
\(698\) −26.0010 21.5099i −0.984151 0.814160i
\(699\) 16.2460 50.0000i 0.614479 1.89117i
\(700\) 0 0
\(701\) −4.01298 12.3507i −0.151568 0.466479i 0.846229 0.532820i \(-0.178868\pi\)
−0.997797 + 0.0663408i \(0.978868\pi\)
\(702\) 8.60156 21.7251i 0.324645 0.819959i
\(703\) 12.1182 12.9045i 0.457046 0.486704i
\(704\) −1.06753 5.59618i −0.0402340 0.210914i
\(705\) 0 0
\(706\) 41.5374 39.0062i 1.56328 1.46802i
\(707\) −7.65269 + 2.48651i −0.287809 + 0.0935149i
\(708\) 48.6915 + 9.28840i 1.82994 + 0.349079i
\(709\) −2.19608 34.9057i −0.0824755 1.31091i −0.793857 0.608104i \(-0.791930\pi\)
0.711382 0.702806i \(-0.248070\pi\)
\(710\) 0 0
\(711\) −39.6823 62.5293i −1.48820 2.34503i
\(712\) −12.0891 + 0.760581i −0.453058 + 0.0285040i
\(713\) 18.1397 + 11.5118i 0.679339 + 0.431121i
\(714\) −14.3450 + 17.3401i −0.536847 + 0.648937i
\(715\) 0 0
\(716\) 27.2470 + 6.99583i 1.01827 + 0.261446i
\(717\) −23.8681 + 11.2315i −0.891370 + 0.419447i
\(718\) 45.6267 + 14.8250i 1.70277 + 0.553265i
\(719\) 27.0272 + 14.8583i 1.00794 + 0.554121i 0.898083 0.439826i \(-0.144960\pi\)
0.109860 + 0.993947i \(0.464960\pi\)
\(720\) 0 0
\(721\) 13.2526 + 1.67419i 0.493553 + 0.0623502i
\(722\) −2.74172 + 21.7029i −0.102036 + 0.807699i
\(723\) −34.3599 + 21.8055i −1.27786 + 0.810954i
\(724\) −72.7867 + 52.8826i −2.70510 + 1.96537i
\(725\) 0 0
\(726\) −66.2692 48.1474i −2.45948 1.78692i
\(727\) −9.26913 0.583164i −0.343773 0.0216284i −0.110034 0.993928i \(-0.535096\pi\)
−0.233739 + 0.972299i \(0.575096\pi\)
\(728\) 1.16435 + 2.11795i 0.0431538 + 0.0784965i
\(729\) 36.0325 76.5729i 1.33454 2.83603i
\(730\) 0 0
\(731\) −1.83934 + 9.64217i −0.0680306 + 0.356629i
\(732\) 61.1377 + 84.1489i 2.25972 + 3.11023i
\(733\) 2.88620 5.24998i 0.106604 0.193913i −0.817624 0.575752i \(-0.804709\pi\)
0.924229 + 0.381840i \(0.124709\pi\)
\(734\) −8.55469 + 13.4800i −0.315759 + 0.497557i
\(735\) 0 0
\(736\) −6.08594 2.40959i −0.224331 0.0888188i
\(737\) 5.20256 + 13.1402i 0.191639 + 0.484024i
\(738\) 174.945 144.727i 6.43982 5.32748i
\(739\) −13.1162 + 3.36768i −0.482489 + 0.123882i −0.482097 0.876118i \(-0.660125\pi\)
−0.000391910 1.00000i \(0.500125\pi\)
\(740\) 0 0
\(741\) 5.55998 2.20135i 0.204251 0.0808686i
\(742\) 4.15841 + 4.42826i 0.152660 + 0.162567i
\(743\) −13.6581 + 18.7987i −0.501066 + 0.689658i −0.982381 0.186890i \(-0.940159\pi\)
0.481315 + 0.876548i \(0.340159\pi\)
\(744\) 48.8072 + 103.721i 1.78936 + 3.80258i
\(745\) 0 0
\(746\) 11.5988 6.37649i 0.424662 0.233460i
\(747\) −1.50507 + 0.287107i −0.0550675 + 0.0105047i
\(748\) −3.73775 14.5576i −0.136666 0.532277i
\(749\) −11.1220 −0.406389
\(750\) 0 0
\(751\) 45.1704 1.64829 0.824146 0.566377i \(-0.191655\pi\)
0.824146 + 0.566377i \(0.191655\pi\)
\(752\) −1.88955 7.35931i −0.0689048 0.268366i
\(753\) −19.9666 + 3.80884i −0.727624 + 0.138802i
\(754\) −2.49941 + 1.37406i −0.0910230 + 0.0500403i
\(755\) 0 0
\(756\) 23.4056 + 49.7395i 0.851254 + 1.80901i
\(757\) 21.7999 30.0050i 0.792332 1.09055i −0.201482 0.979492i \(-0.564576\pi\)
0.993814 0.111059i \(-0.0354242\pi\)
\(758\) −56.8119 60.4985i −2.06350 2.19741i
\(759\) −10.8396 + 4.29169i −0.393451 + 0.155778i
\(760\) 0 0
\(761\) −6.23285 + 1.60032i −0.225941 + 0.0580117i −0.359963 0.932967i \(-0.617211\pi\)
0.134022 + 0.990978i \(0.457211\pi\)
\(762\) 52.9954 43.8416i 1.91982 1.58821i
\(763\) −0.240173 0.606607i −0.00869483 0.0219606i
\(764\) 39.3059 + 15.5623i 1.42204 + 0.563025i
\(765\) 0 0
\(766\) −20.6523 + 32.5429i −0.746199 + 1.17582i
\(767\) −0.969216 + 1.76300i −0.0349964 + 0.0636582i
\(768\) 63.5914 + 87.5261i 2.29466 + 3.15833i
\(769\) −2.99673 + 15.7094i −0.108065 + 0.566495i 0.886531 + 0.462669i \(0.153108\pi\)
−0.994596 + 0.103825i \(0.966892\pi\)
\(770\) 0 0
\(771\) −25.2033 + 53.5596i −0.907673 + 1.92890i
\(772\) −31.7782 57.8042i −1.14372 2.08042i
\(773\) −8.52249 0.536189i −0.306533 0.0192854i −0.0912206 0.995831i \(-0.529077\pi\)
−0.215312 + 0.976545i \(0.569077\pi\)
\(774\) 45.8023 + 33.2773i 1.64633 + 1.19613i
\(775\) 0 0
\(776\) 53.3018 38.7260i 1.91342 1.39018i
\(777\) −12.2436 + 7.77003i −0.439237 + 0.278748i
\(778\) −3.00813 + 23.8118i −0.107847 + 0.853693i
\(779\) 36.0812 + 4.55811i 1.29274 + 0.163311i
\(780\) 0 0
\(781\) 4.75676 + 2.61505i 0.170210 + 0.0935738i
\(782\) 27.6648 + 8.98885i 0.989293 + 0.321441i
\(783\) −30.6522 + 14.4238i −1.09542 + 0.515466i
\(784\) 31.8168 + 8.16916i 1.13631 + 0.291756i
\(785\) 0 0
\(786\) −50.5086 + 61.0544i −1.80158 + 2.17774i
\(787\) 6.35500 + 4.03301i 0.226531 + 0.143761i 0.644249 0.764816i \(-0.277170\pi\)
−0.417718 + 0.908577i \(0.637170\pi\)
\(788\) 65.3731 4.11293i 2.32882 0.146517i
\(789\) 43.8111 + 69.0353i 1.55972 + 2.45772i
\(790\) 0 0
\(791\) 0.322301 + 5.12283i 0.0114597 + 0.182147i
\(792\) −44.4656 8.48226i −1.58002 0.301404i
\(793\) −4.01493 + 1.30453i −0.142574 + 0.0463252i
\(794\) 18.3893 17.2687i 0.652612 0.612843i
\(795\) 0 0
\(796\) 11.0698 + 58.0297i 0.392357 + 2.05681i
\(797\) 19.3269 20.5811i 0.684594 0.729019i −0.288994 0.957331i \(-0.593321\pi\)
0.973588 + 0.228312i \(0.0733207\pi\)
\(798\) −7.65344 + 19.3304i −0.270929 + 0.684288i
\(799\) 1.57650 + 4.85197i 0.0557726 + 0.171650i
\(800\) 0 0
\(801\) 5.52085 16.9914i 0.195069 0.600362i
\(802\) 36.8822 + 30.5116i 1.30236 + 1.07740i
\(803\) 5.86690 + 2.76076i 0.207039 + 0.0974249i
\(804\) −137.856 129.455i −4.86181 4.56554i
\(805\) 0 0
\(806\) −8.83898 + 1.11662i −0.311340 + 0.0393313i
\(807\) 23.6736i 0.833350i
\(808\) 6.95511 + 55.0553i 0.244680 + 1.93684i
\(809\) 7.95125 + 9.61141i 0.279551 + 0.337919i 0.891536 0.452951i \(-0.149629\pi\)
−0.611985 + 0.790870i \(0.709629\pi\)
\(810\) 0 0
\(811\) 2.05459 32.6568i 0.0721464 1.14673i −0.780816 0.624761i \(-0.785196\pi\)
0.852962 0.521973i \(-0.174804\pi\)
\(812\) 1.66875 6.49936i 0.0585617 0.228083i
\(813\) 21.2549 82.7822i 0.745441 2.90330i
\(814\) 0.898643 14.2835i 0.0314974 0.500637i
\(815\) 0 0
\(816\) 37.6787 + 45.5458i 1.31902 + 1.59442i
\(817\) 1.13656 + 8.99681i 0.0397633 + 0.314759i
\(818\) 63.4598i 2.21882i
\(819\) −3.53666 + 0.446784i −0.123581 + 0.0156119i
\(820\) 0 0
\(821\) 6.26838 + 5.88640i 0.218768 + 0.205437i 0.786181 0.617997i \(-0.212056\pi\)
−0.567413 + 0.823434i \(0.692056\pi\)
\(822\) 13.4573 + 6.33253i 0.469378 + 0.220872i
\(823\) −28.4119 23.5043i −0.990375 0.819310i −0.00683079 0.999977i \(-0.502174\pi\)
−0.983544 + 0.180667i \(0.942174\pi\)
\(824\) 28.4676 87.6144i 0.991717 3.05219i
\(825\) 0 0
\(826\) −2.16145 6.65227i −0.0752065 0.231462i
\(827\) −3.60867 + 9.11447i −0.125486 + 0.316941i −0.978915 0.204268i \(-0.934519\pi\)
0.853429 + 0.521209i \(0.174519\pi\)
\(828\) 77.7149 82.7579i 2.70078 2.87604i
\(829\) 3.95671 + 20.7418i 0.137422 + 0.720393i 0.982575 + 0.185868i \(0.0595096\pi\)
−0.845153 + 0.534525i \(0.820490\pi\)
\(830\) 0 0
\(831\) −9.22716 + 8.66488i −0.320087 + 0.300582i
\(832\) −2.94263 + 0.956117i −0.102017 + 0.0331474i
\(833\) −21.6655 4.13292i −0.750666 0.143197i
\(834\) −4.67468 74.3019i −0.161871 2.57286i
\(835\) 0 0
\(836\) −7.43989 11.7234i −0.257314 0.405462i
\(837\) −105.608 + 6.64431i −3.65036 + 0.229661i
\(838\) 77.2285 + 49.0107i 2.66781 + 1.69305i
\(839\) 21.3524 25.8107i 0.737168 0.891083i −0.260052 0.965595i \(-0.583740\pi\)
0.997220 + 0.0745113i \(0.0237397\pi\)
\(840\) 0 0
\(841\) −24.0836 6.18363i −0.830470 0.213229i
\(842\) 51.3500 24.1635i 1.76964 0.832729i
\(843\) −24.5783 7.98598i −0.846522 0.275052i
\(844\) −70.4655 38.7388i −2.42552 1.33344i
\(845\) 0 0
\(846\) 29.1922 + 3.68783i 1.00365 + 0.126790i
\(847\) −0.980289 + 7.75979i −0.0336831 + 0.266629i
\(848\) 13.4720 8.54959i 0.462630 0.293594i
\(849\) 6.43728 4.67696i 0.220927 0.160513i
\(850\) 0 0
\(851\) 15.1637 + 11.0171i 0.519807 + 0.377662i
\(852\) −72.4923 4.56083i −2.48354 0.156251i
\(853\) −21.3979 38.9227i −0.732652 1.33269i −0.935447 0.353467i \(-0.885003\pi\)
0.202795 0.979221i \(-0.434997\pi\)
\(854\) 6.24919 13.2802i 0.213843 0.454439i
\(855\) 0 0
\(856\) −14.3727 + 75.3444i −0.491249 + 2.57522i
\(857\) −18.8965 26.0088i −0.645493 0.888445i 0.353401 0.935472i \(-0.385025\pi\)
−0.998894 + 0.0470273i \(0.985025\pi\)
\(858\) 2.32905 4.23653i 0.0795124 0.144633i
\(859\) 9.16371 14.4397i 0.312662 0.492676i −0.651263 0.758852i \(-0.725760\pi\)
0.963924 + 0.266176i \(0.0857604\pi\)
\(860\) 0 0
\(861\) −27.6989 10.9668i −0.943975 0.373746i
\(862\) −19.1569 48.3848i −0.652487 1.64799i
\(863\) −1.51625 + 1.25435i −0.0516138 + 0.0426986i −0.662873 0.748732i \(-0.730663\pi\)
0.611259 + 0.791430i \(0.290663\pi\)
\(864\) 31.2264 8.01757i 1.06234 0.272763i
\(865\) 0 0
\(866\) −34.0772 + 13.4921i −1.15799 + 0.458481i
\(867\) 11.4597 + 12.2033i 0.389190 + 0.414446i
\(868\) 12.3200 16.9571i 0.418169 0.575560i
\(869\) −4.08332 8.67750i −0.138517 0.294364i
\(870\) 0 0
\(871\) 6.72596 3.69763i 0.227900 0.125289i
\(872\) −4.41974 + 0.843110i −0.149671 + 0.0285513i
\(873\) 24.1665 + 94.1223i 0.817912 + 3.18556i
\(874\) 26.8728 0.908985
\(875\) 0 0
\(876\) −86.7637 −2.93147
\(877\) −6.26965 24.4187i −0.211711 0.824561i −0.982313 0.187244i \(-0.940044\pi\)
0.770602 0.637316i \(-0.219956\pi\)
\(878\) 33.5127 6.39289i 1.13100 0.215750i
\(879\) −32.2330 + 17.7202i −1.08719 + 0.597689i
\(880\) 0 0
\(881\) −7.48675 15.9102i −0.252235 0.536027i 0.738105 0.674686i \(-0.235721\pi\)
−0.990340 + 0.138659i \(0.955721\pi\)
\(882\) −74.7726 + 102.916i −2.51773 + 3.46535i
\(883\) 12.3227 + 13.1224i 0.414693 + 0.441603i 0.902071 0.431588i \(-0.142047\pi\)
−0.487378 + 0.873191i \(0.662047\pi\)
\(884\) −7.58938 + 3.00485i −0.255258 + 0.101064i
\(885\) 0 0
\(886\) −13.7948 + 3.54190i −0.463444 + 0.118992i
\(887\) −0.0957476 + 0.0792093i −0.00321489 + 0.00265959i −0.639030 0.769182i \(-0.720664\pi\)
0.635815 + 0.771841i \(0.280664\pi\)
\(888\) 36.8148 + 92.9837i 1.23542 + 3.12033i
\(889\) −6.10620 2.41762i −0.204795 0.0810842i
\(890\) 0 0
\(891\) 17.3831 27.3914i 0.582356 0.917646i
\(892\) 9.45182 17.1928i 0.316470 0.575657i
\(893\) 2.77026 + 3.81294i 0.0927032 + 0.127595i
\(894\) −9.39804 + 49.2662i −0.314317 + 1.64771i
\(895\) 0 0
\(896\) 5.87928 12.4941i 0.196413 0.417399i
\(897\) 3.05024 + 5.54837i 0.101845 + 0.185255i
\(898\) 2.04457 + 0.128633i 0.0682281 + 0.00429255i
\(899\) 10.4499 + 7.59229i 0.348523 + 0.253217i
\(900\) 0 0
\(901\) −8.66742 + 6.29725i −0.288754 + 0.209792i
\(902\) 24.8250 15.7544i 0.826583 0.524565i
\(903\) 0.931017 7.36976i 0.0309823 0.245250i
\(904\) 35.1204 + 4.43673i 1.16809 + 0.147564i
\(905\) 0 0
\(906\) 79.0544 + 43.4605i 2.62641 + 1.44388i
\(907\) 1.40695 + 0.457146i 0.0467170 + 0.0151793i 0.332282 0.943180i \(-0.392181\pi\)
−0.285565 + 0.958359i \(0.592181\pi\)
\(908\) −27.5435 + 12.9610i −0.914063 + 0.430125i
\(909\) −79.2768 20.3548i −2.62945 0.675127i
\(910\) 0 0
\(911\) 34.6996 41.9446i 1.14965 1.38969i 0.241834 0.970318i \(-0.422251\pi\)
0.907815 0.419370i \(-0.137749\pi\)
\(912\) 46.1073 + 29.2606i 1.52676 + 0.968914i
\(913\) −0.198023 + 0.0124585i −0.00655360 + 0.000412318i
\(914\) −11.3007 17.8071i −0.373794 0.589006i
\(915\) 0 0
\(916\) −4.01737 63.8542i −0.132738 2.10980i
\(917\) 7.43207 + 1.41774i 0.245428 + 0.0468180i
\(918\) −136.259 + 44.2731i −4.49721 + 1.46123i
\(919\) −8.82636 + 8.28850i −0.291155 + 0.273412i −0.816335 0.577578i \(-0.803998\pi\)
0.525181 + 0.850991i \(0.323998\pi\)
\(920\) 0 0
\(921\) −5.69323 29.8450i −0.187598 0.983425i
\(922\) 59.5247 63.3873i 1.96034 2.08755i
\(923\) 1.08524 2.74100i 0.0357211 0.0902212i
\(924\) 3.51471 + 10.8172i 0.115625 + 0.355858i
\(925\) 0 0
\(926\) 5.08016 15.6351i 0.166944 0.513802i
\(927\) 104.694 + 86.6102i 3.43859 + 2.84465i
\(928\) −3.56081 1.67559i −0.116889 0.0550039i
\(929\) −15.2833 14.3520i −0.501430 0.470874i 0.392071 0.919935i \(-0.371759\pi\)
−0.893501 + 0.449061i \(0.851759\pi\)
\(930\) 0 0
\(931\) −20.2154 + 2.55380i −0.662534 + 0.0836975i
\(932\) 66.2960i 2.17160i
\(933\) 11.1533 + 88.2873i 0.365142 + 2.89040i
\(934\) 23.3683 + 28.2474i 0.764633 + 0.924283i
\(935\) 0 0
\(936\) −1.54367 + 24.5360i −0.0504565 + 0.801983i
\(937\) 5.07137 19.7517i 0.165674 0.645259i −0.830434 0.557117i \(-0.811907\pi\)
0.996108 0.0881413i \(-0.0280927\pi\)
\(938\) −6.63627 + 25.8465i −0.216682 + 0.843920i
\(939\) 5.47194 86.9741i 0.178570 2.83829i
\(940\) 0 0
\(941\) −20.3352 24.5810i −0.662908 0.801318i 0.326698 0.945129i \(-0.394064\pi\)
−0.989605 + 0.143811i \(0.954064\pi\)
\(942\) 15.4420 + 122.236i 0.503126 + 3.98265i
\(943\) 38.5065i 1.25394i
\(944\) −18.2273 + 2.30264i −0.593247 + 0.0749445i
\(945\) 0 0
\(946\) 5.34435 + 5.01868i 0.173760 + 0.163171i
\(947\) −45.4700 21.3965i −1.47758 0.695294i −0.492964 0.870050i \(-0.664087\pi\)
−0.984612 + 0.174755i \(0.944087\pi\)
\(948\) 98.8789 + 81.7998i 3.21144 + 2.65673i
\(949\) 1.08818 3.34908i 0.0353239 0.108716i
\(950\) 0 0
\(951\) 12.9558 + 39.8738i 0.420120 + 1.29300i
\(952\) 5.45544 13.7789i 0.176812 0.446576i
\(953\) −14.3314 + 15.2613i −0.464238 + 0.494363i −0.917901 0.396810i \(-0.870117\pi\)
0.453663 + 0.891174i \(0.350117\pi\)
\(954\) 11.5785 + 60.6965i 0.374867 + 1.96512i
\(955\) 0 0
\(956\) 24.2485 22.7708i 0.784252 0.736461i
\(957\) −6.66613 + 2.16596i −0.215486 + 0.0700155i
\(958\) −18.8753 3.60065i −0.609832 0.116332i
\(959\) −0.0891704 1.41732i −0.00287946 0.0457678i
\(960\) 0 0
\(961\) 5.00849 + 7.89212i 0.161564 + 0.254584i
\(962\) −7.75731 + 0.488049i −0.250106 + 0.0157353i
\(963\) −95.5202 60.6190i −3.07810 1.95342i
\(964\) 32.7109 39.5407i 1.05355 1.27352i
\(965\) 0 0
\(966\) −21.3213 5.47438i −0.686002 0.176135i
\(967\) −4.10340 + 1.93091i −0.131956 + 0.0620940i −0.490624 0.871371i \(-0.663231\pi\)
0.358668 + 0.933465i \(0.383231\pi\)
\(968\) 51.3008 + 16.6686i 1.64887 + 0.535750i
\(969\) −32.1311 17.6642i −1.03220 0.567457i
\(970\) 0 0
\(971\) −15.5189 1.96050i −0.498026 0.0629153i −0.127692 0.991814i \(-0.540757\pi\)
−0.370334 + 0.928899i \(0.620757\pi\)
\(972\) −28.1887 + 223.136i −0.904152 + 7.15710i
\(973\) −6.00210 + 3.80905i −0.192418 + 0.122112i
\(974\) −55.9639 + 40.6601i −1.79320 + 1.30284i
\(975\) 0 0
\(976\) −31.1884 22.6597i −0.998317 0.725320i
\(977\) 9.15641 + 0.576072i 0.292940 + 0.0184302i 0.208580 0.978005i \(-0.433116\pi\)
0.0843591 + 0.996435i \(0.473116\pi\)
\(978\) 31.2206 + 56.7901i 0.998325 + 1.81595i
\(979\) 0.985063 2.09337i 0.0314828 0.0669043i
\(980\) 0 0
\(981\) 1.24353 6.51881i 0.0397028 0.208130i
\(982\) 25.0468 + 34.4740i 0.799276 + 1.10011i
\(983\) 19.5778 35.6119i 0.624435 1.13584i −0.355149 0.934810i \(-0.615570\pi\)
0.979584 0.201034i \(-0.0644302\pi\)
\(984\) −110.087 + 173.470i −3.50946 + 5.53002i
\(985\) 0 0
\(986\) 16.2605 + 6.43800i 0.517841 + 0.205028i
\(987\) −1.42122 3.58959i −0.0452379 0.114258i
\(988\) −5.81029 + 4.80669i −0.184850 + 0.152921i
\(989\) −9.29991 + 2.38781i −0.295720 + 0.0759280i
\(990\) 0 0
\(991\) −33.4956 + 13.2619i −1.06402 + 0.421277i −0.833918 0.551888i \(-0.813907\pi\)
−0.230106 + 0.973165i \(0.573907\pi\)
\(992\) −8.41484 8.96089i −0.267171 0.284509i
\(993\) 20.6893 28.4763i 0.656554 0.903669i
\(994\) 4.36398 + 9.27393i 0.138417 + 0.294151i
\(995\) 0 0
\(996\) 2.32661 1.27907i 0.0737216 0.0405288i
\(997\) 7.53095 1.43661i 0.238508 0.0454977i −0.0667415 0.997770i \(-0.521260\pi\)
0.305249 + 0.952273i \(0.401260\pi\)
\(998\) 4.63509 + 18.0525i 0.146721 + 0.571441i
\(999\) −92.3177 −2.92080
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 625.2.h.b.274.21 440
5.2 odd 4 125.2.g.a.21.2 yes 220
5.3 odd 4 625.2.g.a.351.10 220
5.4 even 2 inner 625.2.h.b.274.2 440
125.6 even 25 inner 625.2.h.b.349.2 440
125.33 odd 100 625.2.g.a.276.10 220
125.92 odd 100 125.2.g.a.6.2 220
125.119 even 50 inner 625.2.h.b.349.21 440
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
125.2.g.a.6.2 220 125.92 odd 100
125.2.g.a.21.2 yes 220 5.2 odd 4
625.2.g.a.276.10 220 125.33 odd 100
625.2.g.a.351.10 220 5.3 odd 4
625.2.h.b.274.2 440 5.4 even 2 inner
625.2.h.b.274.21 440 1.1 even 1 trivial
625.2.h.b.349.2 440 125.6 even 25 inner
625.2.h.b.349.21 440 125.119 even 50 inner