Properties

Label 825.2.bx.f.124.3
Level $825$
Weight $2$
Character 825.124
Analytic conductor $6.588$
Analytic rank $0$
Dimension $16$
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] = [825,2,Mod(49,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), 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: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 124.3
Root \(0.701538 - 0.227943i\) of defining polynomial
Character \(\chi\) \(=\) 825.124
Dual form 825.2.bx.f.499.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.154211 + 0.212253i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.596764 - 1.83665i) q^{4} +(0.212253 + 0.154211i) q^{6} +(-3.03722 - 0.986854i) q^{7} +(0.980901 - 0.318714i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.154211 + 0.212253i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.596764 - 1.83665i) q^{4} +(0.212253 + 0.154211i) q^{6} +(-3.03722 - 0.986854i) q^{7} +(0.980901 - 0.318714i) q^{8} +(0.809017 - 0.587785i) q^{9} +(3.27115 - 0.547326i) q^{11} -1.93117i q^{12} +(-0.658088 - 0.905781i) q^{13} +(-0.258911 - 0.796845i) q^{14} +(-2.90578 - 2.11117i) q^{16} +(-0.0518582 + 0.0713767i) q^{17} +(0.249519 + 0.0810736i) q^{18} +(0.0212704 + 0.0654637i) q^{19} -3.19353 q^{21} +(0.620620 + 0.609909i) q^{22} -6.65450i q^{23} +(0.834404 - 0.606230i) q^{24} +(0.0907705 - 0.279363i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-3.62501 + 4.98940i) q^{28} +(-1.15444 + 3.55299i) q^{29} +(7.75430 - 5.63383i) q^{31} -3.00509i q^{32} +(2.94192 - 1.53138i) q^{33} -0.0231471 q^{34} +(-0.596764 - 1.83665i) q^{36} +(-7.92250 - 2.57418i) q^{37} +(-0.0106148 + 0.0146100i) q^{38} +(-0.905781 - 0.658088i) q^{39} +(-3.60489 - 11.0947i) q^{41} +(-0.492478 - 0.677837i) q^{42} +11.8217i q^{43} +(0.946857 - 6.33458i) q^{44} +(1.41244 - 1.02620i) q^{46} +(-0.863579 + 0.280594i) q^{47} +(-3.41595 - 1.10991i) q^{48} +(2.58773 + 1.88010i) q^{49} +(-0.0272635 + 0.0839083i) q^{51} +(-2.05632 + 0.668140i) q^{52} +(0.512771 + 0.705768i) q^{53} +0.262360 q^{54} -3.29374 q^{56} +(0.0404588 + 0.0556868i) q^{57} +(-0.932160 + 0.302877i) q^{58} +(-0.567369 + 1.74618i) q^{59} +(8.13881 + 5.91319i) q^{61} +(2.39160 + 0.777078i) q^{62} +(-3.03722 + 0.986854i) q^{63} +(-5.17372 + 3.75893i) q^{64} +(0.778717 + 0.388276i) q^{66} +9.53916i q^{67} +(0.100147 + 0.137840i) q^{68} +(-2.05635 - 6.32881i) q^{69} +(3.77370 + 2.74175i) q^{71} +(0.606230 - 0.834404i) q^{72} +(6.80989 + 2.21267i) q^{73} +(-0.675360 - 2.07854i) q^{74} +0.132927 q^{76} +(-10.4754 - 1.56580i) q^{77} -0.293740i q^{78} +(0.640209 - 0.465139i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.79898 - 2.47608i) q^{82} +(-0.145318 + 0.200012i) q^{83} +(-1.90578 + 5.86539i) q^{84} +(-2.50920 + 1.82304i) q^{86} +3.73583i q^{87} +(3.03423 - 1.57943i) q^{88} +14.5788 q^{89} +(1.10489 + 3.40050i) q^{91} +(-12.2220 - 3.97116i) q^{92} +(5.63383 - 7.75430i) q^{93} +(-0.192730 - 0.140027i) q^{94} +(-0.928623 - 2.85801i) q^{96} +(2.40521 + 3.31048i) q^{97} +0.839188i q^{98} +(2.32471 - 2.36553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9} + 6 q^{11} + 8 q^{14} - 24 q^{16} - 4 q^{19} - 24 q^{21} - 8 q^{24} + 4 q^{26} - 20 q^{29} + 38 q^{31} + 12 q^{34} + 4 q^{36} + 8 q^{39} - 18 q^{41} - 34 q^{44} - 44 q^{46} - 2 q^{49} + 20 q^{51} + 12 q^{54} - 32 q^{56} - 26 q^{59} + 26 q^{61} - 78 q^{64} - 22 q^{66} - 18 q^{69} - 22 q^{71} + 86 q^{74} - 76 q^{76} + 44 q^{79} - 4 q^{81} - 8 q^{84} + 40 q^{86} + 40 q^{89} - 22 q^{91} + 70 q^{94} - 16 q^{96} + 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.154211 + 0.212253i 0.109044 + 0.150086i 0.860051 0.510208i \(-0.170432\pi\)
−0.751007 + 0.660294i \(0.770432\pi\)
\(3\) 0.951057 0.309017i 0.549093 0.178411i
\(4\) 0.596764 1.83665i 0.298382 0.918325i
\(5\) 0 0
\(6\) 0.212253 + 0.154211i 0.0866521 + 0.0629564i
\(7\) −3.03722 0.986854i −1.14796 0.372996i −0.327587 0.944821i \(-0.606236\pi\)
−0.820376 + 0.571825i \(0.806236\pi\)
\(8\) 0.980901 0.318714i 0.346801 0.112682i
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 0 0
\(11\) 3.27115 0.547326i 0.986289 0.165025i
\(12\) 1.93117i 0.557480i
\(13\) −0.658088 0.905781i −0.182521 0.251218i 0.707946 0.706267i \(-0.249622\pi\)
−0.890467 + 0.455048i \(0.849622\pi\)
\(14\) −0.258911 0.796845i −0.0691968 0.212966i
\(15\) 0 0
\(16\) −2.90578 2.11117i −0.726445 0.527793i
\(17\) −0.0518582 + 0.0713767i −0.0125775 + 0.0173114i −0.815259 0.579096i \(-0.803406\pi\)
0.802682 + 0.596407i \(0.203406\pi\)
\(18\) 0.249519 + 0.0810736i 0.0588122 + 0.0191092i
\(19\) 0.0212704 + 0.0654637i 0.00487977 + 0.0150184i 0.953467 0.301498i \(-0.0974867\pi\)
−0.948587 + 0.316517i \(0.897487\pi\)
\(20\) 0 0
\(21\) −3.19353 −0.696885
\(22\) 0.620620 + 0.609909i 0.132317 + 0.130033i
\(23\) 6.65450i 1.38756i −0.720187 0.693780i \(-0.755944\pi\)
0.720187 0.693780i \(-0.244056\pi\)
\(24\) 0.834404 0.606230i 0.170322 0.123746i
\(25\) 0 0
\(26\) 0.0907705 0.279363i 0.0178016 0.0547876i
\(27\) 0.587785 0.809017i 0.113119 0.155695i
\(28\) −3.62501 + 4.98940i −0.685062 + 0.942908i
\(29\) −1.15444 + 3.55299i −0.214373 + 0.659773i 0.784824 + 0.619718i \(0.212753\pi\)
−0.999197 + 0.0400546i \(0.987247\pi\)
\(30\) 0 0
\(31\) 7.75430 5.63383i 1.39271 1.01187i 0.397152 0.917753i \(-0.369998\pi\)
0.995562 0.0941130i \(-0.0300015\pi\)
\(32\) 3.00509i 0.531230i
\(33\) 2.94192 1.53138i 0.512122 0.266579i
\(34\) −0.0231471 −0.00396969
\(35\) 0 0
\(36\) −0.596764 1.83665i −0.0994606 0.306108i
\(37\) −7.92250 2.57418i −1.30245 0.423192i −0.426017 0.904715i \(-0.640084\pi\)
−0.876433 + 0.481523i \(0.840084\pi\)
\(38\) −0.0106148 + 0.0146100i −0.00172194 + 0.00237005i
\(39\) −0.905781 0.658088i −0.145041 0.105378i
\(40\) 0 0
\(41\) −3.60489 11.0947i −0.562989 1.73270i −0.673852 0.738866i \(-0.735362\pi\)
0.110863 0.993836i \(-0.464638\pi\)
\(42\) −0.492478 0.677837i −0.0759909 0.104593i
\(43\) 11.8217i 1.80280i 0.432989 + 0.901399i \(0.357459\pi\)
−0.432989 + 0.901399i \(0.642541\pi\)
\(44\) 0.946857 6.33458i 0.142744 0.954974i
\(45\) 0 0
\(46\) 1.41244 1.02620i 0.208253 0.151305i
\(47\) −0.863579 + 0.280594i −0.125966 + 0.0409288i −0.371322 0.928504i \(-0.621095\pi\)
0.245356 + 0.969433i \(0.421095\pi\)
\(48\) −3.41595 1.10991i −0.493050 0.160202i
\(49\) 2.58773 + 1.88010i 0.369676 + 0.268586i
\(50\) 0 0
\(51\) −0.0272635 + 0.0839083i −0.00381765 + 0.0117495i
\(52\) −2.05632 + 0.668140i −0.285161 + 0.0926544i
\(53\) 0.512771 + 0.705768i 0.0704344 + 0.0969447i 0.842781 0.538257i \(-0.180917\pi\)
−0.772346 + 0.635202i \(0.780917\pi\)
\(54\) 0.262360 0.0357026
\(55\) 0 0
\(56\) −3.29374 −0.440144
\(57\) 0.0404588 + 0.0556868i 0.00535890 + 0.00737589i
\(58\) −0.932160 + 0.302877i −0.122399 + 0.0397697i
\(59\) −0.567369 + 1.74618i −0.0738651 + 0.227333i −0.981172 0.193135i \(-0.938134\pi\)
0.907307 + 0.420469i \(0.138134\pi\)
\(60\) 0 0
\(61\) 8.13881 + 5.91319i 1.04207 + 0.757107i 0.970688 0.240342i \(-0.0772597\pi\)
0.0713799 + 0.997449i \(0.477260\pi\)
\(62\) 2.39160 + 0.777078i 0.303733 + 0.0986890i
\(63\) −3.03722 + 0.986854i −0.382654 + 0.124332i
\(64\) −5.17372 + 3.75893i −0.646715 + 0.469866i
\(65\) 0 0
\(66\) 0.778717 + 0.388276i 0.0958534 + 0.0477935i
\(67\) 9.53916i 1.16539i 0.812690 + 0.582697i \(0.198003\pi\)
−0.812690 + 0.582697i \(0.801997\pi\)
\(68\) 0.100147 + 0.137840i 0.0121446 + 0.0167156i
\(69\) −2.05635 6.32881i −0.247556 0.761899i
\(70\) 0 0
\(71\) 3.77370 + 2.74175i 0.447855 + 0.325386i 0.788748 0.614716i \(-0.210729\pi\)
−0.340893 + 0.940102i \(0.610729\pi\)
\(72\) 0.606230 0.834404i 0.0714449 0.0983354i
\(73\) 6.80989 + 2.21267i 0.797037 + 0.258973i 0.679098 0.734048i \(-0.262371\pi\)
0.117939 + 0.993021i \(0.462371\pi\)
\(74\) −0.675360 2.07854i −0.0785090 0.241626i
\(75\) 0 0
\(76\) 0.132927 0.0152478
\(77\) −10.4754 1.56580i −1.19378 0.178439i
\(78\) 0.293740i 0.0332595i
\(79\) 0.640209 0.465139i 0.0720292 0.0523323i −0.551188 0.834381i \(-0.685825\pi\)
0.623217 + 0.782049i \(0.285825\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 1.79898 2.47608i 0.198664 0.273437i
\(83\) −0.145318 + 0.200012i −0.0159507 + 0.0219542i −0.816918 0.576754i \(-0.804319\pi\)
0.800967 + 0.598708i \(0.204319\pi\)
\(84\) −1.90578 + 5.86539i −0.207938 + 0.639966i
\(85\) 0 0
\(86\) −2.50920 + 1.82304i −0.270574 + 0.196584i
\(87\) 3.73583i 0.400523i
\(88\) 3.03423 1.57943i 0.323450 0.168368i
\(89\) 14.5788 1.54535 0.772673 0.634804i \(-0.218919\pi\)
0.772673 + 0.634804i \(0.218919\pi\)
\(90\) 0 0
\(91\) 1.10489 + 3.40050i 0.115824 + 0.356469i
\(92\) −12.2220 3.97116i −1.27423 0.414022i
\(93\) 5.63383 7.75430i 0.584201 0.804084i
\(94\) −0.192730 0.140027i −0.0198786 0.0144427i
\(95\) 0 0
\(96\) −0.928623 2.85801i −0.0947772 0.291694i
\(97\) 2.40521 + 3.31048i 0.244212 + 0.336128i 0.913474 0.406898i \(-0.133390\pi\)
−0.669262 + 0.743027i \(0.733390\pi\)
\(98\) 0.839188i 0.0847708i
\(99\) 2.32471 2.36553i 0.233642 0.237745i
\(100\) 0 0
\(101\) −3.47207 + 2.52261i −0.345484 + 0.251009i −0.746972 0.664856i \(-0.768493\pi\)
0.401488 + 0.915864i \(0.368493\pi\)
\(102\) −0.0220142 + 0.00715284i −0.00217973 + 0.000708236i
\(103\) −1.99038 0.646712i −0.196118 0.0637224i 0.209311 0.977849i \(-0.432878\pi\)
−0.405429 + 0.914127i \(0.632878\pi\)
\(104\) −0.934204 0.678739i −0.0916062 0.0665558i
\(105\) 0 0
\(106\) −0.0707268 + 0.217675i −0.00686959 + 0.0211424i
\(107\) 14.9705 4.86421i 1.44725 0.470241i 0.523103 0.852270i \(-0.324774\pi\)
0.924151 + 0.382029i \(0.124774\pi\)
\(108\) −1.13511 1.56235i −0.109226 0.150337i
\(109\) 4.13271 0.395842 0.197921 0.980218i \(-0.436581\pi\)
0.197921 + 0.980218i \(0.436581\pi\)
\(110\) 0 0
\(111\) −8.33021 −0.790668
\(112\) 6.74209 + 9.27969i 0.637067 + 0.876848i
\(113\) 13.0818 4.25053i 1.23063 0.399856i 0.379688 0.925114i \(-0.376031\pi\)
0.850943 + 0.525258i \(0.176031\pi\)
\(114\) −0.00558051 + 0.0171750i −0.000522662 + 0.00160859i
\(115\) 0 0
\(116\) 5.83666 + 4.24059i 0.541921 + 0.393728i
\(117\) −1.06481 0.345977i −0.0984416 0.0319856i
\(118\) −0.458127 + 0.148855i −0.0421740 + 0.0137032i
\(119\) 0.227943 0.165611i 0.0208955 0.0151815i
\(120\) 0 0
\(121\) 10.4009 3.58078i 0.945533 0.325525i
\(122\) 2.63937i 0.238957i
\(123\) −6.85690 9.43772i −0.618266 0.850971i
\(124\) −5.71989 17.6040i −0.513661 1.58089i
\(125\) 0 0
\(126\) −0.677837 0.492478i −0.0603865 0.0438734i
\(127\) 4.64338 6.39106i 0.412033 0.567115i −0.551680 0.834056i \(-0.686013\pi\)
0.963713 + 0.266941i \(0.0860129\pi\)
\(128\) −7.31171 2.37572i −0.646270 0.209986i
\(129\) 3.65312 + 11.2431i 0.321639 + 0.989903i
\(130\) 0 0
\(131\) −16.3539 −1.42884 −0.714422 0.699715i \(-0.753310\pi\)
−0.714422 + 0.699715i \(0.753310\pi\)
\(132\) −1.05698 6.31714i −0.0919982 0.549837i
\(133\) 0.219819i 0.0190607i
\(134\) −2.02472 + 1.47104i −0.174909 + 0.127079i
\(135\) 0 0
\(136\) −0.0281190 + 0.0865414i −0.00241118 + 0.00742086i
\(137\) 4.54480 6.25538i 0.388289 0.534433i −0.569468 0.822013i \(-0.692851\pi\)
0.957757 + 0.287580i \(0.0928508\pi\)
\(138\) 1.02620 1.41244i 0.0873558 0.120235i
\(139\) −6.23796 + 19.1985i −0.529097 + 1.62839i 0.226972 + 0.973901i \(0.427117\pi\)
−0.756069 + 0.654492i \(0.772883\pi\)
\(140\) 0 0
\(141\) −0.734604 + 0.533721i −0.0618648 + 0.0449474i
\(142\) 1.22379i 0.102698i
\(143\) −2.64846 2.60276i −0.221476 0.217653i
\(144\) −3.59174 −0.299312
\(145\) 0 0
\(146\) 0.580514 + 1.78664i 0.0480437 + 0.147863i
\(147\) 3.04206 + 0.988426i 0.250905 + 0.0815240i
\(148\) −9.45572 + 13.0147i −0.777255 + 1.06980i
\(149\) 7.84361 + 5.69872i 0.642573 + 0.466857i 0.860733 0.509056i \(-0.170005\pi\)
−0.218160 + 0.975913i \(0.570005\pi\)
\(150\) 0 0
\(151\) 4.68515 + 14.4194i 0.381272 + 1.17343i 0.939149 + 0.343511i \(0.111616\pi\)
−0.557877 + 0.829924i \(0.688384\pi\)
\(152\) 0.0417284 + 0.0574342i 0.00338462 + 0.00465853i
\(153\) 0.0882264i 0.00713268i
\(154\) −1.28307 2.46489i −0.103393 0.198627i
\(155\) 0 0
\(156\) −1.74921 + 1.27088i −0.140049 + 0.101752i
\(157\) 14.1522 4.59834i 1.12947 0.366987i 0.316096 0.948727i \(-0.397628\pi\)
0.813375 + 0.581740i \(0.197628\pi\)
\(158\) 0.197455 + 0.0641570i 0.0157087 + 0.00510405i
\(159\) 0.705768 + 0.512771i 0.0559710 + 0.0406653i
\(160\) 0 0
\(161\) −6.56702 + 20.2112i −0.517554 + 1.59287i
\(162\) 0.249519 0.0810736i 0.0196041 0.00636974i
\(163\) 1.99914 + 2.75158i 0.156585 + 0.215521i 0.880101 0.474787i \(-0.157475\pi\)
−0.723516 + 0.690308i \(0.757475\pi\)
\(164\) −22.5283 −1.75917
\(165\) 0 0
\(166\) −0.0648629 −0.00503434
\(167\) 13.2936 + 18.2970i 1.02869 + 1.41587i 0.905929 + 0.423429i \(0.139174\pi\)
0.122757 + 0.992437i \(0.460826\pi\)
\(168\) −3.13253 + 1.01782i −0.241680 + 0.0785266i
\(169\) 3.62986 11.1716i 0.279220 0.859351i
\(170\) 0 0
\(171\) 0.0556868 + 0.0404588i 0.00425847 + 0.00309396i
\(172\) 21.7124 + 7.05478i 1.65555 + 0.537922i
\(173\) −12.4506 + 4.04543i −0.946598 + 0.307568i −0.741333 0.671138i \(-0.765806\pi\)
−0.205266 + 0.978706i \(0.565806\pi\)
\(174\) −0.792943 + 0.576107i −0.0601128 + 0.0436745i
\(175\) 0 0
\(176\) −10.6607 5.31556i −0.803584 0.400675i
\(177\) 1.83604i 0.138005i
\(178\) 2.24821 + 3.09439i 0.168510 + 0.231935i
\(179\) 4.69008 + 14.4346i 0.350553 + 1.07889i 0.958543 + 0.284947i \(0.0919759\pi\)
−0.607990 + 0.793944i \(0.708024\pi\)
\(180\) 0 0
\(181\) −1.14353 0.830823i −0.0849978 0.0617546i 0.544475 0.838777i \(-0.316729\pi\)
−0.629473 + 0.777023i \(0.716729\pi\)
\(182\) −0.551381 + 0.758911i −0.0408711 + 0.0562542i
\(183\) 9.56775 + 3.10875i 0.707268 + 0.229805i
\(184\) −2.12088 6.52740i −0.156354 0.481207i
\(185\) 0 0
\(186\) 2.51468 0.184385
\(187\) −0.130570 + 0.261867i −0.00954820 + 0.0191496i
\(188\) 1.75354i 0.127890i
\(189\) −2.58362 + 1.87711i −0.187931 + 0.136540i
\(190\) 0 0
\(191\) 1.51701 4.66887i 0.109767 0.337827i −0.881053 0.473018i \(-0.843165\pi\)
0.990820 + 0.135190i \(0.0431646\pi\)
\(192\) −3.75893 + 5.17372i −0.271277 + 0.373381i
\(193\) −5.71320 + 7.86354i −0.411245 + 0.566030i −0.963522 0.267631i \(-0.913759\pi\)
0.552276 + 0.833661i \(0.313759\pi\)
\(194\) −0.331752 + 1.02103i −0.0238184 + 0.0733054i
\(195\) 0 0
\(196\) 4.99735 3.63079i 0.356953 0.259342i
\(197\) 8.88764i 0.633218i −0.948556 0.316609i \(-0.897456\pi\)
0.948556 0.316609i \(-0.102544\pi\)
\(198\) 0.860588 + 0.128636i 0.0611593 + 0.00914175i
\(199\) −18.0381 −1.27869 −0.639343 0.768921i \(-0.720794\pi\)
−0.639343 + 0.768921i \(0.720794\pi\)
\(200\) 0 0
\(201\) 2.94776 + 9.07228i 0.207919 + 0.639909i
\(202\) −1.07086 0.347945i −0.0753457 0.0244813i
\(203\) 7.01256 9.65196i 0.492185 0.677435i
\(204\) 0.137840 + 0.100147i 0.00965075 + 0.00701168i
\(205\) 0 0
\(206\) −0.169671 0.522194i −0.0118216 0.0363830i
\(207\) −3.91142 5.38361i −0.271862 0.374186i
\(208\) 4.02134i 0.278830i
\(209\) 0.105409 + 0.202500i 0.00729128 + 0.0140072i
\(210\) 0 0
\(211\) −14.5444 + 10.5671i −1.00127 + 0.727469i −0.962361 0.271774i \(-0.912390\pi\)
−0.0389136 + 0.999243i \(0.512390\pi\)
\(212\) 1.60225 0.520603i 0.110043 0.0357552i
\(213\) 4.43625 + 1.44142i 0.303967 + 0.0987647i
\(214\) 3.34106 + 2.42743i 0.228390 + 0.165935i
\(215\) 0 0
\(216\) 0.318714 0.980901i 0.0216857 0.0667418i
\(217\) −29.1113 + 9.45884i −1.97621 + 0.642108i
\(218\) 0.637310 + 0.877182i 0.0431641 + 0.0594103i
\(219\) 7.16034 0.483851
\(220\) 0 0
\(221\) 0.0987789 0.00664459
\(222\) −1.28461 1.76812i −0.0862174 0.118668i
\(223\) −13.0760 + 4.24865i −0.875635 + 0.284511i −0.712144 0.702034i \(-0.752276\pi\)
−0.163491 + 0.986545i \(0.552276\pi\)
\(224\) −2.96558 + 9.12713i −0.198146 + 0.609832i
\(225\) 0 0
\(226\) 2.91955 + 2.12118i 0.194205 + 0.141099i
\(227\) 0.630298 + 0.204796i 0.0418344 + 0.0135928i 0.329859 0.944030i \(-0.392999\pi\)
−0.288025 + 0.957623i \(0.592999\pi\)
\(228\) 0.126421 0.0410768i 0.00837246 0.00272038i
\(229\) −6.05987 + 4.40275i −0.400447 + 0.290942i −0.769723 0.638378i \(-0.779606\pi\)
0.369276 + 0.929320i \(0.379606\pi\)
\(230\) 0 0
\(231\) −10.4465 + 1.74790i −0.687330 + 0.115004i
\(232\) 3.85306i 0.252966i
\(233\) 6.18665 + 8.51520i 0.405301 + 0.557849i 0.962065 0.272822i \(-0.0879570\pi\)
−0.556763 + 0.830671i \(0.687957\pi\)
\(234\) −0.0907705 0.279363i −0.00593385 0.0182625i
\(235\) 0 0
\(236\) 2.86854 + 2.08411i 0.186726 + 0.135664i
\(237\) 0.465139 0.640209i 0.0302140 0.0415861i
\(238\) 0.0703028 + 0.0228428i 0.00455706 + 0.00148068i
\(239\) −5.27684 16.2404i −0.341330 1.05051i −0.963519 0.267640i \(-0.913756\pi\)
0.622189 0.782867i \(-0.286244\pi\)
\(240\) 0 0
\(241\) −16.7082 −1.07627 −0.538135 0.842859i \(-0.680871\pi\)
−0.538135 + 0.842859i \(0.680871\pi\)
\(242\) 2.36396 + 1.65542i 0.151961 + 0.106415i
\(243\) 1.00000i 0.0641500i
\(244\) 15.7174 11.4194i 1.00620 0.731050i
\(245\) 0 0
\(246\) 0.945777 2.91080i 0.0603006 0.185586i
\(247\) 0.0452979 0.0623472i 0.00288224 0.00396706i
\(248\) 5.81062 7.99763i 0.368975 0.507850i
\(249\) −0.0763980 + 0.235129i −0.00484152 + 0.0149007i
\(250\) 0 0
\(251\) 4.15646 3.01984i 0.262353 0.190611i −0.448831 0.893617i \(-0.648159\pi\)
0.711184 + 0.703006i \(0.248159\pi\)
\(252\) 6.16724i 0.388499i
\(253\) −3.64219 21.7679i −0.228982 1.36854i
\(254\) 2.07259 0.130046
\(255\) 0 0
\(256\) 3.32908 + 10.2458i 0.208067 + 0.640366i
\(257\) −3.51724 1.14282i −0.219399 0.0712872i 0.197255 0.980352i \(-0.436797\pi\)
−0.416654 + 0.909065i \(0.636797\pi\)
\(258\) −1.82304 + 2.50920i −0.113498 + 0.156216i
\(259\) 21.5221 + 15.6367i 1.33732 + 0.971617i
\(260\) 0 0
\(261\) 1.15444 + 3.55299i 0.0714577 + 0.219924i
\(262\) −2.52195 3.47116i −0.155806 0.214449i
\(263\) 31.6315i 1.95048i −0.221147 0.975241i \(-0.570980\pi\)
0.221147 0.975241i \(-0.429020\pi\)
\(264\) 2.39766 2.43976i 0.147566 0.150157i
\(265\) 0 0
\(266\) 0.0466573 0.0338985i 0.00286074 0.00207845i
\(267\) 13.8652 4.50509i 0.848539 0.275707i
\(268\) 17.5201 + 5.69262i 1.07021 + 0.347732i
\(269\) −11.9536 8.68479i −0.728823 0.529521i 0.160368 0.987057i \(-0.448732\pi\)
−0.889191 + 0.457536i \(0.848732\pi\)
\(270\) 0 0
\(271\) −6.05269 + 18.6283i −0.367675 + 1.13159i 0.580614 + 0.814179i \(0.302812\pi\)
−0.948289 + 0.317408i \(0.897188\pi\)
\(272\) 0.301377 0.0979234i 0.0182737 0.00593748i
\(273\) 2.10162 + 2.89263i 0.127196 + 0.175070i
\(274\) 2.02859 0.122551
\(275\) 0 0
\(276\) −12.8510 −0.773537
\(277\) −15.1122 20.8001i −0.908002 1.24976i −0.967844 0.251550i \(-0.919060\pi\)
0.0598418 0.998208i \(-0.480940\pi\)
\(278\) −5.03691 + 1.63659i −0.302094 + 0.0981561i
\(279\) 2.96188 9.11573i 0.177323 0.545744i
\(280\) 0 0
\(281\) 21.6096 + 15.7003i 1.28912 + 0.936599i 0.999787 0.0206304i \(-0.00656732\pi\)
0.289331 + 0.957229i \(0.406567\pi\)
\(282\) −0.226568 0.0736165i −0.0134919 0.00438380i
\(283\) 6.87970 2.23535i 0.408956 0.132878i −0.0973123 0.995254i \(-0.531025\pi\)
0.506268 + 0.862376i \(0.331025\pi\)
\(284\) 7.28764 5.29478i 0.432442 0.314187i
\(285\) 0 0
\(286\) 0.144021 0.963520i 0.00851616 0.0569741i
\(287\) 37.2546i 2.19907i
\(288\) −1.76635 2.43117i −0.104083 0.143258i
\(289\) 5.25088 + 16.1606i 0.308876 + 0.950621i
\(290\) 0 0
\(291\) 3.31048 + 2.40521i 0.194064 + 0.140996i
\(292\) 8.12778 11.1869i 0.475643 0.654666i
\(293\) −13.8804 4.51002i −0.810902 0.263478i −0.125922 0.992040i \(-0.540189\pi\)
−0.684980 + 0.728562i \(0.740189\pi\)
\(294\) 0.259323 + 0.798115i 0.0151240 + 0.0465470i
\(295\) 0 0
\(296\) −8.59161 −0.499377
\(297\) 1.47994 2.96813i 0.0858747 0.172228i
\(298\) 2.54364i 0.147349i
\(299\) −6.02752 + 4.37925i −0.348580 + 0.253258i
\(300\) 0 0
\(301\) 11.6663 35.9053i 0.672436 2.06955i
\(302\) −2.33807 + 3.21807i −0.134541 + 0.185179i
\(303\) −2.52261 + 3.47207i −0.144920 + 0.199465i
\(304\) 0.0763980 0.235129i 0.00438172 0.0134856i
\(305\) 0 0
\(306\) −0.0187264 + 0.0136055i −0.00107052 + 0.000777775i
\(307\) 28.5445i 1.62912i 0.580080 + 0.814559i \(0.303021\pi\)
−0.580080 + 0.814559i \(0.696979\pi\)
\(308\) −9.12713 + 18.3051i −0.520066 + 1.04303i
\(309\) −2.09280 −0.119055
\(310\) 0 0
\(311\) −3.07411 9.46113i −0.174317 0.536492i 0.825285 0.564717i \(-0.191015\pi\)
−0.999602 + 0.0282249i \(0.991015\pi\)
\(312\) −1.09822 0.356834i −0.0621746 0.0202018i
\(313\) 9.65786 13.2929i 0.545894 0.751359i −0.443554 0.896248i \(-0.646282\pi\)
0.989448 + 0.144889i \(0.0462824\pi\)
\(314\) 3.15844 + 2.29474i 0.178241 + 0.129500i
\(315\) 0 0
\(316\) −0.472244 1.45342i −0.0265658 0.0817612i
\(317\) −8.35278 11.4966i −0.469139 0.645714i 0.507234 0.861809i \(-0.330668\pi\)
−0.976373 + 0.216094i \(0.930668\pi\)
\(318\) 0.228877i 0.0128348i
\(319\) −1.83169 + 12.2542i −0.102555 + 0.686104i
\(320\) 0 0
\(321\) 12.7347 9.25228i 0.710780 0.516412i
\(322\) −5.30261 + 1.72292i −0.295503 + 0.0960147i
\(323\) −0.00577563 0.00187662i −0.000321365 0.000104418i
\(324\) −1.56235 1.13511i −0.0867971 0.0630618i
\(325\) 0 0
\(326\) −0.275743 + 0.848650i −0.0152720 + 0.0470024i
\(327\) 3.93044 1.27708i 0.217354 0.0706226i
\(328\) −7.07207 9.73387i −0.390490 0.537463i
\(329\) 2.89979 0.159870
\(330\) 0 0
\(331\) −10.9119 −0.599773 −0.299886 0.953975i \(-0.596949\pi\)
−0.299886 + 0.953975i \(0.596949\pi\)
\(332\) 0.280633 + 0.386258i 0.0154017 + 0.0211986i
\(333\) −7.92250 + 2.57418i −0.434150 + 0.141064i
\(334\) −1.83359 + 5.64321i −0.100330 + 0.308783i
\(335\) 0 0
\(336\) 9.27969 + 6.74209i 0.506249 + 0.367811i
\(337\) −5.59800 1.81890i −0.304943 0.0990819i 0.152549 0.988296i \(-0.451252\pi\)
−0.457491 + 0.889214i \(0.651252\pi\)
\(338\) 2.93097 0.952330i 0.159424 0.0517999i
\(339\) 11.1280 8.08499i 0.604392 0.439116i
\(340\) 0 0
\(341\) 22.2820 22.6732i 1.20664 1.22783i
\(342\) 0.0180589i 0.000976514i
\(343\) 7.13561 + 9.82132i 0.385287 + 0.530302i
\(344\) 3.76775 + 11.5959i 0.203144 + 0.625212i
\(345\) 0 0
\(346\) −2.77867 2.01882i −0.149382 0.108533i
\(347\) 20.2811 27.9145i 1.08875 1.49853i 0.239234 0.970962i \(-0.423104\pi\)
0.849512 0.527569i \(-0.176896\pi\)
\(348\) 6.86141 + 2.22941i 0.367810 + 0.119509i
\(349\) 1.70378 + 5.24371i 0.0912014 + 0.280689i 0.986245 0.165289i \(-0.0528558\pi\)
−0.895044 + 0.445978i \(0.852856\pi\)
\(350\) 0 0
\(351\) −1.11961 −0.0597602
\(352\) −1.64476 9.83010i −0.0876662 0.523946i
\(353\) 29.8740i 1.59003i 0.606589 + 0.795016i \(0.292537\pi\)
−0.606589 + 0.795016i \(0.707463\pi\)
\(354\) −0.389706 + 0.283138i −0.0207127 + 0.0150486i
\(355\) 0 0
\(356\) 8.70008 26.7761i 0.461103 1.41913i
\(357\) 0.165611 0.227943i 0.00876504 0.0120640i
\(358\) −2.34053 + 3.22146i −0.123701 + 0.170259i
\(359\) 11.0978 34.1554i 0.585717 1.80265i −0.0106548 0.999943i \(-0.503392\pi\)
0.596372 0.802708i \(-0.296608\pi\)
\(360\) 0 0
\(361\) 15.3675 11.1651i 0.808815 0.587639i
\(362\) 0.370840i 0.0194909i
\(363\) 8.78529 6.61956i 0.461108 0.347437i
\(364\) 6.90488 0.361914
\(365\) 0 0
\(366\) 0.815611 + 2.51019i 0.0426326 + 0.131210i
\(367\) −8.58887 2.79069i −0.448335 0.145673i 0.0761428 0.997097i \(-0.475740\pi\)
−0.524478 + 0.851424i \(0.675740\pi\)
\(368\) −14.0488 + 19.3365i −0.732345 + 1.00799i
\(369\) −9.43772 6.85690i −0.491308 0.356956i
\(370\) 0 0
\(371\) −0.860909 2.64961i −0.0446962 0.137561i
\(372\) −10.8799 14.9749i −0.564095 0.776410i
\(373\) 17.1994i 0.890553i −0.895393 0.445277i \(-0.853105\pi\)
0.895393 0.445277i \(-0.146895\pi\)
\(374\) −0.0757176 + 0.0126690i −0.00391526 + 0.000655098i
\(375\) 0 0
\(376\) −0.757656 + 0.550469i −0.0390731 + 0.0283883i
\(377\) 3.97795 1.29251i 0.204875 0.0665678i
\(378\) −0.796845 0.258911i −0.0409853 0.0133169i
\(379\) −6.47382 4.70350i −0.332538 0.241603i 0.408969 0.912548i \(-0.365888\pi\)
−0.741507 + 0.670946i \(0.765888\pi\)
\(380\) 0 0
\(381\) 2.44117 7.51314i 0.125065 0.384910i
\(382\) 1.22492 0.398002i 0.0626725 0.0203635i
\(383\) 17.4649 + 24.0384i 0.892417 + 1.22831i 0.972824 + 0.231544i \(0.0743778\pi\)
−0.0804076 + 0.996762i \(0.525622\pi\)
\(384\) −7.68799 −0.392326
\(385\) 0 0
\(386\) −2.55010 −0.129797
\(387\) 6.94864 + 9.56399i 0.353219 + 0.486165i
\(388\) 7.51553 2.44194i 0.381543 0.123971i
\(389\) 0.183988 0.566256i 0.00932855 0.0287103i −0.946284 0.323337i \(-0.895195\pi\)
0.955612 + 0.294627i \(0.0951953\pi\)
\(390\) 0 0
\(391\) 0.474976 + 0.345090i 0.0240206 + 0.0174520i
\(392\) 3.13752 + 1.01944i 0.158469 + 0.0514897i
\(393\) −15.5534 + 5.05362i −0.784568 + 0.254922i
\(394\) 1.88643 1.37057i 0.0950371 0.0690485i
\(395\) 0 0
\(396\) −2.95735 5.68133i −0.148612 0.285498i
\(397\) 1.66950i 0.0837898i 0.999122 + 0.0418949i \(0.0133395\pi\)
−0.999122 + 0.0418949i \(0.986661\pi\)
\(398\) −2.78168 3.82865i −0.139433 0.191913i
\(399\) −0.0679277 0.209060i −0.00340064 0.0104661i
\(400\) 0 0
\(401\) 9.19771 + 6.68253i 0.459312 + 0.333710i 0.793261 0.608881i \(-0.208381\pi\)
−0.333949 + 0.942591i \(0.608381\pi\)
\(402\) −1.47104 + 2.02472i −0.0733690 + 0.100984i
\(403\) −10.2060 3.31614i −0.508398 0.165189i
\(404\) 2.56114 + 7.88237i 0.127421 + 0.392163i
\(405\) 0 0
\(406\) 3.13008 0.155343
\(407\) −27.3246 4.08433i −1.35443 0.202453i
\(408\) 0.0909950i 0.00450492i
\(409\) −6.95565 + 5.05358i −0.343935 + 0.249883i −0.746320 0.665587i \(-0.768181\pi\)
0.402385 + 0.915470i \(0.368181\pi\)
\(410\) 0 0
\(411\) 2.38934 7.35364i 0.117858 0.362728i
\(412\) −2.37557 + 3.26969i −0.117036 + 0.161086i
\(413\) 3.44645 4.74363i 0.169589 0.233419i
\(414\) 0.539504 1.66042i 0.0265152 0.0816054i
\(415\) 0 0
\(416\) −2.72195 + 1.97761i −0.133455 + 0.0969604i
\(417\) 20.1865i 0.988536i
\(418\) −0.0267261 + 0.0536011i −0.00130721 + 0.00262172i
\(419\) −31.3915 −1.53358 −0.766789 0.641899i \(-0.778147\pi\)
−0.766789 + 0.641899i \(0.778147\pi\)
\(420\) 0 0
\(421\) −1.41497 4.35482i −0.0689613 0.212241i 0.910637 0.413208i \(-0.135592\pi\)
−0.979598 + 0.200967i \(0.935592\pi\)
\(422\) −4.48580 1.45753i −0.218366 0.0709513i
\(423\) −0.533721 + 0.734604i −0.0259504 + 0.0357177i
\(424\) 0.727915 + 0.528861i 0.0353507 + 0.0256838i
\(425\) 0 0
\(426\) 0.378171 + 1.16389i 0.0183225 + 0.0563908i
\(427\) −18.8839 25.9915i −0.913858 1.25782i
\(428\) 30.3983i 1.46936i
\(429\) −3.32313 1.65695i −0.160442 0.0799982i
\(430\) 0 0
\(431\) −12.8694 + 9.35015i −0.619896 + 0.450381i −0.852885 0.522098i \(-0.825149\pi\)
0.232989 + 0.972479i \(0.425149\pi\)
\(432\) −3.41595 + 1.10991i −0.164350 + 0.0534005i
\(433\) −15.0295 4.88338i −0.722272 0.234680i −0.0752639 0.997164i \(-0.523980\pi\)
−0.647008 + 0.762483i \(0.723980\pi\)
\(434\) −6.49696 4.72032i −0.311864 0.226583i
\(435\) 0 0
\(436\) 2.46625 7.59034i 0.118112 0.363511i
\(437\) 0.435628 0.141544i 0.0208389 0.00677098i
\(438\) 1.10420 + 1.51981i 0.0527609 + 0.0726192i
\(439\) −21.5227 −1.02722 −0.513611 0.858023i \(-0.671693\pi\)
−0.513611 + 0.858023i \(0.671693\pi\)
\(440\) 0 0
\(441\) 3.19862 0.152315
\(442\) 0.0152328 + 0.0209662i 0.000724551 + 0.000997258i
\(443\) 9.67881 3.14484i 0.459854 0.149416i −0.0699233 0.997552i \(-0.522275\pi\)
0.529777 + 0.848137i \(0.322275\pi\)
\(444\) −4.97116 + 15.2997i −0.235921 + 0.726090i
\(445\) 0 0
\(446\) −2.91826 2.12024i −0.138184 0.100396i
\(447\) 9.22071 + 2.99599i 0.436125 + 0.141706i
\(448\) 19.4233 6.31100i 0.917663 0.298167i
\(449\) 31.2352 22.6937i 1.47408 1.07098i 0.494673 0.869079i \(-0.335288\pi\)
0.979406 0.201902i \(-0.0647121\pi\)
\(450\) 0 0
\(451\) −17.8646 34.3194i −0.841209 1.61604i
\(452\) 26.5632i 1.24943i
\(453\) 8.91168 + 12.2659i 0.418707 + 0.576301i
\(454\) 0.0537303 + 0.165365i 0.00252169 + 0.00776096i
\(455\) 0 0
\(456\) 0.0574342 + 0.0417284i 0.00268960 + 0.00195411i
\(457\) 13.7329 18.9017i 0.642396 0.884183i −0.356344 0.934355i \(-0.615977\pi\)
0.998741 + 0.0501720i \(0.0159769\pi\)
\(458\) −1.86900 0.607275i −0.0873326 0.0283761i
\(459\) 0.0272635 + 0.0839083i 0.00127255 + 0.00391651i
\(460\) 0 0
\(461\) 4.93120 0.229669 0.114834 0.993385i \(-0.463366\pi\)
0.114834 + 0.993385i \(0.463366\pi\)
\(462\) −1.98197 1.94776i −0.0922094 0.0906181i
\(463\) 26.9648i 1.25316i −0.779357 0.626580i \(-0.784454\pi\)
0.779357 0.626580i \(-0.215546\pi\)
\(464\) 10.8555 7.88699i 0.503954 0.366144i
\(465\) 0 0
\(466\) −0.853329 + 2.62628i −0.0395297 + 0.121660i
\(467\) −13.9175 + 19.1558i −0.644024 + 0.886423i −0.998822 0.0485201i \(-0.984550\pi\)
0.354798 + 0.934943i \(0.384550\pi\)
\(468\) −1.27088 + 1.74921i −0.0587464 + 0.0808574i
\(469\) 9.41376 28.9726i 0.434687 1.33783i
\(470\) 0 0
\(471\) 12.0386 8.74655i 0.554709 0.403020i
\(472\) 1.89366i 0.0871627i
\(473\) 6.47035 + 38.6707i 0.297507 + 1.77808i
\(474\) 0.207616 0.00953613
\(475\) 0 0
\(476\) −0.168140 0.517482i −0.00770669 0.0237188i
\(477\) 0.829680 + 0.269579i 0.0379884 + 0.0123432i
\(478\) 2.63334 3.62449i 0.120446 0.165780i
\(479\) −10.9412 7.94922i −0.499915 0.363209i 0.309070 0.951039i \(-0.399982\pi\)
−0.808984 + 0.587830i \(0.799982\pi\)
\(480\) 0 0
\(481\) 2.88206 + 8.87008i 0.131411 + 0.404441i
\(482\) −2.57659 3.54637i −0.117361 0.161533i
\(483\) 21.2513i 0.966969i
\(484\) −0.369771 21.2396i −0.0168078 0.965437i
\(485\) 0 0
\(486\) 0.212253 0.154211i 0.00962801 0.00699516i
\(487\) 8.20480 2.66590i 0.371795 0.120803i −0.117159 0.993113i \(-0.537379\pi\)
0.488954 + 0.872310i \(0.337379\pi\)
\(488\) 9.86798 + 3.20630i 0.446703 + 0.145142i
\(489\) 2.75158 + 1.99914i 0.124431 + 0.0904043i
\(490\) 0 0
\(491\) −8.00565 + 24.6388i −0.361290 + 1.11194i 0.590982 + 0.806685i \(0.298740\pi\)
−0.952272 + 0.305251i \(0.901260\pi\)
\(492\) −21.4257 + 6.96164i −0.965947 + 0.313855i
\(493\) −0.193733 0.266651i −0.00872532 0.0120094i
\(494\) 0.0202189 0.000909690
\(495\) 0 0
\(496\) −34.4263 −1.54579
\(497\) −8.75585 12.0514i −0.392754 0.540579i
\(498\) −0.0616883 + 0.0200437i −0.00276432 + 0.000898182i
\(499\) 8.66717 26.6748i 0.387996 1.19413i −0.546288 0.837597i \(-0.683960\pi\)
0.934284 0.356531i \(-0.116040\pi\)
\(500\) 0 0
\(501\) 18.2970 + 13.2936i 0.817450 + 0.593913i
\(502\) 1.28194 + 0.416529i 0.0572160 + 0.0185906i
\(503\) 27.9610 9.08507i 1.24672 0.405083i 0.389974 0.920826i \(-0.372484\pi\)
0.856744 + 0.515743i \(0.172484\pi\)
\(504\) −2.66469 + 1.93601i −0.118695 + 0.0862368i
\(505\) 0 0
\(506\) 4.05864 4.12992i 0.180429 0.183597i
\(507\) 11.7465i 0.521680i
\(508\) −8.96714 12.3422i −0.397853 0.547597i
\(509\) 5.99195 + 18.4413i 0.265589 + 0.817398i 0.991557 + 0.129670i \(0.0413918\pi\)
−0.725969 + 0.687728i \(0.758608\pi\)
\(510\) 0 0
\(511\) −18.4996 13.4407i −0.818373 0.594583i
\(512\) −10.6991 + 14.7261i −0.472838 + 0.650806i
\(513\) 0.0654637 + 0.0212704i 0.00289029 + 0.000939113i
\(514\) −0.299830 0.922782i −0.0132249 0.0407022i
\(515\) 0 0
\(516\) 22.8298 1.00502
\(517\) −2.67132 + 1.39052i −0.117485 + 0.0611552i
\(518\) 6.97949i 0.306661i
\(519\) −10.5911 + 7.69487i −0.464897 + 0.337767i
\(520\) 0 0
\(521\) 7.72734 23.7823i 0.338541 1.04192i −0.626410 0.779493i \(-0.715477\pi\)
0.964951 0.262429i \(-0.0845235\pi\)
\(522\) −0.576107 + 0.792943i −0.0252155 + 0.0347062i
\(523\) 1.28585 1.76982i 0.0562262 0.0773887i −0.779978 0.625807i \(-0.784770\pi\)
0.836204 + 0.548418i \(0.184770\pi\)
\(524\) −9.75939 + 30.0363i −0.426341 + 1.31214i
\(525\) 0 0
\(526\) 6.71389 4.87793i 0.292740 0.212688i
\(527\) 0.845637i 0.0368365i
\(528\) −11.7816 1.76104i −0.512727 0.0766395i
\(529\) −21.2824 −0.925322
\(530\) 0 0
\(531\) 0.567369 + 1.74618i 0.0246217 + 0.0757778i
\(532\) −0.403730 0.131180i −0.0175039 0.00568737i
\(533\) −7.67703 + 10.5665i −0.332529 + 0.457687i
\(534\) 3.09439 + 2.24821i 0.133908 + 0.0972895i
\(535\) 0 0
\(536\) 3.04026 + 9.35697i 0.131319 + 0.404159i
\(537\) 8.92106 + 12.2788i 0.384972 + 0.529869i
\(538\) 3.87648i 0.167127i
\(539\) 9.49390 + 4.73375i 0.408931 + 0.203897i
\(540\) 0 0
\(541\) −10.9689 + 7.96939i −0.471591 + 0.342631i −0.798061 0.602577i \(-0.794141\pi\)
0.326470 + 0.945208i \(0.394141\pi\)
\(542\) −4.88731 + 1.58798i −0.209928 + 0.0682097i
\(543\) −1.34430 0.436789i −0.0576894 0.0187444i
\(544\) 0.214493 + 0.155838i 0.00919632 + 0.00668152i
\(545\) 0 0
\(546\) −0.289878 + 0.892153i −0.0124056 + 0.0381806i
\(547\) 3.53110 1.14732i 0.150979 0.0490560i −0.232553 0.972584i \(-0.574708\pi\)
0.383531 + 0.923528i \(0.374708\pi\)
\(548\) −8.77677 12.0802i −0.374925 0.516040i
\(549\) 10.0601 0.429356
\(550\) 0 0
\(551\) −0.257147 −0.0109548
\(552\) −4.03416 5.55254i −0.171705 0.236332i
\(553\) −2.40348 + 0.780939i −0.102207 + 0.0332089i
\(554\) 2.08443 6.41522i 0.0885590 0.272557i
\(555\) 0 0
\(556\) 31.5383 + 22.9139i 1.33752 + 0.971766i
\(557\) 6.25339 + 2.03185i 0.264964 + 0.0860922i 0.438486 0.898738i \(-0.355515\pi\)
−0.173522 + 0.984830i \(0.555515\pi\)
\(558\) 2.39160 0.777078i 0.101244 0.0328963i
\(559\) 10.7079 7.77974i 0.452896 0.329048i
\(560\) 0 0
\(561\) −0.0432577 + 0.289399i −0.00182634 + 0.0122184i
\(562\) 7.00786i 0.295609i
\(563\) −4.06087 5.58931i −0.171145 0.235561i 0.714825 0.699303i \(-0.246506\pi\)
−0.885970 + 0.463742i \(0.846506\pi\)
\(564\) 0.541873 + 1.66771i 0.0228170 + 0.0702235i
\(565\) 0 0
\(566\) 1.53539 + 1.11552i 0.0645372 + 0.0468890i
\(567\) −1.87711 + 2.58362i −0.0788311 + 0.108502i
\(568\) 4.57545 + 1.48666i 0.191982 + 0.0623787i
\(569\) 2.08515 + 6.41743i 0.0874140 + 0.269033i 0.985203 0.171394i \(-0.0548272\pi\)
−0.897789 + 0.440427i \(0.854827\pi\)
\(570\) 0 0
\(571\) 9.68928 0.405484 0.202742 0.979232i \(-0.435015\pi\)
0.202742 + 0.979232i \(0.435015\pi\)
\(572\) −6.36086 + 3.31107i −0.265961 + 0.138443i
\(573\) 4.90914i 0.205082i
\(574\) −7.90742 + 5.74508i −0.330049 + 0.239795i
\(575\) 0 0
\(576\) −1.97619 + 6.08207i −0.0823411 + 0.253420i
\(577\) 8.90484 12.2565i 0.370713 0.510243i −0.582381 0.812916i \(-0.697879\pi\)
0.953095 + 0.302673i \(0.0978789\pi\)
\(578\) −2.62039 + 3.60666i −0.108994 + 0.150017i
\(579\) −3.00361 + 9.24415i −0.124826 + 0.384174i
\(580\) 0 0
\(581\) 0.638745 0.464076i 0.0264996 0.0192531i
\(582\) 1.07357i 0.0445009i
\(583\) 2.06364 + 2.02802i 0.0854671 + 0.0839921i
\(584\) 7.38503 0.305595
\(585\) 0 0
\(586\) −1.18325 3.64166i −0.0488795 0.150436i
\(587\) −25.6892 8.34693i −1.06031 0.344514i −0.273601 0.961843i \(-0.588215\pi\)
−0.786705 + 0.617329i \(0.788215\pi\)
\(588\) 3.63079 4.99735i 0.149731 0.206087i
\(589\) 0.533749 + 0.387791i 0.0219927 + 0.0159787i
\(590\) 0 0
\(591\) −2.74643 8.45265i −0.112973 0.347696i
\(592\) 17.5865 + 24.2058i 0.722801 + 0.994850i
\(593\) 22.1863i 0.911084i 0.890214 + 0.455542i \(0.150554\pi\)
−0.890214 + 0.455542i \(0.849446\pi\)
\(594\) 0.858218 0.143596i 0.0352131 0.00589183i
\(595\) 0 0
\(596\) 15.1473 11.0052i 0.620458 0.450789i
\(597\) −17.1552 + 5.57408i −0.702118 + 0.228132i
\(598\) −1.85902 0.604033i −0.0760210 0.0247007i
\(599\) 9.50487 + 6.90569i 0.388359 + 0.282159i 0.764783 0.644289i \(-0.222846\pi\)
−0.376424 + 0.926448i \(0.622846\pi\)
\(600\) 0 0
\(601\) 10.6242 32.6979i 0.433370 1.33378i −0.461377 0.887204i \(-0.652645\pi\)
0.894747 0.446572i \(-0.147355\pi\)
\(602\) 9.42010 3.06077i 0.383934 0.124748i
\(603\) 5.60698 + 7.71734i 0.228334 + 0.314274i
\(604\) 29.2793 1.19136
\(605\) 0 0
\(606\) −1.12597 −0.0457395
\(607\) −8.01137 11.0267i −0.325172 0.447560i 0.614866 0.788632i \(-0.289210\pi\)
−0.940037 + 0.341071i \(0.889210\pi\)
\(608\) 0.196724 0.0639196i 0.00797822 0.00259228i
\(609\) 3.68672 11.3466i 0.149393 0.459786i
\(610\) 0 0
\(611\) 0.822467 + 0.597557i 0.0332735 + 0.0241746i
\(612\) 0.162041 + 0.0526503i 0.00655012 + 0.00212826i
\(613\) −6.49565 + 2.11057i −0.262357 + 0.0852450i −0.437242 0.899344i \(-0.644045\pi\)
0.174885 + 0.984589i \(0.444045\pi\)
\(614\) −6.05866 + 4.40187i −0.244508 + 0.177645i
\(615\) 0 0
\(616\) −10.7743 + 1.80275i −0.434110 + 0.0726349i
\(617\) 30.3730i 1.22277i 0.791333 + 0.611386i \(0.209388\pi\)
−0.791333 + 0.611386i \(0.790612\pi\)
\(618\) −0.322734 0.444205i −0.0129823 0.0178685i
\(619\) 7.96890 + 24.5258i 0.320297 + 0.985773i 0.973519 + 0.228607i \(0.0734170\pi\)
−0.653222 + 0.757167i \(0.726583\pi\)
\(620\) 0 0
\(621\) −5.38361 3.91142i −0.216037 0.156960i
\(622\) 1.53410 2.11150i 0.0615117 0.0846635i
\(623\) −44.2790 14.3871i −1.77400 0.576408i
\(624\) 1.24266 + 3.82452i 0.0497463 + 0.153103i
\(625\) 0 0
\(626\) 4.31081 0.172295
\(627\) 0.162826 + 0.160016i 0.00650263 + 0.00639041i
\(628\) 28.7368i 1.14672i
\(629\) 0.594583 0.431990i 0.0237076 0.0172246i
\(630\) 0 0
\(631\) −7.90021 + 24.3143i −0.314502 + 0.967939i 0.661456 + 0.749984i \(0.269939\pi\)
−0.975959 + 0.217955i \(0.930061\pi\)
\(632\) 0.479735 0.660299i 0.0190828 0.0262653i
\(633\) −10.5671 + 14.5444i −0.420004 + 0.578086i
\(634\) 1.15210 3.54581i 0.0457559 0.140822i
\(635\) 0 0
\(636\) 1.36296 0.990246i 0.0540447 0.0392658i
\(637\) 3.58119i 0.141892i
\(638\) −2.88347 + 1.50095i −0.114157 + 0.0594233i
\(639\) 4.66454 0.184527
\(640\) 0 0
\(641\) −1.25851 3.87329i −0.0497081 0.152986i 0.923121 0.384509i \(-0.125629\pi\)
−0.972829 + 0.231523i \(0.925629\pi\)
\(642\) 3.92766 + 1.27617i 0.155012 + 0.0503665i
\(643\) −6.65950 + 9.16601i −0.262625 + 0.361472i −0.919883 0.392194i \(-0.871716\pi\)
0.657258 + 0.753666i \(0.271716\pi\)
\(644\) 33.2020 + 24.1226i 1.30834 + 0.950565i
\(645\) 0 0
\(646\) −0.000492348 0.00151529i −1.93712e−5 5.96184e-5i
\(647\) 21.6587 + 29.8107i 0.851492 + 1.17198i 0.983532 + 0.180734i \(0.0578472\pi\)
−0.132040 + 0.991244i \(0.542153\pi\)
\(648\) 1.03138i 0.0405164i
\(649\) −0.900218 + 6.02256i −0.0353366 + 0.236406i
\(650\) 0 0
\(651\) −24.7636 + 17.9918i −0.970561 + 0.705154i
\(652\) 6.24671 2.02968i 0.244640 0.0794883i
\(653\) −14.5291 4.72079i −0.568568 0.184739i 0.0106050 0.999944i \(-0.496624\pi\)
−0.579173 + 0.815205i \(0.696624\pi\)
\(654\) 0.877182 + 0.637310i 0.0343005 + 0.0249208i
\(655\) 0 0
\(656\) −12.9478 + 39.8493i −0.505528 + 1.55585i
\(657\) 6.80989 2.21267i 0.265679 0.0863243i
\(658\) 0.447180 + 0.615490i 0.0174329 + 0.0239943i
\(659\) −11.8996 −0.463544 −0.231772 0.972770i \(-0.574452\pi\)
−0.231772 + 0.972770i \(0.574452\pi\)
\(660\) 0 0
\(661\) −44.8648 −1.74504 −0.872520 0.488578i \(-0.837516\pi\)
−0.872520 + 0.488578i \(0.837516\pi\)
\(662\) −1.68274 2.31609i −0.0654015 0.0900174i
\(663\) 0.0939443 0.0305244i 0.00364849 0.00118547i
\(664\) −0.0787953 + 0.242507i −0.00305785 + 0.00941110i
\(665\) 0 0
\(666\) −1.76812 1.28461i −0.0685131 0.0497777i
\(667\) 23.6434 + 7.68219i 0.915474 + 0.297456i
\(668\) 41.5383 13.4966i 1.60717 0.522200i
\(669\) −11.1231 + 8.08142i −0.430045 + 0.312446i
\(670\) 0 0
\(671\) 29.8597 + 14.8884i 1.15272 + 0.574759i
\(672\) 9.59683i 0.370206i
\(673\) −11.2306 15.4576i −0.432909 0.595848i 0.535709 0.844403i \(-0.320044\pi\)
−0.968618 + 0.248555i \(0.920044\pi\)
\(674\) −0.477207 1.46869i −0.0183813 0.0565719i
\(675\) 0 0
\(676\) −18.3521 13.3336i −0.705849 0.512830i
\(677\) 27.3093 37.5881i 1.04958 1.44463i 0.160414 0.987050i \(-0.448717\pi\)
0.889170 0.457578i \(-0.151283\pi\)
\(678\) 3.43213 + 1.11517i 0.131810 + 0.0428278i
\(679\) −4.03819 12.4283i −0.154971 0.476953i
\(680\) 0 0
\(681\) 0.662735 0.0253961
\(682\) 8.24860 + 1.23295i 0.315855 + 0.0472122i
\(683\) 42.5651i 1.62871i 0.580367 + 0.814355i \(0.302909\pi\)
−0.580367 + 0.814355i \(0.697091\pi\)
\(684\) 0.107540 0.0781327i 0.00411191 0.00298748i
\(685\) 0 0
\(686\) −0.984219 + 3.02912i −0.0375777 + 0.115652i
\(687\) −4.40275 + 6.05987i −0.167976 + 0.231198i
\(688\) 24.9577 34.3514i 0.951505 1.30963i
\(689\) 0.301823 0.928915i 0.0114985 0.0353888i
\(690\) 0 0
\(691\) −28.4249 + 20.6519i −1.08134 + 0.785636i −0.977915 0.209001i \(-0.932979\pi\)
−0.103420 + 0.994638i \(0.532979\pi\)
\(692\) 25.2815i 0.961057i
\(693\) −9.39509 + 4.89050i −0.356890 + 0.185775i
\(694\) 9.05253 0.343629
\(695\) 0 0
\(696\) 1.19066 + 3.66448i 0.0451319 + 0.138902i
\(697\) 0.978846 + 0.318046i 0.0370764 + 0.0120469i
\(698\) −0.850252 + 1.17027i −0.0321825 + 0.0442954i
\(699\) 8.51520 + 6.18665i 0.322074 + 0.234001i
\(700\) 0 0
\(701\) −9.47794 29.1701i −0.357977 1.10174i −0.954263 0.298968i \(-0.903358\pi\)
0.596286 0.802772i \(-0.296642\pi\)
\(702\) −0.172656 0.237640i −0.00651647 0.00896916i
\(703\) 0.573390i 0.0216258i
\(704\) −14.8667 + 15.1277i −0.560309 + 0.570148i
\(705\) 0 0
\(706\) −6.34086 + 4.60690i −0.238641 + 0.173383i
\(707\) 13.0349 4.23530i 0.490228 0.159285i
\(708\) 3.37217 + 1.09568i 0.126734 + 0.0411783i
\(709\) 12.2100 + 8.87107i 0.458555 + 0.333160i 0.792964 0.609268i \(-0.208537\pi\)
−0.334409 + 0.942428i \(0.608537\pi\)
\(710\) 0 0
\(711\) 0.244538 0.752611i 0.00917090 0.0282251i
\(712\) 14.3003 4.64646i 0.535927 0.174133i
\(713\) −37.4903 51.6010i −1.40402 1.93247i
\(714\) 0.0739208 0.00276642
\(715\) 0 0
\(716\) 29.3101 1.09537
\(717\) −10.0371 13.8149i −0.374844 0.515929i
\(718\) 8.96099 2.91160i 0.334421 0.108660i
\(719\) 1.91288 5.88723i 0.0713383 0.219557i −0.909030 0.416730i \(-0.863176\pi\)
0.980369 + 0.197173i \(0.0631761\pi\)
\(720\) 0 0
\(721\) 5.40701 + 3.92842i 0.201367 + 0.146302i
\(722\) 4.73968 + 1.54001i 0.176393 + 0.0573134i
\(723\) −15.8904 + 5.16312i −0.590972 + 0.192018i
\(724\) −2.20835 + 1.60446i −0.0820725 + 0.0596292i
\(725\) 0 0
\(726\) 2.75982 + 0.843898i 0.102426 + 0.0313200i
\(727\) 18.1515i 0.673200i −0.941648 0.336600i \(-0.890723\pi\)
0.941648 0.336600i \(-0.109277\pi\)
\(728\) 2.16757 + 2.98341i 0.0803355 + 0.110572i
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) 0 0
\(731\) −0.843796 0.613054i −0.0312089 0.0226746i
\(732\) 11.4194 15.7174i 0.422072 0.580932i
\(733\) 27.3342 + 8.88142i 1.00961 + 0.328043i 0.766700 0.642005i \(-0.221897\pi\)
0.242912 + 0.970048i \(0.421897\pi\)
\(734\) −0.732165 2.25337i −0.0270247 0.0831735i
\(735\) 0 0
\(736\) −19.9974 −0.737113
\(737\) 5.22103 + 31.2040i 0.192319 + 1.14942i
\(738\) 3.06060i 0.112662i
\(739\) −37.8896 + 27.5284i −1.39379 + 1.01265i −0.398354 + 0.917232i \(0.630419\pi\)
−0.995437 + 0.0954172i \(0.969581\pi\)
\(740\) 0 0
\(741\) 0.0238145 0.0732936i 0.000874848 0.00269251i
\(742\) 0.429626 0.591330i 0.0157721 0.0217084i
\(743\) −15.6414 + 21.5286i −0.573828 + 0.789806i −0.993002 0.118100i \(-0.962320\pi\)
0.419174 + 0.907906i \(0.362320\pi\)
\(744\) 3.05482 9.40178i 0.111995 0.344686i
\(745\) 0 0
\(746\) 3.65064 2.65235i 0.133659 0.0971093i
\(747\) 0.247229i 0.00904564i
\(748\) 0.403039 + 0.396084i 0.0147366 + 0.0144823i
\(749\) −50.2691 −1.83679
\(750\) 0 0
\(751\) 12.5406 + 38.5959i 0.457612 + 1.40838i 0.868041 + 0.496492i \(0.165379\pi\)
−0.410430 + 0.911892i \(0.634621\pi\)
\(752\) 3.10175 + 1.00782i 0.113109 + 0.0367514i
\(753\) 3.01984 4.15646i 0.110049 0.151470i
\(754\) 0.887784 + 0.645013i 0.0323312 + 0.0234900i
\(755\) 0 0
\(756\) 1.90578 + 5.86539i 0.0693126 + 0.213322i
\(757\) −19.2311 26.4693i −0.698966 0.962045i −0.999965 0.00841989i \(-0.997320\pi\)
0.300998 0.953625i \(-0.402680\pi\)
\(758\) 2.09942i 0.0762545i
\(759\) −10.1906 19.5770i −0.369894 0.710600i
\(760\) 0 0
\(761\) 2.12721 1.54551i 0.0771113 0.0560246i −0.548562 0.836110i \(-0.684824\pi\)
0.625673 + 0.780085i \(0.284824\pi\)
\(762\) 1.97115 0.640464i 0.0714071 0.0232016i
\(763\) −12.5520 4.07838i −0.454412 0.147647i
\(764\) −7.66978 5.57242i −0.277483 0.201603i
\(765\) 0 0
\(766\) −2.40895 + 7.41399i −0.0870389 + 0.267878i
\(767\) 1.95503 0.635229i 0.0705922 0.0229368i
\(768\) 6.33228 + 8.71564i 0.228497 + 0.314499i
\(769\) −3.23559 −0.116678 −0.0583392 0.998297i \(-0.518581\pi\)
−0.0583392 + 0.998297i \(0.518581\pi\)
\(770\) 0 0
\(771\) −3.69824 −0.133189
\(772\) 11.0331 + 15.1858i 0.397092 + 0.546550i
\(773\) 41.5008 13.4844i 1.49268 0.485001i 0.554806 0.831980i \(-0.312792\pi\)
0.937873 + 0.346979i \(0.112792\pi\)
\(774\) −0.958431 + 2.94975i −0.0344501 + 0.106026i
\(775\) 0 0
\(776\) 3.41436 + 2.48068i 0.122569 + 0.0890512i
\(777\) 25.3007 + 8.22070i 0.907658 + 0.294916i
\(778\) 0.148563 0.0482710i 0.00532623 0.00173060i
\(779\) 0.649623 0.471979i 0.0232752 0.0169104i
\(780\) 0 0
\(781\) 13.8450 + 6.90324i 0.495412 + 0.247017i
\(782\) 0.154032i 0.00550818i
\(783\) 2.19587 + 3.02235i 0.0784739 + 0.108010i
\(784\) −3.55017 10.9263i −0.126792 0.390225i
\(785\) 0 0
\(786\) −3.47116 2.52195i −0.123812 0.0899549i
\(787\) −2.68277 + 3.69251i −0.0956304 + 0.131624i −0.854151 0.520025i \(-0.825923\pi\)
0.758521 + 0.651649i \(0.225923\pi\)
\(788\) −16.3235 5.30382i −0.581500 0.188941i
\(789\) −9.77467 30.0833i −0.347987 1.07100i
\(790\) 0 0
\(791\) −43.9270 −1.56186
\(792\) 1.52638 3.06127i 0.0542375 0.108777i
\(793\) 11.2634i 0.399974i
\(794\) −0.354357 + 0.257455i −0.0125757 + 0.00913675i
\(795\) 0 0
\(796\) −10.7645 + 33.1297i −0.381537 + 1.17425i
\(797\) −6.57177 + 9.04526i −0.232784 + 0.320400i −0.909389 0.415946i \(-0.863450\pi\)
0.676605 + 0.736346i \(0.263450\pi\)
\(798\) 0.0338985 0.0466573i 0.00119999 0.00165165i
\(799\) 0.0247558 0.0761905i 0.000875797 0.00269543i
\(800\) 0 0
\(801\) 11.7945 8.56919i 0.416737 0.302777i
\(802\) 2.98277i 0.105325i
\(803\) 23.4872 + 3.51074i 0.828846 + 0.123891i
\(804\) 18.4217 0.649684
\(805\) 0 0
\(806\) −0.870021 2.67765i −0.0306452 0.0943162i
\(807\) −14.0523 4.56586i −0.494664 0.160726i
\(808\) −2.60176 + 3.58102i −0.0915298 + 0.125980i
\(809\) −36.8440 26.7687i −1.29537 0.941139i −0.295468 0.955353i \(-0.595475\pi\)
−0.999899 + 0.0142137i \(0.995475\pi\)
\(810\) 0 0
\(811\) 0.872550 + 2.68543i 0.0306394 + 0.0942983i 0.965207 0.261488i \(-0.0842131\pi\)
−0.934567 + 0.355786i \(0.884213\pi\)
\(812\) −13.5424 18.6395i −0.475246 0.654120i
\(813\) 19.5869i 0.686943i
\(814\) −3.34685 6.42959i −0.117307 0.225357i
\(815\) 0 0
\(816\) 0.256367 0.186261i 0.00897463 0.00652045i
\(817\) −0.773895 + 0.251454i −0.0270751 + 0.00879725i
\(818\) −2.14528 0.697043i −0.0750079 0.0243715i
\(819\) 2.89263 + 2.10162i 0.101077 + 0.0734366i
\(820\) 0 0
\(821\) −7.23460 + 22.2658i −0.252489 + 0.777083i 0.741825 + 0.670594i \(0.233961\pi\)
−0.994314 + 0.106488i \(0.966039\pi\)
\(822\) 1.92930 0.626867i 0.0672920 0.0218645i
\(823\) 27.0996 + 37.2994i 0.944633 + 1.30018i 0.953870 + 0.300218i \(0.0970596\pi\)
−0.00923747 + 0.999957i \(0.502940\pi\)
\(824\) −2.15848 −0.0751941
\(825\) 0 0
\(826\) 1.53833 0.0535255
\(827\) 25.5390 + 35.1515i 0.888079 + 1.22234i 0.974117 + 0.226044i \(0.0725794\pi\)
−0.0860379 + 0.996292i \(0.527421\pi\)
\(828\) −12.2220 + 3.97116i −0.424743 + 0.138007i
\(829\) −4.78085 + 14.7139i −0.166046 + 0.511036i −0.999112 0.0421372i \(-0.986583\pi\)
0.833066 + 0.553173i \(0.186583\pi\)
\(830\) 0 0
\(831\) −20.8001 15.1122i −0.721548 0.524235i
\(832\) 6.80953 + 2.21255i 0.236078 + 0.0767064i
\(833\) −0.268390 + 0.0872053i −0.00929918 + 0.00302149i
\(834\) −4.28465 + 3.11298i −0.148365 + 0.107794i
\(835\) 0 0
\(836\) 0.434825 0.0727546i 0.0150387 0.00251627i
\(837\) 9.58484i 0.331301i
\(838\) −4.84093 6.66296i −0.167227 0.230168i
\(839\) −9.33790 28.7391i −0.322380 0.992184i −0.972609 0.232446i \(-0.925327\pi\)
0.650229 0.759738i \(-0.274673\pi\)
\(840\) 0 0
\(841\) 12.1705 + 8.84239i 0.419673 + 0.304910i
\(842\) 0.706122 0.971894i 0.0243346 0.0334937i
\(843\) 25.4036 + 8.25411i 0.874945 + 0.284287i
\(844\) 10.7285 + 33.0189i 0.369290 + 1.13656i
\(845\) 0 0
\(846\) −0.238228 −0.00819045
\(847\) −35.1235 + 0.611482i −1.20686 + 0.0210108i
\(848\) 3.13335i 0.107600i
\(849\) 5.85223 4.25189i 0.200848 0.145925i
\(850\) 0 0
\(851\) −17.1299 + 52.7203i −0.587204 + 1.80723i
\(852\) 5.29478 7.28764i 0.181396 0.249670i
\(853\) 1.18091 1.62538i 0.0404336 0.0556521i −0.788322 0.615263i \(-0.789050\pi\)
0.828755 + 0.559611i \(0.189050\pi\)
\(854\) 2.60467 8.01636i 0.0891301 0.274314i
\(855\) 0 0
\(856\) 13.1343 9.54262i 0.448921 0.326160i
\(857\) 33.6095i 1.14808i −0.818828 0.574039i \(-0.805376\pi\)
0.818828 0.574039i \(-0.194624\pi\)
\(858\) −0.160771 0.960867i −0.00548865 0.0328034i
\(859\) 13.7301 0.468466 0.234233 0.972180i \(-0.424742\pi\)
0.234233 + 0.972180i \(0.424742\pi\)
\(860\) 0 0
\(861\) 11.5123 + 35.4312i 0.392338 + 1.20749i
\(862\) −3.96920 1.28967i −0.135192 0.0439264i
\(863\) −5.14799 + 7.08560i −0.175240 + 0.241197i −0.887598 0.460620i \(-0.847627\pi\)
0.712358 + 0.701816i \(0.247627\pi\)
\(864\) −2.43117 1.76635i −0.0827100 0.0600923i
\(865\) 0 0
\(866\) −1.28120 3.94314i −0.0435370 0.133993i
\(867\) 9.98777 + 13.7470i 0.339203 + 0.466872i
\(868\) 59.1120i 2.00639i
\(869\) 1.83964 1.87194i 0.0624055 0.0635014i
\(870\) 0 0
\(871\) 8.64038 6.27761i 0.292768 0.212709i
\(872\) 4.05378 1.31715i 0.137278 0.0446044i
\(873\) 3.89170 + 1.26449i 0.131714 + 0.0427965i
\(874\) 0.0972220 + 0.0706359i 0.00328858 + 0.00238930i
\(875\) 0 0
\(876\) 4.27303 13.1510i 0.144372 0.444332i
\(877\) 14.5001 4.71136i 0.489633 0.159091i −0.0537871 0.998552i \(-0.517129\pi\)
0.543420 + 0.839461i \(0.317129\pi\)
\(878\) −3.31904 4.56827i −0.112012 0.154172i
\(879\) −14.5947 −0.492268
\(880\) 0 0
\(881\) −15.8486 −0.533953 −0.266977 0.963703i \(-0.586025\pi\)
−0.266977 + 0.963703i \(0.586025\pi\)
\(882\) 0.493262 + 0.678917i 0.0166090 + 0.0228603i
\(883\) −31.3474 + 10.1854i −1.05492 + 0.342765i −0.784598 0.620004i \(-0.787131\pi\)
−0.270324 + 0.962769i \(0.587131\pi\)
\(884\) 0.0589476 0.181422i 0.00198262 0.00610189i
\(885\) 0 0
\(886\) 2.16008 + 1.56939i 0.0725694 + 0.0527247i
\(887\) 10.7017 + 3.47720i 0.359328 + 0.116753i 0.483117 0.875556i \(-0.339505\pi\)
−0.123789 + 0.992309i \(0.539505\pi\)
\(888\) −8.17111 + 2.65495i −0.274204 + 0.0890944i
\(889\) −20.4100 + 14.8288i −0.684530 + 0.497340i
\(890\) 0 0
\(891\) 0.490303 3.28018i 0.0164258 0.109890i
\(892\) 26.5515i 0.889010i
\(893\) −0.0367374 0.0505647i −0.00122937 0.00169208i
\(894\) 0.786027 + 2.41914i 0.0262887 + 0.0809083i
\(895\) 0 0
\(896\) 19.8628 + 14.4312i 0.663570 + 0.482112i
\(897\) −4.37925 + 6.02752i −0.146219 + 0.201253i
\(898\) 9.63362 + 3.13015i 0.321478 + 0.104455i
\(899\) 11.0651 + 34.0548i 0.369041 + 1.13579i
\(900\) 0 0
\(901\) −0.0769667 −0.00256413
\(902\) 4.52950 9.08425i 0.150816 0.302472i
\(903\) 37.7530i 1.25634i
\(904\) 11.4772 8.33870i 0.381727 0.277341i
\(905\) 0 0
\(906\) −1.22919 + 3.78307i −0.0408372 + 0.125684i
\(907\) −14.9147 + 20.5284i −0.495236 + 0.681634i −0.981343 0.192266i \(-0.938417\pi\)
0.486107 + 0.873899i \(0.338417\pi\)
\(908\) 0.752278 1.03542i 0.0249652 0.0343617i
\(909\) −1.32621 + 4.08166i −0.0439877 + 0.135380i
\(910\) 0 0
\(911\) 14.0825 10.2316i 0.466575 0.338986i −0.329530 0.944145i \(-0.606890\pi\)
0.796105 + 0.605159i \(0.206890\pi\)
\(912\) 0.247229i 0.00818657i
\(913\) −0.365884 + 0.733807i −0.0121090 + 0.0242855i
\(914\) 6.12971 0.202753
\(915\) 0 0
\(916\) 4.47000 + 13.7573i 0.147693 + 0.454553i
\(917\) 49.6704 + 16.1389i 1.64026 + 0.532953i
\(918\) −0.0136055 + 0.0187264i −0.000449048 + 0.000618062i
\(919\) −26.6133 19.3357i −0.877890 0.637825i 0.0548022 0.998497i \(-0.482547\pi\)
−0.932692 + 0.360673i \(0.882547\pi\)
\(920\) 0 0
\(921\) 8.82072 + 27.1474i 0.290653 + 0.894537i
\(922\) 0.760446 + 1.04666i 0.0250440 + 0.0344701i
\(923\) 5.22245i 0.171899i
\(924\) −3.02381 + 20.2297i −0.0994762 + 0.665507i
\(925\) 0 0
\(926\) 5.72337 4.15827i 0.188082 0.136649i
\(927\) −1.99038 + 0.646712i −0.0653725 + 0.0212408i
\(928\) 10.6770 + 3.46918i 0.350491 + 0.113881i
\(929\) 26.9509 + 19.5810i 0.884230 + 0.642431i 0.934367 0.356311i \(-0.115966\pi\)
−0.0501368 + 0.998742i \(0.515966\pi\)
\(930\) 0 0
\(931\) −0.0680360 + 0.209393i −0.00222979 + 0.00686258i
\(932\) 19.3314 6.28115i 0.633221 0.205746i
\(933\) −5.84730 8.04812i −0.191432 0.263484i
\(934\) −6.21211 −0.203266
\(935\) 0 0
\(936\) −1.15474 −0.0377438
\(937\) 14.0267 + 19.3061i 0.458233 + 0.630704i 0.974141 0.225940i \(-0.0725453\pi\)
−0.515908 + 0.856644i \(0.672545\pi\)
\(938\) 7.60123 2.46979i 0.248189 0.0806415i
\(939\) 5.07744 15.6267i 0.165696 0.509959i
\(940\) 0 0
\(941\) 6.41192 + 4.65853i 0.209023 + 0.151864i 0.687371 0.726306i \(-0.258765\pi\)
−0.478349 + 0.878170i \(0.658765\pi\)
\(942\) 3.71297 + 1.20642i 0.120975 + 0.0393072i
\(943\) −73.8297 + 23.9887i −2.40423 + 0.781181i
\(944\) 5.33514 3.87620i 0.173644 0.126160i
\(945\) 0 0
\(946\) −7.21019 + 7.33681i −0.234423 + 0.238540i
\(947\) 2.15429i 0.0700050i −0.999387 0.0350025i \(-0.988856\pi\)
0.999387 0.0350025i \(-0.0111439\pi\)
\(948\) −0.898262 1.23635i −0.0291742 0.0401548i
\(949\) −2.47731 7.62439i −0.0804170 0.247498i
\(950\) 0 0
\(951\) −11.4966 8.35278i −0.372803 0.270858i
\(952\) 0.170807 0.235096i 0.00553590 0.00761951i
\(953\) 5.69971 + 1.85195i 0.184632 + 0.0599904i 0.399874 0.916570i \(-0.369054\pi\)
−0.215242 + 0.976561i \(0.569054\pi\)
\(954\) 0.0707268 + 0.217675i 0.00228986 + 0.00704748i
\(955\) 0 0
\(956\) −32.9770 −1.06655
\(957\) 2.04472 + 12.2205i 0.0660964 + 0.395032i
\(958\) 3.54816i 0.114636i
\(959\) −19.9767 + 14.5139i −0.645082 + 0.468680i
\(960\) 0 0
\(961\) 18.8096 57.8901i 0.606762 1.86742i
\(962\) −1.43826 + 1.97959i −0.0463713 + 0.0638246i
\(963\) 9.25228 12.7347i 0.298151 0.410369i
\(964\) −9.97085 + 30.6871i −0.321139 + 0.988365i
\(965\) 0 0
\(966\) −4.51067 + 3.27719i −0.145128 + 0.105442i
\(967\) 22.2784i 0.716424i 0.933640 + 0.358212i \(0.116613\pi\)
−0.933640 + 0.358212i \(0.883387\pi\)
\(968\) 9.06097 6.82729i 0.291231 0.219437i
\(969\) −0.00607286 −0.000195088
\(970\) 0 0
\(971\) −11.3381 34.8952i −0.363858 1.11984i −0.950693 0.310133i \(-0.899626\pi\)
0.586835 0.809706i \(-0.300374\pi\)
\(972\) −1.83665 0.596764i −0.0589106 0.0191412i
\(973\) 37.8922 52.1541i 1.21477 1.67198i
\(974\) 1.83112 + 1.33039i 0.0586728 + 0.0426283i
\(975\) 0 0
\(976\) −11.1658 34.3649i −0.357409 1.09999i
\(977\) −16.4018 22.5751i −0.524739 0.722242i 0.461578 0.887100i \(-0.347283\pi\)
−0.986317 + 0.164858i \(0.947283\pi\)
\(978\) 0.892323i 0.0285333i
\(979\) 47.6894 7.97935i 1.52416 0.255021i
\(980\) 0 0
\(981\) 3.34343 2.42915i 0.106748 0.0775567i
\(982\) −6.46424 + 2.10036i −0.206282 + 0.0670252i
\(983\) −9.31294 3.02596i −0.297037 0.0965130i 0.156708 0.987645i \(-0.449912\pi\)
−0.453744 + 0.891132i \(0.649912\pi\)
\(984\) −9.73387 7.07207i −0.310305 0.225449i
\(985\) 0 0
\(986\) 0.0267218 0.0822412i 0.000850995 0.00261909i
\(987\) 2.75786 0.896084i 0.0877837 0.0285227i
\(988\) −0.0874779 0.120403i −0.00278304 0.00383053i
\(989\) 78.6678 2.50149
\(990\) 0 0
\(991\) 34.9794 1.11116 0.555578 0.831464i \(-0.312497\pi\)
0.555578 + 0.831464i \(0.312497\pi\)
\(992\) −16.9302 23.3024i −0.537533 0.739851i
\(993\) −10.3778 + 3.37196i −0.329331 + 0.107006i
\(994\) 1.20770 3.71692i 0.0383059 0.117894i
\(995\) 0 0
\(996\) 0.386258 + 0.280633i 0.0122390 + 0.00889218i
\(997\) −12.1501 3.94779i −0.384796 0.125028i 0.110230 0.993906i \(-0.464841\pi\)
−0.495026 + 0.868878i \(0.664841\pi\)
\(998\) 6.99839 2.27392i 0.221530 0.0719795i
\(999\) −6.73928 + 4.89637i −0.213221 + 0.154914i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 825.2.bx.f.124.3 16
5.2 odd 4 825.2.n.g.751.2 8
5.3 odd 4 165.2.m.d.91.1 8
5.4 even 2 inner 825.2.bx.f.124.2 16
11.4 even 5 inner 825.2.bx.f.499.2 16
15.8 even 4 495.2.n.a.91.2 8
55.2 even 20 9075.2.a.cm.1.3 4
55.4 even 10 inner 825.2.bx.f.499.3 16
55.13 even 20 1815.2.a.w.1.2 4
55.37 odd 20 825.2.n.g.301.2 8
55.42 odd 20 9075.2.a.di.1.2 4
55.48 odd 20 165.2.m.d.136.1 yes 8
55.53 odd 20 1815.2.a.p.1.3 4
165.53 even 20 5445.2.a.bt.1.2 4
165.68 odd 20 5445.2.a.bf.1.3 4
165.158 even 20 495.2.n.a.136.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.d.91.1 8 5.3 odd 4
165.2.m.d.136.1 yes 8 55.48 odd 20
495.2.n.a.91.2 8 15.8 even 4
495.2.n.a.136.2 8 165.158 even 20
825.2.n.g.301.2 8 55.37 odd 20
825.2.n.g.751.2 8 5.2 odd 4
825.2.bx.f.124.2 16 5.4 even 2 inner
825.2.bx.f.124.3 16 1.1 even 1 trivial
825.2.bx.f.499.2 16 11.4 even 5 inner
825.2.bx.f.499.3 16 55.4 even 10 inner
1815.2.a.p.1.3 4 55.53 odd 20
1815.2.a.w.1.2 4 55.13 even 20
5445.2.a.bf.1.3 4 165.68 odd 20
5445.2.a.bt.1.2 4 165.53 even 20
9075.2.a.cm.1.3 4 55.2 even 20
9075.2.a.di.1.2 4 55.42 odd 20