Properties

Label 300.3.u.a.47.88
Level $300$
Weight $3$
Character 300.47
Analytic conductor $8.174$
Analytic rank $0$
Dimension $928$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [300,3,Mod(23,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 10, 11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.u (of order \(20\), degree \(8\), 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: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(928\)
Relative dimension: \(116\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 47.88
Character \(\chi\) \(=\) 300.47
Dual form 300.3.u.a.83.88

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.41582 - 1.41260i) q^{2} +(1.99269 + 2.24259i) q^{3} +(0.00911459 - 3.99999i) q^{4} +(-2.76818 - 4.16380i) q^{5} +(5.98918 + 0.360232i) q^{6} +(2.17959 - 2.17959i) q^{7} +(-5.63749 - 5.67616i) q^{8} +(-1.05838 + 8.93755i) q^{9} +O(q^{10})\) \(q+(1.41582 - 1.41260i) q^{2} +(1.99269 + 2.24259i) q^{3} +(0.00911459 - 3.99999i) q^{4} +(-2.76818 - 4.16380i) q^{5} +(5.98918 + 0.360232i) q^{6} +(2.17959 - 2.17959i) q^{7} +(-5.63749 - 5.67616i) q^{8} +(-1.05838 + 8.93755i) q^{9} +(-9.80103 - 1.98488i) q^{10} +(5.18256 - 15.9503i) q^{11} +(8.98848 - 7.95029i) q^{12} +(5.69035 + 2.89938i) q^{13} +(0.00702372 - 6.16480i) q^{14} +(3.82156 - 14.5050i) q^{15} +(-15.9998 - 0.0729166i) q^{16} +(2.94865 - 18.6170i) q^{17} +(11.1267 + 14.1491i) q^{18} +(-0.956694 + 0.695079i) q^{19} +(-16.6804 + 11.0347i) q^{20} +(9.23116 + 0.544674i) q^{21} +(-15.1938 - 29.9037i) q^{22} +(3.62519 + 7.11483i) q^{23} +(1.49551 - 23.9534i) q^{24} +(-9.67441 + 23.0522i) q^{25} +(12.1522 - 3.93318i) q^{26} +(-22.1523 + 15.4362i) q^{27} +(-8.69847 - 8.73820i) q^{28} +(28.2236 + 20.5057i) q^{29} +(-15.0792 - 25.9349i) q^{30} +(-2.12066 - 2.91884i) q^{31} +(-22.7559 + 22.4982i) q^{32} +(46.0971 - 20.1616i) q^{33} +(-22.1237 - 30.5237i) q^{34} +(-15.1089 - 3.04188i) q^{35} +(35.7405 + 4.31499i) q^{36} +(9.94115 - 19.5106i) q^{37} +(-0.372641 + 2.33554i) q^{38} +(4.83699 + 18.5386i) q^{39} +(-8.02881 + 39.1859i) q^{40} +(55.8084 - 18.1332i) q^{41} +(13.8391 - 12.2688i) q^{42} +(-14.0645 - 14.0645i) q^{43} +(-63.7537 - 20.8756i) q^{44} +(40.1439 - 20.3338i) q^{45} +(15.1830 + 4.95240i) q^{46} +(4.21566 + 26.6166i) q^{47} +(-31.7192 - 36.0263i) q^{48} +39.4988i q^{49} +(18.8664 + 46.3040i) q^{50} +(47.6260 - 30.4853i) q^{51} +(11.6493 - 22.7349i) q^{52} +(7.38747 + 46.6427i) q^{53} +(-9.55844 + 53.1473i) q^{54} +(-80.7600 + 22.5740i) q^{55} +(-24.6591 - 0.0842845i) q^{56} +(-3.46517 - 0.760393i) q^{57} +(68.9260 - 10.8363i) q^{58} +(-94.7509 + 30.7864i) q^{59} +(-57.9851 - 15.4184i) q^{60} +(-24.4629 + 75.2889i) q^{61} +(-7.12565 - 1.13692i) q^{62} +(17.1733 + 21.7870i) q^{63} +(-0.437497 + 63.9985i) q^{64} +(-3.67946 - 31.7194i) q^{65} +(36.7851 - 93.6621i) q^{66} +(3.32405 - 20.9872i) q^{67} +(-74.4410 - 11.9642i) q^{68} +(-8.73175 + 22.3074i) q^{69} +(-25.6884 + 17.0360i) q^{70} +(65.5003 + 47.5888i) q^{71} +(56.6976 - 44.3778i) q^{72} +(20.7394 + 40.7033i) q^{73} +(-13.4858 - 41.6665i) q^{74} +(-70.9747 + 24.2402i) q^{75} +(2.77159 + 3.83310i) q^{76} +(-23.4692 - 46.0609i) q^{77} +(33.0360 + 19.4147i) q^{78} +(-13.2556 - 9.63079i) q^{79} +(43.9867 + 66.8219i) q^{80} +(-78.7596 - 18.9187i) q^{81} +(53.3998 - 104.508i) q^{82} +(22.3634 - 141.197i) q^{83} +(2.26283 - 36.9196i) q^{84} +(-85.6799 + 39.2576i) q^{85} +(-39.7805 - 0.0453230i) q^{86} +(10.2552 + 104.155i) q^{87} +(-119.753 + 60.5025i) q^{88} +(35.3586 - 108.823i) q^{89} +(28.1132 - 85.4965i) q^{90} +(18.7221 - 6.08317i) q^{91} +(28.4923 - 14.4359i) q^{92} +(2.31993 - 10.5721i) q^{93} +(43.5673 + 31.7294i) q^{94} +(5.54246 + 2.05938i) q^{95} +(-95.7996 - 6.20037i) q^{96} +(14.4379 + 91.1575i) q^{97} +(55.7960 + 55.9233i) q^{98} +(137.071 + 63.2009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9} - 8 q^{10} + 10 q^{12} - 32 q^{13} - 12 q^{16} + 14 q^{18} - 12 q^{21} + 56 q^{22} - 32 q^{25} + 64 q^{28} - 78 q^{30} + 20 q^{33} - 20 q^{34} - 70 q^{36} - 124 q^{40} + 454 q^{42} + 84 q^{45} - 12 q^{46} - 76 q^{48} - 324 q^{52} - 660 q^{54} + 52 q^{57} - 200 q^{58} - 826 q^{60} - 24 q^{61} - 20 q^{64} + 138 q^{66} - 20 q^{69} + 352 q^{70} + 590 q^{72} - 144 q^{73} + 96 q^{76} + 308 q^{78} - 12 q^{81} + 20 q^{82} - 10 q^{84} + 864 q^{85} - 760 q^{88} - 538 q^{90} - 388 q^{93} - 1420 q^{94} - 6 q^{96} + 288 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{17}{20}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41582 1.41260i 0.707912 0.706301i
\(3\) 1.99269 + 2.24259i 0.664230 + 0.747529i
\(4\) 0.00911459 3.99999i 0.00227865 0.999997i
\(5\) −2.76818 4.16380i −0.553635 0.832759i
\(6\) 5.98918 + 0.360232i 0.998196 + 0.0600387i
\(7\) 2.17959 2.17959i 0.311370 0.311370i −0.534070 0.845440i \(-0.679338\pi\)
0.845440 + 0.534070i \(0.179338\pi\)
\(8\) −5.63749 5.67616i −0.704686 0.709520i
\(9\) −1.05838 + 8.93755i −0.117598 + 0.993061i
\(10\) −9.80103 1.98488i −0.980103 0.198488i
\(11\) 5.18256 15.9503i 0.471142 1.45003i −0.379949 0.925007i \(-0.624059\pi\)
0.851091 0.525018i \(-0.175941\pi\)
\(12\) 8.98848 7.95029i 0.749040 0.662524i
\(13\) 5.69035 + 2.89938i 0.437719 + 0.223029i 0.658941 0.752195i \(-0.271005\pi\)
−0.221222 + 0.975223i \(0.571005\pi\)
\(14\) 0.00702372 6.16480i 0.000501694 0.440343i
\(15\) 3.82156 14.5050i 0.254771 0.967001i
\(16\) −15.9998 0.0729166i −0.999990 0.00455729i
\(17\) 2.94865 18.6170i 0.173450 1.09512i −0.735289 0.677754i \(-0.762954\pi\)
0.908739 0.417365i \(-0.137046\pi\)
\(18\) 11.1267 + 14.1491i 0.618151 + 0.786060i
\(19\) −0.956694 + 0.695079i −0.0503523 + 0.0365831i −0.612677 0.790334i \(-0.709907\pi\)
0.562324 + 0.826917i \(0.309907\pi\)
\(20\) −16.6804 + 11.0347i −0.834019 + 0.551736i
\(21\) 9.23116 + 0.544674i 0.439579 + 0.0259368i
\(22\) −15.1938 29.9037i −0.690627 1.35926i
\(23\) 3.62519 + 7.11483i 0.157617 + 0.309340i 0.956288 0.292428i \(-0.0944631\pi\)
−0.798671 + 0.601768i \(0.794463\pi\)
\(24\) 1.49551 23.9534i 0.0623131 0.998057i
\(25\) −9.67441 + 23.0522i −0.386976 + 0.922090i
\(26\) 12.1522 3.93318i 0.467392 0.151276i
\(27\) −22.1523 + 15.4362i −0.820454 + 0.571713i
\(28\) −8.69847 8.73820i −0.310660 0.312079i
\(29\) 28.2236 + 20.5057i 0.973229 + 0.707092i 0.956185 0.292763i \(-0.0945746\pi\)
0.0170435 + 0.999855i \(0.494575\pi\)
\(30\) −15.0792 25.9349i −0.502639 0.864497i
\(31\) −2.12066 2.91884i −0.0684085 0.0941562i 0.773442 0.633867i \(-0.218533\pi\)
−0.841850 + 0.539711i \(0.818533\pi\)
\(32\) −22.7559 + 22.4982i −0.711123 + 0.703067i
\(33\) 46.0971 20.1616i 1.39688 0.610958i
\(34\) −22.1237 30.5237i −0.650696 0.897755i
\(35\) −15.1089 3.04188i −0.431681 0.0869109i
\(36\) 35.7405 + 4.31499i 0.992791 + 0.119861i
\(37\) 9.94115 19.5106i 0.268680 0.527314i −0.716764 0.697316i \(-0.754377\pi\)
0.985444 + 0.170002i \(0.0543775\pi\)
\(38\) −0.372641 + 2.33554i −0.00980634 + 0.0614615i
\(39\) 4.83699 + 18.5386i 0.124025 + 0.475350i
\(40\) −8.02881 + 39.1859i −0.200720 + 0.979649i
\(41\) 55.8084 18.1332i 1.36118 0.442274i 0.464743 0.885446i \(-0.346147\pi\)
0.896437 + 0.443172i \(0.146147\pi\)
\(42\) 13.8391 12.2688i 0.329502 0.292114i
\(43\) −14.0645 14.0645i −0.327082 0.327082i 0.524394 0.851476i \(-0.324292\pi\)
−0.851476 + 0.524394i \(0.824292\pi\)
\(44\) −63.7537 20.8756i −1.44895 0.474445i
\(45\) 40.1439 20.3338i 0.892088 0.451862i
\(46\) 15.1830 + 4.95240i 0.330066 + 0.107661i
\(47\) 4.21566 + 26.6166i 0.0896948 + 0.566311i 0.991077 + 0.133287i \(0.0425533\pi\)
−0.901383 + 0.433024i \(0.857447\pi\)
\(48\) −31.7192 36.0263i −0.660816 0.750548i
\(49\) 39.4988i 0.806098i
\(50\) 18.8664 + 46.3040i 0.377327 + 0.926080i
\(51\) 47.6260 30.4853i 0.933843 0.597752i
\(52\) 11.6493 22.7349i 0.224026 0.437210i
\(53\) 7.38747 + 46.6427i 0.139386 + 0.880050i 0.953948 + 0.299973i \(0.0969777\pi\)
−0.814561 + 0.580077i \(0.803022\pi\)
\(54\) −9.55844 + 53.1473i −0.177008 + 0.984209i
\(55\) −80.7600 + 22.5740i −1.46836 + 0.410437i
\(56\) −24.6591 0.0842845i −0.440341 0.00150508i
\(57\) −3.46517 0.760393i −0.0607924 0.0133402i
\(58\) 68.9260 10.8363i 1.18838 0.186833i
\(59\) −94.7509 + 30.7864i −1.60595 + 0.521804i −0.968568 0.248747i \(-0.919981\pi\)
−0.637378 + 0.770551i \(0.719981\pi\)
\(60\) −57.9851 15.4184i −0.966418 0.256974i
\(61\) −24.4629 + 75.2889i −0.401030 + 1.23424i 0.523134 + 0.852250i \(0.324763\pi\)
−0.924165 + 0.381994i \(0.875237\pi\)
\(62\) −7.12565 1.13692i −0.114930 0.0183373i
\(63\) 17.1733 + 21.7870i 0.272593 + 0.345826i
\(64\) −0.437497 + 63.9985i −0.00683590 + 0.999977i
\(65\) −3.67946 31.7194i −0.0566071 0.487991i
\(66\) 36.7851 93.6621i 0.557350 1.41912i
\(67\) 3.32405 20.9872i 0.0496127 0.313242i −0.950385 0.311076i \(-0.899311\pi\)
0.999998 0.00216599i \(-0.000689455\pi\)
\(68\) −74.4410 11.9642i −1.09472 0.175945i
\(69\) −8.73175 + 22.3074i −0.126547 + 0.323296i
\(70\) −25.6884 + 17.0360i −0.366978 + 0.243372i
\(71\) 65.5003 + 47.5888i 0.922540 + 0.670264i 0.944155 0.329502i \(-0.106881\pi\)
−0.0216151 + 0.999766i \(0.506881\pi\)
\(72\) 56.6976 44.3778i 0.787466 0.616358i
\(73\) 20.7394 + 40.7033i 0.284101 + 0.557579i 0.988318 0.152405i \(-0.0487019\pi\)
−0.704217 + 0.709984i \(0.748702\pi\)
\(74\) −13.4858 41.6665i −0.182240 0.563060i
\(75\) −70.9747 + 24.2402i −0.946330 + 0.323203i
\(76\) 2.77159 + 3.83310i 0.0364683 + 0.0504355i
\(77\) −23.4692 46.0609i −0.304795 0.598194i
\(78\) 33.0360 + 19.4147i 0.423539 + 0.248907i
\(79\) −13.2556 9.63079i −0.167793 0.121909i 0.500720 0.865609i \(-0.333069\pi\)
−0.668513 + 0.743701i \(0.733069\pi\)
\(80\) 43.9867 + 66.8219i 0.549834 + 0.835274i
\(81\) −78.7596 18.9187i −0.972341 0.233565i
\(82\) 53.3998 104.508i 0.651217 1.27449i
\(83\) 22.3634 141.197i 0.269439 1.70117i −0.367309 0.930099i \(-0.619721\pi\)
0.636748 0.771072i \(-0.280279\pi\)
\(84\) 2.26283 36.9196i 0.0269384 0.439519i
\(85\) −85.6799 + 39.2576i −1.00800 + 0.461854i
\(86\) −39.7805 0.0453230i −0.462564 0.000527011i
\(87\) 10.2552 + 104.155i 0.117876 + 1.19719i
\(88\) −119.753 + 60.5025i −1.36083 + 0.687528i
\(89\) 35.3586 108.823i 0.397288 1.22273i −0.529877 0.848074i \(-0.677762\pi\)
0.927165 0.374653i \(-0.122238\pi\)
\(90\) 28.1132 85.4965i 0.312369 0.949961i
\(91\) 18.7221 6.08317i 0.205737 0.0668480i
\(92\) 28.4923 14.4359i 0.309699 0.156911i
\(93\) 2.31993 10.5721i 0.0249455 0.113679i
\(94\) 43.5673 + 31.7294i 0.463482 + 0.337547i
\(95\) 5.54246 + 2.05938i 0.0583417 + 0.0216777i
\(96\) −95.7996 6.20037i −0.997912 0.0645871i
\(97\) 14.4379 + 91.1575i 0.148845 + 0.939768i 0.943178 + 0.332287i \(0.107820\pi\)
−0.794334 + 0.607482i \(0.792180\pi\)
\(98\) 55.7960 + 55.9233i 0.569347 + 0.570646i
\(99\) 137.071 + 63.2009i 1.38456 + 0.638393i
\(100\) 92.1205 + 38.9077i 0.921205 + 0.389077i
\(101\) 73.1689i 0.724444i 0.932092 + 0.362222i \(0.117982\pi\)
−0.932092 + 0.362222i \(0.882018\pi\)
\(102\) 24.3664 110.438i 0.238886 1.08273i
\(103\) 30.0134 + 189.497i 0.291392 + 1.83978i 0.505323 + 0.862930i \(0.331373\pi\)
−0.213931 + 0.976849i \(0.568627\pi\)
\(104\) −15.6219 48.6445i −0.150211 0.467735i
\(105\) −23.2856 39.9444i −0.221767 0.380423i
\(106\) 76.3469 + 55.6022i 0.720253 + 0.524549i
\(107\) −78.9141 78.9141i −0.737515 0.737515i 0.234582 0.972096i \(-0.424628\pi\)
−0.972096 + 0.234582i \(0.924628\pi\)
\(108\) 61.5429 + 88.7495i 0.569842 + 0.821755i
\(109\) 190.355 61.8502i 1.74638 0.567433i 0.750729 0.660610i \(-0.229702\pi\)
0.995650 + 0.0931770i \(0.0297022\pi\)
\(110\) −82.4538 + 146.043i −0.749580 + 1.32766i
\(111\) 63.5638 16.5847i 0.572647 0.149411i
\(112\) −35.0320 + 34.7141i −0.312786 + 0.309948i
\(113\) −65.5584 + 128.666i −0.580163 + 1.13863i 0.395317 + 0.918545i \(0.370635\pi\)
−0.975480 + 0.220089i \(0.929365\pi\)
\(114\) −5.98020 + 3.81832i −0.0524579 + 0.0334940i
\(115\) 19.5895 34.7896i 0.170344 0.302518i
\(116\) 82.2797 112.707i 0.709308 0.971615i
\(117\) −31.9359 + 47.7891i −0.272956 + 0.408454i
\(118\) −90.6616 + 177.433i −0.768319 + 1.50367i
\(119\) −34.1506 47.0043i −0.286980 0.394994i
\(120\) −103.877 + 60.0801i −0.865640 + 0.500667i
\(121\) −129.661 94.2046i −1.07158 0.778550i
\(122\) 71.7182 + 141.152i 0.587854 + 1.15698i
\(123\) 151.874 + 89.0212i 1.23475 + 0.723749i
\(124\) −11.6947 + 8.45603i −0.0943118 + 0.0681938i
\(125\) 122.765 23.5304i 0.982123 0.188243i
\(126\) 55.0908 + 6.58751i 0.437229 + 0.0522818i
\(127\) −10.0823 19.7875i −0.0793878 0.155807i 0.847900 0.530156i \(-0.177866\pi\)
−0.927288 + 0.374348i \(0.877866\pi\)
\(128\) 89.7850 + 91.2286i 0.701445 + 0.712724i
\(129\) 3.51469 59.5672i 0.0272457 0.461761i
\(130\) −50.0164 39.7115i −0.384741 0.305473i
\(131\) 84.6261 61.4844i 0.646001 0.469347i −0.215906 0.976414i \(-0.569270\pi\)
0.861906 + 0.507067i \(0.169270\pi\)
\(132\) −80.2261 184.572i −0.607773 1.39827i
\(133\) −0.570213 + 3.60019i −0.00428732 + 0.0270691i
\(134\) −24.9403 34.4098i −0.186122 0.256789i
\(135\) 125.595 + 49.5073i 0.930331 + 0.366721i
\(136\) −122.296 + 88.2162i −0.899236 + 0.648649i
\(137\) −51.4204 26.2000i −0.375331 0.191241i 0.256141 0.966640i \(-0.417549\pi\)
−0.631472 + 0.775399i \(0.717549\pi\)
\(138\) 19.1489 + 43.9179i 0.138760 + 0.318245i
\(139\) 33.0322 101.663i 0.237642 0.731386i −0.759118 0.650953i \(-0.774370\pi\)
0.996760 0.0804335i \(-0.0256305\pi\)
\(140\) −12.3052 + 60.4075i −0.0878943 + 0.431482i
\(141\) −51.2895 + 62.4926i −0.363756 + 0.443210i
\(142\) 159.961 25.1485i 1.12649 0.177102i
\(143\) 75.7364 75.7364i 0.529625 0.529625i
\(144\) 17.5857 142.922i 0.122123 0.992515i
\(145\) 7.25348 174.281i 0.0500240 1.20194i
\(146\) 86.8608 + 28.3322i 0.594937 + 0.194056i
\(147\) −88.5794 + 78.7088i −0.602581 + 0.535434i
\(148\) −77.9516 39.9423i −0.526700 0.269881i
\(149\) 98.5283 0.661264 0.330632 0.943760i \(-0.392738\pi\)
0.330632 + 0.943760i \(0.392738\pi\)
\(150\) −66.2459 + 134.579i −0.441639 + 0.897193i
\(151\) 183.847i 1.21753i −0.793350 0.608766i \(-0.791665\pi\)
0.793350 0.608766i \(-0.208335\pi\)
\(152\) 9.33873 + 1.51185i 0.0614390 + 0.00994636i
\(153\) 163.270 + 46.0576i 1.06712 + 0.301030i
\(154\) −98.2940 32.0615i −0.638272 0.208192i
\(155\) −6.28310 + 16.9099i −0.0405361 + 0.109096i
\(156\) 74.1985 19.1789i 0.475631 0.122942i
\(157\) 159.097 + 159.097i 1.01335 + 1.01335i 0.999910 + 0.0134442i \(0.00427954\pi\)
0.0134442 + 0.999910i \(0.495720\pi\)
\(158\) −32.3721 + 5.08944i −0.204887 + 0.0322116i
\(159\) −89.8793 + 109.511i −0.565278 + 0.688751i
\(160\) 156.670 + 32.4723i 0.979189 + 0.202952i
\(161\) 23.4088 + 7.60598i 0.145396 + 0.0472421i
\(162\) −138.234 + 84.4704i −0.853299 + 0.521422i
\(163\) −22.5280 + 44.2136i −0.138208 + 0.271249i −0.949728 0.313076i \(-0.898641\pi\)
0.811520 + 0.584325i \(0.198641\pi\)
\(164\) −72.0241 223.398i −0.439171 1.36218i
\(165\) −211.554 136.128i −1.28214 0.825019i
\(166\) −167.793 231.501i −1.01080 1.39458i
\(167\) −284.229 45.0175i −1.70197 0.269566i −0.771580 0.636132i \(-0.780533\pi\)
−0.930392 + 0.366566i \(0.880533\pi\)
\(168\) −48.9489 55.4681i −0.291362 0.330167i
\(169\) −75.3621 103.727i −0.445929 0.613769i
\(170\) −65.8522 + 176.613i −0.387366 + 1.03890i
\(171\) −5.19975 9.28616i −0.0304079 0.0543050i
\(172\) −56.3862 + 56.1298i −0.327827 + 0.326336i
\(173\) −74.9154 + 38.1713i −0.433037 + 0.220643i −0.656901 0.753977i \(-0.728133\pi\)
0.223864 + 0.974620i \(0.428133\pi\)
\(174\) 161.649 + 132.979i 0.929020 + 0.764248i
\(175\) 29.1582 + 71.3306i 0.166618 + 0.407604i
\(176\) −84.0831 + 254.824i −0.477745 + 1.44786i
\(177\) −257.850 151.139i −1.45678 0.853894i
\(178\) −103.661 204.021i −0.582368 1.14619i
\(179\) 144.076 198.304i 0.804894 1.10784i −0.187198 0.982322i \(-0.559940\pi\)
0.992091 0.125519i \(-0.0400595\pi\)
\(180\) −80.9691 160.761i −0.449829 0.893115i
\(181\) −159.549 + 115.919i −0.881486 + 0.640437i −0.933644 0.358202i \(-0.883390\pi\)
0.0521582 + 0.998639i \(0.483390\pi\)
\(182\) 17.9141 35.0595i 0.0984289 0.192635i
\(183\) −217.589 + 95.1673i −1.18901 + 0.520040i
\(184\) 19.9479 60.6869i 0.108413 0.329820i
\(185\) −108.757 + 12.6158i −0.587876 + 0.0681938i
\(186\) −11.6496 18.2454i −0.0626321 0.0980935i
\(187\) −281.665 143.516i −1.50623 0.767463i
\(188\) 106.505 16.6200i 0.566514 0.0884042i
\(189\) −14.6382 + 81.9275i −0.0774506 + 0.433479i
\(190\) 10.7562 4.91357i 0.0566118 0.0258609i
\(191\) −75.2637 231.638i −0.394051 1.21276i −0.929698 0.368322i \(-0.879932\pi\)
0.535647 0.844442i \(-0.320068\pi\)
\(192\) −144.394 + 126.548i −0.752052 + 0.659104i
\(193\) −44.6628 + 44.6628i −0.231413 + 0.231413i −0.813282 0.581869i \(-0.802322\pi\)
0.581869 + 0.813282i \(0.302322\pi\)
\(194\) 149.211 + 108.668i 0.769128 + 0.560144i
\(195\) 63.8015 71.4584i 0.327187 0.366454i
\(196\) 157.995 + 0.360015i 0.806096 + 0.00183681i
\(197\) −148.228 + 23.4770i −0.752426 + 0.119173i −0.520854 0.853645i \(-0.674387\pi\)
−0.231571 + 0.972818i \(0.574387\pi\)
\(198\) 283.347 104.146i 1.43104 0.525989i
\(199\) 66.3921 0.333628 0.166814 0.985988i \(-0.446652\pi\)
0.166814 + 0.985988i \(0.446652\pi\)
\(200\) 185.387 75.0432i 0.926937 0.375216i
\(201\) 53.6895 34.3665i 0.267112 0.170978i
\(202\) 103.358 + 103.594i 0.511675 + 0.512843i
\(203\) 106.210 16.8220i 0.523201 0.0828669i
\(204\) −121.507 190.781i −0.595622 0.935203i
\(205\) −229.990 182.179i −1.12190 0.888677i
\(206\) 310.178 + 225.898i 1.50572 + 1.09659i
\(207\) −67.4260 + 24.8701i −0.325729 + 0.120145i
\(208\) −90.8332 46.8044i −0.436698 0.225021i
\(209\) 6.12858 + 18.8618i 0.0293233 + 0.0902480i
\(210\) −89.3938 23.6611i −0.425685 0.112672i
\(211\) 227.475 + 73.9112i 1.07808 + 0.350290i 0.793631 0.608400i \(-0.208188\pi\)
0.284452 + 0.958690i \(0.408188\pi\)
\(212\) 186.638 29.1247i 0.880366 0.137381i
\(213\) 23.7998 + 241.720i 0.111736 + 1.13483i
\(214\) −223.203 0.254300i −1.04300 0.00118832i
\(215\) −19.6288 + 97.4950i −0.0912967 + 0.453465i
\(216\) 212.502 + 38.7181i 0.983803 + 0.179250i
\(217\) −10.9841 1.73970i −0.0506177 0.00801706i
\(218\) 182.140 356.465i 0.835504 1.63516i
\(219\) −49.9535 + 127.619i −0.228098 + 0.582734i
\(220\) 89.5598 + 323.245i 0.407090 + 1.46929i
\(221\) 70.7566 97.3880i 0.320165 0.440670i
\(222\) 66.5676 113.271i 0.299854 0.510231i
\(223\) −178.181 + 90.7880i −0.799020 + 0.407121i −0.805306 0.592859i \(-0.797999\pi\)
0.00628630 + 0.999980i \(0.497999\pi\)
\(224\) −0.561895 + 98.6353i −0.00250846 + 0.440336i
\(225\) −195.791 110.864i −0.870184 0.492727i
\(226\) 88.9341 + 274.776i 0.393514 + 1.21582i
\(227\) 139.963 71.3148i 0.616578 0.314162i −0.117660 0.993054i \(-0.537539\pi\)
0.734238 + 0.678892i \(0.237539\pi\)
\(228\) −3.07315 + 13.8537i −0.0134787 + 0.0607619i
\(229\) 232.073 319.421i 1.01342 1.39485i 0.0966999 0.995314i \(-0.469171\pi\)
0.916718 0.399536i \(-0.130829\pi\)
\(230\) −21.4085 76.9282i −0.0930805 0.334470i
\(231\) 56.5287 144.417i 0.244713 0.625181i
\(232\) −42.7170 275.802i −0.184125 1.18880i
\(233\) 149.393 + 23.6616i 0.641173 + 0.101552i 0.468551 0.883436i \(-0.344776\pi\)
0.172622 + 0.984988i \(0.444776\pi\)
\(234\) 22.2913 + 112.774i 0.0952622 + 0.481939i
\(235\) 99.1565 91.2326i 0.421943 0.388224i
\(236\) 122.282 + 379.283i 0.518143 + 1.60713i
\(237\) −4.81650 48.9181i −0.0203228 0.206405i
\(238\) −114.750 18.3086i −0.482141 0.0769268i
\(239\) −19.3151 6.27587i −0.0808164 0.0262589i 0.268330 0.963327i \(-0.413528\pi\)
−0.349146 + 0.937068i \(0.613528\pi\)
\(240\) −62.2020 + 231.799i −0.259175 + 0.965830i
\(241\) −55.1634 169.775i −0.228894 0.704463i −0.997873 0.0651887i \(-0.979235\pi\)
0.768979 0.639274i \(-0.220765\pi\)
\(242\) −316.651 + 49.7829i −1.30848 + 0.205714i
\(243\) −114.517 214.324i −0.471262 0.881993i
\(244\) 300.932 + 98.5374i 1.23333 + 0.403842i
\(245\) 164.465 109.340i 0.671285 0.446284i
\(246\) 340.778 88.4992i 1.38528 0.359753i
\(247\) −7.45921 + 1.18142i −0.0301992 + 0.00478309i
\(248\) −4.61260 + 28.4921i −0.0185992 + 0.114888i
\(249\) 361.210 231.210i 1.45064 0.928555i
\(250\) 140.575 206.733i 0.562300 0.826933i
\(251\) −313.031 −1.24713 −0.623567 0.781770i \(-0.714317\pi\)
−0.623567 + 0.781770i \(0.714317\pi\)
\(252\) 87.3044 68.4946i 0.346446 0.271804i
\(253\) 132.271 20.9497i 0.522811 0.0828052i
\(254\) −42.2266 13.7735i −0.166246 0.0542262i
\(255\) −258.772 113.916i −1.01479 0.446730i
\(256\) 255.989 + 2.33331i 0.999958 + 0.00911448i
\(257\) −320.038 + 320.038i −1.24528 + 1.24528i −0.287504 + 0.957779i \(0.592825\pi\)
−0.957779 + 0.287504i \(0.907175\pi\)
\(258\) −79.1685 89.3016i −0.306855 0.346130i
\(259\) −20.8575 64.1927i −0.0805308 0.247848i
\(260\) −126.911 + 14.4287i −0.488119 + 0.0554950i
\(261\) −213.142 + 230.547i −0.816636 + 0.883323i
\(262\) 32.9626 206.594i 0.125811 0.788527i
\(263\) −300.822 153.276i −1.14381 0.582800i −0.223776 0.974641i \(-0.571838\pi\)
−0.920033 + 0.391841i \(0.871838\pi\)
\(264\) −374.312 147.994i −1.41785 0.560582i
\(265\) 173.761 159.875i 0.655701 0.603302i
\(266\) 4.27831 + 5.90271i 0.0160839 + 0.0221907i
\(267\) 314.503 137.555i 1.17791 0.515187i
\(268\) −83.9184 13.4875i −0.313128 0.0503263i
\(269\) −104.996 + 76.2842i −0.390320 + 0.283584i −0.765587 0.643333i \(-0.777551\pi\)
0.375266 + 0.926917i \(0.377551\pi\)
\(270\) 247.754 107.322i 0.917608 0.397488i
\(271\) −263.327 + 362.439i −0.971688 + 1.33741i −0.0304986 + 0.999535i \(0.509710\pi\)
−0.941190 + 0.337879i \(0.890290\pi\)
\(272\) −48.5353 + 297.654i −0.178439 + 1.09432i
\(273\) 50.9493 + 29.8640i 0.186627 + 0.109392i
\(274\) −109.812 + 35.5419i −0.400775 + 0.129715i
\(275\) 317.551 + 273.779i 1.15473 + 0.995561i
\(276\) 89.1499 + 35.1302i 0.323007 + 0.127283i
\(277\) 269.833 137.487i 0.974125 0.496341i 0.106906 0.994269i \(-0.465906\pi\)
0.867219 + 0.497928i \(0.165906\pi\)
\(278\) −96.8411 190.598i −0.348349 0.685604i
\(279\) 28.3318 15.8643i 0.101548 0.0568612i
\(280\) 67.9097 + 102.909i 0.242535 + 0.367531i
\(281\) −141.333 194.528i −0.502963 0.692270i 0.479750 0.877405i \(-0.340728\pi\)
−0.982713 + 0.185136i \(0.940728\pi\)
\(282\) 15.6602 + 160.930i 0.0555325 + 0.570674i
\(283\) 438.471 + 69.4470i 1.54937 + 0.245396i 0.871725 0.489996i \(-0.163002\pi\)
0.677642 + 0.735392i \(0.263002\pi\)
\(284\) 190.952 261.567i 0.672365 0.921010i
\(285\) 6.42607 + 16.5332i 0.0225476 + 0.0580111i
\(286\) 0.244060 214.215i 0.000853358 0.749003i
\(287\) 82.1163 161.162i 0.286119 0.561541i
\(288\) −176.994 227.194i −0.614562 0.788869i
\(289\) −63.0436 20.4841i −0.218144 0.0708793i
\(290\) −235.920 256.997i −0.813516 0.886197i
\(291\) −175.658 + 214.027i −0.603637 + 0.735488i
\(292\) 163.002 82.5862i 0.558225 0.282829i
\(293\) −365.083 365.083i −1.24602 1.24602i −0.957464 0.288553i \(-0.906826\pi\)
−0.288553 0.957464i \(-0.593174\pi\)
\(294\) −14.2287 + 236.565i −0.0483971 + 0.804643i
\(295\) 390.475 + 309.301i 1.32365 + 1.04848i
\(296\) −166.788 + 53.5632i −0.563474 + 0.180957i
\(297\) 131.407 + 433.334i 0.442448 + 1.45904i
\(298\) 139.499 139.181i 0.468117 0.467051i
\(299\) 50.9966i 0.170557i
\(300\) 96.3138 + 284.119i 0.321046 + 0.947064i
\(301\) −61.3099 −0.203687
\(302\) −259.703 260.295i −0.859943 0.861905i
\(303\) −164.087 + 145.803i −0.541543 + 0.481197i
\(304\) 15.3576 11.0514i 0.0505185 0.0363532i
\(305\) 381.205 106.555i 1.24985 0.349359i
\(306\) 296.222 165.426i 0.968047 0.540607i
\(307\) −118.940 + 118.940i −0.387428 + 0.387428i −0.873769 0.486341i \(-0.838331\pi\)
0.486341 + 0.873769i \(0.338331\pi\)
\(308\) −184.457 + 93.4567i −0.598887 + 0.303431i
\(309\) −365.156 + 444.917i −1.18174 + 1.43986i
\(310\) 14.9912 + 32.8169i 0.0483586 + 0.105861i
\(311\) −23.7306 + 73.0352i −0.0763041 + 0.234840i −0.981932 0.189233i \(-0.939400\pi\)
0.905628 + 0.424073i \(0.139400\pi\)
\(312\) 77.9598 131.967i 0.249871 0.422971i
\(313\) 124.226 + 63.2963i 0.396888 + 0.202225i 0.641032 0.767515i \(-0.278507\pi\)
−0.244143 + 0.969739i \(0.578507\pi\)
\(314\) 449.993 + 0.512688i 1.43310 + 0.00163277i
\(315\) 43.1779 131.817i 0.137073 0.418466i
\(316\) −38.6439 + 52.9346i −0.122291 + 0.167515i
\(317\) −35.7917 + 225.980i −0.112908 + 0.712871i 0.864677 + 0.502328i \(0.167523\pi\)
−0.977585 + 0.210543i \(0.932477\pi\)
\(318\) 27.4427 + 282.012i 0.0862978 + 0.886831i
\(319\) 473.342 343.903i 1.48383 1.07807i
\(320\) 267.688 175.337i 0.836525 0.547929i
\(321\) 19.7204 334.223i 0.0614343 1.04119i
\(322\) 43.8870 22.2986i 0.136295 0.0692503i
\(323\) 10.1193 + 19.8603i 0.0313292 + 0.0614871i
\(324\) −76.3926 + 314.865i −0.235780 + 0.971807i
\(325\) −121.888 + 103.125i −0.375040 + 0.317309i
\(326\) 30.5606 + 94.4217i 0.0937441 + 0.289637i
\(327\) 518.023 + 303.640i 1.58417 + 0.928563i
\(328\) −417.546 214.551i −1.27301 0.654119i
\(329\) 67.2017 + 48.8249i 0.204260 + 0.148404i
\(330\) −491.818 + 106.108i −1.49036 + 0.321538i
\(331\) 57.1886 + 78.7134i 0.172775 + 0.237805i 0.886619 0.462500i \(-0.153047\pi\)
−0.713844 + 0.700305i \(0.753047\pi\)
\(332\) −564.583 90.7405i −1.70055 0.273315i
\(333\) 163.855 + 109.499i 0.492058 + 0.328827i
\(334\) −466.010 + 337.766i −1.39524 + 1.01128i
\(335\) −96.5881 + 44.2557i −0.288323 + 0.132106i
\(336\) −147.657 9.38779i −0.439456 0.0279399i
\(337\) −177.847 + 349.044i −0.527736 + 1.03574i 0.461186 + 0.887303i \(0.347424\pi\)
−0.988922 + 0.148436i \(0.952576\pi\)
\(338\) −253.224 40.4026i −0.749184 0.119534i
\(339\) −419.181 + 109.370i −1.23652 + 0.322626i
\(340\) 156.249 + 343.076i 0.459556 + 1.00905i
\(341\) −57.5468 + 18.6981i −0.168759 + 0.0548331i
\(342\) −20.4796 5.80239i −0.0598818 0.0169661i
\(343\) 192.891 + 192.891i 0.562364 + 0.562364i
\(344\) −0.543875 + 159.121i −0.00158103 + 0.462562i
\(345\) 117.055 25.3936i 0.339289 0.0736048i
\(346\) −52.1462 + 159.870i −0.150712 + 0.462051i
\(347\) 14.5334 + 91.7601i 0.0418829 + 0.264438i 0.999740 0.0228073i \(-0.00726042\pi\)
−0.957857 + 0.287246i \(0.907260\pi\)
\(348\) 416.714 40.0713i 1.19745 0.115147i
\(349\) 188.986i 0.541507i −0.962649 0.270753i \(-0.912727\pi\)
0.962649 0.270753i \(-0.0872728\pi\)
\(350\) 142.045 + 59.8028i 0.405842 + 0.170865i
\(351\) −170.809 + 23.6098i −0.486637 + 0.0672644i
\(352\) 240.918 + 479.562i 0.684425 + 1.36239i
\(353\) 12.6824 + 80.0736i 0.0359275 + 0.226838i 0.999118 0.0419809i \(-0.0133669\pi\)
−0.963191 + 0.268818i \(0.913367\pi\)
\(354\) −578.570 + 150.253i −1.63438 + 0.424443i
\(355\) 16.8336 404.464i 0.0474186 1.13934i
\(356\) −434.967 142.426i −1.22182 0.400073i
\(357\) 37.3596 170.251i 0.104649 0.476892i
\(358\) −76.1377 484.285i −0.212675 1.35275i
\(359\) 120.518 39.1586i 0.335704 0.109077i −0.136314 0.990666i \(-0.543526\pi\)
0.472018 + 0.881589i \(0.343526\pi\)
\(360\) −341.729 113.232i −0.949247 0.314533i
\(361\) −111.123 + 342.001i −0.307820 + 0.947372i
\(362\) −62.1457 + 389.500i −0.171673 + 1.07597i
\(363\) −47.1131 478.497i −0.129788 1.31817i
\(364\) −24.1620 74.9435i −0.0663790 0.205889i
\(365\) 112.070 199.028i 0.307041 0.545283i
\(366\) −173.634 + 442.106i −0.474409 + 1.20794i
\(367\) 45.7739 289.005i 0.124725 0.787480i −0.843451 0.537207i \(-0.819479\pi\)
0.968175 0.250273i \(-0.0805205\pi\)
\(368\) −57.4836 114.100i −0.156205 0.310055i
\(369\) 103.000 + 517.982i 0.279133 + 1.40375i
\(370\) −136.160 + 171.492i −0.367999 + 0.463492i
\(371\) 117.763 + 85.5602i 0.317422 + 0.230620i
\(372\) −42.2672 9.37607i −0.113622 0.0252045i
\(373\) −50.4133 98.9416i −0.135156 0.265259i 0.813502 0.581562i \(-0.197558\pi\)
−0.948658 + 0.316303i \(0.897558\pi\)
\(374\) −601.519 + 194.688i −1.60834 + 0.520556i
\(375\) 297.402 + 228.423i 0.793072 + 0.609128i
\(376\) 127.314 173.980i 0.338602 0.462711i
\(377\) 101.149 + 198.515i 0.268299 + 0.526566i
\(378\) 95.0058 + 136.673i 0.251338 + 0.361568i
\(379\) −420.270 305.344i −1.10889 0.805657i −0.126403 0.991979i \(-0.540343\pi\)
−0.982489 + 0.186322i \(0.940343\pi\)
\(380\) 8.28801 22.1510i 0.0218106 0.0582922i
\(381\) 24.2845 62.0407i 0.0637388 0.162837i
\(382\) −433.772 221.641i −1.13553 0.580212i
\(383\) −70.3288 + 444.039i −0.183626 + 1.15937i 0.707870 + 0.706342i \(0.249656\pi\)
−0.891497 + 0.453027i \(0.850344\pi\)
\(384\) −25.6746 + 383.141i −0.0668609 + 0.997762i
\(385\) −126.821 + 225.226i −0.329406 + 0.585002i
\(386\) −0.143926 + 126.325i −0.000372865 + 0.327268i
\(387\) 140.588 110.817i 0.363277 0.286349i
\(388\) 364.761 56.9207i 0.940105 0.146703i
\(389\) 215.239 662.438i 0.553314 1.70293i −0.147041 0.989130i \(-0.546975\pi\)
0.700355 0.713795i \(-0.253025\pi\)
\(390\) −10.6106 191.299i −0.0272066 0.490509i
\(391\) 143.146 46.5110i 0.366103 0.118954i
\(392\) 224.201 222.674i 0.571942 0.568046i
\(393\) 306.518 + 67.2619i 0.779943 + 0.171150i
\(394\) −176.701 + 242.626i −0.448479 + 0.615802i
\(395\) −3.40670 + 81.8535i −0.00862457 + 0.207224i
\(396\) 254.052 547.708i 0.641546 1.38310i
\(397\) 62.1540 + 392.425i 0.156559 + 0.988476i 0.933415 + 0.358798i \(0.116813\pi\)
−0.776856 + 0.629678i \(0.783187\pi\)
\(398\) 93.9995 93.7855i 0.236180 0.235642i
\(399\) −9.20998 + 5.89530i −0.0230827 + 0.0147752i
\(400\) 156.470 368.127i 0.391175 0.920316i
\(401\) 106.578i 0.265781i −0.991131 0.132891i \(-0.957574\pi\)
0.991131 0.132891i \(-0.0424259\pi\)
\(402\) 27.4686 124.499i 0.0683299 0.309698i
\(403\) −3.60448 22.7578i −0.00894413 0.0564710i
\(404\) 292.675 + 0.666904i 0.724442 + 0.00165075i
\(405\) 139.247 + 380.310i 0.343819 + 0.939036i
\(406\) 126.612 173.849i 0.311851 0.428200i
\(407\) −259.679 259.679i −0.638032 0.638032i
\(408\) −441.530 98.4720i −1.08218 0.241353i
\(409\) 274.286 89.1208i 0.670625 0.217899i 0.0461387 0.998935i \(-0.485308\pi\)
0.624486 + 0.781036i \(0.285308\pi\)
\(410\) −582.972 + 66.9518i −1.42188 + 0.163297i
\(411\) −43.7091 167.523i −0.106348 0.407599i
\(412\) 758.261 118.326i 1.84044 0.287199i
\(413\) −139.416 + 273.620i −0.337569 + 0.662517i
\(414\) −60.3318 + 130.458i −0.145729 + 0.315115i
\(415\) −649.822 + 297.742i −1.56584 + 0.717450i
\(416\) −194.720 + 62.0442i −0.468076 + 0.149145i
\(417\) 293.810 128.505i 0.704581 0.308164i
\(418\) 35.3212 + 18.0478i 0.0845005 + 0.0431765i
\(419\) 308.199 + 424.200i 0.735559 + 1.01241i 0.998862 + 0.0476973i \(0.0151883\pi\)
−0.263302 + 0.964713i \(0.584812\pi\)
\(420\) −159.989 + 92.7779i −0.380927 + 0.220900i
\(421\) 181.099 + 131.576i 0.430163 + 0.312532i 0.781714 0.623637i \(-0.214346\pi\)
−0.351551 + 0.936169i \(0.614346\pi\)
\(422\) 426.472 216.687i 1.01060 0.513476i
\(423\) −242.349 + 9.50705i −0.572929 + 0.0224753i
\(424\) 223.104 304.880i 0.526189 0.719056i
\(425\) 400.638 + 248.082i 0.942677 + 0.583721i
\(426\) 375.150 + 308.613i 0.880634 + 0.724443i
\(427\) 110.780 + 217.418i 0.259438 + 0.509175i
\(428\) −316.375 + 314.936i −0.739193 + 0.735832i
\(429\) 320.765 + 18.9263i 0.747703 + 0.0441173i
\(430\) 109.931 + 165.763i 0.255653 + 0.385496i
\(431\) −460.978 + 334.920i −1.06956 + 0.777078i −0.975832 0.218521i \(-0.929877\pi\)
−0.0937232 + 0.995598i \(0.529877\pi\)
\(432\) 355.558 245.362i 0.823051 0.567968i
\(433\) −96.8426 + 611.440i −0.223655 + 1.41210i 0.578839 + 0.815442i \(0.303506\pi\)
−0.802494 + 0.596660i \(0.796494\pi\)
\(434\) −18.0090 + 13.0530i −0.0414954 + 0.0300760i
\(435\) 405.293 331.021i 0.931709 0.760967i
\(436\) −245.665 761.983i −0.563452 1.74767i
\(437\) −8.41356 4.28692i −0.0192530 0.00980989i
\(438\) 109.549 + 251.250i 0.250112 + 0.573630i
\(439\) −249.881 + 769.055i −0.569205 + 1.75183i 0.0859096 + 0.996303i \(0.472620\pi\)
−0.655114 + 0.755530i \(0.727380\pi\)
\(440\) 583.417 + 331.145i 1.32595 + 0.752603i
\(441\) −353.022 41.8049i −0.800504 0.0947957i
\(442\) −37.3917 237.835i −0.0845965 0.538089i
\(443\) −323.348 + 323.348i −0.729904 + 0.729904i −0.970601 0.240696i \(-0.922624\pi\)
0.240696 + 0.970601i \(0.422624\pi\)
\(444\) −65.7592 254.406i −0.148106 0.572986i
\(445\) −550.995 + 154.014i −1.23819 + 0.346099i
\(446\) −124.026 + 380.239i −0.278086 + 0.852554i
\(447\) 196.336 + 220.958i 0.439231 + 0.494314i
\(448\) 138.537 + 140.444i 0.309234 + 0.313491i
\(449\) 175.927 0.391819 0.195909 0.980622i \(-0.437234\pi\)
0.195909 + 0.980622i \(0.437234\pi\)
\(450\) −433.812 + 119.612i −0.964027 + 0.265804i
\(451\) 984.136i 2.18212i
\(452\) 514.064 + 263.406i 1.13731 + 0.582756i
\(453\) 412.293 366.350i 0.910140 0.808720i
\(454\) 97.4238 298.681i 0.214590 0.657888i
\(455\) −77.1550 61.1156i −0.169571 0.134320i
\(456\) 15.2187 + 23.9555i 0.0333744 + 0.0525341i
\(457\) −518.387 518.387i −1.13433 1.13433i −0.989450 0.144877i \(-0.953721\pi\)
−0.144877 0.989450i \(-0.546279\pi\)
\(458\) −122.640 780.069i −0.267773 1.70321i
\(459\) 222.058 + 457.925i 0.483786 + 0.997658i
\(460\) −138.980 78.6751i −0.302130 0.171033i
\(461\) 595.031 + 193.337i 1.29074 + 0.419387i 0.872351 0.488881i \(-0.162595\pi\)
0.418390 + 0.908268i \(0.362595\pi\)
\(462\) −123.969 284.321i −0.268330 0.615414i
\(463\) −15.4450 + 30.3125i −0.0333586 + 0.0654699i −0.907084 0.420949i \(-0.861697\pi\)
0.873726 + 0.486419i \(0.161697\pi\)
\(464\) −450.078 330.145i −0.969996 0.711520i
\(465\) −50.4421 + 19.6057i −0.108478 + 0.0421629i
\(466\) 244.939 177.533i 0.525620 0.380971i
\(467\) 565.119 + 89.5061i 1.21011 + 0.191662i 0.728698 0.684835i \(-0.240126\pi\)
0.481407 + 0.876497i \(0.340126\pi\)
\(468\) 190.865 + 128.179i 0.407831 + 0.273886i
\(469\) −38.4985 52.9886i −0.0820863 0.112982i
\(470\) 11.5128 269.238i 0.0244954 0.572847i
\(471\) −39.7578 + 673.818i −0.0844115 + 1.43061i
\(472\) 708.905 + 364.263i 1.50192 + 0.771743i
\(473\) −297.224 + 151.443i −0.628380 + 0.320176i
\(474\) −75.9210 62.4556i −0.160171 0.131763i
\(475\) −6.76767 28.7784i −0.0142477 0.0605861i
\(476\) −188.328 + 136.174i −0.395647 + 0.286079i
\(477\) −424.690 + 16.6601i −0.890335 + 0.0349267i
\(478\) −36.2121 + 18.3991i −0.0757576 + 0.0384917i
\(479\) 120.378 165.687i 0.251312 0.345901i −0.664658 0.747147i \(-0.731423\pi\)
0.915970 + 0.401246i \(0.131423\pi\)
\(480\) 239.373 + 416.054i 0.498694 + 0.866778i
\(481\) 113.137 82.1989i 0.235212 0.170892i
\(482\) −317.927 162.448i −0.659599 0.337030i
\(483\) 29.5894 + 67.6526i 0.0612617 + 0.140068i
\(484\) −377.999 + 517.786i −0.780990 + 1.06981i
\(485\) 339.595 312.457i 0.700195 0.644241i
\(486\) −464.890 141.679i −0.956564 0.291521i
\(487\) −558.012 284.321i −1.14581 0.583822i −0.225207 0.974311i \(-0.572306\pi\)
−0.920607 + 0.390489i \(0.872306\pi\)
\(488\) 565.261 285.585i 1.15832 0.585216i
\(489\) −144.044 + 37.5831i −0.294569 + 0.0768570i
\(490\) 78.4002 387.129i 0.160000 0.790059i
\(491\) 80.6454 + 248.201i 0.164247 + 0.505501i 0.998980 0.0451542i \(-0.0143779\pi\)
−0.834733 + 0.550655i \(0.814378\pi\)
\(492\) 357.468 606.683i 0.726561 1.23310i
\(493\) 464.976 464.976i 0.943156 0.943156i
\(494\) −8.89205 + 12.2096i −0.0180001 + 0.0247158i
\(495\) −116.282 745.688i −0.234912 1.50644i
\(496\) 33.7174 + 46.8556i 0.0679787 + 0.0944670i
\(497\) 246.488 39.0398i 0.495951 0.0785510i
\(498\) 184.802 837.599i 0.371089 1.68193i
\(499\) −561.217 −1.12468 −0.562342 0.826905i \(-0.690099\pi\)
−0.562342 + 0.826905i \(0.690099\pi\)
\(500\) −93.0022 491.274i −0.186004 0.982549i
\(501\) −465.425 727.115i −0.928992 1.45133i
\(502\) −443.196 + 442.188i −0.882861 + 0.880852i
\(503\) 347.980 55.1147i 0.691810 0.109572i 0.199378 0.979923i \(-0.436108\pi\)
0.492432 + 0.870351i \(0.336108\pi\)
\(504\) 26.8521 220.303i 0.0532780 0.437108i
\(505\) 304.660 202.544i 0.603288 0.401078i
\(506\) 157.679 216.508i 0.311619 0.427881i
\(507\) 82.4436 375.701i 0.162611 0.741029i
\(508\) −79.2419 + 40.1486i −0.155988 + 0.0790326i
\(509\) 126.449 + 389.169i 0.248426 + 0.764575i 0.995054 + 0.0993340i \(0.0316712\pi\)
−0.746629 + 0.665241i \(0.768329\pi\)
\(510\) −527.294 + 204.256i −1.03391 + 0.400502i
\(511\) 133.920 + 43.5131i 0.262074 + 0.0851529i
\(512\) 365.732 358.307i 0.714320 0.699819i
\(513\) 10.4635 30.1653i 0.0203967 0.0588018i
\(514\) −1.03132 + 905.203i −0.00200646 + 1.76110i
\(515\) 705.946 649.531i 1.37077 1.26123i
\(516\) −238.236 14.6017i −0.461698 0.0282978i
\(517\) 446.390 + 70.7013i 0.863424 + 0.136753i
\(518\) −120.209 61.4223i −0.232064 0.118576i
\(519\) −234.886 91.9408i −0.452573 0.177150i
\(520\) −159.301 + 199.703i −0.306349 + 0.384044i
\(521\) −331.050 + 455.652i −0.635414 + 0.874572i −0.998361 0.0572380i \(-0.981771\pi\)
0.362947 + 0.931810i \(0.381771\pi\)
\(522\) 23.9000 + 627.499i 0.0457854 + 1.20211i
\(523\) −518.988 + 264.438i −0.992329 + 0.505617i −0.873252 0.487268i \(-0.837993\pi\)
−0.119077 + 0.992885i \(0.537993\pi\)
\(524\) −245.166 339.064i −0.467874 0.647068i
\(525\) −101.862 + 207.529i −0.194023 + 0.395294i
\(526\) −642.429 + 207.929i −1.22135 + 0.395302i
\(527\) −60.5932 + 30.8738i −0.114978 + 0.0585841i
\(528\) −739.016 + 319.221i −1.39965 + 0.604585i
\(529\) 273.460 376.385i 0.516937 0.711503i
\(530\) 20.1750 471.810i 0.0380660 0.890207i
\(531\) −174.872 879.424i −0.329327 1.65617i
\(532\) 14.3955 + 2.31366i 0.0270592 + 0.00434899i
\(533\) 370.144 + 58.6250i 0.694454 + 0.109991i
\(534\) 250.971 639.021i 0.469982 1.19667i
\(535\) −110.134 + 547.030i −0.205858 + 1.02249i
\(536\) −137.866 + 99.4474i −0.257213 + 0.185536i
\(537\) 731.811 72.0545i 1.36278 0.134180i
\(538\) −40.8969 + 256.323i −0.0760166 + 0.476436i
\(539\) 630.017 + 204.705i 1.16886 + 0.379786i
\(540\) 199.173 501.926i 0.368840 0.929493i
\(541\) 28.2370 + 86.9046i 0.0521941 + 0.160637i 0.973756 0.227595i \(-0.0730861\pi\)
−0.921562 + 0.388232i \(0.873086\pi\)
\(542\) 139.157 + 885.127i 0.256747 + 1.63308i
\(543\) −577.890 126.812i −1.06425 0.233539i
\(544\) 351.749 + 489.987i 0.646598 + 0.900712i
\(545\) −784.468 621.389i −1.43939 1.14016i
\(546\) 114.321 29.6889i 0.209379 0.0543752i
\(547\) −4.17712 + 0.661591i −0.00763642 + 0.00120949i −0.160252 0.987076i \(-0.551231\pi\)
0.152615 + 0.988286i \(0.451231\pi\)
\(548\) −105.268 + 205.442i −0.192096 + 0.374895i
\(549\) −647.008 298.323i −1.17852 0.543393i
\(550\) 836.338 60.9505i 1.52061 0.110819i
\(551\) −41.2544 −0.0748719
\(552\) 175.846 76.1951i 0.318561 0.138035i
\(553\) −49.8830 + 7.90069i −0.0902043 + 0.0142870i
\(554\) 187.822 575.823i 0.339028 1.03939i
\(555\) −245.011 218.758i −0.441461 0.394158i
\(556\) −406.349 133.055i −0.730843 0.239308i
\(557\) 278.916 278.916i 0.500747 0.500747i −0.410923 0.911670i \(-0.634794\pi\)
0.911670 + 0.410923i \(0.134794\pi\)
\(558\) 17.7029 62.4825i 0.0317256 0.111976i
\(559\) −39.2537 120.811i −0.0702213 0.216119i
\(560\) 241.517 + 49.7713i 0.431281 + 0.0888773i
\(561\) −239.425 917.640i −0.426782 1.63572i
\(562\) −474.892 75.7703i −0.845004 0.134823i
\(563\) −358.482 182.656i −0.636735 0.324433i 0.105653 0.994403i \(-0.466307\pi\)
−0.742388 + 0.669970i \(0.766307\pi\)
\(564\) 249.502 + 205.727i 0.442380 + 0.364765i
\(565\) 717.215 83.1971i 1.26941 0.147251i
\(566\) 718.898 521.060i 1.27014 0.920600i
\(567\) −212.899 + 130.429i −0.375483 + 0.230033i
\(568\) −99.1359 640.071i −0.174535 1.12689i
\(569\) −427.932 + 310.911i −0.752078 + 0.546416i −0.896470 0.443104i \(-0.853877\pi\)
0.144392 + 0.989520i \(0.453877\pi\)
\(570\) 32.4529 + 14.3306i 0.0569350 + 0.0251413i
\(571\) 249.306 343.140i 0.436613 0.600947i −0.532842 0.846215i \(-0.678876\pi\)
0.969455 + 0.245268i \(0.0788760\pi\)
\(572\) −302.255 303.635i −0.528417 0.530831i
\(573\) 369.491 630.368i 0.644836 1.10012i
\(574\) −111.396 344.175i −0.194069 0.599608i
\(575\) −199.084 + 14.7369i −0.346233 + 0.0256294i
\(576\) −571.527 71.6452i −0.992234 0.124384i
\(577\) −416.923 + 212.433i −0.722570 + 0.368168i −0.776279 0.630389i \(-0.782895\pi\)
0.0537098 + 0.998557i \(0.482895\pi\)
\(578\) −118.195 + 60.0536i −0.204489 + 0.103899i
\(579\) −189.159 11.1611i −0.326700 0.0192765i
\(580\) −697.055 30.6024i −1.20182 0.0527627i
\(581\) −259.009 356.495i −0.445798 0.613588i
\(582\) 53.6335 + 551.160i 0.0921537 + 0.947010i
\(583\) 782.250 + 123.896i 1.34177 + 0.212515i
\(584\) 114.120 347.184i 0.195412 0.594493i
\(585\) 287.388 + 0.685966i 0.491262 + 0.00117259i
\(586\) −1032.61 1.17648i −1.76213 0.00200764i
\(587\) −136.846 + 268.574i −0.233127 + 0.457537i −0.977701 0.210003i \(-0.932653\pi\)
0.744574 + 0.667540i \(0.232653\pi\)
\(588\) 314.027 + 355.034i 0.534059 + 0.603800i
\(589\) 4.05765 + 1.31841i 0.00688905 + 0.00223839i
\(590\) 989.764 113.670i 1.67757 0.192661i
\(591\) −348.021 285.631i −0.588868 0.483302i
\(592\) −160.479 + 311.442i −0.271080 + 0.526084i
\(593\) −94.1094 94.1094i −0.158700 0.158700i 0.623290 0.781991i \(-0.285796\pi\)
−0.781991 + 0.623290i \(0.785796\pi\)
\(594\) 798.177 + 427.899i 1.34373 + 0.720369i
\(595\) −101.181 + 272.312i −0.170053 + 0.457668i
\(596\) 0.898046 394.112i 0.00150679 0.661262i
\(597\) 132.299 + 148.890i 0.221606 + 0.249397i
\(598\) 72.0379 + 72.2022i 0.120465 + 0.120739i
\(599\) 350.031i 0.584359i 0.956364 + 0.292179i \(0.0943804\pi\)
−0.956364 + 0.292179i \(0.905620\pi\)
\(600\) 537.710 + 266.210i 0.896184 + 0.443683i
\(601\) −500.921 −0.833479 −0.416739 0.909026i \(-0.636827\pi\)
−0.416739 + 0.909026i \(0.636827\pi\)
\(602\) −86.8040 + 86.6064i −0.144193 + 0.143864i
\(603\) 184.056 + 51.9214i 0.305234 + 0.0861052i
\(604\) −735.387 1.67569i −1.21753 0.00277433i
\(605\) −33.3230 + 800.659i −0.0550794 + 1.32340i
\(606\) −26.3578 + 438.221i −0.0434947 + 0.723137i
\(607\) −169.671 + 169.671i −0.279524 + 0.279524i −0.832919 0.553395i \(-0.813332\pi\)
0.553395 + 0.832919i \(0.313332\pi\)
\(608\) 6.13249 37.3410i 0.0100863 0.0614162i
\(609\) 249.368 + 204.664i 0.409471 + 0.336065i
\(610\) 389.200 689.354i 0.638033 1.13009i
\(611\) −53.1830 + 163.680i −0.0870426 + 0.267889i
\(612\) 185.718 652.658i 0.303461 1.06643i
\(613\) 63.8685 + 32.5427i 0.104190 + 0.0530875i 0.505309 0.862939i \(-0.331379\pi\)
−0.401119 + 0.916026i \(0.631379\pi\)
\(614\) −0.383285 + 336.414i −0.000624242 + 0.547905i
\(615\) −49.7479 878.799i −0.0808909 1.42894i
\(616\) −129.142 + 392.883i −0.209645 + 0.637796i
\(617\) −122.623 + 774.210i −0.198741 + 1.25480i 0.663453 + 0.748218i \(0.269090\pi\)
−0.862193 + 0.506580i \(0.830910\pi\)
\(618\) 111.493 + 1145.74i 0.180409 + 1.85396i
\(619\) 932.506 677.506i 1.50647 1.09452i 0.538760 0.842459i \(-0.318893\pi\)
0.967712 0.252057i \(-0.0811070\pi\)
\(620\) 67.5821 + 25.2865i 0.109003 + 0.0407846i
\(621\) −190.132 101.650i −0.306171 0.163688i
\(622\) 69.5714 + 136.927i 0.111851 + 0.220140i
\(623\) −160.121 314.256i −0.257017 0.504424i
\(624\) −76.0392 296.968i −0.121858 0.475910i
\(625\) −437.812 446.034i −0.700498 0.713654i
\(626\) 265.294 85.8654i 0.423793 0.137165i
\(627\) −30.0869 + 51.3296i −0.0479855 + 0.0818654i
\(628\) 637.835 634.934i 1.01566 1.01104i
\(629\) −333.916 242.604i −0.530869 0.385699i
\(630\) −125.072 247.622i −0.198527 0.393051i
\(631\) 133.329 + 183.511i 0.211297 + 0.290826i 0.901490 0.432800i \(-0.142474\pi\)
−0.690193 + 0.723626i \(0.742474\pi\)
\(632\) 20.0626 + 129.534i 0.0317447 + 0.204960i
\(633\) 287.535 + 657.415i 0.454242 + 1.03857i
\(634\) 268.545 + 370.507i 0.423572 + 0.584396i
\(635\) −54.4819 + 96.7559i −0.0857982 + 0.152371i
\(636\) 437.225 + 360.514i 0.687461 + 0.566846i
\(637\) −114.522 + 224.762i −0.179783 + 0.352844i
\(638\) 184.371 1155.55i 0.288983 1.81121i
\(639\) −494.652 + 535.045i −0.774103 + 0.837317i
\(640\) 131.317 626.383i 0.205183 0.978724i
\(641\) −175.446 + 57.0057i −0.273706 + 0.0889325i −0.442654 0.896692i \(-0.645963\pi\)
0.168948 + 0.985625i \(0.445963\pi\)
\(642\) −444.203 501.058i −0.691905 0.780464i
\(643\) −84.8609 84.8609i −0.131976 0.131976i 0.638033 0.770009i \(-0.279748\pi\)
−0.770009 + 0.638033i \(0.779748\pi\)
\(644\) 30.6372 93.5657i 0.0475733 0.145288i
\(645\) −257.755 + 150.258i −0.399620 + 0.232958i
\(646\) 42.3819 + 13.8241i 0.0656067 + 0.0213996i
\(647\) 26.0576 + 164.521i 0.0402745 + 0.254283i 0.999608 0.0279914i \(-0.00891110\pi\)
−0.959334 + 0.282275i \(0.908911\pi\)
\(648\) 336.621 + 553.706i 0.519476 + 0.854485i
\(649\) 1670.86i 2.57451i
\(650\) −26.8966 + 318.186i −0.0413793 + 0.489518i
\(651\) −17.9864 28.0994i −0.0276288 0.0431634i
\(652\) 176.649 + 90.5146i 0.270934 + 0.138826i
\(653\) −144.435 911.928i −0.221187 1.39652i −0.809135 0.587622i \(-0.800064\pi\)
0.587948 0.808899i \(-0.299936\pi\)
\(654\) 1162.35 301.860i 1.77730 0.461559i
\(655\) −490.268 182.166i −0.748502 0.278116i
\(656\) −894.247 + 286.059i −1.36318 + 0.436066i
\(657\) −385.738 + 142.279i −0.587120 + 0.216559i
\(658\) 164.116 25.8018i 0.249416 0.0392124i
\(659\) −481.105 + 156.320i −0.730053 + 0.237208i −0.650376 0.759612i \(-0.725389\pi\)
−0.0796765 + 0.996821i \(0.525389\pi\)
\(660\) −546.439 + 844.972i −0.827938 + 1.28026i
\(661\) −153.265 + 471.700i −0.231868 + 0.713616i 0.765654 + 0.643253i \(0.222416\pi\)
−0.997521 + 0.0703628i \(0.977584\pi\)
\(662\) 192.160 + 30.6596i 0.290272 + 0.0463136i
\(663\) 359.397 35.3864i 0.542077 0.0533731i
\(664\) −927.531 + 669.059i −1.39688 + 1.00762i
\(665\) 16.5689 7.59169i 0.0249156 0.0114161i
\(666\) 386.669 76.4308i 0.580585 0.114761i
\(667\) −43.5784 + 275.143i −0.0653349 + 0.412508i
\(668\) −182.660 + 1136.50i −0.273443 + 1.70135i
\(669\) −558.660 218.675i −0.835067 0.326868i
\(670\) −74.2362 + 199.099i −0.110800 + 0.297162i
\(671\) 1074.10 + 780.379i 1.60074 + 1.16301i
\(672\) −222.318 + 195.289i −0.330830 + 0.290609i
\(673\) −22.6330 44.4199i −0.0336301 0.0660028i 0.873580 0.486680i \(-0.161792\pi\)
−0.907210 + 0.420678i \(0.861792\pi\)
\(674\) 241.260 + 745.412i 0.357953 + 1.10595i
\(675\) −141.530 659.996i −0.209674 0.977771i
\(676\) −415.594 + 300.502i −0.614784 + 0.444530i
\(677\) −279.282 548.122i −0.412529 0.809634i −1.00000 0.000388497i \(-0.999876\pi\)
0.587471 0.809245i \(-0.300124\pi\)
\(678\) −438.990 + 746.985i −0.647478 + 1.10175i
\(679\) 230.155 + 167.217i 0.338961 + 0.246270i
\(680\) 705.851 + 265.018i 1.03802 + 0.389732i
\(681\) 438.833 + 171.771i 0.644394 + 0.252234i
\(682\) −55.0632 + 107.764i −0.0807378 + 0.158012i
\(683\) 171.460 1082.55i 0.251039 1.58500i −0.463949 0.885862i \(-0.653568\pi\)
0.714988 0.699137i \(-0.246432\pi\)
\(684\) −37.1919 + 20.7143i −0.0543742 + 0.0302841i
\(685\) 33.2492 + 286.630i 0.0485390 + 0.418438i
\(686\) 545.578 + 0.621591i 0.795303 + 0.000906109i
\(687\) 1178.78 116.063i 1.71583 0.168942i
\(688\) 224.005 + 226.056i 0.325588 + 0.328570i
\(689\) −93.1973 + 286.832i −0.135265 + 0.416302i
\(690\) 129.858 201.304i 0.188199 0.291746i
\(691\) 602.145 195.649i 0.871411 0.283138i 0.161024 0.986950i \(-0.448520\pi\)
0.710386 + 0.703812i \(0.248520\pi\)
\(692\) 152.002 + 300.009i 0.219656 + 0.433539i
\(693\) 436.511 161.007i 0.629886 0.232333i
\(694\) 150.197 + 109.386i 0.216422 + 0.157617i
\(695\) −514.742 + 143.881i −0.740636 + 0.207023i
\(696\) 533.388 645.384i 0.766363 0.927276i
\(697\) −173.028 1092.45i −0.248246 1.56737i
\(698\) −266.962 267.571i −0.382467 0.383339i
\(699\) 244.631 + 382.177i 0.349973 + 0.546749i
\(700\) 285.588 115.982i 0.407982 0.165689i
\(701\) 917.097i 1.30827i 0.756378 + 0.654135i \(0.226967\pi\)
−0.756378 + 0.654135i \(0.773033\pi\)
\(702\) −208.485 + 274.713i −0.296987 + 0.391329i
\(703\) 4.05077 + 25.5756i 0.00576212 + 0.0363806i
\(704\) 1018.53 + 338.654i 1.44677 + 0.481043i
\(705\) 402.185 + 40.5688i 0.570475 + 0.0575444i
\(706\) 131.068 + 95.4550i 0.185649 + 0.135205i
\(707\) 159.478 + 159.478i 0.225570 + 0.225570i
\(708\) −606.905 + 1030.02i −0.857211 + 1.45483i
\(709\) −1194.52 + 388.124i −1.68480 + 0.547425i −0.985833 0.167729i \(-0.946357\pi\)
−0.698967 + 0.715154i \(0.746357\pi\)
\(710\) −547.513 596.429i −0.771145 0.840041i
\(711\) 100.105 108.280i 0.140795 0.152292i
\(712\) −817.029 + 412.785i −1.14751 + 0.579755i
\(713\) 13.0793 25.6695i 0.0183440 0.0360021i
\(714\) −187.602 293.819i −0.262747 0.411511i
\(715\) −525.003 105.699i −0.734270 0.147831i
\(716\) −791.899 578.110i −1.10600 0.807416i
\(717\) −24.4149 55.8217i −0.0340514 0.0778545i
\(718\) 115.316 225.685i 0.160608 0.314325i
\(719\) 184.679 + 254.188i 0.256855 + 0.353530i 0.917897 0.396818i \(-0.129886\pi\)
−0.661042 + 0.750348i \(0.729886\pi\)
\(720\) −643.779 + 322.410i −0.894138 + 0.447792i
\(721\) 478.443 + 347.609i 0.663583 + 0.482121i
\(722\) 325.781 + 641.186i 0.451220 + 0.888070i
\(723\) 270.813 462.018i 0.374568 0.639029i
\(724\) 462.221 + 639.251i 0.638427 + 0.882943i
\(725\) −745.749 + 452.238i −1.02862 + 0.623776i
\(726\) −742.630 610.916i −1.02291 0.841482i
\(727\) 180.840 + 354.919i 0.248748 + 0.488196i 0.981292 0.192524i \(-0.0616672\pi\)
−0.732544 + 0.680720i \(0.761667\pi\)
\(728\) −140.074 71.9756i −0.192410 0.0988675i
\(729\) 252.445 683.895i 0.346290 0.938128i
\(730\) −122.476 440.099i −0.167776 0.602876i
\(731\) −303.311 + 220.369i −0.414927 + 0.301462i
\(732\) 378.685 + 871.220i 0.517329 + 1.19019i
\(733\) 14.9604 94.4564i 0.0204098 0.128863i −0.975380 0.220533i \(-0.929220\pi\)
0.995789 + 0.0916699i \(0.0292205\pi\)
\(734\) −343.441 473.841i −0.467904 0.645560i
\(735\) 572.931 + 150.947i 0.779498 + 0.205370i
\(736\) −242.565 80.3447i −0.329572 0.109164i
\(737\) −317.525 161.787i −0.430835 0.219521i
\(738\) 877.532 + 587.873i 1.18907 + 0.796576i
\(739\) 129.280 397.884i 0.174940 0.538409i −0.824691 0.565583i \(-0.808651\pi\)
0.999631 + 0.0271747i \(0.00865104\pi\)
\(740\) 49.4720 + 435.142i 0.0668540 + 0.588030i
\(741\) −17.5133 14.3737i −0.0236347 0.0193977i
\(742\) 287.595 45.2147i 0.387594 0.0609363i
\(743\) 79.3562 79.3562i 0.106805 0.106805i −0.651685 0.758490i \(-0.725938\pi\)
0.758490 + 0.651685i \(0.225938\pi\)
\(744\) −73.0876 + 46.4318i −0.0982360 + 0.0624084i
\(745\) −272.744 410.252i −0.366099 0.550674i
\(746\) −211.141 68.8700i −0.283031 0.0923191i
\(747\) 1238.29 + 349.315i 1.65768 + 0.467624i
\(748\) −576.628 + 1125.35i −0.770893 + 1.50448i
\(749\) −344.000 −0.459280
\(750\) 743.740 96.7034i 0.991653 0.128938i
\(751\) 331.529i 0.441450i 0.975336 + 0.220725i \(0.0708423\pi\)
−0.975336 + 0.220725i \(0.929158\pi\)
\(752\) −65.5090 426.169i −0.0871131 0.566714i
\(753\) −623.773 701.998i −0.828384 0.932269i
\(754\) 423.631 + 138.180i 0.561845 + 0.183263i
\(755\) −765.503 + 508.921i −1.01391 + 0.674068i
\(756\) 327.576 + 59.2992i 0.433301 + 0.0784381i
\(757\) −472.747 472.747i −0.624501 0.624501i 0.322178 0.946679i \(-0.395585\pi\)
−0.946679 + 0.322178i \(0.895585\pi\)
\(758\) −1026.36 + 161.361i −1.35403 + 0.212877i
\(759\) 310.557 + 254.883i 0.409166 + 0.335815i
\(760\) −19.5562 43.0696i −0.0257318 0.0566705i
\(761\) 267.322 + 86.8583i 0.351278 + 0.114137i 0.479341 0.877629i \(-0.340876\pi\)
−0.128063 + 0.991766i \(0.540876\pi\)
\(762\) −53.2563 122.143i −0.0698902 0.160293i
\(763\) 280.088 549.704i 0.367088 0.720451i
\(764\) −927.235 + 298.943i −1.21366 + 0.391286i
\(765\) −260.185 807.318i −0.340111 1.05532i
\(766\) 527.676 + 728.027i 0.688873 + 0.950427i
\(767\) −628.426 99.5330i −0.819330 0.129769i
\(768\) 504.874 + 578.728i 0.657389 + 0.753552i
\(769\) 193.017 + 265.666i 0.250998 + 0.345469i 0.915860 0.401497i \(-0.131510\pi\)
−0.664862 + 0.746966i \(0.731510\pi\)
\(770\) 138.597 + 498.028i 0.179997 + 0.646790i
\(771\) −1355.45 79.9766i −1.75804 0.103731i
\(772\) 178.244 + 179.058i 0.230885 + 0.231940i
\(773\) −1057.61 + 538.881i −1.36819 + 0.697129i −0.974975 0.222316i \(-0.928638\pi\)
−0.393218 + 0.919445i \(0.628638\pi\)
\(774\) 42.5082 355.492i 0.0549201 0.459293i
\(775\) 87.8020 20.6480i 0.113293 0.0266425i
\(776\) 436.031 595.851i 0.561895 0.767850i
\(777\) 102.395 174.691i 0.131783 0.224827i
\(778\) −631.020 1241.94i −0.811080 1.59633i
\(779\) −40.7875 + 56.1392i −0.0523588 + 0.0720657i
\(780\) −285.251 255.857i −0.365707 0.328021i
\(781\) 1098.51 798.117i 1.40655 1.02192i
\(782\) 136.968 268.060i 0.175151 0.342788i
\(783\) −941.747 18.5801i −1.20274 0.0237294i
\(784\) 2.88012 631.974i 0.00367362 0.806089i
\(785\) 222.039 1102.85i 0.282852 1.40491i
\(786\) 528.989 337.756i 0.673014 0.429715i
\(787\) −832.152 424.003i −1.05737 0.538758i −0.163252 0.986584i \(-0.552198\pi\)
−0.894121 + 0.447826i \(0.852198\pi\)
\(788\) 92.5567 + 593.124i 0.117458 + 0.752695i
\(789\) −255.709 980.051i −0.324092 1.24214i
\(790\) 110.803 + 120.702i 0.140257 + 0.152788i
\(791\) 137.548 + 423.329i 0.173891 + 0.535182i
\(792\) −413.999 1134.33i −0.522726 1.43224i
\(793\) −357.493 + 357.493i −0.450811 + 0.450811i
\(794\) 642.339 + 467.806i 0.808991 + 0.589176i
\(795\) 704.785 + 71.0924i 0.886521 + 0.0894244i
\(796\) 0.605137 265.568i 0.000760222 0.333628i
\(797\) −866.798 + 137.287i −1.08758 + 0.172255i −0.674378 0.738386i \(-0.735588\pi\)
−0.413198 + 0.910641i \(0.635588\pi\)
\(798\) −4.71201 + 21.3567i −0.00590478 + 0.0267628i
\(799\) 507.952 0.635735
\(800\) −298.482 742.232i −0.373103 0.927790i
\(801\) 935.185 + 431.196i 1.16752 + 0.538322i
\(802\) −150.553 150.896i −0.187721 0.188150i
\(803\) 756.712 119.851i 0.942356 0.149254i
\(804\) −136.976 215.071i −0.170369 0.267501i
\(805\) −33.1299 118.524i −0.0411552 0.147235i
\(806\) −37.2510 27.1294i −0.0462172 0.0336593i
\(807\) −380.298 83.4523i −0.471250 0.103411i
\(808\) 415.318 412.488i 0.514007 0.510506i
\(809\) −385.397 1186.13i −0.476387 1.46617i −0.844078 0.536221i \(-0.819851\pi\)
0.367690 0.929948i \(-0.380149\pi\)
\(810\) 734.375 + 341.751i 0.906635 + 0.421915i
\(811\) 1006.29 + 326.962i 1.24080 + 0.403159i 0.854614 0.519263i \(-0.173794\pi\)
0.386182 + 0.922422i \(0.373794\pi\)
\(812\) −66.3197 424.992i −0.0816745 0.523389i
\(813\) −1337.53 + 131.694i −1.64518 + 0.161985i
\(814\) −734.483 0.836815i −0.902313 0.00102803i
\(815\) 246.458 28.5892i 0.302402 0.0350787i
\(816\) −764.231 + 484.288i −0.936558 + 0.593490i
\(817\) 23.2314 + 3.67950i 0.0284351 + 0.00450367i
\(818\) 262.448 513.636i 0.320841 0.627916i
\(819\) 34.5535 + 173.768i 0.0421898 + 0.212171i
\(820\) −730.809 + 918.299i −0.891231 + 1.11988i
\(821\) −125.786 + 173.130i −0.153211 + 0.210877i −0.878722 0.477334i \(-0.841603\pi\)
0.725511 + 0.688210i \(0.241603\pi\)
\(822\) −298.528 175.440i −0.363172 0.213430i
\(823\) 96.0032 48.9161i 0.116650 0.0594363i −0.394692 0.918814i \(-0.629149\pi\)
0.511342 + 0.859377i \(0.329149\pi\)
\(824\) 906.416 1238.65i 1.10002 1.50321i
\(825\) 18.8078 + 1257.69i 0.0227973 + 1.52448i
\(826\) 189.127 + 584.337i 0.228967 + 0.707429i
\(827\) −531.346 + 270.734i −0.642498 + 0.327369i −0.744705 0.667394i \(-0.767410\pi\)
0.102207 + 0.994763i \(0.467410\pi\)
\(828\) 98.8654 + 269.930i 0.119403 + 0.326002i
\(829\) 94.1734 129.619i 0.113599 0.156355i −0.748431 0.663212i \(-0.769193\pi\)
0.862030 + 0.506857i \(0.169193\pi\)
\(830\) −499.444 + 1339.49i −0.601739 + 1.61384i
\(831\) 846.018 + 331.155i 1.01807 + 0.398502i
\(832\) −188.045 + 362.905i −0.226016 + 0.436184i
\(833\) 735.350 + 116.468i 0.882773 + 0.139817i
\(834\) 234.458 596.977i 0.281125 0.715799i
\(835\) 599.353 + 1308.09i 0.717788 + 1.56657i
\(836\) 75.5030 24.3423i 0.0903146 0.0291176i
\(837\) 92.0334 + 31.9239i 0.109956 + 0.0381408i
\(838\) 1035.58 + 165.230i 1.23578 + 0.197171i
\(839\) −746.797 242.649i −0.890104 0.289212i −0.171958 0.985104i \(-0.555009\pi\)
−0.718146 + 0.695892i \(0.755009\pi\)
\(840\) −95.4588 + 357.359i −0.113641 + 0.425427i
\(841\) 116.208 + 357.650i 0.138178 + 0.425268i
\(842\) 442.268 69.5319i 0.525259 0.0825794i
\(843\) 154.613 704.584i 0.183408 0.835806i
\(844\) 297.718 909.226i 0.352746 1.07728i
\(845\) −223.283 + 600.927i −0.264240 + 0.711156i
\(846\) −329.694 + 355.803i −0.389709 + 0.420571i
\(847\) −487.936 + 77.2815i −0.576076 + 0.0912414i
\(848\) −114.797 746.814i −0.135374 0.880676i
\(849\) 717.995 + 1121.69i 0.845695 + 1.32120i
\(850\) 917.673 214.701i 1.07962 0.252590i
\(851\) 174.853 0.205468
\(852\) 967.093 92.9959i 1.13509 0.109150i
\(853\) −25.4379 + 4.02897i −0.0298217 + 0.00472330i −0.171328 0.985214i \(-0.554806\pi\)
0.141506 + 0.989937i \(0.454806\pi\)
\(854\) 463.970 + 151.338i 0.543290 + 0.177210i
\(855\) −24.2719 + 47.3564i −0.0283881 + 0.0553876i
\(856\) −3.05160 + 892.806i −0.00356495 + 1.04300i
\(857\) 650.648 650.648i 0.759216 0.759216i −0.216964 0.976180i \(-0.569615\pi\)
0.976180 + 0.216964i \(0.0696153\pi\)
\(858\) 480.881 426.316i 0.560468 0.496872i
\(859\) −295.281 908.782i −0.343750 1.05795i −0.962250 0.272169i \(-0.912259\pi\)
0.618500 0.785785i \(-0.287741\pi\)
\(860\) 389.800 + 79.4036i 0.453256 + 0.0923297i
\(861\) 525.053 136.993i 0.609817 0.159110i
\(862\) −179.555 + 1125.37i −0.208301 + 1.30553i
\(863\) 858.585 + 437.471i 0.994884 + 0.506919i 0.874093 0.485759i \(-0.161457\pi\)
0.120792 + 0.992678i \(0.461457\pi\)
\(864\) 156.809 849.651i 0.181492 0.983392i
\(865\) 366.317 + 206.268i 0.423487 + 0.238460i
\(866\) 726.609 + 1002.49i 0.839041 + 1.15761i
\(867\) −79.6889 182.199i −0.0919134 0.210149i
\(868\) −7.05891 + 43.9202i −0.00813238 + 0.0505993i
\(869\) −222.312 + 161.519i −0.255825 + 0.185868i
\(870\) 106.224 1041.19i 0.122096 1.19676i
\(871\) 79.7649 109.787i 0.0915785 0.126047i
\(872\) −1424.20 731.807i −1.63325 0.839228i
\(873\) −830.006 + 32.5601i −0.950752 + 0.0372968i
\(874\) −17.9678 + 5.81548i −0.0205582 + 0.00665387i
\(875\) 216.291 318.864i 0.247190 0.364416i
\(876\) 510.018 + 200.977i 0.582213 + 0.229426i
\(877\) 961.385 489.850i 1.09622 0.558552i 0.190182 0.981749i \(-0.439092\pi\)
0.906038 + 0.423197i \(0.139092\pi\)
\(878\) 732.580 + 1441.83i 0.834374 + 1.64217i
\(879\) 91.2333 1546.23i 0.103792 1.75908i
\(880\) 1293.79 355.292i 1.47022 0.403741i
\(881\) 145.961 + 200.898i 0.165677 + 0.228035i 0.883781 0.467901i \(-0.154990\pi\)
−0.718104 + 0.695936i \(0.754990\pi\)
\(882\) −558.871 + 439.492i −0.633641 + 0.498290i
\(883\) −826.194 130.856i −0.935667 0.148195i −0.330061 0.943960i \(-0.607069\pi\)
−0.605606 + 0.795764i \(0.707069\pi\)
\(884\) −388.906 283.913i −0.439939 0.321169i
\(885\) 84.4614 + 1492.02i 0.0954367 + 1.68589i
\(886\) −1.04199 + 914.565i −0.00117606 + 1.03224i
\(887\) 73.4581 144.170i 0.0828164 0.162536i −0.845884 0.533366i \(-0.820927\pi\)
0.928701 + 0.370830i \(0.120927\pi\)
\(888\) −452.477 267.302i −0.509547 0.301016i
\(889\) −65.1039 21.1535i −0.0732327 0.0237948i
\(890\) −562.551 + 996.393i −0.632079 + 1.11954i
\(891\) −709.936 + 1158.19i −0.796785 + 1.29988i
\(892\) 361.527 + 713.551i 0.405299 + 0.799945i
\(893\) −22.5337 22.5337i −0.0252337 0.0252337i
\(894\) 590.104 + 35.4931i 0.660071 + 0.0397014i
\(895\) −1224.52 50.9641i −1.36818 0.0569431i
\(896\) 394.535 + 3.14659i 0.440329 + 0.00351182i
\(897\) −114.364 + 101.620i −0.127496 + 0.113289i
\(898\) 249.081 248.514i 0.277373 0.276742i
\(899\) 125.866i 0.140007i
\(900\) −445.238 + 782.153i −0.494709 + 0.869059i
\(901\) 890.131 0.987936
\(902\) −1390.19 1393.36i −1.54123 1.54475i
\(903\) −122.171 137.493i −0.135295 0.152262i
\(904\) 1099.91 353.231i 1.21672 0.390742i
\(905\) 924.323 + 343.445i 1.02135 + 0.379497i
\(906\) 66.2277 1101.09i 0.0730990 1.21533i
\(907\) −265.336 + 265.336i −0.292542 + 0.292542i −0.838084 0.545542i \(-0.816324\pi\)
0.545542 + 0.838084i \(0.316324\pi\)
\(908\) −283.983 560.501i −0.312756 0.617292i
\(909\) −653.950 77.4408i −0.719417 0.0851934i
\(910\) −195.570 + 22.4604i −0.214912 + 0.0246817i
\(911\) 384.973 1184.82i 0.422583 1.30058i −0.482708 0.875782i \(-0.660347\pi\)
0.905290 0.424794i \(-0.139653\pi\)
\(912\) 55.3867 + 12.4188i 0.0607310 + 0.0136171i
\(913\) −2136.23 1088.47i −2.33980 1.19219i
\(914\) −1466.22 1.67050i −1.60418 0.00182768i
\(915\) 998.581 + 642.556i 1.09135 + 0.702247i
\(916\) −1275.56 931.199i −1.39254 1.01659i
\(917\) 50.4392 318.461i 0.0550046 0.347286i
\(918\) 961.260 + 334.662i 1.04712 + 0.364556i
\(919\) 312.229 226.847i 0.339748 0.246842i −0.404807 0.914402i \(-0.632661\pi\)
0.744556 + 0.667560i \(0.232661\pi\)
\(920\) −307.907 + 84.9327i −0.334682 + 0.0923182i
\(921\) −503.745 29.7229i −0.546954 0.0322724i
\(922\) 1115.57 566.810i 1.20994 0.614762i
\(923\) 234.742 + 460.707i 0.254325 + 0.499140i
\(924\) −577.150 227.431i −0.624622 0.246137i
\(925\) 353.588 + 417.919i 0.382258 + 0.451805i
\(926\) 20.9521 + 64.7349i 0.0226265 + 0.0699081i
\(927\) −1725.41 + 67.6855i −1.86128 + 0.0730157i
\(928\) −1103.60 + 168.354i −1.18922 + 0.181415i
\(929\) −768.374 558.257i −0.827098 0.600922i 0.0916387 0.995792i \(-0.470790\pi\)
−0.918737 + 0.394870i \(0.870790\pi\)
\(930\) −43.7221 + 99.0129i −0.0470130 + 0.106465i
\(931\) −27.4548 37.7882i −0.0294895 0.0405889i
\(932\) 96.0077 597.356i 0.103013 0.640940i
\(933\) −211.075 + 92.3186i −0.226233 + 0.0989481i
\(934\) 926.546 671.563i 0.992019 0.719019i
\(935\) 182.129 + 1570.07i 0.194790 + 1.67922i
\(936\) 451.297 88.1373i 0.482154 0.0941638i
\(937\) 522.672 1025.80i 0.557814 1.09477i −0.424130 0.905601i \(-0.639420\pi\)
0.981944 0.189171i \(-0.0605799\pi\)
\(938\) −129.359 20.6395i −0.137909 0.0220038i
\(939\) 105.596 + 404.717i 0.112456 + 0.431009i
\(940\) −364.026 397.456i −0.387261 0.422826i
\(941\) 1219.66 396.290i 1.29613 0.421137i 0.421894 0.906645i \(-0.361365\pi\)
0.874232 + 0.485508i \(0.161365\pi\)
\(942\) 895.546 + 1010.17i 0.950685 + 1.07237i
\(943\) 331.331 + 331.331i 0.351358 + 0.351358i
\(944\) 1518.24 485.669i 1.60831 0.514480i
\(945\) 381.650 165.839i 0.403863 0.175491i
\(946\) −206.888 + 634.276i −0.218698 + 0.670482i
\(947\) −56.4117 356.170i −0.0595689 0.376103i −0.999405 0.0344787i \(-0.989023\pi\)
0.939837 0.341624i \(-0.110977\pi\)
\(948\) −195.716 + 18.8201i −0.206451 + 0.0198524i
\(949\) 291.747i 0.307426i
\(950\) −50.2343 31.1851i −0.0528782 0.0328265i
\(951\) −578.101 + 370.042i −0.607888 + 0.389108i
\(952\) −74.2801 + 458.830i −0.0780253 + 0.481965i
\(953\) −186.945 1180.33i −0.196165 1.23854i −0.867521 0.497401i \(-0.834288\pi\)
0.671356 0.741135i \(-0.265712\pi\)
\(954\) −577.752 + 623.505i −0.605610 + 0.653570i
\(955\) −756.150 + 954.597i −0.791780 + 0.999578i
\(956\) −25.2794 + 77.2031i −0.0264429 + 0.0807564i
\(957\) 1714.45 + 376.218i 1.79149 + 0.393123i
\(958\) −63.6146 404.630i −0.0664035 0.422369i
\(959\) −169.181 + 54.9701i −0.176414 + 0.0573202i
\(960\) 926.628 + 250.920i 0.965237 + 0.261375i
\(961\) 292.943 901.586i 0.304831 0.938174i
\(962\) 44.0679 276.197i 0.0458087 0.287107i
\(963\) 788.820 621.777i 0.819128 0.645667i
\(964\) −679.603 + 219.106i −0.704982 + 0.227288i
\(965\) 309.601 + 62.3323i 0.320830 + 0.0645931i
\(966\) 137.460 + 53.9862i 0.142298 + 0.0558863i
\(967\) 124.218 784.280i 0.128457 0.811045i −0.836371 0.548163i \(-0.815327\pi\)
0.964828 0.262881i \(-0.0846728\pi\)
\(968\) 196.245 + 1267.06i 0.202732 + 1.30894i
\(969\) −24.3738 + 62.2690i −0.0251536 + 0.0642611i
\(970\) 39.4296 922.096i 0.0406491 0.950614i
\(971\) −1331.26 967.215i −1.37102 0.996102i −0.997657 0.0684151i \(-0.978206\pi\)
−0.373360 0.927687i \(-0.621794\pi\)
\(972\) −858.339 + 456.112i −0.883065 + 0.469251i
\(973\) −149.586 293.580i −0.153737 0.301726i
\(974\) −1191.68 + 385.699i −1.22349 + 0.395995i
\(975\) −474.152 67.8471i −0.486310 0.0695867i
\(976\) 396.891 1202.83i 0.406651 1.23240i
\(977\) 364.032 + 714.452i 0.372601 + 0.731271i 0.998830 0.0483684i \(-0.0154021\pi\)
−0.626228 + 0.779640i \(0.715402\pi\)
\(978\) −150.851 + 256.688i −0.154245 + 0.262462i
\(979\) −1552.50 1127.96i −1.58581 1.15216i
\(980\) −435.858 658.855i −0.444753 0.672301i
\(981\) 351.320 + 1766.77i 0.358125 + 1.80099i
\(982\) 464.789 + 237.489i 0.473308 + 0.241842i
\(983\) −130.425 + 823.471i −0.132681 + 0.837712i 0.828136 + 0.560527i \(0.189401\pi\)
−0.960817 + 0.277185i \(0.910599\pi\)
\(984\) −350.890 1363.92i −0.356595 1.38609i
\(985\) 508.074 + 552.202i 0.515811 + 0.560611i
\(986\) 1.49838 1315.15i 0.00151966 1.33382i
\(987\) 24.4180 + 247.998i 0.0247396 + 0.251265i
\(988\) 4.65769 + 29.8475i 0.00471426 + 0.0302101i
\(989\) 49.0802 151.053i 0.0496261 0.152733i
\(990\) −1217.99 891.504i −1.23030 0.900509i
\(991\) 699.711 227.350i 0.706066 0.229415i 0.0660945 0.997813i \(-0.478946\pi\)
0.639972 + 0.768399i \(0.278946\pi\)
\(992\) 113.926 + 18.7100i 0.114845 + 0.0188609i
\(993\) −62.5625 + 285.102i −0.0630035 + 0.287112i
\(994\) 293.836 403.462i 0.295609 0.405898i
\(995\) −183.785 276.443i −0.184708 0.277832i
\(996\) −921.546 1446.94i −0.925247 1.45276i
\(997\) −141.592 893.979i −0.142018 0.896669i −0.951080 0.308945i \(-0.900024\pi\)
0.809061 0.587724i \(-0.199976\pi\)
\(998\) −794.585 + 792.776i −0.796177 + 0.794365i
\(999\) 80.9514 + 585.658i 0.0810325 + 0.586244i
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 300.3.u.a.47.88 yes 928
3.2 odd 2 inner 300.3.u.a.47.29 yes 928
4.3 odd 2 inner 300.3.u.a.47.7 928
12.11 even 2 inner 300.3.u.a.47.110 yes 928
25.8 odd 20 inner 300.3.u.a.83.110 yes 928
75.8 even 20 inner 300.3.u.a.83.7 yes 928
100.83 even 20 inner 300.3.u.a.83.29 yes 928
300.83 odd 20 inner 300.3.u.a.83.88 yes 928
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.3.u.a.47.7 928 4.3 odd 2 inner
300.3.u.a.47.29 yes 928 3.2 odd 2 inner
300.3.u.a.47.88 yes 928 1.1 even 1 trivial
300.3.u.a.47.110 yes 928 12.11 even 2 inner
300.3.u.a.83.7 yes 928 75.8 even 20 inner
300.3.u.a.83.29 yes 928 100.83 even 20 inner
300.3.u.a.83.88 yes 928 300.83 odd 20 inner
300.3.u.a.83.110 yes 928 25.8 odd 20 inner