# Properties

 Label 1600.4.a.bi.1.1 Level $1600$ Weight $4$ Character 1600.1 Self dual yes Analytic conductor $94.403$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,4,Mod(1,1600)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1600.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1600.a (trivial)

## 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: yes Analytic conductor: $$94.4030560092$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 5) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1600.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} -6.00000 q^{7} -23.0000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} -6.00000 q^{7} -23.0000 q^{9} -32.0000 q^{11} -38.0000 q^{13} -26.0000 q^{17} -100.000 q^{19} -12.0000 q^{21} +78.0000 q^{23} -100.000 q^{27} +50.0000 q^{29} -108.000 q^{31} -64.0000 q^{33} +266.000 q^{37} -76.0000 q^{39} +22.0000 q^{41} +442.000 q^{43} +514.000 q^{47} -307.000 q^{49} -52.0000 q^{51} +2.00000 q^{53} -200.000 q^{57} -500.000 q^{59} +518.000 q^{61} +138.000 q^{63} +126.000 q^{67} +156.000 q^{69} +412.000 q^{71} +878.000 q^{73} +192.000 q^{77} +600.000 q^{79} +421.000 q^{81} +282.000 q^{83} +100.000 q^{87} -150.000 q^{89} +228.000 q^{91} -216.000 q^{93} -386.000 q^{97} +736.000 q^{99} +O(q^{100})$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2.00000 0.384900 0.192450 0.981307i $$-0.438357\pi$$
0.192450 + 0.981307i $$0.438357\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −6.00000 −0.323970 −0.161985 0.986793i $$-0.551790\pi$$
−0.161985 + 0.986793i $$0.551790\pi$$
$$8$$ 0 0
$$9$$ −23.0000 −0.851852
$$10$$ 0 0
$$11$$ −32.0000 −0.877124 −0.438562 0.898701i $$-0.644512\pi$$
−0.438562 + 0.898701i $$0.644512\pi$$
$$12$$ 0 0
$$13$$ −38.0000 −0.810716 −0.405358 0.914158i $$-0.632853\pi$$
−0.405358 + 0.914158i $$0.632853\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −26.0000 −0.370937 −0.185468 0.982650i $$-0.559380\pi$$
−0.185468 + 0.982650i $$0.559380\pi$$
$$18$$ 0 0
$$19$$ −100.000 −1.20745 −0.603726 0.797192i $$-0.706318\pi$$
−0.603726 + 0.797192i $$0.706318\pi$$
$$20$$ 0 0
$$21$$ −12.0000 −0.124696
$$22$$ 0 0
$$23$$ 78.0000 0.707136 0.353568 0.935409i $$-0.384968\pi$$
0.353568 + 0.935409i $$0.384968\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −100.000 −0.712778
$$28$$ 0 0
$$29$$ 50.0000 0.320164 0.160082 0.987104i $$-0.448824\pi$$
0.160082 + 0.987104i $$0.448824\pi$$
$$30$$ 0 0
$$31$$ −108.000 −0.625722 −0.312861 0.949799i $$-0.601287\pi$$
−0.312861 + 0.949799i $$0.601287\pi$$
$$32$$ 0 0
$$33$$ −64.0000 −0.337605
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 266.000 1.18190 0.590948 0.806710i $$-0.298754\pi$$
0.590948 + 0.806710i $$0.298754\pi$$
$$38$$ 0 0
$$39$$ −76.0000 −0.312045
$$40$$ 0 0
$$41$$ 22.0000 0.0838006 0.0419003 0.999122i $$-0.486659\pi$$
0.0419003 + 0.999122i $$0.486659\pi$$
$$42$$ 0 0
$$43$$ 442.000 1.56754 0.783772 0.621049i $$-0.213293\pi$$
0.783772 + 0.621049i $$0.213293\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 514.000 1.59520 0.797602 0.603184i $$-0.206101\pi$$
0.797602 + 0.603184i $$0.206101\pi$$
$$48$$ 0 0
$$49$$ −307.000 −0.895044
$$50$$ 0 0
$$51$$ −52.0000 −0.142774
$$52$$ 0 0
$$53$$ 2.00000 0.00518342 0.00259171 0.999997i $$-0.499175\pi$$
0.00259171 + 0.999997i $$0.499175\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −200.000 −0.464748
$$58$$ 0 0
$$59$$ −500.000 −1.10330 −0.551648 0.834077i $$-0.686001\pi$$
−0.551648 + 0.834077i $$0.686001\pi$$
$$60$$ 0 0
$$61$$ 518.000 1.08726 0.543632 0.839324i $$-0.317049\pi$$
0.543632 + 0.839324i $$0.317049\pi$$
$$62$$ 0 0
$$63$$ 138.000 0.275974
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 126.000 0.229751 0.114876 0.993380i $$-0.463353\pi$$
0.114876 + 0.993380i $$0.463353\pi$$
$$68$$ 0 0
$$69$$ 156.000 0.272177
$$70$$ 0 0
$$71$$ 412.000 0.688668 0.344334 0.938847i $$-0.388105\pi$$
0.344334 + 0.938847i $$0.388105\pi$$
$$72$$ 0 0
$$73$$ 878.000 1.40770 0.703850 0.710348i $$-0.251463\pi$$
0.703850 + 0.710348i $$0.251463\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 192.000 0.284161
$$78$$ 0 0
$$79$$ 600.000 0.854497 0.427249 0.904134i $$-0.359483\pi$$
0.427249 + 0.904134i $$0.359483\pi$$
$$80$$ 0 0
$$81$$ 421.000 0.577503
$$82$$ 0 0
$$83$$ 282.000 0.372934 0.186467 0.982461i $$-0.440296\pi$$
0.186467 + 0.982461i $$0.440296\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 100.000 0.123231
$$88$$ 0 0
$$89$$ −150.000 −0.178651 −0.0893257 0.996002i $$-0.528471\pi$$
−0.0893257 + 0.996002i $$0.528471\pi$$
$$90$$ 0 0
$$91$$ 228.000 0.262647
$$92$$ 0 0
$$93$$ −216.000 −0.240840
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −386.000 −0.404045 −0.202022 0.979381i $$-0.564751\pi$$
−0.202022 + 0.979381i $$0.564751\pi$$
$$98$$ 0 0
$$99$$ 736.000 0.747180
$$100$$ 0 0
$$101$$ −702.000 −0.691600 −0.345800 0.938308i $$-0.612392\pi$$
−0.345800 + 0.938308i $$0.612392\pi$$
$$102$$ 0 0
$$103$$ 598.000 0.572065 0.286032 0.958220i $$-0.407663\pi$$
0.286032 + 0.958220i $$0.407663\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1194.00 −1.07877 −0.539385 0.842059i $$-0.681343\pi$$
−0.539385 + 0.842059i $$0.681343\pi$$
$$108$$ 0 0
$$109$$ 550.000 0.483307 0.241653 0.970363i $$-0.422310\pi$$
0.241653 + 0.970363i $$0.422310\pi$$
$$110$$ 0 0
$$111$$ 532.000 0.454912
$$112$$ 0 0
$$113$$ −1562.00 −1.30036 −0.650180 0.759781i $$-0.725306\pi$$
−0.650180 + 0.759781i $$0.725306\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 874.000 0.690610
$$118$$ 0 0
$$119$$ 156.000 0.120172
$$120$$ 0 0
$$121$$ −307.000 −0.230654
$$122$$ 0 0
$$123$$ 44.0000 0.0322548
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −1846.00 −1.28981 −0.644906 0.764262i $$-0.723103\pi$$
−0.644906 + 0.764262i $$0.723103\pi$$
$$128$$ 0 0
$$129$$ 884.000 0.603348
$$130$$ 0 0
$$131$$ 2208.00 1.47262 0.736312 0.676642i $$-0.236565\pi$$
0.736312 + 0.676642i $$0.236565\pi$$
$$132$$ 0 0
$$133$$ 600.000 0.391177
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2334.00 1.45553 0.727763 0.685829i $$-0.240560\pi$$
0.727763 + 0.685829i $$0.240560\pi$$
$$138$$ 0 0
$$139$$ 700.000 0.427146 0.213573 0.976927i $$-0.431490\pi$$
0.213573 + 0.976927i $$0.431490\pi$$
$$140$$ 0 0
$$141$$ 1028.00 0.613994
$$142$$ 0 0
$$143$$ 1216.00 0.711098
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −614.000 −0.344502
$$148$$ 0 0
$$149$$ −2050.00 −1.12713 −0.563566 0.826071i $$-0.690571\pi$$
−0.563566 + 0.826071i $$0.690571\pi$$
$$150$$ 0 0
$$151$$ 1852.00 0.998103 0.499052 0.866572i $$-0.333682\pi$$
0.499052 + 0.866572i $$0.333682\pi$$
$$152$$ 0 0
$$153$$ 598.000 0.315983
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −2494.00 −1.26779 −0.633894 0.773420i $$-0.718545\pi$$
−0.633894 + 0.773420i $$0.718545\pi$$
$$158$$ 0 0
$$159$$ 4.00000 0.00199510
$$160$$ 0 0
$$161$$ −468.000 −0.229090
$$162$$ 0 0
$$163$$ 2762.00 1.32722 0.663609 0.748080i $$-0.269024\pi$$
0.663609 + 0.748080i $$0.269024\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −3126.00 −1.44849 −0.724243 0.689545i $$-0.757811\pi$$
−0.724243 + 0.689545i $$0.757811\pi$$
$$168$$ 0 0
$$169$$ −753.000 −0.342740
$$170$$ 0 0
$$171$$ 2300.00 1.02857
$$172$$ 0 0
$$173$$ −78.0000 −0.0342788 −0.0171394 0.999853i $$-0.505456\pi$$
−0.0171394 + 0.999853i $$0.505456\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −1000.00 −0.424659
$$178$$ 0 0
$$179$$ 1300.00 0.542830 0.271415 0.962462i $$-0.412508\pi$$
0.271415 + 0.962462i $$0.412508\pi$$
$$180$$ 0 0
$$181$$ −1742.00 −0.715369 −0.357685 0.933842i $$-0.616434\pi$$
−0.357685 + 0.933842i $$0.616434\pi$$
$$182$$ 0 0
$$183$$ 1036.00 0.418488
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 832.000 0.325358
$$188$$ 0 0
$$189$$ 600.000 0.230918
$$190$$ 0 0
$$191$$ 3772.00 1.42897 0.714483 0.699653i $$-0.246662\pi$$
0.714483 + 0.699653i $$0.246662\pi$$
$$192$$ 0 0
$$193$$ 358.000 0.133520 0.0667601 0.997769i $$-0.478734\pi$$
0.0667601 + 0.997769i $$0.478734\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2214.00 −0.800716 −0.400358 0.916359i $$-0.631114\pi$$
−0.400358 + 0.916359i $$0.631114\pi$$
$$198$$ 0 0
$$199$$ −2600.00 −0.926176 −0.463088 0.886312i $$-0.653259\pi$$
−0.463088 + 0.886312i $$0.653259\pi$$
$$200$$ 0 0
$$201$$ 252.000 0.0884314
$$202$$ 0 0
$$203$$ −300.000 −0.103724
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1794.00 −0.602375
$$208$$ 0 0
$$209$$ 3200.00 1.05908
$$210$$ 0 0
$$211$$ 1168.00 0.381083 0.190541 0.981679i $$-0.438976\pi$$
0.190541 + 0.981679i $$0.438976\pi$$
$$212$$ 0 0
$$213$$ 824.000 0.265068
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 648.000 0.202715
$$218$$ 0 0
$$219$$ 1756.00 0.541824
$$220$$ 0 0
$$221$$ 988.000 0.300724
$$222$$ 0 0
$$223$$ 6478.00 1.94529 0.972643 0.232303i $$-0.0746262\pi$$
0.972643 + 0.232303i $$0.0746262\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 646.000 0.188883 0.0944417 0.995530i $$-0.469893\pi$$
0.0944417 + 0.995530i $$0.469893\pi$$
$$228$$ 0 0
$$229$$ −3750.00 −1.08213 −0.541063 0.840982i $$-0.681978\pi$$
−0.541063 + 0.840982i $$0.681978\pi$$
$$230$$ 0 0
$$231$$ 384.000 0.109374
$$232$$ 0 0
$$233$$ −1482.00 −0.416691 −0.208346 0.978055i $$-0.566808\pi$$
−0.208346 + 0.978055i $$0.566808\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 1200.00 0.328896
$$238$$ 0 0
$$239$$ 1400.00 0.378906 0.189453 0.981890i $$-0.439329\pi$$
0.189453 + 0.981890i $$0.439329\pi$$
$$240$$ 0 0
$$241$$ 3022.00 0.807735 0.403867 0.914817i $$-0.367666\pi$$
0.403867 + 0.914817i $$0.367666\pi$$
$$242$$ 0 0
$$243$$ 3542.00 0.935059
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3800.00 0.978900
$$248$$ 0 0
$$249$$ 564.000 0.143542
$$250$$ 0 0
$$251$$ 1248.00 0.313837 0.156918 0.987612i $$-0.449844\pi$$
0.156918 + 0.987612i $$0.449844\pi$$
$$252$$ 0 0
$$253$$ −2496.00 −0.620246
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −2106.00 −0.511162 −0.255581 0.966788i $$-0.582267\pi$$
−0.255581 + 0.966788i $$0.582267\pi$$
$$258$$ 0 0
$$259$$ −1596.00 −0.382898
$$260$$ 0 0
$$261$$ −1150.00 −0.272733
$$262$$ 0 0
$$263$$ 3638.00 0.852961 0.426480 0.904497i $$-0.359753\pi$$
0.426480 + 0.904497i $$0.359753\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −300.000 −0.0687629
$$268$$ 0 0
$$269$$ 6550.00 1.48461 0.742306 0.670061i $$-0.233732\pi$$
0.742306 + 0.670061i $$0.233732\pi$$
$$270$$ 0 0
$$271$$ −4388.00 −0.983587 −0.491793 0.870712i $$-0.663658\pi$$
−0.491793 + 0.870712i $$0.663658\pi$$
$$272$$ 0 0
$$273$$ 456.000 0.101093
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 546.000 0.118433 0.0592165 0.998245i $$-0.481140\pi$$
0.0592165 + 0.998245i $$0.481140\pi$$
$$278$$ 0 0
$$279$$ 2484.00 0.533022
$$280$$ 0 0
$$281$$ −6858.00 −1.45592 −0.727961 0.685619i $$-0.759532\pi$$
−0.727961 + 0.685619i $$0.759532\pi$$
$$282$$ 0 0
$$283$$ 9282.00 1.94967 0.974837 0.222920i $$-0.0715588\pi$$
0.974837 + 0.222920i $$0.0715588\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −132.000 −0.0271488
$$288$$ 0 0
$$289$$ −4237.00 −0.862406
$$290$$ 0 0
$$291$$ −772.000 −0.155517
$$292$$ 0 0
$$293$$ 4842.00 0.965436 0.482718 0.875776i $$-0.339650\pi$$
0.482718 + 0.875776i $$0.339650\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 3200.00 0.625195
$$298$$ 0 0
$$299$$ −2964.00 −0.573286
$$300$$ 0 0
$$301$$ −2652.00 −0.507836
$$302$$ 0 0
$$303$$ −1404.00 −0.266197
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −2594.00 −0.482239 −0.241120 0.970495i $$-0.577515\pi$$
−0.241120 + 0.970495i $$0.577515\pi$$
$$308$$ 0 0
$$309$$ 1196.00 0.220188
$$310$$ 0 0
$$311$$ 7332.00 1.33685 0.668424 0.743781i $$-0.266969\pi$$
0.668424 + 0.743781i $$0.266969\pi$$
$$312$$ 0 0
$$313$$ −1562.00 −0.282075 −0.141037 0.990004i $$-0.545044\pi$$
−0.141037 + 0.990004i $$0.545044\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1426.00 0.252657 0.126328 0.991988i $$-0.459681\pi$$
0.126328 + 0.991988i $$0.459681\pi$$
$$318$$ 0 0
$$319$$ −1600.00 −0.280824
$$320$$ 0 0
$$321$$ −2388.00 −0.415219
$$322$$ 0 0
$$323$$ 2600.00 0.447888
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 1100.00 0.186025
$$328$$ 0 0
$$329$$ −3084.00 −0.516798
$$330$$ 0 0
$$331$$ 4008.00 0.665558 0.332779 0.943005i $$-0.392014\pi$$
0.332779 + 0.943005i $$0.392014\pi$$
$$332$$ 0 0
$$333$$ −6118.00 −1.00680
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −8866.00 −1.43312 −0.716561 0.697525i $$-0.754285\pi$$
−0.716561 + 0.697525i $$0.754285\pi$$
$$338$$ 0 0
$$339$$ −3124.00 −0.500509
$$340$$ 0 0
$$341$$ 3456.00 0.548835
$$342$$ 0 0
$$343$$ 3900.00 0.613936
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1714.00 −0.265165 −0.132583 0.991172i $$-0.542327\pi$$
−0.132583 + 0.991172i $$0.542327\pi$$
$$348$$ 0 0
$$349$$ −1150.00 −0.176384 −0.0881921 0.996103i $$-0.528109\pi$$
−0.0881921 + 0.996103i $$0.528109\pi$$
$$350$$ 0 0
$$351$$ 3800.00 0.577860
$$352$$ 0 0
$$353$$ 4398.00 0.663122 0.331561 0.943434i $$-0.392425\pi$$
0.331561 + 0.943434i $$0.392425\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 312.000 0.0462543
$$358$$ 0 0
$$359$$ 1800.00 0.264625 0.132312 0.991208i $$-0.457760\pi$$
0.132312 + 0.991208i $$0.457760\pi$$
$$360$$ 0 0
$$361$$ 3141.00 0.457938
$$362$$ 0 0
$$363$$ −614.000 −0.0887786
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 5874.00 0.835478 0.417739 0.908567i $$-0.362823\pi$$
0.417739 + 0.908567i $$0.362823\pi$$
$$368$$ 0 0
$$369$$ −506.000 −0.0713857
$$370$$ 0 0
$$371$$ −12.0000 −0.00167927
$$372$$ 0 0
$$373$$ −2078.00 −0.288458 −0.144229 0.989544i $$-0.546070\pi$$
−0.144229 + 0.989544i $$0.546070\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −1900.00 −0.259562
$$378$$ 0 0
$$379$$ −7900.00 −1.07070 −0.535351 0.844630i $$-0.679821\pi$$
−0.535351 + 0.844630i $$0.679821\pi$$
$$380$$ 0 0
$$381$$ −3692.00 −0.496449
$$382$$ 0 0
$$383$$ 7518.00 1.00301 0.501504 0.865155i $$-0.332780\pi$$
0.501504 + 0.865155i $$0.332780\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −10166.0 −1.33531
$$388$$ 0 0
$$389$$ 1950.00 0.254162 0.127081 0.991892i $$-0.459439\pi$$
0.127081 + 0.991892i $$0.459439\pi$$
$$390$$ 0 0
$$391$$ −2028.00 −0.262303
$$392$$ 0 0
$$393$$ 4416.00 0.566814
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 13786.0 1.74282 0.871410 0.490555i $$-0.163206\pi$$
0.871410 + 0.490555i $$0.163206\pi$$
$$398$$ 0 0
$$399$$ 1200.00 0.150564
$$400$$ 0 0
$$401$$ 6402.00 0.797258 0.398629 0.917112i $$-0.369486\pi$$
0.398629 + 0.917112i $$0.369486\pi$$
$$402$$ 0 0
$$403$$ 4104.00 0.507282
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −8512.00 −1.03667
$$408$$ 0 0
$$409$$ 11150.0 1.34800 0.674000 0.738731i $$-0.264575\pi$$
0.674000 + 0.738731i $$0.264575\pi$$
$$410$$ 0 0
$$411$$ 4668.00 0.560232
$$412$$ 0 0
$$413$$ 3000.00 0.357434
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 1400.00 0.164408
$$418$$ 0 0
$$419$$ 13700.0 1.59735 0.798674 0.601764i $$-0.205535\pi$$
0.798674 + 0.601764i $$0.205535\pi$$
$$420$$ 0 0
$$421$$ 5438.00 0.629529 0.314765 0.949170i $$-0.398074\pi$$
0.314765 + 0.949170i $$0.398074\pi$$
$$422$$ 0 0
$$423$$ −11822.0 −1.35888
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −3108.00 −0.352240
$$428$$ 0 0
$$429$$ 2432.00 0.273702
$$430$$ 0 0
$$431$$ 7692.00 0.859653 0.429827 0.902911i $$-0.358575\pi$$
0.429827 + 0.902911i $$0.358575\pi$$
$$432$$ 0 0
$$433$$ 1118.00 0.124082 0.0620412 0.998074i $$-0.480239\pi$$
0.0620412 + 0.998074i $$0.480239\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −7800.00 −0.853832
$$438$$ 0 0
$$439$$ −2600.00 −0.282668 −0.141334 0.989962i $$-0.545139\pi$$
−0.141334 + 0.989962i $$0.545139\pi$$
$$440$$ 0 0
$$441$$ 7061.00 0.762445
$$442$$ 0 0
$$443$$ −11958.0 −1.28249 −0.641243 0.767337i $$-0.721581\pi$$
−0.641243 + 0.767337i $$0.721581\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −4100.00 −0.433833
$$448$$ 0 0
$$449$$ −17050.0 −1.79207 −0.896035 0.443984i $$-0.853565\pi$$
−0.896035 + 0.443984i $$0.853565\pi$$
$$450$$ 0 0
$$451$$ −704.000 −0.0735035
$$452$$ 0 0
$$453$$ 3704.00 0.384170
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 9494.00 0.971796 0.485898 0.874016i $$-0.338493\pi$$
0.485898 + 0.874016i $$0.338493\pi$$
$$458$$ 0 0
$$459$$ 2600.00 0.264396
$$460$$ 0 0
$$461$$ 11418.0 1.15356 0.576778 0.816901i $$-0.304310\pi$$
0.576778 + 0.816901i $$0.304310\pi$$
$$462$$ 0 0
$$463$$ −7962.00 −0.799191 −0.399596 0.916692i $$-0.630849\pi$$
−0.399596 + 0.916692i $$0.630849\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6526.00 0.646654 0.323327 0.946287i $$-0.395199\pi$$
0.323327 + 0.946287i $$0.395199\pi$$
$$468$$ 0 0
$$469$$ −756.000 −0.0744325
$$470$$ 0 0
$$471$$ −4988.00 −0.487972
$$472$$ 0 0
$$473$$ −14144.0 −1.37493
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −46.0000 −0.00441550
$$478$$ 0 0
$$479$$ 17400.0 1.65976 0.829881 0.557940i $$-0.188408\pi$$
0.829881 + 0.557940i $$0.188408\pi$$
$$480$$ 0 0
$$481$$ −10108.0 −0.958181
$$482$$ 0 0
$$483$$ −936.000 −0.0881770
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −1166.00 −0.108494 −0.0542469 0.998528i $$-0.517276\pi$$
−0.0542469 + 0.998528i $$0.517276\pi$$
$$488$$ 0 0
$$489$$ 5524.00 0.510846
$$490$$ 0 0
$$491$$ −7072.00 −0.650010 −0.325005 0.945712i $$-0.605366\pi$$
−0.325005 + 0.945712i $$0.605366\pi$$
$$492$$ 0 0
$$493$$ −1300.00 −0.118761
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −2472.00 −0.223107
$$498$$ 0 0
$$499$$ −100.000 −0.00897117 −0.00448559 0.999990i $$-0.501428\pi$$
−0.00448559 + 0.999990i $$0.501428\pi$$
$$500$$ 0 0
$$501$$ −6252.00 −0.557522
$$502$$ 0 0
$$503$$ −2602.00 −0.230651 −0.115325 0.993328i $$-0.536791\pi$$
−0.115325 + 0.993328i $$0.536791\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −1506.00 −0.131921
$$508$$ 0 0
$$509$$ −11150.0 −0.970953 −0.485476 0.874250i $$-0.661354\pi$$
−0.485476 + 0.874250i $$0.661354\pi$$
$$510$$ 0 0
$$511$$ −5268.00 −0.456052
$$512$$ 0 0
$$513$$ 10000.0 0.860645
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −16448.0 −1.39919
$$518$$ 0 0
$$519$$ −156.000 −0.0131939
$$520$$ 0 0
$$521$$ −3638.00 −0.305919 −0.152959 0.988232i $$-0.548880\pi$$
−0.152959 + 0.988232i $$0.548880\pi$$
$$522$$ 0 0
$$523$$ −2078.00 −0.173737 −0.0868686 0.996220i $$-0.527686\pi$$
−0.0868686 + 0.996220i $$0.527686\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 2808.00 0.232103
$$528$$ 0 0
$$529$$ −6083.00 −0.499959
$$530$$ 0 0
$$531$$ 11500.0 0.939845
$$532$$ 0 0
$$533$$ −836.000 −0.0679384
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 2600.00 0.208935
$$538$$ 0 0
$$539$$ 9824.00 0.785064
$$540$$ 0 0
$$541$$ −5622.00 −0.446781 −0.223391 0.974729i $$-0.571713\pi$$
−0.223391 + 0.974729i $$0.571713\pi$$
$$542$$ 0 0
$$543$$ −3484.00 −0.275346
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 16486.0 1.28865 0.644324 0.764753i $$-0.277139\pi$$
0.644324 + 0.764753i $$0.277139\pi$$
$$548$$ 0 0
$$549$$ −11914.0 −0.926188
$$550$$ 0 0
$$551$$ −5000.00 −0.386583
$$552$$ 0 0
$$553$$ −3600.00 −0.276831
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 11706.0 0.890483 0.445242 0.895410i $$-0.353118\pi$$
0.445242 + 0.895410i $$0.353118\pi$$
$$558$$ 0 0
$$559$$ −16796.0 −1.27083
$$560$$ 0 0
$$561$$ 1664.00 0.125230
$$562$$ 0 0
$$563$$ −25038.0 −1.87429 −0.937146 0.348939i $$-0.886542\pi$$
−0.937146 + 0.348939i $$0.886542\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −2526.00 −0.187094
$$568$$ 0 0
$$569$$ 17550.0 1.29303 0.646515 0.762901i $$-0.276226\pi$$
0.646515 + 0.762901i $$0.276226\pi$$
$$570$$ 0 0
$$571$$ −10712.0 −0.785084 −0.392542 0.919734i $$-0.628404\pi$$
−0.392542 + 0.919734i $$0.628404\pi$$
$$572$$ 0 0
$$573$$ 7544.00 0.550009
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 13654.0 0.985136 0.492568 0.870274i $$-0.336058\pi$$
0.492568 + 0.870274i $$0.336058\pi$$
$$578$$ 0 0
$$579$$ 716.000 0.0513920
$$580$$ 0 0
$$581$$ −1692.00 −0.120819
$$582$$ 0 0
$$583$$ −64.0000 −0.00454650
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 14166.0 0.996071 0.498035 0.867157i $$-0.334055\pi$$
0.498035 + 0.867157i $$0.334055\pi$$
$$588$$ 0 0
$$589$$ 10800.0 0.755528
$$590$$ 0 0
$$591$$ −4428.00 −0.308196
$$592$$ 0 0
$$593$$ −17842.0 −1.23555 −0.617777 0.786354i $$-0.711966\pi$$
−0.617777 + 0.786354i $$0.711966\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −5200.00 −0.356485
$$598$$ 0 0
$$599$$ −17600.0 −1.20053 −0.600264 0.799802i $$-0.704938\pi$$
−0.600264 + 0.799802i $$0.704938\pi$$
$$600$$ 0 0
$$601$$ 27302.0 1.85303 0.926516 0.376256i $$-0.122789\pi$$
0.926516 + 0.376256i $$0.122789\pi$$
$$602$$ 0 0
$$603$$ −2898.00 −0.195714
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 3794.00 0.253696 0.126848 0.991922i $$-0.459514\pi$$
0.126848 + 0.991922i $$0.459514\pi$$
$$608$$ 0 0
$$609$$ −600.000 −0.0399232
$$610$$ 0 0
$$611$$ −19532.0 −1.29326
$$612$$ 0 0
$$613$$ −13238.0 −0.872231 −0.436116 0.899891i $$-0.643646\pi$$
−0.436116 + 0.899891i $$0.643646\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 11574.0 0.755189 0.377595 0.925971i $$-0.376751\pi$$
0.377595 + 0.925971i $$0.376751\pi$$
$$618$$ 0 0
$$619$$ −8300.00 −0.538942 −0.269471 0.963008i $$-0.586849\pi$$
−0.269471 + 0.963008i $$0.586849\pi$$
$$620$$ 0 0
$$621$$ −7800.00 −0.504031
$$622$$ 0 0
$$623$$ 900.000 0.0578776
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 6400.00 0.407642
$$628$$ 0 0
$$629$$ −6916.00 −0.438409
$$630$$ 0 0
$$631$$ −7508.00 −0.473675 −0.236837 0.971549i $$-0.576111\pi$$
−0.236837 + 0.971549i $$0.576111\pi$$
$$632$$ 0 0
$$633$$ 2336.00 0.146679
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 11666.0 0.725626
$$638$$ 0 0
$$639$$ −9476.00 −0.586643
$$640$$ 0 0
$$641$$ −27378.0 −1.68700 −0.843499 0.537130i $$-0.819508\pi$$
−0.843499 + 0.537130i $$0.819508\pi$$
$$642$$ 0 0
$$643$$ 1842.00 0.112973 0.0564863 0.998403i $$-0.482010\pi$$
0.0564863 + 0.998403i $$0.482010\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 10114.0 0.614563 0.307282 0.951619i $$-0.400581\pi$$
0.307282 + 0.951619i $$0.400581\pi$$
$$648$$ 0 0
$$649$$ 16000.0 0.967727
$$650$$ 0 0
$$651$$ 1296.00 0.0780250
$$652$$ 0 0
$$653$$ 10402.0 0.623372 0.311686 0.950185i $$-0.399106\pi$$
0.311686 + 0.950185i $$0.399106\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −20194.0 −1.19915
$$658$$ 0 0
$$659$$ −7100.00 −0.419692 −0.209846 0.977734i $$-0.567296\pi$$
−0.209846 + 0.977734i $$0.567296\pi$$
$$660$$ 0 0
$$661$$ 7118.00 0.418847 0.209424 0.977825i $$-0.432841\pi$$
0.209424 + 0.977825i $$0.432841\pi$$
$$662$$ 0 0
$$663$$ 1976.00 0.115749
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3900.00 0.226400
$$668$$ 0 0
$$669$$ 12956.0 0.748741
$$670$$ 0 0
$$671$$ −16576.0 −0.953665
$$672$$ 0 0
$$673$$ 31278.0 1.79150 0.895749 0.444560i $$-0.146640\pi$$
0.895749 + 0.444560i $$0.146640\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −30054.0 −1.70616 −0.853079 0.521782i $$-0.825268\pi$$
−0.853079 + 0.521782i $$0.825268\pi$$
$$678$$ 0 0
$$679$$ 2316.00 0.130898
$$680$$ 0 0
$$681$$ 1292.00 0.0727012
$$682$$ 0 0
$$683$$ −4518.00 −0.253113 −0.126557 0.991959i $$-0.540393\pi$$
−0.126557 + 0.991959i $$0.540393\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −7500.00 −0.416511
$$688$$ 0 0
$$689$$ −76.0000 −0.00420228
$$690$$ 0 0
$$691$$ −29272.0 −1.61152 −0.805759 0.592243i $$-0.798242\pi$$
−0.805759 + 0.592243i $$0.798242\pi$$
$$692$$ 0 0
$$693$$ −4416.00 −0.242063
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −572.000 −0.0310847
$$698$$ 0 0
$$699$$ −2964.00 −0.160385
$$700$$ 0 0
$$701$$ 5798.00 0.312393 0.156196 0.987726i $$-0.450077\pi$$
0.156196 + 0.987726i $$0.450077\pi$$
$$702$$ 0 0
$$703$$ −26600.0 −1.42708
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 4212.00 0.224057
$$708$$ 0 0
$$709$$ −8950.00 −0.474082 −0.237041 0.971500i $$-0.576178\pi$$
−0.237041 + 0.971500i $$0.576178\pi$$
$$710$$ 0 0
$$711$$ −13800.0 −0.727905
$$712$$ 0 0
$$713$$ −8424.00 −0.442470
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 2800.00 0.145841
$$718$$ 0 0
$$719$$ 7800.00 0.404577 0.202289 0.979326i $$-0.435162\pi$$
0.202289 + 0.979326i $$0.435162\pi$$
$$720$$ 0 0
$$721$$ −3588.00 −0.185332
$$722$$ 0 0
$$723$$ 6044.00 0.310897
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 8554.00 0.436383 0.218191 0.975906i $$-0.429984\pi$$
0.218191 + 0.975906i $$0.429984\pi$$
$$728$$ 0 0
$$729$$ −4283.00 −0.217599
$$730$$ 0 0
$$731$$ −11492.0 −0.581460
$$732$$ 0 0
$$733$$ 2882.00 0.145224 0.0726119 0.997360i $$-0.476867\pi$$
0.0726119 + 0.997360i $$0.476867\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −4032.00 −0.201521
$$738$$ 0 0
$$739$$ −18700.0 −0.930840 −0.465420 0.885090i $$-0.654097\pi$$
−0.465420 + 0.885090i $$0.654097\pi$$
$$740$$ 0 0
$$741$$ 7600.00 0.376779
$$742$$ 0 0
$$743$$ −12242.0 −0.604462 −0.302231 0.953235i $$-0.597731\pi$$
−0.302231 + 0.953235i $$0.597731\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −6486.00 −0.317685
$$748$$ 0 0
$$749$$ 7164.00 0.349488
$$750$$ 0 0
$$751$$ −31148.0 −1.51346 −0.756729 0.653729i $$-0.773204\pi$$
−0.756729 + 0.653729i $$0.773204\pi$$
$$752$$ 0 0
$$753$$ 2496.00 0.120796
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −7694.00 −0.369410 −0.184705 0.982794i $$-0.559133\pi$$
−0.184705 + 0.982794i $$0.559133\pi$$
$$758$$ 0 0
$$759$$ −4992.00 −0.238733
$$760$$ 0 0
$$761$$ −4518.00 −0.215213 −0.107607 0.994194i $$-0.534319\pi$$
−0.107607 + 0.994194i $$0.534319\pi$$
$$762$$ 0 0
$$763$$ −3300.00 −0.156577
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 19000.0 0.894459
$$768$$ 0 0
$$769$$ −39550.0 −1.85463 −0.927314 0.374283i $$-0.877889\pi$$
−0.927314 + 0.374283i $$0.877889\pi$$
$$770$$ 0 0
$$771$$ −4212.00 −0.196746
$$772$$ 0 0
$$773$$ 22122.0 1.02933 0.514666 0.857391i $$-0.327916\pi$$
0.514666 + 0.857391i $$0.327916\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −3192.00 −0.147378
$$778$$ 0 0
$$779$$ −2200.00 −0.101185
$$780$$ 0 0
$$781$$ −13184.0 −0.604047
$$782$$ 0 0
$$783$$ −5000.00 −0.228206
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −16634.0 −0.753416 −0.376708 0.926332i $$-0.622944\pi$$
−0.376708 + 0.926332i $$0.622944\pi$$
$$788$$ 0 0
$$789$$ 7276.00 0.328305
$$790$$ 0 0
$$791$$ 9372.00 0.421277
$$792$$ 0 0
$$793$$ −19684.0 −0.881462
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 27586.0 1.22603 0.613015 0.790071i $$-0.289956\pi$$
0.613015 + 0.790071i $$0.289956\pi$$
$$798$$ 0 0
$$799$$ −13364.0 −0.591720
$$800$$ 0 0
$$801$$ 3450.00 0.152184
$$802$$ 0 0
$$803$$ −28096.0 −1.23473
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 13100.0 0.571427
$$808$$ 0 0
$$809$$ 3850.00 0.167316 0.0836581 0.996495i $$-0.473340\pi$$
0.0836581 + 0.996495i $$0.473340\pi$$
$$810$$ 0 0
$$811$$ −10032.0 −0.434366 −0.217183 0.976131i $$-0.569687\pi$$
−0.217183 + 0.976131i $$0.569687\pi$$
$$812$$ 0 0
$$813$$ −8776.00 −0.378583
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −44200.0 −1.89273
$$818$$ 0 0
$$819$$ −5244.00 −0.223736
$$820$$ 0 0
$$821$$ −20562.0 −0.874079 −0.437039 0.899442i $$-0.643973\pi$$
−0.437039 + 0.899442i $$0.643973\pi$$
$$822$$ 0 0
$$823$$ −10322.0 −0.437184 −0.218592 0.975816i $$-0.570146\pi$$
−0.218592 + 0.975816i $$0.570146\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 8846.00 0.371954 0.185977 0.982554i $$-0.440455\pi$$
0.185977 + 0.982554i $$0.440455\pi$$
$$828$$ 0 0
$$829$$ 25350.0 1.06205 0.531026 0.847355i $$-0.321806\pi$$
0.531026 + 0.847355i $$0.321806\pi$$
$$830$$ 0 0
$$831$$ 1092.00 0.0455849
$$832$$ 0 0
$$833$$ 7982.00 0.332005
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 10800.0 0.446001
$$838$$ 0 0
$$839$$ 46000.0 1.89284 0.946422 0.322932i $$-0.104669\pi$$
0.946422 + 0.322932i $$0.104669\pi$$
$$840$$ 0 0
$$841$$ −21889.0 −0.897495
$$842$$ 0 0
$$843$$ −13716.0 −0.560385
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 1842.00 0.0747248
$$848$$ 0 0
$$849$$ 18564.0 0.750430
$$850$$ 0 0
$$851$$ 20748.0 0.835761
$$852$$ 0 0
$$853$$ −16998.0 −0.682298 −0.341149 0.940009i $$-0.610816\pi$$
−0.341149 + 0.940009i $$0.610816\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 26494.0 1.05603 0.528015 0.849235i $$-0.322936\pi$$
0.528015 + 0.849235i $$0.322936\pi$$
$$858$$ 0 0
$$859$$ 21500.0 0.853982 0.426991 0.904256i $$-0.359574\pi$$
0.426991 + 0.904256i $$0.359574\pi$$
$$860$$ 0 0
$$861$$ −264.000 −0.0104496
$$862$$ 0 0
$$863$$ −25762.0 −1.01616 −0.508082 0.861309i $$-0.669645\pi$$
−0.508082 + 0.861309i $$0.669645\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −8474.00 −0.331940
$$868$$ 0 0
$$869$$ −19200.0 −0.749500
$$870$$ 0 0
$$871$$ −4788.00 −0.186263
$$872$$ 0 0
$$873$$ 8878.00 0.344186
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 30546.0 1.17613 0.588064 0.808814i $$-0.299890\pi$$
0.588064 + 0.808814i $$0.299890\pi$$
$$878$$ 0 0
$$879$$ 9684.00 0.371596
$$880$$ 0 0
$$881$$ 32942.0 1.25976 0.629878 0.776694i $$-0.283105\pi$$
0.629878 + 0.776694i $$0.283105\pi$$
$$882$$ 0 0
$$883$$ −27118.0 −1.03351 −0.516757 0.856132i $$-0.672861\pi$$
−0.516757 + 0.856132i $$0.672861\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 38634.0 1.46246 0.731230 0.682131i $$-0.238946\pi$$
0.731230 + 0.682131i $$0.238946\pi$$
$$888$$ 0 0
$$889$$ 11076.0 0.417860
$$890$$ 0 0
$$891$$ −13472.0 −0.506542
$$892$$ 0 0
$$893$$ −51400.0 −1.92613
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −5928.00 −0.220658
$$898$$ 0 0
$$899$$ −5400.00 −0.200334
$$900$$ 0 0
$$901$$ −52.0000 −0.00192272
$$902$$ 0 0
$$903$$ −5304.00 −0.195466
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −1794.00 −0.0656767 −0.0328384 0.999461i $$-0.510455\pi$$
−0.0328384 + 0.999461i $$0.510455\pi$$
$$908$$ 0 0
$$909$$ 16146.0 0.589141
$$910$$ 0 0
$$911$$ 41732.0 1.51772 0.758860 0.651254i $$-0.225757\pi$$
0.758860 + 0.651254i $$0.225757\pi$$
$$912$$ 0 0
$$913$$ −9024.00 −0.327109
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −13248.0 −0.477086
$$918$$ 0 0
$$919$$ 29200.0 1.04812 0.524058 0.851682i $$-0.324417\pi$$
0.524058 + 0.851682i $$0.324417\pi$$
$$920$$ 0 0
$$921$$ −5188.00 −0.185614
$$922$$ 0 0
$$923$$ −15656.0 −0.558314
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −13754.0 −0.487315
$$928$$ 0 0
$$929$$ −48650.0 −1.71814 −0.859071 0.511856i $$-0.828958\pi$$
−0.859071 + 0.511856i $$0.828958\pi$$
$$930$$ 0 0
$$931$$ 30700.0 1.08072
$$932$$ 0 0
$$933$$ 14664.0 0.514553
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 11334.0 0.395161 0.197580 0.980287i $$-0.436692\pi$$
0.197580 + 0.980287i $$0.436692\pi$$
$$938$$ 0 0
$$939$$ −3124.00 −0.108571
$$940$$ 0 0
$$941$$ 31178.0 1.08010 0.540050 0.841633i $$-0.318405\pi$$
0.540050 + 0.841633i $$0.318405\pi$$
$$942$$ 0 0
$$943$$ 1716.00 0.0592584
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 4686.00 0.160797 0.0803984 0.996763i $$-0.474381\pi$$
0.0803984 + 0.996763i $$0.474381\pi$$
$$948$$ 0 0
$$949$$ −33364.0 −1.14124
$$950$$ 0 0
$$951$$ 2852.00 0.0972476
$$952$$ 0 0
$$953$$ 598.000 0.0203265 0.0101632 0.999948i $$-0.496765\pi$$
0.0101632 + 0.999948i $$0.496765\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −3200.00 −0.108089
$$958$$ 0 0
$$959$$ −14004.0 −0.471546
$$960$$ 0 0
$$961$$ −18127.0 −0.608472
$$962$$ 0 0
$$963$$ 27462.0 0.918952
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −41726.0 −1.38761 −0.693804 0.720163i $$-0.744067\pi$$
−0.693804 + 0.720163i $$0.744067\pi$$
$$968$$ 0 0
$$969$$ 5200.00 0.172392
$$970$$ 0 0
$$971$$ −24312.0 −0.803511 −0.401756 0.915747i $$-0.631600\pi$$
−0.401756 + 0.915747i $$0.631600\pi$$
$$972$$ 0 0
$$973$$ −4200.00 −0.138382
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −40946.0 −1.34082 −0.670409 0.741992i $$-0.733881\pi$$
−0.670409 + 0.741992i $$0.733881\pi$$
$$978$$ 0 0
$$979$$ 4800.00 0.156699
$$980$$ 0 0
$$981$$ −12650.0 −0.411706
$$982$$ 0 0
$$983$$ −42282.0 −1.37191 −0.685954 0.727645i $$-0.740615\pi$$
−0.685954 + 0.727645i $$0.740615\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −6168.00 −0.198916
$$988$$ 0 0
$$989$$ 34476.0 1.10847
$$990$$ 0 0
$$991$$ 1172.00 0.0375679 0.0187840 0.999824i $$-0.494021\pi$$
0.0187840 + 0.999824i $$0.494021\pi$$
$$992$$ 0 0
$$993$$ 8016.00 0.256173
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −31614.0 −1.00424 −0.502119 0.864798i $$-0.667446\pi$$
−0.502119 + 0.864798i $$0.667446\pi$$
$$998$$ 0 0
$$999$$ −26600.0 −0.842429
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1600.4.a.bi.1.1 1
4.3 odd 2 1600.4.a.s.1.1 1
5.4 even 2 320.4.a.g.1.1 1
8.3 odd 2 400.4.a.m.1.1 1
8.5 even 2 25.4.a.c.1.1 1
20.19 odd 2 320.4.a.h.1.1 1
24.5 odd 2 225.4.a.b.1.1 1
40.3 even 4 400.4.c.k.49.2 2
40.13 odd 4 25.4.b.a.24.1 2
40.19 odd 2 80.4.a.d.1.1 1
40.27 even 4 400.4.c.k.49.1 2
40.29 even 2 5.4.a.a.1.1 1
40.37 odd 4 25.4.b.a.24.2 2
56.13 odd 2 1225.4.a.k.1.1 1
80.19 odd 4 1280.4.d.l.641.2 2
80.29 even 4 1280.4.d.e.641.1 2
80.59 odd 4 1280.4.d.l.641.1 2
80.69 even 4 1280.4.d.e.641.2 2
120.29 odd 2 45.4.a.d.1.1 1
120.53 even 4 225.4.b.c.199.2 2
120.59 even 2 720.4.a.u.1.1 1
120.77 even 4 225.4.b.c.199.1 2
280.69 odd 2 245.4.a.a.1.1 1
280.109 even 6 245.4.e.f.226.1 2
280.149 even 6 245.4.e.f.116.1 2
280.229 odd 6 245.4.e.g.116.1 2
280.269 odd 6 245.4.e.g.226.1 2
360.29 odd 6 405.4.e.c.271.1 2
360.149 odd 6 405.4.e.c.136.1 2
360.229 even 6 405.4.e.l.136.1 2
360.349 even 6 405.4.e.l.271.1 2
440.109 odd 2 605.4.a.d.1.1 1
520.389 even 2 845.4.a.b.1.1 1
680.509 even 2 1445.4.a.a.1.1 1
760.189 odd 2 1805.4.a.h.1.1 1
840.629 even 2 2205.4.a.q.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
5.4.a.a.1.1 1 40.29 even 2
25.4.a.c.1.1 1 8.5 even 2
25.4.b.a.24.1 2 40.13 odd 4
25.4.b.a.24.2 2 40.37 odd 4
45.4.a.d.1.1 1 120.29 odd 2
80.4.a.d.1.1 1 40.19 odd 2
225.4.a.b.1.1 1 24.5 odd 2
225.4.b.c.199.1 2 120.77 even 4
225.4.b.c.199.2 2 120.53 even 4
245.4.a.a.1.1 1 280.69 odd 2
245.4.e.f.116.1 2 280.149 even 6
245.4.e.f.226.1 2 280.109 even 6
245.4.e.g.116.1 2 280.229 odd 6
245.4.e.g.226.1 2 280.269 odd 6
320.4.a.g.1.1 1 5.4 even 2
320.4.a.h.1.1 1 20.19 odd 2
400.4.a.m.1.1 1 8.3 odd 2
400.4.c.k.49.1 2 40.27 even 4
400.4.c.k.49.2 2 40.3 even 4
405.4.e.c.136.1 2 360.149 odd 6
405.4.e.c.271.1 2 360.29 odd 6
405.4.e.l.136.1 2 360.229 even 6
405.4.e.l.271.1 2 360.349 even 6
605.4.a.d.1.1 1 440.109 odd 2
720.4.a.u.1.1 1 120.59 even 2
845.4.a.b.1.1 1 520.389 even 2
1225.4.a.k.1.1 1 56.13 odd 2
1280.4.d.e.641.1 2 80.29 even 4
1280.4.d.e.641.2 2 80.69 even 4
1280.4.d.l.641.1 2 80.59 odd 4
1280.4.d.l.641.2 2 80.19 odd 4
1445.4.a.a.1.1 1 680.509 even 2
1600.4.a.s.1.1 1 4.3 odd 2
1600.4.a.bi.1.1 1 1.1 even 1 trivial
1805.4.a.h.1.1 1 760.189 odd 2
2205.4.a.q.1.1 1 840.629 even 2