# Properties

 Label 1600.4.a.bk.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 $1$

# Related objects

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 40) 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)

 $$f(q)$$ $$=$$ $$q+4.00000 q^{3} -16.0000 q^{7} -11.0000 q^{9} +O(q^{10})$$ $$q+4.00000 q^{3} -16.0000 q^{7} -11.0000 q^{9} -36.0000 q^{11} -42.0000 q^{13} +110.000 q^{17} +116.000 q^{19} -64.0000 q^{21} -16.0000 q^{23} -152.000 q^{27} -198.000 q^{29} +240.000 q^{31} -144.000 q^{33} -258.000 q^{37} -168.000 q^{39} +442.000 q^{41} -292.000 q^{43} -392.000 q^{47} -87.0000 q^{49} +440.000 q^{51} +142.000 q^{53} +464.000 q^{57} +348.000 q^{59} +570.000 q^{61} +176.000 q^{63} +692.000 q^{67} -64.0000 q^{69} +168.000 q^{71} +134.000 q^{73} +576.000 q^{77} +784.000 q^{79} -311.000 q^{81} +564.000 q^{83} -792.000 q^{87} +1034.00 q^{89} +672.000 q^{91} +960.000 q^{93} +382.000 q^{97} +396.000 q^{99} +O(q^{100})$$

## 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
$$3$$ 4.00000 0.769800 0.384900 0.922958i $$-0.374236\pi$$
0.384900 + 0.922958i $$0.374236\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −16.0000 −0.863919 −0.431959 0.901893i $$-0.642178\pi$$
−0.431959 + 0.901893i $$0.642178\pi$$
$$8$$ 0 0
$$9$$ −11.0000 −0.407407
$$10$$ 0 0
$$11$$ −36.0000 −0.986764 −0.493382 0.869813i $$-0.664240\pi$$
−0.493382 + 0.869813i $$0.664240\pi$$
$$12$$ 0 0
$$13$$ −42.0000 −0.896054 −0.448027 0.894020i $$-0.647873\pi$$
−0.448027 + 0.894020i $$0.647873\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 110.000 1.56935 0.784674 0.619909i $$-0.212830\pi$$
0.784674 + 0.619909i $$0.212830\pi$$
$$18$$ 0 0
$$19$$ 116.000 1.40064 0.700322 0.713827i $$-0.253040\pi$$
0.700322 + 0.713827i $$0.253040\pi$$
$$20$$ 0 0
$$21$$ −64.0000 −0.665045
$$22$$ 0 0
$$23$$ −16.0000 −0.145054 −0.0725268 0.997366i $$-0.523106\pi$$
−0.0725268 + 0.997366i $$0.523106\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −152.000 −1.08342
$$28$$ 0 0
$$29$$ −198.000 −1.26785 −0.633925 0.773394i $$-0.718557\pi$$
−0.633925 + 0.773394i $$0.718557\pi$$
$$30$$ 0 0
$$31$$ 240.000 1.39049 0.695246 0.718772i $$-0.255295\pi$$
0.695246 + 0.718772i $$0.255295\pi$$
$$32$$ 0 0
$$33$$ −144.000 −0.759612
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −258.000 −1.14635 −0.573175 0.819433i $$-0.694288\pi$$
−0.573175 + 0.819433i $$0.694288\pi$$
$$38$$ 0 0
$$39$$ −168.000 −0.689783
$$40$$ 0 0
$$41$$ 442.000 1.68363 0.841815 0.539767i $$-0.181488\pi$$
0.841815 + 0.539767i $$0.181488\pi$$
$$42$$ 0 0
$$43$$ −292.000 −1.03557 −0.517786 0.855510i $$-0.673244\pi$$
−0.517786 + 0.855510i $$0.673244\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −392.000 −1.21658 −0.608288 0.793716i $$-0.708143\pi$$
−0.608288 + 0.793716i $$0.708143\pi$$
$$48$$ 0 0
$$49$$ −87.0000 −0.253644
$$50$$ 0 0
$$51$$ 440.000 1.20808
$$52$$ 0 0
$$53$$ 142.000 0.368023 0.184011 0.982924i $$-0.441092\pi$$
0.184011 + 0.982924i $$0.441092\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 464.000 1.07822
$$58$$ 0 0
$$59$$ 348.000 0.767894 0.383947 0.923355i $$-0.374565\pi$$
0.383947 + 0.923355i $$0.374565\pi$$
$$60$$ 0 0
$$61$$ 570.000 1.19641 0.598205 0.801343i $$-0.295881\pi$$
0.598205 + 0.801343i $$0.295881\pi$$
$$62$$ 0 0
$$63$$ 176.000 0.351967
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 692.000 1.26181 0.630905 0.775860i $$-0.282684\pi$$
0.630905 + 0.775860i $$0.282684\pi$$
$$68$$ 0 0
$$69$$ −64.0000 −0.111662
$$70$$ 0 0
$$71$$ 168.000 0.280816 0.140408 0.990094i $$-0.455159\pi$$
0.140408 + 0.990094i $$0.455159\pi$$
$$72$$ 0 0
$$73$$ 134.000 0.214843 0.107421 0.994214i $$-0.465741\pi$$
0.107421 + 0.994214i $$0.465741\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 576.000 0.852484
$$78$$ 0 0
$$79$$ 784.000 1.11654 0.558271 0.829658i $$-0.311465\pi$$
0.558271 + 0.829658i $$0.311465\pi$$
$$80$$ 0 0
$$81$$ −311.000 −0.426612
$$82$$ 0 0
$$83$$ 564.000 0.745868 0.372934 0.927858i $$-0.378352\pi$$
0.372934 + 0.927858i $$0.378352\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −792.000 −0.975992
$$88$$ 0 0
$$89$$ 1034.00 1.23150 0.615752 0.787940i $$-0.288852\pi$$
0.615752 + 0.787940i $$0.288852\pi$$
$$90$$ 0 0
$$91$$ 672.000 0.774118
$$92$$ 0 0
$$93$$ 960.000 1.07040
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 382.000 0.399858 0.199929 0.979810i $$-0.435929\pi$$
0.199929 + 0.979810i $$0.435929\pi$$
$$98$$ 0 0
$$99$$ 396.000 0.402015
$$100$$ 0 0
$$101$$ 674.000 0.664015 0.332007 0.943277i $$-0.392274\pi$$
0.332007 + 0.943277i $$0.392274\pi$$
$$102$$ 0 0
$$103$$ 992.000 0.948977 0.474489 0.880262i $$-0.342633\pi$$
0.474489 + 0.880262i $$0.342633\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −500.000 −0.451746 −0.225873 0.974157i $$-0.572523\pi$$
−0.225873 + 0.974157i $$0.572523\pi$$
$$108$$ 0 0
$$109$$ −1046.00 −0.919162 −0.459581 0.888136i $$-0.652000\pi$$
−0.459581 + 0.888136i $$0.652000\pi$$
$$110$$ 0 0
$$111$$ −1032.00 −0.882460
$$112$$ 0 0
$$113$$ 558.000 0.464533 0.232266 0.972652i $$-0.425386\pi$$
0.232266 + 0.972652i $$0.425386\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 462.000 0.365059
$$118$$ 0 0
$$119$$ −1760.00 −1.35579
$$120$$ 0 0
$$121$$ −35.0000 −0.0262960
$$122$$ 0 0
$$123$$ 1768.00 1.29606
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 328.000 0.229176 0.114588 0.993413i $$-0.463445\pi$$
0.114588 + 0.993413i $$0.463445\pi$$
$$128$$ 0 0
$$129$$ −1168.00 −0.797183
$$130$$ 0 0
$$131$$ 212.000 0.141393 0.0706967 0.997498i $$-0.477478\pi$$
0.0706967 + 0.997498i $$0.477478\pi$$
$$132$$ 0 0
$$133$$ −1856.00 −1.21004
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1434.00 −0.894269 −0.447135 0.894467i $$-0.647556\pi$$
−0.447135 + 0.894467i $$0.647556\pi$$
$$138$$ 0 0
$$139$$ −2196.00 −1.34002 −0.670008 0.742354i $$-0.733709\pi$$
−0.670008 + 0.742354i $$0.733709\pi$$
$$140$$ 0 0
$$141$$ −1568.00 −0.936521
$$142$$ 0 0
$$143$$ 1512.00 0.884194
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −348.000 −0.195255
$$148$$ 0 0
$$149$$ 2418.00 1.32946 0.664732 0.747081i $$-0.268546\pi$$
0.664732 + 0.747081i $$0.268546\pi$$
$$150$$ 0 0
$$151$$ 3672.00 1.97896 0.989481 0.144666i $$-0.0462108\pi$$
0.989481 + 0.144666i $$0.0462108\pi$$
$$152$$ 0 0
$$153$$ −1210.00 −0.639364
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 358.000 0.181984 0.0909921 0.995852i $$-0.470996\pi$$
0.0909921 + 0.995852i $$0.470996\pi$$
$$158$$ 0 0
$$159$$ 568.000 0.283304
$$160$$ 0 0
$$161$$ 256.000 0.125314
$$162$$ 0 0
$$163$$ 2564.00 1.23207 0.616037 0.787717i $$-0.288737\pi$$
0.616037 + 0.787717i $$0.288737\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3056.00 1.41605 0.708025 0.706187i $$-0.249586\pi$$
0.708025 + 0.706187i $$0.249586\pi$$
$$168$$ 0 0
$$169$$ −433.000 −0.197087
$$170$$ 0 0
$$171$$ −1276.00 −0.570633
$$172$$ 0 0
$$173$$ −234.000 −0.102836 −0.0514182 0.998677i $$-0.516374\pi$$
−0.0514182 + 0.998677i $$0.516374\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 1392.00 0.591125
$$178$$ 0 0
$$179$$ −524.000 −0.218802 −0.109401 0.993998i $$-0.534893\pi$$
−0.109401 + 0.993998i $$0.534893\pi$$
$$180$$ 0 0
$$181$$ 1138.00 0.467331 0.233665 0.972317i $$-0.424928\pi$$
0.233665 + 0.972317i $$0.424928\pi$$
$$182$$ 0 0
$$183$$ 2280.00 0.920997
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −3960.00 −1.54858
$$188$$ 0 0
$$189$$ 2432.00 0.935989
$$190$$ 0 0
$$191$$ 1520.00 0.575829 0.287915 0.957656i $$-0.407038\pi$$
0.287915 + 0.957656i $$0.407038\pi$$
$$192$$ 0 0
$$193$$ 2142.00 0.798884 0.399442 0.916759i $$-0.369204\pi$$
0.399442 + 0.916759i $$0.369204\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2306.00 −0.833988 −0.416994 0.908909i $$-0.636916\pi$$
−0.416994 + 0.908909i $$0.636916\pi$$
$$198$$ 0 0
$$199$$ 3288.00 1.17126 0.585628 0.810580i $$-0.300848\pi$$
0.585628 + 0.810580i $$0.300848\pi$$
$$200$$ 0 0
$$201$$ 2768.00 0.971342
$$202$$ 0 0
$$203$$ 3168.00 1.09532
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 176.000 0.0590959
$$208$$ 0 0
$$209$$ −4176.00 −1.38211
$$210$$ 0 0
$$211$$ 3876.00 1.26462 0.632310 0.774715i $$-0.282107\pi$$
0.632310 + 0.774715i $$0.282107\pi$$
$$212$$ 0 0
$$213$$ 672.000 0.216172
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −3840.00 −1.20127
$$218$$ 0 0
$$219$$ 536.000 0.165386
$$220$$ 0 0
$$221$$ −4620.00 −1.40622
$$222$$ 0 0
$$223$$ 5688.00 1.70806 0.854028 0.520226i $$-0.174152\pi$$
0.854028 + 0.520226i $$0.174152\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −2796.00 −0.817520 −0.408760 0.912642i $$-0.634039\pi$$
−0.408760 + 0.912642i $$0.634039\pi$$
$$228$$ 0 0
$$229$$ −4446.00 −1.28297 −0.641485 0.767136i $$-0.721681\pi$$
−0.641485 + 0.767136i $$0.721681\pi$$
$$230$$ 0 0
$$231$$ 2304.00 0.656243
$$232$$ 0 0
$$233$$ −2522.00 −0.709106 −0.354553 0.935036i $$-0.615367\pi$$
−0.354553 + 0.935036i $$0.615367\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 3136.00 0.859515
$$238$$ 0 0
$$239$$ 816.000 0.220848 0.110424 0.993885i $$-0.464779\pi$$
0.110424 + 0.993885i $$0.464779\pi$$
$$240$$ 0 0
$$241$$ −5422.00 −1.44922 −0.724609 0.689160i $$-0.757980\pi$$
−0.724609 + 0.689160i $$0.757980\pi$$
$$242$$ 0 0
$$243$$ 2860.00 0.755017
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −4872.00 −1.25505
$$248$$ 0 0
$$249$$ 2256.00 0.574169
$$250$$ 0 0
$$251$$ 5900.00 1.48368 0.741842 0.670575i $$-0.233952\pi$$
0.741842 + 0.670575i $$0.233952\pi$$
$$252$$ 0 0
$$253$$ 576.000 0.143134
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5250.00 −1.27426 −0.637132 0.770754i $$-0.719880\pi$$
−0.637132 + 0.770754i $$0.719880\pi$$
$$258$$ 0 0
$$259$$ 4128.00 0.990353
$$260$$ 0 0
$$261$$ 2178.00 0.516532
$$262$$ 0 0
$$263$$ −6240.00 −1.46302 −0.731511 0.681829i $$-0.761185\pi$$
−0.731511 + 0.681829i $$0.761185\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 4136.00 0.948012
$$268$$ 0 0
$$269$$ 714.000 0.161834 0.0809170 0.996721i $$-0.474215\pi$$
0.0809170 + 0.996721i $$0.474215\pi$$
$$270$$ 0 0
$$271$$ 2144.00 0.480586 0.240293 0.970700i $$-0.422757\pi$$
0.240293 + 0.970700i $$0.422757\pi$$
$$272$$ 0 0
$$273$$ 2688.00 0.595916
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −4466.00 −0.968722 −0.484361 0.874868i $$-0.660948\pi$$
−0.484361 + 0.874868i $$0.660948\pi$$
$$278$$ 0 0
$$279$$ −2640.00 −0.566497
$$280$$ 0 0
$$281$$ −5302.00 −1.12559 −0.562795 0.826596i $$-0.690274\pi$$
−0.562795 + 0.826596i $$0.690274\pi$$
$$282$$ 0 0
$$283$$ −6932.00 −1.45606 −0.728029 0.685546i $$-0.759564\pi$$
−0.728029 + 0.685546i $$0.759564\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −7072.00 −1.45452
$$288$$ 0 0
$$289$$ 7187.00 1.46285
$$290$$ 0 0
$$291$$ 1528.00 0.307811
$$292$$ 0 0
$$293$$ −4034.00 −0.804330 −0.402165 0.915567i $$-0.631742\pi$$
−0.402165 + 0.915567i $$0.631742\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 5472.00 1.06908
$$298$$ 0 0
$$299$$ 672.000 0.129976
$$300$$ 0 0
$$301$$ 4672.00 0.894650
$$302$$ 0 0
$$303$$ 2696.00 0.511159
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −3836.00 −0.713134 −0.356567 0.934270i $$-0.616053\pi$$
−0.356567 + 0.934270i $$0.616053\pi$$
$$308$$ 0 0
$$309$$ 3968.00 0.730523
$$310$$ 0 0
$$311$$ 664.000 0.121067 0.0605337 0.998166i $$-0.480720\pi$$
0.0605337 + 0.998166i $$0.480720\pi$$
$$312$$ 0 0
$$313$$ −2986.00 −0.539229 −0.269615 0.962968i $$-0.586896\pi$$
−0.269615 + 0.962968i $$0.586896\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2726.00 0.482989 0.241494 0.970402i $$-0.422362\pi$$
0.241494 + 0.970402i $$0.422362\pi$$
$$318$$ 0 0
$$319$$ 7128.00 1.25107
$$320$$ 0 0
$$321$$ −2000.00 −0.347754
$$322$$ 0 0
$$323$$ 12760.0 2.19810
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −4184.00 −0.707571
$$328$$ 0 0
$$329$$ 6272.00 1.05102
$$330$$ 0 0
$$331$$ 9212.00 1.52972 0.764860 0.644197i $$-0.222808\pi$$
0.764860 + 0.644197i $$0.222808\pi$$
$$332$$ 0 0
$$333$$ 2838.00 0.467031
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 3278.00 0.529864 0.264932 0.964267i $$-0.414651\pi$$
0.264932 + 0.964267i $$0.414651\pi$$
$$338$$ 0 0
$$339$$ 2232.00 0.357598
$$340$$ 0 0
$$341$$ −8640.00 −1.37209
$$342$$ 0 0
$$343$$ 6880.00 1.08305
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4956.00 0.766721 0.383360 0.923599i $$-0.374767\pi$$
0.383360 + 0.923599i $$0.374767\pi$$
$$348$$ 0 0
$$349$$ −4678.00 −0.717500 −0.358750 0.933434i $$-0.616797\pi$$
−0.358750 + 0.933434i $$0.616797\pi$$
$$350$$ 0 0
$$351$$ 6384.00 0.970805
$$352$$ 0 0
$$353$$ −1890.00 −0.284970 −0.142485 0.989797i $$-0.545509\pi$$
−0.142485 + 0.989797i $$0.545509\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −7040.00 −1.04369
$$358$$ 0 0
$$359$$ −6472.00 −0.951474 −0.475737 0.879588i $$-0.657819\pi$$
−0.475737 + 0.879588i $$0.657819\pi$$
$$360$$ 0 0
$$361$$ 6597.00 0.961802
$$362$$ 0 0
$$363$$ −140.000 −0.0202427
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −1960.00 −0.278777 −0.139389 0.990238i $$-0.544514\pi$$
−0.139389 + 0.990238i $$0.544514\pi$$
$$368$$ 0 0
$$369$$ −4862.00 −0.685923
$$370$$ 0 0
$$371$$ −2272.00 −0.317942
$$372$$ 0 0
$$373$$ 8750.00 1.21463 0.607316 0.794460i $$-0.292246\pi$$
0.607316 + 0.794460i $$0.292246\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 8316.00 1.13606
$$378$$ 0 0
$$379$$ 380.000 0.0515021 0.0257510 0.999668i $$-0.491802\pi$$
0.0257510 + 0.999668i $$0.491802\pi$$
$$380$$ 0 0
$$381$$ 1312.00 0.176419
$$382$$ 0 0
$$383$$ 9688.00 1.29252 0.646258 0.763119i $$-0.276333\pi$$
0.646258 + 0.763119i $$0.276333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 3212.00 0.421900
$$388$$ 0 0
$$389$$ −3870.00 −0.504413 −0.252207 0.967673i $$-0.581156\pi$$
−0.252207 + 0.967673i $$0.581156\pi$$
$$390$$ 0 0
$$391$$ −1760.00 −0.227639
$$392$$ 0 0
$$393$$ 848.000 0.108845
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1622.00 0.205053 0.102526 0.994730i $$-0.467307\pi$$
0.102526 + 0.994730i $$0.467307\pi$$
$$398$$ 0 0
$$399$$ −7424.00 −0.931491
$$400$$ 0 0
$$401$$ 9906.00 1.23362 0.616811 0.787112i $$-0.288424\pi$$
0.616811 + 0.787112i $$0.288424\pi$$
$$402$$ 0 0
$$403$$ −10080.0 −1.24596
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 9288.00 1.13118
$$408$$ 0 0
$$409$$ −4214.00 −0.509459 −0.254730 0.967012i $$-0.581986\pi$$
−0.254730 + 0.967012i $$0.581986\pi$$
$$410$$ 0 0
$$411$$ −5736.00 −0.688409
$$412$$ 0 0
$$413$$ −5568.00 −0.663398
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −8784.00 −1.03155
$$418$$ 0 0
$$419$$ 7012.00 0.817562 0.408781 0.912632i $$-0.365954\pi$$
0.408781 + 0.912632i $$0.365954\pi$$
$$420$$ 0 0
$$421$$ 1602.00 0.185455 0.0927277 0.995692i $$-0.470441\pi$$
0.0927277 + 0.995692i $$0.470441\pi$$
$$422$$ 0 0
$$423$$ 4312.00 0.495642
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −9120.00 −1.03360
$$428$$ 0 0
$$429$$ 6048.00 0.680653
$$430$$ 0 0
$$431$$ −3584.00 −0.400546 −0.200273 0.979740i $$-0.564183\pi$$
−0.200273 + 0.979740i $$0.564183\pi$$
$$432$$ 0 0
$$433$$ 3470.00 0.385121 0.192561 0.981285i $$-0.438321\pi$$
0.192561 + 0.981285i $$0.438321\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1856.00 −0.203168
$$438$$ 0 0
$$439$$ −3416.00 −0.371382 −0.185691 0.982608i $$-0.559452\pi$$
−0.185691 + 0.982608i $$0.559452\pi$$
$$440$$ 0 0
$$441$$ 957.000 0.103337
$$442$$ 0 0
$$443$$ 9708.00 1.04118 0.520588 0.853808i $$-0.325713\pi$$
0.520588 + 0.853808i $$0.325713\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 9672.00 1.02342
$$448$$ 0 0
$$449$$ −10366.0 −1.08954 −0.544768 0.838587i $$-0.683382\pi$$
−0.544768 + 0.838587i $$0.683382\pi$$
$$450$$ 0 0
$$451$$ −15912.0 −1.66135
$$452$$ 0 0
$$453$$ 14688.0 1.52340
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 16742.0 1.71369 0.856847 0.515572i $$-0.172420\pi$$
0.856847 + 0.515572i $$0.172420\pi$$
$$458$$ 0 0
$$459$$ −16720.0 −1.70027
$$460$$ 0 0
$$461$$ 1258.00 0.127095 0.0635476 0.997979i $$-0.479759\pi$$
0.0635476 + 0.997979i $$0.479759\pi$$
$$462$$ 0 0
$$463$$ −13528.0 −1.35788 −0.678941 0.734193i $$-0.737561\pi$$
−0.678941 + 0.734193i $$0.737561\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6916.00 0.685298 0.342649 0.939463i $$-0.388676\pi$$
0.342649 + 0.939463i $$0.388676\pi$$
$$468$$ 0 0
$$469$$ −11072.0 −1.09010
$$470$$ 0 0
$$471$$ 1432.00 0.140091
$$472$$ 0 0
$$473$$ 10512.0 1.02187
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −1562.00 −0.149935
$$478$$ 0 0
$$479$$ 1728.00 0.164832 0.0824158 0.996598i $$-0.473736\pi$$
0.0824158 + 0.996598i $$0.473736\pi$$
$$480$$ 0 0
$$481$$ 10836.0 1.02719
$$482$$ 0 0
$$483$$ 1024.00 0.0964671
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −16656.0 −1.54981 −0.774903 0.632080i $$-0.782201\pi$$
−0.774903 + 0.632080i $$0.782201\pi$$
$$488$$ 0 0
$$489$$ 10256.0 0.948451
$$490$$ 0 0
$$491$$ 1084.00 0.0996339 0.0498169 0.998758i $$-0.484136\pi$$
0.0498169 + 0.998758i $$0.484136\pi$$
$$492$$ 0 0
$$493$$ −21780.0 −1.98970
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −2688.00 −0.242602
$$498$$ 0 0
$$499$$ −5804.00 −0.520687 −0.260343 0.965516i $$-0.583836\pi$$
−0.260343 + 0.965516i $$0.583836\pi$$
$$500$$ 0 0
$$501$$ 12224.0 1.09008
$$502$$ 0 0
$$503$$ −10512.0 −0.931823 −0.465911 0.884831i $$-0.654273\pi$$
−0.465911 + 0.884831i $$0.654273\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −1732.00 −0.151718
$$508$$ 0 0
$$509$$ 4314.00 0.375667 0.187834 0.982201i $$-0.439853\pi$$
0.187834 + 0.982201i $$0.439853\pi$$
$$510$$ 0 0
$$511$$ −2144.00 −0.185607
$$512$$ 0 0
$$513$$ −17632.0 −1.51749
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 14112.0 1.20047
$$518$$ 0 0
$$519$$ −936.000 −0.0791635
$$520$$ 0 0
$$521$$ −1190.00 −0.100067 −0.0500334 0.998748i $$-0.515933\pi$$
−0.0500334 + 0.998748i $$0.515933\pi$$
$$522$$ 0 0
$$523$$ −3780.00 −0.316038 −0.158019 0.987436i $$-0.550511\pi$$
−0.158019 + 0.987436i $$0.550511\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 26400.0 2.18217
$$528$$ 0 0
$$529$$ −11911.0 −0.978959
$$530$$ 0 0
$$531$$ −3828.00 −0.312846
$$532$$ 0 0
$$533$$ −18564.0 −1.50862
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −2096.00 −0.168434
$$538$$ 0 0
$$539$$ 3132.00 0.250287
$$540$$ 0 0
$$541$$ 11002.0 0.874331 0.437165 0.899381i $$-0.355982\pi$$
0.437165 + 0.899381i $$0.355982\pi$$
$$542$$ 0 0
$$543$$ 4552.00 0.359751
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 5908.00 0.461806 0.230903 0.972977i $$-0.425832\pi$$
0.230903 + 0.972977i $$0.425832\pi$$
$$548$$ 0 0
$$549$$ −6270.00 −0.487426
$$550$$ 0 0
$$551$$ −22968.0 −1.77581
$$552$$ 0 0
$$553$$ −12544.0 −0.964602
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 14806.0 1.12630 0.563151 0.826354i $$-0.309589\pi$$
0.563151 + 0.826354i $$0.309589\pi$$
$$558$$ 0 0
$$559$$ 12264.0 0.927928
$$560$$ 0 0
$$561$$ −15840.0 −1.19210
$$562$$ 0 0
$$563$$ −684.000 −0.0512028 −0.0256014 0.999672i $$-0.508150\pi$$
−0.0256014 + 0.999672i $$0.508150\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 4976.00 0.368558
$$568$$ 0 0
$$569$$ −2582.00 −0.190234 −0.0951169 0.995466i $$-0.530323\pi$$
−0.0951169 + 0.995466i $$0.530323\pi$$
$$570$$ 0 0
$$571$$ 2540.00 0.186157 0.0930785 0.995659i $$-0.470329\pi$$
0.0930785 + 0.995659i $$0.470329\pi$$
$$572$$ 0 0
$$573$$ 6080.00 0.443273
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −22786.0 −1.64401 −0.822005 0.569480i $$-0.807144\pi$$
−0.822005 + 0.569480i $$0.807144\pi$$
$$578$$ 0 0
$$579$$ 8568.00 0.614981
$$580$$ 0 0
$$581$$ −9024.00 −0.644369
$$582$$ 0 0
$$583$$ −5112.00 −0.363152
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7884.00 0.554357 0.277178 0.960818i $$-0.410601\pi$$
0.277178 + 0.960818i $$0.410601\pi$$
$$588$$ 0 0
$$589$$ 27840.0 1.94758
$$590$$ 0 0
$$591$$ −9224.00 −0.642005
$$592$$ 0 0
$$593$$ 21902.0 1.51671 0.758354 0.651843i $$-0.226004\pi$$
0.758354 + 0.651843i $$0.226004\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 13152.0 0.901634
$$598$$ 0 0
$$599$$ 15080.0 1.02863 0.514317 0.857600i $$-0.328045\pi$$
0.514317 + 0.857600i $$0.328045\pi$$
$$600$$ 0 0
$$601$$ −19702.0 −1.33721 −0.668603 0.743619i $$-0.733108\pi$$
−0.668603 + 0.743619i $$0.733108\pi$$
$$602$$ 0 0
$$603$$ −7612.00 −0.514071
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −7320.00 −0.489472 −0.244736 0.969590i $$-0.578701\pi$$
−0.244736 + 0.969590i $$0.578701\pi$$
$$608$$ 0 0
$$609$$ 12672.0 0.843178
$$610$$ 0 0
$$611$$ 16464.0 1.09012
$$612$$ 0 0
$$613$$ 24350.0 1.60438 0.802192 0.597066i $$-0.203667\pi$$
0.802192 + 0.597066i $$0.203667\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −19546.0 −1.27535 −0.637676 0.770305i $$-0.720104\pi$$
−0.637676 + 0.770305i $$0.720104\pi$$
$$618$$ 0 0
$$619$$ −3476.00 −0.225706 −0.112853 0.993612i $$-0.535999\pi$$
−0.112853 + 0.993612i $$0.535999\pi$$
$$620$$ 0 0
$$621$$ 2432.00 0.157154
$$622$$ 0 0
$$623$$ −16544.0 −1.06392
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −16704.0 −1.06394
$$628$$ 0 0
$$629$$ −28380.0 −1.79902
$$630$$ 0 0
$$631$$ 21880.0 1.38039 0.690197 0.723621i $$-0.257524\pi$$
0.690197 + 0.723621i $$0.257524\pi$$
$$632$$ 0 0
$$633$$ 15504.0 0.973505
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 3654.00 0.227279
$$638$$ 0 0
$$639$$ −1848.00 −0.114406
$$640$$ 0 0
$$641$$ 20994.0 1.29362 0.646812 0.762649i $$-0.276102\pi$$
0.646812 + 0.762649i $$0.276102\pi$$
$$642$$ 0 0
$$643$$ −18204.0 −1.11648 −0.558239 0.829680i $$-0.688523\pi$$
−0.558239 + 0.829680i $$0.688523\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 2064.00 0.125416 0.0627080 0.998032i $$-0.480026\pi$$
0.0627080 + 0.998032i $$0.480026\pi$$
$$648$$ 0 0
$$649$$ −12528.0 −0.757730
$$650$$ 0 0
$$651$$ −15360.0 −0.924740
$$652$$ 0 0
$$653$$ 9942.00 0.595805 0.297902 0.954596i $$-0.403713\pi$$
0.297902 + 0.954596i $$0.403713\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −1474.00 −0.0875285
$$658$$ 0 0
$$659$$ −24236.0 −1.43263 −0.716313 0.697779i $$-0.754172\pi$$
−0.716313 + 0.697779i $$0.754172\pi$$
$$660$$ 0 0
$$661$$ −17614.0 −1.03647 −0.518234 0.855239i $$-0.673410\pi$$
−0.518234 + 0.855239i $$0.673410\pi$$
$$662$$ 0 0
$$663$$ −18480.0 −1.08251
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3168.00 0.183906
$$668$$ 0 0
$$669$$ 22752.0 1.31486
$$670$$ 0 0
$$671$$ −20520.0 −1.18057
$$672$$ 0 0
$$673$$ −13058.0 −0.747918 −0.373959 0.927445i $$-0.622000\pi$$
−0.373959 + 0.927445i $$0.622000\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −33186.0 −1.88396 −0.941980 0.335668i $$-0.891038\pi$$
−0.941980 + 0.335668i $$0.891038\pi$$
$$678$$ 0 0
$$679$$ −6112.00 −0.345445
$$680$$ 0 0
$$681$$ −11184.0 −0.629327
$$682$$ 0 0
$$683$$ −31716.0 −1.77684 −0.888418 0.459035i $$-0.848195\pi$$
−0.888418 + 0.459035i $$0.848195\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −17784.0 −0.987630
$$688$$ 0 0
$$689$$ −5964.00 −0.329768
$$690$$ 0 0
$$691$$ 2084.00 0.114731 0.0573655 0.998353i $$-0.481730\pi$$
0.0573655 + 0.998353i $$0.481730\pi$$
$$692$$ 0 0
$$693$$ −6336.00 −0.347308
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 48620.0 2.64220
$$698$$ 0 0
$$699$$ −10088.0 −0.545870
$$700$$ 0 0
$$701$$ 7418.00 0.399678 0.199839 0.979829i $$-0.435958\pi$$
0.199839 + 0.979829i $$0.435958\pi$$
$$702$$ 0 0
$$703$$ −29928.0 −1.60563
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −10784.0 −0.573655
$$708$$ 0 0
$$709$$ 18242.0 0.966280 0.483140 0.875543i $$-0.339496\pi$$
0.483140 + 0.875543i $$0.339496\pi$$
$$710$$ 0 0
$$711$$ −8624.00 −0.454888
$$712$$ 0 0
$$713$$ −3840.00 −0.201696
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 3264.00 0.170009
$$718$$ 0 0
$$719$$ 3024.00 0.156851 0.0784257 0.996920i $$-0.475011\pi$$
0.0784257 + 0.996920i $$0.475011\pi$$
$$720$$ 0 0
$$721$$ −15872.0 −0.819839
$$722$$ 0 0
$$723$$ −21688.0 −1.11561
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 26176.0 1.33537 0.667685 0.744444i $$-0.267285\pi$$
0.667685 + 0.744444i $$0.267285\pi$$
$$728$$ 0 0
$$729$$ 19837.0 1.00782
$$730$$ 0 0
$$731$$ −32120.0 −1.62517
$$732$$ 0 0
$$733$$ −17818.0 −0.897848 −0.448924 0.893570i $$-0.648193\pi$$
−0.448924 + 0.893570i $$0.648193\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −24912.0 −1.24511
$$738$$ 0 0
$$739$$ 22052.0 1.09769 0.548847 0.835923i $$-0.315067\pi$$
0.548847 + 0.835923i $$0.315067\pi$$
$$740$$ 0 0
$$741$$ −19488.0 −0.966140
$$742$$ 0 0
$$743$$ −15840.0 −0.782117 −0.391059 0.920366i $$-0.627891\pi$$
−0.391059 + 0.920366i $$0.627891\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −6204.00 −0.303872
$$748$$ 0 0
$$749$$ 8000.00 0.390272
$$750$$ 0 0
$$751$$ 21024.0 1.02154 0.510770 0.859717i $$-0.329360\pi$$
0.510770 + 0.859717i $$0.329360\pi$$
$$752$$ 0 0
$$753$$ 23600.0 1.14214
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −38034.0 −1.82612 −0.913058 0.407831i $$-0.866285\pi$$
−0.913058 + 0.407831i $$0.866285\pi$$
$$758$$ 0 0
$$759$$ 2304.00 0.110184
$$760$$ 0 0
$$761$$ 37802.0 1.80069 0.900343 0.435182i $$-0.143316\pi$$
0.900343 + 0.435182i $$0.143316\pi$$
$$762$$ 0 0
$$763$$ 16736.0 0.794081
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −14616.0 −0.688075
$$768$$ 0 0
$$769$$ 15042.0 0.705369 0.352684 0.935742i $$-0.385269\pi$$
0.352684 + 0.935742i $$0.385269\pi$$
$$770$$ 0 0
$$771$$ −21000.0 −0.980929
$$772$$ 0 0
$$773$$ 5950.00 0.276852 0.138426 0.990373i $$-0.455796\pi$$
0.138426 + 0.990373i $$0.455796\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 16512.0 0.762374
$$778$$ 0 0
$$779$$ 51272.0 2.35816
$$780$$ 0 0
$$781$$ −6048.00 −0.277099
$$782$$ 0 0
$$783$$ 30096.0 1.37362
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 23364.0 1.05824 0.529121 0.848546i $$-0.322522\pi$$
0.529121 + 0.848546i $$0.322522\pi$$
$$788$$ 0 0
$$789$$ −24960.0 −1.12624
$$790$$ 0 0
$$791$$ −8928.00 −0.401319
$$792$$ 0 0
$$793$$ −23940.0 −1.07205
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 19846.0 0.882034 0.441017 0.897499i $$-0.354618\pi$$
0.441017 + 0.897499i $$0.354618\pi$$
$$798$$ 0 0
$$799$$ −43120.0 −1.90923
$$800$$ 0 0
$$801$$ −11374.0 −0.501724
$$802$$ 0 0
$$803$$ −4824.00 −0.211999
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 2856.00 0.124580
$$808$$ 0 0
$$809$$ 24762.0 1.07613 0.538063 0.842905i $$-0.319156\pi$$
0.538063 + 0.842905i $$0.319156\pi$$
$$810$$ 0 0
$$811$$ −16644.0 −0.720653 −0.360327 0.932826i $$-0.617335\pi$$
−0.360327 + 0.932826i $$0.617335\pi$$
$$812$$ 0 0
$$813$$ 8576.00 0.369955
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −33872.0 −1.45047
$$818$$ 0 0
$$819$$ −7392.00 −0.315381
$$820$$ 0 0
$$821$$ −3182.00 −0.135265 −0.0676325 0.997710i $$-0.521545\pi$$
−0.0676325 + 0.997710i $$0.521545\pi$$
$$822$$ 0 0
$$823$$ 7504.00 0.317829 0.158914 0.987292i $$-0.449201\pi$$
0.158914 + 0.987292i $$0.449201\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 12604.0 0.529969 0.264984 0.964253i $$-0.414633\pi$$
0.264984 + 0.964253i $$0.414633\pi$$
$$828$$ 0 0
$$829$$ −12230.0 −0.512383 −0.256191 0.966626i $$-0.582468\pi$$
−0.256191 + 0.966626i $$0.582468\pi$$
$$830$$ 0 0
$$831$$ −17864.0 −0.745722
$$832$$ 0 0
$$833$$ −9570.00 −0.398056
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −36480.0 −1.50649
$$838$$ 0 0
$$839$$ 9656.00 0.397333 0.198666 0.980067i $$-0.436339\pi$$
0.198666 + 0.980067i $$0.436339\pi$$
$$840$$ 0 0
$$841$$ 14815.0 0.607446
$$842$$ 0 0
$$843$$ −21208.0 −0.866480
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 560.000 0.0227176
$$848$$ 0 0
$$849$$ −27728.0 −1.12087
$$850$$ 0 0
$$851$$ 4128.00 0.166282
$$852$$ 0 0
$$853$$ 5806.00 0.233052 0.116526 0.993188i $$-0.462824\pi$$
0.116526 + 0.993188i $$0.462824\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 39094.0 1.55826 0.779128 0.626865i $$-0.215662\pi$$
0.779128 + 0.626865i $$0.215662\pi$$
$$858$$ 0 0
$$859$$ 18876.0 0.749756 0.374878 0.927074i $$-0.377685\pi$$
0.374878 + 0.927074i $$0.377685\pi$$
$$860$$ 0 0
$$861$$ −28288.0 −1.11969
$$862$$ 0 0
$$863$$ −32296.0 −1.27389 −0.636946 0.770909i $$-0.719803\pi$$
−0.636946 + 0.770909i $$0.719803\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 28748.0 1.12611
$$868$$ 0 0
$$869$$ −28224.0 −1.10176
$$870$$ 0 0
$$871$$ −29064.0 −1.13065
$$872$$ 0 0
$$873$$ −4202.00 −0.162905
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −9578.00 −0.368787 −0.184393 0.982853i $$-0.559032\pi$$
−0.184393 + 0.982853i $$0.559032\pi$$
$$878$$ 0 0
$$879$$ −16136.0 −0.619174
$$880$$ 0 0
$$881$$ −41710.0 −1.59506 −0.797529 0.603281i $$-0.793860\pi$$
−0.797529 + 0.603281i $$0.793860\pi$$
$$882$$ 0 0
$$883$$ 2260.00 0.0861326 0.0430663 0.999072i $$-0.486287\pi$$
0.0430663 + 0.999072i $$0.486287\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 33696.0 1.27554 0.637768 0.770228i $$-0.279858\pi$$
0.637768 + 0.770228i $$0.279858\pi$$
$$888$$ 0 0
$$889$$ −5248.00 −0.197989
$$890$$ 0 0
$$891$$ 11196.0 0.420965
$$892$$ 0 0
$$893$$ −45472.0 −1.70399
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 2688.00 0.100055
$$898$$ 0 0
$$899$$ −47520.0 −1.76294
$$900$$ 0 0
$$901$$ 15620.0 0.577556
$$902$$ 0 0
$$903$$ 18688.0 0.688702
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 7756.00 0.283940 0.141970 0.989871i $$-0.454656\pi$$
0.141970 + 0.989871i $$0.454656\pi$$
$$908$$ 0 0
$$909$$ −7414.00 −0.270525
$$910$$ 0 0
$$911$$ −5312.00 −0.193188 −0.0965941 0.995324i $$-0.530795\pi$$
−0.0965941 + 0.995324i $$0.530795\pi$$
$$912$$ 0 0
$$913$$ −20304.0 −0.735996
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −3392.00 −0.122152
$$918$$ 0 0
$$919$$ −23576.0 −0.846246 −0.423123 0.906072i $$-0.639066\pi$$
−0.423123 + 0.906072i $$0.639066\pi$$
$$920$$ 0 0
$$921$$ −15344.0 −0.548971
$$922$$ 0 0
$$923$$ −7056.00 −0.251626
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −10912.0 −0.386620
$$928$$ 0 0
$$929$$ −19038.0 −0.672354 −0.336177 0.941799i $$-0.609134\pi$$
−0.336177 + 0.941799i $$0.609134\pi$$
$$930$$ 0 0
$$931$$ −10092.0 −0.355265
$$932$$ 0 0
$$933$$ 2656.00 0.0931978
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −20570.0 −0.717175 −0.358587 0.933496i $$-0.616741\pi$$
−0.358587 + 0.933496i $$0.616741\pi$$
$$938$$ 0 0
$$939$$ −11944.0 −0.415099
$$940$$ 0 0
$$941$$ 21386.0 0.740875 0.370438 0.928857i $$-0.379208\pi$$
0.370438 + 0.928857i $$0.379208\pi$$
$$942$$ 0 0
$$943$$ −7072.00 −0.244216
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 38020.0 1.30463 0.652315 0.757948i $$-0.273798\pi$$
0.652315 + 0.757948i $$0.273798\pi$$
$$948$$ 0 0
$$949$$ −5628.00 −0.192511
$$950$$ 0 0
$$951$$ 10904.0 0.371805
$$952$$ 0 0
$$953$$ −20202.0 −0.686681 −0.343340 0.939211i $$-0.611558\pi$$
−0.343340 + 0.939211i $$0.611558\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 28512.0 0.963074
$$958$$ 0 0
$$959$$ 22944.0 0.772576
$$960$$ 0 0
$$961$$ 27809.0 0.933470
$$962$$ 0 0
$$963$$ 5500.00 0.184045
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −29840.0 −0.992337 −0.496168 0.868226i $$-0.665260\pi$$
−0.496168 + 0.868226i $$0.665260\pi$$
$$968$$ 0 0
$$969$$ 51040.0 1.69210
$$970$$ 0 0
$$971$$ 12476.0 0.412332 0.206166 0.978517i $$-0.433901\pi$$
0.206166 + 0.978517i $$0.433901\pi$$
$$972$$ 0 0
$$973$$ 35136.0 1.15767
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 36974.0 1.21075 0.605375 0.795940i $$-0.293023\pi$$
0.605375 + 0.795940i $$0.293023\pi$$
$$978$$ 0 0
$$979$$ −37224.0 −1.21520
$$980$$ 0 0
$$981$$ 11506.0 0.374473
$$982$$ 0 0
$$983$$ 16368.0 0.531087 0.265543 0.964099i $$-0.414449\pi$$
0.265543 + 0.964099i $$0.414449\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 25088.0 0.809078
$$988$$ 0 0
$$989$$ 4672.00 0.150213
$$990$$ 0 0
$$991$$ −49552.0 −1.58837 −0.794183 0.607678i $$-0.792101\pi$$
−0.794183 + 0.607678i $$0.792101\pi$$
$$992$$ 0 0
$$993$$ 36848.0 1.17758
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 24414.0 0.775526 0.387763 0.921759i $$-0.373248\pi$$
0.387763 + 0.921759i $$0.373248\pi$$
$$998$$ 0 0
$$999$$ 39216.0 1.24198
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.bk.1.1 1
4.3 odd 2 1600.4.a.q.1.1 1
5.4 even 2 320.4.a.e.1.1 1
8.3 odd 2 400.4.a.p.1.1 1
8.5 even 2 200.4.a.d.1.1 1
20.19 odd 2 320.4.a.j.1.1 1
24.5 odd 2 1800.4.a.h.1.1 1
40.3 even 4 400.4.c.h.49.2 2
40.13 odd 4 200.4.c.f.49.1 2
40.19 odd 2 80.4.a.b.1.1 1
40.27 even 4 400.4.c.h.49.1 2
40.29 even 2 40.4.a.b.1.1 1
40.37 odd 4 200.4.c.f.49.2 2
80.19 odd 4 1280.4.d.m.641.2 2
80.29 even 4 1280.4.d.d.641.1 2
80.59 odd 4 1280.4.d.m.641.1 2
80.69 even 4 1280.4.d.d.641.2 2
120.29 odd 2 360.4.a.f.1.1 1
120.53 even 4 1800.4.f.d.649.2 2
120.59 even 2 720.4.a.d.1.1 1
120.77 even 4 1800.4.f.d.649.1 2
280.69 odd 2 1960.4.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.b.1.1 1 40.29 even 2
80.4.a.b.1.1 1 40.19 odd 2
200.4.a.d.1.1 1 8.5 even 2
200.4.c.f.49.1 2 40.13 odd 4
200.4.c.f.49.2 2 40.37 odd 4
320.4.a.e.1.1 1 5.4 even 2
320.4.a.j.1.1 1 20.19 odd 2
360.4.a.f.1.1 1 120.29 odd 2
400.4.a.p.1.1 1 8.3 odd 2
400.4.c.h.49.1 2 40.27 even 4
400.4.c.h.49.2 2 40.3 even 4
720.4.a.d.1.1 1 120.59 even 2
1280.4.d.d.641.1 2 80.29 even 4
1280.4.d.d.641.2 2 80.69 even 4
1280.4.d.m.641.1 2 80.59 odd 4
1280.4.d.m.641.2 2 80.19 odd 4
1600.4.a.q.1.1 1 4.3 odd 2
1600.4.a.bk.1.1 1 1.1 even 1 trivial
1800.4.a.h.1.1 1 24.5 odd 2
1800.4.f.d.649.1 2 120.77 even 4
1800.4.f.d.649.2 2 120.53 even 4
1960.4.a.e.1.1 1 280.69 odd 2