# Properties

 Label 1800.4.a.o.1.1 Level $1800$ Weight $4$ Character 1800.1 Self dual yes Analytic conductor $106.203$ 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] = [1800,4,Mod(1,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1800.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1800.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: $$106.203438010$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 120) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1800.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-4.00000 q^{7} +O(q^{10})$$ $$q-4.00000 q^{7} +28.0000 q^{11} +16.0000 q^{13} +108.000 q^{17} +32.0000 q^{19} -28.0000 q^{23} +238.000 q^{29} -180.000 q^{31} +40.0000 q^{37} -422.000 q^{41} -276.000 q^{43} +60.0000 q^{47} -327.000 q^{49} +220.000 q^{53} +804.000 q^{59} -358.000 q^{61} +884.000 q^{67} +64.0000 q^{71} +152.000 q^{73} -112.000 q^{77} -932.000 q^{79} -1292.00 q^{83} +1146.00 q^{89} -64.0000 q^{91} -824.000 q^{97} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −4.00000 −0.215980 −0.107990 0.994152i $$-0.534441\pi$$
−0.107990 + 0.994152i $$0.534441\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 28.0000 0.767483 0.383742 0.923440i $$-0.374635\pi$$
0.383742 + 0.923440i $$0.374635\pi$$
$$12$$ 0 0
$$13$$ 16.0000 0.341354 0.170677 0.985327i $$-0.445405\pi$$
0.170677 + 0.985327i $$0.445405\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 108.000 1.54081 0.770407 0.637552i $$-0.220053\pi$$
0.770407 + 0.637552i $$0.220053\pi$$
$$18$$ 0 0
$$19$$ 32.0000 0.386384 0.193192 0.981161i $$-0.438116\pi$$
0.193192 + 0.981161i $$0.438116\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −28.0000 −0.253844 −0.126922 0.991913i $$-0.540510\pi$$
−0.126922 + 0.991913i $$0.540510\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 238.000 1.52398 0.761991 0.647587i $$-0.224222\pi$$
0.761991 + 0.647587i $$0.224222\pi$$
$$30$$ 0 0
$$31$$ −180.000 −1.04287 −0.521435 0.853291i $$-0.674603\pi$$
−0.521435 + 0.853291i $$0.674603\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 40.0000 0.177729 0.0888643 0.996044i $$-0.471676\pi$$
0.0888643 + 0.996044i $$0.471676\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −422.000 −1.60745 −0.803724 0.595003i $$-0.797151\pi$$
−0.803724 + 0.595003i $$0.797151\pi$$
$$42$$ 0 0
$$43$$ −276.000 −0.978828 −0.489414 0.872052i $$-0.662789\pi$$
−0.489414 + 0.872052i $$0.662789\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 60.0000 0.186211 0.0931053 0.995656i $$-0.470321\pi$$
0.0931053 + 0.995656i $$0.470321\pi$$
$$48$$ 0 0
$$49$$ −327.000 −0.953353
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 220.000 0.570176 0.285088 0.958501i $$-0.407977\pi$$
0.285088 + 0.958501i $$0.407977\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 804.000 1.77410 0.887050 0.461674i $$-0.152751\pi$$
0.887050 + 0.461674i $$0.152751\pi$$
$$60$$ 0 0
$$61$$ −358.000 −0.751430 −0.375715 0.926735i $$-0.622603\pi$$
−0.375715 + 0.926735i $$0.622603\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 884.000 1.61191 0.805954 0.591979i $$-0.201653\pi$$
0.805954 + 0.591979i $$0.201653\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 64.0000 0.106978 0.0534888 0.998568i $$-0.482966\pi$$
0.0534888 + 0.998568i $$0.482966\pi$$
$$72$$ 0 0
$$73$$ 152.000 0.243702 0.121851 0.992548i $$-0.461117\pi$$
0.121851 + 0.992548i $$0.461117\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −112.000 −0.165761
$$78$$ 0 0
$$79$$ −932.000 −1.32732 −0.663659 0.748035i $$-0.730998\pi$$
−0.663659 + 0.748035i $$0.730998\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1292.00 −1.70862 −0.854310 0.519764i $$-0.826020\pi$$
−0.854310 + 0.519764i $$0.826020\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1146.00 1.36490 0.682448 0.730934i $$-0.260915\pi$$
0.682448 + 0.730934i $$0.260915\pi$$
$$90$$ 0 0
$$91$$ −64.0000 −0.0737255
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −824.000 −0.862521 −0.431260 0.902227i $$-0.641931\pi$$
−0.431260 + 0.902227i $$0.641931\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1290.00 1.27089 0.635445 0.772147i $$-0.280817\pi$$
0.635445 + 0.772147i $$0.280817\pi$$
$$102$$ 0 0
$$103$$ 1604.00 1.53444 0.767218 0.641387i $$-0.221641\pi$$
0.767218 + 0.641387i $$0.221641\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 892.000 0.805915 0.402957 0.915219i $$-0.367982\pi$$
0.402957 + 0.915219i $$0.367982\pi$$
$$108$$ 0 0
$$109$$ 966.000 0.848863 0.424431 0.905460i $$-0.360474\pi$$
0.424431 + 0.905460i $$0.360474\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1124.00 0.935726 0.467863 0.883801i $$-0.345024\pi$$
0.467863 + 0.883801i $$0.345024\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −432.000 −0.332785
$$120$$ 0 0
$$121$$ −547.000 −0.410969
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1884.00 1.31636 0.658181 0.752860i $$-0.271326\pi$$
0.658181 + 0.752860i $$0.271326\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 588.000 0.392166 0.196083 0.980587i $$-0.437178\pi$$
0.196083 + 0.980587i $$0.437178\pi$$
$$132$$ 0 0
$$133$$ −128.000 −0.0834512
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1060.00 0.661036 0.330518 0.943800i $$-0.392777\pi$$
0.330518 + 0.943800i $$0.392777\pi$$
$$138$$ 0 0
$$139$$ −2864.00 −1.74764 −0.873818 0.486254i $$-0.838363\pi$$
−0.873818 + 0.486254i $$0.838363\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 448.000 0.261984
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −342.000 −0.188038 −0.0940192 0.995570i $$-0.529972\pi$$
−0.0940192 + 0.995570i $$0.529972\pi$$
$$150$$ 0 0
$$151$$ 1636.00 0.881694 0.440847 0.897582i $$-0.354678\pi$$
0.440847 + 0.897582i $$0.354678\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 2072.00 1.05327 0.526636 0.850091i $$-0.323453\pi$$
0.526636 + 0.850091i $$0.323453\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 112.000 0.0548251
$$162$$ 0 0
$$163$$ −772.000 −0.370968 −0.185484 0.982647i $$-0.559385\pi$$
−0.185484 + 0.982647i $$0.559385\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1044.00 −0.483755 −0.241878 0.970307i $$-0.577763\pi$$
−0.241878 + 0.970307i $$0.577763\pi$$
$$168$$ 0 0
$$169$$ −1941.00 −0.883477
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 4404.00 1.93543 0.967717 0.252041i $$-0.0811018\pi$$
0.967717 + 0.252041i $$0.0811018\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −3452.00 −1.44142 −0.720711 0.693235i $$-0.756185\pi$$
−0.720711 + 0.693235i $$0.756185\pi$$
$$180$$ 0 0
$$181$$ 526.000 0.216007 0.108004 0.994151i $$-0.465554\pi$$
0.108004 + 0.994151i $$0.465554\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 3024.00 1.18255
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −72.0000 −0.0272761 −0.0136381 0.999907i $$-0.504341\pi$$
−0.0136381 + 0.999907i $$0.504341\pi$$
$$192$$ 0 0
$$193$$ −208.000 −0.0775760 −0.0387880 0.999247i $$-0.512350\pi$$
−0.0387880 + 0.999247i $$0.512350\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 372.000 0.134538 0.0672688 0.997735i $$-0.478571\pi$$
0.0672688 + 0.997735i $$0.478571\pi$$
$$198$$ 0 0
$$199$$ 4348.00 1.54885 0.774426 0.632665i $$-0.218039\pi$$
0.774426 + 0.632665i $$0.218039\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −952.000 −0.329149
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 896.000 0.296544
$$210$$ 0 0
$$211$$ −416.000 −0.135728 −0.0678640 0.997695i $$-0.521618\pi$$
−0.0678640 + 0.997695i $$0.521618\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 720.000 0.225239
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1728.00 0.525963
$$222$$ 0 0
$$223$$ 5748.00 1.72607 0.863037 0.505141i $$-0.168559\pi$$
0.863037 + 0.505141i $$0.168559\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1148.00 0.335663 0.167831 0.985816i $$-0.446324\pi$$
0.167831 + 0.985816i $$0.446324\pi$$
$$228$$ 0 0
$$229$$ 3234.00 0.933226 0.466613 0.884462i $$-0.345474\pi$$
0.466613 + 0.884462i $$0.345474\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −228.000 −0.0641063 −0.0320532 0.999486i $$-0.510205\pi$$
−0.0320532 + 0.999486i $$0.510205\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −4760.00 −1.28828 −0.644140 0.764908i $$-0.722784\pi$$
−0.644140 + 0.764908i $$0.722784\pi$$
$$240$$ 0 0
$$241$$ 3230.00 0.863330 0.431665 0.902034i $$-0.357926\pi$$
0.431665 + 0.902034i $$0.357926\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 512.000 0.131894
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1708.00 −0.429514 −0.214757 0.976668i $$-0.568896\pi$$
−0.214757 + 0.976668i $$0.568896\pi$$
$$252$$ 0 0
$$253$$ −784.000 −0.194821
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 6372.00 1.54659 0.773297 0.634044i $$-0.218606\pi$$
0.773297 + 0.634044i $$0.218606\pi$$
$$258$$ 0 0
$$259$$ −160.000 −0.0383858
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3036.00 −0.711817 −0.355908 0.934521i $$-0.615828\pi$$
−0.355908 + 0.934521i $$0.615828\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 114.000 0.0258390 0.0129195 0.999917i $$-0.495887\pi$$
0.0129195 + 0.999917i $$0.495887\pi$$
$$270$$ 0 0
$$271$$ −5236.00 −1.17367 −0.586835 0.809707i $$-0.699626\pi$$
−0.586835 + 0.809707i $$0.699626\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 5712.00 1.23899 0.619496 0.785000i $$-0.287337\pi$$
0.619496 + 0.785000i $$0.287337\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −3222.00 −0.684016 −0.342008 0.939697i $$-0.611107\pi$$
−0.342008 + 0.939697i $$0.611107\pi$$
$$282$$ 0 0
$$283$$ 4620.00 0.970426 0.485213 0.874396i $$-0.338742\pi$$
0.485213 + 0.874396i $$0.338742\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 1688.00 0.347176
$$288$$ 0 0
$$289$$ 6751.00 1.37411
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −5404.00 −1.07749 −0.538746 0.842468i $$-0.681102\pi$$
−0.538746 + 0.842468i $$0.681102\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −448.000 −0.0866505
$$300$$ 0 0
$$301$$ 1104.00 0.211407
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 9700.00 1.80328 0.901642 0.432483i $$-0.142362\pi$$
0.901642 + 0.432483i $$0.142362\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −9672.00 −1.76350 −0.881750 0.471716i $$-0.843635\pi$$
−0.881750 + 0.471716i $$0.843635\pi$$
$$312$$ 0 0
$$313$$ −4048.00 −0.731011 −0.365506 0.930809i $$-0.619104\pi$$
−0.365506 + 0.930809i $$0.619104\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −84.0000 −0.0148830 −0.00744150 0.999972i $$-0.502369\pi$$
−0.00744150 + 0.999972i $$0.502369\pi$$
$$318$$ 0 0
$$319$$ 6664.00 1.16963
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3456.00 0.595347
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −240.000 −0.0402177
$$330$$ 0 0
$$331$$ 5416.00 0.899366 0.449683 0.893188i $$-0.351537\pi$$
0.449683 + 0.893188i $$0.351537\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 8216.00 1.32805 0.664027 0.747709i $$-0.268846\pi$$
0.664027 + 0.747709i $$0.268846\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −5040.00 −0.800385
$$342$$ 0 0
$$343$$ 2680.00 0.421885
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 3836.00 0.593450 0.296725 0.954963i $$-0.404105\pi$$
0.296725 + 0.954963i $$0.404105\pi$$
$$348$$ 0 0
$$349$$ −2038.00 −0.312583 −0.156292 0.987711i $$-0.549954\pi$$
−0.156292 + 0.987711i $$0.549954\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 5292.00 0.797917 0.398959 0.916969i $$-0.369372\pi$$
0.398959 + 0.916969i $$0.369372\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 3896.00 0.572766 0.286383 0.958115i $$-0.407547\pi$$
0.286383 + 0.958115i $$0.407547\pi$$
$$360$$ 0 0
$$361$$ −5835.00 −0.850707
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −7652.00 −1.08837 −0.544184 0.838966i $$-0.683161\pi$$
−0.544184 + 0.838966i $$0.683161\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −880.000 −0.123146
$$372$$ 0 0
$$373$$ 1576.00 0.218773 0.109386 0.993999i $$-0.465111\pi$$
0.109386 + 0.993999i $$0.465111\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3808.00 0.520217
$$378$$ 0 0
$$379$$ −5416.00 −0.734040 −0.367020 0.930213i $$-0.619622\pi$$
−0.367020 + 0.930213i $$0.619622\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 8292.00 1.10627 0.553135 0.833092i $$-0.313431\pi$$
0.553135 + 0.833092i $$0.313431\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 9642.00 1.25673 0.628366 0.777918i $$-0.283724\pi$$
0.628366 + 0.777918i $$0.283724\pi$$
$$390$$ 0 0
$$391$$ −3024.00 −0.391126
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 13032.0 1.64750 0.823750 0.566954i $$-0.191878\pi$$
0.823750 + 0.566954i $$0.191878\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 13358.0 1.66351 0.831754 0.555144i $$-0.187337\pi$$
0.831754 + 0.555144i $$0.187337\pi$$
$$402$$ 0 0
$$403$$ −2880.00 −0.355988
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1120.00 0.136404
$$408$$ 0 0
$$409$$ 6410.00 0.774949 0.387474 0.921880i $$-0.373348\pi$$
0.387474 + 0.921880i $$0.373348\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −3216.00 −0.383170
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −7644.00 −0.891250 −0.445625 0.895220i $$-0.647019\pi$$
−0.445625 + 0.895220i $$0.647019\pi$$
$$420$$ 0 0
$$421$$ 14674.0 1.69873 0.849367 0.527803i $$-0.176984\pi$$
0.849367 + 0.527803i $$0.176984\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 1432.00 0.162294
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 9704.00 1.08451 0.542257 0.840213i $$-0.317570\pi$$
0.542257 + 0.840213i $$0.317570\pi$$
$$432$$ 0 0
$$433$$ −1296.00 −0.143838 −0.0719189 0.997410i $$-0.522912\pi$$
−0.0719189 + 0.997410i $$0.522912\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −896.000 −0.0980812
$$438$$ 0 0
$$439$$ −15684.0 −1.70514 −0.852570 0.522613i $$-0.824957\pi$$
−0.852570 + 0.522613i $$0.824957\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −5772.00 −0.619043 −0.309521 0.950892i $$-0.600169\pi$$
−0.309521 + 0.950892i $$0.600169\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 4782.00 0.502620 0.251310 0.967907i $$-0.419139\pi$$
0.251310 + 0.967907i $$0.419139\pi$$
$$450$$ 0 0
$$451$$ −11816.0 −1.23369
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −15000.0 −1.53538 −0.767692 0.640819i $$-0.778595\pi$$
−0.767692 + 0.640819i $$0.778595\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 3762.00 0.380073 0.190037 0.981777i $$-0.439139\pi$$
0.190037 + 0.981777i $$0.439139\pi$$
$$462$$ 0 0
$$463$$ −5036.00 −0.505492 −0.252746 0.967533i $$-0.581334\pi$$
−0.252746 + 0.967533i $$0.581334\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2268.00 0.224733 0.112367 0.993667i $$-0.464157\pi$$
0.112367 + 0.993667i $$0.464157\pi$$
$$468$$ 0 0
$$469$$ −3536.00 −0.348139
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −7728.00 −0.751234
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −16208.0 −1.54606 −0.773030 0.634370i $$-0.781260\pi$$
−0.773030 + 0.634370i $$0.781260\pi$$
$$480$$ 0 0
$$481$$ 640.000 0.0606684
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −11572.0 −1.07675 −0.538375 0.842705i $$-0.680962\pi$$
−0.538375 + 0.842705i $$0.680962\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −5636.00 −0.518023 −0.259011 0.965874i $$-0.583397\pi$$
−0.259011 + 0.965874i $$0.583397\pi$$
$$492$$ 0 0
$$493$$ 25704.0 2.34817
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −256.000 −0.0231050
$$498$$ 0 0
$$499$$ −5560.00 −0.498797 −0.249399 0.968401i $$-0.580233\pi$$
−0.249399 + 0.968401i $$0.580233\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 15172.0 1.34490 0.672451 0.740141i $$-0.265241\pi$$
0.672451 + 0.740141i $$0.265241\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 17342.0 1.51016 0.755079 0.655634i $$-0.227598\pi$$
0.755079 + 0.655634i $$0.227598\pi$$
$$510$$ 0 0
$$511$$ −608.000 −0.0526347
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 1680.00 0.142914
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 4886.00 0.410863 0.205431 0.978672i $$-0.434140\pi$$
0.205431 + 0.978672i $$0.434140\pi$$
$$522$$ 0 0
$$523$$ −18548.0 −1.55076 −0.775380 0.631495i $$-0.782442\pi$$
−0.775380 + 0.631495i $$0.782442\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −19440.0 −1.60687
$$528$$ 0 0
$$529$$ −11383.0 −0.935563
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −6752.00 −0.548708
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −9156.00 −0.731682
$$540$$ 0 0
$$541$$ −15770.0 −1.25324 −0.626622 0.779323i $$-0.715563\pi$$
−0.626622 + 0.779323i $$0.715563\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 7700.00 0.601880 0.300940 0.953643i $$-0.402700\pi$$
0.300940 + 0.953643i $$0.402700\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 7616.00 0.588843
$$552$$ 0 0
$$553$$ 3728.00 0.286674
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −19236.0 −1.46330 −0.731648 0.681683i $$-0.761248\pi$$
−0.731648 + 0.681683i $$0.761248\pi$$
$$558$$ 0 0
$$559$$ −4416.00 −0.334127
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 8388.00 0.627908 0.313954 0.949438i $$-0.398346\pi$$
0.313954 + 0.949438i $$0.398346\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 16758.0 1.23468 0.617339 0.786697i $$-0.288211\pi$$
0.617339 + 0.786697i $$0.288211\pi$$
$$570$$ 0 0
$$571$$ 8056.00 0.590426 0.295213 0.955432i $$-0.404609\pi$$
0.295213 + 0.955432i $$0.404609\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −5728.00 −0.413275 −0.206638 0.978418i $$-0.566252\pi$$
−0.206638 + 0.978418i $$0.566252\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 5168.00 0.369027
$$582$$ 0 0
$$583$$ 6160.00 0.437601
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12172.0 0.855864 0.427932 0.903811i $$-0.359242\pi$$
0.427932 + 0.903811i $$0.359242\pi$$
$$588$$ 0 0
$$589$$ −5760.00 −0.402948
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 10708.0 0.741526 0.370763 0.928728i $$-0.379096\pi$$
0.370763 + 0.928728i $$0.379096\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 9416.00 0.642283 0.321141 0.947031i $$-0.395934\pi$$
0.321141 + 0.947031i $$0.395934\pi$$
$$600$$ 0 0
$$601$$ 9270.00 0.629170 0.314585 0.949229i $$-0.398135\pi$$
0.314585 + 0.949229i $$0.398135\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 7996.00 0.534675 0.267337 0.963603i $$-0.413856\pi$$
0.267337 + 0.963603i $$0.413856\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 960.000 0.0635637
$$612$$ 0 0
$$613$$ 232.000 0.0152861 0.00764306 0.999971i $$-0.497567\pi$$
0.00764306 + 0.999971i $$0.497567\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 3740.00 0.244030 0.122015 0.992528i $$-0.461064\pi$$
0.122015 + 0.992528i $$0.461064\pi$$
$$618$$ 0 0
$$619$$ −26000.0 −1.68825 −0.844126 0.536145i $$-0.819880\pi$$
−0.844126 + 0.536145i $$0.819880\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4584.00 −0.294790
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 4320.00 0.273847
$$630$$ 0 0
$$631$$ 11660.0 0.735622 0.367811 0.929901i $$-0.380107\pi$$
0.367811 + 0.929901i $$0.380107\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −5232.00 −0.325431
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 7602.00 0.468426 0.234213 0.972185i $$-0.424749\pi$$
0.234213 + 0.972185i $$0.424749\pi$$
$$642$$ 0 0
$$643$$ −29268.0 −1.79505 −0.897525 0.440963i $$-0.854637\pi$$
−0.897525 + 0.440963i $$0.854637\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 17836.0 1.08378 0.541890 0.840449i $$-0.317709\pi$$
0.541890 + 0.840449i $$0.317709\pi$$
$$648$$ 0 0
$$649$$ 22512.0 1.36159
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −19188.0 −1.14990 −0.574950 0.818189i $$-0.694978\pi$$
−0.574950 + 0.818189i $$0.694978\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −13860.0 −0.819285 −0.409643 0.912246i $$-0.634347\pi$$
−0.409643 + 0.912246i $$0.634347\pi$$
$$660$$ 0 0
$$661$$ −16558.0 −0.974329 −0.487165 0.873310i $$-0.661969\pi$$
−0.487165 + 0.873310i $$0.661969\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −6664.00 −0.386853
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −10024.0 −0.576710
$$672$$ 0 0
$$673$$ 4640.00 0.265764 0.132882 0.991132i $$-0.457577\pi$$
0.132882 + 0.991132i $$0.457577\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −34260.0 −1.94493 −0.972466 0.233045i $$-0.925131\pi$$
−0.972466 + 0.233045i $$0.925131\pi$$
$$678$$ 0 0
$$679$$ 3296.00 0.186287
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −19420.0 −1.08797 −0.543987 0.839094i $$-0.683086\pi$$
−0.543987 + 0.839094i $$0.683086\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 3520.00 0.194632
$$690$$ 0 0
$$691$$ 4608.00 0.253685 0.126843 0.991923i $$-0.459516\pi$$
0.126843 + 0.991923i $$0.459516\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −45576.0 −2.47678
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 2318.00 0.124893 0.0624463 0.998048i $$-0.480110\pi$$
0.0624463 + 0.998048i $$0.480110\pi$$
$$702$$ 0 0
$$703$$ 1280.00 0.0686716
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −5160.00 −0.274486
$$708$$ 0 0
$$709$$ 16834.0 0.891698 0.445849 0.895108i $$-0.352902\pi$$
0.445849 + 0.895108i $$0.352902\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 5040.00 0.264726
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 7400.00 0.383830 0.191915 0.981412i $$-0.438530\pi$$
0.191915 + 0.981412i $$0.438530\pi$$
$$720$$ 0 0
$$721$$ −6416.00 −0.331407
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −20340.0 −1.03765 −0.518823 0.854882i $$-0.673630\pi$$
−0.518823 + 0.854882i $$0.673630\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −29808.0 −1.50819
$$732$$ 0 0
$$733$$ −4896.00 −0.246709 −0.123355 0.992363i $$-0.539365\pi$$
−0.123355 + 0.992363i $$0.539365\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 24752.0 1.23711
$$738$$ 0 0
$$739$$ 26040.0 1.29621 0.648103 0.761552i $$-0.275562\pi$$
0.648103 + 0.761552i $$0.275562\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −6780.00 −0.334770 −0.167385 0.985892i $$-0.553532\pi$$
−0.167385 + 0.985892i $$0.553532\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −3568.00 −0.174061
$$750$$ 0 0
$$751$$ −20692.0 −1.00541 −0.502704 0.864458i $$-0.667662\pi$$
−0.502704 + 0.864458i $$0.667662\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 10816.0 0.519305 0.259653 0.965702i $$-0.416392\pi$$
0.259653 + 0.965702i $$0.416392\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −13978.0 −0.665837 −0.332919 0.942956i $$-0.608033\pi$$
−0.332919 + 0.942956i $$0.608033\pi$$
$$762$$ 0 0
$$763$$ −3864.00 −0.183337
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 12864.0 0.605596
$$768$$ 0 0
$$769$$ 2926.00 0.137210 0.0686048 0.997644i $$-0.478145\pi$$
0.0686048 + 0.997644i $$0.478145\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 13916.0 0.647508 0.323754 0.946141i $$-0.395055\pi$$
0.323754 + 0.946141i $$0.395055\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −13504.0 −0.621092
$$780$$ 0 0
$$781$$ 1792.00 0.0821035
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −29996.0 −1.35863 −0.679315 0.733847i $$-0.737723\pi$$
−0.679315 + 0.733847i $$0.737723\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −4496.00 −0.202098
$$792$$ 0 0
$$793$$ −5728.00 −0.256503
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −8940.00 −0.397329 −0.198664 0.980068i $$-0.563660\pi$$
−0.198664 + 0.980068i $$0.563660\pi$$
$$798$$ 0 0
$$799$$ 6480.00 0.286916
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 4256.00 0.187037
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 10698.0 0.464922 0.232461 0.972606i $$-0.425322\pi$$
0.232461 + 0.972606i $$0.425322\pi$$
$$810$$ 0 0
$$811$$ −6408.00 −0.277454 −0.138727 0.990331i $$-0.544301\pi$$
−0.138727 + 0.990331i $$0.544301\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −8832.00 −0.378204
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −23130.0 −0.983243 −0.491622 0.870809i $$-0.663596\pi$$
−0.491622 + 0.870809i $$0.663596\pi$$
$$822$$ 0 0
$$823$$ −11852.0 −0.501986 −0.250993 0.967989i $$-0.580757\pi$$
−0.250993 + 0.967989i $$0.580757\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −32628.0 −1.37193 −0.685965 0.727634i $$-0.740620\pi$$
−0.685965 + 0.727634i $$0.740620\pi$$
$$828$$ 0 0
$$829$$ 36694.0 1.53732 0.768658 0.639660i $$-0.220925\pi$$
0.768658 + 0.639660i $$0.220925\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −35316.0 −1.46894
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1704.00 0.0701175 0.0350588 0.999385i $$-0.488838\pi$$
0.0350588 + 0.999385i $$0.488838\pi$$
$$840$$ 0 0
$$841$$ 32255.0 1.32252
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 2188.00 0.0887610
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −1120.00 −0.0451153
$$852$$ 0 0
$$853$$ −31880.0 −1.27966 −0.639830 0.768516i $$-0.720995\pi$$
−0.639830 + 0.768516i $$0.720995\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −7972.00 −0.317758 −0.158879 0.987298i $$-0.550788\pi$$
−0.158879 + 0.987298i $$0.550788\pi$$
$$858$$ 0 0
$$859$$ −6008.00 −0.238638 −0.119319 0.992856i $$-0.538071\pi$$
−0.119319 + 0.992856i $$0.538071\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1716.00 0.0676863 0.0338432 0.999427i $$-0.489225\pi$$
0.0338432 + 0.999427i $$0.489225\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −26096.0 −1.01870
$$870$$ 0 0
$$871$$ 14144.0 0.550231
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 9032.00 0.347764 0.173882 0.984767i $$-0.444369\pi$$
0.173882 + 0.984767i $$0.444369\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −27838.0 −1.06457 −0.532285 0.846565i $$-0.678666\pi$$
−0.532285 + 0.846565i $$0.678666\pi$$
$$882$$ 0 0
$$883$$ 4316.00 0.164490 0.0822452 0.996612i $$-0.473791\pi$$
0.0822452 + 0.996612i $$0.473791\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −43524.0 −1.64757 −0.823784 0.566904i $$-0.808141\pi$$
−0.823784 + 0.566904i $$0.808141\pi$$
$$888$$ 0 0
$$889$$ −7536.00 −0.284307
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 1920.00 0.0719489
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −42840.0 −1.58931
$$900$$ 0 0
$$901$$ 23760.0 0.878535
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −10556.0 −0.386446 −0.193223 0.981155i $$-0.561894\pi$$
−0.193223 + 0.981155i $$0.561894\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 47472.0 1.72647 0.863237 0.504799i $$-0.168433\pi$$
0.863237 + 0.504799i $$0.168433\pi$$
$$912$$ 0 0
$$913$$ −36176.0 −1.31134
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −2352.00 −0.0847000
$$918$$ 0 0
$$919$$ 11964.0 0.429441 0.214720 0.976676i $$-0.431116\pi$$
0.214720 + 0.976676i $$0.431116\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 1024.00 0.0365172
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 15214.0 0.537304 0.268652 0.963237i $$-0.413422\pi$$
0.268652 + 0.963237i $$0.413422\pi$$
$$930$$ 0 0
$$931$$ −10464.0 −0.368361
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −39712.0 −1.38456 −0.692281 0.721628i $$-0.743394\pi$$
−0.692281 + 0.721628i $$0.743394\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 36034.0 1.24833 0.624163 0.781294i $$-0.285440\pi$$
0.624163 + 0.781294i $$0.285440\pi$$
$$942$$ 0 0
$$943$$ 11816.0 0.408040
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −2532.00 −0.0868838 −0.0434419 0.999056i $$-0.513832\pi$$
−0.0434419 + 0.999056i $$0.513832\pi$$
$$948$$ 0 0
$$949$$ 2432.00 0.0831887
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 55284.0 1.87914 0.939572 0.342351i $$-0.111223\pi$$
0.939572 + 0.342351i $$0.111223\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −4240.00 −0.142770
$$960$$ 0 0
$$961$$ 2609.00 0.0875768
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −4372.00 −0.145392 −0.0726960 0.997354i $$-0.523160\pi$$
−0.0726960 + 0.997354i $$0.523160\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −24300.0 −0.803114 −0.401557 0.915834i $$-0.631531\pi$$
−0.401557 + 0.915834i $$0.631531\pi$$
$$972$$ 0 0
$$973$$ 11456.0 0.377454
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 46204.0 1.51300 0.756498 0.653996i $$-0.226909\pi$$
0.756498 + 0.653996i $$0.226909\pi$$
$$978$$ 0 0
$$979$$ 32088.0 1.04754
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −25468.0 −0.826351 −0.413176 0.910651i $$-0.635580\pi$$
−0.413176 + 0.910651i $$0.635580\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 7728.00 0.248469
$$990$$ 0 0
$$991$$ 11668.0 0.374012 0.187006 0.982359i $$-0.440122\pi$$
0.187006 + 0.982359i $$0.440122\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 7224.00 0.229475 0.114737 0.993396i $$-0.463397\pi$$
0.114737 + 0.993396i $$0.463397\pi$$
$$998$$ 0 0
$$999$$ 0 0
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 1800.4.a.o.1.1 1
3.2 odd 2 600.4.a.k.1.1 1
5.2 odd 4 360.4.f.a.289.2 2
5.3 odd 4 360.4.f.a.289.1 2
5.4 even 2 1800.4.a.u.1.1 1
12.11 even 2 1200.4.a.l.1.1 1
15.2 even 4 120.4.f.c.49.1 2
15.8 even 4 120.4.f.c.49.2 yes 2
15.14 odd 2 600.4.a.f.1.1 1
20.3 even 4 720.4.f.b.289.1 2
20.7 even 4 720.4.f.b.289.2 2
60.23 odd 4 240.4.f.e.49.1 2
60.47 odd 4 240.4.f.e.49.2 2
60.59 even 2 1200.4.a.z.1.1 1
120.53 even 4 960.4.f.b.769.1 2
120.77 even 4 960.4.f.b.769.2 2
120.83 odd 4 960.4.f.a.769.2 2
120.107 odd 4 960.4.f.a.769.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.f.c.49.1 2 15.2 even 4
120.4.f.c.49.2 yes 2 15.8 even 4
240.4.f.e.49.1 2 60.23 odd 4
240.4.f.e.49.2 2 60.47 odd 4
360.4.f.a.289.1 2 5.3 odd 4
360.4.f.a.289.2 2 5.2 odd 4
600.4.a.f.1.1 1 15.14 odd 2
600.4.a.k.1.1 1 3.2 odd 2
720.4.f.b.289.1 2 20.3 even 4
720.4.f.b.289.2 2 20.7 even 4
960.4.f.a.769.1 2 120.107 odd 4
960.4.f.a.769.2 2 120.83 odd 4
960.4.f.b.769.1 2 120.53 even 4
960.4.f.b.769.2 2 120.77 even 4
1200.4.a.l.1.1 1 12.11 even 2
1200.4.a.z.1.1 1 60.59 even 2
1800.4.a.o.1.1 1 1.1 even 1 trivial
1800.4.a.u.1.1 1 5.4 even 2