# Properties

 Label 1800.4.a.bh.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 200) 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)

 $$f(q)$$ $$=$$ $$q+26.0000 q^{7} +O(q^{10})$$ $$q+26.0000 q^{7} +59.0000 q^{11} +28.0000 q^{13} -5.00000 q^{17} +109.000 q^{19} +194.000 q^{23} +32.0000 q^{29} +10.0000 q^{31} -198.000 q^{37} -117.000 q^{41} +388.000 q^{43} +68.0000 q^{47} +333.000 q^{49} +18.0000 q^{53} -392.000 q^{59} -710.000 q^{61} -253.000 q^{67} +612.000 q^{71} -549.000 q^{73} +1534.00 q^{77} +414.000 q^{79} +121.000 q^{83} +81.0000 q^{89} +728.000 q^{91} -1502.00 q^{97} +O(q^{100})$$

## 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
$$7$$ 26.0000 1.40387 0.701934 0.712242i $$-0.252320\pi$$
0.701934 + 0.712242i $$0.252320\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 59.0000 1.61720 0.808599 0.588361i $$-0.200226\pi$$
0.808599 + 0.588361i $$0.200226\pi$$
$$12$$ 0 0
$$13$$ 28.0000 0.597369 0.298685 0.954352i $$-0.403452\pi$$
0.298685 + 0.954352i $$0.403452\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −5.00000 −0.0713340 −0.0356670 0.999364i $$-0.511356\pi$$
−0.0356670 + 0.999364i $$0.511356\pi$$
$$18$$ 0 0
$$19$$ 109.000 1.31612 0.658061 0.752965i $$-0.271377\pi$$
0.658061 + 0.752965i $$0.271377\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 194.000 1.75877 0.879387 0.476108i $$-0.157953\pi$$
0.879387 + 0.476108i $$0.157953\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 32.0000 0.204905 0.102453 0.994738i $$-0.467331\pi$$
0.102453 + 0.994738i $$0.467331\pi$$
$$30$$ 0 0
$$31$$ 10.0000 0.0579372 0.0289686 0.999580i $$-0.490778\pi$$
0.0289686 + 0.999580i $$0.490778\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −198.000 −0.879757 −0.439878 0.898057i $$-0.644978\pi$$
−0.439878 + 0.898057i $$0.644978\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −117.000 −0.445667 −0.222833 0.974857i $$-0.571531\pi$$
−0.222833 + 0.974857i $$0.571531\pi$$
$$42$$ 0 0
$$43$$ 388.000 1.37603 0.688017 0.725695i $$-0.258482\pi$$
0.688017 + 0.725695i $$0.258482\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 68.0000 0.211039 0.105519 0.994417i $$-0.466350\pi$$
0.105519 + 0.994417i $$0.466350\pi$$
$$48$$ 0 0
$$49$$ 333.000 0.970845
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 18.0000 0.0466508 0.0233254 0.999728i $$-0.492575\pi$$
0.0233254 + 0.999728i $$0.492575\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −392.000 −0.864984 −0.432492 0.901638i $$-0.642366\pi$$
−0.432492 + 0.901638i $$0.642366\pi$$
$$60$$ 0 0
$$61$$ −710.000 −1.49027 −0.745133 0.666916i $$-0.767614\pi$$
−0.745133 + 0.666916i $$0.767614\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −253.000 −0.461326 −0.230663 0.973034i $$-0.574090\pi$$
−0.230663 + 0.973034i $$0.574090\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 612.000 1.02297 0.511486 0.859292i $$-0.329095\pi$$
0.511486 + 0.859292i $$0.329095\pi$$
$$72$$ 0 0
$$73$$ −549.000 −0.880214 −0.440107 0.897945i $$-0.645059\pi$$
−0.440107 + 0.897945i $$0.645059\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1534.00 2.27033
$$78$$ 0 0
$$79$$ 414.000 0.589603 0.294802 0.955559i $$-0.404746\pi$$
0.294802 + 0.955559i $$0.404746\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 121.000 0.160018 0.0800089 0.996794i $$-0.474505\pi$$
0.0800089 + 0.996794i $$0.474505\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 81.0000 0.0964717 0.0482359 0.998836i $$-0.484640\pi$$
0.0482359 + 0.998836i $$0.484640\pi$$
$$90$$ 0 0
$$91$$ 728.000 0.838628
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1502.00 −1.57222 −0.786108 0.618089i $$-0.787907\pi$$
−0.786108 + 0.618089i $$0.787907\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 234.000 0.230533 0.115267 0.993335i $$-0.463228\pi$$
0.115267 + 0.993335i $$0.463228\pi$$
$$102$$ 0 0
$$103$$ −1172.00 −1.12117 −0.560585 0.828097i $$-0.689424\pi$$
−0.560585 + 0.828097i $$0.689424\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1125.00 −1.01643 −0.508214 0.861231i $$-0.669694\pi$$
−0.508214 + 0.861231i $$0.669694\pi$$
$$108$$ 0 0
$$109$$ −1234.00 −1.08436 −0.542182 0.840261i $$-0.682402\pi$$
−0.542182 + 0.840261i $$0.682402\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −567.000 −0.472025 −0.236013 0.971750i $$-0.575841\pi$$
−0.236013 + 0.971750i $$0.575841\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −130.000 −0.100144
$$120$$ 0 0
$$121$$ 2150.00 1.61533
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2358.00 −1.64755 −0.823774 0.566918i $$-0.808136\pi$$
−0.823774 + 0.566918i $$0.808136\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1692.00 1.12848 0.564239 0.825611i $$-0.309169\pi$$
0.564239 + 0.825611i $$0.309169\pi$$
$$132$$ 0 0
$$133$$ 2834.00 1.84766
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −229.000 −0.142809 −0.0714043 0.997447i $$-0.522748\pi$$
−0.0714043 + 0.997447i $$0.522748\pi$$
$$138$$ 0 0
$$139$$ 2781.00 1.69699 0.848494 0.529205i $$-0.177510\pi$$
0.848494 + 0.529205i $$0.177510\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 1652.00 0.966064
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1472.00 −0.809335 −0.404668 0.914464i $$-0.632613\pi$$
−0.404668 + 0.914464i $$0.632613\pi$$
$$150$$ 0 0
$$151$$ 1322.00 0.712469 0.356235 0.934397i $$-0.384060\pi$$
0.356235 + 0.934397i $$0.384060\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 298.000 0.151484 0.0757420 0.997127i $$-0.475867\pi$$
0.0757420 + 0.997127i $$0.475867\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 5044.00 2.46909
$$162$$ 0 0
$$163$$ −341.000 −0.163860 −0.0819300 0.996638i $$-0.526108\pi$$
−0.0819300 + 0.996638i $$0.526108\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −684.000 −0.316943 −0.158472 0.987364i $$-0.550657\pi$$
−0.158472 + 0.987364i $$0.550657\pi$$
$$168$$ 0 0
$$169$$ −1413.00 −0.643150
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2344.00 1.03012 0.515061 0.857154i $$-0.327769\pi$$
0.515061 + 0.857154i $$0.327769\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 1111.00 0.463911 0.231955 0.972726i $$-0.425488\pi$$
0.231955 + 0.972726i $$0.425488\pi$$
$$180$$ 0 0
$$181$$ 2042.00 0.838567 0.419284 0.907855i $$-0.362281\pi$$
0.419284 + 0.907855i $$0.362281\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −295.000 −0.115361
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −5270.00 −1.99646 −0.998230 0.0594735i $$-0.981058\pi$$
−0.998230 + 0.0594735i $$0.981058\pi$$
$$192$$ 0 0
$$193$$ 613.000 0.228625 0.114313 0.993445i $$-0.463533\pi$$
0.114313 + 0.993445i $$0.463533\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1174.00 −0.424589 −0.212295 0.977206i $$-0.568094\pi$$
−0.212295 + 0.977206i $$0.568094\pi$$
$$198$$ 0 0
$$199$$ 3428.00 1.22113 0.610564 0.791967i $$-0.290943\pi$$
0.610564 + 0.791967i $$0.290943\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 832.000 0.287660
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 6431.00 2.12843
$$210$$ 0 0
$$211$$ 2339.00 0.763144 0.381572 0.924339i $$-0.375383\pi$$
0.381572 + 0.924339i $$0.375383\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 260.000 0.0813362
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −140.000 −0.0426128
$$222$$ 0 0
$$223$$ 3932.00 1.18075 0.590373 0.807131i $$-0.298981\pi$$
0.590373 + 0.807131i $$0.298981\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −6084.00 −1.77890 −0.889448 0.457037i $$-0.848911\pi$$
−0.889448 + 0.457037i $$0.848911\pi$$
$$228$$ 0 0
$$229$$ 4996.00 1.44168 0.720841 0.693101i $$-0.243756\pi$$
0.720841 + 0.693101i $$0.243756\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −3222.00 −0.905924 −0.452962 0.891530i $$-0.649633\pi$$
−0.452962 + 0.891530i $$0.649633\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −2736.00 −0.740490 −0.370245 0.928934i $$-0.620726\pi$$
−0.370245 + 0.928934i $$0.620726\pi$$
$$240$$ 0 0
$$241$$ 1673.00 0.447168 0.223584 0.974685i $$-0.428224\pi$$
0.223584 + 0.974685i $$0.428224\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3052.00 0.786211
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −5355.00 −1.34663 −0.673316 0.739355i $$-0.735131\pi$$
−0.673316 + 0.739355i $$0.735131\pi$$
$$252$$ 0 0
$$253$$ 11446.0 2.84428
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 5490.00 1.33252 0.666258 0.745721i $$-0.267895\pi$$
0.666258 + 0.745721i $$0.267895\pi$$
$$258$$ 0 0
$$259$$ −5148.00 −1.23506
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3150.00 −0.738545 −0.369272 0.929321i $$-0.620393\pi$$
−0.369272 + 0.929321i $$0.620393\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −176.000 −0.0398919 −0.0199459 0.999801i $$-0.506349\pi$$
−0.0199459 + 0.999801i $$0.506349\pi$$
$$270$$ 0 0
$$271$$ 2394.00 0.536624 0.268312 0.963332i $$-0.413534\pi$$
0.268312 + 0.963332i $$0.413534\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −6256.00 −1.35699 −0.678496 0.734604i $$-0.737368\pi$$
−0.678496 + 0.734604i $$0.737368\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 4802.00 1.01944 0.509721 0.860340i $$-0.329749\pi$$
0.509721 + 0.860340i $$0.329749\pi$$
$$282$$ 0 0
$$283$$ 2123.00 0.445934 0.222967 0.974826i $$-0.428426\pi$$
0.222967 + 0.974826i $$0.428426\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −3042.00 −0.625657
$$288$$ 0 0
$$289$$ −4888.00 −0.994911
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 8834.00 1.76139 0.880696 0.473682i $$-0.157075\pi$$
0.880696 + 0.473682i $$0.157075\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 5432.00 1.05064
$$300$$ 0 0
$$301$$ 10088.0 1.93177
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1369.00 0.254505 0.127252 0.991870i $$-0.459384\pi$$
0.127252 + 0.991870i $$0.459384\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 10426.0 1.90098 0.950489 0.310758i $$-0.100583\pi$$
0.950489 + 0.310758i $$0.100583\pi$$
$$312$$ 0 0
$$313$$ −3574.00 −0.645413 −0.322707 0.946499i $$-0.604593\pi$$
−0.322707 + 0.946499i $$0.604593\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −9036.00 −1.60099 −0.800493 0.599343i $$-0.795429\pi$$
−0.800493 + 0.599343i $$0.795429\pi$$
$$318$$ 0 0
$$319$$ 1888.00 0.331372
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −545.000 −0.0938842
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1768.00 0.296271
$$330$$ 0 0
$$331$$ 10233.0 1.69926 0.849632 0.527376i $$-0.176824\pi$$
0.849632 + 0.527376i $$0.176824\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 4627.00 0.747919 0.373960 0.927445i $$-0.378000\pi$$
0.373960 + 0.927445i $$0.378000\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 590.000 0.0936959
$$342$$ 0 0
$$343$$ −260.000 −0.0409291
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −4901.00 −0.758212 −0.379106 0.925353i $$-0.623768\pi$$
−0.379106 + 0.925353i $$0.623768\pi$$
$$348$$ 0 0
$$349$$ −4482.00 −0.687438 −0.343719 0.939072i $$-0.611687\pi$$
−0.343719 + 0.939072i $$0.611687\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1210.00 0.182441 0.0912207 0.995831i $$-0.470923\pi$$
0.0912207 + 0.995831i $$0.470923\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 9882.00 1.45279 0.726396 0.687277i $$-0.241194\pi$$
0.726396 + 0.687277i $$0.241194\pi$$
$$360$$ 0 0
$$361$$ 5022.00 0.732177
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −11260.0 −1.60155 −0.800773 0.598968i $$-0.795578\pi$$
−0.800773 + 0.598968i $$0.795578\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 468.000 0.0654915
$$372$$ 0 0
$$373$$ −3230.00 −0.448373 −0.224186 0.974546i $$-0.571972\pi$$
−0.224186 + 0.974546i $$0.571972\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 896.000 0.122404
$$378$$ 0 0
$$379$$ 11575.0 1.56878 0.784390 0.620268i $$-0.212976\pi$$
0.784390 + 0.620268i $$0.212976\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 18.0000 0.00240145 0.00120073 0.999999i $$-0.499618\pi$$
0.00120073 + 0.999999i $$0.499618\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −10710.0 −1.39593 −0.697967 0.716130i $$-0.745912\pi$$
−0.697967 + 0.716130i $$0.745912\pi$$
$$390$$ 0 0
$$391$$ −970.000 −0.125460
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −3788.00 −0.478877 −0.239439 0.970912i $$-0.576963\pi$$
−0.239439 + 0.970912i $$0.576963\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 10539.0 1.31245 0.656225 0.754565i $$-0.272152\pi$$
0.656225 + 0.754565i $$0.272152\pi$$
$$402$$ 0 0
$$403$$ 280.000 0.0346099
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −11682.0 −1.42274
$$408$$ 0 0
$$409$$ 5581.00 0.674725 0.337363 0.941375i $$-0.390465\pi$$
0.337363 + 0.941375i $$0.390465\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −10192.0 −1.21432
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −5193.00 −0.605476 −0.302738 0.953074i $$-0.597901\pi$$
−0.302738 + 0.953074i $$0.597901\pi$$
$$420$$ 0 0
$$421$$ 4788.00 0.554282 0.277141 0.960829i $$-0.410613\pi$$
0.277141 + 0.960829i $$0.410613\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −18460.0 −2.09214
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −8006.00 −0.894746 −0.447373 0.894348i $$-0.647640\pi$$
−0.447373 + 0.894348i $$0.647640\pi$$
$$432$$ 0 0
$$433$$ −2395.00 −0.265811 −0.132906 0.991129i $$-0.542431\pi$$
−0.132906 + 0.991129i $$0.542431\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 21146.0 2.31476
$$438$$ 0 0
$$439$$ 1864.00 0.202651 0.101326 0.994853i $$-0.467692\pi$$
0.101326 + 0.994853i $$0.467692\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −5463.00 −0.585903 −0.292951 0.956127i $$-0.594637\pi$$
−0.292951 + 0.956127i $$0.594637\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −12969.0 −1.36313 −0.681565 0.731758i $$-0.738700\pi$$
−0.681565 + 0.731758i $$0.738700\pi$$
$$450$$ 0 0
$$451$$ −6903.00 −0.720731
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 18313.0 1.87450 0.937249 0.348659i $$-0.113363\pi$$
0.937249 + 0.348659i $$0.113363\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −12492.0 −1.26206 −0.631031 0.775758i $$-0.717368\pi$$
−0.631031 + 0.775758i $$0.717368\pi$$
$$462$$ 0 0
$$463$$ 4428.00 0.444464 0.222232 0.974994i $$-0.428666\pi$$
0.222232 + 0.974994i $$0.428666\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 1084.00 0.107412 0.0537061 0.998557i $$-0.482897\pi$$
0.0537061 + 0.998557i $$0.482897\pi$$
$$468$$ 0 0
$$469$$ −6578.00 −0.647641
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 22892.0 2.22532
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 13082.0 1.24787 0.623937 0.781474i $$-0.285532\pi$$
0.623937 + 0.781474i $$0.285532\pi$$
$$480$$ 0 0
$$481$$ −5544.00 −0.525540
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −3014.00 −0.280446 −0.140223 0.990120i $$-0.544782\pi$$
−0.140223 + 0.990120i $$0.544782\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 3564.00 0.327579 0.163789 0.986495i $$-0.447628\pi$$
0.163789 + 0.986495i $$0.447628\pi$$
$$492$$ 0 0
$$493$$ −160.000 −0.0146167
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 15912.0 1.43612
$$498$$ 0 0
$$499$$ −15796.0 −1.41709 −0.708543 0.705667i $$-0.750647\pi$$
−0.708543 + 0.705667i $$0.750647\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 10908.0 0.966926 0.483463 0.875365i $$-0.339379\pi$$
0.483463 + 0.875365i $$0.339379\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −21946.0 −1.91108 −0.955540 0.294863i $$-0.904726\pi$$
−0.955540 + 0.294863i $$0.904726\pi$$
$$510$$ 0 0
$$511$$ −14274.0 −1.23570
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 4012.00 0.341291
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 6395.00 0.537754 0.268877 0.963174i $$-0.413347\pi$$
0.268877 + 0.963174i $$0.413347\pi$$
$$522$$ 0 0
$$523$$ −5615.00 −0.469459 −0.234729 0.972061i $$-0.575420\pi$$
−0.234729 + 0.972061i $$0.575420\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −50.0000 −0.00413289
$$528$$ 0 0
$$529$$ 25469.0 2.09329
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3276.00 −0.266228
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 19647.0 1.57005
$$540$$ 0 0
$$541$$ −4112.00 −0.326781 −0.163391 0.986561i $$-0.552243\pi$$
−0.163391 + 0.986561i $$0.552243\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2167.00 −0.169386 −0.0846931 0.996407i $$-0.526991\pi$$
−0.0846931 + 0.996407i $$0.526991\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 3488.00 0.269680
$$552$$ 0 0
$$553$$ 10764.0 0.827725
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 19444.0 1.47912 0.739559 0.673092i $$-0.235034\pi$$
0.739559 + 0.673092i $$0.235034\pi$$
$$558$$ 0 0
$$559$$ 10864.0 0.822000
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −20416.0 −1.52830 −0.764149 0.645040i $$-0.776841\pi$$
−0.764149 + 0.645040i $$0.776841\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 3127.00 0.230388 0.115194 0.993343i $$-0.463251\pi$$
0.115194 + 0.993343i $$0.463251\pi$$
$$570$$ 0 0
$$571$$ −22580.0 −1.65489 −0.827446 0.561545i $$-0.810207\pi$$
−0.827446 + 0.561545i $$0.810207\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −829.000 −0.0598123 −0.0299062 0.999553i $$-0.509521\pi$$
−0.0299062 + 0.999553i $$0.509521\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 3146.00 0.224644
$$582$$ 0 0
$$583$$ 1062.00 0.0754435
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −7119.00 −0.500567 −0.250283 0.968173i $$-0.580524\pi$$
−0.250283 + 0.968173i $$0.580524\pi$$
$$588$$ 0 0
$$589$$ 1090.00 0.0762524
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 8217.00 0.569025 0.284512 0.958672i $$-0.408168\pi$$
0.284512 + 0.958672i $$0.408168\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 90.0000 0.00613907 0.00306953 0.999995i $$-0.499023\pi$$
0.00306953 + 0.999995i $$0.499023\pi$$
$$600$$ 0 0
$$601$$ −17117.0 −1.16176 −0.580879 0.813990i $$-0.697291\pi$$
−0.580879 + 0.813990i $$0.697291\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −15120.0 −1.01104 −0.505520 0.862815i $$-0.668699\pi$$
−0.505520 + 0.862815i $$0.668699\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 1904.00 0.126068
$$612$$ 0 0
$$613$$ −6570.00 −0.432887 −0.216444 0.976295i $$-0.569446\pi$$
−0.216444 + 0.976295i $$0.569446\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −18846.0 −1.22968 −0.614839 0.788653i $$-0.710779\pi$$
−0.614839 + 0.788653i $$0.710779\pi$$
$$618$$ 0 0
$$619$$ 16316.0 1.05944 0.529722 0.848172i $$-0.322296\pi$$
0.529722 + 0.848172i $$0.322296\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 2106.00 0.135434
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 990.000 0.0627566
$$630$$ 0 0
$$631$$ 20170.0 1.27251 0.636256 0.771478i $$-0.280482\pi$$
0.636256 + 0.771478i $$0.280482\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 9324.00 0.579953
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 12726.0 0.784160 0.392080 0.919931i $$-0.371756\pi$$
0.392080 + 0.919931i $$0.371756\pi$$
$$642$$ 0 0
$$643$$ 2196.00 0.134684 0.0673420 0.997730i $$-0.478548\pi$$
0.0673420 + 0.997730i $$0.478548\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 16884.0 1.02593 0.512966 0.858409i $$-0.328547\pi$$
0.512966 + 0.858409i $$0.328547\pi$$
$$648$$ 0 0
$$649$$ −23128.0 −1.39885
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 4018.00 0.240791 0.120395 0.992726i $$-0.461584\pi$$
0.120395 + 0.992726i $$0.461584\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −19071.0 −1.12732 −0.563658 0.826009i $$-0.690606\pi$$
−0.563658 + 0.826009i $$0.690606\pi$$
$$660$$ 0 0
$$661$$ 17424.0 1.02529 0.512644 0.858601i $$-0.328666\pi$$
0.512644 + 0.858601i $$0.328666\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 6208.00 0.360382
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −41890.0 −2.41005
$$672$$ 0 0
$$673$$ −5382.00 −0.308263 −0.154131 0.988050i $$-0.549258\pi$$
−0.154131 + 0.988050i $$0.549258\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 4496.00 0.255237 0.127618 0.991823i $$-0.459267\pi$$
0.127618 + 0.991823i $$0.459267\pi$$
$$678$$ 0 0
$$679$$ −39052.0 −2.20718
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −3249.00 −0.182020 −0.0910099 0.995850i $$-0.529009\pi$$
−0.0910099 + 0.995850i $$0.529009\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 504.000 0.0278677
$$690$$ 0 0
$$691$$ −13399.0 −0.737658 −0.368829 0.929497i $$-0.620241\pi$$
−0.368829 + 0.929497i $$0.620241\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 585.000 0.0317912
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 18148.0 0.977804 0.488902 0.872339i $$-0.337398\pi$$
0.488902 + 0.872339i $$0.337398\pi$$
$$702$$ 0 0
$$703$$ −21582.0 −1.15787
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 6084.00 0.323638
$$708$$ 0 0
$$709$$ 4868.00 0.257858 0.128929 0.991654i $$-0.458846\pi$$
0.128929 + 0.991654i $$0.458846\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1940.00 0.101898
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 17366.0 0.900755 0.450377 0.892838i $$-0.351289\pi$$
0.450377 + 0.892838i $$0.351289\pi$$
$$720$$ 0 0
$$721$$ −30472.0 −1.57398
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 21824.0 1.11335 0.556676 0.830729i $$-0.312076\pi$$
0.556676 + 0.830729i $$0.312076\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1940.00 −0.0981580
$$732$$ 0 0
$$733$$ −31428.0 −1.58366 −0.791828 0.610744i $$-0.790870\pi$$
−0.791828 + 0.610744i $$0.790870\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −14927.0 −0.746056
$$738$$ 0 0
$$739$$ −14292.0 −0.711420 −0.355710 0.934596i $$-0.615761\pi$$
−0.355710 + 0.934596i $$0.615761\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −13950.0 −0.688797 −0.344398 0.938824i $$-0.611917\pi$$
−0.344398 + 0.938824i $$0.611917\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −29250.0 −1.42693
$$750$$ 0 0
$$751$$ −38736.0 −1.88215 −0.941076 0.338194i $$-0.890184\pi$$
−0.941076 + 0.338194i $$0.890184\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −3664.00 −0.175919 −0.0879593 0.996124i $$-0.528035\pi$$
−0.0879593 + 0.996124i $$0.528035\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −19557.0 −0.931591 −0.465795 0.884892i $$-0.654232\pi$$
−0.465795 + 0.884892i $$0.654232\pi$$
$$762$$ 0 0
$$763$$ −32084.0 −1.52231
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −10976.0 −0.516715
$$768$$ 0 0
$$769$$ −13283.0 −0.622883 −0.311442 0.950265i $$-0.600812\pi$$
−0.311442 + 0.950265i $$0.600812\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −24840.0 −1.15580 −0.577900 0.816108i $$-0.696127\pi$$
−0.577900 + 0.816108i $$0.696127\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −12753.0 −0.586552
$$780$$ 0 0
$$781$$ 36108.0 1.65435
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 18044.0 0.817280 0.408640 0.912696i $$-0.366003\pi$$
0.408640 + 0.912696i $$0.366003\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −14742.0 −0.662661
$$792$$ 0 0
$$793$$ −19880.0 −0.890239
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 6174.00 0.274397 0.137198 0.990544i $$-0.456190\pi$$
0.137198 + 0.990544i $$0.456190\pi$$
$$798$$ 0 0
$$799$$ −340.000 −0.0150542
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −32391.0 −1.42348
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1998.00 0.0868306 0.0434153 0.999057i $$-0.486176\pi$$
0.0434153 + 0.999057i $$0.486176\pi$$
$$810$$ 0 0
$$811$$ −7156.00 −0.309841 −0.154921 0.987927i $$-0.549512\pi$$
−0.154921 + 0.987927i $$0.549512\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 42292.0 1.81103
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −27922.0 −1.18695 −0.593474 0.804853i $$-0.702244\pi$$
−0.593474 + 0.804853i $$0.702244\pi$$
$$822$$ 0 0
$$823$$ 22636.0 0.958738 0.479369 0.877613i $$-0.340866\pi$$
0.479369 + 0.877613i $$0.340866\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −26559.0 −1.11674 −0.558372 0.829591i $$-0.688574\pi$$
−0.558372 + 0.829591i $$0.688574\pi$$
$$828$$ 0 0
$$829$$ 12580.0 0.527046 0.263523 0.964653i $$-0.415115\pi$$
0.263523 + 0.964653i $$0.415115\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1665.00 −0.0692543
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 11344.0 0.466792 0.233396 0.972382i $$-0.425016\pi$$
0.233396 + 0.972382i $$0.425016\pi$$
$$840$$ 0 0
$$841$$ −23365.0 −0.958014
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 55900.0 2.26771
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −38412.0 −1.54729
$$852$$ 0 0
$$853$$ 14786.0 0.593509 0.296754 0.954954i $$-0.404096\pi$$
0.296754 + 0.954954i $$0.404096\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 29259.0 1.16624 0.583120 0.812386i $$-0.301832\pi$$
0.583120 + 0.812386i $$0.301832\pi$$
$$858$$ 0 0
$$859$$ −13651.0 −0.542219 −0.271109 0.962549i $$-0.587391\pi$$
−0.271109 + 0.962549i $$0.587391\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −29016.0 −1.14451 −0.572257 0.820074i $$-0.693932\pi$$
−0.572257 + 0.820074i $$0.693932\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 24426.0 0.953504
$$870$$ 0 0
$$871$$ −7084.00 −0.275582
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 21412.0 0.824438 0.412219 0.911085i $$-0.364754\pi$$
0.412219 + 0.911085i $$0.364754\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 1170.00 0.0447427 0.0223713 0.999750i $$-0.492878\pi$$
0.0223713 + 0.999750i $$0.492878\pi$$
$$882$$ 0 0
$$883$$ −12655.0 −0.482304 −0.241152 0.970487i $$-0.577525\pi$$
−0.241152 + 0.970487i $$0.577525\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −32764.0 −1.24026 −0.620128 0.784500i $$-0.712919\pi$$
−0.620128 + 0.784500i $$0.712919\pi$$
$$888$$ 0 0
$$889$$ −61308.0 −2.31294
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 7412.00 0.277753
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 320.000 0.0118716
$$900$$ 0 0
$$901$$ −90.0000 −0.00332779
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −29844.0 −1.09256 −0.546281 0.837602i $$-0.683957\pi$$
−0.546281 + 0.837602i $$0.683957\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −15628.0 −0.568363 −0.284182 0.958770i $$-0.591722\pi$$
−0.284182 + 0.958770i $$0.591722\pi$$
$$912$$ 0 0
$$913$$ 7139.00 0.258780
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 43992.0 1.58424
$$918$$ 0 0
$$919$$ 42974.0 1.54253 0.771263 0.636517i $$-0.219625\pi$$
0.771263 + 0.636517i $$0.219625\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 17136.0 0.611092
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −13342.0 −0.471191 −0.235596 0.971851i $$-0.575704\pi$$
−0.235596 + 0.971851i $$0.575704\pi$$
$$930$$ 0 0
$$931$$ 36297.0 1.27775
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −3005.00 −0.104770 −0.0523848 0.998627i $$-0.516682\pi$$
−0.0523848 + 0.998627i $$0.516682\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −16204.0 −0.561355 −0.280678 0.959802i $$-0.590559\pi$$
−0.280678 + 0.959802i $$0.590559\pi$$
$$942$$ 0 0
$$943$$ −22698.0 −0.783827
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 30200.0 1.03629 0.518146 0.855292i $$-0.326622\pi$$
0.518146 + 0.855292i $$0.326622\pi$$
$$948$$ 0 0
$$949$$ −15372.0 −0.525813
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 29583.0 1.00555 0.502774 0.864418i $$-0.332313\pi$$
0.502774 + 0.864418i $$0.332313\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −5954.00 −0.200485
$$960$$ 0 0
$$961$$ −29691.0 −0.996643
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −6480.00 −0.215494 −0.107747 0.994178i $$-0.534364\pi$$
−0.107747 + 0.994178i $$0.534364\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 40171.0 1.32765 0.663825 0.747888i $$-0.268932\pi$$
0.663825 + 0.747888i $$0.268932\pi$$
$$972$$ 0 0
$$973$$ 72306.0 2.38235
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −50801.0 −1.66353 −0.831765 0.555129i $$-0.812669\pi$$
−0.831765 + 0.555129i $$0.812669\pi$$
$$978$$ 0 0
$$979$$ 4779.00 0.156014
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 58338.0 1.89287 0.946436 0.322891i $$-0.104655\pi$$
0.946436 + 0.322891i $$0.104655\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 75272.0 2.42013
$$990$$ 0 0
$$991$$ −51202.0 −1.64126 −0.820628 0.571462i $$-0.806376\pi$$
−0.820628 + 0.571462i $$0.806376\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 1764.00 0.0560345 0.0280173 0.999607i $$-0.491081\pi$$
0.0280173 + 0.999607i $$0.491081\pi$$
$$998$$ 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.bh.1.1 1
3.2 odd 2 200.4.a.j.1.1 yes 1
5.2 odd 4 1800.4.f.w.649.2 2
5.3 odd 4 1800.4.f.w.649.1 2
5.4 even 2 1800.4.a.c.1.1 1
12.11 even 2 400.4.a.a.1.1 1
15.2 even 4 200.4.c.b.49.1 2
15.8 even 4 200.4.c.b.49.2 2
15.14 odd 2 200.4.a.b.1.1 1
24.5 odd 2 1600.4.a.c.1.1 1
24.11 even 2 1600.4.a.by.1.1 1
60.23 odd 4 400.4.c.b.49.1 2
60.47 odd 4 400.4.c.b.49.2 2
60.59 even 2 400.4.a.t.1.1 1
120.29 odd 2 1600.4.a.bz.1.1 1
120.59 even 2 1600.4.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
200.4.a.b.1.1 1 15.14 odd 2
200.4.a.j.1.1 yes 1 3.2 odd 2
200.4.c.b.49.1 2 15.2 even 4
200.4.c.b.49.2 2 15.8 even 4
400.4.a.a.1.1 1 12.11 even 2
400.4.a.t.1.1 1 60.59 even 2
400.4.c.b.49.1 2 60.23 odd 4
400.4.c.b.49.2 2 60.47 odd 4
1600.4.a.b.1.1 1 120.59 even 2
1600.4.a.c.1.1 1 24.5 odd 2
1600.4.a.by.1.1 1 24.11 even 2
1600.4.a.bz.1.1 1 120.29 odd 2
1800.4.a.c.1.1 1 5.4 even 2
1800.4.a.bh.1.1 1 1.1 even 1 trivial
1800.4.f.w.649.1 2 5.3 odd 4
1800.4.f.w.649.2 2 5.2 odd 4