# Properties

 Label 1800.4.a.x.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)

 $$f(q)$$ $$=$$ $$q+10.0000 q^{7} +O(q^{10})$$ $$q+10.0000 q^{7} +14.0000 q^{11} -82.0000 q^{13} -18.0000 q^{17} -136.000 q^{19} +140.000 q^{23} -112.000 q^{29} +72.0000 q^{31} +26.0000 q^{37} +446.000 q^{41} +396.000 q^{43} +144.000 q^{47} -243.000 q^{49} -158.000 q^{53} +342.000 q^{59} +314.000 q^{61} -152.000 q^{67} +932.000 q^{71} -548.000 q^{73} +140.000 q^{77} -512.000 q^{79} -284.000 q^{83} +810.000 q^{89} -820.000 q^{91} +1304.00 q^{97} +O(q^{100})$$

## 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
$$7$$ 10.0000 0.539949 0.269975 0.962867i $$-0.412985\pi$$
0.269975 + 0.962867i $$0.412985\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 14.0000 0.383742 0.191871 0.981420i $$-0.438545\pi$$
0.191871 + 0.981420i $$0.438545\pi$$
$$12$$ 0 0
$$13$$ −82.0000 −1.74944 −0.874720 0.484629i $$-0.838954\pi$$
−0.874720 + 0.484629i $$0.838954\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −18.0000 −0.256802 −0.128401 0.991722i $$-0.540985\pi$$
−0.128401 + 0.991722i $$0.540985\pi$$
$$18$$ 0 0
$$19$$ −136.000 −1.64213 −0.821067 0.570832i $$-0.806621\pi$$
−0.821067 + 0.570832i $$0.806621\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 140.000 1.26922 0.634609 0.772833i $$-0.281161\pi$$
0.634609 + 0.772833i $$0.281161\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −112.000 −0.717168 −0.358584 0.933497i $$-0.616740\pi$$
−0.358584 + 0.933497i $$0.616740\pi$$
$$30$$ 0 0
$$31$$ 72.0000 0.417148 0.208574 0.978007i $$-0.433118\pi$$
0.208574 + 0.978007i $$0.433118\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 26.0000 0.115524 0.0577618 0.998330i $$-0.481604\pi$$
0.0577618 + 0.998330i $$0.481604\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 446.000 1.69887 0.849433 0.527697i $$-0.176944\pi$$
0.849433 + 0.527697i $$0.176944\pi$$
$$42$$ 0 0
$$43$$ 396.000 1.40441 0.702203 0.711977i $$-0.252200\pi$$
0.702203 + 0.711977i $$0.252200\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 144.000 0.446906 0.223453 0.974715i $$-0.428267\pi$$
0.223453 + 0.974715i $$0.428267\pi$$
$$48$$ 0 0
$$49$$ −243.000 −0.708455
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −158.000 −0.409490 −0.204745 0.978815i $$-0.565637\pi$$
−0.204745 + 0.978815i $$0.565637\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 342.000 0.754654 0.377327 0.926080i $$-0.376843\pi$$
0.377327 + 0.926080i $$0.376843\pi$$
$$60$$ 0 0
$$61$$ 314.000 0.659075 0.329538 0.944142i $$-0.393107\pi$$
0.329538 + 0.944142i $$0.393107\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −152.000 −0.277161 −0.138580 0.990351i $$-0.544254\pi$$
−0.138580 + 0.990351i $$0.544254\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 932.000 1.55786 0.778930 0.627111i $$-0.215763\pi$$
0.778930 + 0.627111i $$0.215763\pi$$
$$72$$ 0 0
$$73$$ −548.000 −0.878610 −0.439305 0.898338i $$-0.644775\pi$$
−0.439305 + 0.898338i $$0.644775\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 140.000 0.207201
$$78$$ 0 0
$$79$$ −512.000 −0.729171 −0.364585 0.931170i $$-0.618789\pi$$
−0.364585 + 0.931170i $$0.618789\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −284.000 −0.375579 −0.187789 0.982209i $$-0.560132\pi$$
−0.187789 + 0.982209i $$0.560132\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 810.000 0.964717 0.482359 0.875974i $$-0.339780\pi$$
0.482359 + 0.875974i $$0.339780\pi$$
$$90$$ 0 0
$$91$$ −820.000 −0.944608
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1304.00 1.36496 0.682480 0.730904i $$-0.260901\pi$$
0.682480 + 0.730904i $$0.260901\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −936.000 −0.922133 −0.461067 0.887365i $$-0.652533\pi$$
−0.461067 + 0.887365i $$0.652533\pi$$
$$102$$ 0 0
$$103$$ 1450.00 1.38711 0.693557 0.720402i $$-0.256043\pi$$
0.693557 + 0.720402i $$0.256043\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1292.00 −1.16731 −0.583656 0.812001i $$-0.698378\pi$$
−0.583656 + 0.812001i $$0.698378\pi$$
$$108$$ 0 0
$$109$$ −2142.00 −1.88226 −0.941130 0.338044i $$-0.890235\pi$$
−0.941130 + 0.338044i $$0.890235\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1418.00 1.18048 0.590240 0.807228i $$-0.299033\pi$$
0.590240 + 0.807228i $$0.299033\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −180.000 −0.138660
$$120$$ 0 0
$$121$$ −1135.00 −0.852742
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1674.00 1.16963 0.584817 0.811165i $$-0.301166\pi$$
0.584817 + 0.811165i $$0.301166\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1134.00 −0.756321 −0.378160 0.925740i $$-0.623443\pi$$
−0.378160 + 0.925740i $$0.623443\pi$$
$$132$$ 0 0
$$133$$ −1360.00 −0.886669
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2866.00 1.78729 0.893646 0.448773i $$-0.148139\pi$$
0.893646 + 0.448773i $$0.148139\pi$$
$$138$$ 0 0
$$139$$ −764.000 −0.466199 −0.233099 0.972453i $$-0.574887\pi$$
−0.233099 + 0.972453i $$0.574887\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1148.00 −0.671333
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 3060.00 1.68245 0.841225 0.540686i $$-0.181835\pi$$
0.841225 + 0.540686i $$0.181835\pi$$
$$150$$ 0 0
$$151$$ −1304.00 −0.702768 −0.351384 0.936231i $$-0.614289\pi$$
−0.351384 + 0.936231i $$0.614289\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 1582.00 0.804187 0.402093 0.915599i $$-0.368283\pi$$
0.402093 + 0.915599i $$0.368283\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1400.00 0.685313
$$162$$ 0 0
$$163$$ 3232.00 1.55307 0.776533 0.630077i $$-0.216976\pi$$
0.776533 + 0.630077i $$0.216976\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2988.00 1.38454 0.692271 0.721638i $$-0.256610\pi$$
0.692271 + 0.721638i $$0.256610\pi$$
$$168$$ 0 0
$$169$$ 4527.00 2.06054
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 918.000 0.403435 0.201717 0.979444i $$-0.435348\pi$$
0.201717 + 0.979444i $$0.435348\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 1238.00 0.516941 0.258471 0.966019i $$-0.416781\pi$$
0.258471 + 0.966019i $$0.416781\pi$$
$$180$$ 0 0
$$181$$ 1450.00 0.595457 0.297728 0.954651i $$-0.403771\pi$$
0.297728 + 0.954651i $$0.403771\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −252.000 −0.0985458
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4860.00 −1.84114 −0.920569 0.390581i $$-0.872274\pi$$
−0.920569 + 0.390581i $$0.872274\pi$$
$$192$$ 0 0
$$193$$ −1412.00 −0.526622 −0.263311 0.964711i $$-0.584814\pi$$
−0.263311 + 0.964711i $$0.584814\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1170.00 0.423142 0.211571 0.977363i $$-0.432142\pi$$
0.211571 + 0.977363i $$0.432142\pi$$
$$198$$ 0 0
$$199$$ 2080.00 0.740941 0.370471 0.928844i $$-0.379196\pi$$
0.370471 + 0.928844i $$0.379196\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −1120.00 −0.387234
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −1904.00 −0.630155
$$210$$ 0 0
$$211$$ 2692.00 0.878317 0.439159 0.898410i $$-0.355277\pi$$
0.439159 + 0.898410i $$0.355277\pi$$
$$212$$ 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
$$221$$ 1476.00 0.449260
$$222$$ 0 0
$$223$$ −846.000 −0.254046 −0.127023 0.991900i $$-0.540542\pi$$
−0.127023 + 0.991900i $$0.540542\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −2884.00 −0.843250 −0.421625 0.906770i $$-0.638540\pi$$
−0.421625 + 0.906770i $$0.638540\pi$$
$$228$$ 0 0
$$229$$ 3150.00 0.908986 0.454493 0.890750i $$-0.349820\pi$$
0.454493 + 0.890750i $$0.349820\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 4014.00 1.12861 0.564304 0.825567i $$-0.309144\pi$$
0.564304 + 0.825567i $$0.309144\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −4900.00 −1.32617 −0.663085 0.748544i $$-0.730753\pi$$
−0.663085 + 0.748544i $$0.730753\pi$$
$$240$$ 0 0
$$241$$ −2314.00 −0.618497 −0.309249 0.950981i $$-0.600078\pi$$
−0.309249 + 0.950981i $$0.600078\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 11152.0 2.87281
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2002.00 0.503447 0.251723 0.967799i $$-0.419003\pi$$
0.251723 + 0.967799i $$0.419003\pi$$
$$252$$ 0 0
$$253$$ 1960.00 0.487052
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 450.000 0.109223 0.0546113 0.998508i $$-0.482608\pi$$
0.0546113 + 0.998508i $$0.482608\pi$$
$$258$$ 0 0
$$259$$ 260.000 0.0623769
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −180.000 −0.0422026 −0.0211013 0.999777i $$-0.506717\pi$$
−0.0211013 + 0.999777i $$0.506717\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −2448.00 −0.554859 −0.277430 0.960746i $$-0.589483\pi$$
−0.277430 + 0.960746i $$0.589483\pi$$
$$270$$ 0 0
$$271$$ 6776.00 1.51887 0.759433 0.650586i $$-0.225476\pi$$
0.759433 + 0.650586i $$0.225476\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 6426.00 1.39387 0.696933 0.717136i $$-0.254547\pi$$
0.696933 + 0.717136i $$0.254547\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −2718.00 −0.577019 −0.288509 0.957477i $$-0.593160\pi$$
−0.288509 + 0.957477i $$0.593160\pi$$
$$282$$ 0 0
$$283$$ 6048.00 1.27038 0.635188 0.772358i $$-0.280923\pi$$
0.635188 + 0.772358i $$0.280923\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 4460.00 0.917301
$$288$$ 0 0
$$289$$ −4589.00 −0.934053
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1246.00 −0.248437 −0.124219 0.992255i $$-0.539642\pi$$
−0.124219 + 0.992255i $$0.539642\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −11480.0 −2.22042
$$300$$ 0 0
$$301$$ 3960.00 0.758308
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1244.00 0.231267 0.115633 0.993292i $$-0.463110\pi$$
0.115633 + 0.993292i $$0.463110\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 6372.00 1.16181 0.580905 0.813971i $$-0.302699\pi$$
0.580905 + 0.813971i $$0.302699\pi$$
$$312$$ 0 0
$$313$$ 5500.00 0.993222 0.496611 0.867973i $$-0.334578\pi$$
0.496611 + 0.867973i $$0.334578\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −378.000 −0.0669735 −0.0334867 0.999439i $$-0.510661\pi$$
−0.0334867 + 0.999439i $$0.510661\pi$$
$$318$$ 0 0
$$319$$ −1568.00 −0.275207
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2448.00 0.421704
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1440.00 0.241306
$$330$$ 0 0
$$331$$ −11888.0 −1.97409 −0.987045 0.160446i $$-0.948707\pi$$
−0.987045 + 0.160446i $$0.948707\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −9116.00 −1.47353 −0.736766 0.676148i $$-0.763648\pi$$
−0.736766 + 0.676148i $$0.763648\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1008.00 0.160077
$$342$$ 0 0
$$343$$ −5860.00 −0.922479
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4676.00 0.723403 0.361701 0.932294i $$-0.382196\pi$$
0.361701 + 0.932294i $$0.382196\pi$$
$$348$$ 0 0
$$349$$ 11906.0 1.82611 0.913057 0.407833i $$-0.133715\pi$$
0.913057 + 0.407833i $$0.133715\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2142.00 0.322966 0.161483 0.986875i $$-0.448372\pi$$
0.161483 + 0.986875i $$0.448372\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −9824.00 −1.44426 −0.722132 0.691755i $$-0.756838\pi$$
−0.722132 + 0.691755i $$0.756838\pi$$
$$360$$ 0 0
$$361$$ 11637.0 1.69660
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 5354.00 0.761516 0.380758 0.924675i $$-0.375663\pi$$
0.380758 + 0.924675i $$0.375663\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −1580.00 −0.221104
$$372$$ 0 0
$$373$$ 7694.00 1.06804 0.534022 0.845471i $$-0.320680\pi$$
0.534022 + 0.845471i $$0.320680\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 9184.00 1.25464
$$378$$ 0 0
$$379$$ −6004.00 −0.813733 −0.406866 0.913488i $$-0.633379\pi$$
−0.406866 + 0.913488i $$0.633379\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −9432.00 −1.25836 −0.629181 0.777259i $$-0.716610\pi$$
−0.629181 + 0.777259i $$0.716610\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 6156.00 0.802369 0.401185 0.915997i $$-0.368599\pi$$
0.401185 + 0.915997i $$0.368599\pi$$
$$390$$ 0 0
$$391$$ −2520.00 −0.325938
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 7866.00 0.994416 0.497208 0.867631i $$-0.334359\pi$$
0.497208 + 0.867631i $$0.334359\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 2074.00 0.258281 0.129140 0.991626i $$-0.458778\pi$$
0.129140 + 0.991626i $$0.458778\pi$$
$$402$$ 0 0
$$403$$ −5904.00 −0.729775
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 364.000 0.0443312
$$408$$ 0 0
$$409$$ −2746.00 −0.331983 −0.165991 0.986127i $$-0.553082\pi$$
−0.165991 + 0.986127i $$0.553082\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 3420.00 0.407475
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 6426.00 0.749238 0.374619 0.927179i $$-0.377774\pi$$
0.374619 + 0.927179i $$0.377774\pi$$
$$420$$ 0 0
$$421$$ −10610.0 −1.22827 −0.614133 0.789203i $$-0.710494\pi$$
−0.614133 + 0.789203i $$0.710494\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 3140.00 0.355867
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −8384.00 −0.936991 −0.468495 0.883466i $$-0.655204\pi$$
−0.468495 + 0.883466i $$0.655204\pi$$
$$432$$ 0 0
$$433$$ 1980.00 0.219752 0.109876 0.993945i $$-0.464955\pi$$
0.109876 + 0.993945i $$0.464955\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −19040.0 −2.08423
$$438$$ 0 0
$$439$$ 864.000 0.0939327 0.0469664 0.998896i $$-0.485045\pi$$
0.0469664 + 0.998896i $$0.485045\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 13212.0 1.41698 0.708489 0.705722i $$-0.249377\pi$$
0.708489 + 0.705722i $$0.249377\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 16290.0 1.71219 0.856094 0.516820i $$-0.172884\pi$$
0.856094 + 0.516820i $$0.172884\pi$$
$$450$$ 0 0
$$451$$ 6244.00 0.651926
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 6336.00 0.648546 0.324273 0.945964i $$-0.394880\pi$$
0.324273 + 0.945964i $$0.394880\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 13716.0 1.38572 0.692861 0.721071i $$-0.256350\pi$$
0.692861 + 0.721071i $$0.256350\pi$$
$$462$$ 0 0
$$463$$ −14626.0 −1.46809 −0.734047 0.679098i $$-0.762371\pi$$
−0.734047 + 0.679098i $$0.762371\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 5796.00 0.574319 0.287159 0.957883i $$-0.407289\pi$$
0.287159 + 0.957883i $$0.407289\pi$$
$$468$$ 0 0
$$469$$ −1520.00 −0.149653
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 5544.00 0.538929
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 8348.00 0.796305 0.398152 0.917319i $$-0.369652\pi$$
0.398152 + 0.917319i $$0.369652\pi$$
$$480$$ 0 0
$$481$$ −2132.00 −0.202102
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −1898.00 −0.176605 −0.0883025 0.996094i $$-0.528144\pi$$
−0.0883025 + 0.996094i $$0.528144\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −16654.0 −1.53072 −0.765361 0.643601i $$-0.777440\pi$$
−0.765361 + 0.643601i $$0.777440\pi$$
$$492$$ 0 0
$$493$$ 2016.00 0.184171
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 9320.00 0.841165
$$498$$ 0 0
$$499$$ −10600.0 −0.950944 −0.475472 0.879731i $$-0.657723\pi$$
−0.475472 + 0.879731i $$0.657723\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 10048.0 0.890692 0.445346 0.895359i $$-0.353081\pi$$
0.445346 + 0.895359i $$0.353081\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 15088.0 1.31388 0.656939 0.753944i $$-0.271851\pi$$
0.656939 + 0.753944i $$0.271851\pi$$
$$510$$ 0 0
$$511$$ −5480.00 −0.474405
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 2016.00 0.171496
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −8582.00 −0.721659 −0.360829 0.932632i $$-0.617506\pi$$
−0.360829 + 0.932632i $$0.617506\pi$$
$$522$$ 0 0
$$523$$ 16928.0 1.41532 0.707658 0.706556i $$-0.249752\pi$$
0.707658 + 0.706556i $$0.249752\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −1296.00 −0.107125
$$528$$ 0 0
$$529$$ 7433.00 0.610915
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −36572.0 −2.97206
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −3402.00 −0.271864
$$540$$ 0 0
$$541$$ −11150.0 −0.886092 −0.443046 0.896499i $$-0.646102\pi$$
−0.443046 + 0.896499i $$0.646102\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −19628.0 −1.53425 −0.767123 0.641500i $$-0.778312\pi$$
−0.767123 + 0.641500i $$0.778312\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 15232.0 1.17769
$$552$$ 0 0
$$553$$ −5120.00 −0.393715
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −8694.00 −0.661358 −0.330679 0.943743i $$-0.607278\pi$$
−0.330679 + 0.943743i $$0.607278\pi$$
$$558$$ 0 0
$$559$$ −32472.0 −2.45692
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 828.000 0.0619823 0.0309912 0.999520i $$-0.490134\pi$$
0.0309912 + 0.999520i $$0.490134\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 17514.0 1.29038 0.645189 0.764023i $$-0.276779\pi$$
0.645189 + 0.764023i $$0.276779\pi$$
$$570$$ 0 0
$$571$$ −5552.00 −0.406907 −0.203454 0.979085i $$-0.565217\pi$$
−0.203454 + 0.979085i $$0.565217\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −12896.0 −0.930446 −0.465223 0.885193i $$-0.654026\pi$$
−0.465223 + 0.885193i $$0.654026\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −2840.00 −0.202794
$$582$$ 0 0
$$583$$ −2212.00 −0.157138
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1588.00 0.111659 0.0558295 0.998440i $$-0.482220\pi$$
0.0558295 + 0.998440i $$0.482220\pi$$
$$588$$ 0 0
$$589$$ −9792.00 −0.685012
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −22262.0 −1.54164 −0.770819 0.637055i $$-0.780152\pi$$
−0.770819 + 0.637055i $$0.780152\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −4640.00 −0.316503 −0.158251 0.987399i $$-0.550586\pi$$
−0.158251 + 0.987399i $$0.550586\pi$$
$$600$$ 0 0
$$601$$ −2574.00 −0.174702 −0.0873508 0.996178i $$-0.527840\pi$$
−0.0873508 + 0.996178i $$0.527840\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −11170.0 −0.746913 −0.373457 0.927648i $$-0.621828\pi$$
−0.373457 + 0.927648i $$0.621828\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −11808.0 −0.781834
$$612$$ 0 0
$$613$$ −3646.00 −0.240229 −0.120115 0.992760i $$-0.538326\pi$$
−0.120115 + 0.992760i $$0.538326\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 7646.00 0.498892 0.249446 0.968389i $$-0.419751\pi$$
0.249446 + 0.968389i $$0.419751\pi$$
$$618$$ 0 0
$$619$$ 26668.0 1.73163 0.865814 0.500366i $$-0.166801\pi$$
0.865814 + 0.500366i $$0.166801\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 8100.00 0.520898
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −468.000 −0.0296667
$$630$$ 0 0
$$631$$ 7712.00 0.486545 0.243272 0.969958i $$-0.421779\pi$$
0.243272 + 0.969958i $$0.421779\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 19926.0 1.23940
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 22302.0 1.37422 0.687111 0.726553i $$-0.258879\pi$$
0.687111 + 0.726553i $$0.258879\pi$$
$$642$$ 0 0
$$643$$ 2232.00 0.136892 0.0684459 0.997655i $$-0.478196\pi$$
0.0684459 + 0.997655i $$0.478196\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −9464.00 −0.575067 −0.287533 0.957771i $$-0.592835\pi$$
−0.287533 + 0.957771i $$0.592835\pi$$
$$648$$ 0 0
$$649$$ 4788.00 0.289592
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 4878.00 0.292329 0.146165 0.989260i $$-0.453307\pi$$
0.146165 + 0.989260i $$0.453307\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −10206.0 −0.603292 −0.301646 0.953420i $$-0.597536\pi$$
−0.301646 + 0.953420i $$0.597536\pi$$
$$660$$ 0 0
$$661$$ 20906.0 1.23018 0.615090 0.788457i $$-0.289120\pi$$
0.615090 + 0.788457i $$0.289120\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −15680.0 −0.910243
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 4396.00 0.252915
$$672$$ 0 0
$$673$$ −6812.00 −0.390168 −0.195084 0.980787i $$-0.562498\pi$$
−0.195084 + 0.980787i $$0.562498\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −10026.0 −0.569174 −0.284587 0.958650i $$-0.591856\pi$$
−0.284587 + 0.958650i $$0.591856\pi$$
$$678$$ 0 0
$$679$$ 13040.0 0.737009
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 21236.0 1.18971 0.594856 0.803832i $$-0.297209\pi$$
0.594856 + 0.803832i $$0.297209\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 12956.0 0.716378
$$690$$ 0 0
$$691$$ −11520.0 −0.634213 −0.317107 0.948390i $$-0.602711\pi$$
−0.317107 + 0.948390i $$0.602711\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −8028.00 −0.436273
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 400.000 0.0215518 0.0107759 0.999942i $$-0.496570\pi$$
0.0107759 + 0.999942i $$0.496570\pi$$
$$702$$ 0 0
$$703$$ −3536.00 −0.189705
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −9360.00 −0.497905
$$708$$ 0 0
$$709$$ −5930.00 −0.314113 −0.157056 0.987590i $$-0.550200\pi$$
−0.157056 + 0.987590i $$0.550200\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 10080.0 0.529452
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −7160.00 −0.371381 −0.185691 0.982608i $$-0.559452\pi$$
−0.185691 + 0.982608i $$0.559452\pi$$
$$720$$ 0 0
$$721$$ 14500.0 0.748971
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −8874.00 −0.452708 −0.226354 0.974045i $$-0.572681\pi$$
−0.226354 + 0.974045i $$0.572681\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −7128.00 −0.360655
$$732$$ 0 0
$$733$$ 5562.00 0.280269 0.140134 0.990132i $$-0.455247\pi$$
0.140134 + 0.990132i $$0.455247\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −2128.00 −0.106358
$$738$$ 0 0
$$739$$ −12096.0 −0.602109 −0.301055 0.953607i $$-0.597339\pi$$
−0.301055 + 0.953607i $$0.597339\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −21312.0 −1.05230 −0.526152 0.850391i $$-0.676366\pi$$
−0.526152 + 0.850391i $$0.676366\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −12920.0 −0.630289
$$750$$ 0 0
$$751$$ −6832.00 −0.331962 −0.165981 0.986129i $$-0.553079\pi$$
−0.165981 + 0.986129i $$0.553079\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −7174.00 −0.344443 −0.172222 0.985058i $$-0.555095\pi$$
−0.172222 + 0.985058i $$0.555095\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 15394.0 0.733288 0.366644 0.930361i $$-0.380507\pi$$
0.366644 + 0.930361i $$0.380507\pi$$
$$762$$ 0 0
$$763$$ −21420.0 −1.01633
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −28044.0 −1.32022
$$768$$ 0 0
$$769$$ 9730.00 0.456271 0.228136 0.973629i $$-0.426737\pi$$
0.228136 + 0.973629i $$0.426737\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 24206.0 1.12630 0.563150 0.826355i $$-0.309589\pi$$
0.563150 + 0.826355i $$0.309589\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −60656.0 −2.78976
$$780$$ 0 0
$$781$$ 13048.0 0.597816
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −31312.0 −1.41824 −0.709118 0.705089i $$-0.750907\pi$$
−0.709118 + 0.705089i $$0.750907\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 14180.0 0.637399
$$792$$ 0 0
$$793$$ −25748.0 −1.15301
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −10746.0 −0.477595 −0.238797 0.971069i $$-0.576753\pi$$
−0.238797 + 0.971069i $$0.576753\pi$$
$$798$$ 0 0
$$799$$ −2592.00 −0.114766
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −7672.00 −0.337159
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −30546.0 −1.32749 −0.663745 0.747959i $$-0.731034\pi$$
−0.663745 + 0.747959i $$0.731034\pi$$
$$810$$ 0 0
$$811$$ −2628.00 −0.113787 −0.0568937 0.998380i $$-0.518120\pi$$
−0.0568937 + 0.998380i $$0.518120\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −53856.0 −2.30622
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −26280.0 −1.11715 −0.558574 0.829455i $$-0.688651\pi$$
−0.558574 + 0.829455i $$0.688651\pi$$
$$822$$ 0 0
$$823$$ −26146.0 −1.10740 −0.553701 0.832715i $$-0.686785\pi$$
−0.553701 + 0.832715i $$0.686785\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −29268.0 −1.23065 −0.615325 0.788273i $$-0.710975\pi$$
−0.615325 + 0.788273i $$0.710975\pi$$
$$828$$ 0 0
$$829$$ 6202.00 0.259836 0.129918 0.991525i $$-0.458529\pi$$
0.129918 + 0.991525i $$0.458529\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 4374.00 0.181933
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −4680.00 −0.192576 −0.0962882 0.995353i $$-0.530697\pi$$
−0.0962882 + 0.995353i $$0.530697\pi$$
$$840$$ 0 0
$$841$$ −11845.0 −0.485670
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −11350.0 −0.460438
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 3640.00 0.146625
$$852$$ 0 0
$$853$$ 12122.0 0.486576 0.243288 0.969954i $$-0.421774\pi$$
0.243288 + 0.969954i $$0.421774\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 26006.0 1.03658 0.518289 0.855205i $$-0.326569\pi$$
0.518289 + 0.855205i $$0.326569\pi$$
$$858$$ 0 0
$$859$$ −17684.0 −0.702410 −0.351205 0.936299i $$-0.614228\pi$$
−0.351205 + 0.936299i $$0.614228\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −15084.0 −0.594977 −0.297489 0.954725i $$-0.596149\pi$$
−0.297489 + 0.954725i $$0.596149\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −7168.00 −0.279813
$$870$$ 0 0
$$871$$ 12464.0 0.484875
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 17614.0 0.678201 0.339101 0.940750i $$-0.389877\pi$$
0.339101 + 0.940750i $$0.389877\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 3298.00 0.126121 0.0630604 0.998010i $$-0.479914\pi$$
0.0630604 + 0.998010i $$0.479914\pi$$
$$882$$ 0 0
$$883$$ 9496.00 0.361909 0.180955 0.983491i $$-0.442081\pi$$
0.180955 + 0.983491i $$0.442081\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 50220.0 1.90104 0.950520 0.310663i $$-0.100551\pi$$
0.950520 + 0.310663i $$0.100551\pi$$
$$888$$ 0 0
$$889$$ 16740.0 0.631543
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −19584.0 −0.733879
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −8064.00 −0.299165
$$900$$ 0 0
$$901$$ 2844.00 0.105158
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 20636.0 0.755465 0.377733 0.925915i $$-0.376704\pi$$
0.377733 + 0.925915i $$0.376704\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −13680.0 −0.497518 −0.248759 0.968565i $$-0.580023\pi$$
−0.248759 + 0.968565i $$0.580023\pi$$
$$912$$ 0 0
$$913$$ −3976.00 −0.144125
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −11340.0 −0.408375
$$918$$ 0 0
$$919$$ 21456.0 0.770150 0.385075 0.922885i $$-0.374176\pi$$
0.385075 + 0.922885i $$0.374176\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −76424.0 −2.72538
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −16510.0 −0.583074 −0.291537 0.956560i $$-0.594167\pi$$
−0.291537 + 0.956560i $$0.594167\pi$$
$$930$$ 0 0
$$931$$ 33048.0 1.16338
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −36296.0 −1.26546 −0.632731 0.774371i $$-0.718066\pi$$
−0.632731 + 0.774371i $$0.718066\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −13540.0 −0.469066 −0.234533 0.972108i $$-0.575356\pi$$
−0.234533 + 0.972108i $$0.575356\pi$$
$$942$$ 0 0
$$943$$ 62440.0 2.15623
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −32940.0 −1.13031 −0.565156 0.824984i $$-0.691184\pi$$
−0.565156 + 0.824984i $$0.691184\pi$$
$$948$$ 0 0
$$949$$ 44936.0 1.53708
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 22482.0 0.764180 0.382090 0.924125i $$-0.375204\pi$$
0.382090 + 0.924125i $$0.375204\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 28660.0 0.965047
$$960$$ 0 0
$$961$$ −24607.0 −0.825988
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −9566.00 −0.318120 −0.159060 0.987269i $$-0.550846\pi$$
−0.159060 + 0.987269i $$0.550846\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −10062.0 −0.332549 −0.166274 0.986080i $$-0.553174\pi$$
−0.166274 + 0.986080i $$0.553174\pi$$
$$972$$ 0 0
$$973$$ −7640.00 −0.251724
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −48506.0 −1.58838 −0.794189 0.607671i $$-0.792104\pi$$
−0.794189 + 0.607671i $$0.792104\pi$$
$$978$$ 0 0
$$979$$ 11340.0 0.370202
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 41144.0 1.33498 0.667492 0.744617i $$-0.267368\pi$$
0.667492 + 0.744617i $$0.267368\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 55440.0 1.78250
$$990$$ 0 0
$$991$$ 16120.0 0.516719 0.258360 0.966049i $$-0.416818\pi$$
0.258360 + 0.966049i $$0.416818\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −36666.0 −1.16472 −0.582359 0.812932i $$-0.697870\pi$$
−0.582359 + 0.812932i $$0.697870\pi$$
$$998$$ 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.x.1.1 1
3.2 odd 2 600.4.a.p.1.1 1
5.2 odd 4 360.4.f.b.289.1 2
5.3 odd 4 360.4.f.b.289.2 2
5.4 even 2 1800.4.a.i.1.1 1
12.11 even 2 1200.4.a.e.1.1 1
15.2 even 4 120.4.f.b.49.1 2
15.8 even 4 120.4.f.b.49.2 yes 2
15.14 odd 2 600.4.a.c.1.1 1
20.3 even 4 720.4.f.e.289.2 2
20.7 even 4 720.4.f.e.289.1 2
60.23 odd 4 240.4.f.c.49.1 2
60.47 odd 4 240.4.f.c.49.2 2
60.59 even 2 1200.4.a.bg.1.1 1
120.53 even 4 960.4.f.f.769.1 2
120.77 even 4 960.4.f.f.769.2 2
120.83 odd 4 960.4.f.e.769.2 2
120.107 odd 4 960.4.f.e.769.1 2

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