# Properties

 Label 7605.2.a.h.1.1 Level $7605$ Weight $2$ Character 7605.1 Self dual yes Analytic conductor $60.726$ Analytic rank $1$ 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] = [7605,2,Mod(1,7605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7605, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$7605 = 3^{2} \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7605.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: $$60.7262307372$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 195) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7605.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{8} -1.00000 q^{10} +4.00000 q^{11} -1.00000 q^{16} -2.00000 q^{17} +4.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} -8.00000 q^{23} +1.00000 q^{25} +2.00000 q^{29} +8.00000 q^{31} -5.00000 q^{32} +2.00000 q^{34} -6.00000 q^{37} -4.00000 q^{38} +3.00000 q^{40} -6.00000 q^{41} -4.00000 q^{43} -4.00000 q^{44} +8.00000 q^{46} -8.00000 q^{47} -7.00000 q^{49} -1.00000 q^{50} -6.00000 q^{53} +4.00000 q^{55} -2.00000 q^{58} -12.0000 q^{59} -2.00000 q^{61} -8.00000 q^{62} +7.00000 q^{64} +4.00000 q^{67} +2.00000 q^{68} +6.00000 q^{73} +6.00000 q^{74} -4.00000 q^{76} +16.0000 q^{79} -1.00000 q^{80} +6.00000 q^{82} -4.00000 q^{83} -2.00000 q^{85} +4.00000 q^{86} +12.0000 q^{88} +10.0000 q^{89} +8.00000 q^{92} +8.00000 q^{94} +4.00000 q^{95} -18.0000 q^{97} +7.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107 −0.353553 0.935414i $$-0.615027\pi$$
−0.353553 + 0.935414i $$0.615027\pi$$
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 3.00000 1.06066
$$9$$ 0 0
$$10$$ −1.00000 −0.316228
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ 0 0
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ −4.00000 −0.852803
$$23$$ −8.00000 −1.66812 −0.834058 0.551677i $$-0.813988\pi$$
−0.834058 + 0.551677i $$0.813988\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ −5.00000 −0.883883
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ 0 0
$$40$$ 3.00000 0.474342
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −2.00000 −0.262613
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ −8.00000 −1.01600
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 2.00000 0.242536
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 16.0000 1.80014 0.900070 0.435745i $$-0.143515\pi$$
0.900070 + 0.435745i $$0.143515\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ 12.0000 1.27920
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 8.00000 0.834058
$$93$$ 0 0
$$94$$ 8.00000 0.825137
$$95$$ 4.00000 0.410391
$$96$$ 0 0
$$97$$ −18.0000 −1.82762 −0.913812 0.406138i $$-0.866875\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 7.00000 0.707107
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ −4.00000 −0.381385
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ −8.00000 −0.746004
$$116$$ −2.00000 −0.185695
$$117$$ 0 0
$$118$$ 12.0000 1.10469
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 2.00000 0.181071
$$123$$ 0 0
$$124$$ −8.00000 −0.718421
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ 3.00000 0.265165
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 0 0
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 2.00000 0.166091
$$146$$ −6.00000 −0.496564
$$147$$ 0 0
$$148$$ 6.00000 0.493197
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 12.0000 0.973329
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 8.00000 0.642575
$$156$$ 0 0
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ −16.0000 −1.27289
$$159$$ 0 0
$$160$$ −5.00000 −0.395285
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 16.0000 1.23812 0.619059 0.785345i $$-0.287514\pi$$
0.619059 + 0.785345i $$0.287514\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 2.00000 0.153393
$$171$$ 0 0
$$172$$ 4.00000 0.304997
$$173$$ 2.00000 0.152057 0.0760286 0.997106i $$-0.475776\pi$$
0.0760286 + 0.997106i $$0.475776\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ 0 0
$$178$$ −10.0000 −0.749532
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ 22.0000 1.63525 0.817624 0.575753i $$-0.195291\pi$$
0.817624 + 0.575753i $$0.195291\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −24.0000 −1.76930
$$185$$ −6.00000 −0.441129
$$186$$ 0 0
$$187$$ −8.00000 −0.585018
$$188$$ 8.00000 0.583460
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 0 0
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 18.0000 1.29232
$$195$$ 0 0
$$196$$ 7.00000 0.500000
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 3.00000 0.212132
$$201$$ 0 0
$$202$$ 6.00000 0.422159
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −6.00000 −0.419058
$$206$$ 8.00000 0.557386
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ 20.0000 1.37686 0.688428 0.725304i $$-0.258301\pi$$
0.688428 + 0.725304i $$0.258301\pi$$
$$212$$ 6.00000 0.412082
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ −4.00000 −0.272798
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ 0 0
$$220$$ −4.00000 −0.269680
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 24.0000 1.60716 0.803579 0.595198i $$-0.202926\pi$$
0.803579 + 0.595198i $$0.202926\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 2.00000 0.133038
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 0 0
$$229$$ −22.0000 −1.45380 −0.726900 0.686743i $$-0.759040\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 8.00000 0.527504
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ −26.0000 −1.70332 −0.851658 0.524097i $$-0.824403\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ 0 0
$$235$$ −8.00000 −0.521862
$$236$$ 12.0000 0.781133
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −24.0000 −1.55243 −0.776215 0.630468i $$-0.782863\pi$$
−0.776215 + 0.630468i $$0.782863\pi$$
$$240$$ 0 0
$$241$$ 14.0000 0.901819 0.450910 0.892570i $$-0.351100\pi$$
0.450910 + 0.892570i $$0.351100\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ −7.00000 −0.447214
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 24.0000 1.52400
$$249$$ 0 0
$$250$$ −1.00000 −0.0632456
$$251$$ 4.00000 0.252478 0.126239 0.992000i $$-0.459709\pi$$
0.126239 + 0.992000i $$0.459709\pi$$
$$252$$ 0 0
$$253$$ −32.0000 −2.01182
$$254$$ 16.0000 1.00393
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −12.0000 −0.741362
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −4.00000 −0.244339
$$269$$ −14.0000 −0.853595 −0.426798 0.904347i $$-0.640358\pi$$
−0.426798 + 0.904347i $$0.640358\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 6.00000 0.362473
$$275$$ 4.00000 0.241209
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 20.0000 1.19952
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −22.0000 −1.31241 −0.656205 0.754583i $$-0.727839\pi$$
−0.656205 + 0.754583i $$0.727839\pi$$
$$282$$ 0 0
$$283$$ −20.0000 −1.18888 −0.594438 0.804141i $$-0.702626\pi$$
−0.594438 + 0.804141i $$0.702626\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ −2.00000 −0.117444
$$291$$ 0 0
$$292$$ −6.00000 −0.351123
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 0 0
$$295$$ −12.0000 −0.698667
$$296$$ −18.0000 −1.04623
$$297$$ 0 0
$$298$$ 10.0000 0.579284
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −4.00000 −0.229416
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −8.00000 −0.454369
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ 26.0000 1.46961 0.734803 0.678280i $$-0.237274\pi$$
0.734803 + 0.678280i $$0.237274\pi$$
$$314$$ 2.00000 0.112867
$$315$$ 0 0
$$316$$ −16.0000 −0.900070
$$317$$ 30.0000 1.68497 0.842484 0.538721i $$-0.181092\pi$$
0.842484 + 0.538721i $$0.181092\pi$$
$$318$$ 0 0
$$319$$ 8.00000 0.447914
$$320$$ 7.00000 0.391312
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8.00000 −0.445132
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −20.0000 −1.10770
$$327$$ 0 0
$$328$$ −18.0000 −0.993884
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ 4.00000 0.219529
$$333$$ 0 0
$$334$$ −16.0000 −0.875481
$$335$$ 4.00000 0.218543
$$336$$ 0 0
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 2.00000 0.108465
$$341$$ 32.0000 1.73290
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −12.0000 −0.646997
$$345$$ 0 0
$$346$$ −2.00000 −0.107521
$$347$$ 4.00000 0.214731 0.107366 0.994220i $$-0.465758\pi$$
0.107366 + 0.994220i $$0.465758\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −20.0000 −1.06600
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −22.0000 −1.15629
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 6.00000 0.314054
$$366$$ 0 0
$$367$$ −16.0000 −0.835193 −0.417597 0.908633i $$-0.637127\pi$$
−0.417597 + 0.908633i $$0.637127\pi$$
$$368$$ 8.00000 0.417029
$$369$$ 0 0
$$370$$ 6.00000 0.311925
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ 8.00000 0.413670
$$375$$ 0 0
$$376$$ −24.0000 −1.23771
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −36.0000 −1.84920 −0.924598 0.380945i $$-0.875599\pi$$
−0.924598 + 0.380945i $$0.875599\pi$$
$$380$$ −4.00000 −0.205196
$$381$$ 0 0
$$382$$ 16.0000 0.818631
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −14.0000 −0.712581
$$387$$ 0 0
$$388$$ 18.0000 0.913812
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ −21.0000 −1.06066
$$393$$ 0 0
$$394$$ −6.00000 −0.302276
$$395$$ 16.0000 0.805047
$$396$$ 0 0
$$397$$ −14.0000 −0.702640 −0.351320 0.936255i $$-0.614267\pi$$
−0.351320 + 0.936255i $$0.614267\pi$$
$$398$$ 8.00000 0.401004
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −24.0000 −1.18964
$$408$$ 0 0
$$409$$ 38.0000 1.87898 0.939490 0.342578i $$-0.111300\pi$$
0.939490 + 0.342578i $$0.111300\pi$$
$$410$$ 6.00000 0.296319
$$411$$ 0 0
$$412$$ 8.00000 0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −4.00000 −0.196352
$$416$$ 0 0
$$417$$ 0 0
$$418$$ −16.0000 −0.782586
$$419$$ −20.0000 −0.977064 −0.488532 0.872546i $$-0.662467\pi$$
−0.488532 + 0.872546i $$0.662467\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ −20.0000 −0.973585
$$423$$ 0 0
$$424$$ −18.0000 −0.874157
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 4.00000 0.192897
$$431$$ 8.00000 0.385346 0.192673 0.981263i $$-0.438284\pi$$
0.192673 + 0.981263i $$0.438284\pi$$
$$432$$ 0 0
$$433$$ 18.0000 0.865025 0.432512 0.901628i $$-0.357627\pi$$
0.432512 + 0.901628i $$0.357627\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ −32.0000 −1.53077
$$438$$ 0 0
$$439$$ −24.0000 −1.14546 −0.572729 0.819745i $$-0.694115\pi$$
−0.572729 + 0.819745i $$0.694115\pi$$
$$440$$ 12.0000 0.572078
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4.00000 0.190046 0.0950229 0.995475i $$-0.469708\pi$$
0.0950229 + 0.995475i $$0.469708\pi$$
$$444$$ 0 0
$$445$$ 10.0000 0.474045
$$446$$ −24.0000 −1.13643
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ −24.0000 −1.13012
$$452$$ 2.00000 0.0940721
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −26.0000 −1.21623 −0.608114 0.793849i $$-0.708074\pi$$
−0.608114 + 0.793849i $$0.708074\pi$$
$$458$$ 22.0000 1.02799
$$459$$ 0 0
$$460$$ 8.00000 0.373002
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 0 0
$$466$$ 26.0000 1.20443
$$467$$ −4.00000 −0.185098 −0.0925490 0.995708i $$-0.529501\pi$$
−0.0925490 + 0.995708i $$0.529501\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 8.00000 0.369012
$$471$$ 0 0
$$472$$ −36.0000 −1.65703
$$473$$ −16.0000 −0.735681
$$474$$ 0 0
$$475$$ 4.00000 0.183533
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 24.0000 1.09773
$$479$$ 8.00000 0.365529 0.182765 0.983157i $$-0.441495\pi$$
0.182765 + 0.983157i $$0.441495\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −14.0000 −0.637683
$$483$$ 0 0
$$484$$ −5.00000 −0.227273
$$485$$ −18.0000 −0.817338
$$486$$ 0 0
$$487$$ −16.0000 −0.725029 −0.362515 0.931978i $$-0.618082\pi$$
−0.362515 + 0.931978i $$0.618082\pi$$
$$488$$ −6.00000 −0.271607
$$489$$ 0 0
$$490$$ 7.00000 0.316228
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 0 0
$$493$$ −4.00000 −0.180151
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −8.00000 −0.359211
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −28.0000 −1.25345 −0.626726 0.779240i $$-0.715605\pi$$
−0.626726 + 0.779240i $$0.715605\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 0 0
$$502$$ −4.00000 −0.178529
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 32.0000 1.42257
$$507$$ 0 0
$$508$$ 16.0000 0.709885
$$509$$ 30.0000 1.32973 0.664863 0.746965i $$-0.268490\pi$$
0.664863 + 0.746965i $$0.268490\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 11.0000 0.486136
$$513$$ 0 0
$$514$$ 18.0000 0.793946
$$515$$ −8.00000 −0.352522
$$516$$ 0 0
$$517$$ −32.0000 −1.40736
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 22.0000 0.963837 0.481919 0.876216i $$-0.339940\pi$$
0.481919 + 0.876216i $$0.339940\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ −16.0000 −0.696971
$$528$$ 0 0
$$529$$ 41.0000 1.78261
$$530$$ 6.00000 0.260623
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −12.0000 −0.518805
$$536$$ 12.0000 0.518321
$$537$$ 0 0
$$538$$ 14.0000 0.603583
$$539$$ −28.0000 −1.20605
$$540$$ 0 0
$$541$$ −14.0000 −0.601907 −0.300954 0.953639i $$-0.597305\pi$$
−0.300954 + 0.953639i $$0.597305\pi$$
$$542$$ −8.00000 −0.343629
$$543$$ 0 0
$$544$$ 10.0000 0.428746
$$545$$ 2.00000 0.0856706
$$546$$ 0 0
$$547$$ 36.0000 1.53925 0.769624 0.638497i $$-0.220443\pi$$
0.769624 + 0.638497i $$0.220443\pi$$
$$548$$ 6.00000 0.256307
$$549$$ 0 0
$$550$$ −4.00000 −0.170561
$$551$$ 8.00000 0.340811
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ 20.0000 0.848189
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 22.0000 0.928014
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 0 0
$$565$$ −2.00000 −0.0841406
$$566$$ 20.0000 0.840663
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 38.0000 1.59304 0.796521 0.604610i $$-0.206671\pi$$
0.796521 + 0.604610i $$0.206671\pi$$
$$570$$ 0 0
$$571$$ 44.0000 1.84134 0.920671 0.390339i $$-0.127642\pi$$
0.920671 + 0.390339i $$0.127642\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −8.00000 −0.333623
$$576$$ 0 0
$$577$$ −18.0000 −0.749350 −0.374675 0.927156i $$-0.622246\pi$$
−0.374675 + 0.927156i $$0.622246\pi$$
$$578$$ 13.0000 0.540729
$$579$$ 0 0
$$580$$ −2.00000 −0.0830455
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −24.0000 −0.993978
$$584$$ 18.0000 0.744845
$$585$$ 0 0
$$586$$ −6.00000 −0.247858
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ 32.0000 1.31854
$$590$$ 12.0000 0.494032
$$591$$ 0 0
$$592$$ 6.00000 0.246598
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 10.0000 0.409616
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −40.0000 −1.63436 −0.817178 0.576386i $$-0.804463\pi$$
−0.817178 + 0.576386i $$0.804463\pi$$
$$600$$ 0 0
$$601$$ −38.0000 −1.55005 −0.775026 0.631929i $$-0.782263\pi$$
−0.775026 + 0.631929i $$0.782263\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 5.00000 0.203279
$$606$$ 0 0
$$607$$ 32.0000 1.29884 0.649420 0.760430i $$-0.275012\pi$$
0.649420 + 0.760430i $$0.275012\pi$$
$$608$$ −20.0000 −0.811107
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ −4.00000 −0.161427
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −38.0000 −1.52982 −0.764911 0.644136i $$-0.777217\pi$$
−0.764911 + 0.644136i $$0.777217\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ −8.00000 −0.321288
$$621$$ 0 0
$$622$$ 24.0000 0.962312
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ −26.0000 −1.03917
$$627$$ 0 0
$$628$$ 2.00000 0.0798087
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 48.0000 1.90934
$$633$$ 0 0
$$634$$ −30.0000 −1.19145
$$635$$ −16.0000 −0.634941
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −8.00000 −0.316723
$$639$$ 0 0
$$640$$ 3.00000 0.118585
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ −28.0000 −1.10421 −0.552106 0.833774i $$-0.686176\pi$$
−0.552106 + 0.833774i $$0.686176\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 8.00000 0.314756
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ −48.0000 −1.88416
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −20.0000 −0.783260
$$653$$ −30.0000 −1.17399 −0.586995 0.809590i $$-0.699689\pi$$
−0.586995 + 0.809590i $$0.699689\pi$$
$$654$$ 0 0
$$655$$ 12.0000 0.468879
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −38.0000 −1.47803 −0.739014 0.673690i $$-0.764708\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 20.0000 0.777322
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −16.0000 −0.619522
$$668$$ −16.0000 −0.619059
$$669$$ 0 0
$$670$$ −4.00000 −0.154533
$$671$$ −8.00000 −0.308837
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 14.0000 0.539260
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 10.0000 0.384331 0.192166 0.981363i $$-0.438449\pi$$
0.192166 + 0.981363i $$0.438449\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −6.00000 −0.230089
$$681$$ 0 0
$$682$$ −32.0000 −1.22534
$$683$$ 4.00000 0.153056 0.0765279 0.997067i $$-0.475617\pi$$
0.0765279 + 0.997067i $$0.475617\pi$$
$$684$$ 0 0
$$685$$ −6.00000 −0.229248
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 4.00000 0.152499
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 36.0000 1.36950 0.684752 0.728776i $$-0.259910\pi$$
0.684752 + 0.728776i $$0.259910\pi$$
$$692$$ −2.00000 −0.0760286
$$693$$ 0 0
$$694$$ −4.00000 −0.151838
$$695$$ −20.0000 −0.758643
$$696$$ 0 0
$$697$$ 12.0000 0.454532
$$698$$ 14.0000 0.529908
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 34.0000 1.28416 0.642081 0.766637i $$-0.278071\pi$$
0.642081 + 0.766637i $$0.278071\pi$$
$$702$$ 0 0
$$703$$ −24.0000 −0.905177
$$704$$ 28.0000 1.05529
$$705$$ 0 0
$$706$$ 14.0000 0.526897
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 30.0000 1.12430
$$713$$ −64.0000 −2.39682
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −12.0000 −0.448461
$$717$$ 0 0
$$718$$ −16.0000 −0.597115
$$719$$ 48.0000 1.79010 0.895049 0.445968i $$-0.147140\pi$$
0.895049 + 0.445968i $$0.147140\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 3.00000 0.111648
$$723$$ 0 0
$$724$$ −22.0000 −0.817624
$$725$$ 2.00000 0.0742781
$$726$$ 0 0
$$727$$ −24.0000 −0.890111 −0.445055 0.895503i $$-0.646816\pi$$
−0.445055 + 0.895503i $$0.646816\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −6.00000 −0.222070
$$731$$ 8.00000 0.295891
$$732$$ 0 0
$$733$$ −30.0000 −1.10808 −0.554038 0.832492i $$-0.686914\pi$$
−0.554038 + 0.832492i $$0.686914\pi$$
$$734$$ 16.0000 0.590571
$$735$$ 0 0
$$736$$ 40.0000 1.47442
$$737$$ 16.0000 0.589368
$$738$$ 0 0
$$739$$ 4.00000 0.147142 0.0735712 0.997290i $$-0.476560\pi$$
0.0735712 + 0.997290i $$0.476560\pi$$
$$740$$ 6.00000 0.220564
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ −10.0000 −0.366372
$$746$$ −22.0000 −0.805477
$$747$$ 0 0
$$748$$ 8.00000 0.292509
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 8.00000 0.291730
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −42.0000 −1.52652 −0.763258 0.646094i $$-0.776401\pi$$
−0.763258 + 0.646094i $$0.776401\pi$$
$$758$$ 36.0000 1.30758
$$759$$ 0 0
$$760$$ 12.0000 0.435286
$$761$$ 10.0000 0.362500 0.181250 0.983437i $$-0.441986\pi$$
0.181250 + 0.983437i $$0.441986\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 16.0000 0.578860
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 30.0000 1.08183 0.540914 0.841078i $$-0.318079\pi$$
0.540914 + 0.841078i $$0.318079\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −14.0000 −0.503871
$$773$$ 6.00000 0.215805 0.107903 0.994161i $$-0.465587\pi$$
0.107903 + 0.994161i $$0.465587\pi$$
$$774$$ 0 0
$$775$$ 8.00000 0.287368
$$776$$ −54.0000 −1.93849
$$777$$ 0 0
$$778$$ 6.00000 0.215110
$$779$$ −24.0000 −0.859889
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −16.0000 −0.572159
$$783$$ 0 0
$$784$$ 7.00000 0.250000
$$785$$ −2.00000 −0.0713831
$$786$$ 0 0
$$787$$ 4.00000 0.142585 0.0712923 0.997455i $$-0.477288\pi$$
0.0712923 + 0.997455i $$0.477288\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 0 0
$$790$$ −16.0000 −0.569254
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 14.0000 0.496841
$$795$$ 0 0
$$796$$ 8.00000 0.283552
$$797$$ −46.0000 −1.62940 −0.814702 0.579880i $$-0.803099\pi$$
−0.814702 + 0.579880i $$0.803099\pi$$
$$798$$ 0 0
$$799$$ 16.0000 0.566039
$$800$$ −5.00000 −0.176777
$$801$$ 0 0
$$802$$ 30.0000 1.05934
$$803$$ 24.0000 0.846942
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −18.0000 −0.633238
$$809$$ −42.0000 −1.47664 −0.738321 0.674450i $$-0.764381\pi$$
−0.738321 + 0.674450i $$0.764381\pi$$
$$810$$ 0 0
$$811$$ −20.0000 −0.702295 −0.351147 0.936320i $$-0.614208\pi$$
−0.351147 + 0.936320i $$0.614208\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 24.0000 0.841200
$$815$$ 20.0000 0.700569
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ −38.0000 −1.32864
$$819$$ 0 0
$$820$$ 6.00000 0.209529
$$821$$ 22.0000 0.767805 0.383903 0.923374i $$-0.374580\pi$$
0.383903 + 0.923374i $$0.374580\pi$$
$$822$$ 0 0
$$823$$ −24.0000 −0.836587 −0.418294 0.908312i $$-0.637372\pi$$
−0.418294 + 0.908312i $$0.637372\pi$$
$$824$$ −24.0000 −0.836080
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −12.0000 −0.417281 −0.208640 0.977992i $$-0.566904\pi$$
−0.208640 + 0.977992i $$0.566904\pi$$
$$828$$ 0 0
$$829$$ −34.0000 −1.18087 −0.590434 0.807086i $$-0.701044\pi$$
−0.590434 + 0.807086i $$0.701044\pi$$
$$830$$ 4.00000 0.138842
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 14.0000 0.485071
$$834$$ 0 0
$$835$$ 16.0000 0.553703
$$836$$ −16.0000 −0.553372
$$837$$ 0 0
$$838$$ 20.0000 0.690889
$$839$$ 16.0000 0.552381 0.276191 0.961103i $$-0.410928\pi$$
0.276191 + 0.961103i $$0.410928\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ −10.0000 −0.344623
$$843$$ 0 0
$$844$$ −20.0000 −0.688428
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 6.00000 0.206041
$$849$$ 0 0
$$850$$ 2.00000 0.0685994
$$851$$ 48.0000 1.64542
$$852$$ 0 0
$$853$$ 42.0000 1.43805 0.719026 0.694983i $$-0.244588\pi$$
0.719026 + 0.694983i $$0.244588\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −36.0000 −1.23045
$$857$$ −10.0000 −0.341593 −0.170797 0.985306i $$-0.554634\pi$$
−0.170797 + 0.985306i $$0.554634\pi$$
$$858$$ 0 0
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 4.00000 0.136399
$$861$$ 0 0
$$862$$ −8.00000 −0.272481
$$863$$ −40.0000 −1.36162 −0.680808 0.732462i $$-0.738371\pi$$
−0.680808 + 0.732462i $$0.738371\pi$$
$$864$$ 0 0
$$865$$ 2.00000 0.0680020
$$866$$ −18.0000 −0.611665
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 64.0000 2.17105
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 6.00000 0.203186
$$873$$ 0 0
$$874$$ 32.0000 1.08242
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 50.0000 1.68838 0.844190 0.536044i $$-0.180082\pi$$
0.844190 + 0.536044i $$0.180082\pi$$
$$878$$ 24.0000 0.809961
$$879$$ 0 0
$$880$$ −4.00000 −0.134840
$$881$$ 14.0000 0.471672 0.235836 0.971793i $$-0.424217\pi$$
0.235836 + 0.971793i $$0.424217\pi$$
$$882$$ 0 0
$$883$$ 36.0000 1.21150 0.605748 0.795656i $$-0.292874\pi$$
0.605748 + 0.795656i $$0.292874\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −4.00000 −0.134383
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ −10.0000 −0.335201
$$891$$ 0 0
$$892$$ −24.0000 −0.803579
$$893$$ −32.0000 −1.07084
$$894$$ 0 0
$$895$$ 12.0000 0.401116
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −18.0000 −0.600668
$$899$$ 16.0000 0.533630
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ 24.0000 0.799113
$$903$$ 0 0
$$904$$ −6.00000 −0.199557
$$905$$ 22.0000 0.731305
$$906$$ 0 0
$$907$$ −4.00000 −0.132818 −0.0664089 0.997792i $$-0.521154\pi$$
−0.0664089 + 0.997792i $$0.521154\pi$$
$$908$$ −12.0000 −0.398234
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −32.0000 −1.06021 −0.530104 0.847933i $$-0.677847\pi$$
−0.530104 + 0.847933i $$0.677847\pi$$
$$912$$ 0 0
$$913$$ −16.0000 −0.529523
$$914$$ 26.0000 0.860004
$$915$$ 0 0
$$916$$ 22.0000 0.726900
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −40.0000 −1.31948 −0.659739 0.751495i $$-0.729333\pi$$
−0.659739 + 0.751495i $$0.729333\pi$$
$$920$$ −24.0000 −0.791257
$$921$$ 0 0
$$922$$ 18.0000 0.592798
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −6.00000 −0.197279
$$926$$ 8.00000 0.262896
$$927$$ 0 0
$$928$$ −10.0000 −0.328266
$$929$$ 18.0000 0.590561 0.295280 0.955411i $$-0.404587\pi$$
0.295280 + 0.955411i $$0.404587\pi$$
$$930$$ 0 0
$$931$$ −28.0000 −0.917663
$$932$$ 26.0000 0.851658
$$933$$ 0 0
$$934$$ 4.00000 0.130884
$$935$$ −8.00000 −0.261628
$$936$$ 0 0
$$937$$ −22.0000 −0.718709 −0.359354 0.933201i $$-0.617003\pi$$
−0.359354 + 0.933201i $$0.617003\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 8.00000 0.260931
$$941$$ 46.0000 1.49956 0.749779 0.661689i $$-0.230160\pi$$
0.749779 + 0.661689i $$0.230160\pi$$
$$942$$ 0 0
$$943$$ 48.0000 1.56310
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ 16.0000 0.520205
$$947$$ 12.0000 0.389948 0.194974 0.980808i $$-0.437538\pi$$
0.194974 + 0.980808i $$0.437538\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ −4.00000 −0.129777
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −10.0000 −0.323932 −0.161966 0.986796i $$-0.551783\pi$$
−0.161966 + 0.986796i $$0.551783\pi$$
$$954$$ 0 0
$$955$$ −16.0000 −0.517748
$$956$$ 24.0000 0.776215
$$957$$ 0 0
$$958$$ −8.00000 −0.258468
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −14.0000 −0.450910
$$965$$ 14.0000 0.450676
$$966$$ 0 0
$$967$$ 16.0000 0.514525 0.257263 0.966342i $$-0.417179\pi$$
0.257263 + 0.966342i $$0.417179\pi$$
$$968$$ 15.0000 0.482118
$$969$$ 0 0
$$970$$ 18.0000 0.577945
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 16.0000 0.512673
$$975$$ 0 0
$$976$$ 2.00000 0.0640184
$$977$$ −30.0000 −0.959785 −0.479893 0.877327i $$-0.659324\pi$$
−0.479893 + 0.877327i $$0.659324\pi$$
$$978$$ 0 0
$$979$$ 40.0000 1.27841
$$980$$ 7.00000 0.223607
$$981$$ 0 0
$$982$$ −20.0000 −0.638226
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 6.00000 0.191176
$$986$$ 4.00000 0.127386
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 32.0000 1.01754
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ −40.0000 −1.27000
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −8.00000 −0.253617
$$996$$ 0 0
$$997$$ 38.0000 1.20347 0.601736 0.798695i $$-0.294476\pi$$
0.601736 + 0.798695i $$0.294476\pi$$
$$998$$ 28.0000 0.886325
$$999$$ 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 7605.2.a.h.1.1 1
3.2 odd 2 2535.2.a.k.1.1 1
13.12 even 2 585.2.a.g.1.1 1
39.38 odd 2 195.2.a.a.1.1 1
52.51 odd 2 9360.2.a.o.1.1 1
65.12 odd 4 2925.2.c.f.2224.2 2
65.38 odd 4 2925.2.c.f.2224.1 2
65.64 even 2 2925.2.a.d.1.1 1
156.155 even 2 3120.2.a.k.1.1 1
195.38 even 4 975.2.c.e.274.2 2
195.77 even 4 975.2.c.e.274.1 2
195.194 odd 2 975.2.a.i.1.1 1
273.272 even 2 9555.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.a.1.1 1 39.38 odd 2
585.2.a.g.1.1 1 13.12 even 2
975.2.a.i.1.1 1 195.194 odd 2
975.2.c.e.274.1 2 195.77 even 4
975.2.c.e.274.2 2 195.38 even 4
2535.2.a.k.1.1 1 3.2 odd 2
2925.2.a.d.1.1 1 65.64 even 2
2925.2.c.f.2224.1 2 65.38 odd 4
2925.2.c.f.2224.2 2 65.12 odd 4
3120.2.a.k.1.1 1 156.155 even 2
7605.2.a.h.1.1 1 1.1 even 1 trivial
9360.2.a.o.1.1 1 52.51 odd 2
9555.2.a.b.1.1 1 273.272 even 2