# Properties

 Label 5808.2.a.bh.1.1 Level $5808$ Weight $2$ Character 5808.1 Self dual yes Analytic conductor $46.377$ 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] = [5808,2,Mod(1,5808)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5808, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5808.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$5808 = 2^{4} \cdot 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5808.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: $$46.3771134940$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 363) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 5808.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} +4.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} +4.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} -2.00000 q^{13} +4.00000 q^{15} +4.00000 q^{17} +3.00000 q^{19} -1.00000 q^{21} -2.00000 q^{23} +11.0000 q^{25} +1.00000 q^{27} +6.00000 q^{29} +5.00000 q^{31} -4.00000 q^{35} +3.00000 q^{37} -2.00000 q^{39} -2.00000 q^{41} -12.0000 q^{43} +4.00000 q^{45} -2.00000 q^{47} -6.00000 q^{49} +4.00000 q^{51} +6.00000 q^{53} +3.00000 q^{57} +10.0000 q^{59} +3.00000 q^{61} -1.00000 q^{63} -8.00000 q^{65} +1.00000 q^{67} -2.00000 q^{69} -11.0000 q^{73} +11.0000 q^{75} -11.0000 q^{79} +1.00000 q^{81} -6.00000 q^{83} +16.0000 q^{85} +6.00000 q^{87} +12.0000 q^{89} +2.00000 q^{91} +5.00000 q^{93} +12.0000 q^{95} +5.00000 q^{97} +O(q^{100})$$

## 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
$$3$$ 1.00000 0.577350
$$4$$ 0 0
$$5$$ 4.00000 1.78885 0.894427 0.447214i $$-0.147584\pi$$
0.894427 + 0.447214i $$0.147584\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 4.00000 1.03280
$$16$$ 0 0
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ 0 0
$$19$$ 3.00000 0.688247 0.344124 0.938924i $$-0.388176\pi$$
0.344124 + 0.938924i $$0.388176\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ −2.00000 −0.417029 −0.208514 0.978019i $$-0.566863\pi$$
−0.208514 + 0.978019i $$0.566863\pi$$
$$24$$ 0 0
$$25$$ 11.0000 2.20000
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 5.00000 0.898027 0.449013 0.893525i $$-0.351776\pi$$
0.449013 + 0.893525i $$0.351776\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −4.00000 −0.676123
$$36$$ 0 0
$$37$$ 3.00000 0.493197 0.246598 0.969118i $$-0.420687\pi$$
0.246598 + 0.969118i $$0.420687\pi$$
$$38$$ 0 0
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ −12.0000 −1.82998 −0.914991 0.403473i $$-0.867803\pi$$
−0.914991 + 0.403473i $$0.867803\pi$$
$$44$$ 0 0
$$45$$ 4.00000 0.596285
$$46$$ 0 0
$$47$$ −2.00000 −0.291730 −0.145865 0.989305i $$-0.546597\pi$$
−0.145865 + 0.989305i $$0.546597\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ 3.00000 0.384111 0.192055 0.981384i $$-0.438485\pi$$
0.192055 + 0.981384i $$0.438485\pi$$
$$62$$ 0 0
$$63$$ −1.00000 −0.125988
$$64$$ 0 0
$$65$$ −8.00000 −0.992278
$$66$$ 0 0
$$67$$ 1.00000 0.122169 0.0610847 0.998133i $$-0.480544\pi$$
0.0610847 + 0.998133i $$0.480544\pi$$
$$68$$ 0 0
$$69$$ −2.00000 −0.240772
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −11.0000 −1.28745 −0.643726 0.765256i $$-0.722612\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ 0 0
$$75$$ 11.0000 1.27017
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −11.0000 −1.23760 −0.618798 0.785550i $$-0.712380\pi$$
−0.618798 + 0.785550i $$0.712380\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ 0 0
$$85$$ 16.0000 1.73544
$$86$$ 0 0
$$87$$ 6.00000 0.643268
$$88$$ 0 0
$$89$$ 12.0000 1.27200 0.635999 0.771690i $$-0.280588\pi$$
0.635999 + 0.771690i $$0.280588\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 0 0
$$93$$ 5.00000 0.518476
$$94$$ 0 0
$$95$$ 12.0000 1.23117
$$96$$ 0 0
$$97$$ 5.00000 0.507673 0.253837 0.967247i $$-0.418307\pi$$
0.253837 + 0.967247i $$0.418307\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ 0 0
$$103$$ 7.00000 0.689730 0.344865 0.938652i $$-0.387925\pi$$
0.344865 + 0.938652i $$0.387925\pi$$
$$104$$ 0 0
$$105$$ −4.00000 −0.390360
$$106$$ 0 0
$$107$$ 18.0000 1.74013 0.870063 0.492941i $$-0.164078\pi$$
0.870063 + 0.492941i $$0.164078\pi$$
$$108$$ 0 0
$$109$$ 1.00000 0.0957826 0.0478913 0.998853i $$-0.484750\pi$$
0.0478913 + 0.998853i $$0.484750\pi$$
$$110$$ 0 0
$$111$$ 3.00000 0.284747
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ −8.00000 −0.746004
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ −2.00000 −0.180334
$$124$$ 0 0
$$125$$ 24.0000 2.14663
$$126$$ 0 0
$$127$$ 13.0000 1.15356 0.576782 0.816898i $$-0.304308\pi$$
0.576782 + 0.816898i $$0.304308\pi$$
$$128$$ 0 0
$$129$$ −12.0000 −1.05654
$$130$$ 0 0
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ −3.00000 −0.260133
$$134$$ 0 0
$$135$$ 4.00000 0.344265
$$136$$ 0 0
$$137$$ 8.00000 0.683486 0.341743 0.939793i $$-0.388983\pi$$
0.341743 + 0.939793i $$0.388983\pi$$
$$138$$ 0 0
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ −2.00000 −0.168430
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 24.0000 1.99309
$$146$$ 0 0
$$147$$ −6.00000 −0.494872
$$148$$ 0 0
$$149$$ −16.0000 −1.31077 −0.655386 0.755295i $$-0.727494\pi$$
−0.655386 + 0.755295i $$0.727494\pi$$
$$150$$ 0 0
$$151$$ 16.0000 1.30206 0.651031 0.759051i $$-0.274337\pi$$
0.651031 + 0.759051i $$0.274337\pi$$
$$152$$ 0 0
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 20.0000 1.60644
$$156$$ 0 0
$$157$$ −1.00000 −0.0798087 −0.0399043 0.999204i $$-0.512705\pi$$
−0.0399043 + 0.999204i $$0.512705\pi$$
$$158$$ 0 0
$$159$$ 6.00000 0.475831
$$160$$ 0 0
$$161$$ 2.00000 0.157622
$$162$$ 0 0
$$163$$ −25.0000 −1.95815 −0.979076 0.203497i $$-0.934769\pi$$
−0.979076 + 0.203497i $$0.934769\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 18.0000 1.39288 0.696441 0.717614i $$-0.254766\pi$$
0.696441 + 0.717614i $$0.254766\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 3.00000 0.229416
$$172$$ 0 0
$$173$$ 24.0000 1.82469 0.912343 0.409426i $$-0.134271\pi$$
0.912343 + 0.409426i $$0.134271\pi$$
$$174$$ 0 0
$$175$$ −11.0000 −0.831522
$$176$$ 0 0
$$177$$ 10.0000 0.751646
$$178$$ 0 0
$$179$$ −6.00000 −0.448461 −0.224231 0.974536i $$-0.571987\pi$$
−0.224231 + 0.974536i $$0.571987\pi$$
$$180$$ 0 0
$$181$$ −23.0000 −1.70958 −0.854788 0.518977i $$-0.826313\pi$$
−0.854788 + 0.518977i $$0.826313\pi$$
$$182$$ 0 0
$$183$$ 3.00000 0.221766
$$184$$ 0 0
$$185$$ 12.0000 0.882258
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −1.00000 −0.0727393
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 0 0
$$193$$ −5.00000 −0.359908 −0.179954 0.983675i $$-0.557595\pi$$
−0.179954 + 0.983675i $$0.557595\pi$$
$$194$$ 0 0
$$195$$ −8.00000 −0.572892
$$196$$ 0 0
$$197$$ −8.00000 −0.569976 −0.284988 0.958531i $$-0.591990\pi$$
−0.284988 + 0.958531i $$0.591990\pi$$
$$198$$ 0 0
$$199$$ 21.0000 1.48865 0.744325 0.667817i $$-0.232771\pi$$
0.744325 + 0.667817i $$0.232771\pi$$
$$200$$ 0 0
$$201$$ 1.00000 0.0705346
$$202$$ 0 0
$$203$$ −6.00000 −0.421117
$$204$$ 0 0
$$205$$ −8.00000 −0.558744
$$206$$ 0 0
$$207$$ −2.00000 −0.139010
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 21.0000 1.44570 0.722850 0.691005i $$-0.242832\pi$$
0.722850 + 0.691005i $$0.242832\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −48.0000 −3.27357
$$216$$ 0 0
$$217$$ −5.00000 −0.339422
$$218$$ 0 0
$$219$$ −11.0000 −0.743311
$$220$$ 0 0
$$221$$ −8.00000 −0.538138
$$222$$ 0 0
$$223$$ 17.0000 1.13840 0.569202 0.822198i $$-0.307252\pi$$
0.569202 + 0.822198i $$0.307252\pi$$
$$224$$ 0 0
$$225$$ 11.0000 0.733333
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ −18.0000 −1.18947 −0.594737 0.803921i $$-0.702744\pi$$
−0.594737 + 0.803921i $$0.702744\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ 0 0
$$235$$ −8.00000 −0.521862
$$236$$ 0 0
$$237$$ −11.0000 −0.714527
$$238$$ 0 0
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ 0 0
$$241$$ −14.0000 −0.901819 −0.450910 0.892570i $$-0.648900\pi$$
−0.450910 + 0.892570i $$0.648900\pi$$
$$242$$ 0 0
$$243$$ 1.00000 0.0641500
$$244$$ 0 0
$$245$$ −24.0000 −1.53330
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 0 0
$$249$$ −6.00000 −0.380235
$$250$$ 0 0
$$251$$ 2.00000 0.126239 0.0631194 0.998006i $$-0.479895\pi$$
0.0631194 + 0.998006i $$0.479895\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 16.0000 1.00196
$$256$$ 0 0
$$257$$ −14.0000 −0.873296 −0.436648 0.899632i $$-0.643834\pi$$
−0.436648 + 0.899632i $$0.643834\pi$$
$$258$$ 0 0
$$259$$ −3.00000 −0.186411
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 0 0
$$263$$ 10.0000 0.616626 0.308313 0.951285i $$-0.400236\pi$$
0.308313 + 0.951285i $$0.400236\pi$$
$$264$$ 0 0
$$265$$ 24.0000 1.47431
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ 0 0
$$269$$ −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 $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 0 0
$$273$$ 2.00000 0.121046
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −11.0000 −0.660926 −0.330463 0.943819i $$-0.607205\pi$$
−0.330463 + 0.943819i $$0.607205\pi$$
$$278$$ 0 0
$$279$$ 5.00000 0.299342
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ 11.0000 0.653882 0.326941 0.945045i $$-0.393982\pi$$
0.326941 + 0.945045i $$0.393982\pi$$
$$284$$ 0 0
$$285$$ 12.0000 0.710819
$$286$$ 0 0
$$287$$ 2.00000 0.118056
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 5.00000 0.293105
$$292$$ 0 0
$$293$$ 12.0000 0.701047 0.350524 0.936554i $$-0.386004\pi$$
0.350524 + 0.936554i $$0.386004\pi$$
$$294$$ 0 0
$$295$$ 40.0000 2.32889
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 4.00000 0.231326
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ 0 0
$$303$$ −10.0000 −0.574485
$$304$$ 0 0
$$305$$ 12.0000 0.687118
$$306$$ 0 0
$$307$$ 19.0000 1.08439 0.542194 0.840254i $$-0.317594\pi$$
0.542194 + 0.840254i $$0.317594\pi$$
$$308$$ 0 0
$$309$$ 7.00000 0.398216
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 0 0
$$315$$ −4.00000 −0.225374
$$316$$ 0 0
$$317$$ −20.0000 −1.12331 −0.561656 0.827371i $$-0.689836\pi$$
−0.561656 + 0.827371i $$0.689836\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 18.0000 1.00466
$$322$$ 0 0
$$323$$ 12.0000 0.667698
$$324$$ 0 0
$$325$$ −22.0000 −1.22034
$$326$$ 0 0
$$327$$ 1.00000 0.0553001
$$328$$ 0 0
$$329$$ 2.00000 0.110264
$$330$$ 0 0
$$331$$ 11.0000 0.604615 0.302307 0.953211i $$-0.402243\pi$$
0.302307 + 0.953211i $$0.402243\pi$$
$$332$$ 0 0
$$333$$ 3.00000 0.164399
$$334$$ 0 0
$$335$$ 4.00000 0.218543
$$336$$ 0 0
$$337$$ 5.00000 0.272367 0.136184 0.990684i $$-0.456516\pi$$
0.136184 + 0.990684i $$0.456516\pi$$
$$338$$ 0 0
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 0 0
$$345$$ −8.00000 −0.430706
$$346$$ 0 0
$$347$$ 2.00000 0.107366 0.0536828 0.998558i $$-0.482904\pi$$
0.0536828 + 0.998558i $$0.482904\pi$$
$$348$$ 0 0
$$349$$ 15.0000 0.802932 0.401466 0.915874i $$-0.368501\pi$$
0.401466 + 0.915874i $$0.368501\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ 0 0
$$353$$ −12.0000 −0.638696 −0.319348 0.947638i $$-0.603464\pi$$
−0.319348 + 0.947638i $$0.603464\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −4.00000 −0.211702
$$358$$ 0 0
$$359$$ −4.00000 −0.211112 −0.105556 0.994413i $$-0.533662\pi$$
−0.105556 + 0.994413i $$0.533662\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −44.0000 −2.30307
$$366$$ 0 0
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 0 0
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ −6.00000 −0.311504
$$372$$ 0 0
$$373$$ 7.00000 0.362446 0.181223 0.983442i $$-0.441994\pi$$
0.181223 + 0.983442i $$0.441994\pi$$
$$374$$ 0 0
$$375$$ 24.0000 1.23935
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ −16.0000 −0.821865 −0.410932 0.911666i $$-0.634797\pi$$
−0.410932 + 0.911666i $$0.634797\pi$$
$$380$$ 0 0
$$381$$ 13.0000 0.666010
$$382$$ 0 0
$$383$$ −26.0000 −1.32854 −0.664269 0.747494i $$-0.731257\pi$$
−0.664269 + 0.747494i $$0.731257\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −12.0000 −0.609994
$$388$$ 0 0
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ −8.00000 −0.404577
$$392$$ 0 0
$$393$$ 6.00000 0.302660
$$394$$ 0 0
$$395$$ −44.0000 −2.21388
$$396$$ 0 0
$$397$$ 31.0000 1.55585 0.777923 0.628360i $$-0.216273\pi$$
0.777923 + 0.628360i $$0.216273\pi$$
$$398$$ 0 0
$$399$$ −3.00000 −0.150188
$$400$$ 0 0
$$401$$ −28.0000 −1.39825 −0.699127 0.714998i $$-0.746428\pi$$
−0.699127 + 0.714998i $$0.746428\pi$$
$$402$$ 0 0
$$403$$ −10.0000 −0.498135
$$404$$ 0 0
$$405$$ 4.00000 0.198762
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 21.0000 1.03838 0.519192 0.854658i $$-0.326233\pi$$
0.519192 + 0.854658i $$0.326233\pi$$
$$410$$ 0 0
$$411$$ 8.00000 0.394611
$$412$$ 0 0
$$413$$ −10.0000 −0.492068
$$414$$ 0 0
$$415$$ −24.0000 −1.17811
$$416$$ 0 0
$$417$$ −16.0000 −0.783523
$$418$$ 0 0
$$419$$ −26.0000 −1.27018 −0.635092 0.772437i $$-0.719038\pi$$
−0.635092 + 0.772437i $$0.719038\pi$$
$$420$$ 0 0
$$421$$ −2.00000 −0.0974740 −0.0487370 0.998812i $$-0.515520\pi$$
−0.0487370 + 0.998812i $$0.515520\pi$$
$$422$$ 0 0
$$423$$ −2.00000 −0.0972433
$$424$$ 0 0
$$425$$ 44.0000 2.13431
$$426$$ 0 0
$$427$$ −3.00000 −0.145180
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −18.0000 −0.867029 −0.433515 0.901146i $$-0.642727\pi$$
−0.433515 + 0.901146i $$0.642727\pi$$
$$432$$ 0 0
$$433$$ −17.0000 −0.816968 −0.408484 0.912766i $$-0.633942\pi$$
−0.408484 + 0.912766i $$0.633942\pi$$
$$434$$ 0 0
$$435$$ 24.0000 1.15071
$$436$$ 0 0
$$437$$ −6.00000 −0.287019
$$438$$ 0 0
$$439$$ −37.0000 −1.76591 −0.882957 0.469454i $$-0.844451\pi$$
−0.882957 + 0.469454i $$0.844451\pi$$
$$440$$ 0 0
$$441$$ −6.00000 −0.285714
$$442$$ 0 0
$$443$$ −4.00000 −0.190046 −0.0950229 0.995475i $$-0.530292\pi$$
−0.0950229 + 0.995475i $$0.530292\pi$$
$$444$$ 0 0
$$445$$ 48.0000 2.27542
$$446$$ 0 0
$$447$$ −16.0000 −0.756774
$$448$$ 0 0
$$449$$ 20.0000 0.943858 0.471929 0.881636i $$-0.343558\pi$$
0.471929 + 0.881636i $$0.343558\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 16.0000 0.751746
$$454$$ 0 0
$$455$$ 8.00000 0.375046
$$456$$ 0 0
$$457$$ 18.0000 0.842004 0.421002 0.907060i $$-0.361678\pi$$
0.421002 + 0.907060i $$0.361678\pi$$
$$458$$ 0 0
$$459$$ 4.00000 0.186704
$$460$$ 0 0
$$461$$ −6.00000 −0.279448 −0.139724 0.990190i $$-0.544622\pi$$
−0.139724 + 0.990190i $$0.544622\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 20.0000 0.927478
$$466$$ 0 0
$$467$$ −24.0000 −1.11059 −0.555294 0.831654i $$-0.687394\pi$$
−0.555294 + 0.831654i $$0.687394\pi$$
$$468$$ 0 0
$$469$$ −1.00000 −0.0461757
$$470$$ 0 0
$$471$$ −1.00000 −0.0460776
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 33.0000 1.51414
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ 22.0000 1.00521 0.502603 0.864517i $$-0.332376\pi$$
0.502603 + 0.864517i $$0.332376\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 0 0
$$483$$ 2.00000 0.0910032
$$484$$ 0 0
$$485$$ 20.0000 0.908153
$$486$$ 0 0
$$487$$ 40.0000 1.81257 0.906287 0.422664i $$-0.138905\pi$$
0.906287 + 0.422664i $$0.138905\pi$$
$$488$$ 0 0
$$489$$ −25.0000 −1.13054
$$490$$ 0 0
$$491$$ 14.0000 0.631811 0.315906 0.948791i $$-0.397692\pi$$
0.315906 + 0.948791i $$0.397692\pi$$
$$492$$ 0 0
$$493$$ 24.0000 1.08091
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −23.0000 −1.02962 −0.514811 0.857304i $$-0.672138\pi$$
−0.514811 + 0.857304i $$0.672138\pi$$
$$500$$ 0 0
$$501$$ 18.0000 0.804181
$$502$$ 0 0
$$503$$ 32.0000 1.42681 0.713405 0.700752i $$-0.247152\pi$$
0.713405 + 0.700752i $$0.247152\pi$$
$$504$$ 0 0
$$505$$ −40.0000 −1.77998
$$506$$ 0 0
$$507$$ −9.00000 −0.399704
$$508$$ 0 0
$$509$$ 6.00000 0.265945 0.132973 0.991120i $$-0.457548\pi$$
0.132973 + 0.991120i $$0.457548\pi$$
$$510$$ 0 0
$$511$$ 11.0000 0.486611
$$512$$ 0 0
$$513$$ 3.00000 0.132453
$$514$$ 0 0
$$515$$ 28.0000 1.23383
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 24.0000 1.05348
$$520$$ 0 0
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 0 0
$$523$$ −29.0000 −1.26808 −0.634041 0.773300i $$-0.718605\pi$$
−0.634041 + 0.773300i $$0.718605\pi$$
$$524$$ 0 0
$$525$$ −11.0000 −0.480079
$$526$$ 0 0
$$527$$ 20.0000 0.871214
$$528$$ 0 0
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 10.0000 0.433963
$$532$$ 0 0
$$533$$ 4.00000 0.173259
$$534$$ 0 0
$$535$$ 72.0000 3.11283
$$536$$ 0 0
$$537$$ −6.00000 −0.258919
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 0 0
$$543$$ −23.0000 −0.987024
$$544$$ 0 0
$$545$$ 4.00000 0.171341
$$546$$ 0 0
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ 0 0
$$549$$ 3.00000 0.128037
$$550$$ 0 0
$$551$$ 18.0000 0.766826
$$552$$ 0 0
$$553$$ 11.0000 0.467768
$$554$$ 0 0
$$555$$ 12.0000 0.509372
$$556$$ 0 0
$$557$$ −8.00000 −0.338971 −0.169485 0.985533i $$-0.554211\pi$$
−0.169485 + 0.985533i $$0.554211\pi$$
$$558$$ 0 0
$$559$$ 24.0000 1.01509
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −28.0000 −1.18006 −0.590030 0.807382i $$-0.700884\pi$$
−0.590030 + 0.807382i $$0.700884\pi$$
$$564$$ 0 0
$$565$$ 24.0000 1.00969
$$566$$ 0 0
$$567$$ −1.00000 −0.0419961
$$568$$ 0 0
$$569$$ 12.0000 0.503066 0.251533 0.967849i $$-0.419065\pi$$
0.251533 + 0.967849i $$0.419065\pi$$
$$570$$ 0 0
$$571$$ 25.0000 1.04622 0.523109 0.852266i $$-0.324772\pi$$
0.523109 + 0.852266i $$0.324772\pi$$
$$572$$ 0 0
$$573$$ −8.00000 −0.334205
$$574$$ 0 0
$$575$$ −22.0000 −0.917463
$$576$$ 0 0
$$577$$ 15.0000 0.624458 0.312229 0.950007i $$-0.398924\pi$$
0.312229 + 0.950007i $$0.398924\pi$$
$$578$$ 0 0
$$579$$ −5.00000 −0.207793
$$580$$ 0 0
$$581$$ 6.00000 0.248922
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ −8.00000 −0.330759
$$586$$ 0 0
$$587$$ −4.00000 −0.165098 −0.0825488 0.996587i $$-0.526306\pi$$
−0.0825488 + 0.996587i $$0.526306\pi$$
$$588$$ 0 0
$$589$$ 15.0000 0.618064
$$590$$ 0 0
$$591$$ −8.00000 −0.329076
$$592$$ 0 0
$$593$$ −46.0000 −1.88899 −0.944497 0.328521i $$-0.893450\pi$$
−0.944497 + 0.328521i $$0.893450\pi$$
$$594$$ 0 0
$$595$$ −16.0000 −0.655936
$$596$$ 0 0
$$597$$ 21.0000 0.859473
$$598$$ 0 0
$$599$$ 8.00000 0.326871 0.163436 0.986554i $$-0.447742\pi$$
0.163436 + 0.986554i $$0.447742\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −0.0407909 −0.0203954 0.999792i $$-0.506493\pi$$
−0.0203954 + 0.999792i $$0.506493\pi$$
$$602$$ 0 0
$$603$$ 1.00000 0.0407231
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −8.00000 −0.324710 −0.162355 0.986732i $$-0.551909\pi$$
−0.162355 + 0.986732i $$0.551909\pi$$
$$608$$ 0 0
$$609$$ −6.00000 −0.243132
$$610$$ 0 0
$$611$$ 4.00000 0.161823
$$612$$ 0 0
$$613$$ −13.0000 −0.525065 −0.262533 0.964923i $$-0.584558\pi$$
−0.262533 + 0.964923i $$0.584558\pi$$
$$614$$ 0 0
$$615$$ −8.00000 −0.322591
$$616$$ 0 0
$$617$$ −24.0000 −0.966204 −0.483102 0.875564i $$-0.660490\pi$$
−0.483102 + 0.875564i $$0.660490\pi$$
$$618$$ 0 0
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ 0 0
$$621$$ −2.00000 −0.0802572
$$622$$ 0 0
$$623$$ −12.0000 −0.480770
$$624$$ 0 0
$$625$$ 41.0000 1.64000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ 32.0000 1.27390 0.636950 0.770905i $$-0.280196\pi$$
0.636950 + 0.770905i $$0.280196\pi$$
$$632$$ 0 0
$$633$$ 21.0000 0.834675
$$634$$ 0 0
$$635$$ 52.0000 2.06356
$$636$$ 0 0
$$637$$ 12.0000 0.475457
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −24.0000 −0.947943 −0.473972 0.880540i $$-0.657180\pi$$
−0.473972 + 0.880540i $$0.657180\pi$$
$$642$$ 0 0
$$643$$ 37.0000 1.45914 0.729569 0.683907i $$-0.239721\pi$$
0.729569 + 0.683907i $$0.239721\pi$$
$$644$$ 0 0
$$645$$ −48.0000 −1.89000
$$646$$ 0 0
$$647$$ 4.00000 0.157256 0.0786281 0.996904i $$-0.474946\pi$$
0.0786281 + 0.996904i $$0.474946\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −5.00000 −0.195965
$$652$$ 0 0
$$653$$ 10.0000 0.391330 0.195665 0.980671i $$-0.437313\pi$$
0.195665 + 0.980671i $$0.437313\pi$$
$$654$$ 0 0
$$655$$ 24.0000 0.937758
$$656$$ 0 0
$$657$$ −11.0000 −0.429151
$$658$$ 0 0
$$659$$ −46.0000 −1.79191 −0.895953 0.444149i $$-0.853506\pi$$
−0.895953 + 0.444149i $$0.853506\pi$$
$$660$$ 0 0
$$661$$ −5.00000 −0.194477 −0.0972387 0.995261i $$-0.531001\pi$$
−0.0972387 + 0.995261i $$0.531001\pi$$
$$662$$ 0 0
$$663$$ −8.00000 −0.310694
$$664$$ 0 0
$$665$$ −12.0000 −0.465340
$$666$$ 0 0
$$667$$ −12.0000 −0.464642
$$668$$ 0 0
$$669$$ 17.0000 0.657258
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −13.0000 −0.501113 −0.250557 0.968102i $$-0.580614\pi$$
−0.250557 + 0.968102i $$0.580614\pi$$
$$674$$ 0 0
$$675$$ 11.0000 0.423390
$$676$$ 0 0
$$677$$ 12.0000 0.461197 0.230599 0.973049i $$-0.425932\pi$$
0.230599 + 0.973049i $$0.425932\pi$$
$$678$$ 0 0
$$679$$ −5.00000 −0.191882
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 34.0000 1.30097 0.650487 0.759517i $$-0.274565\pi$$
0.650487 + 0.759517i $$0.274565\pi$$
$$684$$ 0 0
$$685$$ 32.0000 1.22266
$$686$$ 0 0
$$687$$ −18.0000 −0.686743
$$688$$ 0 0
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ −11.0000 −0.418460 −0.209230 0.977866i $$-0.567096\pi$$
−0.209230 + 0.977866i $$0.567096\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −64.0000 −2.42766
$$696$$ 0 0
$$697$$ −8.00000 −0.303022
$$698$$ 0 0
$$699$$ 18.0000 0.680823
$$700$$ 0 0
$$701$$ 50.0000 1.88847 0.944237 0.329267i $$-0.106802\pi$$
0.944237 + 0.329267i $$0.106802\pi$$
$$702$$ 0 0
$$703$$ 9.00000 0.339441
$$704$$ 0 0
$$705$$ −8.00000 −0.301297
$$706$$ 0 0
$$707$$ 10.0000 0.376089
$$708$$ 0 0
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 0 0
$$711$$ −11.0000 −0.412532
$$712$$ 0 0
$$713$$ −10.0000 −0.374503
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −6.00000 −0.224074
$$718$$ 0 0
$$719$$ 6.00000 0.223762 0.111881 0.993722i $$-0.464312\pi$$
0.111881 + 0.993722i $$0.464312\pi$$
$$720$$ 0 0
$$721$$ −7.00000 −0.260694
$$722$$ 0 0
$$723$$ −14.0000 −0.520666
$$724$$ 0 0
$$725$$ 66.0000 2.45118
$$726$$ 0 0
$$727$$ 12.0000 0.445055 0.222528 0.974926i $$-0.428569\pi$$
0.222528 + 0.974926i $$0.428569\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −48.0000 −1.77534
$$732$$ 0 0
$$733$$ −30.0000 −1.10808 −0.554038 0.832492i $$-0.686914\pi$$
−0.554038 + 0.832492i $$0.686914\pi$$
$$734$$ 0 0
$$735$$ −24.0000 −0.885253
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −41.0000 −1.50821 −0.754105 0.656754i $$-0.771929\pi$$
−0.754105 + 0.656754i $$0.771929\pi$$
$$740$$ 0 0
$$741$$ −6.00000 −0.220416
$$742$$ 0 0
$$743$$ 20.0000 0.733729 0.366864 0.930274i $$-0.380431\pi$$
0.366864 + 0.930274i $$0.380431\pi$$
$$744$$ 0 0
$$745$$ −64.0000 −2.34478
$$746$$ 0 0
$$747$$ −6.00000 −0.219529
$$748$$ 0 0
$$749$$ −18.0000 −0.657706
$$750$$ 0 0
$$751$$ −19.0000 −0.693320 −0.346660 0.937991i $$-0.612684\pi$$
−0.346660 + 0.937991i $$0.612684\pi$$
$$752$$ 0 0
$$753$$ 2.00000 0.0728841
$$754$$ 0 0
$$755$$ 64.0000 2.32920
$$756$$ 0 0
$$757$$ 5.00000 0.181728 0.0908640 0.995863i $$-0.471037\pi$$
0.0908640 + 0.995863i $$0.471037\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −24.0000 −0.869999 −0.435000 0.900431i $$-0.643252\pi$$
−0.435000 + 0.900431i $$0.643252\pi$$
$$762$$ 0 0
$$763$$ −1.00000 −0.0362024
$$764$$ 0 0
$$765$$ 16.0000 0.578481
$$766$$ 0 0
$$767$$ −20.0000 −0.722158
$$768$$ 0 0
$$769$$ 11.0000 0.396670 0.198335 0.980134i $$-0.436447\pi$$
0.198335 + 0.980134i $$0.436447\pi$$
$$770$$ 0 0
$$771$$ −14.0000 −0.504198
$$772$$ 0 0
$$773$$ 36.0000 1.29483 0.647415 0.762138i $$-0.275850\pi$$
0.647415 + 0.762138i $$0.275850\pi$$
$$774$$ 0 0
$$775$$ 55.0000 1.97566
$$776$$ 0 0
$$777$$ −3.00000 −0.107624
$$778$$ 0 0
$$779$$ −6.00000 −0.214972
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 6.00000 0.214423
$$784$$ 0 0
$$785$$ −4.00000 −0.142766
$$786$$ 0 0
$$787$$ −4.00000 −0.142585 −0.0712923 0.997455i $$-0.522712\pi$$
−0.0712923 + 0.997455i $$0.522712\pi$$
$$788$$ 0 0
$$789$$ 10.0000 0.356009
$$790$$ 0 0
$$791$$ −6.00000 −0.213335
$$792$$ 0 0
$$793$$ −6.00000 −0.213066
$$794$$ 0 0
$$795$$ 24.0000 0.851192
$$796$$ 0 0
$$797$$ −10.0000 −0.354218 −0.177109 0.984191i $$-0.556675\pi$$
−0.177109 + 0.984191i $$0.556675\pi$$
$$798$$ 0 0
$$799$$ −8.00000 −0.283020
$$800$$ 0 0
$$801$$ 12.0000 0.423999
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 8.00000 0.281963
$$806$$ 0 0
$$807$$ −14.0000 −0.492823
$$808$$ 0 0
$$809$$ −48.0000 −1.68759 −0.843795 0.536666i $$-0.819684\pi$$
−0.843795 + 0.536666i $$0.819684\pi$$
$$810$$ 0 0
$$811$$ 17.0000 0.596951 0.298475 0.954417i $$-0.403522\pi$$
0.298475 + 0.954417i $$0.403522\pi$$
$$812$$ 0 0
$$813$$ −8.00000 −0.280572
$$814$$ 0 0
$$815$$ −100.000 −3.50285
$$816$$ 0 0
$$817$$ −36.0000 −1.25948
$$818$$ 0 0
$$819$$ 2.00000 0.0698857
$$820$$ 0 0
$$821$$ −38.0000 −1.32621 −0.663105 0.748527i $$-0.730762\pi$$
−0.663105 + 0.748527i $$0.730762\pi$$
$$822$$ 0 0
$$823$$ 27.0000 0.941161 0.470580 0.882357i $$-0.344045\pi$$
0.470580 + 0.882357i $$0.344045\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 10.0000 0.347734 0.173867 0.984769i $$-0.444374\pi$$
0.173867 + 0.984769i $$0.444374\pi$$
$$828$$ 0 0
$$829$$ −11.0000 −0.382046 −0.191023 0.981586i $$-0.561180\pi$$
−0.191023 + 0.981586i $$0.561180\pi$$
$$830$$ 0 0
$$831$$ −11.0000 −0.381586
$$832$$ 0 0
$$833$$ −24.0000 −0.831551
$$834$$ 0 0
$$835$$ 72.0000 2.49166
$$836$$ 0 0
$$837$$ 5.00000 0.172825
$$838$$ 0 0
$$839$$ −16.0000 −0.552381 −0.276191 0.961103i $$-0.589072\pi$$
−0.276191 + 0.961103i $$0.589072\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ −12.0000 −0.413302
$$844$$ 0 0
$$845$$ −36.0000 −1.23844
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 11.0000 0.377519
$$850$$ 0 0
$$851$$ −6.00000 −0.205677
$$852$$ 0 0
$$853$$ 11.0000 0.376633 0.188316 0.982108i $$-0.439697\pi$$
0.188316 + 0.982108i $$0.439697\pi$$
$$854$$ 0 0
$$855$$ 12.0000 0.410391
$$856$$ 0 0
$$857$$ −4.00000 −0.136637 −0.0683187 0.997664i $$-0.521763\pi$$
−0.0683187 + 0.997664i $$0.521763\pi$$
$$858$$ 0 0
$$859$$ 45.0000 1.53538 0.767690 0.640821i $$-0.221406\pi$$
0.767690 + 0.640821i $$0.221406\pi$$
$$860$$ 0 0
$$861$$ 2.00000 0.0681598
$$862$$ 0 0
$$863$$ −30.0000 −1.02121 −0.510606 0.859815i $$-0.670579\pi$$
−0.510606 + 0.859815i $$0.670579\pi$$
$$864$$ 0 0
$$865$$ 96.0000 3.26410
$$866$$ 0 0
$$867$$ −1.00000 −0.0339618
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −2.00000 −0.0677674
$$872$$ 0 0
$$873$$ 5.00000 0.169224
$$874$$ 0 0
$$875$$ −24.0000 −0.811348
$$876$$ 0 0
$$877$$ −45.0000 −1.51954 −0.759771 0.650191i $$-0.774689\pi$$
−0.759771 + 0.650191i $$0.774689\pi$$
$$878$$ 0 0
$$879$$ 12.0000 0.404750
$$880$$ 0 0
$$881$$ 2.00000 0.0673817 0.0336909 0.999432i $$-0.489274\pi$$
0.0336909 + 0.999432i $$0.489274\pi$$
$$882$$ 0 0
$$883$$ −49.0000 −1.64898 −0.824491 0.565876i $$-0.808538\pi$$
−0.824491 + 0.565876i $$0.808538\pi$$
$$884$$ 0 0
$$885$$ 40.0000 1.34459
$$886$$ 0 0
$$887$$ 22.0000 0.738688 0.369344 0.929293i $$-0.379582\pi$$
0.369344 + 0.929293i $$0.379582\pi$$
$$888$$ 0 0
$$889$$ −13.0000 −0.436006
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −6.00000 −0.200782
$$894$$ 0 0
$$895$$ −24.0000 −0.802232
$$896$$ 0 0
$$897$$ 4.00000 0.133556
$$898$$ 0 0
$$899$$ 30.0000 1.00056
$$900$$ 0 0
$$901$$ 24.0000 0.799556
$$902$$ 0 0
$$903$$ 12.0000 0.399335
$$904$$ 0 0
$$905$$ −92.0000 −3.05818
$$906$$ 0 0
$$907$$ −33.0000 −1.09575 −0.547874 0.836561i $$-0.684562\pi$$
−0.547874 + 0.836561i $$0.684562\pi$$
$$908$$ 0 0
$$909$$ −10.0000 −0.331679
$$910$$ 0 0
$$911$$ −36.0000 −1.19273 −0.596367 0.802712i $$-0.703390\pi$$
−0.596367 + 0.802712i $$0.703390\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 12.0000 0.396708
$$916$$ 0 0
$$917$$ −6.00000 −0.198137
$$918$$ 0 0
$$919$$ 5.00000 0.164935 0.0824674 0.996594i $$-0.473720\pi$$
0.0824674 + 0.996594i $$0.473720\pi$$
$$920$$ 0 0
$$921$$ 19.0000 0.626071
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 33.0000 1.08503
$$926$$ 0 0
$$927$$ 7.00000 0.229910
$$928$$ 0 0
$$929$$ −18.0000 −0.590561 −0.295280 0.955411i $$-0.595413\pi$$
−0.295280 + 0.955411i $$0.595413\pi$$
$$930$$ 0 0
$$931$$ −18.0000 −0.589926
$$932$$ 0 0
$$933$$ −24.0000 −0.785725
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 23.0000 0.751377 0.375689 0.926746i $$-0.377406\pi$$
0.375689 + 0.926746i $$0.377406\pi$$
$$938$$ 0 0
$$939$$ −10.0000 −0.326338
$$940$$ 0 0
$$941$$ 42.0000 1.36916 0.684580 0.728937i $$-0.259985\pi$$
0.684580 + 0.728937i $$0.259985\pi$$
$$942$$ 0 0
$$943$$ 4.00000 0.130258
$$944$$ 0 0
$$945$$ −4.00000 −0.130120
$$946$$ 0 0
$$947$$ −54.0000 −1.75476 −0.877382 0.479792i $$-0.840712\pi$$
−0.877382 + 0.479792i $$0.840712\pi$$
$$948$$ 0 0
$$949$$ 22.0000 0.714150
$$950$$ 0 0
$$951$$ −20.0000 −0.648544
$$952$$ 0 0
$$953$$ 34.0000 1.10137 0.550684 0.834714i $$-0.314367\pi$$
0.550684 + 0.834714i $$0.314367\pi$$
$$954$$ 0 0
$$955$$ −32.0000 −1.03550
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −8.00000 −0.258333
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ 0 0
$$963$$ 18.0000 0.580042
$$964$$ 0 0
$$965$$ −20.0000 −0.643823
$$966$$ 0 0
$$967$$ −13.0000 −0.418052 −0.209026 0.977910i $$-0.567029\pi$$
−0.209026 + 0.977910i $$0.567029\pi$$
$$968$$ 0 0
$$969$$ 12.0000 0.385496
$$970$$ 0 0
$$971$$ −2.00000 −0.0641831 −0.0320915 0.999485i $$-0.510217\pi$$
−0.0320915 + 0.999485i $$0.510217\pi$$
$$972$$ 0 0
$$973$$ 16.0000 0.512936
$$974$$ 0 0
$$975$$ −22.0000 −0.704564
$$976$$ 0 0
$$977$$ −42.0000 −1.34370 −0.671850 0.740688i $$-0.734500\pi$$
−0.671850 + 0.740688i $$0.734500\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 1.00000 0.0319275
$$982$$ 0 0
$$983$$ −6.00000 −0.191370 −0.0956851 0.995412i $$-0.530504\pi$$
−0.0956851 + 0.995412i $$0.530504\pi$$
$$984$$ 0 0
$$985$$ −32.0000 −1.01960
$$986$$ 0 0
$$987$$ 2.00000 0.0636607
$$988$$ 0 0
$$989$$ 24.0000 0.763156
$$990$$ 0 0
$$991$$ −4.00000 −0.127064 −0.0635321 0.997980i $$-0.520237\pi$$
−0.0635321 + 0.997980i $$0.520237\pi$$
$$992$$ 0 0
$$993$$ 11.0000 0.349074
$$994$$ 0 0
$$995$$ 84.0000 2.66298
$$996$$ 0 0
$$997$$ −49.0000 −1.55185 −0.775923 0.630828i $$-0.782715\pi$$
−0.775923 + 0.630828i $$0.782715\pi$$
$$998$$ 0 0
$$999$$ 3.00000 0.0949158
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 5808.2.a.bh.1.1 1
4.3 odd 2 363.2.a.a.1.1 1
11.10 odd 2 5808.2.a.bi.1.1 1
12.11 even 2 1089.2.a.k.1.1 1
20.19 odd 2 9075.2.a.t.1.1 1
44.3 odd 10 363.2.e.i.130.1 4
44.7 even 10 363.2.e.d.148.1 4
44.15 odd 10 363.2.e.i.148.1 4
44.19 even 10 363.2.e.d.130.1 4
44.27 odd 10 363.2.e.i.124.1 4
44.31 odd 10 363.2.e.i.202.1 4
44.35 even 10 363.2.e.d.202.1 4
44.39 even 10 363.2.e.d.124.1 4
44.43 even 2 363.2.a.c.1.1 yes 1
132.131 odd 2 1089.2.a.a.1.1 1
220.219 even 2 9075.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.a.a.1.1 1 4.3 odd 2
363.2.a.c.1.1 yes 1 44.43 even 2
363.2.e.d.124.1 4 44.39 even 10
363.2.e.d.130.1 4 44.19 even 10
363.2.e.d.148.1 4 44.7 even 10
363.2.e.d.202.1 4 44.35 even 10
363.2.e.i.124.1 4 44.27 odd 10
363.2.e.i.130.1 4 44.3 odd 10
363.2.e.i.148.1 4 44.15 odd 10
363.2.e.i.202.1 4 44.31 odd 10
1089.2.a.a.1.1 1 132.131 odd 2
1089.2.a.k.1.1 1 12.11 even 2
5808.2.a.bh.1.1 1 1.1 even 1 trivial
5808.2.a.bi.1.1 1 11.10 odd 2
9075.2.a.b.1.1 1 220.219 even 2
9075.2.a.t.1.1 1 20.19 odd 2