# Properties

 Label 2925.2.a.t.1.1 Level $2925$ Weight $2$ Character 2925.1 Self dual yes Analytic conductor $23.356$ 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] = [2925,2,Mod(1,2925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2925, 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("2925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2925 = 3^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2925.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: $$23.3562425912$$ Analytic rank: $$0$$ 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 $$\chi$$ $$=$$ 2925.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.00000 q^{2} +2.00000 q^{4} +3.00000 q^{7} +O(q^{10})$$ $$q+2.00000 q^{2} +2.00000 q^{4} +3.00000 q^{7} +5.00000 q^{11} -1.00000 q^{13} +6.00000 q^{14} -4.00000 q^{16} +5.00000 q^{17} +2.00000 q^{19} +10.0000 q^{22} -1.00000 q^{23} -2.00000 q^{26} +6.00000 q^{28} -10.0000 q^{29} -2.00000 q^{31} -8.00000 q^{32} +10.0000 q^{34} +3.00000 q^{37} +4.00000 q^{38} +9.00000 q^{41} +4.00000 q^{43} +10.0000 q^{44} -2.00000 q^{46} +10.0000 q^{47} +2.00000 q^{49} -2.00000 q^{52} +9.00000 q^{53} -20.0000 q^{58} -11.0000 q^{61} -4.00000 q^{62} -8.00000 q^{64} +4.00000 q^{67} +10.0000 q^{68} -15.0000 q^{71} -6.00000 q^{73} +6.00000 q^{74} +4.00000 q^{76} +15.0000 q^{77} -11.0000 q^{79} +18.0000 q^{82} +8.00000 q^{83} +8.00000 q^{86} +11.0000 q^{89} -3.00000 q^{91} -2.00000 q^{92} +20.0000 q^{94} +9.00000 q^{97} +4.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$3$$ 0 0
$$4$$ 2.00000 1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 6.00000 1.60357
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ 5.00000 1.21268 0.606339 0.795206i $$-0.292637\pi$$
0.606339 + 0.795206i $$0.292637\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 10.0000 2.13201
$$23$$ −1.00000 −0.208514 −0.104257 0.994550i $$-0.533247\pi$$
−0.104257 + 0.994550i $$0.533247\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −2.00000 −0.392232
$$27$$ 0 0
$$28$$ 6.00000 1.13389
$$29$$ −10.0000 −1.85695 −0.928477 0.371391i $$-0.878881\pi$$
−0.928477 + 0.371391i $$0.878881\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ −8.00000 −1.41421
$$33$$ 0 0
$$34$$ 10.0000 1.71499
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 3.00000 0.493197 0.246598 0.969118i $$-0.420687\pi$$
0.246598 + 0.969118i $$0.420687\pi$$
$$38$$ 4.00000 0.648886
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 9.00000 1.40556 0.702782 0.711405i $$-0.251941\pi$$
0.702782 + 0.711405i $$0.251941\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 10.0000 1.50756
$$45$$ 0 0
$$46$$ −2.00000 −0.294884
$$47$$ 10.0000 1.45865 0.729325 0.684167i $$-0.239834\pi$$
0.729325 + 0.684167i $$0.239834\pi$$
$$48$$ 0 0
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −2.00000 −0.277350
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −20.0000 −2.62613
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −11.0000 −1.40841 −0.704203 0.709999i $$-0.748695\pi$$
−0.704203 + 0.709999i $$0.748695\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 10.0000 1.21268
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −15.0000 −1.78017 −0.890086 0.455792i $$-0.849356\pi$$
−0.890086 + 0.455792i $$0.849356\pi$$
$$72$$ 0 0
$$73$$ −6.00000 −0.702247 −0.351123 0.936329i $$-0.614200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 0 0
$$76$$ 4.00000 0.458831
$$77$$ 15.0000 1.70941
$$78$$ 0 0
$$79$$ −11.0000 −1.23760 −0.618798 0.785550i $$-0.712380\pi$$
−0.618798 + 0.785550i $$0.712380\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 18.0000 1.98777
$$83$$ 8.00000 0.878114 0.439057 0.898459i $$-0.355313\pi$$
0.439057 + 0.898459i $$0.355313\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 8.00000 0.862662
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 11.0000 1.16600 0.582999 0.812473i $$-0.301879\pi$$
0.582999 + 0.812473i $$0.301879\pi$$
$$90$$ 0 0
$$91$$ −3.00000 −0.314485
$$92$$ −2.00000 −0.208514
$$93$$ 0 0
$$94$$ 20.0000 2.06284
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 9.00000 0.913812 0.456906 0.889515i $$-0.348958\pi$$
0.456906 + 0.889515i $$0.348958\pi$$
$$98$$ 4.00000 0.404061
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 0 0
$$103$$ −4.00000 −0.394132 −0.197066 0.980390i $$-0.563141\pi$$
−0.197066 + 0.980390i $$0.563141\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 18.0000 1.74831
$$107$$ 3.00000 0.290021 0.145010 0.989430i $$-0.453678\pi$$
0.145010 + 0.989430i $$0.453678\pi$$
$$108$$ 0 0
$$109$$ 16.0000 1.53252 0.766261 0.642529i $$-0.222115\pi$$
0.766261 + 0.642529i $$0.222115\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −12.0000 −1.13389
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −20.0000 −1.85695
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 15.0000 1.37505
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ −22.0000 −1.99179
$$123$$ 0 0
$$124$$ −4.00000 −0.359211
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −14.0000 −1.24230 −0.621150 0.783692i $$-0.713334\pi$$
−0.621150 + 0.783692i $$0.713334\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −6.00000 −0.524222 −0.262111 0.965038i $$-0.584419\pi$$
−0.262111 + 0.965038i $$0.584419\pi$$
$$132$$ 0 0
$$133$$ 6.00000 0.520266
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 0 0
$$139$$ −17.0000 −1.44192 −0.720961 0.692976i $$-0.756299\pi$$
−0.720961 + 0.692976i $$0.756299\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −30.0000 −2.51754
$$143$$ −5.00000 −0.418121
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −12.0000 −0.993127
$$147$$ 0 0
$$148$$ 6.00000 0.493197
$$149$$ 7.00000 0.573462 0.286731 0.958011i $$-0.407431\pi$$
0.286731 + 0.958011i $$0.407431\pi$$
$$150$$ 0 0
$$151$$ −12.0000 −0.976546 −0.488273 0.872691i $$-0.662373\pi$$
−0.488273 + 0.872691i $$0.662373\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 30.0000 2.41747
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ −22.0000 −1.75023
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −3.00000 −0.236433
$$162$$ 0 0
$$163$$ 11.0000 0.861586 0.430793 0.902451i $$-0.358234\pi$$
0.430793 + 0.902451i $$0.358234\pi$$
$$164$$ 18.0000 1.40556
$$165$$ 0 0
$$166$$ 16.0000 1.24184
$$167$$ −8.00000 −0.619059 −0.309529 0.950890i $$-0.600171\pi$$
−0.309529 + 0.950890i $$0.600171\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ −2.00000 −0.152057 −0.0760286 0.997106i $$-0.524224\pi$$
−0.0760286 + 0.997106i $$0.524224\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −20.0000 −1.50756
$$177$$ 0 0
$$178$$ 22.0000 1.64897
$$179$$ 6.00000 0.448461 0.224231 0.974536i $$-0.428013\pi$$
0.224231 + 0.974536i $$0.428013\pi$$
$$180$$ 0 0
$$181$$ −23.0000 −1.70958 −0.854788 0.518977i $$-0.826313\pi$$
−0.854788 + 0.518977i $$0.826313\pi$$
$$182$$ −6.00000 −0.444750
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 25.0000 1.82818
$$188$$ 20.0000 1.45865
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 20.0000 1.44715 0.723575 0.690246i $$-0.242498\pi$$
0.723575 + 0.690246i $$0.242498\pi$$
$$192$$ 0 0
$$193$$ −13.0000 −0.935760 −0.467880 0.883792i $$-0.654982\pi$$
−0.467880 + 0.883792i $$0.654982\pi$$
$$194$$ 18.0000 1.29232
$$195$$ 0 0
$$196$$ 4.00000 0.285714
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ 4.00000 0.283552 0.141776 0.989899i $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 24.0000 1.68863
$$203$$ −30.0000 −2.10559
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −8.00000 −0.557386
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ 10.0000 0.691714
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 18.0000 1.23625
$$213$$ 0 0
$$214$$ 6.00000 0.410152
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −6.00000 −0.407307
$$218$$ 32.0000 2.16731
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −5.00000 −0.336336
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ −24.0000 −1.60357
$$225$$ 0 0
$$226$$ 4.00000 0.266076
$$227$$ −18.0000 −1.19470 −0.597351 0.801980i $$-0.703780\pi$$
−0.597351 + 0.801980i $$0.703780\pi$$
$$228$$ 0 0
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −25.0000 −1.63780 −0.818902 0.573933i $$-0.805417\pi$$
−0.818902 + 0.573933i $$0.805417\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 30.0000 1.94461
$$239$$ −15.0000 −0.970269 −0.485135 0.874439i $$-0.661229\pi$$
−0.485135 + 0.874439i $$0.661229\pi$$
$$240$$ 0 0
$$241$$ −14.0000 −0.901819 −0.450910 0.892570i $$-0.648900\pi$$
−0.450910 + 0.892570i $$0.648900\pi$$
$$242$$ 28.0000 1.79991
$$243$$ 0 0
$$244$$ −22.0000 −1.40841
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −2.00000 −0.127257
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −20.0000 −1.26239 −0.631194 0.775625i $$-0.717435\pi$$
−0.631194 + 0.775625i $$0.717435\pi$$
$$252$$ 0 0
$$253$$ −5.00000 −0.314347
$$254$$ −28.0000 −1.75688
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 9.00000 0.559233
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −12.0000 −0.741362
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 12.0000 0.735767
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ −32.0000 −1.95107 −0.975537 0.219834i $$-0.929448\pi$$
−0.975537 + 0.219834i $$0.929448\pi$$
$$270$$ 0 0
$$271$$ −2.00000 −0.121491 −0.0607457 0.998153i $$-0.519348\pi$$
−0.0607457 + 0.998153i $$0.519348\pi$$
$$272$$ −20.0000 −1.21268
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −26.0000 −1.56219 −0.781094 0.624413i $$-0.785338\pi$$
−0.781094 + 0.624413i $$0.785338\pi$$
$$278$$ −34.0000 −2.03918
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ 8.00000 0.475551 0.237775 0.971320i $$-0.423582\pi$$
0.237775 + 0.971320i $$0.423582\pi$$
$$284$$ −30.0000 −1.78017
$$285$$ 0 0
$$286$$ −10.0000 −0.591312
$$287$$ 27.0000 1.59376
$$288$$ 0 0
$$289$$ 8.00000 0.470588
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −12.0000 −0.702247
$$293$$ 24.0000 1.40209 0.701047 0.713115i $$-0.252716\pi$$
0.701047 + 0.713115i $$0.252716\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 14.0000 0.810998
$$299$$ 1.00000 0.0578315
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ −24.0000 −1.38104
$$303$$ 0 0
$$304$$ −8.00000 −0.458831
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 19.0000 1.08439 0.542194 0.840254i $$-0.317594\pi$$
0.542194 + 0.840254i $$0.317594\pi$$
$$308$$ 30.0000 1.70941
$$309$$ 0 0
$$310$$ 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 $$-0.408798\pi$$
0.282617 + 0.959233i $$0.408798\pi$$
$$314$$ −44.0000 −2.48306
$$315$$ 0 0
$$316$$ −22.0000 −1.23760
$$317$$ 12.0000 0.673987 0.336994 0.941507i $$-0.390590\pi$$
0.336994 + 0.941507i $$0.390590\pi$$
$$318$$ 0 0
$$319$$ −50.0000 −2.79946
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −6.00000 −0.334367
$$323$$ 10.0000 0.556415
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 22.0000 1.21847
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 30.0000 1.65395
$$330$$ 0 0
$$331$$ 32.0000 1.75888 0.879440 0.476011i $$-0.157918\pi$$
0.879440 + 0.476011i $$0.157918\pi$$
$$332$$ 16.0000 0.878114
$$333$$ 0 0
$$334$$ −16.0000 −0.875481
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −4.00000 −0.217894 −0.108947 0.994048i $$-0.534748\pi$$
−0.108947 + 0.994048i $$0.534748\pi$$
$$338$$ 2.00000 0.108786
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −10.0000 −0.541530
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −4.00000 −0.215041
$$347$$ −1.00000 −0.0536828 −0.0268414 0.999640i $$-0.508545\pi$$
−0.0268414 + 0.999640i $$0.508545\pi$$
$$348$$ 0 0
$$349$$ 20.0000 1.07058 0.535288 0.844670i $$-0.320203\pi$$
0.535288 + 0.844670i $$0.320203\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −40.0000 −2.13201
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 22.0000 1.16600
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ −16.0000 −0.844448 −0.422224 0.906492i $$-0.638750\pi$$
−0.422224 + 0.906492i $$0.638750\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ −46.0000 −2.41771
$$363$$ 0 0
$$364$$ −6.00000 −0.314485
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 27.0000 1.40177
$$372$$ 0 0
$$373$$ −16.0000 −0.828449 −0.414224 0.910175i $$-0.635947\pi$$
−0.414224 + 0.910175i $$0.635947\pi$$
$$374$$ 50.0000 2.58544
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 10.0000 0.515026
$$378$$ 0 0
$$379$$ 6.00000 0.308199 0.154100 0.988055i $$-0.450752\pi$$
0.154100 + 0.988055i $$0.450752\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 40.0000 2.04658
$$383$$ −18.0000 −0.919757 −0.459879 0.887982i $$-0.652107\pi$$
−0.459879 + 0.887982i $$0.652107\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −26.0000 −1.32337
$$387$$ 0 0
$$388$$ 18.0000 0.913812
$$389$$ 24.0000 1.21685 0.608424 0.793612i $$-0.291802\pi$$
0.608424 + 0.793612i $$0.291802\pi$$
$$390$$ 0 0
$$391$$ −5.00000 −0.252861
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −24.0000 −1.20910
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 19.0000 0.953583 0.476791 0.879017i $$-0.341800\pi$$
0.476791 + 0.879017i $$0.341800\pi$$
$$398$$ 8.00000 0.401004
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 2.00000 0.0996271
$$404$$ 24.0000 1.19404
$$405$$ 0 0
$$406$$ −60.0000 −2.97775
$$407$$ 15.0000 0.743522
$$408$$ 0 0
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 8.00000 0.392232
$$417$$ 0 0
$$418$$ 20.0000 0.978232
$$419$$ −26.0000 −1.27018 −0.635092 0.772437i $$-0.719038\pi$$
−0.635092 + 0.772437i $$0.719038\pi$$
$$420$$ 0 0
$$421$$ 32.0000 1.55958 0.779792 0.626038i $$-0.215325\pi$$
0.779792 + 0.626038i $$0.215325\pi$$
$$422$$ −8.00000 −0.389434
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −33.0000 −1.59698
$$428$$ 6.00000 0.290021
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ −24.0000 −1.15337 −0.576683 0.816968i $$-0.695653\pi$$
−0.576683 + 0.816968i $$0.695653\pi$$
$$434$$ −12.0000 −0.576018
$$435$$ 0 0
$$436$$ 32.0000 1.53252
$$437$$ −2.00000 −0.0956730
$$438$$ 0 0
$$439$$ −33.0000 −1.57500 −0.787502 0.616312i $$-0.788626\pi$$
−0.787502 + 0.616312i $$0.788626\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −10.0000 −0.475651
$$443$$ 35.0000 1.66290 0.831450 0.555599i $$-0.187511\pi$$
0.831450 + 0.555599i $$0.187511\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ −24.0000 −1.13389
$$449$$ −15.0000 −0.707894 −0.353947 0.935266i $$-0.615161\pi$$
−0.353947 + 0.935266i $$0.615161\pi$$
$$450$$ 0 0
$$451$$ 45.0000 2.11897
$$452$$ 4.00000 0.188144
$$453$$ 0 0
$$454$$ −36.0000 −1.68956
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 13.0000 0.608114 0.304057 0.952654i $$-0.401659\pi$$
0.304057 + 0.952654i $$0.401659\pi$$
$$458$$ −28.0000 −1.30835
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −3.00000 −0.139724 −0.0698620 0.997557i $$-0.522256\pi$$
−0.0698620 + 0.997557i $$0.522256\pi$$
$$462$$ 0 0
$$463$$ −5.00000 −0.232370 −0.116185 0.993228i $$-0.537067\pi$$
−0.116185 + 0.993228i $$0.537067\pi$$
$$464$$ 40.0000 1.85695
$$465$$ 0 0
$$466$$ −50.0000 −2.31621
$$467$$ −29.0000 −1.34196 −0.670980 0.741475i $$-0.734126\pi$$
−0.670980 + 0.741475i $$0.734126\pi$$
$$468$$ 0 0
$$469$$ 12.0000 0.554109
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 20.0000 0.919601
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 30.0000 1.37505
$$477$$ 0 0
$$478$$ −30.0000 −1.37217
$$479$$ −5.00000 −0.228456 −0.114228 0.993455i $$-0.536439\pi$$
−0.114228 + 0.993455i $$0.536439\pi$$
$$480$$ 0 0
$$481$$ −3.00000 −0.136788
$$482$$ −28.0000 −1.27537
$$483$$ 0 0
$$484$$ 28.0000 1.27273
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −7.00000 −0.317200 −0.158600 0.987343i $$-0.550698\pi$$
−0.158600 + 0.987343i $$0.550698\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −16.0000 −0.722070 −0.361035 0.932552i $$-0.617576\pi$$
−0.361035 + 0.932552i $$0.617576\pi$$
$$492$$ 0 0
$$493$$ −50.0000 −2.25189
$$494$$ −4.00000 −0.179969
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ −45.0000 −2.01853
$$498$$ 0 0
$$499$$ 34.0000 1.52205 0.761025 0.648723i $$-0.224697\pi$$
0.761025 + 0.648723i $$0.224697\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −40.0000 −1.78529
$$503$$ 12.0000 0.535054 0.267527 0.963550i $$-0.413794\pi$$
0.267527 + 0.963550i $$0.413794\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −10.0000 −0.444554
$$507$$ 0 0
$$508$$ −28.0000 −1.24230
$$509$$ −21.0000 −0.930809 −0.465404 0.885098i $$-0.654091\pi$$
−0.465404 + 0.885098i $$0.654091\pi$$
$$510$$ 0 0
$$511$$ −18.0000 −0.796273
$$512$$ 32.0000 1.41421
$$513$$ 0 0
$$514$$ 36.0000 1.58789
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 50.0000 2.19900
$$518$$ 18.0000 0.790875
$$519$$ 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 $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −10.0000 −0.435607
$$528$$ 0 0
$$529$$ −22.0000 −0.956522
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 12.0000 0.520266
$$533$$ −9.00000 −0.389833
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −64.0000 −2.75924
$$539$$ 10.0000 0.430730
$$540$$ 0 0
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ −4.00000 −0.171815
$$543$$ 0 0
$$544$$ −40.0000 −1.71499
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 12.0000 0.512615
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −20.0000 −0.852029
$$552$$ 0 0
$$553$$ −33.0000 −1.40330
$$554$$ −52.0000 −2.20927
$$555$$ 0 0
$$556$$ −34.0000 −1.44192
$$557$$ −30.0000 −1.27114 −0.635570 0.772043i $$-0.719235\pi$$
−0.635570 + 0.772043i $$0.719235\pi$$
$$558$$ 0 0
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 20.0000 0.843649
$$563$$ −41.0000 −1.72794 −0.863972 0.503540i $$-0.832031\pi$$
−0.863972 + 0.503540i $$0.832031\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 16.0000 0.672530
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −16.0000 −0.670755 −0.335377 0.942084i $$-0.608864\pi$$
−0.335377 + 0.942084i $$0.608864\pi$$
$$570$$ 0 0
$$571$$ 17.0000 0.711428 0.355714 0.934595i $$-0.384238\pi$$
0.355714 + 0.934595i $$0.384238\pi$$
$$572$$ −10.0000 −0.418121
$$573$$ 0 0
$$574$$ 54.0000 2.25392
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 21.0000 0.874241 0.437121 0.899403i $$-0.355998\pi$$
0.437121 + 0.899403i $$0.355998\pi$$
$$578$$ 16.0000 0.665512
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 24.0000 0.995688
$$582$$ 0 0
$$583$$ 45.0000 1.86371
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 48.0000 1.98286
$$587$$ 42.0000 1.73353 0.866763 0.498721i $$-0.166197\pi$$
0.866763 + 0.498721i $$0.166197\pi$$
$$588$$ 0 0
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −12.0000 −0.493197
$$593$$ −36.0000 −1.47834 −0.739171 0.673517i $$-0.764783\pi$$
−0.739171 + 0.673517i $$0.764783\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 14.0000 0.573462
$$597$$ 0 0
$$598$$ 2.00000 0.0817861
$$599$$ −4.00000 −0.163436 −0.0817178 0.996656i $$-0.526041\pi$$
−0.0817178 + 0.996656i $$0.526041\pi$$
$$600$$ 0 0
$$601$$ −5.00000 −0.203954 −0.101977 0.994787i $$-0.532517\pi$$
−0.101977 + 0.994787i $$0.532517\pi$$
$$602$$ 24.0000 0.978167
$$603$$ 0 0
$$604$$ −24.0000 −0.976546
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 40.0000 1.62355 0.811775 0.583970i $$-0.198502\pi$$
0.811775 + 0.583970i $$0.198502\pi$$
$$608$$ −16.0000 −0.648886
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −10.0000 −0.404557
$$612$$ 0 0
$$613$$ −3.00000 −0.121169 −0.0605844 0.998163i $$-0.519296\pi$$
−0.0605844 + 0.998163i $$0.519296\pi$$
$$614$$ 38.0000 1.53356
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 22.0000 0.885687 0.442843 0.896599i $$-0.353970\pi$$
0.442843 + 0.896599i $$0.353970\pi$$
$$618$$ 0 0
$$619$$ −2.00000 −0.0803868 −0.0401934 0.999192i $$-0.512797\pi$$
−0.0401934 + 0.999192i $$0.512797\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −48.0000 −1.92462
$$623$$ 33.0000 1.32212
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 20.0000 0.799361
$$627$$ 0 0
$$628$$ −44.0000 −1.75579
$$629$$ 15.0000 0.598089
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 24.0000 0.953162
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −2.00000 −0.0792429
$$638$$ −100.000 −3.95904
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 36.0000 1.42191 0.710957 0.703235i $$-0.248262\pi$$
0.710957 + 0.703235i $$0.248262\pi$$
$$642$$ 0 0
$$643$$ −1.00000 −0.0394362 −0.0197181 0.999806i $$-0.506277\pi$$
−0.0197181 + 0.999806i $$0.506277\pi$$
$$644$$ −6.00000 −0.236433
$$645$$ 0 0
$$646$$ 20.0000 0.786889
$$647$$ 21.0000 0.825595 0.412798 0.910823i $$-0.364552\pi$$
0.412798 + 0.910823i $$0.364552\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 22.0000 0.861586
$$653$$ −30.0000 −1.17399 −0.586995 0.809590i $$-0.699689\pi$$
−0.586995 + 0.809590i $$0.699689\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −36.0000 −1.40556
$$657$$ 0 0
$$658$$ 60.0000 2.33904
$$659$$ −12.0000 −0.467454 −0.233727 0.972302i $$-0.575092\pi$$
−0.233727 + 0.972302i $$0.575092\pi$$
$$660$$ 0 0
$$661$$ −16.0000 −0.622328 −0.311164 0.950356i $$-0.600719\pi$$
−0.311164 + 0.950356i $$0.600719\pi$$
$$662$$ 64.0000 2.48743
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 10.0000 0.387202
$$668$$ −16.0000 −0.619059
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −55.0000 −2.12325
$$672$$ 0 0
$$673$$ −22.0000 −0.848038 −0.424019 0.905653i $$-0.639381\pi$$
−0.424019 + 0.905653i $$0.639381\pi$$
$$674$$ −8.00000 −0.308148
$$675$$ 0 0
$$676$$ 2.00000 0.0769231
$$677$$ −7.00000 −0.269032 −0.134516 0.990911i $$-0.542948\pi$$
−0.134516 + 0.990911i $$0.542948\pi$$
$$678$$ 0 0
$$679$$ 27.0000 1.03616
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −20.0000 −0.765840
$$683$$ 4.00000 0.153056 0.0765279 0.997067i $$-0.475617\pi$$
0.0765279 + 0.997067i $$0.475617\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −30.0000 −1.14541
$$687$$ 0 0
$$688$$ −16.0000 −0.609994
$$689$$ −9.00000 −0.342873
$$690$$ 0 0
$$691$$ 6.00000 0.228251 0.114125 0.993466i $$-0.463593\pi$$
0.114125 + 0.993466i $$0.463593\pi$$
$$692$$ −4.00000 −0.152057
$$693$$ 0 0
$$694$$ −2.00000 −0.0759190
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 45.0000 1.70450
$$698$$ 40.0000 1.51402
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 4.00000 0.151078 0.0755390 0.997143i $$-0.475932\pi$$
0.0755390 + 0.997143i $$0.475932\pi$$
$$702$$ 0 0
$$703$$ 6.00000 0.226294
$$704$$ −40.0000 −1.50756
$$705$$ 0 0
$$706$$ −28.0000 −1.05379
$$707$$ 36.0000 1.35392
$$708$$ 0 0
$$709$$ 20.0000 0.751116 0.375558 0.926799i $$-0.377451\pi$$
0.375558 + 0.926799i $$0.377451\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2.00000 0.0749006
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 0 0
$$718$$ −32.0000 −1.19423
$$719$$ −12.0000 −0.447524 −0.223762 0.974644i $$-0.571834\pi$$
−0.223762 + 0.974644i $$0.571834\pi$$
$$720$$ 0 0
$$721$$ −12.0000 −0.446903
$$722$$ −30.0000 −1.11648
$$723$$ 0 0
$$724$$ −46.0000 −1.70958
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −6.00000 −0.222528 −0.111264 0.993791i $$-0.535490\pi$$
−0.111264 + 0.993791i $$0.535490\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 20.0000 0.739727
$$732$$ 0 0
$$733$$ 15.0000 0.554038 0.277019 0.960864i $$-0.410654\pi$$
0.277019 + 0.960864i $$0.410654\pi$$
$$734$$ −16.0000 −0.590571
$$735$$ 0 0
$$736$$ 8.00000 0.294884
$$737$$ 20.0000 0.736709
$$738$$ 0 0
$$739$$ 38.0000 1.39785 0.698926 0.715194i $$-0.253662\pi$$
0.698926 + 0.715194i $$0.253662\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 54.0000 1.98240
$$743$$ 6.00000 0.220119 0.110059 0.993925i $$-0.464896\pi$$
0.110059 + 0.993925i $$0.464896\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −32.0000 −1.17160
$$747$$ 0 0
$$748$$ 50.0000 1.82818
$$749$$ 9.00000 0.328853
$$750$$ 0 0
$$751$$ −45.0000 −1.64207 −0.821037 0.570875i $$-0.806604\pi$$
−0.821037 + 0.570875i $$0.806604\pi$$
$$752$$ −40.0000 −1.45865
$$753$$ 0 0
$$754$$ 20.0000 0.728357
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −36.0000 −1.30844 −0.654221 0.756303i $$-0.727003\pi$$
−0.654221 + 0.756303i $$0.727003\pi$$
$$758$$ 12.0000 0.435860
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 14.0000 0.507500 0.253750 0.967270i $$-0.418336\pi$$
0.253750 + 0.967270i $$0.418336\pi$$
$$762$$ 0 0
$$763$$ 48.0000 1.73772
$$764$$ 40.0000 1.44715
$$765$$ 0 0
$$766$$ −36.0000 −1.30073
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −12.0000 −0.432731 −0.216366 0.976312i $$-0.569420\pi$$
−0.216366 + 0.976312i $$0.569420\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −26.0000 −0.935760
$$773$$ 24.0000 0.863220 0.431610 0.902060i $$-0.357946\pi$$
0.431610 + 0.902060i $$0.357946\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 48.0000 1.72088
$$779$$ 18.0000 0.644917
$$780$$ 0 0
$$781$$ −75.0000 −2.68371
$$782$$ −10.0000 −0.357599
$$783$$ 0 0
$$784$$ −8.00000 −0.285714
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −44.0000 −1.56843 −0.784215 0.620489i $$-0.786934\pi$$
−0.784215 + 0.620489i $$0.786934\pi$$
$$788$$ −24.0000 −0.854965
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 6.00000 0.213335
$$792$$ 0 0
$$793$$ 11.0000 0.390621
$$794$$ 38.0000 1.34857
$$795$$ 0 0
$$796$$ 8.00000 0.283552
$$797$$ −5.00000 −0.177109 −0.0885545 0.996071i $$-0.528225\pi$$
−0.0885545 + 0.996071i $$0.528225\pi$$
$$798$$ 0 0
$$799$$ 50.0000 1.76887
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 36.0000 1.27120
$$803$$ −30.0000 −1.05868
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 4.00000 0.140894
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 6.00000 0.210949 0.105474 0.994422i $$-0.466364\pi$$
0.105474 + 0.994422i $$0.466364\pi$$
$$810$$ 0 0
$$811$$ −4.00000 −0.140459 −0.0702295 0.997531i $$-0.522373\pi$$
−0.0702295 + 0.997531i $$0.522373\pi$$
$$812$$ −60.0000 −2.10559
$$813$$ 0 0
$$814$$ 30.0000 1.05150
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 8.00000 0.279885
$$818$$ −52.0000 −1.81814
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 41.0000 1.43091 0.715455 0.698659i $$-0.246219\pi$$
0.715455 + 0.698659i $$0.246219\pi$$
$$822$$ 0 0
$$823$$ 48.0000 1.67317 0.836587 0.547833i $$-0.184547\pi$$
0.836587 + 0.547833i $$0.184547\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −42.0000 −1.46048 −0.730242 0.683189i $$-0.760592\pi$$
−0.730242 + 0.683189i $$0.760592\pi$$
$$828$$ 0 0
$$829$$ 14.0000 0.486240 0.243120 0.969996i $$-0.421829\pi$$
0.243120 + 0.969996i $$0.421829\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 8.00000 0.277350
$$833$$ 10.0000 0.346479
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 20.0000 0.691714
$$837$$ 0 0
$$838$$ −52.0000 −1.79631
$$839$$ −7.00000 −0.241667 −0.120833 0.992673i $$-0.538557\pi$$
−0.120833 + 0.992673i $$0.538557\pi$$
$$840$$ 0 0
$$841$$ 71.0000 2.44828
$$842$$ 64.0000 2.20559
$$843$$ 0 0
$$844$$ −8.00000 −0.275371
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 42.0000 1.44314
$$848$$ −36.0000 −1.23625
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −3.00000 −0.102839
$$852$$ 0 0
$$853$$ −51.0000 −1.74621 −0.873103 0.487535i $$-0.837896\pi$$
−0.873103 + 0.487535i $$0.837896\pi$$
$$854$$ −66.0000 −2.25847
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −17.0000 −0.580709 −0.290354 0.956919i $$-0.593773\pi$$
−0.290354 + 0.956919i $$0.593773\pi$$
$$858$$ 0 0
$$859$$ 35.0000 1.19418 0.597092 0.802173i $$-0.296323\pi$$
0.597092 + 0.802173i $$0.296323\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 32.0000 1.08992
$$863$$ −22.0000 −0.748889 −0.374444 0.927249i $$-0.622167\pi$$
−0.374444 + 0.927249i $$0.622167\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −48.0000 −1.63111
$$867$$ 0 0
$$868$$ −12.0000 −0.407307
$$869$$ −55.0000 −1.86575
$$870$$ 0 0
$$871$$ −4.00000 −0.135535
$$872$$ 0 0
$$873$$ 0 0
$$874$$ −4.00000 −0.135302
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −22.0000 −0.742887 −0.371444 0.928456i $$-0.621137\pi$$
−0.371444 + 0.928456i $$0.621137\pi$$
$$878$$ −66.0000 −2.22739
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 14.0000 0.471672 0.235836 0.971793i $$-0.424217\pi$$
0.235836 + 0.971793i $$0.424217\pi$$
$$882$$ 0 0
$$883$$ −12.0000 −0.403832 −0.201916 0.979403i $$-0.564717\pi$$
−0.201916 + 0.979403i $$0.564717\pi$$
$$884$$ −10.0000 −0.336336
$$885$$ 0 0
$$886$$ 70.0000 2.35170
$$887$$ −15.0000 −0.503651 −0.251825 0.967773i $$-0.581031\pi$$
−0.251825 + 0.967773i $$0.581031\pi$$
$$888$$ 0 0
$$889$$ −42.0000 −1.40863
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 20.0000 0.669274
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −30.0000 −1.00111
$$899$$ 20.0000 0.667037
$$900$$ 0 0
$$901$$ 45.0000 1.49917
$$902$$ 90.0000 2.99667
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −2.00000 −0.0664089 −0.0332045 0.999449i $$-0.510571\pi$$
−0.0332045 + 0.999449i $$0.510571\pi$$
$$908$$ −36.0000 −1.19470
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −8.00000 −0.265052 −0.132526 0.991180i $$-0.542309\pi$$
−0.132526 + 0.991180i $$0.542309\pi$$
$$912$$ 0 0
$$913$$ 40.0000 1.32381
$$914$$ 26.0000 0.860004
$$915$$ 0 0
$$916$$ −28.0000 −0.925146
$$917$$ −18.0000 −0.594412
$$918$$ 0 0
$$919$$ 29.0000 0.956622 0.478311 0.878191i $$-0.341249\pi$$
0.478311 + 0.878191i $$0.341249\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −6.00000 −0.197599
$$923$$ 15.0000 0.493731
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −10.0000 −0.328620
$$927$$ 0 0
$$928$$ 80.0000 2.62613
$$929$$ −21.0000 −0.688988 −0.344494 0.938789i $$-0.611949\pi$$
−0.344494 + 0.938789i $$0.611949\pi$$
$$930$$ 0 0
$$931$$ 4.00000 0.131095
$$932$$ −50.0000 −1.63780
$$933$$ 0 0
$$934$$ −58.0000 −1.89782
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −2.00000 −0.0653372 −0.0326686 0.999466i $$-0.510401\pi$$
−0.0326686 + 0.999466i $$0.510401\pi$$
$$938$$ 24.0000 0.783628
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 23.0000 0.749779 0.374889 0.927070i $$-0.377681\pi$$
0.374889 + 0.927070i $$0.377681\pi$$
$$942$$ 0 0
$$943$$ −9.00000 −0.293080
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 40.0000 1.30051
$$947$$ 36.0000 1.16984 0.584921 0.811090i $$-0.301125\pi$$
0.584921 + 0.811090i $$0.301125\pi$$
$$948$$ 0 0
$$949$$ 6.00000 0.194768
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −11.0000 −0.356325 −0.178162 0.984001i $$-0.557015\pi$$
−0.178162 + 0.984001i $$0.557015\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −30.0000 −0.970269
$$957$$ 0 0
$$958$$ −10.0000 −0.323085
$$959$$ 18.0000 0.581250
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ −6.00000 −0.193448
$$963$$ 0 0
$$964$$ −28.0000 −0.901819
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 40.0000 1.28631 0.643157 0.765735i $$-0.277624\pi$$
0.643157 + 0.765735i $$0.277624\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ −51.0000 −1.63498
$$974$$ −14.0000 −0.448589
$$975$$ 0 0
$$976$$ 44.0000 1.40841
$$977$$ 12.0000 0.383914 0.191957 0.981403i $$-0.438517\pi$$
0.191957 + 0.981403i $$0.438517\pi$$
$$978$$ 0 0
$$979$$ 55.0000 1.75781
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −32.0000 −1.02116
$$983$$ 36.0000 1.14822 0.574111 0.818778i $$-0.305348\pi$$
0.574111 + 0.818778i $$0.305348\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −100.000 −3.18465
$$987$$ 0 0
$$988$$ −4.00000 −0.127257
$$989$$ −4.00000 −0.127193
$$990$$ 0 0
$$991$$ 39.0000 1.23888 0.619438 0.785046i $$-0.287361\pi$$
0.619438 + 0.785046i $$0.287361\pi$$
$$992$$ 16.0000 0.508001
$$993$$ 0 0
$$994$$ −90.0000 −2.85463
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 16.0000 0.506725 0.253363 0.967371i $$-0.418463\pi$$
0.253363 + 0.967371i $$0.418463\pi$$
$$998$$ 68.0000 2.15250
$$999$$ 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 2925.2.a.t.1.1 1
3.2 odd 2 975.2.a.b.1.1 1
5.2 odd 4 2925.2.c.d.2224.2 2
5.3 odd 4 2925.2.c.d.2224.1 2
5.4 even 2 585.2.a.a.1.1 1
15.2 even 4 975.2.c.b.274.1 2
15.8 even 4 975.2.c.b.274.2 2
15.14 odd 2 195.2.a.d.1.1 1
20.19 odd 2 9360.2.a.w.1.1 1
60.59 even 2 3120.2.a.n.1.1 1
65.64 even 2 7605.2.a.v.1.1 1
105.104 even 2 9555.2.a.t.1.1 1
195.194 odd 2 2535.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.d.1.1 1 15.14 odd 2
585.2.a.a.1.1 1 5.4 even 2
975.2.a.b.1.1 1 3.2 odd 2
975.2.c.b.274.1 2 15.2 even 4
975.2.c.b.274.2 2 15.8 even 4
2535.2.a.b.1.1 1 195.194 odd 2
2925.2.a.t.1.1 1 1.1 even 1 trivial
2925.2.c.d.2224.1 2 5.3 odd 4
2925.2.c.d.2224.2 2 5.2 odd 4
3120.2.a.n.1.1 1 60.59 even 2
7605.2.a.v.1.1 1 65.64 even 2
9360.2.a.w.1.1 1 20.19 odd 2
9555.2.a.t.1.1 1 105.104 even 2