# Properties

 Label 1725.2.a.k.1.1 Level $1725$ Weight $2$ Character 1725.1 Self dual yes Analytic conductor $13.774$ 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] = [1725,2,Mod(1,1725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1725, 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("1725.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1725 = 3 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1725.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: $$13.7741943487$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 345) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1725.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} -2.00000 q^{4} +3.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} -2.00000 q^{4} +3.00000 q^{7} +1.00000 q^{9} -4.00000 q^{11} +2.00000 q^{12} +4.00000 q^{16} +3.00000 q^{17} -8.00000 q^{19} -3.00000 q^{21} -1.00000 q^{23} -1.00000 q^{27} -6.00000 q^{28} +9.00000 q^{29} -5.00000 q^{31} +4.00000 q^{33} -2.00000 q^{36} +9.00000 q^{37} +7.00000 q^{41} -4.00000 q^{43} +8.00000 q^{44} +2.00000 q^{47} -4.00000 q^{48} +2.00000 q^{49} -3.00000 q^{51} -13.0000 q^{53} +8.00000 q^{57} -3.00000 q^{59} -14.0000 q^{61} +3.00000 q^{63} -8.00000 q^{64} -13.0000 q^{67} -6.00000 q^{68} +1.00000 q^{69} -13.0000 q^{71} +4.00000 q^{73} +16.0000 q^{76} -12.0000 q^{77} +1.00000 q^{81} +1.00000 q^{83} +6.00000 q^{84} -9.00000 q^{87} -8.00000 q^{89} +2.00000 q^{92} +5.00000 q^{93} -10.0000 q^{97} -4.00000 q^{99} +O(q^{100})$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ −1.00000 −0.577350
$$4$$ −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
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 2.00000 0.577350
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4.00000 1.00000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ −3.00000 −0.654654
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ −6.00000 −1.13389
$$29$$ 9.00000 1.67126 0.835629 0.549294i $$-0.185103\pi$$
0.835629 + 0.549294i $$0.185103\pi$$
$$30$$ 0 0
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ 0 0
$$33$$ 4.00000 0.696311
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ 9.00000 1.47959 0.739795 0.672832i $$-0.234922\pi$$
0.739795 + 0.672832i $$0.234922\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 7.00000 1.09322 0.546608 0.837389i $$-0.315919\pi$$
0.546608 + 0.837389i $$0.315919\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 8.00000 1.20605
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ −4.00000 −0.577350
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ −13.0000 −1.78569 −0.892844 0.450367i $$-0.851293\pi$$
−0.892844 + 0.450367i $$0.851293\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ 0 0
$$59$$ −3.00000 −0.390567 −0.195283 0.980747i $$-0.562563\pi$$
−0.195283 + 0.980747i $$0.562563\pi$$
$$60$$ 0 0
$$61$$ −14.0000 −1.79252 −0.896258 0.443533i $$-0.853725\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 0 0
$$63$$ 3.00000 0.377964
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −13.0000 −1.58820 −0.794101 0.607785i $$-0.792058\pi$$
−0.794101 + 0.607785i $$0.792058\pi$$
$$68$$ −6.00000 −0.727607
$$69$$ 1.00000 0.120386
$$70$$ 0 0
$$71$$ −13.0000 −1.54282 −0.771408 0.636341i $$-0.780447\pi$$
−0.771408 + 0.636341i $$0.780447\pi$$
$$72$$ 0 0
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 16.0000 1.83533
$$77$$ −12.0000 −1.36753
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 1.00000 0.109764 0.0548821 0.998493i $$-0.482522\pi$$
0.0548821 + 0.998493i $$0.482522\pi$$
$$84$$ 6.00000 0.654654
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −9.00000 −0.964901
$$88$$ 0 0
$$89$$ −8.00000 −0.847998 −0.423999 0.905663i $$-0.639374\pi$$
−0.423999 + 0.905663i $$0.639374\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 2.00000 0.208514
$$93$$ 5.00000 0.518476
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ −4.00000 −0.402015
$$100$$ 0 0
$$101$$ 9.00000 0.895533 0.447767 0.894150i $$-0.352219\pi$$
0.447767 + 0.894150i $$0.352219\pi$$
$$102$$ 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
$$106$$ 0 0
$$107$$ −11.0000 −1.06341 −0.531705 0.846930i $$-0.678449\pi$$
−0.531705 + 0.846930i $$0.678449\pi$$
$$108$$ 2.00000 0.192450
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ 0 0
$$111$$ −9.00000 −0.854242
$$112$$ 12.0000 1.13389
$$113$$ −1.00000 −0.0940721 −0.0470360 0.998893i $$-0.514978\pi$$
−0.0470360 + 0.998893i $$0.514978\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −18.0000 −1.67126
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 9.00000 0.825029
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 0 0
$$123$$ −7.00000 −0.631169
$$124$$ 10.0000 0.898027
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 18.0000 1.59724 0.798621 0.601834i $$-0.205563\pi$$
0.798621 + 0.601834i $$0.205563\pi$$
$$128$$ 0 0
$$129$$ 4.00000 0.352180
$$130$$ 0 0
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ −8.00000 −0.696311
$$133$$ −24.0000 −2.08106
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.00000 −0.170872 −0.0854358 0.996344i $$-0.527228\pi$$
−0.0854358 + 0.996344i $$0.527228\pi$$
$$138$$ 0 0
$$139$$ −3.00000 −0.254457 −0.127228 0.991873i $$-0.540608\pi$$
−0.127228 + 0.991873i $$0.540608\pi$$
$$140$$ 0 0
$$141$$ −2.00000 −0.168430
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 4.00000 0.333333
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −2.00000 −0.164957
$$148$$ −18.0000 −1.47959
$$149$$ −14.0000 −1.14692 −0.573462 0.819232i $$-0.694400\pi$$
−0.573462 + 0.819232i $$0.694400\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 3.00000 0.242536
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 3.00000 0.239426 0.119713 0.992809i $$-0.461803\pi$$
0.119713 + 0.992809i $$0.461803\pi$$
$$158$$ 0 0
$$159$$ 13.0000 1.03097
$$160$$ 0 0
$$161$$ −3.00000 −0.236433
$$162$$ 0 0
$$163$$ 2.00000 0.156652 0.0783260 0.996928i $$-0.475042\pi$$
0.0783260 + 0.996928i $$0.475042\pi$$
$$164$$ −14.0000 −1.09322
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 22.0000 1.70241 0.851206 0.524832i $$-0.175872\pi$$
0.851206 + 0.524832i $$0.175872\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ −8.00000 −0.611775
$$172$$ 8.00000 0.609994
$$173$$ 24.0000 1.82469 0.912343 0.409426i $$-0.134271\pi$$
0.912343 + 0.409426i $$0.134271\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −16.0000 −1.20605
$$177$$ 3.00000 0.225494
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 14.0000 1.03491
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −12.0000 −0.877527
$$188$$ −4.00000 −0.291730
$$189$$ −3.00000 −0.218218
$$190$$ 0 0
$$191$$ −2.00000 −0.144715 −0.0723575 0.997379i $$-0.523052\pi$$
−0.0723575 + 0.997379i $$0.523052\pi$$
$$192$$ 8.00000 0.577350
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −4.00000 −0.285714
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ −18.0000 −1.27599 −0.637993 0.770042i $$-0.720235\pi$$
−0.637993 + 0.770042i $$0.720235\pi$$
$$200$$ 0 0
$$201$$ 13.0000 0.916949
$$202$$ 0 0
$$203$$ 27.0000 1.89503
$$204$$ 6.00000 0.420084
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1.00000 −0.0695048
$$208$$ 0 0
$$209$$ 32.0000 2.21349
$$210$$ 0 0
$$211$$ 7.00000 0.481900 0.240950 0.970538i $$-0.422541\pi$$
0.240950 + 0.970538i $$0.422541\pi$$
$$212$$ 26.0000 1.78569
$$213$$ 13.0000 0.890745
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −15.0000 −1.01827
$$218$$ 0 0
$$219$$ −4.00000 −0.270295
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −10.0000 −0.669650 −0.334825 0.942280i $$-0.608677\pi$$
−0.334825 + 0.942280i $$0.608677\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 4.00000 0.265489 0.132745 0.991150i $$-0.457621\pi$$
0.132745 + 0.991150i $$0.457621\pi$$
$$228$$ −16.0000 −1.05963
$$229$$ 4.00000 0.264327 0.132164 0.991228i $$-0.457808\pi$$
0.132164 + 0.991228i $$0.457808\pi$$
$$230$$ 0 0
$$231$$ 12.0000 0.789542
$$232$$ 0 0
$$233$$ 8.00000 0.524097 0.262049 0.965055i $$-0.415602\pi$$
0.262049 + 0.965055i $$0.415602\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 6.00000 0.390567
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 13.0000 0.840900 0.420450 0.907316i $$-0.361872\pi$$
0.420450 + 0.907316i $$0.361872\pi$$
$$240$$ 0 0
$$241$$ 20.0000 1.28831 0.644157 0.764894i $$-0.277208\pi$$
0.644157 + 0.764894i $$0.277208\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 28.0000 1.79252
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.00000 −0.0633724
$$250$$ 0 0
$$251$$ 18.0000 1.13615 0.568075 0.822977i $$-0.307688\pi$$
0.568075 + 0.822977i $$0.307688\pi$$
$$252$$ −6.00000 −0.377964
$$253$$ 4.00000 0.251478
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ 27.0000 1.67770
$$260$$ 0 0
$$261$$ 9.00000 0.557086
$$262$$ 0 0
$$263$$ 23.0000 1.41824 0.709120 0.705087i $$-0.249092\pi$$
0.709120 + 0.705087i $$0.249092\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 8.00000 0.489592
$$268$$ 26.0000 1.58820
$$269$$ −17.0000 −1.03651 −0.518254 0.855227i $$-0.673418\pi$$
−0.518254 + 0.855227i $$0.673418\pi$$
$$270$$ 0 0
$$271$$ −23.0000 −1.39715 −0.698575 0.715537i $$-0.746182\pi$$
−0.698575 + 0.715537i $$0.746182\pi$$
$$272$$ 12.0000 0.727607
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ −2.00000 −0.120386
$$277$$ −18.0000 −1.08152 −0.540758 0.841178i $$-0.681862\pi$$
−0.540758 + 0.841178i $$0.681862\pi$$
$$278$$ 0 0
$$279$$ −5.00000 −0.299342
$$280$$ 0 0
$$281$$ 24.0000 1.43172 0.715860 0.698244i $$-0.246035\pi$$
0.715860 + 0.698244i $$0.246035\pi$$
$$282$$ 0 0
$$283$$ 5.00000 0.297219 0.148610 0.988896i $$-0.452520\pi$$
0.148610 + 0.988896i $$0.452520\pi$$
$$284$$ 26.0000 1.54282
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 21.0000 1.23959
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 10.0000 0.586210
$$292$$ −8.00000 −0.468165
$$293$$ −19.0000 −1.10999 −0.554996 0.831853i $$-0.687280\pi$$
−0.554996 + 0.831853i $$0.687280\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 4.00000 0.232104
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −12.0000 −0.691669
$$302$$ 0 0
$$303$$ −9.00000 −0.517036
$$304$$ −32.0000 −1.83533
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 24.0000 1.36753
$$309$$ 8.00000 0.455104
$$310$$ 0 0
$$311$$ −8.00000 −0.453638 −0.226819 0.973937i $$-0.572833\pi$$
−0.226819 + 0.973937i $$0.572833\pi$$
$$312$$ 0 0
$$313$$ −25.0000 −1.41308 −0.706542 0.707671i $$-0.749746\pi$$
−0.706542 + 0.707671i $$0.749746\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −30.0000 −1.68497 −0.842484 0.538721i $$-0.818908\pi$$
−0.842484 + 0.538721i $$0.818908\pi$$
$$318$$ 0 0
$$319$$ −36.0000 −2.01561
$$320$$ 0 0
$$321$$ 11.0000 0.613960
$$322$$ 0 0
$$323$$ −24.0000 −1.33540
$$324$$ −2.00000 −0.111111
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 16.0000 0.884802
$$328$$ 0 0
$$329$$ 6.00000 0.330791
$$330$$ 0 0
$$331$$ 7.00000 0.384755 0.192377 0.981321i $$-0.438380\pi$$
0.192377 + 0.981321i $$0.438380\pi$$
$$332$$ −2.00000 −0.109764
$$333$$ 9.00000 0.493197
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −12.0000 −0.654654
$$337$$ −10.0000 −0.544735 −0.272367 0.962193i $$-0.587807\pi$$
−0.272367 + 0.962193i $$0.587807\pi$$
$$338$$ 0 0
$$339$$ 1.00000 0.0543125
$$340$$ 0 0
$$341$$ 20.0000 1.08306
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 16.0000 0.858925 0.429463 0.903085i $$-0.358703\pi$$
0.429463 + 0.903085i $$0.358703\pi$$
$$348$$ 18.0000 0.964901
$$349$$ −1.00000 −0.0535288 −0.0267644 0.999642i $$-0.508520\pi$$
−0.0267644 + 0.999642i $$0.508520\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 16.0000 0.847998
$$357$$ −9.00000 −0.476331
$$358$$ 0 0
$$359$$ −2.00000 −0.105556 −0.0527780 0.998606i $$-0.516808\pi$$
−0.0527780 + 0.998606i $$0.516808\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 0 0
$$363$$ −5.00000 −0.262432
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −31.0000 −1.61819 −0.809093 0.587680i $$-0.800041\pi$$
−0.809093 + 0.587680i $$0.800041\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 7.00000 0.364405
$$370$$ 0 0
$$371$$ −39.0000 −2.02478
$$372$$ −10.0000 −0.518476
$$373$$ 6.00000 0.310668 0.155334 0.987862i $$-0.450355\pi$$
0.155334 + 0.987862i $$0.450355\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 0 0
$$381$$ −18.0000 −0.922168
$$382$$ 0 0
$$383$$ 23.0000 1.17525 0.587623 0.809135i $$-0.300064\pi$$
0.587623 + 0.809135i $$0.300064\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −4.00000 −0.203331
$$388$$ 20.0000 1.01535
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ −3.00000 −0.151717
$$392$$ 0 0
$$393$$ 4.00000 0.201773
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 8.00000 0.402015
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 0 0
$$399$$ 24.0000 1.20150
$$400$$ 0 0
$$401$$ 30.0000 1.49813 0.749064 0.662497i $$-0.230503\pi$$
0.749064 + 0.662497i $$0.230503\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −18.0000 −0.895533
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −36.0000 −1.78445
$$408$$ 0 0
$$409$$ 25.0000 1.23617 0.618085 0.786111i $$-0.287909\pi$$
0.618085 + 0.786111i $$0.287909\pi$$
$$410$$ 0 0
$$411$$ 2.00000 0.0986527
$$412$$ 16.0000 0.788263
$$413$$ −9.00000 −0.442861
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 3.00000 0.146911
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 4.00000 0.194948 0.0974740 0.995238i $$-0.468924\pi$$
0.0974740 + 0.995238i $$0.468924\pi$$
$$422$$ 0 0
$$423$$ 2.00000 0.0972433
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −42.0000 −2.03252
$$428$$ 22.0000 1.06341
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 20.0000 0.963366 0.481683 0.876346i $$-0.340026\pi$$
0.481683 + 0.876346i $$0.340026\pi$$
$$432$$ −4.00000 −0.192450
$$433$$ 37.0000 1.77811 0.889053 0.457804i $$-0.151364\pi$$
0.889053 + 0.457804i $$0.151364\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 32.0000 1.53252
$$437$$ 8.00000 0.382692
$$438$$ 0 0
$$439$$ −24.0000 −1.14546 −0.572729 0.819745i $$-0.694115\pi$$
−0.572729 + 0.819745i $$0.694115\pi$$
$$440$$ 0 0
$$441$$ 2.00000 0.0952381
$$442$$ 0 0
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 18.0000 0.854242
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 14.0000 0.662177
$$448$$ −24.0000 −1.13389
$$449$$ −11.0000 −0.519122 −0.259561 0.965727i $$-0.583578\pi$$
−0.259561 + 0.965727i $$0.583578\pi$$
$$450$$ 0 0
$$451$$ −28.0000 −1.31847
$$452$$ 2.00000 0.0940721
$$453$$ 8.00000 0.375873
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 35.0000 1.63723 0.818615 0.574342i $$-0.194742\pi$$
0.818615 + 0.574342i $$0.194742\pi$$
$$458$$ 0 0
$$459$$ −3.00000 −0.140028
$$460$$ 0 0
$$461$$ 26.0000 1.21094 0.605470 0.795868i $$-0.292985\pi$$
0.605470 + 0.795868i $$0.292985\pi$$
$$462$$ 0 0
$$463$$ 20.0000 0.929479 0.464739 0.885448i $$-0.346148\pi$$
0.464739 + 0.885448i $$0.346148\pi$$
$$464$$ 36.0000 1.67126
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 13.0000 0.601568 0.300784 0.953692i $$-0.402752\pi$$
0.300784 + 0.953692i $$0.402752\pi$$
$$468$$ 0 0
$$469$$ −39.0000 −1.80085
$$470$$ 0 0
$$471$$ −3.00000 −0.138233
$$472$$ 0 0
$$473$$ 16.0000 0.735681
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −18.0000 −0.825029
$$477$$ −13.0000 −0.595229
$$478$$ 0 0
$$479$$ 6.00000 0.274147 0.137073 0.990561i $$-0.456230\pi$$
0.137073 + 0.990561i $$0.456230\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 3.00000 0.136505
$$484$$ −10.0000 −0.454545
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 0 0
$$489$$ −2.00000 −0.0904431
$$490$$ 0 0
$$491$$ 3.00000 0.135388 0.0676941 0.997706i $$-0.478436\pi$$
0.0676941 + 0.997706i $$0.478436\pi$$
$$492$$ 14.0000 0.631169
$$493$$ 27.0000 1.21602
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −20.0000 −0.898027
$$497$$ −39.0000 −1.74939
$$498$$ 0 0
$$499$$ 21.0000 0.940089 0.470045 0.882643i $$-0.344238\pi$$
0.470045 + 0.882643i $$0.344238\pi$$
$$500$$ 0 0
$$501$$ −22.0000 −0.982888
$$502$$ 0 0
$$503$$ −21.0000 −0.936344 −0.468172 0.883637i $$-0.655087\pi$$
−0.468172 + 0.883637i $$0.655087\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 13.0000 0.577350
$$508$$ −36.0000 −1.59724
$$509$$ 30.0000 1.32973 0.664863 0.746965i $$-0.268490\pi$$
0.664863 + 0.746965i $$0.268490\pi$$
$$510$$ 0 0
$$511$$ 12.0000 0.530849
$$512$$ 0 0
$$513$$ 8.00000 0.353209
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −8.00000 −0.352180
$$517$$ −8.00000 −0.351840
$$518$$ 0 0
$$519$$ −24.0000 −1.05348
$$520$$ 0 0
$$521$$ −12.0000 −0.525730 −0.262865 0.964833i $$-0.584667\pi$$
−0.262865 + 0.964833i $$0.584667\pi$$
$$522$$ 0 0
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ 8.00000 0.349482
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −15.0000 −0.653410
$$528$$ 16.0000 0.696311
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ −3.00000 −0.130189
$$532$$ 48.0000 2.08106
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −8.00000 −0.344584
$$540$$ 0 0
$$541$$ −10.0000 −0.429934 −0.214967 0.976621i $$-0.568964\pi$$
−0.214967 + 0.976621i $$0.568964\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ 4.00000 0.170872
$$549$$ −14.0000 −0.597505
$$550$$ 0 0
$$551$$ −72.0000 −3.06730
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 6.00000 0.254457
$$557$$ −21.0000 −0.889799 −0.444899 0.895581i $$-0.646761\pi$$
−0.444899 + 0.895581i $$0.646761\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ 0 0
$$563$$ 11.0000 0.463595 0.231797 0.972764i $$-0.425539\pi$$
0.231797 + 0.972764i $$0.425539\pi$$
$$564$$ 4.00000 0.168430
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 3.00000 0.125988
$$568$$ 0 0
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ −22.0000 −0.920671 −0.460336 0.887745i $$-0.652271\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0 0
$$573$$ 2.00000 0.0835512
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −8.00000 −0.333333
$$577$$ 20.0000 0.832611 0.416305 0.909225i $$-0.363325\pi$$
0.416305 + 0.909225i $$0.363325\pi$$
$$578$$ 0 0
$$579$$ 4.00000 0.166234
$$580$$ 0 0
$$581$$ 3.00000 0.124461
$$582$$ 0 0
$$583$$ 52.0000 2.15362
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −14.0000 −0.577842 −0.288921 0.957353i $$-0.593296\pi$$
−0.288921 + 0.957353i $$0.593296\pi$$
$$588$$ 4.00000 0.164957
$$589$$ 40.0000 1.64817
$$590$$ 0 0
$$591$$ 2.00000 0.0822690
$$592$$ 36.0000 1.47959
$$593$$ −18.0000 −0.739171 −0.369586 0.929197i $$-0.620500\pi$$
−0.369586 + 0.929197i $$0.620500\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 28.0000 1.14692
$$597$$ 18.0000 0.736691
$$598$$ 0 0
$$599$$ −4.00000 −0.163436 −0.0817178 0.996656i $$-0.526041\pi$$
−0.0817178 + 0.996656i $$0.526041\pi$$
$$600$$ 0 0
$$601$$ −41.0000 −1.67242 −0.836212 0.548406i $$-0.815235\pi$$
−0.836212 + 0.548406i $$0.815235\pi$$
$$602$$ 0 0
$$603$$ −13.0000 −0.529401
$$604$$ 16.0000 0.651031
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 10.0000 0.405887 0.202944 0.979190i $$-0.434949\pi$$
0.202944 + 0.979190i $$0.434949\pi$$
$$608$$ 0 0
$$609$$ −27.0000 −1.09410
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −6.00000 −0.242536
$$613$$ −14.0000 −0.565455 −0.282727 0.959200i $$-0.591239\pi$$
−0.282727 + 0.959200i $$0.591239\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 33.0000 1.32853 0.664265 0.747497i $$-0.268745\pi$$
0.664265 + 0.747497i $$0.268745\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 1.00000 0.0401286
$$622$$ 0 0
$$623$$ −24.0000 −0.961540
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −32.0000 −1.27796
$$628$$ −6.00000 −0.239426
$$629$$ 27.0000 1.07656
$$630$$ 0 0
$$631$$ 38.0000 1.51276 0.756378 0.654135i $$-0.226967\pi$$
0.756378 + 0.654135i $$0.226967\pi$$
$$632$$ 0 0
$$633$$ −7.00000 −0.278225
$$634$$ 0 0
$$635$$ 0 0
$$636$$ −26.0000 −1.03097
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −13.0000 −0.514272
$$640$$ 0 0
$$641$$ −20.0000 −0.789953 −0.394976 0.918691i $$-0.629247\pi$$
−0.394976 + 0.918691i $$0.629247\pi$$
$$642$$ 0 0
$$643$$ −13.0000 −0.512670 −0.256335 0.966588i $$-0.582515\pi$$
−0.256335 + 0.966588i $$0.582515\pi$$
$$644$$ 6.00000 0.236433
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −12.0000 −0.471769 −0.235884 0.971781i $$-0.575799\pi$$
−0.235884 + 0.971781i $$0.575799\pi$$
$$648$$ 0 0
$$649$$ 12.0000 0.471041
$$650$$ 0 0
$$651$$ 15.0000 0.587896
$$652$$ −4.00000 −0.156652
$$653$$ −16.0000 −0.626128 −0.313064 0.949732i $$-0.601356\pi$$
−0.313064 + 0.949732i $$0.601356\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 28.0000 1.09322
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −9.00000 −0.348481
$$668$$ −44.0000 −1.70241
$$669$$ 10.0000 0.386622
$$670$$ 0 0
$$671$$ 56.0000 2.16186
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 26.0000 1.00000
$$677$$ 45.0000 1.72949 0.864745 0.502211i $$-0.167480\pi$$
0.864745 + 0.502211i $$0.167480\pi$$
$$678$$ 0 0
$$679$$ −30.0000 −1.15129
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 0 0
$$683$$ −26.0000 −0.994862 −0.497431 0.867503i $$-0.665723\pi$$
−0.497431 + 0.867503i $$0.665723\pi$$
$$684$$ 16.0000 0.611775
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −4.00000 −0.152610
$$688$$ −16.0000 −0.609994
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ −48.0000 −1.82469
$$693$$ −12.0000 −0.455842
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 21.0000 0.795432
$$698$$ 0 0
$$699$$ −8.00000 −0.302588
$$700$$ 0 0
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 0 0
$$703$$ −72.0000 −2.71553
$$704$$ 32.0000 1.20605
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 27.0000 1.01544
$$708$$ −6.00000 −0.225494
$$709$$ 22.0000 0.826227 0.413114 0.910679i $$-0.364441\pi$$
0.413114 + 0.910679i $$0.364441\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 5.00000 0.187251
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −13.0000 −0.485494
$$718$$ 0 0
$$719$$ −7.00000 −0.261056 −0.130528 0.991445i $$-0.541667\pi$$
−0.130528 + 0.991445i $$0.541667\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 0 0
$$723$$ −20.0000 −0.743808
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 37.0000 1.37225 0.686127 0.727482i $$-0.259309\pi$$
0.686127 + 0.727482i $$0.259309\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −12.0000 −0.443836
$$732$$ −28.0000 −1.03491
$$733$$ −51.0000 −1.88373 −0.941864 0.335994i $$-0.890928\pi$$
−0.941864 + 0.335994i $$0.890928\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 52.0000 1.91544
$$738$$ 0 0
$$739$$ 27.0000 0.993211 0.496606 0.867976i $$-0.334580\pi$$
0.496606 + 0.867976i $$0.334580\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 48.0000 1.76095 0.880475 0.474093i $$-0.157224\pi$$
0.880475 + 0.474093i $$0.157224\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 1.00000 0.0365881
$$748$$ 24.0000 0.877527
$$749$$ −33.0000 −1.20579
$$750$$ 0 0
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ 8.00000 0.291730
$$753$$ −18.0000 −0.655956
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 6.00000 0.218218
$$757$$ −45.0000 −1.63555 −0.817776 0.575536i $$-0.804793\pi$$
−0.817776 + 0.575536i $$0.804793\pi$$
$$758$$ 0 0
$$759$$ −4.00000 −0.145191
$$760$$ 0 0
$$761$$ −41.0000 −1.48625 −0.743124 0.669153i $$-0.766657\pi$$
−0.743124 + 0.669153i $$0.766657\pi$$
$$762$$ 0 0
$$763$$ −48.0000 −1.73772
$$764$$ 4.00000 0.144715
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −16.0000 −0.577350
$$769$$ 6.00000 0.216366 0.108183 0.994131i $$-0.465497\pi$$
0.108183 + 0.994131i $$0.465497\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 8.00000 0.287926
$$773$$ 46.0000 1.65451 0.827253 0.561830i $$-0.189903\pi$$
0.827253 + 0.561830i $$0.189903\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −27.0000 −0.968620
$$778$$ 0 0
$$779$$ −56.0000 −2.00641
$$780$$ 0 0
$$781$$ 52.0000 1.86071
$$782$$ 0 0
$$783$$ −9.00000 −0.321634
$$784$$ 8.00000 0.285714
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 27.0000 0.962446 0.481223 0.876598i $$-0.340193\pi$$
0.481223 + 0.876598i $$0.340193\pi$$
$$788$$ 4.00000 0.142494
$$789$$ −23.0000 −0.818822
$$790$$ 0 0
$$791$$ −3.00000 −0.106668
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 36.0000 1.27599
$$797$$ −27.0000 −0.956389 −0.478195 0.878254i $$-0.658709\pi$$
−0.478195 + 0.878254i $$0.658709\pi$$
$$798$$ 0 0
$$799$$ 6.00000 0.212265
$$800$$ 0 0
$$801$$ −8.00000 −0.282666
$$802$$ 0 0
$$803$$ −16.0000 −0.564628
$$804$$ −26.0000 −0.916949
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 17.0000 0.598428
$$808$$ 0 0
$$809$$ −39.0000 −1.37117 −0.685583 0.727994i $$-0.740453\pi$$
−0.685583 + 0.727994i $$0.740453\pi$$
$$810$$ 0 0
$$811$$ −25.0000 −0.877869 −0.438934 0.898519i $$-0.644644\pi$$
−0.438934 + 0.898519i $$0.644644\pi$$
$$812$$ −54.0000 −1.89503
$$813$$ 23.0000 0.806645
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −12.0000 −0.420084
$$817$$ 32.0000 1.11954
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −10.0000 −0.349002 −0.174501 0.984657i $$-0.555831\pi$$
−0.174501 + 0.984657i $$0.555831\pi$$
$$822$$ 0 0
$$823$$ 16.0000 0.557725 0.278862 0.960331i $$-0.410043\pi$$
0.278862 + 0.960331i $$0.410043\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −37.0000 −1.28662 −0.643308 0.765607i $$-0.722439\pi$$
−0.643308 + 0.765607i $$0.722439\pi$$
$$828$$ 2.00000 0.0695048
$$829$$ −27.0000 −0.937749 −0.468874 0.883265i $$-0.655340\pi$$
−0.468874 + 0.883265i $$0.655340\pi$$
$$830$$ 0 0
$$831$$ 18.0000 0.624413
$$832$$ 0 0
$$833$$ 6.00000 0.207888
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −64.0000 −2.21349
$$837$$ 5.00000 0.172825
$$838$$ 0 0
$$839$$ −6.00000 −0.207143 −0.103572 0.994622i $$-0.533027\pi$$
−0.103572 + 0.994622i $$0.533027\pi$$
$$840$$ 0 0
$$841$$ 52.0000 1.79310
$$842$$ 0 0
$$843$$ −24.0000 −0.826604
$$844$$ −14.0000 −0.481900
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 15.0000 0.515406
$$848$$ −52.0000 −1.78569
$$849$$ −5.00000 −0.171600
$$850$$ 0 0
$$851$$ −9.00000 −0.308516
$$852$$ −26.0000 −0.890745
$$853$$ 46.0000 1.57501 0.787505 0.616308i $$-0.211372\pi$$
0.787505 + 0.616308i $$0.211372\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 18.0000 0.614868 0.307434 0.951569i $$-0.400530\pi$$
0.307434 + 0.951569i $$0.400530\pi$$
$$858$$ 0 0
$$859$$ 43.0000 1.46714 0.733571 0.679613i $$-0.237852\pi$$
0.733571 + 0.679613i $$0.237852\pi$$
$$860$$ 0 0
$$861$$ −21.0000 −0.715678
$$862$$ 0 0
$$863$$ −54.0000 −1.83818 −0.919091 0.394046i $$-0.871075\pi$$
−0.919091 + 0.394046i $$0.871075\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 8.00000 0.271694
$$868$$ 30.0000 1.01827
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −10.0000 −0.338449
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 8.00000 0.270295
$$877$$ 22.0000 0.742887 0.371444 0.928456i $$-0.378863\pi$$
0.371444 + 0.928456i $$0.378863\pi$$
$$878$$ 0 0
$$879$$ 19.0000 0.640854
$$880$$ 0 0
$$881$$ 30.0000 1.01073 0.505363 0.862907i $$-0.331359\pi$$
0.505363 + 0.862907i $$0.331359\pi$$
$$882$$ 0 0
$$883$$ 34.0000 1.14419 0.572096 0.820187i $$-0.306131\pi$$
0.572096 + 0.820187i $$0.306131\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 46.0000 1.54453 0.772264 0.635301i $$-0.219124\pi$$
0.772264 + 0.635301i $$0.219124\pi$$
$$888$$ 0 0
$$889$$ 54.0000 1.81110
$$890$$ 0 0
$$891$$ −4.00000 −0.134005
$$892$$ 20.0000 0.669650
$$893$$ −16.0000 −0.535420
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −45.0000 −1.50083
$$900$$ 0 0
$$901$$ −39.0000 −1.29928
$$902$$ 0 0
$$903$$ 12.0000 0.399335
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −53.0000 −1.75984 −0.879918 0.475125i $$-0.842403\pi$$
−0.879918 + 0.475125i $$0.842403\pi$$
$$908$$ −8.00000 −0.265489
$$909$$ 9.00000 0.298511
$$910$$ 0 0
$$911$$ −40.0000 −1.32526 −0.662630 0.748947i $$-0.730560\pi$$
−0.662630 + 0.748947i $$0.730560\pi$$
$$912$$ 32.0000 1.05963
$$913$$ −4.00000 −0.132381
$$914$$ 0 0
$$915$$ 0 0
$$916$$ −8.00000 −0.264327
$$917$$ −12.0000 −0.396275
$$918$$ 0 0
$$919$$ 24.0000 0.791687 0.395843 0.918318i $$-0.370452\pi$$
0.395843 + 0.918318i $$0.370452\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ −24.0000 −0.789542
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −8.00000 −0.262754
$$928$$ 0 0
$$929$$ 57.0000 1.87011 0.935055 0.354504i $$-0.115350\pi$$
0.935055 + 0.354504i $$0.115350\pi$$
$$930$$ 0 0
$$931$$ −16.0000 −0.524379
$$932$$ −16.0000 −0.524097
$$933$$ 8.00000 0.261908
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −10.0000 −0.326686 −0.163343 0.986569i $$-0.552228\pi$$
−0.163343 + 0.986569i $$0.552228\pi$$
$$938$$ 0 0
$$939$$ 25.0000 0.815844
$$940$$ 0 0
$$941$$ 10.0000 0.325991 0.162995 0.986627i $$-0.447884\pi$$
0.162995 + 0.986627i $$0.447884\pi$$
$$942$$ 0 0
$$943$$ −7.00000 −0.227951
$$944$$ −12.0000 −0.390567
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 8.00000 0.259965 0.129983 0.991516i $$-0.458508\pi$$
0.129983 + 0.991516i $$0.458508\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 30.0000 0.972817
$$952$$ 0 0
$$953$$ 22.0000 0.712650 0.356325 0.934362i $$-0.384030\pi$$
0.356325 + 0.934362i $$0.384030\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −26.0000 −0.840900
$$957$$ 36.0000 1.16371
$$958$$ 0 0
$$959$$ −6.00000 −0.193750
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ 0 0
$$963$$ −11.0000 −0.354470
$$964$$ −40.0000 −1.28831
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −10.0000 −0.321578 −0.160789 0.986989i $$-0.551404\pi$$
−0.160789 + 0.986989i $$0.551404\pi$$
$$968$$ 0 0
$$969$$ 24.0000 0.770991
$$970$$ 0 0
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 2.00000 0.0641500
$$973$$ −9.00000 −0.288527
$$974$$ 0 0
$$975$$ 0 0
$$976$$ −56.0000 −1.79252
$$977$$ 25.0000 0.799821 0.399910 0.916554i $$-0.369041\pi$$
0.399910 + 0.916554i $$0.369041\pi$$
$$978$$ 0 0
$$979$$ 32.0000 1.02272
$$980$$ 0 0
$$981$$ −16.0000 −0.510841
$$982$$ 0 0
$$983$$ −15.0000 −0.478426 −0.239213 0.970967i $$-0.576889\pi$$
−0.239213 + 0.970967i $$0.576889\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −6.00000 −0.190982
$$988$$ 0 0
$$989$$ 4.00000 0.127193
$$990$$ 0 0
$$991$$ −33.0000 −1.04828 −0.524140 0.851632i $$-0.675613\pi$$
−0.524140 + 0.851632i $$0.675613\pi$$
$$992$$ 0 0
$$993$$ −7.00000 −0.222138
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 2.00000 0.0633724
$$997$$ −8.00000 −0.253363 −0.126681 0.991943i $$-0.540433\pi$$
−0.126681 + 0.991943i $$0.540433\pi$$
$$998$$ 0 0
$$999$$ −9.00000 −0.284747
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 1725.2.a.k.1.1 1
3.2 odd 2 5175.2.a.o.1.1 1
5.2 odd 4 1725.2.b.j.1174.2 2
5.3 odd 4 1725.2.b.j.1174.1 2
5.4 even 2 345.2.a.d.1.1 1
15.14 odd 2 1035.2.a.d.1.1 1
20.19 odd 2 5520.2.a.h.1.1 1
115.114 odd 2 7935.2.a.i.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
345.2.a.d.1.1 1 5.4 even 2
1035.2.a.d.1.1 1 15.14 odd 2
1725.2.a.k.1.1 1 1.1 even 1 trivial
1725.2.b.j.1174.1 2 5.3 odd 4
1725.2.b.j.1174.2 2 5.2 odd 4
5175.2.a.o.1.1 1 3.2 odd 2
5520.2.a.h.1.1 1 20.19 odd 2
7935.2.a.i.1.1 1 115.114 odd 2