# Properties

 Label 1734.2.a.h.1.1 Level $1734$ Weight $2$ Character 1734.1 Self dual yes Analytic conductor $13.846$ 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] = [1734,2,Mod(1,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1734.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1734 = 2 \cdot 3 \cdot 17^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1734.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: $$13.8460597105$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 102) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1734.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{10} +1.00000 q^{12} -6.00000 q^{13} -2.00000 q^{14} +4.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.00000 q^{19} +4.00000 q^{20} +2.00000 q^{21} -6.00000 q^{23} -1.00000 q^{24} +11.0000 q^{25} +6.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} +4.00000 q^{29} -4.00000 q^{30} +6.00000 q^{31} -1.00000 q^{32} +8.00000 q^{35} +1.00000 q^{36} +4.00000 q^{37} -4.00000 q^{38} -6.00000 q^{39} -4.00000 q^{40} +10.0000 q^{41} -2.00000 q^{42} -4.00000 q^{43} +4.00000 q^{45} +6.00000 q^{46} +4.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -11.0000 q^{50} -6.00000 q^{52} -2.00000 q^{53} -1.00000 q^{54} -2.00000 q^{56} +4.00000 q^{57} -4.00000 q^{58} +12.0000 q^{59} +4.00000 q^{60} +4.00000 q^{61} -6.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -24.0000 q^{65} -12.0000 q^{67} -6.00000 q^{69} -8.00000 q^{70} +6.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -4.00000 q^{74} +11.0000 q^{75} +4.00000 q^{76} +6.00000 q^{78} -10.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} -12.0000 q^{83} +2.00000 q^{84} +4.00000 q^{86} +4.00000 q^{87} -2.00000 q^{89} -4.00000 q^{90} -12.0000 q^{91} -6.00000 q^{92} +6.00000 q^{93} -4.00000 q^{94} +16.0000 q^{95} -1.00000 q^{96} -6.00000 q^{97} +3.00000 q^{98} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 1.00000 0.577350
$$4$$ 1.00000 0.500000
$$5$$ 4.00000 1.78885 0.894427 0.447214i $$-0.147584\pi$$
0.894427 + 0.447214i $$0.147584\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ −4.00000 −1.26491
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −6.00000 −1.66410 −0.832050 0.554700i $$-0.812833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ −2.00000 −0.534522
$$15$$ 4.00000 1.03280
$$16$$ 1.00000 0.250000
$$17$$ 0 0
$$18$$ −1.00000 −0.235702
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 4.00000 0.894427
$$21$$ 2.00000 0.436436
$$22$$ 0 0
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 11.0000 2.20000
$$26$$ 6.00000 1.17670
$$27$$ 1.00000 0.192450
$$28$$ 2.00000 0.377964
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ −4.00000 −0.730297
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 8.00000 1.35225
$$36$$ 1.00000 0.166667
$$37$$ 4.00000 0.657596 0.328798 0.944400i $$-0.393356\pi$$
0.328798 + 0.944400i $$0.393356\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ −6.00000 −0.960769
$$40$$ −4.00000 −0.632456
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ −2.00000 −0.308607
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 4.00000 0.596285
$$46$$ 6.00000 0.884652
$$47$$ 4.00000 0.583460 0.291730 0.956501i $$-0.405769\pi$$
0.291730 + 0.956501i $$0.405769\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −3.00000 −0.428571
$$50$$ −11.0000 −1.55563
$$51$$ 0 0
$$52$$ −6.00000 −0.832050
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ −2.00000 −0.267261
$$57$$ 4.00000 0.529813
$$58$$ −4.00000 −0.525226
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ 4.00000 0.516398
$$61$$ 4.00000 0.512148 0.256074 0.966657i $$-0.417571\pi$$
0.256074 + 0.966657i $$0.417571\pi$$
$$62$$ −6.00000 −0.762001
$$63$$ 2.00000 0.251976
$$64$$ 1.00000 0.125000
$$65$$ −24.0000 −2.97683
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ −8.00000 −0.956183
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ −4.00000 −0.464991
$$75$$ 11.0000 1.27017
$$76$$ 4.00000 0.458831
$$77$$ 0 0
$$78$$ 6.00000 0.679366
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 4.00000 0.447214
$$81$$ 1.00000 0.111111
$$82$$ −10.0000 −1.10432
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 2.00000 0.218218
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ 4.00000 0.428845
$$88$$ 0 0
$$89$$ −2.00000 −0.212000 −0.106000 0.994366i $$-0.533804\pi$$
−0.106000 + 0.994366i $$0.533804\pi$$
$$90$$ −4.00000 −0.421637
$$91$$ −12.0000 −1.25794
$$92$$ −6.00000 −0.625543
$$93$$ 6.00000 0.622171
$$94$$ −4.00000 −0.412568
$$95$$ 16.0000 1.64157
$$96$$ −1.00000 −0.102062
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 3.00000 0.303046
$$99$$ 0 0
$$100$$ 11.0000 1.10000
$$101$$ 14.0000 1.39305 0.696526 0.717532i $$-0.254728\pi$$
0.696526 + 0.717532i $$0.254728\pi$$
$$102$$ 0 0
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 8.00000 0.780720
$$106$$ 2.00000 0.194257
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ 0 0
$$111$$ 4.00000 0.379663
$$112$$ 2.00000 0.188982
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ −4.00000 −0.374634
$$115$$ −24.0000 −2.23801
$$116$$ 4.00000 0.371391
$$117$$ −6.00000 −0.554700
$$118$$ −12.0000 −1.10469
$$119$$ 0 0
$$120$$ −4.00000 −0.365148
$$121$$ −11.0000 −1.00000
$$122$$ −4.00000 −0.362143
$$123$$ 10.0000 0.901670
$$124$$ 6.00000 0.538816
$$125$$ 24.0000 2.14663
$$126$$ −2.00000 −0.178174
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −4.00000 −0.352180
$$130$$ 24.0000 2.10494
$$131$$ 16.0000 1.39793 0.698963 0.715158i $$-0.253645\pi$$
0.698963 + 0.715158i $$0.253645\pi$$
$$132$$ 0 0
$$133$$ 8.00000 0.693688
$$134$$ 12.0000 1.03664
$$135$$ 4.00000 0.344265
$$136$$ 0 0
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 6.00000 0.510754
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ 8.00000 0.676123
$$141$$ 4.00000 0.336861
$$142$$ −6.00000 −0.503509
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 16.0000 1.32873
$$146$$ 2.00000 0.165521
$$147$$ −3.00000 −0.247436
$$148$$ 4.00000 0.328798
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ −11.0000 −0.898146
$$151$$ −24.0000 −1.95309 −0.976546 0.215308i $$-0.930924\pi$$
−0.976546 + 0.215308i $$0.930924\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 24.0000 1.92773
$$156$$ −6.00000 −0.480384
$$157$$ 6.00000 0.478852 0.239426 0.970915i $$-0.423041\pi$$
0.239426 + 0.970915i $$0.423041\pi$$
$$158$$ 10.0000 0.795557
$$159$$ −2.00000 −0.158610
$$160$$ −4.00000 −0.316228
$$161$$ −12.0000 −0.945732
$$162$$ −1.00000 −0.0785674
$$163$$ −12.0000 −0.939913 −0.469956 0.882690i $$-0.655730\pi$$
−0.469956 + 0.882690i $$0.655730\pi$$
$$164$$ 10.0000 0.780869
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ −2.00000 −0.154303
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ −4.00000 −0.304997
$$173$$ 4.00000 0.304114 0.152057 0.988372i $$-0.451410\pi$$
0.152057 + 0.988372i $$0.451410\pi$$
$$174$$ −4.00000 −0.303239
$$175$$ 22.0000 1.66304
$$176$$ 0 0
$$177$$ 12.0000 0.901975
$$178$$ 2.00000 0.149906
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 4.00000 0.298142
$$181$$ 20.0000 1.48659 0.743294 0.668965i $$-0.233262\pi$$
0.743294 + 0.668965i $$0.233262\pi$$
$$182$$ 12.0000 0.889499
$$183$$ 4.00000 0.295689
$$184$$ 6.00000 0.442326
$$185$$ 16.0000 1.17634
$$186$$ −6.00000 −0.439941
$$187$$ 0 0
$$188$$ 4.00000 0.291730
$$189$$ 2.00000 0.145479
$$190$$ −16.0000 −1.16076
$$191$$ −4.00000 −0.289430 −0.144715 0.989473i $$-0.546227\pi$$
−0.144715 + 0.989473i $$0.546227\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ 6.00000 0.430775
$$195$$ −24.0000 −1.71868
$$196$$ −3.00000 −0.214286
$$197$$ −8.00000 −0.569976 −0.284988 0.958531i $$-0.591990\pi$$
−0.284988 + 0.958531i $$0.591990\pi$$
$$198$$ 0 0
$$199$$ −14.0000 −0.992434 −0.496217 0.868199i $$-0.665278\pi$$
−0.496217 + 0.868199i $$0.665278\pi$$
$$200$$ −11.0000 −0.777817
$$201$$ −12.0000 −0.846415
$$202$$ −14.0000 −0.985037
$$203$$ 8.00000 0.561490
$$204$$ 0 0
$$205$$ 40.0000 2.79372
$$206$$ −4.00000 −0.278693
$$207$$ −6.00000 −0.417029
$$208$$ −6.00000 −0.416025
$$209$$ 0 0
$$210$$ −8.00000 −0.552052
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ −2.00000 −0.137361
$$213$$ 6.00000 0.411113
$$214$$ 0 0
$$215$$ −16.0000 −1.09119
$$216$$ −1.00000 −0.0680414
$$217$$ 12.0000 0.814613
$$218$$ 16.0000 1.08366
$$219$$ −2.00000 −0.135147
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −4.00000 −0.268462
$$223$$ −4.00000 −0.267860 −0.133930 0.990991i $$-0.542760\pi$$
−0.133930 + 0.990991i $$0.542760\pi$$
$$224$$ −2.00000 −0.133631
$$225$$ 11.0000 0.733333
$$226$$ 2.00000 0.133038
$$227$$ −4.00000 −0.265489 −0.132745 0.991150i $$-0.542379\pi$$
−0.132745 + 0.991150i $$0.542379\pi$$
$$228$$ 4.00000 0.264906
$$229$$ −2.00000 −0.132164 −0.0660819 0.997814i $$-0.521050\pi$$
−0.0660819 + 0.997814i $$0.521050\pi$$
$$230$$ 24.0000 1.58251
$$231$$ 0 0
$$232$$ −4.00000 −0.262613
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 6.00000 0.392232
$$235$$ 16.0000 1.04372
$$236$$ 12.0000 0.781133
$$237$$ −10.0000 −0.649570
$$238$$ 0 0
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 4.00000 0.258199
$$241$$ 18.0000 1.15948 0.579741 0.814801i $$-0.303154\pi$$
0.579741 + 0.814801i $$0.303154\pi$$
$$242$$ 11.0000 0.707107
$$243$$ 1.00000 0.0641500
$$244$$ 4.00000 0.256074
$$245$$ −12.0000 −0.766652
$$246$$ −10.0000 −0.637577
$$247$$ −24.0000 −1.52708
$$248$$ −6.00000 −0.381000
$$249$$ −12.0000 −0.760469
$$250$$ −24.0000 −1.51789
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 2.00000 0.125988
$$253$$ 0 0
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 4.00000 0.249029
$$259$$ 8.00000 0.497096
$$260$$ −24.0000 −1.48842
$$261$$ 4.00000 0.247594
$$262$$ −16.0000 −0.988483
$$263$$ −12.0000 −0.739952 −0.369976 0.929041i $$-0.620634\pi$$
−0.369976 + 0.929041i $$0.620634\pi$$
$$264$$ 0 0
$$265$$ −8.00000 −0.491436
$$266$$ −8.00000 −0.490511
$$267$$ −2.00000 −0.122398
$$268$$ −12.0000 −0.733017
$$269$$ 12.0000 0.731653 0.365826 0.930683i $$-0.380786\pi$$
0.365826 + 0.930683i $$0.380786\pi$$
$$270$$ −4.00000 −0.243432
$$271$$ −16.0000 −0.971931 −0.485965 0.873978i $$-0.661532\pi$$
−0.485965 + 0.873978i $$0.661532\pi$$
$$272$$ 0 0
$$273$$ −12.0000 −0.726273
$$274$$ 6.00000 0.362473
$$275$$ 0 0
$$276$$ −6.00000 −0.361158
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 6.00000 0.359211
$$280$$ −8.00000 −0.478091
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ −4.00000 −0.238197
$$283$$ −32.0000 −1.90220 −0.951101 0.308879i $$-0.900046\pi$$
−0.951101 + 0.308879i $$0.900046\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 16.0000 0.947758
$$286$$ 0 0
$$287$$ 20.0000 1.18056
$$288$$ −1.00000 −0.0589256
$$289$$ 0 0
$$290$$ −16.0000 −0.939552
$$291$$ −6.00000 −0.351726
$$292$$ −2.00000 −0.117041
$$293$$ 2.00000 0.116841 0.0584206 0.998292i $$-0.481394\pi$$
0.0584206 + 0.998292i $$0.481394\pi$$
$$294$$ 3.00000 0.174964
$$295$$ 48.0000 2.79467
$$296$$ −4.00000 −0.232495
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 36.0000 2.08193
$$300$$ 11.0000 0.635085
$$301$$ −8.00000 −0.461112
$$302$$ 24.0000 1.38104
$$303$$ 14.0000 0.804279
$$304$$ 4.00000 0.229416
$$305$$ 16.0000 0.916157
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ 4.00000 0.227552
$$310$$ −24.0000 −1.36311
$$311$$ −30.0000 −1.70114 −0.850572 0.525859i $$-0.823744\pi$$
−0.850572 + 0.525859i $$0.823744\pi$$
$$312$$ 6.00000 0.339683
$$313$$ 26.0000 1.46961 0.734803 0.678280i $$-0.237274\pi$$
0.734803 + 0.678280i $$0.237274\pi$$
$$314$$ −6.00000 −0.338600
$$315$$ 8.00000 0.450749
$$316$$ −10.0000 −0.562544
$$317$$ 16.0000 0.898650 0.449325 0.893368i $$-0.351665\pi$$
0.449325 + 0.893368i $$0.351665\pi$$
$$318$$ 2.00000 0.112154
$$319$$ 0 0
$$320$$ 4.00000 0.223607
$$321$$ 0 0
$$322$$ 12.0000 0.668734
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ −66.0000 −3.66102
$$326$$ 12.0000 0.664619
$$327$$ −16.0000 −0.884802
$$328$$ −10.0000 −0.552158
$$329$$ 8.00000 0.441054
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 4.00000 0.219199
$$334$$ −2.00000 −0.109435
$$335$$ −48.0000 −2.62252
$$336$$ 2.00000 0.109109
$$337$$ 6.00000 0.326841 0.163420 0.986557i $$-0.447747\pi$$
0.163420 + 0.986557i $$0.447747\pi$$
$$338$$ −23.0000 −1.25104
$$339$$ −2.00000 −0.108625
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −4.00000 −0.216295
$$343$$ −20.0000 −1.07990
$$344$$ 4.00000 0.215666
$$345$$ −24.0000 −1.29212
$$346$$ −4.00000 −0.215041
$$347$$ 4.00000 0.214731 0.107366 0.994220i $$-0.465758\pi$$
0.107366 + 0.994220i $$0.465758\pi$$
$$348$$ 4.00000 0.214423
$$349$$ −30.0000 −1.60586 −0.802932 0.596071i $$-0.796728\pi$$
−0.802932 + 0.596071i $$0.796728\pi$$
$$350$$ −22.0000 −1.17595
$$351$$ −6.00000 −0.320256
$$352$$ 0 0
$$353$$ 14.0000 0.745145 0.372572 0.928003i $$-0.378476\pi$$
0.372572 + 0.928003i $$0.378476\pi$$
$$354$$ −12.0000 −0.637793
$$355$$ 24.0000 1.27379
$$356$$ −2.00000 −0.106000
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ −4.00000 −0.210819
$$361$$ −3.00000 −0.157895
$$362$$ −20.0000 −1.05118
$$363$$ −11.0000 −0.577350
$$364$$ −12.0000 −0.628971
$$365$$ −8.00000 −0.418739
$$366$$ −4.00000 −0.209083
$$367$$ −10.0000 −0.521996 −0.260998 0.965339i $$-0.584052\pi$$
−0.260998 + 0.965339i $$0.584052\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 10.0000 0.520579
$$370$$ −16.0000 −0.831800
$$371$$ −4.00000 −0.207670
$$372$$ 6.00000 0.311086
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 0 0
$$375$$ 24.0000 1.23935
$$376$$ −4.00000 −0.206284
$$377$$ −24.0000 −1.23606
$$378$$ −2.00000 −0.102869
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 16.0000 0.820783
$$381$$ 8.00000 0.409852
$$382$$ 4.00000 0.204658
$$383$$ 28.0000 1.43073 0.715367 0.698749i $$-0.246260\pi$$
0.715367 + 0.698749i $$0.246260\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ 6.00000 0.305392
$$387$$ −4.00000 −0.203331
$$388$$ −6.00000 −0.304604
$$389$$ −14.0000 −0.709828 −0.354914 0.934899i $$-0.615490\pi$$
−0.354914 + 0.934899i $$0.615490\pi$$
$$390$$ 24.0000 1.21529
$$391$$ 0 0
$$392$$ 3.00000 0.151523
$$393$$ 16.0000 0.807093
$$394$$ 8.00000 0.403034
$$395$$ −40.0000 −2.01262
$$396$$ 0 0
$$397$$ −20.0000 −1.00377 −0.501886 0.864934i $$-0.667360\pi$$
−0.501886 + 0.864934i $$0.667360\pi$$
$$398$$ 14.0000 0.701757
$$399$$ 8.00000 0.400501
$$400$$ 11.0000 0.550000
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 12.0000 0.598506
$$403$$ −36.0000 −1.79329
$$404$$ 14.0000 0.696526
$$405$$ 4.00000 0.198762
$$406$$ −8.00000 −0.397033
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ −40.0000 −1.97546
$$411$$ −6.00000 −0.295958
$$412$$ 4.00000 0.197066
$$413$$ 24.0000 1.18096
$$414$$ 6.00000 0.294884
$$415$$ −48.0000 −2.35623
$$416$$ 6.00000 0.294174
$$417$$ −8.00000 −0.391762
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 8.00000 0.390360
$$421$$ 34.0000 1.65706 0.828529 0.559946i $$-0.189178\pi$$
0.828529 + 0.559946i $$0.189178\pi$$
$$422$$ 8.00000 0.389434
$$423$$ 4.00000 0.194487
$$424$$ 2.00000 0.0971286
$$425$$ 0 0
$$426$$ −6.00000 −0.290701
$$427$$ 8.00000 0.387147
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 16.0000 0.771589
$$431$$ −14.0000 −0.674356 −0.337178 0.941441i $$-0.609472\pi$$
−0.337178 + 0.941441i $$0.609472\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −18.0000 −0.865025 −0.432512 0.901628i $$-0.642373\pi$$
−0.432512 + 0.901628i $$0.642373\pi$$
$$434$$ −12.0000 −0.576018
$$435$$ 16.0000 0.767141
$$436$$ −16.0000 −0.766261
$$437$$ −24.0000 −1.14808
$$438$$ 2.00000 0.0955637
$$439$$ 10.0000 0.477274 0.238637 0.971109i $$-0.423299\pi$$
0.238637 + 0.971109i $$0.423299\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ 12.0000 0.570137 0.285069 0.958507i $$-0.407984\pi$$
0.285069 + 0.958507i $$0.407984\pi$$
$$444$$ 4.00000 0.189832
$$445$$ −8.00000 −0.379236
$$446$$ 4.00000 0.189405
$$447$$ −6.00000 −0.283790
$$448$$ 2.00000 0.0944911
$$449$$ 26.0000 1.22702 0.613508 0.789689i $$-0.289758\pi$$
0.613508 + 0.789689i $$0.289758\pi$$
$$450$$ −11.0000 −0.518545
$$451$$ 0 0
$$452$$ −2.00000 −0.0940721
$$453$$ −24.0000 −1.12762
$$454$$ 4.00000 0.187729
$$455$$ −48.0000 −2.25027
$$456$$ −4.00000 −0.187317
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 2.00000 0.0934539
$$459$$ 0 0
$$460$$ −24.0000 −1.11901
$$461$$ −10.0000 −0.465746 −0.232873 0.972507i $$-0.574813\pi$$
−0.232873 + 0.972507i $$0.574813\pi$$
$$462$$ 0 0
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 4.00000 0.185695
$$465$$ 24.0000 1.11297
$$466$$ −6.00000 −0.277945
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ −6.00000 −0.277350
$$469$$ −24.0000 −1.10822
$$470$$ −16.0000 −0.738025
$$471$$ 6.00000 0.276465
$$472$$ −12.0000 −0.552345
$$473$$ 0 0
$$474$$ 10.0000 0.459315
$$475$$ 44.0000 2.01886
$$476$$ 0 0
$$477$$ −2.00000 −0.0915737
$$478$$ 20.0000 0.914779
$$479$$ −10.0000 −0.456912 −0.228456 0.973554i $$-0.573368\pi$$
−0.228456 + 0.973554i $$0.573368\pi$$
$$480$$ −4.00000 −0.182574
$$481$$ −24.0000 −1.09431
$$482$$ −18.0000 −0.819878
$$483$$ −12.0000 −0.546019
$$484$$ −11.0000 −0.500000
$$485$$ −24.0000 −1.08978
$$486$$ −1.00000 −0.0453609
$$487$$ 38.0000 1.72194 0.860972 0.508652i $$-0.169856\pi$$
0.860972 + 0.508652i $$0.169856\pi$$
$$488$$ −4.00000 −0.181071
$$489$$ −12.0000 −0.542659
$$490$$ 12.0000 0.542105
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 10.0000 0.450835
$$493$$ 0 0
$$494$$ 24.0000 1.07981
$$495$$ 0 0
$$496$$ 6.00000 0.269408
$$497$$ 12.0000 0.538274
$$498$$ 12.0000 0.537733
$$499$$ −32.0000 −1.43252 −0.716258 0.697835i $$-0.754147\pi$$
−0.716258 + 0.697835i $$0.754147\pi$$
$$500$$ 24.0000 1.07331
$$501$$ 2.00000 0.0893534
$$502$$ −12.0000 −0.535586
$$503$$ 26.0000 1.15928 0.579641 0.814872i $$-0.303193\pi$$
0.579641 + 0.814872i $$0.303193\pi$$
$$504$$ −2.00000 −0.0890871
$$505$$ 56.0000 2.49197
$$506$$ 0 0
$$507$$ 23.0000 1.02147
$$508$$ 8.00000 0.354943
$$509$$ 26.0000 1.15243 0.576215 0.817298i $$-0.304529\pi$$
0.576215 + 0.817298i $$0.304529\pi$$
$$510$$ 0 0
$$511$$ −4.00000 −0.176950
$$512$$ −1.00000 −0.0441942
$$513$$ 4.00000 0.176604
$$514$$ −18.0000 −0.793946
$$515$$ 16.0000 0.705044
$$516$$ −4.00000 −0.176090
$$517$$ 0 0
$$518$$ −8.00000 −0.351500
$$519$$ 4.00000 0.175581
$$520$$ 24.0000 1.05247
$$521$$ 10.0000 0.438108 0.219054 0.975713i $$-0.429703\pi$$
0.219054 + 0.975713i $$0.429703\pi$$
$$522$$ −4.00000 −0.175075
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 16.0000 0.698963
$$525$$ 22.0000 0.960159
$$526$$ 12.0000 0.523225
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 8.00000 0.347498
$$531$$ 12.0000 0.520756
$$532$$ 8.00000 0.346844
$$533$$ −60.0000 −2.59889
$$534$$ 2.00000 0.0865485
$$535$$ 0 0
$$536$$ 12.0000 0.518321
$$537$$ −12.0000 −0.517838
$$538$$ −12.0000 −0.517357
$$539$$ 0 0
$$540$$ 4.00000 0.172133
$$541$$ 12.0000 0.515920 0.257960 0.966156i $$-0.416950\pi$$
0.257960 + 0.966156i $$0.416950\pi$$
$$542$$ 16.0000 0.687259
$$543$$ 20.0000 0.858282
$$544$$ 0 0
$$545$$ −64.0000 −2.74146
$$546$$ 12.0000 0.513553
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 4.00000 0.170716
$$550$$ 0 0
$$551$$ 16.0000 0.681623
$$552$$ 6.00000 0.255377
$$553$$ −20.0000 −0.850487
$$554$$ −8.00000 −0.339887
$$555$$ 16.0000 0.679162
$$556$$ −8.00000 −0.339276
$$557$$ 14.0000 0.593199 0.296600 0.955002i $$-0.404147\pi$$
0.296600 + 0.955002i $$0.404147\pi$$
$$558$$ −6.00000 −0.254000
$$559$$ 24.0000 1.01509
$$560$$ 8.00000 0.338062
$$561$$ 0 0
$$562$$ 18.0000 0.759284
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 4.00000 0.168430
$$565$$ −8.00000 −0.336563
$$566$$ 32.0000 1.34506
$$567$$ 2.00000 0.0839921
$$568$$ −6.00000 −0.251754
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ −16.0000 −0.670166
$$571$$ −44.0000 −1.84134 −0.920671 0.390339i $$-0.872358\pi$$
−0.920671 + 0.390339i $$0.872358\pi$$
$$572$$ 0 0
$$573$$ −4.00000 −0.167102
$$574$$ −20.0000 −0.834784
$$575$$ −66.0000 −2.75239
$$576$$ 1.00000 0.0416667
$$577$$ −30.0000 −1.24892 −0.624458 0.781058i $$-0.714680\pi$$
−0.624458 + 0.781058i $$0.714680\pi$$
$$578$$ 0 0
$$579$$ −6.00000 −0.249351
$$580$$ 16.0000 0.664364
$$581$$ −24.0000 −0.995688
$$582$$ 6.00000 0.248708
$$583$$ 0 0
$$584$$ 2.00000 0.0827606
$$585$$ −24.0000 −0.992278
$$586$$ −2.00000 −0.0826192
$$587$$ 36.0000 1.48588 0.742940 0.669359i $$-0.233431\pi$$
0.742940 + 0.669359i $$0.233431\pi$$
$$588$$ −3.00000 −0.123718
$$589$$ 24.0000 0.988903
$$590$$ −48.0000 −1.97613
$$591$$ −8.00000 −0.329076
$$592$$ 4.00000 0.164399
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −14.0000 −0.572982
$$598$$ −36.0000 −1.47215
$$599$$ −16.0000 −0.653742 −0.326871 0.945069i $$-0.605994\pi$$
−0.326871 + 0.945069i $$0.605994\pi$$
$$600$$ −11.0000 −0.449073
$$601$$ 38.0000 1.55005 0.775026 0.631929i $$-0.217737\pi$$
0.775026 + 0.631929i $$0.217737\pi$$
$$602$$ 8.00000 0.326056
$$603$$ −12.0000 −0.488678
$$604$$ −24.0000 −0.976546
$$605$$ −44.0000 −1.78885
$$606$$ −14.0000 −0.568711
$$607$$ 38.0000 1.54237 0.771186 0.636610i $$-0.219664\pi$$
0.771186 + 0.636610i $$0.219664\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 8.00000 0.324176
$$610$$ −16.0000 −0.647821
$$611$$ −24.0000 −0.970936
$$612$$ 0 0
$$613$$ 30.0000 1.21169 0.605844 0.795583i $$-0.292835\pi$$
0.605844 + 0.795583i $$0.292835\pi$$
$$614$$ 12.0000 0.484281
$$615$$ 40.0000 1.61296
$$616$$ 0 0
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ −4.00000 −0.160904
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 24.0000 0.963863
$$621$$ −6.00000 −0.240772
$$622$$ 30.0000 1.20289
$$623$$ −4.00000 −0.160257
$$624$$ −6.00000 −0.240192
$$625$$ 41.0000 1.64000
$$626$$ −26.0000 −1.03917
$$627$$ 0 0
$$628$$ 6.00000 0.239426
$$629$$ 0 0
$$630$$ −8.00000 −0.318728
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ 10.0000 0.397779
$$633$$ −8.00000 −0.317971
$$634$$ −16.0000 −0.635441
$$635$$ 32.0000 1.26988
$$636$$ −2.00000 −0.0793052
$$637$$ 18.0000 0.713186
$$638$$ 0 0
$$639$$ 6.00000 0.237356
$$640$$ −4.00000 −0.158114
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ −12.0000 −0.472866
$$645$$ −16.0000 −0.629999
$$646$$ 0 0
$$647$$ 28.0000 1.10079 0.550397 0.834903i $$-0.314476\pi$$
0.550397 + 0.834903i $$0.314476\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 0 0
$$650$$ 66.0000 2.58873
$$651$$ 12.0000 0.470317
$$652$$ −12.0000 −0.469956
$$653$$ −20.0000 −0.782660 −0.391330 0.920250i $$-0.627985\pi$$
−0.391330 + 0.920250i $$0.627985\pi$$
$$654$$ 16.0000 0.625650
$$655$$ 64.0000 2.50069
$$656$$ 10.0000 0.390434
$$657$$ −2.00000 −0.0780274
$$658$$ −8.00000 −0.311872
$$659$$ 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 $$0.587774\pi$$
$$662$$ −20.0000 −0.777322
$$663$$ 0 0
$$664$$ 12.0000 0.465690
$$665$$ 32.0000 1.24091
$$666$$ −4.00000 −0.154997
$$667$$ −24.0000 −0.929284
$$668$$ 2.00000 0.0773823
$$669$$ −4.00000 −0.154649
$$670$$ 48.0000 1.85440
$$671$$ 0 0
$$672$$ −2.00000 −0.0771517
$$673$$ 26.0000 1.00223 0.501113 0.865382i $$-0.332924\pi$$
0.501113 + 0.865382i $$0.332924\pi$$
$$674$$ −6.00000 −0.231111
$$675$$ 11.0000 0.423390
$$676$$ 23.0000 0.884615
$$677$$ −8.00000 −0.307465 −0.153732 0.988113i $$-0.549129\pi$$
−0.153732 + 0.988113i $$0.549129\pi$$
$$678$$ 2.00000 0.0768095
$$679$$ −12.0000 −0.460518
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 4.00000 0.152944
$$685$$ −24.0000 −0.916993
$$686$$ 20.0000 0.763604
$$687$$ −2.00000 −0.0763048
$$688$$ −4.00000 −0.152499
$$689$$ 12.0000 0.457164
$$690$$ 24.0000 0.913664
$$691$$ −16.0000 −0.608669 −0.304334 0.952565i $$-0.598434\pi$$
−0.304334 + 0.952565i $$0.598434\pi$$
$$692$$ 4.00000 0.152057
$$693$$ 0 0
$$694$$ −4.00000 −0.151838
$$695$$ −32.0000 −1.21383
$$696$$ −4.00000 −0.151620
$$697$$ 0 0
$$698$$ 30.0000 1.13552
$$699$$ 6.00000 0.226941
$$700$$ 22.0000 0.831522
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 6.00000 0.226455
$$703$$ 16.0000 0.603451
$$704$$ 0 0
$$705$$ 16.0000 0.602595
$$706$$ −14.0000 −0.526897
$$707$$ 28.0000 1.05305
$$708$$ 12.0000 0.450988
$$709$$ 16.0000 0.600893 0.300446 0.953799i $$-0.402864\pi$$
0.300446 + 0.953799i $$0.402864\pi$$
$$710$$ −24.0000 −0.900704
$$711$$ −10.0000 −0.375029
$$712$$ 2.00000 0.0749532
$$713$$ −36.0000 −1.34821
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −12.0000 −0.448461
$$717$$ −20.0000 −0.746914
$$718$$ 0 0
$$719$$ −42.0000 −1.56634 −0.783168 0.621810i $$-0.786397\pi$$
−0.783168 + 0.621810i $$0.786397\pi$$
$$720$$ 4.00000 0.149071
$$721$$ 8.00000 0.297936
$$722$$ 3.00000 0.111648
$$723$$ 18.0000 0.669427
$$724$$ 20.0000 0.743294
$$725$$ 44.0000 1.63412
$$726$$ 11.0000 0.408248
$$727$$ −8.00000 −0.296704 −0.148352 0.988935i $$-0.547397\pi$$
−0.148352 + 0.988935i $$0.547397\pi$$
$$728$$ 12.0000 0.444750
$$729$$ 1.00000 0.0370370
$$730$$ 8.00000 0.296093
$$731$$ 0 0
$$732$$ 4.00000 0.147844
$$733$$ 18.0000 0.664845 0.332423 0.943131i $$-0.392134\pi$$
0.332423 + 0.943131i $$0.392134\pi$$
$$734$$ 10.0000 0.369107
$$735$$ −12.0000 −0.442627
$$736$$ 6.00000 0.221163
$$737$$ 0 0
$$738$$ −10.0000 −0.368105
$$739$$ −12.0000 −0.441427 −0.220714 0.975339i $$-0.570839\pi$$
−0.220714 + 0.975339i $$0.570839\pi$$
$$740$$ 16.0000 0.588172
$$741$$ −24.0000 −0.881662
$$742$$ 4.00000 0.146845
$$743$$ −38.0000 −1.39408 −0.697042 0.717030i $$-0.745501\pi$$
−0.697042 + 0.717030i $$0.745501\pi$$
$$744$$ −6.00000 −0.219971
$$745$$ −24.0000 −0.879292
$$746$$ 14.0000 0.512576
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −24.0000 −0.876356
$$751$$ 34.0000 1.24068 0.620339 0.784334i $$-0.286995\pi$$
0.620339 + 0.784334i $$0.286995\pi$$
$$752$$ 4.00000 0.145865
$$753$$ 12.0000 0.437304
$$754$$ 24.0000 0.874028
$$755$$ −96.0000 −3.49380
$$756$$ 2.00000 0.0727393
$$757$$ 14.0000 0.508839 0.254419 0.967094i $$-0.418116\pi$$
0.254419 + 0.967094i $$0.418116\pi$$
$$758$$ −4.00000 −0.145287
$$759$$ 0 0
$$760$$ −16.0000 −0.580381
$$761$$ 10.0000 0.362500 0.181250 0.983437i $$-0.441986\pi$$
0.181250 + 0.983437i $$0.441986\pi$$
$$762$$ −8.00000 −0.289809
$$763$$ −32.0000 −1.15848
$$764$$ −4.00000 −0.144715
$$765$$ 0 0
$$766$$ −28.0000 −1.01168
$$767$$ −72.0000 −2.59977
$$768$$ 1.00000 0.0360844
$$769$$ 26.0000 0.937584 0.468792 0.883309i $$-0.344689\pi$$
0.468792 + 0.883309i $$0.344689\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ −6.00000 −0.215945
$$773$$ 42.0000 1.51064 0.755318 0.655359i $$-0.227483\pi$$
0.755318 + 0.655359i $$0.227483\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 66.0000 2.37079
$$776$$ 6.00000 0.215387
$$777$$ 8.00000 0.286998
$$778$$ 14.0000 0.501924
$$779$$ 40.0000 1.43315
$$780$$ −24.0000 −0.859338
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 4.00000 0.142948
$$784$$ −3.00000 −0.107143
$$785$$ 24.0000 0.856597
$$786$$ −16.0000 −0.570701
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ −8.00000 −0.284988
$$789$$ −12.0000 −0.427211
$$790$$ 40.0000 1.42314
$$791$$ −4.00000 −0.142224
$$792$$ 0 0
$$793$$ −24.0000 −0.852265
$$794$$ 20.0000 0.709773
$$795$$ −8.00000 −0.283731
$$796$$ −14.0000 −0.496217
$$797$$ 46.0000 1.62940 0.814702 0.579880i $$-0.196901\pi$$
0.814702 + 0.579880i $$0.196901\pi$$
$$798$$ −8.00000 −0.283197
$$799$$ 0 0
$$800$$ −11.0000 −0.388909
$$801$$ −2.00000 −0.0706665
$$802$$ 30.0000 1.05934
$$803$$ 0 0
$$804$$ −12.0000 −0.423207
$$805$$ −48.0000 −1.69178
$$806$$ 36.0000 1.26805
$$807$$ 12.0000 0.422420
$$808$$ −14.0000 −0.492518
$$809$$ 26.0000 0.914111 0.457056 0.889438i $$-0.348904\pi$$
0.457056 + 0.889438i $$0.348904\pi$$
$$810$$ −4.00000 −0.140546
$$811$$ 12.0000 0.421377 0.210688 0.977553i $$-0.432429\pi$$
0.210688 + 0.977553i $$0.432429\pi$$
$$812$$ 8.00000 0.280745
$$813$$ −16.0000 −0.561144
$$814$$ 0 0
$$815$$ −48.0000 −1.68137
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ 26.0000 0.909069
$$819$$ −12.0000 −0.419314
$$820$$ 40.0000 1.39686
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 6.00000 0.209274
$$823$$ −18.0000 −0.627441 −0.313720 0.949515i $$-0.601575\pi$$
−0.313720 + 0.949515i $$0.601575\pi$$
$$824$$ −4.00000 −0.139347
$$825$$ 0 0
$$826$$ −24.0000 −0.835067
$$827$$ −16.0000 −0.556375 −0.278187 0.960527i $$-0.589734\pi$$
−0.278187 + 0.960527i $$0.589734\pi$$
$$828$$ −6.00000 −0.208514
$$829$$ 6.00000 0.208389 0.104194 0.994557i $$-0.466774\pi$$
0.104194 + 0.994557i $$0.466774\pi$$
$$830$$ 48.0000 1.66610
$$831$$ 8.00000 0.277517
$$832$$ −6.00000 −0.208013
$$833$$ 0 0
$$834$$ 8.00000 0.277017
$$835$$ 8.00000 0.276851
$$836$$ 0 0
$$837$$ 6.00000 0.207390
$$838$$ −12.0000 −0.414533
$$839$$ 30.0000 1.03572 0.517858 0.855467i $$-0.326730\pi$$
0.517858 + 0.855467i $$0.326730\pi$$
$$840$$ −8.00000 −0.276026
$$841$$ −13.0000 −0.448276
$$842$$ −34.0000 −1.17172
$$843$$ −18.0000 −0.619953
$$844$$ −8.00000 −0.275371
$$845$$ 92.0000 3.16490
$$846$$ −4.00000 −0.137523
$$847$$ −22.0000 −0.755929
$$848$$ −2.00000 −0.0686803
$$849$$ −32.0000 −1.09824
$$850$$ 0 0
$$851$$ −24.0000 −0.822709
$$852$$ 6.00000 0.205557
$$853$$ 16.0000 0.547830 0.273915 0.961754i $$-0.411681\pi$$
0.273915 + 0.961754i $$0.411681\pi$$
$$854$$ −8.00000 −0.273754
$$855$$ 16.0000 0.547188
$$856$$ 0 0
$$857$$ 10.0000 0.341593 0.170797 0.985306i $$-0.445366\pi$$
0.170797 + 0.985306i $$0.445366\pi$$
$$858$$ 0 0
$$859$$ 20.0000 0.682391 0.341196 0.939992i $$-0.389168\pi$$
0.341196 + 0.939992i $$0.389168\pi$$
$$860$$ −16.0000 −0.545595
$$861$$ 20.0000 0.681598
$$862$$ 14.0000 0.476842
$$863$$ −48.0000 −1.63394 −0.816970 0.576681i $$-0.804348\pi$$
−0.816970 + 0.576681i $$0.804348\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 16.0000 0.544016
$$866$$ 18.0000 0.611665
$$867$$ 0 0
$$868$$ 12.0000 0.407307
$$869$$ 0 0
$$870$$ −16.0000 −0.542451
$$871$$ 72.0000 2.43963
$$872$$ 16.0000 0.541828
$$873$$ −6.00000 −0.203069
$$874$$ 24.0000 0.811812
$$875$$ 48.0000 1.62270
$$876$$ −2.00000 −0.0675737
$$877$$ 24.0000 0.810422 0.405211 0.914223i $$-0.367198\pi$$
0.405211 + 0.914223i $$0.367198\pi$$
$$878$$ −10.0000 −0.337484
$$879$$ 2.00000 0.0674583
$$880$$ 0 0
$$881$$ −50.0000 −1.68454 −0.842271 0.539054i $$-0.818782\pi$$
−0.842271 + 0.539054i $$0.818782\pi$$
$$882$$ 3.00000 0.101015
$$883$$ −52.0000 −1.74994 −0.874970 0.484178i $$-0.839119\pi$$
−0.874970 + 0.484178i $$0.839119\pi$$
$$884$$ 0 0
$$885$$ 48.0000 1.61350
$$886$$ −12.0000 −0.403148
$$887$$ −18.0000 −0.604381 −0.302190 0.953248i $$-0.597718\pi$$
−0.302190 + 0.953248i $$0.597718\pi$$
$$888$$ −4.00000 −0.134231
$$889$$ 16.0000 0.536623
$$890$$ 8.00000 0.268161
$$891$$ 0 0
$$892$$ −4.00000 −0.133930
$$893$$ 16.0000 0.535420
$$894$$ 6.00000 0.200670
$$895$$ −48.0000 −1.60446
$$896$$ −2.00000 −0.0668153
$$897$$ 36.0000 1.20201
$$898$$ −26.0000 −0.867631
$$899$$ 24.0000 0.800445
$$900$$ 11.0000 0.366667
$$901$$ 0 0
$$902$$ 0 0
$$903$$ −8.00000 −0.266223
$$904$$ 2.00000 0.0665190
$$905$$ 80.0000 2.65929
$$906$$ 24.0000 0.797347
$$907$$ −24.0000 −0.796907 −0.398453 0.917189i $$-0.630453\pi$$
−0.398453 + 0.917189i $$0.630453\pi$$
$$908$$ −4.00000 −0.132745
$$909$$ 14.0000 0.464351
$$910$$ 48.0000 1.59118
$$911$$ −26.0000 −0.861418 −0.430709 0.902491i $$-0.641737\pi$$
−0.430709 + 0.902491i $$0.641737\pi$$
$$912$$ 4.00000 0.132453
$$913$$ 0 0
$$914$$ −22.0000 −0.727695
$$915$$ 16.0000 0.528944
$$916$$ −2.00000 −0.0660819
$$917$$ 32.0000 1.05673
$$918$$ 0 0
$$919$$ 16.0000 0.527791 0.263896 0.964551i $$-0.414993\pi$$
0.263896 + 0.964551i $$0.414993\pi$$
$$920$$ 24.0000 0.791257
$$921$$ −12.0000 −0.395413
$$922$$ 10.0000 0.329332
$$923$$ −36.0000 −1.18495
$$924$$ 0 0
$$925$$ 44.0000 1.44671
$$926$$ 4.00000 0.131448
$$927$$ 4.00000 0.131377
$$928$$ −4.00000 −0.131306
$$929$$ 34.0000 1.11550 0.557752 0.830008i $$-0.311664\pi$$
0.557752 + 0.830008i $$0.311664\pi$$
$$930$$ −24.0000 −0.786991
$$931$$ −12.0000 −0.393284
$$932$$ 6.00000 0.196537
$$933$$ −30.0000 −0.982156
$$934$$ 36.0000 1.17796
$$935$$ 0 0
$$936$$ 6.00000 0.196116
$$937$$ 22.0000 0.718709 0.359354 0.933201i $$-0.382997\pi$$
0.359354 + 0.933201i $$0.382997\pi$$
$$938$$ 24.0000 0.783628
$$939$$ 26.0000 0.848478
$$940$$ 16.0000 0.521862
$$941$$ −48.0000 −1.56476 −0.782378 0.622804i $$-0.785993\pi$$
−0.782378 + 0.622804i $$0.785993\pi$$
$$942$$ −6.00000 −0.195491
$$943$$ −60.0000 −1.95387
$$944$$ 12.0000 0.390567
$$945$$ 8.00000 0.260240
$$946$$ 0 0
$$947$$ 24.0000 0.779895 0.389948 0.920837i $$-0.372493\pi$$
0.389948 + 0.920837i $$0.372493\pi$$
$$948$$ −10.0000 −0.324785
$$949$$ 12.0000 0.389536
$$950$$ −44.0000 −1.42755
$$951$$ 16.0000 0.518836
$$952$$ 0 0
$$953$$ 22.0000 0.712650 0.356325 0.934362i $$-0.384030\pi$$
0.356325 + 0.934362i $$0.384030\pi$$
$$954$$ 2.00000 0.0647524
$$955$$ −16.0000 −0.517748
$$956$$ −20.0000 −0.646846
$$957$$ 0 0
$$958$$ 10.0000 0.323085
$$959$$ −12.0000 −0.387500
$$960$$ 4.00000 0.129099
$$961$$ 5.00000 0.161290
$$962$$ 24.0000 0.773791
$$963$$ 0 0
$$964$$ 18.0000 0.579741
$$965$$ −24.0000 −0.772587
$$966$$ 12.0000 0.386094
$$967$$ −44.0000 −1.41494 −0.707472 0.706741i $$-0.750165\pi$$
−0.707472 + 0.706741i $$0.750165\pi$$
$$968$$ 11.0000 0.353553
$$969$$ 0 0
$$970$$ 24.0000 0.770594
$$971$$ 20.0000 0.641831 0.320915 0.947108i $$-0.396010\pi$$
0.320915 + 0.947108i $$0.396010\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ −16.0000 −0.512936
$$974$$ −38.0000 −1.21760
$$975$$ −66.0000 −2.11369
$$976$$ 4.00000 0.128037
$$977$$ 2.00000 0.0639857 0.0319928 0.999488i $$-0.489815\pi$$
0.0319928 + 0.999488i $$0.489815\pi$$
$$978$$ 12.0000 0.383718
$$979$$ 0 0
$$980$$ −12.0000 −0.383326
$$981$$ −16.0000 −0.510841
$$982$$ 20.0000 0.638226
$$983$$ 38.0000 1.21201 0.606006 0.795460i $$-0.292771\pi$$
0.606006 + 0.795460i $$0.292771\pi$$
$$984$$ −10.0000 −0.318788
$$985$$ −32.0000 −1.01960
$$986$$ 0 0
$$987$$ 8.00000 0.254643
$$988$$ −24.0000 −0.763542
$$989$$ 24.0000 0.763156
$$990$$ 0 0
$$991$$ 34.0000 1.08005 0.540023 0.841650i $$-0.318416\pi$$
0.540023 + 0.841650i $$0.318416\pi$$
$$992$$ −6.00000 −0.190500
$$993$$ 20.0000 0.634681
$$994$$ −12.0000 −0.380617
$$995$$ −56.0000 −1.77532
$$996$$ −12.0000 −0.380235
$$997$$ 20.0000 0.633406 0.316703 0.948525i $$-0.397424\pi$$
0.316703 + 0.948525i $$0.397424\pi$$
$$998$$ 32.0000 1.01294
$$999$$ 4.00000 0.126554
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 1734.2.a.h.1.1 1
3.2 odd 2 5202.2.a.g.1.1 1
17.2 even 8 1734.2.f.g.1483.2 4
17.4 even 4 1734.2.b.d.577.1 2
17.8 even 8 1734.2.f.g.829.1 4
17.9 even 8 1734.2.f.g.829.2 4
17.13 even 4 1734.2.b.d.577.2 2
17.15 even 8 1734.2.f.g.1483.1 4
17.16 even 2 102.2.a.a.1.1 1
51.50 odd 2 306.2.a.d.1.1 1
68.67 odd 2 816.2.a.h.1.1 1
85.33 odd 4 2550.2.d.q.2449.2 2
85.67 odd 4 2550.2.d.q.2449.1 2
85.84 even 2 2550.2.a.be.1.1 1
119.118 odd 2 4998.2.a.x.1.1 1
136.67 odd 2 3264.2.a.p.1.1 1
136.101 even 2 3264.2.a.bf.1.1 1
204.203 even 2 2448.2.a.t.1.1 1
255.254 odd 2 7650.2.a.z.1.1 1
408.101 odd 2 9792.2.a.a.1.1 1
408.203 even 2 9792.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
102.2.a.a.1.1 1 17.16 even 2
306.2.a.d.1.1 1 51.50 odd 2
816.2.a.h.1.1 1 68.67 odd 2
1734.2.a.h.1.1 1 1.1 even 1 trivial
1734.2.b.d.577.1 2 17.4 even 4
1734.2.b.d.577.2 2 17.13 even 4
1734.2.f.g.829.1 4 17.8 even 8
1734.2.f.g.829.2 4 17.9 even 8
1734.2.f.g.1483.1 4 17.15 even 8
1734.2.f.g.1483.2 4 17.2 even 8
2448.2.a.t.1.1 1 204.203 even 2
2550.2.a.be.1.1 1 85.84 even 2
2550.2.d.q.2449.1 2 85.67 odd 4
2550.2.d.q.2449.2 2 85.33 odd 4
3264.2.a.p.1.1 1 136.67 odd 2
3264.2.a.bf.1.1 1 136.101 even 2
4998.2.a.x.1.1 1 119.118 odd 2
5202.2.a.g.1.1 1 3.2 odd 2
7650.2.a.z.1.1 1 255.254 odd 2
9792.2.a.a.1.1 1 408.101 odd 2
9792.2.a.b.1.1 1 408.203 even 2