# Properties

 Label 666.2.a.d.1.1 Level $666$ Weight $2$ Character 666.1 Self dual yes Analytic conductor $5.318$ 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] = [666,2,Mod(1,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, 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("666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 666.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: $$5.31803677462$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 222) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 666.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} -4.00000 q^{10} +1.00000 q^{11} -3.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -5.00000 q^{19} -4.00000 q^{20} +1.00000 q^{22} -5.00000 q^{23} +11.0000 q^{25} -3.00000 q^{26} -1.00000 q^{28} -4.00000 q^{29} -10.0000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +4.00000 q^{35} -1.00000 q^{37} -5.00000 q^{38} -4.00000 q^{40} +6.00000 q^{41} +4.00000 q^{43} +1.00000 q^{44} -5.00000 q^{46} -2.00000 q^{47} -6.00000 q^{49} +11.0000 q^{50} -3.00000 q^{52} +11.0000 q^{53} -4.00000 q^{55} -1.00000 q^{56} -4.00000 q^{58} +12.0000 q^{59} +10.0000 q^{61} -10.0000 q^{62} +1.00000 q^{64} +12.0000 q^{65} +14.0000 q^{67} -3.00000 q^{68} +4.00000 q^{70} -11.0000 q^{73} -1.00000 q^{74} -5.00000 q^{76} -1.00000 q^{77} -10.0000 q^{79} -4.00000 q^{80} +6.00000 q^{82} +9.00000 q^{83} +12.0000 q^{85} +4.00000 q^{86} +1.00000 q^{88} -11.0000 q^{89} +3.00000 q^{91} -5.00000 q^{92} -2.00000 q^{94} +20.0000 q^{95} +10.0000 q^{97} -6.00000 q^{98} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −4.00000 −1.78885 −0.894427 0.447214i $$-0.852416\pi$$
−0.894427 + 0.447214i $$0.852416\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −4.00000 −1.26491
$$11$$ 1.00000 0.301511 0.150756 0.988571i $$-0.451829\pi$$
0.150756 + 0.988571i $$0.451829\pi$$
$$12$$ 0 0
$$13$$ −3.00000 −0.832050 −0.416025 0.909353i $$-0.636577\pi$$
−0.416025 + 0.909353i $$0.636577\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ 0 0
$$19$$ −5.00000 −1.14708 −0.573539 0.819178i $$-0.694430\pi$$
−0.573539 + 0.819178i $$0.694430\pi$$
$$20$$ −4.00000 −0.894427
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −5.00000 −1.04257 −0.521286 0.853382i $$-0.674548\pi$$
−0.521286 + 0.853382i $$0.674548\pi$$
$$24$$ 0 0
$$25$$ 11.0000 2.20000
$$26$$ −3.00000 −0.588348
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ −10.0000 −1.79605 −0.898027 0.439941i $$-0.854999\pi$$
−0.898027 + 0.439941i $$0.854999\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −3.00000 −0.514496
$$35$$ 4.00000 0.676123
$$36$$ 0 0
$$37$$ −1.00000 −0.164399
$$38$$ −5.00000 −0.811107
$$39$$ 0 0
$$40$$ −4.00000 −0.632456
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 1.00000 0.150756
$$45$$ 0 0
$$46$$ −5.00000 −0.737210
$$47$$ −2.00000 −0.291730 −0.145865 0.989305i $$-0.546597\pi$$
−0.145865 + 0.989305i $$0.546597\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 11.0000 1.55563
$$51$$ 0 0
$$52$$ −3.00000 −0.416025
$$53$$ 11.0000 1.51097 0.755483 0.655168i $$-0.227402\pi$$
0.755483 + 0.655168i $$0.227402\pi$$
$$54$$ 0 0
$$55$$ −4.00000 −0.539360
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ −4.00000 −0.525226
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ 0 0
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ −10.0000 −1.27000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 12.0000 1.48842
$$66$$ 0 0
$$67$$ 14.0000 1.71037 0.855186 0.518321i $$-0.173443\pi$$
0.855186 + 0.518321i $$0.173443\pi$$
$$68$$ −3.00000 −0.363803
$$69$$ 0 0
$$70$$ 4.00000 0.478091
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −11.0000 −1.28745 −0.643726 0.765256i $$-0.722612\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ −1.00000 −0.116248
$$75$$ 0 0
$$76$$ −5.00000 −0.573539
$$77$$ −1.00000 −0.113961
$$78$$ 0 0
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ −4.00000 −0.447214
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ 9.00000 0.987878 0.493939 0.869496i $$-0.335557\pi$$
0.493939 + 0.869496i $$0.335557\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ 1.00000 0.106600
$$89$$ −11.0000 −1.16600 −0.582999 0.812473i $$-0.698121\pi$$
−0.582999 + 0.812473i $$0.698121\pi$$
$$90$$ 0 0
$$91$$ 3.00000 0.314485
$$92$$ −5.00000 −0.521286
$$93$$ 0 0
$$94$$ −2.00000 −0.206284
$$95$$ 20.0000 2.05196
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ −6.00000 −0.606092
$$99$$ 0 0
$$100$$ 11.0000 1.10000
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ −2.00000 −0.197066 −0.0985329 0.995134i $$-0.531415\pi$$
−0.0985329 + 0.995134i $$0.531415\pi$$
$$104$$ −3.00000 −0.294174
$$105$$ 0 0
$$106$$ 11.0000 1.06841
$$107$$ 3.00000 0.290021 0.145010 0.989430i $$-0.453678\pi$$
0.145010 + 0.989430i $$0.453678\pi$$
$$108$$ 0 0
$$109$$ −9.00000 −0.862044 −0.431022 0.902342i $$-0.641847\pi$$
−0.431022 + 0.902342i $$0.641847\pi$$
$$110$$ −4.00000 −0.381385
$$111$$ 0 0
$$112$$ −1.00000 −0.0944911
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ 20.0000 1.86501
$$116$$ −4.00000 −0.371391
$$117$$ 0 0
$$118$$ 12.0000 1.10469
$$119$$ 3.00000 0.275010
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ 10.0000 0.905357
$$123$$ 0 0
$$124$$ −10.0000 −0.898027
$$125$$ −24.0000 −2.14663
$$126$$ 0 0
$$127$$ −3.00000 −0.266207 −0.133103 0.991102i $$-0.542494\pi$$
−0.133103 + 0.991102i $$0.542494\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 12.0000 1.05247
$$131$$ −22.0000 −1.92215 −0.961074 0.276289i $$-0.910895\pi$$
−0.961074 + 0.276289i $$0.910895\pi$$
$$132$$ 0 0
$$133$$ 5.00000 0.433555
$$134$$ 14.0000 1.20942
$$135$$ 0 0
$$136$$ −3.00000 −0.257248
$$137$$ −20.0000 −1.70872 −0.854358 0.519685i $$-0.826049\pi$$
−0.854358 + 0.519685i $$0.826049\pi$$
$$138$$ 0 0
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 4.00000 0.338062
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −3.00000 −0.250873
$$144$$ 0 0
$$145$$ 16.0000 1.32873
$$146$$ −11.0000 −0.910366
$$147$$ 0 0
$$148$$ −1.00000 −0.0821995
$$149$$ 10.0000 0.819232 0.409616 0.912258i $$-0.365663\pi$$
0.409616 + 0.912258i $$0.365663\pi$$
$$150$$ 0 0
$$151$$ 5.00000 0.406894 0.203447 0.979086i $$-0.434786\pi$$
0.203447 + 0.979086i $$0.434786\pi$$
$$152$$ −5.00000 −0.405554
$$153$$ 0 0
$$154$$ −1.00000 −0.0805823
$$155$$ 40.0000 3.21288
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ −10.0000 −0.795557
$$159$$ 0 0
$$160$$ −4.00000 −0.316228
$$161$$ 5.00000 0.394055
$$162$$ 0 0
$$163$$ 9.00000 0.704934 0.352467 0.935824i $$-0.385343\pi$$
0.352467 + 0.935824i $$0.385343\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ 9.00000 0.698535
$$167$$ 17.0000 1.31550 0.657750 0.753237i $$-0.271508\pi$$
0.657750 + 0.753237i $$0.271508\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 12.0000 0.920358
$$171$$ 0 0
$$172$$ 4.00000 0.304997
$$173$$ 13.0000 0.988372 0.494186 0.869356i $$-0.335466\pi$$
0.494186 + 0.869356i $$0.335466\pi$$
$$174$$ 0 0
$$175$$ −11.0000 −0.831522
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ −11.0000 −0.824485
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 3.00000 0.222375
$$183$$ 0 0
$$184$$ −5.00000 −0.368605
$$185$$ 4.00000 0.294086
$$186$$ 0 0
$$187$$ −3.00000 −0.219382
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ 20.0000 1.45095
$$191$$ −9.00000 −0.651217 −0.325609 0.945505i $$-0.605569\pi$$
−0.325609 + 0.945505i $$0.605569\pi$$
$$192$$ 0 0
$$193$$ 18.0000 1.29567 0.647834 0.761781i $$-0.275675\pi$$
0.647834 + 0.761781i $$0.275675\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ −6.00000 −0.428571
$$197$$ −7.00000 −0.498729 −0.249365 0.968410i $$-0.580222\pi$$
−0.249365 + 0.968410i $$0.580222\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ 11.0000 0.777817
$$201$$ 0 0
$$202$$ −6.00000 −0.422159
$$203$$ 4.00000 0.280745
$$204$$ 0 0
$$205$$ −24.0000 −1.67623
$$206$$ −2.00000 −0.139347
$$207$$ 0 0
$$208$$ −3.00000 −0.208013
$$209$$ −5.00000 −0.345857
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 11.0000 0.755483
$$213$$ 0 0
$$214$$ 3.00000 0.205076
$$215$$ −16.0000 −1.09119
$$216$$ 0 0
$$217$$ 10.0000 0.678844
$$218$$ −9.00000 −0.609557
$$219$$ 0 0
$$220$$ −4.00000 −0.269680
$$221$$ 9.00000 0.605406
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ −14.0000 −0.931266
$$227$$ −16.0000 −1.06196 −0.530979 0.847385i $$-0.678176\pi$$
−0.530979 + 0.847385i $$0.678176\pi$$
$$228$$ 0 0
$$229$$ −8.00000 −0.528655 −0.264327 0.964433i $$-0.585150\pi$$
−0.264327 + 0.964433i $$0.585150\pi$$
$$230$$ 20.0000 1.31876
$$231$$ 0 0
$$232$$ −4.00000 −0.262613
$$233$$ −10.0000 −0.655122 −0.327561 0.944830i $$-0.606227\pi$$
−0.327561 + 0.944830i $$0.606227\pi$$
$$234$$ 0 0
$$235$$ 8.00000 0.521862
$$236$$ 12.0000 0.781133
$$237$$ 0 0
$$238$$ 3.00000 0.194461
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 28.0000 1.80364 0.901819 0.432113i $$-0.142232\pi$$
0.901819 + 0.432113i $$0.142232\pi$$
$$242$$ −10.0000 −0.642824
$$243$$ 0 0
$$244$$ 10.0000 0.640184
$$245$$ 24.0000 1.53330
$$246$$ 0 0
$$247$$ 15.0000 0.954427
$$248$$ −10.0000 −0.635001
$$249$$ 0 0
$$250$$ −24.0000 −1.51789
$$251$$ 6.00000 0.378717 0.189358 0.981908i $$-0.439359\pi$$
0.189358 + 0.981908i $$0.439359\pi$$
$$252$$ 0 0
$$253$$ −5.00000 −0.314347
$$254$$ −3.00000 −0.188237
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −27.0000 −1.68421 −0.842107 0.539311i $$-0.818685\pi$$
−0.842107 + 0.539311i $$0.818685\pi$$
$$258$$ 0 0
$$259$$ 1.00000 0.0621370
$$260$$ 12.0000 0.744208
$$261$$ 0 0
$$262$$ −22.0000 −1.35916
$$263$$ −18.0000 −1.10993 −0.554964 0.831875i $$-0.687268\pi$$
−0.554964 + 0.831875i $$0.687268\pi$$
$$264$$ 0 0
$$265$$ −44.0000 −2.70290
$$266$$ 5.00000 0.306570
$$267$$ 0 0
$$268$$ 14.0000 0.855186
$$269$$ −27.0000 −1.64622 −0.823110 0.567883i $$-0.807763\pi$$
−0.823110 + 0.567883i $$0.807763\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ −3.00000 −0.181902
$$273$$ 0 0
$$274$$ −20.0000 −1.20824
$$275$$ 11.0000 0.663325
$$276$$ 0 0
$$277$$ −5.00000 −0.300421 −0.150210 0.988654i $$-0.547995\pi$$
−0.150210 + 0.988654i $$0.547995\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 0 0
$$280$$ 4.00000 0.239046
$$281$$ 9.00000 0.536895 0.268447 0.963294i $$-0.413489\pi$$
0.268447 + 0.963294i $$0.413489\pi$$
$$282$$ 0 0
$$283$$ 21.0000 1.24832 0.624160 0.781296i $$-0.285441\pi$$
0.624160 + 0.781296i $$0.285441\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −3.00000 −0.177394
$$287$$ −6.00000 −0.354169
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 16.0000 0.939552
$$291$$ 0 0
$$292$$ −11.0000 −0.643726
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ −48.0000 −2.79467
$$296$$ −1.00000 −0.0581238
$$297$$ 0 0
$$298$$ 10.0000 0.579284
$$299$$ 15.0000 0.867472
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 5.00000 0.287718
$$303$$ 0 0
$$304$$ −5.00000 −0.286770
$$305$$ −40.0000 −2.29039
$$306$$ 0 0
$$307$$ 32.0000 1.82634 0.913168 0.407583i $$-0.133628\pi$$
0.913168 + 0.407583i $$0.133628\pi$$
$$308$$ −1.00000 −0.0569803
$$309$$ 0 0
$$310$$ 40.0000 2.27185
$$311$$ 16.0000 0.907277 0.453638 0.891186i $$-0.350126\pi$$
0.453638 + 0.891186i $$0.350126\pi$$
$$312$$ 0 0
$$313$$ −14.0000 −0.791327 −0.395663 0.918396i $$-0.629485\pi$$
−0.395663 + 0.918396i $$0.629485\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ −4.00000 −0.223957
$$320$$ −4.00000 −0.223607
$$321$$ 0 0
$$322$$ 5.00000 0.278639
$$323$$ 15.0000 0.834622
$$324$$ 0 0
$$325$$ −33.0000 −1.83051
$$326$$ 9.00000 0.498464
$$327$$ 0 0
$$328$$ 6.00000 0.331295
$$329$$ 2.00000 0.110264
$$330$$ 0 0
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ 9.00000 0.493939
$$333$$ 0 0
$$334$$ 17.0000 0.930199
$$335$$ −56.0000 −3.05961
$$336$$ 0 0
$$337$$ 5.00000 0.272367 0.136184 0.990684i $$-0.456516\pi$$
0.136184 + 0.990684i $$0.456516\pi$$
$$338$$ −4.00000 −0.217571
$$339$$ 0 0
$$340$$ 12.0000 0.650791
$$341$$ −10.0000 −0.541530
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ 13.0000 0.698884
$$347$$ −18.0000 −0.966291 −0.483145 0.875540i $$-0.660506\pi$$
−0.483145 + 0.875540i $$0.660506\pi$$
$$348$$ 0 0
$$349$$ −30.0000 −1.60586 −0.802932 0.596071i $$-0.796728\pi$$
−0.802932 + 0.596071i $$0.796728\pi$$
$$350$$ −11.0000 −0.587975
$$351$$ 0 0
$$352$$ 1.00000 0.0533002
$$353$$ 26.0000 1.38384 0.691920 0.721974i $$-0.256765\pi$$
0.691920 + 0.721974i $$0.256765\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −11.0000 −0.582999
$$357$$ 0 0
$$358$$ −4.00000 −0.211407
$$359$$ −6.00000 −0.316668 −0.158334 0.987386i $$-0.550612\pi$$
−0.158334 + 0.987386i $$0.550612\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ −16.0000 −0.840941
$$363$$ 0 0
$$364$$ 3.00000 0.157243
$$365$$ 44.0000 2.30307
$$366$$ 0 0
$$367$$ 15.0000 0.782994 0.391497 0.920179i $$-0.371957\pi$$
0.391497 + 0.920179i $$0.371957\pi$$
$$368$$ −5.00000 −0.260643
$$369$$ 0 0
$$370$$ 4.00000 0.207950
$$371$$ −11.0000 −0.571092
$$372$$ 0 0
$$373$$ −28.0000 −1.44979 −0.724893 0.688862i $$-0.758111\pi$$
−0.724893 + 0.688862i $$0.758111\pi$$
$$374$$ −3.00000 −0.155126
$$375$$ 0 0
$$376$$ −2.00000 −0.103142
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 20.0000 1.02598
$$381$$ 0 0
$$382$$ −9.00000 −0.460480
$$383$$ 21.0000 1.07305 0.536525 0.843884i $$-0.319737\pi$$
0.536525 + 0.843884i $$0.319737\pi$$
$$384$$ 0 0
$$385$$ 4.00000 0.203859
$$386$$ 18.0000 0.916176
$$387$$ 0 0
$$388$$ 10.0000 0.507673
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 15.0000 0.758583
$$392$$ −6.00000 −0.303046
$$393$$ 0 0
$$394$$ −7.00000 −0.352655
$$395$$ 40.0000 2.01262
$$396$$ 0 0
$$397$$ −32.0000 −1.60603 −0.803017 0.595956i $$-0.796773\pi$$
−0.803017 + 0.595956i $$0.796773\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ 11.0000 0.550000
$$401$$ −19.0000 −0.948815 −0.474407 0.880305i $$-0.657338\pi$$
−0.474407 + 0.880305i $$0.657338\pi$$
$$402$$ 0 0
$$403$$ 30.0000 1.49441
$$404$$ −6.00000 −0.298511
$$405$$ 0 0
$$406$$ 4.00000 0.198517
$$407$$ −1.00000 −0.0495682
$$408$$ 0 0
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ −24.0000 −1.18528
$$411$$ 0 0
$$412$$ −2.00000 −0.0985329
$$413$$ −12.0000 −0.590481
$$414$$ 0 0
$$415$$ −36.0000 −1.76717
$$416$$ −3.00000 −0.147087
$$417$$ 0 0
$$418$$ −5.00000 −0.244558
$$419$$ −5.00000 −0.244266 −0.122133 0.992514i $$-0.538973\pi$$
−0.122133 + 0.992514i $$0.538973\pi$$
$$420$$ 0 0
$$421$$ −6.00000 −0.292422 −0.146211 0.989253i $$-0.546708\pi$$
−0.146211 + 0.989253i $$0.546708\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 11.0000 0.534207
$$425$$ −33.0000 −1.60074
$$426$$ 0 0
$$427$$ −10.0000 −0.483934
$$428$$ 3.00000 0.145010
$$429$$ 0 0
$$430$$ −16.0000 −0.771589
$$431$$ −15.0000 −0.722525 −0.361262 0.932464i $$-0.617654\pi$$
−0.361262 + 0.932464i $$0.617654\pi$$
$$432$$ 0 0
$$433$$ −25.0000 −1.20142 −0.600712 0.799466i $$-0.705116\pi$$
−0.600712 + 0.799466i $$0.705116\pi$$
$$434$$ 10.0000 0.480015
$$435$$ 0 0
$$436$$ −9.00000 −0.431022
$$437$$ 25.0000 1.19591
$$438$$ 0 0
$$439$$ −14.0000 −0.668184 −0.334092 0.942541i $$-0.608430\pi$$
−0.334092 + 0.942541i $$0.608430\pi$$
$$440$$ −4.00000 −0.190693
$$441$$ 0 0
$$442$$ 9.00000 0.428086
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ 0 0
$$445$$ 44.0000 2.08580
$$446$$ 0 0
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ 0 0
$$451$$ 6.00000 0.282529
$$452$$ −14.0000 −0.658505
$$453$$ 0 0
$$454$$ −16.0000 −0.750917
$$455$$ −12.0000 −0.562569
$$456$$ 0 0
$$457$$ 28.0000 1.30978 0.654892 0.755722i $$-0.272714\pi$$
0.654892 + 0.755722i $$0.272714\pi$$
$$458$$ −8.00000 −0.373815
$$459$$ 0 0
$$460$$ 20.0000 0.932505
$$461$$ 14.0000 0.652045 0.326023 0.945362i $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 0 0
$$463$$ −22.0000 −1.02243 −0.511213 0.859454i $$-0.670804\pi$$
−0.511213 + 0.859454i $$0.670804\pi$$
$$464$$ −4.00000 −0.185695
$$465$$ 0 0
$$466$$ −10.0000 −0.463241
$$467$$ 34.0000 1.57333 0.786666 0.617379i $$-0.211805\pi$$
0.786666 + 0.617379i $$0.211805\pi$$
$$468$$ 0 0
$$469$$ −14.0000 −0.646460
$$470$$ 8.00000 0.369012
$$471$$ 0 0
$$472$$ 12.0000 0.552345
$$473$$ 4.00000 0.183920
$$474$$ 0 0
$$475$$ −55.0000 −2.52357
$$476$$ 3.00000 0.137505
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −15.0000 −0.685367 −0.342684 0.939451i $$-0.611336\pi$$
−0.342684 + 0.939451i $$0.611336\pi$$
$$480$$ 0 0
$$481$$ 3.00000 0.136788
$$482$$ 28.0000 1.27537
$$483$$ 0 0
$$484$$ −10.0000 −0.454545
$$485$$ −40.0000 −1.81631
$$486$$ 0 0
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 10.0000 0.452679
$$489$$ 0 0
$$490$$ 24.0000 1.08421
$$491$$ 29.0000 1.30875 0.654376 0.756169i $$-0.272931\pi$$
0.654376 + 0.756169i $$0.272931\pi$$
$$492$$ 0 0
$$493$$ 12.0000 0.540453
$$494$$ 15.0000 0.674882
$$495$$ 0 0
$$496$$ −10.0000 −0.449013
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −15.0000 −0.671492 −0.335746 0.941953i $$-0.608988\pi$$
−0.335746 + 0.941953i $$0.608988\pi$$
$$500$$ −24.0000 −1.07331
$$501$$ 0 0
$$502$$ 6.00000 0.267793
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 24.0000 1.06799
$$506$$ −5.00000 −0.222277
$$507$$ 0 0
$$508$$ −3.00000 −0.133103
$$509$$ 15.0000 0.664863 0.332432 0.943127i $$-0.392131\pi$$
0.332432 + 0.943127i $$0.392131\pi$$
$$510$$ 0 0
$$511$$ 11.0000 0.486611
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −27.0000 −1.19092
$$515$$ 8.00000 0.352522
$$516$$ 0 0
$$517$$ −2.00000 −0.0879599
$$518$$ 1.00000 0.0439375
$$519$$ 0 0
$$520$$ 12.0000 0.526235
$$521$$ −2.00000 −0.0876216 −0.0438108 0.999040i $$-0.513950\pi$$
−0.0438108 + 0.999040i $$0.513950\pi$$
$$522$$ 0 0
$$523$$ −16.0000 −0.699631 −0.349816 0.936819i $$-0.613756\pi$$
−0.349816 + 0.936819i $$0.613756\pi$$
$$524$$ −22.0000 −0.961074
$$525$$ 0 0
$$526$$ −18.0000 −0.784837
$$527$$ 30.0000 1.30682
$$528$$ 0 0
$$529$$ 2.00000 0.0869565
$$530$$ −44.0000 −1.91124
$$531$$ 0 0
$$532$$ 5.00000 0.216777
$$533$$ −18.0000 −0.779667
$$534$$ 0 0
$$535$$ −12.0000 −0.518805
$$536$$ 14.0000 0.604708
$$537$$ 0 0
$$538$$ −27.0000 −1.16405
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 1.00000 0.0429934 0.0214967 0.999769i $$-0.493157\pi$$
0.0214967 + 0.999769i $$0.493157\pi$$
$$542$$ 8.00000 0.343629
$$543$$ 0 0
$$544$$ −3.00000 −0.128624
$$545$$ 36.0000 1.54207
$$546$$ 0 0
$$547$$ 17.0000 0.726868 0.363434 0.931620i $$-0.381604\pi$$
0.363434 + 0.931620i $$0.381604\pi$$
$$548$$ −20.0000 −0.854358
$$549$$ 0 0
$$550$$ 11.0000 0.469042
$$551$$ 20.0000 0.852029
$$552$$ 0 0
$$553$$ 10.0000 0.425243
$$554$$ −5.00000 −0.212430
$$555$$ 0 0
$$556$$ −14.0000 −0.593732
$$557$$ 30.0000 1.27114 0.635570 0.772043i $$-0.280765\pi$$
0.635570 + 0.772043i $$0.280765\pi$$
$$558$$ 0 0
$$559$$ −12.0000 −0.507546
$$560$$ 4.00000 0.169031
$$561$$ 0 0
$$562$$ 9.00000 0.379642
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ 0 0
$$565$$ 56.0000 2.35594
$$566$$ 21.0000 0.882696
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 3.00000 0.125767 0.0628833 0.998021i $$-0.479970\pi$$
0.0628833 + 0.998021i $$0.479970\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ −3.00000 −0.125436
$$573$$ 0 0
$$574$$ −6.00000 −0.250435
$$575$$ −55.0000 −2.29366
$$576$$ 0 0
$$577$$ −34.0000 −1.41544 −0.707719 0.706494i $$-0.750276\pi$$
−0.707719 + 0.706494i $$0.750276\pi$$
$$578$$ −8.00000 −0.332756
$$579$$ 0 0
$$580$$ 16.0000 0.664364
$$581$$ −9.00000 −0.373383
$$582$$ 0 0
$$583$$ 11.0000 0.455573
$$584$$ −11.0000 −0.455183
$$585$$ 0 0
$$586$$ −21.0000 −0.867502
$$587$$ −28.0000 −1.15568 −0.577842 0.816149i $$-0.696105\pi$$
−0.577842 + 0.816149i $$0.696105\pi$$
$$588$$ 0 0
$$589$$ 50.0000 2.06021
$$590$$ −48.0000 −1.97613
$$591$$ 0 0
$$592$$ −1.00000 −0.0410997
$$593$$ −28.0000 −1.14982 −0.574911 0.818216i $$-0.694963\pi$$
−0.574911 + 0.818216i $$0.694963\pi$$
$$594$$ 0 0
$$595$$ −12.0000 −0.491952
$$596$$ 10.0000 0.409616
$$597$$ 0 0
$$598$$ 15.0000 0.613396
$$599$$ −42.0000 −1.71607 −0.858037 0.513588i $$-0.828316\pi$$
−0.858037 + 0.513588i $$0.828316\pi$$
$$600$$ 0 0
$$601$$ −9.00000 −0.367118 −0.183559 0.983009i $$-0.558762\pi$$
−0.183559 + 0.983009i $$0.558762\pi$$
$$602$$ −4.00000 −0.163028
$$603$$ 0 0
$$604$$ 5.00000 0.203447
$$605$$ 40.0000 1.62623
$$606$$ 0 0
$$607$$ 14.0000 0.568242 0.284121 0.958788i $$-0.408298\pi$$
0.284121 + 0.958788i $$0.408298\pi$$
$$608$$ −5.00000 −0.202777
$$609$$ 0 0
$$610$$ −40.0000 −1.61955
$$611$$ 6.00000 0.242734
$$612$$ 0 0
$$613$$ −10.0000 −0.403896 −0.201948 0.979396i $$-0.564727\pi$$
−0.201948 + 0.979396i $$0.564727\pi$$
$$614$$ 32.0000 1.29141
$$615$$ 0 0
$$616$$ −1.00000 −0.0402911
$$617$$ 28.0000 1.12724 0.563619 0.826035i $$-0.309409\pi$$
0.563619 + 0.826035i $$0.309409\pi$$
$$618$$ 0 0
$$619$$ 26.0000 1.04503 0.522514 0.852631i $$-0.324994\pi$$
0.522514 + 0.852631i $$0.324994\pi$$
$$620$$ 40.0000 1.60644
$$621$$ 0 0
$$622$$ 16.0000 0.641542
$$623$$ 11.0000 0.440706
$$624$$ 0 0
$$625$$ 41.0000 1.64000
$$626$$ −14.0000 −0.559553
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ 44.0000 1.75161 0.875806 0.482663i $$-0.160330\pi$$
0.875806 + 0.482663i $$0.160330\pi$$
$$632$$ −10.0000 −0.397779
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ 12.0000 0.476205
$$636$$ 0 0
$$637$$ 18.0000 0.713186
$$638$$ −4.00000 −0.158362
$$639$$ 0 0
$$640$$ −4.00000 −0.158114
$$641$$ 12.0000 0.473972 0.236986 0.971513i $$-0.423841\pi$$
0.236986 + 0.971513i $$0.423841\pi$$
$$642$$ 0 0
$$643$$ −41.0000 −1.61688 −0.808441 0.588577i $$-0.799688\pi$$
−0.808441 + 0.588577i $$0.799688\pi$$
$$644$$ 5.00000 0.197028
$$645$$ 0 0
$$646$$ 15.0000 0.590167
$$647$$ 11.0000 0.432455 0.216227 0.976343i $$-0.430625\pi$$
0.216227 + 0.976343i $$0.430625\pi$$
$$648$$ 0 0
$$649$$ 12.0000 0.471041
$$650$$ −33.0000 −1.29437
$$651$$ 0 0
$$652$$ 9.00000 0.352467
$$653$$ 20.0000 0.782660 0.391330 0.920250i $$-0.372015\pi$$
0.391330 + 0.920250i $$0.372015\pi$$
$$654$$ 0 0
$$655$$ 88.0000 3.43844
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 2.00000 0.0779681
$$659$$ −16.0000 −0.623272 −0.311636 0.950202i $$-0.600877\pi$$
−0.311636 + 0.950202i $$0.600877\pi$$
$$660$$ 0 0
$$661$$ 5.00000 0.194477 0.0972387 0.995261i $$-0.468999\pi$$
0.0972387 + 0.995261i $$0.468999\pi$$
$$662$$ 28.0000 1.08825
$$663$$ 0 0
$$664$$ 9.00000 0.349268
$$665$$ −20.0000 −0.775567
$$666$$ 0 0
$$667$$ 20.0000 0.774403
$$668$$ 17.0000 0.657750
$$669$$ 0 0
$$670$$ −56.0000 −2.16347
$$671$$ 10.0000 0.386046
$$672$$ 0 0
$$673$$ 37.0000 1.42625 0.713123 0.701039i $$-0.247280\pi$$
0.713123 + 0.701039i $$0.247280\pi$$
$$674$$ 5.00000 0.192593
$$675$$ 0 0
$$676$$ −4.00000 −0.153846
$$677$$ −15.0000 −0.576497 −0.288248 0.957556i $$-0.593073\pi$$
−0.288248 + 0.957556i $$0.593073\pi$$
$$678$$ 0 0
$$679$$ −10.0000 −0.383765
$$680$$ 12.0000 0.460179
$$681$$ 0 0
$$682$$ −10.0000 −0.382920
$$683$$ 22.0000 0.841807 0.420903 0.907106i $$-0.361713\pi$$
0.420903 + 0.907106i $$0.361713\pi$$
$$684$$ 0 0
$$685$$ 80.0000 3.05664
$$686$$ 13.0000 0.496342
$$687$$ 0 0
$$688$$ 4.00000 0.152499
$$689$$ −33.0000 −1.25720
$$690$$ 0 0
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ 13.0000 0.494186
$$693$$ 0 0
$$694$$ −18.0000 −0.683271
$$695$$ 56.0000 2.12420
$$696$$ 0 0
$$697$$ −18.0000 −0.681799
$$698$$ −30.0000 −1.13552
$$699$$ 0 0
$$700$$ −11.0000 −0.415761
$$701$$ 40.0000 1.51078 0.755390 0.655276i $$-0.227448\pi$$
0.755390 + 0.655276i $$0.227448\pi$$
$$702$$ 0 0
$$703$$ 5.00000 0.188579
$$704$$ 1.00000 0.0376889
$$705$$ 0 0
$$706$$ 26.0000 0.978523
$$707$$ 6.00000 0.225653
$$708$$ 0 0
$$709$$ −19.0000 −0.713560 −0.356780 0.934188i $$-0.616125\pi$$
−0.356780 + 0.934188i $$0.616125\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −11.0000 −0.412242
$$713$$ 50.0000 1.87251
$$714$$ 0 0
$$715$$ 12.0000 0.448775
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ −6.00000 −0.223918
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ 2.00000 0.0744839
$$722$$ 6.00000 0.223297
$$723$$ 0 0
$$724$$ −16.0000 −0.594635
$$725$$ −44.0000 −1.63412
$$726$$ 0 0
$$727$$ 20.0000 0.741759 0.370879 0.928681i $$-0.379056\pi$$
0.370879 + 0.928681i $$0.379056\pi$$
$$728$$ 3.00000 0.111187
$$729$$ 0 0
$$730$$ 44.0000 1.62851
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ 15.0000 0.553660
$$735$$ 0 0
$$736$$ −5.00000 −0.184302
$$737$$ 14.0000 0.515697
$$738$$ 0 0
$$739$$ −38.0000 −1.39785 −0.698926 0.715194i $$-0.746338\pi$$
−0.698926 + 0.715194i $$0.746338\pi$$
$$740$$ 4.00000 0.147043
$$741$$ 0 0
$$742$$ −11.0000 −0.403823
$$743$$ −8.00000 −0.293492 −0.146746 0.989174i $$-0.546880\pi$$
−0.146746 + 0.989174i $$0.546880\pi$$
$$744$$ 0 0
$$745$$ −40.0000 −1.46549
$$746$$ −28.0000 −1.02515
$$747$$ 0 0
$$748$$ −3.00000 −0.109691
$$749$$ −3.00000 −0.109618
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ −2.00000 −0.0729325
$$753$$ 0 0
$$754$$ 12.0000 0.437014
$$755$$ −20.0000 −0.727875
$$756$$ 0 0
$$757$$ 15.0000 0.545184 0.272592 0.962130i $$-0.412119\pi$$
0.272592 + 0.962130i $$0.412119\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 0 0
$$760$$ 20.0000 0.725476
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 0 0
$$763$$ 9.00000 0.325822
$$764$$ −9.00000 −0.325609
$$765$$ 0 0
$$766$$ 21.0000 0.758761
$$767$$ −36.0000 −1.29988
$$768$$ 0 0
$$769$$ −4.00000 −0.144244 −0.0721218 0.997396i $$-0.522977\pi$$
−0.0721218 + 0.997396i $$0.522977\pi$$
$$770$$ 4.00000 0.144150
$$771$$ 0 0
$$772$$ 18.0000 0.647834
$$773$$ 33.0000 1.18693 0.593464 0.804861i $$-0.297760\pi$$
0.593464 + 0.804861i $$0.297760\pi$$
$$774$$ 0 0
$$775$$ −110.000 −3.95132
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ 6.00000 0.215110
$$779$$ −30.0000 −1.07486
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 15.0000 0.536399
$$783$$ 0 0
$$784$$ −6.00000 −0.214286
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 38.0000 1.35455 0.677277 0.735728i $$-0.263160\pi$$
0.677277 + 0.735728i $$0.263160\pi$$
$$788$$ −7.00000 −0.249365
$$789$$ 0 0
$$790$$ 40.0000 1.42314
$$791$$ 14.0000 0.497783
$$792$$ 0 0
$$793$$ −30.0000 −1.06533
$$794$$ −32.0000 −1.13564
$$795$$ 0 0
$$796$$ 16.0000 0.567105
$$797$$ −4.00000 −0.141687 −0.0708436 0.997487i $$-0.522569\pi$$
−0.0708436 + 0.997487i $$0.522569\pi$$
$$798$$ 0 0
$$799$$ 6.00000 0.212265
$$800$$ 11.0000 0.388909
$$801$$ 0 0
$$802$$ −19.0000 −0.670913
$$803$$ −11.0000 −0.388182
$$804$$ 0 0
$$805$$ −20.0000 −0.704907
$$806$$ 30.0000 1.05670
$$807$$ 0 0
$$808$$ −6.00000 −0.211079
$$809$$ −19.0000 −0.668004 −0.334002 0.942572i $$-0.608399\pi$$
−0.334002 + 0.942572i $$0.608399\pi$$
$$810$$ 0 0
$$811$$ −32.0000 −1.12367 −0.561836 0.827249i $$-0.689905\pi$$
−0.561836 + 0.827249i $$0.689905\pi$$
$$812$$ 4.00000 0.140372
$$813$$ 0 0
$$814$$ −1.00000 −0.0350500
$$815$$ −36.0000 −1.26102
$$816$$ 0 0
$$817$$ −20.0000 −0.699711
$$818$$ 10.0000 0.349642
$$819$$ 0 0
$$820$$ −24.0000 −0.838116
$$821$$ −33.0000 −1.15171 −0.575854 0.817553i $$-0.695330\pi$$
−0.575854 + 0.817553i $$0.695330\pi$$
$$822$$ 0 0
$$823$$ 9.00000 0.313720 0.156860 0.987621i $$-0.449863\pi$$
0.156860 + 0.987621i $$0.449863\pi$$
$$824$$ −2.00000 −0.0696733
$$825$$ 0 0
$$826$$ −12.0000 −0.417533
$$827$$ 14.0000 0.486828 0.243414 0.969923i $$-0.421733\pi$$
0.243414 + 0.969923i $$0.421733\pi$$
$$828$$ 0 0
$$829$$ 19.0000 0.659897 0.329949 0.943999i $$-0.392969\pi$$
0.329949 + 0.943999i $$0.392969\pi$$
$$830$$ −36.0000 −1.24958
$$831$$ 0 0
$$832$$ −3.00000 −0.104006
$$833$$ 18.0000 0.623663
$$834$$ 0 0
$$835$$ −68.0000 −2.35324
$$836$$ −5.00000 −0.172929
$$837$$ 0 0
$$838$$ −5.00000 −0.172722
$$839$$ 4.00000 0.138095 0.0690477 0.997613i $$-0.478004\pi$$
0.0690477 + 0.997613i $$0.478004\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ −6.00000 −0.206774
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 16.0000 0.550417
$$846$$ 0 0
$$847$$ 10.0000 0.343604
$$848$$ 11.0000 0.377742
$$849$$ 0 0
$$850$$ −33.0000 −1.13189
$$851$$ 5.00000 0.171398
$$852$$ 0 0
$$853$$ −55.0000 −1.88316 −0.941582 0.336784i $$-0.890661\pi$$
−0.941582 + 0.336784i $$0.890661\pi$$
$$854$$ −10.0000 −0.342193
$$855$$ 0 0
$$856$$ 3.00000 0.102538
$$857$$ 3.00000 0.102478 0.0512390 0.998686i $$-0.483683\pi$$
0.0512390 + 0.998686i $$0.483683\pi$$
$$858$$ 0 0
$$859$$ −23.0000 −0.784750 −0.392375 0.919805i $$-0.628346\pi$$
−0.392375 + 0.919805i $$0.628346\pi$$
$$860$$ −16.0000 −0.545595
$$861$$ 0 0
$$862$$ −15.0000 −0.510902
$$863$$ 22.0000 0.748889 0.374444 0.927249i $$-0.377833\pi$$
0.374444 + 0.927249i $$0.377833\pi$$
$$864$$ 0 0
$$865$$ −52.0000 −1.76805
$$866$$ −25.0000 −0.849535
$$867$$ 0 0
$$868$$ 10.0000 0.339422
$$869$$ −10.0000 −0.339227
$$870$$ 0 0
$$871$$ −42.0000 −1.42312
$$872$$ −9.00000 −0.304778
$$873$$ 0 0
$$874$$ 25.0000 0.845638
$$875$$ 24.0000 0.811348
$$876$$ 0 0
$$877$$ −14.0000 −0.472746 −0.236373 0.971662i $$-0.575959\pi$$
−0.236373 + 0.971662i $$0.575959\pi$$
$$878$$ −14.0000 −0.472477
$$879$$ 0 0
$$880$$ −4.00000 −0.134840
$$881$$ 36.0000 1.21287 0.606435 0.795133i $$-0.292599\pi$$
0.606435 + 0.795133i $$0.292599\pi$$
$$882$$ 0 0
$$883$$ −11.0000 −0.370179 −0.185090 0.982722i $$-0.559258\pi$$
−0.185090 + 0.982722i $$0.559258\pi$$
$$884$$ 9.00000 0.302703
$$885$$ 0 0
$$886$$ −36.0000 −1.20944
$$887$$ −6.00000 −0.201460 −0.100730 0.994914i $$-0.532118\pi$$
−0.100730 + 0.994914i $$0.532118\pi$$
$$888$$ 0 0
$$889$$ 3.00000 0.100617
$$890$$ 44.0000 1.47488
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 10.0000 0.334637
$$894$$ 0 0
$$895$$ 16.0000 0.534821
$$896$$ −1.00000 −0.0334077
$$897$$ 0 0
$$898$$ −2.00000 −0.0667409
$$899$$ 40.0000 1.33407
$$900$$ 0 0
$$901$$ −33.0000 −1.09939
$$902$$ 6.00000 0.199778
$$903$$ 0 0
$$904$$ −14.0000 −0.465633
$$905$$ 64.0000 2.12743
$$906$$ 0 0
$$907$$ −11.0000 −0.365249 −0.182625 0.983183i $$-0.558459\pi$$
−0.182625 + 0.983183i $$0.558459\pi$$
$$908$$ −16.0000 −0.530979
$$909$$ 0 0
$$910$$ −12.0000 −0.397796
$$911$$ −40.0000 −1.32526 −0.662630 0.748947i $$-0.730560\pi$$
−0.662630 + 0.748947i $$0.730560\pi$$
$$912$$ 0 0
$$913$$ 9.00000 0.297857
$$914$$ 28.0000 0.926158
$$915$$ 0 0
$$916$$ −8.00000 −0.264327
$$917$$ 22.0000 0.726504
$$918$$ 0 0
$$919$$ 46.0000 1.51740 0.758700 0.651440i $$-0.225835\pi$$
0.758700 + 0.651440i $$0.225835\pi$$
$$920$$ 20.0000 0.659380
$$921$$ 0 0
$$922$$ 14.0000 0.461065
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −11.0000 −0.361678
$$926$$ −22.0000 −0.722965
$$927$$ 0 0
$$928$$ −4.00000 −0.131306
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 30.0000 0.983210
$$932$$ −10.0000 −0.327561
$$933$$ 0 0
$$934$$ 34.0000 1.11251
$$935$$ 12.0000 0.392442
$$936$$ 0 0
$$937$$ 22.0000 0.718709 0.359354 0.933201i $$-0.382997\pi$$
0.359354 + 0.933201i $$0.382997\pi$$
$$938$$ −14.0000 −0.457116
$$939$$ 0 0
$$940$$ 8.00000 0.260931
$$941$$ −50.0000 −1.62995 −0.814977 0.579494i $$-0.803250\pi$$
−0.814977 + 0.579494i $$0.803250\pi$$
$$942$$ 0 0
$$943$$ −30.0000 −0.976934
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ 4.00000 0.130051
$$947$$ 26.0000 0.844886 0.422443 0.906389i $$-0.361173\pi$$
0.422443 + 0.906389i $$0.361173\pi$$
$$948$$ 0 0
$$949$$ 33.0000 1.07123
$$950$$ −55.0000 −1.78444
$$951$$ 0 0
$$952$$ 3.00000 0.0972306
$$953$$ −8.00000 −0.259145 −0.129573 0.991570i $$-0.541361\pi$$
−0.129573 + 0.991570i $$0.541361\pi$$
$$954$$ 0 0
$$955$$ 36.0000 1.16493
$$956$$ 0 0
$$957$$ 0 0
$$958$$ −15.0000 −0.484628
$$959$$ 20.0000 0.645834
$$960$$ 0 0
$$961$$ 69.0000 2.22581
$$962$$ 3.00000 0.0967239
$$963$$ 0 0
$$964$$ 28.0000 0.901819
$$965$$ −72.0000 −2.31776
$$966$$ 0 0
$$967$$ −12.0000 −0.385894 −0.192947 0.981209i $$-0.561805\pi$$
−0.192947 + 0.981209i $$0.561805\pi$$
$$968$$ −10.0000 −0.321412
$$969$$ 0 0
$$970$$ −40.0000 −1.28432
$$971$$ 60.0000 1.92549 0.962746 0.270408i $$-0.0871586\pi$$
0.962746 + 0.270408i $$0.0871586\pi$$
$$972$$ 0 0
$$973$$ 14.0000 0.448819
$$974$$ −2.00000 −0.0640841
$$975$$ 0 0
$$976$$ 10.0000 0.320092
$$977$$ −27.0000 −0.863807 −0.431903 0.901920i $$-0.642158\pi$$
−0.431903 + 0.901920i $$0.642158\pi$$
$$978$$ 0 0
$$979$$ −11.0000 −0.351562
$$980$$ 24.0000 0.766652
$$981$$ 0 0
$$982$$ 29.0000 0.925427
$$983$$ 14.0000 0.446531 0.223265 0.974758i $$-0.428328\pi$$
0.223265 + 0.974758i $$0.428328\pi$$
$$984$$ 0 0
$$985$$ 28.0000 0.892154
$$986$$ 12.0000 0.382158
$$987$$ 0 0
$$988$$ 15.0000 0.477214
$$989$$ −20.0000 −0.635963
$$990$$ 0 0
$$991$$ 20.0000 0.635321 0.317660 0.948205i $$-0.397103\pi$$
0.317660 + 0.948205i $$0.397103\pi$$
$$992$$ −10.0000 −0.317500
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −64.0000 −2.02894
$$996$$ 0 0
$$997$$ −9.00000 −0.285033 −0.142516 0.989792i $$-0.545519\pi$$
−0.142516 + 0.989792i $$0.545519\pi$$
$$998$$ −15.0000 −0.474817
$$999$$ 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 666.2.a.d.1.1 1
3.2 odd 2 222.2.a.c.1.1 1
4.3 odd 2 5328.2.a.b.1.1 1
12.11 even 2 1776.2.a.e.1.1 1
15.14 odd 2 5550.2.a.z.1.1 1
24.5 odd 2 7104.2.a.a.1.1 1
24.11 even 2 7104.2.a.p.1.1 1
111.110 odd 2 8214.2.a.j.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
222.2.a.c.1.1 1 3.2 odd 2
666.2.a.d.1.1 1 1.1 even 1 trivial
1776.2.a.e.1.1 1 12.11 even 2
5328.2.a.b.1.1 1 4.3 odd 2
5550.2.a.z.1.1 1 15.14 odd 2
7104.2.a.a.1.1 1 24.5 odd 2
7104.2.a.p.1.1 1 24.11 even 2
8214.2.a.j.1.1 1 111.110 odd 2