# Properties

 Label 950.2.a.c.1.1 Level $950$ Weight $2$ Character 950.1 Self dual yes Analytic conductor $7.586$ 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] = [950,2,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.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: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 950.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{6} +5.00000 q^{7} -1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{6} +5.00000 q^{7} -1.00000 q^{8} +6.00000 q^{9} -4.00000 q^{11} +3.00000 q^{12} +1.00000 q^{13} -5.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -6.00000 q^{18} +1.00000 q^{19} +15.0000 q^{21} +4.00000 q^{22} -7.00000 q^{23} -3.00000 q^{24} -1.00000 q^{26} +9.00000 q^{27} +5.00000 q^{28} -3.00000 q^{29} -2.00000 q^{31} -1.00000 q^{32} -12.0000 q^{33} -3.00000 q^{34} +6.00000 q^{36} +2.00000 q^{37} -1.00000 q^{38} +3.00000 q^{39} -6.00000 q^{41} -15.0000 q^{42} -6.00000 q^{43} -4.00000 q^{44} +7.00000 q^{46} +3.00000 q^{48} +18.0000 q^{49} +9.00000 q^{51} +1.00000 q^{52} +13.0000 q^{53} -9.00000 q^{54} -5.00000 q^{56} +3.00000 q^{57} +3.00000 q^{58} -9.00000 q^{59} -12.0000 q^{61} +2.00000 q^{62} +30.0000 q^{63} +1.00000 q^{64} +12.0000 q^{66} +3.00000 q^{67} +3.00000 q^{68} -21.0000 q^{69} -6.00000 q^{72} -11.0000 q^{73} -2.00000 q^{74} +1.00000 q^{76} -20.0000 q^{77} -3.00000 q^{78} -2.00000 q^{79} +9.00000 q^{81} +6.00000 q^{82} +10.0000 q^{83} +15.0000 q^{84} +6.00000 q^{86} -9.00000 q^{87} +4.00000 q^{88} +2.00000 q^{89} +5.00000 q^{91} -7.00000 q^{92} -6.00000 q^{93} -3.00000 q^{96} +2.00000 q^{97} -18.0000 q^{98} -24.0000 q^{99} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 3.00000 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −3.00000 −1.22474
$$7$$ 5.00000 1.88982 0.944911 0.327327i $$-0.106148\pi$$
0.944911 + 0.327327i $$0.106148\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 6.00000 2.00000
$$10$$ 0 0
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 3.00000 0.866025
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ −5.00000 −1.33631
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ −6.00000 −1.41421
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ 15.0000 3.27327
$$22$$ 4.00000 0.852803
$$23$$ −7.00000 −1.45960 −0.729800 0.683660i $$-0.760387\pi$$
−0.729800 + 0.683660i $$0.760387\pi$$
$$24$$ −3.00000 −0.612372
$$25$$ 0 0
$$26$$ −1.00000 −0.196116
$$27$$ 9.00000 1.73205
$$28$$ 5.00000 0.944911
$$29$$ −3.00000 −0.557086 −0.278543 0.960424i $$-0.589851\pi$$
−0.278543 + 0.960424i $$0.589851\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −12.0000 −2.08893
$$34$$ −3.00000 −0.514496
$$35$$ 0 0
$$36$$ 6.00000 1.00000
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 3.00000 0.480384
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ −15.0000 −2.31455
$$43$$ −6.00000 −0.914991 −0.457496 0.889212i $$-0.651253\pi$$
−0.457496 + 0.889212i $$0.651253\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ 7.00000 1.03209
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 3.00000 0.433013
$$49$$ 18.0000 2.57143
$$50$$ 0 0
$$51$$ 9.00000 1.26025
$$52$$ 1.00000 0.138675
$$53$$ 13.0000 1.78569 0.892844 0.450367i $$-0.148707\pi$$
0.892844 + 0.450367i $$0.148707\pi$$
$$54$$ −9.00000 −1.22474
$$55$$ 0 0
$$56$$ −5.00000 −0.668153
$$57$$ 3.00000 0.397360
$$58$$ 3.00000 0.393919
$$59$$ −9.00000 −1.17170 −0.585850 0.810419i $$-0.699239\pi$$
−0.585850 + 0.810419i $$0.699239\pi$$
$$60$$ 0 0
$$61$$ −12.0000 −1.53644 −0.768221 0.640184i $$-0.778858\pi$$
−0.768221 + 0.640184i $$0.778858\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 30.0000 3.77964
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 12.0000 1.47710
$$67$$ 3.00000 0.366508 0.183254 0.983066i $$-0.441337\pi$$
0.183254 + 0.983066i $$0.441337\pi$$
$$68$$ 3.00000 0.363803
$$69$$ −21.0000 −2.52810
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ −6.00000 −0.707107
$$73$$ −11.0000 −1.28745 −0.643726 0.765256i $$-0.722612\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ −20.0000 −2.27921
$$78$$ −3.00000 −0.339683
$$79$$ −2.00000 −0.225018 −0.112509 0.993651i $$-0.535889\pi$$
−0.112509 + 0.993651i $$0.535889\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 6.00000 0.662589
$$83$$ 10.0000 1.09764 0.548821 0.835940i $$-0.315077\pi$$
0.548821 + 0.835940i $$0.315077\pi$$
$$84$$ 15.0000 1.63663
$$85$$ 0 0
$$86$$ 6.00000 0.646997
$$87$$ −9.00000 −0.964901
$$88$$ 4.00000 0.426401
$$89$$ 2.00000 0.212000 0.106000 0.994366i $$-0.466196\pi$$
0.106000 + 0.994366i $$0.466196\pi$$
$$90$$ 0 0
$$91$$ 5.00000 0.524142
$$92$$ −7.00000 −0.729800
$$93$$ −6.00000 −0.622171
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −3.00000 −0.306186
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ −18.0000 −1.81827
$$99$$ −24.0000 −2.41209
$$100$$ 0 0
$$101$$ −8.00000 −0.796030 −0.398015 0.917379i $$-0.630301\pi$$
−0.398015 + 0.917379i $$0.630301\pi$$
$$102$$ −9.00000 −0.891133
$$103$$ −4.00000 −0.394132 −0.197066 0.980390i $$-0.563141\pi$$
−0.197066 + 0.980390i $$0.563141\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ −13.0000 −1.26267
$$107$$ 13.0000 1.25676 0.628379 0.777908i $$-0.283719\pi$$
0.628379 + 0.777908i $$0.283719\pi$$
$$108$$ 9.00000 0.866025
$$109$$ 19.0000 1.81987 0.909935 0.414751i $$-0.136131\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 0 0
$$111$$ 6.00000 0.569495
$$112$$ 5.00000 0.472456
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ −3.00000 −0.280976
$$115$$ 0 0
$$116$$ −3.00000 −0.278543
$$117$$ 6.00000 0.554700
$$118$$ 9.00000 0.828517
$$119$$ 15.0000 1.37505
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 12.0000 1.08643
$$123$$ −18.0000 −1.62301
$$124$$ −2.00000 −0.179605
$$125$$ 0 0
$$126$$ −30.0000 −2.67261
$$127$$ 6.00000 0.532414 0.266207 0.963916i $$-0.414230\pi$$
0.266207 + 0.963916i $$0.414230\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −18.0000 −1.58481
$$130$$ 0 0
$$131$$ 16.0000 1.39793 0.698963 0.715158i $$-0.253645\pi$$
0.698963 + 0.715158i $$0.253645\pi$$
$$132$$ −12.0000 −1.04447
$$133$$ 5.00000 0.433555
$$134$$ −3.00000 −0.259161
$$135$$ 0 0
$$136$$ −3.00000 −0.257248
$$137$$ −9.00000 −0.768922 −0.384461 0.923141i $$-0.625613\pi$$
−0.384461 + 0.923141i $$0.625613\pi$$
$$138$$ 21.0000 1.78764
$$139$$ 16.0000 1.35710 0.678551 0.734553i $$-0.262608\pi$$
0.678551 + 0.734553i $$0.262608\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −4.00000 −0.334497
$$144$$ 6.00000 0.500000
$$145$$ 0 0
$$146$$ 11.0000 0.910366
$$147$$ 54.0000 4.45384
$$148$$ 2.00000 0.164399
$$149$$ −4.00000 −0.327693 −0.163846 0.986486i $$-0.552390\pi$$
−0.163846 + 0.986486i $$0.552390\pi$$
$$150$$ 0 0
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ 18.0000 1.45521
$$154$$ 20.0000 1.61165
$$155$$ 0 0
$$156$$ 3.00000 0.240192
$$157$$ −6.00000 −0.478852 −0.239426 0.970915i $$-0.576959\pi$$
−0.239426 + 0.970915i $$0.576959\pi$$
$$158$$ 2.00000 0.159111
$$159$$ 39.0000 3.09290
$$160$$ 0 0
$$161$$ −35.0000 −2.75839
$$162$$ −9.00000 −0.707107
$$163$$ −22.0000 −1.72317 −0.861586 0.507611i $$-0.830529\pi$$
−0.861586 + 0.507611i $$0.830529\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ −10.0000 −0.776151
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ −15.0000 −1.15728
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 6.00000 0.458831
$$172$$ −6.00000 −0.457496
$$173$$ 14.0000 1.06440 0.532200 0.846619i $$-0.321365\pi$$
0.532200 + 0.846619i $$0.321365\pi$$
$$174$$ 9.00000 0.682288
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ −27.0000 −2.02944
$$178$$ −2.00000 −0.149906
$$179$$ −8.00000 −0.597948 −0.298974 0.954261i $$-0.596644\pi$$
−0.298974 + 0.954261i $$0.596644\pi$$
$$180$$ 0 0
$$181$$ 26.0000 1.93256 0.966282 0.257485i $$-0.0828937\pi$$
0.966282 + 0.257485i $$0.0828937\pi$$
$$182$$ −5.00000 −0.370625
$$183$$ −36.0000 −2.66120
$$184$$ 7.00000 0.516047
$$185$$ 0 0
$$186$$ 6.00000 0.439941
$$187$$ −12.0000 −0.877527
$$188$$ 0 0
$$189$$ 45.0000 3.27327
$$190$$ 0 0
$$191$$ 9.00000 0.651217 0.325609 0.945505i $$-0.394431\pi$$
0.325609 + 0.945505i $$0.394431\pi$$
$$192$$ 3.00000 0.216506
$$193$$ −10.0000 −0.719816 −0.359908 0.932988i $$-0.617192\pi$$
−0.359908 + 0.932988i $$0.617192\pi$$
$$194$$ −2.00000 −0.143592
$$195$$ 0 0
$$196$$ 18.0000 1.28571
$$197$$ 22.0000 1.56744 0.783718 0.621117i $$-0.213321\pi$$
0.783718 + 0.621117i $$0.213321\pi$$
$$198$$ 24.0000 1.70561
$$199$$ −15.0000 −1.06332 −0.531661 0.846957i $$-0.678432\pi$$
−0.531661 + 0.846957i $$0.678432\pi$$
$$200$$ 0 0
$$201$$ 9.00000 0.634811
$$202$$ 8.00000 0.562878
$$203$$ −15.0000 −1.05279
$$204$$ 9.00000 0.630126
$$205$$ 0 0
$$206$$ 4.00000 0.278693
$$207$$ −42.0000 −2.91920
$$208$$ 1.00000 0.0693375
$$209$$ −4.00000 −0.276686
$$210$$ 0 0
$$211$$ −5.00000 −0.344214 −0.172107 0.985078i $$-0.555058\pi$$
−0.172107 + 0.985078i $$0.555058\pi$$
$$212$$ 13.0000 0.892844
$$213$$ 0 0
$$214$$ −13.0000 −0.888662
$$215$$ 0 0
$$216$$ −9.00000 −0.612372
$$217$$ −10.0000 −0.678844
$$218$$ −19.0000 −1.28684
$$219$$ −33.0000 −2.22993
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ −6.00000 −0.402694
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ −5.00000 −0.334077
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −5.00000 −0.331862 −0.165931 0.986137i $$-0.553063\pi$$
−0.165931 + 0.986137i $$0.553063\pi$$
$$228$$ 3.00000 0.198680
$$229$$ −6.00000 −0.396491 −0.198246 0.980152i $$-0.563524\pi$$
−0.198246 + 0.980152i $$0.563524\pi$$
$$230$$ 0 0
$$231$$ −60.0000 −3.94771
$$232$$ 3.00000 0.196960
$$233$$ −10.0000 −0.655122 −0.327561 0.944830i $$-0.606227\pi$$
−0.327561 + 0.944830i $$0.606227\pi$$
$$234$$ −6.00000 −0.392232
$$235$$ 0 0
$$236$$ −9.00000 −0.585850
$$237$$ −6.00000 −0.389742
$$238$$ −15.0000 −0.972306
$$239$$ −11.0000 −0.711531 −0.355765 0.934575i $$-0.615780\pi$$
−0.355765 + 0.934575i $$0.615780\pi$$
$$240$$ 0 0
$$241$$ −12.0000 −0.772988 −0.386494 0.922292i $$-0.626314\pi$$
−0.386494 + 0.922292i $$0.626314\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 0 0
$$244$$ −12.0000 −0.768221
$$245$$ 0 0
$$246$$ 18.0000 1.14764
$$247$$ 1.00000 0.0636285
$$248$$ 2.00000 0.127000
$$249$$ 30.0000 1.90117
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 30.0000 1.88982
$$253$$ 28.0000 1.76034
$$254$$ −6.00000 −0.376473
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −22.0000 −1.37232 −0.686161 0.727450i $$-0.740706\pi$$
−0.686161 + 0.727450i $$0.740706\pi$$
$$258$$ 18.0000 1.12063
$$259$$ 10.0000 0.621370
$$260$$ 0 0
$$261$$ −18.0000 −1.11417
$$262$$ −16.0000 −0.988483
$$263$$ −8.00000 −0.493301 −0.246651 0.969104i $$-0.579330\pi$$
−0.246651 + 0.969104i $$0.579330\pi$$
$$264$$ 12.0000 0.738549
$$265$$ 0 0
$$266$$ −5.00000 −0.306570
$$267$$ 6.00000 0.367194
$$268$$ 3.00000 0.183254
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ 0 0
$$271$$ −27.0000 −1.64013 −0.820067 0.572268i $$-0.806064\pi$$
−0.820067 + 0.572268i $$0.806064\pi$$
$$272$$ 3.00000 0.181902
$$273$$ 15.0000 0.907841
$$274$$ 9.00000 0.543710
$$275$$ 0 0
$$276$$ −21.0000 −1.26405
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ −12.0000 −0.718421
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 2.00000 0.118888 0.0594438 0.998232i $$-0.481067\pi$$
0.0594438 + 0.998232i $$0.481067\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 4.00000 0.236525
$$287$$ −30.0000 −1.77084
$$288$$ −6.00000 −0.353553
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 6.00000 0.351726
$$292$$ −11.0000 −0.643726
$$293$$ 27.0000 1.57736 0.788678 0.614806i $$-0.210766\pi$$
0.788678 + 0.614806i $$0.210766\pi$$
$$294$$ −54.0000 −3.14934
$$295$$ 0 0
$$296$$ −2.00000 −0.116248
$$297$$ −36.0000 −2.08893
$$298$$ 4.00000 0.231714
$$299$$ −7.00000 −0.404820
$$300$$ 0 0
$$301$$ −30.0000 −1.72917
$$302$$ 10.0000 0.575435
$$303$$ −24.0000 −1.37876
$$304$$ 1.00000 0.0573539
$$305$$ 0 0
$$306$$ −18.0000 −1.02899
$$307$$ −4.00000 −0.228292 −0.114146 0.993464i $$-0.536413\pi$$
−0.114146 + 0.993464i $$0.536413\pi$$
$$308$$ −20.0000 −1.13961
$$309$$ −12.0000 −0.682656
$$310$$ 0 0
$$311$$ 25.0000 1.41762 0.708810 0.705399i $$-0.249232\pi$$
0.708810 + 0.705399i $$0.249232\pi$$
$$312$$ −3.00000 −0.169842
$$313$$ 1.00000 0.0565233 0.0282617 0.999601i $$-0.491003\pi$$
0.0282617 + 0.999601i $$0.491003\pi$$
$$314$$ 6.00000 0.338600
$$315$$ 0 0
$$316$$ −2.00000 −0.112509
$$317$$ −9.00000 −0.505490 −0.252745 0.967533i $$-0.581333\pi$$
−0.252745 + 0.967533i $$0.581333\pi$$
$$318$$ −39.0000 −2.18701
$$319$$ 12.0000 0.671871
$$320$$ 0 0
$$321$$ 39.0000 2.17677
$$322$$ 35.0000 1.95047
$$323$$ 3.00000 0.166924
$$324$$ 9.00000 0.500000
$$325$$ 0 0
$$326$$ 22.0000 1.21847
$$327$$ 57.0000 3.15211
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −7.00000 −0.384755 −0.192377 0.981321i $$-0.561620\pi$$
−0.192377 + 0.981321i $$0.561620\pi$$
$$332$$ 10.0000 0.548821
$$333$$ 12.0000 0.657596
$$334$$ −2.00000 −0.109435
$$335$$ 0 0
$$336$$ 15.0000 0.818317
$$337$$ −6.00000 −0.326841 −0.163420 0.986557i $$-0.552253\pi$$
−0.163420 + 0.986557i $$0.552253\pi$$
$$338$$ 12.0000 0.652714
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.00000 0.433224
$$342$$ −6.00000 −0.324443
$$343$$ 55.0000 2.96972
$$344$$ 6.00000 0.323498
$$345$$ 0 0
$$346$$ −14.0000 −0.752645
$$347$$ 6.00000 0.322097 0.161048 0.986947i $$-0.448512\pi$$
0.161048 + 0.986947i $$0.448512\pi$$
$$348$$ −9.00000 −0.482451
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 9.00000 0.480384
$$352$$ 4.00000 0.213201
$$353$$ −7.00000 −0.372572 −0.186286 0.982496i $$-0.559645\pi$$
−0.186286 + 0.982496i $$0.559645\pi$$
$$354$$ 27.0000 1.43503
$$355$$ 0 0
$$356$$ 2.00000 0.106000
$$357$$ 45.0000 2.38165
$$358$$ 8.00000 0.422813
$$359$$ −5.00000 −0.263890 −0.131945 0.991257i $$-0.542122\pi$$
−0.131945 + 0.991257i $$0.542122\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ −26.0000 −1.36653
$$363$$ 15.0000 0.787296
$$364$$ 5.00000 0.262071
$$365$$ 0 0
$$366$$ 36.0000 1.88175
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ −7.00000 −0.364900
$$369$$ −36.0000 −1.87409
$$370$$ 0 0
$$371$$ 65.0000 3.37463
$$372$$ −6.00000 −0.311086
$$373$$ 23.0000 1.19089 0.595447 0.803394i $$-0.296975\pi$$
0.595447 + 0.803394i $$0.296975\pi$$
$$374$$ 12.0000 0.620505
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −3.00000 −0.154508
$$378$$ −45.0000 −2.31455
$$379$$ −33.0000 −1.69510 −0.847548 0.530719i $$-0.821922\pi$$
−0.847548 + 0.530719i $$0.821922\pi$$
$$380$$ 0 0
$$381$$ 18.0000 0.922168
$$382$$ −9.00000 −0.460480
$$383$$ 4.00000 0.204390 0.102195 0.994764i $$-0.467413\pi$$
0.102195 + 0.994764i $$0.467413\pi$$
$$384$$ −3.00000 −0.153093
$$385$$ 0 0
$$386$$ 10.0000 0.508987
$$387$$ −36.0000 −1.82998
$$388$$ 2.00000 0.101535
$$389$$ −4.00000 −0.202808 −0.101404 0.994845i $$-0.532333\pi$$
−0.101404 + 0.994845i $$0.532333\pi$$
$$390$$ 0 0
$$391$$ −21.0000 −1.06202
$$392$$ −18.0000 −0.909137
$$393$$ 48.0000 2.42128
$$394$$ −22.0000 −1.10834
$$395$$ 0 0
$$396$$ −24.0000 −1.20605
$$397$$ 16.0000 0.803017 0.401508 0.915855i $$-0.368486\pi$$
0.401508 + 0.915855i $$0.368486\pi$$
$$398$$ 15.0000 0.751882
$$399$$ 15.0000 0.750939
$$400$$ 0 0
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ −9.00000 −0.448879
$$403$$ −2.00000 −0.0996271
$$404$$ −8.00000 −0.398015
$$405$$ 0 0
$$406$$ 15.0000 0.744438
$$407$$ −8.00000 −0.396545
$$408$$ −9.00000 −0.445566
$$409$$ 22.0000 1.08783 0.543915 0.839140i $$-0.316941\pi$$
0.543915 + 0.839140i $$0.316941\pi$$
$$410$$ 0 0
$$411$$ −27.0000 −1.33181
$$412$$ −4.00000 −0.197066
$$413$$ −45.0000 −2.21431
$$414$$ 42.0000 2.06419
$$415$$ 0 0
$$416$$ −1.00000 −0.0490290
$$417$$ 48.0000 2.35057
$$418$$ 4.00000 0.195646
$$419$$ 14.0000 0.683945 0.341972 0.939710i $$-0.388905\pi$$
0.341972 + 0.939710i $$0.388905\pi$$
$$420$$ 0 0
$$421$$ 1.00000 0.0487370 0.0243685 0.999703i $$-0.492242\pi$$
0.0243685 + 0.999703i $$0.492242\pi$$
$$422$$ 5.00000 0.243396
$$423$$ 0 0
$$424$$ −13.0000 −0.631336
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −60.0000 −2.90360
$$428$$ 13.0000 0.628379
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ −36.0000 −1.73406 −0.867029 0.498257i $$-0.833974\pi$$
−0.867029 + 0.498257i $$0.833974\pi$$
$$432$$ 9.00000 0.433013
$$433$$ 16.0000 0.768911 0.384455 0.923144i $$-0.374389\pi$$
0.384455 + 0.923144i $$0.374389\pi$$
$$434$$ 10.0000 0.480015
$$435$$ 0 0
$$436$$ 19.0000 0.909935
$$437$$ −7.00000 −0.334855
$$438$$ 33.0000 1.57680
$$439$$ 26.0000 1.24091 0.620456 0.784241i $$-0.286947\pi$$
0.620456 + 0.784241i $$0.286947\pi$$
$$440$$ 0 0
$$441$$ 108.000 5.14286
$$442$$ −3.00000 −0.142695
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ 6.00000 0.284747
$$445$$ 0 0
$$446$$ −2.00000 −0.0947027
$$447$$ −12.0000 −0.567581
$$448$$ 5.00000 0.236228
$$449$$ −22.0000 −1.03824 −0.519122 0.854700i $$-0.673741\pi$$
−0.519122 + 0.854700i $$0.673741\pi$$
$$450$$ 0 0
$$451$$ 24.0000 1.13012
$$452$$ 0 0
$$453$$ −30.0000 −1.40952
$$454$$ 5.00000 0.234662
$$455$$ 0 0
$$456$$ −3.00000 −0.140488
$$457$$ 29.0000 1.35656 0.678281 0.734802i $$-0.262725\pi$$
0.678281 + 0.734802i $$0.262725\pi$$
$$458$$ 6.00000 0.280362
$$459$$ 27.0000 1.26025
$$460$$ 0 0
$$461$$ 18.0000 0.838344 0.419172 0.907907i $$-0.362320\pi$$
0.419172 + 0.907907i $$0.362320\pi$$
$$462$$ 60.0000 2.79145
$$463$$ 8.00000 0.371792 0.185896 0.982569i $$-0.440481\pi$$
0.185896 + 0.982569i $$0.440481\pi$$
$$464$$ −3.00000 −0.139272
$$465$$ 0 0
$$466$$ 10.0000 0.463241
$$467$$ 8.00000 0.370196 0.185098 0.982720i $$-0.440740\pi$$
0.185098 + 0.982720i $$0.440740\pi$$
$$468$$ 6.00000 0.277350
$$469$$ 15.0000 0.692636
$$470$$ 0 0
$$471$$ −18.0000 −0.829396
$$472$$ 9.00000 0.414259
$$473$$ 24.0000 1.10352
$$474$$ 6.00000 0.275589
$$475$$ 0 0
$$476$$ 15.0000 0.687524
$$477$$ 78.0000 3.57137
$$478$$ 11.0000 0.503128
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 2.00000 0.0911922
$$482$$ 12.0000 0.546585
$$483$$ −105.000 −4.77767
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 38.0000 1.72194 0.860972 0.508652i $$-0.169856\pi$$
0.860972 + 0.508652i $$0.169856\pi$$
$$488$$ 12.0000 0.543214
$$489$$ −66.0000 −2.98462
$$490$$ 0 0
$$491$$ 18.0000 0.812329 0.406164 0.913800i $$-0.366866\pi$$
0.406164 + 0.913800i $$0.366866\pi$$
$$492$$ −18.0000 −0.811503
$$493$$ −9.00000 −0.405340
$$494$$ −1.00000 −0.0449921
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ 0 0
$$498$$ −30.0000 −1.34433
$$499$$ 42.0000 1.88018 0.940089 0.340929i $$-0.110742\pi$$
0.940089 + 0.340929i $$0.110742\pi$$
$$500$$ 0 0
$$501$$ 6.00000 0.268060
$$502$$ 12.0000 0.535586
$$503$$ 21.0000 0.936344 0.468172 0.883637i $$-0.344913\pi$$
0.468172 + 0.883637i $$0.344913\pi$$
$$504$$ −30.0000 −1.33631
$$505$$ 0 0
$$506$$ −28.0000 −1.24475
$$507$$ −36.0000 −1.59882
$$508$$ 6.00000 0.266207
$$509$$ 2.00000 0.0886484 0.0443242 0.999017i $$-0.485887\pi$$
0.0443242 + 0.999017i $$0.485887\pi$$
$$510$$ 0 0
$$511$$ −55.0000 −2.43306
$$512$$ −1.00000 −0.0441942
$$513$$ 9.00000 0.397360
$$514$$ 22.0000 0.970378
$$515$$ 0 0
$$516$$ −18.0000 −0.792406
$$517$$ 0 0
$$518$$ −10.0000 −0.439375
$$519$$ 42.0000 1.84360
$$520$$ 0 0
$$521$$ 24.0000 1.05146 0.525730 0.850652i $$-0.323792\pi$$
0.525730 + 0.850652i $$0.323792\pi$$
$$522$$ 18.0000 0.787839
$$523$$ 9.00000 0.393543 0.196771 0.980449i $$-0.436954\pi$$
0.196771 + 0.980449i $$0.436954\pi$$
$$524$$ 16.0000 0.698963
$$525$$ 0 0
$$526$$ 8.00000 0.348817
$$527$$ −6.00000 −0.261364
$$528$$ −12.0000 −0.522233
$$529$$ 26.0000 1.13043
$$530$$ 0 0
$$531$$ −54.0000 −2.34340
$$532$$ 5.00000 0.216777
$$533$$ −6.00000 −0.259889
$$534$$ −6.00000 −0.259645
$$535$$ 0 0
$$536$$ −3.00000 −0.129580
$$537$$ −24.0000 −1.03568
$$538$$ −2.00000 −0.0862261
$$539$$ −72.0000 −3.10126
$$540$$ 0 0
$$541$$ 16.0000 0.687894 0.343947 0.938989i $$-0.388236\pi$$
0.343947 + 0.938989i $$0.388236\pi$$
$$542$$ 27.0000 1.15975
$$543$$ 78.0000 3.34730
$$544$$ −3.00000 −0.128624
$$545$$ 0 0
$$546$$ −15.0000 −0.641941
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ −9.00000 −0.384461
$$549$$ −72.0000 −3.07289
$$550$$ 0 0
$$551$$ −3.00000 −0.127804
$$552$$ 21.0000 0.893819
$$553$$ −10.0000 −0.425243
$$554$$ −8.00000 −0.339887
$$555$$ 0 0
$$556$$ 16.0000 0.678551
$$557$$ −12.0000 −0.508456 −0.254228 0.967144i $$-0.581821\pi$$
−0.254228 + 0.967144i $$0.581821\pi$$
$$558$$ 12.0000 0.508001
$$559$$ −6.00000 −0.253773
$$560$$ 0 0
$$561$$ −36.0000 −1.51992
$$562$$ 18.0000 0.759284
$$563$$ −20.0000 −0.842900 −0.421450 0.906852i $$-0.638479\pi$$
−0.421450 + 0.906852i $$0.638479\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −2.00000 −0.0840663
$$567$$ 45.0000 1.88982
$$568$$ 0 0
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ 6.00000 0.251092 0.125546 0.992088i $$-0.459932\pi$$
0.125546 + 0.992088i $$0.459932\pi$$
$$572$$ −4.00000 −0.167248
$$573$$ 27.0000 1.12794
$$574$$ 30.0000 1.25218
$$575$$ 0 0
$$576$$ 6.00000 0.250000
$$577$$ 7.00000 0.291414 0.145707 0.989328i $$-0.453454\pi$$
0.145707 + 0.989328i $$0.453454\pi$$
$$578$$ 8.00000 0.332756
$$579$$ −30.0000 −1.24676
$$580$$ 0 0
$$581$$ 50.0000 2.07435
$$582$$ −6.00000 −0.248708
$$583$$ −52.0000 −2.15362
$$584$$ 11.0000 0.455183
$$585$$ 0 0
$$586$$ −27.0000 −1.11536
$$587$$ −18.0000 −0.742940 −0.371470 0.928445i $$-0.621146\pi$$
−0.371470 + 0.928445i $$0.621146\pi$$
$$588$$ 54.0000 2.22692
$$589$$ −2.00000 −0.0824086
$$590$$ 0 0
$$591$$ 66.0000 2.71488
$$592$$ 2.00000 0.0821995
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 36.0000 1.47710
$$595$$ 0 0
$$596$$ −4.00000 −0.163846
$$597$$ −45.0000 −1.84173
$$598$$ 7.00000 0.286251
$$599$$ −26.0000 −1.06233 −0.531166 0.847268i $$-0.678246\pi$$
−0.531166 + 0.847268i $$0.678246\pi$$
$$600$$ 0 0
$$601$$ 42.0000 1.71322 0.856608 0.515968i $$-0.172568\pi$$
0.856608 + 0.515968i $$0.172568\pi$$
$$602$$ 30.0000 1.22271
$$603$$ 18.0000 0.733017
$$604$$ −10.0000 −0.406894
$$605$$ 0 0
$$606$$ 24.0000 0.974933
$$607$$ 26.0000 1.05531 0.527654 0.849460i $$-0.323072\pi$$
0.527654 + 0.849460i $$0.323072\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ −45.0000 −1.82349
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 18.0000 0.727607
$$613$$ 20.0000 0.807792 0.403896 0.914805i $$-0.367656\pi$$
0.403896 + 0.914805i $$0.367656\pi$$
$$614$$ 4.00000 0.161427
$$615$$ 0 0
$$616$$ 20.0000 0.805823
$$617$$ −14.0000 −0.563619 −0.281809 0.959470i $$-0.590935\pi$$
−0.281809 + 0.959470i $$0.590935\pi$$
$$618$$ 12.0000 0.482711
$$619$$ −24.0000 −0.964641 −0.482321 0.875995i $$-0.660206\pi$$
−0.482321 + 0.875995i $$0.660206\pi$$
$$620$$ 0 0
$$621$$ −63.0000 −2.52810
$$622$$ −25.0000 −1.00241
$$623$$ 10.0000 0.400642
$$624$$ 3.00000 0.120096
$$625$$ 0 0
$$626$$ −1.00000 −0.0399680
$$627$$ −12.0000 −0.479234
$$628$$ −6.00000 −0.239426
$$629$$ 6.00000 0.239236
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 2.00000 0.0795557
$$633$$ −15.0000 −0.596196
$$634$$ 9.00000 0.357436
$$635$$ 0 0
$$636$$ 39.0000 1.54645
$$637$$ 18.0000 0.713186
$$638$$ −12.0000 −0.475085
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.00000 0.315981 0.157991 0.987441i $$-0.449498\pi$$
0.157991 + 0.987441i $$0.449498\pi$$
$$642$$ −39.0000 −1.53921
$$643$$ −26.0000 −1.02534 −0.512670 0.858586i $$-0.671344\pi$$
−0.512670 + 0.858586i $$0.671344\pi$$
$$644$$ −35.0000 −1.37919
$$645$$ 0 0
$$646$$ −3.00000 −0.118033
$$647$$ 21.0000 0.825595 0.412798 0.910823i $$-0.364552\pi$$
0.412798 + 0.910823i $$0.364552\pi$$
$$648$$ −9.00000 −0.353553
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ −30.0000 −1.17579
$$652$$ −22.0000 −0.861586
$$653$$ 16.0000 0.626128 0.313064 0.949732i $$-0.398644\pi$$
0.313064 + 0.949732i $$0.398644\pi$$
$$654$$ −57.0000 −2.22888
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ −66.0000 −2.57491
$$658$$ 0 0
$$659$$ 33.0000 1.28550 0.642749 0.766077i $$-0.277794\pi$$
0.642749 + 0.766077i $$0.277794\pi$$
$$660$$ 0 0
$$661$$ 15.0000 0.583432 0.291716 0.956505i $$-0.405774\pi$$
0.291716 + 0.956505i $$0.405774\pi$$
$$662$$ 7.00000 0.272063
$$663$$ 9.00000 0.349531
$$664$$ −10.0000 −0.388075
$$665$$ 0 0
$$666$$ −12.0000 −0.464991
$$667$$ 21.0000 0.813123
$$668$$ 2.00000 0.0773823
$$669$$ 6.00000 0.231973
$$670$$ 0 0
$$671$$ 48.0000 1.85302
$$672$$ −15.0000 −0.578638
$$673$$ 44.0000 1.69608 0.848038 0.529936i $$-0.177784\pi$$
0.848038 + 0.529936i $$0.177784\pi$$
$$674$$ 6.00000 0.231111
$$675$$ 0 0
$$676$$ −12.0000 −0.461538
$$677$$ 39.0000 1.49889 0.749446 0.662066i $$-0.230320\pi$$
0.749446 + 0.662066i $$0.230320\pi$$
$$678$$ 0 0
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ −15.0000 −0.574801
$$682$$ −8.00000 −0.306336
$$683$$ 44.0000 1.68361 0.841807 0.539779i $$-0.181492\pi$$
0.841807 + 0.539779i $$0.181492\pi$$
$$684$$ 6.00000 0.229416
$$685$$ 0 0
$$686$$ −55.0000 −2.09991
$$687$$ −18.0000 −0.686743
$$688$$ −6.00000 −0.228748
$$689$$ 13.0000 0.495261
$$690$$ 0 0
$$691$$ −42.0000 −1.59776 −0.798878 0.601494i $$-0.794573\pi$$
−0.798878 + 0.601494i $$0.794573\pi$$
$$692$$ 14.0000 0.532200
$$693$$ −120.000 −4.55842
$$694$$ −6.00000 −0.227757
$$695$$ 0 0
$$696$$ 9.00000 0.341144
$$697$$ −18.0000 −0.681799
$$698$$ −14.0000 −0.529908
$$699$$ −30.0000 −1.13470
$$700$$ 0 0
$$701$$ 24.0000 0.906467 0.453234 0.891392i $$-0.350270\pi$$
0.453234 + 0.891392i $$0.350270\pi$$
$$702$$ −9.00000 −0.339683
$$703$$ 2.00000 0.0754314
$$704$$ −4.00000 −0.150756
$$705$$ 0 0
$$706$$ 7.00000 0.263448
$$707$$ −40.0000 −1.50435
$$708$$ −27.0000 −1.01472
$$709$$ 2.00000 0.0751116 0.0375558 0.999295i $$-0.488043\pi$$
0.0375558 + 0.999295i $$0.488043\pi$$
$$710$$ 0 0
$$711$$ −12.0000 −0.450035
$$712$$ −2.00000 −0.0749532
$$713$$ 14.0000 0.524304
$$714$$ −45.0000 −1.68408
$$715$$ 0 0
$$716$$ −8.00000 −0.298974
$$717$$ −33.0000 −1.23241
$$718$$ 5.00000 0.186598
$$719$$ −27.0000 −1.00693 −0.503465 0.864016i $$-0.667942\pi$$
−0.503465 + 0.864016i $$0.667942\pi$$
$$720$$ 0 0
$$721$$ −20.0000 −0.744839
$$722$$ −1.00000 −0.0372161
$$723$$ −36.0000 −1.33885
$$724$$ 26.0000 0.966282
$$725$$ 0 0
$$726$$ −15.0000 −0.556702
$$727$$ −23.0000 −0.853023 −0.426511 0.904482i $$-0.640258\pi$$
−0.426511 + 0.904482i $$0.640258\pi$$
$$728$$ −5.00000 −0.185312
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −18.0000 −0.665754
$$732$$ −36.0000 −1.33060
$$733$$ −36.0000 −1.32969 −0.664845 0.746981i $$-0.731502\pi$$
−0.664845 + 0.746981i $$0.731502\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ 7.00000 0.258023
$$737$$ −12.0000 −0.442026
$$738$$ 36.0000 1.32518
$$739$$ −10.0000 −0.367856 −0.183928 0.982940i $$-0.558881\pi$$
−0.183928 + 0.982940i $$0.558881\pi$$
$$740$$ 0 0
$$741$$ 3.00000 0.110208
$$742$$ −65.0000 −2.38623
$$743$$ 18.0000 0.660356 0.330178 0.943919i $$-0.392891\pi$$
0.330178 + 0.943919i $$0.392891\pi$$
$$744$$ 6.00000 0.219971
$$745$$ 0 0
$$746$$ −23.0000 −0.842090
$$747$$ 60.0000 2.19529
$$748$$ −12.0000 −0.438763
$$749$$ 65.0000 2.37505
$$750$$ 0 0
$$751$$ −26.0000 −0.948753 −0.474377 0.880322i $$-0.657327\pi$$
−0.474377 + 0.880322i $$0.657327\pi$$
$$752$$ 0 0
$$753$$ −36.0000 −1.31191
$$754$$ 3.00000 0.109254
$$755$$ 0 0
$$756$$ 45.0000 1.63663
$$757$$ 6.00000 0.218074 0.109037 0.994038i $$-0.465223\pi$$
0.109037 + 0.994038i $$0.465223\pi$$
$$758$$ 33.0000 1.19861
$$759$$ 84.0000 3.04901
$$760$$ 0 0
$$761$$ 11.0000 0.398750 0.199375 0.979923i $$-0.436109\pi$$
0.199375 + 0.979923i $$0.436109\pi$$
$$762$$ −18.0000 −0.652071
$$763$$ 95.0000 3.43923
$$764$$ 9.00000 0.325609
$$765$$ 0 0
$$766$$ −4.00000 −0.144526
$$767$$ −9.00000 −0.324971
$$768$$ 3.00000 0.108253
$$769$$ −47.0000 −1.69486 −0.847432 0.530904i $$-0.821852\pi$$
−0.847432 + 0.530904i $$0.821852\pi$$
$$770$$ 0 0
$$771$$ −66.0000 −2.37693
$$772$$ −10.0000 −0.359908
$$773$$ 51.0000 1.83434 0.917171 0.398493i $$-0.130467\pi$$
0.917171 + 0.398493i $$0.130467\pi$$
$$774$$ 36.0000 1.29399
$$775$$ 0 0
$$776$$ −2.00000 −0.0717958
$$777$$ 30.0000 1.07624
$$778$$ 4.00000 0.143407
$$779$$ −6.00000 −0.214972
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 21.0000 0.750958
$$783$$ −27.0000 −0.964901
$$784$$ 18.0000 0.642857
$$785$$ 0 0
$$786$$ −48.0000 −1.71210
$$787$$ 39.0000 1.39020 0.695100 0.718913i $$-0.255360\pi$$
0.695100 + 0.718913i $$0.255360\pi$$
$$788$$ 22.0000 0.783718
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 24.0000 0.852803
$$793$$ −12.0000 −0.426132
$$794$$ −16.0000 −0.567819
$$795$$ 0 0
$$796$$ −15.0000 −0.531661
$$797$$ −31.0000 −1.09808 −0.549038 0.835797i $$-0.685006\pi$$
−0.549038 + 0.835797i $$0.685006\pi$$
$$798$$ −15.0000 −0.530994
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 12.0000 0.423999
$$802$$ 6.00000 0.211867
$$803$$ 44.0000 1.55273
$$804$$ 9.00000 0.317406
$$805$$ 0 0
$$806$$ 2.00000 0.0704470
$$807$$ 6.00000 0.211210
$$808$$ 8.00000 0.281439
$$809$$ 25.0000 0.878953 0.439477 0.898254i $$-0.355164\pi$$
0.439477 + 0.898254i $$0.355164\pi$$
$$810$$ 0 0
$$811$$ 37.0000 1.29925 0.649623 0.760257i $$-0.274927\pi$$
0.649623 + 0.760257i $$0.274927\pi$$
$$812$$ −15.0000 −0.526397
$$813$$ −81.0000 −2.84079
$$814$$ 8.00000 0.280400
$$815$$ 0 0
$$816$$ 9.00000 0.315063
$$817$$ −6.00000 −0.209913
$$818$$ −22.0000 −0.769212
$$819$$ 30.0000 1.04828
$$820$$ 0 0
$$821$$ −52.0000 −1.81481 −0.907406 0.420255i $$-0.861941\pi$$
−0.907406 + 0.420255i $$0.861941\pi$$
$$822$$ 27.0000 0.941733
$$823$$ 43.0000 1.49889 0.749443 0.662069i $$-0.230321\pi$$
0.749443 + 0.662069i $$0.230321\pi$$
$$824$$ 4.00000 0.139347
$$825$$ 0 0
$$826$$ 45.0000 1.56575
$$827$$ 3.00000 0.104320 0.0521601 0.998639i $$-0.483389\pi$$
0.0521601 + 0.998639i $$0.483389\pi$$
$$828$$ −42.0000 −1.45960
$$829$$ 35.0000 1.21560 0.607800 0.794090i $$-0.292052\pi$$
0.607800 + 0.794090i $$0.292052\pi$$
$$830$$ 0 0
$$831$$ 24.0000 0.832551
$$832$$ 1.00000 0.0346688
$$833$$ 54.0000 1.87099
$$834$$ −48.0000 −1.66210
$$835$$ 0 0
$$836$$ −4.00000 −0.138343
$$837$$ −18.0000 −0.622171
$$838$$ −14.0000 −0.483622
$$839$$ −4.00000 −0.138095 −0.0690477 0.997613i $$-0.521996\pi$$
−0.0690477 + 0.997613i $$0.521996\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ −1.00000 −0.0344623
$$843$$ −54.0000 −1.85986
$$844$$ −5.00000 −0.172107
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 25.0000 0.859010
$$848$$ 13.0000 0.446422
$$849$$ 6.00000 0.205919
$$850$$ 0 0
$$851$$ −14.0000 −0.479914
$$852$$ 0 0
$$853$$ −42.0000 −1.43805 −0.719026 0.694983i $$-0.755412\pi$$
−0.719026 + 0.694983i $$0.755412\pi$$
$$854$$ 60.0000 2.05316
$$855$$ 0 0
$$856$$ −13.0000 −0.444331
$$857$$ 40.0000 1.36637 0.683187 0.730243i $$-0.260593\pi$$
0.683187 + 0.730243i $$0.260593\pi$$
$$858$$ 12.0000 0.409673
$$859$$ −28.0000 −0.955348 −0.477674 0.878537i $$-0.658520\pi$$
−0.477674 + 0.878537i $$0.658520\pi$$
$$860$$ 0 0
$$861$$ −90.0000 −3.06719
$$862$$ 36.0000 1.22616
$$863$$ −56.0000 −1.90626 −0.953131 0.302558i $$-0.902160\pi$$
−0.953131 + 0.302558i $$0.902160\pi$$
$$864$$ −9.00000 −0.306186
$$865$$ 0 0
$$866$$ −16.0000 −0.543702
$$867$$ −24.0000 −0.815083
$$868$$ −10.0000 −0.339422
$$869$$ 8.00000 0.271381
$$870$$ 0 0
$$871$$ 3.00000 0.101651
$$872$$ −19.0000 −0.643421
$$873$$ 12.0000 0.406138
$$874$$ 7.00000 0.236779
$$875$$ 0 0
$$876$$ −33.0000 −1.11497
$$877$$ −33.0000 −1.11433 −0.557165 0.830402i $$-0.688111\pi$$
−0.557165 + 0.830402i $$0.688111\pi$$
$$878$$ −26.0000 −0.877457
$$879$$ 81.0000 2.73206
$$880$$ 0 0
$$881$$ 10.0000 0.336909 0.168454 0.985709i $$-0.446122\pi$$
0.168454 + 0.985709i $$0.446122\pi$$
$$882$$ −108.000 −3.63655
$$883$$ −30.0000 −1.00958 −0.504790 0.863242i $$-0.668430\pi$$
−0.504790 + 0.863242i $$0.668430\pi$$
$$884$$ 3.00000 0.100901
$$885$$ 0 0
$$886$$ 36.0000 1.20944
$$887$$ 28.0000 0.940148 0.470074 0.882627i $$-0.344227\pi$$
0.470074 + 0.882627i $$0.344227\pi$$
$$888$$ −6.00000 −0.201347
$$889$$ 30.0000 1.00617
$$890$$ 0 0
$$891$$ −36.0000 −1.20605
$$892$$ 2.00000 0.0669650
$$893$$ 0 0
$$894$$ 12.0000 0.401340
$$895$$ 0 0
$$896$$ −5.00000 −0.167038
$$897$$ −21.0000 −0.701170
$$898$$ 22.0000 0.734150
$$899$$ 6.00000 0.200111
$$900$$ 0 0
$$901$$ 39.0000 1.29928
$$902$$ −24.0000 −0.799113
$$903$$ −90.0000 −2.99501
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 30.0000 0.996683
$$907$$ 1.00000 0.0332045 0.0166022 0.999862i $$-0.494715\pi$$
0.0166022 + 0.999862i $$0.494715\pi$$
$$908$$ −5.00000 −0.165931
$$909$$ −48.0000 −1.59206
$$910$$ 0 0
$$911$$ −12.0000 −0.397578 −0.198789 0.980042i $$-0.563701\pi$$
−0.198789 + 0.980042i $$0.563701\pi$$
$$912$$ 3.00000 0.0993399
$$913$$ −40.0000 −1.32381
$$914$$ −29.0000 −0.959235
$$915$$ 0 0
$$916$$ −6.00000 −0.198246
$$917$$ 80.0000 2.64183
$$918$$ −27.0000 −0.891133
$$919$$ −5.00000 −0.164935 −0.0824674 0.996594i $$-0.526280\pi$$
−0.0824674 + 0.996594i $$0.526280\pi$$
$$920$$ 0 0
$$921$$ −12.0000 −0.395413
$$922$$ −18.0000 −0.592798
$$923$$ 0 0
$$924$$ −60.0000 −1.97386
$$925$$ 0 0
$$926$$ −8.00000 −0.262896
$$927$$ −24.0000 −0.788263
$$928$$ 3.00000 0.0984798
$$929$$ −3.00000 −0.0984268 −0.0492134 0.998788i $$-0.515671\pi$$
−0.0492134 + 0.998788i $$0.515671\pi$$
$$930$$ 0 0
$$931$$ 18.0000 0.589926
$$932$$ −10.0000 −0.327561
$$933$$ 75.0000 2.45539
$$934$$ −8.00000 −0.261768
$$935$$ 0 0
$$936$$ −6.00000 −0.196116
$$937$$ −47.0000 −1.53542 −0.767712 0.640796i $$-0.778605\pi$$
−0.767712 + 0.640796i $$0.778605\pi$$
$$938$$ −15.0000 −0.489767
$$939$$ 3.00000 0.0979013
$$940$$ 0 0
$$941$$ −51.0000 −1.66255 −0.831276 0.555860i $$-0.812389\pi$$
−0.831276 + 0.555860i $$0.812389\pi$$
$$942$$ 18.0000 0.586472
$$943$$ 42.0000 1.36771
$$944$$ −9.00000 −0.292925
$$945$$ 0 0
$$946$$ −24.0000 −0.780307
$$947$$ 24.0000 0.779895 0.389948 0.920837i $$-0.372493\pi$$
0.389948 + 0.920837i $$0.372493\pi$$
$$948$$ −6.00000 −0.194871
$$949$$ −11.0000 −0.357075
$$950$$ 0 0
$$951$$ −27.0000 −0.875535
$$952$$ −15.0000 −0.486153
$$953$$ 24.0000 0.777436 0.388718 0.921357i $$-0.372918\pi$$
0.388718 + 0.921357i $$0.372918\pi$$
$$954$$ −78.0000 −2.52534
$$955$$ 0 0
$$956$$ −11.0000 −0.355765
$$957$$ 36.0000 1.16371
$$958$$ 0 0
$$959$$ −45.0000 −1.45313
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ −2.00000 −0.0644826
$$963$$ 78.0000 2.51351
$$964$$ −12.0000 −0.386494
$$965$$ 0 0
$$966$$ 105.000 3.37832
$$967$$ 44.0000 1.41494 0.707472 0.706741i $$-0.249835\pi$$
0.707472 + 0.706741i $$0.249835\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ 9.00000 0.289122
$$970$$ 0 0
$$971$$ 28.0000 0.898563 0.449281 0.893390i $$-0.351680\pi$$
0.449281 + 0.893390i $$0.351680\pi$$
$$972$$ 0 0
$$973$$ 80.0000 2.56468
$$974$$ −38.0000 −1.21760
$$975$$ 0 0
$$976$$ −12.0000 −0.384111
$$977$$ 62.0000 1.98356 0.991778 0.127971i $$-0.0408466\pi$$
0.991778 + 0.127971i $$0.0408466\pi$$
$$978$$ 66.0000 2.11045
$$979$$ −8.00000 −0.255681
$$980$$ 0 0
$$981$$ 114.000 3.63974
$$982$$ −18.0000 −0.574403
$$983$$ 42.0000 1.33959 0.669796 0.742545i $$-0.266382\pi$$
0.669796 + 0.742545i $$0.266382\pi$$
$$984$$ 18.0000 0.573819
$$985$$ 0 0
$$986$$ 9.00000 0.286618
$$987$$ 0 0
$$988$$ 1.00000 0.0318142
$$989$$ 42.0000 1.33552
$$990$$ 0 0
$$991$$ 30.0000 0.952981 0.476491 0.879180i $$-0.341909\pi$$
0.476491 + 0.879180i $$0.341909\pi$$
$$992$$ 2.00000 0.0635001
$$993$$ −21.0000 −0.666415
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 30.0000 0.950586
$$997$$ 50.0000 1.58352 0.791758 0.610835i $$-0.209166\pi$$
0.791758 + 0.610835i $$0.209166\pi$$
$$998$$ −42.0000 −1.32949
$$999$$ 18.0000 0.569495
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 950.2.a.c.1.1 1
3.2 odd 2 8550.2.a.bm.1.1 1
4.3 odd 2 7600.2.a.a.1.1 1
5.2 odd 4 950.2.b.a.799.1 2
5.3 odd 4 950.2.b.a.799.2 2
5.4 even 2 190.2.a.b.1.1 1
15.14 odd 2 1710.2.a.g.1.1 1
20.19 odd 2 1520.2.a.j.1.1 1
35.34 odd 2 9310.2.a.u.1.1 1
40.19 odd 2 6080.2.a.b.1.1 1
40.29 even 2 6080.2.a.x.1.1 1
95.94 odd 2 3610.2.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.b.1.1 1 5.4 even 2
950.2.a.c.1.1 1 1.1 even 1 trivial
950.2.b.a.799.1 2 5.2 odd 4
950.2.b.a.799.2 2 5.3 odd 4
1520.2.a.j.1.1 1 20.19 odd 2
1710.2.a.g.1.1 1 15.14 odd 2
3610.2.a.e.1.1 1 95.94 odd 2
6080.2.a.b.1.1 1 40.19 odd 2
6080.2.a.x.1.1 1 40.29 even 2
7600.2.a.a.1.1 1 4.3 odd 2
8550.2.a.bm.1.1 1 3.2 odd 2
9310.2.a.u.1.1 1 35.34 odd 2