# Properties

 Label 9025.2.a.bn.1.4 Level $9025$ Weight $2$ Character 9025.1 Self dual yes Analytic conductor $72.065$ Analytic rank $1$ Dimension $4$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, 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("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$9025 = 5^{2} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9025.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: $$72.0649878242$$ Analytic rank: $$1$$ Dimension: $$4$$ Coefficient field: 4.4.7168.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 6x^{2} + 7$$ x^4 - 6*x^2 + 7 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1805) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.4 Root $$2.10100$$ of defining polynomial Character $$\chi$$ $$=$$ 9025.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.10100 q^{2} -2.97127 q^{3} +2.41421 q^{4} -6.24264 q^{6} -4.82843 q^{7} +0.870264 q^{8} +5.82843 q^{9} +O(q^{10})$$ $$q+2.10100 q^{2} -2.97127 q^{3} +2.41421 q^{4} -6.24264 q^{6} -4.82843 q^{7} +0.870264 q^{8} +5.82843 q^{9} +2.00000 q^{11} -7.17327 q^{12} +1.23074 q^{13} -10.1445 q^{14} -3.00000 q^{16} +3.65685 q^{17} +12.2455 q^{18} +14.3465 q^{21} +4.20201 q^{22} -4.82843 q^{23} -2.58579 q^{24} +2.58579 q^{26} -8.40401 q^{27} -11.6569 q^{28} -2.46148 q^{29} +5.94253 q^{31} -8.04354 q^{32} -5.94253 q^{33} +7.68306 q^{34} +14.0711 q^{36} +7.17327 q^{37} -3.65685 q^{39} +30.1421 q^{42} -0.828427 q^{43} +4.82843 q^{44} -10.1445 q^{46} +6.48528 q^{47} +8.91380 q^{48} +16.3137 q^{49} -10.8655 q^{51} +2.97127 q^{52} +4.71179 q^{53} -17.6569 q^{54} -4.20201 q^{56} -5.17157 q^{58} -11.8851 q^{59} +2.82843 q^{61} +12.4853 q^{62} -28.1421 q^{63} -10.8995 q^{64} -12.4853 q^{66} +5.43275 q^{67} +8.82843 q^{68} +14.3465 q^{69} -10.8655 q^{71} +5.07227 q^{72} +0.343146 q^{73} +15.0711 q^{74} -9.65685 q^{77} -7.68306 q^{78} +11.8851 q^{79} +7.48528 q^{81} -3.17157 q^{83} +34.6356 q^{84} -1.74053 q^{86} +7.31371 q^{87} +1.74053 q^{88} -9.42359 q^{89} -5.94253 q^{91} -11.6569 q^{92} -17.6569 q^{93} +13.6256 q^{94} +23.8995 q^{96} +1.23074 q^{97} +34.2752 q^{98} +11.6569 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{4} - 8 q^{6} - 8 q^{7} + 12 q^{9}+O(q^{10})$$ 4 * q + 4 * q^4 - 8 * q^6 - 8 * q^7 + 12 * q^9 $$4 q + 4 q^{4} - 8 q^{6} - 8 q^{7} + 12 q^{9} + 8 q^{11} - 12 q^{16} - 8 q^{17} - 8 q^{23} - 16 q^{24} + 16 q^{26} - 24 q^{28} + 28 q^{36} + 8 q^{39} + 64 q^{42} + 8 q^{43} + 8 q^{44} - 8 q^{47} + 20 q^{49} - 48 q^{54} - 32 q^{58} + 16 q^{62} - 56 q^{63} - 4 q^{64} - 16 q^{66} + 24 q^{68} + 24 q^{73} + 32 q^{74} - 16 q^{77} - 4 q^{81} - 24 q^{83} - 16 q^{87} - 24 q^{92} - 48 q^{93} + 56 q^{96} + 24 q^{99}+O(q^{100})$$ 4 * q + 4 * q^4 - 8 * q^6 - 8 * q^7 + 12 * q^9 + 8 * q^11 - 12 * q^16 - 8 * q^17 - 8 * q^23 - 16 * q^24 + 16 * q^26 - 24 * q^28 + 28 * q^36 + 8 * q^39 + 64 * q^42 + 8 * q^43 + 8 * q^44 - 8 * q^47 + 20 * q^49 - 48 * q^54 - 32 * q^58 + 16 * q^62 - 56 * q^63 - 4 * q^64 - 16 * q^66 + 24 * q^68 + 24 * q^73 + 32 * q^74 - 16 * q^77 - 4 * q^81 - 24 * q^83 - 16 * q^87 - 24 * q^92 - 48 * q^93 + 56 * q^96 + 24 * q^99

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.10100 1.48563 0.742817 0.669495i $$-0.233489\pi$$
0.742817 + 0.669495i $$0.233489\pi$$
$$3$$ −2.97127 −1.71546 −0.857731 0.514099i $$-0.828126\pi$$
−0.857731 + 0.514099i $$0.828126\pi$$
$$4$$ 2.41421 1.20711
$$5$$ 0 0
$$6$$ −6.24264 −2.54855
$$7$$ −4.82843 −1.82497 −0.912487 0.409106i $$-0.865841\pi$$
−0.912487 + 0.409106i $$0.865841\pi$$
$$8$$ 0.870264 0.307685
$$9$$ 5.82843 1.94281
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ −7.17327 −2.07075
$$13$$ 1.23074 0.341346 0.170673 0.985328i $$-0.445406\pi$$
0.170673 + 0.985328i $$0.445406\pi$$
$$14$$ −10.1445 −2.71124
$$15$$ 0 0
$$16$$ −3.00000 −0.750000
$$17$$ 3.65685 0.886917 0.443459 0.896295i $$-0.353751\pi$$
0.443459 + 0.896295i $$0.353751\pi$$
$$18$$ 12.2455 2.88630
$$19$$ 0 0
$$20$$ 0 0
$$21$$ 14.3465 3.13067
$$22$$ 4.20201 0.895871
$$23$$ −4.82843 −1.00680 −0.503398 0.864054i $$-0.667917\pi$$
−0.503398 + 0.864054i $$0.667917\pi$$
$$24$$ −2.58579 −0.527821
$$25$$ 0 0
$$26$$ 2.58579 0.507114
$$27$$ −8.40401 −1.61735
$$28$$ −11.6569 −2.20294
$$29$$ −2.46148 −0.457085 −0.228543 0.973534i $$-0.573396\pi$$
−0.228543 + 0.973534i $$0.573396\pi$$
$$30$$ 0 0
$$31$$ 5.94253 1.06731 0.533655 0.845702i $$-0.320818\pi$$
0.533655 + 0.845702i $$0.320818\pi$$
$$32$$ −8.04354 −1.42191
$$33$$ −5.94253 −1.03446
$$34$$ 7.68306 1.31763
$$35$$ 0 0
$$36$$ 14.0711 2.34518
$$37$$ 7.17327 1.17928 0.589639 0.807667i $$-0.299270\pi$$
0.589639 + 0.807667i $$0.299270\pi$$
$$38$$ 0 0
$$39$$ −3.65685 −0.585565
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 30.1421 4.65103
$$43$$ −0.828427 −0.126334 −0.0631670 0.998003i $$-0.520120\pi$$
−0.0631670 + 0.998003i $$0.520120\pi$$
$$44$$ 4.82843 0.727913
$$45$$ 0 0
$$46$$ −10.1445 −1.49573
$$47$$ 6.48528 0.945976 0.472988 0.881069i $$-0.343175\pi$$
0.472988 + 0.881069i $$0.343175\pi$$
$$48$$ 8.91380 1.28660
$$49$$ 16.3137 2.33053
$$50$$ 0 0
$$51$$ −10.8655 −1.52147
$$52$$ 2.97127 0.412041
$$53$$ 4.71179 0.647215 0.323607 0.946191i $$-0.395104\pi$$
0.323607 + 0.946191i $$0.395104\pi$$
$$54$$ −17.6569 −2.40279
$$55$$ 0 0
$$56$$ −4.20201 −0.561517
$$57$$ 0 0
$$58$$ −5.17157 −0.679061
$$59$$ −11.8851 −1.54730 −0.773652 0.633611i $$-0.781572\pi$$
−0.773652 + 0.633611i $$0.781572\pi$$
$$60$$ 0 0
$$61$$ 2.82843 0.362143 0.181071 0.983470i $$-0.442043\pi$$
0.181071 + 0.983470i $$0.442043\pi$$
$$62$$ 12.4853 1.58563
$$63$$ −28.1421 −3.54558
$$64$$ −10.8995 −1.36244
$$65$$ 0 0
$$66$$ −12.4853 −1.53683
$$67$$ 5.43275 0.663715 0.331858 0.943329i $$-0.392325\pi$$
0.331858 + 0.943329i $$0.392325\pi$$
$$68$$ 8.82843 1.07060
$$69$$ 14.3465 1.72712
$$70$$ 0 0
$$71$$ −10.8655 −1.28950 −0.644748 0.764395i $$-0.723038\pi$$
−0.644748 + 0.764395i $$0.723038\pi$$
$$72$$ 5.07227 0.597773
$$73$$ 0.343146 0.0401622 0.0200811 0.999798i $$-0.493608\pi$$
0.0200811 + 0.999798i $$0.493608\pi$$
$$74$$ 15.0711 1.75198
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −9.65685 −1.10050
$$78$$ −7.68306 −0.869935
$$79$$ 11.8851 1.33717 0.668587 0.743634i $$-0.266899\pi$$
0.668587 + 0.743634i $$0.266899\pi$$
$$80$$ 0 0
$$81$$ 7.48528 0.831698
$$82$$ 0 0
$$83$$ −3.17157 −0.348125 −0.174063 0.984735i $$-0.555690\pi$$
−0.174063 + 0.984735i $$0.555690\pi$$
$$84$$ 34.6356 3.77906
$$85$$ 0 0
$$86$$ −1.74053 −0.187686
$$87$$ 7.31371 0.784112
$$88$$ 1.74053 0.185541
$$89$$ −9.42359 −0.998898 −0.499449 0.866343i $$-0.666464\pi$$
−0.499449 + 0.866343i $$0.666464\pi$$
$$90$$ 0 0
$$91$$ −5.94253 −0.622947
$$92$$ −11.6569 −1.21531
$$93$$ −17.6569 −1.83093
$$94$$ 13.6256 1.40537
$$95$$ 0 0
$$96$$ 23.8995 2.43923
$$97$$ 1.23074 0.124963 0.0624813 0.998046i $$-0.480099\pi$$
0.0624813 + 0.998046i $$0.480099\pi$$
$$98$$ 34.2752 3.46231
$$99$$ 11.6569 1.17156
$$100$$ 0 0
$$101$$ −16.4853 −1.64035 −0.820173 0.572115i $$-0.806123\pi$$
−0.820173 + 0.572115i $$0.806123\pi$$
$$102$$ −22.8284 −2.26035
$$103$$ 8.91380 0.878303 0.439151 0.898413i $$-0.355279\pi$$
0.439151 + 0.898413i $$0.355279\pi$$
$$104$$ 1.07107 0.105027
$$105$$ 0 0
$$106$$ 9.89949 0.961524
$$107$$ 6.45232 0.623770 0.311885 0.950120i $$-0.399040\pi$$
0.311885 + 0.950120i $$0.399040\pi$$
$$108$$ −20.2891 −1.95232
$$109$$ 19.2695 1.84568 0.922842 0.385179i $$-0.125860\pi$$
0.922842 + 0.385179i $$0.125860\pi$$
$$110$$ 0 0
$$111$$ −21.3137 −2.02301
$$112$$ 14.4853 1.36873
$$113$$ −9.63475 −0.906361 −0.453181 0.891419i $$-0.649711\pi$$
−0.453181 + 0.891419i $$0.649711\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −5.94253 −0.551750
$$117$$ 7.17327 0.663169
$$118$$ −24.9706 −2.29873
$$119$$ −17.6569 −1.61860
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 5.94253 0.538012
$$123$$ 0 0
$$124$$ 14.3465 1.28836
$$125$$ 0 0
$$126$$ −59.1267 −5.26743
$$127$$ 12.3949 1.09987 0.549933 0.835209i $$-0.314653\pi$$
0.549933 + 0.835209i $$0.314653\pi$$
$$128$$ −6.81280 −0.602172
$$129$$ 2.46148 0.216721
$$130$$ 0 0
$$131$$ −7.31371 −0.639002 −0.319501 0.947586i $$-0.603515\pi$$
−0.319501 + 0.947586i $$0.603515\pi$$
$$132$$ −14.3465 −1.24871
$$133$$ 0 0
$$134$$ 11.4142 0.986038
$$135$$ 0 0
$$136$$ 3.18243 0.272891
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 30.1421 2.56587
$$139$$ 8.34315 0.707656 0.353828 0.935310i $$-0.384880\pi$$
0.353828 + 0.935310i $$0.384880\pi$$
$$140$$ 0 0
$$141$$ −19.2695 −1.62278
$$142$$ −22.8284 −1.91572
$$143$$ 2.46148 0.205839
$$144$$ −17.4853 −1.45711
$$145$$ 0 0
$$146$$ 0.720950 0.0596663
$$147$$ −48.4724 −3.99793
$$148$$ 17.3178 1.42352
$$149$$ −9.17157 −0.751365 −0.375682 0.926749i $$-0.622592\pi$$
−0.375682 + 0.926749i $$0.622592\pi$$
$$150$$ 0 0
$$151$$ −17.8276 −1.45079 −0.725395 0.688333i $$-0.758343\pi$$
−0.725395 + 0.688333i $$0.758343\pi$$
$$152$$ 0 0
$$153$$ 21.3137 1.72311
$$154$$ −20.2891 −1.63494
$$155$$ 0 0
$$156$$ −8.82843 −0.706840
$$157$$ −18.0000 −1.43656 −0.718278 0.695756i $$-0.755069\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ 24.9706 1.98655
$$159$$ −14.0000 −1.11027
$$160$$ 0 0
$$161$$ 23.3137 1.83738
$$162$$ 15.7266 1.23560
$$163$$ −12.8284 −1.00480 −0.502400 0.864635i $$-0.667549\pi$$
−0.502400 + 0.864635i $$0.667549\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −6.66348 −0.517187
$$167$$ −22.2408 −1.72104 −0.860521 0.509415i $$-0.829862\pi$$
−0.860521 + 0.509415i $$0.829862\pi$$
$$168$$ 12.4853 0.963260
$$169$$ −11.4853 −0.883483
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −2.00000 −0.152499
$$173$$ −13.1158 −0.997176 −0.498588 0.866839i $$-0.666148\pi$$
−0.498588 + 0.866839i $$0.666148\pi$$
$$174$$ 15.3661 1.16490
$$175$$ 0 0
$$176$$ −6.00000 −0.452267
$$177$$ 35.3137 2.65434
$$178$$ −19.7990 −1.48400
$$179$$ −4.92296 −0.367959 −0.183980 0.982930i $$-0.558898\pi$$
−0.183980 + 0.982930i $$0.558898\pi$$
$$180$$ 0 0
$$181$$ 16.8080 1.24933 0.624665 0.780893i $$-0.285235\pi$$
0.624665 + 0.780893i $$0.285235\pi$$
$$182$$ −12.4853 −0.925471
$$183$$ −8.40401 −0.621242
$$184$$ −4.20201 −0.309776
$$185$$ 0 0
$$186$$ −37.0971 −2.72009
$$187$$ 7.31371 0.534831
$$188$$ 15.6569 1.14189
$$189$$ 40.5782 2.95163
$$190$$ 0 0
$$191$$ −13.6569 −0.988175 −0.494088 0.869412i $$-0.664498\pi$$
−0.494088 + 0.869412i $$0.664498\pi$$
$$192$$ 32.3853 2.33721
$$193$$ 8.19285 0.589734 0.294867 0.955538i $$-0.404725\pi$$
0.294867 + 0.955538i $$0.404725\pi$$
$$194$$ 2.58579 0.185649
$$195$$ 0 0
$$196$$ 39.3848 2.81320
$$197$$ 13.3137 0.948562 0.474281 0.880373i $$-0.342708\pi$$
0.474281 + 0.880373i $$0.342708\pi$$
$$198$$ 24.4911 1.74051
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 0 0
$$201$$ −16.1421 −1.13858
$$202$$ −34.6356 −2.43695
$$203$$ 11.8851 0.834168
$$204$$ −26.2316 −1.83658
$$205$$ 0 0
$$206$$ 18.7279 1.30484
$$207$$ −28.1421 −1.95601
$$208$$ −3.69222 −0.256009
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 10.8655 0.748011 0.374006 0.927426i $$-0.377984\pi$$
0.374006 + 0.927426i $$0.377984\pi$$
$$212$$ 11.3753 0.781257
$$213$$ 32.2843 2.21208
$$214$$ 13.5563 0.926693
$$215$$ 0 0
$$216$$ −7.31371 −0.497635
$$217$$ −28.6931 −1.94781
$$218$$ 40.4853 2.74201
$$219$$ −1.01958 −0.0688967
$$220$$ 0 0
$$221$$ 4.50063 0.302745
$$222$$ −44.7802 −3.00545
$$223$$ −17.3178 −1.15969 −0.579843 0.814728i $$-0.696886\pi$$
−0.579843 + 0.814728i $$0.696886\pi$$
$$224$$ 38.8376 2.59495
$$225$$ 0 0
$$226$$ −20.2426 −1.34652
$$227$$ −22.2408 −1.47617 −0.738086 0.674707i $$-0.764270\pi$$
−0.738086 + 0.674707i $$0.764270\pi$$
$$228$$ 0 0
$$229$$ 12.4853 0.825051 0.412525 0.910946i $$-0.364647\pi$$
0.412525 + 0.910946i $$0.364647\pi$$
$$230$$ 0 0
$$231$$ 28.6931 1.88787
$$232$$ −2.14214 −0.140638
$$233$$ −13.3137 −0.872210 −0.436105 0.899896i $$-0.643642\pi$$
−0.436105 + 0.899896i $$0.643642\pi$$
$$234$$ 15.0711 0.985227
$$235$$ 0 0
$$236$$ −28.6931 −1.86776
$$237$$ −35.3137 −2.29387
$$238$$ −37.0971 −2.40465
$$239$$ −1.65685 −0.107173 −0.0535865 0.998563i $$-0.517065\pi$$
−0.0535865 + 0.998563i $$0.517065\pi$$
$$240$$ 0 0
$$241$$ 6.96211 0.448469 0.224235 0.974535i $$-0.428012\pi$$
0.224235 + 0.974535i $$0.428012\pi$$
$$242$$ −14.7070 −0.945403
$$243$$ 2.97127 0.190607
$$244$$ 6.82843 0.437145
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 5.17157 0.328395
$$249$$ 9.42359 0.597196
$$250$$ 0 0
$$251$$ −12.9706 −0.818695 −0.409347 0.912379i $$-0.634244\pi$$
−0.409347 + 0.912379i $$0.634244\pi$$
$$252$$ −67.9411 −4.27989
$$253$$ −9.65685 −0.607121
$$254$$ 26.0416 1.63400
$$255$$ 0 0
$$256$$ 7.48528 0.467830
$$257$$ −8.19285 −0.511056 −0.255528 0.966802i $$-0.582249\pi$$
−0.255528 + 0.966802i $$0.582249\pi$$
$$258$$ 5.17157 0.321968
$$259$$ −34.6356 −2.15215
$$260$$ 0 0
$$261$$ −14.3465 −0.888029
$$262$$ −15.3661 −0.949322
$$263$$ −12.1421 −0.748716 −0.374358 0.927284i $$-0.622137\pi$$
−0.374358 + 0.927284i $$0.622137\pi$$
$$264$$ −5.17157 −0.318288
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 28.0000 1.71357
$$268$$ 13.1158 0.801175
$$269$$ −2.46148 −0.150079 −0.0750395 0.997181i $$-0.523908\pi$$
−0.0750395 + 0.997181i $$0.523908\pi$$
$$270$$ 0 0
$$271$$ −2.97056 −0.180449 −0.0902244 0.995921i $$-0.528758\pi$$
−0.0902244 + 0.995921i $$0.528758\pi$$
$$272$$ −10.9706 −0.665188
$$273$$ 17.6569 1.06864
$$274$$ 4.20201 0.253852
$$275$$ 0 0
$$276$$ 34.6356 2.08482
$$277$$ −5.31371 −0.319270 −0.159635 0.987176i $$-0.551032\pi$$
−0.159635 + 0.987176i $$0.551032\pi$$
$$278$$ 17.5290 1.05132
$$279$$ 34.6356 2.07358
$$280$$ 0 0
$$281$$ 23.7701 1.41801 0.709004 0.705205i $$-0.249145\pi$$
0.709004 + 0.705205i $$0.249145\pi$$
$$282$$ −40.4853 −2.41086
$$283$$ −29.7990 −1.77137 −0.885683 0.464290i $$-0.846309\pi$$
−0.885683 + 0.464290i $$0.846309\pi$$
$$284$$ −26.2316 −1.55656
$$285$$ 0 0
$$286$$ 5.17157 0.305802
$$287$$ 0 0
$$288$$ −46.8812 −2.76250
$$289$$ −3.62742 −0.213377
$$290$$ 0 0
$$291$$ −3.65685 −0.214369
$$292$$ 0.828427 0.0484800
$$293$$ −12.0962 −0.706669 −0.353335 0.935497i $$-0.614952\pi$$
−0.353335 + 0.935497i $$0.614952\pi$$
$$294$$ −101.841 −5.93947
$$295$$ 0 0
$$296$$ 6.24264 0.362846
$$297$$ −16.8080 −0.975300
$$298$$ −19.2695 −1.11625
$$299$$ −5.94253 −0.343666
$$300$$ 0 0
$$301$$ 4.00000 0.230556
$$302$$ −37.4558 −2.15534
$$303$$ 48.9822 2.81395
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 44.7802 2.55991
$$307$$ 11.3753 0.649221 0.324611 0.945848i $$-0.394767\pi$$
0.324611 + 0.945848i $$0.394767\pi$$
$$308$$ −23.3137 −1.32842
$$309$$ −26.4853 −1.50670
$$310$$ 0 0
$$311$$ −31.6569 −1.79510 −0.897548 0.440917i $$-0.854653\pi$$
−0.897548 + 0.440917i $$0.854653\pi$$
$$312$$ −3.18243 −0.180170
$$313$$ 20.6274 1.16593 0.582965 0.812497i $$-0.301892\pi$$
0.582965 + 0.812497i $$0.301892\pi$$
$$314$$ −37.8181 −2.13420
$$315$$ 0 0
$$316$$ 28.6931 1.61411
$$317$$ −15.5773 −0.874907 −0.437454 0.899241i $$-0.644120\pi$$
−0.437454 + 0.899241i $$0.644120\pi$$
$$318$$ −29.4140 −1.64946
$$319$$ −4.92296 −0.275633
$$320$$ 0 0
$$321$$ −19.1716 −1.07005
$$322$$ 48.9822 2.72967
$$323$$ 0 0
$$324$$ 18.0711 1.00395
$$325$$ 0 0
$$326$$ −26.9526 −1.49276
$$327$$ −57.2548 −3.16620
$$328$$ 0 0
$$329$$ −31.3137 −1.72638
$$330$$ 0 0
$$331$$ −29.7127 −1.63316 −0.816578 0.577235i $$-0.804132\pi$$
−0.816578 + 0.577235i $$0.804132\pi$$
$$332$$ −7.65685 −0.420224
$$333$$ 41.8089 2.29111
$$334$$ −46.7279 −2.55684
$$335$$ 0 0
$$336$$ −43.0396 −2.34800
$$337$$ 30.9434 1.68559 0.842797 0.538231i $$-0.180907\pi$$
0.842797 + 0.538231i $$0.180907\pi$$
$$338$$ −24.1306 −1.31253
$$339$$ 28.6274 1.55483
$$340$$ 0 0
$$341$$ 11.8851 0.643612
$$342$$ 0 0
$$343$$ −44.9706 −2.42818
$$344$$ −0.720950 −0.0388710
$$345$$ 0 0
$$346$$ −27.5563 −1.48144
$$347$$ −24.8284 −1.33286 −0.666430 0.745568i $$-0.732178\pi$$
−0.666430 + 0.745568i $$0.732178\pi$$
$$348$$ 17.6569 0.946507
$$349$$ −6.68629 −0.357909 −0.178954 0.983857i $$-0.557271\pi$$
−0.178954 + 0.983857i $$0.557271\pi$$
$$350$$ 0 0
$$351$$ −10.3431 −0.552076
$$352$$ −16.0871 −0.857444
$$353$$ 3.65685 0.194635 0.0973174 0.995253i $$-0.468974\pi$$
0.0973174 + 0.995253i $$0.468974\pi$$
$$354$$ 74.1942 3.94338
$$355$$ 0 0
$$356$$ −22.7506 −1.20578
$$357$$ 52.4632 2.77665
$$358$$ −10.3431 −0.546652
$$359$$ −25.3137 −1.33601 −0.668003 0.744158i $$-0.732851\pi$$
−0.668003 + 0.744158i $$0.732851\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 35.3137 1.85605
$$363$$ 20.7989 1.09166
$$364$$ −14.3465 −0.751963
$$365$$ 0 0
$$366$$ −17.6569 −0.922939
$$367$$ −8.82843 −0.460840 −0.230420 0.973091i $$-0.574010\pi$$
−0.230420 + 0.973091i $$0.574010\pi$$
$$368$$ 14.4853 0.755097
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −22.7506 −1.18115
$$372$$ −42.6274 −2.21013
$$373$$ −23.9813 −1.24170 −0.620852 0.783928i $$-0.713213\pi$$
−0.620852 + 0.783928i $$0.713213\pi$$
$$374$$ 15.3661 0.794563
$$375$$ 0 0
$$376$$ 5.64391 0.291062
$$377$$ −3.02944 −0.156024
$$378$$ 85.2548 4.38504
$$379$$ 4.92296 0.252875 0.126438 0.991975i $$-0.459646\pi$$
0.126438 + 0.991975i $$0.459646\pi$$
$$380$$ 0 0
$$381$$ −36.8284 −1.88678
$$382$$ −28.6931 −1.46807
$$383$$ 12.8172 0.654927 0.327464 0.944864i $$-0.393806\pi$$
0.327464 + 0.944864i $$0.393806\pi$$
$$384$$ 20.2426 1.03300
$$385$$ 0 0
$$386$$ 17.2132 0.876129
$$387$$ −4.82843 −0.245443
$$388$$ 2.97127 0.150843
$$389$$ 24.6274 1.24866 0.624330 0.781161i $$-0.285372\pi$$
0.624330 + 0.781161i $$0.285372\pi$$
$$390$$ 0 0
$$391$$ −17.6569 −0.892946
$$392$$ 14.1972 0.717069
$$393$$ 21.7310 1.09618
$$394$$ 27.9721 1.40922
$$395$$ 0 0
$$396$$ 28.1421 1.41420
$$397$$ 14.0000 0.702640 0.351320 0.936255i $$-0.385733\pi$$
0.351320 + 0.936255i $$0.385733\pi$$
$$398$$ −8.40401 −0.421255
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 16.8080 0.839353 0.419676 0.907674i $$-0.362144\pi$$
0.419676 + 0.907674i $$0.362144\pi$$
$$402$$ −33.9147 −1.69151
$$403$$ 7.31371 0.364322
$$404$$ −39.7990 −1.98007
$$405$$ 0 0
$$406$$ 24.9706 1.23927
$$407$$ 14.3465 0.711132
$$408$$ −9.45584 −0.468134
$$409$$ 38.1167 1.88475 0.942374 0.334560i $$-0.108588\pi$$
0.942374 + 0.334560i $$0.108588\pi$$
$$410$$ 0 0
$$411$$ −5.94253 −0.293124
$$412$$ 21.5198 1.06021
$$413$$ 57.3862 2.82379
$$414$$ −59.1267 −2.90592
$$415$$ 0 0
$$416$$ −9.89949 −0.485363
$$417$$ −24.7897 −1.21396
$$418$$ 0 0
$$419$$ 8.97056 0.438241 0.219120 0.975698i $$-0.429681\pi$$
0.219120 + 0.975698i $$0.429681\pi$$
$$420$$ 0 0
$$421$$ 16.8080 0.819173 0.409586 0.912271i $$-0.365673\pi$$
0.409586 + 0.912271i $$0.365673\pi$$
$$422$$ 22.8284 1.11127
$$423$$ 37.7990 1.83785
$$424$$ 4.10051 0.199138
$$425$$ 0 0
$$426$$ 67.8294 3.28634
$$427$$ −13.6569 −0.660901
$$428$$ 15.5773 0.752956
$$429$$ −7.31371 −0.353109
$$430$$ 0 0
$$431$$ 5.94253 0.286242 0.143121 0.989705i $$-0.454286\pi$$
0.143121 + 0.989705i $$0.454286\pi$$
$$432$$ 25.2120 1.21301
$$433$$ −33.4049 −1.60534 −0.802668 0.596426i $$-0.796587\pi$$
−0.802668 + 0.596426i $$0.796587\pi$$
$$434$$ −60.2843 −2.89374
$$435$$ 0 0
$$436$$ 46.5207 2.22794
$$437$$ 0 0
$$438$$ −2.14214 −0.102355
$$439$$ −28.6931 −1.36945 −0.684723 0.728803i $$-0.740077\pi$$
−0.684723 + 0.728803i $$0.740077\pi$$
$$440$$ 0 0
$$441$$ 95.0833 4.52777
$$442$$ 9.45584 0.449769
$$443$$ 8.14214 0.386845 0.193422 0.981116i $$-0.438041\pi$$
0.193422 + 0.981116i $$0.438041\pi$$
$$444$$ −51.4558 −2.44199
$$445$$ 0 0
$$446$$ −36.3848 −1.72287
$$447$$ 27.2512 1.28894
$$448$$ 52.6274 2.48641
$$449$$ 2.46148 0.116164 0.0580822 0.998312i $$-0.481501\pi$$
0.0580822 + 0.998312i $$0.481501\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −23.2603 −1.09407
$$453$$ 52.9706 2.48877
$$454$$ −46.7279 −2.19305
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.3137 0.809901 0.404951 0.914339i $$-0.367289\pi$$
0.404951 + 0.914339i $$0.367289\pi$$
$$458$$ 26.2316 1.22572
$$459$$ −30.7322 −1.43446
$$460$$ 0 0
$$461$$ −33.3137 −1.55157 −0.775787 0.630995i $$-0.782647\pi$$
−0.775787 + 0.630995i $$0.782647\pi$$
$$462$$ 60.2843 2.80468
$$463$$ 27.1716 1.26277 0.631385 0.775469i $$-0.282487\pi$$
0.631385 + 0.775469i $$0.282487\pi$$
$$464$$ 7.38443 0.342814
$$465$$ 0 0
$$466$$ −27.9721 −1.29578
$$467$$ −21.5147 −0.995582 −0.497791 0.867297i $$-0.665855\pi$$
−0.497791 + 0.867297i $$0.665855\pi$$
$$468$$ 17.3178 0.800516
$$469$$ −26.2316 −1.21126
$$470$$ 0 0
$$471$$ 53.4828 2.46436
$$472$$ −10.3431 −0.476082
$$473$$ −1.65685 −0.0761822
$$474$$ −74.1942 −3.40785
$$475$$ 0 0
$$476$$ −42.6274 −1.95382
$$477$$ 27.4624 1.25741
$$478$$ −3.48106 −0.159220
$$479$$ 10.0000 0.456912 0.228456 0.973554i $$-0.426632\pi$$
0.228456 + 0.973554i $$0.426632\pi$$
$$480$$ 0 0
$$481$$ 8.82843 0.402542
$$482$$ 14.6274 0.666261
$$483$$ −69.2713 −3.15195
$$484$$ −16.8995 −0.768159
$$485$$ 0 0
$$486$$ 6.24264 0.283172
$$487$$ 15.8759 0.719406 0.359703 0.933067i $$-0.382878\pi$$
0.359703 + 0.933067i $$0.382878\pi$$
$$488$$ 2.46148 0.111426
$$489$$ 38.1167 1.72370
$$490$$ 0 0
$$491$$ −24.2843 −1.09593 −0.547967 0.836500i $$-0.684598\pi$$
−0.547967 + 0.836500i $$0.684598\pi$$
$$492$$ 0 0
$$493$$ −9.00127 −0.405397
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −17.8276 −0.800483
$$497$$ 52.4632 2.35330
$$498$$ 19.7990 0.887214
$$499$$ 34.9706 1.56550 0.782749 0.622338i $$-0.213817\pi$$
0.782749 + 0.622338i $$0.213817\pi$$
$$500$$ 0 0
$$501$$ 66.0833 2.95238
$$502$$ −27.2512 −1.21628
$$503$$ 14.4853 0.645867 0.322933 0.946422i $$-0.395331\pi$$
0.322933 + 0.946422i $$0.395331\pi$$
$$504$$ −24.4911 −1.09092
$$505$$ 0 0
$$506$$ −20.2891 −0.901960
$$507$$ 34.1258 1.51558
$$508$$ 29.9238 1.32766
$$509$$ −4.50063 −0.199487 −0.0997435 0.995013i $$-0.531802\pi$$
−0.0997435 + 0.995013i $$0.531802\pi$$
$$510$$ 0 0
$$511$$ −1.65685 −0.0732949
$$512$$ 29.3522 1.29720
$$513$$ 0 0
$$514$$ −17.2132 −0.759242
$$515$$ 0 0
$$516$$ 5.94253 0.261605
$$517$$ 12.9706 0.570445
$$518$$ −72.7696 −3.19731
$$519$$ 38.9706 1.71062
$$520$$ 0 0
$$521$$ 4.92296 0.215679 0.107839 0.994168i $$-0.465607\pi$$
0.107839 + 0.994168i $$0.465607\pi$$
$$522$$ −30.1421 −1.31929
$$523$$ 7.89422 0.345190 0.172595 0.984993i $$-0.444785\pi$$
0.172595 + 0.984993i $$0.444785\pi$$
$$524$$ −17.6569 −0.771343
$$525$$ 0 0
$$526$$ −25.5107 −1.11232
$$527$$ 21.7310 0.946616
$$528$$ 17.8276 0.775847
$$529$$ 0.313708 0.0136395
$$530$$ 0 0
$$531$$ −69.2713 −3.00612
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 58.8281 2.54574
$$535$$ 0 0
$$536$$ 4.72792 0.204215
$$537$$ 14.6274 0.631220
$$538$$ −5.17157 −0.222962
$$539$$ 32.6274 1.40536
$$540$$ 0 0
$$541$$ −6.14214 −0.264071 −0.132036 0.991245i $$-0.542151\pi$$
−0.132036 + 0.991245i $$0.542151\pi$$
$$542$$ −6.24116 −0.268081
$$543$$ −49.9411 −2.14318
$$544$$ −29.4140 −1.26112
$$545$$ 0 0
$$546$$ 37.0971 1.58761
$$547$$ 13.8368 0.591617 0.295809 0.955247i $$-0.404411\pi$$
0.295809 + 0.955247i $$0.404411\pi$$
$$548$$ 4.82843 0.206260
$$549$$ 16.4853 0.703575
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 12.4853 0.531409
$$553$$ −57.3862 −2.44031
$$554$$ −11.1641 −0.474318
$$555$$ 0 0
$$556$$ 20.1421 0.854217
$$557$$ −16.6274 −0.704526 −0.352263 0.935901i $$-0.614588\pi$$
−0.352263 + 0.935901i $$0.614588\pi$$
$$558$$ 72.7696 3.08058
$$559$$ −1.01958 −0.0431235
$$560$$ 0 0
$$561$$ −21.7310 −0.917483
$$562$$ 49.9411 2.10664
$$563$$ 9.93338 0.418642 0.209321 0.977847i $$-0.432875\pi$$
0.209321 + 0.977847i $$0.432875\pi$$
$$564$$ −46.5207 −1.95887
$$565$$ 0 0
$$566$$ −62.6078 −2.63160
$$567$$ −36.1421 −1.51783
$$568$$ −9.45584 −0.396758
$$569$$ −9.42359 −0.395057 −0.197529 0.980297i $$-0.563292\pi$$
−0.197529 + 0.980297i $$0.563292\pi$$
$$570$$ 0 0
$$571$$ −9.31371 −0.389767 −0.194883 0.980826i $$-0.562433\pi$$
−0.194883 + 0.980826i $$0.562433\pi$$
$$572$$ 5.94253 0.248470
$$573$$ 40.5782 1.69518
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −63.5269 −2.64695
$$577$$ −10.0000 −0.416305 −0.208153 0.978096i $$-0.566745\pi$$
−0.208153 + 0.978096i $$0.566745\pi$$
$$578$$ −7.62121 −0.317001
$$579$$ −24.3431 −1.01167
$$580$$ 0 0
$$581$$ 15.3137 0.635320
$$582$$ −7.68306 −0.318473
$$583$$ 9.42359 0.390285
$$584$$ 0.298627 0.0123573
$$585$$ 0 0
$$586$$ −25.4142 −1.04985
$$587$$ −1.51472 −0.0625191 −0.0312596 0.999511i $$-0.509952\pi$$
−0.0312596 + 0.999511i $$0.509952\pi$$
$$588$$ −117.023 −4.82593
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −39.5586 −1.62722
$$592$$ −21.5198 −0.884459
$$593$$ −13.3137 −0.546728 −0.273364 0.961911i $$-0.588136\pi$$
−0.273364 + 0.961911i $$0.588136\pi$$
$$594$$ −35.3137 −1.44894
$$595$$ 0 0
$$596$$ −22.1421 −0.906977
$$597$$ 11.8851 0.486423
$$598$$ −12.4853 −0.510561
$$599$$ 9.84591 0.402293 0.201147 0.979561i $$-0.435533\pi$$
0.201147 + 0.979561i $$0.435533\pi$$
$$600$$ 0 0
$$601$$ 4.92296 0.200812 0.100406 0.994947i $$-0.467986\pi$$
0.100406 + 0.994947i $$0.467986\pi$$
$$602$$ 8.40401 0.342522
$$603$$ 31.6644 1.28947
$$604$$ −43.0396 −1.75126
$$605$$ 0 0
$$606$$ 102.912 4.18050
$$607$$ −21.8184 −0.885583 −0.442792 0.896625i $$-0.646012\pi$$
−0.442792 + 0.896625i $$0.646012\pi$$
$$608$$ 0 0
$$609$$ −35.3137 −1.43098
$$610$$ 0 0
$$611$$ 7.98169 0.322905
$$612$$ 51.4558 2.07998
$$613$$ −42.2843 −1.70785 −0.853923 0.520400i $$-0.825783\pi$$
−0.853923 + 0.520400i $$0.825783\pi$$
$$614$$ 23.8995 0.964505
$$615$$ 0 0
$$616$$ −8.40401 −0.338607
$$617$$ 26.2843 1.05816 0.529082 0.848570i $$-0.322536\pi$$
0.529082 + 0.848570i $$0.322536\pi$$
$$618$$ −55.6457 −2.23840
$$619$$ 14.9706 0.601718 0.300859 0.953669i $$-0.402727\pi$$
0.300859 + 0.953669i $$0.402727\pi$$
$$620$$ 0 0
$$621$$ 40.5782 1.62835
$$622$$ −66.5111 −2.66685
$$623$$ 45.5011 1.82296
$$624$$ 10.9706 0.439174
$$625$$ 0 0
$$626$$ 43.3383 1.73215
$$627$$ 0 0
$$628$$ −43.4558 −1.73408
$$629$$ 26.2316 1.04592
$$630$$ 0 0
$$631$$ −38.2843 −1.52407 −0.762036 0.647534i $$-0.775800\pi$$
−0.762036 + 0.647534i $$0.775800\pi$$
$$632$$ 10.3431 0.411428
$$633$$ −32.2843 −1.28318
$$634$$ −32.7279 −1.29979
$$635$$ 0 0
$$636$$ −33.7990 −1.34022
$$637$$ 20.0779 0.795516
$$638$$ −10.3431 −0.409489
$$639$$ −63.3287 −2.50525
$$640$$ 0 0
$$641$$ −35.6552 −1.40830 −0.704148 0.710053i $$-0.748671\pi$$
−0.704148 + 0.710053i $$0.748671\pi$$
$$642$$ −40.2795 −1.58971
$$643$$ −26.4853 −1.04448 −0.522239 0.852799i $$-0.674903\pi$$
−0.522239 + 0.852799i $$0.674903\pi$$
$$644$$ 56.2843 2.21791
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 32.8284 1.29062 0.645309 0.763921i $$-0.276728\pi$$
0.645309 + 0.763921i $$0.276728\pi$$
$$648$$ 6.51417 0.255901
$$649$$ −23.7701 −0.933059
$$650$$ 0 0
$$651$$ 85.2548 3.34140
$$652$$ −30.9706 −1.21290
$$653$$ −16.3431 −0.639557 −0.319778 0.947492i $$-0.603608\pi$$
−0.319778 + 0.947492i $$0.603608\pi$$
$$654$$ −120.293 −4.70381
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 2.00000 0.0780274
$$658$$ −65.7902 −2.56477
$$659$$ 33.6160 1.30950 0.654748 0.755848i $$-0.272775\pi$$
0.654748 + 0.755848i $$0.272775\pi$$
$$660$$ 0 0
$$661$$ −28.6931 −1.11603 −0.558016 0.829830i $$-0.688437\pi$$
−0.558016 + 0.829830i $$0.688437\pi$$
$$662$$ −62.4264 −2.42627
$$663$$ −13.3726 −0.519348
$$664$$ −2.76011 −0.107113
$$665$$ 0 0
$$666$$ 87.8406 3.40375
$$667$$ 11.8851 0.460192
$$668$$ −53.6940 −2.07748
$$669$$ 51.4558 1.98940
$$670$$ 0 0
$$671$$ 5.65685 0.218380
$$672$$ −115.397 −4.45153
$$673$$ 7.59560 0.292789 0.146394 0.989226i $$-0.453233\pi$$
0.146394 + 0.989226i $$0.453233\pi$$
$$674$$ 65.0122 2.50418
$$675$$ 0 0
$$676$$ −27.7279 −1.06646
$$677$$ 21.5198 0.827074 0.413537 0.910487i $$-0.364293\pi$$
0.413537 + 0.910487i $$0.364293\pi$$
$$678$$ 60.1463 2.30990
$$679$$ −5.94253 −0.228054
$$680$$ 0 0
$$681$$ 66.0833 2.53232
$$682$$ 24.9706 0.956172
$$683$$ −13.8368 −0.529449 −0.264724 0.964324i $$-0.585281\pi$$
−0.264724 + 0.964324i $$0.585281\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −94.4833 −3.60739
$$687$$ −37.0971 −1.41534
$$688$$ 2.48528 0.0947505
$$689$$ 5.79899 0.220924
$$690$$ 0 0
$$691$$ −28.6274 −1.08904 −0.544519 0.838748i $$-0.683288\pi$$
−0.544519 + 0.838748i $$0.683288\pi$$
$$692$$ −31.6644 −1.20370
$$693$$ −56.2843 −2.13806
$$694$$ −52.1646 −1.98014
$$695$$ 0 0
$$696$$ 6.36486 0.241259
$$697$$ 0 0
$$698$$ −14.0479 −0.531722
$$699$$ 39.5586 1.49624
$$700$$ 0 0
$$701$$ −7.51472 −0.283827 −0.141914 0.989879i $$-0.545325\pi$$
−0.141914 + 0.989879i $$0.545325\pi$$
$$702$$ −21.7310 −0.820183
$$703$$ 0 0
$$704$$ −21.7990 −0.821580
$$705$$ 0 0
$$706$$ 7.68306 0.289156
$$707$$ 79.5980 2.99359
$$708$$ 85.2548 3.20407
$$709$$ 17.3137 0.650230 0.325115 0.945674i $$-0.394597\pi$$
0.325115 + 0.945674i $$0.394597\pi$$
$$710$$ 0 0
$$711$$ 69.2713 2.59787
$$712$$ −8.20101 −0.307346
$$713$$ −28.6931 −1.07456
$$714$$ 110.225 4.12508
$$715$$ 0 0
$$716$$ −11.8851 −0.444166
$$717$$ 4.92296 0.183851
$$718$$ −53.1842 −1.98482
$$719$$ −35.9411 −1.34038 −0.670189 0.742191i $$-0.733787\pi$$
−0.670189 + 0.742191i $$0.733787\pi$$
$$720$$ 0 0
$$721$$ −43.0396 −1.60288
$$722$$ 0 0
$$723$$ −20.6863 −0.769331
$$724$$ 40.5782 1.50808
$$725$$ 0 0
$$726$$ 43.6985 1.62180
$$727$$ 10.4853 0.388878 0.194439 0.980915i $$-0.437711\pi$$
0.194439 + 0.980915i $$0.437711\pi$$
$$728$$ −5.17157 −0.191671
$$729$$ −31.2843 −1.15868
$$730$$ 0 0
$$731$$ −3.02944 −0.112048
$$732$$ −20.2891 −0.749906
$$733$$ 24.3431 0.899135 0.449567 0.893246i $$-0.351578\pi$$
0.449567 + 0.893246i $$0.351578\pi$$
$$734$$ −18.5486 −0.684640
$$735$$ 0 0
$$736$$ 38.8376 1.43157
$$737$$ 10.8655 0.400235
$$738$$ 0 0
$$739$$ 46.6274 1.71522 0.857609 0.514303i $$-0.171949\pi$$
0.857609 + 0.514303i $$0.171949\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −47.7990 −1.75476
$$743$$ 5.43275 0.199308 0.0996540 0.995022i $$-0.468226\pi$$
0.0996540 + 0.995022i $$0.468226\pi$$
$$744$$ −15.3661 −0.563349
$$745$$ 0 0
$$746$$ −50.3848 −1.84472
$$747$$ −18.4853 −0.676341
$$748$$ 17.6569 0.645599
$$749$$ −31.1546 −1.13836
$$750$$ 0 0
$$751$$ 22.7506 0.830180 0.415090 0.909780i $$-0.363750\pi$$
0.415090 + 0.909780i $$0.363750\pi$$
$$752$$ −19.4558 −0.709482
$$753$$ 38.5390 1.40444
$$754$$ −6.36486 −0.231794
$$755$$ 0 0
$$756$$ 97.9643 3.56293
$$757$$ 29.3137 1.06542 0.532712 0.846296i $$-0.321173\pi$$
0.532712 + 0.846296i $$0.321173\pi$$
$$758$$ 10.3431 0.375680
$$759$$ 28.6931 1.04149
$$760$$ 0 0
$$761$$ −14.8284 −0.537530 −0.268765 0.963206i $$-0.586616\pi$$
−0.268765 + 0.963206i $$0.586616\pi$$
$$762$$ −77.3766 −2.80306
$$763$$ −93.0414 −3.36832
$$764$$ −32.9706 −1.19283
$$765$$ 0 0
$$766$$ 26.9289 0.972982
$$767$$ −14.6274 −0.528165
$$768$$ −22.2408 −0.802545
$$769$$ −14.1421 −0.509978 −0.254989 0.966944i $$-0.582072\pi$$
−0.254989 + 0.966944i $$0.582072\pi$$
$$770$$ 0 0
$$771$$ 24.3431 0.876697
$$772$$ 19.7793 0.711872
$$773$$ −22.5394 −0.810686 −0.405343 0.914165i $$-0.632848\pi$$
−0.405343 + 0.914165i $$0.632848\pi$$
$$774$$ −10.1445 −0.364638
$$775$$ 0 0
$$776$$ 1.07107 0.0384491
$$777$$ 102.912 3.69194
$$778$$ 51.7423 1.85505
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −21.7310 −0.777596
$$782$$ −37.0971 −1.32659
$$783$$ 20.6863 0.739268
$$784$$ −48.9411 −1.74790
$$785$$ 0 0
$$786$$ 45.6569 1.62853
$$787$$ 23.6827 0.844196 0.422098 0.906550i $$-0.361294\pi$$
0.422098 + 0.906550i $$0.361294\pi$$
$$788$$ 32.1421 1.14502
$$789$$ 36.0775 1.28439
$$790$$ 0 0
$$791$$ 46.5207 1.65409
$$792$$ 10.1445 0.360471
$$793$$ 3.48106 0.123616
$$794$$ 29.4140 1.04387
$$795$$ 0 0
$$796$$ −9.65685 −0.342278
$$797$$ −7.17327 −0.254090 −0.127045 0.991897i $$-0.540549\pi$$
−0.127045 + 0.991897i $$0.540549\pi$$
$$798$$ 0 0
$$799$$ 23.7157 0.839002
$$800$$ 0 0
$$801$$ −54.9247 −1.94067
$$802$$ 35.3137 1.24697
$$803$$ 0.686292 0.0242187
$$804$$ −38.9706 −1.37439
$$805$$ 0 0
$$806$$ 15.3661 0.541249
$$807$$ 7.31371 0.257455
$$808$$ −14.3465 −0.504710
$$809$$ 9.31371 0.327453 0.163726 0.986506i $$-0.447649\pi$$
0.163726 + 0.986506i $$0.447649\pi$$
$$810$$ 0 0
$$811$$ 44.4815 1.56196 0.780979 0.624557i $$-0.214721\pi$$
0.780979 + 0.624557i $$0.214721\pi$$
$$812$$ 28.6931 1.00693
$$813$$ 8.82633 0.309553
$$814$$ 30.1421 1.05648
$$815$$ 0 0
$$816$$ 32.5965 1.14110
$$817$$ 0 0
$$818$$ 80.0833 2.80005
$$819$$ −34.6356 −1.21027
$$820$$ 0 0
$$821$$ 25.3137 0.883455 0.441727 0.897149i $$-0.354366\pi$$
0.441727 + 0.897149i $$0.354366\pi$$
$$822$$ −12.4853 −0.435474
$$823$$ 54.0833 1.88522 0.942612 0.333890i $$-0.108361\pi$$
0.942612 + 0.333890i $$0.108361\pi$$
$$824$$ 7.75736 0.270240
$$825$$ 0 0
$$826$$ 120.569 4.19512
$$827$$ −1.95169 −0.0678669 −0.0339334 0.999424i $$-0.510803\pi$$
−0.0339334 + 0.999424i $$0.510803\pi$$
$$828$$ −67.9411 −2.36112
$$829$$ −12.3074 −0.427453 −0.213727 0.976893i $$-0.568560\pi$$
−0.213727 + 0.976893i $$0.568560\pi$$
$$830$$ 0 0
$$831$$ 15.7884 0.547695
$$832$$ −13.4144 −0.465062
$$833$$ 59.6569 2.06699
$$834$$ −52.0833 −1.80350
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −49.9411 −1.72622
$$838$$ 18.8472 0.651065
$$839$$ −18.8472 −0.650677 −0.325338 0.945598i $$-0.605478\pi$$
−0.325338 + 0.945598i $$0.605478\pi$$
$$840$$ 0 0
$$841$$ −22.9411 −0.791073
$$842$$ 35.3137 1.21699
$$843$$ −70.6274 −2.43254
$$844$$ 26.2316 0.902929
$$845$$ 0 0
$$846$$ 79.4158 2.73037
$$847$$ 33.7990 1.16135
$$848$$ −14.1354 −0.485411
$$849$$ 88.5408 3.03871
$$850$$ 0 0
$$851$$ −34.6356 −1.18729
$$852$$ 77.9411 2.67022
$$853$$ −47.6569 −1.63174 −0.815870 0.578236i $$-0.803741\pi$$
−0.815870 + 0.578236i $$0.803741\pi$$
$$854$$ −28.6931 −0.981857
$$855$$ 0 0
$$856$$ 5.61522 0.191924
$$857$$ −36.8859 −1.26000 −0.630000 0.776595i $$-0.716945\pi$$
−0.630000 + 0.776595i $$0.716945\pi$$
$$858$$ −15.3661 −0.524591
$$859$$ 12.2843 0.419134 0.209567 0.977794i $$-0.432795\pi$$
0.209567 + 0.977794i $$0.432795\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 12.4853 0.425250
$$863$$ 24.2799 0.826498 0.413249 0.910618i $$-0.364394\pi$$
0.413249 + 0.910618i $$0.364394\pi$$
$$864$$ 67.5980 2.29973
$$865$$ 0 0
$$866$$ −70.1838 −2.38494
$$867$$ 10.7780 0.366041
$$868$$ −69.2713 −2.35122
$$869$$ 23.7701 0.806347
$$870$$ 0 0
$$871$$ 6.68629 0.226556
$$872$$ 16.7696 0.567889
$$873$$ 7.17327 0.242779
$$874$$ 0 0
$$875$$ 0 0
$$876$$ −2.46148 −0.0831656
$$877$$ −23.9813 −0.809791 −0.404895 0.914363i $$-0.632692\pi$$
−0.404895 + 0.914363i $$0.632692\pi$$
$$878$$ −60.2843 −2.03450
$$879$$ 35.9411 1.21226
$$880$$ 0 0
$$881$$ −12.4853 −0.420640 −0.210320 0.977633i $$-0.567451\pi$$
−0.210320 + 0.977633i $$0.567451\pi$$
$$882$$ 199.770 6.72661
$$883$$ −32.1421 −1.08167 −0.540834 0.841129i $$-0.681891\pi$$
−0.540834 + 0.841129i $$0.681891\pi$$
$$884$$ 10.8655 0.365446
$$885$$ 0 0
$$886$$ 17.1067 0.574709
$$887$$ 31.6644 1.06319 0.531593 0.847000i $$-0.321594\pi$$
0.531593 + 0.847000i $$0.321594\pi$$
$$888$$ −18.5486 −0.622449
$$889$$ −59.8477 −2.00723
$$890$$ 0 0
$$891$$ 14.9706 0.501533
$$892$$ −41.8089 −1.39987
$$893$$ 0 0
$$894$$ 57.2548 1.91489
$$895$$ 0 0
$$896$$ 32.8951 1.09895
$$897$$ 17.6569 0.589545
$$898$$ 5.17157 0.172578
$$899$$ −14.6274 −0.487852
$$900$$ 0 0
$$901$$ 17.2303 0.574026
$$902$$ 0 0
$$903$$ −11.8851 −0.395510
$$904$$ −8.38478 −0.278874
$$905$$ 0 0
$$906$$ 111.291 3.69741
$$907$$ 33.1063 1.09928 0.549638 0.835403i $$-0.314766\pi$$
0.549638 + 0.835403i $$0.314766\pi$$
$$908$$ −53.6940 −1.78190
$$909$$ −96.0833 −3.18688
$$910$$ 0 0
$$911$$ 56.3666 1.86751 0.933754 0.357914i $$-0.116512\pi$$
0.933754 + 0.357914i $$0.116512\pi$$
$$912$$ 0 0
$$913$$ −6.34315 −0.209927
$$914$$ 36.3762 1.20322
$$915$$ 0 0
$$916$$ 30.1421 0.995924
$$917$$ 35.3137 1.16616
$$918$$ −64.5685 −2.13108
$$919$$ −56.2843 −1.85665 −0.928323 0.371774i $$-0.878750\pi$$
−0.928323 + 0.371774i $$0.878750\pi$$
$$920$$ 0 0
$$921$$ −33.7990 −1.11371
$$922$$ −69.9922 −2.30507
$$923$$ −13.3726 −0.440164
$$924$$ 69.2713 2.27886
$$925$$ 0 0
$$926$$ 57.0876 1.87601
$$927$$ 51.9534 1.70637
$$928$$ 19.7990 0.649934
$$929$$ −6.00000 −0.196854 −0.0984268 0.995144i $$-0.531381\pi$$
−0.0984268 + 0.995144i $$0.531381\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −32.1421 −1.05285
$$933$$ 94.0610 3.07942
$$934$$ −45.2025 −1.47907
$$935$$ 0 0
$$936$$ 6.24264 0.204047
$$937$$ 22.9706 0.750416 0.375208 0.926941i $$-0.377571\pi$$
0.375208 + 0.926941i $$0.377571\pi$$
$$938$$ −55.1127 −1.79949
$$939$$ −61.2896 −2.00011
$$940$$ 0 0
$$941$$ −28.6931 −0.935368 −0.467684 0.883896i $$-0.654911\pi$$
−0.467684 + 0.883896i $$0.654911\pi$$
$$942$$ 112.368 3.66113
$$943$$ 0 0
$$944$$ 35.6552 1.16048
$$945$$ 0 0
$$946$$ −3.48106 −0.113179
$$947$$ −24.1421 −0.784514 −0.392257 0.919856i $$-0.628306\pi$$
−0.392257 + 0.919856i $$0.628306\pi$$
$$948$$ −85.2548 −2.76895
$$949$$ 0.422323 0.0137092
$$950$$ 0 0
$$951$$ 46.2843 1.50087
$$952$$ −15.3661 −0.498019
$$953$$ 27.4624 0.889593 0.444796 0.895632i $$-0.353276\pi$$
0.444796 + 0.895632i $$0.353276\pi$$
$$954$$ 57.6985 1.86806
$$955$$ 0 0
$$956$$ −4.00000 −0.129369
$$957$$ 14.6274 0.472837
$$958$$ 21.0100 0.678803
$$959$$ −9.65685 −0.311836
$$960$$ 0 0
$$961$$ 4.31371 0.139152
$$962$$ 18.5486 0.598029
$$963$$ 37.6069 1.21187
$$964$$ 16.8080 0.541350
$$965$$ 0 0
$$966$$ −145.539 −4.68264
$$967$$ −38.4853 −1.23760 −0.618802 0.785547i $$-0.712382\pi$$
−0.618802 + 0.785547i $$0.712382\pi$$
$$968$$ −6.09185 −0.195799
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 46.5207 1.49292 0.746460 0.665430i $$-0.231752\pi$$
0.746460 + 0.665430i $$0.231752\pi$$
$$972$$ 7.17327 0.230083
$$973$$ −40.2843 −1.29145
$$974$$ 33.3553 1.06877
$$975$$ 0 0
$$976$$ −8.48528 −0.271607
$$977$$ −21.0975 −0.674969 −0.337484 0.941331i $$-0.609576\pi$$
−0.337484 + 0.941331i $$0.609576\pi$$
$$978$$ 80.0833 2.56078
$$979$$ −18.8472 −0.602358
$$980$$ 0 0
$$981$$ 112.311 3.58581
$$982$$ −51.0213 −1.62816
$$983$$ −56.4541 −1.80061 −0.900303 0.435265i $$-0.856655\pi$$
−0.900303 + 0.435265i $$0.856655\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −18.9117 −0.602271
$$987$$ 93.0414 2.96154
$$988$$ 0 0
$$989$$ 4.00000 0.127193
$$990$$ 0 0
$$991$$ 12.9046 0.409930 0.204965 0.978769i $$-0.434292\pi$$
0.204965 + 0.978769i $$0.434292\pi$$
$$992$$ −47.7990 −1.51762
$$993$$ 88.2843 2.80162
$$994$$ 110.225 3.49614
$$995$$ 0 0
$$996$$ 22.7506 0.720879
$$997$$ −3.65685 −0.115814 −0.0579069 0.998322i $$-0.518443\pi$$
−0.0579069 + 0.998322i $$0.518443\pi$$
$$998$$ 73.4733 2.32576
$$999$$ −60.2843 −1.90731
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 9025.2.a.bn.1.4 4
5.4 even 2 1805.2.a.m.1.1 4
19.18 odd 2 inner 9025.2.a.bn.1.1 4
95.94 odd 2 1805.2.a.m.1.4 yes 4

By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.m.1.1 4 5.4 even 2
1805.2.a.m.1.4 yes 4 95.94 odd 2
9025.2.a.bn.1.1 4 19.18 odd 2 inner
9025.2.a.bn.1.4 4 1.1 even 1 trivial