# Properties

 Label 2960.2.a.h.1.1 Level $2960$ Weight $2$ Character 2960.1 Self dual yes Analytic conductor $23.636$ 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] = [2960,2,Mod(1,2960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2960, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2960.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2960 = 2^{4} \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2960.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: $$23.6357189983$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 740) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2960.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{9} +3.00000 q^{11} -6.00000 q^{13} +1.00000 q^{15} -1.00000 q^{21} -2.00000 q^{23} +1.00000 q^{25} -5.00000 q^{27} -6.00000 q^{29} +3.00000 q^{33} -1.00000 q^{35} -1.00000 q^{37} -6.00000 q^{39} -9.00000 q^{41} +10.0000 q^{43} -2.00000 q^{45} -1.00000 q^{47} -6.00000 q^{49} +1.00000 q^{53} +3.00000 q^{55} -12.0000 q^{61} +2.00000 q^{63} -6.00000 q^{65} -2.00000 q^{69} +5.00000 q^{71} +3.00000 q^{73} +1.00000 q^{75} -3.00000 q^{77} -16.0000 q^{79} +1.00000 q^{81} -11.0000 q^{83} -6.00000 q^{87} +6.00000 q^{91} +8.00000 q^{97} -6.00000 q^{99} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.00000 0.577350 0.288675 0.957427i $$-0.406785\pi$$
0.288675 + 0.957427i $$0.406785\pi$$
$$4$$ 0 0
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 0 0
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ −6.00000 −1.66410 −0.832050 0.554700i $$-0.812833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ −2.00000 −0.417029 −0.208514 0.978019i $$-0.566863\pi$$
−0.208514 + 0.978019i $$0.566863\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 3.00000 0.522233
$$34$$ 0 0
$$35$$ −1.00000 −0.169031
$$36$$ 0 0
$$37$$ −1.00000 −0.164399
$$38$$ 0 0
$$39$$ −6.00000 −0.960769
$$40$$ 0 0
$$41$$ −9.00000 −1.40556 −0.702782 0.711405i $$-0.748059\pi$$
−0.702782 + 0.711405i $$0.748059\pi$$
$$42$$ 0 0
$$43$$ 10.0000 1.52499 0.762493 0.646997i $$-0.223975\pi$$
0.762493 + 0.646997i $$0.223975\pi$$
$$44$$ 0 0
$$45$$ −2.00000 −0.298142
$$46$$ 0 0
$$47$$ −1.00000 −0.145865 −0.0729325 0.997337i $$-0.523236\pi$$
−0.0729325 + 0.997337i $$0.523236\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.00000 0.137361 0.0686803 0.997639i $$-0.478121\pi$$
0.0686803 + 0.997639i $$0.478121\pi$$
$$54$$ 0 0
$$55$$ 3.00000 0.404520
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −12.0000 −1.53644 −0.768221 0.640184i $$-0.778858\pi$$
−0.768221 + 0.640184i $$0.778858\pi$$
$$62$$ 0 0
$$63$$ 2.00000 0.251976
$$64$$ 0 0
$$65$$ −6.00000 −0.744208
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ −2.00000 −0.240772
$$70$$ 0 0
$$71$$ 5.00000 0.593391 0.296695 0.954972i $$-0.404115\pi$$
0.296695 + 0.954972i $$0.404115\pi$$
$$72$$ 0 0
$$73$$ 3.00000 0.351123 0.175562 0.984468i $$-0.443826\pi$$
0.175562 + 0.984468i $$0.443826\pi$$
$$74$$ 0 0
$$75$$ 1.00000 0.115470
$$76$$ 0 0
$$77$$ −3.00000 −0.341882
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −11.0000 −1.20741 −0.603703 0.797209i $$-0.706309\pi$$
−0.603703 + 0.797209i $$0.706309\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −6.00000 −0.643268
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 6.00000 0.628971
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −1.00000 −0.0995037 −0.0497519 0.998762i $$-0.515843\pi$$
−0.0497519 + 0.998762i $$0.515843\pi$$
$$102$$ 0 0
$$103$$ 10.0000 0.985329 0.492665 0.870219i $$-0.336023\pi$$
0.492665 + 0.870219i $$0.336023\pi$$
$$104$$ 0 0
$$105$$ −1.00000 −0.0975900
$$106$$ 0 0
$$107$$ −20.0000 −1.93347 −0.966736 0.255774i $$-0.917670\pi$$
−0.966736 + 0.255774i $$0.917670\pi$$
$$108$$ 0 0
$$109$$ −12.0000 −1.14939 −0.574696 0.818367i $$-0.694880\pi$$
−0.574696 + 0.818367i $$0.694880\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ −2.00000 −0.186501
$$116$$ 0 0
$$117$$ 12.0000 1.10940
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ −9.00000 −0.811503
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 1.00000 0.0887357 0.0443678 0.999015i $$-0.485873\pi$$
0.0443678 + 0.999015i $$0.485873\pi$$
$$128$$ 0 0
$$129$$ 10.0000 0.880451
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −5.00000 −0.430331
$$136$$ 0 0
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 0 0
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 0 0
$$141$$ −1.00000 −0.0842152
$$142$$ 0 0
$$143$$ −18.0000 −1.50524
$$144$$ 0 0
$$145$$ −6.00000 −0.498273
$$146$$ 0 0
$$147$$ −6.00000 −0.494872
$$148$$ 0 0
$$149$$ −9.00000 −0.737309 −0.368654 0.929567i $$-0.620181\pi$$
−0.368654 + 0.929567i $$0.620181\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 15.0000 1.19713 0.598565 0.801074i $$-0.295738\pi$$
0.598565 + 0.801074i $$0.295738\pi$$
$$158$$ 0 0
$$159$$ 1.00000 0.0793052
$$160$$ 0 0
$$161$$ 2.00000 0.157622
$$162$$ 0 0
$$163$$ 2.00000 0.156652 0.0783260 0.996928i $$-0.475042\pi$$
0.0783260 + 0.996928i $$0.475042\pi$$
$$164$$ 0 0
$$165$$ 3.00000 0.233550
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −15.0000 −1.14043 −0.570214 0.821496i $$-0.693140\pi$$
−0.570214 + 0.821496i $$0.693140\pi$$
$$174$$ 0 0
$$175$$ −1.00000 −0.0755929
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −18.0000 −1.34538 −0.672692 0.739923i $$-0.734862\pi$$
−0.672692 + 0.739923i $$0.734862\pi$$
$$180$$ 0 0
$$181$$ 17.0000 1.26360 0.631800 0.775131i $$-0.282316\pi$$
0.631800 + 0.775131i $$0.282316\pi$$
$$182$$ 0 0
$$183$$ −12.0000 −0.887066
$$184$$ 0 0
$$185$$ −1.00000 −0.0735215
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 5.00000 0.363696
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ −22.0000 −1.58359 −0.791797 0.610784i $$-0.790854\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ 0 0
$$195$$ −6.00000 −0.429669
$$196$$ 0 0
$$197$$ 3.00000 0.213741 0.106871 0.994273i $$-0.465917\pi$$
0.106871 + 0.994273i $$0.465917\pi$$
$$198$$ 0 0
$$199$$ −14.0000 −0.992434 −0.496217 0.868199i $$-0.665278\pi$$
−0.496217 + 0.868199i $$0.665278\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 6.00000 0.421117
$$204$$ 0 0
$$205$$ −9.00000 −0.628587
$$206$$ 0 0
$$207$$ 4.00000 0.278019
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 27.0000 1.85876 0.929378 0.369129i $$-0.120344\pi$$
0.929378 + 0.369129i $$0.120344\pi$$
$$212$$ 0 0
$$213$$ 5.00000 0.342594
$$214$$ 0 0
$$215$$ 10.0000 0.681994
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 3.00000 0.202721
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −17.0000 −1.13840 −0.569202 0.822198i $$-0.692748\pi$$
−0.569202 + 0.822198i $$0.692748\pi$$
$$224$$ 0 0
$$225$$ −2.00000 −0.133333
$$226$$ 0 0
$$227$$ 8.00000 0.530979 0.265489 0.964114i $$-0.414466\pi$$
0.265489 + 0.964114i $$0.414466\pi$$
$$228$$ 0 0
$$229$$ 3.00000 0.198246 0.0991228 0.995075i $$-0.468396\pi$$
0.0991228 + 0.995075i $$0.468396\pi$$
$$230$$ 0 0
$$231$$ −3.00000 −0.197386
$$232$$ 0 0
$$233$$ −2.00000 −0.131024 −0.0655122 0.997852i $$-0.520868\pi$$
−0.0655122 + 0.997852i $$0.520868\pi$$
$$234$$ 0 0
$$235$$ −1.00000 −0.0652328
$$236$$ 0 0
$$237$$ −16.0000 −1.03931
$$238$$ 0 0
$$239$$ −30.0000 −1.94054 −0.970269 0.242028i $$-0.922188\pi$$
−0.970269 + 0.242028i $$0.922188\pi$$
$$240$$ 0 0
$$241$$ −6.00000 −0.386494 −0.193247 0.981150i $$-0.561902\pi$$
−0.193247 + 0.981150i $$0.561902\pi$$
$$242$$ 0 0
$$243$$ 16.0000 1.02640
$$244$$ 0 0
$$245$$ −6.00000 −0.383326
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −11.0000 −0.697097
$$250$$ 0 0
$$251$$ −6.00000 −0.378717 −0.189358 0.981908i $$-0.560641\pi$$
−0.189358 + 0.981908i $$0.560641\pi$$
$$252$$ 0 0
$$253$$ −6.00000 −0.377217
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 20.0000 1.24757 0.623783 0.781598i $$-0.285595\pi$$
0.623783 + 0.781598i $$0.285595\pi$$
$$258$$ 0 0
$$259$$ 1.00000 0.0621370
$$260$$ 0 0
$$261$$ 12.0000 0.742781
$$262$$ 0 0
$$263$$ −5.00000 −0.308313 −0.154157 0.988046i $$-0.549266\pi$$
−0.154157 + 0.988046i $$0.549266\pi$$
$$264$$ 0 0
$$265$$ 1.00000 0.0614295
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ 0 0
$$271$$ 13.0000 0.789694 0.394847 0.918747i $$-0.370798\pi$$
0.394847 + 0.918747i $$0.370798\pi$$
$$272$$ 0 0
$$273$$ 6.00000 0.363137
$$274$$ 0 0
$$275$$ 3.00000 0.180907
$$276$$ 0 0
$$277$$ −8.00000 −0.480673 −0.240337 0.970690i $$-0.577258\pi$$
−0.240337 + 0.970690i $$0.577258\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 9.00000 0.531253
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ 0 0
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −15.0000 −0.870388
$$298$$ 0 0
$$299$$ 12.0000 0.693978
$$300$$ 0 0
$$301$$ −10.0000 −0.576390
$$302$$ 0 0
$$303$$ −1.00000 −0.0574485
$$304$$ 0 0
$$305$$ −12.0000 −0.687118
$$306$$ 0 0
$$307$$ 11.0000 0.627803 0.313902 0.949456i $$-0.398364\pi$$
0.313902 + 0.949456i $$0.398364\pi$$
$$308$$ 0 0
$$309$$ 10.0000 0.568880
$$310$$ 0 0
$$311$$ −16.0000 −0.907277 −0.453638 0.891186i $$-0.649874\pi$$
−0.453638 + 0.891186i $$0.649874\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 0 0
$$315$$ 2.00000 0.112687
$$316$$ 0 0
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 0 0
$$319$$ −18.0000 −1.00781
$$320$$ 0 0
$$321$$ −20.0000 −1.11629
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −6.00000 −0.332820
$$326$$ 0 0
$$327$$ −12.0000 −0.663602
$$328$$ 0 0
$$329$$ 1.00000 0.0551318
$$330$$ 0 0
$$331$$ −6.00000 −0.329790 −0.164895 0.986311i $$-0.552728\pi$$
−0.164895 + 0.986311i $$0.552728\pi$$
$$332$$ 0 0
$$333$$ 2.00000 0.109599
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 3.00000 0.163420 0.0817102 0.996656i $$-0.473962\pi$$
0.0817102 + 0.996656i $$0.473962\pi$$
$$338$$ 0 0
$$339$$ 14.0000 0.760376
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 0 0
$$345$$ −2.00000 −0.107676
$$346$$ 0 0
$$347$$ 34.0000 1.82522 0.912608 0.408836i $$-0.134065\pi$$
0.912608 + 0.408836i $$0.134065\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 30.0000 1.60128
$$352$$ 0 0
$$353$$ 4.00000 0.212899 0.106449 0.994318i $$-0.466052\pi$$
0.106449 + 0.994318i $$0.466052\pi$$
$$354$$ 0 0
$$355$$ 5.00000 0.265372
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −19.0000 −1.00278 −0.501391 0.865221i $$-0.667178\pi$$
−0.501391 + 0.865221i $$0.667178\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 0 0
$$363$$ −2.00000 −0.104973
$$364$$ 0 0
$$365$$ 3.00000 0.157027
$$366$$ 0 0
$$367$$ −16.0000 −0.835193 −0.417597 0.908633i $$-0.637127\pi$$
−0.417597 + 0.908633i $$0.637127\pi$$
$$368$$ 0 0
$$369$$ 18.0000 0.937043
$$370$$ 0 0
$$371$$ −1.00000 −0.0519174
$$372$$ 0 0
$$373$$ −11.0000 −0.569558 −0.284779 0.958593i $$-0.591920\pi$$
−0.284779 + 0.958593i $$0.591920\pi$$
$$374$$ 0 0
$$375$$ 1.00000 0.0516398
$$376$$ 0 0
$$377$$ 36.0000 1.85409
$$378$$ 0 0
$$379$$ 23.0000 1.18143 0.590715 0.806880i $$-0.298846\pi$$
0.590715 + 0.806880i $$0.298846\pi$$
$$380$$ 0 0
$$381$$ 1.00000 0.0512316
$$382$$ 0 0
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ −3.00000 −0.152894
$$386$$ 0 0
$$387$$ −20.0000 −1.01666
$$388$$ 0 0
$$389$$ −36.0000 −1.82527 −0.912636 0.408773i $$-0.865957\pi$$
−0.912636 + 0.408773i $$0.865957\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −16.0000 −0.805047
$$396$$ 0 0
$$397$$ −21.0000 −1.05396 −0.526980 0.849878i $$-0.676676\pi$$
−0.526980 + 0.849878i $$0.676676\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 34.0000 1.69788 0.848939 0.528490i $$-0.177242\pi$$
0.848939 + 0.528490i $$0.177242\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 1.00000 0.0496904
$$406$$ 0 0
$$407$$ −3.00000 −0.148704
$$408$$ 0 0
$$409$$ −12.0000 −0.593362 −0.296681 0.954977i $$-0.595880\pi$$
−0.296681 + 0.954977i $$0.595880\pi$$
$$410$$ 0 0
$$411$$ 2.00000 0.0986527
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −11.0000 −0.539969
$$416$$ 0 0
$$417$$ 12.0000 0.587643
$$418$$ 0 0
$$419$$ 15.0000 0.732798 0.366399 0.930458i $$-0.380591\pi$$
0.366399 + 0.930458i $$0.380591\pi$$
$$420$$ 0 0
$$421$$ −32.0000 −1.55958 −0.779792 0.626038i $$-0.784675\pi$$
−0.779792 + 0.626038i $$0.784675\pi$$
$$422$$ 0 0
$$423$$ 2.00000 0.0972433
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 12.0000 0.580721
$$428$$ 0 0
$$429$$ −18.0000 −0.869048
$$430$$ 0 0
$$431$$ −26.0000 −1.25238 −0.626188 0.779672i $$-0.715386\pi$$
−0.626188 + 0.779672i $$0.715386\pi$$
$$432$$ 0 0
$$433$$ −19.0000 −0.913082 −0.456541 0.889702i $$-0.650912\pi$$
−0.456541 + 0.889702i $$0.650912\pi$$
$$434$$ 0 0
$$435$$ −6.00000 −0.287678
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −4.00000 −0.190910 −0.0954548 0.995434i $$-0.530431\pi$$
−0.0954548 + 0.995434i $$0.530431\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 0 0
$$443$$ 13.0000 0.617649 0.308824 0.951119i $$-0.400064\pi$$
0.308824 + 0.951119i $$0.400064\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −9.00000 −0.425685
$$448$$ 0 0
$$449$$ −16.0000 −0.755087 −0.377543 0.925992i $$-0.623231\pi$$
−0.377543 + 0.925992i $$0.623231\pi$$
$$450$$ 0 0
$$451$$ −27.0000 −1.27138
$$452$$ 0 0
$$453$$ 8.00000 0.375873
$$454$$ 0 0
$$455$$ 6.00000 0.281284
$$456$$ 0 0
$$457$$ −30.0000 −1.40334 −0.701670 0.712502i $$-0.747562\pi$$
−0.701670 + 0.712502i $$0.747562\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 14.0000 0.652045 0.326023 0.945362i $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 0 0
$$463$$ −6.00000 −0.278844 −0.139422 0.990233i $$-0.544524\pi$$
−0.139422 + 0.990233i $$0.544524\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 22.0000 1.01804 0.509019 0.860755i $$-0.330008\pi$$
0.509019 + 0.860755i $$0.330008\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 15.0000 0.691164
$$472$$ 0 0
$$473$$ 30.0000 1.37940
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −2.00000 −0.0915737
$$478$$ 0 0
$$479$$ 26.0000 1.18797 0.593985 0.804476i $$-0.297554\pi$$
0.593985 + 0.804476i $$0.297554\pi$$
$$480$$ 0 0
$$481$$ 6.00000 0.273576
$$482$$ 0 0
$$483$$ 2.00000 0.0910032
$$484$$ 0 0
$$485$$ 8.00000 0.363261
$$486$$ 0 0
$$487$$ −16.0000 −0.725029 −0.362515 0.931978i $$-0.618082\pi$$
−0.362515 + 0.931978i $$0.618082\pi$$
$$488$$ 0 0
$$489$$ 2.00000 0.0904431
$$490$$ 0 0
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −6.00000 −0.269680
$$496$$ 0 0
$$497$$ −5.00000 −0.224281
$$498$$ 0 0
$$499$$ 40.0000 1.79065 0.895323 0.445418i $$-0.146945\pi$$
0.895323 + 0.445418i $$0.146945\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ −1.00000 −0.0444994
$$506$$ 0 0
$$507$$ 23.0000 1.02147
$$508$$ 0 0
$$509$$ −27.0000 −1.19675 −0.598377 0.801215i $$-0.704187\pi$$
−0.598377 + 0.801215i $$0.704187\pi$$
$$510$$ 0 0
$$511$$ −3.00000 −0.132712
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 10.0000 0.440653
$$516$$ 0 0
$$517$$ −3.00000 −0.131940
$$518$$ 0 0
$$519$$ −15.0000 −0.658427
$$520$$ 0 0
$$521$$ 7.00000 0.306676 0.153338 0.988174i $$-0.450998\pi$$
0.153338 + 0.988174i $$0.450998\pi$$
$$522$$ 0 0
$$523$$ 26.0000 1.13690 0.568450 0.822718i $$-0.307543\pi$$
0.568450 + 0.822718i $$0.307543\pi$$
$$524$$ 0 0
$$525$$ −1.00000 −0.0436436
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 54.0000 2.33900
$$534$$ 0 0
$$535$$ −20.0000 −0.864675
$$536$$ 0 0
$$537$$ −18.0000 −0.776757
$$538$$ 0 0
$$539$$ −18.0000 −0.775315
$$540$$ 0 0
$$541$$ −8.00000 −0.343947 −0.171973 0.985102i $$-0.555014\pi$$
−0.171973 + 0.985102i $$0.555014\pi$$
$$542$$ 0 0
$$543$$ 17.0000 0.729540
$$544$$ 0 0
$$545$$ −12.0000 −0.514024
$$546$$ 0 0
$$547$$ 40.0000 1.71028 0.855138 0.518400i $$-0.173472\pi$$
0.855138 + 0.518400i $$0.173472\pi$$
$$548$$ 0 0
$$549$$ 24.0000 1.02430
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ 0 0
$$555$$ −1.00000 −0.0424476
$$556$$ 0 0
$$557$$ 26.0000 1.10166 0.550828 0.834619i $$-0.314312\pi$$
0.550828 + 0.834619i $$0.314312\pi$$
$$558$$ 0 0
$$559$$ −60.0000 −2.53773
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 38.0000 1.60151 0.800755 0.598993i $$-0.204432\pi$$
0.800755 + 0.598993i $$0.204432\pi$$
$$564$$ 0 0
$$565$$ 14.0000 0.588984
$$566$$ 0 0
$$567$$ −1.00000 −0.0419961
$$568$$ 0 0
$$569$$ 28.0000 1.17382 0.586911 0.809652i $$-0.300344\pi$$
0.586911 + 0.809652i $$0.300344\pi$$
$$570$$ 0 0
$$571$$ −17.0000 −0.711428 −0.355714 0.934595i $$-0.615762\pi$$
−0.355714 + 0.934595i $$0.615762\pi$$
$$572$$ 0 0
$$573$$ 12.0000 0.501307
$$574$$ 0 0
$$575$$ −2.00000 −0.0834058
$$576$$ 0 0
$$577$$ −24.0000 −0.999133 −0.499567 0.866276i $$-0.666507\pi$$
−0.499567 + 0.866276i $$0.666507\pi$$
$$578$$ 0 0
$$579$$ −22.0000 −0.914289
$$580$$ 0 0
$$581$$ 11.0000 0.456357
$$582$$ 0 0
$$583$$ 3.00000 0.124247
$$584$$ 0 0
$$585$$ 12.0000 0.496139
$$586$$ 0 0
$$587$$ −20.0000 −0.825488 −0.412744 0.910847i $$-0.635430\pi$$
−0.412744 + 0.910847i $$0.635430\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 3.00000 0.123404
$$592$$ 0 0
$$593$$ −33.0000 −1.35515 −0.677574 0.735455i $$-0.736969\pi$$
−0.677574 + 0.735455i $$0.736969\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −14.0000 −0.572982
$$598$$ 0 0
$$599$$ 21.0000 0.858037 0.429018 0.903296i $$-0.358860\pi$$
0.429018 + 0.903296i $$0.358860\pi$$
$$600$$ 0 0
$$601$$ 42.0000 1.71322 0.856608 0.515968i $$-0.172568\pi$$
0.856608 + 0.515968i $$0.172568\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −2.00000 −0.0813116
$$606$$ 0 0
$$607$$ −16.0000 −0.649420 −0.324710 0.945814i $$-0.605267\pi$$
−0.324710 + 0.945814i $$0.605267\pi$$
$$608$$ 0 0
$$609$$ 6.00000 0.243132
$$610$$ 0 0
$$611$$ 6.00000 0.242734
$$612$$ 0 0
$$613$$ 23.0000 0.928961 0.464481 0.885583i $$-0.346241\pi$$
0.464481 + 0.885583i $$0.346241\pi$$
$$614$$ 0 0
$$615$$ −9.00000 −0.362915
$$616$$ 0 0
$$617$$ −3.00000 −0.120775 −0.0603877 0.998175i $$-0.519234\pi$$
−0.0603877 + 0.998175i $$0.519234\pi$$
$$618$$ 0 0
$$619$$ 31.0000 1.24600 0.622998 0.782224i $$-0.285915\pi$$
0.622998 + 0.782224i $$0.285915\pi$$
$$620$$ 0 0
$$621$$ 10.0000 0.401286
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 0 0
$$633$$ 27.0000 1.07315
$$634$$ 0 0
$$635$$ 1.00000 0.0396838
$$636$$ 0 0
$$637$$ 36.0000 1.42637
$$638$$ 0 0
$$639$$ −10.0000 −0.395594
$$640$$ 0 0
$$641$$ 15.0000 0.592464 0.296232 0.955116i $$-0.404270\pi$$
0.296232 + 0.955116i $$0.404270\pi$$
$$642$$ 0 0
$$643$$ 34.0000 1.34083 0.670415 0.741987i $$-0.266116\pi$$
0.670415 + 0.741987i $$0.266116\pi$$
$$644$$ 0 0
$$645$$ 10.0000 0.393750
$$646$$ 0 0
$$647$$ 12.0000 0.471769 0.235884 0.971781i $$-0.424201\pi$$
0.235884 + 0.971781i $$0.424201\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −36.0000 −1.40879 −0.704394 0.709809i $$-0.748781\pi$$
−0.704394 + 0.709809i $$0.748781\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −6.00000 −0.234082
$$658$$ 0 0
$$659$$ −15.0000 −0.584317 −0.292159 0.956370i $$-0.594373\pi$$
−0.292159 + 0.956370i $$0.594373\pi$$
$$660$$ 0 0
$$661$$ 32.0000 1.24466 0.622328 0.782757i $$-0.286187\pi$$
0.622328 + 0.782757i $$0.286187\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 12.0000 0.464642
$$668$$ 0 0
$$669$$ −17.0000 −0.657258
$$670$$ 0 0
$$671$$ −36.0000 −1.38976
$$672$$ 0 0
$$673$$ 47.0000 1.81172 0.905858 0.423581i $$-0.139227\pi$$
0.905858 + 0.423581i $$0.139227\pi$$
$$674$$ 0 0
$$675$$ −5.00000 −0.192450
$$676$$ 0 0
$$677$$ 37.0000 1.42203 0.711013 0.703179i $$-0.248237\pi$$
0.711013 + 0.703179i $$0.248237\pi$$
$$678$$ 0 0
$$679$$ −8.00000 −0.307012
$$680$$ 0 0
$$681$$ 8.00000 0.306561
$$682$$ 0 0
$$683$$ −26.0000 −0.994862 −0.497431 0.867503i $$-0.665723\pi$$
−0.497431 + 0.867503i $$0.665723\pi$$
$$684$$ 0 0
$$685$$ 2.00000 0.0764161
$$686$$ 0 0
$$687$$ 3.00000 0.114457
$$688$$ 0 0
$$689$$ −6.00000 −0.228582
$$690$$ 0 0
$$691$$ −20.0000 −0.760836 −0.380418 0.924815i $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ 0 0
$$693$$ 6.00000 0.227921
$$694$$ 0 0
$$695$$ 12.0000 0.455186
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −2.00000 −0.0756469
$$700$$ 0 0
$$701$$ 20.0000 0.755390 0.377695 0.925930i $$-0.376717\pi$$
0.377695 + 0.925930i $$0.376717\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −1.00000 −0.0376622
$$706$$ 0 0
$$707$$ 1.00000 0.0376089
$$708$$ 0 0
$$709$$ −40.0000 −1.50223 −0.751116 0.660171i $$-0.770484\pi$$
−0.751116 + 0.660171i $$0.770484\pi$$
$$710$$ 0 0
$$711$$ 32.0000 1.20009
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −18.0000 −0.673162
$$716$$ 0 0
$$717$$ −30.0000 −1.12037
$$718$$ 0 0
$$719$$ 3.00000 0.111881 0.0559406 0.998434i $$-0.482184\pi$$
0.0559406 + 0.998434i $$0.482184\pi$$
$$720$$ 0 0
$$721$$ −10.0000 −0.372419
$$722$$ 0 0
$$723$$ −6.00000 −0.223142
$$724$$ 0 0
$$725$$ −6.00000 −0.222834
$$726$$ 0 0
$$727$$ −28.0000 −1.03846 −0.519231 0.854634i $$-0.673782\pi$$
−0.519231 + 0.854634i $$0.673782\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −17.0000 −0.627909 −0.313955 0.949438i $$-0.601654\pi$$
−0.313955 + 0.949438i $$0.601654\pi$$
$$734$$ 0 0
$$735$$ −6.00000 −0.221313
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −33.0000 −1.21392 −0.606962 0.794731i $$-0.707612\pi$$
−0.606962 + 0.794731i $$0.707612\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 45.0000 1.65089 0.825445 0.564483i $$-0.190924\pi$$
0.825445 + 0.564483i $$0.190924\pi$$
$$744$$ 0 0
$$745$$ −9.00000 −0.329734
$$746$$ 0 0
$$747$$ 22.0000 0.804938
$$748$$ 0 0
$$749$$ 20.0000 0.730784
$$750$$ 0 0
$$751$$ −11.0000 −0.401396 −0.200698 0.979653i $$-0.564321\pi$$
−0.200698 + 0.979653i $$0.564321\pi$$
$$752$$ 0 0
$$753$$ −6.00000 −0.218652
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ 10.0000 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$758$$ 0 0
$$759$$ −6.00000 −0.217786
$$760$$ 0 0
$$761$$ 21.0000 0.761249 0.380625 0.924730i $$-0.375709\pi$$
0.380625 + 0.924730i $$0.375709\pi$$
$$762$$ 0 0
$$763$$ 12.0000 0.434429
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −10.0000 −0.360609 −0.180305 0.983611i $$-0.557708\pi$$
−0.180305 + 0.983611i $$0.557708\pi$$
$$770$$ 0 0
$$771$$ 20.0000 0.720282
$$772$$ 0 0
$$773$$ 31.0000 1.11499 0.557496 0.830179i $$-0.311762\pi$$
0.557496 + 0.830179i $$0.311762\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 1.00000 0.0358748
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 15.0000 0.536742
$$782$$ 0 0
$$783$$ 30.0000 1.07211
$$784$$ 0 0
$$785$$ 15.0000 0.535373
$$786$$ 0 0
$$787$$ −17.0000 −0.605985 −0.302992 0.952993i $$-0.597986\pi$$
−0.302992 + 0.952993i $$0.597986\pi$$
$$788$$ 0 0
$$789$$ −5.00000 −0.178005
$$790$$ 0 0
$$791$$ −14.0000 −0.497783
$$792$$ 0 0
$$793$$ 72.0000 2.55679
$$794$$ 0 0
$$795$$ 1.00000 0.0354663
$$796$$ 0 0
$$797$$ 28.0000 0.991811 0.495905 0.868377i $$-0.334836\pi$$
0.495905 + 0.868377i $$0.334836\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 9.00000 0.317603
$$804$$ 0 0
$$805$$ 2.00000 0.0704907
$$806$$ 0 0
$$807$$ 2.00000 0.0704033
$$808$$ 0 0
$$809$$ −50.0000 −1.75791 −0.878953 0.476908i $$-0.841757\pi$$
−0.878953 + 0.476908i $$0.841757\pi$$
$$810$$ 0 0
$$811$$ −41.0000 −1.43970 −0.719852 0.694127i $$-0.755791\pi$$
−0.719852 + 0.694127i $$0.755791\pi$$
$$812$$ 0 0
$$813$$ 13.0000 0.455930
$$814$$ 0 0
$$815$$ 2.00000 0.0700569
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ −12.0000 −0.419314
$$820$$ 0 0
$$821$$ −19.0000 −0.663105 −0.331552 0.943437i $$-0.607572\pi$$
−0.331552 + 0.943437i $$0.607572\pi$$
$$822$$ 0 0
$$823$$ −24.0000 −0.836587 −0.418294 0.908312i $$-0.637372\pi$$
−0.418294 + 0.908312i $$0.637372\pi$$
$$824$$ 0 0
$$825$$ 3.00000 0.104447
$$826$$ 0 0
$$827$$ 2.00000 0.0695468 0.0347734 0.999395i $$-0.488929\pi$$
0.0347734 + 0.999395i $$0.488929\pi$$
$$828$$ 0 0
$$829$$ −12.0000 −0.416777 −0.208389 0.978046i $$-0.566822\pi$$
−0.208389 + 0.978046i $$0.566822\pi$$
$$830$$ 0 0
$$831$$ −8.00000 −0.277517
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 36.0000 1.24286 0.621429 0.783470i $$-0.286552\pi$$
0.621429 + 0.783470i $$0.286552\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 23.0000 0.791224
$$846$$ 0 0
$$847$$ 2.00000 0.0687208
$$848$$ 0 0
$$849$$ −4.00000 −0.137280
$$850$$ 0 0
$$851$$ 2.00000 0.0685591
$$852$$ 0 0
$$853$$ −2.00000 −0.0684787 −0.0342393 0.999414i $$-0.510901\pi$$
−0.0342393 + 0.999414i $$0.510901\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −12.0000 −0.409912 −0.204956 0.978771i $$-0.565705\pi$$
−0.204956 + 0.978771i $$0.565705\pi$$
$$858$$ 0 0
$$859$$ −36.0000 −1.22830 −0.614152 0.789188i $$-0.710502\pi$$
−0.614152 + 0.789188i $$0.710502\pi$$
$$860$$ 0 0
$$861$$ 9.00000 0.306719
$$862$$ 0 0
$$863$$ 24.0000 0.816970 0.408485 0.912765i $$-0.366057\pi$$
0.408485 + 0.912765i $$0.366057\pi$$
$$864$$ 0 0
$$865$$ −15.0000 −0.510015
$$866$$ 0 0
$$867$$ −17.0000 −0.577350
$$868$$ 0 0
$$869$$ −48.0000 −1.62829
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −16.0000 −0.541518
$$874$$ 0 0
$$875$$ −1.00000 −0.0338062
$$876$$ 0 0
$$877$$ −46.0000 −1.55331 −0.776655 0.629926i $$-0.783085\pi$$
−0.776655 + 0.629926i $$0.783085\pi$$
$$878$$ 0 0
$$879$$ 30.0000 1.01187
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ 16.0000 0.538443 0.269221 0.963078i $$-0.413234\pi$$
0.269221 + 0.963078i $$0.413234\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 33.0000 1.10803 0.554016 0.832506i $$-0.313095\pi$$
0.554016 + 0.832506i $$0.313095\pi$$
$$888$$ 0 0
$$889$$ −1.00000 −0.0335389
$$890$$ 0 0
$$891$$ 3.00000 0.100504
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −18.0000 −0.601674
$$896$$ 0 0
$$897$$ 12.0000 0.400668
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ −10.0000 −0.332779
$$904$$ 0 0
$$905$$ 17.0000 0.565099
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 2.00000 0.0663358
$$910$$ 0 0
$$911$$ −30.0000 −0.993944 −0.496972 0.867766i $$-0.665555\pi$$
−0.496972 + 0.867766i $$0.665555\pi$$
$$912$$ 0 0
$$913$$ −33.0000 −1.09214
$$914$$ 0 0
$$915$$ −12.0000 −0.396708
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −14.0000 −0.461817 −0.230909 0.972975i $$-0.574170\pi$$
−0.230909 + 0.972975i $$0.574170\pi$$
$$920$$ 0 0
$$921$$ 11.0000 0.362462
$$922$$ 0 0
$$923$$ −30.0000 −0.987462
$$924$$ 0 0
$$925$$ −1.00000 −0.0328798
$$926$$ 0 0
$$927$$ −20.0000 −0.656886
$$928$$ 0 0
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ −16.0000 −0.523816
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 1.00000 0.0326686 0.0163343 0.999867i $$-0.494800\pi$$
0.0163343 + 0.999867i $$0.494800\pi$$
$$938$$ 0 0
$$939$$ −10.0000 −0.326338
$$940$$ 0 0
$$941$$ 30.0000 0.977972 0.488986 0.872292i $$-0.337367\pi$$
0.488986 + 0.872292i $$0.337367\pi$$
$$942$$ 0 0
$$943$$ 18.0000 0.586161
$$944$$ 0 0
$$945$$ 5.00000 0.162650
$$946$$ 0 0
$$947$$ 36.0000 1.16984 0.584921 0.811090i $$-0.301125\pi$$
0.584921 + 0.811090i $$0.301125\pi$$
$$948$$ 0 0
$$949$$ −18.0000 −0.584305
$$950$$ 0 0
$$951$$ 6.00000 0.194563
$$952$$ 0 0
$$953$$ 9.00000 0.291539 0.145769 0.989319i $$-0.453434\pi$$
0.145769 + 0.989319i $$0.453434\pi$$
$$954$$ 0 0
$$955$$ 12.0000 0.388311
$$956$$ 0 0
$$957$$ −18.0000 −0.581857
$$958$$ 0 0
$$959$$ −2.00000 −0.0645834
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ 40.0000 1.28898
$$964$$ 0 0
$$965$$ −22.0000 −0.708205
$$966$$ 0 0
$$967$$ −6.00000 −0.192947 −0.0964735 0.995336i $$-0.530756\pi$$
−0.0964735 + 0.995336i $$0.530756\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −24.0000 −0.770197 −0.385098 0.922876i $$-0.625832\pi$$
−0.385098 + 0.922876i $$0.625832\pi$$
$$972$$ 0 0
$$973$$ −12.0000 −0.384702
$$974$$ 0 0
$$975$$ −6.00000 −0.192154
$$976$$ 0 0
$$977$$ −52.0000 −1.66363 −0.831814 0.555055i $$-0.812697\pi$$
−0.831814 + 0.555055i $$0.812697\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 24.0000 0.766261
$$982$$ 0 0
$$983$$ −39.0000 −1.24391 −0.621953 0.783054i $$-0.713661\pi$$
−0.621953 + 0.783054i $$0.713661\pi$$
$$984$$ 0 0
$$985$$ 3.00000 0.0955879
$$986$$ 0 0
$$987$$ 1.00000 0.0318304
$$988$$ 0 0
$$989$$ −20.0000 −0.635963
$$990$$ 0 0
$$991$$ 30.0000 0.952981 0.476491 0.879180i $$-0.341909\pi$$
0.476491 + 0.879180i $$0.341909\pi$$
$$992$$ 0 0
$$993$$ −6.00000 −0.190404
$$994$$ 0 0
$$995$$ −14.0000 −0.443830
$$996$$ 0 0
$$997$$ 42.0000 1.33015 0.665077 0.746775i $$-0.268399\pi$$
0.665077 + 0.746775i $$0.268399\pi$$
$$998$$ 0 0
$$999$$ 5.00000 0.158193
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 2960.2.a.h.1.1 1
4.3 odd 2 740.2.a.a.1.1 1
12.11 even 2 6660.2.a.a.1.1 1
20.3 even 4 3700.2.d.c.149.1 2
20.7 even 4 3700.2.d.c.149.2 2
20.19 odd 2 3700.2.a.d.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
740.2.a.a.1.1 1 4.3 odd 2
2960.2.a.h.1.1 1 1.1 even 1 trivial
3700.2.a.d.1.1 1 20.19 odd 2
3700.2.d.c.149.1 2 20.3 even 4
3700.2.d.c.149.2 2 20.7 even 4
6660.2.a.a.1.1 1 12.11 even 2