# Properties

 Label 1386.2.a.j.1.1 Level $1386$ Weight $2$ Character 1386.1 Self dual yes Analytic conductor $11.067$ 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] = [1386,2,Mod(1,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1386.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.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: $$11.0672657201$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 462) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1386.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{11} +6.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} +6.00000 q^{19} +1.00000 q^{22} +4.00000 q^{23} -5.00000 q^{25} +6.00000 q^{26} -1.00000 q^{28} -6.00000 q^{29} -2.00000 q^{31} +1.00000 q^{32} -4.00000 q^{34} +10.0000 q^{37} +6.00000 q^{38} +4.00000 q^{41} +8.00000 q^{43} +1.00000 q^{44} +4.00000 q^{46} +6.00000 q^{47} +1.00000 q^{49} -5.00000 q^{50} +6.00000 q^{52} +10.0000 q^{53} -1.00000 q^{56} -6.00000 q^{58} -2.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} -4.00000 q^{68} -16.0000 q^{71} +12.0000 q^{73} +10.0000 q^{74} +6.00000 q^{76} -1.00000 q^{77} -16.0000 q^{79} +4.00000 q^{82} +2.00000 q^{83} +8.00000 q^{86} +1.00000 q^{88} +6.00000 q^{89} -6.00000 q^{91} +4.00000 q^{92} +6.00000 q^{94} -6.00000 q^{97} +1.00000 q^{98} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.00000 0.301511
$$12$$ 0 0
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ 6.00000 1.37649 0.688247 0.725476i $$-0.258380\pi$$
0.688247 + 0.725476i $$0.258380\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 6.00000 1.17670
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 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
$$33$$ 0 0
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 6.00000 0.973329
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.00000 0.624695 0.312348 0.949968i $$-0.398885\pi$$
0.312348 + 0.949968i $$0.398885\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 1.00000 0.150756
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ −5.00000 −0.707107
$$51$$ 0 0
$$52$$ 6.00000 0.832050
$$53$$ 10.0000 1.37361 0.686803 0.726844i $$-0.259014\pi$$
0.686803 + 0.726844i $$0.259014\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ −6.00000 −0.787839
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −16.0000 −1.89885 −0.949425 0.313993i $$-0.898333\pi$$
−0.949425 + 0.313993i $$0.898333\pi$$
$$72$$ 0 0
$$73$$ 12.0000 1.40449 0.702247 0.711934i $$-0.252180\pi$$
0.702247 + 0.711934i $$0.252180\pi$$
$$74$$ 10.0000 1.16248
$$75$$ 0 0
$$76$$ 6.00000 0.688247
$$77$$ −1.00000 −0.113961
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 4.00000 0.441726
$$83$$ 2.00000 0.219529 0.109764 0.993958i $$-0.464990\pi$$
0.109764 + 0.993958i $$0.464990\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 8.00000 0.862662
$$87$$ 0 0
$$88$$ 1.00000 0.106600
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ −6.00000 −0.628971
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ 6.00000 0.618853
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ −5.00000 −0.500000
$$101$$ 14.0000 1.39305 0.696526 0.717532i $$-0.254728\pi$$
0.696526 + 0.717532i $$0.254728\pi$$
$$102$$ 0 0
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ 10.0000 0.971286
$$107$$ −8.00000 −0.773389 −0.386695 0.922208i $$-0.626383\pi$$
−0.386695 + 0.922208i $$0.626383\pi$$
$$108$$ 0 0
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −1.00000 −0.0944911
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 4.00000 0.366679
$$120$$ 0 0
$$121$$ 1.00000 0.0909091
$$122$$ −2.00000 −0.181071
$$123$$ 0 0
$$124$$ −2.00000 −0.179605
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 22.0000 1.92215 0.961074 0.276289i $$-0.0891049\pi$$
0.961074 + 0.276289i $$0.0891049\pi$$
$$132$$ 0 0
$$133$$ −6.00000 −0.520266
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ −4.00000 −0.342997
$$137$$ −22.0000 −1.87959 −0.939793 0.341743i $$-0.888983\pi$$
−0.939793 + 0.341743i $$0.888983\pi$$
$$138$$ 0 0
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −16.0000 −1.34269
$$143$$ 6.00000 0.501745
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 12.0000 0.993127
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 6.00000 0.486664
$$153$$ 0 0
$$154$$ −1.00000 −0.0805823
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 12.0000 0.957704 0.478852 0.877896i $$-0.341053\pi$$
0.478852 + 0.877896i $$0.341053\pi$$
$$158$$ −16.0000 −1.27289
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −4.00000 −0.315244
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 4.00000 0.312348
$$165$$ 0 0
$$166$$ 2.00000 0.155230
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 0 0
$$175$$ 5.00000 0.377964
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ 6.00000 0.449719
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ 8.00000 0.594635 0.297318 0.954779i $$-0.403908\pi$$
0.297318 + 0.954779i $$0.403908\pi$$
$$182$$ −6.00000 −0.444750
$$183$$ 0 0
$$184$$ 4.00000 0.294884
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −4.00000 −0.292509
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ −6.00000 −0.430775
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ −14.0000 −0.992434 −0.496217 0.868199i $$-0.665278\pi$$
−0.496217 + 0.868199i $$0.665278\pi$$
$$200$$ −5.00000 −0.353553
$$201$$ 0 0
$$202$$ 14.0000 0.985037
$$203$$ 6.00000 0.421117
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −14.0000 −0.975426
$$207$$ 0 0
$$208$$ 6.00000 0.416025
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ 10.0000 0.686803
$$213$$ 0 0
$$214$$ −8.00000 −0.546869
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 2.00000 0.135769
$$218$$ −14.0000 −0.948200
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −24.0000 −1.61441
$$222$$ 0 0
$$223$$ −26.0000 −1.74109 −0.870544 0.492090i $$-0.836233\pi$$
−0.870544 + 0.492090i $$0.836233\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ 2.00000 0.133038
$$227$$ −18.0000 −1.19470 −0.597351 0.801980i $$-0.703780\pi$$
−0.597351 + 0.801980i $$0.703780\pi$$
$$228$$ 0 0
$$229$$ 8.00000 0.528655 0.264327 0.964433i $$-0.414850\pi$$
0.264327 + 0.964433i $$0.414850\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ −22.0000 −1.44127 −0.720634 0.693316i $$-0.756149\pi$$
−0.720634 + 0.693316i $$0.756149\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 4.00000 0.259281
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ −20.0000 −1.28831 −0.644157 0.764894i $$-0.722792\pi$$
−0.644157 + 0.764894i $$0.722792\pi$$
$$242$$ 1.00000 0.0642824
$$243$$ 0 0
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 36.0000 2.29063
$$248$$ −2.00000 −0.127000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ −16.0000 −1.00393
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −10.0000 −0.623783 −0.311891 0.950118i $$-0.600963\pi$$
−0.311891 + 0.950118i $$0.600963\pi$$
$$258$$ 0 0
$$259$$ −10.0000 −0.621370
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 22.0000 1.35916
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −6.00000 −0.367884
$$267$$ 0 0
$$268$$ −4.00000 −0.244339
$$269$$ 24.0000 1.46331 0.731653 0.681677i $$-0.238749\pi$$
0.731653 + 0.681677i $$0.238749\pi$$
$$270$$ 0 0
$$271$$ 12.0000 0.728948 0.364474 0.931214i $$-0.381249\pi$$
0.364474 + 0.931214i $$0.381249\pi$$
$$272$$ −4.00000 −0.242536
$$273$$ 0 0
$$274$$ −22.0000 −1.32907
$$275$$ −5.00000 −0.301511
$$276$$ 0 0
$$277$$ −6.00000 −0.360505 −0.180253 0.983620i $$-0.557691\pi$$
−0.180253 + 0.983620i $$0.557691\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −14.0000 −0.835170 −0.417585 0.908638i $$-0.637123\pi$$
−0.417585 + 0.908638i $$0.637123\pi$$
$$282$$ 0 0
$$283$$ 18.0000 1.06999 0.534994 0.844856i $$-0.320314\pi$$
0.534994 + 0.844856i $$0.320314\pi$$
$$284$$ −16.0000 −0.949425
$$285$$ 0 0
$$286$$ 6.00000 0.354787
$$287$$ −4.00000 −0.236113
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 12.0000 0.702247
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 10.0000 0.581238
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 24.0000 1.38796
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 6.00000 0.344124
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −30.0000 −1.71219 −0.856095 0.516818i $$-0.827116\pi$$
−0.856095 + 0.516818i $$0.827116\pi$$
$$308$$ −1.00000 −0.0569803
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 0 0
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 12.0000 0.677199
$$315$$ 0 0
$$316$$ −16.0000 −0.900070
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ −6.00000 −0.335936
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −4.00000 −0.222911
$$323$$ −24.0000 −1.33540
$$324$$ 0 0
$$325$$ −30.0000 −1.66410
$$326$$ −4.00000 −0.221540
$$327$$ 0 0
$$328$$ 4.00000 0.220863
$$329$$ −6.00000 −0.330791
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ 2.00000 0.109764
$$333$$ 0 0
$$334$$ −12.0000 −0.656611
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 22.0000 1.19842 0.599208 0.800593i $$-0.295482\pi$$
0.599208 + 0.800593i $$0.295482\pi$$
$$338$$ 23.0000 1.25104
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −2.00000 −0.108306
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ −16.0000 −0.858925 −0.429463 0.903085i $$-0.641297\pi$$
−0.429463 + 0.903085i $$0.641297\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 5.00000 0.267261
$$351$$ 0 0
$$352$$ 1.00000 0.0533002
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −4.00000 −0.211407
$$359$$ −8.00000 −0.422224 −0.211112 0.977462i $$-0.567708\pi$$
−0.211112 + 0.977462i $$0.567708\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 8.00000 0.420471
$$363$$ 0 0
$$364$$ −6.00000 −0.314485
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −2.00000 −0.104399 −0.0521996 0.998637i $$-0.516623\pi$$
−0.0521996 + 0.998637i $$0.516623\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −10.0000 −0.519174
$$372$$ 0 0
$$373$$ −10.0000 −0.517780 −0.258890 0.965907i $$-0.583357\pi$$
−0.258890 + 0.965907i $$0.583357\pi$$
$$374$$ −4.00000 −0.206835
$$375$$ 0 0
$$376$$ 6.00000 0.309426
$$377$$ −36.0000 −1.85409
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 12.0000 0.613973
$$383$$ 34.0000 1.73732 0.868659 0.495410i $$-0.164982\pi$$
0.868659 + 0.495410i $$0.164982\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −6.00000 −0.305392
$$387$$ 0 0
$$388$$ −6.00000 −0.304604
$$389$$ 30.0000 1.52106 0.760530 0.649303i $$-0.224939\pi$$
0.760530 + 0.649303i $$0.224939\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ −6.00000 −0.302276
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −4.00000 −0.200754 −0.100377 0.994949i $$-0.532005\pi$$
−0.100377 + 0.994949i $$0.532005\pi$$
$$398$$ −14.0000 −0.701757
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 0 0
$$403$$ −12.0000 −0.597763
$$404$$ 14.0000 0.696526
$$405$$ 0 0
$$406$$ 6.00000 0.297775
$$407$$ 10.0000 0.495682
$$408$$ 0 0
$$409$$ 16.0000 0.791149 0.395575 0.918434i $$-0.370545\pi$$
0.395575 + 0.918434i $$0.370545\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −14.0000 −0.689730
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 6.00000 0.294174
$$417$$ 0 0
$$418$$ 6.00000 0.293470
$$419$$ −4.00000 −0.195413 −0.0977064 0.995215i $$-0.531151\pi$$
−0.0977064 + 0.995215i $$0.531151\pi$$
$$420$$ 0 0
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ 8.00000 0.389434
$$423$$ 0 0
$$424$$ 10.0000 0.485643
$$425$$ 20.0000 0.970143
$$426$$ 0 0
$$427$$ 2.00000 0.0967868
$$428$$ −8.00000 −0.386695
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −40.0000 −1.92673 −0.963366 0.268190i $$-0.913575\pi$$
−0.963366 + 0.268190i $$0.913575\pi$$
$$432$$ 0 0
$$433$$ 26.0000 1.24948 0.624740 0.780833i $$-0.285205\pi$$
0.624740 + 0.780833i $$0.285205\pi$$
$$434$$ 2.00000 0.0960031
$$435$$ 0 0
$$436$$ −14.0000 −0.670478
$$437$$ 24.0000 1.14808
$$438$$ 0 0
$$439$$ −20.0000 −0.954548 −0.477274 0.878755i $$-0.658375\pi$$
−0.477274 + 0.878755i $$0.658375\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −24.0000 −1.14156
$$443$$ 4.00000 0.190046 0.0950229 0.995475i $$-0.469708\pi$$
0.0950229 + 0.995475i $$0.469708\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −26.0000 −1.23114
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ 34.0000 1.60456 0.802280 0.596948i $$-0.203620\pi$$
0.802280 + 0.596948i $$0.203620\pi$$
$$450$$ 0 0
$$451$$ 4.00000 0.188353
$$452$$ 2.00000 0.0940721
$$453$$ 0 0
$$454$$ −18.0000 −0.844782
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 10.0000 0.467780 0.233890 0.972263i $$-0.424854\pi$$
0.233890 + 0.972263i $$0.424854\pi$$
$$458$$ 8.00000 0.373815
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.00000 −0.0931493 −0.0465746 0.998915i $$-0.514831\pi$$
−0.0465746 + 0.998915i $$0.514831\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ −22.0000 −1.01913
$$467$$ −28.0000 −1.29569 −0.647843 0.761774i $$-0.724329\pi$$
−0.647843 + 0.761774i $$0.724329\pi$$
$$468$$ 0 0
$$469$$ 4.00000 0.184703
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 8.00000 0.367840
$$474$$ 0 0
$$475$$ −30.0000 −1.37649
$$476$$ 4.00000 0.183340
$$477$$ 0 0
$$478$$ −8.00000 −0.365911
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 60.0000 2.73576
$$482$$ −20.0000 −0.910975
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 20.0000 0.906287 0.453143 0.891438i $$-0.350303\pi$$
0.453143 + 0.891438i $$0.350303\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 0 0
$$493$$ 24.0000 1.08091
$$494$$ 36.0000 1.61972
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ 16.0000 0.717698
$$498$$ 0 0
$$499$$ 36.0000 1.61158 0.805791 0.592200i $$-0.201741\pi$$
0.805791 + 0.592200i $$0.201741\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 4.00000 0.177822
$$507$$ 0 0
$$508$$ −16.0000 −0.709885
$$509$$ 16.0000 0.709188 0.354594 0.935020i $$-0.384619\pi$$
0.354594 + 0.935020i $$0.384619\pi$$
$$510$$ 0 0
$$511$$ −12.0000 −0.530849
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −10.0000 −0.441081
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 6.00000 0.263880
$$518$$ −10.0000 −0.439375
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −2.00000 −0.0876216 −0.0438108 0.999040i $$-0.513950\pi$$
−0.0438108 + 0.999040i $$0.513950\pi$$
$$522$$ 0 0
$$523$$ −6.00000 −0.262362 −0.131181 0.991358i $$-0.541877\pi$$
−0.131181 + 0.991358i $$0.541877\pi$$
$$524$$ 22.0000 0.961074
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 8.00000 0.348485
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −6.00000 −0.260133
$$533$$ 24.0000 1.03956
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −4.00000 −0.172774
$$537$$ 0 0
$$538$$ 24.0000 1.03471
$$539$$ 1.00000 0.0430730
$$540$$ 0 0
$$541$$ 30.0000 1.28980 0.644900 0.764267i $$-0.276899\pi$$
0.644900 + 0.764267i $$0.276899\pi$$
$$542$$ 12.0000 0.515444
$$543$$ 0 0
$$544$$ −4.00000 −0.171499
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ −22.0000 −0.939793
$$549$$ 0 0
$$550$$ −5.00000 −0.213201
$$551$$ −36.0000 −1.53365
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ −6.00000 −0.254916
$$555$$ 0 0
$$556$$ −14.0000 −0.593732
$$557$$ 2.00000 0.0847427 0.0423714 0.999102i $$-0.486509\pi$$
0.0423714 + 0.999102i $$0.486509\pi$$
$$558$$ 0 0
$$559$$ 48.0000 2.03018
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −14.0000 −0.590554
$$563$$ 22.0000 0.927189 0.463595 0.886047i $$-0.346559\pi$$
0.463595 + 0.886047i $$0.346559\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 18.0000 0.756596
$$567$$ 0 0
$$568$$ −16.0000 −0.671345
$$569$$ 42.0000 1.76073 0.880366 0.474295i $$-0.157297\pi$$
0.880366 + 0.474295i $$0.157297\pi$$
$$570$$ 0 0
$$571$$ −28.0000 −1.17176 −0.585882 0.810397i $$-0.699252\pi$$
−0.585882 + 0.810397i $$0.699252\pi$$
$$572$$ 6.00000 0.250873
$$573$$ 0 0
$$574$$ −4.00000 −0.166957
$$575$$ −20.0000 −0.834058
$$576$$ 0 0
$$577$$ −34.0000 −1.41544 −0.707719 0.706494i $$-0.750276\pi$$
−0.707719 + 0.706494i $$0.750276\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −2.00000 −0.0829740
$$582$$ 0 0
$$583$$ 10.0000 0.414158
$$584$$ 12.0000 0.496564
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ −24.0000 −0.990586 −0.495293 0.868726i $$-0.664939\pi$$
−0.495293 + 0.868726i $$0.664939\pi$$
$$588$$ 0 0
$$589$$ −12.0000 −0.494451
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 10.0000 0.410997
$$593$$ −20.0000 −0.821302 −0.410651 0.911793i $$-0.634698\pi$$
−0.410651 + 0.911793i $$0.634698\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ 0 0
$$598$$ 24.0000 0.981433
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −32.0000 −1.30531 −0.652654 0.757656i $$-0.726344\pi$$
−0.652654 + 0.757656i $$0.726344\pi$$
$$602$$ −8.00000 −0.326056
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 24.0000 0.974130 0.487065 0.873366i $$-0.338067\pi$$
0.487065 + 0.873366i $$0.338067\pi$$
$$608$$ 6.00000 0.243332
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 36.0000 1.45640
$$612$$ 0 0
$$613$$ −26.0000 −1.05013 −0.525065 0.851062i $$-0.675959\pi$$
−0.525065 + 0.851062i $$0.675959\pi$$
$$614$$ −30.0000 −1.21070
$$615$$ 0 0
$$616$$ −1.00000 −0.0402911
$$617$$ 30.0000 1.20775 0.603877 0.797077i $$-0.293622\pi$$
0.603877 + 0.797077i $$0.293622\pi$$
$$618$$ 0 0
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 18.0000 0.721734
$$623$$ −6.00000 −0.240385
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 6.00000 0.239808
$$627$$ 0 0
$$628$$ 12.0000 0.478852
$$629$$ −40.0000 −1.59490
$$630$$ 0 0
$$631$$ 4.00000 0.159237 0.0796187 0.996825i $$-0.474630\pi$$
0.0796187 + 0.996825i $$0.474630\pi$$
$$632$$ −16.0000 −0.636446
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.00000 0.237729
$$638$$ −6.00000 −0.237542
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −26.0000 −1.02694 −0.513469 0.858108i $$-0.671640\pi$$
−0.513469 + 0.858108i $$0.671640\pi$$
$$642$$ 0 0
$$643$$ −24.0000 −0.946468 −0.473234 0.880937i $$-0.656913\pi$$
−0.473234 + 0.880937i $$0.656913\pi$$
$$644$$ −4.00000 −0.157622
$$645$$ 0 0
$$646$$ −24.0000 −0.944267
$$647$$ 34.0000 1.33668 0.668339 0.743857i $$-0.267006\pi$$
0.668339 + 0.743857i $$0.267006\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ −30.0000 −1.17670
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 4.00000 0.156174
$$657$$ 0 0
$$658$$ −6.00000 −0.233904
$$659$$ −16.0000 −0.623272 −0.311636 0.950202i $$-0.600877\pi$$
−0.311636 + 0.950202i $$0.600877\pi$$
$$660$$ 0 0
$$661$$ −32.0000 −1.24466 −0.622328 0.782757i $$-0.713813\pi$$
−0.622328 + 0.782757i $$0.713813\pi$$
$$662$$ −4.00000 −0.155464
$$663$$ 0 0
$$664$$ 2.00000 0.0776151
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −24.0000 −0.929284
$$668$$ −12.0000 −0.464294
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −2.00000 −0.0772091
$$672$$ 0 0
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ 22.0000 0.847408
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −30.0000 −1.15299 −0.576497 0.817099i $$-0.695581\pi$$
−0.576497 + 0.817099i $$0.695581\pi$$
$$678$$ 0 0
$$679$$ 6.00000 0.230259
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −2.00000 −0.0765840
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −1.00000 −0.0381802
$$687$$ 0 0
$$688$$ 8.00000 0.304997
$$689$$ 60.0000 2.28582
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ −16.0000 −0.607352
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −16.0000 −0.606043
$$698$$ 26.0000 0.984115
$$699$$ 0 0
$$700$$ 5.00000 0.188982
$$701$$ 46.0000 1.73740 0.868698 0.495342i $$-0.164957\pi$$
0.868698 + 0.495342i $$0.164957\pi$$
$$702$$ 0 0
$$703$$ 60.0000 2.26294
$$704$$ 1.00000 0.0376889
$$705$$ 0 0
$$706$$ 6.00000 0.225813
$$707$$ −14.0000 −0.526524
$$708$$ 0 0
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 6.00000 0.224860
$$713$$ −8.00000 −0.299602
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ −8.00000 −0.298557
$$719$$ 50.0000 1.86469 0.932343 0.361576i $$-0.117761\pi$$
0.932343 + 0.361576i $$0.117761\pi$$
$$720$$ 0 0
$$721$$ 14.0000 0.521387
$$722$$ 17.0000 0.632674
$$723$$ 0 0
$$724$$ 8.00000 0.297318
$$725$$ 30.0000 1.11417
$$726$$ 0 0
$$727$$ 22.0000 0.815935 0.407967 0.912996i $$-0.366238\pi$$
0.407967 + 0.912996i $$0.366238\pi$$
$$728$$ −6.00000 −0.222375
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −32.0000 −1.18356
$$732$$ 0 0
$$733$$ 6.00000 0.221615 0.110808 0.993842i $$-0.464656\pi$$
0.110808 + 0.993842i $$0.464656\pi$$
$$734$$ −2.00000 −0.0738213
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ −4.00000 −0.147342
$$738$$ 0 0
$$739$$ −52.0000 −1.91285 −0.956425 0.291977i $$-0.905687\pi$$
−0.956425 + 0.291977i $$0.905687\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −10.0000 −0.367112
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −10.0000 −0.366126
$$747$$ 0 0
$$748$$ −4.00000 −0.146254
$$749$$ 8.00000 0.292314
$$750$$ 0 0
$$751$$ 28.0000 1.02173 0.510867 0.859660i $$-0.329324\pi$$
0.510867 + 0.859660i $$0.329324\pi$$
$$752$$ 6.00000 0.218797
$$753$$ 0 0
$$754$$ −36.0000 −1.31104
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −14.0000 −0.508839 −0.254419 0.967094i $$-0.581884\pi$$
−0.254419 + 0.967094i $$0.581884\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −8.00000 −0.290000 −0.145000 0.989432i $$-0.546318\pi$$
−0.145000 + 0.989432i $$0.546318\pi$$
$$762$$ 0 0
$$763$$ 14.0000 0.506834
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ 34.0000 1.22847
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 16.0000 0.576975 0.288487 0.957484i $$-0.406848\pi$$
0.288487 + 0.957484i $$0.406848\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −6.00000 −0.215945
$$773$$ −20.0000 −0.719350 −0.359675 0.933078i $$-0.617112\pi$$
−0.359675 + 0.933078i $$0.617112\pi$$
$$774$$ 0 0
$$775$$ 10.0000 0.359211
$$776$$ −6.00000 −0.215387
$$777$$ 0 0
$$778$$ 30.0000 1.07555
$$779$$ 24.0000 0.859889
$$780$$ 0 0
$$781$$ −16.0000 −0.572525
$$782$$ −16.0000 −0.572159
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 22.0000 0.784215 0.392108 0.919919i $$-0.371746\pi$$
0.392108 + 0.919919i $$0.371746\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −2.00000 −0.0711118
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ −4.00000 −0.141955
$$795$$ 0 0
$$796$$ −14.0000 −0.496217
$$797$$ 20.0000 0.708436 0.354218 0.935163i $$-0.384747\pi$$
0.354218 + 0.935163i $$0.384747\pi$$
$$798$$ 0 0
$$799$$ −24.0000 −0.849059
$$800$$ −5.00000 −0.176777
$$801$$ 0 0
$$802$$ −30.0000 −1.05934
$$803$$ 12.0000 0.423471
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −12.0000 −0.422682
$$807$$ 0 0
$$808$$ 14.0000 0.492518
$$809$$ −18.0000 −0.632846 −0.316423 0.948618i $$-0.602482\pi$$
−0.316423 + 0.948618i $$0.602482\pi$$
$$810$$ 0 0
$$811$$ 18.0000 0.632065 0.316033 0.948748i $$-0.397649\pi$$
0.316033 + 0.948748i $$0.397649\pi$$
$$812$$ 6.00000 0.210559
$$813$$ 0 0
$$814$$ 10.0000 0.350500
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 48.0000 1.67931
$$818$$ 16.0000 0.559427
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 38.0000 1.32621 0.663105 0.748527i $$-0.269238\pi$$
0.663105 + 0.748527i $$0.269238\pi$$
$$822$$ 0 0
$$823$$ 28.0000 0.976019 0.488009 0.872838i $$-0.337723\pi$$
0.488009 + 0.872838i $$0.337723\pi$$
$$824$$ −14.0000 −0.487713
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ 0 0
$$829$$ 24.0000 0.833554 0.416777 0.909009i $$-0.363160\pi$$
0.416777 + 0.909009i $$0.363160\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 6.00000 0.208013
$$833$$ −4.00000 −0.138592
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 6.00000 0.207514
$$837$$ 0 0
$$838$$ −4.00000 −0.138178
$$839$$ 42.0000 1.45000 0.725001 0.688748i $$-0.241839\pi$$
0.725001 + 0.688748i $$0.241839\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ −10.0000 −0.344623
$$843$$ 0 0
$$844$$ 8.00000 0.275371
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −1.00000 −0.0343604
$$848$$ 10.0000 0.343401
$$849$$ 0 0
$$850$$ 20.0000 0.685994
$$851$$ 40.0000 1.37118
$$852$$ 0 0
$$853$$ −42.0000 −1.43805 −0.719026 0.694983i $$-0.755412\pi$$
−0.719026 + 0.694983i $$0.755412\pi$$
$$854$$ 2.00000 0.0684386
$$855$$ 0 0
$$856$$ −8.00000 −0.273434
$$857$$ −24.0000 −0.819824 −0.409912 0.912125i $$-0.634441\pi$$
−0.409912 + 0.912125i $$0.634441\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −40.0000 −1.36241
$$863$$ −12.0000 −0.408485 −0.204242 0.978920i $$-0.565473\pi$$
−0.204242 + 0.978920i $$0.565473\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 26.0000 0.883516
$$867$$ 0 0
$$868$$ 2.00000 0.0678844
$$869$$ −16.0000 −0.542763
$$870$$ 0 0
$$871$$ −24.0000 −0.813209
$$872$$ −14.0000 −0.474100
$$873$$ 0 0
$$874$$ 24.0000 0.811812
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 18.0000 0.607817 0.303908 0.952701i $$-0.401708\pi$$
0.303908 + 0.952701i $$0.401708\pi$$
$$878$$ −20.0000 −0.674967
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 50.0000 1.68454 0.842271 0.539054i $$-0.181218\pi$$
0.842271 + 0.539054i $$0.181218\pi$$
$$882$$ 0 0
$$883$$ −28.0000 −0.942275 −0.471138 0.882060i $$-0.656156\pi$$
−0.471138 + 0.882060i $$0.656156\pi$$
$$884$$ −24.0000 −0.807207
$$885$$ 0 0
$$886$$ 4.00000 0.134383
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 0 0
$$889$$ 16.0000 0.536623
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −26.0000 −0.870544
$$893$$ 36.0000 1.20469
$$894$$ 0 0
$$895$$ 0 0
$$896$$ −1.00000 −0.0334077
$$897$$ 0 0
$$898$$ 34.0000 1.13459
$$899$$ 12.0000 0.400222
$$900$$ 0 0
$$901$$ −40.0000 −1.33259
$$902$$ 4.00000 0.133185
$$903$$ 0 0
$$904$$ 2.00000 0.0665190
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 20.0000 0.664089 0.332045 0.943264i $$-0.392262\pi$$
0.332045 + 0.943264i $$0.392262\pi$$
$$908$$ −18.0000 −0.597351
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ 2.00000 0.0661903
$$914$$ 10.0000 0.330771
$$915$$ 0 0
$$916$$ 8.00000 0.264327
$$917$$ −22.0000 −0.726504
$$918$$ 0 0
$$919$$ −8.00000 −0.263896 −0.131948 0.991257i $$-0.542123\pi$$
−0.131948 + 0.991257i $$0.542123\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −2.00000 −0.0658665
$$923$$ −96.0000 −3.15988
$$924$$ 0 0
$$925$$ −50.0000 −1.64399
$$926$$ 16.0000 0.525793
$$927$$ 0 0
$$928$$ −6.00000 −0.196960
$$929$$ −10.0000 −0.328089 −0.164045 0.986453i $$-0.552454\pi$$
−0.164045 + 0.986453i $$0.552454\pi$$
$$930$$ 0 0
$$931$$ 6.00000 0.196642
$$932$$ −22.0000 −0.720634
$$933$$ 0 0
$$934$$ −28.0000 −0.916188
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −12.0000 −0.392023 −0.196011 0.980602i $$-0.562799\pi$$
−0.196011 + 0.980602i $$0.562799\pi$$
$$938$$ 4.00000 0.130605
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 18.0000 0.586783 0.293392 0.955992i $$-0.405216\pi$$
0.293392 + 0.955992i $$0.405216\pi$$
$$942$$ 0 0
$$943$$ 16.0000 0.521032
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 8.00000 0.260102
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ 0 0
$$949$$ 72.0000 2.33722
$$950$$ −30.0000 −0.973329
$$951$$ 0 0
$$952$$ 4.00000 0.129641
$$953$$ −18.0000 −0.583077 −0.291539 0.956559i $$-0.594167\pi$$
−0.291539 + 0.956559i $$0.594167\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −8.00000 −0.258738
$$957$$ 0 0
$$958$$ 24.0000 0.775405
$$959$$ 22.0000 0.710417
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 60.0000 1.93448
$$963$$ 0 0
$$964$$ −20.0000 −0.644157
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 24.0000 0.771788 0.385894 0.922543i $$-0.373893\pi$$
0.385894 + 0.922543i $$0.373893\pi$$
$$968$$ 1.00000 0.0321412
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −20.0000 −0.641831 −0.320915 0.947108i $$-0.603990\pi$$
−0.320915 + 0.947108i $$0.603990\pi$$
$$972$$ 0 0
$$973$$ 14.0000 0.448819
$$974$$ 20.0000 0.640841
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ 46.0000 1.47167 0.735835 0.677161i $$-0.236790\pi$$
0.735835 + 0.677161i $$0.236790\pi$$
$$978$$ 0 0
$$979$$ 6.00000 0.191761
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −12.0000 −0.382935
$$983$$ −10.0000 −0.318950 −0.159475 0.987202i $$-0.550980\pi$$
−0.159475 + 0.987202i $$0.550980\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 24.0000 0.764316
$$987$$ 0 0
$$988$$ 36.0000 1.14531
$$989$$ 32.0000 1.01754
$$990$$ 0 0
$$991$$ 16.0000 0.508257 0.254128 0.967170i $$-0.418211\pi$$
0.254128 + 0.967170i $$0.418211\pi$$
$$992$$ −2.00000 −0.0635001
$$993$$ 0 0
$$994$$ 16.0000 0.507489
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −46.0000 −1.45683 −0.728417 0.685134i $$-0.759744\pi$$
−0.728417 + 0.685134i $$0.759744\pi$$
$$998$$ 36.0000 1.13956
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1386.2.a.j.1.1 1
3.2 odd 2 462.2.a.d.1.1 1
7.6 odd 2 9702.2.a.bp.1.1 1
12.11 even 2 3696.2.a.j.1.1 1
21.20 even 2 3234.2.a.b.1.1 1
33.32 even 2 5082.2.a.ba.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.a.d.1.1 1 3.2 odd 2
1386.2.a.j.1.1 1 1.1 even 1 trivial
3234.2.a.b.1.1 1 21.20 even 2
3696.2.a.j.1.1 1 12.11 even 2
5082.2.a.ba.1.1 1 33.32 even 2
9702.2.a.bp.1.1 1 7.6 odd 2