# Properties

 Label 9025.2.a.g.1.1 Level $9025$ Weight $2$ Character 9025.1 Self dual yes Analytic conductor $72.065$ 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] = [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: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 95) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 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)

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} -2.00000 q^{4} +4.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} -2.00000 q^{4} +4.00000 q^{7} +1.00000 q^{9} +3.00000 q^{11} -4.00000 q^{12} -2.00000 q^{13} +4.00000 q^{16} -6.00000 q^{17} +8.00000 q^{21} -4.00000 q^{27} -8.00000 q^{28} -3.00000 q^{29} -7.00000 q^{31} +6.00000 q^{33} -2.00000 q^{36} -8.00000 q^{37} -4.00000 q^{39} -6.00000 q^{41} +4.00000 q^{43} -6.00000 q^{44} -6.00000 q^{47} +8.00000 q^{48} +9.00000 q^{49} -12.0000 q^{51} +4.00000 q^{52} +6.00000 q^{53} -15.0000 q^{59} +5.00000 q^{61} +4.00000 q^{63} -8.00000 q^{64} -2.00000 q^{67} +12.0000 q^{68} -3.00000 q^{71} -8.00000 q^{73} +12.0000 q^{77} +5.00000 q^{79} -11.0000 q^{81} -12.0000 q^{83} -16.0000 q^{84} -6.00000 q^{87} -15.0000 q^{89} -8.00000 q^{91} -14.0000 q^{93} -8.00000 q^{97} +3.00000 q^{99} +O(q^{100})$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ −2.00000 −1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 4.00000 1.51186 0.755929 0.654654i $$-0.227186\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ −4.00000 −1.15470
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4.00000 1.00000
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ 0 0
$$20$$ 0 0
$$21$$ 8.00000 1.74574
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ −8.00000 −1.51186
$$29$$ −3.00000 −0.557086 −0.278543 0.960424i $$-0.589851\pi$$
−0.278543 + 0.960424i $$0.589851\pi$$
$$30$$ 0 0
$$31$$ −7.00000 −1.25724 −0.628619 0.777714i $$-0.716379\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ 0 0
$$33$$ 6.00000 1.04447
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 0 0
$$39$$ −4.00000 −0.640513
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ −6.00000 −0.904534
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 8.00000 1.15470
$$49$$ 9.00000 1.28571
$$50$$ 0 0
$$51$$ −12.0000 −1.68034
$$52$$ 4.00000 0.554700
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −15.0000 −1.95283 −0.976417 0.215894i $$-0.930733\pi$$
−0.976417 + 0.215894i $$0.930733\pi$$
$$60$$ 0 0
$$61$$ 5.00000 0.640184 0.320092 0.947386i $$-0.396286\pi$$
0.320092 + 0.947386i $$0.396286\pi$$
$$62$$ 0 0
$$63$$ 4.00000 0.503953
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 12.0000 1.45521
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3.00000 −0.356034 −0.178017 0.984027i $$-0.556968\pi$$
−0.178017 + 0.984027i $$0.556968\pi$$
$$72$$ 0 0
$$73$$ −8.00000 −0.936329 −0.468165 0.883641i $$-0.655085\pi$$
−0.468165 + 0.883641i $$0.655085\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 12.0000 1.36753
$$78$$ 0 0
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ −16.0000 −1.74574
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −6.00000 −0.643268
$$88$$ 0 0
$$89$$ −15.0000 −1.59000 −0.794998 0.606612i $$-0.792528\pi$$
−0.794998 + 0.606612i $$0.792528\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ 0 0
$$93$$ −14.0000 −1.45173
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −8.00000 −0.812277 −0.406138 0.913812i $$-0.633125\pi$$
−0.406138 + 0.913812i $$0.633125\pi$$
$$98$$ 0 0
$$99$$ 3.00000 0.301511
$$100$$ 0 0
$$101$$ 15.0000 1.49256 0.746278 0.665635i $$-0.231839\pi$$
0.746278 + 0.665635i $$0.231839\pi$$
$$102$$ 0 0
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 8.00000 0.769800
$$109$$ 11.0000 1.05361 0.526804 0.849987i $$-0.323390\pi$$
0.526804 + 0.849987i $$0.323390\pi$$
$$110$$ 0 0
$$111$$ −16.0000 −1.51865
$$112$$ 16.0000 1.51186
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 6.00000 0.557086
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ −24.0000 −2.20008
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ −12.0000 −1.08200
$$124$$ 14.0000 1.25724
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ 0 0
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ −12.0000 −1.04447
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ 0 0
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ −12.0000 −1.01058
$$142$$ 0 0
$$143$$ −6.00000 −0.501745
$$144$$ 4.00000 0.333333
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 18.0000 1.48461
$$148$$ 16.0000 1.31519
$$149$$ 3.00000 0.245770 0.122885 0.992421i $$-0.460785\pi$$
0.122885 + 0.992421i $$0.460785\pi$$
$$150$$ 0 0
$$151$$ 17.0000 1.38344 0.691720 0.722166i $$-0.256853\pi$$
0.691720 + 0.722166i $$0.256853\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 8.00000 0.640513
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ 0 0
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 10.0000 0.783260 0.391630 0.920123i $$-0.371911\pi$$
0.391630 + 0.920123i $$0.371911\pi$$
$$164$$ 12.0000 0.937043
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −8.00000 −0.609994
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 12.0000 0.904534
$$177$$ −30.0000 −2.25494
$$178$$ 0 0
$$179$$ −9.00000 −0.672692 −0.336346 0.941739i $$-0.609191\pi$$
−0.336346 + 0.941739i $$0.609191\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 10.0000 0.739221
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −18.0000 −1.31629
$$188$$ 12.0000 0.875190
$$189$$ −16.0000 −1.16383
$$190$$ 0 0
$$191$$ −15.0000 −1.08536 −0.542681 0.839939i $$-0.682591\pi$$
−0.542681 + 0.839939i $$0.682591\pi$$
$$192$$ −16.0000 −1.15470
$$193$$ 16.0000 1.15171 0.575853 0.817554i $$-0.304670\pi$$
0.575853 + 0.817554i $$0.304670\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −18.0000 −1.28571
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ −19.0000 −1.34687 −0.673437 0.739244i $$-0.735183\pi$$
−0.673437 + 0.739244i $$0.735183\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 0 0
$$203$$ −12.0000 −0.842235
$$204$$ 24.0000 1.68034
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −8.00000 −0.554700
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −7.00000 −0.481900 −0.240950 0.970538i $$-0.577459\pi$$
−0.240950 + 0.970538i $$0.577459\pi$$
$$212$$ −12.0000 −0.824163
$$213$$ −6.00000 −0.411113
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −28.0000 −1.90076
$$218$$ 0 0
$$219$$ −16.0000 −1.08118
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 24.0000 1.59294 0.796468 0.604681i $$-0.206699\pi$$
0.796468 + 0.604681i $$0.206699\pi$$
$$228$$ 0 0
$$229$$ −7.00000 −0.462573 −0.231287 0.972886i $$-0.574293\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ 0 0
$$231$$ 24.0000 1.57908
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 30.0000 1.95283
$$237$$ 10.0000 0.649570
$$238$$ 0 0
$$239$$ −3.00000 −0.194054 −0.0970269 0.995282i $$-0.530933\pi$$
−0.0970269 + 0.995282i $$0.530933\pi$$
$$240$$ 0 0
$$241$$ 5.00000 0.322078 0.161039 0.986948i $$-0.448515\pi$$
0.161039 + 0.986948i $$0.448515\pi$$
$$242$$ 0 0
$$243$$ −10.0000 −0.641500
$$244$$ −10.0000 −0.640184
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −24.0000 −1.52094
$$250$$ 0 0
$$251$$ −15.0000 −0.946792 −0.473396 0.880850i $$-0.656972\pi$$
−0.473396 + 0.880850i $$0.656972\pi$$
$$252$$ −8.00000 −0.503953
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ −32.0000 −1.98838
$$260$$ 0 0
$$261$$ −3.00000 −0.185695
$$262$$ 0 0
$$263$$ 18.0000 1.10993 0.554964 0.831875i $$-0.312732\pi$$
0.554964 + 0.831875i $$0.312732\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −30.0000 −1.83597
$$268$$ 4.00000 0.244339
$$269$$ −21.0000 −1.28039 −0.640196 0.768211i $$-0.721147\pi$$
−0.640196 + 0.768211i $$0.721147\pi$$
$$270$$ 0 0
$$271$$ 11.0000 0.668202 0.334101 0.942537i $$-0.391567\pi$$
0.334101 + 0.942537i $$0.391567\pi$$
$$272$$ −24.0000 −1.45521
$$273$$ −16.0000 −0.968364
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −8.00000 −0.480673 −0.240337 0.970690i $$-0.577258\pi$$
−0.240337 + 0.970690i $$0.577258\pi$$
$$278$$ 0 0
$$279$$ −7.00000 −0.419079
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ −14.0000 −0.832214 −0.416107 0.909316i $$-0.636606\pi$$
−0.416107 + 0.909316i $$0.636606\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −24.0000 −1.41668
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −16.0000 −0.937937
$$292$$ 16.0000 0.936329
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −12.0000 −0.696311
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 16.0000 0.922225
$$302$$ 0 0
$$303$$ 30.0000 1.72345
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 34.0000 1.94048 0.970241 0.242140i $$-0.0778494\pi$$
0.970241 + 0.242140i $$0.0778494\pi$$
$$308$$ −24.0000 −1.36753
$$309$$ 32.0000 1.82042
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 0 0
$$313$$ 10.0000 0.565233 0.282617 0.959233i $$-0.408798\pi$$
0.282617 + 0.959233i $$0.408798\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ −24.0000 −1.34797 −0.673987 0.738743i $$-0.735420\pi$$
−0.673987 + 0.738743i $$0.735420\pi$$
$$318$$ 0 0
$$319$$ −9.00000 −0.503903
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 22.0000 1.22222
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 22.0000 1.21660
$$328$$ 0 0
$$329$$ −24.0000 −1.32316
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ 24.0000 1.31717
$$333$$ −8.00000 −0.438397
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 32.0000 1.74574
$$337$$ 16.0000 0.871576 0.435788 0.900049i $$-0.356470\pi$$
0.435788 + 0.900049i $$0.356470\pi$$
$$338$$ 0 0
$$339$$ −12.0000 −0.651751
$$340$$ 0 0
$$341$$ −21.0000 −1.13721
$$342$$ 0 0
$$343$$ 8.00000 0.431959
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 12.0000 0.643268
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 8.00000 0.427008
$$352$$ 0 0
$$353$$ −12.0000 −0.638696 −0.319348 0.947638i $$-0.603464\pi$$
−0.319348 + 0.947638i $$0.603464\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 30.0000 1.59000
$$357$$ −48.0000 −2.54043
$$358$$ 0 0
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0 0
$$363$$ −4.00000 −0.209946
$$364$$ 16.0000 0.838628
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4.00000 0.208798 0.104399 0.994535i $$-0.466708\pi$$
0.104399 + 0.994535i $$0.466708\pi$$
$$368$$ 0 0
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ 24.0000 1.24602
$$372$$ 28.0000 1.45173
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 6.00000 0.309016
$$378$$ 0 0
$$379$$ −37.0000 −1.90056 −0.950281 0.311393i $$-0.899204\pi$$
−0.950281 + 0.311393i $$0.899204\pi$$
$$380$$ 0 0
$$381$$ −4.00000 −0.204926
$$382$$ 0 0
$$383$$ −30.0000 −1.53293 −0.766464 0.642287i $$-0.777986\pi$$
−0.766464 + 0.642287i $$0.777986\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.00000 0.203331
$$388$$ 16.0000 0.812277
$$389$$ 15.0000 0.760530 0.380265 0.924878i $$-0.375833\pi$$
0.380265 + 0.924878i $$0.375833\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 24.0000 1.21064
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −6.00000 −0.301511
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −33.0000 −1.64794 −0.823971 0.566632i $$-0.808246\pi$$
−0.823971 + 0.566632i $$0.808246\pi$$
$$402$$ 0 0
$$403$$ 14.0000 0.697390
$$404$$ −30.0000 −1.49256
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −24.0000 −1.18964
$$408$$ 0 0
$$409$$ 23.0000 1.13728 0.568638 0.822588i $$-0.307470\pi$$
0.568638 + 0.822588i $$0.307470\pi$$
$$410$$ 0 0
$$411$$ 24.0000 1.18383
$$412$$ −32.0000 −1.57653
$$413$$ −60.0000 −2.95241
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −32.0000 −1.56705
$$418$$ 0 0
$$419$$ −3.00000 −0.146560 −0.0732798 0.997311i $$-0.523347\pi$$
−0.0732798 + 0.997311i $$0.523347\pi$$
$$420$$ 0 0
$$421$$ −19.0000 −0.926003 −0.463002 0.886357i $$-0.653228\pi$$
−0.463002 + 0.886357i $$0.653228\pi$$
$$422$$ 0 0
$$423$$ −6.00000 −0.291730
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 20.0000 0.967868
$$428$$ 0 0
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ −15.0000 −0.722525 −0.361262 0.932464i $$-0.617654\pi$$
−0.361262 + 0.932464i $$0.617654\pi$$
$$432$$ −16.0000 −0.769800
$$433$$ −8.00000 −0.384455 −0.192228 0.981350i $$-0.561571\pi$$
−0.192228 + 0.981350i $$0.561571\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −22.0000 −1.05361
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −13.0000 −0.620456 −0.310228 0.950662i $$-0.600405\pi$$
−0.310228 + 0.950662i $$0.600405\pi$$
$$440$$ 0 0
$$441$$ 9.00000 0.428571
$$442$$ 0 0
$$443$$ 12.0000 0.570137 0.285069 0.958507i $$-0.407984\pi$$
0.285069 + 0.958507i $$0.407984\pi$$
$$444$$ 32.0000 1.51865
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 6.00000 0.283790
$$448$$ −32.0000 −1.51186
$$449$$ −9.00000 −0.424736 −0.212368 0.977190i $$-0.568118\pi$$
−0.212368 + 0.977190i $$0.568118\pi$$
$$450$$ 0 0
$$451$$ −18.0000 −0.847587
$$452$$ 12.0000 0.564433
$$453$$ 34.0000 1.59746
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 0 0
$$459$$ 24.0000 1.12022
$$460$$ 0 0
$$461$$ −9.00000 −0.419172 −0.209586 0.977790i $$-0.567212\pi$$
−0.209586 + 0.977790i $$0.567212\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −12.0000 −0.557086
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 4.00000 0.184900
$$469$$ −8.00000 −0.369406
$$470$$ 0 0
$$471$$ −4.00000 −0.184310
$$472$$ 0 0
$$473$$ 12.0000 0.551761
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 48.0000 2.20008
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ 15.0000 0.685367 0.342684 0.939451i $$-0.388664\pi$$
0.342684 + 0.939451i $$0.388664\pi$$
$$480$$ 0 0
$$481$$ 16.0000 0.729537
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 4.00000 0.181818
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 0 0
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ −15.0000 −0.676941 −0.338470 0.940977i $$-0.609909\pi$$
−0.338470 + 0.940977i $$0.609909\pi$$
$$492$$ 24.0000 1.08200
$$493$$ 18.0000 0.810679
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −28.0000 −1.25724
$$497$$ −12.0000 −0.538274
$$498$$ 0 0
$$499$$ 20.0000 0.895323 0.447661 0.894203i $$-0.352257\pi$$
0.447661 + 0.894203i $$0.352257\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 42.0000 1.87269 0.936344 0.351085i $$-0.114187\pi$$
0.936344 + 0.351085i $$0.114187\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −18.0000 −0.799408
$$508$$ 4.00000 0.177471
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ −32.0000 −1.41560
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −16.0000 −0.704361
$$517$$ −18.0000 −0.791639
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −45.0000 −1.97149 −0.985743 0.168259i $$-0.946186\pi$$
−0.985743 + 0.168259i $$0.946186\pi$$
$$522$$ 0 0
$$523$$ −26.0000 −1.13690 −0.568450 0.822718i $$-0.692457\pi$$
−0.568450 + 0.822718i $$0.692457\pi$$
$$524$$ −24.0000 −1.04844
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 42.0000 1.82955
$$528$$ 24.0000 1.04447
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ −15.0000 −0.650945
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −18.0000 −0.776757
$$538$$ 0 0
$$539$$ 27.0000 1.16297
$$540$$ 0 0
$$541$$ −37.0000 −1.59075 −0.795377 0.606115i $$-0.792727\pi$$
−0.795377 + 0.606115i $$0.792727\pi$$
$$542$$ 0 0
$$543$$ 4.00000 0.171656
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ −24.0000 −1.02523
$$549$$ 5.00000 0.213395
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 20.0000 0.850487
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 32.0000 1.35710
$$557$$ −12.0000 −0.508456 −0.254228 0.967144i $$-0.581821\pi$$
−0.254228 + 0.967144i $$0.581821\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ −36.0000 −1.51992
$$562$$ 0 0
$$563$$ −6.00000 −0.252870 −0.126435 0.991975i $$-0.540353\pi$$
−0.126435 + 0.991975i $$0.540353\pi$$
$$564$$ 24.0000 1.01058
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −44.0000 −1.84783
$$568$$ 0 0
$$569$$ 39.0000 1.63497 0.817483 0.575953i $$-0.195369\pi$$
0.817483 + 0.575953i $$0.195369\pi$$
$$570$$ 0 0
$$571$$ −7.00000 −0.292941 −0.146470 0.989215i $$-0.546791\pi$$
−0.146470 + 0.989215i $$0.546791\pi$$
$$572$$ 12.0000 0.501745
$$573$$ −30.0000 −1.25327
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −8.00000 −0.333333
$$577$$ 16.0000 0.666089 0.333044 0.942911i $$-0.391924\pi$$
0.333044 + 0.942911i $$0.391924\pi$$
$$578$$ 0 0
$$579$$ 32.0000 1.32987
$$580$$ 0 0
$$581$$ −48.0000 −1.99138
$$582$$ 0 0
$$583$$ 18.0000 0.745484
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 36.0000 1.48588 0.742940 0.669359i $$-0.233431\pi$$
0.742940 + 0.669359i $$0.233431\pi$$
$$588$$ −36.0000 −1.48461
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 36.0000 1.48084
$$592$$ −32.0000 −1.31519
$$593$$ −12.0000 −0.492781 −0.246390 0.969171i $$-0.579245\pi$$
−0.246390 + 0.969171i $$0.579245\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −38.0000 −1.55524
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −31.0000 −1.26452 −0.632258 0.774758i $$-0.717872\pi$$
−0.632258 + 0.774758i $$0.717872\pi$$
$$602$$ 0 0
$$603$$ −2.00000 −0.0814463
$$604$$ −34.0000 −1.38344
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −2.00000 −0.0811775 −0.0405887 0.999176i $$-0.512923\pi$$
−0.0405887 + 0.999176i $$0.512923\pi$$
$$608$$ 0 0
$$609$$ −24.0000 −0.972529
$$610$$ 0 0
$$611$$ 12.0000 0.485468
$$612$$ 12.0000 0.485071
$$613$$ −2.00000 −0.0807792 −0.0403896 0.999184i $$-0.512860\pi$$
−0.0403896 + 0.999184i $$0.512860\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −36.0000 −1.44931 −0.724653 0.689114i $$-0.758000\pi$$
−0.724653 + 0.689114i $$0.758000\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −60.0000 −2.40385
$$624$$ −16.0000 −0.640513
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 4.00000 0.159617
$$629$$ 48.0000 1.91389
$$630$$ 0 0
$$631$$ −19.0000 −0.756378 −0.378189 0.925728i $$-0.623453\pi$$
−0.378189 + 0.925728i $$0.623453\pi$$
$$632$$ 0 0
$$633$$ −14.0000 −0.556450
$$634$$ 0 0
$$635$$ 0 0
$$636$$ −24.0000 −0.951662
$$637$$ −18.0000 −0.713186
$$638$$ 0 0
$$639$$ −3.00000 −0.118678
$$640$$ 0 0
$$641$$ 9.00000 0.355479 0.177739 0.984078i $$-0.443122\pi$$
0.177739 + 0.984078i $$0.443122\pi$$
$$642$$ 0 0
$$643$$ 34.0000 1.34083 0.670415 0.741987i $$-0.266116\pi$$
0.670415 + 0.741987i $$0.266116\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 0 0
$$649$$ −45.0000 −1.76640
$$650$$ 0 0
$$651$$ −56.0000 −2.19481
$$652$$ −20.0000 −0.783260
$$653$$ −24.0000 −0.939193 −0.469596 0.882881i $$-0.655601\pi$$
−0.469596 + 0.882881i $$0.655601\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −24.0000 −0.937043
$$657$$ −8.00000 −0.312110
$$658$$ 0 0
$$659$$ −12.0000 −0.467454 −0.233727 0.972302i $$-0.575092\pi$$
−0.233727 + 0.972302i $$0.575092\pi$$
$$660$$ 0 0
$$661$$ 5.00000 0.194477 0.0972387 0.995261i $$-0.468999\pi$$
0.0972387 + 0.995261i $$0.468999\pi$$
$$662$$ 0 0
$$663$$ 24.0000 0.932083
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 8.00000 0.309298
$$670$$ 0 0
$$671$$ 15.0000 0.579069
$$672$$ 0 0
$$673$$ 4.00000 0.154189 0.0770943 0.997024i $$-0.475436\pi$$
0.0770943 + 0.997024i $$0.475436\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 18.0000 0.692308
$$677$$ −48.0000 −1.84479 −0.922395 0.386248i $$-0.873771\pi$$
−0.922395 + 0.386248i $$0.873771\pi$$
$$678$$ 0 0
$$679$$ −32.0000 −1.22805
$$680$$ 0 0
$$681$$ 48.0000 1.83936
$$682$$ 0 0
$$683$$ 18.0000 0.688751 0.344375 0.938832i $$-0.388091\pi$$
0.344375 + 0.938832i $$0.388091\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −14.0000 −0.534133
$$688$$ 16.0000 0.609994
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ −37.0000 −1.40755 −0.703773 0.710425i $$-0.748503\pi$$
−0.703773 + 0.710425i $$0.748503\pi$$
$$692$$ 0 0
$$693$$ 12.0000 0.455842
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 36.0000 1.36360
$$698$$ 0 0
$$699$$ −12.0000 −0.453882
$$700$$ 0 0
$$701$$ 6.00000 0.226617 0.113308 0.993560i $$-0.463855\pi$$
0.113308 + 0.993560i $$0.463855\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −24.0000 −0.904534
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 60.0000 2.25653
$$708$$ 60.0000 2.25494
$$709$$ −31.0000 −1.16423 −0.582115 0.813107i $$-0.697775\pi$$
−0.582115 + 0.813107i $$0.697775\pi$$
$$710$$ 0 0
$$711$$ 5.00000 0.187515
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 18.0000 0.672692
$$717$$ −6.00000 −0.224074
$$718$$ 0 0
$$719$$ 15.0000 0.559406 0.279703 0.960087i $$-0.409764\pi$$
0.279703 + 0.960087i $$0.409764\pi$$
$$720$$ 0 0
$$721$$ 64.0000 2.38348
$$722$$ 0 0
$$723$$ 10.0000 0.371904
$$724$$ −4.00000 −0.148659
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −14.0000 −0.519231 −0.259616 0.965712i $$-0.583596\pi$$
−0.259616 + 0.965712i $$0.583596\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −24.0000 −0.887672
$$732$$ −20.0000 −0.739221
$$733$$ −32.0000 −1.18195 −0.590973 0.806691i $$-0.701256\pi$$
−0.590973 + 0.806691i $$0.701256\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −6.00000 −0.221013
$$738$$ 0 0
$$739$$ 35.0000 1.28750 0.643748 0.765238i $$-0.277379\pi$$
0.643748 + 0.765238i $$0.277379\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −12.0000 −0.439057
$$748$$ 36.0000 1.31629
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −7.00000 −0.255434 −0.127717 0.991811i $$-0.540765\pi$$
−0.127717 + 0.991811i $$0.540765\pi$$
$$752$$ −24.0000 −0.875190
$$753$$ −30.0000 −1.09326
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 32.0000 1.16383
$$757$$ 10.0000 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 0 0
$$763$$ 44.0000 1.59291
$$764$$ 30.0000 1.08536
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 30.0000 1.08324
$$768$$ 32.0000 1.15470
$$769$$ 29.0000 1.04577 0.522883 0.852404i $$-0.324856\pi$$
0.522883 + 0.852404i $$0.324856\pi$$
$$770$$ 0 0
$$771$$ 36.0000 1.29651
$$772$$ −32.0000 −1.15171
$$773$$ −30.0000 −1.07903 −0.539513 0.841978i $$-0.681391\pi$$
−0.539513 + 0.841978i $$0.681391\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −64.0000 −2.29599
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −9.00000 −0.322045
$$782$$ 0 0
$$783$$ 12.0000 0.428845
$$784$$ 36.0000 1.28571
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 34.0000 1.21197 0.605985 0.795476i $$-0.292779\pi$$
0.605985 + 0.795476i $$0.292779\pi$$
$$788$$ −36.0000 −1.28245
$$789$$ 36.0000 1.28163
$$790$$ 0 0
$$791$$ −24.0000 −0.853342
$$792$$ 0 0
$$793$$ −10.0000 −0.355110
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 38.0000 1.34687
$$797$$ 30.0000 1.06265 0.531327 0.847167i $$-0.321693\pi$$
0.531327 + 0.847167i $$0.321693\pi$$
$$798$$ 0 0
$$799$$ 36.0000 1.27359
$$800$$ 0 0
$$801$$ −15.0000 −0.529999
$$802$$ 0 0
$$803$$ −24.0000 −0.846942
$$804$$ 8.00000 0.282138
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −42.0000 −1.47847
$$808$$ 0 0
$$809$$ −27.0000 −0.949269 −0.474635 0.880183i $$-0.657420\pi$$
−0.474635 + 0.880183i $$0.657420\pi$$
$$810$$ 0 0
$$811$$ −43.0000 −1.50993 −0.754967 0.655763i $$-0.772347\pi$$
−0.754967 + 0.655763i $$0.772347\pi$$
$$812$$ 24.0000 0.842235
$$813$$ 22.0000 0.771574
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −48.0000 −1.68034
$$817$$ 0 0
$$818$$ 0 0
$$819$$ −8.00000 −0.279543
$$820$$ 0 0
$$821$$ −3.00000 −0.104701 −0.0523504 0.998629i $$-0.516671\pi$$
−0.0523504 + 0.998629i $$0.516671\pi$$
$$822$$ 0 0
$$823$$ 22.0000 0.766872 0.383436 0.923567i $$-0.374741\pi$$
0.383436 + 0.923567i $$0.374741\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 42.0000 1.46048 0.730242 0.683189i $$-0.239408\pi$$
0.730242 + 0.683189i $$0.239408\pi$$
$$828$$ 0 0
$$829$$ 26.0000 0.903017 0.451509 0.892267i $$-0.350886\pi$$
0.451509 + 0.892267i $$0.350886\pi$$
$$830$$ 0 0
$$831$$ −16.0000 −0.555034
$$832$$ 16.0000 0.554700
$$833$$ −54.0000 −1.87099
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 28.0000 0.967822
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ 0 0
$$843$$ 12.0000 0.413302
$$844$$ 14.0000 0.481900
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −8.00000 −0.274883
$$848$$ 24.0000 0.824163
$$849$$ −28.0000 −0.960958
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 12.0000 0.411113
$$853$$ −14.0000 −0.479351 −0.239675 0.970853i $$-0.577041\pi$$
−0.239675 + 0.970853i $$0.577041\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −36.0000 −1.22974 −0.614868 0.788630i $$-0.710791\pi$$
−0.614868 + 0.788630i $$0.710791\pi$$
$$858$$ 0 0
$$859$$ −7.00000 −0.238837 −0.119418 0.992844i $$-0.538103\pi$$
−0.119418 + 0.992844i $$0.538103\pi$$
$$860$$ 0 0
$$861$$ −48.0000 −1.63584
$$862$$ 0 0
$$863$$ −18.0000 −0.612727 −0.306364 0.951915i $$-0.599112\pi$$
−0.306364 + 0.951915i $$0.599112\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 38.0000 1.29055
$$868$$ 56.0000 1.90076
$$869$$ 15.0000 0.508840
$$870$$ 0 0
$$871$$ 4.00000 0.135535
$$872$$ 0 0
$$873$$ −8.00000 −0.270759
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 32.0000 1.08118
$$877$$ 52.0000 1.75592 0.877958 0.478738i $$-0.158906\pi$$
0.877958 + 0.478738i $$0.158906\pi$$
$$878$$ 0 0
$$879$$ −48.0000 −1.61900
$$880$$ 0 0
$$881$$ 9.00000 0.303218 0.151609 0.988441i $$-0.451555\pi$$
0.151609 + 0.988441i $$0.451555\pi$$
$$882$$ 0 0
$$883$$ −8.00000 −0.269221 −0.134611 0.990899i $$-0.542978\pi$$
−0.134611 + 0.990899i $$0.542978\pi$$
$$884$$ −24.0000 −0.807207
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −36.0000 −1.20876 −0.604381 0.796696i $$-0.706579\pi$$
−0.604381 + 0.796696i $$0.706579\pi$$
$$888$$ 0 0
$$889$$ −8.00000 −0.268311
$$890$$ 0 0
$$891$$ −33.0000 −1.10554
$$892$$ −8.00000 −0.267860
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 21.0000 0.700389
$$900$$ 0 0
$$901$$ −36.0000 −1.19933
$$902$$ 0 0
$$903$$ 32.0000 1.06489
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −8.00000 −0.265636 −0.132818 0.991140i $$-0.542403\pi$$
−0.132818 + 0.991140i $$0.542403\pi$$
$$908$$ −48.0000 −1.59294
$$909$$ 15.0000 0.497519
$$910$$ 0 0
$$911$$ 21.0000 0.695761 0.347881 0.937539i $$-0.386901\pi$$
0.347881 + 0.937539i $$0.386901\pi$$
$$912$$ 0 0
$$913$$ −36.0000 −1.19143
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 14.0000 0.462573
$$917$$ 48.0000 1.58510
$$918$$ 0 0
$$919$$ 8.00000 0.263896 0.131948 0.991257i $$-0.457877\pi$$
0.131948 + 0.991257i $$0.457877\pi$$
$$920$$ 0 0
$$921$$ 68.0000 2.24068
$$922$$ 0 0
$$923$$ 6.00000 0.197492
$$924$$ −48.0000 −1.57908
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 16.0000 0.525509
$$928$$ 0 0
$$929$$ 27.0000 0.885841 0.442921 0.896561i $$-0.353942\pi$$
0.442921 + 0.896561i $$0.353942\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 12.0000 0.393073
$$933$$ 48.0000 1.57145
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 46.0000 1.50275 0.751377 0.659873i $$-0.229390\pi$$
0.751377 + 0.659873i $$0.229390\pi$$
$$938$$ 0 0
$$939$$ 20.0000 0.652675
$$940$$ 0 0
$$941$$ −9.00000 −0.293392 −0.146696 0.989182i $$-0.546864\pi$$
−0.146696 + 0.989182i $$0.546864\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −60.0000 −1.95283
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 18.0000 0.584921 0.292461 0.956278i $$-0.405526\pi$$
0.292461 + 0.956278i $$0.405526\pi$$
$$948$$ −20.0000 −0.649570
$$949$$ 16.0000 0.519382
$$950$$ 0 0
$$951$$ −48.0000 −1.55651
$$952$$ 0 0
$$953$$ 12.0000 0.388718 0.194359 0.980930i $$-0.437737\pi$$
0.194359 + 0.980930i $$0.437737\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 6.00000 0.194054
$$957$$ −18.0000 −0.581857
$$958$$ 0 0
$$959$$ 48.0000 1.55000
$$960$$ 0 0
$$961$$ 18.0000 0.580645
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −10.0000 −0.322078
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 16.0000 0.514525 0.257263 0.966342i $$-0.417179\pi$$
0.257263 + 0.966342i $$0.417179\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 20.0000 0.641500
$$973$$ −64.0000 −2.05175
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 20.0000 0.640184
$$977$$ 12.0000 0.383914 0.191957 0.981403i $$-0.438517\pi$$
0.191957 + 0.981403i $$0.438517\pi$$
$$978$$ 0 0
$$979$$ −45.0000 −1.43821
$$980$$ 0 0
$$981$$ 11.0000 0.351203
$$982$$ 0 0
$$983$$ 36.0000 1.14822 0.574111 0.818778i $$-0.305348\pi$$
0.574111 + 0.818778i $$0.305348\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −48.0000 −1.52786
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 8.00000 0.254128 0.127064 0.991894i $$-0.459445\pi$$
0.127064 + 0.991894i $$0.459445\pi$$
$$992$$ 0 0
$$993$$ −8.00000 −0.253872
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 48.0000 1.52094
$$997$$ 22.0000 0.696747 0.348373 0.937356i $$-0.386734\pi$$
0.348373 + 0.937356i $$0.386734\pi$$
$$998$$ 0 0
$$999$$ 32.0000 1.01244
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.g.1.1 1
5.4 even 2 1805.2.a.a.1.1 1
19.7 even 3 475.2.e.b.201.1 2
19.11 even 3 475.2.e.b.26.1 2
19.18 odd 2 9025.2.a.e.1.1 1
95.7 odd 12 475.2.j.a.49.2 4
95.49 even 6 95.2.e.a.26.1 yes 2
95.64 even 6 95.2.e.a.11.1 2
95.68 odd 12 475.2.j.a.349.2 4
95.83 odd 12 475.2.j.a.49.1 4
95.87 odd 12 475.2.j.a.349.1 4
95.94 odd 2 1805.2.a.b.1.1 1
285.239 odd 6 855.2.k.b.406.1 2
285.254 odd 6 855.2.k.b.676.1 2
380.159 odd 6 1520.2.q.c.961.1 2
380.239 odd 6 1520.2.q.c.881.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.e.a.11.1 2 95.64 even 6
95.2.e.a.26.1 yes 2 95.49 even 6
475.2.e.b.26.1 2 19.11 even 3
475.2.e.b.201.1 2 19.7 even 3
475.2.j.a.49.1 4 95.83 odd 12
475.2.j.a.49.2 4 95.7 odd 12
475.2.j.a.349.1 4 95.87 odd 12
475.2.j.a.349.2 4 95.68 odd 12
855.2.k.b.406.1 2 285.239 odd 6
855.2.k.b.676.1 2 285.254 odd 6
1520.2.q.c.881.1 2 380.239 odd 6
1520.2.q.c.961.1 2 380.159 odd 6
1805.2.a.a.1.1 1 5.4 even 2
1805.2.a.b.1.1 1 95.94 odd 2
9025.2.a.e.1.1 1 19.18 odd 2
9025.2.a.g.1.1 1 1.1 even 1 trivial