Properties

 Label 666.2.a.j.1.2 Level $666$ Weight $2$ Character 666.1 Self dual yes Analytic conductor $5.318$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(1,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, 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("666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 666.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: $$5.31803677462$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{13})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 3$$ x^2 - x - 3 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 74) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.2 Root $$2.30278$$ of defining polynomial Character $$\chi$$ $$=$$ 666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +2.30278 q^{5} -2.60555 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +2.30278 q^{5} -2.60555 q^{7} +1.00000 q^{8} +2.30278 q^{10} +2.30278 q^{11} +1.30278 q^{13} -2.60555 q^{14} +1.00000 q^{16} +6.00000 q^{17} +2.00000 q^{19} +2.30278 q^{20} +2.30278 q^{22} -3.90833 q^{23} +0.302776 q^{25} +1.30278 q^{26} -2.60555 q^{28} +3.90833 q^{29} -0.302776 q^{31} +1.00000 q^{32} +6.00000 q^{34} -6.00000 q^{35} +1.00000 q^{37} +2.00000 q^{38} +2.30278 q^{40} -9.90833 q^{41} +0.605551 q^{43} +2.30278 q^{44} -3.90833 q^{46} -4.60555 q^{47} -0.211103 q^{49} +0.302776 q^{50} +1.30278 q^{52} +6.00000 q^{53} +5.30278 q^{55} -2.60555 q^{56} +3.90833 q^{58} -10.6056 q^{59} +7.51388 q^{61} -0.302776 q^{62} +1.00000 q^{64} +3.00000 q^{65} -3.51388 q^{67} +6.00000 q^{68} -6.00000 q^{70} -6.00000 q^{71} -12.3028 q^{73} +1.00000 q^{74} +2.00000 q^{76} -6.00000 q^{77} +9.11943 q^{79} +2.30278 q^{80} -9.90833 q^{82} -2.78890 q^{83} +13.8167 q^{85} +0.605551 q^{86} +2.30278 q^{88} +9.21110 q^{89} -3.39445 q^{91} -3.90833 q^{92} -4.60555 q^{94} +4.60555 q^{95} -16.4222 q^{97} -0.211103 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 2 q^{4} + q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 + 2 * q^4 + q^5 + 2 * q^7 + 2 * q^8 $$2 q + 2 q^{2} + 2 q^{4} + q^{5} + 2 q^{7} + 2 q^{8} + q^{10} + q^{11} - q^{13} + 2 q^{14} + 2 q^{16} + 12 q^{17} + 4 q^{19} + q^{20} + q^{22} + 3 q^{23} - 3 q^{25} - q^{26} + 2 q^{28} - 3 q^{29} + 3 q^{31} + 2 q^{32} + 12 q^{34} - 12 q^{35} + 2 q^{37} + 4 q^{38} + q^{40} - 9 q^{41} - 6 q^{43} + q^{44} + 3 q^{46} - 2 q^{47} + 14 q^{49} - 3 q^{50} - q^{52} + 12 q^{53} + 7 q^{55} + 2 q^{56} - 3 q^{58} - 14 q^{59} - 3 q^{61} + 3 q^{62} + 2 q^{64} + 6 q^{65} + 11 q^{67} + 12 q^{68} - 12 q^{70} - 12 q^{71} - 21 q^{73} + 2 q^{74} + 4 q^{76} - 12 q^{77} - 7 q^{79} + q^{80} - 9 q^{82} - 20 q^{83} + 6 q^{85} - 6 q^{86} + q^{88} + 4 q^{89} - 14 q^{91} + 3 q^{92} - 2 q^{94} + 2 q^{95} - 4 q^{97} + 14 q^{98}+O(q^{100})$$ 2 * q + 2 * q^2 + 2 * q^4 + q^5 + 2 * q^7 + 2 * q^8 + q^10 + q^11 - q^13 + 2 * q^14 + 2 * q^16 + 12 * q^17 + 4 * q^19 + q^20 + q^22 + 3 * q^23 - 3 * q^25 - q^26 + 2 * q^28 - 3 * q^29 + 3 * q^31 + 2 * q^32 + 12 * q^34 - 12 * q^35 + 2 * q^37 + 4 * q^38 + q^40 - 9 * q^41 - 6 * q^43 + q^44 + 3 * q^46 - 2 * q^47 + 14 * q^49 - 3 * q^50 - q^52 + 12 * q^53 + 7 * q^55 + 2 * q^56 - 3 * q^58 - 14 * q^59 - 3 * q^61 + 3 * q^62 + 2 * q^64 + 6 * q^65 + 11 * q^67 + 12 * q^68 - 12 * q^70 - 12 * q^71 - 21 * q^73 + 2 * q^74 + 4 * q^76 - 12 * q^77 - 7 * q^79 + q^80 - 9 * q^82 - 20 * q^83 + 6 * q^85 - 6 * q^86 + q^88 + 4 * q^89 - 14 * q^91 + 3 * q^92 - 2 * q^94 + 2 * q^95 - 4 * q^97 + 14 * q^98

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
$$5$$ 2.30278 1.02983 0.514916 0.857240i $$-0.327823\pi$$
0.514916 + 0.857240i $$0.327823\pi$$
$$6$$ 0 0
$$7$$ −2.60555 −0.984806 −0.492403 0.870367i $$-0.663881\pi$$
−0.492403 + 0.870367i $$0.663881\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 2.30278 0.728202
$$11$$ 2.30278 0.694313 0.347156 0.937807i $$-0.387147\pi$$
0.347156 + 0.937807i $$0.387147\pi$$
$$12$$ 0 0
$$13$$ 1.30278 0.361325 0.180662 0.983545i $$-0.442176\pi$$
0.180662 + 0.983545i $$0.442176\pi$$
$$14$$ −2.60555 −0.696363
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 2.30278 0.514916
$$21$$ 0 0
$$22$$ 2.30278 0.490953
$$23$$ −3.90833 −0.814942 −0.407471 0.913218i $$-0.633589\pi$$
−0.407471 + 0.913218i $$0.633589\pi$$
$$24$$ 0 0
$$25$$ 0.302776 0.0605551
$$26$$ 1.30278 0.255495
$$27$$ 0 0
$$28$$ −2.60555 −0.492403
$$29$$ 3.90833 0.725758 0.362879 0.931836i $$-0.381794\pi$$
0.362879 + 0.931836i $$0.381794\pi$$
$$30$$ 0 0
$$31$$ −0.302776 −0.0543801 −0.0271901 0.999630i $$-0.508656\pi$$
−0.0271901 + 0.999630i $$0.508656\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ −6.00000 −1.01419
$$36$$ 0 0
$$37$$ 1.00000 0.164399
$$38$$ 2.00000 0.324443
$$39$$ 0 0
$$40$$ 2.30278 0.364101
$$41$$ −9.90833 −1.54742 −0.773710 0.633540i $$-0.781601\pi$$
−0.773710 + 0.633540i $$0.781601\pi$$
$$42$$ 0 0
$$43$$ 0.605551 0.0923457 0.0461729 0.998933i $$-0.485297\pi$$
0.0461729 + 0.998933i $$0.485297\pi$$
$$44$$ 2.30278 0.347156
$$45$$ 0 0
$$46$$ −3.90833 −0.576251
$$47$$ −4.60555 −0.671789 −0.335894 0.941900i $$-0.609039\pi$$
−0.335894 + 0.941900i $$0.609039\pi$$
$$48$$ 0 0
$$49$$ −0.211103 −0.0301575
$$50$$ 0.302776 0.0428189
$$51$$ 0 0
$$52$$ 1.30278 0.180662
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 5.30278 0.715026
$$56$$ −2.60555 −0.348181
$$57$$ 0 0
$$58$$ 3.90833 0.513188
$$59$$ −10.6056 −1.38073 −0.690363 0.723464i $$-0.742549\pi$$
−0.690363 + 0.723464i $$0.742549\pi$$
$$60$$ 0 0
$$61$$ 7.51388 0.962054 0.481027 0.876706i $$-0.340264\pi$$
0.481027 + 0.876706i $$0.340264\pi$$
$$62$$ −0.302776 −0.0384525
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 3.00000 0.372104
$$66$$ 0 0
$$67$$ −3.51388 −0.429289 −0.214644 0.976692i $$-0.568859\pi$$
−0.214644 + 0.976692i $$0.568859\pi$$
$$68$$ 6.00000 0.727607
$$69$$ 0 0
$$70$$ −6.00000 −0.717137
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0 0
$$73$$ −12.3028 −1.43993 −0.719965 0.694010i $$-0.755842\pi$$
−0.719965 + 0.694010i $$0.755842\pi$$
$$74$$ 1.00000 0.116248
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ −6.00000 −0.683763
$$78$$ 0 0
$$79$$ 9.11943 1.02602 0.513008 0.858384i $$-0.328531\pi$$
0.513008 + 0.858384i $$0.328531\pi$$
$$80$$ 2.30278 0.257458
$$81$$ 0 0
$$82$$ −9.90833 −1.09419
$$83$$ −2.78890 −0.306121 −0.153061 0.988217i $$-0.548913\pi$$
−0.153061 + 0.988217i $$0.548913\pi$$
$$84$$ 0 0
$$85$$ 13.8167 1.49863
$$86$$ 0.605551 0.0652983
$$87$$ 0 0
$$88$$ 2.30278 0.245477
$$89$$ 9.21110 0.976375 0.488187 0.872739i $$-0.337658\pi$$
0.488187 + 0.872739i $$0.337658\pi$$
$$90$$ 0 0
$$91$$ −3.39445 −0.355835
$$92$$ −3.90833 −0.407471
$$93$$ 0 0
$$94$$ −4.60555 −0.475026
$$95$$ 4.60555 0.472520
$$96$$ 0 0
$$97$$ −16.4222 −1.66742 −0.833711 0.552201i $$-0.813788\pi$$
−0.833711 + 0.552201i $$0.813788\pi$$
$$98$$ −0.211103 −0.0213246
$$99$$ 0 0
$$100$$ 0.302776 0.0302776
$$101$$ 12.4222 1.23606 0.618028 0.786156i $$-0.287932\pi$$
0.618028 + 0.786156i $$0.287932\pi$$
$$102$$ 0 0
$$103$$ −0.302776 −0.0298334 −0.0149167 0.999889i $$-0.504748\pi$$
−0.0149167 + 0.999889i $$0.504748\pi$$
$$104$$ 1.30278 0.127748
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −0.697224 −0.0674032 −0.0337016 0.999432i $$-0.510730\pi$$
−0.0337016 + 0.999432i $$0.510730\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 5.30278 0.505600
$$111$$ 0 0
$$112$$ −2.60555 −0.246201
$$113$$ 3.21110 0.302075 0.151038 0.988528i $$-0.451739\pi$$
0.151038 + 0.988528i $$0.451739\pi$$
$$114$$ 0 0
$$115$$ −9.00000 −0.839254
$$116$$ 3.90833 0.362879
$$117$$ 0 0
$$118$$ −10.6056 −0.976320
$$119$$ −15.6333 −1.43310
$$120$$ 0 0
$$121$$ −5.69722 −0.517929
$$122$$ 7.51388 0.680275
$$123$$ 0 0
$$124$$ −0.302776 −0.0271901
$$125$$ −10.8167 −0.967471
$$126$$ 0 0
$$127$$ −19.2111 −1.70471 −0.852355 0.522964i $$-0.824826\pi$$
−0.852355 + 0.522964i $$0.824826\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 3.00000 0.263117
$$131$$ −10.6056 −0.926611 −0.463306 0.886199i $$-0.653337\pi$$
−0.463306 + 0.886199i $$0.653337\pi$$
$$132$$ 0 0
$$133$$ −5.21110 −0.451860
$$134$$ −3.51388 −0.303553
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ −0.908327 −0.0776036 −0.0388018 0.999247i $$-0.512354\pi$$
−0.0388018 + 0.999247i $$0.512354\pi$$
$$138$$ 0 0
$$139$$ −1.90833 −0.161862 −0.0809311 0.996720i $$-0.525789\pi$$
−0.0809311 + 0.996720i $$0.525789\pi$$
$$140$$ −6.00000 −0.507093
$$141$$ 0 0
$$142$$ −6.00000 −0.503509
$$143$$ 3.00000 0.250873
$$144$$ 0 0
$$145$$ 9.00000 0.747409
$$146$$ −12.3028 −1.01818
$$147$$ 0 0
$$148$$ 1.00000 0.0821995
$$149$$ −19.8167 −1.62344 −0.811722 0.584044i $$-0.801469\pi$$
−0.811722 + 0.584044i $$0.801469\pi$$
$$150$$ 0 0
$$151$$ −20.6056 −1.67686 −0.838428 0.545012i $$-0.816525\pi$$
−0.838428 + 0.545012i $$0.816525\pi$$
$$152$$ 2.00000 0.162221
$$153$$ 0 0
$$154$$ −6.00000 −0.483494
$$155$$ −0.697224 −0.0560024
$$156$$ 0 0
$$157$$ −7.21110 −0.575509 −0.287754 0.957704i $$-0.592909\pi$$
−0.287754 + 0.957704i $$0.592909\pi$$
$$158$$ 9.11943 0.725503
$$159$$ 0 0
$$160$$ 2.30278 0.182050
$$161$$ 10.1833 0.802560
$$162$$ 0 0
$$163$$ 8.42221 0.659678 0.329839 0.944037i $$-0.393006\pi$$
0.329839 + 0.944037i $$0.393006\pi$$
$$164$$ −9.90833 −0.773710
$$165$$ 0 0
$$166$$ −2.78890 −0.216460
$$167$$ 5.51388 0.426677 0.213338 0.976978i $$-0.431566\pi$$
0.213338 + 0.976978i $$0.431566\pi$$
$$168$$ 0 0
$$169$$ −11.3028 −0.869444
$$170$$ 13.8167 1.05969
$$171$$ 0 0
$$172$$ 0.605551 0.0461729
$$173$$ 8.78890 0.668207 0.334104 0.942536i $$-0.391566\pi$$
0.334104 + 0.942536i $$0.391566\pi$$
$$174$$ 0 0
$$175$$ −0.788897 −0.0596350
$$176$$ 2.30278 0.173578
$$177$$ 0 0
$$178$$ 9.21110 0.690401
$$179$$ 13.8167 1.03271 0.516353 0.856376i $$-0.327289\pi$$
0.516353 + 0.856376i $$0.327289\pi$$
$$180$$ 0 0
$$181$$ 20.0000 1.48659 0.743294 0.668965i $$-0.233262\pi$$
0.743294 + 0.668965i $$0.233262\pi$$
$$182$$ −3.39445 −0.251613
$$183$$ 0 0
$$184$$ −3.90833 −0.288126
$$185$$ 2.30278 0.169303
$$186$$ 0 0
$$187$$ 13.8167 1.01037
$$188$$ −4.60555 −0.335894
$$189$$ 0 0
$$190$$ 4.60555 0.334122
$$191$$ 5.51388 0.398970 0.199485 0.979901i $$-0.436073\pi$$
0.199485 + 0.979901i $$0.436073\pi$$
$$192$$ 0 0
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ −16.4222 −1.17905
$$195$$ 0 0
$$196$$ −0.211103 −0.0150788
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 26.4222 1.87302 0.936510 0.350640i $$-0.114036\pi$$
0.936510 + 0.350640i $$0.114036\pi$$
$$200$$ 0.302776 0.0214095
$$201$$ 0 0
$$202$$ 12.4222 0.874023
$$203$$ −10.1833 −0.714731
$$204$$ 0 0
$$205$$ −22.8167 −1.59358
$$206$$ −0.302776 −0.0210954
$$207$$ 0 0
$$208$$ 1.30278 0.0903312
$$209$$ 4.60555 0.318573
$$210$$ 0 0
$$211$$ 10.3028 0.709272 0.354636 0.935004i $$-0.384605\pi$$
0.354636 + 0.935004i $$0.384605\pi$$
$$212$$ 6.00000 0.412082
$$213$$ 0 0
$$214$$ −0.697224 −0.0476613
$$215$$ 1.39445 0.0951006
$$216$$ 0 0
$$217$$ 0.788897 0.0535538
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ 5.30278 0.357513
$$221$$ 7.81665 0.525805
$$222$$ 0 0
$$223$$ −5.81665 −0.389512 −0.194756 0.980852i $$-0.562391\pi$$
−0.194756 + 0.980852i $$0.562391\pi$$
$$224$$ −2.60555 −0.174091
$$225$$ 0 0
$$226$$ 3.21110 0.213599
$$227$$ −13.8167 −0.917044 −0.458522 0.888683i $$-0.651621\pi$$
−0.458522 + 0.888683i $$0.651621\pi$$
$$228$$ 0 0
$$229$$ 24.6056 1.62598 0.812990 0.582277i $$-0.197838\pi$$
0.812990 + 0.582277i $$0.197838\pi$$
$$230$$ −9.00000 −0.593442
$$231$$ 0 0
$$232$$ 3.90833 0.256594
$$233$$ −8.51388 −0.557763 −0.278881 0.960326i $$-0.589964\pi$$
−0.278881 + 0.960326i $$0.589964\pi$$
$$234$$ 0 0
$$235$$ −10.6056 −0.691830
$$236$$ −10.6056 −0.690363
$$237$$ 0 0
$$238$$ −15.6333 −1.01336
$$239$$ 17.5139 1.13288 0.566439 0.824103i $$-0.308321\pi$$
0.566439 + 0.824103i $$0.308321\pi$$
$$240$$ 0 0
$$241$$ 8.00000 0.515325 0.257663 0.966235i $$-0.417048\pi$$
0.257663 + 0.966235i $$0.417048\pi$$
$$242$$ −5.69722 −0.366231
$$243$$ 0 0
$$244$$ 7.51388 0.481027
$$245$$ −0.486122 −0.0310572
$$246$$ 0 0
$$247$$ 2.60555 0.165787
$$248$$ −0.302776 −0.0192263
$$249$$ 0 0
$$250$$ −10.8167 −0.684105
$$251$$ 21.2111 1.33883 0.669416 0.742887i $$-0.266544\pi$$
0.669416 + 0.742887i $$0.266544\pi$$
$$252$$ 0 0
$$253$$ −9.00000 −0.565825
$$254$$ −19.2111 −1.20541
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −3.21110 −0.200303 −0.100152 0.994972i $$-0.531933\pi$$
−0.100152 + 0.994972i $$0.531933\pi$$
$$258$$ 0 0
$$259$$ −2.60555 −0.161901
$$260$$ 3.00000 0.186052
$$261$$ 0 0
$$262$$ −10.6056 −0.655213
$$263$$ −13.8167 −0.851971 −0.425986 0.904730i $$-0.640073\pi$$
−0.425986 + 0.904730i $$0.640073\pi$$
$$264$$ 0 0
$$265$$ 13.8167 0.848750
$$266$$ −5.21110 −0.319513
$$267$$ 0 0
$$268$$ −3.51388 −0.214644
$$269$$ 21.2111 1.29326 0.646632 0.762802i $$-0.276177\pi$$
0.646632 + 0.762802i $$0.276177\pi$$
$$270$$ 0 0
$$271$$ −22.4222 −1.36205 −0.681026 0.732259i $$-0.738466\pi$$
−0.681026 + 0.732259i $$0.738466\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ −0.908327 −0.0548740
$$275$$ 0.697224 0.0420442
$$276$$ 0 0
$$277$$ 0.119429 0.00717582 0.00358791 0.999994i $$-0.498858\pi$$
0.00358791 + 0.999994i $$0.498858\pi$$
$$278$$ −1.90833 −0.114454
$$279$$ 0 0
$$280$$ −6.00000 −0.358569
$$281$$ 12.0000 0.715860 0.357930 0.933748i $$-0.383483\pi$$
0.357930 + 0.933748i $$0.383483\pi$$
$$282$$ 0 0
$$283$$ 24.6056 1.46265 0.731324 0.682030i $$-0.238903\pi$$
0.731324 + 0.682030i $$0.238903\pi$$
$$284$$ −6.00000 −0.356034
$$285$$ 0 0
$$286$$ 3.00000 0.177394
$$287$$ 25.8167 1.52391
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 9.00000 0.528498
$$291$$ 0 0
$$292$$ −12.3028 −0.719965
$$293$$ −11.0278 −0.644248 −0.322124 0.946697i $$-0.604397\pi$$
−0.322124 + 0.946697i $$0.604397\pi$$
$$294$$ 0 0
$$295$$ −24.4222 −1.42192
$$296$$ 1.00000 0.0581238
$$297$$ 0 0
$$298$$ −19.8167 −1.14795
$$299$$ −5.09167 −0.294459
$$300$$ 0 0
$$301$$ −1.57779 −0.0909426
$$302$$ −20.6056 −1.18572
$$303$$ 0 0
$$304$$ 2.00000 0.114708
$$305$$ 17.3028 0.990754
$$306$$ 0 0
$$307$$ 17.9083 1.02208 0.511041 0.859556i $$-0.329260\pi$$
0.511041 + 0.859556i $$0.329260\pi$$
$$308$$ −6.00000 −0.341882
$$309$$ 0 0
$$310$$ −0.697224 −0.0395997
$$311$$ −15.9083 −0.902078 −0.451039 0.892504i $$-0.648947\pi$$
−0.451039 + 0.892504i $$0.648947\pi$$
$$312$$ 0 0
$$313$$ −9.02776 −0.510279 −0.255139 0.966904i $$-0.582121\pi$$
−0.255139 + 0.966904i $$0.582121\pi$$
$$314$$ −7.21110 −0.406946
$$315$$ 0 0
$$316$$ 9.11943 0.513008
$$317$$ −9.21110 −0.517347 −0.258674 0.965965i $$-0.583285\pi$$
−0.258674 + 0.965965i $$0.583285\pi$$
$$318$$ 0 0
$$319$$ 9.00000 0.503903
$$320$$ 2.30278 0.128729
$$321$$ 0 0
$$322$$ 10.1833 0.567496
$$323$$ 12.0000 0.667698
$$324$$ 0 0
$$325$$ 0.394449 0.0218801
$$326$$ 8.42221 0.466463
$$327$$ 0 0
$$328$$ −9.90833 −0.547096
$$329$$ 12.0000 0.661581
$$330$$ 0 0
$$331$$ −13.2111 −0.726148 −0.363074 0.931760i $$-0.618273\pi$$
−0.363074 + 0.931760i $$0.618273\pi$$
$$332$$ −2.78890 −0.153061
$$333$$ 0 0
$$334$$ 5.51388 0.301706
$$335$$ −8.09167 −0.442095
$$336$$ 0 0
$$337$$ 6.11943 0.333347 0.166673 0.986012i $$-0.446697\pi$$
0.166673 + 0.986012i $$0.446697\pi$$
$$338$$ −11.3028 −0.614790
$$339$$ 0 0
$$340$$ 13.8167 0.749313
$$341$$ −0.697224 −0.0377568
$$342$$ 0 0
$$343$$ 18.7889 1.01451
$$344$$ 0.605551 0.0326491
$$345$$ 0 0
$$346$$ 8.78890 0.472494
$$347$$ −10.1833 −0.546671 −0.273335 0.961919i $$-0.588127\pi$$
−0.273335 + 0.961919i $$0.588127\pi$$
$$348$$ 0 0
$$349$$ 28.2389 1.51159 0.755796 0.654807i $$-0.227250\pi$$
0.755796 + 0.654807i $$0.227250\pi$$
$$350$$ −0.788897 −0.0421683
$$351$$ 0 0
$$352$$ 2.30278 0.122738
$$353$$ −10.1833 −0.542005 −0.271002 0.962579i $$-0.587355\pi$$
−0.271002 + 0.962579i $$0.587355\pi$$
$$354$$ 0 0
$$355$$ −13.8167 −0.733312
$$356$$ 9.21110 0.488187
$$357$$ 0 0
$$358$$ 13.8167 0.730233
$$359$$ −3.21110 −0.169476 −0.0847378 0.996403i $$-0.527005\pi$$
−0.0847378 + 0.996403i $$0.527005\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 20.0000 1.05118
$$363$$ 0 0
$$364$$ −3.39445 −0.177917
$$365$$ −28.3305 −1.48289
$$366$$ 0 0
$$367$$ 3.81665 0.199228 0.0996139 0.995026i $$-0.468239\pi$$
0.0996139 + 0.995026i $$0.468239\pi$$
$$368$$ −3.90833 −0.203736
$$369$$ 0 0
$$370$$ 2.30278 0.119716
$$371$$ −15.6333 −0.811641
$$372$$ 0 0
$$373$$ −17.8167 −0.922511 −0.461256 0.887267i $$-0.652601\pi$$
−0.461256 + 0.887267i $$0.652601\pi$$
$$374$$ 13.8167 0.714442
$$375$$ 0 0
$$376$$ −4.60555 −0.237513
$$377$$ 5.09167 0.262235
$$378$$ 0 0
$$379$$ 24.3305 1.24978 0.624888 0.780715i $$-0.285145\pi$$
0.624888 + 0.780715i $$0.285145\pi$$
$$380$$ 4.60555 0.236260
$$381$$ 0 0
$$382$$ 5.51388 0.282115
$$383$$ 36.8444 1.88266 0.941331 0.337486i $$-0.109576\pi$$
0.941331 + 0.337486i $$0.109576\pi$$
$$384$$ 0 0
$$385$$ −13.8167 −0.704162
$$386$$ −4.00000 −0.203595
$$387$$ 0 0
$$388$$ −16.4222 −0.833711
$$389$$ 37.1194 1.88203 0.941015 0.338365i $$-0.109874\pi$$
0.941015 + 0.338365i $$0.109874\pi$$
$$390$$ 0 0
$$391$$ −23.4500 −1.18592
$$392$$ −0.211103 −0.0106623
$$393$$ 0 0
$$394$$ 6.00000 0.302276
$$395$$ 21.0000 1.05662
$$396$$ 0 0
$$397$$ 6.18335 0.310333 0.155167 0.987888i $$-0.450409\pi$$
0.155167 + 0.987888i $$0.450409\pi$$
$$398$$ 26.4222 1.32443
$$399$$ 0 0
$$400$$ 0.302776 0.0151388
$$401$$ 7.81665 0.390345 0.195173 0.980769i $$-0.437473\pi$$
0.195173 + 0.980769i $$0.437473\pi$$
$$402$$ 0 0
$$403$$ −0.394449 −0.0196489
$$404$$ 12.4222 0.618028
$$405$$ 0 0
$$406$$ −10.1833 −0.505391
$$407$$ 2.30278 0.114144
$$408$$ 0 0
$$409$$ 31.0278 1.53422 0.767112 0.641513i $$-0.221693\pi$$
0.767112 + 0.641513i $$0.221693\pi$$
$$410$$ −22.8167 −1.12683
$$411$$ 0 0
$$412$$ −0.302776 −0.0149167
$$413$$ 27.6333 1.35975
$$414$$ 0 0
$$415$$ −6.42221 −0.315254
$$416$$ 1.30278 0.0638738
$$417$$ 0 0
$$418$$ 4.60555 0.225265
$$419$$ −36.1472 −1.76591 −0.882953 0.469462i $$-0.844448\pi$$
−0.882953 + 0.469462i $$0.844448\pi$$
$$420$$ 0 0
$$421$$ −3.72498 −0.181544 −0.0907722 0.995872i $$-0.528934\pi$$
−0.0907722 + 0.995872i $$0.528934\pi$$
$$422$$ 10.3028 0.501531
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ 1.81665 0.0881207
$$426$$ 0 0
$$427$$ −19.5778 −0.947436
$$428$$ −0.697224 −0.0337016
$$429$$ 0 0
$$430$$ 1.39445 0.0672463
$$431$$ −9.21110 −0.443683 −0.221842 0.975083i $$-0.571207\pi$$
−0.221842 + 0.975083i $$0.571207\pi$$
$$432$$ 0 0
$$433$$ 34.9361 1.67892 0.839461 0.543421i $$-0.182871\pi$$
0.839461 + 0.543421i $$0.182871\pi$$
$$434$$ 0.788897 0.0378683
$$435$$ 0 0
$$436$$ 2.00000 0.0957826
$$437$$ −7.81665 −0.373921
$$438$$ 0 0
$$439$$ 30.3305 1.44760 0.723799 0.690011i $$-0.242394\pi$$
0.723799 + 0.690011i $$0.242394\pi$$
$$440$$ 5.30278 0.252800
$$441$$ 0 0
$$442$$ 7.81665 0.371800
$$443$$ −32.7250 −1.55481 −0.777405 0.629000i $$-0.783465\pi$$
−0.777405 + 0.629000i $$0.783465\pi$$
$$444$$ 0 0
$$445$$ 21.2111 1.00550
$$446$$ −5.81665 −0.275427
$$447$$ 0 0
$$448$$ −2.60555 −0.123101
$$449$$ 15.2111 0.717856 0.358928 0.933365i $$-0.383142\pi$$
0.358928 + 0.933365i $$0.383142\pi$$
$$450$$ 0 0
$$451$$ −22.8167 −1.07439
$$452$$ 3.21110 0.151038
$$453$$ 0 0
$$454$$ −13.8167 −0.648448
$$455$$ −7.81665 −0.366450
$$456$$ 0 0
$$457$$ −2.60555 −0.121883 −0.0609413 0.998141i $$-0.519410\pi$$
−0.0609413 + 0.998141i $$0.519410\pi$$
$$458$$ 24.6056 1.14974
$$459$$ 0 0
$$460$$ −9.00000 −0.419627
$$461$$ −12.4222 −0.578560 −0.289280 0.957245i $$-0.593416\pi$$
−0.289280 + 0.957245i $$0.593416\pi$$
$$462$$ 0 0
$$463$$ 26.6972 1.24073 0.620363 0.784315i $$-0.286985\pi$$
0.620363 + 0.784315i $$0.286985\pi$$
$$464$$ 3.90833 0.181440
$$465$$ 0 0
$$466$$ −8.51388 −0.394398
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 9.15559 0.422766
$$470$$ −10.6056 −0.489198
$$471$$ 0 0
$$472$$ −10.6056 −0.488160
$$473$$ 1.39445 0.0641168
$$474$$ 0 0
$$475$$ 0.605551 0.0277846
$$476$$ −15.6333 −0.716551
$$477$$ 0 0
$$478$$ 17.5139 0.801066
$$479$$ 13.1194 0.599442 0.299721 0.954027i $$-0.403106\pi$$
0.299721 + 0.954027i $$0.403106\pi$$
$$480$$ 0 0
$$481$$ 1.30278 0.0594015
$$482$$ 8.00000 0.364390
$$483$$ 0 0
$$484$$ −5.69722 −0.258965
$$485$$ −37.8167 −1.71717
$$486$$ 0 0
$$487$$ −37.2111 −1.68620 −0.843098 0.537760i $$-0.819271\pi$$
−0.843098 + 0.537760i $$0.819271\pi$$
$$488$$ 7.51388 0.340137
$$489$$ 0 0
$$490$$ −0.486122 −0.0219607
$$491$$ −17.7250 −0.799917 −0.399959 0.916533i $$-0.630975\pi$$
−0.399959 + 0.916533i $$0.630975\pi$$
$$492$$ 0 0
$$493$$ 23.4500 1.05613
$$494$$ 2.60555 0.117229
$$495$$ 0 0
$$496$$ −0.302776 −0.0135950
$$497$$ 15.6333 0.701250
$$498$$ 0 0
$$499$$ −42.2389 −1.89087 −0.945436 0.325809i $$-0.894363\pi$$
−0.945436 + 0.325809i $$0.894363\pi$$
$$500$$ −10.8167 −0.483735
$$501$$ 0 0
$$502$$ 21.2111 0.946698
$$503$$ 6.48612 0.289202 0.144601 0.989490i $$-0.453810\pi$$
0.144601 + 0.989490i $$0.453810\pi$$
$$504$$ 0 0
$$505$$ 28.6056 1.27293
$$506$$ −9.00000 −0.400099
$$507$$ 0 0
$$508$$ −19.2111 −0.852355
$$509$$ 4.18335 0.185424 0.0927118 0.995693i $$-0.470446\pi$$
0.0927118 + 0.995693i $$0.470446\pi$$
$$510$$ 0 0
$$511$$ 32.0555 1.41805
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −3.21110 −0.141636
$$515$$ −0.697224 −0.0307234
$$516$$ 0 0
$$517$$ −10.6056 −0.466432
$$518$$ −2.60555 −0.114481
$$519$$ 0 0
$$520$$ 3.00000 0.131559
$$521$$ −33.6333 −1.47350 −0.736751 0.676164i $$-0.763641\pi$$
−0.736751 + 0.676164i $$0.763641\pi$$
$$522$$ 0 0
$$523$$ −18.2389 −0.797530 −0.398765 0.917053i $$-0.630561\pi$$
−0.398765 + 0.917053i $$0.630561\pi$$
$$524$$ −10.6056 −0.463306
$$525$$ 0 0
$$526$$ −13.8167 −0.602435
$$527$$ −1.81665 −0.0791347
$$528$$ 0 0
$$529$$ −7.72498 −0.335869
$$530$$ 13.8167 0.600157
$$531$$ 0 0
$$532$$ −5.21110 −0.225930
$$533$$ −12.9083 −0.559122
$$534$$ 0 0
$$535$$ −1.60555 −0.0694140
$$536$$ −3.51388 −0.151776
$$537$$ 0 0
$$538$$ 21.2111 0.914476
$$539$$ −0.486122 −0.0209387
$$540$$ 0 0
$$541$$ 25.9361 1.11508 0.557540 0.830150i $$-0.311745\pi$$
0.557540 + 0.830150i $$0.311745\pi$$
$$542$$ −22.4222 −0.963116
$$543$$ 0 0
$$544$$ 6.00000 0.257248
$$545$$ 4.60555 0.197280
$$546$$ 0 0
$$547$$ −20.6056 −0.881030 −0.440515 0.897745i $$-0.645204\pi$$
−0.440515 + 0.897745i $$0.645204\pi$$
$$548$$ −0.908327 −0.0388018
$$549$$ 0 0
$$550$$ 0.697224 0.0297297
$$551$$ 7.81665 0.333001
$$552$$ 0 0
$$553$$ −23.7611 −1.01043
$$554$$ 0.119429 0.00507407
$$555$$ 0 0
$$556$$ −1.90833 −0.0809311
$$557$$ −11.5139 −0.487859 −0.243929 0.969793i $$-0.578436\pi$$
−0.243929 + 0.969793i $$0.578436\pi$$
$$558$$ 0 0
$$559$$ 0.788897 0.0333668
$$560$$ −6.00000 −0.253546
$$561$$ 0 0
$$562$$ 12.0000 0.506189
$$563$$ 28.0555 1.18240 0.591199 0.806525i $$-0.298655\pi$$
0.591199 + 0.806525i $$0.298655\pi$$
$$564$$ 0 0
$$565$$ 7.39445 0.311087
$$566$$ 24.6056 1.03425
$$567$$ 0 0
$$568$$ −6.00000 −0.251754
$$569$$ −18.4222 −0.772299 −0.386150 0.922436i $$-0.626195\pi$$
−0.386150 + 0.922436i $$0.626195\pi$$
$$570$$ 0 0
$$571$$ −16.6972 −0.698757 −0.349379 0.936982i $$-0.613607\pi$$
−0.349379 + 0.936982i $$0.613607\pi$$
$$572$$ 3.00000 0.125436
$$573$$ 0 0
$$574$$ 25.8167 1.07757
$$575$$ −1.18335 −0.0493489
$$576$$ 0 0
$$577$$ 22.2389 0.925816 0.462908 0.886406i $$-0.346806\pi$$
0.462908 + 0.886406i $$0.346806\pi$$
$$578$$ 19.0000 0.790296
$$579$$ 0 0
$$580$$ 9.00000 0.373705
$$581$$ 7.26662 0.301470
$$582$$ 0 0
$$583$$ 13.8167 0.572227
$$584$$ −12.3028 −0.509092
$$585$$ 0 0
$$586$$ −11.0278 −0.455552
$$587$$ 45.6333 1.88349 0.941744 0.336330i $$-0.109186\pi$$
0.941744 + 0.336330i $$0.109186\pi$$
$$588$$ 0 0
$$589$$ −0.605551 −0.0249513
$$590$$ −24.4222 −1.00545
$$591$$ 0 0
$$592$$ 1.00000 0.0410997
$$593$$ −18.4861 −0.759134 −0.379567 0.925164i $$-0.623927\pi$$
−0.379567 + 0.925164i $$0.623927\pi$$
$$594$$ 0 0
$$595$$ −36.0000 −1.47586
$$596$$ −19.8167 −0.811722
$$597$$ 0 0
$$598$$ −5.09167 −0.208214
$$599$$ 20.7889 0.849411 0.424706 0.905331i $$-0.360378\pi$$
0.424706 + 0.905331i $$0.360378\pi$$
$$600$$ 0 0
$$601$$ −24.3028 −0.991331 −0.495665 0.868514i $$-0.665076\pi$$
−0.495665 + 0.868514i $$0.665076\pi$$
$$602$$ −1.57779 −0.0643061
$$603$$ 0 0
$$604$$ −20.6056 −0.838428
$$605$$ −13.1194 −0.533381
$$606$$ 0 0
$$607$$ −13.4861 −0.547385 −0.273692 0.961817i $$-0.588245\pi$$
−0.273692 + 0.961817i $$0.588245\pi$$
$$608$$ 2.00000 0.0811107
$$609$$ 0 0
$$610$$ 17.3028 0.700569
$$611$$ −6.00000 −0.242734
$$612$$ 0 0
$$613$$ −29.8167 −1.20428 −0.602142 0.798389i $$-0.705686\pi$$
−0.602142 + 0.798389i $$0.705686\pi$$
$$614$$ 17.9083 0.722721
$$615$$ 0 0
$$616$$ −6.00000 −0.241747
$$617$$ 42.5694 1.71378 0.856890 0.515500i $$-0.172394\pi$$
0.856890 + 0.515500i $$0.172394\pi$$
$$618$$ 0 0
$$619$$ −6.30278 −0.253330 −0.126665 0.991946i $$-0.540427\pi$$
−0.126665 + 0.991946i $$0.540427\pi$$
$$620$$ −0.697224 −0.0280012
$$621$$ 0 0
$$622$$ −15.9083 −0.637866
$$623$$ −24.0000 −0.961540
$$624$$ 0 0
$$625$$ −26.4222 −1.05689
$$626$$ −9.02776 −0.360822
$$627$$ 0 0
$$628$$ −7.21110 −0.287754
$$629$$ 6.00000 0.239236
$$630$$ 0 0
$$631$$ 14.6972 0.585087 0.292544 0.956252i $$-0.405498\pi$$
0.292544 + 0.956252i $$0.405498\pi$$
$$632$$ 9.11943 0.362751
$$633$$ 0 0
$$634$$ −9.21110 −0.365820
$$635$$ −44.2389 −1.75557
$$636$$ 0 0
$$637$$ −0.275019 −0.0108967
$$638$$ 9.00000 0.356313
$$639$$ 0 0
$$640$$ 2.30278 0.0910252
$$641$$ 20.5139 0.810249 0.405125 0.914261i $$-0.367228\pi$$
0.405125 + 0.914261i $$0.367228\pi$$
$$642$$ 0 0
$$643$$ −8.18335 −0.322720 −0.161360 0.986896i $$-0.551588\pi$$
−0.161360 + 0.986896i $$0.551588\pi$$
$$644$$ 10.1833 0.401280
$$645$$ 0 0
$$646$$ 12.0000 0.472134
$$647$$ −20.9361 −0.823082 −0.411541 0.911391i $$-0.635009\pi$$
−0.411541 + 0.911391i $$0.635009\pi$$
$$648$$ 0 0
$$649$$ −24.4222 −0.958655
$$650$$ 0.394449 0.0154716
$$651$$ 0 0
$$652$$ 8.42221 0.329839
$$653$$ 3.90833 0.152945 0.0764723 0.997072i $$-0.475634\pi$$
0.0764723 + 0.997072i $$0.475634\pi$$
$$654$$ 0 0
$$655$$ −24.4222 −0.954255
$$656$$ −9.90833 −0.386855
$$657$$ 0 0
$$658$$ 12.0000 0.467809
$$659$$ 16.8806 0.657574 0.328787 0.944404i $$-0.393360\pi$$
0.328787 + 0.944404i $$0.393360\pi$$
$$660$$ 0 0
$$661$$ −30.5139 −1.18685 −0.593426 0.804888i $$-0.702225\pi$$
−0.593426 + 0.804888i $$0.702225\pi$$
$$662$$ −13.2111 −0.513464
$$663$$ 0 0
$$664$$ −2.78890 −0.108230
$$665$$ −12.0000 −0.465340
$$666$$ 0 0
$$667$$ −15.2750 −0.591451
$$668$$ 5.51388 0.213338
$$669$$ 0 0
$$670$$ −8.09167 −0.312609
$$671$$ 17.3028 0.667966
$$672$$ 0 0
$$673$$ 20.6972 0.797819 0.398910 0.916990i $$-0.369389\pi$$
0.398910 + 0.916990i $$0.369389\pi$$
$$674$$ 6.11943 0.235712
$$675$$ 0 0
$$676$$ −11.3028 −0.434722
$$677$$ −14.2389 −0.547244 −0.273622 0.961837i $$-0.588222\pi$$
−0.273622 + 0.961837i $$0.588222\pi$$
$$678$$ 0 0
$$679$$ 42.7889 1.64209
$$680$$ 13.8167 0.529844
$$681$$ 0 0
$$682$$ −0.697224 −0.0266981
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ −2.09167 −0.0799187
$$686$$ 18.7889 0.717363
$$687$$ 0 0
$$688$$ 0.605551 0.0230864
$$689$$ 7.81665 0.297791
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ 8.78890 0.334104
$$693$$ 0 0
$$694$$ −10.1833 −0.386555
$$695$$ −4.39445 −0.166691
$$696$$ 0 0
$$697$$ −59.4500 −2.25183
$$698$$ 28.2389 1.06886
$$699$$ 0 0
$$700$$ −0.788897 −0.0298175
$$701$$ −40.1194 −1.51529 −0.757645 0.652667i $$-0.773650\pi$$
−0.757645 + 0.652667i $$0.773650\pi$$
$$702$$ 0 0
$$703$$ 2.00000 0.0754314
$$704$$ 2.30278 0.0867891
$$705$$ 0 0
$$706$$ −10.1833 −0.383255
$$707$$ −32.3667 −1.21727
$$708$$ 0 0
$$709$$ −41.3305 −1.55220 −0.776100 0.630609i $$-0.782805\pi$$
−0.776100 + 0.630609i $$0.782805\pi$$
$$710$$ −13.8167 −0.518530
$$711$$ 0 0
$$712$$ 9.21110 0.345201
$$713$$ 1.18335 0.0443167
$$714$$ 0 0
$$715$$ 6.90833 0.258357
$$716$$ 13.8167 0.516353
$$717$$ 0 0
$$718$$ −3.21110 −0.119837
$$719$$ 51.6333 1.92560 0.962799 0.270220i $$-0.0870963\pi$$
0.962799 + 0.270220i $$0.0870963\pi$$
$$720$$ 0 0
$$721$$ 0.788897 0.0293801
$$722$$ −15.0000 −0.558242
$$723$$ 0 0
$$724$$ 20.0000 0.743294
$$725$$ 1.18335 0.0439484
$$726$$ 0 0
$$727$$ 19.0917 0.708071 0.354035 0.935232i $$-0.384809\pi$$
0.354035 + 0.935232i $$0.384809\pi$$
$$728$$ −3.39445 −0.125807
$$729$$ 0 0
$$730$$ −28.3305 −1.04856
$$731$$ 3.63331 0.134383
$$732$$ 0 0
$$733$$ −13.6333 −0.503558 −0.251779 0.967785i $$-0.581016\pi$$
−0.251779 + 0.967785i $$0.581016\pi$$
$$734$$ 3.81665 0.140875
$$735$$ 0 0
$$736$$ −3.90833 −0.144063
$$737$$ −8.09167 −0.298061
$$738$$ 0 0
$$739$$ −2.66947 −0.0981980 −0.0490990 0.998794i $$-0.515635\pi$$
−0.0490990 + 0.998794i $$0.515635\pi$$
$$740$$ 2.30278 0.0846517
$$741$$ 0 0
$$742$$ −15.6333 −0.573917
$$743$$ 29.4500 1.08041 0.540207 0.841532i $$-0.318346\pi$$
0.540207 + 0.841532i $$0.318346\pi$$
$$744$$ 0 0
$$745$$ −45.6333 −1.67188
$$746$$ −17.8167 −0.652314
$$747$$ 0 0
$$748$$ 13.8167 0.505187
$$749$$ 1.81665 0.0663791
$$750$$ 0 0
$$751$$ 14.0000 0.510867 0.255434 0.966827i $$-0.417782\pi$$
0.255434 + 0.966827i $$0.417782\pi$$
$$752$$ −4.60555 −0.167947
$$753$$ 0 0
$$754$$ 5.09167 0.185428
$$755$$ −47.4500 −1.72688
$$756$$ 0 0
$$757$$ 5.69722 0.207069 0.103535 0.994626i $$-0.466985\pi$$
0.103535 + 0.994626i $$0.466985\pi$$
$$758$$ 24.3305 0.883725
$$759$$ 0 0
$$760$$ 4.60555 0.167061
$$761$$ −16.8806 −0.611920 −0.305960 0.952044i $$-0.598977\pi$$
−0.305960 + 0.952044i $$0.598977\pi$$
$$762$$ 0 0
$$763$$ −5.21110 −0.188655
$$764$$ 5.51388 0.199485
$$765$$ 0 0
$$766$$ 36.8444 1.33124
$$767$$ −13.8167 −0.498890
$$768$$ 0 0
$$769$$ −22.0000 −0.793340 −0.396670 0.917961i $$-0.629834\pi$$
−0.396670 + 0.917961i $$0.629834\pi$$
$$770$$ −13.8167 −0.497918
$$771$$ 0 0
$$772$$ −4.00000 −0.143963
$$773$$ −22.0555 −0.793282 −0.396641 0.917974i $$-0.629824\pi$$
−0.396641 + 0.917974i $$0.629824\pi$$
$$774$$ 0 0
$$775$$ −0.0916731 −0.00329299
$$776$$ −16.4222 −0.589523
$$777$$ 0 0
$$778$$ 37.1194 1.33080
$$779$$ −19.8167 −0.710005
$$780$$ 0 0
$$781$$ −13.8167 −0.494399
$$782$$ −23.4500 −0.838569
$$783$$ 0 0
$$784$$ −0.211103 −0.00753938
$$785$$ −16.6056 −0.592678
$$786$$ 0 0
$$787$$ 10.7889 0.384583 0.192291 0.981338i $$-0.438408\pi$$
0.192291 + 0.981338i $$0.438408\pi$$
$$788$$ 6.00000 0.213741
$$789$$ 0 0
$$790$$ 21.0000 0.747146
$$791$$ −8.36669 −0.297485
$$792$$ 0 0
$$793$$ 9.78890 0.347614
$$794$$ 6.18335 0.219439
$$795$$ 0 0
$$796$$ 26.4222 0.936510
$$797$$ −22.3305 −0.790988 −0.395494 0.918469i $$-0.629427\pi$$
−0.395494 + 0.918469i $$0.629427\pi$$
$$798$$ 0 0
$$799$$ −27.6333 −0.977596
$$800$$ 0.302776 0.0107047
$$801$$ 0 0
$$802$$ 7.81665 0.276016
$$803$$ −28.3305 −0.999763
$$804$$ 0 0
$$805$$ 23.4500 0.826503
$$806$$ −0.394449 −0.0138939
$$807$$ 0 0
$$808$$ 12.4222 0.437012
$$809$$ 35.4500 1.24635 0.623177 0.782081i $$-0.285842\pi$$
0.623177 + 0.782081i $$0.285842\pi$$
$$810$$ 0 0
$$811$$ −7.14719 −0.250972 −0.125486 0.992095i $$-0.540049\pi$$
−0.125486 + 0.992095i $$0.540049\pi$$
$$812$$ −10.1833 −0.357365
$$813$$ 0 0
$$814$$ 2.30278 0.0807122
$$815$$ 19.3944 0.679358
$$816$$ 0 0
$$817$$ 1.21110 0.0423711
$$818$$ 31.0278 1.08486
$$819$$ 0 0
$$820$$ −22.8167 −0.796792
$$821$$ 3.21110 0.112068 0.0560341 0.998429i $$-0.482154\pi$$
0.0560341 + 0.998429i $$0.482154\pi$$
$$822$$ 0 0
$$823$$ 44.8444 1.56318 0.781589 0.623794i $$-0.214410\pi$$
0.781589 + 0.623794i $$0.214410\pi$$
$$824$$ −0.302776 −0.0105477
$$825$$ 0 0
$$826$$ 27.6333 0.961486
$$827$$ −34.6056 −1.20335 −0.601676 0.798740i $$-0.705500\pi$$
−0.601676 + 0.798740i $$0.705500\pi$$
$$828$$ 0 0
$$829$$ −27.7250 −0.962928 −0.481464 0.876466i $$-0.659895\pi$$
−0.481464 + 0.876466i $$0.659895\pi$$
$$830$$ −6.42221 −0.222918
$$831$$ 0 0
$$832$$ 1.30278 0.0451656
$$833$$ −1.26662 −0.0438856
$$834$$ 0 0
$$835$$ 12.6972 0.439406
$$836$$ 4.60555 0.159286
$$837$$ 0 0
$$838$$ −36.1472 −1.24868
$$839$$ 12.9722 0.447852 0.223926 0.974606i $$-0.428113\pi$$
0.223926 + 0.974606i $$0.428113\pi$$
$$840$$ 0 0
$$841$$ −13.7250 −0.473275
$$842$$ −3.72498 −0.128371
$$843$$ 0 0
$$844$$ 10.3028 0.354636
$$845$$ −26.0278 −0.895382
$$846$$ 0 0
$$847$$ 14.8444 0.510060
$$848$$ 6.00000 0.206041
$$849$$ 0 0
$$850$$ 1.81665 0.0623107
$$851$$ −3.90833 −0.133976
$$852$$ 0 0
$$853$$ 42.5416 1.45660 0.728299 0.685260i $$-0.240311\pi$$
0.728299 + 0.685260i $$0.240311\pi$$
$$854$$ −19.5778 −0.669938
$$855$$ 0 0
$$856$$ −0.697224 −0.0238306
$$857$$ −42.8444 −1.46354 −0.731769 0.681553i $$-0.761305\pi$$
−0.731769 + 0.681553i $$0.761305\pi$$
$$858$$ 0 0
$$859$$ 48.0555 1.63963 0.819816 0.572626i $$-0.194075\pi$$
0.819816 + 0.572626i $$0.194075\pi$$
$$860$$ 1.39445 0.0475503
$$861$$ 0 0
$$862$$ −9.21110 −0.313731
$$863$$ −12.0000 −0.408485 −0.204242 0.978920i $$-0.565473\pi$$
−0.204242 + 0.978920i $$0.565473\pi$$
$$864$$ 0 0
$$865$$ 20.2389 0.688142
$$866$$ 34.9361 1.18718
$$867$$ 0 0
$$868$$ 0.788897 0.0267769
$$869$$ 21.0000 0.712376
$$870$$ 0 0
$$871$$ −4.57779 −0.155113
$$872$$ 2.00000 0.0677285
$$873$$ 0 0
$$874$$ −7.81665 −0.264402
$$875$$ 28.1833 0.952771
$$876$$ 0 0
$$877$$ −7.21110 −0.243502 −0.121751 0.992561i $$-0.538851\pi$$
−0.121751 + 0.992561i $$0.538851\pi$$
$$878$$ 30.3305 1.02361
$$879$$ 0 0
$$880$$ 5.30278 0.178757
$$881$$ 28.5416 0.961592 0.480796 0.876832i $$-0.340348\pi$$
0.480796 + 0.876832i $$0.340348\pi$$
$$882$$ 0 0
$$883$$ 26.4222 0.889178 0.444589 0.895735i $$-0.353350\pi$$
0.444589 + 0.895735i $$0.353350\pi$$
$$884$$ 7.81665 0.262903
$$885$$ 0 0
$$886$$ −32.7250 −1.09942
$$887$$ 0.422205 0.0141763 0.00708813 0.999975i $$-0.497744\pi$$
0.00708813 + 0.999975i $$0.497744\pi$$
$$888$$ 0 0
$$889$$ 50.0555 1.67881
$$890$$ 21.2111 0.710998
$$891$$ 0 0
$$892$$ −5.81665 −0.194756
$$893$$ −9.21110 −0.308238
$$894$$ 0 0
$$895$$ 31.8167 1.06351
$$896$$ −2.60555 −0.0870454
$$897$$ 0 0
$$898$$ 15.2111 0.507601
$$899$$ −1.18335 −0.0394668
$$900$$ 0 0
$$901$$ 36.0000 1.19933
$$902$$ −22.8167 −0.759711
$$903$$ 0 0
$$904$$ 3.21110 0.106800
$$905$$ 46.0555 1.53094
$$906$$ 0 0
$$907$$ 26.0000 0.863316 0.431658 0.902037i $$-0.357929\pi$$
0.431658 + 0.902037i $$0.357929\pi$$
$$908$$ −13.8167 −0.458522
$$909$$ 0 0
$$910$$ −7.81665 −0.259120
$$911$$ 17.5778 0.582378 0.291189 0.956665i $$-0.405949\pi$$
0.291189 + 0.956665i $$0.405949\pi$$
$$912$$ 0 0
$$913$$ −6.42221 −0.212544
$$914$$ −2.60555 −0.0861840
$$915$$ 0 0
$$916$$ 24.6056 0.812990
$$917$$ 27.6333 0.912532
$$918$$ 0 0
$$919$$ −9.57779 −0.315942 −0.157971 0.987444i $$-0.550495\pi$$
−0.157971 + 0.987444i $$0.550495\pi$$
$$920$$ −9.00000 −0.296721
$$921$$ 0 0
$$922$$ −12.4222 −0.409104
$$923$$ −7.81665 −0.257288
$$924$$ 0 0
$$925$$ 0.302776 0.00995520
$$926$$ 26.6972 0.877325
$$927$$ 0 0
$$928$$ 3.90833 0.128297
$$929$$ 18.4861 0.606510 0.303255 0.952909i $$-0.401927\pi$$
0.303255 + 0.952909i $$0.401927\pi$$
$$930$$ 0 0
$$931$$ −0.422205 −0.0138372
$$932$$ −8.51388 −0.278881
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 31.8167 1.04052
$$936$$ 0 0
$$937$$ −18.0917 −0.591029 −0.295515 0.955338i $$-0.595491\pi$$
−0.295515 + 0.955338i $$0.595491\pi$$
$$938$$ 9.15559 0.298941
$$939$$ 0 0
$$940$$ −10.6056 −0.345915
$$941$$ −13.8167 −0.450410 −0.225205 0.974311i $$-0.572305\pi$$
−0.225205 + 0.974311i $$0.572305\pi$$
$$942$$ 0 0
$$943$$ 38.7250 1.26106
$$944$$ −10.6056 −0.345181
$$945$$ 0 0
$$946$$ 1.39445 0.0453374
$$947$$ 3.63331 0.118067 0.0590333 0.998256i $$-0.481198\pi$$
0.0590333 + 0.998256i $$0.481198\pi$$
$$948$$ 0 0
$$949$$ −16.0278 −0.520283
$$950$$ 0.605551 0.0196467
$$951$$ 0 0
$$952$$ −15.6333 −0.506678
$$953$$ −49.7527 −1.61165 −0.805825 0.592154i $$-0.798278\pi$$
−0.805825 + 0.592154i $$0.798278\pi$$
$$954$$ 0 0
$$955$$ 12.6972 0.410873
$$956$$ 17.5139 0.566439
$$957$$ 0 0
$$958$$ 13.1194 0.423870
$$959$$ 2.36669 0.0764245
$$960$$ 0 0
$$961$$ −30.9083 −0.997043
$$962$$ 1.30278 0.0420032
$$963$$ 0 0
$$964$$ 8.00000 0.257663
$$965$$ −9.21110 −0.296516
$$966$$ 0 0
$$967$$ −6.72498 −0.216261 −0.108130 0.994137i $$-0.534486\pi$$
−0.108130 + 0.994137i $$0.534486\pi$$
$$968$$ −5.69722 −0.183116
$$969$$ 0 0
$$970$$ −37.8167 −1.21422
$$971$$ 22.5416 0.723395 0.361698 0.932295i $$-0.382197\pi$$
0.361698 + 0.932295i $$0.382197\pi$$
$$972$$ 0 0
$$973$$ 4.97224 0.159403
$$974$$ −37.2111 −1.19232
$$975$$ 0 0
$$976$$ 7.51388 0.240513
$$977$$ −18.0000 −0.575871 −0.287936 0.957650i $$-0.592969\pi$$
−0.287936 + 0.957650i $$0.592969\pi$$
$$978$$ 0 0
$$979$$ 21.2111 0.677910
$$980$$ −0.486122 −0.0155286
$$981$$ 0 0
$$982$$ −17.7250 −0.565627
$$983$$ 12.0000 0.382741 0.191370 0.981518i $$-0.438707\pi$$
0.191370 + 0.981518i $$0.438707\pi$$
$$984$$ 0 0
$$985$$ 13.8167 0.440235
$$986$$ 23.4500 0.746799
$$987$$ 0 0
$$988$$ 2.60555 0.0828936
$$989$$ −2.36669 −0.0752564
$$990$$ 0 0
$$991$$ 50.6972 1.61045 0.805225 0.592969i $$-0.202044\pi$$
0.805225 + 0.592969i $$0.202044\pi$$
$$992$$ −0.302776 −0.00961314
$$993$$ 0 0
$$994$$ 15.6333 0.495858
$$995$$ 60.8444 1.92890
$$996$$ 0 0
$$997$$ −52.4222 −1.66023 −0.830114 0.557594i $$-0.811725\pi$$
−0.830114 + 0.557594i $$0.811725\pi$$
$$998$$ −42.2389 −1.33705
$$999$$ 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 666.2.a.j.1.2 2
3.2 odd 2 74.2.a.a.1.2 2
4.3 odd 2 5328.2.a.bf.1.2 2
12.11 even 2 592.2.a.f.1.1 2
15.2 even 4 1850.2.b.i.149.1 4
15.8 even 4 1850.2.b.i.149.4 4
15.14 odd 2 1850.2.a.u.1.1 2
21.20 even 2 3626.2.a.a.1.1 2
24.5 odd 2 2368.2.a.s.1.1 2
24.11 even 2 2368.2.a.ba.1.2 2
33.32 even 2 8954.2.a.p.1.2 2
111.110 odd 2 2738.2.a.l.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
74.2.a.a.1.2 2 3.2 odd 2
592.2.a.f.1.1 2 12.11 even 2
666.2.a.j.1.2 2 1.1 even 1 trivial
1850.2.a.u.1.1 2 15.14 odd 2
1850.2.b.i.149.1 4 15.2 even 4
1850.2.b.i.149.4 4 15.8 even 4
2368.2.a.s.1.1 2 24.5 odd 2
2368.2.a.ba.1.2 2 24.11 even 2
2738.2.a.l.1.2 2 111.110 odd 2
3626.2.a.a.1.1 2 21.20 even 2
5328.2.a.bf.1.2 2 4.3 odd 2
8954.2.a.p.1.2 2 33.32 even 2