# Properties

 Label 1840.2.a.l.1.1 Level $1840$ Weight $2$ Character 1840.1 Self dual yes Analytic conductor $14.692$ Analytic rank $1$ 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] = [1840,2,Mod(1,1840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1840, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1840.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.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: $$14.6924739719$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 230) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$1.61803$$ of defining polynomial Character $$\chi$$ $$=$$ 1840.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.61803 q^{3} +1.00000 q^{5} +0.618034 q^{7} -0.381966 q^{9} +O(q^{10})$$ $$q-1.61803 q^{3} +1.00000 q^{5} +0.618034 q^{7} -0.381966 q^{9} +2.85410 q^{11} -7.09017 q^{13} -1.61803 q^{15} +6.09017 q^{17} -1.85410 q^{19} -1.00000 q^{21} -1.00000 q^{23} +1.00000 q^{25} +5.47214 q^{27} -9.23607 q^{29} -9.09017 q^{31} -4.61803 q^{33} +0.618034 q^{35} +6.47214 q^{37} +11.4721 q^{39} +3.32624 q^{41} -0.381966 q^{45} +3.70820 q^{47} -6.61803 q^{49} -9.85410 q^{51} +0.472136 q^{53} +2.85410 q^{55} +3.00000 q^{57} -1.70820 q^{59} -9.32624 q^{61} -0.236068 q^{63} -7.09017 q^{65} -14.4721 q^{67} +1.61803 q^{69} +4.09017 q^{71} +3.23607 q^{73} -1.61803 q^{75} +1.76393 q^{77} -1.52786 q^{79} -7.70820 q^{81} +6.94427 q^{83} +6.09017 q^{85} +14.9443 q^{87} -10.4721 q^{89} -4.38197 q^{91} +14.7082 q^{93} -1.85410 q^{95} +12.3820 q^{97} -1.09017 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{3} + 2 q^{5} - q^{7} - 3 q^{9}+O(q^{10})$$ 2 * q - q^3 + 2 * q^5 - q^7 - 3 * q^9 $$2 q - q^{3} + 2 q^{5} - q^{7} - 3 q^{9} - q^{11} - 3 q^{13} - q^{15} + q^{17} + 3 q^{19} - 2 q^{21} - 2 q^{23} + 2 q^{25} + 2 q^{27} - 14 q^{29} - 7 q^{31} - 7 q^{33} - q^{35} + 4 q^{37} + 14 q^{39} - 9 q^{41} - 3 q^{45} - 6 q^{47} - 11 q^{49} - 13 q^{51} - 8 q^{53} - q^{55} + 6 q^{57} + 10 q^{59} - 3 q^{61} + 4 q^{63} - 3 q^{65} - 20 q^{67} + q^{69} - 3 q^{71} + 2 q^{73} - q^{75} + 8 q^{77} - 12 q^{79} - 2 q^{81} - 4 q^{83} + q^{85} + 12 q^{87} - 12 q^{89} - 11 q^{91} + 16 q^{93} + 3 q^{95} + 27 q^{97} + 9 q^{99}+O(q^{100})$$ 2 * q - q^3 + 2 * q^5 - q^7 - 3 * q^9 - q^11 - 3 * q^13 - q^15 + q^17 + 3 * q^19 - 2 * q^21 - 2 * q^23 + 2 * q^25 + 2 * q^27 - 14 * q^29 - 7 * q^31 - 7 * q^33 - q^35 + 4 * q^37 + 14 * q^39 - 9 * q^41 - 3 * q^45 - 6 * q^47 - 11 * q^49 - 13 * q^51 - 8 * q^53 - q^55 + 6 * q^57 + 10 * q^59 - 3 * q^61 + 4 * q^63 - 3 * q^65 - 20 * q^67 + q^69 - 3 * q^71 + 2 * q^73 - q^75 + 8 * q^77 - 12 * q^79 - 2 * q^81 - 4 * q^83 + q^85 + 12 * q^87 - 12 * q^89 - 11 * q^91 + 16 * q^93 + 3 * q^95 + 27 * q^97 + 9 * q^99

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.61803 −0.934172 −0.467086 0.884212i $$-0.654696\pi$$
−0.467086 + 0.884212i $$0.654696\pi$$
$$4$$ 0 0
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 0.618034 0.233595 0.116797 0.993156i $$-0.462737\pi$$
0.116797 + 0.993156i $$0.462737\pi$$
$$8$$ 0 0
$$9$$ −0.381966 −0.127322
$$10$$ 0 0
$$11$$ 2.85410 0.860544 0.430272 0.902699i $$-0.358418\pi$$
0.430272 + 0.902699i $$0.358418\pi$$
$$12$$ 0 0
$$13$$ −7.09017 −1.96646 −0.983230 0.182372i $$-0.941623\pi$$
−0.983230 + 0.182372i $$0.941623\pi$$
$$14$$ 0 0
$$15$$ −1.61803 −0.417775
$$16$$ 0 0
$$17$$ 6.09017 1.47708 0.738542 0.674208i $$-0.235515\pi$$
0.738542 + 0.674208i $$0.235515\pi$$
$$18$$ 0 0
$$19$$ −1.85410 −0.425360 −0.212680 0.977122i $$-0.568219\pi$$
−0.212680 + 0.977122i $$0.568219\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 5.47214 1.05311
$$28$$ 0 0
$$29$$ −9.23607 −1.71509 −0.857547 0.514405i $$-0.828013\pi$$
−0.857547 + 0.514405i $$0.828013\pi$$
$$30$$ 0 0
$$31$$ −9.09017 −1.63264 −0.816321 0.577598i $$-0.803990\pi$$
−0.816321 + 0.577598i $$0.803990\pi$$
$$32$$ 0 0
$$33$$ −4.61803 −0.803897
$$34$$ 0 0
$$35$$ 0.618034 0.104467
$$36$$ 0 0
$$37$$ 6.47214 1.06401 0.532006 0.846740i $$-0.321438\pi$$
0.532006 + 0.846740i $$0.321438\pi$$
$$38$$ 0 0
$$39$$ 11.4721 1.83701
$$40$$ 0 0
$$41$$ 3.32624 0.519471 0.259736 0.965680i $$-0.416365\pi$$
0.259736 + 0.965680i $$0.416365\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ −0.381966 −0.0569401
$$46$$ 0 0
$$47$$ 3.70820 0.540897 0.270449 0.962734i $$-0.412828\pi$$
0.270449 + 0.962734i $$0.412828\pi$$
$$48$$ 0 0
$$49$$ −6.61803 −0.945433
$$50$$ 0 0
$$51$$ −9.85410 −1.37985
$$52$$ 0 0
$$53$$ 0.472136 0.0648529 0.0324264 0.999474i $$-0.489677\pi$$
0.0324264 + 0.999474i $$0.489677\pi$$
$$54$$ 0 0
$$55$$ 2.85410 0.384847
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ −1.70820 −0.222389 −0.111195 0.993799i $$-0.535468\pi$$
−0.111195 + 0.993799i $$0.535468\pi$$
$$60$$ 0 0
$$61$$ −9.32624 −1.19410 −0.597051 0.802203i $$-0.703661\pi$$
−0.597051 + 0.802203i $$0.703661\pi$$
$$62$$ 0 0
$$63$$ −0.236068 −0.0297418
$$64$$ 0 0
$$65$$ −7.09017 −0.879427
$$66$$ 0 0
$$67$$ −14.4721 −1.76805 −0.884026 0.467437i $$-0.845177\pi$$
−0.884026 + 0.467437i $$0.845177\pi$$
$$68$$ 0 0
$$69$$ 1.61803 0.194788
$$70$$ 0 0
$$71$$ 4.09017 0.485414 0.242707 0.970100i $$-0.421965\pi$$
0.242707 + 0.970100i $$0.421965\pi$$
$$72$$ 0 0
$$73$$ 3.23607 0.378753 0.189377 0.981905i $$-0.439353\pi$$
0.189377 + 0.981905i $$0.439353\pi$$
$$74$$ 0 0
$$75$$ −1.61803 −0.186834
$$76$$ 0 0
$$77$$ 1.76393 0.201019
$$78$$ 0 0
$$79$$ −1.52786 −0.171898 −0.0859491 0.996300i $$-0.527392\pi$$
−0.0859491 + 0.996300i $$0.527392\pi$$
$$80$$ 0 0
$$81$$ −7.70820 −0.856467
$$82$$ 0 0
$$83$$ 6.94427 0.762233 0.381116 0.924527i $$-0.375540\pi$$
0.381116 + 0.924527i $$0.375540\pi$$
$$84$$ 0 0
$$85$$ 6.09017 0.660572
$$86$$ 0 0
$$87$$ 14.9443 1.60219
$$88$$ 0 0
$$89$$ −10.4721 −1.11004 −0.555022 0.831836i $$-0.687290\pi$$
−0.555022 + 0.831836i $$0.687290\pi$$
$$90$$ 0 0
$$91$$ −4.38197 −0.459355
$$92$$ 0 0
$$93$$ 14.7082 1.52517
$$94$$ 0 0
$$95$$ −1.85410 −0.190227
$$96$$ 0 0
$$97$$ 12.3820 1.25720 0.628599 0.777730i $$-0.283629\pi$$
0.628599 + 0.777730i $$0.283629\pi$$
$$98$$ 0 0
$$99$$ −1.09017 −0.109566
$$100$$ 0 0
$$101$$ −0.291796 −0.0290348 −0.0145174 0.999895i $$-0.504621\pi$$
−0.0145174 + 0.999895i $$0.504621\pi$$
$$102$$ 0 0
$$103$$ −16.5623 −1.63193 −0.815966 0.578100i $$-0.803795\pi$$
−0.815966 + 0.578100i $$0.803795\pi$$
$$104$$ 0 0
$$105$$ −1.00000 −0.0975900
$$106$$ 0 0
$$107$$ −18.1803 −1.75756 −0.878780 0.477227i $$-0.841642\pi$$
−0.878780 + 0.477227i $$0.841642\pi$$
$$108$$ 0 0
$$109$$ −11.5623 −1.10747 −0.553734 0.832694i $$-0.686798\pi$$
−0.553734 + 0.832694i $$0.686798\pi$$
$$110$$ 0 0
$$111$$ −10.4721 −0.993971
$$112$$ 0 0
$$113$$ 1.05573 0.0993145 0.0496573 0.998766i $$-0.484187\pi$$
0.0496573 + 0.998766i $$0.484187\pi$$
$$114$$ 0 0
$$115$$ −1.00000 −0.0932505
$$116$$ 0 0
$$117$$ 2.70820 0.250374
$$118$$ 0 0
$$119$$ 3.76393 0.345039
$$120$$ 0 0
$$121$$ −2.85410 −0.259464
$$122$$ 0 0
$$123$$ −5.38197 −0.485276
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −16.1803 −1.43577 −0.717886 0.696160i $$-0.754890\pi$$
−0.717886 + 0.696160i $$0.754890\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −2.94427 −0.257242 −0.128621 0.991694i $$-0.541055\pi$$
−0.128621 + 0.991694i $$0.541055\pi$$
$$132$$ 0 0
$$133$$ −1.14590 −0.0993620
$$134$$ 0 0
$$135$$ 5.47214 0.470966
$$136$$ 0 0
$$137$$ −10.3262 −0.882230 −0.441115 0.897451i $$-0.645417\pi$$
−0.441115 + 0.897451i $$0.645417\pi$$
$$138$$ 0 0
$$139$$ −12.7639 −1.08262 −0.541311 0.840822i $$-0.682072\pi$$
−0.541311 + 0.840822i $$0.682072\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ −20.2361 −1.69223
$$144$$ 0 0
$$145$$ −9.23607 −0.767014
$$146$$ 0 0
$$147$$ 10.7082 0.883198
$$148$$ 0 0
$$149$$ −7.85410 −0.643433 −0.321717 0.946836i $$-0.604260\pi$$
−0.321717 + 0.946836i $$0.604260\pi$$
$$150$$ 0 0
$$151$$ 2.56231 0.208517 0.104259 0.994550i $$-0.466753\pi$$
0.104259 + 0.994550i $$0.466753\pi$$
$$152$$ 0 0
$$153$$ −2.32624 −0.188065
$$154$$ 0 0
$$155$$ −9.09017 −0.730140
$$156$$ 0 0
$$157$$ −3.70820 −0.295947 −0.147973 0.988991i $$-0.547275\pi$$
−0.147973 + 0.988991i $$0.547275\pi$$
$$158$$ 0 0
$$159$$ −0.763932 −0.0605838
$$160$$ 0 0
$$161$$ −0.618034 −0.0487079
$$162$$ 0 0
$$163$$ −1.38197 −0.108244 −0.0541220 0.998534i $$-0.517236\pi$$
−0.0541220 + 0.998534i $$0.517236\pi$$
$$164$$ 0 0
$$165$$ −4.61803 −0.359513
$$166$$ 0 0
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 37.2705 2.86696
$$170$$ 0 0
$$171$$ 0.708204 0.0541577
$$172$$ 0 0
$$173$$ −1.43769 −0.109306 −0.0546529 0.998505i $$-0.517405\pi$$
−0.0546529 + 0.998505i $$0.517405\pi$$
$$174$$ 0 0
$$175$$ 0.618034 0.0467190
$$176$$ 0 0
$$177$$ 2.76393 0.207750
$$178$$ 0 0
$$179$$ −2.18034 −0.162966 −0.0814831 0.996675i $$-0.525966\pi$$
−0.0814831 + 0.996675i $$0.525966\pi$$
$$180$$ 0 0
$$181$$ −12.1459 −0.902797 −0.451399 0.892322i $$-0.649075\pi$$
−0.451399 + 0.892322i $$0.649075\pi$$
$$182$$ 0 0
$$183$$ 15.0902 1.11550
$$184$$ 0 0
$$185$$ 6.47214 0.475841
$$186$$ 0 0
$$187$$ 17.3820 1.27110
$$188$$ 0 0
$$189$$ 3.38197 0.246002
$$190$$ 0 0
$$191$$ 13.7082 0.991891 0.495945 0.868354i $$-0.334822\pi$$
0.495945 + 0.868354i $$0.334822\pi$$
$$192$$ 0 0
$$193$$ 0.763932 0.0549890 0.0274945 0.999622i $$-0.491247\pi$$
0.0274945 + 0.999622i $$0.491247\pi$$
$$194$$ 0 0
$$195$$ 11.4721 0.821537
$$196$$ 0 0
$$197$$ −22.5623 −1.60750 −0.803749 0.594969i $$-0.797164\pi$$
−0.803749 + 0.594969i $$0.797164\pi$$
$$198$$ 0 0
$$199$$ −2.00000 −0.141776 −0.0708881 0.997484i $$-0.522583\pi$$
−0.0708881 + 0.997484i $$0.522583\pi$$
$$200$$ 0 0
$$201$$ 23.4164 1.65167
$$202$$ 0 0
$$203$$ −5.70820 −0.400637
$$204$$ 0 0
$$205$$ 3.32624 0.232315
$$206$$ 0 0
$$207$$ 0.381966 0.0265485
$$208$$ 0 0
$$209$$ −5.29180 −0.366041
$$210$$ 0 0
$$211$$ −14.0000 −0.963800 −0.481900 0.876226i $$-0.660053\pi$$
−0.481900 + 0.876226i $$0.660053\pi$$
$$212$$ 0 0
$$213$$ −6.61803 −0.453460
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −5.61803 −0.381377
$$218$$ 0 0
$$219$$ −5.23607 −0.353821
$$220$$ 0 0
$$221$$ −43.1803 −2.90462
$$222$$ 0 0
$$223$$ 20.9443 1.40253 0.701266 0.712900i $$-0.252618\pi$$
0.701266 + 0.712900i $$0.252618\pi$$
$$224$$ 0 0
$$225$$ −0.381966 −0.0254644
$$226$$ 0 0
$$227$$ 18.7639 1.24541 0.622703 0.782458i $$-0.286035\pi$$
0.622703 + 0.782458i $$0.286035\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ −2.85410 −0.187786
$$232$$ 0 0
$$233$$ 6.29180 0.412189 0.206095 0.978532i $$-0.433925\pi$$
0.206095 + 0.978532i $$0.433925\pi$$
$$234$$ 0 0
$$235$$ 3.70820 0.241897
$$236$$ 0 0
$$237$$ 2.47214 0.160582
$$238$$ 0 0
$$239$$ 20.3607 1.31702 0.658511 0.752571i $$-0.271186\pi$$
0.658511 + 0.752571i $$0.271186\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 0 0
$$243$$ −3.94427 −0.253025
$$244$$ 0 0
$$245$$ −6.61803 −0.422811
$$246$$ 0 0
$$247$$ 13.1459 0.836453
$$248$$ 0 0
$$249$$ −11.2361 −0.712057
$$250$$ 0 0
$$251$$ −6.14590 −0.387926 −0.193963 0.981009i $$-0.562134\pi$$
−0.193963 + 0.981009i $$0.562134\pi$$
$$252$$ 0 0
$$253$$ −2.85410 −0.179436
$$254$$ 0 0
$$255$$ −9.85410 −0.617088
$$256$$ 0 0
$$257$$ −7.81966 −0.487777 −0.243888 0.969803i $$-0.578423\pi$$
−0.243888 + 0.969803i $$0.578423\pi$$
$$258$$ 0 0
$$259$$ 4.00000 0.248548
$$260$$ 0 0
$$261$$ 3.52786 0.218369
$$262$$ 0 0
$$263$$ −20.7426 −1.27905 −0.639523 0.768772i $$-0.720868\pi$$
−0.639523 + 0.768772i $$0.720868\pi$$
$$264$$ 0 0
$$265$$ 0.472136 0.0290031
$$266$$ 0 0
$$267$$ 16.9443 1.03697
$$268$$ 0 0
$$269$$ −14.1803 −0.864591 −0.432295 0.901732i $$-0.642296\pi$$
−0.432295 + 0.901732i $$0.642296\pi$$
$$270$$ 0 0
$$271$$ 30.3262 1.84219 0.921094 0.389341i $$-0.127297\pi$$
0.921094 + 0.389341i $$0.127297\pi$$
$$272$$ 0 0
$$273$$ 7.09017 0.429117
$$274$$ 0 0
$$275$$ 2.85410 0.172109
$$276$$ 0 0
$$277$$ 29.4164 1.76746 0.883730 0.467996i $$-0.155024\pi$$
0.883730 + 0.467996i $$0.155024\pi$$
$$278$$ 0 0
$$279$$ 3.47214 0.207871
$$280$$ 0 0
$$281$$ 22.7639 1.35798 0.678991 0.734146i $$-0.262417\pi$$
0.678991 + 0.734146i $$0.262417\pi$$
$$282$$ 0 0
$$283$$ 26.9443 1.60167 0.800835 0.598885i $$-0.204389\pi$$
0.800835 + 0.598885i $$0.204389\pi$$
$$284$$ 0 0
$$285$$ 3.00000 0.177705
$$286$$ 0 0
$$287$$ 2.05573 0.121346
$$288$$ 0 0
$$289$$ 20.0902 1.18177
$$290$$ 0 0
$$291$$ −20.0344 −1.17444
$$292$$ 0 0
$$293$$ −19.8885 −1.16190 −0.580951 0.813939i $$-0.697319\pi$$
−0.580951 + 0.813939i $$0.697319\pi$$
$$294$$ 0 0
$$295$$ −1.70820 −0.0994555
$$296$$ 0 0
$$297$$ 15.6180 0.906250
$$298$$ 0 0
$$299$$ 7.09017 0.410035
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0.472136 0.0271235
$$304$$ 0 0
$$305$$ −9.32624 −0.534019
$$306$$ 0 0
$$307$$ 28.4508 1.62378 0.811888 0.583813i $$-0.198440\pi$$
0.811888 + 0.583813i $$0.198440\pi$$
$$308$$ 0 0
$$309$$ 26.7984 1.52451
$$310$$ 0 0
$$311$$ −4.00000 −0.226819 −0.113410 0.993548i $$-0.536177\pi$$
−0.113410 + 0.993548i $$0.536177\pi$$
$$312$$ 0 0
$$313$$ 12.7984 0.723407 0.361703 0.932293i $$-0.382195\pi$$
0.361703 + 0.932293i $$0.382195\pi$$
$$314$$ 0 0
$$315$$ −0.236068 −0.0133009
$$316$$ 0 0
$$317$$ −11.0902 −0.622886 −0.311443 0.950265i $$-0.600812\pi$$
−0.311443 + 0.950265i $$0.600812\pi$$
$$318$$ 0 0
$$319$$ −26.3607 −1.47591
$$320$$ 0 0
$$321$$ 29.4164 1.64186
$$322$$ 0 0
$$323$$ −11.2918 −0.628292
$$324$$ 0 0
$$325$$ −7.09017 −0.393292
$$326$$ 0 0
$$327$$ 18.7082 1.03457
$$328$$ 0 0
$$329$$ 2.29180 0.126351
$$330$$ 0 0
$$331$$ −19.2361 −1.05731 −0.528655 0.848837i $$-0.677303\pi$$
−0.528655 + 0.848837i $$0.677303\pi$$
$$332$$ 0 0
$$333$$ −2.47214 −0.135472
$$334$$ 0 0
$$335$$ −14.4721 −0.790697
$$336$$ 0 0
$$337$$ 13.6738 0.744857 0.372429 0.928061i $$-0.378525\pi$$
0.372429 + 0.928061i $$0.378525\pi$$
$$338$$ 0 0
$$339$$ −1.70820 −0.0927769
$$340$$ 0 0
$$341$$ −25.9443 −1.40496
$$342$$ 0 0
$$343$$ −8.41641 −0.454443
$$344$$ 0 0
$$345$$ 1.61803 0.0871120
$$346$$ 0 0
$$347$$ 6.38197 0.342602 0.171301 0.985219i $$-0.445203\pi$$
0.171301 + 0.985219i $$0.445203\pi$$
$$348$$ 0 0
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 0 0
$$351$$ −38.7984 −2.07090
$$352$$ 0 0
$$353$$ 24.0000 1.27739 0.638696 0.769460i $$-0.279474\pi$$
0.638696 + 0.769460i $$0.279474\pi$$
$$354$$ 0 0
$$355$$ 4.09017 0.217084
$$356$$ 0 0
$$357$$ −6.09017 −0.322326
$$358$$ 0 0
$$359$$ −26.3607 −1.39126 −0.695632 0.718399i $$-0.744875\pi$$
−0.695632 + 0.718399i $$0.744875\pi$$
$$360$$ 0 0
$$361$$ −15.5623 −0.819069
$$362$$ 0 0
$$363$$ 4.61803 0.242384
$$364$$ 0 0
$$365$$ 3.23607 0.169384
$$366$$ 0 0
$$367$$ −6.47214 −0.337843 −0.168921 0.985630i $$-0.554028\pi$$
−0.168921 + 0.985630i $$0.554028\pi$$
$$368$$ 0 0
$$369$$ −1.27051 −0.0661401
$$370$$ 0 0
$$371$$ 0.291796 0.0151493
$$372$$ 0 0
$$373$$ 20.1803 1.04490 0.522449 0.852670i $$-0.325018\pi$$
0.522449 + 0.852670i $$0.325018\pi$$
$$374$$ 0 0
$$375$$ −1.61803 −0.0835549
$$376$$ 0 0
$$377$$ 65.4853 3.37266
$$378$$ 0 0
$$379$$ 22.4508 1.15322 0.576611 0.817019i $$-0.304375\pi$$
0.576611 + 0.817019i $$0.304375\pi$$
$$380$$ 0 0
$$381$$ 26.1803 1.34126
$$382$$ 0 0
$$383$$ 17.8885 0.914062 0.457031 0.889451i $$-0.348913\pi$$
0.457031 + 0.889451i $$0.348913\pi$$
$$384$$ 0 0
$$385$$ 1.76393 0.0898983
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 21.3262 1.08128 0.540642 0.841253i $$-0.318182\pi$$
0.540642 + 0.841253i $$0.318182\pi$$
$$390$$ 0 0
$$391$$ −6.09017 −0.307993
$$392$$ 0 0
$$393$$ 4.76393 0.240309
$$394$$ 0 0
$$395$$ −1.52786 −0.0768752
$$396$$ 0 0
$$397$$ 7.32624 0.367693 0.183847 0.982955i $$-0.441145\pi$$
0.183847 + 0.982955i $$0.441145\pi$$
$$398$$ 0 0
$$399$$ 1.85410 0.0928212
$$400$$ 0 0
$$401$$ −1.70820 −0.0853036 −0.0426518 0.999090i $$-0.513581\pi$$
−0.0426518 + 0.999090i $$0.513581\pi$$
$$402$$ 0 0
$$403$$ 64.4508 3.21053
$$404$$ 0 0
$$405$$ −7.70820 −0.383024
$$406$$ 0 0
$$407$$ 18.4721 0.915630
$$408$$ 0 0
$$409$$ −30.2148 −1.49402 −0.747012 0.664810i $$-0.768512\pi$$
−0.747012 + 0.664810i $$0.768512\pi$$
$$410$$ 0 0
$$411$$ 16.7082 0.824155
$$412$$ 0 0
$$413$$ −1.05573 −0.0519490
$$414$$ 0 0
$$415$$ 6.94427 0.340881
$$416$$ 0 0
$$417$$ 20.6525 1.01136
$$418$$ 0 0
$$419$$ −14.4721 −0.707010 −0.353505 0.935433i $$-0.615010\pi$$
−0.353505 + 0.935433i $$0.615010\pi$$
$$420$$ 0 0
$$421$$ 13.7426 0.669776 0.334888 0.942258i $$-0.391302\pi$$
0.334888 + 0.942258i $$0.391302\pi$$
$$422$$ 0 0
$$423$$ −1.41641 −0.0688681
$$424$$ 0 0
$$425$$ 6.09017 0.295417
$$426$$ 0 0
$$427$$ −5.76393 −0.278936
$$428$$ 0 0
$$429$$ 32.7426 1.58083
$$430$$ 0 0
$$431$$ −3.34752 −0.161245 −0.0806223 0.996745i $$-0.525691\pi$$
−0.0806223 + 0.996745i $$0.525691\pi$$
$$432$$ 0 0
$$433$$ 8.50658 0.408800 0.204400 0.978887i $$-0.434476\pi$$
0.204400 + 0.978887i $$0.434476\pi$$
$$434$$ 0 0
$$435$$ 14.9443 0.716523
$$436$$ 0 0
$$437$$ 1.85410 0.0886937
$$438$$ 0 0
$$439$$ 13.3820 0.638686 0.319343 0.947639i $$-0.396538\pi$$
0.319343 + 0.947639i $$0.396538\pi$$
$$440$$ 0 0
$$441$$ 2.52786 0.120374
$$442$$ 0 0
$$443$$ −25.0902 −1.19207 −0.596035 0.802958i $$-0.703258\pi$$
−0.596035 + 0.802958i $$0.703258\pi$$
$$444$$ 0 0
$$445$$ −10.4721 −0.496427
$$446$$ 0 0
$$447$$ 12.7082 0.601077
$$448$$ 0 0
$$449$$ −1.56231 −0.0737298 −0.0368649 0.999320i $$-0.511737\pi$$
−0.0368649 + 0.999320i $$0.511737\pi$$
$$450$$ 0 0
$$451$$ 9.49342 0.447028
$$452$$ 0 0
$$453$$ −4.14590 −0.194791
$$454$$ 0 0
$$455$$ −4.38197 −0.205430
$$456$$ 0 0
$$457$$ −37.7771 −1.76714 −0.883569 0.468301i $$-0.844866\pi$$
−0.883569 + 0.468301i $$0.844866\pi$$
$$458$$ 0 0
$$459$$ 33.3262 1.55554
$$460$$ 0 0
$$461$$ −39.2361 −1.82741 −0.913703 0.406383i $$-0.866790\pi$$
−0.913703 + 0.406383i $$0.866790\pi$$
$$462$$ 0 0
$$463$$ −2.00000 −0.0929479 −0.0464739 0.998920i $$-0.514798\pi$$
−0.0464739 + 0.998920i $$0.514798\pi$$
$$464$$ 0 0
$$465$$ 14.7082 0.682077
$$466$$ 0 0
$$467$$ 17.1246 0.792433 0.396216 0.918157i $$-0.370323\pi$$
0.396216 + 0.918157i $$0.370323\pi$$
$$468$$ 0 0
$$469$$ −8.94427 −0.413008
$$470$$ 0 0
$$471$$ 6.00000 0.276465
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −1.85410 −0.0850720
$$476$$ 0 0
$$477$$ −0.180340 −0.00825720
$$478$$ 0 0
$$479$$ 31.8885 1.45702 0.728512 0.685033i $$-0.240212\pi$$
0.728512 + 0.685033i $$0.240212\pi$$
$$480$$ 0 0
$$481$$ −45.8885 −2.09234
$$482$$ 0 0
$$483$$ 1.00000 0.0455016
$$484$$ 0 0
$$485$$ 12.3820 0.562236
$$486$$ 0 0
$$487$$ 19.8197 0.898115 0.449057 0.893503i $$-0.351760\pi$$
0.449057 + 0.893503i $$0.351760\pi$$
$$488$$ 0 0
$$489$$ 2.23607 0.101118
$$490$$ 0 0
$$491$$ −6.18034 −0.278915 −0.139457 0.990228i $$-0.544536\pi$$
−0.139457 + 0.990228i $$0.544536\pi$$
$$492$$ 0 0
$$493$$ −56.2492 −2.53334
$$494$$ 0 0
$$495$$ −1.09017 −0.0489995
$$496$$ 0 0
$$497$$ 2.52786 0.113390
$$498$$ 0 0
$$499$$ −12.3607 −0.553340 −0.276670 0.960965i $$-0.589231\pi$$
−0.276670 + 0.960965i $$0.589231\pi$$
$$500$$ 0 0
$$501$$ −12.9443 −0.578307
$$502$$ 0 0
$$503$$ −36.3262 −1.61971 −0.809853 0.586632i $$-0.800453\pi$$
−0.809853 + 0.586632i $$0.800453\pi$$
$$504$$ 0 0
$$505$$ −0.291796 −0.0129848
$$506$$ 0 0
$$507$$ −60.3050 −2.67824
$$508$$ 0 0
$$509$$ 36.6525 1.62459 0.812296 0.583245i $$-0.198217\pi$$
0.812296 + 0.583245i $$0.198217\pi$$
$$510$$ 0 0
$$511$$ 2.00000 0.0884748
$$512$$ 0 0
$$513$$ −10.1459 −0.447952
$$514$$ 0 0
$$515$$ −16.5623 −0.729822
$$516$$ 0 0
$$517$$ 10.5836 0.465466
$$518$$ 0 0
$$519$$ 2.32624 0.102111
$$520$$ 0 0
$$521$$ −15.5279 −0.680288 −0.340144 0.940373i $$-0.610476\pi$$
−0.340144 + 0.940373i $$0.610476\pi$$
$$522$$ 0 0
$$523$$ 26.0000 1.13690 0.568450 0.822718i $$-0.307543\pi$$
0.568450 + 0.822718i $$0.307543\pi$$
$$524$$ 0 0
$$525$$ −1.00000 −0.0436436
$$526$$ 0 0
$$527$$ −55.3607 −2.41155
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 0.652476 0.0283150
$$532$$ 0 0
$$533$$ −23.5836 −1.02152
$$534$$ 0 0
$$535$$ −18.1803 −0.786005
$$536$$ 0 0
$$537$$ 3.52786 0.152239
$$538$$ 0 0
$$539$$ −18.8885 −0.813587
$$540$$ 0 0
$$541$$ 22.8328 0.981659 0.490830 0.871256i $$-0.336694\pi$$
0.490830 + 0.871256i $$0.336694\pi$$
$$542$$ 0 0
$$543$$ 19.6525 0.843368
$$544$$ 0 0
$$545$$ −11.5623 −0.495275
$$546$$ 0 0
$$547$$ −27.9230 −1.19390 −0.596950 0.802278i $$-0.703621\pi$$
−0.596950 + 0.802278i $$0.703621\pi$$
$$548$$ 0 0
$$549$$ 3.56231 0.152036
$$550$$ 0 0
$$551$$ 17.1246 0.729533
$$552$$ 0 0
$$553$$ −0.944272 −0.0401545
$$554$$ 0 0
$$555$$ −10.4721 −0.444517
$$556$$ 0 0
$$557$$ −22.8328 −0.967457 −0.483729 0.875218i $$-0.660718\pi$$
−0.483729 + 0.875218i $$0.660718\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −28.1246 −1.18742
$$562$$ 0 0
$$563$$ 13.8885 0.585332 0.292666 0.956215i $$-0.405458\pi$$
0.292666 + 0.956215i $$0.405458\pi$$
$$564$$ 0 0
$$565$$ 1.05573 0.0444148
$$566$$ 0 0
$$567$$ −4.76393 −0.200066
$$568$$ 0 0
$$569$$ −2.00000 −0.0838444 −0.0419222 0.999121i $$-0.513348\pi$$
−0.0419222 + 0.999121i $$0.513348\pi$$
$$570$$ 0 0
$$571$$ −15.9787 −0.668688 −0.334344 0.942451i $$-0.608515\pi$$
−0.334344 + 0.942451i $$0.608515\pi$$
$$572$$ 0 0
$$573$$ −22.1803 −0.926597
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −3.52786 −0.146867 −0.0734335 0.997300i $$-0.523396\pi$$
−0.0734335 + 0.997300i $$0.523396\pi$$
$$578$$ 0 0
$$579$$ −1.23607 −0.0513692
$$580$$ 0 0
$$581$$ 4.29180 0.178054
$$582$$ 0 0
$$583$$ 1.34752 0.0558087
$$584$$ 0 0
$$585$$ 2.70820 0.111970
$$586$$ 0 0
$$587$$ −13.6180 −0.562076 −0.281038 0.959697i $$-0.590679\pi$$
−0.281038 + 0.959697i $$0.590679\pi$$
$$588$$ 0 0
$$589$$ 16.8541 0.694461
$$590$$ 0 0
$$591$$ 36.5066 1.50168
$$592$$ 0 0
$$593$$ 39.2361 1.61123 0.805616 0.592438i $$-0.201834\pi$$
0.805616 + 0.592438i $$0.201834\pi$$
$$594$$ 0 0
$$595$$ 3.76393 0.154306
$$596$$ 0 0
$$597$$ 3.23607 0.132443
$$598$$ 0 0
$$599$$ 18.3820 0.751067 0.375533 0.926809i $$-0.377460\pi$$
0.375533 + 0.926809i $$0.377460\pi$$
$$600$$ 0 0
$$601$$ −33.2705 −1.35713 −0.678566 0.734539i $$-0.737398\pi$$
−0.678566 + 0.734539i $$0.737398\pi$$
$$602$$ 0 0
$$603$$ 5.52786 0.225112
$$604$$ 0 0
$$605$$ −2.85410 −0.116036
$$606$$ 0 0
$$607$$ −26.4721 −1.07447 −0.537235 0.843432i $$-0.680531\pi$$
−0.537235 + 0.843432i $$0.680531\pi$$
$$608$$ 0 0
$$609$$ 9.23607 0.374264
$$610$$ 0 0
$$611$$ −26.2918 −1.06365
$$612$$ 0 0
$$613$$ 19.3050 0.779720 0.389860 0.920874i $$-0.372523\pi$$
0.389860 + 0.920874i $$0.372523\pi$$
$$614$$ 0 0
$$615$$ −5.38197 −0.217022
$$616$$ 0 0
$$617$$ 34.0902 1.37242 0.686209 0.727404i $$-0.259273\pi$$
0.686209 + 0.727404i $$0.259273\pi$$
$$618$$ 0 0
$$619$$ 2.79837 0.112476 0.0562381 0.998417i $$-0.482089\pi$$
0.0562381 + 0.998417i $$0.482089\pi$$
$$620$$ 0 0
$$621$$ −5.47214 −0.219589
$$622$$ 0 0
$$623$$ −6.47214 −0.259301
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 8.56231 0.341946
$$628$$ 0 0
$$629$$ 39.4164 1.57164
$$630$$ 0 0
$$631$$ −42.0689 −1.67474 −0.837368 0.546640i $$-0.815907\pi$$
−0.837368 + 0.546640i $$0.815907\pi$$
$$632$$ 0 0
$$633$$ 22.6525 0.900355
$$634$$ 0 0
$$635$$ −16.1803 −0.642097
$$636$$ 0 0
$$637$$ 46.9230 1.85916
$$638$$ 0 0
$$639$$ −1.56231 −0.0618039
$$640$$ 0 0
$$641$$ 0.360680 0.0142460 0.00712300 0.999975i $$-0.497733\pi$$
0.00712300 + 0.999975i $$0.497733\pi$$
$$642$$ 0 0
$$643$$ 8.29180 0.326997 0.163498 0.986544i $$-0.447722\pi$$
0.163498 + 0.986544i $$0.447722\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 36.2492 1.42510 0.712552 0.701619i $$-0.247539\pi$$
0.712552 + 0.701619i $$0.247539\pi$$
$$648$$ 0 0
$$649$$ −4.87539 −0.191376
$$650$$ 0 0
$$651$$ 9.09017 0.356272
$$652$$ 0 0
$$653$$ −8.03444 −0.314412 −0.157206 0.987566i $$-0.550249\pi$$
−0.157206 + 0.987566i $$0.550249\pi$$
$$654$$ 0 0
$$655$$ −2.94427 −0.115042
$$656$$ 0 0
$$657$$ −1.23607 −0.0482236
$$658$$ 0 0
$$659$$ 46.2492 1.80161 0.900807 0.434220i $$-0.142976\pi$$
0.900807 + 0.434220i $$0.142976\pi$$
$$660$$ 0 0
$$661$$ 18.6738 0.726325 0.363163 0.931726i $$-0.381697\pi$$
0.363163 + 0.931726i $$0.381697\pi$$
$$662$$ 0 0
$$663$$ 69.8673 2.71342
$$664$$ 0 0
$$665$$ −1.14590 −0.0444360
$$666$$ 0 0
$$667$$ 9.23607 0.357622
$$668$$ 0 0
$$669$$ −33.8885 −1.31021
$$670$$ 0 0
$$671$$ −26.6180 −1.02758
$$672$$ 0 0
$$673$$ −10.9443 −0.421871 −0.210935 0.977500i $$-0.567651\pi$$
−0.210935 + 0.977500i $$0.567651\pi$$
$$674$$ 0 0
$$675$$ 5.47214 0.210623
$$676$$ 0 0
$$677$$ −50.9443 −1.95795 −0.978974 0.203986i $$-0.934610\pi$$
−0.978974 + 0.203986i $$0.934610\pi$$
$$678$$ 0 0
$$679$$ 7.65248 0.293675
$$680$$ 0 0
$$681$$ −30.3607 −1.16342
$$682$$ 0 0
$$683$$ 31.5623 1.20770 0.603849 0.797099i $$-0.293633\pi$$
0.603849 + 0.797099i $$0.293633\pi$$
$$684$$ 0 0
$$685$$ −10.3262 −0.394545
$$686$$ 0 0
$$687$$ −16.1803 −0.617318
$$688$$ 0 0
$$689$$ −3.34752 −0.127531
$$690$$ 0 0
$$691$$ 29.2361 1.11219 0.556096 0.831118i $$-0.312299\pi$$
0.556096 + 0.831118i $$0.312299\pi$$
$$692$$ 0 0
$$693$$ −0.673762 −0.0255941
$$694$$ 0 0
$$695$$ −12.7639 −0.484164
$$696$$ 0 0
$$697$$ 20.2574 0.767302
$$698$$ 0 0
$$699$$ −10.1803 −0.385056
$$700$$ 0 0
$$701$$ 43.3394 1.63691 0.818453 0.574573i $$-0.194832\pi$$
0.818453 + 0.574573i $$0.194832\pi$$
$$702$$ 0 0
$$703$$ −12.0000 −0.452589
$$704$$ 0 0
$$705$$ −6.00000 −0.225973
$$706$$ 0 0
$$707$$ −0.180340 −0.00678238
$$708$$ 0 0
$$709$$ −26.0902 −0.979837 −0.489918 0.871768i $$-0.662973\pi$$
−0.489918 + 0.871768i $$0.662973\pi$$
$$710$$ 0 0
$$711$$ 0.583592 0.0218864
$$712$$ 0 0
$$713$$ 9.09017 0.340430
$$714$$ 0 0
$$715$$ −20.2361 −0.756786
$$716$$ 0 0
$$717$$ −32.9443 −1.23033
$$718$$ 0 0
$$719$$ −35.2705 −1.31537 −0.657684 0.753294i $$-0.728464\pi$$
−0.657684 + 0.753294i $$0.728464\pi$$
$$720$$ 0 0
$$721$$ −10.2361 −0.381211
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −9.23607 −0.343019
$$726$$ 0 0
$$727$$ −28.2016 −1.04594 −0.522970 0.852351i $$-0.675176\pi$$
−0.522970 + 0.852351i $$0.675176\pi$$
$$728$$ 0 0
$$729$$ 29.5066 1.09284
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −29.4164 −1.08652 −0.543260 0.839565i $$-0.682810\pi$$
−0.543260 + 0.839565i $$0.682810\pi$$
$$734$$ 0 0
$$735$$ 10.7082 0.394978
$$736$$ 0 0
$$737$$ −41.3050 −1.52149
$$738$$ 0 0
$$739$$ 13.8885 0.510898 0.255449 0.966822i $$-0.417777\pi$$
0.255449 + 0.966822i $$0.417777\pi$$
$$740$$ 0 0
$$741$$ −21.2705 −0.781392
$$742$$ 0 0
$$743$$ −33.6312 −1.23381 −0.616904 0.787038i $$-0.711613\pi$$
−0.616904 + 0.787038i $$0.711613\pi$$
$$744$$ 0 0
$$745$$ −7.85410 −0.287752
$$746$$ 0 0
$$747$$ −2.65248 −0.0970490
$$748$$ 0 0
$$749$$ −11.2361 −0.410557
$$750$$ 0 0
$$751$$ 47.0132 1.71553 0.857767 0.514038i $$-0.171851\pi$$
0.857767 + 0.514038i $$0.171851\pi$$
$$752$$ 0 0
$$753$$ 9.94427 0.362389
$$754$$ 0 0
$$755$$ 2.56231 0.0932519
$$756$$ 0 0
$$757$$ −17.8885 −0.650170 −0.325085 0.945685i $$-0.605393\pi$$
−0.325085 + 0.945685i $$0.605393\pi$$
$$758$$ 0 0
$$759$$ 4.61803 0.167624
$$760$$ 0 0
$$761$$ 46.8673 1.69894 0.849468 0.527640i $$-0.176923\pi$$
0.849468 + 0.527640i $$0.176923\pi$$
$$762$$ 0 0
$$763$$ −7.14590 −0.258699
$$764$$ 0 0
$$765$$ −2.32624 −0.0841053
$$766$$ 0 0
$$767$$ 12.1115 0.437319
$$768$$ 0 0
$$769$$ −6.58359 −0.237410 −0.118705 0.992930i $$-0.537874\pi$$
−0.118705 + 0.992930i $$0.537874\pi$$
$$770$$ 0 0
$$771$$ 12.6525 0.455668
$$772$$ 0 0
$$773$$ 28.9443 1.04105 0.520527 0.853845i $$-0.325736\pi$$
0.520527 + 0.853845i $$0.325736\pi$$
$$774$$ 0 0
$$775$$ −9.09017 −0.326529
$$776$$ 0 0
$$777$$ −6.47214 −0.232187
$$778$$ 0 0
$$779$$ −6.16718 −0.220962
$$780$$ 0 0
$$781$$ 11.6738 0.417720
$$782$$ 0 0
$$783$$ −50.5410 −1.80619
$$784$$ 0 0
$$785$$ −3.70820 −0.132351
$$786$$ 0 0
$$787$$ 2.87539 0.102497 0.0512483 0.998686i $$-0.483680\pi$$
0.0512483 + 0.998686i $$0.483680\pi$$
$$788$$ 0 0
$$789$$ 33.5623 1.19485
$$790$$ 0 0
$$791$$ 0.652476 0.0231994
$$792$$ 0 0
$$793$$ 66.1246 2.34815
$$794$$ 0 0
$$795$$ −0.763932 −0.0270939
$$796$$ 0 0
$$797$$ 13.7082 0.485569 0.242785 0.970080i $$-0.421939\pi$$
0.242785 + 0.970080i $$0.421939\pi$$
$$798$$ 0 0
$$799$$ 22.5836 0.798950
$$800$$ 0 0
$$801$$ 4.00000 0.141333
$$802$$ 0 0
$$803$$ 9.23607 0.325934
$$804$$ 0 0
$$805$$ −0.618034 −0.0217828
$$806$$ 0 0
$$807$$ 22.9443 0.807677
$$808$$ 0 0
$$809$$ −46.7426 −1.64338 −0.821692 0.569932i $$-0.806970\pi$$
−0.821692 + 0.569932i $$0.806970\pi$$
$$810$$ 0 0
$$811$$ −21.8197 −0.766192 −0.383096 0.923709i $$-0.625142\pi$$
−0.383096 + 0.923709i $$0.625142\pi$$
$$812$$ 0 0
$$813$$ −49.0689 −1.72092
$$814$$ 0 0
$$815$$ −1.38197 −0.0484082
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 1.67376 0.0584860
$$820$$ 0 0
$$821$$ −33.0557 −1.15365 −0.576826 0.816867i $$-0.695709\pi$$
−0.576826 + 0.816867i $$0.695709\pi$$
$$822$$ 0 0
$$823$$ −25.4164 −0.885960 −0.442980 0.896531i $$-0.646079\pi$$
−0.442980 + 0.896531i $$0.646079\pi$$
$$824$$ 0 0
$$825$$ −4.61803 −0.160779
$$826$$ 0 0
$$827$$ −21.7082 −0.754868 −0.377434 0.926036i $$-0.623194\pi$$
−0.377434 + 0.926036i $$0.623194\pi$$
$$828$$ 0 0
$$829$$ 18.9443 0.657962 0.328981 0.944337i $$-0.393295\pi$$
0.328981 + 0.944337i $$0.393295\pi$$
$$830$$ 0 0
$$831$$ −47.5967 −1.65111
$$832$$ 0 0
$$833$$ −40.3050 −1.39648
$$834$$ 0 0
$$835$$ 8.00000 0.276851
$$836$$ 0 0
$$837$$ −49.7426 −1.71936
$$838$$ 0 0
$$839$$ −33.0132 −1.13974 −0.569870 0.821735i $$-0.693007\pi$$
−0.569870 + 0.821735i $$0.693007\pi$$
$$840$$ 0 0
$$841$$ 56.3050 1.94155
$$842$$ 0 0
$$843$$ −36.8328 −1.26859
$$844$$ 0 0
$$845$$ 37.2705 1.28214
$$846$$ 0 0
$$847$$ −1.76393 −0.0606094
$$848$$ 0 0
$$849$$ −43.5967 −1.49624
$$850$$ 0 0
$$851$$ −6.47214 −0.221862
$$852$$ 0 0
$$853$$ −10.7984 −0.369729 −0.184865 0.982764i $$-0.559185\pi$$
−0.184865 + 0.982764i $$0.559185\pi$$
$$854$$ 0 0
$$855$$ 0.708204 0.0242201
$$856$$ 0 0
$$857$$ −6.58359 −0.224891 −0.112446 0.993658i $$-0.535868\pi$$
−0.112446 + 0.993658i $$0.535868\pi$$
$$858$$ 0 0
$$859$$ 24.0689 0.821220 0.410610 0.911811i $$-0.365316\pi$$
0.410610 + 0.911811i $$0.365316\pi$$
$$860$$ 0 0
$$861$$ −3.32624 −0.113358
$$862$$ 0 0
$$863$$ −32.7639 −1.11530 −0.557649 0.830077i $$-0.688296\pi$$
−0.557649 + 0.830077i $$0.688296\pi$$
$$864$$ 0 0
$$865$$ −1.43769 −0.0488831
$$866$$ 0 0
$$867$$ −32.5066 −1.10398
$$868$$ 0 0
$$869$$ −4.36068 −0.147926
$$870$$ 0 0
$$871$$ 102.610 3.47680
$$872$$ 0 0
$$873$$ −4.72949 −0.160069
$$874$$ 0 0
$$875$$ 0.618034 0.0208934
$$876$$ 0 0
$$877$$ 18.7426 0.632894 0.316447 0.948610i $$-0.397510\pi$$
0.316447 + 0.948610i $$0.397510\pi$$
$$878$$ 0 0
$$879$$ 32.1803 1.08542
$$880$$ 0 0
$$881$$ 8.58359 0.289189 0.144594 0.989491i $$-0.453812\pi$$
0.144594 + 0.989491i $$0.453812\pi$$
$$882$$ 0 0
$$883$$ −15.5623 −0.523713 −0.261857 0.965107i $$-0.584335\pi$$
−0.261857 + 0.965107i $$0.584335\pi$$
$$884$$ 0 0
$$885$$ 2.76393 0.0929086
$$886$$ 0 0
$$887$$ 5.16718 0.173497 0.0867485 0.996230i $$-0.472352\pi$$
0.0867485 + 0.996230i $$0.472352\pi$$
$$888$$ 0 0
$$889$$ −10.0000 −0.335389
$$890$$ 0 0
$$891$$ −22.0000 −0.737028
$$892$$ 0 0
$$893$$ −6.87539 −0.230076
$$894$$ 0 0
$$895$$ −2.18034 −0.0728807
$$896$$ 0 0
$$897$$ −11.4721 −0.383043
$$898$$ 0 0
$$899$$ 83.9574 2.80014
$$900$$ 0 0
$$901$$ 2.87539 0.0957931
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −12.1459 −0.403743
$$906$$ 0 0
$$907$$ −7.12461 −0.236569 −0.118284 0.992980i $$-0.537739\pi$$
−0.118284 + 0.992980i $$0.537739\pi$$
$$908$$ 0 0
$$909$$ 0.111456 0.00369677
$$910$$ 0 0
$$911$$ −36.0689 −1.19502 −0.597508 0.801863i $$-0.703842\pi$$
−0.597508 + 0.801863i $$0.703842\pi$$
$$912$$ 0 0
$$913$$ 19.8197 0.655935
$$914$$ 0 0
$$915$$ 15.0902 0.498866
$$916$$ 0 0
$$917$$ −1.81966 −0.0600905
$$918$$ 0 0
$$919$$ −40.0000 −1.31948 −0.659739 0.751495i $$-0.729333\pi$$
−0.659739 + 0.751495i $$0.729333\pi$$
$$920$$ 0 0
$$921$$ −46.0344 −1.51689
$$922$$ 0 0
$$923$$ −29.0000 −0.954547
$$924$$ 0 0
$$925$$ 6.47214 0.212803
$$926$$ 0 0
$$927$$ 6.32624 0.207781
$$928$$ 0 0
$$929$$ −3.52786 −0.115745 −0.0578727 0.998324i $$-0.518432\pi$$
−0.0578727 + 0.998324i $$0.518432\pi$$
$$930$$ 0 0
$$931$$ 12.2705 0.402150
$$932$$ 0 0
$$933$$ 6.47214 0.211888
$$934$$ 0 0
$$935$$ 17.3820 0.568451
$$936$$ 0 0
$$937$$ −36.7984 −1.20215 −0.601075 0.799192i $$-0.705261\pi$$
−0.601075 + 0.799192i $$0.705261\pi$$
$$938$$ 0 0
$$939$$ −20.7082 −0.675787
$$940$$ 0 0
$$941$$ −22.4934 −0.733265 −0.366632 0.930366i $$-0.619489\pi$$
−0.366632 + 0.930366i $$0.619489\pi$$
$$942$$ 0 0
$$943$$ −3.32624 −0.108317
$$944$$ 0 0
$$945$$ 3.38197 0.110015
$$946$$ 0 0
$$947$$ 54.6869 1.77709 0.888543 0.458793i $$-0.151718\pi$$
0.888543 + 0.458793i $$0.151718\pi$$
$$948$$ 0 0
$$949$$ −22.9443 −0.744803
$$950$$ 0 0
$$951$$ 17.9443 0.581883
$$952$$ 0 0
$$953$$ 3.79837 0.123041 0.0615207 0.998106i $$-0.480405\pi$$
0.0615207 + 0.998106i $$0.480405\pi$$
$$954$$ 0 0
$$955$$ 13.7082 0.443587
$$956$$ 0 0
$$957$$ 42.6525 1.37876
$$958$$ 0 0
$$959$$ −6.38197 −0.206084
$$960$$ 0 0
$$961$$ 51.6312 1.66552
$$962$$ 0 0
$$963$$ 6.94427 0.223776
$$964$$ 0 0
$$965$$ 0.763932 0.0245918
$$966$$ 0 0
$$967$$ 16.5410 0.531923 0.265962 0.963984i $$-0.414311\pi$$
0.265962 + 0.963984i $$0.414311\pi$$
$$968$$ 0 0
$$969$$ 18.2705 0.586933
$$970$$ 0 0
$$971$$ −34.2705 −1.09979 −0.549896 0.835233i $$-0.685333\pi$$
−0.549896 + 0.835233i $$0.685333\pi$$
$$972$$ 0 0
$$973$$ −7.88854 −0.252895
$$974$$ 0 0
$$975$$ 11.4721 0.367402
$$976$$ 0 0
$$977$$ −23.5623 −0.753825 −0.376912 0.926249i $$-0.623014\pi$$
−0.376912 + 0.926249i $$0.623014\pi$$
$$978$$ 0 0
$$979$$ −29.8885 −0.955242
$$980$$ 0 0
$$981$$ 4.41641 0.141005
$$982$$ 0 0
$$983$$ 14.2705 0.455159 0.227579 0.973760i $$-0.426919\pi$$
0.227579 + 0.973760i $$0.426919\pi$$
$$984$$ 0 0
$$985$$ −22.5623 −0.718895
$$986$$ 0 0
$$987$$ −3.70820 −0.118033
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −27.5066 −0.873775 −0.436888 0.899516i $$-0.643919\pi$$
−0.436888 + 0.899516i $$0.643919\pi$$
$$992$$ 0 0
$$993$$ 31.1246 0.987710
$$994$$ 0 0
$$995$$ −2.00000 −0.0634043
$$996$$ 0 0
$$997$$ 57.1935 1.81134 0.905668 0.423987i $$-0.139370\pi$$
0.905668 + 0.423987i $$0.139370\pi$$
$$998$$ 0 0
$$999$$ 35.4164 1.12053
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 1840.2.a.l.1.1 2
4.3 odd 2 230.2.a.c.1.2 2
5.4 even 2 9200.2.a.bu.1.2 2
8.3 odd 2 7360.2.a.bh.1.1 2
8.5 even 2 7360.2.a.bn.1.2 2
12.11 even 2 2070.2.a.u.1.1 2
20.3 even 4 1150.2.b.i.599.2 4
20.7 even 4 1150.2.b.i.599.3 4
20.19 odd 2 1150.2.a.j.1.1 2
92.91 even 2 5290.2.a.o.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.c.1.2 2 4.3 odd 2
1150.2.a.j.1.1 2 20.19 odd 2
1150.2.b.i.599.2 4 20.3 even 4
1150.2.b.i.599.3 4 20.7 even 4
1840.2.a.l.1.1 2 1.1 even 1 trivial
2070.2.a.u.1.1 2 12.11 even 2
5290.2.a.o.1.2 2 92.91 even 2
7360.2.a.bh.1.1 2 8.3 odd 2
7360.2.a.bn.1.2 2 8.5 even 2
9200.2.a.bu.1.2 2 5.4 even 2