# Properties

 Label 841.2.a.a.1.2 Level $841$ Weight $2$ Character 841.1 Self dual yes Analytic conductor $6.715$ 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] = [841,2,Mod(1,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("841.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$841 = 29^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 841.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: $$6.71541880999$$ 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: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 841.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+0.618034 q^{2} -0.618034 q^{3} -1.61803 q^{4} +3.85410 q^{5} -0.381966 q^{6} -2.23607 q^{7} -2.23607 q^{8} -2.61803 q^{9} +O(q^{10})$$ $$q+0.618034 q^{2} -0.618034 q^{3} -1.61803 q^{4} +3.85410 q^{5} -0.381966 q^{6} -2.23607 q^{7} -2.23607 q^{8} -2.61803 q^{9} +2.38197 q^{10} -1.38197 q^{11} +1.00000 q^{12} -0.236068 q^{13} -1.38197 q^{14} -2.38197 q^{15} +1.85410 q^{16} -4.38197 q^{17} -1.61803 q^{18} -4.85410 q^{19} -6.23607 q^{20} +1.38197 q^{21} -0.854102 q^{22} -1.23607 q^{23} +1.38197 q^{24} +9.85410 q^{25} -0.145898 q^{26} +3.47214 q^{27} +3.61803 q^{28} -1.47214 q^{30} -10.0902 q^{31} +5.61803 q^{32} +0.854102 q^{33} -2.70820 q^{34} -8.61803 q^{35} +4.23607 q^{36} +4.70820 q^{37} -3.00000 q^{38} +0.145898 q^{39} -8.61803 q^{40} +3.85410 q^{41} +0.854102 q^{42} -7.23607 q^{43} +2.23607 q^{44} -10.0902 q^{45} -0.763932 q^{46} -7.00000 q^{47} -1.14590 q^{48} -2.00000 q^{49} +6.09017 q^{50} +2.70820 q^{51} +0.381966 q^{52} -2.00000 q^{53} +2.14590 q^{54} -5.32624 q^{55} +5.00000 q^{56} +3.00000 q^{57} +6.09017 q^{59} +3.85410 q^{60} -0.618034 q^{61} -6.23607 q^{62} +5.85410 q^{63} -0.236068 q^{64} -0.909830 q^{65} +0.527864 q^{66} -1.52786 q^{67} +7.09017 q^{68} +0.763932 q^{69} -5.32624 q^{70} +10.4721 q^{71} +5.85410 q^{72} -13.7082 q^{73} +2.90983 q^{74} -6.09017 q^{75} +7.85410 q^{76} +3.09017 q^{77} +0.0901699 q^{78} -6.09017 q^{79} +7.14590 q^{80} +5.70820 q^{81} +2.38197 q^{82} -9.94427 q^{83} -2.23607 q^{84} -16.8885 q^{85} -4.47214 q^{86} +3.09017 q^{88} +4.70820 q^{89} -6.23607 q^{90} +0.527864 q^{91} +2.00000 q^{92} +6.23607 q^{93} -4.32624 q^{94} -18.7082 q^{95} -3.47214 q^{96} +3.56231 q^{97} -1.23607 q^{98} +3.61803 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + q^{3} - q^{4} + q^{5} - 3 q^{6} - 3 q^{9}+O(q^{10})$$ 2 * q - q^2 + q^3 - q^4 + q^5 - 3 * q^6 - 3 * q^9 $$2 q - q^{2} + q^{3} - q^{4} + q^{5} - 3 q^{6} - 3 q^{9} + 7 q^{10} - 5 q^{11} + 2 q^{12} + 4 q^{13} - 5 q^{14} - 7 q^{15} - 3 q^{16} - 11 q^{17} - q^{18} - 3 q^{19} - 8 q^{20} + 5 q^{21} + 5 q^{22} + 2 q^{23} + 5 q^{24} + 13 q^{25} - 7 q^{26} - 2 q^{27} + 5 q^{28} + 6 q^{30} - 9 q^{31} + 9 q^{32} - 5 q^{33} + 8 q^{34} - 15 q^{35} + 4 q^{36} - 4 q^{37} - 6 q^{38} + 7 q^{39} - 15 q^{40} + q^{41} - 5 q^{42} - 10 q^{43} - 9 q^{45} - 6 q^{46} - 14 q^{47} - 9 q^{48} - 4 q^{49} + q^{50} - 8 q^{51} + 3 q^{52} - 4 q^{53} + 11 q^{54} + 5 q^{55} + 10 q^{56} + 6 q^{57} + q^{59} + q^{60} + q^{61} - 8 q^{62} + 5 q^{63} + 4 q^{64} - 13 q^{65} + 10 q^{66} - 12 q^{67} + 3 q^{68} + 6 q^{69} + 5 q^{70} + 12 q^{71} + 5 q^{72} - 14 q^{73} + 17 q^{74} - q^{75} + 9 q^{76} - 5 q^{77} - 11 q^{78} - q^{79} + 21 q^{80} - 2 q^{81} + 7 q^{82} - 2 q^{83} + 2 q^{85} - 5 q^{88} - 4 q^{89} - 8 q^{90} + 10 q^{91} + 4 q^{92} + 8 q^{93} + 7 q^{94} - 24 q^{95} + 2 q^{96} - 13 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100})$$ 2 * q - q^2 + q^3 - q^4 + q^5 - 3 * q^6 - 3 * q^9 + 7 * q^10 - 5 * q^11 + 2 * q^12 + 4 * q^13 - 5 * q^14 - 7 * q^15 - 3 * q^16 - 11 * q^17 - q^18 - 3 * q^19 - 8 * q^20 + 5 * q^21 + 5 * q^22 + 2 * q^23 + 5 * q^24 + 13 * q^25 - 7 * q^26 - 2 * q^27 + 5 * q^28 + 6 * q^30 - 9 * q^31 + 9 * q^32 - 5 * q^33 + 8 * q^34 - 15 * q^35 + 4 * q^36 - 4 * q^37 - 6 * q^38 + 7 * q^39 - 15 * q^40 + q^41 - 5 * q^42 - 10 * q^43 - 9 * q^45 - 6 * q^46 - 14 * q^47 - 9 * q^48 - 4 * q^49 + q^50 - 8 * q^51 + 3 * q^52 - 4 * q^53 + 11 * q^54 + 5 * q^55 + 10 * q^56 + 6 * q^57 + q^59 + q^60 + q^61 - 8 * q^62 + 5 * q^63 + 4 * q^64 - 13 * q^65 + 10 * q^66 - 12 * q^67 + 3 * q^68 + 6 * q^69 + 5 * q^70 + 12 * q^71 + 5 * q^72 - 14 * q^73 + 17 * q^74 - q^75 + 9 * q^76 - 5 * q^77 - 11 * q^78 - q^79 + 21 * q^80 - 2 * q^81 + 7 * q^82 - 2 * q^83 + 2 * q^85 - 5 * q^88 - 4 * q^89 - 8 * q^90 + 10 * q^91 + 4 * q^92 + 8 * q^93 + 7 * q^94 - 24 * q^95 + 2 * q^96 - 13 * q^97 + 2 * q^98 + 5 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.618034 0.437016 0.218508 0.975835i $$-0.429881\pi$$
0.218508 + 0.975835i $$0.429881\pi$$
$$3$$ −0.618034 −0.356822 −0.178411 0.983956i $$-0.557096\pi$$
−0.178411 + 0.983956i $$0.557096\pi$$
$$4$$ −1.61803 −0.809017
$$5$$ 3.85410 1.72361 0.861803 0.507242i $$-0.169335\pi$$
0.861803 + 0.507242i $$0.169335\pi$$
$$6$$ −0.381966 −0.155937
$$7$$ −2.23607 −0.845154 −0.422577 0.906327i $$-0.638874\pi$$
−0.422577 + 0.906327i $$0.638874\pi$$
$$8$$ −2.23607 −0.790569
$$9$$ −2.61803 −0.872678
$$10$$ 2.38197 0.753244
$$11$$ −1.38197 −0.416678 −0.208339 0.978057i $$-0.566806\pi$$
−0.208339 + 0.978057i $$0.566806\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −0.236068 −0.0654735 −0.0327367 0.999464i $$-0.510422\pi$$
−0.0327367 + 0.999464i $$0.510422\pi$$
$$14$$ −1.38197 −0.369346
$$15$$ −2.38197 −0.615021
$$16$$ 1.85410 0.463525
$$17$$ −4.38197 −1.06278 −0.531391 0.847126i $$-0.678331\pi$$
−0.531391 + 0.847126i $$0.678331\pi$$
$$18$$ −1.61803 −0.381374
$$19$$ −4.85410 −1.11361 −0.556804 0.830644i $$-0.687972\pi$$
−0.556804 + 0.830644i $$0.687972\pi$$
$$20$$ −6.23607 −1.39443
$$21$$ 1.38197 0.301570
$$22$$ −0.854102 −0.182095
$$23$$ −1.23607 −0.257738 −0.128869 0.991662i $$-0.541135\pi$$
−0.128869 + 0.991662i $$0.541135\pi$$
$$24$$ 1.38197 0.282093
$$25$$ 9.85410 1.97082
$$26$$ −0.145898 −0.0286130
$$27$$ 3.47214 0.668213
$$28$$ 3.61803 0.683744
$$29$$ 0 0
$$30$$ −1.47214 −0.268774
$$31$$ −10.0902 −1.81225 −0.906124 0.423012i $$-0.860973\pi$$
−0.906124 + 0.423012i $$0.860973\pi$$
$$32$$ 5.61803 0.993137
$$33$$ 0.854102 0.148680
$$34$$ −2.70820 −0.464453
$$35$$ −8.61803 −1.45671
$$36$$ 4.23607 0.706011
$$37$$ 4.70820 0.774024 0.387012 0.922075i $$-0.373507\pi$$
0.387012 + 0.922075i $$0.373507\pi$$
$$38$$ −3.00000 −0.486664
$$39$$ 0.145898 0.0233624
$$40$$ −8.61803 −1.36263
$$41$$ 3.85410 0.601910 0.300955 0.953638i $$-0.402695\pi$$
0.300955 + 0.953638i $$0.402695\pi$$
$$42$$ 0.854102 0.131791
$$43$$ −7.23607 −1.10349 −0.551745 0.834013i $$-0.686038\pi$$
−0.551745 + 0.834013i $$0.686038\pi$$
$$44$$ 2.23607 0.337100
$$45$$ −10.0902 −1.50415
$$46$$ −0.763932 −0.112636
$$47$$ −7.00000 −1.02105 −0.510527 0.859861i $$-0.670550\pi$$
−0.510527 + 0.859861i $$0.670550\pi$$
$$48$$ −1.14590 −0.165396
$$49$$ −2.00000 −0.285714
$$50$$ 6.09017 0.861280
$$51$$ 2.70820 0.379224
$$52$$ 0.381966 0.0529692
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 2.14590 0.292020
$$55$$ −5.32624 −0.718190
$$56$$ 5.00000 0.668153
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ 6.09017 0.792873 0.396436 0.918062i $$-0.370247\pi$$
0.396436 + 0.918062i $$0.370247\pi$$
$$60$$ 3.85410 0.497562
$$61$$ −0.618034 −0.0791311 −0.0395656 0.999217i $$-0.512597\pi$$
−0.0395656 + 0.999217i $$0.512597\pi$$
$$62$$ −6.23607 −0.791981
$$63$$ 5.85410 0.737548
$$64$$ −0.236068 −0.0295085
$$65$$ −0.909830 −0.112851
$$66$$ 0.527864 0.0649756
$$67$$ −1.52786 −0.186658 −0.0933292 0.995635i $$-0.529751\pi$$
−0.0933292 + 0.995635i $$0.529751\pi$$
$$68$$ 7.09017 0.859809
$$69$$ 0.763932 0.0919666
$$70$$ −5.32624 −0.636607
$$71$$ 10.4721 1.24281 0.621407 0.783488i $$-0.286561\pi$$
0.621407 + 0.783488i $$0.286561\pi$$
$$72$$ 5.85410 0.689913
$$73$$ −13.7082 −1.60442 −0.802212 0.597039i $$-0.796344\pi$$
−0.802212 + 0.597039i $$0.796344\pi$$
$$74$$ 2.90983 0.338261
$$75$$ −6.09017 −0.703232
$$76$$ 7.85410 0.900927
$$77$$ 3.09017 0.352158
$$78$$ 0.0901699 0.0102097
$$79$$ −6.09017 −0.685198 −0.342599 0.939482i $$-0.611307\pi$$
−0.342599 + 0.939482i $$0.611307\pi$$
$$80$$ 7.14590 0.798936
$$81$$ 5.70820 0.634245
$$82$$ 2.38197 0.263044
$$83$$ −9.94427 −1.09153 −0.545763 0.837940i $$-0.683760\pi$$
−0.545763 + 0.837940i $$0.683760\pi$$
$$84$$ −2.23607 −0.243975
$$85$$ −16.8885 −1.83182
$$86$$ −4.47214 −0.482243
$$87$$ 0 0
$$88$$ 3.09017 0.329413
$$89$$ 4.70820 0.499069 0.249534 0.968366i $$-0.419722\pi$$
0.249534 + 0.968366i $$0.419722\pi$$
$$90$$ −6.23607 −0.657339
$$91$$ 0.527864 0.0553352
$$92$$ 2.00000 0.208514
$$93$$ 6.23607 0.646650
$$94$$ −4.32624 −0.446217
$$95$$ −18.7082 −1.91942
$$96$$ −3.47214 −0.354373
$$97$$ 3.56231 0.361697 0.180849 0.983511i $$-0.442116\pi$$
0.180849 + 0.983511i $$0.442116\pi$$
$$98$$ −1.23607 −0.124862
$$99$$ 3.61803 0.363626
$$100$$ −15.9443 −1.59443
$$101$$ −0.618034 −0.0614967 −0.0307483 0.999527i $$-0.509789\pi$$
−0.0307483 + 0.999527i $$0.509789\pi$$
$$102$$ 1.67376 0.165727
$$103$$ 9.18034 0.904566 0.452283 0.891875i $$-0.350610\pi$$
0.452283 + 0.891875i $$0.350610\pi$$
$$104$$ 0.527864 0.0517613
$$105$$ 5.32624 0.519788
$$106$$ −1.23607 −0.120058
$$107$$ 6.76393 0.653894 0.326947 0.945043i $$-0.393980\pi$$
0.326947 + 0.945043i $$0.393980\pi$$
$$108$$ −5.61803 −0.540596
$$109$$ −14.3820 −1.37754 −0.688771 0.724979i $$-0.741850\pi$$
−0.688771 + 0.724979i $$0.741850\pi$$
$$110$$ −3.29180 −0.313860
$$111$$ −2.90983 −0.276189
$$112$$ −4.14590 −0.391751
$$113$$ 7.94427 0.747334 0.373667 0.927563i $$-0.378100\pi$$
0.373667 + 0.927563i $$0.378100\pi$$
$$114$$ 1.85410 0.173653
$$115$$ −4.76393 −0.444239
$$116$$ 0 0
$$117$$ 0.618034 0.0571373
$$118$$ 3.76393 0.346498
$$119$$ 9.79837 0.898215
$$120$$ 5.32624 0.486217
$$121$$ −9.09017 −0.826379
$$122$$ −0.381966 −0.0345816
$$123$$ −2.38197 −0.214775
$$124$$ 16.3262 1.46614
$$125$$ 18.7082 1.67331
$$126$$ 3.61803 0.322320
$$127$$ 15.9443 1.41483 0.707413 0.706801i $$-0.249862\pi$$
0.707413 + 0.706801i $$0.249862\pi$$
$$128$$ −11.3820 −1.00603
$$129$$ 4.47214 0.393750
$$130$$ −0.562306 −0.0493175
$$131$$ 14.3262 1.25169 0.625845 0.779948i $$-0.284754\pi$$
0.625845 + 0.779948i $$0.284754\pi$$
$$132$$ −1.38197 −0.120285
$$133$$ 10.8541 0.941170
$$134$$ −0.944272 −0.0815727
$$135$$ 13.3820 1.15174
$$136$$ 9.79837 0.840204
$$137$$ 7.14590 0.610515 0.305258 0.952270i $$-0.401257\pi$$
0.305258 + 0.952270i $$0.401257\pi$$
$$138$$ 0.472136 0.0401909
$$139$$ 1.29180 0.109569 0.0547844 0.998498i $$-0.482553\pi$$
0.0547844 + 0.998498i $$0.482553\pi$$
$$140$$ 13.9443 1.17851
$$141$$ 4.32624 0.364335
$$142$$ 6.47214 0.543130
$$143$$ 0.326238 0.0272814
$$144$$ −4.85410 −0.404508
$$145$$ 0 0
$$146$$ −8.47214 −0.701159
$$147$$ 1.23607 0.101949
$$148$$ −7.61803 −0.626199
$$149$$ 9.61803 0.787940 0.393970 0.919123i $$-0.371101\pi$$
0.393970 + 0.919123i $$0.371101\pi$$
$$150$$ −3.76393 −0.307324
$$151$$ 2.67376 0.217588 0.108794 0.994064i $$-0.465301\pi$$
0.108794 + 0.994064i $$0.465301\pi$$
$$152$$ 10.8541 0.880384
$$153$$ 11.4721 0.927467
$$154$$ 1.90983 0.153898
$$155$$ −38.8885 −3.12360
$$156$$ −0.236068 −0.0189006
$$157$$ 14.5623 1.16220 0.581099 0.813833i $$-0.302623\pi$$
0.581099 + 0.813833i $$0.302623\pi$$
$$158$$ −3.76393 −0.299442
$$159$$ 1.23607 0.0980266
$$160$$ 21.6525 1.71178
$$161$$ 2.76393 0.217828
$$162$$ 3.52786 0.277175
$$163$$ −6.03444 −0.472654 −0.236327 0.971674i $$-0.575944\pi$$
−0.236327 + 0.971674i $$0.575944\pi$$
$$164$$ −6.23607 −0.486955
$$165$$ 3.29180 0.256266
$$166$$ −6.14590 −0.477014
$$167$$ 10.5279 0.814671 0.407335 0.913279i $$-0.366458\pi$$
0.407335 + 0.913279i $$0.366458\pi$$
$$168$$ −3.09017 −0.238412
$$169$$ −12.9443 −0.995713
$$170$$ −10.4377 −0.800535
$$171$$ 12.7082 0.971821
$$172$$ 11.7082 0.892742
$$173$$ 4.09017 0.310970 0.155485 0.987838i $$-0.450306\pi$$
0.155485 + 0.987838i $$0.450306\pi$$
$$174$$ 0 0
$$175$$ −22.0344 −1.66565
$$176$$ −2.56231 −0.193141
$$177$$ −3.76393 −0.282914
$$178$$ 2.90983 0.218101
$$179$$ −16.0000 −1.19590 −0.597948 0.801535i $$-0.704017\pi$$
−0.597948 + 0.801535i $$0.704017\pi$$
$$180$$ 16.3262 1.21689
$$181$$ 5.94427 0.441834 0.220917 0.975293i $$-0.429095\pi$$
0.220917 + 0.975293i $$0.429095\pi$$
$$182$$ 0.326238 0.0241824
$$183$$ 0.381966 0.0282357
$$184$$ 2.76393 0.203760
$$185$$ 18.1459 1.33411
$$186$$ 3.85410 0.282596
$$187$$ 6.05573 0.442839
$$188$$ 11.3262 0.826051
$$189$$ −7.76393 −0.564743
$$190$$ −11.5623 −0.838818
$$191$$ 17.0344 1.23257 0.616284 0.787524i $$-0.288637\pi$$
0.616284 + 0.787524i $$0.288637\pi$$
$$192$$ 0.145898 0.0105293
$$193$$ 12.4721 0.897764 0.448882 0.893591i $$-0.351822\pi$$
0.448882 + 0.893591i $$0.351822\pi$$
$$194$$ 2.20163 0.158068
$$195$$ 0.562306 0.0402676
$$196$$ 3.23607 0.231148
$$197$$ −6.29180 −0.448272 −0.224136 0.974558i $$-0.571956\pi$$
−0.224136 + 0.974558i $$0.571956\pi$$
$$198$$ 2.23607 0.158910
$$199$$ −5.85410 −0.414986 −0.207493 0.978236i $$-0.566530\pi$$
−0.207493 + 0.978236i $$0.566530\pi$$
$$200$$ −22.0344 −1.55807
$$201$$ 0.944272 0.0666038
$$202$$ −0.381966 −0.0268750
$$203$$ 0 0
$$204$$ −4.38197 −0.306799
$$205$$ 14.8541 1.03746
$$206$$ 5.67376 0.395310
$$207$$ 3.23607 0.224922
$$208$$ −0.437694 −0.0303486
$$209$$ 6.70820 0.464016
$$210$$ 3.29180 0.227156
$$211$$ −11.6525 −0.802190 −0.401095 0.916037i $$-0.631370\pi$$
−0.401095 + 0.916037i $$0.631370\pi$$
$$212$$ 3.23607 0.222254
$$213$$ −6.47214 −0.443463
$$214$$ 4.18034 0.285762
$$215$$ −27.8885 −1.90198
$$216$$ −7.76393 −0.528269
$$217$$ 22.5623 1.53163
$$218$$ −8.88854 −0.602008
$$219$$ 8.47214 0.572494
$$220$$ 8.61803 0.581028
$$221$$ 1.03444 0.0695841
$$222$$ −1.79837 −0.120699
$$223$$ 2.67376 0.179048 0.0895242 0.995985i $$-0.471465\pi$$
0.0895242 + 0.995985i $$0.471465\pi$$
$$224$$ −12.5623 −0.839354
$$225$$ −25.7984 −1.71989
$$226$$ 4.90983 0.326597
$$227$$ −20.8885 −1.38642 −0.693211 0.720735i $$-0.743804\pi$$
−0.693211 + 0.720735i $$0.743804\pi$$
$$228$$ −4.85410 −0.321471
$$229$$ 2.29180 0.151446 0.0757231 0.997129i $$-0.475874\pi$$
0.0757231 + 0.997129i $$0.475874\pi$$
$$230$$ −2.94427 −0.194140
$$231$$ −1.90983 −0.125658
$$232$$ 0 0
$$233$$ 15.2361 0.998148 0.499074 0.866559i $$-0.333674\pi$$
0.499074 + 0.866559i $$0.333674\pi$$
$$234$$ 0.381966 0.0249699
$$235$$ −26.9787 −1.75990
$$236$$ −9.85410 −0.641447
$$237$$ 3.76393 0.244494
$$238$$ 6.05573 0.392535
$$239$$ −27.7426 −1.79452 −0.897261 0.441500i $$-0.854447\pi$$
−0.897261 + 0.441500i $$0.854447\pi$$
$$240$$ −4.41641 −0.285078
$$241$$ −4.65248 −0.299692 −0.149846 0.988709i $$-0.547878\pi$$
−0.149846 + 0.988709i $$0.547878\pi$$
$$242$$ −5.61803 −0.361141
$$243$$ −13.9443 −0.894525
$$244$$ 1.00000 0.0640184
$$245$$ −7.70820 −0.492459
$$246$$ −1.47214 −0.0938600
$$247$$ 1.14590 0.0729117
$$248$$ 22.5623 1.43271
$$249$$ 6.14590 0.389480
$$250$$ 11.5623 0.731264
$$251$$ −19.6525 −1.24045 −0.620227 0.784423i $$-0.712959\pi$$
−0.620227 + 0.784423i $$0.712959\pi$$
$$252$$ −9.47214 −0.596688
$$253$$ 1.70820 0.107394
$$254$$ 9.85410 0.618301
$$255$$ 10.4377 0.653634
$$256$$ −6.56231 −0.410144
$$257$$ −23.1803 −1.44595 −0.722975 0.690874i $$-0.757226\pi$$
−0.722975 + 0.690874i $$0.757226\pi$$
$$258$$ 2.76393 0.172075
$$259$$ −10.5279 −0.654170
$$260$$ 1.47214 0.0912980
$$261$$ 0 0
$$262$$ 8.85410 0.547008
$$263$$ −16.7082 −1.03027 −0.515136 0.857108i $$-0.672259\pi$$
−0.515136 + 0.857108i $$0.672259\pi$$
$$264$$ −1.90983 −0.117542
$$265$$ −7.70820 −0.473511
$$266$$ 6.70820 0.411306
$$267$$ −2.90983 −0.178079
$$268$$ 2.47214 0.151010
$$269$$ −6.00000 −0.365826 −0.182913 0.983129i $$-0.558553\pi$$
−0.182913 + 0.983129i $$0.558553\pi$$
$$270$$ 8.27051 0.503327
$$271$$ 10.1803 0.618412 0.309206 0.950995i $$-0.399937\pi$$
0.309206 + 0.950995i $$0.399937\pi$$
$$272$$ −8.12461 −0.492627
$$273$$ −0.326238 −0.0197448
$$274$$ 4.41641 0.266805
$$275$$ −13.6180 −0.821198
$$276$$ −1.23607 −0.0744025
$$277$$ −21.3820 −1.28472 −0.642359 0.766404i $$-0.722044\pi$$
−0.642359 + 0.766404i $$0.722044\pi$$
$$278$$ 0.798374 0.0478833
$$279$$ 26.4164 1.58151
$$280$$ 19.2705 1.15163
$$281$$ 23.1246 1.37950 0.689749 0.724048i $$-0.257721\pi$$
0.689749 + 0.724048i $$0.257721\pi$$
$$282$$ 2.67376 0.159220
$$283$$ −5.23607 −0.311252 −0.155626 0.987816i $$-0.549739\pi$$
−0.155626 + 0.987816i $$0.549739\pi$$
$$284$$ −16.9443 −1.00546
$$285$$ 11.5623 0.684892
$$286$$ 0.201626 0.0119224
$$287$$ −8.61803 −0.508706
$$288$$ −14.7082 −0.866689
$$289$$ 2.20163 0.129507
$$290$$ 0 0
$$291$$ −2.20163 −0.129062
$$292$$ 22.1803 1.29801
$$293$$ 8.52786 0.498203 0.249102 0.968477i $$-0.419865\pi$$
0.249102 + 0.968477i $$0.419865\pi$$
$$294$$ 0.763932 0.0445534
$$295$$ 23.4721 1.36660
$$296$$ −10.5279 −0.611920
$$297$$ −4.79837 −0.278430
$$298$$ 5.94427 0.344342
$$299$$ 0.291796 0.0168750
$$300$$ 9.85410 0.568927
$$301$$ 16.1803 0.932619
$$302$$ 1.65248 0.0950893
$$303$$ 0.381966 0.0219434
$$304$$ −9.00000 −0.516185
$$305$$ −2.38197 −0.136391
$$306$$ 7.09017 0.405318
$$307$$ −19.1803 −1.09468 −0.547340 0.836910i $$-0.684360\pi$$
−0.547340 + 0.836910i $$0.684360\pi$$
$$308$$ −5.00000 −0.284901
$$309$$ −5.67376 −0.322769
$$310$$ −24.0344 −1.36506
$$311$$ 2.09017 0.118523 0.0592613 0.998243i $$-0.481125\pi$$
0.0592613 + 0.998243i $$0.481125\pi$$
$$312$$ −0.326238 −0.0184696
$$313$$ −12.9098 −0.729707 −0.364853 0.931065i $$-0.618881\pi$$
−0.364853 + 0.931065i $$0.618881\pi$$
$$314$$ 9.00000 0.507899
$$315$$ 22.5623 1.27124
$$316$$ 9.85410 0.554337
$$317$$ 27.7082 1.55625 0.778124 0.628111i $$-0.216172\pi$$
0.778124 + 0.628111i $$0.216172\pi$$
$$318$$ 0.763932 0.0428392
$$319$$ 0 0
$$320$$ −0.909830 −0.0508610
$$321$$ −4.18034 −0.233324
$$322$$ 1.70820 0.0951945
$$323$$ 21.2705 1.18352
$$324$$ −9.23607 −0.513115
$$325$$ −2.32624 −0.129036
$$326$$ −3.72949 −0.206557
$$327$$ 8.88854 0.491538
$$328$$ −8.61803 −0.475851
$$329$$ 15.6525 0.862949
$$330$$ 2.03444 0.111992
$$331$$ 21.1803 1.16418 0.582088 0.813126i $$-0.302236\pi$$
0.582088 + 0.813126i $$0.302236\pi$$
$$332$$ 16.0902 0.883063
$$333$$ −12.3262 −0.675474
$$334$$ 6.50658 0.356024
$$335$$ −5.88854 −0.321726
$$336$$ 2.56231 0.139785
$$337$$ −34.0689 −1.85585 −0.927925 0.372767i $$-0.878409\pi$$
−0.927925 + 0.372767i $$0.878409\pi$$
$$338$$ −8.00000 −0.435143
$$339$$ −4.90983 −0.266665
$$340$$ 27.3262 1.48197
$$341$$ 13.9443 0.755125
$$342$$ 7.85410 0.424701
$$343$$ 20.1246 1.08663
$$344$$ 16.1803 0.872385
$$345$$ 2.94427 0.158514
$$346$$ 2.52786 0.135899
$$347$$ −32.1246 −1.72454 −0.862270 0.506449i $$-0.830958\pi$$
−0.862270 + 0.506449i $$0.830958\pi$$
$$348$$ 0 0
$$349$$ 4.52786 0.242371 0.121186 0.992630i $$-0.461330\pi$$
0.121186 + 0.992630i $$0.461330\pi$$
$$350$$ −13.6180 −0.727915
$$351$$ −0.819660 −0.0437502
$$352$$ −7.76393 −0.413819
$$353$$ −19.1246 −1.01790 −0.508950 0.860796i $$-0.669966\pi$$
−0.508950 + 0.860796i $$0.669966\pi$$
$$354$$ −2.32624 −0.123638
$$355$$ 40.3607 2.14212
$$356$$ −7.61803 −0.403755
$$357$$ −6.05573 −0.320503
$$358$$ −9.88854 −0.522626
$$359$$ −23.7639 −1.25421 −0.627106 0.778934i $$-0.715761\pi$$
−0.627106 + 0.778934i $$0.715761\pi$$
$$360$$ 22.5623 1.18914
$$361$$ 4.56231 0.240121
$$362$$ 3.67376 0.193089
$$363$$ 5.61803 0.294870
$$364$$ −0.854102 −0.0447671
$$365$$ −52.8328 −2.76540
$$366$$ 0.236068 0.0123395
$$367$$ 27.2705 1.42351 0.711755 0.702428i $$-0.247901\pi$$
0.711755 + 0.702428i $$0.247901\pi$$
$$368$$ −2.29180 −0.119468
$$369$$ −10.0902 −0.525273
$$370$$ 11.2148 0.583029
$$371$$ 4.47214 0.232182
$$372$$ −10.0902 −0.523151
$$373$$ 20.6180 1.06756 0.533781 0.845623i $$-0.320771\pi$$
0.533781 + 0.845623i $$0.320771\pi$$
$$374$$ 3.74265 0.193528
$$375$$ −11.5623 −0.597075
$$376$$ 15.6525 0.807215
$$377$$ 0 0
$$378$$ −4.79837 −0.246802
$$379$$ −24.2918 −1.24779 −0.623893 0.781510i $$-0.714450\pi$$
−0.623893 + 0.781510i $$0.714450\pi$$
$$380$$ 30.2705 1.55284
$$381$$ −9.85410 −0.504841
$$382$$ 10.5279 0.538652
$$383$$ −28.8541 −1.47438 −0.737188 0.675688i $$-0.763847\pi$$
−0.737188 + 0.675688i $$0.763847\pi$$
$$384$$ 7.03444 0.358975
$$385$$ 11.9098 0.606981
$$386$$ 7.70820 0.392337
$$387$$ 18.9443 0.962991
$$388$$ −5.76393 −0.292619
$$389$$ −19.1246 −0.969656 −0.484828 0.874609i $$-0.661118\pi$$
−0.484828 + 0.874609i $$0.661118\pi$$
$$390$$ 0.347524 0.0175976
$$391$$ 5.41641 0.273920
$$392$$ 4.47214 0.225877
$$393$$ −8.85410 −0.446630
$$394$$ −3.88854 −0.195902
$$395$$ −23.4721 −1.18101
$$396$$ −5.85410 −0.294180
$$397$$ −14.0557 −0.705437 −0.352718 0.935730i $$-0.614743\pi$$
−0.352718 + 0.935730i $$0.614743\pi$$
$$398$$ −3.61803 −0.181356
$$399$$ −6.70820 −0.335830
$$400$$ 18.2705 0.913525
$$401$$ 25.0689 1.25188 0.625940 0.779871i $$-0.284715\pi$$
0.625940 + 0.779871i $$0.284715\pi$$
$$402$$ 0.583592 0.0291069
$$403$$ 2.38197 0.118654
$$404$$ 1.00000 0.0497519
$$405$$ 22.0000 1.09319
$$406$$ 0 0
$$407$$ −6.50658 −0.322519
$$408$$ −6.05573 −0.299803
$$409$$ 27.4164 1.35565 0.677827 0.735221i $$-0.262922\pi$$
0.677827 + 0.735221i $$0.262922\pi$$
$$410$$ 9.18034 0.453385
$$411$$ −4.41641 −0.217845
$$412$$ −14.8541 −0.731809
$$413$$ −13.6180 −0.670100
$$414$$ 2.00000 0.0982946
$$415$$ −38.3262 −1.88136
$$416$$ −1.32624 −0.0650242
$$417$$ −0.798374 −0.0390965
$$418$$ 4.14590 0.202783
$$419$$ −17.5623 −0.857975 −0.428987 0.903310i $$-0.641130\pi$$
−0.428987 + 0.903310i $$0.641130\pi$$
$$420$$ −8.61803 −0.420517
$$421$$ −31.0344 −1.51253 −0.756263 0.654268i $$-0.772977\pi$$
−0.756263 + 0.654268i $$0.772977\pi$$
$$422$$ −7.20163 −0.350570
$$423$$ 18.3262 0.891052
$$424$$ 4.47214 0.217186
$$425$$ −43.1803 −2.09455
$$426$$ −4.00000 −0.193801
$$427$$ 1.38197 0.0668780
$$428$$ −10.9443 −0.529011
$$429$$ −0.201626 −0.00973460
$$430$$ −17.2361 −0.831197
$$431$$ 14.5967 0.703101 0.351550 0.936169i $$-0.385655\pi$$
0.351550 + 0.936169i $$0.385655\pi$$
$$432$$ 6.43769 0.309734
$$433$$ 10.3820 0.498925 0.249463 0.968384i $$-0.419746\pi$$
0.249463 + 0.968384i $$0.419746\pi$$
$$434$$ 13.9443 0.669346
$$435$$ 0 0
$$436$$ 23.2705 1.11446
$$437$$ 6.00000 0.287019
$$438$$ 5.23607 0.250189
$$439$$ −20.9443 −0.999616 −0.499808 0.866136i $$-0.666596\pi$$
−0.499808 + 0.866136i $$0.666596\pi$$
$$440$$ 11.9098 0.567779
$$441$$ 5.23607 0.249337
$$442$$ 0.639320 0.0304094
$$443$$ −1.90983 −0.0907388 −0.0453694 0.998970i $$-0.514446\pi$$
−0.0453694 + 0.998970i $$0.514446\pi$$
$$444$$ 4.70820 0.223441
$$445$$ 18.1459 0.860198
$$446$$ 1.65248 0.0782470
$$447$$ −5.94427 −0.281154
$$448$$ 0.527864 0.0249392
$$449$$ −26.1246 −1.23290 −0.616448 0.787395i $$-0.711429\pi$$
−0.616448 + 0.787395i $$0.711429\pi$$
$$450$$ −15.9443 −0.751620
$$451$$ −5.32624 −0.250803
$$452$$ −12.8541 −0.604606
$$453$$ −1.65248 −0.0776401
$$454$$ −12.9098 −0.605888
$$455$$ 2.03444 0.0953761
$$456$$ −6.70820 −0.314140
$$457$$ 18.7082 0.875133 0.437566 0.899186i $$-0.355840\pi$$
0.437566 + 0.899186i $$0.355840\pi$$
$$458$$ 1.41641 0.0661844
$$459$$ −15.2148 −0.710165
$$460$$ 7.70820 0.359397
$$461$$ −38.9787 −1.81542 −0.907710 0.419598i $$-0.862171\pi$$
−0.907710 + 0.419598i $$0.862171\pi$$
$$462$$ −1.18034 −0.0549144
$$463$$ 10.7082 0.497652 0.248826 0.968548i $$-0.419955\pi$$
0.248826 + 0.968548i $$0.419955\pi$$
$$464$$ 0 0
$$465$$ 24.0344 1.11457
$$466$$ 9.41641 0.436207
$$467$$ −17.9443 −0.830362 −0.415181 0.909739i $$-0.636282\pi$$
−0.415181 + 0.909739i $$0.636282\pi$$
$$468$$ −1.00000 −0.0462250
$$469$$ 3.41641 0.157755
$$470$$ −16.6738 −0.769103
$$471$$ −9.00000 −0.414698
$$472$$ −13.6180 −0.626821
$$473$$ 10.0000 0.459800
$$474$$ 2.32624 0.106848
$$475$$ −47.8328 −2.19472
$$476$$ −15.8541 −0.726672
$$477$$ 5.23607 0.239743
$$478$$ −17.1459 −0.784235
$$479$$ −11.1803 −0.510843 −0.255421 0.966830i $$-0.582214\pi$$
−0.255421 + 0.966830i $$0.582214\pi$$
$$480$$ −13.3820 −0.610800
$$481$$ −1.11146 −0.0506780
$$482$$ −2.87539 −0.130970
$$483$$ −1.70820 −0.0777260
$$484$$ 14.7082 0.668555
$$485$$ 13.7295 0.623424
$$486$$ −8.61803 −0.390922
$$487$$ 42.5623 1.92868 0.964341 0.264663i $$-0.0852606\pi$$
0.964341 + 0.264663i $$0.0852606\pi$$
$$488$$ 1.38197 0.0625587
$$489$$ 3.72949 0.168653
$$490$$ −4.76393 −0.215213
$$491$$ −15.1246 −0.682564 −0.341282 0.939961i $$-0.610861\pi$$
−0.341282 + 0.939961i $$0.610861\pi$$
$$492$$ 3.85410 0.173756
$$493$$ 0 0
$$494$$ 0.708204 0.0318636
$$495$$ 13.9443 0.626748
$$496$$ −18.7082 −0.840023
$$497$$ −23.4164 −1.05037
$$498$$ 3.79837 0.170209
$$499$$ 24.6869 1.10514 0.552569 0.833467i $$-0.313648\pi$$
0.552569 + 0.833467i $$0.313648\pi$$
$$500$$ −30.2705 −1.35374
$$501$$ −6.50658 −0.290692
$$502$$ −12.1459 −0.542098
$$503$$ 14.2705 0.636291 0.318145 0.948042i $$-0.396940\pi$$
0.318145 + 0.948042i $$0.396940\pi$$
$$504$$ −13.0902 −0.583083
$$505$$ −2.38197 −0.105996
$$506$$ 1.05573 0.0469328
$$507$$ 8.00000 0.355292
$$508$$ −25.7984 −1.14462
$$509$$ 31.5623 1.39897 0.699487 0.714645i $$-0.253412\pi$$
0.699487 + 0.714645i $$0.253412\pi$$
$$510$$ 6.45085 0.285648
$$511$$ 30.6525 1.35599
$$512$$ 18.7082 0.826794
$$513$$ −16.8541 −0.744127
$$514$$ −14.3262 −0.631903
$$515$$ 35.3820 1.55912
$$516$$ −7.23607 −0.318550
$$517$$ 9.67376 0.425452
$$518$$ −6.50658 −0.285883
$$519$$ −2.52786 −0.110961
$$520$$ 2.03444 0.0892162
$$521$$ 4.09017 0.179194 0.0895968 0.995978i $$-0.471442\pi$$
0.0895968 + 0.995978i $$0.471442\pi$$
$$522$$ 0 0
$$523$$ −20.3820 −0.891241 −0.445621 0.895222i $$-0.647017\pi$$
−0.445621 + 0.895222i $$0.647017\pi$$
$$524$$ −23.1803 −1.01264
$$525$$ 13.6180 0.594340
$$526$$ −10.3262 −0.450245
$$527$$ 44.2148 1.92603
$$528$$ 1.58359 0.0689170
$$529$$ −21.4721 −0.933571
$$530$$ −4.76393 −0.206932
$$531$$ −15.9443 −0.691922
$$532$$ −17.5623 −0.761423
$$533$$ −0.909830 −0.0394091
$$534$$ −1.79837 −0.0778232
$$535$$ 26.0689 1.12706
$$536$$ 3.41641 0.147566
$$537$$ 9.88854 0.426722
$$538$$ −3.70820 −0.159872
$$539$$ 2.76393 0.119051
$$540$$ −21.6525 −0.931774
$$541$$ −14.5967 −0.627563 −0.313782 0.949495i $$-0.601596\pi$$
−0.313782 + 0.949495i $$0.601596\pi$$
$$542$$ 6.29180 0.270256
$$543$$ −3.67376 −0.157656
$$544$$ −24.6180 −1.05549
$$545$$ −55.4296 −2.37434
$$546$$ −0.201626 −0.00862880
$$547$$ 7.38197 0.315630 0.157815 0.987469i $$-0.449555\pi$$
0.157815 + 0.987469i $$0.449555\pi$$
$$548$$ −11.5623 −0.493917
$$549$$ 1.61803 0.0690560
$$550$$ −8.41641 −0.358877
$$551$$ 0 0
$$552$$ −1.70820 −0.0727060
$$553$$ 13.6180 0.579098
$$554$$ −13.2148 −0.561442
$$555$$ −11.2148 −0.476041
$$556$$ −2.09017 −0.0886430
$$557$$ −5.50658 −0.233321 −0.116661 0.993172i $$-0.537219\pi$$
−0.116661 + 0.993172i $$0.537219\pi$$
$$558$$ 16.3262 0.691145
$$559$$ 1.70820 0.0722493
$$560$$ −15.9787 −0.675224
$$561$$ −3.74265 −0.158015
$$562$$ 14.2918 0.602863
$$563$$ 28.3951 1.19671 0.598356 0.801230i $$-0.295821\pi$$
0.598356 + 0.801230i $$0.295821\pi$$
$$564$$ −7.00000 −0.294753
$$565$$ 30.6180 1.28811
$$566$$ −3.23607 −0.136022
$$567$$ −12.7639 −0.536035
$$568$$ −23.4164 −0.982531
$$569$$ −1.94427 −0.0815081 −0.0407541 0.999169i $$-0.512976\pi$$
−0.0407541 + 0.999169i $$0.512976\pi$$
$$570$$ 7.14590 0.299309
$$571$$ −34.5066 −1.44406 −0.722028 0.691864i $$-0.756790\pi$$
−0.722028 + 0.691864i $$0.756790\pi$$
$$572$$ −0.527864 −0.0220711
$$573$$ −10.5279 −0.439808
$$574$$ −5.32624 −0.222313
$$575$$ −12.1803 −0.507955
$$576$$ 0.618034 0.0257514
$$577$$ −2.76393 −0.115064 −0.0575320 0.998344i $$-0.518323\pi$$
−0.0575320 + 0.998344i $$0.518323\pi$$
$$578$$ 1.36068 0.0565968
$$579$$ −7.70820 −0.320342
$$580$$ 0 0
$$581$$ 22.2361 0.922508
$$582$$ −1.36068 −0.0564020
$$583$$ 2.76393 0.114470
$$584$$ 30.6525 1.26841
$$585$$ 2.38197 0.0984822
$$586$$ 5.27051 0.217723
$$587$$ 46.6180 1.92413 0.962066 0.272816i $$-0.0879552\pi$$
0.962066 + 0.272816i $$0.0879552\pi$$
$$588$$ −2.00000 −0.0824786
$$589$$ 48.9787 2.01813
$$590$$ 14.5066 0.597226
$$591$$ 3.88854 0.159953
$$592$$ 8.72949 0.358780
$$593$$ −14.4377 −0.592885 −0.296443 0.955051i $$-0.595800\pi$$
−0.296443 + 0.955051i $$0.595800\pi$$
$$594$$ −2.96556 −0.121678
$$595$$ 37.7639 1.54817
$$596$$ −15.5623 −0.637457
$$597$$ 3.61803 0.148076
$$598$$ 0.180340 0.00737465
$$599$$ 13.0689 0.533980 0.266990 0.963699i $$-0.413971\pi$$
0.266990 + 0.963699i $$0.413971\pi$$
$$600$$ 13.6180 0.555954
$$601$$ 29.1591 1.18942 0.594711 0.803939i $$-0.297266\pi$$
0.594711 + 0.803939i $$0.297266\pi$$
$$602$$ 10.0000 0.407570
$$603$$ 4.00000 0.162893
$$604$$ −4.32624 −0.176032
$$605$$ −35.0344 −1.42435
$$606$$ 0.236068 0.00958961
$$607$$ 10.9787 0.445612 0.222806 0.974863i $$-0.428478\pi$$
0.222806 + 0.974863i $$0.428478\pi$$
$$608$$ −27.2705 −1.10597
$$609$$ 0 0
$$610$$ −1.47214 −0.0596050
$$611$$ 1.65248 0.0668520
$$612$$ −18.5623 −0.750337
$$613$$ 27.5410 1.11237 0.556186 0.831058i $$-0.312264\pi$$
0.556186 + 0.831058i $$0.312264\pi$$
$$614$$ −11.8541 −0.478393
$$615$$ −9.18034 −0.370187
$$616$$ −6.90983 −0.278405
$$617$$ −14.1803 −0.570879 −0.285439 0.958397i $$-0.592140\pi$$
−0.285439 + 0.958397i $$0.592140\pi$$
$$618$$ −3.50658 −0.141055
$$619$$ 7.05573 0.283594 0.141797 0.989896i $$-0.454712\pi$$
0.141797 + 0.989896i $$0.454712\pi$$
$$620$$ 62.9230 2.52705
$$621$$ −4.29180 −0.172224
$$622$$ 1.29180 0.0517963
$$623$$ −10.5279 −0.421790
$$624$$ 0.270510 0.0108291
$$625$$ 22.8328 0.913313
$$626$$ −7.97871 −0.318894
$$627$$ −4.14590 −0.165571
$$628$$ −23.5623 −0.940238
$$629$$ −20.6312 −0.822619
$$630$$ 13.9443 0.555553
$$631$$ −28.2148 −1.12321 −0.561606 0.827405i $$-0.689816\pi$$
−0.561606 + 0.827405i $$0.689816\pi$$
$$632$$ 13.6180 0.541696
$$633$$ 7.20163 0.286239
$$634$$ 17.1246 0.680105
$$635$$ 61.4508 2.43860
$$636$$ −2.00000 −0.0793052
$$637$$ 0.472136 0.0187067
$$638$$ 0 0
$$639$$ −27.4164 −1.08458
$$640$$ −43.8673 −1.73401
$$641$$ 11.0557 0.436675 0.218338 0.975873i $$-0.429937\pi$$
0.218338 + 0.975873i $$0.429937\pi$$
$$642$$ −2.58359 −0.101966
$$643$$ −37.4164 −1.47556 −0.737780 0.675042i $$-0.764126\pi$$
−0.737780 + 0.675042i $$0.764126\pi$$
$$644$$ −4.47214 −0.176227
$$645$$ 17.2361 0.678670
$$646$$ 13.1459 0.517218
$$647$$ −30.5279 −1.20017 −0.600087 0.799935i $$-0.704867\pi$$
−0.600087 + 0.799935i $$0.704867\pi$$
$$648$$ −12.7639 −0.501415
$$649$$ −8.41641 −0.330373
$$650$$ −1.43769 −0.0563910
$$651$$ −13.9443 −0.546519
$$652$$ 9.76393 0.382385
$$653$$ 48.0132 1.87890 0.939450 0.342686i $$-0.111337\pi$$
0.939450 + 0.342686i $$0.111337\pi$$
$$654$$ 5.49342 0.214810
$$655$$ 55.2148 2.15742
$$656$$ 7.14590 0.279000
$$657$$ 35.8885 1.40015
$$658$$ 9.67376 0.377123
$$659$$ −7.05573 −0.274852 −0.137426 0.990512i $$-0.543883\pi$$
−0.137426 + 0.990512i $$0.543883\pi$$
$$660$$ −5.32624 −0.207324
$$661$$ −37.4508 −1.45667 −0.728335 0.685222i $$-0.759705\pi$$
−0.728335 + 0.685222i $$0.759705\pi$$
$$662$$ 13.0902 0.508764
$$663$$ −0.639320 −0.0248291
$$664$$ 22.2361 0.862927
$$665$$ 41.8328 1.62221
$$666$$ −7.61803 −0.295193
$$667$$ 0 0
$$668$$ −17.0344 −0.659082
$$669$$ −1.65248 −0.0638884
$$670$$ −3.63932 −0.140599
$$671$$ 0.854102 0.0329722
$$672$$ 7.76393 0.299500
$$673$$ −6.47214 −0.249483 −0.124741 0.992189i $$-0.539810\pi$$
−0.124741 + 0.992189i $$0.539810\pi$$
$$674$$ −21.0557 −0.811036
$$675$$ 34.2148 1.31693
$$676$$ 20.9443 0.805549
$$677$$ −40.8328 −1.56933 −0.784666 0.619918i $$-0.787166\pi$$
−0.784666 + 0.619918i $$0.787166\pi$$
$$678$$ −3.03444 −0.116537
$$679$$ −7.96556 −0.305690
$$680$$ 37.7639 1.44818
$$681$$ 12.9098 0.494706
$$682$$ 8.61803 0.330002
$$683$$ 20.8541 0.797960 0.398980 0.916960i $$-0.369364\pi$$
0.398980 + 0.916960i $$0.369364\pi$$
$$684$$ −20.5623 −0.786219
$$685$$ 27.5410 1.05229
$$686$$ 12.4377 0.474873
$$687$$ −1.41641 −0.0540393
$$688$$ −13.4164 −0.511496
$$689$$ 0.472136 0.0179869
$$690$$ 1.81966 0.0692733
$$691$$ 11.8328 0.450142 0.225071 0.974342i $$-0.427739\pi$$
0.225071 + 0.974342i $$0.427739\pi$$
$$692$$ −6.61803 −0.251580
$$693$$ −8.09017 −0.307320
$$694$$ −19.8541 −0.753651
$$695$$ 4.97871 0.188853
$$696$$ 0 0
$$697$$ −16.8885 −0.639699
$$698$$ 2.79837 0.105920
$$699$$ −9.41641 −0.356161
$$700$$ 35.6525 1.34754
$$701$$ −21.0557 −0.795264 −0.397632 0.917545i $$-0.630168\pi$$
−0.397632 + 0.917545i $$0.630168\pi$$
$$702$$ −0.506578 −0.0191195
$$703$$ −22.8541 −0.861959
$$704$$ 0.326238 0.0122956
$$705$$ 16.6738 0.627970
$$706$$ −11.8197 −0.444839
$$707$$ 1.38197 0.0519742
$$708$$ 6.09017 0.228883
$$709$$ −41.5066 −1.55881 −0.779406 0.626519i $$-0.784479\pi$$
−0.779406 + 0.626519i $$0.784479\pi$$
$$710$$ 24.9443 0.936142
$$711$$ 15.9443 0.597957
$$712$$ −10.5279 −0.394548
$$713$$ 12.4721 0.467085
$$714$$ −3.74265 −0.140065
$$715$$ 1.25735 0.0470224
$$716$$ 25.8885 0.967500
$$717$$ 17.1459 0.640325
$$718$$ −14.6869 −0.548111
$$719$$ 8.50658 0.317242 0.158621 0.987340i $$-0.449295\pi$$
0.158621 + 0.987340i $$0.449295\pi$$
$$720$$ −18.7082 −0.697214
$$721$$ −20.5279 −0.764498
$$722$$ 2.81966 0.104937
$$723$$ 2.87539 0.106937
$$724$$ −9.61803 −0.357451
$$725$$ 0 0
$$726$$ 3.47214 0.128863
$$727$$ 28.0557 1.04053 0.520265 0.854005i $$-0.325833\pi$$
0.520265 + 0.854005i $$0.325833\pi$$
$$728$$ −1.18034 −0.0437463
$$729$$ −8.50658 −0.315058
$$730$$ −32.6525 −1.20852
$$731$$ 31.7082 1.17277
$$732$$ −0.618034 −0.0228432
$$733$$ 14.8197 0.547377 0.273688 0.961818i $$-0.411756\pi$$
0.273688 + 0.961818i $$0.411756\pi$$
$$734$$ 16.8541 0.622096
$$735$$ 4.76393 0.175720
$$736$$ −6.94427 −0.255969
$$737$$ 2.11146 0.0777765
$$738$$ −6.23607 −0.229553
$$739$$ −50.0689 −1.84181 −0.920907 0.389783i $$-0.872550\pi$$
−0.920907 + 0.389783i $$0.872550\pi$$
$$740$$ −29.3607 −1.07932
$$741$$ −0.708204 −0.0260165
$$742$$ 2.76393 0.101467
$$743$$ 35.2361 1.29269 0.646343 0.763047i $$-0.276298\pi$$
0.646343 + 0.763047i $$0.276298\pi$$
$$744$$ −13.9443 −0.511222
$$745$$ 37.0689 1.35810
$$746$$ 12.7426 0.466541
$$747$$ 26.0344 0.952550
$$748$$ −9.79837 −0.358264
$$749$$ −15.1246 −0.552641
$$750$$ −7.14590 −0.260931
$$751$$ −18.5279 −0.676091 −0.338046 0.941130i $$-0.609766\pi$$
−0.338046 + 0.941130i $$0.609766\pi$$
$$752$$ −12.9787 −0.473285
$$753$$ 12.1459 0.442621
$$754$$ 0 0
$$755$$ 10.3050 0.375036
$$756$$ 12.5623 0.456887
$$757$$ −0.0212862 −0.000773661 0 −0.000386831 1.00000i $$-0.500123\pi$$
−0.000386831 1.00000i $$0.500123\pi$$
$$758$$ −15.0132 −0.545302
$$759$$ −1.05573 −0.0383205
$$760$$ 41.8328 1.51744
$$761$$ 25.2016 0.913558 0.456779 0.889580i $$-0.349003\pi$$
0.456779 + 0.889580i $$0.349003\pi$$
$$762$$ −6.09017 −0.220624
$$763$$ 32.1591 1.16424
$$764$$ −27.5623 −0.997169
$$765$$ 44.2148 1.59859
$$766$$ −17.8328 −0.644326
$$767$$ −1.43769 −0.0519121
$$768$$ 4.05573 0.146348
$$769$$ −19.3607 −0.698164 −0.349082 0.937092i $$-0.613507\pi$$
−0.349082 + 0.937092i $$0.613507\pi$$
$$770$$ 7.36068 0.265260
$$771$$ 14.3262 0.515947
$$772$$ −20.1803 −0.726306
$$773$$ −14.0000 −0.503545 −0.251773 0.967786i $$-0.581013\pi$$
−0.251773 + 0.967786i $$0.581013\pi$$
$$774$$ 11.7082 0.420843
$$775$$ −99.4296 −3.57162
$$776$$ −7.96556 −0.285947
$$777$$ 6.50658 0.233422
$$778$$ −11.8197 −0.423755
$$779$$ −18.7082 −0.670291
$$780$$ −0.909830 −0.0325771
$$781$$ −14.4721 −0.517854
$$782$$ 3.34752 0.119707
$$783$$ 0 0
$$784$$ −3.70820 −0.132436
$$785$$ 56.1246 2.00317
$$786$$ −5.47214 −0.195185
$$787$$ 19.3607 0.690134 0.345067 0.938578i $$-0.387856\pi$$
0.345067 + 0.938578i $$0.387856\pi$$
$$788$$ 10.1803 0.362660
$$789$$ 10.3262 0.367624
$$790$$ −14.5066 −0.516121
$$791$$ −17.7639 −0.631613
$$792$$ −8.09017 −0.287472
$$793$$ 0.145898 0.00518099
$$794$$ −8.68692 −0.308287
$$795$$ 4.76393 0.168959
$$796$$ 9.47214 0.335731
$$797$$ 43.1803 1.52953 0.764763 0.644312i $$-0.222856\pi$$
0.764763 + 0.644312i $$0.222856\pi$$
$$798$$ −4.14590 −0.146763
$$799$$ 30.6738 1.08516
$$800$$ 55.3607 1.95730
$$801$$ −12.3262 −0.435526
$$802$$ 15.4934 0.547092
$$803$$ 18.9443 0.668529
$$804$$ −1.52786 −0.0538836
$$805$$ 10.6525 0.375450
$$806$$ 1.47214 0.0518538
$$807$$ 3.70820 0.130535
$$808$$ 1.38197 0.0486174
$$809$$ −43.0689 −1.51422 −0.757111 0.653287i $$-0.773390\pi$$
−0.757111 + 0.653287i $$0.773390\pi$$
$$810$$ 13.5967 0.477741
$$811$$ 5.65248 0.198485 0.0992426 0.995063i $$-0.468358\pi$$
0.0992426 + 0.995063i $$0.468358\pi$$
$$812$$ 0 0
$$813$$ −6.29180 −0.220663
$$814$$ −4.02129 −0.140946
$$815$$ −23.2574 −0.814670
$$816$$ 5.02129 0.175780
$$817$$ 35.1246 1.22885
$$818$$ 16.9443 0.592443
$$819$$ −1.38197 −0.0482898
$$820$$ −24.0344 −0.839319
$$821$$ 8.58359 0.299569 0.149785 0.988719i $$-0.452142\pi$$
0.149785 + 0.988719i $$0.452142\pi$$
$$822$$ −2.72949 −0.0952019
$$823$$ −5.47214 −0.190747 −0.0953733 0.995442i $$-0.530404\pi$$
−0.0953733 + 0.995442i $$0.530404\pi$$
$$824$$ −20.5279 −0.715122
$$825$$ 8.41641 0.293022
$$826$$ −8.41641 −0.292844
$$827$$ 26.9656 0.937684 0.468842 0.883282i $$-0.344671\pi$$
0.468842 + 0.883282i $$0.344671\pi$$
$$828$$ −5.23607 −0.181966
$$829$$ 32.7984 1.13913 0.569567 0.821945i $$-0.307111\pi$$
0.569567 + 0.821945i $$0.307111\pi$$
$$830$$ −23.6869 −0.822185
$$831$$ 13.2148 0.458416
$$832$$ 0.0557281 0.00193202
$$833$$ 8.76393 0.303652
$$834$$ −0.493422 −0.0170858
$$835$$ 40.5755 1.40417
$$836$$ −10.8541 −0.375397
$$837$$ −35.0344 −1.21097
$$838$$ −10.8541 −0.374949
$$839$$ −48.2148 −1.66456 −0.832280 0.554356i $$-0.812965\pi$$
−0.832280 + 0.554356i $$0.812965\pi$$
$$840$$ −11.9098 −0.410928
$$841$$ 0 0
$$842$$ −19.1803 −0.660998
$$843$$ −14.2918 −0.492236
$$844$$ 18.8541 0.648985
$$845$$ −49.8885 −1.71622
$$846$$ 11.3262 0.389404
$$847$$ 20.3262 0.698418
$$848$$ −3.70820 −0.127340
$$849$$ 3.23607 0.111062
$$850$$ −26.6869 −0.915354
$$851$$ −5.81966 −0.199495
$$852$$ 10.4721 0.358769
$$853$$ −45.0000 −1.54077 −0.770385 0.637579i $$-0.779936\pi$$
−0.770385 + 0.637579i $$0.779936\pi$$
$$854$$ 0.854102 0.0292268
$$855$$ 48.9787 1.67504
$$856$$ −15.1246 −0.516949
$$857$$ −45.3262 −1.54831 −0.774157 0.632993i $$-0.781826\pi$$
−0.774157 + 0.632993i $$0.781826\pi$$
$$858$$ −0.124612 −0.00425418
$$859$$ 32.7082 1.11599 0.557995 0.829844i $$-0.311571\pi$$
0.557995 + 0.829844i $$0.311571\pi$$
$$860$$ 45.1246 1.53874
$$861$$ 5.32624 0.181518
$$862$$ 9.02129 0.307266
$$863$$ 17.7426 0.603967 0.301983 0.953313i $$-0.402351\pi$$
0.301983 + 0.953313i $$0.402351\pi$$
$$864$$ 19.5066 0.663627
$$865$$ 15.7639 0.535990
$$866$$ 6.41641 0.218038
$$867$$ −1.36068 −0.0462111
$$868$$ −36.5066 −1.23911
$$869$$ 8.41641 0.285507
$$870$$ 0 0
$$871$$ 0.360680 0.0122212
$$872$$ 32.1591 1.08904
$$873$$ −9.32624 −0.315645
$$874$$ 3.70820 0.125432
$$875$$ −41.8328 −1.41421
$$876$$ −13.7082 −0.463157
$$877$$ 4.38197 0.147968 0.0739842 0.997259i $$-0.476429\pi$$
0.0739842 + 0.997259i $$0.476429\pi$$
$$878$$ −12.9443 −0.436848
$$879$$ −5.27051 −0.177770
$$880$$ −9.87539 −0.332899
$$881$$ 4.27051 0.143877 0.0719386 0.997409i $$-0.477081\pi$$
0.0719386 + 0.997409i $$0.477081\pi$$
$$882$$ 3.23607 0.108964
$$883$$ −20.6869 −0.696170 −0.348085 0.937463i $$-0.613168\pi$$
−0.348085 + 0.937463i $$0.613168\pi$$
$$884$$ −1.67376 −0.0562947
$$885$$ −14.5066 −0.487633
$$886$$ −1.18034 −0.0396543
$$887$$ −38.0689 −1.27823 −0.639114 0.769112i $$-0.720699\pi$$
−0.639114 + 0.769112i $$0.720699\pi$$
$$888$$ 6.50658 0.218346
$$889$$ −35.6525 −1.19575
$$890$$ 11.2148 0.375920
$$891$$ −7.88854 −0.264276
$$892$$ −4.32624 −0.144853
$$893$$ 33.9787 1.13705
$$894$$ −3.67376 −0.122869
$$895$$ −61.6656 −2.06125
$$896$$ 25.4508 0.850253
$$897$$ −0.180340 −0.00602137
$$898$$ −16.1459 −0.538796
$$899$$ 0 0
$$900$$ 41.7426 1.39142
$$901$$ 8.76393 0.291969
$$902$$ −3.29180 −0.109605
$$903$$ −10.0000 −0.332779
$$904$$ −17.7639 −0.590820
$$905$$ 22.9098 0.761549
$$906$$ −1.02129 −0.0339300
$$907$$ 9.76393 0.324206 0.162103 0.986774i $$-0.448172\pi$$
0.162103 + 0.986774i $$0.448172\pi$$
$$908$$ 33.7984 1.12164
$$909$$ 1.61803 0.0536668
$$910$$ 1.25735 0.0416809
$$911$$ −10.9443 −0.362600 −0.181300 0.983428i $$-0.558030\pi$$
−0.181300 + 0.983428i $$0.558030\pi$$
$$912$$ 5.56231 0.184186
$$913$$ 13.7426 0.454815
$$914$$ 11.5623 0.382447
$$915$$ 1.47214 0.0486673
$$916$$ −3.70820 −0.122523
$$917$$ −32.0344 −1.05787
$$918$$ −9.40325 −0.310354
$$919$$ 31.3050 1.03266 0.516328 0.856391i $$-0.327299\pi$$
0.516328 + 0.856391i $$0.327299\pi$$
$$920$$ 10.6525 0.351202
$$921$$ 11.8541 0.390606
$$922$$ −24.0902 −0.793367
$$923$$ −2.47214 −0.0813713
$$924$$ 3.09017 0.101659
$$925$$ 46.3951 1.52546
$$926$$ 6.61803 0.217482
$$927$$ −24.0344 −0.789395
$$928$$ 0 0
$$929$$ −3.65248 −0.119834 −0.0599169 0.998203i $$-0.519084\pi$$
−0.0599169 + 0.998203i $$0.519084\pi$$
$$930$$ 14.8541 0.487085
$$931$$ 9.70820 0.318174
$$932$$ −24.6525 −0.807519
$$933$$ −1.29180 −0.0422915
$$934$$ −11.0902 −0.362881
$$935$$ 23.3394 0.763280
$$936$$ −1.38197 −0.0451710
$$937$$ 6.65248 0.217327 0.108663 0.994079i $$-0.465343\pi$$
0.108663 + 0.994079i $$0.465343\pi$$
$$938$$ 2.11146 0.0689415
$$939$$ 7.97871 0.260375
$$940$$ 43.6525 1.42379
$$941$$ −34.8885 −1.13733 −0.568667 0.822568i $$-0.692541\pi$$
−0.568667 + 0.822568i $$0.692541\pi$$
$$942$$ −5.56231 −0.181230
$$943$$ −4.76393 −0.155135
$$944$$ 11.2918 0.367517
$$945$$ −29.9230 −0.973395
$$946$$ 6.18034 0.200940
$$947$$ 43.0344 1.39843 0.699216 0.714911i $$-0.253533\pi$$
0.699216 + 0.714911i $$0.253533\pi$$
$$948$$ −6.09017 −0.197800
$$949$$ 3.23607 0.105047
$$950$$ −29.5623 −0.959128
$$951$$ −17.1246 −0.555304
$$952$$ −21.9098 −0.710102
$$953$$ 42.6312 1.38096 0.690480 0.723352i $$-0.257399\pi$$
0.690480 + 0.723352i $$0.257399\pi$$
$$954$$ 3.23607 0.104772
$$955$$ 65.6525 2.12446
$$956$$ 44.8885 1.45180
$$957$$ 0 0
$$958$$ −6.90983 −0.223246
$$959$$ −15.9787 −0.515980
$$960$$ 0.562306 0.0181483
$$961$$ 70.8115 2.28424
$$962$$ −0.686918 −0.0221471
$$963$$ −17.7082 −0.570639
$$964$$ 7.52786 0.242456
$$965$$ 48.0689 1.54739
$$966$$ −1.05573 −0.0339675
$$967$$ 3.56231 0.114556 0.0572780 0.998358i $$-0.481758\pi$$
0.0572780 + 0.998358i $$0.481758\pi$$
$$968$$ 20.3262 0.653310
$$969$$ −13.1459 −0.422307
$$970$$ 8.48529 0.272446
$$971$$ −19.5066 −0.625996 −0.312998 0.949754i $$-0.601333\pi$$
−0.312998 + 0.949754i $$0.601333\pi$$
$$972$$ 22.5623 0.723686
$$973$$ −2.88854 −0.0926025
$$974$$ 26.3050 0.842865
$$975$$ 1.43769 0.0460431
$$976$$ −1.14590 −0.0366793
$$977$$ −45.2148 −1.44655 −0.723275 0.690561i $$-0.757364\pi$$
−0.723275 + 0.690561i $$0.757364\pi$$
$$978$$ 2.30495 0.0737042
$$979$$ −6.50658 −0.207951
$$980$$ 12.4721 0.398408
$$981$$ 37.6525 1.20215
$$982$$ −9.34752 −0.298291
$$983$$ −10.9443 −0.349068 −0.174534 0.984651i $$-0.555842\pi$$
−0.174534 + 0.984651i $$0.555842\pi$$
$$984$$ 5.32624 0.169794
$$985$$ −24.2492 −0.772645
$$986$$ 0 0
$$987$$ −9.67376 −0.307919
$$988$$ −1.85410 −0.0589868
$$989$$ 8.94427 0.284411
$$990$$ 8.61803 0.273899
$$991$$ 7.34752 0.233402 0.116701 0.993167i $$-0.462768\pi$$
0.116701 + 0.993167i $$0.462768\pi$$
$$992$$ −56.6869 −1.79981
$$993$$ −13.0902 −0.415404
$$994$$ −14.4721 −0.459028
$$995$$ −22.5623 −0.715273
$$996$$ −9.94427 −0.315096
$$997$$ 16.9098 0.535540 0.267770 0.963483i $$-0.413713\pi$$
0.267770 + 0.963483i $$0.413713\pi$$
$$998$$ 15.2574 0.482963
$$999$$ 16.3475 0.517213
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 841.2.a.a.1.2 2
3.2 odd 2 7569.2.a.l.1.1 2
29.2 odd 28 841.2.e.j.236.3 24
29.3 odd 28 841.2.e.j.270.3 24
29.4 even 14 841.2.d.g.190.2 12
29.5 even 14 841.2.d.g.605.2 12
29.6 even 14 841.2.d.g.645.2 12
29.7 even 7 841.2.d.i.571.1 12
29.8 odd 28 841.2.e.j.267.3 24
29.9 even 14 841.2.d.g.574.1 12
29.10 odd 28 841.2.e.j.651.3 24
29.11 odd 28 841.2.e.j.63.3 24
29.12 odd 4 841.2.b.b.840.3 4
29.13 even 14 841.2.d.g.778.1 12
29.14 odd 28 841.2.e.j.196.2 24
29.15 odd 28 841.2.e.j.196.3 24
29.16 even 7 841.2.d.i.778.2 12
29.17 odd 4 841.2.b.b.840.2 4
29.18 odd 28 841.2.e.j.63.2 24
29.19 odd 28 841.2.e.j.651.2 24
29.20 even 7 841.2.d.i.574.2 12
29.21 odd 28 841.2.e.j.267.2 24
29.22 even 14 841.2.d.g.571.2 12
29.23 even 7 841.2.d.i.645.1 12
29.24 even 7 841.2.d.i.605.1 12
29.25 even 7 841.2.d.i.190.1 12
29.26 odd 28 841.2.e.j.270.2 24
29.27 odd 28 841.2.e.j.236.2 24
29.28 even 2 841.2.a.c.1.1 yes 2
87.86 odd 2 7569.2.a.d.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
841.2.a.a.1.2 2 1.1 even 1 trivial
841.2.a.c.1.1 yes 2 29.28 even 2
841.2.b.b.840.2 4 29.17 odd 4
841.2.b.b.840.3 4 29.12 odd 4
841.2.d.g.190.2 12 29.4 even 14
841.2.d.g.571.2 12 29.22 even 14
841.2.d.g.574.1 12 29.9 even 14
841.2.d.g.605.2 12 29.5 even 14
841.2.d.g.645.2 12 29.6 even 14
841.2.d.g.778.1 12 29.13 even 14
841.2.d.i.190.1 12 29.25 even 7
841.2.d.i.571.1 12 29.7 even 7
841.2.d.i.574.2 12 29.20 even 7
841.2.d.i.605.1 12 29.24 even 7
841.2.d.i.645.1 12 29.23 even 7
841.2.d.i.778.2 12 29.16 even 7
841.2.e.j.63.2 24 29.18 odd 28
841.2.e.j.63.3 24 29.11 odd 28
841.2.e.j.196.2 24 29.14 odd 28
841.2.e.j.196.3 24 29.15 odd 28
841.2.e.j.236.2 24 29.27 odd 28
841.2.e.j.236.3 24 29.2 odd 28
841.2.e.j.267.2 24 29.21 odd 28
841.2.e.j.267.3 24 29.8 odd 28
841.2.e.j.270.2 24 29.26 odd 28
841.2.e.j.270.3 24 29.3 odd 28
841.2.e.j.651.2 24 29.19 odd 28
841.2.e.j.651.3 24 29.10 odd 28
7569.2.a.d.1.2 2 87.86 odd 2
7569.2.a.l.1.1 2 3.2 odd 2