# Properties

 Label 11.6.a.b.1.2 Level $11$ Weight $6$ Character 11.1 Self dual yes Analytic conductor $1.764$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,6,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 11.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: $$1.76422201794$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.54492.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - x^{2} - 52x - 38$$ x^3 - x^2 - 52*x - 38 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$8.04796$$ of defining polynomial Character $$\chi$$ $$=$$ 11.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.20859 q^{2} +16.8394 q^{3} -27.1221 q^{4} +75.2230 q^{5} +37.1913 q^{6} -225.525 q^{7} -130.577 q^{8} +40.5643 q^{9} +O(q^{10})$$ $$q+2.20859 q^{2} +16.8394 q^{3} -27.1221 q^{4} +75.2230 q^{5} +37.1913 q^{6} -225.525 q^{7} -130.577 q^{8} +40.5643 q^{9} +166.137 q^{10} +121.000 q^{11} -456.719 q^{12} +455.465 q^{13} -498.092 q^{14} +1266.71 q^{15} +579.518 q^{16} +190.657 q^{17} +89.5900 q^{18} -135.393 q^{19} -2040.21 q^{20} -3797.69 q^{21} +267.240 q^{22} +2796.65 q^{23} -2198.83 q^{24} +2533.51 q^{25} +1005.94 q^{26} -3408.89 q^{27} +6116.71 q^{28} -2608.58 q^{29} +2797.64 q^{30} -1056.76 q^{31} +5458.37 q^{32} +2037.56 q^{33} +421.082 q^{34} -16964.7 q^{35} -1100.19 q^{36} +12536.8 q^{37} -299.028 q^{38} +7669.74 q^{39} -9822.37 q^{40} +1130.09 q^{41} -8387.55 q^{42} -14671.0 q^{43} -3281.78 q^{44} +3051.37 q^{45} +6176.65 q^{46} -16882.2 q^{47} +9758.71 q^{48} +34054.4 q^{49} +5595.48 q^{50} +3210.54 q^{51} -12353.2 q^{52} +3313.02 q^{53} -7528.84 q^{54} +9101.99 q^{55} +29448.3 q^{56} -2279.93 q^{57} -5761.29 q^{58} +11454.0 q^{59} -34355.8 q^{60} -28227.5 q^{61} -2333.95 q^{62} -9148.26 q^{63} -6489.25 q^{64} +34261.4 q^{65} +4500.15 q^{66} -51431.0 q^{67} -5171.01 q^{68} +47093.8 q^{69} -37468.0 q^{70} -16218.0 q^{71} -5296.75 q^{72} -10168.8 q^{73} +27688.7 q^{74} +42662.6 q^{75} +3672.15 q^{76} -27288.5 q^{77} +16939.3 q^{78} +60841.2 q^{79} +43593.1 q^{80} -67260.7 q^{81} +2495.90 q^{82} +45770.6 q^{83} +103002. q^{84} +14341.8 q^{85} -32402.3 q^{86} -43926.9 q^{87} -15799.8 q^{88} -82267.9 q^{89} +6739.23 q^{90} -102719. q^{91} -75851.0 q^{92} -17795.1 q^{93} -37285.8 q^{94} -10184.7 q^{95} +91915.5 q^{96} +53097.0 q^{97} +75212.2 q^{98} +4908.28 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9}+O(q^{10})$$ 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9 $$3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9} - 414 q^{10} + 363 q^{11} + 992 q^{12} + 486 q^{13} - 1020 q^{14} + 1654 q^{15} + 1992 q^{16} + 1086 q^{17} - 3706 q^{18} + 1380 q^{19} - 3480 q^{20} - 908 q^{21} - 3066 q^{23} - 11748 q^{24} - 57 q^{25} + 12132 q^{26} - 2990 q^{27} + 23712 q^{28} - 3426 q^{29} + 2650 q^{30} - 4098 q^{31} - 12408 q^{32} + 4114 q^{33} + 25320 q^{34} - 24228 q^{35} + 4756 q^{36} + 17724 q^{37} - 9240 q^{38} - 6560 q^{39} - 15276 q^{40} + 5994 q^{41} - 47828 q^{42} - 26208 q^{43} + 10164 q^{44} + 18458 q^{45} - 16806 q^{46} - 17232 q^{47} + 61064 q^{48} + 48531 q^{49} + 41070 q^{50} - 22724 q^{51} - 35304 q^{52} + 50586 q^{53} + 18814 q^{54} + 2904 q^{55} - 42312 q^{56} + 20160 q^{57} - 29172 q^{58} - 3738 q^{59} - 13456 q^{60} + 18486 q^{61} - 19974 q^{62} - 12496 q^{63} - 20352 q^{64} - 7668 q^{65} - 24926 q^{66} - 47754 q^{67} - 12600 q^{68} + 35042 q^{69} - 123372 q^{70} + 39282 q^{71} - 95040 q^{72} + 15426 q^{73} + 153294 q^{74} - 21916 q^{75} + 103920 q^{76} + 10164 q^{77} + 124984 q^{78} + 125148 q^{79} + 118680 q^{80} - 86917 q^{81} - 255372 q^{82} - 143928 q^{83} + 343616 q^{84} - 104040 q^{85} + 243060 q^{86} - 19368 q^{87} - 68244 q^{88} - 106824 q^{89} + 103424 q^{90} - 109632 q^{91} - 336528 q^{92} - 16622 q^{93} - 74928 q^{94} - 22200 q^{95} - 76456 q^{96} + 9684 q^{97} + 3480 q^{98} - 847 q^{99}+O(q^{100})$$ 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9 - 414 * q^10 + 363 * q^11 + 992 * q^12 + 486 * q^13 - 1020 * q^14 + 1654 * q^15 + 1992 * q^16 + 1086 * q^17 - 3706 * q^18 + 1380 * q^19 - 3480 * q^20 - 908 * q^21 - 3066 * q^23 - 11748 * q^24 - 57 * q^25 + 12132 * q^26 - 2990 * q^27 + 23712 * q^28 - 3426 * q^29 + 2650 * q^30 - 4098 * q^31 - 12408 * q^32 + 4114 * q^33 + 25320 * q^34 - 24228 * q^35 + 4756 * q^36 + 17724 * q^37 - 9240 * q^38 - 6560 * q^39 - 15276 * q^40 + 5994 * q^41 - 47828 * q^42 - 26208 * q^43 + 10164 * q^44 + 18458 * q^45 - 16806 * q^46 - 17232 * q^47 + 61064 * q^48 + 48531 * q^49 + 41070 * q^50 - 22724 * q^51 - 35304 * q^52 + 50586 * q^53 + 18814 * q^54 + 2904 * q^55 - 42312 * q^56 + 20160 * q^57 - 29172 * q^58 - 3738 * q^59 - 13456 * q^60 + 18486 * q^61 - 19974 * q^62 - 12496 * q^63 - 20352 * q^64 - 7668 * q^65 - 24926 * q^66 - 47754 * q^67 - 12600 * q^68 + 35042 * q^69 - 123372 * q^70 + 39282 * q^71 - 95040 * q^72 + 15426 * q^73 + 153294 * q^74 - 21916 * q^75 + 103920 * q^76 + 10164 * q^77 + 124984 * q^78 + 125148 * q^79 + 118680 * q^80 - 86917 * q^81 - 255372 * q^82 - 143928 * q^83 + 343616 * q^84 - 104040 * q^85 + 243060 * q^86 - 19368 * q^87 - 68244 * q^88 - 106824 * q^89 + 103424 * q^90 - 109632 * q^91 - 336528 * q^92 - 16622 * q^93 - 74928 * q^94 - 22200 * q^95 - 76456 * q^96 + 9684 * q^97 + 3480 * q^98 - 847 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.20859 0.390428 0.195214 0.980761i $$-0.437460\pi$$
0.195214 + 0.980761i $$0.437460\pi$$
$$3$$ 16.8394 1.08025 0.540123 0.841586i $$-0.318378\pi$$
0.540123 + 0.841586i $$0.318378\pi$$
$$4$$ −27.1221 −0.847566
$$5$$ 75.2230 1.34563 0.672815 0.739810i $$-0.265085\pi$$
0.672815 + 0.739810i $$0.265085\pi$$
$$6$$ 37.1913 0.421758
$$7$$ −225.525 −1.73960 −0.869799 0.493406i $$-0.835752\pi$$
−0.869799 + 0.493406i $$0.835752\pi$$
$$8$$ −130.577 −0.721341
$$9$$ 40.5643 0.166931
$$10$$ 166.137 0.525371
$$11$$ 121.000 0.301511
$$12$$ −456.719 −0.915580
$$13$$ 455.465 0.747474 0.373737 0.927535i $$-0.378076\pi$$
0.373737 + 0.927535i $$0.378076\pi$$
$$14$$ −498.092 −0.679187
$$15$$ 1266.71 1.45361
$$16$$ 579.518 0.565935
$$17$$ 190.657 0.160003 0.0800017 0.996795i $$-0.474507\pi$$
0.0800017 + 0.996795i $$0.474507\pi$$
$$18$$ 89.5900 0.0651746
$$19$$ −135.393 −0.0860424 −0.0430212 0.999074i $$-0.513698\pi$$
−0.0430212 + 0.999074i $$0.513698\pi$$
$$20$$ −2040.21 −1.14051
$$21$$ −3797.69 −1.87919
$$22$$ 267.240 0.117718
$$23$$ 2796.65 1.10235 0.551173 0.834391i $$-0.314180\pi$$
0.551173 + 0.834391i $$0.314180\pi$$
$$24$$ −2198.83 −0.779225
$$25$$ 2533.51 0.810722
$$26$$ 1005.94 0.291835
$$27$$ −3408.89 −0.899919
$$28$$ 6116.71 1.47443
$$29$$ −2608.58 −0.575983 −0.287991 0.957633i $$-0.592987\pi$$
−0.287991 + 0.957633i $$0.592987\pi$$
$$30$$ 2797.64 0.567530
$$31$$ −1056.76 −0.197502 −0.0987510 0.995112i $$-0.531485\pi$$
−0.0987510 + 0.995112i $$0.531485\pi$$
$$32$$ 5458.37 0.942297
$$33$$ 2037.56 0.325706
$$34$$ 421.082 0.0624697
$$35$$ −16964.7 −2.34086
$$36$$ −1100.19 −0.141485
$$37$$ 12536.8 1.50550 0.752752 0.658304i $$-0.228726\pi$$
0.752752 + 0.658304i $$0.228726\pi$$
$$38$$ −299.028 −0.0335933
$$39$$ 7669.74 0.807456
$$40$$ −9822.37 −0.970658
$$41$$ 1130.09 0.104991 0.0524954 0.998621i $$-0.483282\pi$$
0.0524954 + 0.998621i $$0.483282\pi$$
$$42$$ −8387.55 −0.733689
$$43$$ −14671.0 −1.21001 −0.605005 0.796222i $$-0.706829\pi$$
−0.605005 + 0.796222i $$0.706829\pi$$
$$44$$ −3281.78 −0.255551
$$45$$ 3051.37 0.224628
$$46$$ 6176.65 0.430386
$$47$$ −16882.2 −1.11477 −0.557383 0.830256i $$-0.688194\pi$$
−0.557383 + 0.830256i $$0.688194\pi$$
$$48$$ 9758.71 0.611349
$$49$$ 34054.4 2.02620
$$50$$ 5595.48 0.316528
$$51$$ 3210.54 0.172843
$$52$$ −12353.2 −0.633534
$$53$$ 3313.02 0.162007 0.0810035 0.996714i $$-0.474187\pi$$
0.0810035 + 0.996714i $$0.474187\pi$$
$$54$$ −7528.84 −0.351353
$$55$$ 9101.99 0.405723
$$56$$ 29448.3 1.25484
$$57$$ −2279.93 −0.0929469
$$58$$ −5761.29 −0.224880
$$59$$ 11454.0 0.428378 0.214189 0.976792i $$-0.431289\pi$$
0.214189 + 0.976792i $$0.431289\pi$$
$$60$$ −34355.8 −1.23203
$$61$$ −28227.5 −0.971286 −0.485643 0.874157i $$-0.661415\pi$$
−0.485643 + 0.874157i $$0.661415\pi$$
$$62$$ −2333.95 −0.0771102
$$63$$ −9148.26 −0.290394
$$64$$ −6489.25 −0.198036
$$65$$ 34261.4 1.00582
$$66$$ 4500.15 0.127165
$$67$$ −51431.0 −1.39971 −0.699855 0.714285i $$-0.746752\pi$$
−0.699855 + 0.714285i $$0.746752\pi$$
$$68$$ −5171.01 −0.135614
$$69$$ 47093.8 1.19081
$$70$$ −37468.0 −0.913935
$$71$$ −16218.0 −0.381814 −0.190907 0.981608i $$-0.561143\pi$$
−0.190907 + 0.981608i $$0.561143\pi$$
$$72$$ −5296.75 −0.120414
$$73$$ −10168.8 −0.223337 −0.111669 0.993745i $$-0.535620\pi$$
−0.111669 + 0.993745i $$0.535620\pi$$
$$74$$ 27688.7 0.587791
$$75$$ 42662.6 0.875779
$$76$$ 3672.15 0.0729266
$$77$$ −27288.5 −0.524509
$$78$$ 16939.3 0.315253
$$79$$ 60841.2 1.09681 0.548404 0.836214i $$-0.315236\pi$$
0.548404 + 0.836214i $$0.315236\pi$$
$$80$$ 43593.1 0.761540
$$81$$ −67260.7 −1.13907
$$82$$ 2495.90 0.0409913
$$83$$ 45770.6 0.729275 0.364638 0.931150i $$-0.381193\pi$$
0.364638 + 0.931150i $$0.381193\pi$$
$$84$$ 103002. 1.59274
$$85$$ 14341.8 0.215306
$$86$$ −32402.3 −0.472421
$$87$$ −43926.9 −0.622203
$$88$$ −15799.8 −0.217492
$$89$$ −82267.9 −1.10092 −0.550460 0.834862i $$-0.685548\pi$$
−0.550460 + 0.834862i $$0.685548\pi$$
$$90$$ 6739.23 0.0877009
$$91$$ −102719. −1.30031
$$92$$ −75851.0 −0.934312
$$93$$ −17795.1 −0.213351
$$94$$ −37285.8 −0.435235
$$95$$ −10184.7 −0.115781
$$96$$ 91915.5 1.01791
$$97$$ 53097.0 0.572981 0.286491 0.958083i $$-0.407511\pi$$
0.286491 + 0.958083i $$0.407511\pi$$
$$98$$ 75212.2 0.791085
$$99$$ 4908.28 0.0503317
$$100$$ −68714.1 −0.687141
$$101$$ 186821. 1.82231 0.911153 0.412069i $$-0.135194\pi$$
0.911153 + 0.412069i $$0.135194\pi$$
$$102$$ 7090.76 0.0674827
$$103$$ 34290.5 0.318479 0.159240 0.987240i $$-0.449096\pi$$
0.159240 + 0.987240i $$0.449096\pi$$
$$104$$ −59473.0 −0.539184
$$105$$ −285674. −2.52870
$$106$$ 7317.10 0.0632520
$$107$$ −224117. −1.89241 −0.946206 0.323565i $$-0.895119\pi$$
−0.946206 + 0.323565i $$0.895119\pi$$
$$108$$ 92456.3 0.762741
$$109$$ 162229. 1.30786 0.653931 0.756554i $$-0.273118\pi$$
0.653931 + 0.756554i $$0.273118\pi$$
$$110$$ 20102.6 0.158405
$$111$$ 211112. 1.62632
$$112$$ −130696. −0.984500
$$113$$ 92225.0 0.679442 0.339721 0.940526i $$-0.389667\pi$$
0.339721 + 0.940526i $$0.389667\pi$$
$$114$$ −5035.44 −0.0362890
$$115$$ 210372. 1.48335
$$116$$ 70750.3 0.488184
$$117$$ 18475.6 0.124777
$$118$$ 25297.2 0.167251
$$119$$ −42997.8 −0.278342
$$120$$ −165403. −1.04855
$$121$$ 14641.0 0.0909091
$$122$$ −62342.9 −0.379217
$$123$$ 19029.9 0.113416
$$124$$ 28661.5 0.167396
$$125$$ −44493.9 −0.254698
$$126$$ −20204.8 −0.113378
$$127$$ 138299. 0.760868 0.380434 0.924808i $$-0.375775\pi$$
0.380434 + 0.924808i $$0.375775\pi$$
$$128$$ −189000. −1.01962
$$129$$ −247051. −1.30711
$$130$$ 75669.5 0.392702
$$131$$ −54420.4 −0.277066 −0.138533 0.990358i $$-0.544239\pi$$
−0.138533 + 0.990358i $$0.544239\pi$$
$$132$$ −55263.0 −0.276058
$$133$$ 30534.5 0.149679
$$134$$ −113590. −0.546485
$$135$$ −256427. −1.21096
$$136$$ −24895.3 −0.115417
$$137$$ 40555.1 0.184605 0.0923025 0.995731i $$-0.470577\pi$$
0.0923025 + 0.995731i $$0.470577\pi$$
$$138$$ 104011. 0.464923
$$139$$ 140537. 0.616955 0.308477 0.951232i $$-0.400181\pi$$
0.308477 + 0.951232i $$0.400181\pi$$
$$140$$ 460117. 1.98403
$$141$$ −284285. −1.20422
$$142$$ −35818.9 −0.149071
$$143$$ 55111.2 0.225372
$$144$$ 23507.7 0.0944723
$$145$$ −196225. −0.775060
$$146$$ −22458.7 −0.0871971
$$147$$ 573454. 2.18880
$$148$$ −340024. −1.27602
$$149$$ 176073. 0.649722 0.324861 0.945762i $$-0.394683\pi$$
0.324861 + 0.945762i $$0.394683\pi$$
$$150$$ 94224.4 0.341928
$$151$$ 409241. 1.46062 0.730309 0.683117i $$-0.239376\pi$$
0.730309 + 0.683117i $$0.239376\pi$$
$$152$$ 17679.2 0.0620659
$$153$$ 7733.85 0.0267096
$$154$$ −60269.1 −0.204783
$$155$$ −79492.6 −0.265765
$$156$$ −208020. −0.684373
$$157$$ 14294.5 0.0462829 0.0231414 0.999732i $$-0.492633\pi$$
0.0231414 + 0.999732i $$0.492633\pi$$
$$158$$ 134373. 0.428224
$$159$$ 55789.1 0.175007
$$160$$ 410595. 1.26798
$$161$$ −630713. −1.91764
$$162$$ −148551. −0.444722
$$163$$ −418474. −1.23367 −0.616836 0.787091i $$-0.711586\pi$$
−0.616836 + 0.787091i $$0.711586\pi$$
$$164$$ −30650.3 −0.0889868
$$165$$ 153272. 0.438281
$$166$$ 101089. 0.284729
$$167$$ −139747. −0.387749 −0.193875 0.981026i $$-0.562106\pi$$
−0.193875 + 0.981026i $$0.562106\pi$$
$$168$$ 495890. 1.35554
$$169$$ −163845. −0.441282
$$170$$ 31675.1 0.0840612
$$171$$ −5492.13 −0.0143632
$$172$$ 397909. 1.02556
$$173$$ −687104. −1.74545 −0.872725 0.488213i $$-0.837649\pi$$
−0.872725 + 0.488213i $$0.837649\pi$$
$$174$$ −97016.5 −0.242925
$$175$$ −571368. −1.41033
$$176$$ 70121.6 0.170636
$$177$$ 192878. 0.462754
$$178$$ −181696. −0.429829
$$179$$ 35496.4 0.0828042 0.0414021 0.999143i $$-0.486818\pi$$
0.0414021 + 0.999143i $$0.486818\pi$$
$$180$$ −82759.7 −0.190387
$$181$$ 260469. 0.590963 0.295481 0.955349i $$-0.404520\pi$$
0.295481 + 0.955349i $$0.404520\pi$$
$$182$$ −226863. −0.507675
$$183$$ −475333. −1.04923
$$184$$ −365177. −0.795167
$$185$$ 943056. 2.02585
$$186$$ −39302.2 −0.0832980
$$187$$ 23069.4 0.0482429
$$188$$ 457880. 0.944837
$$189$$ 768789. 1.56550
$$190$$ −22493.8 −0.0452042
$$191$$ 392051. 0.777605 0.388803 0.921321i $$-0.372889\pi$$
0.388803 + 0.921321i $$0.372889\pi$$
$$192$$ −109275. −0.213928
$$193$$ 15776.8 0.0304878 0.0152439 0.999884i $$-0.495148\pi$$
0.0152439 + 0.999884i $$0.495148\pi$$
$$194$$ 117270. 0.223708
$$195$$ 576941. 1.08654
$$196$$ −923627. −1.71734
$$197$$ 545551. 1.00154 0.500771 0.865580i $$-0.333050\pi$$
0.500771 + 0.865580i $$0.333050\pi$$
$$198$$ 10840.4 0.0196509
$$199$$ −546514. −0.978293 −0.489146 0.872202i $$-0.662692\pi$$
−0.489146 + 0.872202i $$0.662692\pi$$
$$200$$ −330817. −0.584807
$$201$$ −866065. −1.51203
$$202$$ 412610. 0.711478
$$203$$ 588300. 1.00198
$$204$$ −87076.5 −0.146496
$$205$$ 85008.5 0.141279
$$206$$ 75733.7 0.124343
$$207$$ 113444. 0.184016
$$208$$ 263950. 0.423022
$$209$$ −16382.6 −0.0259428
$$210$$ −630937. −0.987275
$$211$$ 537150. 0.830596 0.415298 0.909686i $$-0.363677\pi$$
0.415298 + 0.909686i $$0.363677\pi$$
$$212$$ −89856.0 −0.137312
$$213$$ −273101. −0.412453
$$214$$ −494983. −0.738850
$$215$$ −1.10360e6 −1.62823
$$216$$ 445121. 0.649148
$$217$$ 238325. 0.343574
$$218$$ 358298. 0.510626
$$219$$ −171236. −0.241259
$$220$$ −246865. −0.343877
$$221$$ 86837.3 0.119598
$$222$$ 466259. 0.634958
$$223$$ −189640. −0.255368 −0.127684 0.991815i $$-0.540754\pi$$
−0.127684 + 0.991815i $$0.540754\pi$$
$$224$$ −1.23100e6 −1.63922
$$225$$ 102770. 0.135335
$$226$$ 203687. 0.265273
$$227$$ 363428. 0.468116 0.234058 0.972223i $$-0.424799\pi$$
0.234058 + 0.972223i $$0.424799\pi$$
$$228$$ 61836.6 0.0787787
$$229$$ 504331. 0.635516 0.317758 0.948172i $$-0.397070\pi$$
0.317758 + 0.948172i $$0.397070\pi$$
$$230$$ 464627. 0.579141
$$231$$ −459521. −0.566598
$$232$$ 340620. 0.415480
$$233$$ −1.20159e6 −1.45000 −0.724999 0.688750i $$-0.758160\pi$$
−0.724999 + 0.688750i $$0.758160\pi$$
$$234$$ 40805.1 0.0487163
$$235$$ −1.26993e6 −1.50006
$$236$$ −310657. −0.363079
$$237$$ 1.02453e6 1.18482
$$238$$ −94964.5 −0.108672
$$239$$ −185929. −0.210549 −0.105275 0.994443i $$-0.533572\pi$$
−0.105275 + 0.994443i $$0.533572\pi$$
$$240$$ 734080. 0.822650
$$241$$ 174842. 0.193911 0.0969556 0.995289i $$-0.469090\pi$$
0.0969556 + 0.995289i $$0.469090\pi$$
$$242$$ 32336.0 0.0354934
$$243$$ −304267. −0.330552
$$244$$ 765589. 0.823229
$$245$$ 2.56168e6 2.72652
$$246$$ 42029.3 0.0442807
$$247$$ −61666.8 −0.0643145
$$248$$ 137988. 0.142466
$$249$$ 770748. 0.787797
$$250$$ −98269.0 −0.0994412
$$251$$ 447906. 0.448748 0.224374 0.974503i $$-0.427966\pi$$
0.224374 + 0.974503i $$0.427966\pi$$
$$252$$ 248120. 0.246128
$$253$$ 338394. 0.332370
$$254$$ 305446. 0.297064
$$255$$ 241506. 0.232583
$$256$$ −209768. −0.200050
$$257$$ −1.14572e6 −1.08204 −0.541022 0.841009i $$-0.681962\pi$$
−0.541022 + 0.841009i $$0.681962\pi$$
$$258$$ −545634. −0.510331
$$259$$ −2.82736e6 −2.61897
$$260$$ −929243. −0.852503
$$261$$ −105815. −0.0961496
$$262$$ −120192. −0.108174
$$263$$ 443228. 0.395128 0.197564 0.980290i $$-0.436697\pi$$
0.197564 + 0.980290i $$0.436697\pi$$
$$264$$ −266058. −0.234945
$$265$$ 249215. 0.218002
$$266$$ 67438.2 0.0584389
$$267$$ −1.38534e6 −1.18926
$$268$$ 1.39492e6 1.18635
$$269$$ −1.88722e6 −1.59016 −0.795082 0.606502i $$-0.792572\pi$$
−0.795082 + 0.606502i $$0.792572\pi$$
$$270$$ −566343. −0.472792
$$271$$ 2.24203e6 1.85446 0.927230 0.374491i $$-0.122183\pi$$
0.927230 + 0.374491i $$0.122183\pi$$
$$272$$ 110489. 0.0905516
$$273$$ −1.72972e6 −1.40465
$$274$$ 89569.6 0.0720749
$$275$$ 306554. 0.244442
$$276$$ −1.27728e6 −1.00929
$$277$$ 1.27824e6 1.00095 0.500474 0.865751i $$-0.333159\pi$$
0.500474 + 0.865751i $$0.333159\pi$$
$$278$$ 310389. 0.240876
$$279$$ −42866.7 −0.0329693
$$280$$ 2.21519e6 1.68856
$$281$$ 549325. 0.415015 0.207508 0.978233i $$-0.433465\pi$$
0.207508 + 0.978233i $$0.433465\pi$$
$$282$$ −627869. −0.470161
$$283$$ −135813. −0.100803 −0.0504016 0.998729i $$-0.516050\pi$$
−0.0504016 + 0.998729i $$0.516050\pi$$
$$284$$ 439867. 0.323612
$$285$$ −171504. −0.125072
$$286$$ 121718. 0.0879914
$$287$$ −254862. −0.182642
$$288$$ 221415. 0.157299
$$289$$ −1.38351e6 −0.974399
$$290$$ −433382. −0.302605
$$291$$ 894120. 0.618961
$$292$$ 275799. 0.189293
$$293$$ −1.76403e6 −1.20043 −0.600215 0.799839i $$-0.704918\pi$$
−0.600215 + 0.799839i $$0.704918\pi$$
$$294$$ 1.26653e6 0.854567
$$295$$ 861606. 0.576439
$$296$$ −1.63701e6 −1.08598
$$297$$ −412476. −0.271336
$$298$$ 388874. 0.253669
$$299$$ 1.27377e6 0.823976
$$300$$ −1.15710e6 −0.742281
$$301$$ 3.30868e6 2.10493
$$302$$ 903846. 0.570266
$$303$$ 3.14594e6 1.96854
$$304$$ −78462.7 −0.0486944
$$305$$ −2.12336e6 −1.30699
$$306$$ 17080.9 0.0104282
$$307$$ −1.93533e6 −1.17195 −0.585975 0.810329i $$-0.699288\pi$$
−0.585975 + 0.810329i $$0.699288\pi$$
$$308$$ 740122. 0.444556
$$309$$ 577431. 0.344036
$$310$$ −175567. −0.103762
$$311$$ 2.98327e6 1.74901 0.874504 0.485019i $$-0.161187\pi$$
0.874504 + 0.485019i $$0.161187\pi$$
$$312$$ −1.00149e6 −0.582451
$$313$$ −10701.5 −0.00617426 −0.00308713 0.999995i $$-0.500983\pi$$
−0.00308713 + 0.999995i $$0.500983\pi$$
$$314$$ 31570.8 0.0180701
$$315$$ −688160. −0.390762
$$316$$ −1.65014e6 −0.929617
$$317$$ −2.43658e6 −1.36186 −0.680929 0.732349i $$-0.738424\pi$$
−0.680929 + 0.732349i $$0.738424\pi$$
$$318$$ 123215. 0.0683277
$$319$$ −315638. −0.173665
$$320$$ −488141. −0.266484
$$321$$ −3.77399e6 −2.04427
$$322$$ −1.39299e6 −0.748699
$$323$$ −25813.6 −0.0137671
$$324$$ 1.82425e6 0.965433
$$325$$ 1.15392e6 0.605994
$$326$$ −924239. −0.481660
$$327$$ 2.73183e6 1.41281
$$328$$ −147563. −0.0757342
$$329$$ 3.80734e6 1.93924
$$330$$ 338515. 0.171117
$$331$$ 119576. 0.0599894 0.0299947 0.999550i $$-0.490451\pi$$
0.0299947 + 0.999550i $$0.490451\pi$$
$$332$$ −1.24140e6 −0.618109
$$333$$ 508546. 0.251316
$$334$$ −308644. −0.151388
$$335$$ −3.86880e6 −1.88349
$$336$$ −2.20083e6 −1.06350
$$337$$ −2.02195e6 −0.969830 −0.484915 0.874561i $$-0.661149\pi$$
−0.484915 + 0.874561i $$0.661149\pi$$
$$338$$ −361867. −0.172289
$$339$$ 1.55301e6 0.733965
$$340$$ −388979. −0.182486
$$341$$ −127868. −0.0595491
$$342$$ −12129.9 −0.00560778
$$343$$ −3.88971e6 −1.78518
$$344$$ 1.91569e6 0.872829
$$345$$ 3.54254e6 1.60238
$$346$$ −1.51753e6 −0.681471
$$347$$ 3.01864e6 1.34582 0.672912 0.739723i $$-0.265043\pi$$
0.672912 + 0.739723i $$0.265043\pi$$
$$348$$ 1.19139e6 0.527358
$$349$$ 2.40399e6 1.05650 0.528250 0.849089i $$-0.322848\pi$$
0.528250 + 0.849089i $$0.322848\pi$$
$$350$$ −1.26192e6 −0.550632
$$351$$ −1.55263e6 −0.672666
$$352$$ 660463. 0.284113
$$353$$ 3.62981e6 1.55041 0.775206 0.631709i $$-0.217646\pi$$
0.775206 + 0.631709i $$0.217646\pi$$
$$354$$ 425989. 0.180672
$$355$$ −1.21997e6 −0.513780
$$356$$ 2.23128e6 0.933102
$$357$$ −724055. −0.300678
$$358$$ 78397.1 0.0323290
$$359$$ 939181. 0.384603 0.192302 0.981336i $$-0.438405\pi$$
0.192302 + 0.981336i $$0.438405\pi$$
$$360$$ −398438. −0.162033
$$361$$ −2.45777e6 −0.992597
$$362$$ 575270. 0.230728
$$363$$ 246545. 0.0982042
$$364$$ 2.78594e6 1.10210
$$365$$ −764926. −0.300530
$$366$$ −1.04982e6 −0.409647
$$367$$ −2.26697e6 −0.878577 −0.439288 0.898346i $$-0.644769\pi$$
−0.439288 + 0.898346i $$0.644769\pi$$
$$368$$ 1.62071e6 0.623857
$$369$$ 45841.1 0.0175263
$$370$$ 2.08283e6 0.790949
$$371$$ −747167. −0.281827
$$372$$ 482642. 0.180829
$$373$$ −4.55029e6 −1.69343 −0.846714 0.532048i $$-0.821423\pi$$
−0.846714 + 0.532048i $$0.821423\pi$$
$$374$$ 50951.0 0.0188353
$$375$$ −749250. −0.275137
$$376$$ 2.20442e6 0.804125
$$377$$ −1.18812e6 −0.430532
$$378$$ 1.69794e6 0.611213
$$379$$ 618788. 0.221281 0.110641 0.993860i $$-0.464710\pi$$
0.110641 + 0.993860i $$0.464710\pi$$
$$380$$ 276230. 0.0981323
$$381$$ 2.32886e6 0.821924
$$382$$ 865881. 0.303599
$$383$$ 2.23829e6 0.779686 0.389843 0.920881i $$-0.372529\pi$$
0.389843 + 0.920881i $$0.372529\pi$$
$$384$$ −3.18264e6 −1.10144
$$385$$ −2.05272e6 −0.705795
$$386$$ 34844.5 0.0119033
$$387$$ −595120. −0.201989
$$388$$ −1.44010e6 −0.485640
$$389$$ −4.60206e6 −1.54198 −0.770989 0.636848i $$-0.780238\pi$$
−0.770989 + 0.636848i $$0.780238\pi$$
$$390$$ 1.27423e6 0.424214
$$391$$ 533199. 0.176379
$$392$$ −4.44671e6 −1.46158
$$393$$ −916405. −0.299299
$$394$$ 1.20490e6 0.391030
$$395$$ 4.57666e6 1.47590
$$396$$ −133123. −0.0426595
$$397$$ −4.35532e6 −1.38690 −0.693448 0.720506i $$-0.743909\pi$$
−0.693448 + 0.720506i $$0.743909\pi$$
$$398$$ −1.20703e6 −0.381952
$$399$$ 514181. 0.161690
$$400$$ 1.46821e6 0.458816
$$401$$ 3.62515e6 1.12581 0.562905 0.826522i $$-0.309684\pi$$
0.562905 + 0.826522i $$0.309684\pi$$
$$402$$ −1.91278e6 −0.590338
$$403$$ −481316. −0.147628
$$404$$ −5.06697e6 −1.54453
$$405$$ −5.05955e6 −1.53276
$$406$$ 1.29931e6 0.391200
$$407$$ 1.51695e6 0.453927
$$408$$ −419221. −0.124679
$$409$$ 4.13585e6 1.22252 0.611260 0.791430i $$-0.290663\pi$$
0.611260 + 0.791430i $$0.290663\pi$$
$$410$$ 187749. 0.0551592
$$411$$ 682922. 0.199419
$$412$$ −930032. −0.269932
$$413$$ −2.58316e6 −0.745206
$$414$$ 250552. 0.0718450
$$415$$ 3.44300e6 0.981335
$$416$$ 2.48609e6 0.704343
$$417$$ 2.36655e6 0.666463
$$418$$ −36182.4 −0.0101288
$$419$$ −2.46691e6 −0.686464 −0.343232 0.939251i $$-0.611522\pi$$
−0.343232 + 0.939251i $$0.611522\pi$$
$$420$$ 7.74809e6 2.14324
$$421$$ 3.45258e6 0.949376 0.474688 0.880154i $$-0.342561\pi$$
0.474688 + 0.880154i $$0.342561\pi$$
$$422$$ 1.18635e6 0.324287
$$423$$ −684813. −0.186089
$$424$$ −432602. −0.116862
$$425$$ 483029. 0.129718
$$426$$ −603168. −0.161033
$$427$$ 6.36599e6 1.68965
$$428$$ 6.07853e6 1.60394
$$429$$ 928038. 0.243457
$$430$$ −2.43740e6 −0.635704
$$431$$ −3.65893e6 −0.948770 −0.474385 0.880318i $$-0.657329\pi$$
−0.474385 + 0.880318i $$0.657329\pi$$
$$432$$ −1.97551e6 −0.509296
$$433$$ −1.59716e6 −0.409381 −0.204690 0.978827i $$-0.565619\pi$$
−0.204690 + 0.978827i $$0.565619\pi$$
$$434$$ 526363. 0.134141
$$435$$ −3.30431e6 −0.837256
$$436$$ −4.39999e6 −1.10850
$$437$$ −378647. −0.0948485
$$438$$ −378190. −0.0941943
$$439$$ −1.58464e6 −0.392437 −0.196219 0.980560i $$-0.562866\pi$$
−0.196219 + 0.980560i $$0.562866\pi$$
$$440$$ −1.18851e6 −0.292664
$$441$$ 1.38139e6 0.338237
$$442$$ 191788. 0.0466945
$$443$$ 2.29633e6 0.555936 0.277968 0.960590i $$-0.410339\pi$$
0.277968 + 0.960590i $$0.410339\pi$$
$$444$$ −5.72580e6 −1.37841
$$445$$ −6.18844e6 −1.48143
$$446$$ −418837. −0.0997029
$$447$$ 2.96496e6 0.701859
$$448$$ 1.46349e6 0.344504
$$449$$ 3.31569e6 0.776171 0.388086 0.921623i $$-0.373136\pi$$
0.388086 + 0.921623i $$0.373136\pi$$
$$450$$ 226977. 0.0528385
$$451$$ 136740. 0.0316559
$$452$$ −2.50134e6 −0.575872
$$453$$ 6.89136e6 1.57783
$$454$$ 802664. 0.182765
$$455$$ −7.72680e6 −1.74973
$$456$$ 297706. 0.0670464
$$457$$ 2.20892e6 0.494754 0.247377 0.968919i $$-0.420431\pi$$
0.247377 + 0.968919i $$0.420431\pi$$
$$458$$ 1.11386e6 0.248123
$$459$$ −649927. −0.143990
$$460$$ −5.70574e6 −1.25724
$$461$$ −1.86064e6 −0.407764 −0.203882 0.978995i $$-0.565356\pi$$
−0.203882 + 0.978995i $$0.565356\pi$$
$$462$$ −1.01489e6 −0.221216
$$463$$ 1.20592e6 0.261437 0.130718 0.991420i $$-0.458272\pi$$
0.130718 + 0.991420i $$0.458272\pi$$
$$464$$ −1.51172e6 −0.325969
$$465$$ −1.33861e6 −0.287091
$$466$$ −2.65383e6 −0.566119
$$467$$ 2.29388e6 0.486719 0.243360 0.969936i $$-0.421750\pi$$
0.243360 + 0.969936i $$0.421750\pi$$
$$468$$ −501098. −0.105757
$$469$$ 1.15990e7 2.43493
$$470$$ −2.80475e6 −0.585666
$$471$$ 240711. 0.0499969
$$472$$ −1.49563e6 −0.309007
$$473$$ −1.77519e6 −0.364832
$$474$$ 2.26276e6 0.462587
$$475$$ −343019. −0.0697565
$$476$$ 1.16619e6 0.235913
$$477$$ 134390. 0.0270441
$$478$$ −410642. −0.0822041
$$479$$ −7.90892e6 −1.57499 −0.787496 0.616320i $$-0.788623\pi$$
−0.787496 + 0.616320i $$0.788623\pi$$
$$480$$ 6.91416e6 1.36973
$$481$$ 5.71007e6 1.12533
$$482$$ 386154. 0.0757083
$$483$$ −1.06208e7 −2.07152
$$484$$ −397095. −0.0770515
$$485$$ 3.99412e6 0.771021
$$486$$ −672002. −0.129056
$$487$$ 3.48410e6 0.665684 0.332842 0.942983i $$-0.391992\pi$$
0.332842 + 0.942983i $$0.391992\pi$$
$$488$$ 3.68585e6 0.700628
$$489$$ −7.04684e6 −1.33267
$$490$$ 5.65769e6 1.06451
$$491$$ −8.98096e6 −1.68120 −0.840599 0.541658i $$-0.817797\pi$$
−0.840599 + 0.541658i $$0.817797\pi$$
$$492$$ −516132. −0.0961276
$$493$$ −497343. −0.0921592
$$494$$ −136197. −0.0251101
$$495$$ 369216. 0.0677279
$$496$$ −612410. −0.111773
$$497$$ 3.65756e6 0.664203
$$498$$ 1.70227e6 0.307577
$$499$$ 6.67736e6 1.20048 0.600238 0.799821i $$-0.295072\pi$$
0.600238 + 0.799821i $$0.295072\pi$$
$$500$$ 1.20677e6 0.215874
$$501$$ −2.35325e6 −0.418865
$$502$$ 989242. 0.175204
$$503$$ 7.58428e6 1.33658 0.668289 0.743902i $$-0.267027\pi$$
0.668289 + 0.743902i $$0.267027\pi$$
$$504$$ 1.19455e6 0.209473
$$505$$ 1.40532e7 2.45215
$$506$$ 747375. 0.129766
$$507$$ −2.75905e6 −0.476693
$$508$$ −3.75096e6 −0.644886
$$509$$ −6.02580e6 −1.03091 −0.515454 0.856917i $$-0.672377\pi$$
−0.515454 + 0.856917i $$0.672377\pi$$
$$510$$ 533389. 0.0908068
$$511$$ 2.29331e6 0.388518
$$512$$ 5.58471e6 0.941511
$$513$$ 461540. 0.0774312
$$514$$ −2.53042e6 −0.422460
$$515$$ 2.57944e6 0.428555
$$516$$ 6.70054e6 1.10786
$$517$$ −2.04274e6 −0.336114
$$518$$ −6.24448e6 −1.02252
$$519$$ −1.15704e7 −1.88551
$$520$$ −4.47374e6 −0.725542
$$521$$ −4.58541e6 −0.740088 −0.370044 0.929014i $$-0.620657\pi$$
−0.370044 + 0.929014i $$0.620657\pi$$
$$522$$ −233703. −0.0375394
$$523$$ −4.88145e6 −0.780359 −0.390179 0.920739i $$-0.627587\pi$$
−0.390179 + 0.920739i $$0.627587\pi$$
$$524$$ 1.47600e6 0.234832
$$525$$ −9.62148e6 −1.52350
$$526$$ 978910. 0.154269
$$527$$ −201478. −0.0316010
$$528$$ 1.18080e6 0.184329
$$529$$ 1.38489e6 0.215168
$$530$$ 550414. 0.0851138
$$531$$ 464624. 0.0715098
$$532$$ −828160. −0.126863
$$533$$ 514714. 0.0784780
$$534$$ −3.05965e6 −0.464321
$$535$$ −1.68588e7 −2.54649
$$536$$ 6.71568e6 1.00967
$$537$$ 597738. 0.0894489
$$538$$ −4.16810e6 −0.620844
$$539$$ 4.12058e6 0.610923
$$540$$ 6.95484e6 1.02637
$$541$$ 6.21940e6 0.913598 0.456799 0.889570i $$-0.348996\pi$$
0.456799 + 0.889570i $$0.348996\pi$$
$$542$$ 4.95172e6 0.724033
$$543$$ 4.38614e6 0.638385
$$544$$ 1.04067e6 0.150771
$$545$$ 1.22034e7 1.75990
$$546$$ −3.82023e6 −0.548414
$$547$$ −9.49047e6 −1.35619 −0.678093 0.734976i $$-0.737193\pi$$
−0.678093 + 0.734976i $$0.737193\pi$$
$$548$$ −1.09994e6 −0.156465
$$549$$ −1.14503e6 −0.162138
$$550$$ 677053. 0.0954368
$$551$$ 353184. 0.0495589
$$552$$ −6.14935e6 −0.858976
$$553$$ −1.37212e7 −1.90800
$$554$$ 2.82310e6 0.390798
$$555$$ 1.58805e7 2.18842
$$556$$ −3.81166e6 −0.522910
$$557$$ −2.92907e6 −0.400029 −0.200014 0.979793i $$-0.564099\pi$$
−0.200014 + 0.979793i $$0.564099\pi$$
$$558$$ −94675.0 −0.0128721
$$559$$ −6.68213e6 −0.904451
$$560$$ −9.83131e6 −1.32477
$$561$$ 388475. 0.0521141
$$562$$ 1.21324e6 0.162033
$$563$$ −455079. −0.0605084 −0.0302542 0.999542i $$-0.509632\pi$$
−0.0302542 + 0.999542i $$0.509632\pi$$
$$564$$ 7.71041e6 1.02066
$$565$$ 6.93744e6 0.914278
$$566$$ −299955. −0.0393563
$$567$$ 1.51689e7 1.98152
$$568$$ 2.11769e6 0.275418
$$569$$ −6.27664e6 −0.812730 −0.406365 0.913711i $$-0.633204\pi$$
−0.406365 + 0.913711i $$0.633204\pi$$
$$570$$ −378781. −0.0488316
$$571$$ −621794. −0.0798098 −0.0399049 0.999203i $$-0.512706\pi$$
−0.0399049 + 0.999203i $$0.512706\pi$$
$$572$$ −1.49473e6 −0.191018
$$573$$ 6.60189e6 0.840005
$$574$$ −562886. −0.0713085
$$575$$ 7.08532e6 0.893697
$$576$$ −263232. −0.0330585
$$577$$ 1.28776e7 1.61026 0.805130 0.593098i $$-0.202095\pi$$
0.805130 + 0.593098i $$0.202095\pi$$
$$578$$ −3.05560e6 −0.380432
$$579$$ 265671. 0.0329343
$$580$$ 5.32205e6 0.656915
$$581$$ −1.03224e7 −1.26865
$$582$$ 1.97475e6 0.241659
$$583$$ 400875. 0.0488470
$$584$$ 1.32780e6 0.161102
$$585$$ 1.38979e6 0.167904
$$586$$ −3.89602e6 −0.468681
$$587$$ 1.08775e7 1.30296 0.651482 0.758664i $$-0.274148\pi$$
0.651482 + 0.758664i $$0.274148\pi$$
$$588$$ −1.55533e7 −1.85515
$$589$$ 143078. 0.0169935
$$590$$ 1.90293e6 0.225058
$$591$$ 9.18673e6 1.08191
$$592$$ 7.26529e6 0.852018
$$593$$ −7.50449e6 −0.876364 −0.438182 0.898886i $$-0.644378\pi$$
−0.438182 + 0.898886i $$0.644378\pi$$
$$594$$ −910990. −0.105937
$$595$$ −3.23442e6 −0.374545
$$596$$ −4.77548e6 −0.550682
$$597$$ −9.20295e6 −1.05680
$$598$$ 2.81325e6 0.321703
$$599$$ −7.69438e6 −0.876207 −0.438104 0.898925i $$-0.644350\pi$$
−0.438104 + 0.898925i $$0.644350\pi$$
$$600$$ −5.57074e6 −0.631735
$$601$$ 3.14770e6 0.355473 0.177737 0.984078i $$-0.443123\pi$$
0.177737 + 0.984078i $$0.443123\pi$$
$$602$$ 7.30751e6 0.821823
$$603$$ −2.08626e6 −0.233655
$$604$$ −1.10995e7 −1.23797
$$605$$ 1.10134e6 0.122330
$$606$$ 6.94810e6 0.768572
$$607$$ −4.57397e6 −0.503874 −0.251937 0.967744i $$-0.581068\pi$$
−0.251937 + 0.967744i $$0.581068\pi$$
$$608$$ −739025. −0.0810775
$$609$$ 9.90660e6 1.08238
$$610$$ −4.68962e6 −0.510286
$$611$$ −7.68923e6 −0.833258
$$612$$ −209758. −0.0226381
$$613$$ −1.56075e7 −1.67758 −0.838790 0.544455i $$-0.816736\pi$$
−0.838790 + 0.544455i $$0.816736\pi$$
$$614$$ −4.27436e6 −0.457562
$$615$$ 1.43149e6 0.152616
$$616$$ 3.56324e6 0.378349
$$617$$ −1.18602e7 −1.25424 −0.627119 0.778924i $$-0.715766\pi$$
−0.627119 + 0.778924i $$0.715766\pi$$
$$618$$ 1.27531e6 0.134321
$$619$$ 7.91821e6 0.830616 0.415308 0.909681i $$-0.363674\pi$$
0.415308 + 0.909681i $$0.363674\pi$$
$$620$$ 2.15601e6 0.225253
$$621$$ −9.53346e6 −0.992023
$$622$$ 6.58883e6 0.682861
$$623$$ 1.85534e7 1.91516
$$624$$ 4.44475e6 0.456968
$$625$$ −1.12642e7 −1.15345
$$626$$ −23635.3 −0.00241060
$$627$$ −275872. −0.0280246
$$628$$ −387698. −0.0392278
$$629$$ 2.39022e6 0.240886
$$630$$ −1.51986e6 −0.152564
$$631$$ −1.11561e7 −1.11542 −0.557709 0.830037i $$-0.688319\pi$$
−0.557709 + 0.830037i $$0.688319\pi$$
$$632$$ −7.94444e6 −0.791172
$$633$$ 9.04527e6 0.897248
$$634$$ −5.38140e6 −0.531707
$$635$$ 1.04033e7 1.02385
$$636$$ −1.51312e6 −0.148330
$$637$$ 1.55106e7 1.51453
$$638$$ −697116. −0.0678037
$$639$$ −657872. −0.0637367
$$640$$ −1.42172e7 −1.37203
$$641$$ 7.17389e6 0.689620 0.344810 0.938672i $$-0.387943\pi$$
0.344810 + 0.938672i $$0.387943\pi$$
$$642$$ −8.33521e6 −0.798139
$$643$$ 7.14025e6 0.681061 0.340531 0.940233i $$-0.389393\pi$$
0.340531 + 0.940233i $$0.389393\pi$$
$$644$$ 1.71063e7 1.62533
$$645$$ −1.85839e7 −1.75889
$$646$$ −57011.6 −0.00537505
$$647$$ 1.56897e7 1.47351 0.736756 0.676159i $$-0.236357\pi$$
0.736756 + 0.676159i $$0.236357\pi$$
$$648$$ 8.78267e6 0.821654
$$649$$ 1.38594e6 0.129161
$$650$$ 2.54854e6 0.236597
$$651$$ 4.01324e6 0.371145
$$652$$ 1.13499e7 1.04562
$$653$$ −5.04236e6 −0.462755 −0.231378 0.972864i $$-0.574323\pi$$
−0.231378 + 0.972864i $$0.574323\pi$$
$$654$$ 6.03350e6 0.551601
$$655$$ −4.09367e6 −0.372829
$$656$$ 654904. 0.0594180
$$657$$ −412489. −0.0372820
$$658$$ 8.40887e6 0.757134
$$659$$ −9.10902e6 −0.817068 −0.408534 0.912743i $$-0.633960\pi$$
−0.408534 + 0.912743i $$0.633960\pi$$
$$660$$ −4.15705e6 −0.371472
$$661$$ 1.31308e7 1.16893 0.584464 0.811420i $$-0.301305\pi$$
0.584464 + 0.811420i $$0.301305\pi$$
$$662$$ 264095. 0.0234215
$$663$$ 1.46229e6 0.129196
$$664$$ −5.97657e6 −0.526056
$$665$$ 2.29690e6 0.201413
$$666$$ 1.12317e6 0.0981207
$$667$$ −7.29528e6 −0.634933
$$668$$ 3.79023e6 0.328643
$$669$$ −3.19341e6 −0.275861
$$670$$ −8.54459e6 −0.735367
$$671$$ −3.41552e6 −0.292854
$$672$$ −2.07292e7 −1.77076
$$673$$ 1.55171e7 1.32061 0.660303 0.750999i $$-0.270428\pi$$
0.660303 + 0.750999i $$0.270428\pi$$
$$674$$ −4.46566e6 −0.378648
$$675$$ −8.63644e6 −0.729584
$$676$$ 4.44382e6 0.374016
$$677$$ −1.40356e7 −1.17695 −0.588476 0.808515i $$-0.700272\pi$$
−0.588476 + 0.808515i $$0.700272\pi$$
$$678$$ 3.42997e6 0.286560
$$679$$ −1.19747e7 −0.996758
$$680$$ −1.87270e6 −0.155309
$$681$$ 6.11990e6 0.505681
$$682$$ −282408. −0.0232496
$$683$$ 5.34969e6 0.438810 0.219405 0.975634i $$-0.429588\pi$$
0.219405 + 0.975634i $$0.429588\pi$$
$$684$$ 148958. 0.0121737
$$685$$ 3.05068e6 0.248410
$$686$$ −8.59079e6 −0.696984
$$687$$ 8.49261e6 0.686514
$$688$$ −8.50211e6 −0.684787
$$689$$ 1.50896e6 0.121096
$$690$$ 7.82402e6 0.625615
$$691$$ 1.31390e7 1.04681 0.523404 0.852084i $$-0.324662\pi$$
0.523404 + 0.852084i $$0.324662\pi$$
$$692$$ 1.86357e7 1.47938
$$693$$ −1.10694e6 −0.0875569
$$694$$ 6.66695e6 0.525447
$$695$$ 1.05716e7 0.830194
$$696$$ 5.73582e6 0.448820
$$697$$ 215458. 0.0167989
$$698$$ 5.30944e6 0.412487
$$699$$ −2.02341e7 −1.56636
$$700$$ 1.54967e7 1.19535
$$701$$ −2.49888e7 −1.92066 −0.960330 0.278865i $$-0.910042\pi$$
−0.960330 + 0.278865i $$0.910042\pi$$
$$702$$ −3.42912e6 −0.262627
$$703$$ −1.69740e6 −0.129537
$$704$$ −785200. −0.0597102
$$705$$ −2.13848e7 −1.62044
$$706$$ 8.01676e6 0.605323
$$707$$ −4.21327e7 −3.17008
$$708$$ −5.23127e6 −0.392215
$$709$$ −8.86200e6 −0.662089 −0.331044 0.943615i $$-0.607401\pi$$
−0.331044 + 0.943615i $$0.607401\pi$$
$$710$$ −2.69441e6 −0.200594
$$711$$ 2.46798e6 0.183092
$$712$$ 1.07423e7 0.794138
$$713$$ −2.95538e6 −0.217716
$$714$$ −1.59914e6 −0.117393
$$715$$ 4.14563e6 0.303268
$$716$$ −962739. −0.0701820
$$717$$ −3.13093e6 −0.227445
$$718$$ 2.07427e6 0.150160
$$719$$ 2.58635e7 1.86580 0.932901 0.360132i $$-0.117268\pi$$
0.932901 + 0.360132i $$0.117268\pi$$
$$720$$ 1.76832e6 0.127125
$$721$$ −7.73336e6 −0.554026
$$722$$ −5.42820e6 −0.387537
$$723$$ 2.94423e6 0.209472
$$724$$ −7.06448e6 −0.500880
$$725$$ −6.60886e6 −0.466962
$$726$$ 544518. 0.0383416
$$727$$ −1.71871e7 −1.20605 −0.603026 0.797721i $$-0.706039\pi$$
−0.603026 + 0.797721i $$0.706039\pi$$
$$728$$ 1.34126e7 0.937963
$$729$$ 1.12207e7 0.781988
$$730$$ −1.68941e6 −0.117335
$$731$$ −2.79712e6 −0.193606
$$732$$ 1.28920e7 0.889290
$$733$$ 1.85650e7 1.27625 0.638125 0.769932i $$-0.279710\pi$$
0.638125 + 0.769932i $$0.279710\pi$$
$$734$$ −5.00680e6 −0.343021
$$735$$ 4.31370e7 2.94531
$$736$$ 1.52651e7 1.03874
$$737$$ −6.22315e6 −0.422028
$$738$$ 101244. 0.00684274
$$739$$ 5.94724e6 0.400594 0.200297 0.979735i $$-0.435809\pi$$
0.200297 + 0.979735i $$0.435809\pi$$
$$740$$ −2.55777e7 −1.71705
$$741$$ −1.03843e6 −0.0694755
$$742$$ −1.65019e6 −0.110033
$$743$$ −2.72654e7 −1.81193 −0.905963 0.423357i $$-0.860852\pi$$
−0.905963 + 0.423357i $$0.860852\pi$$
$$744$$ 2.32363e6 0.153899
$$745$$ 1.32448e7 0.874285
$$746$$ −1.00497e7 −0.661161
$$747$$ 1.85665e6 0.121739
$$748$$ −625692. −0.0408890
$$749$$ 5.05440e7 3.29204
$$750$$ −1.65479e6 −0.107421
$$751$$ 1.30069e7 0.841541 0.420770 0.907167i $$-0.361760\pi$$
0.420770 + 0.907167i $$0.361760\pi$$
$$752$$ −9.78351e6 −0.630885
$$753$$ 7.54245e6 0.484758
$$754$$ −2.62407e6 −0.168092
$$755$$ 3.07844e7 1.96545
$$756$$ −2.08512e7 −1.32686
$$757$$ −9.22009e6 −0.584784 −0.292392 0.956299i $$-0.594451\pi$$
−0.292392 + 0.956299i $$0.594451\pi$$
$$758$$ 1.36665e6 0.0863942
$$759$$ 5.69835e6 0.359041
$$760$$ 1.32988e6 0.0835177
$$761$$ 328083. 0.0205363 0.0102682 0.999947i $$-0.496731\pi$$
0.0102682 + 0.999947i $$0.496731\pi$$
$$762$$ 5.14351e6 0.320902
$$763$$ −3.65866e7 −2.27516
$$764$$ −1.06333e7 −0.659072
$$765$$ 581764. 0.0359412
$$766$$ 4.94347e6 0.304411
$$767$$ 5.21690e6 0.320202
$$768$$ −3.53235e6 −0.216103
$$769$$ 2.19214e6 0.133676 0.0668380 0.997764i $$-0.478709\pi$$
0.0668380 + 0.997764i $$0.478709\pi$$
$$770$$ −4.53363e6 −0.275562
$$771$$ −1.92932e7 −1.16887
$$772$$ −427900. −0.0258404
$$773$$ 2.18539e7 1.31547 0.657735 0.753249i $$-0.271515\pi$$
0.657735 + 0.753249i $$0.271515\pi$$
$$774$$ −1.31438e6 −0.0788619
$$775$$ −2.67730e6 −0.160119
$$776$$ −6.93323e6 −0.413315
$$777$$ −4.76109e7 −2.82914
$$778$$ −1.01641e7 −0.602031
$$779$$ −153006. −0.00903367
$$780$$ −1.56479e7 −0.920913
$$781$$ −1.96238e6 −0.115121
$$782$$ 1.17762e6 0.0688633
$$783$$ 8.89237e6 0.518338
$$784$$ 1.97351e7 1.14670
$$785$$ 1.07528e6 0.0622797
$$786$$ −2.02396e6 −0.116855
$$787$$ 2.61010e7 1.50217 0.751087 0.660203i $$-0.229530\pi$$
0.751087 + 0.660203i $$0.229530\pi$$
$$788$$ −1.47965e7 −0.848874
$$789$$ 7.46368e6 0.426835
$$790$$ 1.01080e7 0.576231
$$791$$ −2.07990e7 −1.18196
$$792$$ −640907. −0.0363063
$$793$$ −1.28566e7 −0.726011
$$794$$ −9.61913e6 −0.541483
$$795$$ 4.19663e6 0.235495
$$796$$ 1.48226e7 0.829168
$$797$$ 1.39846e7 0.779840 0.389920 0.920849i $$-0.372503\pi$$
0.389920 + 0.920849i $$0.372503\pi$$
$$798$$ 1.13562e6 0.0631284
$$799$$ −3.21869e6 −0.178366
$$800$$ 1.38288e7 0.763941
$$801$$ −3.33714e6 −0.183778
$$802$$ 8.00647e6 0.439547
$$803$$ −1.23042e6 −0.0673388
$$804$$ 2.34895e7 1.28155
$$805$$ −4.74442e7 −2.58044
$$806$$ −1.06303e6 −0.0576379
$$807$$ −3.17796e7 −1.71777
$$808$$ −2.43944e7 −1.31450
$$809$$ 2.70989e7 1.45573 0.727865 0.685721i $$-0.240513\pi$$
0.727865 + 0.685721i $$0.240513\pi$$
$$810$$ −1.11745e7 −0.598432
$$811$$ 1.99644e7 1.06587 0.532936 0.846156i $$-0.321089\pi$$
0.532936 + 0.846156i $$0.321089\pi$$
$$812$$ −1.59559e7 −0.849244
$$813$$ 3.77543e7 2.00327
$$814$$ 3.35033e6 0.177226
$$815$$ −3.14789e7 −1.66007
$$816$$ 1.86056e6 0.0978180
$$817$$ 1.98635e6 0.104112
$$818$$ 9.13439e6 0.477306
$$819$$ −4.16671e6 −0.217062
$$820$$ −2.30561e6 −0.119743
$$821$$ 3.18829e7 1.65082 0.825410 0.564533i $$-0.190944\pi$$
0.825410 + 0.564533i $$0.190944\pi$$
$$822$$ 1.50829e6 0.0778586
$$823$$ −1.34203e7 −0.690655 −0.345328 0.938482i $$-0.612232\pi$$
−0.345328 + 0.938482i $$0.612232\pi$$
$$824$$ −4.47754e6 −0.229732
$$825$$ 5.16218e6 0.264057
$$826$$ −5.70515e6 −0.290949
$$827$$ 1.19386e7 0.607002 0.303501 0.952831i $$-0.401844\pi$$
0.303501 + 0.952831i $$0.401844\pi$$
$$828$$ −3.07684e6 −0.155966
$$829$$ 2.59274e7 1.31031 0.655153 0.755497i $$-0.272604\pi$$
0.655153 + 0.755497i $$0.272604\pi$$
$$830$$ 7.60419e6 0.383140
$$831$$ 2.15247e7 1.08127
$$832$$ −2.95563e6 −0.148027
$$833$$ 6.49269e6 0.324199
$$834$$ 5.22675e6 0.260206
$$835$$ −1.05122e7 −0.521768
$$836$$ 444330. 0.0219882
$$837$$ 3.60237e6 0.177736
$$838$$ −5.44839e6 −0.268015
$$839$$ −3.21482e7 −1.57671 −0.788354 0.615222i $$-0.789067\pi$$
−0.788354 + 0.615222i $$0.789067\pi$$
$$840$$ 3.73024e7 1.82406
$$841$$ −1.37064e7 −0.668244
$$842$$ 7.62533e6 0.370662
$$843$$ 9.25029e6 0.448318
$$844$$ −1.45687e7 −0.703985
$$845$$ −1.23249e7 −0.593803
$$846$$ −1.51247e6 −0.0726544
$$847$$ −3.30191e6 −0.158145
$$848$$ 1.91995e6 0.0916855
$$849$$ −2.28700e6 −0.108892
$$850$$ 1.06681e6 0.0506456
$$851$$ 3.50610e7 1.65959
$$852$$ 7.40708e6 0.349581
$$853$$ −5.64308e6 −0.265548 −0.132774 0.991146i $$-0.542388\pi$$
−0.132774 + 0.991146i $$0.542388\pi$$
$$854$$ 1.40599e7 0.659685
$$855$$ −413135. −0.0193275
$$856$$ 2.92645e7 1.36507
$$857$$ −1.77067e7 −0.823543 −0.411772 0.911287i $$-0.635090\pi$$
−0.411772 + 0.911287i $$0.635090\pi$$
$$858$$ 2.04966e6 0.0950524
$$859$$ 1.57119e7 0.726515 0.363258 0.931689i $$-0.381664\pi$$
0.363258 + 0.931689i $$0.381664\pi$$
$$860$$ 2.99319e7 1.38003
$$861$$ −4.29172e6 −0.197298
$$862$$ −8.08108e6 −0.370426
$$863$$ 245263. 0.0112100 0.00560500 0.999984i $$-0.498216\pi$$
0.00560500 + 0.999984i $$0.498216\pi$$
$$864$$ −1.86070e7 −0.847991
$$865$$ −5.16861e7 −2.34873
$$866$$ −3.52747e6 −0.159834
$$867$$ −2.32974e7 −1.05259
$$868$$ −6.46388e6 −0.291202
$$869$$ 7.36179e6 0.330700
$$870$$ −7.29788e6 −0.326888
$$871$$ −2.34250e7 −1.04625
$$872$$ −2.11833e7 −0.943415
$$873$$ 2.15384e6 0.0956486
$$874$$ −836276. −0.0370315
$$875$$ 1.00345e7 0.443073
$$876$$ 4.64428e6 0.204483
$$877$$ 1.04352e7 0.458142 0.229071 0.973410i $$-0.426431\pi$$
0.229071 + 0.973410i $$0.426431\pi$$
$$878$$ −3.49983e6 −0.153218
$$879$$ −2.97051e7 −1.29676
$$880$$ 5.27476e6 0.229613
$$881$$ −1.10430e7 −0.479344 −0.239672 0.970854i $$-0.577040\pi$$
−0.239672 + 0.970854i $$0.577040\pi$$
$$882$$ 3.05093e6 0.132057
$$883$$ 5.41498e6 0.233720 0.116860 0.993148i $$-0.462717\pi$$
0.116860 + 0.993148i $$0.462717\pi$$
$$884$$ −2.35521e6 −0.101368
$$885$$ 1.45089e7 0.622696
$$886$$ 5.07166e6 0.217053
$$887$$ −1.52663e7 −0.651515 −0.325757 0.945453i $$-0.605619\pi$$
−0.325757 + 0.945453i $$0.605619\pi$$
$$888$$ −2.75663e7 −1.17313
$$889$$ −3.11898e7 −1.32360
$$890$$ −1.36677e7 −0.578391
$$891$$ −8.13854e6 −0.343441
$$892$$ 5.14343e6 0.216442
$$893$$ 2.28573e6 0.0959170
$$894$$ 6.54838e6 0.274025
$$895$$ 2.67015e6 0.111424
$$896$$ 4.26242e7 1.77372
$$897$$ 2.14496e7 0.890096
$$898$$ 7.32300e6 0.303039
$$899$$ 2.75664e6 0.113758
$$900$$ −2.78734e6 −0.114705
$$901$$ 631648. 0.0259217
$$902$$ 302004. 0.0123594
$$903$$ 5.57160e7 2.27384
$$904$$ −1.20424e7 −0.490109
$$905$$ 1.95933e7 0.795218
$$906$$ 1.52202e7 0.616027
$$907$$ 2.02437e7 0.817094 0.408547 0.912737i $$-0.366036\pi$$
0.408547 + 0.912737i $$0.366036\pi$$
$$908$$ −9.85694e6 −0.396759
$$909$$ 7.57825e6 0.304200
$$910$$ −1.70653e7 −0.683143
$$911$$ −1.17158e7 −0.467708 −0.233854 0.972272i $$-0.575134\pi$$
−0.233854 + 0.972272i $$0.575134\pi$$
$$912$$ −1.32126e6 −0.0526019
$$913$$ 5.53824e6 0.219885
$$914$$ 4.87860e6 0.193166
$$915$$ −3.57560e7 −1.41187
$$916$$ −1.36785e7 −0.538642
$$917$$ 1.22731e7 0.481984
$$918$$ −1.43542e6 −0.0562177
$$919$$ −1.95296e7 −0.762788 −0.381394 0.924413i $$-0.624556\pi$$
−0.381394 + 0.924413i $$0.624556\pi$$
$$920$$ −2.74697e7 −1.07000
$$921$$ −3.25898e7 −1.26599
$$922$$ −4.10939e6 −0.159202
$$923$$ −7.38673e6 −0.285396
$$924$$ 1.24632e7 0.480230
$$925$$ 3.17620e7 1.22055
$$926$$ 2.66339e6 0.102072
$$927$$ 1.39097e6 0.0531641
$$928$$ −1.42386e7 −0.542747
$$929$$ −4.29425e7 −1.63248 −0.816240 0.577713i $$-0.803945\pi$$
−0.816240 + 0.577713i $$0.803945\pi$$
$$930$$ −2.95643e6 −0.112088
$$931$$ −4.61073e6 −0.174339
$$932$$ 3.25898e7 1.22897
$$933$$ 5.02364e7 1.88936
$$934$$ 5.06625e6 0.190029
$$935$$ 1.73535e6 0.0649171
$$936$$ −2.41248e6 −0.0900067
$$937$$ 2.27191e7 0.845361 0.422681 0.906279i $$-0.361089\pi$$
0.422681 + 0.906279i $$0.361089\pi$$
$$938$$ 2.56174e7 0.950665
$$939$$ −180207. −0.00666972
$$940$$ 3.44431e7 1.27140
$$941$$ 3.98095e6 0.146559 0.0732795 0.997311i $$-0.476653\pi$$
0.0732795 + 0.997311i $$0.476653\pi$$
$$942$$ 531632. 0.0195202
$$943$$ 3.16045e6 0.115736
$$944$$ 6.63780e6 0.242434
$$945$$ 5.78306e7 2.10658
$$946$$ −3.92067e6 −0.142440
$$947$$ −2.43639e7 −0.882818 −0.441409 0.897306i $$-0.645521\pi$$
−0.441409 + 0.897306i $$0.645521\pi$$
$$948$$ −2.77874e7 −1.00422
$$949$$ −4.63152e6 −0.166939
$$950$$ −757589. −0.0272348
$$951$$ −4.10304e7 −1.47114
$$952$$ 5.61450e6 0.200779
$$953$$ 1.39017e7 0.495833 0.247916 0.968781i $$-0.420254\pi$$
0.247916 + 0.968781i $$0.420254\pi$$
$$954$$ 296813. 0.0105587
$$955$$ 2.94913e7 1.04637
$$956$$ 5.04280e6 0.178454
$$957$$ −5.31515e6 −0.187601
$$958$$ −1.74676e7 −0.614920
$$959$$ −9.14617e6 −0.321139
$$960$$ −8.21999e6 −0.287868
$$961$$ −2.75124e7 −0.960993
$$962$$ 1.26112e7 0.439358
$$963$$ −9.09116e6 −0.315903
$$964$$ −4.74208e6 −0.164353
$$965$$ 1.18678e6 0.0410253
$$966$$ −2.34570e7 −0.808780
$$967$$ 5.16682e7 1.77688 0.888438 0.458998i $$-0.151791\pi$$
0.888438 + 0.458998i $$0.151791\pi$$
$$968$$ −1.91177e6 −0.0655764
$$969$$ −434684. −0.0148718
$$970$$ 8.82137e6 0.301028
$$971$$ −1.45794e7 −0.496240 −0.248120 0.968729i $$-0.579813\pi$$
−0.248120 + 0.968729i $$0.579813\pi$$
$$972$$ 8.25237e6 0.280164
$$973$$ −3.16945e7 −1.07325
$$974$$ 7.69495e6 0.259901
$$975$$ 1.94313e7 0.654623
$$976$$ −1.63583e7 −0.549685
$$977$$ −3.09921e6 −0.103876 −0.0519379 0.998650i $$-0.516540\pi$$
−0.0519379 + 0.998650i $$0.516540\pi$$
$$978$$ −1.55636e7 −0.520311
$$979$$ −9.95442e6 −0.331940
$$980$$ −6.94781e7 −2.31091
$$981$$ 6.58071e6 0.218323
$$982$$ −1.98353e7 −0.656386
$$983$$ 1.53445e7 0.506489 0.253245 0.967402i $$-0.418502\pi$$
0.253245 + 0.967402i $$0.418502\pi$$
$$984$$ −2.48486e6 −0.0818116
$$985$$ 4.10380e7 1.34771
$$986$$ −1.09843e6 −0.0359815
$$987$$ 6.41133e7 2.09486
$$988$$ 1.67253e6 0.0545108
$$989$$ −4.10296e7 −1.33385
$$990$$ 815447. 0.0264428
$$991$$ 1.57747e7 0.510244 0.255122 0.966909i $$-0.417884\pi$$
0.255122 + 0.966909i $$0.417884\pi$$
$$992$$ −5.76818e6 −0.186106
$$993$$ 2.01359e6 0.0648033
$$994$$ 8.07806e6 0.259323
$$995$$ −4.11105e7 −1.31642
$$996$$ −2.09043e7 −0.667710
$$997$$ 1.85577e6 0.0591270 0.0295635 0.999563i $$-0.490588\pi$$
0.0295635 + 0.999563i $$0.490588\pi$$
$$998$$ 1.47476e7 0.468699
$$999$$ −4.27365e7 −1.35483
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 11.6.a.b.1.2 3
3.2 odd 2 99.6.a.g.1.2 3
4.3 odd 2 176.6.a.i.1.2 3
5.2 odd 4 275.6.b.b.199.4 6
5.3 odd 4 275.6.b.b.199.3 6
5.4 even 2 275.6.a.b.1.2 3
7.6 odd 2 539.6.a.e.1.2 3
8.3 odd 2 704.6.a.t.1.2 3
8.5 even 2 704.6.a.q.1.2 3
11.10 odd 2 121.6.a.d.1.2 3
33.32 even 2 1089.6.a.r.1.2 3

By twisted newform
Twist Min Dim Char Parity Ord Type
11.6.a.b.1.2 3 1.1 even 1 trivial
99.6.a.g.1.2 3 3.2 odd 2
121.6.a.d.1.2 3 11.10 odd 2
176.6.a.i.1.2 3 4.3 odd 2
275.6.a.b.1.2 3 5.4 even 2
275.6.b.b.199.3 6 5.3 odd 4
275.6.b.b.199.4 6 5.2 odd 4
539.6.a.e.1.2 3 7.6 odd 2
704.6.a.q.1.2 3 8.5 even 2
704.6.a.t.1.2 3 8.3 odd 2
1089.6.a.r.1.2 3 33.32 even 2