# Properties

 Label 165.6.a.e.1.3 Level $165$ Weight $6$ Character 165.1 Self dual yes Analytic conductor $26.463$ 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] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.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: $$26.4633302691$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.307532.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - x^{2} - 76x + 168$$ x^3 - x^2 - 76*x + 168 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$7.91848$$ of defining polynomial Character $$\chi$$ $$=$$ 165.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+9.91848 q^{2} -9.00000 q^{3} +66.3762 q^{4} -25.0000 q^{5} -89.2663 q^{6} +92.6461 q^{7} +340.959 q^{8} +81.0000 q^{9} +O(q^{10})$$ $$q+9.91848 q^{2} -9.00000 q^{3} +66.3762 q^{4} -25.0000 q^{5} -89.2663 q^{6} +92.6461 q^{7} +340.959 q^{8} +81.0000 q^{9} -247.962 q^{10} +121.000 q^{11} -597.386 q^{12} +800.249 q^{13} +918.908 q^{14} +225.000 q^{15} +1257.76 q^{16} -117.742 q^{17} +803.397 q^{18} +831.422 q^{19} -1659.40 q^{20} -833.814 q^{21} +1200.14 q^{22} +2952.23 q^{23} -3068.63 q^{24} +625.000 q^{25} +7937.25 q^{26} -729.000 q^{27} +6149.49 q^{28} +5765.87 q^{29} +2231.66 q^{30} -61.7803 q^{31} +1564.36 q^{32} -1089.00 q^{33} -1167.83 q^{34} -2316.15 q^{35} +5376.47 q^{36} -10236.6 q^{37} +8246.44 q^{38} -7202.24 q^{39} -8523.98 q^{40} +9599.21 q^{41} -8270.17 q^{42} -17473.2 q^{43} +8031.52 q^{44} -2025.00 q^{45} +29281.7 q^{46} +18748.3 q^{47} -11319.8 q^{48} -8223.71 q^{49} +6199.05 q^{50} +1059.68 q^{51} +53117.5 q^{52} -9703.45 q^{53} -7230.57 q^{54} -3025.00 q^{55} +31588.5 q^{56} -7482.79 q^{57} +57188.6 q^{58} -24401.4 q^{59} +14934.6 q^{60} +33910.3 q^{61} -612.766 q^{62} +7504.33 q^{63} -24732.2 q^{64} -20006.2 q^{65} -10801.2 q^{66} -4989.24 q^{67} -7815.29 q^{68} -26570.1 q^{69} -22972.7 q^{70} -62961.6 q^{71} +27617.7 q^{72} -54232.5 q^{73} -101531. q^{74} -5625.00 q^{75} +55186.6 q^{76} +11210.2 q^{77} -71435.2 q^{78} -56996.4 q^{79} -31444.0 q^{80} +6561.00 q^{81} +95209.6 q^{82} +49685.9 q^{83} -55345.4 q^{84} +2943.56 q^{85} -173308. q^{86} -51892.8 q^{87} +41256.1 q^{88} -87990.1 q^{89} -20084.9 q^{90} +74139.9 q^{91} +195958. q^{92} +556.022 q^{93} +185954. q^{94} -20785.5 q^{95} -14079.3 q^{96} -44817.9 q^{97} -81566.7 q^{98} +9801.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9}+O(q^{10})$$ 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9 $$3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9} - 175 q^{10} + 363 q^{11} - 657 q^{12} - 90 q^{13} - 784 q^{14} + 675 q^{15} - 415 q^{16} + 1934 q^{17} + 567 q^{18} + 2084 q^{19} - 1825 q^{20} - 828 q^{21} + 847 q^{22} + 1220 q^{23} - 2079 q^{24} + 1875 q^{25} + 17062 q^{26} - 2187 q^{27} + 11120 q^{28} + 4402 q^{29} + 1575 q^{30} - 10688 q^{31} + 12439 q^{32} - 3267 q^{33} - 4094 q^{34} - 2300 q^{35} + 5913 q^{36} - 8190 q^{37} + 13792 q^{38} + 810 q^{39} - 5775 q^{40} + 5974 q^{41} + 7056 q^{42} + 18868 q^{43} + 8833 q^{44} - 6075 q^{45} + 46220 q^{46} + 55500 q^{47} + 3735 q^{48} + 1907 q^{49} + 4375 q^{50} - 17406 q^{51} + 27330 q^{52} + 9206 q^{53} - 5103 q^{54} - 9075 q^{55} + 73248 q^{56} - 18756 q^{57} + 15366 q^{58} - 59196 q^{59} + 16425 q^{60} + 79902 q^{61} + 64616 q^{62} + 7452 q^{63} + 2129 q^{64} + 2250 q^{65} - 7623 q^{66} + 4468 q^{67} - 1218 q^{68} - 10980 q^{69} + 19600 q^{70} - 75164 q^{71} + 18711 q^{72} - 61290 q^{73} - 56766 q^{74} - 16875 q^{75} + 37816 q^{76} + 11132 q^{77} - 153558 q^{78} - 83564 q^{79} + 10375 q^{80} + 19683 q^{81} + 147410 q^{82} + 74764 q^{83} - 100080 q^{84} - 48350 q^{85} - 253432 q^{86} - 39618 q^{87} + 27951 q^{88} + 37342 q^{89} - 14175 q^{90} - 126488 q^{91} + 148164 q^{92} + 96192 q^{93} + 59252 q^{94} - 52100 q^{95} - 111951 q^{96} + 33486 q^{97} - 95249 q^{98} + 29403 q^{99}+O(q^{100})$$ 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9 - 175 * q^10 + 363 * q^11 - 657 * q^12 - 90 * q^13 - 784 * q^14 + 675 * q^15 - 415 * q^16 + 1934 * q^17 + 567 * q^18 + 2084 * q^19 - 1825 * q^20 - 828 * q^21 + 847 * q^22 + 1220 * q^23 - 2079 * q^24 + 1875 * q^25 + 17062 * q^26 - 2187 * q^27 + 11120 * q^28 + 4402 * q^29 + 1575 * q^30 - 10688 * q^31 + 12439 * q^32 - 3267 * q^33 - 4094 * q^34 - 2300 * q^35 + 5913 * q^36 - 8190 * q^37 + 13792 * q^38 + 810 * q^39 - 5775 * q^40 + 5974 * q^41 + 7056 * q^42 + 18868 * q^43 + 8833 * q^44 - 6075 * q^45 + 46220 * q^46 + 55500 * q^47 + 3735 * q^48 + 1907 * q^49 + 4375 * q^50 - 17406 * q^51 + 27330 * q^52 + 9206 * q^53 - 5103 * q^54 - 9075 * q^55 + 73248 * q^56 - 18756 * q^57 + 15366 * q^58 - 59196 * q^59 + 16425 * q^60 + 79902 * q^61 + 64616 * q^62 + 7452 * q^63 + 2129 * q^64 + 2250 * q^65 - 7623 * q^66 + 4468 * q^67 - 1218 * q^68 - 10980 * q^69 + 19600 * q^70 - 75164 * q^71 + 18711 * q^72 - 61290 * q^73 - 56766 * q^74 - 16875 * q^75 + 37816 * q^76 + 11132 * q^77 - 153558 * q^78 - 83564 * q^79 + 10375 * q^80 + 19683 * q^81 + 147410 * q^82 + 74764 * q^83 - 100080 * q^84 - 48350 * q^85 - 253432 * q^86 - 39618 * q^87 + 27951 * q^88 + 37342 * q^89 - 14175 * q^90 - 126488 * q^91 + 148164 * q^92 + 96192 * q^93 + 59252 * q^94 - 52100 * q^95 - 111951 * q^96 + 33486 * q^97 - 95249 * q^98 + 29403 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 9.91848 1.75336 0.876678 0.481078i $$-0.159755\pi$$
0.876678 + 0.481078i $$0.159755\pi$$
$$3$$ −9.00000 −0.577350
$$4$$ 66.3762 2.07426
$$5$$ −25.0000 −0.447214
$$6$$ −89.2663 −1.01230
$$7$$ 92.6461 0.714631 0.357315 0.933984i $$-0.383692\pi$$
0.357315 + 0.933984i $$0.383692\pi$$
$$8$$ 340.959 1.88355
$$9$$ 81.0000 0.333333
$$10$$ −247.962 −0.784124
$$11$$ 121.000 0.301511
$$12$$ −597.386 −1.19757
$$13$$ 800.249 1.31331 0.656654 0.754192i $$-0.271971\pi$$
0.656654 + 0.754192i $$0.271971\pi$$
$$14$$ 918.908 1.25300
$$15$$ 225.000 0.258199
$$16$$ 1257.76 1.22828
$$17$$ −117.742 −0.0988122 −0.0494061 0.998779i $$-0.515733\pi$$
−0.0494061 + 0.998779i $$0.515733\pi$$
$$18$$ 803.397 0.584452
$$19$$ 831.422 0.528369 0.264185 0.964472i $$-0.414897\pi$$
0.264185 + 0.964472i $$0.414897\pi$$
$$20$$ −1659.40 −0.927635
$$21$$ −833.814 −0.412592
$$22$$ 1200.14 0.528657
$$23$$ 2952.23 1.16367 0.581837 0.813306i $$-0.302334\pi$$
0.581837 + 0.813306i $$0.302334\pi$$
$$24$$ −3068.63 −1.08747
$$25$$ 625.000 0.200000
$$26$$ 7937.25 2.30270
$$27$$ −729.000 −0.192450
$$28$$ 6149.49 1.48233
$$29$$ 5765.87 1.27312 0.636560 0.771227i $$-0.280357\pi$$
0.636560 + 0.771227i $$0.280357\pi$$
$$30$$ 2231.66 0.452714
$$31$$ −61.7803 −0.0115464 −0.00577319 0.999983i $$-0.501838\pi$$
−0.00577319 + 0.999983i $$0.501838\pi$$
$$32$$ 1564.36 0.270061
$$33$$ −1089.00 −0.174078
$$34$$ −1167.83 −0.173253
$$35$$ −2316.15 −0.319593
$$36$$ 5376.47 0.691419
$$37$$ −10236.6 −1.22928 −0.614640 0.788808i $$-0.710699\pi$$
−0.614640 + 0.788808i $$0.710699\pi$$
$$38$$ 8246.44 0.926419
$$39$$ −7202.24 −0.758239
$$40$$ −8523.98 −0.842350
$$41$$ 9599.21 0.891818 0.445909 0.895078i $$-0.352881\pi$$
0.445909 + 0.895078i $$0.352881\pi$$
$$42$$ −8270.17 −0.723421
$$43$$ −17473.2 −1.44113 −0.720563 0.693389i $$-0.756117\pi$$
−0.720563 + 0.693389i $$0.756117\pi$$
$$44$$ 8031.52 0.625412
$$45$$ −2025.00 −0.149071
$$46$$ 29281.7 2.04033
$$47$$ 18748.3 1.23799 0.618995 0.785395i $$-0.287540\pi$$
0.618995 + 0.785395i $$0.287540\pi$$
$$48$$ −11319.8 −0.709148
$$49$$ −8223.71 −0.489303
$$50$$ 6199.05 0.350671
$$51$$ 1059.68 0.0570493
$$52$$ 53117.5 2.72414
$$53$$ −9703.45 −0.474500 −0.237250 0.971449i $$-0.576246\pi$$
−0.237250 + 0.971449i $$0.576246\pi$$
$$54$$ −7230.57 −0.337433
$$55$$ −3025.00 −0.134840
$$56$$ 31588.5 1.34604
$$57$$ −7482.79 −0.305054
$$58$$ 57188.6 2.23223
$$59$$ −24401.4 −0.912609 −0.456305 0.889824i $$-0.650827\pi$$
−0.456305 + 0.889824i $$0.650827\pi$$
$$60$$ 14934.6 0.535571
$$61$$ 33910.3 1.16683 0.583413 0.812175i $$-0.301717\pi$$
0.583413 + 0.812175i $$0.301717\pi$$
$$62$$ −612.766 −0.0202449
$$63$$ 7504.33 0.238210
$$64$$ −24732.2 −0.754768
$$65$$ −20006.2 −0.587329
$$66$$ −10801.2 −0.305220
$$67$$ −4989.24 −0.135784 −0.0678918 0.997693i $$-0.521627\pi$$
−0.0678918 + 0.997693i $$0.521627\pi$$
$$68$$ −7815.29 −0.204962
$$69$$ −26570.1 −0.671847
$$70$$ −22972.7 −0.560360
$$71$$ −62961.6 −1.48228 −0.741140 0.671351i $$-0.765714\pi$$
−0.741140 + 0.671351i $$0.765714\pi$$
$$72$$ 27617.7 0.627851
$$73$$ −54232.5 −1.19111 −0.595556 0.803314i $$-0.703068\pi$$
−0.595556 + 0.803314i $$0.703068\pi$$
$$74$$ −101531. −2.15537
$$75$$ −5625.00 −0.115470
$$76$$ 55186.6 1.09597
$$77$$ 11210.2 0.215469
$$78$$ −71435.2 −1.32946
$$79$$ −56996.4 −1.02750 −0.513748 0.857941i $$-0.671743\pi$$
−0.513748 + 0.857941i $$0.671743\pi$$
$$80$$ −31444.0 −0.549304
$$81$$ 6561.00 0.111111
$$82$$ 95209.6 1.56367
$$83$$ 49685.9 0.791659 0.395830 0.918324i $$-0.370457\pi$$
0.395830 + 0.918324i $$0.370457\pi$$
$$84$$ −55345.4 −0.855822
$$85$$ 2943.56 0.0441902
$$86$$ −173308. −2.52681
$$87$$ −51892.8 −0.735037
$$88$$ 41256.1 0.567912
$$89$$ −87990.1 −1.17749 −0.588747 0.808317i $$-0.700379\pi$$
−0.588747 + 0.808317i $$0.700379\pi$$
$$90$$ −20084.9 −0.261375
$$91$$ 74139.9 0.938531
$$92$$ 195958. 2.41376
$$93$$ 556.022 0.00666630
$$94$$ 185954. 2.17064
$$95$$ −20785.5 −0.236294
$$96$$ −14079.3 −0.155920
$$97$$ −44817.9 −0.483640 −0.241820 0.970321i $$-0.577744\pi$$
−0.241820 + 0.970321i $$0.577744\pi$$
$$98$$ −81566.7 −0.857921
$$99$$ 9801.00 0.100504
$$100$$ 41485.1 0.414851
$$101$$ 82871.7 0.808356 0.404178 0.914680i $$-0.367558\pi$$
0.404178 + 0.914680i $$0.367558\pi$$
$$102$$ 10510.4 0.100028
$$103$$ 153697. 1.42749 0.713744 0.700406i $$-0.246998\pi$$
0.713744 + 0.700406i $$0.246998\pi$$
$$104$$ 272852. 2.47368
$$105$$ 20845.4 0.184517
$$106$$ −96243.5 −0.831968
$$107$$ 41662.3 0.351790 0.175895 0.984409i $$-0.443718\pi$$
0.175895 + 0.984409i $$0.443718\pi$$
$$108$$ −48388.2 −0.399191
$$109$$ 39745.0 0.320417 0.160209 0.987083i $$-0.448783\pi$$
0.160209 + 0.987083i $$0.448783\pi$$
$$110$$ −30003.4 −0.236422
$$111$$ 92129.3 0.709725
$$112$$ 116526. 0.877768
$$113$$ −191157. −1.40829 −0.704147 0.710054i $$-0.748671\pi$$
−0.704147 + 0.710054i $$0.748671\pi$$
$$114$$ −74217.9 −0.534868
$$115$$ −73805.8 −0.520411
$$116$$ 382716. 2.64078
$$117$$ 64820.1 0.437769
$$118$$ −242025. −1.60013
$$119$$ −10908.4 −0.0706143
$$120$$ 76715.9 0.486331
$$121$$ 14641.0 0.0909091
$$122$$ 336338. 2.04586
$$123$$ −86392.9 −0.514891
$$124$$ −4100.74 −0.0239501
$$125$$ −15625.0 −0.0894427
$$126$$ 74431.5 0.417667
$$127$$ −212879. −1.17118 −0.585590 0.810608i $$-0.699137\pi$$
−0.585590 + 0.810608i $$0.699137\pi$$
$$128$$ −295366. −1.59344
$$129$$ 157259. 0.832035
$$130$$ −198431. −1.02980
$$131$$ −146592. −0.746333 −0.373166 0.927764i $$-0.621728\pi$$
−0.373166 + 0.927764i $$0.621728\pi$$
$$132$$ −72283.7 −0.361082
$$133$$ 77027.9 0.377589
$$134$$ −49485.7 −0.238077
$$135$$ 18225.0 0.0860663
$$136$$ −40145.4 −0.186118
$$137$$ 335075. 1.52525 0.762623 0.646843i $$-0.223911\pi$$
0.762623 + 0.646843i $$0.223911\pi$$
$$138$$ −263535. −1.17799
$$139$$ 30053.6 0.131935 0.0659674 0.997822i $$-0.478987\pi$$
0.0659674 + 0.997822i $$0.478987\pi$$
$$140$$ −153737. −0.662917
$$141$$ −168735. −0.714754
$$142$$ −624483. −2.59896
$$143$$ 96830.1 0.395977
$$144$$ 101879. 0.409427
$$145$$ −144147. −0.569357
$$146$$ −537904. −2.08844
$$147$$ 74013.4 0.282499
$$148$$ −679466. −2.54984
$$149$$ 240256. 0.886559 0.443280 0.896383i $$-0.353815\pi$$
0.443280 + 0.896383i $$0.353815\pi$$
$$150$$ −55791.4 −0.202460
$$151$$ 37997.8 0.135617 0.0678087 0.997698i $$-0.478399\pi$$
0.0678087 + 0.997698i $$0.478399\pi$$
$$152$$ 283481. 0.995211
$$153$$ −9537.13 −0.0329374
$$154$$ 111188. 0.377794
$$155$$ 1544.51 0.00516369
$$156$$ −478057. −1.57278
$$157$$ −260511. −0.843483 −0.421742 0.906716i $$-0.638581\pi$$
−0.421742 + 0.906716i $$0.638581\pi$$
$$158$$ −565318. −1.80157
$$159$$ 87331.1 0.273953
$$160$$ −39109.0 −0.120775
$$161$$ 273513. 0.831597
$$162$$ 65075.1 0.194817
$$163$$ −364741. −1.07527 −0.537633 0.843179i $$-0.680681\pi$$
−0.537633 + 0.843179i $$0.680681\pi$$
$$164$$ 637159. 1.84986
$$165$$ 27225.0 0.0778499
$$166$$ 492809. 1.38806
$$167$$ 70995.9 0.196989 0.0984945 0.995138i $$-0.468597\pi$$
0.0984945 + 0.995138i $$0.468597\pi$$
$$168$$ −284297. −0.777139
$$169$$ 269105. 0.724778
$$170$$ 29195.6 0.0774811
$$171$$ 67345.2 0.176123
$$172$$ −1.15981e6 −2.98927
$$173$$ 295710. 0.751192 0.375596 0.926783i $$-0.377438\pi$$
0.375596 + 0.926783i $$0.377438\pi$$
$$174$$ −514698. −1.28878
$$175$$ 57903.8 0.142926
$$176$$ 152189. 0.370341
$$177$$ 219613. 0.526895
$$178$$ −872727. −2.06457
$$179$$ −567691. −1.32428 −0.662139 0.749381i $$-0.730351\pi$$
−0.662139 + 0.749381i $$0.730351\pi$$
$$180$$ −134412. −0.309212
$$181$$ −361118. −0.819319 −0.409660 0.912239i $$-0.634352\pi$$
−0.409660 + 0.912239i $$0.634352\pi$$
$$182$$ 735355. 1.64558
$$183$$ −305192. −0.673668
$$184$$ 1.00659e6 2.19184
$$185$$ 255915. 0.549751
$$186$$ 5514.90 0.0116884
$$187$$ −14246.8 −0.0297930
$$188$$ 1.24444e6 2.56791
$$189$$ −67539.0 −0.137531
$$190$$ −206161. −0.414307
$$191$$ 334871. 0.664193 0.332096 0.943245i $$-0.392244\pi$$
0.332096 + 0.943245i $$0.392244\pi$$
$$192$$ 222590. 0.435765
$$193$$ −286645. −0.553926 −0.276963 0.960881i $$-0.589328\pi$$
−0.276963 + 0.960881i $$0.589328\pi$$
$$194$$ −444525. −0.847992
$$195$$ 180056. 0.339095
$$196$$ −545858. −1.01494
$$197$$ 402554. 0.739024 0.369512 0.929226i $$-0.379525\pi$$
0.369512 + 0.929226i $$0.379525\pi$$
$$198$$ 97211.0 0.176219
$$199$$ 506857. 0.907304 0.453652 0.891179i $$-0.350121\pi$$
0.453652 + 0.891179i $$0.350121\pi$$
$$200$$ 213100. 0.376710
$$201$$ 44903.2 0.0783948
$$202$$ 821961. 1.41734
$$203$$ 534185. 0.909812
$$204$$ 70337.6 0.118335
$$205$$ −239980. −0.398833
$$206$$ 1.52444e6 2.50289
$$207$$ 239131. 0.387891
$$208$$ 1.00652e6 1.61311
$$209$$ 100602. 0.159309
$$210$$ 206754. 0.323524
$$211$$ 166764. 0.257867 0.128934 0.991653i $$-0.458845\pi$$
0.128934 + 0.991653i $$0.458845\pi$$
$$212$$ −644078. −0.984235
$$213$$ 566655. 0.855794
$$214$$ 413227. 0.616813
$$215$$ 436831. 0.644492
$$216$$ −248559. −0.362490
$$217$$ −5723.70 −0.00825140
$$218$$ 394209. 0.561805
$$219$$ 488093. 0.687689
$$220$$ −200788. −0.279693
$$221$$ −94223.2 −0.129771
$$222$$ 913782. 1.24440
$$223$$ 556053. 0.748780 0.374390 0.927271i $$-0.377852\pi$$
0.374390 + 0.927271i $$0.377852\pi$$
$$224$$ 144932. 0.192994
$$225$$ 50625.0 0.0666667
$$226$$ −1.89598e6 −2.46924
$$227$$ 507849. 0.654139 0.327069 0.945000i $$-0.393939\pi$$
0.327069 + 0.945000i $$0.393939\pi$$
$$228$$ −496679. −0.632760
$$229$$ −627193. −0.790337 −0.395169 0.918609i $$-0.629314\pi$$
−0.395169 + 0.918609i $$0.629314\pi$$
$$230$$ −732042. −0.912465
$$231$$ −100892. −0.124401
$$232$$ 1.96593e6 2.39799
$$233$$ 955870. 1.15348 0.576738 0.816929i $$-0.304325\pi$$
0.576738 + 0.816929i $$0.304325\pi$$
$$234$$ 642917. 0.767565
$$235$$ −468707. −0.553646
$$236$$ −1.61967e6 −1.89298
$$237$$ 512968. 0.593225
$$238$$ −108194. −0.123812
$$239$$ −509255. −0.576687 −0.288344 0.957527i $$-0.593105\pi$$
−0.288344 + 0.957527i $$0.593105\pi$$
$$240$$ 282996. 0.317141
$$241$$ −666125. −0.738776 −0.369388 0.929275i $$-0.620433\pi$$
−0.369388 + 0.929275i $$0.620433\pi$$
$$242$$ 145216. 0.159396
$$243$$ −59049.0 −0.0641500
$$244$$ 2.25083e6 2.42030
$$245$$ 205593. 0.218823
$$246$$ −856886. −0.902787
$$247$$ 665344. 0.693911
$$248$$ −21064.6 −0.0217482
$$249$$ −447173. −0.457065
$$250$$ −154976. −0.156825
$$251$$ 505010. 0.505960 0.252980 0.967472i $$-0.418589\pi$$
0.252980 + 0.967472i $$0.418589\pi$$
$$252$$ 498109. 0.494109
$$253$$ 357220. 0.350861
$$254$$ −2.11144e6 −2.05349
$$255$$ −26492.0 −0.0255132
$$256$$ −2.13815e6 −2.03909
$$257$$ −2.02669e6 −1.91405 −0.957027 0.290000i $$-0.906345\pi$$
−0.957027 + 0.290000i $$0.906345\pi$$
$$258$$ 1.55977e6 1.45885
$$259$$ −948379. −0.878482
$$260$$ −1.32794e6 −1.21827
$$261$$ 467035. 0.424374
$$262$$ −1.45397e6 −1.30859
$$263$$ 1.57349e6 1.40273 0.701366 0.712801i $$-0.252574\pi$$
0.701366 + 0.712801i $$0.252574\pi$$
$$264$$ −371305. −0.327884
$$265$$ 242586. 0.212203
$$266$$ 764000. 0.662048
$$267$$ 791911. 0.679826
$$268$$ −331167. −0.281650
$$269$$ −1.55958e6 −1.31409 −0.657046 0.753850i $$-0.728194\pi$$
−0.657046 + 0.753850i $$0.728194\pi$$
$$270$$ 180764. 0.150905
$$271$$ 1.35274e6 1.11890 0.559451 0.828864i $$-0.311012\pi$$
0.559451 + 0.828864i $$0.311012\pi$$
$$272$$ −148092. −0.121369
$$273$$ −667259. −0.541861
$$274$$ 3.32343e6 2.67430
$$275$$ 75625.0 0.0603023
$$276$$ −1.76362e6 −1.39358
$$277$$ 2.47205e6 1.93579 0.967895 0.251353i $$-0.0808755\pi$$
0.967895 + 0.251353i $$0.0808755\pi$$
$$278$$ 298086. 0.231328
$$279$$ −5004.20 −0.00384879
$$280$$ −789714. −0.601970
$$281$$ 769611. 0.581441 0.290721 0.956808i $$-0.406105\pi$$
0.290721 + 0.956808i $$0.406105\pi$$
$$282$$ −1.67359e6 −1.25322
$$283$$ 2.52887e6 1.87698 0.938490 0.345305i $$-0.112225\pi$$
0.938490 + 0.345305i $$0.112225\pi$$
$$284$$ −4.17915e6 −3.07463
$$285$$ 187070. 0.136424
$$286$$ 960407. 0.694289
$$287$$ 889329. 0.637320
$$288$$ 126713. 0.0900204
$$289$$ −1.40599e6 −0.990236
$$290$$ −1.42972e6 −0.998285
$$291$$ 403361. 0.279229
$$292$$ −3.59975e6 −2.47067
$$293$$ 2.06542e6 1.40553 0.702764 0.711423i $$-0.251949\pi$$
0.702764 + 0.711423i $$0.251949\pi$$
$$294$$ 734100. 0.495321
$$295$$ 610035. 0.408131
$$296$$ −3.49026e6 −2.31541
$$297$$ −88209.0 −0.0580259
$$298$$ 2.38297e6 1.55445
$$299$$ 2.36252e6 1.52826
$$300$$ −373366. −0.239514
$$301$$ −1.61883e6 −1.02987
$$302$$ 376880. 0.237786
$$303$$ −745845. −0.466704
$$304$$ 1.04573e6 0.648986
$$305$$ −847756. −0.521821
$$306$$ −94593.9 −0.0577510
$$307$$ −2.17085e6 −1.31457 −0.657286 0.753641i $$-0.728296\pi$$
−0.657286 + 0.753641i $$0.728296\pi$$
$$308$$ 744088. 0.446939
$$309$$ −1.38327e6 −0.824161
$$310$$ 15319.2 0.00905379
$$311$$ −198576. −0.116420 −0.0582098 0.998304i $$-0.518539\pi$$
−0.0582098 + 0.998304i $$0.518539\pi$$
$$312$$ −2.45567e6 −1.42818
$$313$$ −483762. −0.279107 −0.139554 0.990215i $$-0.544567\pi$$
−0.139554 + 0.990215i $$0.544567\pi$$
$$314$$ −2.58387e6 −1.47893
$$315$$ −187608. −0.106531
$$316$$ −3.78321e6 −2.13129
$$317$$ −1.68099e6 −0.939542 −0.469771 0.882788i $$-0.655664\pi$$
−0.469771 + 0.882788i $$0.655664\pi$$
$$318$$ 866191. 0.480337
$$319$$ 697670. 0.383860
$$320$$ 618306. 0.337542
$$321$$ −374961. −0.203106
$$322$$ 2.71283e6 1.45809
$$323$$ −97893.6 −0.0522093
$$324$$ 435494. 0.230473
$$325$$ 500155. 0.262662
$$326$$ −3.61768e6 −1.88532
$$327$$ −357705. −0.184993
$$328$$ 3.27294e6 1.67979
$$329$$ 1.73696e6 0.884706
$$330$$ 270031. 0.136499
$$331$$ −1.18881e6 −0.596407 −0.298204 0.954502i $$-0.596387\pi$$
−0.298204 + 0.954502i $$0.596387\pi$$
$$332$$ 3.29796e6 1.64210
$$333$$ −829164. −0.409760
$$334$$ 704171. 0.345392
$$335$$ 124731. 0.0607243
$$336$$ −1.04874e6 −0.506779
$$337$$ 1.78561e6 0.856470 0.428235 0.903667i $$-0.359135\pi$$
0.428235 + 0.903667i $$0.359135\pi$$
$$338$$ 2.66911e6 1.27079
$$339$$ 1.72041e6 0.813079
$$340$$ 195382. 0.0916617
$$341$$ −7475.41 −0.00348136
$$342$$ 667961. 0.308806
$$343$$ −2.31900e6 −1.06430
$$344$$ −5.95766e6 −2.71444
$$345$$ 664253. 0.300459
$$346$$ 2.93299e6 1.31711
$$347$$ 2.71689e6 1.21129 0.605645 0.795735i $$-0.292915\pi$$
0.605645 + 0.795735i $$0.292915\pi$$
$$348$$ −3.44445e6 −1.52465
$$349$$ −1.87050e6 −0.822044 −0.411022 0.911626i $$-0.634828\pi$$
−0.411022 + 0.911626i $$0.634828\pi$$
$$350$$ 574317. 0.250600
$$351$$ −583381. −0.252746
$$352$$ 189288. 0.0814265
$$353$$ −4.27952e6 −1.82793 −0.913963 0.405798i $$-0.866994\pi$$
−0.913963 + 0.405798i $$0.866994\pi$$
$$354$$ 2.17822e6 0.923835
$$355$$ 1.57404e6 0.662896
$$356$$ −5.84045e6 −2.44242
$$357$$ 98175.3 0.0407692
$$358$$ −5.63063e6 −2.32193
$$359$$ −1.39681e6 −0.572007 −0.286003 0.958229i $$-0.592327\pi$$
−0.286003 + 0.958229i $$0.592327\pi$$
$$360$$ −690443. −0.280783
$$361$$ −1.78484e6 −0.720826
$$362$$ −3.58174e6 −1.43656
$$363$$ −131769. −0.0524864
$$364$$ 4.92112e6 1.94675
$$365$$ 1.35581e6 0.532681
$$366$$ −3.02704e6 −1.18118
$$367$$ −5.05674e6 −1.95977 −0.979885 0.199561i $$-0.936049\pi$$
−0.979885 + 0.199561i $$0.936049\pi$$
$$368$$ 3.71320e6 1.42932
$$369$$ 777536. 0.297273
$$370$$ 2.53828e6 0.963909
$$371$$ −898987. −0.339093
$$372$$ 36906.6 0.0138276
$$373$$ −4.68117e6 −1.74214 −0.871069 0.491161i $$-0.836573\pi$$
−0.871069 + 0.491161i $$0.836573\pi$$
$$374$$ −141307. −0.0522377
$$375$$ 140625. 0.0516398
$$376$$ 6.39241e6 2.33182
$$377$$ 4.61413e6 1.67200
$$378$$ −669884. −0.241140
$$379$$ −3.76641e6 −1.34688 −0.673442 0.739240i $$-0.735185\pi$$
−0.673442 + 0.739240i $$0.735185\pi$$
$$380$$ −1.37966e6 −0.490134
$$381$$ 1.91591e6 0.676181
$$382$$ 3.32141e6 1.16457
$$383$$ 4.17276e6 1.45354 0.726770 0.686881i $$-0.241021\pi$$
0.726770 + 0.686881i $$0.241021\pi$$
$$384$$ 2.65829e6 0.919972
$$385$$ −280254. −0.0963608
$$386$$ −2.84308e6 −0.971228
$$387$$ −1.41533e6 −0.480376
$$388$$ −2.97484e6 −1.00319
$$389$$ −3.73222e6 −1.25053 −0.625265 0.780413i $$-0.715009\pi$$
−0.625265 + 0.780413i $$0.715009\pi$$
$$390$$ 1.78588e6 0.594553
$$391$$ −347603. −0.114985
$$392$$ −2.80395e6 −0.921627
$$393$$ 1.31933e6 0.430896
$$394$$ 3.99272e6 1.29577
$$395$$ 1.42491e6 0.459510
$$396$$ 650553. 0.208471
$$397$$ 5.71418e6 1.81961 0.909804 0.415038i $$-0.136232\pi$$
0.909804 + 0.415038i $$0.136232\pi$$
$$398$$ 5.02725e6 1.59083
$$399$$ −693251. −0.218001
$$400$$ 786100. 0.245656
$$401$$ 3.60785e6 1.12044 0.560219 0.828345i $$-0.310717\pi$$
0.560219 + 0.828345i $$0.310717\pi$$
$$402$$ 445371. 0.137454
$$403$$ −49439.6 −0.0151639
$$404$$ 5.50070e6 1.67674
$$405$$ −164025. −0.0496904
$$406$$ 5.29830e6 1.59522
$$407$$ −1.23863e6 −0.370642
$$408$$ 361308. 0.107455
$$409$$ −4.59452e6 −1.35810 −0.679050 0.734092i $$-0.737608\pi$$
−0.679050 + 0.734092i $$0.737608\pi$$
$$410$$ −2.38024e6 −0.699296
$$411$$ −3.01567e6 −0.880601
$$412$$ 1.02018e7 2.96098
$$413$$ −2.26069e6 −0.652179
$$414$$ 2.37181e6 0.680111
$$415$$ −1.24215e6 −0.354041
$$416$$ 1.25188e6 0.354673
$$417$$ −270482. −0.0761725
$$418$$ 997819. 0.279326
$$419$$ 1.92383e6 0.535343 0.267671 0.963510i $$-0.413746\pi$$
0.267671 + 0.963510i $$0.413746\pi$$
$$420$$ 1.38364e6 0.382735
$$421$$ −4.28936e6 −1.17947 −0.589736 0.807596i $$-0.700768\pi$$
−0.589736 + 0.807596i $$0.700768\pi$$
$$422$$ 1.65404e6 0.452133
$$423$$ 1.51861e6 0.412663
$$424$$ −3.30848e6 −0.893746
$$425$$ −73589.0 −0.0197624
$$426$$ 5.62035e6 1.50051
$$427$$ 3.14165e6 0.833851
$$428$$ 2.76538e6 0.729703
$$429$$ −871471. −0.228618
$$430$$ 4.33270e6 1.13002
$$431$$ 477444. 0.123802 0.0619012 0.998082i $$-0.480284\pi$$
0.0619012 + 0.998082i $$0.480284\pi$$
$$432$$ −916907. −0.236383
$$433$$ −6.24919e6 −1.60178 −0.800892 0.598808i $$-0.795641\pi$$
−0.800892 + 0.598808i $$0.795641\pi$$
$$434$$ −56770.4 −0.0144676
$$435$$ 1.29732e6 0.328718
$$436$$ 2.63812e6 0.664627
$$437$$ 2.45455e6 0.614849
$$438$$ 4.84113e6 1.20576
$$439$$ 5.45632e6 1.35126 0.675629 0.737241i $$-0.263872\pi$$
0.675629 + 0.737241i $$0.263872\pi$$
$$440$$ −1.03140e6 −0.253978
$$441$$ −666120. −0.163101
$$442$$ −934551. −0.227534
$$443$$ −3.75783e6 −0.909762 −0.454881 0.890552i $$-0.650318\pi$$
−0.454881 + 0.890552i $$0.650318\pi$$
$$444$$ 6.11519e6 1.47215
$$445$$ 2.19975e6 0.526591
$$446$$ 5.51520e6 1.31288
$$447$$ −2.16230e6 −0.511855
$$448$$ −2.29134e6 −0.539380
$$449$$ −7.17310e6 −1.67916 −0.839578 0.543239i $$-0.817198\pi$$
−0.839578 + 0.543239i $$0.817198\pi$$
$$450$$ 502123. 0.116890
$$451$$ 1.16150e6 0.268893
$$452$$ −1.26883e7 −2.92116
$$453$$ −341980. −0.0782988
$$454$$ 5.03709e6 1.14694
$$455$$ −1.85350e6 −0.419724
$$456$$ −2.55133e6 −0.574585
$$457$$ −3.21240e6 −0.719513 −0.359757 0.933046i $$-0.617140\pi$$
−0.359757 + 0.933046i $$0.617140\pi$$
$$458$$ −6.22080e6 −1.38574
$$459$$ 85834.2 0.0190164
$$460$$ −4.89895e6 −1.07946
$$461$$ −5.17808e6 −1.13479 −0.567396 0.823445i $$-0.692049\pi$$
−0.567396 + 0.823445i $$0.692049\pi$$
$$462$$ −1.00069e6 −0.218120
$$463$$ 2.95142e6 0.639851 0.319926 0.947443i $$-0.396342\pi$$
0.319926 + 0.947443i $$0.396342\pi$$
$$464$$ 7.25208e6 1.56375
$$465$$ −13900.6 −0.00298126
$$466$$ 9.48077e6 2.02245
$$467$$ 7.26608e6 1.54173 0.770865 0.636999i $$-0.219825\pi$$
0.770865 + 0.636999i $$0.219825\pi$$
$$468$$ 4.30251e6 0.908045
$$469$$ −462234. −0.0970352
$$470$$ −4.64886e6 −0.970738
$$471$$ 2.34460e6 0.486985
$$472$$ −8.31989e6 −1.71895
$$473$$ −2.11426e6 −0.434516
$$474$$ 5.08786e6 1.04013
$$475$$ 519639. 0.105674
$$476$$ −724056. −0.146472
$$477$$ −785980. −0.158167
$$478$$ −5.05103e6 −1.01114
$$479$$ −4.09584e6 −0.815651 −0.407826 0.913060i $$-0.633713\pi$$
−0.407826 + 0.913060i $$0.633713\pi$$
$$480$$ 351981. 0.0697295
$$481$$ −8.19181e6 −1.61442
$$482$$ −6.60694e6 −1.29534
$$483$$ −2.46162e6 −0.480123
$$484$$ 971814. 0.188569
$$485$$ 1.12045e6 0.216290
$$486$$ −585676. −0.112478
$$487$$ 218477. 0.0417429 0.0208715 0.999782i $$-0.493356\pi$$
0.0208715 + 0.999782i $$0.493356\pi$$
$$488$$ 1.15620e7 2.19778
$$489$$ 3.28267e6 0.620805
$$490$$ 2.03917e6 0.383674
$$491$$ −3.49848e6 −0.654901 −0.327451 0.944868i $$-0.606190\pi$$
−0.327451 + 0.944868i $$0.606190\pi$$
$$492$$ −5.73443e6 −1.06802
$$493$$ −678887. −0.125800
$$494$$ 6.59920e6 1.21667
$$495$$ −245025. −0.0449467
$$496$$ −77704.7 −0.0141822
$$497$$ −5.83315e6 −1.05928
$$498$$ −4.43528e6 −0.801397
$$499$$ −3.62715e6 −0.652100 −0.326050 0.945353i $$-0.605718\pi$$
−0.326050 + 0.945353i $$0.605718\pi$$
$$500$$ −1.03713e6 −0.185527
$$501$$ −638963. −0.113732
$$502$$ 5.00893e6 0.887127
$$503$$ 6.00845e6 1.05887 0.529435 0.848351i $$-0.322404\pi$$
0.529435 + 0.848351i $$0.322404\pi$$
$$504$$ 2.55867e6 0.448682
$$505$$ −2.07179e6 −0.361508
$$506$$ 3.54308e6 0.615184
$$507$$ −2.42194e6 −0.418451
$$508$$ −1.41301e7 −2.42933
$$509$$ 4.28786e6 0.733578 0.366789 0.930304i $$-0.380457\pi$$
0.366789 + 0.930304i $$0.380457\pi$$
$$510$$ −262761. −0.0447337
$$511$$ −5.02443e6 −0.851205
$$512$$ −1.17554e7 −1.98182
$$513$$ −606106. −0.101685
$$514$$ −2.01017e7 −3.35602
$$515$$ −3.84243e6 −0.638392
$$516$$ 1.04383e7 1.72585
$$517$$ 2.26854e6 0.373268
$$518$$ −9.40648e6 −1.54029
$$519$$ −2.66139e6 −0.433701
$$520$$ −6.82131e6 −1.10627
$$521$$ 1.06243e7 1.71477 0.857386 0.514673i $$-0.172087\pi$$
0.857386 + 0.514673i $$0.172087\pi$$
$$522$$ 4.63228e6 0.744078
$$523$$ 123402. 0.0197273 0.00986367 0.999951i $$-0.496860\pi$$
0.00986367 + 0.999951i $$0.496860\pi$$
$$524$$ −9.73023e6 −1.54809
$$525$$ −521134. −0.0825185
$$526$$ 1.56066e7 2.45949
$$527$$ 7274.16 0.00114092
$$528$$ −1.36970e6 −0.213816
$$529$$ 2.27934e6 0.354136
$$530$$ 2.40609e6 0.372067
$$531$$ −1.97651e6 −0.304203
$$532$$ 5.11282e6 0.783216
$$533$$ 7.68176e6 1.17123
$$534$$ 7.85455e6 1.19198
$$535$$ −1.04156e6 −0.157325
$$536$$ −1.70113e6 −0.255756
$$537$$ 5.10922e6 0.764573
$$538$$ −1.54686e7 −2.30407
$$539$$ −995069. −0.147530
$$540$$ 1.20971e6 0.178524
$$541$$ −5.60908e6 −0.823946 −0.411973 0.911196i $$-0.635160\pi$$
−0.411973 + 0.911196i $$0.635160\pi$$
$$542$$ 1.34171e7 1.96183
$$543$$ 3.25006e6 0.473034
$$544$$ −184192. −0.0266853
$$545$$ −993624. −0.143295
$$546$$ −6.61819e6 −0.950075
$$547$$ 2.72729e6 0.389729 0.194864 0.980830i $$-0.437573\pi$$
0.194864 + 0.980830i $$0.437573\pi$$
$$548$$ 2.22410e7 3.16375
$$549$$ 2.74673e6 0.388942
$$550$$ 750085. 0.105731
$$551$$ 4.79387e6 0.672678
$$552$$ −9.05933e6 −1.26546
$$553$$ −5.28050e6 −0.734280
$$554$$ 2.45190e7 3.39413
$$555$$ −2.30323e6 −0.317399
$$556$$ 1.99484e6 0.273666
$$557$$ 3.50042e6 0.478059 0.239030 0.971012i $$-0.423171\pi$$
0.239030 + 0.971012i $$0.423171\pi$$
$$558$$ −49634.1 −0.00674830
$$559$$ −1.39829e7 −1.89264
$$560$$ −2.91316e6 −0.392550
$$561$$ 128221. 0.0172010
$$562$$ 7.63337e6 1.01947
$$563$$ 1.03320e7 1.37377 0.686886 0.726766i $$-0.258977\pi$$
0.686886 + 0.726766i $$0.258977\pi$$
$$564$$ −1.12000e7 −1.48258
$$565$$ 4.77892e6 0.629809
$$566$$ 2.50825e7 3.29101
$$567$$ 607851. 0.0794034
$$568$$ −2.14674e7 −2.79195
$$569$$ −1.31943e7 −1.70846 −0.854229 0.519897i $$-0.825970\pi$$
−0.854229 + 0.519897i $$0.825970\pi$$
$$570$$ 1.85545e6 0.239200
$$571$$ −5.98575e6 −0.768295 −0.384148 0.923272i $$-0.625505\pi$$
−0.384148 + 0.923272i $$0.625505\pi$$
$$572$$ 6.42721e6 0.821358
$$573$$ −3.01384e6 −0.383472
$$574$$ 8.82079e6 1.11745
$$575$$ 1.84515e6 0.232735
$$576$$ −2.00331e6 −0.251589
$$577$$ 7.74177e6 0.968056 0.484028 0.875052i $$-0.339173\pi$$
0.484028 + 0.875052i $$0.339173\pi$$
$$578$$ −1.39453e7 −1.73624
$$579$$ 2.57981e6 0.319809
$$580$$ −9.56791e6 −1.18099
$$581$$ 4.60321e6 0.565744
$$582$$ 4.00072e6 0.489589
$$583$$ −1.17412e6 −0.143067
$$584$$ −1.84911e7 −2.24352
$$585$$ −1.62050e6 −0.195776
$$586$$ 2.04858e7 2.46439
$$587$$ 1.19577e7 1.43236 0.716181 0.697915i $$-0.245889\pi$$
0.716181 + 0.697915i $$0.245889\pi$$
$$588$$ 4.91273e6 0.585975
$$589$$ −51365.5 −0.00610075
$$590$$ 6.05062e6 0.715599
$$591$$ −3.62298e6 −0.426676
$$592$$ −1.28752e7 −1.50990
$$593$$ −1.08502e7 −1.26707 −0.633536 0.773713i $$-0.718397\pi$$
−0.633536 + 0.773713i $$0.718397\pi$$
$$594$$ −874899. −0.101740
$$595$$ 272709. 0.0315797
$$596$$ 1.59472e7 1.83895
$$597$$ −4.56171e6 −0.523832
$$598$$ 2.34326e7 2.67959
$$599$$ −1.23306e7 −1.40416 −0.702082 0.712096i $$-0.747746\pi$$
−0.702082 + 0.712096i $$0.747746\pi$$
$$600$$ −1.91790e6 −0.217494
$$601$$ 1.17382e7 1.32561 0.662807 0.748790i $$-0.269365\pi$$
0.662807 + 0.748790i $$0.269365\pi$$
$$602$$ −1.60563e7 −1.80574
$$603$$ −404129. −0.0452612
$$604$$ 2.52215e6 0.281305
$$605$$ −366025. −0.0406558
$$606$$ −7.39765e6 −0.818299
$$607$$ 9.20559e6 1.01410 0.507049 0.861917i $$-0.330736\pi$$
0.507049 + 0.861917i $$0.330736\pi$$
$$608$$ 1.30064e6 0.142692
$$609$$ −4.80766e6 −0.525280
$$610$$ −8.40845e6 −0.914938
$$611$$ 1.50033e7 1.62586
$$612$$ −633039. −0.0683206
$$613$$ 5.83164e6 0.626815 0.313408 0.949619i $$-0.398529\pi$$
0.313408 + 0.949619i $$0.398529\pi$$
$$614$$ −2.15316e7 −2.30491
$$615$$ 2.15982e6 0.230266
$$616$$ 3.82221e6 0.405848
$$617$$ −9.28462e6 −0.981863 −0.490932 0.871198i $$-0.663344\pi$$
−0.490932 + 0.871198i $$0.663344\pi$$
$$618$$ −1.37200e7 −1.44505
$$619$$ 2.47650e6 0.259784 0.129892 0.991528i $$-0.458537\pi$$
0.129892 + 0.991528i $$0.458537\pi$$
$$620$$ 102518. 0.0107108
$$621$$ −2.15218e6 −0.223949
$$622$$ −1.96957e6 −0.204125
$$623$$ −8.15193e6 −0.841474
$$624$$ −9.05869e6 −0.931330
$$625$$ 390625. 0.0400000
$$626$$ −4.79819e6 −0.489374
$$627$$ −905418. −0.0919772
$$628$$ −1.72917e7 −1.74960
$$629$$ 1.20528e6 0.121468
$$630$$ −1.86079e6 −0.186787
$$631$$ 8.58315e6 0.858170 0.429085 0.903264i $$-0.358836\pi$$
0.429085 + 0.903264i $$0.358836\pi$$
$$632$$ −1.94335e7 −1.93534
$$633$$ −1.50087e6 −0.148880
$$634$$ −1.66728e7 −1.64735
$$635$$ 5.32197e6 0.523767
$$636$$ 5.79670e6 0.568248
$$637$$ −6.58101e6 −0.642605
$$638$$ 6.91982e6 0.673044
$$639$$ −5.09989e6 −0.494093
$$640$$ 7.38414e6 0.712607
$$641$$ 4.59033e6 0.441264 0.220632 0.975357i $$-0.429188\pi$$
0.220632 + 0.975357i $$0.429188\pi$$
$$642$$ −3.71904e6 −0.356117
$$643$$ 9.70391e6 0.925592 0.462796 0.886465i $$-0.346846\pi$$
0.462796 + 0.886465i $$0.346846\pi$$
$$644$$ 1.81547e7 1.72494
$$645$$ −3.93148e6 −0.372097
$$646$$ −970955. −0.0915415
$$647$$ −9.01887e6 −0.847015 −0.423508 0.905892i $$-0.639201\pi$$
−0.423508 + 0.905892i $$0.639201\pi$$
$$648$$ 2.23703e6 0.209284
$$649$$ −2.95257e6 −0.275162
$$650$$ 4.96078e6 0.460539
$$651$$ 51513.3 0.00476395
$$652$$ −2.42101e7 −2.23038
$$653$$ 1.94337e6 0.178349 0.0891747 0.996016i $$-0.471577\pi$$
0.0891747 + 0.996016i $$0.471577\pi$$
$$654$$ −3.54789e6 −0.324358
$$655$$ 3.66481e6 0.333770
$$656$$ 1.20735e7 1.09540
$$657$$ −4.39283e6 −0.397037
$$658$$ 1.72279e7 1.55120
$$659$$ −6.36990e6 −0.571372 −0.285686 0.958323i $$-0.592221\pi$$
−0.285686 + 0.958323i $$0.592221\pi$$
$$660$$ 1.80709e6 0.161481
$$661$$ −7.88417e6 −0.701863 −0.350931 0.936401i $$-0.614135\pi$$
−0.350931 + 0.936401i $$0.614135\pi$$
$$662$$ −1.17912e7 −1.04571
$$663$$ 848009. 0.0749232
$$664$$ 1.69409e7 1.49113
$$665$$ −1.92570e6 −0.168863
$$666$$ −8.22404e6 −0.718455
$$667$$ 1.70222e7 1.48150
$$668$$ 4.71244e6 0.408606
$$669$$ −5.00448e6 −0.432308
$$670$$ 1.23714e6 0.106471
$$671$$ 4.10314e6 0.351812
$$672$$ −1.30439e6 −0.111425
$$673$$ −4.51895e6 −0.384592 −0.192296 0.981337i $$-0.561593\pi$$
−0.192296 + 0.981337i $$0.561593\pi$$
$$674$$ 1.77106e7 1.50170
$$675$$ −455625. −0.0384900
$$676$$ 1.78622e7 1.50337
$$677$$ 1.17659e7 0.986624 0.493312 0.869852i $$-0.335786\pi$$
0.493312 + 0.869852i $$0.335786\pi$$
$$678$$ 1.70639e7 1.42562
$$679$$ −4.15220e6 −0.345624
$$680$$ 1.00363e6 0.0832345
$$681$$ −4.57064e6 −0.377667
$$682$$ −74144.7 −0.00610407
$$683$$ −1.27636e7 −1.04694 −0.523470 0.852044i $$-0.675363\pi$$
−0.523470 + 0.852044i $$0.675363\pi$$
$$684$$ 4.47011e6 0.365324
$$685$$ −8.37686e6 −0.682111
$$686$$ −2.30009e7 −1.86610
$$687$$ 5.64474e6 0.456302
$$688$$ −2.19771e7 −1.77011
$$689$$ −7.76518e6 −0.623165
$$690$$ 6.58837e6 0.526812
$$691$$ 1.94008e7 1.54570 0.772849 0.634590i $$-0.218831\pi$$
0.772849 + 0.634590i $$0.218831\pi$$
$$692$$ 1.96281e7 1.55816
$$693$$ 908024. 0.0718231
$$694$$ 2.69474e7 2.12382
$$695$$ −751339. −0.0590030
$$696$$ −1.76933e7 −1.38448
$$697$$ −1.13023e6 −0.0881225
$$698$$ −1.85525e7 −1.44133
$$699$$ −8.60283e6 −0.665960
$$700$$ 3.84343e6 0.296465
$$701$$ 1.81026e7 1.39138 0.695690 0.718342i $$-0.255099\pi$$
0.695690 + 0.718342i $$0.255099\pi$$
$$702$$ −5.78625e6 −0.443154
$$703$$ −8.51092e6 −0.649514
$$704$$ −2.99260e6 −0.227571
$$705$$ 4.21837e6 0.319648
$$706$$ −4.24463e7 −3.20500
$$707$$ 7.67773e6 0.577676
$$708$$ 1.45771e7 1.09292
$$709$$ 1.55411e7 1.16109 0.580547 0.814227i $$-0.302839\pi$$
0.580547 + 0.814227i $$0.302839\pi$$
$$710$$ 1.56121e7 1.16229
$$711$$ −4.61671e6 −0.342499
$$712$$ −3.00010e7 −2.21787
$$713$$ −182390. −0.0134362
$$714$$ 973750. 0.0714828
$$715$$ −2.42075e6 −0.177086
$$716$$ −3.76812e7 −2.74689
$$717$$ 4.58329e6 0.332951
$$718$$ −1.38542e7 −1.00293
$$719$$ 8.88792e6 0.641177 0.320589 0.947219i $$-0.396119\pi$$
0.320589 + 0.947219i $$0.396119\pi$$
$$720$$ −2.54696e6 −0.183101
$$721$$ 1.42394e7 1.02013
$$722$$ −1.77029e7 −1.26386
$$723$$ 5.99512e6 0.426533
$$724$$ −2.39697e7 −1.69948
$$725$$ 3.60367e6 0.254624
$$726$$ −1.30695e6 −0.0920273
$$727$$ −5.73697e6 −0.402575 −0.201287 0.979532i $$-0.564513\pi$$
−0.201287 + 0.979532i $$0.564513\pi$$
$$728$$ 2.52787e7 1.76777
$$729$$ 531441. 0.0370370
$$730$$ 1.34476e7 0.933980
$$731$$ 2.05734e6 0.142401
$$732$$ −2.02575e7 −1.39736
$$733$$ 1.77002e6 0.121680 0.0608399 0.998148i $$-0.480622\pi$$
0.0608399 + 0.998148i $$0.480622\pi$$
$$734$$ −5.01551e7 −3.43618
$$735$$ −1.85033e6 −0.126337
$$736$$ 4.61836e6 0.314263
$$737$$ −603698. −0.0409403
$$738$$ 7.71198e6 0.521224
$$739$$ 1.53957e7 1.03702 0.518512 0.855070i $$-0.326486\pi$$
0.518512 + 0.855070i $$0.326486\pi$$
$$740$$ 1.69866e7 1.14032
$$741$$ −5.98810e6 −0.400630
$$742$$ −8.91658e6 −0.594550
$$743$$ 1.65861e7 1.10223 0.551115 0.834429i $$-0.314202\pi$$
0.551115 + 0.834429i $$0.314202\pi$$
$$744$$ 189581. 0.0125563
$$745$$ −6.00639e6 −0.396481
$$746$$ −4.64301e7 −3.05459
$$747$$ 4.02456e6 0.263886
$$748$$ −945650. −0.0617983
$$749$$ 3.85985e6 0.251400
$$750$$ 1.39479e6 0.0905429
$$751$$ 9.40157e6 0.608276 0.304138 0.952628i $$-0.401632\pi$$
0.304138 + 0.952628i $$0.401632\pi$$
$$752$$ 2.35808e7 1.52060
$$753$$ −4.54509e6 −0.292116
$$754$$ 4.57651e7 2.93161
$$755$$ −949944. −0.0606500
$$756$$ −4.48298e6 −0.285274
$$757$$ 1.22686e7 0.778134 0.389067 0.921209i $$-0.372797\pi$$
0.389067 + 0.921209i $$0.372797\pi$$
$$758$$ −3.73571e7 −2.36157
$$759$$ −3.21498e6 −0.202570
$$760$$ −7.08703e6 −0.445072
$$761$$ −2.14104e7 −1.34018 −0.670090 0.742280i $$-0.733744\pi$$
−0.670090 + 0.742280i $$0.733744\pi$$
$$762$$ 1.90029e7 1.18559
$$763$$ 3.68221e6 0.228980
$$764$$ 2.22275e7 1.37771
$$765$$ 238428. 0.0147301
$$766$$ 4.13875e7 2.54857
$$767$$ −1.95272e7 −1.19854
$$768$$ 1.92433e7 1.17727
$$769$$ 8.34064e6 0.508609 0.254304 0.967124i $$-0.418154\pi$$
0.254304 + 0.967124i $$0.418154\pi$$
$$770$$ −2.77970e6 −0.168955
$$771$$ 1.82402e7 1.10508
$$772$$ −1.90264e7 −1.14898
$$773$$ 3.00417e7 1.80832 0.904162 0.427191i $$-0.140497\pi$$
0.904162 + 0.427191i $$0.140497\pi$$
$$774$$ −1.40379e7 −0.842269
$$775$$ −38612.7 −0.00230927
$$776$$ −1.52811e7 −0.910960
$$777$$ 8.53541e6 0.507192
$$778$$ −3.70180e7 −2.19262
$$779$$ 7.98099e6 0.471209
$$780$$ 1.19514e7 0.703369
$$781$$ −7.61836e6 −0.446924
$$782$$ −3.44769e6 −0.201610
$$783$$ −4.20332e6 −0.245012
$$784$$ −1.03434e7 −0.601001
$$785$$ 6.51277e6 0.377217
$$786$$ 1.30857e7 0.755513
$$787$$ −1.55411e7 −0.894427 −0.447213 0.894427i $$-0.647584\pi$$
−0.447213 + 0.894427i $$0.647584\pi$$
$$788$$ 2.67200e7 1.53292
$$789$$ −1.41614e7 −0.809868
$$790$$ 1.41329e7 0.805684
$$791$$ −1.77099e7 −1.00641
$$792$$ 3.34174e6 0.189304
$$793$$ 2.71366e7 1.53240
$$794$$ 5.66760e7 3.19042
$$795$$ −2.18328e6 −0.122515
$$796$$ 3.36432e7 1.88198
$$797$$ −2.13571e7 −1.19096 −0.595478 0.803371i $$-0.703037\pi$$
−0.595478 + 0.803371i $$0.703037\pi$$
$$798$$ −6.87600e6 −0.382233
$$799$$ −2.20747e6 −0.122328
$$800$$ 977726. 0.0540122
$$801$$ −7.12720e6 −0.392498
$$802$$ 3.57844e7 1.96453
$$803$$ −6.56213e6 −0.359134
$$804$$ 2.98050e6 0.162611
$$805$$ −6.83782e6 −0.371902
$$806$$ −490365. −0.0265878
$$807$$ 1.40362e7 0.758692
$$808$$ 2.82559e7 1.52258
$$809$$ 9.58699e6 0.515004 0.257502 0.966278i $$-0.417101\pi$$
0.257502 + 0.966278i $$0.417101\pi$$
$$810$$ −1.62688e6 −0.0871249
$$811$$ 2.27762e6 0.121599 0.0607995 0.998150i $$-0.480635\pi$$
0.0607995 + 0.998150i $$0.480635\pi$$
$$812$$ 3.54572e7 1.88718
$$813$$ −1.21747e7 −0.645998
$$814$$ −1.22853e7 −0.649867
$$815$$ 9.11853e6 0.480874
$$816$$ 1.33282e6 0.0700725
$$817$$ −1.45276e7 −0.761447
$$818$$ −4.55706e7 −2.38123
$$819$$ 6.00533e6 0.312844
$$820$$ −1.59290e7 −0.827282
$$821$$ 2.31851e7 1.20047 0.600234 0.799824i $$-0.295074\pi$$
0.600234 + 0.799824i $$0.295074\pi$$
$$822$$ −2.99109e7 −1.54401
$$823$$ 3.30629e7 1.70153 0.850767 0.525542i $$-0.176138\pi$$
0.850767 + 0.525542i $$0.176138\pi$$
$$824$$ 5.24045e7 2.68875
$$825$$ −680625. −0.0348155
$$826$$ −2.24226e7 −1.14350
$$827$$ 2.84571e7 1.44686 0.723431 0.690396i $$-0.242564\pi$$
0.723431 + 0.690396i $$0.242564\pi$$
$$828$$ 1.58726e7 0.804585
$$829$$ −3.34334e7 −1.68964 −0.844821 0.535050i $$-0.820293\pi$$
−0.844821 + 0.535050i $$0.820293\pi$$
$$830$$ −1.23202e7 −0.620759
$$831$$ −2.22485e7 −1.11763
$$832$$ −1.97919e7 −0.991243
$$833$$ 968279. 0.0483491
$$834$$ −2.68277e6 −0.133558
$$835$$ −1.77490e6 −0.0880962
$$836$$ 6.67758e6 0.330448
$$837$$ 45037.8 0.00222210
$$838$$ 1.90815e7 0.938646
$$839$$ −1.79019e7 −0.877999 −0.438999 0.898487i $$-0.644667\pi$$
−0.438999 + 0.898487i $$0.644667\pi$$
$$840$$ 7.10742e6 0.347547
$$841$$ 1.27341e7 0.620837
$$842$$ −4.25440e7 −2.06803
$$843$$ −6.92650e6 −0.335695
$$844$$ 1.10691e7 0.534882
$$845$$ −6.72762e6 −0.324130
$$846$$ 1.50623e7 0.723545
$$847$$ 1.35643e6 0.0649665
$$848$$ −1.22046e7 −0.582820
$$849$$ −2.27598e7 −1.08368
$$850$$ −729891. −0.0346506
$$851$$ −3.02208e7 −1.43048
$$852$$ 3.76124e7 1.77514
$$853$$ −2.79631e7 −1.31587 −0.657934 0.753076i $$-0.728569\pi$$
−0.657934 + 0.753076i $$0.728569\pi$$
$$854$$ 3.11604e7 1.46204
$$855$$ −1.68363e6 −0.0787646
$$856$$ 1.42052e7 0.662615
$$857$$ 9.24668e6 0.430065 0.215032 0.976607i $$-0.431014\pi$$
0.215032 + 0.976607i $$0.431014\pi$$
$$858$$ −8.64366e6 −0.400848
$$859$$ 1.46860e7 0.679081 0.339540 0.940591i $$-0.389728\pi$$
0.339540 + 0.940591i $$0.389728\pi$$
$$860$$ 2.89952e7 1.33684
$$861$$ −8.00396e6 −0.367957
$$862$$ 4.73551e6 0.217070
$$863$$ 1.14915e7 0.525231 0.262615 0.964901i $$-0.415415\pi$$
0.262615 + 0.964901i $$0.415415\pi$$
$$864$$ −1.14042e6 −0.0519733
$$865$$ −7.39275e6 −0.335943
$$866$$ −6.19825e7 −2.80850
$$867$$ 1.26539e7 0.571713
$$868$$ −379917. −0.0171155
$$869$$ −6.89657e6 −0.309802
$$870$$ 1.28674e7 0.576360
$$871$$ −3.99263e6 −0.178326
$$872$$ 1.35514e7 0.603523
$$873$$ −3.63025e6 −0.161213
$$874$$ 2.43454e7 1.07805
$$875$$ −1.44759e6 −0.0639185
$$876$$ 3.23977e7 1.42644
$$877$$ 2.92652e7 1.28485 0.642426 0.766348i $$-0.277928\pi$$
0.642426 + 0.766348i $$0.277928\pi$$
$$878$$ 5.41184e7 2.36924
$$879$$ −1.85888e7 −0.811481
$$880$$ −3.80472e6 −0.165621
$$881$$ −6.92950e6 −0.300789 −0.150395 0.988626i $$-0.548054\pi$$
−0.150395 + 0.988626i $$0.548054\pi$$
$$882$$ −6.60690e6 −0.285974
$$883$$ 4.40887e7 1.90294 0.951470 0.307740i $$-0.0995727\pi$$
0.951470 + 0.307740i $$0.0995727\pi$$
$$884$$ −6.25418e6 −0.269178
$$885$$ −5.49032e6 −0.235635
$$886$$ −3.72719e7 −1.59514
$$887$$ 4.26047e7 1.81823 0.909115 0.416545i $$-0.136759\pi$$
0.909115 + 0.416545i $$0.136759\pi$$
$$888$$ 3.14123e7 1.33680
$$889$$ −1.97224e7 −0.836961
$$890$$ 2.18182e7 0.923302
$$891$$ 793881. 0.0335013
$$892$$ 3.69087e7 1.55316
$$893$$ 1.55877e7 0.654115
$$894$$ −2.14467e7 −0.897464
$$895$$ 1.41923e7 0.592236
$$896$$ −2.73645e7 −1.13872
$$897$$ −2.12627e7 −0.882342
$$898$$ −7.11462e7 −2.94416
$$899$$ −356217. −0.0146999
$$900$$ 3.36029e6 0.138284
$$901$$ 1.14251e6 0.0468864
$$902$$ 1.15204e7 0.471465
$$903$$ 1.45694e7 0.594598
$$904$$ −6.51767e7 −2.65260
$$905$$ 9.02796e6 0.366411
$$906$$ −3.39192e6 −0.137286
$$907$$ 2.03750e7 0.822392 0.411196 0.911547i $$-0.365111\pi$$
0.411196 + 0.911547i $$0.365111\pi$$
$$908$$ 3.37091e7 1.35685
$$909$$ 6.71260e6 0.269452
$$910$$ −1.83839e7 −0.735925
$$911$$ 1.25015e7 0.499077 0.249538 0.968365i $$-0.419721\pi$$
0.249538 + 0.968365i $$0.419721\pi$$
$$912$$ −9.41156e6 −0.374692
$$913$$ 6.01200e6 0.238694
$$914$$ −3.18621e7 −1.26156
$$915$$ 7.62981e6 0.301273
$$916$$ −4.16307e7 −1.63936
$$917$$ −1.35812e7 −0.533353
$$918$$ 851345. 0.0333425
$$919$$ 2.12364e7 0.829455 0.414728 0.909946i $$-0.363877\pi$$
0.414728 + 0.909946i $$0.363877\pi$$
$$920$$ −2.51648e7 −0.980221
$$921$$ 1.95377e7 0.758969
$$922$$ −5.13586e7 −1.98969
$$923$$ −5.03850e7 −1.94669
$$924$$ −6.69680e6 −0.258040
$$925$$ −6.39787e6 −0.245856
$$926$$ 2.92736e7 1.12189
$$927$$ 1.24495e7 0.475829
$$928$$ 9.01990e6 0.343821
$$929$$ 2.38747e7 0.907608 0.453804 0.891102i $$-0.350067\pi$$
0.453804 + 0.891102i $$0.350067\pi$$
$$930$$ −137872. −0.00522721
$$931$$ −6.83737e6 −0.258532
$$932$$ 6.34470e7 2.39261
$$933$$ 1.78719e6 0.0672149
$$934$$ 7.20685e7 2.70320
$$935$$ 356171. 0.0133238
$$936$$ 2.21010e7 0.824561
$$937$$ −1.33814e7 −0.497914 −0.248957 0.968515i $$-0.580088\pi$$
−0.248957 + 0.968515i $$0.580088\pi$$
$$938$$ −4.58465e6 −0.170137
$$939$$ 4.35386e6 0.161143
$$940$$ −3.11110e7 −1.14840
$$941$$ 5.91644e6 0.217814 0.108907 0.994052i $$-0.465265\pi$$
0.108907 + 0.994052i $$0.465265\pi$$
$$942$$ 2.32548e7 0.853858
$$943$$ 2.83391e7 1.03778
$$944$$ −3.06911e7 −1.12094
$$945$$ 1.68847e6 0.0615056
$$946$$ −2.09703e7 −0.761861
$$947$$ −4.78035e7 −1.73215 −0.866074 0.499916i $$-0.833364\pi$$
−0.866074 + 0.499916i $$0.833364\pi$$
$$948$$ 3.40489e7 1.23050
$$949$$ −4.33995e7 −1.56430
$$950$$ 5.15402e6 0.185284
$$951$$ 1.51289e7 0.542445
$$952$$ −3.71931e6 −0.133006
$$953$$ −3.75680e7 −1.33994 −0.669971 0.742387i $$-0.733694\pi$$
−0.669971 + 0.742387i $$0.733694\pi$$
$$954$$ −7.79572e6 −0.277323
$$955$$ −8.37177e6 −0.297036
$$956$$ −3.38024e7 −1.19620
$$957$$ −6.27903e6 −0.221622
$$958$$ −4.06245e7 −1.43013
$$959$$ 3.10433e7 1.08999
$$960$$ −5.56475e6 −0.194880
$$961$$ −2.86253e7 −0.999867
$$962$$ −8.12503e7 −2.83066
$$963$$ 3.37465e6 0.117263
$$964$$ −4.42148e7 −1.53241
$$965$$ 7.16613e6 0.247723
$$966$$ −2.44155e7 −0.841826
$$967$$ −2.07684e7 −0.714228 −0.357114 0.934061i $$-0.616239\pi$$
−0.357114 + 0.934061i $$0.616239\pi$$
$$968$$ 4.99199e6 0.171232
$$969$$ 881042. 0.0301431
$$970$$ 1.11131e7 0.379234
$$971$$ 1.39451e7 0.474650 0.237325 0.971430i $$-0.423729\pi$$
0.237325 + 0.971430i $$0.423729\pi$$
$$972$$ −3.91945e6 −0.133064
$$973$$ 2.78434e6 0.0942846
$$974$$ 2.16696e6 0.0731902
$$975$$ −4.50140e6 −0.151648
$$976$$ 4.26510e7 1.43319
$$977$$ 2.07797e7 0.696471 0.348236 0.937407i $$-0.386781\pi$$
0.348236 + 0.937407i $$0.386781\pi$$
$$978$$ 3.25591e7 1.08849
$$979$$ −1.06468e7 −0.355028
$$980$$ 1.36465e7 0.453894
$$981$$ 3.21934e6 0.106806
$$982$$ −3.46996e7 −1.14828
$$983$$ 1.16598e7 0.384864 0.192432 0.981310i $$-0.438363\pi$$
0.192432 + 0.981310i $$0.438363\pi$$
$$984$$ −2.94565e7 −0.969824
$$985$$ −1.00638e7 −0.330501
$$986$$ −6.73353e6 −0.220572
$$987$$ −1.56326e7 −0.510785
$$988$$ 4.41630e7 1.43935
$$989$$ −5.15851e7 −1.67700
$$990$$ −2.43027e6 −0.0788075
$$991$$ −2.35287e7 −0.761050 −0.380525 0.924771i $$-0.624257\pi$$
−0.380525 + 0.924771i $$0.624257\pi$$
$$992$$ −96646.7 −0.00311823
$$993$$ 1.06993e7 0.344336
$$994$$ −5.78559e7 −1.85730
$$995$$ −1.26714e7 −0.405759
$$996$$ −2.96817e7 −0.948069
$$997$$ −4.85989e7 −1.54842 −0.774210 0.632929i $$-0.781853\pi$$
−0.774210 + 0.632929i $$0.781853\pi$$
$$998$$ −3.59758e7 −1.14336
$$999$$ 7.46247e6 0.236575
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 165.6.a.e.1.3 3
3.2 odd 2 495.6.a.a.1.1 3
5.4 even 2 825.6.a.f.1.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.a.e.1.3 3 1.1 even 1 trivial
495.6.a.a.1.1 3 3.2 odd 2
825.6.a.f.1.1 3 5.4 even 2