# Properties

 Label 147.6.e.n.67.2 Level $147$ Weight $6$ Character 147.67 Analytic conductor $23.576$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 147.e (of order $$3$$, degree $$2$$, not minimal)

## 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: no Analytic conductor: $$23.5764215125$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{193})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} + 49x^{2} + 48x + 2304$$ x^4 - x^3 + 49*x^2 + 48*x + 2304 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.2 Root $$3.72311 + 6.44862i$$ of defining polynomial Character $$\chi$$ $$=$$ 147.67 Dual form 147.6.e.n.79.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(4.22311 + 7.31464i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-19.6693 + 34.0683i) q^{4} +(-18.0000 - 31.1769i) q^{5} +76.0160 q^{6} -61.9840 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$$ $$q+(4.22311 + 7.31464i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-19.6693 + 34.0683i) q^{4} +(-18.0000 - 31.1769i) q^{5} +76.0160 q^{6} -61.9840 q^{8} +(-40.5000 - 70.1481i) q^{9} +(152.032 - 263.327i) q^{10} +(-147.785 + 255.971i) q^{11} +(177.024 + 306.615i) q^{12} +1148.13 q^{13} -324.000 q^{15} +(367.653 + 636.794i) q^{16} +(516.192 - 894.071i) q^{17} +(342.072 - 592.486i) q^{18} +(1054.26 + 1826.02i) q^{19} +1416.19 q^{20} -2496.45 q^{22} +(320.494 + 555.112i) q^{23} +(-278.928 + 483.117i) q^{24} +(914.500 - 1583.96i) q^{25} +(4848.67 + 8398.15i) q^{26} -729.000 q^{27} +7631.58 q^{29} +(-1368.29 - 2369.94i) q^{30} +(-483.488 + 837.426i) q^{31} +(-4097.03 + 7096.26i) q^{32} +(1330.06 + 2303.74i) q^{33} +8719.74 q^{34} +3186.43 q^{36} +(886.605 + 1535.65i) q^{37} +(-8904.48 + 15423.0i) q^{38} +(5166.58 - 8948.77i) q^{39} +(1115.71 + 1932.47i) q^{40} +11976.4 q^{41} -19802.9 q^{43} +(-5813.66 - 10069.6i) q^{44} +(-1458.00 + 2525.33i) q^{45} +(-2706.97 + 4688.60i) q^{46} +(-13983.1 - 24219.4i) q^{47} +6617.76 q^{48} +15448.1 q^{50} +(-4645.73 - 8046.64i) q^{51} +(-22582.9 + 39114.8i) q^{52} +(3557.16 - 6161.19i) q^{53} +(-3078.65 - 5332.37i) q^{54} +10640.5 q^{55} +18976.6 q^{57} +(32229.0 + 55822.3i) q^{58} +(-10434.8 + 18073.5i) q^{59} +(6372.86 - 11038.1i) q^{60} +(-11934.2 - 20670.6i) q^{61} -8167.30 q^{62} -45679.0 q^{64} +(-20666.3 - 35795.1i) q^{65} +(-11234.0 + 19457.9i) q^{66} +(-17335.8 + 30026.4i) q^{67} +(20306.3 + 35171.5i) q^{68} +5768.90 q^{69} -28413.2 q^{71} +(2510.35 + 4348.06i) q^{72} +(-7646.34 + 13243.8i) q^{73} +(-7488.46 + 12970.4i) q^{74} +(-8230.50 - 14255.6i) q^{75} -82946.0 q^{76} +87276.1 q^{78} +(36529.8 + 63271.4i) q^{79} +(13235.5 - 22924.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(50577.6 + 87603.0i) q^{82} +30340.9 q^{83} -37165.8 q^{85} +(-83630.0 - 144851. i) q^{86} +(34342.1 - 59482.3i) q^{87} +(9160.30 - 15866.1i) q^{88} +(-18044.7 - 31254.4i) q^{89} -24629.2 q^{90} -25215.6 q^{92} +(4351.39 + 7536.83i) q^{93} +(118104. - 204562. i) q^{94} +(37953.2 - 65736.9i) q^{95} +(36873.2 + 63866.3i) q^{96} +153963. q^{97} +23941.2 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 3 q^{2} + 18 q^{3} - 37 q^{4} - 72 q^{5} + 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10})$$ 4 * q + 3 * q^2 + 18 * q^3 - 37 * q^4 - 72 * q^5 + 54 * q^6 - 498 * q^8 - 162 * q^9 $$4 q + 3 q^{2} + 18 q^{3} - 37 q^{4} - 72 q^{5} + 54 q^{6} - 498 q^{8} - 162 q^{9} + 108 q^{10} - 480 q^{11} + 333 q^{12} + 2592 q^{13} - 1296 q^{15} + 1679 q^{16} - 936 q^{17} + 243 q^{18} + 216 q^{19} + 2664 q^{20} - 2984 q^{22} + 504 q^{23} - 2241 q^{24} + 3658 q^{25} + 8892 q^{26} - 2916 q^{27} + 12744 q^{29} - 972 q^{30} - 9936 q^{31} - 9039 q^{32} + 4320 q^{33} + 38880 q^{34} + 5994 q^{36} - 11124 q^{37} - 28116 q^{38} + 11664 q^{39} + 8964 q^{40} + 41904 q^{41} - 12528 q^{43} - 11196 q^{44} - 5832 q^{45} - 6160 q^{46} - 7920 q^{47} + 30222 q^{48} + 10974 q^{50} + 8424 q^{51} - 44820 q^{52} - 2220 q^{53} - 2187 q^{54} + 34560 q^{55} + 3888 q^{57} + 71318 q^{58} - 29736 q^{59} + 11988 q^{60} + 17280 q^{61} + 81360 q^{62} - 21758 q^{64} - 46656 q^{65} - 13428 q^{66} + 20680 q^{67} + 45216 q^{68} + 9072 q^{69} - 184560 q^{71} + 20169 q^{72} - 56592 q^{73} - 85218 q^{74} - 32922 q^{75} - 174744 q^{76} + 160056 q^{78} + 56096 q^{79} + 60444 q^{80} - 13122 q^{81} + 52272 q^{82} - 142704 q^{83} + 67392 q^{85} - 240996 q^{86} + 57348 q^{87} + 52812 q^{88} - 123192 q^{89} - 17496 q^{90} - 51072 q^{92} + 89424 q^{93} + 345384 q^{94} + 7776 q^{95} + 81351 q^{96} + 71712 q^{97} + 77760 q^{99}+O(q^{100})$$ 4 * q + 3 * q^2 + 18 * q^3 - 37 * q^4 - 72 * q^5 + 54 * q^6 - 498 * q^8 - 162 * q^9 + 108 * q^10 - 480 * q^11 + 333 * q^12 + 2592 * q^13 - 1296 * q^15 + 1679 * q^16 - 936 * q^17 + 243 * q^18 + 216 * q^19 + 2664 * q^20 - 2984 * q^22 + 504 * q^23 - 2241 * q^24 + 3658 * q^25 + 8892 * q^26 - 2916 * q^27 + 12744 * q^29 - 972 * q^30 - 9936 * q^31 - 9039 * q^32 + 4320 * q^33 + 38880 * q^34 + 5994 * q^36 - 11124 * q^37 - 28116 * q^38 + 11664 * q^39 + 8964 * q^40 + 41904 * q^41 - 12528 * q^43 - 11196 * q^44 - 5832 * q^45 - 6160 * q^46 - 7920 * q^47 + 30222 * q^48 + 10974 * q^50 + 8424 * q^51 - 44820 * q^52 - 2220 * q^53 - 2187 * q^54 + 34560 * q^55 + 3888 * q^57 + 71318 * q^58 - 29736 * q^59 + 11988 * q^60 + 17280 * q^61 + 81360 * q^62 - 21758 * q^64 - 46656 * q^65 - 13428 * q^66 + 20680 * q^67 + 45216 * q^68 + 9072 * q^69 - 184560 * q^71 + 20169 * q^72 - 56592 * q^73 - 85218 * q^74 - 32922 * q^75 - 174744 * q^76 + 160056 * q^78 + 56096 * q^79 + 60444 * q^80 - 13122 * q^81 + 52272 * q^82 - 142704 * q^83 + 67392 * q^85 - 240996 * q^86 + 57348 * q^87 + 52812 * q^88 - 123192 * q^89 - 17496 * q^90 - 51072 * q^92 + 89424 * q^93 + 345384 * q^94 + 7776 * q^95 + 81351 * q^96 + 71712 * q^97 + 77760 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$$.

 $$n$$ $$50$$ $$52$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.22311 + 7.31464i 0.746548 + 1.29306i 0.949468 + 0.313863i $$0.101623\pi$$
−0.202921 + 0.979195i $$0.565043\pi$$
$$3$$ 4.50000 7.79423i 0.288675 0.500000i
$$4$$ −19.6693 + 34.0683i −0.614667 + 1.06463i
$$5$$ −18.0000 31.1769i −0.321994 0.557710i 0.658906 0.752226i $$-0.271020\pi$$
−0.980899 + 0.194516i $$0.937686\pi$$
$$6$$ 76.0160 0.862039
$$7$$ 0 0
$$8$$ −61.9840 −0.342416
$$9$$ −40.5000 70.1481i −0.166667 0.288675i
$$10$$ 152.032 263.327i 0.480767 0.832714i
$$11$$ −147.785 + 255.971i −0.368255 + 0.637836i −0.989293 0.145945i $$-0.953378\pi$$
0.621038 + 0.783780i $$0.286711\pi$$
$$12$$ 177.024 + 306.615i 0.354878 + 0.614667i
$$13$$ 1148.13 1.88422 0.942111 0.335302i $$-0.108838\pi$$
0.942111 + 0.335302i $$0.108838\pi$$
$$14$$ 0 0
$$15$$ −324.000 −0.371806
$$16$$ 367.653 + 636.794i 0.359036 + 0.621869i
$$17$$ 516.192 894.071i 0.433200 0.750325i −0.563946 0.825811i $$-0.690718\pi$$
0.997147 + 0.0754862i $$0.0240509\pi$$
$$18$$ 342.072 592.486i 0.248849 0.431019i
$$19$$ 1054.26 + 1826.02i 0.669980 + 1.16044i 0.977909 + 0.209031i $$0.0670308\pi$$
−0.307929 + 0.951409i $$0.599636\pi$$
$$20$$ 1416.19 0.791675
$$21$$ 0 0
$$22$$ −2496.45 −1.09968
$$23$$ 320.494 + 555.112i 0.126328 + 0.218807i 0.922251 0.386591i $$-0.126347\pi$$
−0.795923 + 0.605398i $$0.793014\pi$$
$$24$$ −278.928 + 483.117i −0.0988471 + 0.171208i
$$25$$ 914.500 1583.96i 0.292640 0.506867i
$$26$$ 4848.67 + 8398.15i 1.40666 + 2.43641i
$$27$$ −729.000 −0.192450
$$28$$ 0 0
$$29$$ 7631.58 1.68508 0.842538 0.538637i $$-0.181060\pi$$
0.842538 + 0.538637i $$0.181060\pi$$
$$30$$ −1368.29 2369.94i −0.277571 0.480767i
$$31$$ −483.488 + 837.426i −0.0903611 + 0.156510i −0.907663 0.419700i $$-0.862135\pi$$
0.817302 + 0.576210i $$0.195469\pi$$
$$32$$ −4097.03 + 7096.26i −0.707284 + 1.22505i
$$33$$ 1330.06 + 2303.74i 0.212612 + 0.368255i
$$34$$ 8719.74 1.29362
$$35$$ 0 0
$$36$$ 3186.43 0.409778
$$37$$ 886.605 + 1535.65i 0.106470 + 0.184411i 0.914338 0.404953i $$-0.132712\pi$$
−0.807868 + 0.589363i $$0.799379\pi$$
$$38$$ −8904.48 + 15423.0i −1.00034 + 1.73265i
$$39$$ 5166.58 8948.77i 0.543928 0.942111i
$$40$$ 1115.71 + 1932.47i 0.110256 + 0.190969i
$$41$$ 11976.4 1.11267 0.556335 0.830958i $$-0.312207\pi$$
0.556335 + 0.830958i $$0.312207\pi$$
$$42$$ 0 0
$$43$$ −19802.9 −1.63327 −0.816636 0.577153i $$-0.804163\pi$$
−0.816636 + 0.577153i $$0.804163\pi$$
$$44$$ −5813.66 10069.6i −0.452708 0.784113i
$$45$$ −1458.00 + 2525.33i −0.107331 + 0.185903i
$$46$$ −2706.97 + 4688.60i −0.188620 + 0.326700i
$$47$$ −13983.1 24219.4i −0.923332 1.59926i −0.794222 0.607628i $$-0.792121\pi$$
−0.129110 0.991630i $$-0.541212\pi$$
$$48$$ 6617.76 0.414580
$$49$$ 0 0
$$50$$ 15448.1 0.873879
$$51$$ −4645.73 8046.64i −0.250108 0.433200i
$$52$$ −22582.9 + 39114.8i −1.15817 + 2.00601i
$$53$$ 3557.16 6161.19i 0.173946 0.301283i −0.765850 0.643019i $$-0.777682\pi$$
0.939796 + 0.341736i $$0.111015\pi$$
$$54$$ −3078.65 5332.37i −0.143673 0.248849i
$$55$$ 10640.5 0.474303
$$56$$ 0 0
$$57$$ 18976.6 0.773627
$$58$$ 32229.0 + 55822.3i 1.25799 + 2.17890i
$$59$$ −10434.8 + 18073.5i −0.390259 + 0.675948i −0.992484 0.122379i $$-0.960948\pi$$
0.602225 + 0.798327i $$0.294281\pi$$
$$60$$ 6372.86 11038.1i 0.228537 0.395838i
$$61$$ −11934.2 20670.6i −0.410646 0.711259i 0.584315 0.811527i $$-0.301363\pi$$
−0.994960 + 0.100268i $$0.968030\pi$$
$$62$$ −8167.30 −0.269835
$$63$$ 0 0
$$64$$ −45679.0 −1.39401
$$65$$ −20666.3 35795.1i −0.606708 1.05085i
$$66$$ −11234.0 + 19457.9i −0.317450 + 0.549839i
$$67$$ −17335.8 + 30026.4i −0.471798 + 0.817178i −0.999479 0.0322646i $$-0.989728\pi$$
0.527682 + 0.849442i $$0.323061\pi$$
$$68$$ 20306.3 + 35171.5i 0.532548 + 0.922400i
$$69$$ 5768.90 0.145871
$$70$$ 0 0
$$71$$ −28413.2 −0.668921 −0.334461 0.942410i $$-0.608554\pi$$
−0.334461 + 0.942410i $$0.608554\pi$$
$$72$$ 2510.35 + 4348.06i 0.0570694 + 0.0988471i
$$73$$ −7646.34 + 13243.8i −0.167937 + 0.290875i −0.937694 0.347461i $$-0.887044\pi$$
0.769757 + 0.638337i $$0.220377\pi$$
$$74$$ −7488.46 + 12970.4i −0.158969 + 0.275343i
$$75$$ −8230.50 14255.6i −0.168956 0.292640i
$$76$$ −82946.0 −1.64726
$$77$$ 0 0
$$78$$ 87276.1 1.62427
$$79$$ 36529.8 + 63271.4i 0.658535 + 1.14062i 0.980995 + 0.194033i $$0.0621570\pi$$
−0.322460 + 0.946583i $$0.604510\pi$$
$$80$$ 13235.5 22924.6i 0.231215 0.400476i
$$81$$ −3280.50 + 5681.99i −0.0555556 + 0.0962250i
$$82$$ 50577.6 + 87603.0i 0.830661 + 1.43875i
$$83$$ 30340.9 0.483429 0.241715 0.970347i $$-0.422290\pi$$
0.241715 + 0.970347i $$0.422290\pi$$
$$84$$ 0 0
$$85$$ −37165.8 −0.557951
$$86$$ −83630.0 144851.i −1.21931 2.11192i
$$87$$ 34342.1 59482.3i 0.486440 0.842538i
$$88$$ 9160.30 15866.1i 0.126096 0.218406i
$$89$$ −18044.7 31254.4i −0.241477 0.418250i 0.719658 0.694328i $$-0.244298\pi$$
−0.961135 + 0.276078i $$0.910965\pi$$
$$90$$ −24629.2 −0.320512
$$91$$ 0 0
$$92$$ −25215.6 −0.310599
$$93$$ 4351.39 + 7536.83i 0.0521700 + 0.0903611i
$$94$$ 118104. 204562.i 1.37862 2.38784i
$$95$$ 37953.2 65736.9i 0.431459 0.747309i
$$96$$ 36873.2 + 63866.3i 0.408351 + 0.707284i
$$97$$ 153963. 1.66145 0.830724 0.556685i $$-0.187927\pi$$
0.830724 + 0.556685i $$0.187927\pi$$
$$98$$ 0 0
$$99$$ 23941.2 0.245503
$$100$$ 35975.2 + 62310.9i 0.359752 + 0.623109i
$$101$$ 69904.4 121078.i 0.681869 1.18103i −0.292541 0.956253i $$-0.594501\pi$$
0.974410 0.224779i $$-0.0721659\pi$$
$$102$$ 39238.8 67963.7i 0.373436 0.646810i
$$103$$ −57962.7 100394.i −0.538339 0.932430i −0.998994 0.0448508i $$-0.985719\pi$$
0.460655 0.887579i $$-0.347615\pi$$
$$104$$ −71165.6 −0.645188
$$105$$ 0 0
$$106$$ 60089.2 0.519436
$$107$$ −41530.9 71933.6i −0.350681 0.607397i 0.635688 0.771946i $$-0.280716\pi$$
−0.986369 + 0.164549i $$0.947383\pi$$
$$108$$ 14338.9 24835.8i 0.118293 0.204889i
$$109$$ −22678.1 + 39279.7i −0.182827 + 0.316666i −0.942842 0.333240i $$-0.891858\pi$$
0.760015 + 0.649906i $$0.225192\pi$$
$$110$$ 44936.1 + 77831.5i 0.354090 + 0.613301i
$$111$$ 15958.9 0.122941
$$112$$ 0 0
$$113$$ −355.533 −0.00261929 −0.00130965 0.999999i $$-0.500417\pi$$
−0.00130965 + 0.999999i $$0.500417\pi$$
$$114$$ 80140.3 + 138807.i 0.577549 + 1.00034i
$$115$$ 11537.8 19984.0i 0.0813538 0.140909i
$$116$$ −150108. + 259995.i −1.03576 + 1.79399i
$$117$$ −46499.2 80538.9i −0.314037 0.543928i
$$118$$ −176269. −1.16539
$$119$$ 0 0
$$120$$ 20082.8 0.127313
$$121$$ 36844.8 + 63817.0i 0.228777 + 0.396253i
$$122$$ 100799. 174588.i 0.613133 1.06198i
$$123$$ 53893.7 93346.7i 0.321200 0.556335i
$$124$$ −19019.8 32943.2i −0.111084 0.192403i
$$125$$ −178344. −1.02090
$$126$$ 0 0
$$127$$ 168967. 0.929593 0.464797 0.885417i $$-0.346127\pi$$
0.464797 + 0.885417i $$0.346127\pi$$
$$128$$ −61802.5 107045.i −0.333412 0.577486i
$$129$$ −89113.2 + 154349.i −0.471485 + 0.816636i
$$130$$ 174552. 302333.i 0.905872 1.56902i
$$131$$ −86984.6 150662.i −0.442858 0.767052i 0.555043 0.831822i $$-0.312702\pi$$
−0.997900 + 0.0647701i $$0.979369\pi$$
$$132$$ −104646. −0.522742
$$133$$ 0 0
$$134$$ −292843. −1.40888
$$135$$ 13122.0 + 22728.0i 0.0619677 + 0.107331i
$$136$$ −31995.6 + 55418.1i −0.148335 + 0.256924i
$$137$$ −183862. + 318458.i −0.836931 + 1.44961i 0.0555168 + 0.998458i $$0.482319\pi$$
−0.892448 + 0.451150i $$0.851014\pi$$
$$138$$ 24362.7 + 42197.4i 0.108900 + 0.188620i
$$139$$ −217967. −0.956870 −0.478435 0.878123i $$-0.658796\pi$$
−0.478435 + 0.878123i $$0.658796\pi$$
$$140$$ 0 0
$$141$$ −251695. −1.06617
$$142$$ −119992. 207833.i −0.499381 0.864954i
$$143$$ −169676. + 293887.i −0.693873 + 1.20182i
$$144$$ 29779.9 51580.3i 0.119679 0.207290i
$$145$$ −137368. 237929.i −0.542584 0.939783i
$$146$$ −129165. −0.501492
$$147$$ 0 0
$$148$$ −69755.7 −0.261773
$$149$$ 32453.0 + 56210.3i 0.119754 + 0.207420i 0.919670 0.392692i $$-0.128456\pi$$
−0.799916 + 0.600112i $$0.795123\pi$$
$$150$$ 69516.6 120406.i 0.252267 0.436939i
$$151$$ 111889. 193797.i 0.399341 0.691678i −0.594304 0.804240i $$-0.702572\pi$$
0.993645 + 0.112562i $$0.0359057\pi$$
$$152$$ −65347.0 113184.i −0.229412 0.397354i
$$153$$ −83623.1 −0.288800
$$154$$ 0 0
$$155$$ 34811.1 0.116383
$$156$$ 203246. + 352033.i 0.668669 + 1.15817i
$$157$$ −229986. + 398348.i −0.744652 + 1.28977i 0.205706 + 0.978614i $$0.434051\pi$$
−0.950357 + 0.311161i $$0.899282\pi$$
$$158$$ −308538. + 534404.i −0.983256 + 1.70305i
$$159$$ −32014.5 55450.7i −0.100428 0.173946i
$$160$$ 294986. 0.910964
$$161$$ 0 0
$$162$$ −55415.7 −0.165899
$$163$$ −45534.3 78867.7i −0.134236 0.232504i 0.791069 0.611727i $$-0.209525\pi$$
−0.925305 + 0.379223i $$0.876191\pi$$
$$164$$ −235567. + 408015.i −0.683921 + 1.18459i
$$165$$ 47882.3 82934.6i 0.136919 0.237151i
$$166$$ 128133. + 221933.i 0.360903 + 0.625103i
$$167$$ 314772. 0.873384 0.436692 0.899611i $$-0.356150\pi$$
0.436692 + 0.899611i $$0.356150\pi$$
$$168$$ 0 0
$$169$$ 946905. 2.55029
$$170$$ −156955. 271855.i −0.416537 0.721464i
$$171$$ 85394.7 147908.i 0.223327 0.386813i
$$172$$ 389510. 674652.i 1.00392 1.73884i
$$173$$ −181071. 313625.i −0.459975 0.796701i 0.538984 0.842316i $$-0.318808\pi$$
−0.998959 + 0.0456154i $$0.985475\pi$$
$$174$$ 580122. 1.45260
$$175$$ 0 0
$$176$$ −217334. −0.528867
$$177$$ 93912.9 + 162662.i 0.225316 + 0.390259i
$$178$$ 152410. 263982.i 0.360548 0.624487i
$$179$$ 86948.1 150599.i 0.202828 0.351308i −0.746611 0.665261i $$-0.768320\pi$$
0.949438 + 0.313953i $$0.101653\pi$$
$$180$$ −57355.8 99343.1i −0.131946 0.228537i
$$181$$ −134973. −0.306233 −0.153116 0.988208i $$-0.548931\pi$$
−0.153116 + 0.988208i $$0.548931\pi$$
$$182$$ 0 0
$$183$$ −214815. −0.474173
$$184$$ −19865.5 34408.1i −0.0432569 0.0749231i
$$185$$ 31917.8 55283.2i 0.0685652 0.118758i
$$186$$ −36752.8 + 63657.8i −0.0778948 + 0.134918i
$$187$$ 152571. + 264260.i 0.319056 + 0.552622i
$$188$$ 1.10015e6 2.27017
$$189$$ 0 0
$$190$$ 641123. 1.28842
$$191$$ −90706.7 157109.i −0.179910 0.311614i 0.761939 0.647648i $$-0.224247\pi$$
−0.941850 + 0.336035i $$0.890914\pi$$
$$192$$ −205555. + 356032.i −0.402416 + 0.697006i
$$193$$ −482999. + 836579.i −0.933369 + 1.61664i −0.155851 + 0.987781i $$0.549812\pi$$
−0.777517 + 0.628861i $$0.783521\pi$$
$$194$$ 650202. + 1.12618e6i 1.24035 + 2.14835i
$$195$$ −371993. −0.700566
$$196$$ 0 0
$$197$$ −699058. −1.28336 −0.641679 0.766974i $$-0.721762\pi$$
−0.641679 + 0.766974i $$0.721762\pi$$
$$198$$ 101106. + 175121.i 0.183280 + 0.317450i
$$199$$ −208095. + 360432.i −0.372503 + 0.645194i −0.989950 0.141419i $$-0.954834\pi$$
0.617447 + 0.786612i $$0.288167\pi$$
$$200$$ −56684.4 + 98180.2i −0.100205 + 0.173560i
$$201$$ 156022. + 270238.i 0.272393 + 0.471798i
$$202$$ 1.18086e6 2.03619
$$203$$ 0 0
$$204$$ 365513. 0.614933
$$205$$ −215575. 373387.i −0.358273 0.620546i
$$206$$ 489566. 847953.i 0.803791 1.39221i
$$207$$ 25960.0 44964.1i 0.0421094 0.0729357i
$$208$$ 422113. + 731121.i 0.676504 + 1.17174i
$$209$$ −623212. −0.986894
$$210$$ 0 0
$$211$$ −407152. −0.629580 −0.314790 0.949161i $$-0.601934\pi$$
−0.314790 + 0.949161i $$0.601934\pi$$
$$212$$ 139934. + 242373.i 0.213837 + 0.370377i
$$213$$ −127860. + 221459.i −0.193101 + 0.334461i
$$214$$ 350779. 607567.i 0.523600 0.906901i
$$215$$ 356453. + 617394.i 0.525903 + 0.910891i
$$216$$ 45186.3 0.0658981
$$217$$ 0 0
$$218$$ −383089. −0.545957
$$219$$ 68817.0 + 119195.i 0.0969584 + 0.167937i
$$220$$ −209292. + 362504.i −0.291538 + 0.504959i
$$221$$ 592654. 1.02651e6i 0.816246 1.41378i
$$222$$ 67396.2 + 116734.i 0.0917810 + 0.158969i
$$223$$ −882022. −1.18773 −0.593865 0.804565i $$-0.702398\pi$$
−0.593865 + 0.804565i $$0.702398\pi$$
$$224$$ 0 0
$$225$$ −148149. −0.195093
$$226$$ −1501.45 2600.60i −0.00195542 0.00338690i
$$227$$ −563251. + 975579.i −0.725499 + 1.25660i 0.233269 + 0.972412i $$0.425058\pi$$
−0.958768 + 0.284189i $$0.908276\pi$$
$$228$$ −373257. + 646500.i −0.475523 + 0.823629i
$$229$$ 155042. + 268541.i 0.195371 + 0.338393i 0.947022 0.321168i $$-0.104075\pi$$
−0.751651 + 0.659561i $$0.770742\pi$$
$$230$$ 194902. 0.242938
$$231$$ 0 0
$$232$$ −473036. −0.576998
$$233$$ −568268. 984268.i −0.685746 1.18775i −0.973202 0.229953i $$-0.926143\pi$$
0.287456 0.957794i $$-0.407190\pi$$
$$234$$ 392742. 680250.i 0.468887 0.812136i
$$235$$ −503391. + 871898.i −0.594614 + 1.02990i
$$236$$ −410490. 710989.i −0.479758 0.830966i
$$237$$ 657536. 0.760411
$$238$$ 0 0
$$239$$ 87506.8 0.0990940 0.0495470 0.998772i $$-0.484222\pi$$
0.0495470 + 0.998772i $$0.484222\pi$$
$$240$$ −119120. 206321.i −0.133492 0.231215i
$$241$$ 268884. 465721.i 0.298210 0.516515i −0.677516 0.735508i $$-0.736944\pi$$
0.975727 + 0.218992i $$0.0702770\pi$$
$$242$$ −311199. + 539012.i −0.341586 + 0.591644i
$$243$$ 29524.5 + 51137.9i 0.0320750 + 0.0555556i
$$244$$ 938948. 1.00964
$$245$$ 0 0
$$246$$ 910397. 0.959164
$$247$$ 1.21042e6 + 2.09651e6i 1.26239 + 2.18653i
$$248$$ 29968.5 51907.0i 0.0309411 0.0535916i
$$249$$ 136534. 236484.i 0.139554 0.241715i
$$250$$ −753167. 1.30452e6i −0.762151 1.32008i
$$251$$ −1.35353e6 −1.35607 −0.678036 0.735028i $$-0.737169\pi$$
−0.678036 + 0.735028i $$0.737169\pi$$
$$252$$ 0 0
$$253$$ −189457. −0.186084
$$254$$ 713567. + 1.23593e6i 0.693986 + 1.20202i
$$255$$ −167246. + 289679.i −0.161067 + 0.278976i
$$256$$ −208866. + 361766.i −0.199190 + 0.345007i
$$257$$ −488450. 846020.i −0.461304 0.799002i 0.537722 0.843122i $$-0.319285\pi$$
−0.999026 + 0.0441199i $$0.985952\pi$$
$$258$$ −1.50534e6 −1.40794
$$259$$ 0 0
$$260$$ 1.62597e6 1.49169
$$261$$ −309079. 535341.i −0.280846 0.486440i
$$262$$ 734691. 1.27252e6i 0.661229 1.14528i
$$263$$ 621874. 1.07712e6i 0.554387 0.960227i −0.443564 0.896243i $$-0.646286\pi$$
0.997951 0.0639842i $$-0.0203807\pi$$
$$264$$ −82442.7 142795.i −0.0728018 0.126096i
$$265$$ −256116. −0.224038
$$266$$ 0 0
$$267$$ −324805. −0.278833
$$268$$ −681966. 1.18120e6i −0.579997 1.00458i
$$269$$ −542042. + 938844.i −0.456722 + 0.791066i −0.998785 0.0492716i $$-0.984310\pi$$
0.542063 + 0.840338i $$0.317643\pi$$
$$270$$ −110831. + 191965.i −0.0925237 + 0.160256i
$$271$$ −1.08314e6 1.87605e6i −0.895900 1.55174i −0.832687 0.553744i $$-0.813199\pi$$
−0.0632128 0.998000i $$-0.520135\pi$$
$$272$$ 759119. 0.622139
$$273$$ 0 0
$$274$$ −3.10587e6 −2.49924
$$275$$ 270299. + 468171.i 0.215532 + 0.373313i
$$276$$ −113470. + 196536.i −0.0896622 + 0.155300i
$$277$$ −126929. + 219848.i −0.0993946 + 0.172157i −0.911434 0.411446i $$-0.865024\pi$$
0.812040 + 0.583602i $$0.198357\pi$$
$$278$$ −920497. 1.59435e6i −0.714349 1.23729i
$$279$$ 78325.1 0.0602407
$$280$$ 0 0
$$281$$ 1.14116e6 0.862143 0.431072 0.902318i $$-0.358136\pi$$
0.431072 + 0.902318i $$0.358136\pi$$
$$282$$ −1.06294e6 1.84106e6i −0.795948 1.37862i
$$283$$ −304959. + 528204.i −0.226347 + 0.392045i −0.956723 0.291001i $$-0.906012\pi$$
0.730376 + 0.683046i $$0.239345\pi$$
$$284$$ 558870. 967990.i 0.411164 0.712156i
$$285$$ −341579. 591632.i −0.249103 0.431459i
$$286$$ −2.86624e6 −2.07204
$$287$$ 0 0
$$288$$ 663718. 0.471523
$$289$$ 177020. + 306608.i 0.124675 + 0.215943i
$$290$$ 1.16024e6 2.00960e6i 0.810130 1.40319i
$$291$$ 692833. 1.20002e6i 0.479618 0.830724i
$$292$$ −300797. 520995.i −0.206450 0.357583i
$$293$$ −156438. −0.106457 −0.0532283 0.998582i $$-0.516951\pi$$
−0.0532283 + 0.998582i $$0.516951\pi$$
$$294$$ 0 0
$$295$$ 751303. 0.502644
$$296$$ −54955.3 95185.4i −0.0364570 0.0631453i
$$297$$ 107735. 186603.i 0.0708707 0.122752i
$$298$$ −274106. + 474765.i −0.178804 + 0.309698i
$$299$$ 367968. + 637340.i 0.238030 + 0.412281i
$$300$$ 647554. 0.415406
$$301$$ 0 0
$$302$$ 1.89007e6 1.19251
$$303$$ −629139. 1.08970e6i −0.393677 0.681869i
$$304$$ −775201. + 1.34269e6i −0.481095 + 0.833281i
$$305$$ −429630. + 744141.i −0.264451 + 0.458042i
$$306$$ −353150. 611673.i −0.215603 0.373436i
$$307$$ −293229. −0.177566 −0.0887831 0.996051i $$-0.528298\pi$$
−0.0887831 + 0.996051i $$0.528298\pi$$
$$308$$ 0 0
$$309$$ −1.04333e6 −0.621620
$$310$$ 147011. + 254631.i 0.0868853 + 0.150490i
$$311$$ 1.22608e6 2.12363e6i 0.718816 1.24503i −0.242653 0.970113i $$-0.578018\pi$$
0.961469 0.274913i $$-0.0886491\pi$$
$$312$$ −320245. + 554681.i −0.186250 + 0.322594i
$$313$$ 917705. + 1.58951e6i 0.529471 + 0.917071i 0.999409 + 0.0343716i $$0.0109430\pi$$
−0.469938 + 0.882700i $$0.655724\pi$$
$$314$$ −3.88503e6 −2.22367
$$315$$ 0 0
$$316$$ −2.87406e6 −1.61912
$$317$$ −294980. 510920.i −0.164871 0.285565i 0.771738 0.635940i $$-0.219387\pi$$
−0.936609 + 0.350375i $$0.886054\pi$$
$$318$$ 270401. 468349.i 0.149948 0.259718i
$$319$$ −1.12783e6 + 1.95346e6i −0.620537 + 1.07480i
$$320$$ 822221. + 1.42413e6i 0.448863 + 0.777454i
$$321$$ −747556. −0.404931
$$322$$ 0 0
$$323$$ 2.17679e6 1.16094
$$324$$ −129050. 223522.i −0.0682963 0.118293i
$$325$$ 1.04996e6 1.81859e6i 0.551399 0.955050i
$$326$$ 384593. 666134.i 0.200427 0.347151i
$$327$$ 204103. + 353517.i 0.105555 + 0.182827i
$$328$$ −742344. −0.380996
$$329$$ 0 0
$$330$$ 808849. 0.408868
$$331$$ −88659.2 153562.i −0.0444789 0.0770396i 0.842929 0.538025i $$-0.180829\pi$$
−0.887408 + 0.460985i $$0.847496\pi$$
$$332$$ −596785. + 1.03366e6i −0.297148 + 0.514675i
$$333$$ 71815.0 124387.i 0.0354899 0.0614703i
$$334$$ 1.32932e6 + 2.30245e6i 0.652023 + 1.12934i
$$335$$ 1.24817e6 0.607664
$$336$$ 0 0
$$337$$ −3.04781e6 −1.46189 −0.730943 0.682438i $$-0.760920\pi$$
−0.730943 + 0.682438i $$0.760920\pi$$
$$338$$ 3.99888e6 + 6.92627e6i 1.90391 + 3.29767i
$$339$$ −1599.90 + 2771.10i −0.000756124 + 0.00130965i
$$340$$ 731027. 1.26618e6i 0.342954 0.594014i
$$341$$ −142904. 247518.i −0.0665518 0.115271i
$$342$$ 1.44253e6 0.666896
$$343$$ 0 0
$$344$$ 1.22747e6 0.559259
$$345$$ −103840. 179856.i −0.0469697 0.0813538i
$$346$$ 1.52937e6 2.64895e6i 0.686787 1.18955i
$$347$$ 1.21180e6 2.09891e6i 0.540268 0.935771i −0.458621 0.888632i $$-0.651656\pi$$
0.998888 0.0471388i $$-0.0150103\pi$$
$$348$$ 1.35097e6 + 2.33995e6i 0.597996 + 1.03576i
$$349$$ 2.67690e6 1.17644 0.588218 0.808702i $$-0.299830\pi$$
0.588218 + 0.808702i $$0.299830\pi$$
$$350$$ 0 0
$$351$$ −836985. −0.362619
$$352$$ −1.21096e6 2.09744e6i −0.520921 0.902262i
$$353$$ 475206. 823081.i 0.202976 0.351565i −0.746510 0.665374i $$-0.768272\pi$$
0.949486 + 0.313809i $$0.101605\pi$$
$$354$$ −793209. + 1.37388e6i −0.336418 + 0.582694i
$$355$$ 511438. + 885837.i 0.215388 + 0.373064i
$$356$$ 1.41971e6 0.593711
$$357$$ 0 0
$$358$$ 1.46877e6 0.605683
$$359$$ −1.39441e6 2.41518e6i −0.571022 0.989039i −0.996461 0.0840524i $$-0.973214\pi$$
0.425439 0.904987i $$-0.360120\pi$$
$$360$$ 90372.7 156530.i 0.0367520 0.0636563i
$$361$$ −984862. + 1.70583e6i −0.397747 + 0.688919i
$$362$$ −570007. 987282.i −0.228617 0.395977i
$$363$$ 663206. 0.264169
$$364$$ 0 0
$$365$$ 550536. 0.216299
$$366$$ −907187. 1.57129e6i −0.353993 0.613133i
$$367$$ 76940.7 133265.i 0.0298189 0.0516478i −0.850731 0.525602i $$-0.823840\pi$$
0.880550 + 0.473954i $$0.157174\pi$$
$$368$$ −235662. + 408178.i −0.0907129 + 0.157119i
$$369$$ −485044. 840120.i −0.185445 0.321200i
$$370$$ 539169. 0.204749
$$371$$ 0 0
$$372$$ −342356. −0.128269
$$373$$ 1.19191e6 + 2.06444e6i 0.443578 + 0.768299i 0.997952 0.0639683i $$-0.0203757\pi$$
−0.554374 + 0.832268i $$0.687042\pi$$
$$374$$ −1.28865e6 + 2.23200e6i −0.476381 + 0.825117i
$$375$$ −802548. + 1.39005e6i −0.294709 + 0.510450i
$$376$$ 866727. + 1.50121e6i 0.316164 + 0.547612i
$$377$$ 8.76203e6 3.17506
$$378$$ 0 0
$$379$$ 3.65191e6 1.30594 0.652969 0.757385i $$-0.273523\pi$$
0.652969 + 0.757385i $$0.273523\pi$$
$$380$$ 1.49303e6 + 2.58600e6i 0.530407 + 0.918692i
$$381$$ 760352. 1.31697e6i 0.268350 0.464797i
$$382$$ 766129. 1.32697e6i 0.268623 0.465269i
$$383$$ 1.07865e6 + 1.86827e6i 0.375736 + 0.650794i 0.990437 0.137967i $$-0.0440566\pi$$
−0.614701 + 0.788760i $$0.710723\pi$$
$$384$$ −1.11245e6 −0.384991
$$385$$ 0 0
$$386$$ −8.15904e6 −2.78722
$$387$$ 802019. + 1.38914e6i 0.272212 + 0.471485i
$$388$$ −3.02835e6 + 5.24525e6i −1.02124 + 1.76883i
$$389$$ 1.83236e6 3.17373e6i 0.613954 1.06340i −0.376613 0.926371i $$-0.622911\pi$$
0.990567 0.137029i $$-0.0437553\pi$$
$$390$$ −1.57097e6 2.72100e6i −0.523006 0.905872i
$$391$$ 661746. 0.218902
$$392$$ 0 0
$$393$$ −1.56572e6 −0.511368
$$394$$ −2.95220e6 5.11336e6i −0.958087 1.65946i
$$395$$ 1.31507e6 2.27777e6i 0.424089 0.734543i
$$396$$ −470906. + 815634.i −0.150903 + 0.261371i
$$397$$ −1.97324e6 3.41775e6i −0.628353 1.08834i −0.987882 0.155205i $$-0.950396\pi$$
0.359529 0.933134i $$-0.382937\pi$$
$$398$$ −3.51524e6 −1.11236
$$399$$ 0 0
$$400$$ 1.34488e6 0.420274
$$401$$ −12508.0 21664.5i −0.00388444 0.00672804i 0.864077 0.503360i $$-0.167903\pi$$
−0.867961 + 0.496632i $$0.834570\pi$$
$$402$$ −1.31780e6 + 2.28249e6i −0.406708 + 0.704439i
$$403$$ −555106. + 961472.i −0.170260 + 0.294900i
$$404$$ 2.74994e6 + 4.76304e6i 0.838244 + 1.45188i
$$405$$ 236196. 0.0715542
$$406$$ 0 0
$$407$$ −524107. −0.156832
$$408$$ 287961. + 498763.i 0.0856412 + 0.148335i
$$409$$ 416350. 721139.i 0.123069 0.213163i −0.797907 0.602780i $$-0.794060\pi$$
0.920977 + 0.389618i $$0.127393\pi$$
$$410$$ 1.82079e6 3.15371e6i 0.534935 0.926535i
$$411$$ 1.65476e6 + 2.86612e6i 0.483203 + 0.836931i
$$412$$ 4.56035e6 1.32360
$$413$$ 0 0
$$414$$ 438528. 0.125747
$$415$$ −546136. 945935.i −0.155661 0.269613i
$$416$$ −4.70391e6 + 8.14741e6i −1.33268 + 2.30827i
$$417$$ −980850. + 1.69888e6i −0.276225 + 0.478435i
$$418$$ −2.63190e6 4.55858e6i −0.736763 1.27611i
$$419$$ −3.95178e6 −1.09966 −0.549828 0.835278i $$-0.685307\pi$$
−0.549828 + 0.835278i $$0.685307\pi$$
$$420$$ 0 0
$$421$$ 4.72285e6 1.29867 0.649336 0.760502i $$-0.275047\pi$$
0.649336 + 0.760502i $$0.275047\pi$$
$$422$$ −1.71945e6 2.97817e6i −0.470011 0.814084i
$$423$$ −1.13263e6 + 1.96177e6i −0.307777 + 0.533086i
$$424$$ −220487. + 381895.i −0.0595619 + 0.103164i
$$425$$ −944115. 1.63526e6i −0.253544 0.439150i
$$426$$ −2.15986e6 −0.576636
$$427$$ 0 0
$$428$$ 3.26754e6 0.862207
$$429$$ 1.52708e6 + 2.64499e6i 0.400608 + 0.693873i
$$430$$ −3.01068e6 + 5.21465e6i −0.785224 + 1.36005i
$$431$$ −2.03905e6 + 3.53174e6i −0.528731 + 0.915789i 0.470708 + 0.882289i $$0.343999\pi$$
−0.999439 + 0.0334995i $$0.989335\pi$$
$$432$$ −268019. 464223.i −0.0690966 0.119679i
$$433$$ 1.79927e6 0.461186 0.230593 0.973050i $$-0.425933\pi$$
0.230593 + 0.973050i $$0.425933\pi$$
$$434$$ 0 0
$$435$$ −2.47263e6 −0.626522
$$436$$ −892127. 1.54521e6i −0.224756 0.389288i
$$437$$ −675766. + 1.17046e6i −0.169275 + 0.293193i
$$438$$ −581244. + 1.00674e6i −0.144768 + 0.250746i
$$439$$ 2.25913e6 + 3.91293e6i 0.559475 + 0.969039i 0.997540 + 0.0700959i $$0.0223305\pi$$
−0.438065 + 0.898943i $$0.644336\pi$$
$$440$$ −659542. −0.162409
$$441$$ 0 0
$$442$$ 1.00114e7 2.43746
$$443$$ 1.42628e6 + 2.47039e6i 0.345299 + 0.598075i 0.985408 0.170209i $$-0.0544443\pi$$
−0.640109 + 0.768284i $$0.721111\pi$$
$$444$$ −313901. + 543692.i −0.0755675 + 0.130887i
$$445$$ −649611. + 1.12516e6i −0.155508 + 0.269348i
$$446$$ −3.72488e6 6.45168e6i −0.886696 1.53580i
$$447$$ 584155. 0.138280
$$448$$ 0 0
$$449$$ −1.90246e6 −0.445348 −0.222674 0.974893i $$-0.571478\pi$$
−0.222674 + 0.974893i $$0.571478\pi$$
$$450$$ −625650. 1.08366e6i −0.145646 0.252267i
$$451$$ −1.76993e6 + 3.06561e6i −0.409746 + 0.709700i
$$452$$ 6993.09 12112.4i 0.00160999 0.00278859i
$$453$$ −1.00700e6 1.74417e6i −0.230559 0.399341i
$$454$$ −9.51468e6 −2.16648
$$455$$ 0 0
$$456$$ −1.17625e6 −0.264903
$$457$$ −1.32417e6 2.29353e6i −0.296588 0.513705i 0.678765 0.734355i $$-0.262515\pi$$
−0.975353 + 0.220650i $$0.929182\pi$$
$$458$$ −1.30952e6 + 2.26815e6i −0.291708 + 0.505253i
$$459$$ −376304. + 651778.i −0.0833695 + 0.144400i
$$460$$ 453881. + 786146.i 0.100011 + 0.173224i
$$461$$ −1.09031e6 −0.238944 −0.119472 0.992838i $$-0.538120\pi$$
−0.119472 + 0.992838i $$0.538120\pi$$
$$462$$ 0 0
$$463$$ −2.50851e6 −0.543831 −0.271916 0.962321i $$-0.587657\pi$$
−0.271916 + 0.962321i $$0.587657\pi$$
$$464$$ 2.80578e6 + 4.85975e6i 0.605004 + 1.04790i
$$465$$ 156650. 271326.i 0.0335968 0.0581914i
$$466$$ 4.79971e6 8.31335e6i 1.02388 1.77342i
$$467$$ −1.60468e6 2.77938e6i −0.340483 0.589734i 0.644040 0.764992i $$-0.277257\pi$$
−0.984522 + 0.175259i $$0.943924\pi$$
$$468$$ 3.65843e6 0.772112
$$469$$ 0 0
$$470$$ −8.50350e6 −1.77563
$$471$$ 2.06988e6 + 3.58513e6i 0.429925 + 0.744652i
$$472$$ 646789. 1.12027e6i 0.133631 0.231456i
$$473$$ 2.92657e6 5.06898e6i 0.601460 1.04176i
$$474$$ 2.77685e6 + 4.80964e6i 0.567683 + 0.983256i
$$475$$ 3.85647e6 0.784252
$$476$$ 0 0
$$477$$ −576260. −0.115964
$$478$$ 369551. + 640081.i 0.0739784 + 0.128134i
$$479$$ 1.15731e6 2.00452e6i 0.230468 0.399182i −0.727478 0.686131i $$-0.759308\pi$$
0.957946 + 0.286949i $$0.0926410\pi$$
$$480$$ 1.32744e6 2.29919e6i 0.262973 0.455482i
$$481$$ 1.01794e6 + 1.76312e6i 0.200612 + 0.347471i
$$482$$ 4.54211e6 0.890513
$$483$$ 0 0
$$484$$ −2.89885e6 −0.562486
$$485$$ −2.77133e6 4.80009e6i −0.534976 0.926605i
$$486$$ −249370. + 431922.i −0.0478911 + 0.0829497i
$$487$$ 2.31867e6 4.01606e6i 0.443014 0.767322i −0.554898 0.831919i $$-0.687243\pi$$
0.997911 + 0.0645962i $$0.0205759\pi$$
$$488$$ 739727. + 1.28124e6i 0.140612 + 0.243547i
$$489$$ −819618. −0.155003
$$490$$ 0 0
$$491$$ 5.02151e6 0.940007 0.470003 0.882665i $$-0.344253\pi$$
0.470003 + 0.882665i $$0.344253\pi$$
$$492$$ 2.12011e6 + 3.67213e6i 0.394862 + 0.683921i
$$493$$ 3.93936e6 6.82317e6i 0.729976 1.26436i
$$494$$ −1.02235e7 + 1.77076e7i −1.88487 + 3.26469i
$$495$$ −430941. 746411.i −0.0790505 0.136919i
$$496$$ −711024. −0.129772
$$497$$ 0 0
$$498$$ 2.30639e6 0.416735
$$499$$ −1.68911e6 2.92562e6i −0.303673 0.525978i 0.673292 0.739377i $$-0.264880\pi$$
−0.976965 + 0.213399i $$0.931546\pi$$
$$500$$ 3.50791e6 6.07587e6i 0.627514 1.08689i
$$501$$ 1.41648e6 2.45341e6i 0.252124 0.436692i
$$502$$ −5.71610e6 9.90057e6i −1.01237 1.75348i
$$503$$ −5.03743e6 −0.887747 −0.443873 0.896090i $$-0.646396\pi$$
−0.443873 + 0.896090i $$0.646396\pi$$
$$504$$ 0 0
$$505$$ −5.03311e6 −0.878230
$$506$$ −800097. 1.38581e6i −0.138921 0.240617i
$$507$$ 4.26107e6 7.38039e6i 0.736205 1.27515i
$$508$$ −3.32347e6 + 5.75642e6i −0.571390 + 0.989677i
$$509$$ 3.36233e6 + 5.82373e6i 0.575236 + 0.996338i 0.996016 + 0.0891752i $$0.0284231\pi$$
−0.420780 + 0.907163i $$0.638244\pi$$
$$510$$ −2.82520e6 −0.480976
$$511$$ 0 0
$$512$$ −7.48361e6 −1.26164
$$513$$ −768553. 1.33117e6i −0.128938 0.223327i
$$514$$ 4.12556e6 7.14568e6i 0.688771 1.19299i
$$515$$ −2.08666e6 + 3.61420e6i −0.346684 + 0.600473i
$$516$$ −3.50559e6 6.07187e6i −0.579612 1.00392i
$$517$$ 8.26595e6 1.36009
$$518$$ 0 0
$$519$$ −3.25929e6 −0.531134
$$520$$ 1.28098e6 + 2.21872e6i 0.207747 + 0.359828i
$$521$$ 2.21385e6 3.83450e6i 0.357317 0.618892i −0.630194 0.776437i $$-0.717025\pi$$
0.987512 + 0.157546i $$0.0503582\pi$$
$$522$$ 2.61055e6 4.52161e6i 0.419330 0.726301i
$$523$$ 4.47955e6 + 7.75882e6i 0.716111 + 1.24034i 0.962529 + 0.271178i $$0.0874131\pi$$
−0.246418 + 0.969164i $$0.579254\pi$$
$$524$$ 6.84372e6 1.08884
$$525$$ 0 0
$$526$$ 1.05050e7 1.65551
$$527$$ 499145. + 864545.i 0.0782889 + 0.135600i
$$528$$ −978005. + 1.69395e6i −0.152671 + 0.264434i
$$529$$ 3.01274e6 5.21822e6i 0.468082 0.810742i
$$530$$ −1.08161e6 1.87340e6i −0.167255 0.289694i
$$531$$ 1.69043e6 0.260173
$$532$$ 0 0
$$533$$ 1.37504e7 2.09652
$$534$$ −1.37169e6 2.37583e6i −0.208162 0.360548i
$$535$$ −1.49511e6 + 2.58961e6i −0.225834 + 0.391156i
$$536$$ 1.07454e6 1.86116e6i 0.161551 0.279815i
$$537$$ −782533. 1.35539e6i −0.117103 0.202828i
$$538$$ −9.15641e6 −1.36386
$$539$$ 0 0
$$540$$ −1.03240e6 −0.152358
$$541$$ 5.02337e6 + 8.70073e6i 0.737907 + 1.27809i 0.953436 + 0.301595i $$0.0975192\pi$$
−0.215529 + 0.976498i $$0.569147\pi$$
$$542$$ 9.14840e6 1.58455e7i 1.33766 2.31690i
$$543$$ −607380. + 1.05201e6i −0.0884018 + 0.153116i
$$544$$ 4.22970e6 + 7.32606e6i 0.612791 + 1.06139i
$$545$$ 1.63282e6 0.235477
$$546$$ 0 0
$$547$$ −1.31426e7 −1.87808 −0.939039 0.343811i $$-0.888282\pi$$
−0.939039 + 0.343811i $$0.888282\pi$$
$$548$$ −7.23287e6 1.25277e7i −1.02887 1.78205i
$$549$$ −966667. + 1.67432e6i −0.136882 + 0.237086i
$$550$$ −2.28300e6 + 3.95427e6i −0.321810 + 0.557391i
$$551$$ 8.04564e6 + 1.39355e7i 1.12897 + 1.95543i
$$552$$ −357579. −0.0499487
$$553$$ 0 0
$$554$$ −2.14415e6 −0.296811
$$555$$ −287260. 497549.i −0.0395861 0.0685652i
$$556$$ 4.28726e6 7.42575e6i 0.588156 1.01872i
$$557$$ −4.53376e6 + 7.85270e6i −0.619185 + 1.07246i 0.370450 + 0.928853i $$0.379204\pi$$
−0.989635 + 0.143607i $$0.954130\pi$$
$$558$$ 330775. + 572920.i 0.0449726 + 0.0778948i
$$559$$ −2.27363e7 −3.07744
$$560$$ 0 0
$$561$$ 2.74627e6 0.368414
$$562$$ 4.81923e6 + 8.34715e6i 0.643631 + 1.11480i
$$563$$ −5.25898e6 + 9.10882e6i −0.699247 + 1.21113i 0.269481 + 0.963006i $$0.413148\pi$$
−0.968728 + 0.248126i $$0.920185\pi$$
$$564$$ 4.95068e6 8.57483e6i 0.655340 1.13508i
$$565$$ 6399.59 + 11084.4i 0.000843395 + 0.00146080i
$$566$$ −5.15150e6 −0.675916
$$567$$ 0 0
$$568$$ 1.76117e6 0.229050
$$569$$ −3.66153e6 6.34196e6i −0.474114 0.821189i 0.525447 0.850826i $$-0.323898\pi$$
−0.999561 + 0.0296373i $$0.990565\pi$$
$$570$$ 2.88505e6 4.99706e6i 0.371934 0.644209i
$$571$$ 3.48990e6 6.04469e6i 0.447943 0.775861i −0.550309 0.834961i $$-0.685490\pi$$
0.998252 + 0.0591007i $$0.0188233\pi$$
$$572$$ −6.67483e6 1.15611e7i −0.853002 1.47744i
$$573$$ −1.63272e6 −0.207743
$$574$$ 0 0
$$575$$ 1.17237e6 0.147875
$$576$$ 1.85000e6 + 3.20429e6i 0.232335 + 0.402416i
$$577$$ 2.90605e6 5.03343e6i 0.363382 0.629397i −0.625133 0.780518i $$-0.714955\pi$$
0.988515 + 0.151122i $$0.0482886\pi$$
$$578$$ −1.49515e6 + 2.58968e6i −0.186151 + 0.322423i
$$579$$ 4.34699e6 + 7.52921e6i 0.538881 + 0.933369i
$$580$$ 1.08078e7 1.33403
$$581$$ 0 0
$$582$$ 1.17036e7 1.43223
$$583$$ 1.05139e6 + 1.82106e6i 0.128113 + 0.221898i
$$584$$ 473951. 820906.i 0.0575044 0.0996005i
$$585$$ −1.67397e6 + 2.89940e6i −0.202236 + 0.350283i
$$586$$ −660654. 1.14429e6i −0.0794750 0.137655i
$$587$$ −7.37446e6 −0.883355 −0.441677 0.897174i $$-0.645616\pi$$
−0.441677 + 0.897174i $$0.645616\pi$$
$$588$$ 0 0
$$589$$ −2.03888e6 −0.242161
$$590$$ 3.17284e6 + 5.49552e6i 0.375247 + 0.649948i
$$591$$ −3.14576e6 + 5.44862e6i −0.370473 + 0.641679i
$$592$$ −651927. + 1.12917e6i −0.0764530 + 0.132420i
$$593$$ −4.73264e6 8.19717e6i −0.552671 0.957254i −0.998081 0.0619274i $$-0.980275\pi$$
0.445410 0.895327i $$-0.353058\pi$$
$$594$$ 1.81991e6 0.211633
$$595$$ 0 0
$$596$$ −2.55332e6 −0.294435
$$597$$ 1.87286e6 + 3.24388e6i 0.215065 + 0.372503i
$$598$$ −3.10794e6 + 5.38311e6i −0.355402 + 0.615575i
$$599$$ 4.26098e6 7.38023e6i 0.485224 0.840432i −0.514632 0.857411i $$-0.672071\pi$$
0.999856 + 0.0169788i $$0.00540478\pi$$
$$600$$ 510159. + 883622.i 0.0578532 + 0.100205i
$$601$$ −657065. −0.0742031 −0.0371016 0.999311i $$-0.511813\pi$$
−0.0371016 + 0.999311i $$0.511813\pi$$
$$602$$ 0 0
$$603$$ 2.80839e6 0.314532
$$604$$ 4.40155e6 + 7.62371e6i 0.490923 + 0.850303i
$$605$$ 1.32641e6 2.29741e6i 0.147330 0.255182i
$$606$$ 5.31385e6 9.20386e6i 0.587798 1.01810i
$$607$$ −2.93443e6 5.08257e6i −0.323260 0.559902i 0.657899 0.753106i $$-0.271445\pi$$
−0.981159 + 0.193204i $$0.938112\pi$$
$$608$$ −1.72773e7 −1.89547
$$609$$ 0 0
$$610$$ −7.25750e6 −0.789700
$$611$$ −1.60544e7 2.78070e7i −1.73976 3.01336i
$$612$$ 1.64481e6 2.84890e6i 0.177516 0.307467i
$$613$$ −1.92201e6 + 3.32902e6i −0.206588 + 0.357820i −0.950637 0.310304i $$-0.899569\pi$$
0.744050 + 0.668124i $$0.232902\pi$$
$$614$$ −1.23834e6 2.14486e6i −0.132562 0.229603i
$$615$$ −3.88035e6 −0.413698
$$616$$ 0 0
$$617$$ 6.44660e6 0.681739 0.340869 0.940111i $$-0.389279\pi$$
0.340869 + 0.940111i $$0.389279\pi$$
$$618$$ −4.40609e6 7.63158e6i −0.464069 0.803791i
$$619$$ −3.36870e6 + 5.83476e6i −0.353375 + 0.612063i −0.986838 0.161709i $$-0.948299\pi$$
0.633464 + 0.773772i $$0.281633\pi$$
$$620$$ −684712. + 1.18596e6i −0.0715367 + 0.123905i
$$621$$ −233640. 404677.i −0.0243119 0.0421094i
$$622$$ 2.07115e7 2.14652
$$623$$ 0 0
$$624$$ 7.59804e6 0.781160
$$625$$ 352380. + 610339.i 0.0360837 + 0.0624987i
$$626$$ −7.75114e6 + 1.34254e7i −0.790551 + 1.36927i
$$627$$ −2.80446e6 + 4.85746e6i −0.284892 + 0.493447i
$$628$$ −9.04736e6 1.56705e7i −0.915425 1.58556i
$$629$$ 1.83063e6 0.184491
$$630$$ 0 0
$$631$$ −9.14514e6 −0.914360 −0.457180 0.889374i $$-0.651140\pi$$
−0.457180 + 0.889374i $$0.651140\pi$$
$$632$$ −2.26426e6 3.92181e6i −0.225493 0.390566i
$$633$$ −1.83219e6 + 3.17344e6i −0.181744 + 0.314790i
$$634$$ 2.49147e6 4.31534e6i 0.246168 0.426376i
$$635$$ −3.04141e6 5.26787e6i −0.299323 0.518443i
$$636$$ 2.51881e6 0.246918
$$637$$ 0 0
$$638$$ −1.90518e7 −1.85304
$$639$$ 1.15074e6 + 1.99313e6i 0.111487 + 0.193101i
$$640$$ −2.22489e6 + 3.85362e6i −0.214713 + 0.371894i
$$641$$ 520442. 901432.i 0.0500296 0.0866538i −0.839926 0.542701i $$-0.817402\pi$$
0.889956 + 0.456047i $$0.150735\pi$$
$$642$$ −3.15701e6 5.46811e6i −0.302300 0.523600i
$$643$$ −9.08713e6 −0.866761 −0.433381 0.901211i $$-0.642679\pi$$
−0.433381 + 0.901211i $$0.642679\pi$$
$$644$$ 0 0
$$645$$ 6.41615e6 0.607261
$$646$$ 9.19284e6 + 1.59225e7i 0.866699 + 1.50117i
$$647$$ −1.10356e6 + 1.91141e6i −0.103641 + 0.179512i −0.913182 0.407551i $$-0.866383\pi$$
0.809541 + 0.587064i $$0.199716\pi$$
$$648$$ 203339. 352193.i 0.0190231 0.0329490i
$$649$$ −3.08420e6 5.34199e6i −0.287429 0.497842i
$$650$$ 1.77364e7 1.64658
$$651$$ 0 0
$$652$$ 3.58252e6 0.330042
$$653$$ 9.18048e6 + 1.59011e7i 0.842524 + 1.45929i 0.887754 + 0.460318i $$0.152265\pi$$
−0.0452296 + 0.998977i $$0.514402\pi$$
$$654$$ −1.72390e6 + 2.98588e6i −0.157604 + 0.272978i
$$655$$ −3.13145e6 + 5.42382e6i −0.285195 + 0.493972i
$$656$$ 4.40316e6 + 7.62649e6i 0.399489 + 0.691935i
$$657$$ 1.23871e6 0.111958
$$658$$ 0 0
$$659$$ 6.21208e6 0.557216 0.278608 0.960405i $$-0.410127\pi$$
0.278608 + 0.960405i $$0.410127\pi$$
$$660$$ 1.88363e6 + 3.26254e6i 0.168320 + 0.291538i
$$661$$ −7.71149e6 + 1.33567e7i −0.686491 + 1.18904i 0.286475 + 0.958088i $$0.407517\pi$$
−0.972966 + 0.230950i $$0.925817\pi$$
$$662$$ 748835. 1.29702e6i 0.0664112 0.115028i
$$663$$ −5.33389e6 9.23857e6i −0.471260 0.816246i
$$664$$ −1.88065e6 −0.165534
$$665$$ 0 0
$$666$$ 1.21313e6 0.105980
$$667$$ 2.44588e6 + 4.23638e6i 0.212873 + 0.368707i
$$668$$ −6.19136e6 + 1.07238e7i −0.536840 + 0.929834i
$$669$$ −3.96910e6 + 6.87468e6i −0.342868 + 0.593865i
$$670$$ 5.27118e6 + 9.12995e6i 0.453650 + 0.785745i
$$671$$ 7.05475e6 0.604889
$$672$$ 0 0
$$673$$ −2.27201e7 −1.93362 −0.966811 0.255491i $$-0.917763\pi$$
−0.966811 + 0.255491i $$0.917763\pi$$
$$674$$ −1.28713e7 2.22937e7i −1.09137 1.89030i
$$675$$ −666670. + 1.15471e6i −0.0563186 + 0.0975467i
$$676$$ −1.86250e7 + 3.22594e7i −1.56758 + 2.71513i
$$677$$ −6.80867e6 1.17930e7i −0.570940 0.988897i −0.996470 0.0839525i $$-0.973246\pi$$
0.425530 0.904944i $$-0.360088\pi$$
$$678$$ −27026.2 −0.00225793
$$679$$ 0 0
$$680$$ 2.30369e6 0.191052
$$681$$ 5.06926e6 + 8.78021e6i 0.418867 + 0.725499i
$$682$$ 1.20700e6 2.09059e6i 0.0993682 0.172111i
$$683$$ −1.19993e6 + 2.07833e6i −0.0984245 + 0.170476i −0.911033 0.412334i $$-0.864714\pi$$
0.812608 + 0.582810i $$0.198047\pi$$
$$684$$ 3.35931e6 + 5.81850e6i 0.274543 + 0.475523i
$$685$$ 1.32380e7 1.07795
$$686$$ 0 0
$$687$$ 2.79076e6 0.225595
$$688$$ −7.28061e6 1.26104e7i −0.586404 1.01568i
$$689$$ 4.08408e6 7.07383e6i 0.327753 0.567684i
$$690$$ 877057. 1.51911e6i 0.0701302 0.121469i
$$691$$ 701824. + 1.21560e6i 0.0559156 + 0.0968487i 0.892628 0.450793i $$-0.148859\pi$$
−0.836713 + 0.547642i $$0.815526\pi$$
$$692$$ 1.42462e7 1.13093
$$693$$ 0 0
$$694$$ 2.04703e7 1.61334
$$695$$ 3.92340e6 + 6.79553e6i 0.308106 + 0.533656i
$$696$$ −2.12866e6 + 3.68695e6i −0.166565 + 0.288499i
$$697$$ 6.18211e6 1.07077e7i 0.482009 0.834864i
$$698$$ 1.13048e7 + 1.95806e7i 0.878266 + 1.52120i
$$699$$ −1.02288e7 −0.791831
$$700$$ 0 0
$$701$$ −5.78991e6 −0.445017 −0.222509 0.974931i $$-0.571425\pi$$
−0.222509 + 0.974931i $$0.571425\pi$$
$$702$$ −3.53468e6 6.12225e6i −0.270712 0.468887i
$$703$$ −1.86942e6 + 3.23793e6i −0.142665 + 0.247103i
$$704$$ 6.75066e6 1.16925e7i 0.513351 0.889150i
$$705$$ 4.53052e6 + 7.84708e6i 0.343301 + 0.594614i
$$706$$ 8.02739e6 0.606126
$$707$$ 0 0
$$708$$ −7.38882e6 −0.553977
$$709$$ 5.65716e6 + 9.79849e6i 0.422652 + 0.732055i 0.996198 0.0871187i $$-0.0277659\pi$$
−0.573546 + 0.819173i $$0.694433\pi$$
$$710$$ −4.31972e6 + 7.48198e6i −0.321595 + 0.557020i
$$711$$ 2.95891e6 5.12498e6i 0.219512 0.380206i
$$712$$ 1.11848e6 + 1.93727e6i 0.0826857 + 0.143216i
$$713$$ −619821. −0.0456607
$$714$$ 0 0
$$715$$ 1.22167e7 0.893692
$$716$$ 3.42042e6 + 5.92435e6i 0.249343 + 0.431875i
$$717$$ 393781. 682048.i 0.0286060 0.0495470i
$$718$$ 1.17775e7 2.03992e7i 0.852591 1.47673i
$$719$$ 1.36890e7 + 2.37101e7i 0.987529 + 1.71045i 0.630109 + 0.776507i $$0.283010\pi$$
0.357420 + 0.933944i $$0.383656\pi$$
$$720$$ −2.14415e6 −0.154143
$$721$$ 0 0
$$722$$ −1.66367e7 −1.18775
$$723$$ −2.41996e6 4.19149e6i −0.172172 0.298210i
$$724$$ 2.65484e6 4.59831e6i 0.188231 0.326026i
$$725$$ 6.97908e6 1.20881e7i 0.493121 0.854110i
$$726$$ 2.80079e6 + 4.85111e6i 0.197215 + 0.341586i
$$727$$ −9.86471e6 −0.692226 −0.346113 0.938193i $$-0.612499\pi$$
−0.346113 + 0.938193i $$0.612499\pi$$
$$728$$ 0 0
$$729$$ 531441. 0.0370370
$$730$$ 2.32498e6 + 4.02698e6i 0.161477 + 0.279687i
$$731$$ −1.02221e7 + 1.77052e7i −0.707534 + 1.22548i
$$732$$ 4.22527e6 7.31837e6i 0.291458 0.504820i
$$733$$ −1.93938e6 3.35911e6i −0.133322 0.230921i 0.791633 0.610997i $$-0.209231\pi$$
−0.924955 + 0.380076i $$0.875898\pi$$
$$734$$ 1.29972e6 0.0890448
$$735$$ 0 0
$$736$$ −5.25229e6 −0.357400
$$737$$ −5.12393e6 8.87490e6i −0.347483 0.601859i
$$738$$ 4.09679e6 7.09584e6i 0.276887 0.479582i
$$739$$ 3.97749e6 6.88922e6i 0.267916 0.464044i −0.700408 0.713743i $$-0.746998\pi$$
0.968323 + 0.249699i $$0.0803318\pi$$
$$740$$ 1.25560e6 + 2.17477e6i 0.0842894 + 0.145994i
$$741$$ 2.17876e7 1.45768
$$742$$ 0 0
$$743$$ 1.65977e7 1.10300 0.551500 0.834175i $$-0.314056\pi$$
0.551500 + 0.834175i $$0.314056\pi$$
$$744$$ −269717. 467163.i −0.0178639 0.0309411i
$$745$$ 1.16831e6 2.02357e6i 0.0771200 0.133576i
$$746$$ −1.00671e7 + 1.74367e7i −0.662304 + 1.14714i
$$747$$ −1.22881e6 2.12835e6i −0.0805716 0.139554i
$$748$$ −1.20039e7 −0.784453
$$749$$ 0 0
$$750$$ −1.35570e7 −0.880056
$$751$$ −7.55359e6 1.30832e7i −0.488713 0.846475i 0.511203 0.859460i $$-0.329200\pi$$
−0.999916 + 0.0129846i $$0.995867\pi$$
$$752$$ 1.02818e7 1.78087e7i 0.663020 1.14838i
$$753$$ −6.09088e6 + 1.05497e7i −0.391464 + 0.678036i
$$754$$ 3.70030e7 + 6.40911e7i 2.37033 + 4.10553i
$$755$$ −8.05598e6 −0.514341
$$756$$ 0 0
$$757$$ 5.80923e6 0.368450 0.184225 0.982884i $$-0.441022\pi$$
0.184225 + 0.982884i $$0.441022\pi$$
$$758$$ 1.54224e7 + 2.67124e7i 0.974944 + 1.68865i
$$759$$ −852556. + 1.47667e6i −0.0537178 + 0.0930420i
$$760$$ −2.35249e6 + 4.07464e6i −0.147739 + 0.255891i
$$761$$ −1.27135e7 2.20204e7i −0.795799 1.37836i −0.922331 0.386402i $$-0.873718\pi$$
0.126531 0.991963i $$-0.459616\pi$$
$$762$$ 1.28442e7 0.801346
$$763$$ 0 0
$$764$$ 7.13656e6 0.442340
$$765$$ 1.50522e6 + 2.60711e6i 0.0929919 + 0.161067i
$$766$$ −9.11050e6 + 1.57798e7i −0.561010 + 0.971697i
$$767$$ −1.19804e7 + 2.07507e7i −0.735334 + 1.27364i
$$768$$ 1.87979e6 + 3.25589e6i 0.115002 + 0.199190i
$$769$$ 1.53909e7