# Properties

 Label 294.6.e.p.67.1 Level $294$ Weight $6$ Character 294.67 Analytic conductor $47.153$ Analytic rank $1$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$294 = 2 \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 294.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: $$47.1528430250$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 294.67 Dual form 294.6.e.p.79.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(13.0000 + 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$$ $$q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(13.0000 + 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-52.0000 + 90.0666i) q^{10} +(-332.000 + 575.041i) q^{11} +(72.0000 + 124.708i) q^{12} -318.000 q^{13} +234.000 q^{15} +(-128.000 - 221.703i) q^{16} +(791.000 - 1370.05i) q^{17} +(162.000 - 280.592i) q^{18} +(118.000 + 204.382i) q^{19} -416.000 q^{20} -2656.00 q^{22} +(-1106.00 - 1915.65i) q^{23} +(-288.000 + 498.831i) q^{24} +(1224.50 - 2120.90i) q^{25} +(-636.000 - 1101.58i) q^{26} -729.000 q^{27} -4954.00 q^{29} +(468.000 + 810.600i) q^{30} +(-3564.00 + 6173.03i) q^{31} +(512.000 - 886.810i) q^{32} +(2988.00 + 5175.37i) q^{33} +6328.00 q^{34} +1296.00 q^{36} +(-2179.00 - 3774.14i) q^{37} +(-472.000 + 817.528i) q^{38} +(-1431.00 + 2478.56i) q^{39} +(-832.000 - 1441.07i) q^{40} -10542.0 q^{41} -8452.00 q^{43} +(-5312.00 - 9200.65i) q^{44} +(1053.00 - 1823.85i) q^{45} +(4424.00 - 7662.59i) q^{46} +(2676.00 + 4634.97i) q^{47} -2304.00 q^{48} +9796.00 q^{50} +(-7119.00 - 12330.5i) q^{51} +(2544.00 - 4406.34i) q^{52} +(16677.0 - 28885.4i) q^{53} +(-1458.00 - 2525.33i) q^{54} -17264.0 q^{55} +2124.00 q^{57} +(-9908.00 - 17161.2i) q^{58} +(-7718.00 + 13368.0i) q^{59} +(-1872.00 + 3242.40i) q^{60} +(-18381.0 - 31836.8i) q^{61} -28512.0 q^{62} +4096.00 q^{64} +(-4134.00 - 7160.30i) q^{65} +(-11952.0 + 20701.5i) q^{66} +(-20486.0 + 35482.8i) q^{67} +(12656.0 + 21920.8i) q^{68} -19908.0 q^{69} -9092.00 q^{71} +(2592.00 + 4489.48i) q^{72} +(-36727.0 + 63613.0i) q^{73} +(8716.00 - 15096.6i) q^{74} +(-11020.5 - 19088.1i) q^{75} -3776.00 q^{76} -11448.0 q^{78} +(-44700.0 - 77422.7i) q^{79} +(3328.00 - 5764.27i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-21084.0 - 36518.6i) q^{82} +6428.00 q^{83} +41132.0 q^{85} +(-16904.0 - 29278.6i) q^{86} +(-22293.0 + 38612.6i) q^{87} +(21248.0 - 36802.6i) q^{88} +(-61329.0 - 106225. i) q^{89} +8424.00 q^{90} +35392.0 q^{92} +(32076.0 + 55557.3i) q^{93} +(-10704.0 + 18539.9i) q^{94} +(-3068.00 + 5313.93i) q^{95} +(-4608.00 - 7981.29i) q^{96} -21370.0 q^{97} +53784.0 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9}+O(q^{10})$$ 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 + 26 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 $$2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} - 104 q^{10} - 664 q^{11} + 144 q^{12} - 636 q^{13} + 468 q^{15} - 256 q^{16} + 1582 q^{17} + 324 q^{18} + 236 q^{19} - 832 q^{20} - 5312 q^{22} - 2212 q^{23} - 576 q^{24} + 2449 q^{25} - 1272 q^{26} - 1458 q^{27} - 9908 q^{29} + 936 q^{30} - 7128 q^{31} + 1024 q^{32} + 5976 q^{33} + 12656 q^{34} + 2592 q^{36} - 4358 q^{37} - 944 q^{38} - 2862 q^{39} - 1664 q^{40} - 21084 q^{41} - 16904 q^{43} - 10624 q^{44} + 2106 q^{45} + 8848 q^{46} + 5352 q^{47} - 4608 q^{48} + 19592 q^{50} - 14238 q^{51} + 5088 q^{52} + 33354 q^{53} - 2916 q^{54} - 34528 q^{55} + 4248 q^{57} - 19816 q^{58} - 15436 q^{59} - 3744 q^{60} - 36762 q^{61} - 57024 q^{62} + 8192 q^{64} - 8268 q^{65} - 23904 q^{66} - 40972 q^{67} + 25312 q^{68} - 39816 q^{69} - 18184 q^{71} + 5184 q^{72} - 73454 q^{73} + 17432 q^{74} - 22041 q^{75} - 7552 q^{76} - 22896 q^{78} - 89400 q^{79} + 6656 q^{80} - 6561 q^{81} - 42168 q^{82} + 12856 q^{83} + 82264 q^{85} - 33808 q^{86} - 44586 q^{87} + 42496 q^{88} - 122658 q^{89} + 16848 q^{90} + 70784 q^{92} + 64152 q^{93} - 21408 q^{94} - 6136 q^{95} - 9216 q^{96} - 42740 q^{97} + 107568 q^{99}+O(q^{100})$$ 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 + 26 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 - 104 * q^10 - 664 * q^11 + 144 * q^12 - 636 * q^13 + 468 * q^15 - 256 * q^16 + 1582 * q^17 + 324 * q^18 + 236 * q^19 - 832 * q^20 - 5312 * q^22 - 2212 * q^23 - 576 * q^24 + 2449 * q^25 - 1272 * q^26 - 1458 * q^27 - 9908 * q^29 + 936 * q^30 - 7128 * q^31 + 1024 * q^32 + 5976 * q^33 + 12656 * q^34 + 2592 * q^36 - 4358 * q^37 - 944 * q^38 - 2862 * q^39 - 1664 * q^40 - 21084 * q^41 - 16904 * q^43 - 10624 * q^44 + 2106 * q^45 + 8848 * q^46 + 5352 * q^47 - 4608 * q^48 + 19592 * q^50 - 14238 * q^51 + 5088 * q^52 + 33354 * q^53 - 2916 * q^54 - 34528 * q^55 + 4248 * q^57 - 19816 * q^58 - 15436 * q^59 - 3744 * q^60 - 36762 * q^61 - 57024 * q^62 + 8192 * q^64 - 8268 * q^65 - 23904 * q^66 - 40972 * q^67 + 25312 * q^68 - 39816 * q^69 - 18184 * q^71 + 5184 * q^72 - 73454 * q^73 + 17432 * q^74 - 22041 * q^75 - 7552 * q^76 - 22896 * q^78 - 89400 * q^79 + 6656 * q^80 - 6561 * q^81 - 42168 * q^82 + 12856 * q^83 + 82264 * q^85 - 33808 * q^86 - 44586 * q^87 + 42496 * q^88 - 122658 * q^89 + 16848 * q^90 + 70784 * q^92 + 64152 * q^93 - 21408 * q^94 - 6136 * q^95 - 9216 * q^96 - 42740 * q^97 + 107568 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$199$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 + 3.46410i 0.353553 + 0.612372i
$$3$$ 4.50000 7.79423i 0.288675 0.500000i
$$4$$ −8.00000 + 13.8564i −0.250000 + 0.433013i
$$5$$ 13.0000 + 22.5167i 0.232551 + 0.402790i 0.958558 0.284897i $$-0.0919594\pi$$
−0.726007 + 0.687687i $$0.758626\pi$$
$$6$$ 36.0000 0.408248
$$7$$ 0 0
$$8$$ −64.0000 −0.353553
$$9$$ −40.5000 70.1481i −0.166667 0.288675i
$$10$$ −52.0000 + 90.0666i −0.164438 + 0.284816i
$$11$$ −332.000 + 575.041i −0.827287 + 1.43290i 0.0728713 + 0.997341i $$0.476784\pi$$
−0.900159 + 0.435562i $$0.856550\pi$$
$$12$$ 72.0000 + 124.708i 0.144338 + 0.250000i
$$13$$ −318.000 −0.521878 −0.260939 0.965355i $$-0.584032\pi$$
−0.260939 + 0.965355i $$0.584032\pi$$
$$14$$ 0 0
$$15$$ 234.000 0.268527
$$16$$ −128.000 221.703i −0.125000 0.216506i
$$17$$ 791.000 1370.05i 0.663826 1.14978i −0.315776 0.948834i $$-0.602265\pi$$
0.979602 0.200946i $$-0.0644017\pi$$
$$18$$ 162.000 280.592i 0.117851 0.204124i
$$19$$ 118.000 + 204.382i 0.0749891 + 0.129885i 0.901082 0.433650i $$-0.142774\pi$$
−0.826092 + 0.563535i $$0.809441\pi$$
$$20$$ −416.000 −0.232551
$$21$$ 0 0
$$22$$ −2656.00 −1.16996
$$23$$ −1106.00 1915.65i −0.435949 0.755086i 0.561424 0.827529i $$-0.310254\pi$$
−0.997373 + 0.0724429i $$0.976920\pi$$
$$24$$ −288.000 + 498.831i −0.102062 + 0.176777i
$$25$$ 1224.50 2120.90i 0.391840 0.678687i
$$26$$ −636.000 1101.58i −0.184512 0.319584i
$$27$$ −729.000 −0.192450
$$28$$ 0 0
$$29$$ −4954.00 −1.09386 −0.546929 0.837179i $$-0.684203\pi$$
−0.546929 + 0.837179i $$0.684203\pi$$
$$30$$ 468.000 + 810.600i 0.0949386 + 0.164438i
$$31$$ −3564.00 + 6173.03i −0.666091 + 1.15370i 0.312897 + 0.949787i $$0.398700\pi$$
−0.978988 + 0.203916i $$0.934633\pi$$
$$32$$ 512.000 886.810i 0.0883883 0.153093i
$$33$$ 2988.00 + 5175.37i 0.477635 + 0.827287i
$$34$$ 6328.00 0.938792
$$35$$ 0 0
$$36$$ 1296.00 0.166667
$$37$$ −2179.00 3774.14i −0.261669 0.453225i 0.705016 0.709191i $$-0.250940\pi$$
−0.966686 + 0.255966i $$0.917606\pi$$
$$38$$ −472.000 + 817.528i −0.0530253 + 0.0918425i
$$39$$ −1431.00 + 2478.56i −0.150653 + 0.260939i
$$40$$ −832.000 1441.07i −0.0822192 0.142408i
$$41$$ −10542.0 −0.979407 −0.489704 0.871889i $$-0.662895\pi$$
−0.489704 + 0.871889i $$0.662895\pi$$
$$42$$ 0 0
$$43$$ −8452.00 −0.697089 −0.348545 0.937292i $$-0.613324\pi$$
−0.348545 + 0.937292i $$0.613324\pi$$
$$44$$ −5312.00 9200.65i −0.413644 0.716452i
$$45$$ 1053.00 1823.85i 0.0775170 0.134263i
$$46$$ 4424.00 7662.59i 0.308262 0.533926i
$$47$$ 2676.00 + 4634.97i 0.176702 + 0.306057i 0.940749 0.339104i $$-0.110124\pi$$
−0.764047 + 0.645161i $$0.776790\pi$$
$$48$$ −2304.00 −0.144338
$$49$$ 0 0
$$50$$ 9796.00 0.554145
$$51$$ −7119.00 12330.5i −0.383260 0.663826i
$$52$$ 2544.00 4406.34i 0.130469 0.225980i
$$53$$ 16677.0 28885.4i 0.815508 1.41250i −0.0934545 0.995624i $$-0.529791\pi$$
0.908963 0.416878i $$-0.136876\pi$$
$$54$$ −1458.00 2525.33i −0.0680414 0.117851i
$$55$$ −17264.0 −0.769546
$$56$$ 0 0
$$57$$ 2124.00 0.0865899
$$58$$ −9908.00 17161.2i −0.386737 0.669849i
$$59$$ −7718.00 + 13368.0i −0.288652 + 0.499960i −0.973488 0.228737i $$-0.926540\pi$$
0.684836 + 0.728697i $$0.259874\pi$$
$$60$$ −1872.00 + 3242.40i −0.0671317 + 0.116276i
$$61$$ −18381.0 31836.8i −0.632477 1.09548i −0.987044 0.160451i $$-0.948705\pi$$
0.354567 0.935031i $$-0.384628\pi$$
$$62$$ −28512.0 −0.941995
$$63$$ 0 0
$$64$$ 4096.00 0.125000
$$65$$ −4134.00 7160.30i −0.121363 0.210207i
$$66$$ −11952.0 + 20701.5i −0.337739 + 0.584980i
$$67$$ −20486.0 + 35482.8i −0.557532 + 0.965675i 0.440169 + 0.897915i $$0.354918\pi$$
−0.997702 + 0.0677597i $$0.978415\pi$$
$$68$$ 12656.0 + 21920.8i 0.331913 + 0.574890i
$$69$$ −19908.0 −0.503390
$$70$$ 0 0
$$71$$ −9092.00 −0.214049 −0.107025 0.994256i $$-0.534132\pi$$
−0.107025 + 0.994256i $$0.534132\pi$$
$$72$$ 2592.00 + 4489.48i 0.0589256 + 0.102062i
$$73$$ −36727.0 + 63613.0i −0.806637 + 1.39714i 0.108543 + 0.994092i $$0.465382\pi$$
−0.915180 + 0.403045i $$0.867952\pi$$
$$74$$ 8716.00 15096.6i 0.185028 0.320478i
$$75$$ −11020.5 19088.1i −0.226229 0.391840i
$$76$$ −3776.00 −0.0749891
$$77$$ 0 0
$$78$$ −11448.0 −0.213056
$$79$$ −44700.0 77422.7i −0.805823 1.39573i −0.915734 0.401785i $$-0.868390\pi$$
0.109911 0.993941i $$-0.464944\pi$$
$$80$$ 3328.00 5764.27i 0.0581378 0.100698i
$$81$$ −3280.50 + 5681.99i −0.0555556 + 0.0962250i
$$82$$ −21084.0 36518.6i −0.346273 0.599762i
$$83$$ 6428.00 0.102419 0.0512095 0.998688i $$-0.483692\pi$$
0.0512095 + 0.998688i $$0.483692\pi$$
$$84$$ 0 0
$$85$$ 41132.0 0.617494
$$86$$ −16904.0 29278.6i −0.246458 0.426878i
$$87$$ −22293.0 + 38612.6i −0.315770 + 0.546929i
$$88$$ 21248.0 36802.6i 0.292490 0.506608i
$$89$$ −61329.0 106225.i −0.820712 1.42152i −0.905153 0.425087i $$-0.860244\pi$$
0.0844405 0.996429i $$-0.473090\pi$$
$$90$$ 8424.00 0.109626
$$91$$ 0 0
$$92$$ 35392.0 0.435949
$$93$$ 32076.0 + 55557.3i 0.384568 + 0.666091i
$$94$$ −10704.0 + 18539.9i −0.124947 + 0.216415i
$$95$$ −3068.00 + 5313.93i −0.0348776 + 0.0604097i
$$96$$ −4608.00 7981.29i −0.0510310 0.0883883i
$$97$$ −21370.0 −0.230608 −0.115304 0.993330i $$-0.536784\pi$$
−0.115304 + 0.993330i $$0.536784\pi$$
$$98$$ 0 0
$$99$$ 53784.0 0.551525
$$100$$ 19592.0 + 33934.3i 0.195920 + 0.339343i
$$101$$ −18407.0 + 31881.9i −0.179548 + 0.310986i −0.941726 0.336382i $$-0.890797\pi$$
0.762178 + 0.647367i $$0.224130\pi$$
$$102$$ 28476.0 49321.9i 0.271006 0.469396i
$$103$$ 52264.0 + 90523.9i 0.485411 + 0.840756i 0.999859 0.0167648i $$-0.00533666\pi$$
−0.514448 + 0.857521i $$0.672003\pi$$
$$104$$ 20352.0 0.184512
$$105$$ 0 0
$$106$$ 133416. 1.15330
$$107$$ −107220. 185710.i −0.905350 1.56811i −0.820447 0.571722i $$-0.806275\pi$$
−0.0849026 0.996389i $$-0.527058\pi$$
$$108$$ 5832.00 10101.3i 0.0481125 0.0833333i
$$109$$ −14399.0 + 24939.8i −0.116082 + 0.201060i −0.918212 0.396090i $$-0.870367\pi$$
0.802130 + 0.597150i $$0.203700\pi$$
$$110$$ −34528.0 59804.3i −0.272076 0.471249i
$$111$$ −39222.0 −0.302150
$$112$$ 0 0
$$113$$ −56014.0 −0.412668 −0.206334 0.978482i $$-0.566153\pi$$
−0.206334 + 0.978482i $$0.566153\pi$$
$$114$$ 4248.00 + 7357.75i 0.0306142 + 0.0530253i
$$115$$ 28756.0 49806.9i 0.202761 0.351192i
$$116$$ 39632.0 68644.6i 0.273465 0.473654i
$$117$$ 12879.0 + 22307.1i 0.0869796 + 0.150653i
$$118$$ −61744.0 −0.408216
$$119$$ 0 0
$$120$$ −14976.0 −0.0949386
$$121$$ −139922. 242353.i −0.868809 1.50482i
$$122$$ 73524.0 127347.i 0.447229 0.774623i
$$123$$ −47439.0 + 82166.8i −0.282731 + 0.489704i
$$124$$ −57024.0 98768.5i −0.333045 0.576852i
$$125$$ 144924. 0.829593
$$126$$ 0 0
$$127$$ 185400. 1.02000 0.510000 0.860174i $$-0.329645\pi$$
0.510000 + 0.860174i $$0.329645\pi$$
$$128$$ 8192.00 + 14189.0i 0.0441942 + 0.0765466i
$$129$$ −38034.0 + 65876.8i −0.201232 + 0.348545i
$$130$$ 16536.0 28641.2i 0.0858168 0.148639i
$$131$$ 32266.0 + 55886.4i 0.164273 + 0.284530i 0.936397 0.350943i $$-0.114139\pi$$
−0.772124 + 0.635472i $$0.780805\pi$$
$$132$$ −95616.0 −0.477635
$$133$$ 0 0
$$134$$ −163888. −0.788470
$$135$$ −9477.00 16414.6i −0.0447545 0.0775170i
$$136$$ −50624.0 + 87683.3i −0.234698 + 0.406509i
$$137$$ −76465.0 + 132441.i −0.348066 + 0.602868i −0.985906 0.167301i $$-0.946495\pi$$
0.637840 + 0.770169i $$0.279828\pi$$
$$138$$ −39816.0 68963.3i −0.177975 0.308262i
$$139$$ 343460. 1.50778 0.753892 0.656998i $$-0.228174\pi$$
0.753892 + 0.656998i $$0.228174\pi$$
$$140$$ 0 0
$$141$$ 48168.0 0.204038
$$142$$ −18184.0 31495.6i −0.0756778 0.131078i
$$143$$ 105576. 182863.i 0.431743 0.747800i
$$144$$ −10368.0 + 17957.9i −0.0416667 + 0.0721688i
$$145$$ −64402.0 111548.i −0.254378 0.440595i
$$146$$ −293816. −1.14076
$$147$$ 0 0
$$148$$ 69728.0 0.261669
$$149$$ 87429.0 + 151431.i 0.322619 + 0.558792i 0.981028 0.193868i $$-0.0621034\pi$$
−0.658409 + 0.752661i $$0.728770\pi$$
$$150$$ 44082.0 76352.3i 0.159968 0.277073i
$$151$$ 226276. 391922.i 0.807600 1.39880i −0.106922 0.994267i $$-0.534100\pi$$
0.914522 0.404536i $$-0.132567\pi$$
$$152$$ −7552.00 13080.4i −0.0265126 0.0459212i
$$153$$ −128142. −0.442551
$$154$$ 0 0
$$155$$ −185328. −0.619601
$$156$$ −22896.0 39657.0i −0.0753266 0.130469i
$$157$$ −249533. + 432204.i −0.807940 + 1.39939i 0.106349 + 0.994329i $$0.466084\pi$$
−0.914289 + 0.405063i $$0.867249\pi$$
$$158$$ 178800. 309691.i 0.569803 0.986928i
$$159$$ −150093. 259969.i −0.470834 0.815508i
$$160$$ 26624.0 0.0822192
$$161$$ 0 0
$$162$$ −26244.0 −0.0785674
$$163$$ 237794. + 411871.i 0.701022 + 1.21421i 0.968108 + 0.250534i $$0.0806060\pi$$
−0.267086 + 0.963673i $$0.586061\pi$$
$$164$$ 84336.0 146074.i 0.244852 0.424096i
$$165$$ −77688.0 + 134560.i −0.222149 + 0.384773i
$$166$$ 12856.0 + 22267.2i 0.0362106 + 0.0627186i
$$167$$ −120224. −0.333580 −0.166790 0.985992i $$-0.553340\pi$$
−0.166790 + 0.985992i $$0.553340\pi$$
$$168$$ 0 0
$$169$$ −270169. −0.727644
$$170$$ 82264.0 + 142485.i 0.218317 + 0.378136i
$$171$$ 9558.00 16554.9i 0.0249964 0.0432950i
$$172$$ 67616.0 117114.i 0.174272 0.301848i
$$173$$ 254437. + 440698.i 0.646346 + 1.11950i 0.983989 + 0.178230i $$0.0570370\pi$$
−0.337643 + 0.941274i $$0.609630\pi$$
$$174$$ −178344. −0.446566
$$175$$ 0 0
$$176$$ 169984. 0.413644
$$177$$ 69462.0 + 120312.i 0.166653 + 0.288652i
$$178$$ 245316. 424900.i 0.580331 1.00516i
$$179$$ −243780. + 422239.i −0.568677 + 0.984977i 0.428020 + 0.903769i $$0.359211\pi$$
−0.996697 + 0.0812080i $$0.974122\pi$$
$$180$$ 16848.0 + 29181.6i 0.0387585 + 0.0671317i
$$181$$ 544410. 1.23518 0.617589 0.786501i $$-0.288109\pi$$
0.617589 + 0.786501i $$0.288109\pi$$
$$182$$ 0 0
$$183$$ −330858. −0.730321
$$184$$ 70784.0 + 122601.i 0.154131 + 0.266963i
$$185$$ 56654.0 98127.6i 0.121703 0.210796i
$$186$$ −128304. + 222229.i −0.271930 + 0.470997i
$$187$$ 525224. + 909715.i 1.09835 + 1.90240i
$$188$$ −85632.0 −0.176702
$$189$$ 0 0
$$190$$ −24544.0 −0.0493243
$$191$$ −188202. 325975.i −0.373285 0.646549i 0.616784 0.787133i $$-0.288435\pi$$
−0.990069 + 0.140584i $$0.955102\pi$$
$$192$$ 18432.0 31925.2i 0.0360844 0.0625000i
$$193$$ −422473. + 731745.i −0.816405 + 1.41406i 0.0919095 + 0.995767i $$0.470703\pi$$
−0.908315 + 0.418288i $$0.862630\pi$$
$$194$$ −42740.0 74027.9i −0.0815324 0.141218i
$$195$$ −74412.0 −0.140138
$$196$$ 0 0
$$197$$ −492794. −0.904690 −0.452345 0.891843i $$-0.649412\pi$$
−0.452345 + 0.891843i $$0.649412\pi$$
$$198$$ 107568. + 186313.i 0.194993 + 0.337739i
$$199$$ −457388. + 792219.i −0.818751 + 1.41812i 0.0878512 + 0.996134i $$0.472000\pi$$
−0.906603 + 0.421985i $$0.861333\pi$$
$$200$$ −78368.0 + 135737.i −0.138536 + 0.239952i
$$201$$ 184374. + 319345.i 0.321892 + 0.557532i
$$202$$ −147256. −0.253919
$$203$$ 0 0
$$204$$ 227808. 0.383260
$$205$$ −137046. 237371.i −0.227762 0.394496i
$$206$$ −209056. + 362096.i −0.343237 + 0.594505i
$$207$$ −89586.0 + 155168.i −0.145316 + 0.251695i
$$208$$ 40704.0 + 70501.4i 0.0652347 + 0.112990i
$$209$$ −156704. −0.248150
$$210$$ 0 0
$$211$$ 311780. 0.482106 0.241053 0.970512i $$-0.422507\pi$$
0.241053 + 0.970512i $$0.422507\pi$$
$$212$$ 266832. + 462167.i 0.407754 + 0.706251i
$$213$$ −40914.0 + 70865.1i −0.0617907 + 0.107025i
$$214$$ 428880. 742842.i 0.640179 1.10882i
$$215$$ −109876. 190311.i −0.162109 0.280781i
$$216$$ 46656.0 0.0680414
$$217$$ 0 0
$$218$$ −115192. −0.164165
$$219$$ 330543. + 572517.i 0.465712 + 0.806637i
$$220$$ 138112. 239217.i 0.192387 0.333223i
$$221$$ −251538. + 435677.i −0.346436 + 0.600045i
$$222$$ −78444.0 135869.i −0.106826 0.185028i
$$223$$ 1.28776e6 1.73409 0.867047 0.498226i $$-0.166015\pi$$
0.867047 + 0.498226i $$0.166015\pi$$
$$224$$ 0 0
$$225$$ −198369. −0.261227
$$226$$ −112028. 194038.i −0.145900 0.252706i
$$227$$ 644526. 1.11635e6i 0.830187 1.43793i −0.0677031 0.997706i $$-0.521567\pi$$
0.897890 0.440220i $$-0.145100\pi$$
$$228$$ −16992.0 + 29431.0i −0.0216475 + 0.0374945i
$$229$$ 339107. + 587351.i 0.427315 + 0.740131i 0.996633 0.0819859i $$-0.0261262\pi$$
−0.569319 + 0.822117i $$0.692793\pi$$
$$230$$ 230048. 0.286747
$$231$$ 0 0
$$232$$ 317056. 0.386737
$$233$$ 558655. + 967619.i 0.674146 + 1.16765i 0.976718 + 0.214528i $$0.0688214\pi$$
−0.302572 + 0.953127i $$0.597845\pi$$
$$234$$ −51516.0 + 89228.3i −0.0615039 + 0.106528i
$$235$$ −69576.0 + 120509.i −0.0821845 + 0.142348i
$$236$$ −123488. 213887.i −0.144326 0.249980i
$$237$$ −804600. −0.930485
$$238$$ 0 0
$$239$$ −1.26196e6 −1.42906 −0.714528 0.699606i $$-0.753359\pi$$
−0.714528 + 0.699606i $$0.753359\pi$$
$$240$$ −29952.0 51878.4i −0.0335659 0.0581378i
$$241$$ 474109. 821181.i 0.525818 0.910744i −0.473730 0.880670i $$-0.657093\pi$$
0.999548 0.0300734i $$-0.00957410\pi$$
$$242$$ 559690. 969412.i 0.614340 1.06407i
$$243$$ 29524.5 + 51137.9i 0.0320750 + 0.0555556i
$$244$$ 588192. 0.632477
$$245$$ 0 0
$$246$$ −379512. −0.399841
$$247$$ −37524.0 64993.5i −0.0391351 0.0677840i
$$248$$ 228096. 395074.i 0.235499 0.407896i
$$249$$ 28926.0 50101.3i 0.0295658 0.0512095i
$$250$$ 289848. + 502031.i 0.293306 + 0.508020i
$$251$$ 486396. 0.487310 0.243655 0.969862i $$-0.421653\pi$$
0.243655 + 0.969862i $$0.421653\pi$$
$$252$$ 0 0
$$253$$ 1.46877e6 1.44262
$$254$$ 370800. + 642244.i 0.360625 + 0.624620i
$$255$$ 185094. 320592.i 0.178255 0.308747i
$$256$$ −32768.0 + 56755.8i −0.0312500 + 0.0541266i
$$257$$ −519549. 899885.i −0.490675 0.849874i 0.509268 0.860608i $$-0.329916\pi$$
−0.999942 + 0.0107346i $$0.996583\pi$$
$$258$$ −304272. −0.284585
$$259$$ 0 0
$$260$$ 132288. 0.121363
$$261$$ 200637. + 347513.i 0.182310 + 0.315770i
$$262$$ −129064. + 223545.i −0.116159 + 0.201193i
$$263$$ −675522. + 1.17004e6i −0.602213 + 1.04306i 0.390272 + 0.920699i $$0.372381\pi$$
−0.992485 + 0.122364i $$0.960952\pi$$
$$264$$ −191232. 331224.i −0.168869 0.292490i
$$265$$ 867204. 0.758589
$$266$$ 0 0
$$267$$ −1.10392e6 −0.947677
$$268$$ −327776. 567725.i −0.278766 0.482837i
$$269$$ −559055. + 968312.i −0.471057 + 0.815895i −0.999452 0.0331036i $$-0.989461\pi$$
0.528395 + 0.848999i $$0.322794\pi$$
$$270$$ 37908.0 65658.6i 0.0316462 0.0548128i
$$271$$ −95052.0 164635.i −0.0786209 0.136175i 0.824034 0.566540i $$-0.191718\pi$$
−0.902655 + 0.430365i $$0.858385\pi$$
$$272$$ −404992. −0.331913
$$273$$ 0 0
$$274$$ −611720. −0.492239
$$275$$ 813068. + 1.40828e6i 0.648329 + 1.12294i
$$276$$ 159264. 275853.i 0.125848 0.217974i
$$277$$ 100253. 173643.i 0.0785051 0.135975i −0.824100 0.566444i $$-0.808319\pi$$
0.902605 + 0.430469i $$0.141652\pi$$
$$278$$ 686920. + 1.18978e6i 0.533082 + 0.923325i
$$279$$ 577368. 0.444061
$$280$$ 0 0
$$281$$ 1.09237e6 0.825285 0.412643 0.910893i $$-0.364606\pi$$
0.412643 + 0.910893i $$0.364606\pi$$
$$282$$ 96336.0 + 166859.i 0.0721383 + 0.124947i
$$283$$ 906290. 1.56974e6i 0.672669 1.16510i −0.304476 0.952520i $$-0.598481\pi$$
0.977145 0.212576i $$-0.0681853\pi$$
$$284$$ 72736.0 125982.i 0.0535123 0.0926860i
$$285$$ 27612.0 + 47825.4i 0.0201366 + 0.0348776i
$$286$$ 844608. 0.610577
$$287$$ 0 0
$$288$$ −82944.0 −0.0589256
$$289$$ −541434. 937790.i −0.381330 0.660482i
$$290$$ 257608. 446190.i 0.179872 0.311548i
$$291$$ −96165.0 + 166563.i −0.0665709 + 0.115304i
$$292$$ −587632. 1.01781e6i −0.403319 0.698568i
$$293$$ −2.10031e6 −1.42927 −0.714634 0.699499i $$-0.753407\pi$$
−0.714634 + 0.699499i $$0.753407\pi$$
$$294$$ 0 0
$$295$$ −401336. −0.268505
$$296$$ 139456. + 241545.i 0.0925141 + 0.160239i
$$297$$ 242028. 419205.i 0.159212 0.275762i
$$298$$ −349716. + 605726.i −0.228126 + 0.395126i
$$299$$ 351708. + 609176.i 0.227512 + 0.394062i
$$300$$ 352656. 0.226229
$$301$$ 0 0
$$302$$ 1.81021e6 1.14212
$$303$$ 165663. + 286937.i 0.103662 + 0.179548i
$$304$$ 30208.0 52321.8i 0.0187473 0.0324712i
$$305$$ 477906. 827757.i 0.294166 0.509511i
$$306$$ −256284. 443897.i −0.156465 0.271006i
$$307$$ 1.64104e6 0.993743 0.496872 0.867824i $$-0.334482\pi$$
0.496872 + 0.867824i $$0.334482\pi$$
$$308$$ 0 0
$$309$$ 940752. 0.560504
$$310$$ −370656. 641995.i −0.219062 0.379426i
$$311$$ −472616. + 818595.i −0.277081 + 0.479919i −0.970658 0.240464i $$-0.922701\pi$$
0.693577 + 0.720383i $$0.256034\pi$$
$$312$$ 91584.0 158628.i 0.0532639 0.0922558i
$$313$$ 207677. + 359707.i 0.119820 + 0.207533i 0.919696 0.392631i $$-0.128435\pi$$
−0.799877 + 0.600165i $$0.795102\pi$$
$$314$$ −1.99626e6 −1.14260
$$315$$ 0 0
$$316$$ 1.43040e6 0.805823
$$317$$ −592407. 1.02608e6i −0.331110 0.573499i 0.651620 0.758546i $$-0.274090\pi$$
−0.982730 + 0.185047i $$0.940756\pi$$
$$318$$ 600372. 1.03987e6i 0.332930 0.576651i
$$319$$ 1.64473e6 2.84875e6i 0.904935 1.56739i
$$320$$ 53248.0 + 92228.2i 0.0290689 + 0.0503488i
$$321$$ −1.92996e6 −1.04541
$$322$$ 0 0
$$323$$ 373352. 0.199119
$$324$$ −52488.0 90911.9i −0.0277778 0.0481125i
$$325$$ −389391. + 674445.i −0.204493 + 0.354191i
$$326$$ −951176. + 1.64749e6i −0.495698 + 0.858574i
$$327$$ 129591. + 224458.i 0.0670202 + 0.116082i
$$328$$ 674688. 0.346273
$$329$$ 0 0
$$330$$ −621504. −0.314166
$$331$$ −685774. 1.18780e6i −0.344042 0.595898i 0.641138 0.767426i $$-0.278463\pi$$
−0.985179 + 0.171528i $$0.945129\pi$$
$$332$$ −51424.0 + 89069.0i −0.0256048 + 0.0443487i
$$333$$ −176499. + 305705.i −0.0872231 + 0.151075i
$$334$$ −240448. 416468.i −0.117938 0.204275i
$$335$$ −1.06527e6 −0.518619
$$336$$ 0 0
$$337$$ 963522. 0.462154 0.231077 0.972935i $$-0.425775\pi$$
0.231077 + 0.972935i $$0.425775\pi$$
$$338$$ −540338. 935893.i −0.257261 0.445589i
$$339$$ −252063. + 436586.i −0.119127 + 0.206334i
$$340$$ −329056. + 569942.i −0.154373 + 0.267383i
$$341$$ −2.36650e6 4.09889e6i −1.10210 1.90889i
$$342$$ 76464.0 0.0353502
$$343$$ 0 0
$$344$$ 540928. 0.246458
$$345$$ −258804. 448262.i −0.117064 0.202761i
$$346$$ −1.01775e6 + 1.76279e6i −0.457036 + 0.791609i
$$347$$ −1.28866e6 + 2.23202e6i −0.574531 + 0.995117i 0.421562 + 0.906800i $$0.361482\pi$$
−0.996092 + 0.0883168i $$0.971851\pi$$
$$348$$ −356688. 617802.i −0.157885 0.273465i
$$349$$ 3.06751e6 1.34810 0.674051 0.738684i $$-0.264553\pi$$
0.674051 + 0.738684i $$0.264553\pi$$
$$350$$ 0 0
$$351$$ 231822. 0.100435
$$352$$ 339968. + 588842.i 0.146245 + 0.253304i
$$353$$ −1.55072e6 + 2.68593e6i −0.662364 + 1.14725i 0.317628 + 0.948215i $$0.397114\pi$$
−0.979993 + 0.199033i $$0.936220\pi$$
$$354$$ −277848. + 481247.i −0.117842 + 0.204108i
$$355$$ −118196. 204721.i −0.0497774 0.0862169i
$$356$$ 1.96253e6 0.820712
$$357$$ 0 0
$$358$$ −1.95024e6 −0.804230
$$359$$ 163754. + 283630.i 0.0670588 + 0.116149i 0.897605 0.440800i $$-0.145305\pi$$
−0.830547 + 0.556949i $$0.811972\pi$$
$$360$$ −67392.0 + 116726.i −0.0274064 + 0.0474693i
$$361$$ 1.21020e6 2.09613e6i 0.488753 0.846546i
$$362$$ 1.08882e6 + 1.88589e6i 0.436701 + 0.756389i
$$363$$ −2.51860e6 −1.00321
$$364$$ 0 0
$$365$$ −1.90980e6 −0.750337
$$366$$ −661716. 1.14613e6i −0.258208 0.447229i
$$367$$ −1.43370e6 + 2.48323e6i −0.555638 + 0.962393i 0.442216 + 0.896909i $$0.354193\pi$$
−0.997854 + 0.0654844i $$0.979141\pi$$
$$368$$ −283136. + 490406.i −0.108987 + 0.188771i
$$369$$ 426951. + 739501.i 0.163235 + 0.282731i
$$370$$ 453232. 0.172114
$$371$$ 0 0
$$372$$ −1.02643e6 −0.384568
$$373$$ −1.79015e6 3.10063e6i −0.666218 1.15392i −0.978953 0.204084i $$-0.934579\pi$$
0.312735 0.949840i $$-0.398755\pi$$
$$374$$ −2.10090e6 + 3.63886e6i −0.776650 + 1.34520i
$$375$$ 652158. 1.12957e6i 0.239483 0.414797i
$$376$$ −171264. 296638.i −0.0624736 0.108207i
$$377$$ 1.57537e6 0.570860
$$378$$ 0 0
$$379$$ 1.64235e6 0.587310 0.293655 0.955912i $$-0.405128\pi$$
0.293655 + 0.955912i $$0.405128\pi$$
$$380$$ −49088.0 85022.9i −0.0174388 0.0302049i
$$381$$ 834300. 1.44505e6i 0.294449 0.510000i
$$382$$ 752808. 1.30390e6i 0.263953 0.457179i
$$383$$ −1.02849e6 1.78139e6i −0.358263 0.620530i 0.629408 0.777075i $$-0.283298\pi$$
−0.987671 + 0.156545i $$0.949964\pi$$
$$384$$ 147456. 0.0510310
$$385$$ 0 0
$$386$$ −3.37978e6 −1.15457
$$387$$ 342306. + 592891.i 0.116182 + 0.201232i
$$388$$ 170960. 296111.i 0.0576521 0.0998564i
$$389$$ −308071. + 533595.i −0.103223 + 0.178788i −0.913011 0.407935i $$-0.866249\pi$$
0.809788 + 0.586723i $$0.199582\pi$$
$$390$$ −148824. 257771.i −0.0495463 0.0858168i
$$391$$ −3.49938e6 −1.15758
$$392$$ 0 0
$$393$$ 580788. 0.189686
$$394$$ −985588. 1.70709e6i −0.319856 0.554007i
$$395$$ 1.16220e6 2.01299e6i 0.374790 0.649156i
$$396$$ −430272. + 745253.i −0.137881 + 0.238817i
$$397$$ 1.09606e6 + 1.89843e6i 0.349026 + 0.604531i 0.986077 0.166291i $$-0.0531792\pi$$
−0.637051 + 0.770822i $$0.719846\pi$$
$$398$$ −3.65910e6 −1.15789
$$399$$ 0 0
$$400$$ −626944. −0.195920
$$401$$ −1.64227e6 2.84449e6i −0.510015 0.883373i −0.999933 0.0116038i $$-0.996306\pi$$
0.489917 0.871769i $$-0.337027\pi$$
$$402$$ −737496. + 1.27738e6i −0.227612 + 0.394235i
$$403$$ 1.13335e6 1.96302e6i 0.347618 0.602092i
$$404$$ −294512. 510110.i −0.0897738 0.155493i
$$405$$ −170586. −0.0516780
$$406$$ 0 0
$$407$$ 2.89371e6 0.865903
$$408$$ 455616. + 789150.i 0.135503 + 0.234698i
$$409$$ −1.80610e6 + 3.12825e6i −0.533866 + 0.924683i 0.465351 + 0.885126i $$0.345928\pi$$
−0.999217 + 0.0395571i $$0.987405\pi$$
$$410$$ 548184. 949483.i 0.161052 0.278951i
$$411$$ 688185. + 1.19197e6i 0.200956 + 0.348066i
$$412$$ −1.67245e6 −0.485411
$$413$$ 0 0
$$414$$ −716688. −0.205508
$$415$$ 83564.0 + 144737.i 0.0238177 + 0.0412534i
$$416$$ −162816. + 282006.i −0.0461279 + 0.0798959i
$$417$$ 1.54557e6 2.67701e6i 0.435260 0.753892i
$$418$$ −313408. 542839.i −0.0877343 0.151960i
$$419$$ −5.41489e6 −1.50680 −0.753398 0.657564i $$-0.771587\pi$$
−0.753398 + 0.657564i $$0.771587\pi$$
$$420$$ 0 0
$$421$$ 3.60629e6 0.991644 0.495822 0.868424i $$-0.334867\pi$$
0.495822 + 0.868424i $$0.334867\pi$$
$$422$$ 623560. + 1.08004e6i 0.170450 + 0.295228i
$$423$$ 216756. 375432.i 0.0589007 0.102019i
$$424$$ −1.06733e6 + 1.84867e6i −0.288326 + 0.499395i
$$425$$ −1.93716e6 3.35526e6i −0.520227 0.901060i
$$426$$ −327312. −0.0873852
$$427$$ 0 0
$$428$$ 3.43104e6 0.905350
$$429$$ −950184. 1.64577e6i −0.249267 0.431743i
$$430$$ 439504. 761243.i 0.114628 0.198542i
$$431$$ 1.39107e6 2.40940e6i 0.360708 0.624765i −0.627370 0.778722i $$-0.715868\pi$$
0.988078 + 0.153957i $$0.0492018\pi$$
$$432$$ 93312.0 + 161621.i 0.0240563 + 0.0416667i
$$433$$ −6.27619e6 −1.60871 −0.804353 0.594152i $$-0.797488\pi$$
−0.804353 + 0.594152i $$0.797488\pi$$
$$434$$ 0 0
$$435$$ −1.15924e6 −0.293730
$$436$$ −230384. 399037.i −0.0580412 0.100530i
$$437$$ 261016. 452093.i 0.0653828 0.113246i
$$438$$ −1.32217e6 + 2.29007e6i −0.329308 + 0.570379i
$$439$$ 320796. + 555635.i 0.0794452 + 0.137603i 0.903011 0.429618i $$-0.141352\pi$$
−0.823566 + 0.567221i $$0.808018\pi$$
$$440$$ 1.10490e6 0.272076
$$441$$ 0 0
$$442$$ −2.01230e6 −0.489934
$$443$$ −3.02773e6 5.24418e6i −0.733006 1.26960i −0.955593 0.294691i $$-0.904783\pi$$
0.222587 0.974913i $$-0.428550\pi$$
$$444$$ 313776. 543476.i 0.0755374 0.130835i
$$445$$ 1.59455e6 2.76185e6i 0.381715 0.661150i
$$446$$ 2.57552e6 + 4.46093e6i 0.613095 + 1.06191i
$$447$$ 1.57372e6 0.372528
$$448$$ 0 0
$$449$$ −5.16681e6 −1.20950 −0.604752 0.796414i $$-0.706728\pi$$
−0.604752 + 0.796414i $$0.706728\pi$$
$$450$$ −396738. 687170.i −0.0923576 0.159968i
$$451$$ 3.49994e6 6.06208e6i 0.810251 1.40340i
$$452$$ 448112. 776153.i 0.103167 0.178690i
$$453$$ −2.03648e6 3.52729e6i −0.466268 0.807600i
$$454$$ 5.15621e6 1.17406
$$455$$ 0 0
$$456$$ −135936. −0.0306142
$$457$$ 113899. + 197279.i 0.0255111 + 0.0441865i 0.878499 0.477744i $$-0.158545\pi$$
−0.852988 + 0.521931i $$0.825212\pi$$
$$458$$ −1.35643e6 + 2.34940e6i −0.302157 + 0.523352i
$$459$$ −576639. + 998768.i −0.127753 + 0.221275i
$$460$$ 460096. + 796910.i 0.101380 + 0.175596i
$$461$$ −585146. −0.128237 −0.0641183 0.997942i $$-0.520423\pi$$
−0.0641183 + 0.997942i $$0.520423\pi$$
$$462$$ 0 0
$$463$$ −3.41454e6 −0.740251 −0.370126 0.928982i $$-0.620685\pi$$
−0.370126 + 0.928982i $$0.620685\pi$$
$$464$$ 634112. + 1.09831e6i 0.136732 + 0.236827i
$$465$$ −833976. + 1.44449e6i −0.178863 + 0.309800i
$$466$$ −2.23462e6 + 3.87048e6i −0.476693 + 0.825657i
$$467$$ 358150. + 620334.i 0.0759929 + 0.131623i 0.901518 0.432742i $$-0.142454\pi$$
−0.825525 + 0.564366i $$0.809121\pi$$
$$468$$ −412128. −0.0869796
$$469$$ 0 0
$$470$$ −556608. −0.116226
$$471$$ 2.24580e6 + 3.88983e6i 0.466464 + 0.807940i
$$472$$ 493952. 855550.i 0.102054 0.176763i
$$473$$ 2.80606e6 4.86025e6i 0.576693 0.998862i
$$474$$ −1.60920e6 2.78722e6i −0.328976 0.569803i
$$475$$ 577964. 0.117535
$$476$$ 0 0
$$477$$ −2.70167e6 −0.543672
$$478$$ −2.52391e6 4.37154e6i −0.505248 0.875115i
$$479$$ 2.62046e6 4.53877e6i 0.521842 0.903856i −0.477836 0.878449i $$-0.658579\pi$$
0.999677 0.0254070i $$-0.00808816\pi$$
$$480$$ 119808. 207514.i 0.0237346 0.0411096i
$$481$$ 692922. + 1.20018e6i 0.136559 + 0.236528i
$$482$$ 3.79287e6 0.743619
$$483$$ 0 0
$$484$$ 4.47752e6 0.868809
$$485$$ −277810. 481181.i −0.0536282 0.0928868i
$$486$$ −118098. + 204552.i −0.0226805 + 0.0392837i
$$487$$ −558508. + 967364.i −0.106710 + 0.184828i −0.914436 0.404731i $$-0.867365\pi$$
0.807725 + 0.589559i $$0.200698\pi$$
$$488$$ 1.17638e6 + 2.03756e6i 0.223614 + 0.387311i
$$489$$ 4.28029e6 0.809471
$$490$$ 0 0
$$491$$ 1.34458e6 0.251699 0.125850 0.992049i $$-0.459834\pi$$
0.125850 + 0.992049i $$0.459834\pi$$
$$492$$ −759024. 1.31467e6i −0.141365 0.244852i
$$493$$ −3.91861e6 + 6.78724e6i −0.726131 + 1.25770i
$$494$$ 150096. 259974.i 0.0276727 0.0479305i
$$495$$ 699192. + 1.21104e6i 0.128258 + 0.222149i
$$496$$ 1.82477e6 0.333045
$$497$$ 0 0
$$498$$ 231408. 0.0418124
$$499$$ 3.27324e6 + 5.66941e6i 0.588473 + 1.01926i 0.994433 + 0.105374i $$0.0336038\pi$$
−0.405960 + 0.913891i $$0.633063\pi$$
$$500$$ −1.15939e6 + 2.00813e6i −0.207398 + 0.359224i
$$501$$ −541008. + 937053.i −0.0962962 + 0.166790i
$$502$$ 972792. + 1.68493e6i 0.172290 + 0.298415i
$$503$$ 8.22050e6 1.44870 0.724350 0.689432i $$-0.242140\pi$$
0.724350 + 0.689432i $$0.242140\pi$$
$$504$$ 0 0
$$505$$ −957164. −0.167016
$$506$$ 2.93754e6 + 5.08796e6i 0.510043 + 0.883421i
$$507$$ −1.21576e6 + 2.10576e6i −0.210053 + 0.363822i
$$508$$ −1.48320e6 + 2.56898e6i −0.255000 + 0.441673i
$$509$$ −2.55522e6 4.42578e6i −0.437154 0.757173i 0.560315 0.828280i $$-0.310680\pi$$
−0.997469 + 0.0711070i $$0.977347\pi$$
$$510$$ 1.48075e6 0.252091
$$511$$ 0 0
$$512$$ −262144. −0.0441942
$$513$$ −86022.0 148994.i −0.0144317 0.0249964i
$$514$$ 2.07820e6 3.59954e6i 0.346959 0.600951i
$$515$$ −1.35886e6 + 2.35362e6i −0.225766 + 0.391038i
$$516$$ −608544. 1.05403e6i −0.100616 0.174272i
$$517$$ −3.55373e6 −0.584733
$$518$$ 0 0
$$519$$ 4.57987e6 0.746336
$$520$$ 264576. + 458259.i 0.0429084 + 0.0743195i
$$521$$ 4.85000e6 8.40044e6i 0.782793 1.35584i −0.147516 0.989060i $$-0.547128\pi$$
0.930309 0.366778i $$-0.119539\pi$$
$$522$$ −802548. + 1.39005e6i −0.128912 + 0.223283i
$$523$$ −1.58647e6 2.74785e6i −0.253617 0.439278i 0.710902 0.703291i $$-0.248287\pi$$
−0.964519 + 0.264013i $$0.914954\pi$$
$$524$$ −1.03251e6 −0.164273
$$525$$ 0 0
$$526$$ −5.40418e6 −0.851658
$$527$$ 5.63825e6 + 9.76573e6i 0.884337 + 1.53172i
$$528$$ 764928. 1.32489e6i 0.119409 0.206822i
$$529$$ 771700. 1.33662e6i 0.119897 0.207668i
$$530$$ 1.73441e6 + 3.00408e6i 0.268202 + 0.464539i
$$531$$ 1.25032e6 0.192435
$$532$$ 0 0
$$533$$ 3.35236e6 0.511131
$$534$$ −2.20784e6 3.82410e6i −0.335054 0.580331i
$$535$$ 2.78772e6 4.82847e6i 0.421080 0.729332i
$$536$$ 1.31110e6 2.27090e6i 0.197117 0.341418i
$$537$$ 2.19402e6 + 3.80015e6i 0.328326 + 0.568677i
$$538$$ −4.47244e6 −0.666176
$$539$$ 0 0
$$540$$ 303264. 0.0447545
$$541$$ 3.31287e6 + 5.73806e6i 0.486644 + 0.842893i 0.999882 0.0153538i $$-0.00488746\pi$$
−0.513238 + 0.858246i $$0.671554\pi$$
$$542$$ 380208. 658540.i 0.0555934 0.0962905i
$$543$$ 2.44984e6 4.24326e6i 0.356565 0.617589i
$$544$$ −809984. 1.40293e6i −0.117349 0.203254i
$$545$$ −748748. −0.107980
$$546$$ 0 0
$$547$$ 3.84707e6 0.549745 0.274873 0.961481i $$-0.411364\pi$$
0.274873 + 0.961481i $$0.411364\pi$$
$$548$$ −1.22344e6 2.11906e6i −0.174033 0.301434i
$$549$$ −1.48886e6 + 2.57878e6i −0.210826 + 0.365161i
$$550$$ −3.25227e6 + 5.63310e6i −0.458438 + 0.794037i
$$551$$ −584572. 1.01251e6i −0.0820274 0.142076i
$$552$$ 1.27411e6 0.177975
$$553$$ 0 0
$$554$$ 802024. 0.111023
$$555$$ −509886. 883148.i −0.0702653 0.121703i
$$556$$ −2.74768e6 + 4.75912e6i −0.376946 + 0.652890i
$$557$$ −2.50088e6 + 4.33165e6i −0.341550 + 0.591583i −0.984721 0.174140i $$-0.944285\pi$$
0.643171 + 0.765723i $$0.277619\pi$$
$$558$$ 1.15474e6 + 2.00006e6i 0.156999 + 0.271930i
$$559$$ 2.68774e6 0.363795
$$560$$ 0 0
$$561$$ 9.45403e6 1.26826
$$562$$ 2.18474e6 + 3.78408e6i 0.291782 + 0.505382i
$$563$$ 1.13886e6 1.97257e6i 0.151426 0.262277i −0.780326 0.625373i $$-0.784947\pi$$
0.931752 + 0.363096i $$0.118280\pi$$
$$564$$ −385344. + 667435.i −0.0510095 + 0.0883510i
$$565$$ −728182. 1.26125e6i −0.0959663 0.166219i
$$566$$ 7.25032e6 0.951297
$$567$$ 0 0
$$568$$ 581888. 0.0756778
$$569$$ −4.43490e6 7.68147e6i −0.574252 0.994634i −0.996122 0.0879781i $$-0.971959\pi$$
0.421870 0.906656i $$-0.361374\pi$$
$$570$$ −110448. + 191302.i −0.0142387 + 0.0246622i
$$571$$ −7.00509e6 + 1.21332e7i −0.899132 + 1.55734i −0.0705261 + 0.997510i $$0.522468\pi$$
−0.828606 + 0.559832i $$0.810866\pi$$
$$572$$ 1.68922e6 + 2.92581e6i 0.215871 + 0.373900i
$$573$$ −3.38764e6 −0.431033
$$574$$ 0 0
$$575$$ −5.41719e6 −0.683289
$$576$$ −165888. 287326.i −0.0208333 0.0360844i
$$577$$ 4.37663e6 7.58055e6i 0.547269 0.947897i −0.451192 0.892427i $$-0.649001\pi$$
0.998460 0.0554701i $$-0.0176657\pi$$
$$578$$ 2.16573e6 3.75116e6i 0.269641 0.467031i
$$579$$ 3.80226e6 + 6.58570e6i 0.471352 + 0.816405i
$$580$$ 2.06086e6 0.254378
$$581$$ 0 0
$$582$$ −769320. −0.0941455
$$583$$ 1.10735e7 + 1.91799e7i 1.34932 + 2.33709i
$$584$$ 2.35053e6 4.07123e6i 0.285189 0.493962i
$$585$$ −334854. + 579984.i −0.0404544 + 0.0700691i
$$586$$ −4.20061e6 7.27567e6i −0.505322 0.875244i
$$587$$ 1.06117e7 1.27113 0.635564 0.772048i $$-0.280768\pi$$
0.635564 + 0.772048i $$0.280768\pi$$
$$588$$ 0 0
$$589$$ −1.68221e6 −0.199798
$$590$$ −802672. 1.39027e6i −0.0949310 0.164425i
$$591$$ −2.21757e6 + 3.84095e6i −0.261162 + 0.452345i
$$592$$ −557824. + 966180.i −0.0654173 + 0.113306i
$$593$$ 942759. + 1.63291e6i 0.110094 + 0.190689i 0.915808 0.401616i $$-0.131551\pi$$
−0.805714 + 0.592305i $$0.798218\pi$$
$$594$$ 1.93622e6 0.225159
$$595$$ 0 0
$$596$$ −2.79773e6 −0.322619
$$597$$ 4.11649e6 + 7.12997e6i 0.472706 + 0.818751i
$$598$$ −1.40683e6 + 2.43670e6i −0.160875 + 0.278644i
$$599$$ −6.36281e6 + 1.10207e7i −0.724573 + 1.25500i 0.234576 + 0.972098i $$0.424630\pi$$
−0.959150 + 0.282900i $$0.908704\pi$$
$$600$$ 705312. + 1.22164e6i 0.0799840 + 0.138536i
$$601$$ −7.18846e6 −0.811801 −0.405900 0.913917i $$-0.633042\pi$$
−0.405900 + 0.913917i $$0.633042\pi$$
$$602$$ 0 0
$$603$$ 3.31873e6 0.371688
$$604$$ 3.62042e6 + 6.27074e6i 0.403800 + 0.699402i
$$605$$ 3.63798e6 6.30117e6i 0.404085 0.699895i
$$606$$ −662652. + 1.14775e6i −0.0733000 + 0.126959i
$$607$$ 5.42472e6 + 9.39589e6i 0.597593 + 1.03506i 0.993175 + 0.116631i $$0.0372095\pi$$
−0.395582 + 0.918431i $$0.629457\pi$$
$$608$$ 241664. 0.0265126
$$609$$ 0 0
$$610$$ 3.82325e6 0.416014
$$611$$ −850968. 1.47392e6i −0.0922168 0.159724i
$$612$$ 1.02514e6 1.77559e6i 0.110638 0.191630i
$$613$$ 2.45256e6 4.24795e6i 0.263614 0.456592i −0.703586 0.710610i $$-0.748419\pi$$
0.967199 + 0.254018i $$0.0817523\pi$$
$$614$$ 3.28209e6 + 5.68474e6i 0.351341 + 0.608541i
$$615$$ −2.46683e6 −0.262997
$$616$$ 0 0
$$617$$ 2.58445e6 0.273310 0.136655 0.990619i $$-0.456365\pi$$
0.136655 + 0.990619i $$0.456365\pi$$
$$618$$ 1.88150e6 + 3.25886e6i 0.198168 + 0.343237i
$$619$$ −2.49668e6 + 4.32438e6i −0.261901 + 0.453625i −0.966747 0.255735i $$-0.917683\pi$$
0.704846 + 0.709360i $$0.251016\pi$$
$$620$$ 1.48262e6 2.56798e6i 0.154900 0.268295i
$$621$$ 806274. + 1.39651e6i 0.0838984 + 0.145316i
$$622$$ −3.78093e6 −0.391852
$$623$$ 0 0
$$624$$ 732672. 0.0753266
$$625$$ −1.94255e6 3.36460e6i −0.198917 0.344535i
$$626$$ −830708. + 1.43883e6i −0.0847252 + 0.146748i
$$627$$ −705168. + 1.22139e6i −0.0716347 + 0.124075i
$$628$$ −3.99253e6 6.91526e6i −0.403970 0.699696i
$$629$$ −6.89436e6 −0.694812
$$630$$ 0 0
$$631$$ −1.18219e7 −1.18199 −0.590997 0.806674i $$-0.701265\pi$$
−0.590997 + 0.806674i $$0.701265\pi$$
$$632$$ 2.86080e6 + 4.95505e6i 0.284902 + 0.493464i
$$633$$ 1.40301e6 2.43008e6i 0.139172 0.241053i
$$634$$ 2.36963e6 4.10432e6i 0.234130 0.405525i
$$635$$ 2.41020e6 + 4.17459e6i 0.237202 + 0.410846i
$$636$$ 4.80298e6 0.470834
$$637$$ 0 0
$$638$$ 1.31578e7 1.27977
$$639$$ 368226. + 637786.i 0.0356749 + 0.0617907i
$$640$$ −212992. + 368913.i −0.0205548 + 0.0356020i
$$641$$ 2.73503e6 4.73722e6i 0.262916 0.455385i −0.704099 0.710102i $$-0.748649\pi$$
0.967016 + 0.254717i $$0.0819823\pi$$
$$642$$ −3.85992e6 6.68558e6i −0.369607 0.640179i
$$643$$ −9.64934e6 −0.920386 −0.460193 0.887819i $$-0.652220\pi$$
−0.460193 + 0.887819i $$0.652220\pi$$
$$644$$ 0 0
$$645$$ −1.97777e6 −0.187187
$$646$$ 746704. + 1.29333e6i 0.0703991 + 0.121935i
$$647$$ 146184. 253198.i 0.0137290 0.0237793i −0.859079 0.511843i $$-0.828963\pi$$
0.872808 + 0.488063i $$0.162296\pi$$
$$648$$ 209952. 363648.i 0.0196419 0.0340207i
$$649$$ −5.12475e6 8.87633e6i −0.477596 0.827221i
$$650$$ −3.11513e6 −0.289196
$$651$$ 0 0
$$652$$ −7.60941e6 −0.701022
$$653$$ −3.47040e6 6.01091e6i −0.318491 0.551642i 0.661683 0.749784i $$-0.269843\pi$$
−0.980173 + 0.198142i $$0.936509\pi$$
$$654$$ −518364. + 897833.i −0.0473904 + 0.0820826i
$$655$$ −838916. + 1.45305e6i −0.0764038 + 0.132335i
$$656$$ 1.34938e6 + 2.33719e6i 0.122426 + 0.212048i
$$657$$ 5.94977e6 0.537758
$$658$$ 0 0
$$659$$ −1.32912e7 −1.19221 −0.596104 0.802908i $$-0.703285\pi$$
−0.596104 + 0.802908i $$0.703285\pi$$
$$660$$ −1.24301e6 2.15295e6i −0.111074 0.192387i
$$661$$ 1.02609e6 1.77725e6i 0.0913448 0.158214i −0.816732 0.577017i $$-0.804217\pi$$
0.908077 + 0.418803i $$0.137550\pi$$
$$662$$ 2.74310e6 4.75118e6i 0.243274 0.421363i
$$663$$ 2.26384e6 + 3.92109e6i 0.200015 + 0.346436i
$$664$$ −411392. −0.0362106
$$665$$ 0 0
$$666$$ −1.41199e6 −0.123352
$$667$$ 5.47912e6 + 9.49012e6i 0.476866 + 0.825956i
$$668$$ 961792. 1.66587e6i 0.0833950 0.144444i
$$669$$ 5.79492e6 1.00371e7i 0.500590 0.867047i
$$670$$ −2.13054e6 3.69021e6i −0.183360 0.317588i
$$671$$ 2.44100e7 2.09296
$$672$$ 0 0
$$673$$ −1.57039e7 −1.33650 −0.668252 0.743935i $$-0.732957\pi$$
−0.668252 + 0.743935i $$0.732957\pi$$
$$674$$ 1.92704e6 + 3.33774e6i 0.163396 + 0.283010i
$$675$$ −892660. + 1.54613e6i −0.0754096 + 0.130613i
$$676$$ 2.16135e6 3.74357e6i 0.181911 0.315079i
$$677$$ −484767. 839641.i −0.0406501 0.0704080i 0.844985 0.534791i $$-0.179610\pi$$
−0.885635 + 0.464383i $$0.846276\pi$$
$$678$$ −2.01650e6 −0.168471
$$679$$ 0 0
$$680$$ −2.63245e6 −0.218317
$$681$$ −5.80073e6 1.00472e7i −0.479309 0.830187i
$$682$$ 9.46598e6 1.63956e7i 0.779300 1.34979i
$$683$$ 7.49539e6 1.29824e7i 0.614812 1.06489i −0.375605 0.926780i $$-0.622565\pi$$
0.990417 0.138106i $$-0.0441016\pi$$
$$684$$ 152928. + 264879.i 0.0124982 + 0.0216475i
$$685$$ −3.97618e6 −0.323772
$$686$$ 0 0
$$687$$ 6.10393e6 0.493421
$$688$$ 1.08186e6 + 1.87383e6i 0.0871361 + 0.150924i
$$689$$ −5.30329e6 + 9.18556e6i −0.425595 + 0.737153i
$$690$$ 1.03522e6 1.79305e6i 0.0827767 0.143373i
$$691$$ −3.58019e6 6.20107e6i −0.285240 0.494051i 0.687427 0.726253i $$-0.258740\pi$$
−0.972667 + 0.232203i $$0.925407\pi$$
$$692$$ −8.14198e6 −0.646346
$$693$$ 0 0
$$694$$ −1.03092e7 −0.812509
$$695$$ 4.46498e6 + 7.73357e6i 0.350637 + 0.607321i
$$696$$ 1.42675e6 2.47121e6i 0.111641 0.193369i
$$697$$ −8.33872e6 + 1.44431e7i −0.650156 + 1.12610i
$$698$$ 6.13503e6 + 1.06262e7i 0.476626 + 0.825541i
$$699$$ 1.00558e7 0.778437
$$700$$ 0 0
$$701$$ −91834.0 −0.00705844 −0.00352922 0.999994i $$-0.501123\pi$$
−0.00352922 + 0.999994i $$0.501123\pi$$
$$702$$ 463644. + 803055.i 0.0355093 + 0.0615039i
$$703$$ 514244. 890697.i 0.0392447 0.0679738i
$$704$$ −1.35987e6 + 2.35537e6i −0.103411 + 0.179113i
$$705$$ 626184. + 1.08458e6i 0.0474492 + 0.0821845i
$$706$$ −1.24058e7 −0.936725
$$707$$ 0 0
$$708$$ −2.22278e6 −0.166653
$$709$$ −1.10491e7 1.91375e7i −0.825487 1.42978i −0.901547 0.432681i $$-0.857567\pi$$
0.0760603 0.997103i $$-0.475766\pi$$
$$710$$ 472784. 818886.i 0.0351979 0.0609646i
$$711$$ −3.62070e6 + 6.27124e6i −0.268608 + 0.465242i
$$712$$ 3.92506e6 + 6.79840e6i 0.290166 + 0.502582i
$$713$$ 1.57671e7 1.16153
$$714$$ 0 0
$$715$$ 5.48995e6 0.401609
$$716$$ −3.90048e6 6.75583e6i −0.284338 0.492489i
$$717$$ −5.67880e6 + 9.83597e6i −0.412533 + 0.714528i
$$718$$ −655016. + 1.13452e6i −0.0474177 + 0.0821299i
$$719$$ 7.91940e6 + 1.37168e7i 0.571308 + 0.989534i 0.996432 + 0.0843990i $$0.0268970\pi$$
−0.425124 + 0.905135i $$0.639770\pi$$
$$720$$ −539136. −0.0387585
$$721$$ 0 0
$$722$$ 9.68161e6 0.691202
$$723$$ −4.26698e6 7.39063e6i −0.303581 0.525818i
$$724$$ −4.35528e6 + 7.54357e6i −0.308795 + 0.534848i
$$725$$ −6.06617e6 + 1.05069e7i −0.428617 + 0.742387i
$$726$$ −5.03721e6 8.72470e6i −0.354690 0.614340i
$$727$$ −6.31418e6 −0.443078 −0.221539 0.975151i $$-0.571108\pi$$
−0.221539 + 0.975151i $$0.571108\pi$$
$$728$$ 0 0
$$729$$ 531441. 0.0370370
$$730$$ −3.81961e6 6.61576e6i −0.265284 0.459486i
$$731$$ −6.68553e6 + 1.15797e7i −0.462746 + 0.801499i
$$732$$ 2.64686e6 4.58450e6i 0.182580 0.316238i
$$733$$ 3.46502e6 + 6.00158e6i 0.238202 + 0.412578i 0.960198 0.279319i $$-0.0901087\pi$$
−0.721996 + 0.691897i $$0.756775\pi$$
$$734$$ −1.14696e7 −0.785791
$$735$$ 0 0
$$736$$ −2.26509e6 −0.154131
$$737$$ −1.36027e7 2.35606e7i −0.922479 1.59778i
$$738$$ −1.70780e6 + 2.95800e6i −0.115424 + 0.199921i
$$739$$ −7.11656e6 + 1.23262e7i −0.479357 + 0.830270i −0.999720 0.0236749i $$-0.992463\pi$$
0.520363 + 0.853945i $$0.325797\pi$$
$$740$$ 906464. + 1.57004e6i 0.0608515 + 0.105398i
$$741$$ −675432. −0.0451894
$$742$$ 0 0
$$743$$ −5.94460e6 −0.395048 −0.197524 0.980298i $$-0.563290\pi$$
−0.197524 + 0.980298i $$0.563290\pi$$
$$744$$ −2.05286e6 3.55566e6i −0.135965 0.235499i
$$745$$ −2.27315e6 + 3.93722e6i −0.150051 + 0.259896i
$$746$$ 7.16059e6 1.24025e7i 0.471088 0.815948i
$$747$$ −260334. 450912.i −0.0170698 0.0295658i
$$748$$ −1.68072e7 −1.09835
$$749$$ 0 0
$$750$$ 5.21726e6 0.338680
$$751$$ 341376. + 591281.i 0.0220868 + 0.0382555i 0.876858 0.480750i $$-0.159636\pi$$
−0.854771 + 0.519006i $$0.826302\pi$$
$$752$$ 685056. 1.18655e6i 0.0441755 0.0765142i
$$753$$ 2.18878e6 3.79108e6i 0.140674 0.243655i
$$754$$ 3.15074e6 + 5.45725e6i 0.201830 + 0.349579i
$$755$$ 1.17664e7 0.751233
$$756$$ 0 0
$$757$$ 1.46333e7 0.928116 0.464058 0.885805i $$-0.346393\pi$$
0.464058 + 0.885805i $$0.346393\pi$$
$$758$$ 3.28470e6 + 5.68926e6i 0.207645 + 0.359652i
$$759$$ 6.60946e6 1.14479e7i 0.416448 0.721310i
$$760$$ 196352. 340092.i 0.0123311 0.0213581i
$$761$$ −5.81837e6 1.00777e7i −0.364200 0.630812i 0.624448 0.781067i $$-0.285324\pi$$
−0.988647 + 0.150254i $$0.951991\pi$$
$$762$$ 6.67440e6 0.416414
$$763$$ 0 0
$$764$$ 6.02246e6 0.373285
$$765$$ −1.66585e6 2.88533e6i −0.102916 0.178255i
$$766$$ 4.11395e6 7.12557e6i 0.253330 0.438781i
$$767$$ 2.45432e6 4.25101e6i 0.150641 0.260918i
$$768$$ 294912. + 510803.i 0.0180422 + 0.0312500i
$$769$$ −1.91472e7 −1.16759 −0.583793 0.811902i $$-0.698432\pi$$