# Properties

 Label 18.6.c.b.7.2 Level $18$ Weight $6$ Character 18.7 Analytic conductor $2.887$ Analytic rank $0$ Dimension $6$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,6,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 18.c (of order $$3$$, degree $$2$$, 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: $$2.88690875663$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.47347183152.3 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331$$ x^6 - 3*x^5 + 118*x^4 - 231*x^3 + 3700*x^2 - 3585*x + 32331 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}\cdot 3^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 7.2 Root $$0.500000 + 8.40123i$$ of defining polynomial Character $$\chi$$ $$=$$ 18.7 Dual form 18.6.c.b.13.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-2.00000 + 3.46410i) q^{2} +(-2.43381 - 15.3973i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-20.8014 - 36.0292i) q^{5} +(58.2054 + 22.3636i) q^{6} +(101.661 - 176.082i) q^{7} +64.0000 q^{8} +(-231.153 + 74.9483i) q^{9} +O(q^{10})$$ $$q+(-2.00000 + 3.46410i) q^{2} +(-2.43381 - 15.3973i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-20.8014 - 36.0292i) q^{5} +(58.2054 + 22.3636i) q^{6} +(101.661 - 176.082i) q^{7} +64.0000 q^{8} +(-231.153 + 74.9483i) q^{9} +166.412 q^{10} +(-235.168 + 407.323i) q^{11} +(-193.881 + 156.902i) q^{12} +(-241.506 - 418.300i) q^{13} +(406.643 + 704.326i) q^{14} +(-504.125 + 407.974i) q^{15} +(-128.000 + 221.703i) q^{16} +1259.86 q^{17} +(202.678 - 950.634i) q^{18} +1978.94 q^{19} +(-332.823 + 576.466i) q^{20} +(-2958.60 - 1136.75i) q^{21} +(-940.672 - 1629.29i) q^{22} +(-239.119 - 414.166i) q^{23} +(-155.764 - 985.427i) q^{24} +(697.100 - 1207.41i) q^{25} +1932.04 q^{26} +(1716.58 + 3376.72i) q^{27} -3253.14 q^{28} +(580.249 - 1005.02i) q^{29} +(-405.015 - 2562.29i) q^{30} +(1186.50 + 2055.07i) q^{31} +(-512.000 - 886.810i) q^{32} +(6844.02 + 2629.60i) q^{33} +(-2519.72 + 4364.28i) q^{34} -8458.76 q^{35} +(2887.74 + 2603.37i) q^{36} +8185.10 q^{37} +(-3957.89 + 6855.26i) q^{38} +(-5852.91 + 4736.60i) q^{39} +(-1331.29 - 2305.87i) q^{40} +(-8758.87 - 15170.8i) q^{41} +(9855.02 - 7975.40i) q^{42} +(-11435.0 + 19806.1i) q^{43} +7525.37 q^{44} +(7508.64 + 6769.22i) q^{45} +1912.95 q^{46} +(8685.43 - 15043.6i) q^{47} +(3725.15 + 1431.27i) q^{48} +(-12266.3 - 21245.9i) q^{49} +(2788.40 + 4829.65i) q^{50} +(-3066.26 - 19398.4i) q^{51} +(-3864.09 + 6692.80i) q^{52} -5390.58 q^{53} +(-15130.5 - 807.021i) q^{54} +19567.3 q^{55} +(6506.29 - 11269.2i) q^{56} +(-4816.38 - 30470.4i) q^{57} +(2321.00 + 4020.09i) q^{58} +(22281.8 + 38593.2i) q^{59} +(9686.05 + 3721.56i) q^{60} +(-2084.17 + 3609.88i) q^{61} -9491.97 q^{62} +(-10302.2 + 48321.1i) q^{63} +4096.00 q^{64} +(-10047.3 + 17402.5i) q^{65} +(-22797.3 + 18449.2i) q^{66} +(-1228.46 - 2127.76i) q^{67} +(-10078.9 - 17457.1i) q^{68} +(-5795.07 + 4689.79i) q^{69} +(16917.5 - 29302.0i) q^{70} +2184.37 q^{71} +(-14793.8 + 4796.69i) q^{72} +3037.34 q^{73} +(-16370.2 + 28354.0i) q^{74} +(-20287.5 - 7794.83i) q^{75} +(-15831.5 - 27421.0i) q^{76} +(47814.7 + 82817.5i) q^{77} +(-4702.24 - 29748.3i) q^{78} +(25266.2 - 43762.3i) q^{79} +10650.3 q^{80} +(47814.5 - 34649.1i) q^{81} +70070.9 q^{82} +(25913.9 - 44884.2i) q^{83} +(7917.55 + 50089.6i) q^{84} +(-26206.9 - 45391.7i) q^{85} +(-45740.1 - 79224.3i) q^{86} +(-16886.8 - 6488.23i) q^{87} +(-15050.7 + 26068.7i) q^{88} -20154.7 q^{89} +(-38466.5 + 12472.3i) q^{90} -98206.5 q^{91} +(-3825.91 + 6626.66i) q^{92} +(28754.8 - 23270.5i) q^{93} +(34741.7 + 60174.4i) q^{94} +(-41164.9 - 71299.6i) q^{95} +(-12408.4 + 10041.7i) q^{96} +(-40214.4 + 69653.3i) q^{97} +98130.4 q^{98} +(23831.7 - 111779. i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9}+O(q^{10})$$ 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9 $$6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9} + 432 q^{10} - 315 q^{11} - 96 q^{12} - 744 q^{13} - 528 q^{14} + 2286 q^{15} - 768 q^{16} + 2898 q^{17} + 1056 q^{18} + 2262 q^{19} - 864 q^{20} - 11076 q^{21} - 1260 q^{22} - 3168 q^{23} + 576 q^{24} - 2883 q^{25} + 5952 q^{26} + 18144 q^{27} + 4224 q^{28} - 5148 q^{29} - 14400 q^{30} - 8610 q^{31} - 3072 q^{32} + 17469 q^{33} - 5796 q^{34} + 2700 q^{35} - 1392 q^{36} + 39936 q^{37} - 4524 q^{38} - 49026 q^{39} - 3456 q^{40} + 5049 q^{41} + 41352 q^{42} - 31389 q^{43} + 10080 q^{44} + 2538 q^{45} + 25344 q^{46} + 12924 q^{47} - 768 q^{48} - 52857 q^{49} - 11532 q^{50} + 36837 q^{51} - 11904 q^{52} - 96048 q^{53} - 71892 q^{54} + 126252 q^{55} - 8448 q^{56} - 17469 q^{57} - 20592 q^{58} + 62955 q^{59} + 21024 q^{60} - 75966 q^{61} + 68880 q^{62} + 49578 q^{63} + 24576 q^{64} + 108702 q^{65} + 2952 q^{66} - 32991 q^{67} - 23184 q^{68} - 29250 q^{69} - 5400 q^{70} - 129672 q^{71} - 11328 q^{72} - 8466 q^{73} - 79872 q^{74} - 105483 q^{75} - 18096 q^{76} + 88740 q^{77} + 171720 q^{78} + 89202 q^{79} + 27648 q^{80} + 123435 q^{81} - 40392 q^{82} + 32634 q^{83} + 11808 q^{84} + 71388 q^{85} - 125556 q^{86} - 151524 q^{87} - 20160 q^{88} + 66132 q^{89} - 263088 q^{90} - 301836 q^{91} - 50688 q^{92} + 57678 q^{93} + 51696 q^{94} - 82944 q^{95} - 6144 q^{96} + 46245 q^{97} + 422856 q^{98} + 282168 q^{99}+O(q^{100})$$ 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9 + 432 * q^10 - 315 * q^11 - 96 * q^12 - 744 * q^13 - 528 * q^14 + 2286 * q^15 - 768 * q^16 + 2898 * q^17 + 1056 * q^18 + 2262 * q^19 - 864 * q^20 - 11076 * q^21 - 1260 * q^22 - 3168 * q^23 + 576 * q^24 - 2883 * q^25 + 5952 * q^26 + 18144 * q^27 + 4224 * q^28 - 5148 * q^29 - 14400 * q^30 - 8610 * q^31 - 3072 * q^32 + 17469 * q^33 - 5796 * q^34 + 2700 * q^35 - 1392 * q^36 + 39936 * q^37 - 4524 * q^38 - 49026 * q^39 - 3456 * q^40 + 5049 * q^41 + 41352 * q^42 - 31389 * q^43 + 10080 * q^44 + 2538 * q^45 + 25344 * q^46 + 12924 * q^47 - 768 * q^48 - 52857 * q^49 - 11532 * q^50 + 36837 * q^51 - 11904 * q^52 - 96048 * q^53 - 71892 * q^54 + 126252 * q^55 - 8448 * q^56 - 17469 * q^57 - 20592 * q^58 + 62955 * q^59 + 21024 * q^60 - 75966 * q^61 + 68880 * q^62 + 49578 * q^63 + 24576 * q^64 + 108702 * q^65 + 2952 * q^66 - 32991 * q^67 - 23184 * q^68 - 29250 * q^69 - 5400 * q^70 - 129672 * q^71 - 11328 * q^72 - 8466 * q^73 - 79872 * q^74 - 105483 * q^75 - 18096 * q^76 + 88740 * q^77 + 171720 * q^78 + 89202 * q^79 + 27648 * q^80 + 123435 * q^81 - 40392 * q^82 + 32634 * q^83 + 11808 * q^84 + 71388 * q^85 - 125556 * q^86 - 151524 * q^87 - 20160 * q^88 + 66132 * q^89 - 263088 * q^90 - 301836 * q^91 - 50688 * q^92 + 57678 * q^93 + 51696 * q^94 - 82944 * q^95 - 6144 * q^96 + 46245 * q^97 + 422856 * q^98 + 282168 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$$.

 $$n$$ $$11$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$3$$ −2.43381 15.3973i −0.156129 0.987737i
$$4$$ −8.00000 13.8564i −0.250000 0.433013i
$$5$$ −20.8014 36.0292i −0.372108 0.644509i 0.617782 0.786349i $$-0.288031\pi$$
−0.989890 + 0.141840i $$0.954698\pi$$
$$6$$ 58.2054 + 22.3636i 0.660063 + 0.253608i
$$7$$ 101.661 176.082i 0.784166 1.35822i −0.145330 0.989383i $$-0.546424\pi$$
0.929496 0.368832i $$-0.120242\pi$$
$$8$$ 64.0000 0.353553
$$9$$ −231.153 + 74.9483i −0.951247 + 0.308429i
$$10$$ 166.412 0.526239
$$11$$ −235.168 + 407.323i −0.585998 + 1.01498i 0.408752 + 0.912646i $$0.365964\pi$$
−0.994750 + 0.102333i $$0.967369\pi$$
$$12$$ −193.881 + 156.902i −0.388670 + 0.314540i
$$13$$ −241.506 418.300i −0.396341 0.686482i 0.596931 0.802293i $$-0.296387\pi$$
−0.993271 + 0.115811i $$0.963053\pi$$
$$14$$ 406.643 + 704.326i 0.554489 + 0.960403i
$$15$$ −504.125 + 407.974i −0.578508 + 0.468171i
$$16$$ −128.000 + 221.703i −0.125000 + 0.216506i
$$17$$ 1259.86 1.05730 0.528652 0.848839i $$-0.322698\pi$$
0.528652 + 0.848839i $$0.322698\pi$$
$$18$$ 202.678 950.634i 0.147443 0.691564i
$$19$$ 1978.94 1.25762 0.628810 0.777559i $$-0.283542\pi$$
0.628810 + 0.777559i $$0.283542\pi$$
$$20$$ −332.823 + 576.466i −0.186054 + 0.322255i
$$21$$ −2958.60 1136.75i −1.46399 0.562492i
$$22$$ −940.672 1629.29i −0.414363 0.717698i
$$23$$ −239.119 414.166i −0.0942529 0.163251i 0.815044 0.579400i $$-0.196713\pi$$
−0.909297 + 0.416149i $$0.863380\pi$$
$$24$$ −155.764 985.427i −0.0552000 0.349218i
$$25$$ 697.100 1207.41i 0.223072 0.386372i
$$26$$ 1932.04 0.560511
$$27$$ 1716.58 + 3376.72i 0.453164 + 0.891427i
$$28$$ −3253.14 −0.784166
$$29$$ 580.249 1005.02i 0.128121 0.221912i −0.794828 0.606835i $$-0.792439\pi$$
0.922949 + 0.384923i $$0.125772\pi$$
$$30$$ −405.015 2562.29i −0.0821614 0.519786i
$$31$$ 1186.50 + 2055.07i 0.221749 + 0.384081i 0.955339 0.295511i $$-0.0954901\pi$$
−0.733590 + 0.679592i $$0.762157\pi$$
$$32$$ −512.000 886.810i −0.0883883 0.153093i
$$33$$ 6844.02 + 2629.60i 1.09402 + 0.420344i
$$34$$ −2519.72 + 4364.28i −0.373813 + 0.647464i
$$35$$ −8458.76 −1.16718
$$36$$ 2887.74 + 2603.37i 0.371366 + 0.334795i
$$37$$ 8185.10 0.982923 0.491462 0.870899i $$-0.336463\pi$$
0.491462 + 0.870899i $$0.336463\pi$$
$$38$$ −3957.89 + 6855.26i −0.444636 + 0.770132i
$$39$$ −5852.91 + 4736.60i −0.616183 + 0.498660i
$$40$$ −1331.29 2305.87i −0.131560 0.227868i
$$41$$ −8758.87 15170.8i −0.813745 1.40945i −0.910226 0.414113i $$-0.864092\pi$$
0.0964809 0.995335i $$-0.469241\pi$$
$$42$$ 9855.02 7975.40i 0.862054 0.697636i
$$43$$ −11435.0 + 19806.1i −0.943119 + 1.63353i −0.183644 + 0.982993i $$0.558789\pi$$
−0.759475 + 0.650537i $$0.774544\pi$$
$$44$$ 7525.37 0.585998
$$45$$ 7508.64 + 6769.22i 0.552752 + 0.498319i
$$46$$ 1912.95 0.133294
$$47$$ 8685.43 15043.6i 0.573518 0.993362i −0.422683 0.906277i $$-0.638912\pi$$
0.996201 0.0870843i $$-0.0277550\pi$$
$$48$$ 3725.15 + 1431.27i 0.233367 + 0.0896641i
$$49$$ −12266.3 21245.9i −0.729833 1.26411i
$$50$$ 2788.40 + 4829.65i 0.157736 + 0.273206i
$$51$$ −3066.26 19398.4i −0.165076 1.04434i
$$52$$ −3864.09 + 6692.80i −0.198170 + 0.343241i
$$53$$ −5390.58 −0.263600 −0.131800 0.991276i $$-0.542076\pi$$
−0.131800 + 0.991276i $$0.542076\pi$$
$$54$$ −15130.5 807.021i −0.706103 0.0376617i
$$55$$ 19567.3 0.872218
$$56$$ 6506.29 11269.2i 0.277245 0.480202i
$$57$$ −4816.38 30470.4i −0.196351 1.24220i
$$58$$ 2321.00 + 4020.09i 0.0905951 + 0.156915i
$$59$$ 22281.8 + 38593.2i 0.833335 + 1.44338i 0.895379 + 0.445306i $$0.146905\pi$$
−0.0620431 + 0.998073i $$0.519762\pi$$
$$60$$ 9686.05 + 3721.56i 0.347351 + 0.133459i
$$61$$ −2084.17 + 3609.88i −0.0717147 + 0.124213i −0.899653 0.436606i $$-0.856180\pi$$
0.827938 + 0.560819i $$0.189514\pi$$
$$62$$ −9491.97 −0.313601
$$63$$ −10302.2 + 48321.1i −0.327023 + 1.53386i
$$64$$ 4096.00 0.125000
$$65$$ −10047.3 + 17402.5i −0.294963 + 0.510891i
$$66$$ −22797.3 + 18449.2i −0.644203 + 0.521336i
$$67$$ −1228.46 2127.76i −0.0334330 0.0579076i 0.848825 0.528674i $$-0.177311\pi$$
−0.882258 + 0.470767i $$0.843977\pi$$
$$68$$ −10078.9 17457.1i −0.264326 0.457826i
$$69$$ −5795.07 + 4689.79i −0.146533 + 0.118585i
$$70$$ 16917.5 29302.0i 0.412659 0.714747i
$$71$$ 2184.37 0.0514256 0.0257128 0.999669i $$-0.491814\pi$$
0.0257128 + 0.999669i $$0.491814\pi$$
$$72$$ −14793.8 + 4796.69i −0.336317 + 0.109046i
$$73$$ 3037.34 0.0667093 0.0333546 0.999444i $$-0.489381\pi$$
0.0333546 + 0.999444i $$0.489381\pi$$
$$74$$ −16370.2 + 28354.0i −0.347516 + 0.601915i
$$75$$ −20287.5 7794.83i −0.416462 0.160012i
$$76$$ −15831.5 27421.0i −0.314405 0.544565i
$$77$$ 47814.7 + 82817.5i 0.919040 + 1.59182i
$$78$$ −4702.24 29748.3i −0.0875121 0.553637i
$$79$$ 25266.2 43762.3i 0.455482 0.788918i −0.543234 0.839582i $$-0.682800\pi$$
0.998716 + 0.0506633i $$0.0161335\pi$$
$$80$$ 10650.3 0.186054
$$81$$ 47814.5 34649.1i 0.809743 0.586785i
$$82$$ 70070.9 1.15081
$$83$$ 25913.9 44884.2i 0.412893 0.715152i −0.582311 0.812966i $$-0.697852\pi$$
0.995205 + 0.0978135i $$0.0311849\pi$$
$$84$$ 7917.55 + 50089.6i 0.122431 + 0.774550i
$$85$$ −26206.9 45391.7i −0.393431 0.681442i
$$86$$ −45740.1 79224.3i −0.666886 1.15508i
$$87$$ −16886.8 6488.23i −0.239194 0.0919027i
$$88$$ −15050.7 + 26068.7i −0.207182 + 0.358849i
$$89$$ −20154.7 −0.269713 −0.134857 0.990865i $$-0.543057\pi$$
−0.134857 + 0.990865i $$0.543057\pi$$
$$90$$ −38466.5 + 12472.3i −0.500584 + 0.162308i
$$91$$ −98206.5 −1.24319
$$92$$ −3825.91 + 6626.66i −0.0471264 + 0.0816254i
$$93$$ 28754.8 23270.5i 0.344749 0.278996i
$$94$$ 34741.7 + 60174.4i 0.405538 + 0.702413i
$$95$$ −41164.9 71299.6i −0.467970 0.810547i
$$96$$ −12408.4 + 10041.7i −0.137416 + 0.111207i
$$97$$ −40214.4 + 69653.3i −0.433962 + 0.751644i −0.997210 0.0746433i $$-0.976218\pi$$
0.563248 + 0.826288i $$0.309552\pi$$
$$98$$ 98130.4 1.03214
$$99$$ 23831.7 111779.i 0.244380 1.14623i
$$100$$ −22307.2 −0.223072
$$101$$ −28450.2 + 49277.2i −0.277512 + 0.480665i −0.970766 0.240028i $$-0.922843\pi$$
0.693254 + 0.720694i $$0.256177\pi$$
$$102$$ 73330.7 + 28175.0i 0.697887 + 0.268141i
$$103$$ 98505.0 + 170616.i 0.914882 + 1.58462i 0.807074 + 0.590451i $$0.201050\pi$$
0.107808 + 0.994172i $$0.465617\pi$$
$$104$$ −15456.4 26771.2i −0.140128 0.242708i
$$105$$ 20587.0 + 130242.i 0.182230 + 1.15286i
$$106$$ 10781.2 18673.5i 0.0931967 0.161421i
$$107$$ −23482.4 −0.198282 −0.0991411 0.995073i $$-0.531610\pi$$
−0.0991411 + 0.995073i $$0.531610\pi$$
$$108$$ 33056.5 50799.5i 0.272708 0.419083i
$$109$$ −118550. −0.955727 −0.477863 0.878434i $$-0.658589\pi$$
−0.477863 + 0.878434i $$0.658589\pi$$
$$110$$ −39134.7 + 67783.2i −0.308375 + 0.534122i
$$111$$ −19921.0 126028.i −0.153463 0.970869i
$$112$$ 26025.1 + 45076.9i 0.196042 + 0.339554i
$$113$$ 223.401 + 386.942i 0.00164585 + 0.00285069i 0.866847 0.498574i $$-0.166143\pi$$
−0.865201 + 0.501425i $$0.832809\pi$$
$$114$$ 115185. + 44256.3i 0.830108 + 0.318943i
$$115$$ −9948.04 + 17230.5i −0.0701444 + 0.121494i
$$116$$ −18568.0 −0.128121
$$117$$ 87175.6 + 78590.9i 0.588749 + 0.530772i
$$118$$ −178254. −1.17851
$$119$$ 128078. 221838.i 0.829102 1.43605i
$$120$$ −32264.0 + 26110.3i −0.204534 + 0.165523i
$$121$$ −30082.4 52104.3i −0.186788 0.323527i
$$122$$ −8336.67 14439.5i −0.0507099 0.0878322i
$$123$$ −212272. + 171786.i −1.26511 + 1.02382i
$$124$$ 18983.9 32881.1i 0.110875 0.192040i
$$125$$ −188012. −1.07624
$$126$$ −146785. 132330.i −0.823673 0.742561i
$$127$$ 193803. 1.06623 0.533116 0.846042i $$-0.321021\pi$$
0.533116 + 0.846042i $$0.321021\pi$$
$$128$$ −8192.00 + 14189.0i −0.0441942 + 0.0765466i
$$129$$ 332790. + 127864.i 1.76075 + 0.676511i
$$130$$ −40189.3 69609.9i −0.208570 0.361254i
$$131$$ −48037.8 83203.8i −0.244571 0.423609i 0.717440 0.696620i $$-0.245314\pi$$
−0.962011 + 0.273011i $$0.911980\pi$$
$$132$$ −18315.4 115870.i −0.0914915 0.578812i
$$133$$ 201181. 348455.i 0.986183 1.70812i
$$134$$ 9827.70 0.0472813
$$135$$ 85953.0 132088.i 0.405907 0.623775i
$$136$$ 80631.0 0.373813
$$137$$ −116089. + 201071.i −0.528431 + 0.915269i 0.471020 + 0.882123i $$0.343886\pi$$
−0.999451 + 0.0331465i $$0.989447\pi$$
$$138$$ −4655.77 29454.3i −0.0208110 0.131659i
$$139$$ 80284.0 + 139056.i 0.352445 + 0.610453i 0.986677 0.162689i $$-0.0520169\pi$$
−0.634232 + 0.773143i $$0.718684\pi$$
$$140$$ 67670.1 + 117208.i 0.291794 + 0.505402i
$$141$$ −252770. 97118.8i −1.07072 0.411392i
$$142$$ −4368.73 + 7566.87i −0.0181817 + 0.0314916i
$$143$$ 227177. 0.929020
$$144$$ 12971.4 60840.6i 0.0521290 0.244505i
$$145$$ −48280.1 −0.190699
$$146$$ −6074.68 + 10521.7i −0.0235853 + 0.0408509i
$$147$$ −297275. + 240576.i −1.13466 + 0.918247i
$$148$$ −65480.8 113416.i −0.245731 0.425618i
$$149$$ 139592. + 241781.i 0.515105 + 0.892189i 0.999846 + 0.0175309i $$0.00558055\pi$$
−0.484741 + 0.874658i $$0.661086\pi$$
$$150$$ 67577.1 54688.3i 0.245229 0.198457i
$$151$$ 14288.8 24749.0i 0.0509981 0.0883314i −0.839399 0.543515i $$-0.817093\pi$$
0.890398 + 0.455184i $$0.150426\pi$$
$$152$$ 126652. 0.444636
$$153$$ −291221. + 94424.3i −1.00576 + 0.326103i
$$154$$ −382517. −1.29972
$$155$$ 49361.6 85496.9i 0.165029 0.285839i
$$156$$ 112455. + 43207.5i 0.369972 + 0.142150i
$$157$$ 62127.0 + 107607.i 0.201155 + 0.348411i 0.948901 0.315574i $$-0.102197\pi$$
−0.747746 + 0.663985i $$0.768864\pi$$
$$158$$ 101065. + 175049.i 0.322075 + 0.557850i
$$159$$ 13119.7 + 83000.3i 0.0411557 + 0.260367i
$$160$$ −21300.7 + 36893.9i −0.0657799 + 0.113934i
$$161$$ −97236.1 −0.295640
$$162$$ 24398.8 + 234932.i 0.0730435 + 0.703324i
$$163$$ 163892. 0.483159 0.241579 0.970381i $$-0.422335\pi$$
0.241579 + 0.970381i $$0.422335\pi$$
$$164$$ −140142. + 242733.i −0.406872 + 0.704724i
$$165$$ −47623.2 301284.i −0.136179 0.861521i
$$166$$ 103656. + 179537.i 0.291960 + 0.505689i
$$167$$ 81164.7 + 140581.i 0.225204 + 0.390065i 0.956381 0.292123i $$-0.0943618\pi$$
−0.731177 + 0.682188i $$0.761028\pi$$
$$168$$ −189351. 72752.0i −0.517599 0.198871i
$$169$$ 68996.6 119506.i 0.185828 0.321863i
$$170$$ 209655. 0.556395
$$171$$ −457439. + 148318.i −1.19631 + 0.387887i
$$172$$ 365921. 0.943119
$$173$$ 192179. 332863.i 0.488191 0.845572i −0.511716 0.859154i $$-0.670990\pi$$
0.999908 + 0.0135821i $$0.00432345\pi$$
$$174$$ 56249.6 45521.2i 0.140846 0.113983i
$$175$$ −141735. 245493.i −0.349851 0.605960i
$$176$$ −60203.0 104275.i −0.146500 0.253745i
$$177$$ 540001. 437008.i 1.29557 1.04847i
$$178$$ 40309.5 69818.1i 0.0953581 0.165165i
$$179$$ −511991. −1.19434 −0.597172 0.802113i $$-0.703709\pi$$
−0.597172 + 0.802113i $$0.703709\pi$$
$$180$$ 33727.9 158197.i 0.0775904 0.363928i
$$181$$ −285832. −0.648507 −0.324254 0.945970i $$-0.605113\pi$$
−0.324254 + 0.945970i $$0.605113\pi$$
$$182$$ 196413. 340197.i 0.439533 0.761294i
$$183$$ 60654.9 + 23304.7i 0.133887 + 0.0514419i
$$184$$ −15303.6 26506.7i −0.0333234 0.0577179i
$$185$$ −170262. 294902.i −0.365753 0.633503i
$$186$$ 23101.7 + 146151.i 0.0489622 + 0.309755i
$$187$$ −296279. + 513170.i −0.619578 + 1.07314i
$$188$$ −277934. −0.573518
$$189$$ 769087. + 41021.1i 1.56611 + 0.0835321i
$$190$$ 329319. 0.661809
$$191$$ −18626.1 + 32261.4i −0.0369436 + 0.0639882i −0.883906 0.467665i $$-0.845096\pi$$
0.846962 + 0.531653i $$0.178429\pi$$
$$192$$ −9968.90 63067.3i −0.0195162 0.123467i
$$193$$ −289378. 501217.i −0.559206 0.968573i −0.997563 0.0697722i $$-0.977773\pi$$
0.438357 0.898801i $$-0.355561\pi$$
$$194$$ −160857. 278613.i −0.306858 0.531493i
$$195$$ 292404. + 112347.i 0.550678 + 0.211581i
$$196$$ −196261. + 339934.i −0.364917 + 0.632054i
$$197$$ 234386. 0.430294 0.215147 0.976582i $$-0.430977\pi$$
0.215147 + 0.976582i $$0.430977\pi$$
$$198$$ 339552. + 306114.i 0.615521 + 0.554907i
$$199$$ 200551. 0.358997 0.179499 0.983758i $$-0.442552\pi$$
0.179499 + 0.983758i $$0.442552\pi$$
$$200$$ 44614.4 77274.4i 0.0788679 0.136603i
$$201$$ −29771.9 + 24093.6i −0.0519776 + 0.0420640i
$$202$$ −113801. 197109.i −0.196231 0.339882i
$$203$$ −117977. 204342.i −0.200936 0.348031i
$$204$$ −244262. + 197675.i −0.410943 + 0.332565i
$$205$$ −364394. + 631149.i −0.605601 + 1.04893i
$$206$$ −788040. −1.29384
$$207$$ 86314.2 + 77814.3i 0.140009 + 0.126222i
$$208$$ 123651. 0.198170
$$209$$ −465384. + 806069.i −0.736963 + 1.27646i
$$210$$ −492345. 189168.i −0.770410 0.296006i
$$211$$ 269826. + 467352.i 0.417232 + 0.722667i 0.995660 0.0930667i $$-0.0296670\pi$$
−0.578428 + 0.815733i $$0.696334\pi$$
$$212$$ 43124.6 + 74694.0i 0.0659000 + 0.114142i
$$213$$ −5316.34 33633.3i −0.00802905 0.0507950i
$$214$$ 46964.9 81345.5i 0.0701033 0.121423i
$$215$$ 951461. 1.40377
$$216$$ 109861. + 216110.i 0.160218 + 0.315167i
$$217$$ 482480. 0.695553
$$218$$ 237099. 410668.i 0.337900 0.585261i
$$219$$ −7392.32 46766.8i −0.0104153 0.0658912i
$$220$$ −156539. 271133.i −0.218054 0.377681i
$$221$$ −304263. 526999.i −0.419053 0.725821i
$$222$$ 476417. + 183048.i 0.648791 + 0.249278i
$$223$$ −442584. + 766578.i −0.595983 + 1.03227i 0.397424 + 0.917635i $$0.369904\pi$$
−0.993407 + 0.114638i $$0.963429\pi$$
$$224$$ −208201. −0.277245
$$225$$ −70643.3 + 331344.i −0.0930282 + 0.436337i
$$226$$ −1787.21 −0.00232758
$$227$$ −159067. + 275512.i −0.204887 + 0.354875i −0.950097 0.311955i $$-0.899016\pi$$
0.745210 + 0.666830i $$0.232349\pi$$
$$228$$ −383679. + 310501.i −0.488799 + 0.395572i
$$229$$ −246934. 427703.i −0.311166 0.538956i 0.667449 0.744656i $$-0.267386\pi$$
−0.978615 + 0.205700i $$0.934053\pi$$
$$230$$ −39792.2 68922.1i −0.0495996 0.0859090i
$$231$$ 1.15879e6 937779.i 1.42881 1.15630i
$$232$$ 37136.0 64321.4i 0.0452976 0.0784577i
$$233$$ 1.16189e6 1.40208 0.701041 0.713121i $$-0.252719\pi$$
0.701041 + 0.713121i $$0.252719\pi$$
$$234$$ −446598. + 144803.i −0.533184 + 0.172878i
$$235$$ −722678. −0.853641
$$236$$ 356508. 617491.i 0.416668 0.721690i
$$237$$ −735313. 282521.i −0.850358 0.326723i
$$238$$ 512313. + 887352.i 0.586264 + 1.01544i
$$239$$ 579263. + 1.00331e6i 0.655965 + 1.13617i 0.981651 + 0.190687i $$0.0610716\pi$$
−0.325685 + 0.945478i $$0.605595\pi$$
$$240$$ −25920.9 163986.i −0.0290484 0.183772i
$$241$$ 410557. 711106.i 0.455335 0.788663i −0.543372 0.839492i $$-0.682853\pi$$
0.998707 + 0.0508285i $$0.0161862\pi$$
$$242$$ 240659. 0.264158
$$243$$ −649873. 651885.i −0.706013 0.708198i
$$244$$ 66693.4 0.0717147
$$245$$ −510314. + 883889.i −0.543153 + 0.940768i
$$246$$ −170540. 1.07890e6i −0.179675 1.13670i
$$247$$ −477926. 827792.i −0.498446 0.863334i
$$248$$ 75935.7 + 131525.i 0.0784002 + 0.135793i
$$249$$ −754165. 289764.i −0.770847 0.296174i
$$250$$ 376024. 651292.i 0.380509 0.659061i
$$251$$ −852357. −0.853959 −0.426980 0.904261i $$-0.640422\pi$$
−0.426980 + 0.904261i $$0.640422\pi$$
$$252$$ 751974. 243817.i 0.745936 0.241860i
$$253$$ 224933. 0.220928
$$254$$ −387606. + 671354.i −0.376970 + 0.652931i
$$255$$ −635126. + 513990.i −0.611659 + 0.494999i
$$256$$ −32768.0 56755.8i −0.0312500 0.0541266i
$$257$$ −650171. 1.12613e6i −0.614037 1.06354i −0.990553 0.137133i $$-0.956211\pi$$
0.376515 0.926410i $$-0.377122\pi$$
$$258$$ −1.10852e6 + 897091.i −1.03679 + 0.839049i
$$259$$ 832103. 1.44124e6i 0.770775 1.33502i
$$260$$ 321515. 0.294963
$$261$$ −58801.8 + 275803.i −0.0534305 + 0.250609i
$$262$$ 384302. 0.345875
$$263$$ 572288. 991232.i 0.510182 0.883662i −0.489748 0.871864i $$-0.662911\pi$$
0.999930 0.0117977i $$-0.00375542\pi$$
$$264$$ 438017. + 168294.i 0.386796 + 0.148614i
$$265$$ 112132. + 194218.i 0.0980876 + 0.169893i
$$266$$ 804723. + 1.39382e6i 0.697336 + 1.20782i
$$267$$ 49052.9 + 310329.i 0.0421101 + 0.266406i
$$268$$ −19655.4 + 34044.1i −0.0167165 + 0.0289538i
$$269$$ 1.54095e6 1.29840 0.649199 0.760619i $$-0.275104\pi$$
0.649199 + 0.760619i $$0.275104\pi$$
$$270$$ 285659. + 561925.i 0.238473 + 0.469104i
$$271$$ 1.42397e6 1.17782 0.588908 0.808200i $$-0.299558\pi$$
0.588908 + 0.808200i $$0.299558\pi$$
$$272$$ −161262. + 279314.i −0.132163 + 0.228913i
$$273$$ 239016. + 1.51211e6i 0.194098 + 1.22794i
$$274$$ −464355. 804286.i −0.373657 0.647193i
$$275$$ 327871. + 567889.i 0.261440 + 0.452827i
$$276$$ 111344. + 42780.5i 0.0879822 + 0.0338044i
$$277$$ −798009. + 1.38219e6i −0.624897 + 1.08235i 0.363664 + 0.931530i $$0.381526\pi$$
−0.988561 + 0.150823i $$0.951808\pi$$
$$278$$ −642272. −0.498433
$$279$$ −428286. 386110.i −0.329400 0.296962i
$$280$$ −541361. −0.412659
$$281$$ −200767. + 347738.i −0.151679 + 0.262716i −0.931845 0.362857i $$-0.881801\pi$$
0.780166 + 0.625573i $$0.215135\pi$$
$$282$$ 841968. 681382.i 0.630483 0.510232i
$$283$$ −535582. 927656.i −0.397521 0.688527i 0.595898 0.803060i $$-0.296796\pi$$
−0.993419 + 0.114533i $$0.963463\pi$$
$$284$$ −17474.9 30267.5i −0.0128564 0.0222680i
$$285$$ −997634. + 807358.i −0.727544 + 0.588781i
$$286$$ −454355. + 786966.i −0.328458 + 0.568906i
$$287$$ −3.56173e6 −2.55244
$$288$$ 184815. + 166615.i 0.131298 + 0.118368i
$$289$$ 167390. 0.117892
$$290$$ 96560.2 167247.i 0.0674222 0.116779i
$$291$$ 1.17035e6 + 449669.i 0.810181 + 0.311287i
$$292$$ −24298.7 42086.6i −0.0166773 0.0288860i
$$293$$ 358830. + 621511.i 0.244185 + 0.422941i 0.961902 0.273394i $$-0.0881462\pi$$
−0.717717 + 0.696335i $$0.754813\pi$$
$$294$$ −238831. 1.51094e6i −0.161147 1.01948i
$$295$$ 926986. 1.60559e6i 0.620181 1.07418i
$$296$$ 523846. 0.347516
$$297$$ −1.77910e6 94892.7i −1.17033 0.0624226i
$$298$$ −1.11674e6 −0.728469
$$299$$ −115497. + 200047.i −0.0747125 + 0.129406i
$$300$$ 54291.6 + 343470.i 0.0348281 + 0.220336i
$$301$$ 2.32499e6 + 4.02700e6i 1.47912 + 2.56192i
$$302$$ 57155.3 + 98995.9i 0.0360611 + 0.0624597i
$$303$$ 827978. + 318125.i 0.518098 + 0.199063i
$$304$$ −253305. + 438737.i −0.157202 + 0.272283i
$$305$$ 173415. 0.106742
$$306$$ 255346. 1.19767e6i 0.155892 0.731193i
$$307$$ −2.25621e6 −1.36626 −0.683131 0.730296i $$-0.739382\pi$$
−0.683131 + 0.730296i $$0.739382\pi$$
$$308$$ 765035. 1.32508e6i 0.459520 0.795912i
$$309$$ 2.38728e6 1.93196e6i 1.42235 1.15107i
$$310$$ 197447. + 341988.i 0.116693 + 0.202118i
$$311$$ −897190. 1.55398e6i −0.525997 0.911054i −0.999541 0.0302837i $$-0.990359\pi$$
0.473544 0.880770i $$-0.342974\pi$$
$$312$$ −374586. + 303142.i −0.217854 + 0.176303i
$$313$$ 281895. 488257.i 0.162640 0.281701i −0.773175 0.634193i $$-0.781332\pi$$
0.935815 + 0.352492i $$0.114666\pi$$
$$314$$ −497016. −0.284476
$$315$$ 1.95527e6 633969.i 1.11027 0.359991i
$$316$$ −808517. −0.455482
$$317$$ 1.59153e6 2.75662e6i 0.889544 1.54074i 0.0491288 0.998792i $$-0.484356\pi$$
0.840415 0.541943i $$-0.182311\pi$$
$$318$$ −313761. 120553.i −0.173993 0.0668512i
$$319$$ 272912. + 472698.i 0.150157 + 0.260080i
$$320$$ −85202.7 147575.i −0.0465134 0.0805636i
$$321$$ 57151.9 + 361566.i 0.0309576 + 0.195851i
$$322$$ 194472. 336836.i 0.104524 0.181042i
$$323$$ 2.49319e6 1.32969
$$324$$ −862627. 385345.i −0.456521 0.203933i
$$325$$ −673414. −0.353650
$$326$$ −327785. + 567740.i −0.170822 + 0.295873i
$$327$$ 288528. + 1.82534e6i 0.149217 + 0.944006i
$$328$$ −560567. 970931.i −0.287702 0.498315i
$$329$$ −1.76593e6 3.05869e6i −0.899466 1.55792i
$$330$$ 1.13892e6 + 437596.i 0.575718 + 0.221202i
$$331$$ 3762.47 6516.79i 0.00188757 0.00326937i −0.865080 0.501634i $$-0.832733\pi$$
0.866968 + 0.498364i $$0.166066\pi$$
$$332$$ −829246. −0.412893
$$333$$ −1.89201e6 + 613459.i −0.935003 + 0.303162i
$$334$$ −649318. −0.318487
$$335$$ −51107.6 + 88520.9i −0.0248813 + 0.0430957i
$$336$$ 630721. 510425.i 0.304782 0.246652i
$$337$$ 734831. + 1.27277e6i 0.352463 + 0.610483i 0.986680 0.162671i $$-0.0520111\pi$$
−0.634218 + 0.773154i $$0.718678\pi$$
$$338$$ 275986. + 478023.i 0.131400 + 0.227592i
$$339$$ 5414.14 4381.51i 0.00255876 0.00207074i
$$340$$ −419310. + 726267.i −0.196715 + 0.340721i
$$341$$ −1.11610e6 −0.519779
$$342$$ 401088. 1.88125e6i 0.185427 0.869724i
$$343$$ −1.57078e6 −0.720909
$$344$$ −731842. + 1.26759e6i −0.333443 + 0.577540i
$$345$$ 289515. + 111237.i 0.130955 + 0.0503155i
$$346$$ 768715. + 1.33145e6i 0.345203 + 0.597910i
$$347$$ 1.31149e6 + 2.27156e6i 0.584709 + 1.01275i 0.994912 + 0.100751i $$0.0321246\pi$$
−0.410203 + 0.911994i $$0.634542\pi$$
$$348$$ 45191.0 + 285897.i 0.0200034 + 0.126550i
$$349$$ −582327. + 1.00862e6i −0.255919 + 0.443265i −0.965145 0.261716i $$-0.915711\pi$$
0.709225 + 0.704982i $$0.249045\pi$$
$$350$$ 1.13388e6 0.494764
$$351$$ 997918. 1.53354e6i 0.432341 0.664398i
$$352$$ 481624. 0.207182
$$353$$ −1.57339e6 + 2.72518e6i −0.672045 + 1.16402i 0.305278 + 0.952263i $$0.401251\pi$$
−0.977323 + 0.211753i $$0.932083\pi$$
$$354$$ 433838. + 2.74463e6i 0.184001 + 1.16406i
$$355$$ −45438.0 78700.9i −0.0191359 0.0331443i
$$356$$ 161238. + 279272.i 0.0674283 + 0.116789i
$$357$$ −3.72742e6 1.43215e6i −1.54788 0.594726i
$$358$$ 1.02398e6 1.77359e6i 0.422264 0.731383i
$$359$$ −720847. −0.295194 −0.147597 0.989048i $$-0.547154\pi$$
−0.147597 + 0.989048i $$0.547154\pi$$
$$360$$ 480553. + 433230.i 0.195427 + 0.176182i
$$361$$ 1.44012e6 0.581607
$$362$$ 571664. 990152.i 0.229282 0.397128i
$$363$$ −729050. + 590000.i −0.290396 + 0.235009i
$$364$$ 785652. + 1.36079e6i 0.310797 + 0.538316i
$$365$$ −63181.1 109433.i −0.0248230 0.0429947i
$$366$$ −202040. + 163505.i −0.0788378 + 0.0638012i
$$367$$ −41258.2 + 71461.4i −0.0159899 + 0.0276953i −0.873910 0.486088i $$-0.838423\pi$$
0.857920 + 0.513784i $$0.171757\pi$$
$$368$$ 122429. 0.0471264
$$369$$ 3.16166e6 + 2.85032e6i 1.20879 + 1.08975i
$$370$$ 1.36209e6 0.517253
$$371$$ −548010. + 949181.i −0.206706 + 0.358026i
$$372$$ −552484. 212275.i −0.206996 0.0795318i
$$373$$ −2.65152e6 4.59256e6i −0.986784 1.70916i −0.633724 0.773560i $$-0.718474\pi$$
−0.353060 0.935601i $$-0.614859\pi$$
$$374$$ −1.18511e6 2.05268e6i −0.438108 0.758826i
$$375$$ 457586. + 2.89487e6i 0.168033 + 1.06304i
$$376$$ 555868. 962791.i 0.202769 0.351206i
$$377$$ −560534. −0.203118
$$378$$ −1.68028e6 + 2.58215e6i −0.604855 + 0.929507i
$$379$$ −49534.8 −0.0177138 −0.00885691 0.999961i $$-0.502819\pi$$
−0.00885691 + 0.999961i $$0.502819\pi$$
$$380$$ −658638. + 1.14079e6i −0.233985 + 0.405274i
$$381$$ −471681. 2.98404e6i −0.166470 1.05316i
$$382$$ −74504.6 129046.i −0.0261231 0.0452465i
$$383$$ 1.92179e6 + 3.32863e6i 0.669434 + 1.15949i 0.978063 + 0.208311i $$0.0667968\pi$$
−0.308628 + 0.951183i $$0.599870\pi$$
$$384$$ 238409. + 91601.3i 0.0825078 + 0.0317010i
$$385$$ 1.98923e6 3.44545e6i 0.683963 1.18466i
$$386$$ 2.31502e6 0.790837
$$387$$ 1.15881e6 5.43527e6i 0.393311 1.84478i
$$388$$ 1.28686e6 0.433962
$$389$$ 1.96659e6 3.40623e6i 0.658930 1.14130i −0.321963 0.946752i $$-0.604343\pi$$
0.980893 0.194548i $$-0.0623240\pi$$
$$390$$ −973991. + 788224.i −0.324260 + 0.262415i
$$391$$ −301257. 521792.i −0.0996540 0.172606i
$$392$$ −785044. 1.35974e6i −0.258035 0.446930i
$$393$$ −1.16420e6 + 942154.i −0.380229 + 0.307709i
$$394$$ −468771. + 811935.i −0.152132 + 0.263500i
$$395$$ −2.10229e6 −0.677953
$$396$$ −1.73951e6 + 564014.i −0.557429 + 0.180739i
$$397$$ 1.48840e6 0.473960 0.236980 0.971514i $$-0.423842\pi$$
0.236980 + 0.971514i $$0.423842\pi$$
$$398$$ −401101. + 694727.i −0.126925 + 0.219840i
$$399$$ −5.85490e6 2.24956e6i −1.84114 0.707402i
$$400$$ 178458. + 309098.i 0.0557680 + 0.0965930i
$$401$$ 1.84020e6 + 3.18731e6i 0.571483 + 0.989837i 0.996414 + 0.0846115i $$0.0269649\pi$$
−0.424931 + 0.905226i $$0.639702\pi$$
$$402$$ −23918.8 151320.i −0.00738200 0.0467015i
$$403$$ 573091. 992622.i 0.175776 0.304454i
$$404$$ 910407. 0.277512
$$405$$ −2.24299e6 1.00197e6i −0.679500 0.303540i
$$406$$ 943817. 0.284166
$$407$$ −1.92487e6 + 3.33398e6i −0.575991 + 0.997646i
$$408$$ −196241. 1.24150e6i −0.0583632 0.369229i
$$409$$ −290013. 502318.i −0.0857254 0.148481i 0.819975 0.572400i $$-0.193987\pi$$
−0.905700 + 0.423919i $$0.860654\pi$$
$$410$$ −1.45758e6 2.52460e6i −0.428225 0.741707i
$$411$$ 3.37849e6 + 1.29808e6i 0.986549 + 0.379050i
$$412$$ 1.57608e6 2.72985e6i 0.457441 0.792311i
$$413$$ 9.06073e6 2.61389
$$414$$ −442185. + 143373.i −0.126795 + 0.0411117i
$$415$$ −2.15619e6 −0.614563
$$416$$ −247302. + 428339.i −0.0700638 + 0.121354i
$$417$$ 1.94569e6 1.57459e6i 0.547940 0.443433i
$$418$$ −1.86154e6 3.22427e6i −0.521112 0.902592i
$$419$$ 759450. + 1.31541e6i 0.211331 + 0.366037i 0.952131 0.305689i $$-0.0988868\pi$$
−0.740800 + 0.671726i $$0.765553\pi$$
$$420$$ 1.63999e6 1.32720e6i 0.453647 0.367124i
$$421$$ −2.70128e6 + 4.67875e6i −0.742787 + 1.28654i 0.208435 + 0.978036i $$0.433163\pi$$
−0.951222 + 0.308508i $$0.900170\pi$$
$$422$$ −2.15861e6 −0.590055
$$423$$ −880172. + 4.12834e6i −0.239175 + 1.12182i
$$424$$ −344997. −0.0931967
$$425$$ 878248. 1.52117e6i 0.235855 0.408513i
$$426$$ 127142. + 48850.3i 0.0339441 + 0.0130420i
$$427$$ 423756. + 733967.i 0.112472 + 0.194808i
$$428$$ 187859. + 325382.i 0.0495705 + 0.0858587i
$$429$$ −552908. 3.49792e6i −0.145047 0.917627i
$$430$$ −1.90292e6 + 3.29596e6i −0.496306 + 0.859628i
$$431$$ −3.04614e6 −0.789871 −0.394935 0.918709i $$-0.629233\pi$$
−0.394935 + 0.918709i $$0.629233\pi$$
$$432$$ −968350. 51649.3i −0.249645 0.0133154i
$$433$$ −1.07293e6 −0.275011 −0.137505 0.990501i $$-0.543908\pi$$
−0.137505 + 0.990501i $$0.543908\pi$$
$$434$$ −964960. + 1.67136e6i −0.245915 + 0.425937i
$$435$$ 117505. + 743383.i 0.0297737 + 0.188360i
$$436$$ 948397. + 1.64267e6i 0.238932 + 0.413842i
$$437$$ −473203. 819612.i −0.118534 0.205307i
$$438$$ 176790. + 67925.9i 0.0440323 + 0.0169180i
$$439$$ −3.81738e6 + 6.61190e6i −0.945376 + 1.63744i −0.190380 + 0.981710i $$0.560972\pi$$
−0.754996 + 0.655729i $$0.772361\pi$$
$$440$$ 1.25231e6 0.308375
$$441$$ 4.42774e6 + 3.99171e6i 1.08414 + 0.977378i
$$442$$ 2.43411e6 0.592630
$$443$$ 3.30067e6 5.71693e6i 0.799085 1.38406i −0.121127 0.992637i $$-0.538651\pi$$
0.920213 0.391419i $$-0.128016\pi$$
$$444$$ −1.58693e6 + 1.28426e6i −0.382033 + 0.309169i
$$445$$ 419248. + 726159.i 0.100362 + 0.173833i
$$446$$ −1.77034e6 3.06631e6i −0.421424 0.729927i
$$447$$ 3.38303e6 2.73779e6i 0.800824 0.648085i
$$448$$ 416402. 721230.i 0.0980208 0.169777i
$$449$$ −5.52311e6 −1.29291 −0.646454 0.762953i $$-0.723749\pi$$
−0.646454 + 0.762953i $$0.723749\pi$$
$$450$$ −1.00652e6 907403.i −0.234310 0.211236i
$$451$$ 8.23922e6 1.90741
$$452$$ 3574.42 6191.07i 0.000822923 0.00142534i
$$453$$ −415844. 159775.i −0.0952104 0.0365816i
$$454$$ −636267. 1.10205e6i −0.144877 0.250935i
$$455$$ 2.04284e6 + 3.53830e6i 0.462600 + 0.801246i
$$456$$ −308248. 1.95010e6i −0.0694206 0.439183i
$$457$$ −706717. + 1.22407e6i −0.158291 + 0.274167i −0.934252 0.356613i $$-0.883932\pi$$
0.775962 + 0.630780i $$0.217265\pi$$
$$458$$ 1.97547e6 0.440056
$$459$$ 2.16266e6 + 4.25420e6i 0.479132 + 0.942509i
$$460$$ 318337. 0.0701444
$$461$$ −4.25416e6 + 7.36841e6i −0.932312 + 1.61481i −0.152953 + 0.988234i $$0.548878\pi$$
−0.779359 + 0.626578i $$0.784455\pi$$
$$462$$ 930976. + 5.88973e6i 0.202924 + 1.28378i
$$463$$ −2.04077e6 3.53472e6i −0.442427 0.766307i 0.555442 0.831555i $$-0.312549\pi$$
−0.997869 + 0.0652489i $$0.979216\pi$$
$$464$$ 148544. + 257285.i 0.0320302 + 0.0554779i
$$465$$ −1.43656e6 551952.i −0.308099 0.118377i
$$466$$ −2.32377e6 + 4.02489e6i −0.495711 + 0.858597i
$$467$$ −5.38239e6 −1.14204 −0.571022 0.820935i $$-0.693453\pi$$
−0.571022 + 0.820935i $$0.693453\pi$$
$$468$$ 391582. 1.83667e6i 0.0826435 0.387629i
$$469$$ −499545. −0.104868
$$470$$ 1.44536e6 2.50343e6i 0.301808 0.522746i
$$471$$ 1.50565e6 1.21848e6i 0.312732 0.253085i
$$472$$ 1.42603e6 + 2.46996e6i 0.294629 + 0.510312i
$$473$$ −5.37831e6 9.31550e6i −1.10533 1.91449i
$$474$$ 2.44931e6 1.98216e6i 0.500723 0.405221i
$$475$$ 1.37952e6 2.38940e6i 0.280540 0.485909i
$$476$$ −4.09850e6 −0.829102
$$477$$ 1.24605e6 404014.i 0.250749 0.0813019i
$$478$$ −4.63410e6 −0.927675
$$479$$ 4.29153e6 7.43315e6i 0.854621 1.48025i −0.0223760 0.999750i $$-0.507123\pi$$
0.876997 0.480497i $$-0.159544\pi$$
$$480$$ 619907. + 238180.i 0.122807 + 0.0471848i
$$481$$ −1.97675e6 3.42383e6i −0.389573 0.674760i
$$482$$ 1.64223e6 + 2.84442e6i 0.321970 + 0.557669i
$$483$$ 236655. + 1.49717e6i 0.0461580 + 0.292014i
$$484$$ −481319. + 833668.i −0.0933941 + 0.161763i
$$485$$ 3.34607e6 0.645922
$$486$$ 3.55794e6 947458.i 0.683295 0.181957i
$$487$$ −3.96670e6 −0.757891 −0.378946 0.925419i $$-0.623713\pi$$
−0.378946 + 0.925419i $$0.623713\pi$$
$$488$$ −133387. + 231033.i −0.0253550 + 0.0439161i
$$489$$ −398884. 2.52350e6i −0.0754352 0.477234i
$$490$$ −2.04125e6 3.53556e6i −0.384067 0.665224i
$$491$$ −2.88205e6 4.99185e6i −0.539507 0.934454i −0.998931 0.0462362i $$-0.985277\pi$$
0.459424 0.888217i $$-0.348056\pi$$
$$492$$ 4.07851e6 + 1.56704e6i 0.759606 + 0.291855i
$$493$$ 731033. 1.26619e6i 0.135463 0.234628i
$$494$$ 3.82341e6 0.704909
$$495$$ −4.52305e6 + 1.46654e6i −0.829695 + 0.269017i
$$496$$ −607486. −0.110875
$$497$$ 222064. 384627.i 0.0403262 0.0698471i
$$498$$ 2.51210e6 2.03298e6i 0.453904 0.367332i
$$499$$ 2.32003e6 + 4.01841e6i 0.417102 + 0.722442i 0.995647 0.0932088i $$-0.0297124\pi$$
−0.578544 + 0.815651i $$0.696379\pi$$
$$500$$ 1.50409e6 + 2.60517e6i 0.269061 + 0.466026i
$$501$$ 1.96703e6 1.59187e6i 0.350120 0.283343i
$$502$$ 1.70471e6 2.95265e6i 0.301920 0.522941i
$$503$$ −2.73360e6 −0.481743 −0.240872 0.970557i $$-0.577433\pi$$
−0.240872 + 0.970557i $$0.577433\pi$$
$$504$$ −659340. + 3.09255e6i −0.115620 + 0.542301i
$$505$$ 2.36722e6 0.413057
$$506$$ −449865. + 779189.i −0.0781099 + 0.135290i
$$507$$ −2.00799e6 771506.i −0.346929 0.133297i
$$508$$ −1.55042e6 2.68541e6i −0.266558 0.461692i
$$509$$ 2.97841e6 + 5.15877e6i 0.509555 + 0.882574i 0.999939 + 0.0110680i $$0.00352313\pi$$
−0.490384 + 0.871506i $$0.663144\pi$$
$$510$$ −510262. 3.22812e6i −0.0868696 0.549572i
$$511$$ 308778. 534820.i 0.0523112 0.0906056i
$$512$$ 262144. 0.0441942
$$513$$ 3.39702e6 + 6.68234e6i 0.569908 + 1.12108i
$$514$$ 5.20137e6 0.868380
$$515$$ 4.09809e6 7.09810e6i 0.680869 1.17930i
$$516$$ −890584. 5.63419e6i −0.147248 0.931553i
$$517$$ 4.08507e6 + 7.07555e6i 0.672161 + 1.16422i
$$518$$ 3.32841e6 + 5.76498e6i 0.545020 + 0.944003i
$$519$$ −5.59292e6 2.14890e6i −0.911424 0.350186i
$$520$$ −643029. + 1.11376e6i −0.104285 + 0.180627i
$$521$$ −1.11813e7 −1.80468 −0.902339 0.431027i $$-0.858151\pi$$
−0.902339 + 0.431027i $$0.858151\pi$$
$$522$$ −837804. 755301.i −0.134576 0.121323i
$$523$$ 4.60970e6 0.736917 0.368458 0.929644i $$-0.379886\pi$$
0.368458 + 0.929644i $$0.379886\pi$$
$$524$$ −768604. + 1.33126e6i −0.122285 + 0.211804i
$$525$$ −3.43497e6 + 2.77982e6i −0.543907 + 0.440169i
$$526$$ 2.28915e6 + 3.96493e6i 0.360753 + 0.624843i
$$527$$ 1.49482e6 + 2.58910e6i 0.234456 + 0.406090i
$$528$$ −1.45902e6 + 1.18075e6i −0.227760 + 0.184320i
$$529$$ 3.10382e6 5.37597e6i 0.482233 0.835252i
$$530$$ −897054. −0.138717
$$531$$ −8.04299e6 7.25095e6i −1.23789 1.11599i
$$532$$ −6.43779e6 −0.986183
$$533$$ −4.23063e6 + 7.32767e6i −0.645041 + 1.11724i
$$534$$ −1.17312e6 450733.i −0.178028 0.0684016i
$$535$$ 488468. + 846052.i 0.0737823 + 0.127795i
$$536$$ −78621.6 136177.i −0.0118203 0.0204734i
$$537$$ 1.24609e6 + 7.88327e6i 0.186472 + 1.17970i
$$538$$ −3.08190e6 + 5.33801e6i −0.459053 + 0.795103i
$$539$$ 1.15386e7 1.71072
$$540$$ −2.51789e6 134298.i −0.371579 0.0198191i
$$541$$ −8.65572e6 −1.27148 −0.635741 0.771902i $$-0.719305\pi$$
−0.635741 + 0.771902i $$0.719305\pi$$
$$542$$ −2.84794e6 + 4.93277e6i −0.416421 + 0.721262i
$$543$$ 695662. + 4.40104e6i 0.101251 + 0.640554i
$$544$$ −645048. 1.11726e6i −0.0934534 0.161866i
$$545$$ 2.46600e6 + 4.27124e6i 0.355633 + 0.615975i
$$546$$ −5.71615e6 2.19625e6i −0.820582 0.315283i
$$547$$ −581626. + 1.00741e6i −0.0831143 + 0.143958i −0.904586 0.426291i $$-0.859820\pi$$
0.821472 + 0.570249i $$0.193153\pi$$
$$548$$ 3.71484e6 0.528431
$$549$$ 211207. 990641.i 0.0299073 0.140277i
$$550$$ −2.62297e6 −0.369731
$$551$$ 1.14828e6 1.98888e6i 0.161127 0.279081i
$$552$$ −370884. + 300147.i −0.0518073 + 0.0419262i
$$553$$ −5.13715e6 8.89781e6i −0.714347 1.23729i
$$554$$ −3.19204e6 5.52877e6i −0.441869 0.765339i
$$555$$ −4.12631e6 + 3.33931e6i −0.568629 + 0.460176i
$$556$$ 1.28454e6 2.22489e6i 0.176223 0.305227i
$$557$$ 1.23037e7 1.68034 0.840168 0.542326i $$-0.182456\pi$$
0.840168 + 0.542326i $$0.182456\pi$$
$$558$$ 2.19410e6 711407.i 0.298312 0.0967236i
$$559$$ 1.10465e7 1.49519
$$560$$ 1.08272e6 1.87533e6i 0.145897 0.252701i
$$561$$ 8.62251e6 + 3.31293e6i 1.15672 + 0.444432i
$$562$$ −803067. 1.39095e6i −0.107253 0.185768i
$$563$$ 2.76949e6 + 4.79690e6i 0.368239 + 0.637808i 0.989290 0.145962i $$-0.0466276\pi$$
−0.621052 + 0.783770i $$0.713294\pi$$
$$564$$ 676439. + 4.27943e6i 0.0895429 + 0.566484i
$$565$$ 9294.13 16097.9i 0.00122486 0.00212152i
$$566$$ 4.28466e6 0.562180
$$567$$ −1.24020e6 1.19417e7i −0.162007 1.55994i
$$568$$ 139799. 0.0181817
$$569$$ −6.91495e6 + 1.19770e7i −0.895382 + 1.55085i −0.0620514 + 0.998073i $$0.519764\pi$$
−0.833331 + 0.552775i $$0.813569\pi$$
$$570$$ −801501. 5.07062e6i −0.103328 0.653693i
$$571$$ −990947. 1.71637e6i −0.127192 0.220303i 0.795396 0.606091i $$-0.207263\pi$$
−0.922588 + 0.385787i $$0.873930\pi$$
$$572$$ −1.81742e6 3.14786e6i −0.232255 0.402278i
$$573$$ 542071. + 208274.i 0.0689715 + 0.0265001i
$$574$$ 7.12346e6 1.23382e7i 0.902425 1.56305i
$$575$$ −666760. −0.0841007
$$576$$ −946803. + 306988.i −0.118906 + 0.0385536i
$$577$$ 9.36673e6 1.17125 0.585623 0.810583i $$-0.300850\pi$$
0.585623 + 0.810583i $$0.300850\pi$$
$$578$$ −334780. + 579855.i −0.0416811 + 0.0721938i
$$579$$ −7.01309e6 + 5.67550e6i −0.869387 + 0.703571i
$$580$$ 386241. + 668989.i 0.0476747 + 0.0825750i
$$581$$ −5.26886e6 9.12593e6i −0.647554 1.12160i
$$582$$ −3.89839e6 + 3.15486e6i −0.477066 + 0.386076i
$$583$$ 1.26769e6 2.19570e6i 0.154469 0.267549i
$$584$$ 194390. 0.0235853
$$585$$ 1.01818e6 4.77567e6i 0.123009 0.576958i
$$586$$ −2.87064e6 −0.345330
$$587$$ 929269. 1.60954e6i 0.111313 0.192800i −0.804987 0.593293i $$-0.797828\pi$$
0.916300 + 0.400493i $$0.131161\pi$$
$$588$$ 5.71172e6 + 2.19455e6i 0.681277 + 0.261759i
$$589$$ 2.34801e6 + 4.06687e6i 0.278876 + 0.483028i
$$590$$ 3.70795e6 + 6.42235e6i 0.438534 + 0.759563i
$$591$$ −570451. 3.60890e6i −0.0671815 0.425017i
$$592$$ −1.04769e6 + 1.81466e6i −0.122865 + 0.212809i
$$593$$ 1.50844e6 0.176154 0.0880770 0.996114i $$-0.471928\pi$$
0.0880770 + 0.996114i $$0.471928\pi$$
$$594$$ 3.88692e6 5.97320e6i 0.452001 0.694610i
$$595$$ −1.06568e7 −1.23406
$$596$$ 2.23348e6 3.86850e6i 0.257553 0.446094i
$$597$$ −488103. 3.08793e6i −0.0560500 0.354595i
$$598$$ −461989. 800188.i −0.0528297 0.0915038i
$$599$$ −6.50791e6 1.12720e7i −0.741096 1.28362i −0.951997 0.306108i $$-0.900973\pi$$
0.210901 0.977507i $$-0.432360\pi$$
$$600$$ −1.29840e6 498869.i −0.147242 0.0565729i
$$601$$ 6.92629e6 1.19967e7i 0.782194 1.35480i −0.148467 0.988917i $$-0.547434\pi$$
0.930661 0.365882i $$-0.119233\pi$$
$$602$$ −1.85999e7 −2.09180
$$603$$ 443435. + 399767.i 0.0496634 + 0.0447727i
$$604$$ −457243. −0.0509981
$$605$$ −1.25152e6 + 2.16769e6i −0.139011 + 0.240773i
$$606$$ −2.75797e6 + 2.23195e6i −0.305076 + 0.246890i
$$607$$ 4.75435e6 + 8.23478e6i 0.523745 + 0.907153i 0.999618 + 0.0276388i $$0.00879883\pi$$
−0.475873 + 0.879514i $$0.657868\pi$$
$$608$$ −1.01322e6 1.75495e6i −0.111159 0.192533i
$$609$$ −2.85919e6 + 2.31386e6i −0.312391 + 0.252810i
$$610$$ −346830. + 600726.i −0.0377391 + 0.0653660i
$$611$$ −8.39032e6 −0.909234
$$612$$ 3.63815e6 + 3.27987e6i 0.392646 + 0.353980i
$$613$$ −1.65462e7 −1.77848 −0.889238 0.457445i $$-0.848765\pi$$
−0.889238 + 0.457445i $$0.848765\pi$$
$$614$$ 4.51242e6 7.81574e6i 0.483046 0.836661i
$$615$$ 1.06049e7 + 4.07458e6i 1.13062 + 0.434405i
$$616$$ 3.06014e6 + 5.30032e6i 0.324930 + 0.562795i
$$617$$ 2.75765e6 + 4.77638e6i 0.291626 + 0.505111i 0.974194 0.225711i $$-0.0724705\pi$$
−0.682569 + 0.730822i $$0.739137\pi$$
$$618$$ 1.91794e6 + 1.21337e7i 0.202006 + 1.27797i
$$619$$ −1.24124e6 + 2.14989e6i −0.130205 + 0.225522i −0.923756 0.382982i $$-0.874897\pi$$
0.793550 + 0.608505i $$0.208230\pi$$
$$620$$ −1.57957e6 −0.165029
$$621$$ 988056. 1.51839e6i 0.102814 0.157999i
$$622$$ 7.17752e6 0.743872
$$623$$ −2.04895e6 + 3.54888e6i −0.211500 + 0.366329i
$$624$$ −300943. 1.90389e6i −0.0309402 0.195740i
$$625$$ 1.73248e6 + 3.00074e6i 0.177406 + 0.307276i
$$626$$ 1.12758e6 + 1.95303e6i 0.115004 + 0.199192i
$$627$$ 1.35439e7 + 5.20383e6i 1.37587 + 0.528633i
$$628$$ 994032. 1.72171e6i 0.100578 0.174205i
$$629$$ 1.03121e7 1.03925
$$630$$ −1.71440e6 + 8.04119e6i −0.172092 + 0.807177i
$$631$$ −9.16852e6 −0.916697 −0.458349 0.888772i $$-0.651559\pi$$
−0.458349 + 0.888772i $$0.651559\pi$$
$$632$$ 1.61703e6 2.80078e6i 0.161037 0.278925i
$$633$$ 6.53925e6 5.29204e6i 0.648662 0.524945i
$$634$$ 6.36613e6 + 1.10265e7i 0.629003 + 1.08946i
$$635$$ −4.03138e6 6.98256e6i −0.396753 0.687196i
$$636$$ 1.04513e6 845794.i 0.102453 0.0829128i
$$637$$ −5.92476e6 + 1.02620e7i −0.578525 + 1.00204i
$$638$$ −2.18330e6 −0.212354
$$639$$ −504923. + 163715.i −0.0489185 + 0.0158612i
$$640$$ 681622. 0.0657799
$$641$$ 994072. 1.72178e6i 0.0955593 0.165514i −0.814283 0.580469i $$-0.802869\pi$$
0.909842 + 0.414955i $$0.136203\pi$$
$$642$$ −1.36680e6 525152.i −0.130879 0.0502860i
$$643$$ 2.62237e6 + 4.54208e6i 0.250130 + 0.433239i 0.963562 0.267487i $$-0.0861932\pi$$
−0.713431 + 0.700725i $$0.752860\pi$$
$$644$$ 777889. + 1.34734e6i 0.0739099 + 0.128016i
$$645$$ −2.31568e6 1.46499e7i −0.219169 1.38655i
$$646$$ −4.98638e6 + 8.63667e6i −0.470115 + 0.814263i
$$647$$ 9.94212e6 0.933723 0.466862 0.884330i $$-0.345385\pi$$
0.466862 + 0.884330i $$0.345385\pi$$
$$648$$ 3.06013e6 2.21754e6i 0.286287 0.207460i
$$649$$ −2.09598e7 −1.95333
$$650$$ 1.34683e6 2.33278e6i 0.125034 0.216566i
$$651$$ −1.17427e6 7.42889e6i −0.108596 0.687023i
$$652$$ −1.31114e6 2.27096e6i −0.120790 0.209214i
$$653$$ 1.21132e6 + 2.09806e6i 0.111167 + 0.192547i 0.916241 0.400628i $$-0.131208\pi$$
−0.805074 + 0.593174i $$0.797875\pi$$
$$654$$ −6.90023e6 2.65120e6i −0.630840 0.242380i
$$655$$ −1.99851e6 + 3.46152e6i −0.182013 + 0.315256i
$$656$$ 4.48454e6 0.406872
$$657$$ −702091. + 227643.i −0.0634570 + 0.0205751i
$$658$$ 1.41275e7 1.27204
$$659$$ −7.70304e6 + 1.33421e7i −0.690953 + 1.19677i 0.280573 + 0.959833i $$0.409476\pi$$
−0.971526 + 0.236933i $$0.923858\pi$$
$$660$$ −3.79373e6 + 3.07016e6i −0.339005 + 0.274347i
$$661$$ −3.40975e6 5.90586e6i −0.303542 0.525751i 0.673393 0.739284i $$-0.264836\pi$$
−0.976936 + 0.213534i $$0.931503\pi$$
$$662$$ 15049.9 + 26067.2i 0.00133471 + 0.00231179i
$$663$$ −7.37384e6 + 5.96745e6i −0.651493 + 0.527236i
$$664$$ 1.65849e6 2.87259e6i 0.145980 0.252845i
$$665$$ −1.67394e7 −1.46786
$$666$$ 1.65894e6 7.78104e6i 0.144925 0.679754i
$$667$$ −554995. −0.0483030
$$668$$ 1.29864e6 2.24930e6i 0.112602 0.195032i
$$669$$ 1.28804e7 + 4.94889e6i 1.11266 + 0.427506i
$$670$$ −204430. 354084.i −0.0175937 0.0304733i
$$671$$ −980259. 1.69786e6i −0.0840494 0.145578i
$$672$$ 506723. + 3.20573e6i 0.0432860 + 0.273845i
$$673$$ 114441. 198218.i 0.00973969 0.0168696i −0.861114 0.508411i $$-0.830233\pi$$
0.870854 + 0.491541i $$0.163566\pi$$
$$674$$ −5.87865e6 −0.498457
$$675$$ 5.27373e6 + 281287.i 0.445511 + 0.0237624i
$$676$$ −2.20789e6 −0.185828
$$677$$ 1.00487e7 1.74048e7i 0.842629 1.45948i −0.0450356 0.998985i $$-0.514340\pi$$
0.887665 0.460491i $$-0.152327\pi$$
$$678$$ 4349.73 + 27518.2i 0.000363403 + 0.00229903i
$$679$$ 8.17644e6 + 1.41620e7i 0.680597 + 1.17883i
$$680$$ −1.67724e6 2.90507e6i −0.139099 0.240926i
$$681$$ 4.62928e6 + 1.77865e6i 0.382512 + 0.146968i
$$682$$ 2.23221e6 3.86629e6i 0.183769 0.318298i
$$683$$ 1.34916e7 1.10665 0.553325 0.832965i $$-0.313359\pi$$
0.553325 + 0.832965i $$0.313359\pi$$
$$684$$ 5.71467e6 + 5.15191e6i 0.467037 + 0.421045i
$$685$$ 9.65924e6 0.786533
$$686$$ 3.14156e6 5.44135e6i 0.254880 0.441465i
$$687$$ −5.98447e6 + 4.84307e6i −0.483764 + 0.391497i
$$688$$ −2.92737e6 5.07035e6i −0.235780 0.408382i
$$689$$ 1.30185e6 + 2.25488e6i 0.104475 + 0.180957i
$$690$$ −964366. + 780435.i −0.0771115 + 0.0624042i
$$691$$ −2.16664e6 + 3.75273e6i −0.172620 + 0.298987i −0.939335 0.343001i $$-0.888557\pi$$
0.766715 + 0.641988i $$0.221890\pi$$
$$692$$ −6.14972e6 −0.488191
$$693$$ −1.72595e7 1.55599e7i −1.36520 1.23076i
$$694$$ −1.04919e7 −0.826903
$$695$$ 3.34005e6 5.78513e6i 0.262295 0.454309i
$$696$$ −1.08076e6 415247.i −0.0845678 0.0324925i
$$697$$ −1.10349e7 1.91131e7i −0.860376 1.49021i
$$698$$ −2.32931e6 4.03448e6i −0.180962 0.313436i
$$699$$ −2.82781e6 1.78899e7i −0.218906 1.38489i
$$700$$ −2.26777e6 + 3.92789e6i −0.174926 + 0.302980i
$$701$$ −4.00999e6 −0.308211 −0.154106 0.988054i $$-0.549250\pi$$
−0.154106 + 0.988054i $$0.549250\pi$$
$$702$$ 3.31652e6 + 6.52398e6i 0.254003 + 0.499654i
$$703$$ 1.61978e7 1.23614
$$704$$ −963248. + 1.66839e6i −0.0732498 + 0.126872i
$$705$$ 1.75886e6 + 1.11273e7i 0.133278 + 0.843172i
$$706$$ −6.29354e6 1.09007e7i −0.475208 0.823084i
$$707$$ 5.78454e6 + 1.00191e7i 0.435231 + 0.753843i
$$708$$ −1.03754e7 3.98641e6i −0.777893 0.298881i
$$709$$ −2.57127e6 + 4.45358e6i −0.192102 + 0.332731i −0.945947 0.324322i $$-0.894864\pi$$
0.753844 + 0.657053i $$0.228197\pi$$
$$710$$ 363504. 0.0270622
$$711$$ −2.56044e6 + 1.20094e7i −0.189951 + 0.890940i
$$712$$ −1.28990e6 −0.0953581
$$713$$ 567428. 982813.i 0.0418010 0.0724014i
$$714$$ 1.24159e7 1.00479e7i 0.911453 0.737614i
$$715$$ −4.72562e6 8.18501e6i −0.345695 0.598762i
$$716$$ 4.09593e6 + 7.09435e6i 0.298586 + 0.517166i
$$717$$ 1.40385e7 1.13610e7i 1.01982 0.825310i
$$718$$ 1.44169e6 2.49709e6i 0.104367 0.180769i
$$719$$ −1.15318e6 −0.0831906 −0.0415953 0.999135i $$-0.513244\pi$$
−0.0415953 + 0.999135i $$0.513244\pi$$
$$720$$ −2.46186e6 + 798225.i −0.176983 + 0.0573844i
$$721$$ 4.00564e7 2.86968
$$722$$ −2.88023e6 + 4.98871e6i −0.205629 + 0.356160i
$$723$$ −1.19483e7 4.59077e6i −0.850083 0.326618i
$$724$$ 2.28666e6 + 3.96061e6i 0.162127 + 0.280812i
$$725$$ −808984. 1.40120e6i −0.0571603 0.0990046i
$$726$$ −585720. 3.70550e6i −0.0412428 0.260919i
$$727$$ 9.27449e6 1.60639e7i 0.650810 1.12724i −0.332117 0.943238i $$-0.607763\pi$$
0.982927 0.183997i $$-0.0589038\pi$$
$$728$$ −6.28522e6 −0.439533
$$729$$ −8.45558e6 + 1.15929e7i −0.589284 + 0.807926i
$$730$$ 505449. 0.0351051
$$731$$ −1.44065e7 + 2.49529e7i −0.997163 + 1.72714i
$$732$$ −162319. 1.02690e6i −0.0111968 0.0708352i
$$733$$ 2.05765e6 + 3.56395e6i 0.141453 + 0.245003i 0.928044 0.372471i $$-0.121489\pi$$
−0.786591 + 0.617474i $$0.788156\pi$$
$$734$$ −165033. 285845.i −0.0113066 0.0195835i
$$735$$ 1.48515e7 + 5.70623e6i 1.01403 + 0.389610i
$$736$$ −244858. + 424106.i −0.0166617 + 0.0288589i
$$737$$ 1.15558e6 0.0783666
$$738$$ −1.61971e7 + 5.25170e6i −1.09470 + 0.354943i
$$739$$ −2.27852e7 −1.53477 −0.767384 0.641188i $$-0.778442\pi$$
−0.767384 + 0.641188i $$0.778442\pi$$
$$740$$ −2.72419e6 + 4.71844e6i −0.182877 + 0.316752i
$$741$$ −1.15826e7 + 9.37345e6i −0.774924 + 0.627125i
$$742$$ −2.19204e6 3.79672e6i −0.146163 0.253162i
$$743$$ 1.05194e7 + 1.82202e7i 0.699068 + 1.21082i 0.968790 + 0.247884i $$0.0797351\pi$$
−0.269721 + 0.962938i $$0.586932\pi$$
$$744$$ 1.84031e6 1.48931e6i 0.121887 0.0986400i
$$745$$ 5.80745e6 1.00588e7i 0.383349 0.663980i
$$746$$ 2.12121e7 1.39552
$$747$$ −2.62609e6 + 1.23173e7i −0.172190 + 0.807635i
$$748$$ 9.48092e6 0.619578
$$749$$ −2.38724e6 + 4.13482e6i −0.155486 + 0.269310i
$$750$$ −1.09433e7 4.20462e6i −0.710387 0.272944i
$$751$$ −1.03484e7 1.79240e7i −0.669537 1.15967i −0.978034 0.208446i $$-0.933159\pi$$
0.308497 0.951225i $$-0.400174\pi$$
$$752$$ 2.22347e6 + 3.85116e6i 0.143379 + 0.248340i
$$753$$ 2.07448e6 + 1.31240e7i 0.133328 + 0.843487i
$$754$$ 1.12107e6 1.94175e6i 0.0718131 0.124384i
$$755$$ −1.18891e6 −0.0759072
$$756$$ −5.58429e6 1.09850e7i −0.355356 0.699027i
$$757$$ 1.22154e7 0.774761 0.387380 0.921920i $$-0.373380\pi$$
0.387380 + 0.921920i $$0.373380\pi$$
$$758$$ 99069.5 171593.i 0.00626278 0.0108475i
$$759$$ −547444. 3.46335e6i −0.0344933 0.218219i
$$760$$ −2.63455e6 4.56318e6i −0.165452 0.286572i
$$761$$ −642893.