# Properties

 Label 26.8.c.b.3.2 Level $26$ Weight $8$ Character 26.3 Analytic conductor $8.122$ Analytic rank $0$ Dimension $8$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,8,Mod(3,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("26.3");

S:= CuspForms(chi, 8);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 26.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: $$8.12201066259$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} + 4654x^{6} + 7012369x^{4} + 3763719168x^{2} + 637953638400$$ x^8 + 4654*x^6 + 7012369*x^4 + 3763719168*x^2 + 637953638400 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{6}\cdot 3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 3.2 Root $$-18.4011i$$ of defining polynomial Character $$\chi$$ $$=$$ 26.3 Dual form 26.8.c.b.9.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(4.00000 + 6.92820i) q^{2} +(-15.9358 - 27.6017i) q^{3} +(-32.0000 + 55.4256i) q^{4} -54.4265 q^{5} +(127.487 - 220.813i) q^{6} +(556.354 - 963.633i) q^{7} -512.000 q^{8} +(585.599 - 1014.29i) q^{9} +O(q^{10})$$ $$q+(4.00000 + 6.92820i) q^{2} +(-15.9358 - 27.6017i) q^{3} +(-32.0000 + 55.4256i) q^{4} -54.4265 q^{5} +(127.487 - 220.813i) q^{6} +(556.354 - 963.633i) q^{7} -512.000 q^{8} +(585.599 - 1014.29i) q^{9} +(-217.706 - 377.078i) q^{10} +(-3566.84 - 6177.94i) q^{11} +2039.79 q^{12} +(7565.86 + 2346.53i) q^{13} +8901.66 q^{14} +(867.331 + 1502.26i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(10252.8 - 17758.4i) q^{17} +9369.59 q^{18} +(-14035.8 + 24310.8i) q^{19} +(1741.65 - 3016.62i) q^{20} -35463.8 q^{21} +(28534.7 - 49423.6i) q^{22} +(-16961.2 - 29377.7i) q^{23} +(8159.14 + 14132.0i) q^{24} -75162.8 q^{25} +(14006.2 + 61804.0i) q^{26} -107031. q^{27} +(35606.6 + 61672.5i) q^{28} +(87734.9 + 151961. i) q^{29} +(-6938.65 + 12018.1i) q^{30} +15690.1 q^{31} +(16384.0 - 28377.9i) q^{32} +(-113681. + 196901. i) q^{33} +164045. q^{34} +(-30280.4 + 52447.2i) q^{35} +(37478.3 + 64914.4i) q^{36} +(-998.478 - 1729.41i) q^{37} -224573. q^{38} +(-55800.0 - 246224. i) q^{39} +27866.4 q^{40} +(-111820. - 193678. i) q^{41} +(-141855. - 245701. i) q^{42} +(268966. - 465862. i) q^{43} +456555. q^{44} +(-31872.1 + 55204.1i) q^{45} +(135690. - 235022. i) q^{46} +542249. q^{47} +(-65273.1 + 113056. i) q^{48} +(-207288. - 359033. i) q^{49} +(-300651. - 520743. i) q^{50} -653549. q^{51} +(-372166. + 344254. i) q^{52} +1.85685e6 q^{53} +(-428125. - 741535. i) q^{54} +(194131. + 336244. i) q^{55} +(-284853. + 493380. i) q^{56} +894691. q^{57} +(-701879. + 1.21569e6i) q^{58} +(665225. - 1.15220e6i) q^{59} -111018. q^{60} +(-1.43331e6 + 2.48257e6i) q^{61} +(62760.3 + 108704. i) q^{62} +(-651601. - 1.12861e6i) q^{63} +262144. q^{64} +(-411784. - 127714. i) q^{65} -1.81890e6 q^{66} +(1.41579e6 + 2.45222e6i) q^{67} +(656181. + 1.13654e6i) q^{68} +(-540583. + 936317. i) q^{69} -484486. q^{70} +(800929. - 1.38725e6i) q^{71} +(-299827. + 519315. i) q^{72} +1.39213e6 q^{73} +(7987.82 - 13835.3i) q^{74} +(1.19778e6 + 2.07462e6i) q^{75} +(-898294. - 1.55589e6i) q^{76} -7.93770e6 q^{77} +(1.48269e6 - 1.37149e6i) q^{78} -2.33505e6 q^{79} +(111466. + 193064. i) q^{80} +(424927. + 735994. i) q^{81} +(894559. - 1.54942e6i) q^{82} +2.37338e6 q^{83} +(1.13484e6 - 1.96560e6i) q^{84} +(-558025. + 966528. i) q^{85} +4.30345e6 q^{86} +(2.79625e6 - 4.84325e6i) q^{87} +(1.82622e6 + 3.16311e6i) q^{88} +(-3.52575e6 - 6.10678e6i) q^{89} -509954. q^{90} +(6.47050e6 - 5.98521e6i) q^{91} +2.17104e6 q^{92} +(-250034. - 433072. i) q^{93} +(2.16899e6 + 3.75681e6i) q^{94} +(763922. - 1.32315e6i) q^{95} -1.04437e6 q^{96} +(-4.25685e6 + 7.37308e6i) q^{97} +(1.65830e6 - 2.87226e6i) q^{98} -8.35495e6 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9}+O(q^{10})$$ 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9 $$8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9} + 2224 q^{10} - 7392 q^{11} - 25818 q^{13} - 8768 q^{14} + 15528 q^{15} - 16384 q^{16} + 28316 q^{17} - 83424 q^{18} - 99888 q^{19} - 17792 q^{20} + 182148 q^{21} + 59136 q^{22} - 33388 q^{23} + 173756 q^{25} - 156000 q^{26} + 212544 q^{27} - 35072 q^{28} + 93140 q^{29} - 124224 q^{30} + 622320 q^{31} + 131072 q^{32} + 238638 q^{33} + 453056 q^{34} + 141544 q^{35} - 333696 q^{36} - 9636 q^{37} - 1598208 q^{38} - 22932 q^{39} - 284672 q^{40} + 82892 q^{41} + 728592 q^{42} - 569264 q^{43} + 946176 q^{44} - 2303394 q^{45} + 267104 q^{46} - 1148400 q^{47} - 717798 q^{49} + 695024 q^{50} - 5459856 q^{51} + 404352 q^{52} + 2470700 q^{53} + 850176 q^{54} - 1092512 q^{55} + 280576 q^{56} + 7056924 q^{57} - 745120 q^{58} + 231504 q^{59} - 1987584 q^{60} + 685684 q^{61} + 2489280 q^{62} - 5951712 q^{63} + 2097152 q^{64} - 6216678 q^{65} + 3818208 q^{66} + 3271056 q^{67} + 1812224 q^{68} + 5600034 q^{69} + 2264704 q^{70} - 175012 q^{71} + 2669568 q^{72} + 14275780 q^{73} + 77088 q^{74} + 22200960 q^{75} - 6392832 q^{76} - 27830412 q^{77} + 5028192 q^{78} - 14107904 q^{79} - 1138688 q^{80} + 3758004 q^{81} - 663136 q^{82} + 1314576 q^{83} - 5828736 q^{84} + 11814998 q^{85} - 9108224 q^{86} - 7182900 q^{87} + 3784704 q^{88} - 11452234 q^{89} - 36854304 q^{90} + 16457168 q^{91} + 4273664 q^{92} + 2984688 q^{93} - 4593600 q^{94} - 23334088 q^{95} - 428002 q^{97} + 5742384 q^{98} - 20715312 q^{99}+O(q^{100})$$ 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9 + 2224 * q^10 - 7392 * q^11 - 25818 * q^13 - 8768 * q^14 + 15528 * q^15 - 16384 * q^16 + 28316 * q^17 - 83424 * q^18 - 99888 * q^19 - 17792 * q^20 + 182148 * q^21 + 59136 * q^22 - 33388 * q^23 + 173756 * q^25 - 156000 * q^26 + 212544 * q^27 - 35072 * q^28 + 93140 * q^29 - 124224 * q^30 + 622320 * q^31 + 131072 * q^32 + 238638 * q^33 + 453056 * q^34 + 141544 * q^35 - 333696 * q^36 - 9636 * q^37 - 1598208 * q^38 - 22932 * q^39 - 284672 * q^40 + 82892 * q^41 + 728592 * q^42 - 569264 * q^43 + 946176 * q^44 - 2303394 * q^45 + 267104 * q^46 - 1148400 * q^47 - 717798 * q^49 + 695024 * q^50 - 5459856 * q^51 + 404352 * q^52 + 2470700 * q^53 + 850176 * q^54 - 1092512 * q^55 + 280576 * q^56 + 7056924 * q^57 - 745120 * q^58 + 231504 * q^59 - 1987584 * q^60 + 685684 * q^61 + 2489280 * q^62 - 5951712 * q^63 + 2097152 * q^64 - 6216678 * q^65 + 3818208 * q^66 + 3271056 * q^67 + 1812224 * q^68 + 5600034 * q^69 + 2264704 * q^70 - 175012 * q^71 + 2669568 * q^72 + 14275780 * q^73 + 77088 * q^74 + 22200960 * q^75 - 6392832 * q^76 - 27830412 * q^77 + 5028192 * q^78 - 14107904 * q^79 - 1138688 * q^80 + 3758004 * q^81 - 663136 * q^82 + 1314576 * q^83 - 5828736 * q^84 + 11814998 * q^85 - 9108224 * q^86 - 7182900 * q^87 + 3784704 * q^88 - 11452234 * q^89 - 36854304 * q^90 + 16457168 * q^91 + 4273664 * q^92 + 2984688 * q^93 - 4593600 * q^94 - 23334088 * q^95 - 428002 * q^97 + 5742384 * q^98 - 20715312 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$$.

 $$n$$ $$15$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.00000 + 6.92820i 0.353553 + 0.612372i
$$3$$ −15.9358 27.6017i −0.340761 0.590216i 0.643813 0.765183i $$-0.277351\pi$$
−0.984574 + 0.174967i $$0.944018\pi$$
$$4$$ −32.0000 + 55.4256i −0.250000 + 0.433013i
$$5$$ −54.4265 −0.194722 −0.0973611 0.995249i $$-0.531040\pi$$
−0.0973611 + 0.995249i $$0.531040\pi$$
$$6$$ 127.487 220.813i 0.240955 0.417345i
$$7$$ 556.354 963.633i 0.613067 1.06186i −0.377653 0.925947i $$-0.623269\pi$$
0.990720 0.135916i $$-0.0433978\pi$$
$$8$$ −512.000 −0.353553
$$9$$ 585.599 1014.29i 0.267764 0.463780i
$$10$$ −217.706 377.078i −0.0688447 0.119243i
$$11$$ −3566.84 6177.94i −0.807996 1.39949i −0.914250 0.405150i $$-0.867219\pi$$
0.106255 0.994339i $$-0.466114\pi$$
$$12$$ 2039.79 0.340761
$$13$$ 7565.86 + 2346.53i 0.955117 + 0.296227i
$$14$$ 8901.66 0.867008
$$15$$ 867.331 + 1502.26i 0.0663538 + 0.114928i
$$16$$ −2048.00 3547.24i −0.125000 0.216506i
$$17$$ 10252.8 17758.4i 0.506142 0.876663i −0.493833 0.869557i $$-0.664405\pi$$
0.999975 0.00710642i $$-0.00226206\pi$$
$$18$$ 9369.59 0.378675
$$19$$ −14035.8 + 24310.8i −0.469462 + 0.813133i −0.999390 0.0349098i $$-0.988886\pi$$
0.529928 + 0.848043i $$0.322219\pi$$
$$20$$ 1741.65 3016.62i 0.0486806 0.0843172i
$$21$$ −35463.8 −0.835638
$$22$$ 28534.7 49423.6i 0.571339 0.989588i
$$23$$ −16961.2 29377.7i −0.290677 0.503467i 0.683293 0.730144i $$-0.260547\pi$$
−0.973970 + 0.226677i $$0.927214\pi$$
$$24$$ 8159.14 + 14132.0i 0.120477 + 0.208673i
$$25$$ −75162.8 −0.962083
$$26$$ 14006.2 + 61804.0i 0.156284 + 0.689620i
$$27$$ −107031. −1.04650
$$28$$ 35606.6 + 61672.5i 0.306534 + 0.530932i
$$29$$ 87734.9 + 151961.i 0.668004 + 1.15702i 0.978461 + 0.206430i $$0.0661845\pi$$
−0.310457 + 0.950587i $$0.600482\pi$$
$$30$$ −6938.65 + 12018.1i −0.0469192 + 0.0812664i
$$31$$ 15690.1 0.0945930 0.0472965 0.998881i $$-0.484939\pi$$
0.0472965 + 0.998881i $$0.484939\pi$$
$$32$$ 16384.0 28377.9i 0.0883883 0.153093i
$$33$$ −113681. + 196901.i −0.550667 + 0.953783i
$$34$$ 164045. 0.715792
$$35$$ −30280.4 + 52447.2i −0.119378 + 0.206768i
$$36$$ 37478.3 + 64914.4i 0.133882 + 0.231890i
$$37$$ −998.478 1729.41i −0.00324065 0.00561297i 0.864401 0.502804i $$-0.167698\pi$$
−0.867641 + 0.497191i $$0.834365\pi$$
$$38$$ −224573. −0.663920
$$39$$ −55800.0 246224.i −0.150629 0.664668i
$$40$$ 27866.4 0.0688447
$$41$$ −111820. 193678.i −0.253382 0.438870i 0.711073 0.703118i $$-0.248210\pi$$
−0.964455 + 0.264248i $$0.914876\pi$$
$$42$$ −141855. 245701.i −0.295443 0.511722i
$$43$$ 268966. 465862.i 0.515890 0.893548i −0.483940 0.875101i $$-0.660795\pi$$
0.999830 0.0184468i $$-0.00587213\pi$$
$$44$$ 456555. 0.807996
$$45$$ −31872.1 + 55204.1i −0.0521395 + 0.0903083i
$$46$$ 135690. 235022.i 0.205540 0.356005i
$$47$$ 542249. 0.761826 0.380913 0.924611i $$-0.375610\pi$$
0.380913 + 0.924611i $$0.375610\pi$$
$$48$$ −65273.1 + 113056.i −0.0851903 + 0.147554i
$$49$$ −207288. 359033.i −0.251702 0.435961i
$$50$$ −300651. 520743.i −0.340148 0.589153i
$$51$$ −653549. −0.689894
$$52$$ −372166. + 344254.i −0.367050 + 0.339521i
$$53$$ 1.85685e6 1.71322 0.856609 0.515967i $$-0.172567\pi$$
0.856609 + 0.515967i $$0.172567\pi$$
$$54$$ −428125. 741535.i −0.369992 0.640845i
$$55$$ 194131. + 336244.i 0.157335 + 0.272512i
$$56$$ −284853. + 493380.i −0.216752 + 0.375425i
$$57$$ 894691. 0.639898
$$58$$ −701879. + 1.21569e6i −0.472350 + 0.818135i
$$59$$ 665225. 1.15220e6i 0.421684 0.730377i −0.574421 0.818560i $$-0.694773\pi$$
0.996104 + 0.0881828i $$0.0281060\pi$$
$$60$$ −111018. −0.0663538
$$61$$ −1.43331e6 + 2.48257e6i −0.808512 + 1.40038i 0.105383 + 0.994432i $$0.466393\pi$$
−0.913895 + 0.405952i $$0.866940\pi$$
$$62$$ 62760.3 + 108704.i 0.0334437 + 0.0579261i
$$63$$ −651601. 1.12861e6i −0.328314 0.568657i
$$64$$ 262144. 0.125000
$$65$$ −411784. 127714.i −0.185983 0.0576821i
$$66$$ −1.81890e6 −0.778761
$$67$$ 1.41579e6 + 2.45222e6i 0.575091 + 0.996086i 0.996032 + 0.0889982i $$0.0283665\pi$$
−0.420941 + 0.907088i $$0.638300\pi$$
$$68$$ 656181. + 1.13654e6i 0.253071 + 0.438332i
$$69$$ −540583. + 936317.i −0.198103 + 0.343124i
$$70$$ −484486. −0.168826
$$71$$ 800929. 1.38725e6i 0.265576 0.459992i −0.702138 0.712041i $$-0.747771\pi$$
0.967714 + 0.252049i $$0.0811044\pi$$
$$72$$ −299827. + 519315.i −0.0946687 + 0.163971i
$$73$$ 1.39213e6 0.418841 0.209420 0.977826i $$-0.432842\pi$$
0.209420 + 0.977826i $$0.432842\pi$$
$$74$$ 7987.82 13835.3i 0.00229149 0.00396897i
$$75$$ 1.19778e6 + 2.07462e6i 0.327841 + 0.567837i
$$76$$ −898294. 1.55589e6i −0.234731 0.406566i
$$77$$ −7.93770e6 −1.98142
$$78$$ 1.48269e6 1.37149e6i 0.353769 0.327237i
$$79$$ −2.33505e6 −0.532847 −0.266423 0.963856i $$-0.585842\pi$$
−0.266423 + 0.963856i $$0.585842\pi$$
$$80$$ 111466. + 193064.i 0.0243403 + 0.0421586i
$$81$$ 424927. + 735994.i 0.0888416 + 0.153878i
$$82$$ 894559. 1.54942e6i 0.179168 0.310328i
$$83$$ 2.37338e6 0.455610 0.227805 0.973707i $$-0.426845\pi$$
0.227805 + 0.973707i $$0.426845\pi$$
$$84$$ 1.13484e6 1.96560e6i 0.208909 0.361842i
$$85$$ −558025. + 966528.i −0.0985570 + 0.170706i
$$86$$ 4.30345e6 0.729579
$$87$$ 2.79625e6 4.84325e6i 0.455260 0.788533i
$$88$$ 1.82622e6 + 3.16311e6i 0.285670 + 0.494794i
$$89$$ −3.52575e6 6.10678e6i −0.530135 0.918221i −0.999382 0.0351542i $$-0.988808\pi$$
0.469247 0.883067i $$-0.344526\pi$$
$$90$$ −509954. −0.0737364
$$91$$ 6.47050e6 5.98521e6i 0.900104 0.832597i
$$92$$ 2.17104e6 0.290677
$$93$$ −250034. 433072.i −0.0322336 0.0558302i
$$94$$ 2.16899e6 + 3.75681e6i 0.269346 + 0.466521i
$$95$$ 763922. 1.32315e6i 0.0914148 0.158335i
$$96$$ −1.04437e6 −0.120477
$$97$$ −4.25685e6 + 7.37308e6i −0.473573 + 0.820253i −0.999542 0.0302508i $$-0.990369\pi$$
0.525969 + 0.850504i $$0.323703\pi$$
$$98$$ 1.65830e6 2.87226e6i 0.177980 0.308271i
$$99$$ −8.35495e6 −0.865407
$$100$$ 2.40521e6 4.16594e6i 0.240521 0.416594i
$$101$$ 5.28711e6 + 9.15754e6i 0.510615 + 0.884411i 0.999924 + 0.0123007i $$0.00391555\pi$$
−0.489309 + 0.872110i $$0.662751\pi$$
$$102$$ −2.61419e6 4.52792e6i −0.243914 0.422472i
$$103$$ 3.01542e6 0.271905 0.135952 0.990715i $$-0.456591\pi$$
0.135952 + 0.990715i $$0.456591\pi$$
$$104$$ −3.87372e6 1.20143e6i −0.337685 0.104732i
$$105$$ 1.93017e6 0.162717
$$106$$ 7.42742e6 + 1.28647e7i 0.605714 + 1.04913i
$$107$$ −1.14119e7 1.97661e7i −0.900568 1.55983i −0.826758 0.562557i $$-0.809818\pi$$
−0.0738099 0.997272i $$-0.523516\pi$$
$$108$$ 3.42500e6 5.93228e6i 0.261624 0.453146i
$$109$$ 4.55907e6 0.337197 0.168598 0.985685i $$-0.446076\pi$$
0.168598 + 0.985685i $$0.446076\pi$$
$$110$$ −1.55304e6 + 2.68995e6i −0.111252 + 0.192695i
$$111$$ −31823.1 + 55119.3i −0.00220858 + 0.00382537i
$$112$$ −4.55765e6 −0.306534
$$113$$ −1.03660e7 + 1.79544e7i −0.675826 + 1.17056i 0.300401 + 0.953813i $$0.402880\pi$$
−0.976227 + 0.216752i $$0.930454\pi$$
$$114$$ 3.57876e6 + 6.19860e6i 0.226238 + 0.391856i
$$115$$ 923142. + 1.59893e6i 0.0566012 + 0.0980362i
$$116$$ −1.12301e7 −0.668004
$$117$$ 6.81062e6 6.29983e6i 0.393130 0.363646i
$$118$$ 1.06436e7 0.596351
$$119$$ −1.14084e7 1.97599e7i −0.620598 1.07491i
$$120$$ −444074. 769158.i −0.0234596 0.0406332i
$$121$$ −1.57011e7 + 2.71951e7i −0.805714 + 1.39554i
$$122$$ −2.29330e7 −1.14341
$$123$$ −3.56388e6 + 6.17283e6i −0.172685 + 0.299100i
$$124$$ −502082. + 869632.i −0.0236482 + 0.0409600i
$$125$$ 8.34292e6 0.382061
$$126$$ 5.21281e6 9.02884e6i 0.232153 0.402101i
$$127$$ 2.03935e7 + 3.53227e7i 0.883445 + 1.53017i 0.847485 + 0.530819i $$0.178116\pi$$
0.0359603 + 0.999353i $$0.488551\pi$$
$$128$$ 1.04858e6 + 1.81619e6i 0.0441942 + 0.0765466i
$$129$$ −1.71448e7 −0.703182
$$130$$ −762308. 3.36378e6i −0.0304319 0.134284i
$$131$$ 4.11026e7 1.59742 0.798711 0.601715i $$-0.205516\pi$$
0.798711 + 0.601715i $$0.205516\pi$$
$$132$$ −7.27558e6 1.26017e7i −0.275333 0.476892i
$$133$$ 1.56178e7 + 2.70508e7i 0.575624 + 0.997010i
$$134$$ −1.13263e7 + 1.96177e7i −0.406650 + 0.704339i
$$135$$ 5.82534e6 0.203776
$$136$$ −5.24944e6 + 9.09230e6i −0.178948 + 0.309947i
$$137$$ −7.36036e6 + 1.27485e7i −0.244555 + 0.423582i −0.962006 0.273027i $$-0.911975\pi$$
0.717451 + 0.696609i $$0.245309\pi$$
$$138$$ −8.64933e6 −0.280160
$$139$$ 2.84245e7 4.92326e7i 0.897719 1.55490i 0.0673168 0.997732i $$-0.478556\pi$$
0.830403 0.557164i $$-0.188110\pi$$
$$140$$ −1.93795e6 3.35662e6i −0.0596889 0.103384i
$$141$$ −8.64118e6 1.49670e7i −0.259601 0.449642i
$$142$$ 1.28149e7 0.375582
$$143$$ −1.24894e7 5.51112e7i −0.357164 1.57603i
$$144$$ −4.79723e6 −0.133882
$$145$$ −4.77510e6 8.27072e6i −0.130075 0.225297i
$$146$$ 5.56851e6 + 9.64494e6i 0.148082 + 0.256486i
$$147$$ −6.60660e6 + 1.14430e7i −0.171541 + 0.297117i
$$148$$ 127805. 0.00324065
$$149$$ 1.92631e7 3.33646e7i 0.477061 0.826294i −0.522594 0.852582i $$-0.675035\pi$$
0.999654 + 0.0262884i $$0.00836881\pi$$
$$150$$ −9.58224e6 + 1.65969e7i −0.231818 + 0.401521i
$$151$$ 2.94587e7 0.696297 0.348148 0.937439i $$-0.386811\pi$$
0.348148 + 0.937439i $$0.386811\pi$$
$$152$$ 7.18635e6 1.24471e7i 0.165980 0.287486i
$$153$$ −1.20081e7 2.07986e7i −0.271053 0.469477i
$$154$$ −3.17508e7 5.49940e7i −0.700538 1.21337i
$$155$$ −853956. −0.0184194
$$156$$ 1.54327e7 + 4.78643e6i 0.325467 + 0.100943i
$$157$$ 6.77251e7 1.39669 0.698346 0.715760i $$-0.253919\pi$$
0.698346 + 0.715760i $$0.253919\pi$$
$$158$$ −9.34022e6 1.61777e7i −0.188390 0.326301i
$$159$$ −2.95905e7 5.12523e7i −0.583798 1.01117i
$$160$$ −891724. + 1.54451e6i −0.0172112 + 0.0298106i
$$161$$ −3.77458e7 −0.712817
$$162$$ −3.39941e6 + 5.88796e6i −0.0628205 + 0.108808i
$$163$$ −4.98183e7 + 8.62878e7i −0.901015 + 1.56060i −0.0748357 + 0.997196i $$0.523843\pi$$
−0.826179 + 0.563408i $$0.809490\pi$$
$$164$$ 1.43129e7 0.253382
$$165$$ 6.18726e6 1.07166e7i 0.107227 0.185723i
$$166$$ 9.49351e6 + 1.64432e7i 0.161083 + 0.279003i
$$167$$ −1.65811e7 2.87193e7i −0.275490 0.477162i 0.694769 0.719233i $$-0.255507\pi$$
−0.970259 + 0.242071i $$0.922173\pi$$
$$168$$ 1.81575e7 0.295443
$$169$$ 5.17361e7 + 3.55071e7i 0.824499 + 0.565864i
$$170$$ −8.92840e6 −0.139381
$$171$$ 1.64388e7 + 2.84728e7i 0.251410 + 0.435455i
$$172$$ 1.72138e7 + 2.98152e7i 0.257945 + 0.446774i
$$173$$ −2.13081e7 + 3.69067e7i −0.312884 + 0.541931i −0.978985 0.203930i $$-0.934628\pi$$
0.666101 + 0.745861i $$0.267962\pi$$
$$174$$ 4.47401e7 0.643834
$$175$$ −4.18171e7 + 7.24293e7i −0.589822 + 1.02160i
$$176$$ −1.46098e7 + 2.53049e7i −0.201999 + 0.349872i
$$177$$ −4.24037e7 −0.574774
$$178$$ 2.82060e7 4.88543e7i 0.374862 0.649281i
$$179$$ 1.01329e7 + 1.75507e7i 0.132053 + 0.228722i 0.924468 0.381260i $$-0.124510\pi$$
−0.792415 + 0.609982i $$0.791177\pi$$
$$180$$ −2.03982e6 3.53306e6i −0.0260698 0.0451542i
$$181$$ −3.09055e7 −0.387401 −0.193700 0.981061i $$-0.562049\pi$$
−0.193700 + 0.981061i $$0.562049\pi$$
$$182$$ 6.73488e7 + 2.08881e7i 0.828094 + 0.256831i
$$183$$ 9.13640e7 1.10204
$$184$$ 8.68416e6 + 1.50414e7i 0.102770 + 0.178002i
$$185$$ 54343.7 + 94126.0i 0.000631027 + 0.00109297i
$$186$$ 2.00027e6 3.46457e6i 0.0227926 0.0394779i
$$187$$ −1.46281e8 −1.63584
$$188$$ −1.73520e7 + 3.00545e7i −0.190457 + 0.329881i
$$189$$ −5.95473e7 + 1.03139e8i −0.641572 + 1.11124i
$$190$$ 1.22228e7 0.129280
$$191$$ −4.03566e7 + 6.98997e7i −0.419081 + 0.725870i −0.995847 0.0910397i $$-0.970981\pi$$
0.576766 + 0.816909i $$0.304314\pi$$
$$192$$ −4.17748e6 7.23561e6i −0.0425951 0.0737770i
$$193$$ −6.91934e7 1.19846e8i −0.692810 1.19998i −0.970913 0.239431i $$-0.923039\pi$$
0.278104 0.960551i $$-0.410294\pi$$
$$194$$ −6.81096e7 −0.669734
$$195$$ 3.03700e6 + 1.34011e7i 0.0293308 + 0.129426i
$$196$$ 2.65328e7 0.251702
$$197$$ −8.69235e7 1.50556e8i −0.810038 1.40303i −0.912837 0.408325i $$-0.866113\pi$$
0.102798 0.994702i $$-0.467220\pi$$
$$198$$ −3.34198e7 5.78848e7i −0.305968 0.529952i
$$199$$ −1.19505e7 + 2.06988e7i −0.107498 + 0.186191i −0.914756 0.404007i $$-0.867617\pi$$
0.807258 + 0.590198i $$0.200950\pi$$
$$200$$ 3.84833e7 0.340148
$$201$$ 4.51235e7 7.81562e7i 0.391937 0.678855i
$$202$$ −4.22969e7 + 7.32603e7i −0.361059 + 0.625373i
$$203$$ 1.95246e8 1.63813
$$204$$ 2.09136e7 3.62233e7i 0.172473 0.298733i
$$205$$ 6.08596e6 + 1.05412e7i 0.0493391 + 0.0854578i
$$206$$ 1.20617e7 + 2.08914e7i 0.0961329 + 0.166507i
$$207$$ −3.97300e7 −0.311331
$$208$$ −7.17117e6 3.16436e7i −0.0552546 0.243817i
$$209$$ 2.00254e8 1.51729
$$210$$ 7.72069e6 + 1.33726e7i 0.0575292 + 0.0996436i
$$211$$ 2.73880e7 + 4.74375e7i 0.200711 + 0.347642i 0.948758 0.316004i $$-0.102341\pi$$
−0.748046 + 0.663646i $$0.769008\pi$$
$$212$$ −5.94194e7 + 1.02917e8i −0.428304 + 0.741845i
$$213$$ −5.10538e7 −0.361993
$$214$$ 9.12956e7 1.58129e8i 0.636798 1.10297i
$$215$$ −1.46389e7 + 2.53553e7i −0.100455 + 0.173994i
$$216$$ 5.48000e7 0.369992
$$217$$ 8.72923e6 1.51195e7i 0.0579918 0.100445i
$$218$$ 1.82363e7 + 3.15862e7i 0.119217 + 0.206490i
$$219$$ −2.21847e7 3.84250e7i −0.142725 0.247206i
$$220$$ −2.48487e7 −0.157335
$$221$$ 1.19242e8 1.10299e8i 0.743116 0.687383i
$$222$$ −509170. −0.00312340
$$223$$ −1.36109e8 2.35747e8i −0.821901 1.42357i −0.904265 0.426972i $$-0.859580\pi$$
0.0823641 0.996602i $$-0.473753\pi$$
$$224$$ −1.82306e7 3.15763e7i −0.108376 0.187713i
$$225$$ −4.40152e7 + 7.62366e7i −0.257611 + 0.446195i
$$226$$ −1.65855e8 −0.955762
$$227$$ 2.24777e7 3.89325e7i 0.127544 0.220914i −0.795180 0.606373i $$-0.792624\pi$$
0.922725 + 0.385460i $$0.125957\pi$$
$$228$$ −2.86301e7 + 4.95888e7i −0.159975 + 0.277084i
$$229$$ 1.23460e8 0.679362 0.339681 0.940541i $$-0.389681\pi$$
0.339681 + 0.940541i $$0.389681\pi$$
$$230$$ −7.38513e6 + 1.27914e7i −0.0400231 + 0.0693221i
$$231$$ 1.26494e8 + 2.19094e8i 0.675192 + 1.16947i
$$232$$ −4.49202e7 7.78041e7i −0.236175 0.409067i
$$233$$ 1.26541e8 0.655371 0.327685 0.944787i $$-0.393731\pi$$
0.327685 + 0.944787i $$0.393731\pi$$
$$234$$ 7.08890e7 + 2.19861e7i 0.361679 + 0.112174i
$$235$$ −2.95127e7 −0.148345
$$236$$ 4.25744e7 + 7.37411e7i 0.210842 + 0.365189i
$$237$$ 3.72110e7 + 6.44514e7i 0.181573 + 0.314494i
$$238$$ 9.12671e7 1.58079e8i 0.438829 0.760074i
$$239$$ 8.04943e6 0.0381393 0.0190696 0.999818i $$-0.493930\pi$$
0.0190696 + 0.999818i $$0.493930\pi$$
$$240$$ 3.55259e6 6.15326e6i 0.0165884 0.0287320i
$$241$$ 1.93788e8 3.35651e8i 0.891801 1.54464i 0.0540864 0.998536i $$-0.482775\pi$$
0.837715 0.546108i $$-0.183891\pi$$
$$242$$ −2.51217e8 −1.13945
$$243$$ −1.03496e8 + 1.79260e8i −0.462701 + 0.801421i
$$244$$ −9.17320e7 1.58884e8i −0.404256 0.700192i
$$245$$ 1.12819e7 + 1.95409e7i 0.0490120 + 0.0848913i
$$246$$ −5.70221e7 −0.244214
$$247$$ −1.63239e8 + 1.50997e8i −0.689264 + 0.637570i
$$248$$ −8.03331e6 −0.0334437
$$249$$ −3.78217e7 6.55091e7i −0.155254 0.268908i
$$250$$ 3.33717e7 + 5.78014e7i 0.135079 + 0.233964i
$$251$$ −3.70235e7 + 6.41265e7i −0.147781 + 0.255965i −0.930407 0.366528i $$-0.880546\pi$$
0.782626 + 0.622492i $$0.213880\pi$$
$$252$$ 8.34049e7 0.328314
$$253$$ −1.20996e8 + 2.09571e8i −0.469731 + 0.813598i
$$254$$ −1.63148e8 + 2.82581e8i −0.624690 + 1.08200i
$$255$$ 3.55704e7 0.134338
$$256$$ −8.38861e6 + 1.45295e7i −0.0312500 + 0.0541266i
$$257$$ 7.46504e7 + 1.29298e8i 0.274326 + 0.475146i 0.969965 0.243246i $$-0.0782121\pi$$
−0.695639 + 0.718391i $$0.744879\pi$$
$$258$$ −6.85790e7 1.18782e8i −0.248612 0.430609i
$$259$$ −2.22203e6 −0.00794695
$$260$$ 2.02557e7 1.87365e7i 0.0714727 0.0661123i
$$261$$ 2.05510e8 0.715469
$$262$$ 1.64410e8 + 2.84767e8i 0.564774 + 0.978217i
$$263$$ −8.67285e7 1.50218e8i −0.293979 0.509187i 0.680768 0.732499i $$-0.261646\pi$$
−0.974747 + 0.223313i $$0.928313\pi$$
$$264$$ 5.82047e7 1.00813e8i 0.194690 0.337213i
$$265$$ −1.01062e8 −0.333601
$$266$$ −1.24942e8 + 2.16406e8i −0.407028 + 0.704992i
$$267$$ −1.12372e8 + 1.94633e8i −0.361299 + 0.625788i
$$268$$ −1.81221e8 −0.575091
$$269$$ 2.15455e8 3.73179e8i 0.674875 1.16892i −0.301631 0.953425i $$-0.597531\pi$$
0.976506 0.215492i $$-0.0691357\pi$$
$$270$$ 2.33014e7 + 4.03591e7i 0.0720457 + 0.124787i
$$271$$ −1.55116e8 2.68669e8i −0.473439 0.820021i 0.526099 0.850424i $$-0.323654\pi$$
−0.999538 + 0.0304029i $$0.990321\pi$$
$$272$$ −8.39911e7 −0.253071
$$273$$ −2.68314e8 8.32171e7i −0.798132 0.247539i
$$274$$ −1.17766e8 −0.345853
$$275$$ 2.68093e8 + 4.64351e8i 0.777359 + 1.34643i
$$276$$ −3.45973e7 5.99243e7i −0.0990514 0.171562i
$$277$$ −1.95019e8 + 3.37783e8i −0.551313 + 0.954902i 0.446867 + 0.894600i $$0.352540\pi$$
−0.998180 + 0.0603016i $$0.980794\pi$$
$$278$$ 4.54792e8 1.26957
$$279$$ 9.18809e6 1.59142e7i 0.0253286 0.0438704i
$$280$$ 1.55036e7 2.68530e7i 0.0422064 0.0731037i
$$281$$ −2.24392e8 −0.603303 −0.301652 0.953418i $$-0.597538\pi$$
−0.301652 + 0.953418i $$0.597538\pi$$
$$282$$ 6.91294e7 1.19736e8i 0.183566 0.317945i
$$283$$ 6.25944e6 + 1.08417e7i 0.0164166 + 0.0284344i 0.874117 0.485715i $$-0.161441\pi$$
−0.857700 + 0.514150i $$0.828108\pi$$
$$284$$ 5.12594e7 + 8.87839e7i 0.132788 + 0.229996i
$$285$$ −4.86949e7 −0.124602
$$286$$ 3.31864e8 3.06974e8i 0.838839 0.775927i
$$287$$ −2.48846e8 −0.621360
$$288$$ −1.91889e7 3.32362e7i −0.0473344 0.0819855i
$$289$$ −5.07133e6 8.78379e6i −0.0123589 0.0214062i
$$290$$ 3.82008e7 6.61658e7i 0.0919771 0.159309i
$$291$$ 2.71346e8 0.645501
$$292$$ −4.45481e7 + 7.71595e7i −0.104710 + 0.181363i
$$293$$ 2.13337e8 3.69510e8i 0.495483 0.858201i −0.504504 0.863410i $$-0.668325\pi$$
0.999986 + 0.00520823i $$0.00165784\pi$$
$$294$$ −1.05706e8 −0.242595
$$295$$ −3.62059e7 + 6.27105e7i −0.0821112 + 0.142221i
$$296$$ 511221. + 885460.i 0.00114574 + 0.00198449i
$$297$$ 3.81763e8 + 6.61233e8i 0.845564 + 1.46456i
$$298$$ 3.08209e8 0.674666
$$299$$ −5.93906e7 2.62068e8i −0.128490 0.566977i
$$300$$ −1.53316e8 −0.327841
$$301$$ −2.99280e8 5.18369e8i −0.632551 1.09561i
$$302$$ 1.17835e8 + 2.04096e8i 0.246178 + 0.426393i
$$303$$ 1.68509e8 2.91866e8i 0.347995 0.602746i
$$304$$ 1.14982e8 0.234731
$$305$$ 7.80102e7 1.35118e8i 0.157435 0.272686i
$$306$$ 9.60647e7 1.66389e8i 0.191663 0.331970i
$$307$$ 2.83423e8 0.559051 0.279525 0.960138i $$-0.409823\pi$$
0.279525 + 0.960138i $$0.409823\pi$$
$$308$$ 2.54006e8 4.39952e8i 0.495355 0.857981i
$$309$$ −4.80532e7 8.32305e7i −0.0926547 0.160483i
$$310$$ −3.41582e6 5.91638e6i −0.00651222 0.0112795i
$$311$$ −7.14238e8 −1.34642 −0.673212 0.739450i $$-0.735086\pi$$
−0.673212 + 0.739450i $$0.735086\pi$$
$$312$$ 2.85696e7 + 1.26067e8i 0.0532554 + 0.234996i
$$313$$ −3.51984e8 −0.648811 −0.324406 0.945918i $$-0.605164\pi$$
−0.324406 + 0.945918i $$0.605164\pi$$
$$314$$ 2.70900e8 + 4.69213e8i 0.493806 + 0.855296i
$$315$$ 3.54644e7 + 6.14261e7i 0.0639301 + 0.110730i
$$316$$ 7.47217e7 1.29422e8i 0.133212 0.230729i
$$317$$ −4.55628e8 −0.803346 −0.401673 0.915783i $$-0.631571\pi$$
−0.401673 + 0.915783i $$0.631571\pi$$
$$318$$ 2.36724e8 4.10018e8i 0.412807 0.715003i
$$319$$ 6.25872e8 1.08404e9i 1.07949 1.86973i
$$320$$ −1.42676e7 −0.0243403
$$321$$ −3.63718e8 + 6.29977e8i −0.613757 + 1.06306i
$$322$$ −1.50983e8 2.61511e8i −0.252019 0.436510i
$$323$$ 2.87814e8 + 4.98508e8i 0.475229 + 0.823121i
$$324$$ −5.43906e7 −0.0888416
$$325$$ −5.68671e8 1.76372e8i −0.918902 0.284995i
$$326$$ −7.97092e8 −1.27423
$$327$$ −7.26526e7 1.25838e8i −0.114904 0.199019i
$$328$$ 5.72518e7 + 9.91630e7i 0.0895840 + 0.155164i
$$329$$ 3.01682e8 5.22529e8i 0.467051 0.808955i
$$330$$ 9.89962e7 0.151642
$$331$$ −3.32605e8 + 5.76089e8i −0.504117 + 0.873156i 0.495872 + 0.868396i $$0.334849\pi$$
−0.999989 + 0.00476004i $$0.998485\pi$$
$$332$$ −7.59481e7 + 1.31546e8i −0.113903 + 0.197285i
$$333$$ −2.33883e6 −0.00347091
$$334$$ 1.32649e8 2.29754e8i 0.194801 0.337405i
$$335$$ −7.70564e7 1.33466e8i −0.111983 0.193960i
$$336$$ 7.26299e7 + 1.25799e8i 0.104455 + 0.180921i
$$337$$ 9.20291e8 1.30985 0.654924 0.755695i $$-0.272701\pi$$
0.654924 + 0.755695i $$0.272701\pi$$
$$338$$ −3.90563e7 + 5.00466e8i −0.0550152 + 0.704963i
$$339$$ 6.60760e8 0.921181
$$340$$ −3.57136e7 6.18578e7i −0.0492785 0.0853529i
$$341$$ −5.59639e7 9.69324e7i −0.0764307 0.132382i
$$342$$ −1.31510e8 + 2.27782e8i −0.177774 + 0.307913i
$$343$$ 4.55061e8 0.608892
$$344$$ −1.37710e8 + 2.38522e8i −0.182395 + 0.315917i
$$345$$ 2.94220e7 5.09605e7i 0.0385750 0.0668139i
$$346$$ −3.40930e8 −0.442485
$$347$$ −6.82493e8 + 1.18211e9i −0.876890 + 1.51882i −0.0221539 + 0.999755i $$0.507052\pi$$
−0.854736 + 0.519063i $$0.826281\pi$$
$$348$$ 1.78960e8 + 3.09968e8i 0.227630 + 0.394266i
$$349$$ 4.48612e8 + 7.77018e8i 0.564913 + 0.978458i 0.997058 + 0.0766537i $$0.0244236\pi$$
−0.432145 + 0.901804i $$0.642243\pi$$
$$350$$ −6.69073e8 −0.834134
$$351$$ −8.09784e8 2.51153e8i −0.999527 0.310001i
$$352$$ −2.33756e8 −0.285670
$$353$$ 1.34803e8 + 2.33485e8i 0.163112 + 0.282519i 0.935983 0.352044i $$-0.114513\pi$$
−0.772871 + 0.634563i $$0.781180\pi$$
$$354$$ −1.69615e8 2.93781e8i −0.203213 0.351976i
$$355$$ −4.35918e7 + 7.55031e7i −0.0517136 + 0.0895707i
$$356$$ 4.51296e8 0.530135
$$357$$ −3.63604e8 + 6.29781e8i −0.422951 + 0.732573i
$$358$$ −8.10630e7 + 1.40405e8i −0.0933753 + 0.161731i
$$359$$ −2.23928e8 −0.255433 −0.127717 0.991811i $$-0.540765\pi$$
−0.127717 + 0.991811i $$0.540765\pi$$
$$360$$ 1.63185e7 2.82645e7i 0.0184341 0.0319288i
$$361$$ 5.29262e7 + 9.16708e7i 0.0592100 + 0.102555i
$$362$$ −1.23622e8 2.14119e8i −0.136967 0.237234i
$$363$$ 1.00084e9 1.09822
$$364$$ 1.24678e8 + 5.50158e8i 0.135499 + 0.597906i
$$365$$ −7.57686e7 −0.0815576
$$366$$ 3.65456e8 + 6.32989e8i 0.389629 + 0.674857i
$$367$$ 1.40428e8 + 2.43229e8i 0.148294 + 0.256853i 0.930597 0.366045i $$-0.119288\pi$$
−0.782303 + 0.622898i $$0.785955\pi$$
$$368$$ −6.94733e7 + 1.20331e8i −0.0726692 + 0.125867i
$$369$$ −2.61926e8 −0.271386
$$370$$ −434749. + 753008.i −0.000446203 + 0.000772847i
$$371$$ 1.03307e9 1.78933e9i 1.05032 1.81920i
$$372$$ 3.20044e7 0.0322336
$$373$$ −8.77622e8 + 1.52009e9i −0.875642 + 1.51666i −0.0195647 + 0.999809i $$0.506228\pi$$
−0.856077 + 0.516848i $$0.827105\pi$$
$$374$$ −5.85122e8 1.01346e9i −0.578357 1.00174i
$$375$$ −1.32951e8 2.30278e8i −0.130192 0.225499i
$$376$$ −2.77631e8 −0.269346
$$377$$ 3.07208e8 + 1.35559e9i 0.295282 + 1.30297i
$$378$$ −9.52756e8 −0.907320
$$379$$ −1.79617e8 3.11105e8i −0.169477 0.293542i 0.768759 0.639538i $$-0.220874\pi$$
−0.938236 + 0.345996i $$0.887541\pi$$
$$380$$ 4.88910e7 + 8.46817e7i 0.0457074 + 0.0791675i
$$381$$ 6.49976e8 1.12579e9i 0.602088 1.04285i
$$382$$ −6.45706e8 −0.592670
$$383$$ 9.39346e8 1.62699e9i 0.854338 1.47976i −0.0229197 0.999737i $$-0.507296\pi$$
0.877258 0.480020i $$-0.159370\pi$$
$$384$$ 3.34198e7 5.78849e7i 0.0301193 0.0521682i
$$385$$ 4.32021e8 0.385827
$$386$$ 5.53547e8 9.58772e8i 0.489891 0.848515i
$$387$$ −3.15012e8 5.45617e8i −0.276273 0.478519i
$$388$$ −2.72438e8 4.71877e8i −0.236787 0.410126i
$$389$$ 4.34490e8 0.374245 0.187122 0.982337i $$-0.440084\pi$$
0.187122 + 0.982337i $$0.440084\pi$$
$$390$$ −8.06978e7 + 7.46455e7i −0.0688867 + 0.0637202i
$$391$$ −6.95603e8 −0.588495
$$392$$ 1.06131e8 + 1.83825e8i 0.0889902 + 0.154136i
$$393$$ −6.55004e8 1.13450e9i −0.544339 0.942824i
$$394$$ 6.95388e8 1.20445e9i 0.572784 0.992090i
$$395$$ 1.27089e8 0.103757
$$396$$ 2.67358e8 4.63078e8i 0.216352 0.374732i
$$397$$ −1.01579e9 + 1.75940e9i −0.814772 + 1.41123i 0.0947188 + 0.995504i $$0.469805\pi$$
−0.909491 + 0.415723i $$0.863529\pi$$
$$398$$ −1.91207e8 −0.152025
$$399$$ 4.97765e8 8.62154e8i 0.392301 0.679484i
$$400$$ 1.53933e8 + 2.66620e8i 0.120260 + 0.208297i
$$401$$ 4.01539e8 + 6.95485e8i 0.310973 + 0.538620i 0.978573 0.205899i $$-0.0660119\pi$$
−0.667601 + 0.744520i $$0.732679\pi$$
$$402$$ 7.21976e8 0.554283
$$403$$ 1.18709e8 + 3.68173e7i 0.0903474 + 0.0280210i
$$404$$ −6.76750e8 −0.510615
$$405$$ −2.31273e7 4.00576e7i −0.0172994 0.0299635i
$$406$$ 7.80986e8 + 1.35271e9i 0.579165 + 1.00314i
$$407$$ −7.12282e6 + 1.23371e7i −0.00523686 + 0.00907051i
$$408$$ 3.34617e8 0.243914
$$409$$ 1.26870e9 2.19745e9i 0.916912 1.58814i 0.112835 0.993614i $$-0.464007\pi$$
0.804077 0.594525i $$-0.202660\pi$$
$$410$$ −4.86877e7 + 8.43296e7i −0.0348880 + 0.0604278i
$$411$$ 4.69174e8 0.333340
$$412$$ −9.64934e7 + 1.67131e8i −0.0679762 + 0.117738i
$$413$$ −7.40201e8 1.28207e9i −0.517041 0.895541i
$$414$$ −1.58920e8 2.75257e8i −0.110072 0.190650i
$$415$$ −1.29175e8 −0.0887174
$$416$$ 1.90549e8 1.76258e8i 0.129772 0.120039i
$$417$$ −1.81187e9 −1.22363
$$418$$ 8.01017e8 + 1.38740e9i 0.536445 + 0.929149i
$$419$$ 8.92968e7 + 1.54667e8i 0.0593044 + 0.102718i 0.894153 0.447761i $$-0.147778\pi$$
−0.834849 + 0.550479i $$0.814445\pi$$
$$420$$ −6.17655e7 + 1.06981e8i −0.0406793 + 0.0704586i
$$421$$ 2.07782e9 1.35713 0.678563 0.734542i $$-0.262603\pi$$
0.678563 + 0.734542i $$0.262603\pi$$
$$422$$ −2.19104e8 + 3.79500e8i −0.141924 + 0.245820i
$$423$$ 3.17540e8 5.49996e8i 0.203989 0.353320i
$$424$$ −9.50710e8 −0.605714
$$425$$ −7.70630e8 + 1.33477e9i −0.486950 + 0.843423i
$$426$$ −2.04215e8 3.53711e8i −0.127984 0.221674i
$$427$$ 1.59486e9 + 2.76237e9i 0.991344 + 1.71706i
$$428$$ 1.46073e9 0.900568
$$429$$ −1.32213e9 + 1.22297e9i −0.808488 + 0.747852i
$$430$$ −2.34222e8 −0.142065
$$431$$ −7.90928e8 1.36993e9i −0.475846 0.824190i 0.523771 0.851859i $$-0.324525\pi$$
−0.999617 + 0.0276692i $$0.991192\pi$$
$$432$$ 2.19200e8 + 3.79666e8i 0.130812 + 0.226573i
$$433$$ −6.68261e8 + 1.15746e9i −0.395584 + 0.685171i −0.993176 0.116629i $$-0.962791\pi$$
0.597592 + 0.801801i $$0.296124\pi$$
$$434$$ 1.39668e8 0.0820128
$$435$$ −1.52190e8 + 2.63601e8i −0.0886492 + 0.153545i
$$436$$ −1.45890e8 + 2.52689e8i −0.0842992 + 0.146011i
$$437$$ 9.52262e8 0.545847
$$438$$ 1.77477e8 3.07400e8i 0.100922 0.174801i
$$439$$ −9.97662e8 1.72800e9i −0.562805 0.974806i −0.997250 0.0741082i $$-0.976389\pi$$
0.434445 0.900698i $$-0.356944\pi$$
$$440$$ −9.93948e7 1.72157e8i −0.0556262 0.0963474i
$$441$$ −4.85550e8 −0.269587
$$442$$ 1.24114e9 + 3.84938e8i 0.683666 + 0.212037i
$$443$$ 1.51862e8 0.0829921 0.0414960 0.999139i $$-0.486788\pi$$
0.0414960 + 0.999139i $$0.486788\pi$$
$$444$$ −2.03668e6 3.52763e6i −0.00110429 0.00191268i
$$445$$ 1.91894e8 + 3.32371e8i 0.103229 + 0.178798i
$$446$$ 1.08887e9 1.88598e9i 0.581172 1.00662i
$$447$$ −1.22789e9 −0.650255
$$448$$ 1.45845e8 2.52611e8i 0.0766334 0.132733i
$$449$$ 8.03256e7 1.39128e8i 0.0418786 0.0725358i −0.844326 0.535829i $$-0.819999\pi$$
0.886205 + 0.463293i $$0.153332\pi$$
$$450$$ −7.04244e8 −0.364317
$$451$$ −7.97686e8 + 1.38163e9i −0.409463 + 0.709210i
$$452$$ −6.63421e8 1.14908e9i −0.337913 0.585282i
$$453$$ −4.69449e8 8.13109e8i −0.237271 0.410965i
$$454$$ 3.59643e8 0.180375
$$455$$ −3.52167e8 + 3.25754e8i −0.175270 + 0.162125i
$$456$$ −4.58082e8 −0.226238
$$457$$ −5.10839e8 8.84800e8i −0.250367 0.433649i 0.713260 0.700900i $$-0.247218\pi$$
−0.963627 + 0.267251i $$0.913885\pi$$
$$458$$ 4.93839e8 + 8.55354e8i 0.240191 + 0.416022i
$$459$$ −1.09737e9 + 1.90071e9i −0.529675 + 0.917425i
$$460$$ −1.18162e8 −0.0566012
$$461$$ −1.35144e9 + 2.34077e9i −0.642458 + 1.11277i 0.342424 + 0.939546i $$0.388752\pi$$
−0.984882 + 0.173225i $$0.944581\pi$$
$$462$$ −1.01195e9 + 1.75275e9i −0.477433 + 0.826937i
$$463$$ −2.68582e9 −1.25760 −0.628801 0.777566i $$-0.716454\pi$$
−0.628801 + 0.777566i $$0.716454\pi$$
$$464$$ 3.59362e8 6.22433e8i 0.167001 0.289254i
$$465$$ 1.36085e7 + 2.35706e7i 0.00627660 + 0.0108714i
$$466$$ 5.06166e8 + 8.76705e8i 0.231709 + 0.401331i
$$467$$ −4.54161e8 −0.206348 −0.103174 0.994663i $$-0.532900\pi$$
−0.103174 + 0.994663i $$0.532900\pi$$
$$468$$ 1.31232e8 + 5.79078e8i 0.0591807 + 0.261142i
$$469$$ 3.15072e9 1.41028
$$470$$ −1.18051e8 2.04470e8i −0.0524477 0.0908421i
$$471$$ −1.07926e9 1.86933e9i −0.475939 0.824350i
$$472$$ −3.40595e8 + 5.89928e8i −0.149088 + 0.258227i
$$473$$ −3.83743e9 −1.66735
$$474$$ −2.97688e8 + 5.15611e8i −0.128392 + 0.222381i
$$475$$ 1.05497e9 1.82727e9i 0.451662 0.782301i
$$476$$ 1.46027e9 0.620598
$$477$$ 1.08737e9 1.88338e9i 0.458737 0.794556i
$$478$$ 3.21977e7 + 5.57681e7i 0.0134843 + 0.0233554i
$$479$$ 9.98214e8 + 1.72896e9i 0.415001 + 0.718803i 0.995429 0.0955088i $$-0.0304478\pi$$
−0.580427 + 0.814312i $$0.697114\pi$$
$$480$$ 5.68414e7 0.0234596
$$481$$ −3.49622e6 1.54275e7i −0.00143249 0.00632102i
$$482$$ 3.10061e9 1.26120
$$483$$ 6.01511e8 + 1.04185e9i 0.242901 + 0.420716i
$$484$$ −1.00487e9 1.74048e9i −0.402857 0.697768i
$$485$$ 2.31685e8 4.01291e8i 0.0922152 0.159721i
$$486$$ −1.65593e9 −0.654357
$$487$$ −8.06060e8 + 1.39614e9i −0.316240 + 0.547743i −0.979700 0.200468i $$-0.935754\pi$$
0.663461 + 0.748211i $$0.269087\pi$$
$$488$$ 7.33856e8 1.27108e9i 0.285852 0.495110i
$$489$$ 3.17558e9 1.22812
$$490$$ −9.02556e7 + 1.56327e8i −0.0346567 + 0.0600272i
$$491$$ 2.59072e9 + 4.48725e9i 0.987722 + 1.71078i 0.629152 + 0.777282i $$0.283402\pi$$
0.358570 + 0.933503i $$0.383264\pi$$
$$492$$ −2.28088e8 3.95061e8i −0.0863427 0.149550i
$$493$$ 3.59812e9 1.35242
$$494$$ −1.69909e9 5.26969e8i −0.634122 0.196671i
$$495$$ 4.54731e8 0.168514
$$496$$ −3.21333e7 5.56564e7i −0.0118241 0.0204800i
$$497$$ −8.91199e8 1.54360e9i −0.325632 0.564012i
$$498$$ 3.02574e8 5.24073e8i 0.109781 0.190147i
$$499$$ 2.11935e9 0.763574 0.381787 0.924250i $$-0.375309\pi$$
0.381787 + 0.924250i $$0.375309\pi$$
$$500$$ −2.66973e8 + 4.62411e8i −0.0955153 + 0.165437i
$$501$$ −5.28466e8 + 9.15331e8i −0.187752 + 0.325197i
$$502$$ −5.92376e8 −0.208994
$$503$$ 9.53790e7 1.65201e8i 0.0334168 0.0578796i −0.848833 0.528661i $$-0.822694\pi$$
0.882250 + 0.470781i $$0.156028\pi$$
$$504$$ 3.33620e8 + 5.77846e8i 0.116077 + 0.201051i
$$505$$ −2.87759e8 4.98413e8i −0.0994281 0.172214i
$$506$$ −1.93594e9 −0.664300
$$507$$ 1.55598e8 1.99384e9i 0.0530246 0.679456i
$$508$$ −2.61037e9 −0.883445
$$509$$ −2.57239e9 4.45550e9i −0.864617 1.49756i −0.867427 0.497565i $$-0.834228\pi$$
0.00280918 0.999996i $$-0.499106\pi$$
$$510$$ 1.42281e8 + 2.46439e8i 0.0474955 + 0.0822647i
$$511$$ 7.74515e8 1.34150e9i 0.256777 0.444751i
$$512$$ −1.34218e8 −0.0441942
$$513$$ 1.50227e9 2.60202e9i 0.491291 0.850940i
$$514$$ −5.97203e8 + 1.03439e9i −0.193977 + 0.335979i
$$515$$ −1.64119e8 −0.0529459
$$516$$ 5.48632e8 9.50259e8i 0.175795 0.304487i
$$517$$ −1.93411e9 3.34998e9i −0.615552 1.06617i
$$518$$ −8.88811e6 1.53947e7i −0.00280967 0.00486649i
$$519$$ 1.35825e9 0.426475
$$520$$ 2.10833e8 + 6.53894e7i 0.0657548 + 0.0203937i
$$521$$ 1.41370e9 0.437950 0.218975 0.975730i $$-0.429729\pi$$
0.218975 + 0.975730i $$0.429729\pi$$
$$522$$ 8.22039e8 + 1.42381e9i 0.252956 + 0.438133i
$$523$$ 1.73475e9 + 3.00468e9i 0.530251 + 0.918421i 0.999377 + 0.0352902i $$0.0112356\pi$$
−0.469126 + 0.883131i $$0.655431\pi$$
$$524$$ −1.31528e9 + 2.27814e9i −0.399356 + 0.691704i
$$525$$ 2.66556e9 0.803953
$$526$$ 6.93828e8 1.20174e9i 0.207875 0.360049i
$$527$$ 1.60867e8 2.78631e8i 0.0478774 0.0829262i
$$528$$ 9.31275e8 0.275333
$$529$$ 1.12704e9 1.95210e9i 0.331014 0.573333i
$$530$$ −4.04249e8 7.00179e8i −0.117946 0.204288i
$$531$$ −7.79111e8 1.34946e9i −0.225823 0.391137i
$$532$$ −1.99908e9 −0.575624
$$533$$ −3.91542e8 1.72773e9i −0.112004 0.494231i
$$534$$ −1.79794e9 −0.510954
$$535$$ 6.21113e8 + 1.07580e9i 0.175361 + 0.303734i
$$536$$ −7.24883e8 1.25553e9i −0.203325 0.352170i
$$537$$ 3.22951e8 5.59368e8i 0.0899968 0.155879i
$$538$$ 3.44728e9 0.954417
$$539$$ −1.47872e9 + 2.56122e9i −0.406749 + 0.704510i
$$540$$ −1.86411e8 + 3.22873e8i −0.0509440 + 0.0882376i
$$541$$ −2.01148e9 −0.546166 −0.273083 0.961990i $$-0.588043\pi$$
−0.273083 + 0.961990i $$0.588043\pi$$
$$542$$ 1.24093e9 2.14935e9i 0.334772 0.579842i
$$543$$ 4.92504e8 + 8.53042e8i 0.132011 + 0.228650i
$$544$$ −3.35964e8 5.81907e8i −0.0894741 0.154974i
$$545$$ −2.48134e8 −0.0656597
$$546$$ −4.96713e8 2.19181e9i −0.130596 0.576272i
$$547$$ −1.25989e8 −0.0329137 −0.0164569 0.999865i $$-0.505239\pi$$
−0.0164569 + 0.999865i $$0.505239\pi$$
$$548$$ −4.71063e8 8.15905e8i −0.122278 0.211791i
$$549$$ 1.67869e9 + 2.90758e9i 0.432980 + 0.749944i
$$550$$ −2.14475e9 + 3.71481e9i −0.549676 + 0.952066i
$$551$$ −4.92573e9 −1.25441
$$552$$ 2.76778e8 4.79394e8i 0.0700399 0.121313i
$$553$$ −1.29912e9 + 2.25014e9i −0.326671 + 0.565810i
$$554$$ −3.12031e9 −0.779674
$$555$$ 1.73202e6 2.99995e6i 0.000430059 0.000744884i
$$556$$ 1.81917e9 + 3.15089e9i 0.448860 + 0.777448i
$$557$$ 1.13089e7 + 1.95875e7i 0.00277284 + 0.00480270i 0.867408 0.497597i $$-0.165784\pi$$
−0.864636 + 0.502399i $$0.832451\pi$$
$$558$$ 1.47009e8 0.0358200
$$559$$ 3.12812e9 2.89351e9i 0.757429 0.700623i
$$560$$ 2.48057e8 0.0596889
$$561$$ 2.33110e9 + 4.03759e9i 0.557431 + 0.965499i
$$562$$ −8.97569e8 1.55463e9i −0.213300 0.369446i
$$563$$ −1.70004e9 + 2.94455e9i −0.401494 + 0.695408i −0.993906 0.110227i $$-0.964842\pi$$
0.592412 + 0.805635i $$0.298176\pi$$
$$564$$ 1.10607e9 0.259601
$$565$$ 5.64183e8 9.77194e8i 0.131598 0.227935i
$$566$$ −5.00755e7 + 8.67333e7i −0.0116083 + 0.0201061i
$$567$$ 9.45638e8 0.217863
$$568$$ −4.10075e8 + 7.10272e8i −0.0938955 + 0.162632i
$$569$$ 4.22095e9 + 7.31090e9i 0.960544 + 1.66371i 0.721138 + 0.692792i $$0.243619\pi$$
0.239406 + 0.970919i $$0.423047\pi$$
$$570$$ −1.94780e8 3.37368e8i −0.0440536 0.0763031i
$$571$$ −8.49495e9 −1.90956 −0.954782 0.297307i $$-0.903912\pi$$
−0.954782 + 0.297307i $$0.903912\pi$$
$$572$$ 3.45423e9 + 1.07132e9i 0.771731 + 0.239350i
$$573$$ 2.57246e9 0.571226
$$574$$ −9.95382e8 1.72405e9i −0.219684 0.380504i
$$575$$ 1.27485e9 + 2.20811e9i 0.279655 + 0.484377i
$$576$$ 1.53511e8 2.65889e8i 0.0334705 0.0579725i
$$577$$ −3.24606e9 −0.703462 −0.351731 0.936101i $$-0.614407\pi$$
−0.351731 + 0.936101i $$0.614407\pi$$
$$578$$ 4.05706e7 7.02704e7i 0.00873905 0.0151365i
$$579$$ −2.20531e9 + 3.81970e9i −0.472165 + 0.817814i
$$580$$ 6.11213e8 0.130075
$$581$$ 1.32044e9 2.28707e9i 0.279320 0.483796i
$$582$$ 1.08538e9 + 1.87994e9i 0.228219 + 0.395287i
$$583$$ −6.62310e9 1.14715e10i −1.38427 2.39763i
$$584$$ −7.12769e8 −0.148082
$$585$$ −3.70679e8 + 3.42878e8i −0.0765512 + 0.0708099i
$$586$$ 3.41338e9 0.700718
$$587$$ 2.87126e9 + 4.97318e9i 0.585922 + 1.01485i 0.994760 + 0.102240i $$0.0326009\pi$$
−0.408838 + 0.912607i $$0.634066\pi$$
$$588$$ −4.22822e8 7.32350e8i −0.0857704 0.148559i
$$589$$ −2.20223e8 + 3.81438e8i −0.0444078 + 0.0769166i
$$590$$ −5.79294e8 −0.116123
$$591$$ −2.77040e9 + 4.79847e9i −0.552059 + 0.956195i
$$592$$ −4.08976e6 + 7.08368e6i −0.000810163 + 0.00140324i
$$593$$ −5.53884e9 −1.09076 −0.545378 0.838190i $$-0.683614\pi$$
−0.545378 + 0.838190i $$0.683614\pi$$
$$594$$ −3.05411e9 + 5.28987e9i −0.597904 + 1.03560i
$$595$$ 6.20919e8 + 1.07546e9i 0.120844 + 0.209308i
$$596$$ 1.23284e9 + 2.13534e9i 0.238530 + 0.413147i
$$597$$ 7.61761e8 0.146524
$$598$$ 1.57810e9 1.45974e9i 0.301773 0.279140i
$$599$$ −5.75425e8 −0.109394 −0.0546971 0.998503i $$-0.517419\pi$$
−0.0546971 + 0.998503i $$0.517419\pi$$
$$600$$ −6.13264e8 1.06220e9i −0.115909 0.200761i
$$601$$ −1.81762e9 3.14821e9i −0.341541 0.591566i 0.643178 0.765717i $$-0.277615\pi$$
−0.984719 + 0.174150i $$0.944282\pi$$
$$602$$ 2.39424e9 4.14695e9i 0.447281 0.774713i
$$603$$ 3.31634e9 0.615953
$$604$$ −9.42679e8 + 1.63277e9i −0.174074 + 0.301505i
$$605$$ 8.54555e8 1.48013e9i 0.156890 0.271742i
$$606$$ 2.69614e9 0.492140
$$607$$ −4.49966e8 + 7.79364e8i −0.0816619 + 0.141443i −0.903964 0.427609i $$-0.859356\pi$$
0.822302 + 0.569051i $$0.192689\pi$$
$$608$$ 4.59926e8 + 7.96616e8i 0.0829900 + 0.143743i
$$609$$ −3.11141e9 5.38913e9i −0.558209 0.966847i
$$610$$ 1.24816e9 0.222647
$$611$$ 4.10258e9 + 1.27241e9i 0.727634 + 0.225674i
$$612$$ 1.53703e9 0.271053
$$613$$ −9.74743e8 1.68830e9i −0.170914 0.296032i 0.767825 0.640659i $$-0.221339\pi$$
−0.938740 + 0.344627i $$0.888005\pi$$
$$614$$ 1.13369e9 + 1.96361e9i 0.197654 + 0.342347i
$$615$$ 1.93970e8 3.35965e8i 0.0336257 0.0582414i
$$616$$ 4.06410e9 0.700538
$$617$$ 2.94732e9 5.10490e9i 0.505160 0.874962i −0.494822 0.868994i $$-0.664767\pi$$
0.999982 0.00596820i $$-0.00189975\pi$$
$$618$$ 3.84425e8 6.65844e8i 0.0655167 0.113478i
$$619$$ 5.43625e9 0.921259 0.460630 0.887592i $$-0.347624\pi$$
0.460630 + 0.887592i $$0.347624\pi$$
$$620$$ 2.73266e7 4.73310e7i 0.00460484 0.00797581i
$$621$$ 1.81538e9 + 3.14434e9i 0.304192 + 0.526876i
$$622$$ −2.85695e9 4.94839e9i −0.476033 0.824512i
$$623$$ −7.84626e9 −1.30003
$$624$$ −7.59138e8 + 7.02203e8i −0.125076 + 0.115696i
$$625$$ 5.41801e9 0.887687
$$626$$ −1.40794e9 2.43862e9i −0.229389 0.397314i
$$627$$ −3.19122e9 5.52735e9i −0.517035 0.895531i
$$628$$ −2.16720e9 + 3.75371e9i −0.349173 + 0.604786i
$$629$$ −4.09488e7 −0.00656092
$$630$$ −2.83715e8 + 4.91408e8i −0.0452054 + 0.0782980i
$$631$$ 5.81666e8 1.00747e9i 0.0921660 0.159636i −0.816256 0.577690i $$-0.803954\pi$$
0.908422 + 0.418054i $$0.137288\pi$$
$$632$$ 1.19555e9 0.188390
$$633$$ 8.72901e8 1.51191e9i 0.136789 0.236926i
$$634$$ −1.82251e9 3.15668e9i −0.284026 0.491947i
$$635$$ −1.10995e9 1.92249e9i −0.172026 0.297959i
$$636$$ 3.78759e9 0.583798
$$637$$ −7.25828e8 3.20280e9i −0.111262 0.490955i
$$638$$ 1.00140e10 1.52663
$$639$$ −9.38046e8 1.62474e9i −0.142223 0.246338i
$$640$$ −5.70703e7 9.88487e7i −0.00860559 0.0149053i
$$641$$ −1.31488e9 + 2.27743e9i −0.197189 + 0.341541i −0.947616 0.319412i $$-0.896515\pi$$
0.750427 + 0.660953i $$0.229848\pi$$
$$642$$ −5.81948e9 −0.867984
$$643$$ 1.46295e9 2.53391e9i 0.217016 0.375883i −0.736878 0.676025i $$-0.763701\pi$$
0.953894 + 0.300143i $$0.0970343\pi$$
$$644$$ 1.20787e9 2.09209e9i 0.178204 0.308659i
$$645$$ 9.33130e8 0.136925
$$646$$ −2.30251e9 + 3.98807e9i −0.336038 + 0.582034i
$$647$$ 6.86472e8 + 1.18900e9i 0.0996455 + 0.172591i 0.911538 0.411216i $$-0.134896\pi$$
−0.811892 + 0.583807i $$0.801562\pi$$
$$648$$ −2.17562e8 3.76829e8i −0.0314102 0.0544041i
$$649$$ −9.49100e9 −1.36287
$$650$$ −1.05274e9 4.64536e9i −0.150358 0.663472i
$$651$$ −5.56430e8 −0.0790455
$$652$$ −3.18837e9 5.52242e9i −0.450507 0.780302i
$$653$$ 2.25639e9 + 3.90819e9i 0.317116 + 0.549262i 0.979885 0.199563i $$-0.0639521\pi$$
−0.662769 + 0.748824i $$0.730619\pi$$
$$654$$ 5.81220e8 1.00670e9i 0.0812491 0.140728i
$$655$$ −2.23707e9 −0.311054
$$656$$ −4.58014e8 + 7.93304e8i −0.0633454 + 0.109718i
$$657$$ 8.15228e8 1.41202e9i 0.112150 0.194250i
$$658$$ 4.82691e9 0.660509
$$659$$ 2.70823e9 4.69079e9i 0.368626 0.638479i −0.620725 0.784028i $$-0.713162\pi$$
0.989351 + 0.145549i $$0.0464949\pi$$
$$660$$ 3.95985e8 + 6.85866e8i 0.0536136 + 0.0928614i
$$661$$ 7.09561e8 + 1.22900e9i 0.0955618 + 0.165518i 0.909843 0.414953i $$-0.136202\pi$$
−0.814281 + 0.580471i $$0.802869\pi$$
$$662$$ −5.32168e9 −0.712929
$$663$$ −4.94466e9 1.53357e9i −0.658930 0.204365i
$$664$$ −1.21517e9 −0.161083
$$665$$ −8.50022e8 1.47228e9i −0.112087 0.194140i
$$666$$ −9.35532e6 1.62039e7i −0.00122715 0.00212549i
$$667$$ 2.97619e9 5.15490e9i 0.388347 0.672636i
$$668$$ 2.12238e9 0.275490
$$669$$ −4.33801e9 + 7.51366e9i −0.560144 + 0.970198i
$$670$$ 6.16451e8 1.06772e9i 0.0791839 0.137151i
$$671$$ 2.04496e10 2.61310
$$672$$ −5.81039e8 + 1.00639e9i −0.0738606 + 0.127930i
$$673$$ 2.75030e9 + 4.76366e9i 0.347799 + 0.602405i 0.985858 0.167582i $$-0.0535960\pi$$
−0.638060 + 0.769987i $$0.720263\pi$$
$$674$$ 3.68117e9 + 6.37597e9i 0.463101 + 0.802114i
$$675$$ 8.04477e9 1.00682
$$676$$ −3.62356e9 + 1.73128e9i −0.451151 + 0.215552i
$$677$$ −8.33416e9 −1.03229 −0.516145 0.856501i $$-0.672633\pi$$
−0.516145 + 0.856501i $$0.672633\pi$$
$$678$$ 2.64304e9 + 4.57788e9i 0.325687 + 0.564106i
$$679$$ 4.73663e9 + 8.20408e9i 0.580664 + 1.00574i
$$680$$ 2.85709e8 4.94862e8i 0.0348452 0.0603536i
$$681$$ −1.43280e9 −0.173849
$$682$$ 4.47711e8 7.75459e8i 0.0540447 0.0936081i
$$683$$ −7.46024e9 + 1.29215e10i −0.895943 + 1.55182i −0.0633104 + 0.997994i $$0.520166\pi$$
−0.832633 + 0.553825i $$0.813168\pi$$
$$684$$ −2.10416e9 −0.251410
$$685$$ 4.00599e8 6.93857e8i 0.0476204 0.0824809i
$$686$$ 1.82025e9 + 3.15276e9i 0.215276 + 0.372869i
$$687$$ −1.96743e9 3.40769e9i −0.231500 0.400970i
$$688$$ −2.20337e9 −0.257945
$$689$$ 1.40487e10 + 4.35717e9i 1.63632 + 0.507502i
$$690$$ 4.70753e8 0.0545533
$$691$$ −2.44866e9 4.24121e9i −0.282329 0.489009i 0.689629 0.724163i $$-0.257774\pi$$
−0.971958 + 0.235154i $$0.924440\pi$$
$$692$$ −1.36372e9 2.36203e9i −0.156442 0.270965i
$$693$$ −4.64831e9 + 8.05111e9i −0.530553 + 0.918944i
$$694$$ −1.09199e10 −1.24011
$$695$$ −1.54704e9 + 2.67956e9i −0.174806 + 0.302773i
$$696$$ −1.43168e9 + 2.47975e9i −0.160959 + 0.278789i
$$697$$ −4.58588e9 −0.512988
$$698$$ −3.58889e9 + 6.21615e9i −0.399454 + 0.691874i
$$699$$ −2.01654e9 3.49275e9i −0.223325 0.386810i
$$700$$ −2.67629e9 4.63548e9i −0.294911 0.510800i
$$701$$ −2.20310e9 −0.241558 −0.120779 0.992679i $$-0.538539\pi$$
−0.120779 + 0.992679i $$0.538539\pi$$
$$702$$ −1.49910e9 6.61496e9i −0.163550 0.721684i
$$703$$ 5.60579e7 0.00608546
$$704$$ −9.35025e8 1.61951e9i −0.100999 0.174936i
$$705$$ 4.70309e8 + 8.14600e8i 0.0505501 + 0.0875553i
$$706$$ −1.07842e9 + 1.86788e9i −0.115338 + 0.199771i
$$707$$ 1.17660e10 1.25216
$$708$$ 1.35692e9 2.35025e9i 0.143693 0.248884i
$$709$$ −4.34938e9 + 7.53334e9i −0.458316 + 0.793827i −0.998872 0.0474812i $$-0.984881\pi$$
0.540556 + 0.841308i $$0.318214\pi$$
$$710$$ −6.97468e8 −0.0731341
$$711$$ −1.36741e9 + 2.36842e9i −0.142677 + 0.247124i
$$712$$ 1.80519e9 + 3.12667e9i 0.187431 + 0.324640i
$$713$$ −2.66123e8 4.60939e8i −0.0274960 0.0476244i
$$714$$ −5.81767e9 −0.598143
$$715$$ 6.79757e8 + 2.99951e9i 0.0695477 + 0.306887i
$$716$$ −1.29701e9 −0.132053
$$717$$ −1.28274e8 2.22177e8i −0.0129964 0.0225104i
$$718$$ −8.95711e8 1.55142e9i −0.0903093 0.156420i
$$719$$ 5.46812e8 9.47107e8i 0.0548640 0.0950272i −0.837289 0.546761i $$-0.815861\pi$$
0.892153 + 0.451733i $$0.149194\pi$$
$$720$$ 2.61096e8 0.0260698
$$721$$ 1.67764e9 2.90576e9i 0.166696 0.288726i
$$722$$ −4.23409e8 + 7.33367e8i −0.0418678 + 0.0725172i
$$723$$ −1.23527e10 −1.21556
$$724$$ 9.88975e8 1.71296e9i 0.0968502 0.167749i
$$725$$ −6.59439e9 1.14218e10i −0.642676 1.11315i
$$726$$ 4.00335e9 + 6.93401e9i 0.388281 + 0.672522i
$$727$$ 9.47790e9 0.914832 0.457416 0.889253i $$-0.348775\pi$$
0.457416 + 0.889253i $$0.348775\pi$$
$$728$$ −3.31289e9 + 3.06443e9i −0.318235 + 0.294367i
$$729$$ 8.45578e9 0.808365
$$730$$ −3.03074e8 5.24940e8i −0.0288350 0.0499436i
$$731$$ −5.51532e9 9.55281e9i −0.522227 0.904524i
$$732$$ −2.92365e9 + 5.06391e9i −0.275509 + 0.477196i
$$733$$ 5.75895e9 0.540107 0.270053 0.962845i $$-0.412959\pi$$
0.270053 + 0.962845i $$0.412959\pi$$
$$734$$ −1.12343e9 + 1.94583e9i −0.104860 + 0.181622i
$$735$$ 3.59574e8 6.22801e8i 0.0334028 0.0578553i
$$736$$ −1.11157e9 −0.102770
$$737$$ 1.00998e10 1.74933e10i 0.929341 1.60967i
$$738$$ −1.04771e9 1.81468e9i −0.0959493 0.166189i
$$739$$ −3.55253e9 6.15316e9i −0.323804 0.560845i 0.657466 0.753485i $$-0.271628\pi$$
−0.981270 + 0.192640i $$0.938295\pi$$
$$740$$ −6.95599e6 −0.000631027
$$741$$ 6.76911e9 + 2.09942e9i 0.611178 + 0.189555i
$$742$$ 1.65291e10 1.48537
$$743$$ 4.92054e9 + 8.52263e9i 0.440101 + 0.762277i 0.997697 0.0678357i $$-0.0216094\pi$$
−0.557596 + 0.830113i $$0.688276\pi$$
$$744$$ 1.28017e8 + 2.21733e8i 0.0113963 + 0.0197390i
$$745$$ −1.04842e9 + 1.81592e9i −0.0928943 + 0.160898i
$$746$$ −1.40420e10 −1.23834
$$747$$ 1.38985e9 2.40729e9i 0.121996 0.211303i
$$748$$ 4.68098e9 8.10769e9i 0.408960 0.708340i
$$749$$ −2.53963e10 −2.20843
$$750$$ 1.06361e9 1.84223e9i 0.0920594 0.159452i
$$751$$ −6.46148e9 1.11916e10i −0.556663 0.964169i −0.997772 0.0667151i $$-0.978748\pi$$
0.441109 0.897454i $$-0.354585\pi$$
$$752$$ −1.11053e9 1.92349e9i −0.0952283 0.164940i
$$753$$ 2.36000e9 0.201432
$$754$$ −8.16298e9 + 7.55076e9i −0.693504 + 0.641492i
$$755$$ −1.60333e9 −0.135584
$$756$$ −3.81103e9 6.60089e9i −0.320786 0.555618i
$$757$$ 7.59753e9 + 1.31593e10i 0.636556 + 1.10255i 0.986183 + 0.165659i $$0.0529750\pi$$
−0.349627 + 0.936889i $$0.613692\pi$$
$$758$$ 1.43693e9 2.48884e9i 0.119838 0.207565i