# Properties

 Label 26.8.c.b.3.3 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 3.3 Root $$23.0850i$$ of defining polynomial Character $$\chi$$ $$=$$ 26.3 Dual form 26.8.c.b.9.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(4.00000 + 6.92820i) q^{2} +(19.9922 + 34.6275i) q^{3} +(-32.0000 + 55.4256i) q^{4} -323.700 q^{5} +(-159.938 + 277.020i) q^{6} +(-284.296 + 492.415i) q^{7} -512.000 q^{8} +(294.123 - 509.436i) q^{9} +O(q^{10})$$ $$q+(4.00000 + 6.92820i) q^{2} +(19.9922 + 34.6275i) q^{3} +(-32.0000 + 55.4256i) q^{4} -323.700 q^{5} +(-159.938 + 277.020i) q^{6} +(-284.296 + 492.415i) q^{7} -512.000 q^{8} +(294.123 - 509.436i) q^{9} +(-1294.80 - 2242.66i) q^{10} +(119.113 + 206.309i) q^{11} -2559.00 q^{12} +(-5815.88 + 5378.11i) q^{13} -4548.73 q^{14} +(-6471.49 - 11208.9i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-10233.3 + 17724.6i) q^{17} +4705.97 q^{18} +(4821.16 - 8350.49i) q^{19} +(10358.4 - 17941.3i) q^{20} -22734.8 q^{21} +(-952.901 + 1650.47i) q^{22} +(39132.3 + 67779.1i) q^{23} +(-10236.0 - 17729.3i) q^{24} +26657.0 q^{25} +(-60524.2 - 18781.2i) q^{26} +110967. q^{27} +(-18194.9 - 31514.5i) q^{28} +(69432.3 + 120260. i) q^{29} +(51771.9 - 89671.6i) q^{30} +160571. q^{31} +(16384.0 - 28377.9i) q^{32} +(-4762.65 + 8249.15i) q^{33} -163733. q^{34} +(92026.6 - 159395. i) q^{35} +(18823.9 + 32603.9i) q^{36} +(76477.6 + 132463. i) q^{37} +77138.6 q^{38} +(-302503. - 93869.2i) q^{39} +165735. q^{40} +(-92718.0 - 160592. i) q^{41} +(-90939.2 - 157511. i) q^{42} +(-42504.5 + 73620.0i) q^{43} -15246.4 q^{44} +(-95207.7 + 164905. i) q^{45} +(-313058. + 542233. i) q^{46} -1.20335e6 q^{47} +(81888.1 - 141834. i) q^{48} +(250123. + 433227. i) q^{49} +(106628. + 184685. i) q^{50} -818346. q^{51} +(-111977. - 494448. i) q^{52} -665967. q^{53} +(443866. + 768799. i) q^{54} +(-38556.8 - 66782.3i) q^{55} +(145559. - 252116. i) q^{56} +385543. q^{57} +(-555458. + 962082. i) q^{58} +(1.24309e6 - 2.15310e6i) q^{59} +828351. q^{60} +(1.52300e6 - 2.63791e6i) q^{61} +(642282. + 1.11247e6i) q^{62} +(167236. + 289661. i) q^{63} +262144. q^{64} +(1.88260e6 - 1.74090e6i) q^{65} -76202.4 q^{66} +(193938. + 335910. i) q^{67} +(-654932. - 1.13437e6i) q^{68} +(-1.56468e6 + 2.71011e6i) q^{69} +1.47243e6 q^{70} +(-1.84016e6 + 3.18724e6i) q^{71} +(-150591. + 260831. i) q^{72} +1.57546e6 q^{73} +(-611821. + 1.05970e6i) q^{74} +(532932. + 923066. i) q^{75} +(308554. + 534432. i) q^{76} -135453. q^{77} +(-559667. - 2.47128e6i) q^{78} +2.29576e6 q^{79} +(662939. + 1.14824e6i) q^{80} +(1.57522e6 + 2.72836e6i) q^{81} +(741744. - 1.28474e6i) q^{82} -7.93544e6 q^{83} +(727514. - 1.26009e6i) q^{84} +(3.31253e6 - 5.73746e6i) q^{85} -680072. q^{86} +(-2.77621e6 + 4.80854e6i) q^{87} +(-60985.6 - 105630. i) q^{88} +(-4.07541e6 - 7.05882e6i) q^{89} -1.52332e6 q^{90} +(-994830. - 4.39280e6i) q^{91} -5.00893e6 q^{92} +(3.21016e6 + 5.56016e6i) q^{93} +(-4.81339e6 - 8.33704e6i) q^{94} +(-1.56061e6 + 2.70306e6i) q^{95} +1.31021e6 q^{96} +(669795. - 1.16012e6i) q^{97} +(-2.00099e6 + 3.46581e6i) q^{98} +140135. 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
$$3$$ 19.9922 + 34.6275i 0.427500 + 0.740452i 0.996650 0.0817814i $$-0.0260609\pi$$
−0.569150 + 0.822234i $$0.692728\pi$$
$$4$$ −32.0000 + 55.4256i −0.250000 + 0.433013i
$$5$$ −323.700 −1.15811 −0.579053 0.815290i $$-0.696578\pi$$
−0.579053 + 0.815290i $$0.696578\pi$$
$$6$$ −159.938 + 277.020i −0.302288 + 0.523579i
$$7$$ −284.296 + 492.415i −0.313276 + 0.542610i −0.979070 0.203526i $$-0.934760\pi$$
0.665794 + 0.746136i $$0.268093\pi$$
$$8$$ −512.000 −0.353553
$$9$$ 294.123 509.436i 0.134487 0.232938i
$$10$$ −1294.80 2242.66i −0.409452 0.709192i
$$11$$ 119.113 + 206.309i 0.0269826 + 0.0467352i 0.879201 0.476450i $$-0.158077\pi$$
−0.852219 + 0.523186i $$0.824743\pi$$
$$12$$ −2559.00 −0.427500
$$13$$ −5815.88 + 5378.11i −0.734199 + 0.678935i
$$14$$ −4548.73 −0.443039
$$15$$ −6471.49 11208.9i −0.495091 0.857522i
$$16$$ −2048.00 3547.24i −0.125000 0.216506i
$$17$$ −10233.3 + 17724.6i −0.505178 + 0.874994i 0.494804 + 0.869005i $$0.335240\pi$$
−0.999982 + 0.00598975i $$0.998093\pi$$
$$18$$ 4705.97 0.190193
$$19$$ 4821.16 8350.49i 0.161255 0.279302i −0.774064 0.633108i $$-0.781779\pi$$
0.935319 + 0.353805i $$0.115112\pi$$
$$20$$ 10358.4 17941.3i 0.289527 0.501475i
$$21$$ −22734.8 −0.535702
$$22$$ −952.901 + 1650.47i −0.0190796 + 0.0330468i
$$23$$ 39132.3 + 67779.1i 0.670638 + 1.16158i 0.977724 + 0.209897i $$0.0673128\pi$$
−0.307086 + 0.951682i $$0.599354\pi$$
$$24$$ −10236.0 17729.3i −0.151144 0.261789i
$$25$$ 26657.0 0.341210
$$26$$ −60524.2 18781.2i −0.675339 0.209563i
$$27$$ 110967. 1.08497
$$28$$ −18194.9 31514.5i −0.156638 0.271305i
$$29$$ 69432.3 + 120260.i 0.528650 + 0.915649i 0.999442 + 0.0334046i $$0.0106350\pi$$
−0.470792 + 0.882244i $$0.656032\pi$$
$$30$$ 51771.9 89671.6i 0.350082 0.606360i
$$31$$ 160571. 0.968055 0.484027 0.875053i $$-0.339174\pi$$
0.484027 + 0.875053i $$0.339174\pi$$
$$32$$ 16384.0 28377.9i 0.0883883 0.153093i
$$33$$ −4762.65 + 8249.15i −0.0230701 + 0.0399586i
$$34$$ −163733. −0.714430
$$35$$ 92026.6 159395.i 0.362807 0.628400i
$$36$$ 18823.9 + 32603.9i 0.0672435 + 0.116469i
$$37$$ 76477.6 + 132463.i 0.248215 + 0.429921i 0.963031 0.269392i $$-0.0868227\pi$$
−0.714816 + 0.699313i $$0.753489\pi$$
$$38$$ 77138.6 0.228049
$$39$$ −302503. 93869.2i −0.816589 0.253394i
$$40$$ 165735. 0.409452
$$41$$ −92718.0 160592.i −0.210097 0.363899i 0.741647 0.670790i $$-0.234045\pi$$
−0.951745 + 0.306891i $$0.900711\pi$$
$$42$$ −90939.2 157511.i −0.189399 0.328049i
$$43$$ −42504.5 + 73620.0i −0.0815259 + 0.141207i −0.903906 0.427732i $$-0.859313\pi$$
0.822380 + 0.568939i $$0.192646\pi$$
$$44$$ −15246.4 −0.0269826
$$45$$ −95207.7 + 164905.i −0.155750 + 0.269767i
$$46$$ −313058. + 542233.i −0.474212 + 0.821360i
$$47$$ −1.20335e6 −1.69063 −0.845315 0.534268i $$-0.820587\pi$$
−0.845315 + 0.534268i $$0.820587\pi$$
$$48$$ 81888.1 141834.i 0.106875 0.185113i
$$49$$ 250123. + 433227.i 0.303716 + 0.526052i
$$50$$ 106628. + 184685.i 0.120636 + 0.208947i
$$51$$ −818346. −0.863856
$$52$$ −111977. 494448.i −0.110438 0.487651i
$$53$$ −665967. −0.614451 −0.307225 0.951637i $$-0.599401\pi$$
−0.307225 + 0.951637i $$0.599401\pi$$
$$54$$ 443866. + 768799.i 0.383596 + 0.664408i
$$55$$ −38556.8 66782.3i −0.0312487 0.0541243i
$$56$$ 145559. 252116.i 0.110760 0.191842i
$$57$$ 385543. 0.275747
$$58$$ −555458. + 962082.i −0.373812 + 0.647462i
$$59$$ 1.24309e6 2.15310e6i 0.787992 1.36484i −0.139204 0.990264i $$-0.544454\pi$$
0.927195 0.374578i $$-0.122212\pi$$
$$60$$ 828351. 0.495091
$$61$$ 1.52300e6 2.63791e6i 0.859104 1.48801i −0.0136811 0.999906i $$-0.504355\pi$$
0.872785 0.488105i $$-0.162312\pi$$
$$62$$ 642282. + 1.11247e6i 0.342259 + 0.592810i
$$63$$ 167236. + 289661.i 0.0842630 + 0.145948i
$$64$$ 262144. 0.125000
$$65$$ 1.88260e6 1.74090e6i 0.850280 0.786278i
$$66$$ −76202.4 −0.0326261
$$67$$ 193938. + 335910.i 0.0787772 + 0.136446i 0.902723 0.430223i $$-0.141565\pi$$
−0.823945 + 0.566669i $$0.808232\pi$$
$$68$$ −654932. 1.13437e6i −0.252589 0.437497i
$$69$$ −1.56468e6 + 2.71011e6i −0.573396 + 0.993150i
$$70$$ 1.47243e6 0.513086
$$71$$ −1.84016e6 + 3.18724e6i −0.610170 + 1.05684i 0.381042 + 0.924558i $$0.375565\pi$$
−0.991211 + 0.132287i $$0.957768\pi$$
$$72$$ −150591. + 260831.i −0.0475483 + 0.0823561i
$$73$$ 1.57546e6 0.473998 0.236999 0.971510i $$-0.423836\pi$$
0.236999 + 0.971510i $$0.423836\pi$$
$$74$$ −611821. + 1.05970e6i −0.175515 + 0.304000i
$$75$$ 532932. + 923066.i 0.145867 + 0.252649i
$$76$$ 308554. + 534432.i 0.0806276 + 0.139651i
$$77$$ −135453. −0.0338120
$$78$$ −559667. 2.47128e6i −0.133536 0.589645i
$$79$$ 2.29576e6 0.523880 0.261940 0.965084i $$-0.415638\pi$$
0.261940 + 0.965084i $$0.415638\pi$$
$$80$$ 662939. + 1.14824e6i 0.144763 + 0.250737i
$$81$$ 1.57522e6 + 2.72836e6i 0.329340 + 0.570433i
$$82$$ 741744. 1.28474e6i 0.148561 0.257316i
$$83$$ −7.93544e6 −1.52334 −0.761672 0.647963i $$-0.775621\pi$$
−0.761672 + 0.647963i $$0.775621\pi$$
$$84$$ 727514. 1.26009e6i 0.133926 0.231966i
$$85$$ 3.31253e6 5.73746e6i 0.585050 1.01334i
$$86$$ −680072. −0.115295
$$87$$ −2.77621e6 + 4.80854e6i −0.451996 + 0.782881i
$$88$$ −60985.6 105630.i −0.00953978 0.0165234i
$$89$$ −4.07541e6 7.05882e6i −0.612782 1.06137i −0.990769 0.135559i $$-0.956717\pi$$
0.377987 0.925811i $$-0.376616\pi$$
$$90$$ −1.52332e6 −0.220264
$$91$$ −994830. 4.39280e6i −0.138390 0.611077i
$$92$$ −5.00893e6 −0.670638
$$93$$ 3.21016e6 + 5.56016e6i 0.413844 + 0.716798i
$$94$$ −4.81339e6 8.33704e6i −0.597728 1.03530i
$$95$$ −1.56061e6 + 2.70306e6i −0.186751 + 0.323462i
$$96$$ 1.31021e6 0.151144
$$97$$ 669795. 1.16012e6i 0.0745145 0.129063i −0.826361 0.563141i $$-0.809593\pi$$
0.900875 + 0.434079i $$0.142926\pi$$
$$98$$ −2.00099e6 + 3.46581e6i −0.214760 + 0.371975i
$$99$$ 140135. 0.0145152
$$100$$ −853024. + 1.47748e6i −0.0853024 + 0.147748i
$$101$$ 9.63841e6 + 1.66942e7i 0.930852 + 1.61228i 0.781868 + 0.623444i $$0.214267\pi$$
0.148984 + 0.988840i $$0.452400\pi$$
$$102$$ −3.27338e6 5.66966e6i −0.305419 0.529001i
$$103$$ −1.54295e7 −1.39130 −0.695652 0.718379i $$-0.744884\pi$$
−0.695652 + 0.718379i $$0.744884\pi$$
$$104$$ 2.97773e6 2.75359e6i 0.259578 0.240040i
$$105$$ 7.35926e6 0.620400
$$106$$ −2.66387e6 4.61395e6i −0.217241 0.376273i
$$107$$ 5.21244e6 + 9.02820e6i 0.411337 + 0.712456i 0.995036 0.0995137i $$-0.0317287\pi$$
−0.583699 + 0.811970i $$0.698395\pi$$
$$108$$ −3.55093e6 + 6.15039e6i −0.271243 + 0.469807i
$$109$$ 1.55544e7 1.15043 0.575216 0.818001i $$-0.304918\pi$$
0.575216 + 0.818001i $$0.304918\pi$$
$$110$$ 308454. 534259.i 0.0220961 0.0382716i
$$111$$ −3.05791e6 + 5.29646e6i −0.212224 + 0.367583i
$$112$$ 2.32895e6 0.156638
$$113$$ 468038. 810666.i 0.0305145 0.0528527i −0.850365 0.526194i $$-0.823619\pi$$
0.880879 + 0.473341i $$0.156952\pi$$
$$114$$ 1.54217e6 + 2.67112e6i 0.0974912 + 0.168860i
$$115$$ −1.26671e7 2.19401e7i −0.776670 1.34523i
$$116$$ −8.88733e6 −0.528650
$$117$$ 1.02922e6 + 4.54464e6i 0.0594096 + 0.262331i
$$118$$ 1.98895e7 1.11439
$$119$$ −5.81857e6 1.00781e7i −0.316520 0.548230i
$$120$$ 3.31340e6 + 5.73898e6i 0.175041 + 0.303180i
$$121$$ 9.71521e6 1.68272e7i 0.498544 0.863503i
$$122$$ 2.43680e7 1.21496
$$123$$ 3.70727e6 6.42119e6i 0.179633 0.311134i
$$124$$ −5.13826e6 + 8.89972e6i −0.242014 + 0.419180i
$$125$$ 1.66602e7 0.762949
$$126$$ −1.33789e6 + 2.31729e6i −0.0595830 + 0.103201i
$$127$$ 4.23586e6 + 7.33673e6i 0.183497 + 0.317826i 0.943069 0.332597i $$-0.107925\pi$$
−0.759572 + 0.650423i $$0.774592\pi$$
$$128$$ 1.04858e6 + 1.81619e6i 0.0441942 + 0.0765466i
$$129$$ −3.39904e6 −0.139409
$$130$$ 1.95917e7 + 6.07947e6i 0.782114 + 0.242697i
$$131$$ 1.17131e7 0.455219 0.227610 0.973752i $$-0.426909\pi$$
0.227610 + 0.973752i $$0.426909\pi$$
$$132$$ −304809. 527945.i −0.0115351 0.0199793i
$$133$$ 2.74127e6 + 4.74802e6i 0.101035 + 0.174997i
$$134$$ −1.55150e6 + 2.68728e6i −0.0557039 + 0.0964820i
$$135$$ −3.59199e7 −1.25651
$$136$$ 5.23945e6 9.07500e6i 0.178608 0.309357i
$$137$$ −1.87496e7 + 3.24753e7i −0.622975 + 1.07902i 0.365954 + 0.930633i $$0.380743\pi$$
−0.988929 + 0.148391i $$0.952591\pi$$
$$138$$ −2.50349e7 −0.810904
$$139$$ 1.40529e7 2.43404e7i 0.443828 0.768733i −0.554142 0.832422i $$-0.686953\pi$$
0.997970 + 0.0636896i $$0.0202867\pi$$
$$140$$ 5.88970e6 + 1.02013e7i 0.181403 + 0.314200i
$$141$$ −2.40576e7 4.16690e7i −0.722745 1.25183i
$$142$$ −2.94425e7 −0.862910
$$143$$ −1.80230e6 559268.i −0.0515407 0.0159935i
$$144$$ −2.40945e6 −0.0672435
$$145$$ −2.24753e7 3.89283e7i −0.612233 1.06042i
$$146$$ 6.30182e6 + 1.09151e7i 0.167584 + 0.290263i
$$147$$ −1.00010e7 + 1.73223e7i −0.259678 + 0.449775i
$$148$$ −9.78913e6 −0.248215
$$149$$ −2.29505e7 + 3.97514e7i −0.568381 + 0.984465i 0.428345 + 0.903615i $$0.359097\pi$$
−0.996726 + 0.0808495i $$0.974237\pi$$
$$150$$ −4.26346e6 + 7.38453e6i −0.103144 + 0.178650i
$$151$$ 4.77305e7 1.12818 0.564088 0.825714i $$-0.309228\pi$$
0.564088 + 0.825714i $$0.309228\pi$$
$$152$$ −2.46843e6 + 4.27545e6i −0.0570124 + 0.0987483i
$$153$$ 6.01970e6 + 1.04264e7i 0.135880 + 0.235351i
$$154$$ −541811. 938444.i −0.0119543 0.0207055i
$$155$$ −5.19768e7 −1.12111
$$156$$ 1.48829e7 1.37626e7i 0.313870 0.290245i
$$157$$ 7.12033e7 1.46842 0.734212 0.678921i $$-0.237552\pi$$
0.734212 + 0.678921i $$0.237552\pi$$
$$158$$ 9.18305e6 + 1.59055e7i 0.185220 + 0.320810i
$$159$$ −1.33141e7 2.30608e7i −0.262678 0.454971i
$$160$$ −5.30351e6 + 9.18595e6i −0.102363 + 0.177298i
$$161$$ −4.45006e7 −0.840379
$$162$$ −1.26018e7 + 2.18269e7i −0.232878 + 0.403357i
$$163$$ −3.11031e7 + 5.38721e7i −0.562531 + 0.974332i 0.434744 + 0.900554i $$0.356839\pi$$
−0.997275 + 0.0737781i $$0.976494\pi$$
$$164$$ 1.18679e7 0.210097
$$165$$ 1.54167e6 2.67025e6i 0.0267176 0.0462763i
$$166$$ −3.17418e7 5.49784e7i −0.538583 0.932854i
$$167$$ −1.12288e7 1.94489e7i −0.186563 0.323137i 0.757539 0.652790i $$-0.226402\pi$$
−0.944102 + 0.329653i $$0.893068\pi$$
$$168$$ 1.16402e7 0.189399
$$169$$ 4.90039e6 6.25569e7i 0.0780957 0.996946i
$$170$$ 5.30004e7 0.827386
$$171$$ −2.83603e6 4.91214e6i −0.0433734 0.0751250i
$$172$$ −2.72029e6 4.71168e6i −0.0407629 0.0706035i
$$173$$ −4.30844e7 + 7.46244e7i −0.632643 + 1.09577i 0.354366 + 0.935107i $$0.384697\pi$$
−0.987009 + 0.160664i $$0.948637\pi$$
$$174$$ −4.44194e7 −0.639219
$$175$$ −7.57847e6 + 1.31263e7i −0.106893 + 0.185144i
$$176$$ 487885. 845042.i 0.00674564 0.0116838i
$$177$$ 9.94087e7 1.34747
$$178$$ 3.26033e7 5.64705e7i 0.433303 0.750502i
$$179$$ 3.55570e7 + 6.15865e7i 0.463382 + 0.802602i 0.999127 0.0417785i $$-0.0133024\pi$$
−0.535745 + 0.844380i $$0.679969\pi$$
$$180$$ −6.09329e6 1.05539e7i −0.0778750 0.134884i
$$181$$ 1.39420e8 1.74763 0.873817 0.486254i $$-0.161637\pi$$
0.873817 + 0.486254i $$0.161637\pi$$
$$182$$ 2.64549e7 2.44636e7i 0.325279 0.300795i
$$183$$ 1.21793e8 1.46907
$$184$$ −2.00357e7 3.47029e7i −0.237106 0.410680i
$$185$$ −2.47558e7 4.28784e7i −0.287459 0.497894i
$$186$$ −2.56813e7 + 4.44813e7i −0.292632 + 0.506853i
$$187$$ −4.87566e6 −0.0545240
$$188$$ 3.85071e7 6.66963e7i 0.422658 0.732064i
$$189$$ −3.15473e7 + 5.46416e7i −0.339896 + 0.588717i
$$190$$ −2.49698e7 −0.264105
$$191$$ 4.29014e7 7.43074e7i 0.445507 0.771641i −0.552580 0.833460i $$-0.686357\pi$$
0.998087 + 0.0618185i $$0.0196900\pi$$
$$192$$ 5.24084e6 + 9.07740e6i 0.0534375 + 0.0925565i
$$193$$ −1.17723e7 2.03903e7i −0.117872 0.204161i 0.801052 0.598595i $$-0.204274\pi$$
−0.918924 + 0.394434i $$0.870941\pi$$
$$194$$ 1.07167e7 0.105379
$$195$$ 9.79203e7 + 3.03855e7i 0.945697 + 0.293458i
$$196$$ −3.20158e7 −0.303716
$$197$$ −3.57372e7 6.18986e7i −0.333034 0.576832i 0.650071 0.759873i $$-0.274739\pi$$
−0.983105 + 0.183041i $$0.941406\pi$$
$$198$$ 560540. + 970883.i 0.00513190 + 0.00888871i
$$199$$ −1.07802e8 + 1.86718e8i −0.969706 + 1.67958i −0.273306 + 0.961927i $$0.588117\pi$$
−0.696400 + 0.717654i $$0.745216\pi$$
$$200$$ −1.36484e7 −0.120636
$$201$$ −7.75449e6 + 1.34312e7i −0.0673546 + 0.116662i
$$202$$ −7.71073e7 + 1.33554e8i −0.658212 + 1.14006i
$$203$$ −7.89572e7 −0.662454
$$204$$ 2.61871e7 4.53573e7i 0.215964 0.374060i
$$205$$ 3.00129e7 + 5.19838e7i 0.243315 + 0.421434i
$$206$$ −6.17180e7 1.06899e8i −0.491900 0.851996i
$$207$$ 4.60388e7 0.360768
$$208$$ 3.09884e7 + 9.61595e6i 0.238768 + 0.0740919i
$$209$$ 2.29704e6 0.0174043
$$210$$ 2.94371e7 + 5.09865e7i 0.219345 + 0.379916i
$$211$$ −4.46978e7 7.74188e7i −0.327565 0.567359i 0.654463 0.756094i $$-0.272895\pi$$
−0.982028 + 0.188735i $$0.939561\pi$$
$$212$$ 2.13109e7 3.69116e7i 0.153613 0.266065i
$$213$$ −1.47155e8 −1.04339
$$214$$ −4.16995e7 + 7.22256e7i −0.290859 + 0.503783i
$$215$$ 1.37587e7 2.38308e7i 0.0944156 0.163533i
$$216$$ −5.68149e7 −0.383596
$$217$$ −4.56495e7 + 7.90673e7i −0.303268 + 0.525276i
$$218$$ 6.22177e7 + 1.07764e8i 0.406739 + 0.704493i
$$219$$ 3.14969e7 + 5.45541e7i 0.202634 + 0.350973i
$$220$$ 4.93527e6 0.0312487
$$221$$ −3.58092e7 1.58120e8i −0.223163 0.985403i
$$222$$ −4.89266e7 −0.300130
$$223$$ −5.37637e7 9.31215e7i −0.324655 0.562319i 0.656787 0.754076i $$-0.271915\pi$$
−0.981443 + 0.191757i $$0.938582\pi$$
$$224$$ 9.31580e6 + 1.61354e7i 0.0553799 + 0.0959208i
$$225$$ 7.84043e6 1.35800e7i 0.0458882 0.0794807i
$$226$$ 7.48861e6 0.0431541
$$227$$ 1.07539e8 1.86264e8i 0.610207 1.05691i −0.380999 0.924576i $$-0.624420\pi$$
0.991205 0.132333i $$-0.0422470\pi$$
$$228$$ −1.23374e7 + 2.13689e7i −0.0689367 + 0.119402i
$$229$$ −3.12216e8 −1.71803 −0.859016 0.511949i $$-0.828924\pi$$
−0.859016 + 0.511949i $$0.828924\pi$$
$$230$$ 1.01337e8 1.75521e8i 0.549188 0.951222i
$$231$$ −2.70800e6 4.69039e6i −0.0144546 0.0250361i
$$232$$ −3.55493e7 6.15732e7i −0.186906 0.323731i
$$233$$ −2.62733e8 −1.36072 −0.680360 0.732878i $$-0.738177\pi$$
−0.680360 + 0.732878i $$0.738177\pi$$
$$234$$ −2.73693e7 + 2.53092e7i −0.139640 + 0.129129i
$$235$$ 3.89524e8 1.95793
$$236$$ 7.95580e7 + 1.37798e8i 0.393996 + 0.682421i
$$237$$ 4.58974e7 + 7.94965e7i 0.223959 + 0.387908i
$$238$$ 4.65485e7 8.06244e7i 0.223814 0.387657i
$$239$$ −8.68087e7 −0.411311 −0.205656 0.978624i $$-0.565933\pi$$
−0.205656 + 0.978624i $$0.565933\pi$$
$$240$$ −2.65072e7 + 4.59118e7i −0.123773 + 0.214381i
$$241$$ −1.06288e8 + 1.84096e8i −0.489130 + 0.847198i −0.999922 0.0125066i $$-0.996019\pi$$
0.510792 + 0.859704i $$0.329352\pi$$
$$242$$ 1.55443e8 0.705048
$$243$$ 5.83577e7 1.01078e8i 0.260901 0.451894i
$$244$$ 9.74720e7 + 1.68827e8i 0.429552 + 0.744006i
$$245$$ −8.09651e7 1.40236e8i −0.351736 0.609224i
$$246$$ 5.93164e7 0.254040
$$247$$ 1.68706e7 + 7.44942e7i 0.0712346 + 0.314545i
$$248$$ −8.22121e7 −0.342259
$$249$$ −1.58647e8 2.74785e8i −0.651230 1.12796i
$$250$$ 6.66409e7 + 1.15425e8i 0.269743 + 0.467209i
$$251$$ 5.96185e7 1.03262e8i 0.237970 0.412177i −0.722161 0.691725i $$-0.756851\pi$$
0.960132 + 0.279548i $$0.0901846\pi$$
$$252$$ −2.14062e7 −0.0842630
$$253$$ −9.32230e6 + 1.61467e7i −0.0361910 + 0.0626847i
$$254$$ −3.38869e7 + 5.86938e7i −0.129752 + 0.224737i
$$255$$ 2.64899e8 1.00044
$$256$$ −8.38861e6 + 1.45295e7i −0.0312500 + 0.0541266i
$$257$$ 1.72292e8 + 2.98419e8i 0.633139 + 1.09663i 0.986906 + 0.161296i $$0.0515673\pi$$
−0.353767 + 0.935334i $$0.615099\pi$$
$$258$$ −1.35962e7 2.35492e7i −0.0492887 0.0853705i
$$259$$ −8.69690e7 −0.311039
$$260$$ 3.62470e7 + 1.60053e8i 0.127898 + 0.564752i
$$261$$ 8.16865e7 0.284386
$$262$$ 4.68522e7 + 8.11504e7i 0.160944 + 0.278764i
$$263$$ −1.51825e7 2.62969e7i −0.0514634 0.0891373i 0.839146 0.543906i $$-0.183055\pi$$
−0.890610 + 0.454769i $$0.849722\pi$$
$$264$$ 2.43848e6 4.22356e6i 0.00815652 0.0141275i
$$265$$ 2.15574e8 0.711599
$$266$$ −2.19302e7 + 3.79841e7i −0.0714424 + 0.123742i
$$267$$ 1.62953e8 2.82243e8i 0.523929 0.907472i
$$268$$ −2.48240e7 −0.0787772
$$269$$ −2.52890e8 + 4.38018e8i −0.792134 + 1.37202i 0.132510 + 0.991182i $$0.457696\pi$$
−0.924643 + 0.380834i $$0.875637\pi$$
$$270$$ −1.43680e8 2.48861e8i −0.444245 0.769455i
$$271$$ 1.82110e8 + 3.15424e8i 0.555829 + 0.962724i 0.997839 + 0.0657138i $$0.0209324\pi$$
−0.442009 + 0.897010i $$0.645734\pi$$
$$272$$ 8.38312e7 0.252589
$$273$$ 1.32223e8 1.22270e8i 0.393312 0.363707i
$$274$$ −2.99994e8 −0.881020
$$275$$ 3.17518e6 + 5.49958e6i 0.00920671 + 0.0159465i
$$276$$ −1.00140e8 1.73447e8i −0.286698 0.496575i
$$277$$ 5.83761e7 1.01110e8i 0.165027 0.285836i −0.771638 0.636062i $$-0.780562\pi$$
0.936665 + 0.350227i $$0.113895\pi$$
$$278$$ 2.24847e8 0.627668
$$279$$ 4.72275e7 8.18004e7i 0.130191 0.225497i
$$280$$ −4.71176e7 + 8.16101e7i −0.128272 + 0.222173i
$$281$$ 3.12559e8 0.840349 0.420174 0.907443i $$-0.361969\pi$$
0.420174 + 0.907443i $$0.361969\pi$$
$$282$$ 1.92461e8 3.33352e8i 0.511058 0.885178i
$$283$$ −1.05637e8 1.82969e8i −0.277054 0.479872i 0.693597 0.720363i $$-0.256025\pi$$
−0.970651 + 0.240491i $$0.922692\pi$$
$$284$$ −1.17770e8 2.03984e8i −0.305085 0.528422i
$$285$$ −1.24800e8 −0.319344
$$286$$ −3.33447e6 1.47238e7i −0.00842840 0.0372167i
$$287$$ 1.05437e8 0.263274
$$288$$ −9.63782e6 1.66932e7i −0.0237742 0.0411780i
$$289$$ −4.27172e6 7.39884e6i −0.0104102 0.0180311i
$$290$$ 1.79802e8 3.11426e8i 0.432914 0.749829i
$$291$$ 5.35627e7 0.127420
$$292$$ −5.04146e7 + 8.73206e7i −0.118499 + 0.205247i
$$293$$ 3.49752e8 6.05788e8i 0.812313 1.40697i −0.0989278 0.995095i $$-0.531541\pi$$
0.911241 0.411873i $$-0.135125\pi$$
$$294$$ −1.60017e8 −0.367240
$$295$$ −4.02390e8 + 6.96960e8i −0.912578 + 1.58063i
$$296$$ −3.91565e7 6.78211e7i −0.0877573 0.152000i
$$297$$ 1.32175e7 + 2.28934e7i 0.0292754 + 0.0507064i
$$298$$ −3.67207e8 −0.803812
$$299$$ −5.92112e8 1.83737e8i −1.28102 0.397510i
$$300$$ −6.82153e7 −0.145867
$$301$$ −2.41677e7 4.18597e7i −0.0510802 0.0884735i
$$302$$ 1.90922e8 + 3.30687e8i 0.398871 + 0.690864i
$$303$$ −3.85386e8 + 6.67509e8i −0.795879 + 1.37850i
$$304$$ −3.94949e7 −0.0806276
$$305$$ −4.92996e8 + 8.53894e8i −0.994933 + 1.72327i
$$306$$ −4.81576e7 + 8.34114e7i −0.0960815 + 0.166418i
$$307$$ 4.84159e8 0.955001 0.477500 0.878632i $$-0.341543\pi$$
0.477500 + 0.878632i $$0.341543\pi$$
$$308$$ 4.33449e6 7.50755e6i 0.00845299 0.0146410i
$$309$$ −3.08470e8 5.34286e8i −0.594783 1.03019i
$$310$$ −2.07907e8 3.60106e8i −0.396372 0.686537i
$$311$$ −5.82462e8 −1.09801 −0.549005 0.835819i $$-0.684993\pi$$
−0.549005 + 0.835819i $$0.684993\pi$$
$$312$$ 1.54882e8 + 4.80610e7i 0.288708 + 0.0895885i
$$313$$ −6.04523e8 −1.11431 −0.557157 0.830407i $$-0.688108\pi$$
−0.557157 + 0.830407i $$0.688108\pi$$
$$314$$ 2.84813e8 + 4.93311e8i 0.519166 + 0.899222i
$$315$$ −5.41343e7 9.37633e7i −0.0975855 0.169023i
$$316$$ −7.34644e7 + 1.27244e8i −0.130970 + 0.226847i
$$317$$ 9.32561e8 1.64426 0.822129 0.569301i $$-0.192786\pi$$
0.822129 + 0.569301i $$0.192786\pi$$
$$318$$ 1.06513e8 1.84486e8i 0.185741 0.321713i
$$319$$ −1.65405e7 + 2.86490e7i −0.0285287 + 0.0494131i
$$320$$ −8.48561e7 −0.144763
$$321$$ −2.08416e8 + 3.60988e8i −0.351693 + 0.609150i
$$322$$ −1.78002e8 3.08309e8i −0.297119 0.514625i
$$323$$ 9.86728e7 + 1.70906e8i 0.162925 + 0.282195i
$$324$$ −2.01628e8 −0.329340
$$325$$ −1.55034e8 + 1.43364e8i −0.250516 + 0.231659i
$$326$$ −4.97649e8 −0.795539
$$327$$ 3.10967e8 + 5.38611e8i 0.491810 + 0.851840i
$$328$$ 4.74716e7 + 8.22232e7i 0.0742806 + 0.128658i
$$329$$ 3.42107e8 5.92546e8i 0.529634 0.917353i
$$330$$ 2.46667e7 0.0377844
$$331$$ 3.41829e8 5.92065e8i 0.518096 0.897369i −0.481683 0.876346i $$-0.659974\pi$$
0.999779 0.0210234i $$-0.00669245\pi$$
$$332$$ 2.53934e8 4.39827e8i 0.380836 0.659627i
$$333$$ 8.99753e7 0.133527
$$334$$ 8.98305e7 1.55591e8i 0.131920 0.228492i
$$335$$ −6.27778e7 1.08734e8i −0.0912324 0.158019i
$$336$$ 4.65609e7 + 8.06458e7i 0.0669628 + 0.115983i
$$337$$ 1.36368e9 1.94092 0.970459 0.241264i $$-0.0775621\pi$$
0.970459 + 0.241264i $$0.0775621\pi$$
$$338$$ 4.53008e8 2.16277e8i 0.638113 0.304650i
$$339$$ 3.74285e7 0.0521799
$$340$$ 2.12002e8 + 3.67198e8i 0.292525 + 0.506668i
$$341$$ 1.91260e7 + 3.31271e7i 0.0261206 + 0.0452422i
$$342$$ 2.26882e7 3.92971e7i 0.0306697 0.0531214i
$$343$$ −7.52695e8 −1.00714
$$344$$ 2.17623e7 3.76934e7i 0.0288238 0.0499242i
$$345$$ 5.06488e8 8.77264e8i 0.664053 1.15017i
$$346$$ −6.89351e8 −0.894693
$$347$$ 9.07095e7 1.57113e8i 0.116547 0.201865i −0.801850 0.597525i $$-0.796151\pi$$
0.918397 + 0.395660i $$0.129484\pi$$
$$348$$ −1.77677e8 3.07746e8i −0.225998 0.391440i
$$349$$ 2.23486e8 + 3.87090e8i 0.281425 + 0.487442i 0.971736 0.236071i $$-0.0758598\pi$$
−0.690311 + 0.723512i $$0.742526\pi$$
$$350$$ −1.21255e8 −0.151169
$$351$$ −6.45368e8 + 5.96791e8i −0.796586 + 0.736626i
$$352$$ 7.80616e6 0.00953978
$$353$$ −6.06158e7 1.04990e8i −0.0733456 0.127038i 0.827020 0.562172i $$-0.190034\pi$$
−0.900366 + 0.435134i $$0.856701\pi$$
$$354$$ 3.97635e8 + 6.88724e8i 0.476402 + 0.825152i
$$355$$ 5.95660e8 1.03171e9i 0.706641 1.22394i
$$356$$ 5.21653e8 0.612782
$$357$$ 2.32652e8 4.02965e8i 0.270625 0.468737i
$$358$$ −2.84456e8 + 4.92692e8i −0.327661 + 0.567525i
$$359$$ −1.84724e8 −0.210714 −0.105357 0.994434i $$-0.533599\pi$$
−0.105357 + 0.994434i $$0.533599\pi$$
$$360$$ 4.87463e7 8.44312e7i 0.0550660 0.0953771i
$$361$$ 4.00449e8 + 6.93597e8i 0.447993 + 0.775947i
$$362$$ 5.57681e8 + 9.65932e8i 0.617882 + 1.07020i
$$363$$ 7.76914e8 0.852511
$$364$$ 2.75308e8 + 8.54304e7i 0.299202 + 0.0928448i
$$365$$ −5.09976e8 −0.548940
$$366$$ 4.87170e8 + 8.43804e8i 0.519394 + 0.899617i
$$367$$ −4.45347e8 7.71364e8i −0.470292 0.814569i 0.529131 0.848540i $$-0.322518\pi$$
−0.999423 + 0.0339709i $$0.989185\pi$$
$$368$$ 1.60286e8 2.77623e8i 0.167659 0.290395i
$$369$$ −1.09082e8 −0.113021
$$370$$ 1.98047e8 3.43027e8i 0.203265 0.352064i
$$371$$ 1.89331e8 3.27932e8i 0.192493 0.333407i
$$372$$ −4.10901e8 −0.413844
$$373$$ −2.21327e8 + 3.83349e8i −0.220828 + 0.382485i −0.955060 0.296414i $$-0.904209\pi$$
0.734232 + 0.678899i $$0.237542\pi$$
$$374$$ −1.95026e7 3.37796e7i −0.0192772 0.0333890i
$$375$$ 3.33075e8 + 5.76902e8i 0.326161 + 0.564928i
$$376$$ 6.16114e8 0.597728
$$377$$ −1.05058e9 3.26005e8i −1.00980 0.313349i
$$378$$ −5.04757e8 −0.480686
$$379$$ −7.43553e8 1.28787e9i −0.701576 1.21517i −0.967913 0.251285i $$-0.919147\pi$$
0.266337 0.963880i $$-0.414187\pi$$
$$380$$ −9.98792e7 1.72996e8i −0.0933754 0.161731i
$$381$$ −1.69368e8 + 2.93355e8i −0.156890 + 0.271741i
$$382$$ 6.86423e8 0.630042
$$383$$ −4.46769e8 + 7.73827e8i −0.406338 + 0.703798i −0.994476 0.104962i $$-0.966528\pi$$
0.588138 + 0.808761i $$0.299861\pi$$
$$384$$ −4.19267e7 + 7.26192e7i −0.0377860 + 0.0654474i
$$385$$ 4.38461e7 0.0391578
$$386$$ 9.41787e7 1.63122e8i 0.0833484 0.144364i
$$387$$ 2.50031e7 + 4.33066e7i 0.0219283 + 0.0379810i
$$388$$ 4.28669e7 + 7.42476e7i 0.0372572 + 0.0645314i
$$389$$ −5.98070e8 −0.515143 −0.257572 0.966259i $$-0.582922\pi$$
−0.257572 + 0.966259i $$0.582922\pi$$
$$390$$ 1.81164e8 + 7.99954e8i 0.154649 + 0.682871i
$$391$$ −1.60181e9 −1.35517
$$392$$ −1.28063e8 2.21812e8i −0.107380 0.185988i
$$393$$ 2.34170e8 + 4.05594e8i 0.194606 + 0.337068i
$$394$$ 2.85898e8 4.95189e8i 0.235491 0.407882i
$$395$$ −7.43139e8 −0.606709
$$396$$ −4.48432e6 + 7.76707e6i −0.00362880 + 0.00628527i
$$397$$ 1.02106e9 1.76852e9i 0.818999 1.41855i −0.0874217 0.996171i $$-0.527863\pi$$
0.906421 0.422376i $$-0.138804\pi$$
$$398$$ −1.72483e9 −1.37137
$$399$$ −1.09608e8 + 1.89847e8i −0.0863848 + 0.149623i
$$400$$ −5.45935e7 9.45588e7i −0.0426512 0.0738740i
$$401$$ 8.12903e8 + 1.40799e9i 0.629555 + 1.09042i 0.987641 + 0.156732i $$0.0500960\pi$$
−0.358086 + 0.933689i $$0.616571\pi$$
$$402$$ −1.24072e8 −0.0952538
$$403$$ −9.33859e8 + 8.63566e8i −0.710745 + 0.657246i
$$404$$ −1.23372e9 −0.930852
$$405$$ −5.09900e8 8.83172e8i −0.381410 0.660622i
$$406$$ −3.15829e8 5.47031e8i −0.234213 0.405668i
$$407$$ −1.82189e7 + 3.15560e7i −0.0133950 + 0.0232008i
$$408$$ 4.18993e8 0.305419
$$409$$ 3.53619e7 6.12486e7i 0.0255567 0.0442655i −0.852964 0.521969i $$-0.825198\pi$$
0.878521 + 0.477704i $$0.158531\pi$$
$$410$$ −2.40103e8 + 4.15870e8i −0.172050 + 0.297999i
$$411$$ −1.49939e9 −1.06529
$$412$$ 4.93744e8 8.55190e8i 0.347826 0.602452i
$$413$$ 7.06812e8 + 1.22423e9i 0.493718 + 0.855144i
$$414$$ 1.84155e8 + 3.18966e8i 0.127551 + 0.220924i
$$415$$ 2.56871e9 1.76419
$$416$$ 5.73322e7 + 2.53158e8i 0.0390456 + 0.172411i
$$417$$ 1.12380e9 0.758947
$$418$$ 9.18817e6 + 1.59144e7i 0.00615336 + 0.0106579i
$$419$$ −7.58892e8 1.31444e9i −0.504000 0.872954i −0.999989 0.00462522i $$-0.998528\pi$$
0.495989 0.868329i $$-0.334806\pi$$
$$420$$ −2.35496e8 + 4.07892e8i −0.155100 + 0.268641i
$$421$$ −6.23005e8 −0.406916 −0.203458 0.979084i $$-0.565218\pi$$
−0.203458 + 0.979084i $$0.565218\pi$$
$$422$$ 3.57582e8 6.19351e8i 0.231623 0.401183i
$$423$$ −3.53932e8 + 6.13028e8i −0.227368 + 0.393812i
$$424$$ 3.40975e8 0.217241
$$425$$ −2.72789e8 + 4.72485e8i −0.172372 + 0.298556i
$$426$$ −5.88621e8 1.01952e9i −0.368894 0.638944i
$$427$$ 8.65965e8 + 1.49990e9i 0.538273 + 0.932316i
$$428$$ −6.67192e8 −0.411337
$$429$$ −1.66658e7 7.35901e7i −0.0101912 0.0450007i
$$430$$ 2.20140e8 0.133524
$$431$$ 3.99315e8 + 6.91634e8i 0.240240 + 0.416108i 0.960783 0.277303i $$-0.0894406\pi$$
−0.720543 + 0.693411i $$0.756107\pi$$
$$432$$ −2.27260e8 3.93625e8i −0.135622 0.234904i
$$433$$ 5.32611e8 9.22509e8i 0.315284 0.546088i −0.664214 0.747543i $$-0.731233\pi$$
0.979498 + 0.201455i $$0.0645668\pi$$
$$434$$ −7.30392e8 −0.428886
$$435$$ 8.98660e8 1.55653e9i 0.523460 0.906659i
$$436$$ −4.97741e8 + 8.62114e8i −0.287608 + 0.498152i
$$437$$ 7.54652e8 0.432575
$$438$$ −2.51975e8 + 4.36433e8i −0.143284 + 0.248175i
$$439$$ −1.39630e9 2.41846e9i −0.787685 1.36431i −0.927382 0.374115i $$-0.877946\pi$$
0.139698 0.990194i $$-0.455387\pi$$
$$440$$ 1.97411e7 + 3.41926e7i 0.0110481 + 0.0191358i
$$441$$ 2.94268e8 0.163383
$$442$$ 9.52251e8 8.80573e8i 0.524534 0.485051i
$$443$$ 1.37114e9 0.749323 0.374661 0.927162i $$-0.377759\pi$$
0.374661 + 0.927162i $$0.377759\pi$$
$$444$$ −1.95706e8 3.38973e8i −0.106112 0.183791i
$$445$$ 1.31921e9 + 2.28494e9i 0.709667 + 1.22918i
$$446$$ 4.30110e8 7.44972e8i 0.229566 0.397620i
$$447$$ −1.83532e9 −0.971932
$$448$$ −7.45264e7 + 1.29084e8i −0.0391595 + 0.0678262i
$$449$$ 4.30186e8 7.45104e8i 0.224282 0.388467i −0.731822 0.681496i $$-0.761330\pi$$
0.956104 + 0.293028i $$0.0946631\pi$$
$$450$$ 1.25447e8 0.0648957
$$451$$ 2.20878e7 3.82571e7i 0.0113379 0.0196379i
$$452$$ 2.99545e7 + 5.18826e7i 0.0152573 + 0.0264264i
$$453$$ 9.54239e8 + 1.65279e9i 0.482296 + 0.835361i
$$454$$ 1.72063e9 0.862963
$$455$$ 3.22027e8 + 1.42195e9i 0.160270 + 0.707692i
$$456$$ −1.97398e8 −0.0974912
$$457$$ 4.03429e8 + 6.98760e8i 0.197725 + 0.342469i 0.947790 0.318894i $$-0.103311\pi$$
−0.750066 + 0.661363i $$0.769978\pi$$
$$458$$ −1.24886e9 2.16310e9i −0.607416 1.05208i
$$459$$ −1.13556e9 + 1.96684e9i −0.548105 + 0.949346i
$$460$$ 1.62139e9 0.776670
$$461$$ 7.54447e7 1.30674e8i 0.0358654 0.0621207i −0.847536 0.530739i $$-0.821915\pi$$
0.883401 + 0.468618i $$0.155248\pi$$
$$462$$ 2.16640e7 3.75231e7i 0.0102210 0.0177032i
$$463$$ 2.52574e9 1.18265 0.591324 0.806434i $$-0.298605\pi$$
0.591324 + 0.806434i $$0.298605\pi$$
$$464$$ 2.84395e8 4.92586e8i 0.132163 0.228912i
$$465$$ −1.03913e9 1.79983e9i −0.479275 0.830129i
$$466$$ −1.05093e9 1.82027e9i −0.481087 0.833268i
$$467$$ 2.68879e9 1.22165 0.610827 0.791764i $$-0.290837\pi$$
0.610827 + 0.791764i $$0.290837\pi$$
$$468$$ −2.84825e8 8.83835e7i −0.128445 0.0398576i
$$469$$ −2.20543e8 −0.0987161
$$470$$ 1.55810e9 + 2.69870e9i 0.692233 + 1.19898i
$$471$$ 1.42351e9 + 2.46559e9i 0.627751 + 1.08730i
$$472$$ −6.36464e8 + 1.10239e9i −0.278597 + 0.482544i
$$473$$ −2.02513e7 −0.00879911
$$474$$ −3.67179e8 + 6.35972e8i −0.158363 + 0.274293i
$$475$$ 1.28518e8 2.22599e8i 0.0550218 0.0953006i
$$476$$ 7.44777e8 0.316520
$$477$$ −1.95876e8 + 3.39267e8i −0.0826356 + 0.143129i
$$478$$ −3.47235e8 6.01428e8i −0.145420 0.251876i
$$479$$ −1.31293e8 2.27405e8i −0.0545841 0.0945424i 0.837442 0.546526i $$-0.184050\pi$$
−0.892026 + 0.451983i $$0.850717\pi$$
$$480$$ −4.24115e8 −0.175041
$$481$$ −1.15719e9 3.59084e8i −0.474128 0.147126i
$$482$$ −1.70061e9 −0.691734
$$483$$ −8.89665e8 1.54094e9i −0.359262 0.622260i
$$484$$ 6.21773e8 + 1.07694e9i 0.249272 + 0.431752i
$$485$$ −2.16813e8 + 3.75531e8i −0.0862957 + 0.149468i
$$486$$ 9.33723e8 0.368970
$$487$$ −1.13272e9 + 1.96193e9i −0.444398 + 0.769720i −0.998010 0.0630549i $$-0.979916\pi$$
0.553612 + 0.832775i $$0.313249\pi$$
$$488$$ −7.79776e8 + 1.35061e9i −0.303739 + 0.526091i
$$489$$ −2.48728e9 −0.961929
$$490$$ 6.47721e8 1.12189e9i 0.248715 0.430786i
$$491$$ −1.38389e9 2.39696e9i −0.527613 0.913852i −0.999482 0.0321836i $$-0.989754\pi$$
0.471869 0.881669i $$-0.343579\pi$$
$$492$$ 2.37266e8 + 4.10956e8i 0.0898167 + 0.155567i
$$493$$ −2.84209e9 −1.06825
$$494$$ −4.48629e8 + 4.14860e8i −0.167434 + 0.154831i
$$495$$ −4.53617e7 −0.0168101
$$496$$ −3.28848e8 5.69582e8i −0.121007 0.209590i
$$497$$ −1.04630e9 1.81224e9i −0.382303 0.662168i
$$498$$ 1.26918e9 2.19828e9i 0.460489 0.797590i
$$499$$ 1.33804e9 0.482078 0.241039 0.970515i $$-0.422512\pi$$
0.241039 + 0.970515i $$0.422512\pi$$
$$500$$ −5.33127e8 + 9.23403e8i −0.190737 + 0.330367i
$$501$$ 4.48978e8 7.77652e8i 0.159512 0.276283i
$$502$$ 9.53896e8 0.336541
$$503$$ −2.20403e8 + 3.81749e8i −0.0772199 + 0.133749i −0.902049 0.431633i $$-0.857938\pi$$
0.824830 + 0.565381i $$0.191271\pi$$
$$504$$ −8.56247e7 1.48306e8i −0.0297915 0.0516004i
$$505$$ −3.11996e9 5.40393e9i −1.07803 1.86719i
$$506$$ −1.49157e8 −0.0511819
$$507$$ 2.26416e9 1.08096e9i 0.771577 0.368369i
$$508$$ −5.42190e8 −0.183497
$$509$$ 1.62285e8 + 2.81086e8i 0.0545464 + 0.0944771i 0.892009 0.452017i $$-0.149295\pi$$
−0.837463 + 0.546494i $$0.815962\pi$$
$$510$$ 1.05960e9 + 1.83527e9i 0.353708 + 0.612640i
$$511$$ −4.47895e8 + 7.75777e8i −0.148492 + 0.257196i
$$512$$ −1.34218e8 −0.0441942
$$513$$ 5.34988e8 9.26626e8i 0.174958 0.303036i
$$514$$ −1.37834e9 + 2.38735e9i −0.447697 + 0.775434i
$$515$$ 4.99454e9 1.61128
$$516$$ 1.08769e8 1.88394e8i 0.0348523 0.0603660i
$$517$$ −1.43334e8 2.48262e8i −0.0456175 0.0790119i
$$518$$ −3.47876e8 6.02539e8i −0.109969 0.190472i
$$519$$ −3.44541e9 −1.08182
$$520$$ −9.63893e8 + 8.91339e8i −0.300619 + 0.277991i
$$521$$ 1.45685e9 0.451320 0.225660 0.974206i $$-0.427546\pi$$
0.225660 + 0.974206i $$0.427546\pi$$
$$522$$ 3.26746e8 + 5.65941e8i 0.100546 + 0.174150i
$$523$$ −9.45984e8 1.63849e9i −0.289153 0.500828i 0.684455 0.729055i $$-0.260040\pi$$
−0.973608 + 0.228227i $$0.926707\pi$$
$$524$$ −3.74818e8 + 6.49203e8i −0.113805 + 0.197116i
$$525$$ −6.06041e8 −0.182787
$$526$$ 1.21460e8 2.10375e8i 0.0363901 0.0630296i
$$527$$ −1.64317e9 + 2.84605e9i −0.489040 + 0.847043i
$$528$$ 3.90156e7 0.0115351
$$529$$ −1.36026e9 + 2.35604e9i −0.399510 + 0.691971i
$$530$$ 8.62295e8 + 1.49354e9i 0.251588 + 0.435764i
$$531$$ −7.31244e8 1.26655e9i −0.211949 0.367107i
$$532$$ −3.50883e8 −0.101035
$$533$$ 1.40292e9 + 4.35338e8i 0.401317 + 0.124532i
$$534$$ 2.60725e9 0.740948
$$535$$ −1.68727e9 2.92243e9i −0.476372 0.825100i
$$536$$ −9.92962e7 1.71986e8i −0.0278520 0.0482410i
$$537$$ −1.42173e9 + 2.46250e9i −0.396192 + 0.686225i
$$538$$ −4.04624e9 −1.12025
$$539$$ −5.95857e7 + 1.03205e8i −0.0163901 + 0.0283885i
$$540$$ 1.14944e9 1.99089e9i 0.314129 0.544087i
$$541$$ −1.32498e9 −0.359765 −0.179883 0.983688i $$-0.557572\pi$$
−0.179883 + 0.983688i $$0.557572\pi$$
$$542$$ −1.45688e9 + 2.52339e9i −0.393030 + 0.680749i
$$543$$ 2.78732e9 + 4.82778e9i 0.747115 + 1.29404i
$$544$$ 3.35325e8 + 5.80800e8i 0.0893038 + 0.154679i
$$545$$ −5.03497e9 −1.33232
$$546$$ 1.37600e9 + 4.26986e8i 0.361781 + 0.112264i
$$547$$ 1.87811e9 0.490643 0.245321 0.969442i $$-0.421107\pi$$
0.245321 + 0.969442i $$0.421107\pi$$
$$548$$ −1.19998e9 2.07842e9i −0.311487 0.539512i
$$549$$ −8.95899e8 1.55174e9i −0.231076 0.400236i
$$550$$ −2.54015e7 + 4.39966e7i −0.00651013 + 0.0112759i
$$551$$ 1.33898e9 0.340991
$$552$$ 8.01117e8 1.38758e9i 0.202726 0.351132i
$$553$$ −6.52675e8 + 1.13047e9i −0.164119 + 0.284263i
$$554$$ 9.34018e8 0.233384
$$555$$ 9.89848e8 1.71447e9i 0.245778 0.425700i
$$556$$ 8.99387e8 + 1.55778e9i 0.221914 + 0.384366i
$$557$$ 7.25064e7 + 1.25585e8i 0.0177780 + 0.0307924i 0.874778 0.484525i $$-0.161007\pi$$
−0.857000 + 0.515317i $$0.827674\pi$$
$$558$$ 7.55639e8 0.184117
$$559$$ −1.48735e8 6.56759e8i −0.0360141 0.159025i
$$560$$ −7.53882e8 −0.181403
$$561$$ −9.74752e7 1.68832e8i −0.0233090 0.0403724i
$$562$$ 1.25023e9 + 2.16547e9i 0.297108 + 0.514606i
$$563$$ 2.40050e9 4.15779e9i 0.566921 0.981936i −0.429947 0.902854i $$-0.641468\pi$$
0.996868 0.0790818i $$-0.0251988\pi$$
$$564$$ 3.07937e9 0.722745
$$565$$ −1.51504e8 + 2.62413e8i −0.0353391 + 0.0612091i
$$566$$ 8.45099e8 1.46375e9i 0.195907 0.339321i
$$567$$ −1.79131e9 −0.412697
$$568$$ 9.42160e8 1.63187e9i 0.215728 0.373651i
$$569$$ 3.18665e9 + 5.51944e9i 0.725173 + 1.25604i 0.958903 + 0.283735i $$0.0915736\pi$$
−0.233730 + 0.972302i $$0.575093\pi$$
$$570$$ −4.99201e8 8.64642e8i −0.112905 0.195557i
$$571$$ 3.01445e9 0.677613 0.338807 0.940856i $$-0.389977\pi$$
0.338807 + 0.940856i $$0.389977\pi$$
$$572$$ 8.86713e7 8.19969e7i 0.0198106 0.0183194i
$$573$$ 3.43078e9 0.761818
$$574$$ 4.21749e8 + 7.30491e8i 0.0930813 + 0.161222i
$$575$$ 1.04315e9 + 1.80679e9i 0.228828 + 0.396342i
$$576$$ 7.71025e7 1.33546e8i 0.0168109 0.0291173i
$$577$$ 5.46768e9 1.18492 0.592458 0.805601i $$-0.298158\pi$$
0.592458 + 0.805601i $$0.298158\pi$$
$$578$$ 3.41738e7 5.91907e7i 0.00736115 0.0127499i
$$579$$ 4.70710e8 8.15294e8i 0.100781 0.174558i
$$580$$ 2.87683e9 0.612233
$$581$$ 2.25601e9 3.90753e9i 0.477227 0.826581i
$$582$$ 2.14251e8 + 3.71093e8i 0.0450497 + 0.0780284i
$$583$$ −7.93250e7 1.37395e8i −0.0165794 0.0287164i
$$584$$ −8.06634e8 −0.167584
$$585$$ −3.33158e8 1.47110e9i −0.0688027 0.303807i
$$586$$ 5.59603e9 1.14878
$$587$$ −2.05914e9 3.56654e9i −0.420197 0.727803i 0.575761 0.817618i $$-0.304706\pi$$
−0.995958 + 0.0898148i $$0.971372\pi$$
$$588$$ −6.40067e8 1.10863e9i −0.129839 0.224887i
$$589$$ 7.74136e8 1.34084e9i 0.156104 0.270380i
$$590$$ −6.43824e9 −1.29058
$$591$$ 1.42893e9 2.47498e9i 0.284744 0.493192i
$$592$$ 3.13252e8 5.42569e8i 0.0620538 0.107480i
$$593$$ 6.94912e8 0.136848 0.0684240 0.997656i $$-0.478203\pi$$
0.0684240 + 0.997656i $$0.478203\pi$$
$$594$$ −1.05740e8 + 1.83147e8i −0.0207008 + 0.0358549i
$$595$$ 1.88347e9 + 3.26227e9i 0.366564 + 0.634908i
$$596$$ −1.46883e9 2.54409e9i −0.284190 0.492232i
$$597$$ −8.62079e9 −1.65820
$$598$$ −1.09548e9 4.83722e9i −0.209484 0.925001i
$$599$$ 5.53945e9 1.05311 0.526554 0.850142i $$-0.323484\pi$$
0.526554 + 0.850142i $$0.323484\pi$$
$$600$$ −2.72861e8 4.72610e8i −0.0515718 0.0893250i
$$601$$ −9.34647e8 1.61886e9i −0.175625 0.304192i 0.764752 0.644324i $$-0.222861\pi$$
−0.940377 + 0.340133i $$0.889528\pi$$
$$602$$ 1.93342e8 3.34878e8i 0.0361192 0.0625602i
$$603$$ 2.28166e8 0.0423780
$$604$$ −1.52738e9 + 2.64550e9i −0.282044 + 0.488515i
$$605$$ −3.14482e9 + 5.44698e9i −0.577367 + 1.00003i
$$606$$ −6.16618e9 −1.12554
$$607$$ −3.92775e9 + 6.80306e9i −0.712825 + 1.23465i 0.250967 + 0.967996i $$0.419251\pi$$
−0.963792 + 0.266654i $$0.914082\pi$$
$$608$$ −1.57980e8 2.73629e8i −0.0285062 0.0493741i
$$609$$ −1.57853e9 2.73409e9i −0.283199 0.490515i
$$610$$ −7.88794e9 −1.40705
$$611$$ 6.99853e9 6.47174e9i 1.24126 1.14783i
$$612$$ −7.70521e8 −0.135880
$$613$$ 5.55641e9 + 9.62398e9i 0.974277 + 1.68750i 0.682302 + 0.731070i $$0.260979\pi$$
0.291974 + 0.956426i $$0.405688\pi$$
$$614$$ 1.93664e9 + 3.35435e9i 0.337644 + 0.584816i
$$615$$ −1.20005e9 + 2.07854e9i −0.208034 + 0.360326i
$$616$$ 6.93518e7 0.0119543
$$617$$ −1.49482e9 + 2.58911e9i −0.256207 + 0.443764i −0.965223 0.261429i $$-0.915806\pi$$
0.709016 + 0.705193i $$0.249140\pi$$
$$618$$ 2.46776e9 4.27429e9i 0.420575 0.728457i
$$619$$ −4.26716e9 −0.723138 −0.361569 0.932345i $$-0.617759\pi$$
−0.361569 + 0.932345i $$0.617759\pi$$
$$620$$ 1.66326e9 2.88084e9i 0.280278 0.485455i
$$621$$ 4.34238e9 + 7.52122e9i 0.727624 + 1.26028i
$$622$$ −2.32985e9 4.03541e9i −0.388205 0.672391i
$$623$$ 4.63449e9 0.767880
$$624$$ 2.86549e8 + 1.26529e9i 0.0472121 + 0.208471i
$$625$$ −7.47550e9 −1.22479
$$626$$ −2.41809e9 4.18826e9i −0.393970 0.682375i
$$627$$ 4.59230e7 + 7.95409e7i 0.00744035 + 0.0128871i
$$628$$ −2.27850e9 + 3.94649e9i −0.367106 + 0.635846i
$$629$$ −3.13047e9 −0.501572
$$630$$ 4.33074e8 7.50107e8i 0.0690034 0.119517i
$$631$$ −3.57540e9 + 6.19277e9i −0.566528 + 0.981256i 0.430377 + 0.902649i $$0.358380\pi$$
−0.996906 + 0.0786066i $$0.974953\pi$$
$$632$$ −1.17543e9 −0.185220
$$633$$ 1.78721e9 3.09555e9i 0.280068 0.485092i
$$634$$ 3.73024e9 + 6.46097e9i 0.581333 + 1.00690i
$$635$$ −1.37115e9 2.37490e9i −0.212509 0.368076i
$$636$$ 1.70421e9 0.262678
$$637$$ −3.78463e9 1.17440e9i −0.580143 0.180023i
$$638$$ −2.64648e8 −0.0403456
$$639$$ 1.08246e9 + 1.87488e9i 0.164120 + 0.284264i
$$640$$ −3.39425e8 5.87901e8i −0.0511815 0.0886490i
$$641$$ −1.54411e9 + 2.67448e9i −0.231566 + 0.401085i −0.958269 0.285867i $$-0.907718\pi$$
0.726703 + 0.686952i $$0.241052\pi$$
$$642$$ −3.33466e9 −0.497369
$$643$$ −3.08662e9 + 5.34619e9i −0.457873 + 0.793060i −0.998848 0.0479788i $$-0.984722\pi$$
0.540975 + 0.841039i $$0.318055\pi$$
$$644$$ 1.42402e9 2.46647e9i 0.210095 0.363895i
$$645$$ 1.10027e9 0.161451
$$646$$ −7.89382e8 + 1.36725e9i −0.115206 + 0.199542i
$$647$$ −1.89760e9 3.28675e9i −0.275449 0.477091i 0.694800 0.719203i $$-0.255493\pi$$
−0.970248 + 0.242112i $$0.922160\pi$$
$$648$$ −8.06513e8 1.39692e9i −0.116439 0.201679i
$$649$$ 5.92272e8 0.0850481
$$650$$ −1.61339e9 5.00649e8i −0.230432 0.0715051i
$$651$$ −3.65054e9 −0.518589
$$652$$ −1.99060e9 3.44781e9i −0.281266 0.487166i
$$653$$ −5.33607e9 9.24234e9i −0.749938 1.29893i −0.947852 0.318711i $$-0.896750\pi$$
0.197914 0.980219i $$-0.436583\pi$$
$$654$$ −2.48774e9 + 4.30889e9i −0.347762 + 0.602342i
$$655$$ −3.79152e9 −0.527192
$$656$$ −3.79773e8 + 6.57786e8i −0.0525243 + 0.0909748i
$$657$$ 4.63378e8 8.02594e8i 0.0637465 0.110412i
$$658$$ 5.47371e9 0.749015
$$659$$ 6.14106e9 1.06366e10i 0.835880 1.44779i −0.0574313 0.998349i $$-0.518291\pi$$
0.893312 0.449438i $$-0.148376\pi$$
$$660$$ 9.86670e7 + 1.70896e8i 0.0133588 + 0.0231381i
$$661$$ −3.63672e9 6.29899e9i −0.489785 0.848332i 0.510146 0.860088i $$-0.329591\pi$$
−0.999931 + 0.0117556i $$0.996258\pi$$
$$662$$ 5.46926e9 0.732699
$$663$$ 4.75940e9 4.40115e9i 0.634242 0.586501i
$$664$$ 4.06295e9 0.538583
$$665$$ −8.87350e8 1.53694e9i −0.117009 0.202666i
$$666$$ 3.59901e8 + 6.23367e8i 0.0472088 + 0.0817681i
$$667$$ −5.43409e9 + 9.41212e9i −0.709065 + 1.22814i
$$668$$ 1.43729e9 0.186563
$$669$$ 2.14971e9 3.72341e9i 0.277580 0.480783i
$$670$$ 5.02222e8 8.69874e8i 0.0645110 0.111736i
$$671$$ 7.25634e8 0.0927233
$$672$$ −3.72487e8 + 6.45166e8i −0.0473498 + 0.0820123i
$$673$$ 2.43285e8 + 4.21381e8i 0.0307654 + 0.0532872i 0.880998 0.473120i $$-0.156872\pi$$
−0.850233 + 0.526407i $$0.823539\pi$$
$$674$$ 5.45471e9 + 9.44784e9i 0.686218 + 1.18857i
$$675$$ 2.95804e9 0.370203
$$676$$ 3.31044e9 + 2.27343e9i 0.412166 + 0.283053i
$$677$$ 4.31885e9 0.534944 0.267472 0.963566i $$-0.413812\pi$$
0.267472 + 0.963566i $$0.413812\pi$$
$$678$$ 1.49714e8 + 2.59312e8i 0.0184484 + 0.0319535i
$$679$$ 3.80839e8 + 6.59633e8i 0.0466872 + 0.0808646i
$$680$$ −1.69601e9 + 2.93758e9i −0.206846 + 0.358269i
$$681$$ 8.59980e9 1.04345
$$682$$ −1.53008e8 + 2.65017e8i −0.0184701 + 0.0319911i
$$683$$ −3.89016e9 + 6.73796e9i −0.467192 + 0.809201i −0.999297 0.0374776i $$-0.988068\pi$$
0.532105 + 0.846678i $$0.321401\pi$$
$$684$$ 3.63011e8 0.0433734
$$685$$ 6.06926e9 1.05123e10i 0.721471 1.24962i
$$686$$ −3.01078e9 5.21483e9i −0.356078 0.616745i
$$687$$ −6.24189e9 1.08113e10i −0.734459 1.27212i
$$688$$ 3.48197e8 0.0407629
$$689$$ 3.87318e9 3.58164e9i 0.451129 0.417172i
$$690$$ 8.10382e9 0.939113
$$691$$ 7.63764e9 + 1.32288e10i 0.880614 + 1.52527i 0.850659 + 0.525718i $$0.176203\pi$$
0.0299552 + 0.999551i $$0.490464\pi$$
$$692$$ −2.75740e9 4.77596e9i −0.316322 0.547885i
$$693$$ −3.98397e7 + 6.90045e7i −0.00454727 + 0.00787609i
$$694$$ 1.45135e9 0.164822
$$695$$ −4.54894e9 + 7.87899e9i −0.514000 + 0.890274i
$$696$$ 1.42142e9 2.46197e9i 0.159805 0.276790i
$$697$$ 3.79525e9 0.424546
$$698$$ −1.78789e9 + 3.09672e9i −0.198997 + 0.344673i
$$699$$ −5.25262e9 9.09780e9i −0.581709 1.00755i
$$700$$ −4.85022e8 8.40083e8i −0.0534464 0.0925718i
$$701$$ −1.39687e9 −0.153159 −0.0765794 0.997063i $$-0.524400\pi$$
−0.0765794 + 0.997063i $$0.524400\pi$$
$$702$$ −6.71616e9 2.08408e9i −0.732725 0.227371i
$$703$$ 1.47484e9 0.160104
$$704$$ 3.12246e7 + 5.40827e7i 0.00337282 + 0.00584190i
$$705$$ 7.78745e9 + 1.34883e10i 0.837015 + 1.44975i
$$706$$ 4.84926e8 8.39917e8i 0.0518632 0.0898297i
$$707$$ −1.09606e10 −1.16645
$$708$$ −3.18108e9 + 5.50979e9i −0.336867 + 0.583470i
$$709$$ 6.96858e8 1.20699e9i 0.0734315 0.127187i −0.826972 0.562244i $$-0.809938\pi$$
0.900403 + 0.435057i $$0.143272\pi$$
$$710$$ 9.53055e9 0.999341
$$711$$ 6.75236e8 1.16954e9i 0.0704550 0.122032i
$$712$$ 2.08661e9 + 3.61411e9i 0.216651 + 0.375251i
$$713$$ 6.28349e9 + 1.08833e10i 0.649214 + 1.12447i
$$714$$ 3.72243e9 0.382722
$$715$$ 5.83404e8 + 1.81035e8i 0.0596896 + 0.0185222i
$$716$$ −4.55129e9 −0.463382
$$717$$ −1.73550e9 3.00597e9i −0.175836 0.304556i
$$718$$ −7.38898e8 1.27981e9i −0.0744987 0.129036i
$$719$$ 4.06923e9 7.04812e9i 0.408283 0.707167i −0.586414 0.810011i $$-0.699461\pi$$
0.994697 + 0.102844i $$0.0327943\pi$$
$$720$$ 7.79942e8 0.0778750
$$721$$ 4.38654e9 7.59771e9i 0.435862 0.754935i
$$722$$ −3.20359e9 + 5.54878e9i −0.316779 + 0.548678i
$$723$$ −8.49972e9 −0.836413
$$724$$ −4.46145e9 + 7.72745e9i −0.436909 + 0.756748i
$$725$$ 1.85086e9 + 3.20578e9i 0.180380 + 0.312428i
$$726$$ 3.10766e9 + 5.38262e9i 0.301408 + 0.522054i
$$727$$ −9.98246e9 −0.963534 −0.481767 0.876299i $$-0.660005\pi$$
−0.481767 + 0.876299i $$0.660005\pi$$
$$728$$ 5.09353e8 + 2.24911e9i 0.0489282 + 0.216048i
$$729$$ 1.15568e10 1.10482
$$730$$ −2.03990e9 3.53322e9i −0.194079 0.336156i
$$731$$ −8.69923e8 1.50675e9i −0.0823702 0.142669i
$$732$$ −3.89736e9 + 6.75043e9i −0.367267 + 0.636125i
$$733$$ 6.61890e9 0.620758 0.310379 0.950613i $$-0.399544\pi$$
0.310379 + 0.950613i $$0.399544\pi$$
$$734$$ 3.56278e9 6.17091e9i 0.332546 0.575987i
$$735$$ 3.23734e9 5.60724e9i 0.300734 0.520887i
$$736$$ 2.56457e9 0.237106
$$737$$ −4.62009e7 + 8.00222e7i −0.00425122 + 0.00736333i
$$738$$ −4.36328e8 7.55742e8i −0.0399591 0.0692112i
$$739$$ 2.02110e9 + 3.50065e9i 0.184218 + 0.319075i 0.943313 0.331905i $$-0.107691\pi$$
−0.759095 + 0.650980i $$0.774358\pi$$
$$740$$ 3.16875e9 0.287459
$$741$$ −2.24227e9 + 2.07349e9i −0.202453 + 0.187214i
$$742$$ 3.02930e9 0.272226
$$743$$ −5.12883e9 8.88339e9i −0.458730 0.794544i 0.540164 0.841560i $$-0.318362\pi$$
−0.998894 + 0.0470156i $$0.985029\pi$$
$$744$$ −1.64360e9 2.84680e9i −0.146316 0.253426i
$$745$$ 7.42908e9 1.28675e10i 0.658245 1.14011i
$$746$$ −3.54123e9 −0.312297
$$747$$ −2.33400e9 + 4.04260e9i −0.204870 + 0.354845i
$$748$$ 1.56021e8 2.70237e8i 0.0136310 0.0236096i
$$749$$ −5.92749e9 −0.515448
$$750$$ −2.66460e9 + 4.61522e9i −0.230631 + 0.399464i
$$751$$ −8.25795e9 1.43032e10i −0.711431 1.23223i −0.964320 0.264739i $$-0.914714\pi$$
0.252890 0.967495i $$-0.418619\pi$$
$$752$$ 2.46446e9 + 4.26856e9i 0.211329 + 0.366032i
$$753$$ 4.76762e9 0.406930
$$754$$ −1.94370e9 8.58267e9i −0.165132 0.729160i
$$755$$ −1.54504e10 −1.30655
$$756$$ −2.01903e9 3.49706e9i −0.169948 0.294359i
$$757$$ −1.73903e9 3.01209e9i −0.145704 0.252367i 0.783931 0.620848i $$-0.213211\pi$$
−0.929635 + 0.368481i $$0.879878\pi$$
$$758$$ 5.94842e9 1.03030e10i 0.496089 0.859251i
$$759$$ −7.45493e8