# Properties

 Label 54.9.f.a.5.13 Level $54$ Weight $9$ Character 54.5 Analytic conductor $21.998$ Analytic rank $0$ Dimension $144$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$54 = 2 \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 54.f (of order $$18$$, degree $$6$$, 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: $$21.9984449433$$ Analytic rank: $$0$$ Dimension: $$144$$ Relative dimension: $$24$$ over $$\Q(\zeta_{18})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

## Embedding invariants

 Embedding label 5.13 Character $$\chi$$ $$=$$ 54.5 Dual form 54.9.f.a.11.13

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(7.27231 + 8.66680i) q^{2} +(-80.9968 + 0.714754i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-52.9870 - 145.581i) q^{5} +(-595.229 - 696.786i) q^{6} +(710.104 + 4027.20i) q^{7} +(-1254.14 + 724.077i) q^{8} +(6559.98 - 115.786i) q^{9} +O(q^{10})$$ $$q+(7.27231 + 8.66680i) q^{2} +(-80.9968 + 0.714754i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-52.9870 - 145.581i) q^{5} +(-595.229 - 696.786i) q^{6} +(710.104 + 4027.20i) q^{7} +(-1254.14 + 724.077i) q^{8} +(6559.98 - 115.786i) q^{9} +(876.380 - 1517.93i) q^{10} +(-3975.80 + 10923.4i) q^{11} +(1710.22 - 10226.0i) q^{12} +(-27255.2 - 22869.8i) q^{13} +(-29738.9 + 35441.4i) q^{14} +(4395.83 + 11753.7i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(13598.0 + 7850.80i) q^{17} +(48709.7 + 56012.0i) q^{18} +(-98965.7 - 171414. i) q^{19} +(19528.9 - 3443.48i) q^{20} +(-60394.7 - 325683. i) q^{21} +(-123584. + 44981.0i) q^{22} +(-90004.7 - 15870.2i) q^{23} +(101064. - 59544.4i) q^{24} +(280850. - 235661. i) q^{25} -402532. i q^{26} +(-531255. + 14067.0i) q^{27} -523434. q^{28} +(-357065. - 425533. i) q^{29} +(-69899.1 + 123574. i) q^{30} +(-140814. + 798598. i) q^{31} +(-63398.2 - 174185. i) q^{32} +(314220. - 887604. i) q^{33} +(30847.4 + 174944. i) q^{34} +(548656. - 316767. i) q^{35} +(-131213. + 829494. i) q^{36} +(1.10342e6 - 1.91117e6i) q^{37} +(765899. - 2.10429e6i) q^{38} +(2.22393e6 + 1.83290e6i) q^{39} +(171865. + 144211. i) q^{40} +(-716625. + 854041. i) q^{41} +(2.38342e6 - 2.89190e6i) q^{42} +(-1.02832e6 - 374279. i) q^{43} +(-1.28859e6 - 743965. i) q^{44} +(-364450. - 948870. i) q^{45} +(-516998. - 895466. i) q^{46} +(-8.47930e6 + 1.49513e6i) q^{47} +(1.25103e6 + 442874. i) q^{48} +(-1.02970e7 + 3.74779e6i) q^{49} +(4.08486e6 + 720271. i) q^{50} +(-1.10700e6 - 626170. i) q^{51} +(3.48866e6 - 2.92734e6i) q^{52} -1.10951e7i q^{53} +(-3.98537e6 - 4.50198e6i) q^{54} +1.80090e6 q^{55} +(-3.80657e6 - 4.53650e6i) q^{56} +(8.13843e6 + 1.38132e7i) q^{57} +(1.09133e6 - 6.18922e6i) q^{58} +(-1.24036e6 - 3.40786e6i) q^{59} +(-1.57932e6 + 292869. i) q^{60} +(1.58203e6 + 8.97211e6i) q^{61} +(-7.94534e6 + 4.58724e6i) q^{62} +(5.12456e6 + 2.63361e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(-1.88523e6 + 5.17963e6i) q^{65} +(9.97779e6 - 3.73165e6i) q^{66} +(6.53405e6 + 5.48272e6i) q^{67} +(-1.29188e6 + 1.53960e6i) q^{68} +(7.30144e6 + 1.22111e6i) q^{69} +(6.73535e6 + 2.45147e6i) q^{70} +(5.65174e6 + 3.26303e6i) q^{71} +(-8.14329e6 + 4.89514e6i) q^{72} +(1.47593e7 + 2.55638e7i) q^{73} +(2.45881e7 - 4.33555e6i) q^{74} +(-2.25795e7 + 1.92886e7i) q^{75} +(2.38073e7 - 8.66515e6i) q^{76} +(-4.68140e7 - 8.25458e6i) q^{77} +(287711. + 3.26038e7i) q^{78} +(1.18277e7 - 9.92459e6i) q^{79} +2.53827e6i q^{80} +(4.30199e7 - 1.51910e6i) q^{81} -1.26133e7 q^{82} +(4.78941e7 + 5.70779e7i) q^{83} +(4.23965e7 - 374127. i) q^{84} +(422407. - 2.39559e6i) q^{85} +(-4.23448e6 - 1.16341e7i) q^{86} +(2.92253e7 + 3.42116e7i) q^{87} +(-2.92320e6 - 1.65783e7i) q^{88} +(-1.07469e8 + 6.20470e7i) q^{89} +(5.57328e6 - 1.00591e7i) q^{90} +(7.27473e7 - 1.26002e8i) q^{91} +(4.00106e6 - 1.09928e7i) q^{92} +(1.08347e7 - 6.47846e7i) q^{93} +(-7.46221e7 - 6.26154e7i) q^{94} +(-1.97106e7 + 2.34902e7i) q^{95} +(5.25955e6 + 1.40631e7i) q^{96} +(-1.51140e8 - 5.50103e7i) q^{97} +(-1.07364e8 - 6.19867e7i) q^{98} +(-2.48164e7 + 7.21177e7i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10})$$ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 $$144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100})$$ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$\chi(n)$$ $$e\left(\frac{5}{18}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 7.27231 + 8.66680i 0.454519 + 0.541675i
$$3$$ −80.9968 + 0.714754i −0.999961 + 0.00882412i
$$4$$ −22.2270 + 126.055i −0.0868241 + 0.492404i
$$5$$ −52.9870 145.581i −0.0847792 0.232929i 0.890058 0.455848i $$-0.150664\pi$$
−0.974837 + 0.222919i $$0.928442\pi$$
$$6$$ −595.229 696.786i −0.459282 0.537643i
$$7$$ 710.104 + 4027.20i 0.295754 + 1.67730i 0.664124 + 0.747623i $$0.268805\pi$$
−0.368370 + 0.929679i $$0.620084\pi$$
$$8$$ −1254.14 + 724.077i −0.306186 + 0.176777i
$$9$$ 6559.98 115.786i 0.999844 0.0176476i
$$10$$ 876.380 1517.93i 0.0876380 0.151793i
$$11$$ −3975.80 + 10923.4i −0.271552 + 0.746084i 0.726698 + 0.686957i $$0.241054\pi$$
−0.998250 + 0.0591271i $$0.981168\pi$$
$$12$$ 1710.22 10226.0i 0.0824757 0.493151i
$$13$$ −27255.2 22869.8i −0.954280 0.800736i 0.0257333 0.999669i $$-0.491808\pi$$
−0.980013 + 0.198933i $$0.936252\pi$$
$$14$$ −29738.9 + 35441.4i −0.774127 + 0.922569i
$$15$$ 4395.83 + 11753.7i 0.0868312 + 0.232172i
$$16$$ −15395.9 5603.66i −0.234923 0.0855050i
$$17$$ 13598.0 + 7850.80i 0.162809 + 0.0939979i 0.579191 0.815192i $$-0.303369\pi$$
−0.416382 + 0.909190i $$0.636702\pi$$
$$18$$ 48709.7 + 56012.0i 0.464008 + 0.533570i
$$19$$ −98965.7 171414.i −0.759399 1.31532i −0.943157 0.332347i $$-0.892160\pi$$
0.183758 0.982971i $$-0.441174\pi$$
$$20$$ 19528.9 3443.48i 0.122056 0.0215218i
$$21$$ −60394.7 325683.i −0.310543 1.67463i
$$22$$ −123584. + 44981.0i −0.527561 + 0.192017i
$$23$$ −90004.7 15870.2i −0.321628 0.0567117i 0.0105034 0.999945i $$-0.496657\pi$$
−0.332131 + 0.943233i $$0.607768\pi$$
$$24$$ 101064. 59544.4i 0.304614 0.179472i
$$25$$ 280850. 235661.i 0.718976 0.603293i
$$26$$ 402532.i 0.880860i
$$27$$ −531255. + 14067.0i −0.999650 + 0.0264696i
$$28$$ −523434. −0.851588
$$29$$ −357065. 425533.i −0.504841 0.601646i 0.452086 0.891974i $$-0.350680\pi$$
−0.956927 + 0.290328i $$0.906236\pi$$
$$30$$ −69899.1 + 123574.i −0.0862951 + 0.152561i
$$31$$ −140814. + 798598.i −0.152476 + 0.864732i 0.808582 + 0.588384i $$0.200236\pi$$
−0.961058 + 0.276348i $$0.910876\pi$$
$$32$$ −63398.2 174185.i −0.0604612 0.166116i
$$33$$ 314220. 887604.i 0.264958 0.748451i
$$34$$ 30847.4 + 174944.i 0.0230836 + 0.130914i
$$35$$ 548656. 316767.i 0.365618 0.211090i
$$36$$ −131213. + 829494.i −0.0781208 + 0.493859i
$$37$$ 1.10342e6 1.91117e6i 0.588752 1.01975i −0.405644 0.914031i $$-0.632953\pi$$
0.994396 0.105717i $$-0.0337139\pi$$
$$38$$ 765899. 2.10429e6i 0.367313 1.00919i
$$39$$ 2.22393e6 + 1.83290e6i 0.961308 + 0.792284i
$$40$$ 171865. + 144211.i 0.0671346 + 0.0563326i
$$41$$ −716625. + 854041.i −0.253604 + 0.302234i −0.877793 0.479039i $$-0.840985\pi$$
0.624189 + 0.781273i $$0.285430\pi$$
$$42$$ 2.38342e6 2.89190e6i 0.765956 0.929364i
$$43$$ −1.02832e6 374279.i −0.300784 0.109477i 0.187219 0.982318i $$-0.440053\pi$$
−0.488004 + 0.872842i $$0.662275\pi$$
$$44$$ −1.28859e6 743965.i −0.343797 0.198492i
$$45$$ −364450. 948870.i −0.0888766 0.231396i
$$46$$ −516998. 895466.i −0.115467 0.199994i
$$47$$ −8.47930e6 + 1.49513e6i −1.73768 + 0.306399i −0.950591 0.310446i $$-0.899522\pi$$
−0.787085 + 0.616845i $$0.788410\pi$$
$$48$$ 1.25103e6 + 442874.i 0.235669 + 0.0834287i
$$49$$ −1.02970e7 + 3.74779e6i −1.78618 + 0.650116i
$$50$$ 4.08486e6 + 720271.i 0.653577 + 0.115243i
$$51$$ −1.10700e6 626170.i −0.163632 0.0925576i
$$52$$ 3.48866e6 2.92734e6i 0.477140 0.400368i
$$53$$ 1.10951e7i 1.40614i −0.711123 0.703068i $$-0.751813\pi$$
0.711123 0.703068i $$-0.248187\pi$$
$$54$$ −3.98537e6 4.50198e6i −0.468698 0.529454i
$$55$$ 1.80090e6 0.196806
$$56$$ −3.80657e6 4.53650e6i −0.387064 0.461284i
$$57$$ 8.13843e6 + 1.38132e7i 0.770976 + 1.30857i
$$58$$ 1.09133e6 6.18922e6i 0.0964368 0.546920i
$$59$$ −1.24036e6 3.40786e6i −0.102362 0.281238i 0.877931 0.478788i $$-0.158924\pi$$
−0.980293 + 0.197550i $$0.936701\pi$$
$$60$$ −1.57932e6 + 292869.i −0.121861 + 0.0225980i
$$61$$ 1.58203e6 + 8.97211e6i 0.114260 + 0.648000i 0.987114 + 0.160019i $$0.0511555\pi$$
−0.872854 + 0.487981i $$0.837733\pi$$
$$62$$ −7.94534e6 + 4.58724e6i −0.537707 + 0.310445i
$$63$$ 5.12456e6 + 2.63361e7i 0.325308 + 1.67182i
$$64$$ 1.04858e6 1.81619e6i 0.0625000 0.108253i
$$65$$ −1.88523e6 + 5.17963e6i −0.105611 + 0.290165i
$$66$$ 9.97779e6 3.73165e6i 0.525846 0.196664i
$$67$$ 6.53405e6 + 5.48272e6i 0.324252 + 0.272080i 0.790353 0.612652i $$-0.209897\pi$$
−0.466101 + 0.884732i $$0.654342\pi$$
$$68$$ −1.29188e6 + 1.53960e6i −0.0604207 + 0.0720065i
$$69$$ 7.30144e6 + 1.22111e6i 0.322116 + 0.0538714i
$$70$$ 6.73535e6 + 2.45147e6i 0.280523 + 0.102102i
$$71$$ 5.65174e6 + 3.26303e6i 0.222407 + 0.128407i 0.607064 0.794653i $$-0.292347\pi$$
−0.384657 + 0.923059i $$0.625680\pi$$
$$72$$ −8.14329e6 + 4.89514e6i −0.303019 + 0.182153i
$$73$$ 1.47593e7 + 2.55638e7i 0.519725 + 0.900191i 0.999737 + 0.0229286i $$0.00729905\pi$$
−0.480012 + 0.877262i $$0.659368\pi$$
$$74$$ 2.45881e7 4.33555e6i 0.819972 0.144583i
$$75$$ −2.25795e7 + 1.92886e7i −0.713625 + 0.609613i
$$76$$ 2.38073e7 8.66515e6i 0.713602 0.259730i
$$77$$ −4.68140e7 8.25458e6i −1.33172 0.234818i
$$78$$ 287711. + 3.26038e7i 0.00777282 + 0.880825i
$$79$$ 1.18277e7 9.92459e6i 0.303662 0.254803i −0.478204 0.878249i $$-0.658712\pi$$
0.781867 + 0.623446i $$0.214268\pi$$
$$80$$ 2.53827e6i 0.0619694i
$$81$$ 4.30199e7 1.51910e6i 0.999377 0.0352896i
$$82$$ −1.26133e7 −0.278981
$$83$$ 4.78941e7 + 5.70779e7i 1.00918 + 1.20270i 0.979148 + 0.203147i $$0.0651170\pi$$
0.0300338 + 0.999549i $$0.490439\pi$$
$$84$$ 4.23965e7 374127.i 0.851555 0.00751452i
$$85$$ 422407. 2.39559e6i 0.00809200 0.0458920i
$$86$$ −4.23448e6 1.16341e7i −0.0774116 0.212687i
$$87$$ 2.92253e7 + 3.42116e7i 0.510131 + 0.597168i
$$88$$ −2.92320e6 1.65783e7i −0.0487447 0.276445i
$$89$$ −1.07469e8 + 6.20470e7i −1.71286 + 0.988919i −0.782200 + 0.623028i $$0.785902\pi$$
−0.930658 + 0.365891i $$0.880764\pi$$
$$90$$ 5.57328e6 1.00591e7i 0.0849456 0.153316i
$$91$$ 7.27473e7 1.26002e8i 1.06084 1.83744i
$$92$$ 4.00106e6 1.09928e7i 0.0558501 0.153447i
$$93$$ 1.08347e7 6.47846e7i 0.144839 0.866044i
$$94$$ −7.46221e7 6.26154e7i −0.955776 0.801991i
$$95$$ −1.97106e7 + 2.34902e7i −0.241994 + 0.288398i
$$96$$ 5.25955e6 + 1.40631e7i 0.0619247 + 0.165576i
$$97$$ −1.51140e8 5.50103e7i −1.70723 0.621379i −0.710611 0.703585i $$-0.751581\pi$$
−0.996615 + 0.0822058i $$0.973804\pi$$
$$98$$ −1.07364e8 6.19867e7i −1.16400 0.672038i
$$99$$ −2.48164e7 + 7.21177e7i −0.258344 + 0.750760i
$$100$$ 2.34639e7 + 4.06407e7i 0.234639 + 0.406407i
$$101$$ −1.12553e8 + 1.98461e7i −1.08161 + 0.190717i −0.685928 0.727670i $$-0.740603\pi$$
−0.395684 + 0.918387i $$0.629492\pi$$
$$102$$ −2.62359e6 1.41479e7i −0.0242379 0.130705i
$$103$$ 1.34783e8 4.90572e7i 1.19753 0.435867i 0.335171 0.942157i $$-0.391206\pi$$
0.862363 + 0.506291i $$0.168984\pi$$
$$104$$ 5.07413e7 + 8.94706e6i 0.433739 + 0.0764798i
$$105$$ −4.42130e7 + 2.60492e7i −0.363741 + 0.214308i
$$106$$ 9.61589e7 8.06869e7i 0.761669 0.639116i
$$107$$ 7.07714e7i 0.539912i −0.962873 0.269956i $$-0.912991\pi$$
0.962873 0.269956i $$-0.0870091\pi$$
$$108$$ 1.00350e7 6.72802e7i 0.0737599 0.494530i
$$109$$ 1.86458e8 1.32092 0.660458 0.750863i $$-0.270362\pi$$
0.660458 + 0.750863i $$0.270362\pi$$
$$110$$ 1.30967e7 + 1.56081e7i 0.0894524 + 0.106605i
$$111$$ −8.80072e7 + 1.55588e8i −0.579731 + 1.02490i
$$112$$ 1.16343e7 6.59817e7i 0.0739384 0.419325i
$$113$$ −6.38335e7 1.75381e8i −0.391503 1.07564i −0.966316 0.257360i $$-0.917147\pi$$
0.574813 0.818285i $$-0.305075\pi$$
$$114$$ −6.05313e7 + 1.70988e8i −0.358394 + 1.01239i
$$115$$ 2.45868e6 + 1.39438e7i 0.0140576 + 0.0797244i
$$116$$ 6.15772e7 3.55516e7i 0.340085 0.196348i
$$117$$ −1.81441e8 1.46870e8i −0.968262 0.783770i
$$118$$ 2.05150e7 3.55330e7i 0.105814 0.183275i
$$119$$ −2.19608e7 + 6.03367e7i −0.109511 + 0.300880i
$$120$$ −1.40236e7 1.15578e7i −0.0676291 0.0557380i
$$121$$ 6.06944e7 + 5.09286e7i 0.283144 + 0.237586i
$$122$$ −6.62545e7 + 7.89591e7i −0.299072 + 0.356421i
$$123$$ 5.74340e7 6.96868e7i 0.250928 0.304460i
$$124$$ −9.75377e7 3.55008e7i −0.412559 0.150159i
$$125$$ −1.01598e8 5.86578e7i −0.416147 0.240262i
$$126$$ −1.90983e8 + 2.35938e8i −0.757725 + 0.936086i
$$127$$ −1.27172e8 2.20268e8i −0.488851 0.846714i 0.511067 0.859541i $$-0.329250\pi$$
−0.999918 + 0.0128267i $$0.995917\pi$$
$$128$$ 2.33661e7 4.12008e6i 0.0870455 0.0153485i
$$129$$ 8.35584e7 + 2.95804e7i 0.301739 + 0.106818i
$$130$$ −5.86008e7 + 2.13289e7i −0.205178 + 0.0746785i
$$131$$ −3.85139e8 6.79104e7i −1.30777 0.230596i −0.524041 0.851693i $$-0.675576\pi$$
−0.783733 + 0.621098i $$0.786687\pi$$
$$132$$ 1.04903e8 + 5.93378e7i 0.345536 + 0.195450i
$$133$$ 6.20041e8 5.20276e8i 1.98159 1.66275i
$$134$$ 9.65014e7i 0.299305i
$$135$$ 3.01975e7 + 7.65950e7i 0.0909150 + 0.230603i
$$136$$ −2.27383e7 −0.0664665
$$137$$ −6.28308e7 7.48788e7i −0.178357 0.212558i 0.669458 0.742850i $$-0.266527\pi$$
−0.847815 + 0.530293i $$0.822082\pi$$
$$138$$ 4.25152e7 + 7.21604e7i 0.117227 + 0.198968i
$$139$$ −4.98521e7 + 2.82725e8i −0.133544 + 0.757365i 0.842319 + 0.538980i $$0.181190\pi$$
−0.975863 + 0.218385i $$0.929921\pi$$
$$140$$ 2.77352e7 + 7.62018e7i 0.0721969 + 0.198359i
$$141$$ 6.85728e8 1.27161e8i 1.73490 0.321721i
$$142$$ 1.28211e7 + 7.27123e7i 0.0315336 + 0.178836i
$$143$$ 3.58178e8 2.06794e8i 0.856553 0.494531i
$$144$$ −1.01646e8 3.49772e7i −0.236396 0.0813459i
$$145$$ −4.30296e7 + 7.45294e7i −0.0973408 + 0.168599i
$$146$$ −1.14223e8 + 3.13824e8i −0.251386 + 0.690677i
$$147$$ 8.31343e8 3.10919e8i 1.78037 0.665852i
$$148$$ 2.16388e8 + 1.81571e8i 0.451010 + 0.378443i
$$149$$ −3.42144e8 + 4.07751e8i −0.694167 + 0.827276i −0.991853 0.127388i $$-0.959341\pi$$
0.297686 + 0.954664i $$0.403785\pi$$
$$150$$ −3.31375e8 5.54200e7i −0.654569 0.109472i
$$151$$ −1.70935e7 6.22152e6i −0.0328793 0.0119671i 0.325528 0.945532i $$-0.394458\pi$$
−0.358407 + 0.933565i $$0.616680\pi$$
$$152$$ 2.48233e8 + 1.43318e8i 0.465035 + 0.268488i
$$153$$ 9.01114e7 + 4.99266e7i 0.164443 + 0.0911100i
$$154$$ −2.68905e8 4.65758e8i −0.478098 0.828090i
$$155$$ 1.23722e8 2.18155e7i 0.214348 0.0377953i
$$156$$ −2.80478e8 + 2.39599e8i −0.473588 + 0.404563i
$$157$$ −9.78838e8 + 3.56268e8i −1.61106 + 0.586379i −0.981650 0.190693i $$-0.938927\pi$$
−0.629412 + 0.777071i $$0.716704\pi$$
$$158$$ 1.72029e8 + 3.03333e7i 0.276041 + 0.0486734i
$$159$$ 7.93026e6 + 8.98667e8i 0.0124079 + 1.40608i
$$160$$ −2.19987e7 + 1.84591e7i −0.0335673 + 0.0281663i
$$161$$ 3.73736e8i 0.556240i
$$162$$ 3.26020e8 + 3.61798e8i 0.473352 + 0.525298i
$$163$$ −1.24749e8 −0.176721 −0.0883605 0.996089i $$-0.528163\pi$$
−0.0883605 + 0.996089i $$0.528163\pi$$
$$164$$ −9.17280e7 1.09317e8i −0.126802 0.151117i
$$165$$ −1.45867e8 + 1.28720e6i −0.196799 + 0.00173664i
$$166$$ −1.46383e8 + 8.30177e8i −0.192778 + 1.09330i
$$167$$ 2.12724e8 + 5.84455e8i 0.273496 + 0.751424i 0.998063 + 0.0622191i $$0.0198178\pi$$
−0.724567 + 0.689205i $$0.757960\pi$$
$$168$$ 3.11563e8 + 3.64721e8i 0.391119 + 0.457851i
$$169$$ 7.81665e7 + 4.43304e8i 0.0958239 + 0.543444i
$$170$$ 2.38340e7 1.37606e7i 0.0285365 0.0164756i
$$171$$ −6.69060e8 1.11301e9i −0.782493 1.30171i
$$172$$ 7.00363e7 1.21306e8i 0.0800220 0.138602i
$$173$$ 1.11528e8 3.06419e8i 0.124508 0.342083i −0.861741 0.507348i $$-0.830626\pi$$
0.986249 + 0.165265i $$0.0528480\pi$$
$$174$$ −8.39702e7 + 5.02087e8i −0.0916069 + 0.547750i
$$175$$ 1.14849e9 + 9.63696e8i 1.22454 + 1.02751i
$$176$$ 1.22422e8 1.45897e8i 0.127588 0.152053i
$$177$$ 1.02901e8 + 2.75139e8i 0.104840 + 0.280324i
$$178$$ −1.31929e9 4.80184e8i −1.31420 0.478330i
$$179$$ −1.03207e9 5.95866e8i −1.00530 0.580412i −0.0954901 0.995430i $$-0.530442\pi$$
−0.909813 + 0.415018i $$0.863775\pi$$
$$180$$ 1.27711e8 2.48503e7i 0.121657 0.0236724i
$$181$$ 7.34232e8 + 1.27173e9i 0.684099 + 1.18489i 0.973719 + 0.227753i $$0.0731377\pi$$
−0.289620 + 0.957142i $$0.593529\pi$$
$$182$$ 1.62108e9 2.85840e8i 1.47747 0.260517i
$$183$$ −1.34552e8 7.25582e8i −0.119974 0.646967i
$$184$$ 1.24370e8 4.52668e7i 0.108503 0.0394920i
$$185$$ −3.36696e8 5.93686e7i −0.287443 0.0506839i
$$186$$ 6.40269e8 3.77231e8i 0.534947 0.315178i
$$187$$ −1.39820e8 + 1.17323e8i −0.114341 + 0.0959439i
$$188$$ 1.10209e9i 0.882241i
$$189$$ −4.33897e8 2.12948e9i −0.340047 1.66889i
$$190$$ −3.46926e8 −0.266209
$$191$$ 1.03574e9 + 1.23434e9i 0.778245 + 0.927476i 0.998853 0.0478866i $$-0.0152486\pi$$
−0.220608 + 0.975363i $$0.570804\pi$$
$$192$$ −8.36332e7 + 1.47855e8i −0.0615423 + 0.108800i
$$193$$ −8.72037e7 + 4.94556e8i −0.0628500 + 0.356440i 0.937122 + 0.349001i $$0.113479\pi$$
−0.999972 + 0.00743907i $$0.997632\pi$$
$$194$$ −6.22370e8 1.70995e9i −0.439382 1.20719i
$$195$$ 1.48995e8 4.20881e8i 0.103047 0.291086i
$$196$$ −2.43559e8 1.38129e9i −0.165036 0.935967i
$$197$$ −2.07396e9 + 1.19740e9i −1.37701 + 0.795014i −0.991798 0.127816i $$-0.959203\pi$$
−0.385207 + 0.922830i $$0.625870\pi$$
$$198$$ −8.05502e8 + 3.09384e8i −0.524090 + 0.201297i
$$199$$ −3.18402e8 + 5.51488e8i −0.203031 + 0.351661i −0.949504 0.313756i $$-0.898413\pi$$
0.746472 + 0.665417i $$0.231746\pi$$
$$200$$ −1.81588e8 + 4.98909e8i −0.113493 + 0.311818i
$$201$$ −5.33156e8 4.39413e8i −0.326641 0.269208i
$$202$$ −9.90522e8 8.31147e8i −0.594920 0.499197i
$$203$$ 1.46015e9 1.74014e9i 0.859834 1.02471i
$$204$$ 1.03538e8 1.25626e8i 0.0597829 0.0725369i
$$205$$ 1.62303e8 + 5.90736e7i 0.0918993 + 0.0334486i
$$206$$ 1.40536e9 + 8.11383e8i 0.780400 + 0.450564i
$$207$$ −5.92266e8 9.36872e7i −0.322579 0.0510269i
$$208$$ 2.91464e8 + 5.04831e8i 0.155715 + 0.269707i
$$209$$ 2.26589e9 3.99537e8i 1.18755 0.209398i
$$210$$ −5.47294e8 1.93747e8i −0.281413 0.0996226i
$$211$$ −4.42585e7 + 1.61088e7i −0.0223289 + 0.00812705i −0.353160 0.935563i $$-0.614893\pi$$
0.330832 + 0.943690i $$0.392671\pi$$
$$212$$ 1.39860e9 + 2.46610e8i 0.692387 + 0.122086i
$$213$$ −4.60105e8 2.60256e8i −0.223531 0.126439i
$$214$$ 6.13362e8 5.14672e8i 0.292457 0.245400i
$$215$$ 1.69536e8i 0.0793427i
$$216$$ 6.56082e8 4.02312e8i 0.301400 0.184819i
$$217$$ −3.31611e9 −1.49551
$$218$$ 1.35598e9 + 1.61600e9i 0.600382 + 0.715507i
$$219$$ −1.21373e9 2.06004e9i −0.527649 0.895570i
$$220$$ −4.00286e7 + 2.27013e8i −0.0170875 + 0.0969083i
$$221$$ −1.91069e8 5.24958e8i −0.0800980 0.220067i
$$222$$ −1.98846e9 + 3.68741e8i −0.818664 + 0.151813i
$$223$$ 4.87350e7 + 2.76390e8i 0.0197070 + 0.111764i 0.993075 0.117486i $$-0.0374836\pi$$
−0.973367 + 0.229250i $$0.926373\pi$$
$$224$$ 6.56459e8 3.79007e8i 0.260745 0.150541i
$$225$$ 1.81508e9 1.57845e9i 0.708218 0.615887i
$$226$$ 1.05578e9 1.82866e9i 0.404704 0.700969i
$$227$$ −8.36529e8 + 2.29835e9i −0.315049 + 0.865589i 0.676569 + 0.736380i $$0.263466\pi$$
−0.991617 + 0.129210i $$0.958756\pi$$
$$228$$ −1.92212e9 + 7.18866e8i −0.711282 + 0.266017i
$$229$$ −6.10044e7 5.11888e7i −0.0221830 0.0186137i 0.631629 0.775271i $$-0.282387\pi$$
−0.653812 + 0.756657i $$0.726831\pi$$
$$230$$ −1.02968e8 + 1.22713e8i −0.0367953 + 0.0438509i
$$231$$ 3.79769e9 + 6.35134e8i 1.33374 + 0.223058i
$$232$$ 7.55928e8 + 2.75135e8i 0.260933 + 0.0949717i
$$233$$ 2.74734e8 + 1.58618e8i 0.0932155 + 0.0538180i 0.545883 0.837861i $$-0.316194\pi$$
−0.452668 + 0.891679i $$0.649528\pi$$
$$234$$ −4.66074e7 2.64060e9i −0.0155450 0.880723i
$$235$$ 6.66954e8 + 1.15520e9i 0.218688 + 0.378778i
$$236$$ 4.57149e8 8.06076e7i 0.147370 0.0259853i
$$237$$ −9.50910e8 + 8.12314e8i −0.301402 + 0.257472i
$$238$$ −6.82632e8 + 2.48458e8i −0.212754 + 0.0774363i
$$239$$ −2.55120e9 4.49846e8i −0.781904 0.137871i −0.231573 0.972818i $$-0.574387\pi$$
−0.550331 + 0.834947i $$0.685498\pi$$
$$240$$ −1.81424e6 2.05592e8i −0.000546826 0.0619670i
$$241$$ −1.45808e8 + 1.22348e8i −0.0432229 + 0.0362683i −0.664143 0.747605i $$-0.731203\pi$$
0.620920 + 0.783874i $$0.286759\pi$$
$$242$$ 8.96395e8i 0.261359i
$$243$$ −3.48339e9 + 1.53791e8i −0.999027 + 0.0441069i
$$244$$ −1.16615e9 −0.328998
$$245$$ 1.09121e9 + 1.30045e9i 0.302861 + 0.360936i
$$246$$ 1.02164e9 9.01543e6i 0.278970 0.00246176i
$$247$$ −1.22287e9 + 6.93523e9i −0.328543 + 1.86326i
$$248$$ −4.01646e8 1.10351e9i −0.106179 0.291723i
$$249$$ −3.92007e9 4.58890e9i −1.01976 1.19374i
$$250$$ −2.30479e8 1.30711e9i −0.0590026 0.334620i
$$251$$ −3.20228e9 + 1.84884e9i −0.806797 + 0.465804i −0.845842 0.533433i $$-0.820902\pi$$
0.0390456 + 0.999237i $$0.487568\pi$$
$$252$$ −3.43372e9 + 6.06061e7i −0.851456 + 0.0150285i
$$253$$ 5.31198e8 9.20061e8i 0.129650 0.224561i
$$254$$ 9.84187e8 2.70403e9i 0.236452 0.649646i
$$255$$ −3.25014e7 + 1.94337e8i −0.00768672 + 0.0459616i
$$256$$ 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
$$257$$ 4.01594e9 4.78601e9i 0.920565 1.09709i −0.0744361 0.997226i $$-0.523716\pi$$
0.995001 0.0998612i $$-0.0318399\pi$$
$$258$$ 3.51295e8 + 9.39302e8i 0.0792854 + 0.211995i
$$259$$ 8.48022e9 + 3.08655e9i 1.88455 + 0.685921i
$$260$$ −6.11017e8 3.52771e8i −0.133709 0.0771968i
$$261$$ −2.39161e9 2.75014e9i −0.515380 0.592644i
$$262$$ −2.21229e9 3.83179e9i −0.469501 0.813199i
$$263$$ 1.60079e9 2.82262e8i 0.334588 0.0589969i −0.00383041 0.999993i $$-0.501219\pi$$
0.338418 + 0.940996i $$0.390108\pi$$
$$264$$ 2.48619e8 + 1.34070e9i 0.0511822 + 0.276004i
$$265$$ −1.61523e9 + 5.87895e8i −0.327529 + 0.119211i
$$266$$ 9.01826e9 + 1.59016e9i 1.80134 + 0.317625i
$$267$$ 8.66026e9 5.10242e9i 1.70406 1.00399i
$$268$$ −8.36359e8 + 7.01788e8i −0.162126 + 0.136040i
$$269$$ 3.33410e9i 0.636751i 0.947965 + 0.318375i $$0.103137\pi$$
−0.947965 + 0.318375i $$0.896863\pi$$
$$270$$ −4.44228e8 + 8.18738e8i −0.0835894 + 0.154060i
$$271$$ −4.48377e9 −0.831316 −0.415658 0.909521i $$-0.636449\pi$$
−0.415658 + 0.909521i $$0.636449\pi$$
$$272$$ −1.65360e8 1.97069e8i −0.0302103 0.0360033i
$$273$$ −5.80224e9 + 1.02578e10i −1.04459 + 1.84673i
$$274$$ 1.92035e8 1.08908e9i 0.0340704 0.193223i
$$275$$ 1.45762e9 + 4.00478e9i 0.254867 + 0.700242i
$$276$$ −3.16216e8 + 8.93244e8i −0.0544939 + 0.153934i
$$277$$ −1.24240e9 7.04602e9i −0.211030 1.19681i −0.887665 0.460490i $$-0.847674\pi$$
0.676635 0.736318i $$-0.263437\pi$$
$$278$$ −2.81286e9 + 1.62401e9i −0.470944 + 0.271900i
$$279$$ −8.31273e8 + 5.25509e9i −0.137191 + 0.867288i
$$280$$ −4.58727e8 + 7.94538e8i −0.0746315 + 0.129266i
$$281$$ −3.75232e9 + 1.03094e10i −0.601831 + 1.65352i 0.145729 + 0.989324i $$0.453447\pi$$
−0.747561 + 0.664193i $$0.768775\pi$$
$$282$$ 6.08891e9 + 5.01831e9i 0.962816 + 0.793526i
$$283$$ 9.01440e9 + 7.56398e9i 1.40537 + 1.17925i 0.958655 + 0.284571i $$0.0918511\pi$$
0.446716 + 0.894676i $$0.352593\pi$$
$$284$$ −5.36944e8 + 6.39905e8i −0.0825383 + 0.0983653i
$$285$$ 1.57971e9 1.91672e9i 0.239440 0.290522i
$$286$$ 4.39702e9 + 1.60039e9i 0.657195 + 0.239200i
$$287$$ −3.94827e9 2.27954e9i −0.581942 0.335984i
$$288$$ −4.36059e8 1.13531e9i −0.0633833 0.165023i
$$289$$ −3.36461e9 5.82767e9i −0.482329 0.835418i
$$290$$ −9.58856e8 + 1.69072e8i −0.135569 + 0.0239045i
$$291$$ 1.22811e10 + 4.34763e9i 1.71264 + 0.606291i
$$292$$ −3.55051e9 + 1.29228e9i −0.488382 + 0.177757i
$$293$$ −8.36842e9 1.47558e9i −1.13546 0.200213i −0.425843 0.904797i $$-0.640022\pi$$
−0.709620 + 0.704584i $$0.751133\pi$$
$$294$$ 8.74046e9 + 4.94399e9i 1.16989 + 0.661741i
$$295$$ −4.30395e8 + 3.61144e8i −0.0568302 + 0.0476862i
$$296$$ 3.19583e9i 0.416311i
$$297$$ 1.95850e9 5.85905e9i 0.251709 0.753011i
$$298$$ −6.02208e9 −0.763627
$$299$$ 2.09014e9 + 2.49094e9i 0.261512 + 0.311658i
$$300$$ −1.92955e9 3.27500e9i −0.238216 0.404321i
$$301$$ 7.77080e8 4.40704e9i 0.0946672 0.536884i
$$302$$ −7.03885e7 1.93391e8i −0.00846202 0.0232492i
$$303$$ 9.10225e9 1.68792e9i 1.07989 0.200254i
$$304$$ 5.63125e8 + 3.19364e9i 0.0659341 + 0.373931i
$$305$$ 1.22234e9 7.05717e8i 0.141251 0.0815514i
$$306$$ 2.22614e8 + 1.14406e9i 0.0253903 + 0.130486i
$$307$$ 2.02536e9 3.50802e9i 0.228007 0.394920i −0.729210 0.684290i $$-0.760112\pi$$
0.957217 + 0.289370i $$0.0934457\pi$$
$$308$$ 2.08107e9 5.71769e9i 0.231251 0.635357i
$$309$$ −1.08820e10 + 4.06981e9i −1.19364 + 0.446417i
$$310$$ 1.08881e9 + 9.13623e8i 0.117898 + 0.0989282i
$$311$$ 9.57663e9 1.14130e10i 1.02370 1.21999i 0.0484606 0.998825i $$-0.484568\pi$$
0.975236 0.221169i $$-0.0709871\pi$$
$$312$$ −4.11628e9 6.88416e8i −0.434397 0.0726495i
$$313$$ 1.48507e10 + 5.40522e9i 1.54729 + 0.563166i 0.967779 0.251802i $$-0.0810231\pi$$
0.579507 + 0.814968i $$0.303245\pi$$
$$314$$ −1.02061e10 5.89251e9i −1.04989 0.606152i
$$315$$ 3.56249e9 2.14151e9i 0.361836 0.217509i
$$316$$ 9.88155e8 + 1.71153e9i 0.0991007 + 0.171647i
$$317$$ −4.91725e9 + 8.67044e8i −0.486951 + 0.0858627i −0.411733 0.911304i $$-0.635076\pi$$
−0.0752182 + 0.997167i $$0.523965\pi$$
$$318$$ −7.73090e9 + 6.60412e9i −0.755999 + 0.645812i
$$319$$ 6.06789e9 2.20853e9i 0.585970 0.213276i
$$320$$ −3.19962e8 5.64180e7i −0.0305140 0.00538044i
$$321$$ 5.05842e7 + 5.73226e9i 0.00476425 + 0.539891i
$$322$$ 3.23910e9 2.71793e9i 0.301301 0.252822i
$$323$$ 3.10784e9i 0.285528i
$$324$$ −7.64711e8 + 5.45666e9i −0.0693933 + 0.495161i
$$325$$ −1.30441e10 −1.16918
$$326$$ −9.07216e8 1.08118e9i −0.0803231 0.0957253i
$$327$$ −1.51025e10 + 1.33272e8i −1.32086 + 0.0116559i
$$328$$ 2.80356e8 1.58998e9i 0.0242222 0.137371i
$$329$$ −1.20424e10 3.30862e10i −1.02785 2.82399i
$$330$$ −1.07195e9 1.25484e9i −0.0903896 0.105812i
$$331$$ −1.24567e9 7.06453e9i −0.103774 0.588533i −0.991703 0.128552i $$-0.958967\pi$$
0.887928 0.459982i $$-0.152144\pi$$
$$332$$ −8.25952e9 + 4.76864e9i −0.679834 + 0.392502i
$$333$$ 7.01710e9 1.26650e10i 0.570664 1.02998i
$$334$$ −3.51836e9 + 6.09398e9i −0.282719 + 0.489683i
$$335$$ 4.51958e8 1.24174e9i 0.0358855 0.0985945i
$$336$$ −8.95185e8 + 5.35262e9i −0.0702353 + 0.419962i
$$337$$ −7.45021e9 6.25147e9i −0.577629 0.484688i 0.306538 0.951858i $$-0.400829\pi$$
−0.884168 + 0.467170i $$0.845274\pi$$
$$338$$ −3.27358e9 + 3.90130e9i −0.250816 + 0.298911i
$$339$$ 5.29566e9 + 1.41597e10i 0.400979 + 1.07215i
$$340$$ 2.92588e8 + 1.06493e8i 0.0218948 + 0.00796906i
$$341$$ −8.16357e9 4.71324e9i −0.603758 0.348580i
$$342$$ 4.78063e9 1.38928e10i 0.349447 1.01551i
$$343$$ −1.06179e10 1.83908e10i −0.767121 1.32869i
$$344$$ 1.56067e9 2.75187e8i 0.111449 0.0196515i
$$345$$ −2.09111e8 1.12765e9i −0.0147605 0.0795972i
$$346$$ 3.46674e9 1.26179e9i 0.241889 0.0880405i
$$347$$ 4.85807e8 + 8.56608e7i 0.0335078 + 0.00590832i 0.190377 0.981711i $$-0.439029\pi$$
−0.156869 + 0.987619i $$0.550140\pi$$
$$348$$ −4.96215e9 + 2.92358e9i −0.338340 + 0.199342i
$$349$$ 1.74105e10 1.46092e10i 1.17357 0.984744i 0.173573 0.984821i $$-0.444469\pi$$
1.00000 7.66482e-5i $$2.43979e-5\pi$$
$$350$$ 1.69620e10i 1.13033i
$$351$$ 1.48012e10 + 1.17663e10i 0.975141 + 0.775196i
$$352$$ 2.15475e9 0.140355
$$353$$ −1.30297e10 1.55281e10i −0.839140 1.00005i −0.999915 0.0130565i $$-0.995844\pi$$
0.160775 0.986991i $$-0.448601\pi$$
$$354$$ −1.63625e9 + 2.89272e9i −0.104193 + 0.184202i
$$355$$ 1.75565e8 9.95681e8i 0.0110542 0.0626912i
$$356$$ −5.43266e9 1.49261e10i −0.338230 0.929280i
$$357$$ 1.73563e9 4.90278e9i 0.106852 0.301835i
$$358$$ −2.34128e9 1.32781e10i −0.142535 0.808356i
$$359$$ −2.63293e10 + 1.52012e10i −1.58512 + 0.915169i −0.591024 + 0.806654i $$0.701276\pi$$
−0.994095 + 0.108515i $$0.965391\pi$$
$$360$$ 1.14413e9 + 9.26125e8i 0.0681183 + 0.0551391i
$$361$$ −1.10966e10 + 1.92199e10i −0.653374 + 1.13168i
$$362$$ −5.68224e9 + 1.56118e10i −0.330892 + 0.909117i
$$363$$ −4.95245e9 4.08168e9i −0.285229 0.235078i
$$364$$ 1.42663e10 + 1.19708e10i 0.812654 + 0.681897i
$$365$$ 2.93955e9 3.50321e9i 0.165618 0.197376i
$$366$$ 5.30997e9 6.44279e9i 0.295916 0.359046i
$$367$$ −1.54241e10 5.61393e9i −0.850231 0.309459i −0.120096 0.992762i $$-0.538320\pi$$
−0.730135 + 0.683303i $$0.760543\pi$$
$$368$$ 1.29677e9 + 7.48692e8i 0.0707087 + 0.0408237i
$$369$$ −4.60216e9 + 5.68546e9i −0.248231 + 0.306662i
$$370$$ −1.93402e9 3.34983e9i −0.103194 0.178737i
$$371$$ 4.46821e10 7.87867e9i 2.35851 0.415870i
$$372$$ 7.92562e9 + 2.80574e9i 0.413868 + 0.146513i
$$373$$ 1.38305e10 5.03388e9i 0.714499 0.260057i 0.0409106 0.999163i $$-0.486974\pi$$
0.673589 + 0.739106i $$0.264752\pi$$
$$374$$ −2.03363e9 3.58585e8i −0.103941 0.0183276i
$$375$$ 8.27107e9 + 4.67848e9i 0.418251 + 0.236581i
$$376$$ 9.55163e9 8.01477e9i 0.477888 0.400996i
$$377$$ 1.97640e10i 0.978384i
$$378$$ 1.53004e10 1.92468e10i 0.749436 0.942736i
$$379$$ −5.31521e9 −0.257611 −0.128805 0.991670i $$-0.541114\pi$$
−0.128805 + 0.991670i $$0.541114\pi$$
$$380$$ −2.52295e9 3.00674e9i −0.120997 0.144199i
$$381$$ 1.04580e10 + 1.77501e10i 0.496303 + 0.842367i
$$382$$ −3.16561e9 + 1.79531e10i −0.148663 + 0.843112i
$$383$$ 9.08773e9 + 2.49683e10i 0.422338 + 1.16036i 0.950365 + 0.311137i $$0.100710\pi$$
−0.528027 + 0.849227i $$0.677068\pi$$
$$384$$ −1.88964e9 + 3.50414e8i −0.0869067 + 0.0161160i
$$385$$ 1.27883e9 + 7.25260e9i 0.0582062 + 0.330104i
$$386$$ −4.92040e9 + 2.84079e9i −0.221641 + 0.127965i
$$387$$ −6.78911e9 2.33619e9i −0.302670 0.104151i
$$388$$ 1.02937e10 1.78292e10i 0.454198 0.786694i
$$389$$ −1.21906e10 + 3.34935e10i −0.532387 + 1.46272i 0.323835 + 0.946113i $$0.395028\pi$$
−0.856222 + 0.516608i $$0.827195\pi$$
$$390$$ 4.73123e9 1.76946e9i 0.204511 0.0764861i
$$391$$ −1.09929e9 9.22411e8i −0.0470332 0.0394655i
$$392$$ 1.02001e10 1.21560e10i 0.431978 0.514811i
$$393$$ 3.12436e10 + 5.22525e9i 1.30976 + 0.219047i
$$394$$ −2.54601e10 9.26673e9i −1.05652 0.384540i
$$395$$ −2.07154e9 1.19600e9i −0.0850951 0.0491297i
$$396$$ −8.53923e9 4.73120e9i −0.347247 0.192393i
$$397$$ −2.49086e9 4.31430e9i −0.100274 0.173680i 0.811524 0.584320i $$-0.198639\pi$$
−0.911797 + 0.410640i $$0.865305\pi$$
$$398$$ −7.09516e9 + 1.25107e9i −0.282768 + 0.0498596i
$$399$$ −4.98495e10 + 4.25839e10i −1.96684 + 1.68017i
$$400$$ −5.64451e9 + 2.05443e9i −0.220489 + 0.0802513i
$$401$$ 1.83536e10 + 3.23624e9i 0.709813 + 0.125159i 0.516886 0.856054i $$-0.327091\pi$$
0.192927 + 0.981213i $$0.438202\pi$$
$$402$$ −6.89748e7 7.81631e9i −0.00264111 0.299294i
$$403$$ 2.21017e10 1.85455e10i 0.837926 0.703104i
$$404$$ 1.46290e10i 0.549148i
$$405$$ −2.50065e9 6.18237e9i −0.0929463 0.229792i
$$406$$ 2.57002e10 0.945872
$$407$$ 1.64896e10 + 1.96515e10i 0.600941 + 0.716174i
$$408$$ 1.84173e9 1.62523e7i 0.0664639 0.000586509i
$$409$$ 1.70687e9 9.68011e9i 0.0609966 0.345929i −0.939001 0.343914i $$-0.888247\pi$$
0.999998 0.00201563i $$-0.000641597\pi$$
$$410$$ 6.68342e8 + 1.83625e9i 0.0236518 + 0.0649827i
$$411$$ 5.14261e9 + 6.02004e9i 0.180226 + 0.210975i
$$412$$ 3.18809e9 + 1.80806e10i 0.110648 + 0.627514i
$$413$$ 1.28434e10 7.41511e9i 0.441447 0.254869i
$$414$$ −3.49517e9 5.81438e9i −0.118978 0.197926i
$$415$$ 5.77167e9 9.99683e9i 0.194585 0.337031i
$$416$$ −2.25565e9 + 6.19735e9i −0.0753179 + 0.206934i
$$417$$ 3.83578e9 2.29355e10i 0.126856 0.758514i
$$418$$ 1.99410e10 + 1.67325e10i 0.653192 + 0.548093i
$$419$$ −1.00979e10 + 1.20342e10i −0.327622 + 0.390445i −0.904562 0.426342i $$-0.859802\pi$$
0.576940 + 0.816786i $$0.304247\pi$$
$$420$$ −2.30093e9 6.15228e9i −0.0739445 0.197715i
$$421$$ 4.57745e10 + 1.66606e10i 1.45712 + 0.530348i 0.944570 0.328309i $$-0.106479\pi$$
0.512550 + 0.858657i $$0.328701\pi$$
$$422$$ −4.61473e8 2.66432e8i −0.0145511 0.00840110i
$$423$$ −5.54509e10 + 1.07898e10i −1.73200 + 0.337017i
$$424$$ 8.03370e9 + 1.39148e10i 0.248572 + 0.430539i
$$425$$ 5.66912e9 9.99619e8i 0.173764 0.0306393i
$$426$$ −1.09044e9 5.88030e9i −0.0331104 0.178551i
$$427$$ −3.50091e10 + 1.27423e10i −1.05310 + 0.383297i
$$428$$ 8.92112e9 + 1.57303e9i 0.265855 + 0.0468774i
$$429$$ −2.88635e10 + 1.70057e10i −0.852156 + 0.502070i
$$430$$ −1.46933e9 + 1.23292e9i −0.0429780 + 0.0360628i
$$431$$ 3.61544e10i 1.04774i −0.851799 0.523868i $$-0.824488\pi$$
0.851799 0.523868i $$-0.175512\pi$$
$$432$$ 8.25799e9 + 2.76040e9i 0.237104 + 0.0792567i
$$433$$ −5.26000e10 −1.49635 −0.748176 0.663500i $$-0.769070\pi$$
−0.748176 + 0.663500i $$0.769070\pi$$
$$434$$ −2.41158e10 2.87401e10i −0.679739 0.810082i
$$435$$ 3.43199e9 6.06740e9i 0.0958492 0.169452i
$$436$$ −4.14440e9 + 2.35040e10i −0.114687 + 0.650424i
$$437$$ 6.18699e9 + 1.69986e10i 0.169650 + 0.466110i
$$438$$ 9.02736e9 2.55004e10i 0.245281 0.692868i
$$439$$ 6.18375e9 + 3.50698e10i 0.166492 + 0.944225i 0.947512 + 0.319719i $$0.103588\pi$$
−0.781020 + 0.624506i $$0.785300\pi$$
$$440$$ −2.25858e9 + 1.30399e9i −0.0602594 + 0.0347908i
$$441$$ −6.71139e10 + 2.57776e10i −1.77443 + 0.681536i
$$442$$ 3.16019e9 5.47362e9i 0.0827989 0.143412i
$$443$$ 1.31423e9 3.61083e9i 0.0341239 0.0937545i −0.921461 0.388472i $$-0.873003\pi$$
0.955585 + 0.294717i $$0.0952254\pi$$
$$444$$ −1.76565e10 1.45520e10i −0.454332 0.374448i
$$445$$ 1.47273e10 + 1.23576e10i 0.375562 + 0.315134i
$$446$$ −2.04100e9 + 2.43237e9i −0.0515826 + 0.0614738i
$$447$$ 2.74211e10 3.32711e10i 0.686840 0.833369i
$$448$$ 8.05875e9 + 2.93314e9i 0.200058 + 0.0728151i
$$449$$ 3.15809e10 + 1.82332e10i 0.777031 + 0.448619i 0.835377 0.549677i $$-0.185249\pi$$
−0.0583457 + 0.998296i $$0.518583\pi$$
$$450$$ 2.68800e10 + 4.25199e9i 0.655509 + 0.103691i
$$451$$ −6.47989e9 1.12235e10i −0.156625 0.271282i
$$452$$ 2.35265e10 4.14836e9i 0.563643 0.0993855i
$$453$$ 1.38897e9 + 4.91706e8i 0.0329837 + 0.0116765i
$$454$$ −2.60028e10 + 9.46425e9i −0.612064 + 0.222773i
$$455$$ −2.21981e10 3.91413e9i −0.517929 0.0913249i
$$456$$ −2.02086e10 1.14308e10i −0.467386 0.264374i
$$457$$ 2.28530e10 1.91759e10i 0.523936 0.439635i −0.342065 0.939676i $$-0.611126\pi$$
0.866001 + 0.500042i $$0.166682\pi$$
$$458$$ 9.00974e8i 0.0204763i
$$459$$ −7.33443e9 3.97949e9i −0.165240 0.0896554i
$$460$$ −1.81235e9 −0.0404771
$$461$$ 3.02114e10 + 3.60046e10i 0.668910 + 0.797176i 0.988635 0.150335i $$-0.0480351\pi$$
−0.319725 + 0.947510i $$0.603591\pi$$
$$462$$ 2.21134e10 + 3.75327e10i 0.485386 + 0.823839i
$$463$$ −8.60616e8 + 4.88079e9i −0.0187277 + 0.106210i −0.992739 0.120290i $$-0.961617\pi$$
0.974011 + 0.226501i $$0.0727285\pi$$
$$464$$ 3.11280e9 + 8.55234e9i 0.0671551 + 0.184507i
$$465$$ −1.00055e10 + 1.85541e9i −0.214006 + 0.0396853i
$$466$$ 6.23242e8 + 3.53458e9i 0.0132164 + 0.0749539i
$$467$$ 5.51561e10 3.18444e10i 1.15965 0.669523i 0.208428 0.978038i $$-0.433165\pi$$
0.951219 + 0.308515i $$0.0998321\pi$$
$$468$$ 2.25466e10 1.96072e10i 0.470000 0.408726i
$$469$$ −1.74402e10 + 3.02072e10i −0.360462 + 0.624338i
$$470$$ −5.16158e9 + 1.41813e10i −0.105777 + 0.290620i
$$471$$ 7.90282e10 2.95562e10i 1.60583 0.600572i
$$472$$ 4.02314e9 + 3.37581e9i 0.0810582 + 0.0680159i
$$473$$ 8.17680e9 9.74473e9i 0.163357 0.194682i
$$474$$ −1.39555e10 2.33395e9i −0.276459 0.0462357i
$$475$$ −6.81900e10 2.48191e10i −1.33951 0.487542i
$$476$$ −7.11764e9 4.10937e9i −0.138646 0.0800475i
$$477$$ −1.28465e9 7.27835e10i −0.0248149 1.40592i
$$478$$ −1.46544e10 2.53822e10i −0.280709 0.486203i
$$479$$ 6.28490e10 1.10820e10i 1.19387 0.210511i 0.458822 0.888528i $$-0.348272\pi$$
0.735046 + 0.678017i $$0.237160\pi$$
$$480$$ 1.76863e9 1.51085e9i 0.0333174 0.0284614i
$$481$$ −7.37820e10 + 2.68544e10i −1.37838 + 0.501691i
$$482$$ −2.12072e9 3.73941e8i −0.0392913 0.00692811i
$$483$$ 2.67130e8 + 3.02715e10i 0.00490833 + 0.556218i
$$484$$ −7.76888e9 + 6.51886e9i −0.141572 + 0.118793i
$$485$$ 2.49178e10i 0.450342i
$$486$$ −2.66652e10 2.90714e10i −0.477969 0.521101i
$$487$$ 1.10506e10 0.196459 0.0982294 0.995164i $$-0.468682\pi$$
0.0982294 + 0.995164i $$0.468682\pi$$
$$488$$ −8.48058e9 1.01068e10i −0.149536 0.178210i
$$489$$ 1.01043e10 8.91651e7i 0.176714 0.00155941i
$$490$$ −3.33515e9 + 1.89146e10i −0.0578538 + 0.328105i
$$491$$ −3.51172e10 9.64836e10i −0.604218 1.66007i −0.742632 0.669700i $$-0.766423\pi$$
0.138414 0.990374i $$-0.455799\pi$$
$$492$$ 7.50782e9 + 8.78879e9i 0.128131 + 0.149992i
$$493$$ −1.51458e9 8.58963e9i −0.0256393 0.145408i
$$494$$ −6.89994e10 + 3.98368e10i −1.15861 + 0.668924i
$$495$$ 1.18139e10 2.08519e8i 0.196776 0.00347315i
$$496$$ 6.64304e9 1.15061e10i 0.109759 0.190108i
$$497$$ −9.12756e9 + 2.50778e10i −0.149599 + 0.411020i
$$498$$ 1.12632e10 6.73464e10i 0.183123 1.09496i
$$499$$ −2.13955e10 1.79529e10i −0.345080 0.289556i 0.453731 0.891139i $$-0.350093\pi$$
−0.798811 + 0.601582i $$0.794537\pi$$
$$500$$ 9.65236e9 1.15032e10i 0.154438 0.184052i
$$501$$ −1.76477e10 4.71870e10i −0.280116 0.748981i
$$502$$ −3.93115e10 1.43082e10i −0.619019 0.225305i
$$503$$ −3.72001e10 2.14775e10i −0.581129 0.335515i 0.180453 0.983584i $$-0.442244\pi$$
−0.761582 + 0.648069i $$0.775577\pi$$
$$504$$ −2.54963e10 2.93186e10i −0.395144 0.454382i
$$505$$ 8.85304e9 + 1.53339e10i 0.136122 + 0.235770i
$$506$$ 1.18370e10 2.08719e9i 0.180568 0.0318390i
$$507$$ −6.64809e9 3.58504e10i −0.100616 0.542577i
$$508$$ 3.05926e10 1.11348e10i 0.459369 0.167197i
$$509$$ 2.68012e10 + 4.72577e9i 0.399284 + 0.0704046i 0.369685 0.929157i $$-0.379466\pi$$
0.0295996 + 0.999562i $$0.490577\pi$$
$$510$$ −1.92064e9 + 1.13160e9i −0.0283900 + 0.0167267i
$$511$$ −9.24701e10 + 7.75916e10i −1.35618 + 1.13797i
$$512$$ 3.03700e9i 0.0441942i
$$513$$ 5.49873e10 + 8.96721e10i 0.793949 + 1.29476i
$$514$$ 7.06846e10 1.01268
$$515$$ −1.42835e10 1.70225e10i −0.203052 0.241988i
$$516$$ −5.58602e9 + 9.87550e9i −0.0787959 + 0.139303i
$$517$$ 1.73801e10 9.85673e10i 0.243270 1.37966i
$$518$$ 3.49203e10 + 9.59427e10i 0.485019 + 1.33258i
$$519$$ −8.81436e9 + 2.48987e10i −0.121485 + 0.343169i
$$520$$ −1.38611e9 7.86102e9i −0.0189576 0.107514i
$$521$$ 1.19984e11 6.92729e10i 1.62844 0.940183i 0.643887 0.765120i $$-0.277321\pi$$
0.984557 0.175062i $$-0.0560127\pi$$
$$522$$ 6.44245e9 4.07275e10i 0.0867699 0.548537i
$$523$$ −3.01972e10 + 5.23032e10i −0.403609 + 0.699071i −0.994158 0.107930i $$-0.965578\pi$$
0.590550 + 0.807001i $$0.298911\pi$$
$$524$$ 1.71210e10 4.70394e10i 0.227093 0.623932i
$$525$$ −9.37127e10 7.72354e10i −1.23356 1.01667i
$$526$$ 1.40877e10 + 1.18210e10i 0.184034 + 0.154423i
$$527$$ −8.18442e9 + 9.75382e9i −0.106107 + 0.126454i
$$528$$ −9.81153e9 + 1.19047e10i −0.126241 + 0.153173i
$$529$$ −6.57393e10 2.39271e10i −0.839464 0.305540i
$$530$$ −1.68416e10 9.72351e9i −0.213442 0.123231i
$$531$$ −8.53131e9 2.22119e10i −0.107309 0.279388i
$$532$$ 5.18020e10 + 8.97237e10i 0.646696 + 1.12011i
$$533$$ 3.90635e10 6.88795e9i 0.484019 0.0853456i
$$534$$ 1.07202e11 + 3.79504e10i 1.31837 + 0.466714i
$$535$$ −1.03029e10 + 3.74996e9i −0.125761 + 0.0457733i
$$536$$ −1.21645e10 2.14493e9i −0.147379 0.0259869i
$$537$$ 8.40203e10 + 4.75256e10i 1.01039 + 0.571519i
$$538$$ −2.88960e10 + 2.42466e10i −0.344912 + 0.289416i
$$539$$ 1.27378e11i 1.50918i
$$540$$ −1.03264e10 + 2.10408e9i −0.121443 + 0.0247450i
$$541$$ 1.43171e11 1.67134 0.835671 0.549231i $$-0.185079\pi$$
0.835671 + 0.549231i $$0.185079\pi$$
$$542$$ −3.26074e10 3.88600e10i −0.377850 0.450304i
$$543$$ −6.03794e10 1.02481e11i −0.694528 1.17881i
$$544$$ 5.05404e8 2.86629e9i 0.00577090 0.0327284i
$$545$$ −9.87985e9 2.71447e10i −0.111986 0.307679i
$$546$$ −1.31098e11 + 2.43108e10i −1.47511 + 0.273545i
$$547$$ 7.96790e9 + 4.51882e10i 0.0890009 + 0.504749i 0.996421 + 0.0845254i $$0.0269374\pi$$
−0.907420 + 0.420224i $$0.861951\pi$$
$$548$$ 1.08354e10 6.25583e9i 0.120150 0.0693685i
$$549$$ 1.14169e10 + 5.86737e10i 0.125678 + 0.645883i
$$550$$ −2.41084e10 + 4.17570e10i −0.263462 + 0.456329i
$$551$$ −3.76050e10 + 1.03319e11i −0.407980 + 1.12092i
$$552$$ −1.00412e10 + 3.75536e9i −0.108151 + 0.0404479i
$$553$$ 4.83672e10 + 4.05849e10i 0.517190 + 0.433974i
$$554$$ 5.20313e10 6.20085e10i 0.552364 0.658282i
$$555$$ 2.73138e10 + 4.56802e9i 0.287879 + 0.0481455i
$$556$$ −3.45310e10 1.25683e10i −0.361335 0.131515i
$$557$$ 1.86421e10 + 1.07630e10i 0.193675 + 0.111818i 0.593702 0.804685i $$-0.297666\pi$$
−0.400027 + 0.916503i $$0.630999\pi$$
$$558$$ −5.15901e10 + 3.10122e10i −0.532145 + 0.319886i
$$559$$ 1.94674e10 + 3.37186e10i 0.199371 + 0.345320i
$$560$$ −1.02221e10 + 1.80243e9i −0.103941 + 0.0183277i
$$561$$ 1.12411e10 9.60275e9i 0.113490 0.0969491i
$$562$$ −1.16638e11 + 4.24527e10i −1.16921 + 0.425559i
$$563$$ −8.65075e10 1.52536e10i −0.861033 0.151823i −0.274340 0.961633i $$-0.588459\pi$$
−0.586693 + 0.809809i $$0.699571\pi$$
$$564$$ 7.87726e8 + 8.92661e10i 0.00778500 + 0.882207i
$$565$$ −2.21497e10 + 1.85858e10i −0.217357 + 0.182384i
$$566$$ 1.33134e11i 1.29725i
$$567$$ 3.66664e10 + 1.72171e11i 0.354761 + 1.66582i
$$568$$ −9.45075e9 −0.0907973
$$569$$ 7.25537e10 + 8.64662e10i 0.692167 + 0.824892i 0.991616 0.129220i $$-0.0412474\pi$$
−0.299449 + 0.954112i $$0.596803\pi$$
$$570$$ 2.80999e10 2.47967e8i 0.266199 0.00234906i
$$571$$ 1.93065e10 1.09493e11i 0.181618 1.03001i −0.748606 0.663015i $$-0.769276\pi$$
0.930224 0.366992i $$-0.119613\pi$$
$$572$$ 1.81063e10 + 4.97466e10i 0.169140 + 0.464707i
$$573$$ −8.47737e10 9.92377e10i −0.786399 0.920572i
$$574$$ −8.95678e9 5.07964e10i −0.0825095 0.467935i
$$575$$ −2.90178e10 + 1.67534e10i −0.265456 + 0.153261i
$$576$$ 6.66835e9 1.20356e10i 0.0605799 0.109339i
$$577$$ 3.94895e10 6.83978e10i 0.356269 0.617076i −0.631065 0.775730i $$-0.717382\pi$$
0.987334 + 0.158654i $$0.0507153\pi$$
$$578$$ 2.60388e10 7.15411e10i 0.233297 0.640979i
$$579$$ 6.70973e9 4.01198e10i 0.0597023 0.356981i
$$580$$ −8.43841e9 7.08067e9i −0.0745674 0.0625694i
$$581$$ −1.95855e11 + 2.33410e11i −1.71882 + 2.04840i
$$582$$ 5.16322e10 + 1.38056e11i 0.450017 + 1.20327i
$$583$$ 1.21196e11 + 4.41118e10i 1.04910 + 0.381839i
$$584$$ −3.70204e10 2.13737e10i −0.318265 0.183751i
$$585$$ −1.17673e10 + 3.41965e10i −0.100474 + 0.291984i
$$586$$ −4.80692e10 8.32583e10i −0.407640 0.706053i
$$587$$ −6.09522e10 + 1.07475e10i −0.513377 + 0.0905223i −0.424335 0.905505i $$-0.639492\pi$$
−0.0890429 + 0.996028i $$0.528381\pi$$
$$588$$ 2.07148e10 + 1.11706e11i 0.173289 + 0.934474i
$$589$$ 1.50826e11 5.48963e10i 1.25319 0.456123i
$$590$$ −6.25994e9 1.10380e9i −0.0516609 0.00910921i
$$591$$ 1.67128e11 9.84681e10i 1.36994 0.807134i
$$592$$ −2.76977e10 + 2.32411e10i −0.225505 + 0.189221i
$$593$$ 4.85917e10i 0.392956i −0.980508 0.196478i $$-0.937050\pi$$
0.980508 0.196478i $$-0.0629504\pi$$
$$594$$ 6.50220e10 2.56349e10i 0.522294 0.205914i
$$595$$ 9.94748e9 0.0793679
$$596$$ −4.37944e10 5.21922e10i −0.347083 0.413638i
$$597$$ 2.53954e10 4.48964e10i 0.199920 0.353439i
$$598$$ −6.38828e9 + 3.62297e10i −0.0499550 + 0.283309i
$$599$$ 1.48815e10 + 4.08865e10i 0.115595 + 0.317594i 0.983975 0.178304i $$-0.0570611\pi$$
−0.868381 + 0.495898i $$0.834839\pi$$
$$600$$ 1.43515e10 4.05398e10i 0.110737 0.312807i
$$601$$ −2.36720e10 1.34251e11i −0.181442 1.02901i −0.930443 0.366438i $$-0.880577\pi$$
0.749001 0.662569i $$-0.230534\pi$$
$$602$$ 4.38461e10 2.53146e10i 0.333845 0.192746i
$$603$$ 4.34981e10 + 3.52100e10i 0.329004 + 0.266316i
$$604$$ 1.16419e9 2.01644e9i 0.00874736 0.0151509i
$$605$$ 4.19820e9 1.15345e10i 0.0313359 0.0860947i
$$606$$ 8.08232e10 + 6.66123e10i 0.599302 + 0.493928i
$$607$$ −1.01399e10 8.50841e9i −0.0746930 0.0626749i 0.604677 0.796471i $$-0.293302\pi$$
−0.679370 + 0.733796i $$0.737747\pi$$
$$608$$ −2.35834e10 + 2.81056e10i −0.172581 + 0.205674i
$$609$$ −1.17024e11 + 1.41990e11i −0.850758 + 1.03226i
$$610$$ 1.50055e10 + 5.46157e9i 0.108376 + 0.0394455i
$$611$$ 2.65298e11 + 1.53170e11i 1.90357 + 1.09903i
$$612$$ −8.29642e9 + 1.02493e10i −0.0591405 + 0.0730616i
$$613$$ −1.33386e10 2.31031e10i −0.0944642 0.163617i 0.814921 0.579573i $$-0.196780\pi$$
−0.909385 + 0.415956i $$0.863447\pi$$
$$614$$ 4.51324e10 7.95806e9i 0.317552 0.0559930i
$$615$$ −1.31883e10 4.66877e9i −0.0921909 0.0326364i
$$616$$ 6.46882e10 2.35446e10i 0.449265 0.163519i
$$617$$ −3.40660e10 6.00676e9i −0.235061 0.0414476i 0.0548765 0.998493i $$-0.482523\pi$$
−0.289938 + 0.957046i $$0.593635\pi$$
$$618$$ −1.14409e11 6.47149e10i −0.784346 0.443660i
$$619$$ 1.03240e10 8.66288e9i 0.0703212 0.0590065i −0.606950 0.794740i $$-0.707607\pi$$
0.677271 + 0.735734i $$0.263163\pi$$
$$620$$ 1.60807e10i 0.108827i
$$621$$ 4.80387e10 + 7.16505e9i 0.323016 + 0.0481784i
$$622$$ 1.68558e11 1.12613
$$623$$ −3.26190e11 3.88738e11i −2.16530 2.58050i
$$624$$ −2.39685e10 4.06814e10i −0.158089 0.268323i
$$625$$ 2.17125e10 1.23138e11i 0.142295 0.806996i
$$626$$ 6.11531e10 + 1.68017e11i 0.398218 + 1.09410i
$$627$$ −1.83244e11 + 3.39808e10i −1.18566 + 0.219869i
$$628$$ −2.31529e10 1.31307e11i −0.148856 0.844205i
$$629$$ 3.00085e10 1.73254e10i 0.191708 0.110683i
$$630$$ 4.44676e10 + 1.53017e10i 0.282281 + 0.0971355i
$$631$$ −5.61310e10 + 9.72218e10i −0.354067 + 0.613262i −0.986958 0.160979i $$-0.948535\pi$$
0.632891 + 0.774241i $$0.281868\pi$$
$$632$$ −7.64736e9 + 2.10110e10i −0.0479340 + 0.131697i
$$633$$ 3.57329e9 1.33639e9i 0.0222563 0.00832377i
$$634$$ −4.32743e10 3.63115e10i −0.267839 0.224743i
$$635$$ −2.53283e10 + 3.01851e10i −0.155780 + 0.185651i
$$636$$ −1.13458e11 1.89750e10i −0.693437 0.115972i
$$637$$ 3.66357e11 + 1.33343e11i 2.22508 + 0.809865i
$$638$$ 6.32685e10 + 3.65281e10i 0.381861 + 0.220467i
$$639$$ 3.74531e10 + 2.07510e10i 0.224638 + 0.124462i
$$640$$ −1.83790e9 3.18334e9i −0.0109547 0.0189742i
$$641$$ −2.25968e11 + 3.98442e10i −1.33849 + 0.236011i −0.796634 0.604462i $$-0.793388\pi$$
−0.541853 + 0.840473i $$0.682277\pi$$
$$642$$ −4.93125e10 + 4.21252e10i −0.290280 + 0.247972i
$$643$$ −1.80052e11 + 6.55336e10i −1.05330 + 0.383372i −0.809909 0.586556i $$-0.800484\pi$$
−0.243396 + 0.969927i $$0.578261\pi$$
$$644$$ 4.71115e10 + 8.30703e9i 0.273895 + 0.0482950i
$$645$$ −1.21176e8 1.37318e10i −0.000700130 0.0793396i
$$646$$ 2.69350e10 2.26012e10i 0.154663 0.129778i
$$647$$ 1.79065e11i 1.02187i −0.859621 0.510933i $$-0.829300\pi$$
0.859621 0.510933i $$-0.170700\pi$$
$$648$$ −5.28530e10 + 3.30549e10i −0.299757 + 0.187472i
$$649$$ 4.21569e10 0.237624
$$650$$ −9.48611e10 1.13051e11i −0.531416 0.633317i
$$651$$ 2.68594e11 2.37020e9i 1.49545 0.0131966i
$$652$$ 2.77280e9 1.57253e10i 0.0153436 0.0870181i
$$653$$ 7.05168e10 + 1.93743e11i 0.387829 + 1.06555i 0.967977 + 0.251040i $$0.0807724\pi$$
−0.580148 + 0.814511i $$0.697005\pi$$
$$654$$ −1.10985e11 1.29921e11i −0.606672 0.710182i
$$655$$ 1.05209e10 + 5.96671e10i 0.0571596 + 0.324168i
$$656$$ 1.58189e10 9.13302e9i 0.0854201 0.0493173i
$$657$$ 9.97805e10 + 1.65989e11i 0.535531 + 0.890879i
$$658$$ 1.99175e11 3.44982e11i 1.06251 1.84032i
$$659$$ −7.40481e10 + 2.03446e11i −0.392620 + 1.07871i 0.573181 + 0.819429i $$0.305709\pi$$
−0.965801 + 0.259286i $$0.916513\pi$$
$$660$$ 3.07993e9 1.84160e10i 0.0162317 0.0970553i
$$661$$ 5.27631e10 + 4.42735e10i 0.276391 + 0.231920i 0.770437 0.637516i $$-0.220038\pi$$
−0.494046 + 0.869436i $$0.664482\pi$$
$$662$$ 5.21680e10 6.21714e10i 0.271626 0.323712i
$$663$$ 1.58512e10 + 4.23834e10i 0.0820367 + 0.219352i
$$664$$ −1.01395e11 3.69046e10i −0.521606 0.189849i
$$665$$ −1.08596e11 6.26980e10i −0.555300 0.320603i
$$666$$ 1.60796e11 3.12881e10i 0.817293 0.159031i
$$667$$ 2.53842e10 + 4.39667e10i 0.128251 + 0.222137i
$$668$$ −7.84019e10 + 1.38244e10i −0.393750 + 0.0694288i
$$669$$ −4.14493e9 2.23519e10i −0.0206925 0.111586i
$$670$$ 1.40487e10 5.11332e9i 0.0697168 0.0253748i
$$671$$ −1.04296e11 1.83902e10i −0.514490 0.0907185i
$$672$$ −5.29002e10 + 3.11676e10i −0.259406 + 0.152836i
$$673$$ −1.98524e11 + 1.66582e11i −0.967728 + 0.812020i −0.982193 0.187875i $$-0.939840\pi$$
0.0144652 + 0.999895i $$0.495395\pi$$
$$674$$ 1.10032e11i 0.533188i
$$675$$ −1.45888e11 + 1.29147e11i −0.702755 + 0.622112i
$$676$$ −5.76183e10 −0.275914
$$677$$ −5.23020e10 6.23311e10i −0.248979 0.296722i 0.627051 0.778978i $$-0.284262\pi$$
−0.876030 + 0.482256i $$0.839817\pi$$
$$678$$ −8.42075e10 + 1.48870e11i −0.398503 + 0.704512i
$$679$$ 1.14213e11 6.47732e11i 0.537323 3.04731i
$$680$$ 1.20484e9 + 3.31026e9i 0.00563498 + 0.0154820i
$$681$$ 6.61135e10 1.86757e11i 0.307398 0.868336i
$$682$$ −1.85193e10 1.05028e11i −0.0856027 0.485477i
$$683$$ −3.18031e10 + 1.83615e10i −0.146146 + 0.0843774i −0.571290 0.820748i $$-0.693557\pi$$
0.425144 + 0.905126i $$0.360223\pi$$
$$684$$ 1.55172e11 5.95998e10i 0.708907 0.272283i
$$685$$ −7.57168e9 + 1.31145e10i −0.0343898 + 0.0595649i
$$686$$ 8.21726e10 2.25767e11i 0.371048 1.01945i
$$687$$ 4.97775e9 + 4.10253e9i 0.0223463 + 0.0184172i
$$688$$ 1.37346e10 + 1.15247e10i 0.0613004 + 0.0514372i
$$689$$ −2.53743e11 + 3.02399e11i −1.12594 + 1.34185i
$$690$$ 8.25240e9 1.00129e10i 0.0364069 0.0441739i
$$691$$ −1.26237e11 4.59465e10i −0.553699 0.201530i 0.0499900 0.998750i $$-0.484081\pi$$
−0.603689 + 0.797220i $$0.706303\pi$$
$$692$$ 3.61469e10 + 2.08694e10i 0.157633 + 0.0910093i
$$693$$ −3.08055e11 4.87295e10i −1.33566 0.211280i
$$694$$ 2.79053e9 + 4.83334e9i 0.0120295 + 0.0208358i
$$695$$ 4.38008e10 7.72326e9i 0.187734 0.0331026i
$$696$$ −6.14244e10 2.17448e10i −0.261760 0.0926655i
$$697$$ −1.64496e10 + 5.98715e9i −0.0696984 + 0.0253682i
$$698$$ 2.53229e11 + 4.46512e10i 1.06682 + 0.188110i
$$699$$ −2.23659e10 1.26512e10i −0.0936868 0.0529934i
$$700$$ −1.47006e11 + 1.23353e11i −0.612272 + 0.513757i
$$701$$ 5.79495e10i 0.239981i 0.992775 + 0.119991i $$0.0382865\pi$$
−0.992775 + 0.119991i $$0.961714\pi$$
$$702$$ 5.66243e9 + 2.13847e11i 0.0233160 + 0.880551i
$$703$$ −4.36801e11 −1.78839
$$704$$ 1.56700e10 + 1.86748e10i 0.0637939 + 0.0760267i
$$705$$ −5.48469e10 9.30908e10i −0.222022 0.376834i
$$706$$ 3.98236e10 2.25851e11i 0.160296 0.909082i
$$707$$ −1.59849e11 4.39180e11i −0.639781 1.75778i
$$708$$ −3.69700e10 + 6.85571e9i −0.147135 + 0.0272847i
$$709$$ 5.57568e10 + 3.16213e11i 0.220655 + 1.25139i 0.870820 + 0.491602i $$0.163589\pi$$
−0.650165 + 0.759793i $$0.725300\pi$$
$$710$$ 9.90614e9 5.71931e9i 0.0389826 0.0225066i
$$711$$ 7.64401e10 6.64746e10i 0.299118 0.260122i
$$712$$ 8.98536e10 1.55631e11i 0.349636 0.605587i
$$713$$ 2.53479e10 6.96428e10i 0.0980808 0.269475i
$$714$$ 5.51134e10 2.06122e10i 0.212063 0.0793106i
$$715$$ −4.90839e10 4.11863e10i −0.187808 0.157590i
$$716$$ 9.80519e10 1.16854e11i 0.373082 0.444621i
$$717$$ 2.06961e11 + 3.46126e10i 0.783090 + 0.130966i
$$718$$ −3.23221e11 1.17643e11i −1.21619 0.442658i
$$719$$ 3.93948e10 + 2.27446e10i 0.147409 + 0.0851065i 0.571890 0.820330i $$-0.306210\pi$$
−0.424482 + 0.905437i $$0.639544\pi$$
$$720$$ 2.93895e8 + 1.66510e10i 0.00109361 + 0.0619598i
$$721$$ 2.93273e11 + 5.07964e11i 1.08525 + 1.87972i
$$722$$ −2.47273e11 + 4.36010e10i −0.909973 + 0.160453i
$$723$$ 1.17225e10 1.00140e10i 0.0429011 0.0366483i
$$724$$ −1.76628e11 + 6.42873e10i −0.642843 + 0.233976i
$$725$$ −2.00563e11 3.53647e10i −0.725938 0.128002i
$$726$$ −6.40702e8 7.26052e10i −0.00230627 0.261349i
$$727$$ 1.15111e11 9.65896e10i 0.412078 0.345774i −0.413062 0.910703i $$-0.635541\pi$$
0.825140 + 0.564929i $$0.191096\pi$$
$$728$$ 2.10699e11i 0.750130i
$$729$$ 2.82034e11 1.49464e10i 0.998599 0.0529207i
$$730$$ 5.17390e10 0.182191
$$731$$ −1.10447e10 1.31626e10i −0.0386799 0.0460969i
$$732$$ 9.44542e10 8.33508e8i 0.328986 0.00290312i
$$733$$ 8.87309e10 5.03218e11i 0.307368 1.74317i −0.304774 0.952425i $$-0.598581\pi$$
0.612142 0.790748i $$-0.290308\pi$$
$$734$$ −6.35144e10 1.74504e11i −0.218820 0.601204i
$$735$$ −8.93141e10 1.04553e11i −0.306035 0.358250i
$$736$$ 2.94177e9 + 1.66836e10i 0.0100253 + 0.0568563i
$$737$$ −8.58681e10 + 4.95760e10i −0.291046 + 0.168036i
$$738$$ −8.27431e10 + 1.46044e9i −0.278937 + 0.00492333i
$$739$$ −1.39896e11 + 2.42306e11i −0.469058 + 0.812432i −0.999374 0.0353675i $$-0.988740\pi$$
0.530316 + 0.847800i $$0.322073\pi$$
$$740$$ 1.49675e10 4.11228e10i 0.0499139 0.137137i
$$741$$ 9.40915e10 5.62606e11i 0.312089 1.86609i
$$742$$ 3.93225e11 + 3.29955e11i 1.29726 + 1.08853i
$$743$$ 1.66102e11 1.97953e11i 0.545031 0.649542i −0.421277 0.906932i $$-0.638418\pi$$
0.966308 + 0.257390i $$0.0828624\pi$$
$$744$$ 3.33208e10 + 8.90940e10i 0.108749 + 0.290775i
$$745$$ 7.74898e10 + 2.82040e10i 0.251547 + 0.0915557i
$$746$$ 1.44207e11 + 8.32581e10i 0.465620 + 0.268826i
$$747$$ 3.20793e11 + 3.68885e11i 1.03025 + 1.18470i
$$748$$ −1.16814e10 2.02328e10i −0.0373156 0.0646324i
$$749$$ 2.85011e11 5.02551e10i 0.905595 0.159681i
$$750$$ 1.96023e10 + 1.05707e11i 0.0619530 + 0.334087i
$$751$$ −9.53482e10 + 3.47039e10i −0.299746 + 0.109098i −0.487515 0.873115i $$-0.662096\pi$$
0.187769 + 0.982213i $$0.439874\pi$$
$$752$$ 1.38925e11 + 2.44962e10i 0.434419 + 0.0765998i
$$753$$ 2.58053e11 1.52039e11i 0.802655 0.472905i
$$754$$ −1.71291e11 + 1.43730e11i −0.529966 + 0.444694i
$$755$$ 2.81814e9i 0.00867310i