LMFDB - Embedded newform 27.7.f.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	27.5
Dual form			27.7.f.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.78575 - 10.4705i) q^{2} +(21.2323 - 16.6790i) q^{3} +(-21.3274 + 120.954i) q^{4} +(-83.1319 - 228.403i) q^{5} +(-361.178 - 75.7744i) q^{6} +(3.85901 + 21.8856i) q^{7} +(696.250 - 401.980i) q^{8} +(172.622 - 708.267i) q^{9} +O(q^{10})$	\(q+(-8.78575 - 10.4705i) q^{2} +(21.2323 - 16.6790i) q^{3} +(-21.3274 + 120.954i) q^{4} +(-83.1319 - 228.403i) q^{5} +(-361.178 - 75.7744i) q^{6} +(3.85901 + 21.8856i) q^{7} +(696.250 - 401.980i) q^{8} +(172.622 - 708.267i) q^{9} +(-1661.11 + 2877.12i) q^{10} +(-470.609 + 1292.99i) q^{11} +(1564.56 + 2923.85i) q^{12} +(1442.04 + 1210.02i) q^{13} +(195.247 - 232.687i) q^{14} +(-5574.62 - 3462.97i) q^{15} +(-2939.57 - 1069.92i) q^{16} +(739.593 + 427.004i) q^{17} +(-8932.49 + 4415.23i) q^{18} +(-4651.50 - 8056.63i) q^{19} +(29399.2 - 5183.88i) q^{20} +(446.965 + 400.317i) q^{21} +(17672.8 - 6432.38i) q^{22} +(-845.594 - 149.101i) q^{23} +(8078.38 - 20147.7i) q^{24} +(-33287.6 + 27931.6i) q^{25} -25729.7i q^{26} +(-8148.01 - 17917.3i) q^{27} -2729.44 q^{28} +(-6312.41 - 7522.84i) q^{29} +(12718.3 + 88793.5i) q^{30} +(5062.00 - 28708.0i) q^{31} +(-2974.27 - 8171.75i) q^{32} +(11573.6 + 35302.4i) q^{33} +(-2026.95 - 11495.4i) q^{34} +(4677.92 - 2700.80i) q^{35} +(81986.1 + 35984.9i) q^{36} +(18624.3 - 32258.2i) q^{37} +(-43489.6 + 119487. i) q^{38} +(50799.7 + 1639.65i) q^{39} +(-149694. - 125608. i) q^{40} +(31749.6 - 37837.7i) q^{41} +(264.573 - 8197.00i) q^{42} +(10987.9 + 3999.26i) q^{43} +(-146355. - 84498.1i) q^{44} +(-176121. + 19452.1i) q^{45} +(5868.03 + 10163.7i) q^{46} +(-123131. + 21711.4i) q^{47} +(-80259.1 + 26312.3i) q^{48} +(110090. - 40069.4i) q^{49} +(584913. + 103136. i) q^{50} +(22825.3 - 3269.38i) q^{51} +(-177111. + 148614. i) q^{52} -23116.5i q^{53} +(-116016. + 242730. i) q^{54} +334445. q^{55} +(11484.4 + 13686.6i) q^{56} +(-233139. - 93478.6i) q^{57} +(-23308.2 + 132188. i) q^{58} +(-98982.2 - 271951. i) q^{59} +(537752. - 600415. i) q^{60} +(42313.0 + 239969. i) q^{61} +(-345060. + 199220. i) q^{62} +(16167.0 + 1044.72i) q^{63} +(-159534. + 276321. i) q^{64} +(156492. - 429957. i) q^{65} +(267949. - 431339. i) q^{66} +(-216191. - 181406. i) q^{67} +(-67421.4 + 80349.7i) q^{68} +(-20440.8 + 10937.9i) q^{69} +(-69377.6 - 25251.4i) q^{70} +(242393. + 139946. i) q^{71} +(-164521. - 562522. i) q^{72} +(131842. + 228357. i) q^{73} +(-501386. + 88407.8i) q^{74} +(-240902. + 1.14826e6i) q^{75} +(1.07368e6 - 390789. i) q^{76} +(-30113.8 - 5309.88i) q^{77} +(-429146. - 546301. i) q^{78} +(252610. - 211965. i) q^{79} +760352. i q^{80} +(-471844. - 244526. i) q^{81} -675121. q^{82} +(104427. + 124451. i) q^{83} +(-57952.4 + 45524.4i) q^{84} +(36045.3 - 204423. i) q^{85} +(-54662.7 - 150184. i) q^{86} +(-259501. - 54442.6i) q^{87} +(192094. + 1.08942e6i) q^{88} +(-430492. + 248545. i) q^{89} +(1.75103e6 + 1.67316e6i) q^{90} +(-20917.0 + 36229.3i) q^{91} +(36068.7 - 99098.0i) q^{92} +(-371343. - 693967. i) q^{93} +(1.30913e6 + 1.09849e6i) q^{94} +(-1.45347e6 + 1.73218e6i) q^{95} +(-199447. - 123897. i) q^{96} +(-35417.3 - 12890.8i) q^{97} +(-1.38677e6 - 800650. i) q^{98} +(834543. + 556516. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−8.78575	−	10.4705i	−1.09822	−	1.30881i	−0.947331	−	0.320255i	$-0.896231\pi$
$2$	−8.78575	−	10.4705i	−1.09822	−	1.30881i	−0.150888	−	0.988551i	$-0.548213\pi$
$3$	21.2323	−	16.6790i	0.786382	−	0.617740i
$3$	21.2323	−	16.6790i	0.786382	−	0.617740i
$4$	−21.3274	+	120.954i	−0.333241	+	1.88990i
$5$	−83.1319	−	228.403i	−0.665055	−	1.82722i	−0.552379	−	0.833593i	$-0.686280\pi$
$5$	−83.1319	−	228.403i	−0.665055	−	1.82722i	−0.112676	−	0.993632i	$-0.535942\pi$
$6$	−361.178	−	75.7744i	−1.67212	−	0.350808i
$7$	3.85901	+	21.8856i	0.0112508	+	0.0638063i	0.989916	−	0.141654i	$-0.0452420\pi$
$7$	3.85901	+	21.8856i	0.0112508	+	0.0638063i	−0.978665	+	0.205460i	$0.934131\pi$
$8$	696.250	−	401.980i	1.35986	−	0.785118i
$9$	172.622	−	708.267i	0.236793	−	0.971560i
$10$	−1661.11	+	2877.12i	−1.66111	+	2.87712i
$11$	−470.609	+	1292.99i	−0.353576	+	0.971441i	0.627636	+	0.778507i	$0.284023\pi$
$11$	−470.609	+	1292.99i	−0.353576	+	0.971441i	−0.981212	+	0.192934i	$0.938200\pi$
$12$	1564.56	+	2923.85i	0.905415	+	1.69204i
$13$	1442.04	+	1210.02i	0.656368	+	0.550758i	0.908996	−	0.416805i	$-0.136850\pi$
$13$	1442.04	+	1210.02i	0.656368	+	0.550758i	−0.252628	+	0.967564i	$0.581295\pi$
$14$	195.247	−	232.687i	0.0711543	−	0.0847983i
$15$	−5574.62	−	3462.97i	−1.65174	−	1.02607i
$16$	−2939.57	−	1069.92i	−0.717669	−	0.261210i
$17$	739.593	+	427.004i	0.150538	+	0.0869131i	0.573377	−	0.819292i	$-0.305633\pi$
$17$	739.593	+	427.004i	0.150538	+	0.0869131i	−0.422839	+	0.906205i	$0.638966\pi$
$18$	−8932.49	+	4415.23i	−1.53163	+	0.757069i
$19$	−4651.50	−	8056.63i	−0.678160	−	1.17461i	−0.975535	−	0.219846i	$-0.929444\pi$
$19$	−4651.50	−	8056.63i	−0.678160	−	1.17461i	0.297375	−	0.954761i	$-0.403889\pi$
$20$	29399.2	−	5183.88i	3.67490	−	0.647985i
$21$	446.965	+	400.317i	0.0482631	+	0.0432261i
$22$	17672.8	−	6432.38i	1.65973	−	0.604093i
$23$	−845.594	−	149.101i	−0.0694990	−	0.0122546i	0.138791	−	0.990322i	$-0.455679\pi$
$23$	−845.594	−	149.101i	−0.0694990	−	0.0122546i	−0.208290	+	0.978067i	$0.566790\pi$
$24$	8078.38	−	20147.7i	0.584373	−	1.45745i
$25$	−33287.6	+	27931.6i	−2.13041	+	1.78762i
$26$		−	25729.7i		−	1.46391i
$27$	−8148.01	−	17917.3i	−0.413962	−	0.910294i
$28$	−2729.44			−0.124337
$29$	−6312.41	−	7522.84i	−0.258822	−	0.308452i	0.620948	−	0.783852i	$-0.286748\pi$
$29$	−6312.41	−	7522.84i	−0.258822	−	0.308452i	−0.879770	+	0.475400i	$0.842303\pi$
$30$	12718.3	+	88793.5i	0.471050	+	3.28865i
$31$	5062.00	−	28708.0i	0.169917	−	0.963648i	−0.773931	−	0.633269i	$-0.781713\pi$
$31$	5062.00	−	28708.0i	0.169917	−	0.963648i	0.943849	−	0.330378i	$-0.107176\pi$
$32$	−2974.27	−	8171.75i	−0.0907677	−	0.249382i
$33$	11573.6	+	35302.4i	0.322053	+	0.982342i
$34$	−2026.95	−	11495.4i	−0.0515711	−	0.292475i
$35$	4677.92	−	2700.80i	0.109106	−	0.0629924i
$36$	81986.1	+	35984.9i	1.75725	+	0.771281i
$37$	18624.3	−	32258.2i	0.367683	−	0.636846i	−0.621520	−	0.783399i	$-0.713484\pi$
$37$	18624.3	−	32258.2i	0.367683	−	0.636846i	0.989203	+	0.146553i	$0.0468177\pi$
$38$	−43489.6	+	119487.i	−0.792565	+	2.17756i
$39$	50799.7	+	1639.65i	0.856381	+	0.0276412i
$40$	−149694.	−	125608.i	−2.33897	−	1.96263i
$41$	31749.6	−	37837.7i	0.460666	−	0.549001i	−0.484841	−	0.874602i	$-0.661122\pi$
$41$	31749.6	−	37837.7i	0.460666	−	0.549001i	0.945507	+	0.325602i	$0.105567\pi$
$42$	264.573	−	8197.00i	0.00357106	−	0.110639i
$43$	10987.9	+	3999.26i	0.138200	+	0.0503007i	0.410194	−	0.911998i	$-0.365461\pi$
$43$	10987.9	+	3999.26i	0.138200	+	0.0503007i	−0.271994	+	0.962299i	$0.587683\pi$
$44$	−146355.	−	84498.1i	−1.71810	−	0.991948i
$45$	−176121.	+	19452.1i	−1.93274	+	0.213466i
$46$	5868.03	+	10163.7i	0.0602863	+	0.104419i
$47$	−123131.	+	21711.4i	−1.18597	+	0.209119i	−0.731627	−	0.681705i	$-0.761239\pi$
$47$	−123131.	+	21711.4i	−1.18597	+	0.209119i	−0.454348	+	0.890824i	$0.650128\pi$
$48$	−80259.1	+	26312.3i	−0.725722	+	0.237922i
$49$	110090.	−	40069.4i	0.935748	−	0.340584i
$50$	584913.	+	103136.i	4.67931	+	0.825088i
$51$	22825.3	−	3269.38i	0.172070	−	0.0246464i
$52$	−177111.	+	148614.i	−1.25961	+	1.05694i
$53$		−	23116.5i		−	0.155272i	−0.996982	−	0.0776362i	$-0.975263\pi$
$53$		−	23116.5i		−	0.155272i	0.996982	−	0.0776362i	$-0.0247373\pi$
$54$	−116016.	+	242730.i	−0.736778	+	1.54150i
$55$	334445.			2.01019
$56$	11484.4	+	13686.6i	0.0653949	+	0.0779347i
$57$	−233139.	−	93478.6i	−1.25890	−	0.504763i
$58$	−23308.2	+	132188.i	−0.119461	+	0.677496i
$59$	−98982.2	−	271951.i	−0.481949	−	1.32414i	−0.907820	−	0.419360i	$-0.862254\pi$
$59$	−98982.2	−	271951.i	−0.481949	−	1.32414i	0.425871	−	0.904784i	$-0.359968\pi$
$60$	537752.	−	600415.i	2.48959	−	2.77970i
$61$	42313.0	+	239969.i	0.186416	+	1.05722i	0.924122	+	0.382097i	$0.124798\pi$
$61$	42313.0	+	239969.i	0.186416	+	1.05722i	−0.737706	+	0.675122i	$0.764091\pi$
$62$	−345060.	+	199220.i	−1.44783	+	0.835908i
$63$	16167.0	+	1044.72i	0.0646557	+	0.00417811i
$64$	−159534.	+	276321.i	−0.608574	+	1.05408i
$65$	156492.	−	429957.i	0.569838	−	1.56562i
$66$	267949.	−	431339.i	0.932010	−	1.50033i
$67$	−216191.	−	181406.i	−0.718808	−	0.603151i	0.208248	−	0.978076i	$-0.433224\pi$
$67$	−216191.	−	181406.i	−0.718808	−	0.603151i	−0.927055	+	0.374925i	$0.877668\pi$
$68$	−67421.4	+	80349.7i	−0.214423	+	0.255539i
$69$	−20440.8	+	10937.9i	−0.0622229	+	0.0332956i
$70$	−69377.6	−	25251.4i	−0.202267	−	0.0736192i
$71$	242393.	+	139946.i	0.677244	+	0.391007i	0.798816	−	0.601576i	$-0.205460\pi$
$71$	242393.	+	139946.i	0.677244	+	0.391007i	−0.121572	+	0.992583i	$0.538793\pi$
$72$	−164521.	−	562522.i	−0.440782	−	1.50710i
$73$	131842.	+	228357.i	0.338910	+	0.587009i	0.984228	−	0.176905i	$-0.0566084\pi$
$73$	131842.	+	228357.i	0.338910	+	0.587009i	−0.645318	+	0.763914i	$0.723275\pi$
$74$	−501386.	+	88407.8i	−1.23730	+	0.218170i
$75$	−240902.	+	1.14826e6i	−0.571026	+	2.72179i
$76$	1.07368e6	−	390789.i	2.44589	−	0.890229i
$77$	−30113.8	−	5309.88i	−0.0659620	−	0.0116309i
$78$	−429146.	−	546301.i	−0.904317	−	1.15119i
$79$	252610.	−	211965.i	0.512353	−	0.429915i	−0.349603	−	0.936898i	$-0.613684\pi$
$79$	252610.	−	211965.i	0.512353	−	0.429915i	0.861956	+	0.506983i	$0.169239\pi$
$80$			760352.i			1.48506i
$81$	−471844.	−	244526.i	−0.887858	−	0.460118i
$82$	−675121.			−1.22445
$83$	104427.	+	124451.i	0.182633	+	0.217653i	0.849591	−	0.527441i	$-0.176849\pi$
$83$	104427.	+	124451.i	0.182633	+	0.217653i	−0.666958	+	0.745095i	$0.732404\pi$
$84$	−57952.4	+	45524.4i	−0.0977764	+	0.0768080i
$85$	36045.3	−	204423.i	0.0586937	−	0.332869i
$86$	−54662.7	−	150184.i	−0.0859400	−	0.236118i
$87$	−259501.	−	54442.6i	−0.394076	−	0.0826764i
$88$	192094.	+	1.08942e6i	0.281881	+	1.59863i
$89$	−430492.	+	248545.i	−0.610654	+	0.352561i	−0.773221	−	0.634136i	$-0.781356\pi$
$89$	−430492.	+	248545.i	−0.610654	+	0.352561i	0.162567	+	0.986697i	$0.448023\pi$
$90$	1.75103e6	+	1.67316e6i	2.40196	+	2.29515i
$91$	−20917.0	+	36229.3i	−0.0277572	+	0.0480768i
$92$	36068.7	−	99098.0i	0.0463198	−	0.127263i
$93$	−371343.	−	693967.i	−0.461665	−	0.862760i
$94$	1.30913e6	+	1.09849e6i	1.57616	+	1.32255i
$95$	−1.45347e6	+	1.73218e6i	−1.69526	+	2.02033i
$96$	−199447.	−	123897.i	−0.225431	−	0.140039i
$97$	−35417.3	−	12890.8i	−0.0388061	−	0.0141243i	0.322544	−	0.946554i	$-0.395462\pi$
$97$	−35417.3	−	12890.8i	−0.0388061	−	0.0141243i	−0.361350	+	0.932430i	$0.617684\pi$
$98$	−1.38677e6	−	800650.i	−1.47342	−	0.850677i
$99$	834543.	+	556516.i	0.860089	+	0.573551i
$100$	−2.66850e6	−	4.62197e6i	−2.66850	−	4.62197i
$101$	1.57540e6	−	277786.i	1.52907	−	0.269616i	0.655080	−	0.755560i	$-0.272635\pi$
$101$	1.57540e6	−	277786.i	1.52907	−	0.269616i	0.873990	+	0.485943i	$0.161524\pi$
$102$	−234769.	−	210267.i	−0.221228	−	0.198139i
$103$	465026.	−	169255.i	0.425564	−	0.154893i	−0.120354	−	0.992731i	$-0.538403\pi$
$103$	465026.	−	169255.i	0.425564	−	0.154893i	0.545919	+	0.837838i	$0.316181\pi$
$104$	1.49042e6	+	262802.i	1.32498	+	0.233630i
$105$	54276.5	−	135367.i	0.0468861	−	0.116935i
$106$	−242040.	+	203096.i	−0.203222	+	0.170523i
$107$		−	389907.i		−	0.318280i	−0.987256	−	0.159140i	$-0.949128\pi$
$107$		−	389907.i		−	0.318280i	0.987256	−	0.159140i	$-0.0508722\pi$
$108$	2.34095e6	−	603403.i	1.85832	−	0.479001i
$109$	985297.			0.760830			0.380415	−	0.924816i	$-0.375781\pi$
$109$	985297.			0.760830			0.380415	+	0.924816i	$0.375781\pi$
$110$	−2.93835e6	−	3.50179e6i	−2.20763	−	2.63095i
$111$	−142598.	−	995549.i	−0.104266	−	0.727937i
$112$	12071.9	−	68463.0i	0.00859252	−	0.0487306i
$113$	177822.	+	488563.i	0.123240	+	0.338599i	0.985936	−	0.167124i	$-0.0534481\pi$
$113$	177822.	+	488563.i	0.123240	+	0.338599i	−0.862696	+	0.505723i	$0.831226\pi$
$114$	1.06953e6	+	3.26235e6i	0.721905	+	2.20199i
$115$	36240.7	+	205531.i	0.0238289	+	0.135140i
$116$	1.04454e6	−	603068.i	0.669195	−	0.386360i
$117$	1.10594e6	−	812474.i	0.690518	−	0.507285i
$118$	−1.97782e6	+	3.42569e6i	−1.20376	+	2.08498i
$119$	−6491.12	+	17834.2i	−0.00385193	+	0.0105831i
$120$	−5.27337e6	−	170208.i	−3.05172	−	0.0984997i
$121$	−93250.3	−	78246.3i	−0.0526374	−	0.0441680i
$122$	2.14083e6	−	2.55134e6i	1.17897	−	1.40504i
$123$	43022.8	−	1.33293e6i	0.0231197	−	0.716296i
$124$	3.36439e6	+	1.22454e6i	1.76458	+	0.642254i
$125$	5.85791e6	+	3.38207e6i	2.99925	+	1.73162i
$126$	−131100.	−	178454.i	−0.0655378	−	0.0892103i
$127$	−765143.	−	1.32527e6i	−0.373535	−	0.646982i	0.616572	−	0.787299i	$-0.288521\pi$
$127$	−765143.	−	1.32527e6i	−0.373535	−	0.646982i	−0.990107	+	0.140317i	$0.955188\pi$
$128$	3.74673e6	−	660650.i	1.78658	−	0.315022i
$129$	300001.	−	98353.1i	0.139751	−	0.0458162i
$130$	−5.87674e6	+	2.13896e6i	−2.67490	+	0.973582i
$131$	74162.3	+	13076.8i	0.0329890	+	0.00581685i	0.190118	−	0.981761i	$-0.439113\pi$
$131$	74162.3	+	13076.8i	0.0329890	+	0.00581685i	−0.157129	+	0.987578i	$0.550224\pi$
$132$	−4.51680e6	+	646964.i	−1.96385	+	0.281292i
$133$	158374.	−	132891.i	0.0673175	−	0.0564861i
$134$			3.85740e6i			1.60317i
$135$	−3.41501e6	+	3.35053e6i	−1.38800	+	1.36180i
$136$	686589.			0.272948
$137$	−1.18880e6	−	1.41675e6i	−0.462323	−	0.550975i	0.483632	−	0.875271i	$-0.339317\pi$
$137$	−1.18880e6	−	1.41675e6i	−0.462323	−	0.550975i	−0.945956	+	0.324296i	$0.894873\pi$
$138$	294112.	+	117927.i	0.111912	+	0.0448719i
$139$	430915.	−	2.44384e6i	0.160453	−	0.909973i	−0.793177	−	0.608991i	$-0.791574\pi$
$139$	430915.	−	2.44384e6i	0.160453	−	0.909973i	0.953630	−	0.300982i	$-0.0973144\pi$
$140$	226904.	+	623414.i	0.0826910	+	0.227192i
$141$	−2.25224e6	+	2.51469e6i	−0.803448	+	0.897072i
$142$	−664311.	−	3.76749e6i	−0.232010	−	1.31579i
$143$	−2.24317e6	+	1.29510e6i	−0.767105	+	0.442888i
$144$	−1.26522e6	+	1.89731e6i	−0.423721	+	0.635406i
$145$	−1.19348e6	+	2.06716e6i	−0.391480	+	0.678064i
$146$	1.23267e6	−	3.38673e6i	0.396084	−	1.08823i
$147$	1.66914e6	−	2.68695e6i	0.525463	−	0.845879i
$148$	3.50454e6	+	2.94066e6i	1.08105	+	0.907109i
$149$	1.56215e6	−	1.86170e6i	0.472241	−	0.562794i	−0.476368	−	0.879246i	$-0.658047\pi$
$149$	1.56215e6	−	1.86170e6i	0.472241	−	0.562794i	0.948609	+	0.316452i	$0.102491\pi$
$150$	1.41393e7	−	7.56595e6i	4.18941	−	2.24176i
$151$	−5.29857e6	−	1.92852e6i	−1.53896	−	0.560136i	−0.573165	−	0.819440i	$-0.694285\pi$
$151$	−5.29857e6	−	1.92852e6i	−1.53896	−	0.560136i	−0.965796	+	0.259304i	$0.916507\pi$
$152$	−6.47721e6	−	3.73962e6i	−1.84441	−	1.06487i
$153$	430103.	−	450119.i	0.120088	−	0.125676i
$154$	208976.	+	361957.i	0.0572182	+	0.0991048i
$155$	−6.97782e6	+	1.23038e6i	−1.87381	+	0.330402i
$156$	−1.28175e6	+	6.10945e6i	−0.337621	+	1.60927i
$157$	5.42578e6	−	1.97482e6i	1.40205	−	0.510304i	0.473263	−	0.880921i	$-0.343076\pi$
$157$	5.42578e6	−	1.97482e6i	1.40205	−	0.510304i	0.928786	+	0.370618i	$0.120854\pi$
$158$	−4.43874e6	−	782669.i	−1.12535	−	0.198430i
$159$	−385560.	−	490817.i	−0.0959181	−	0.122103i
$160$	−1.61920e6	+	1.35867e6i	−0.395312	+	0.331706i
$161$		−	19081.7i		−	0.00457235i
$162$	1.58521e6	+	7.08876e6i	0.372857	+	1.66734i
$163$	1.90116e6			0.438991			0.219495	−	0.975614i	$-0.429559\pi$
$163$	1.90116e6			0.438991			0.219495	+	0.975614i	$0.429559\pi$
$164$	3.89947e6	+	4.64721e6i	0.884045	+	1.05356i
$165$	7.10104e6	−	5.57821e6i	1.58078	−	1.24177i
$166$	385592.	−	2.18680e6i	0.0842953	−	0.478062i
$167$	2.29944e6	+	6.31767e6i	0.493712	+	1.35646i	0.897259	+	0.441504i	$0.145555\pi$
$167$	2.29944e6	+	6.31767e6i	0.493712	+	1.35646i	−0.403548	+	0.914959i	$0.632223\pi$
$168$	472119.	+	99049.4i	0.0995688	+	0.0208893i
$169$	−222824.	−	1.26370e6i	−0.0461638	−	0.261808i
$170$	−2.45708e6	+	1.41860e6i	−0.500119	+	0.288744i
$171$	−6.50920e6	+	1.90375e6i	−1.30179	+	0.380734i
$172$	−718068.	+	1.24373e6i	−0.141117	+	0.244422i
$173$	−1.27941e6	+	3.51515e6i	−0.247099	+	0.678900i	0.752690	+	0.658375i	$0.228756\pi$
$173$	−1.27941e6	+	3.51515e6i	−0.247099	+	0.678900i	−0.999789	+	0.0205248i	$0.993466\pi$
$174$	1.70987e6	+	3.19541e6i	0.324575	+	0.606567i
$175$	−739756.	−	620729.i	−0.138030	−	0.115821i
$176$	2.76678e6	−	3.29732e6i	0.507501	−	0.604816i
$177$	−6.63750e6	−	4.12324e6i	−1.19697	−	0.743564i
$178$	6.38458e6	+	2.32380e6i	1.13207	+	0.412039i
$179$	−856838.	−	494696.i	−0.149396	−	0.0862539i	0.423438	−	0.905925i	$-0.360823\pi$
$179$	−856838.	−	494696.i	−0.149396	−	0.0862539i	−0.572835	+	0.819671i	$0.694156\pi$
$180$	1.40340e6	−	2.17174e7i	0.240637	−	3.72383i
$181$	−2.27777e6	−	3.94522e6i	−0.384127	−	0.665328i	0.607521	−	0.794304i	$-0.292164\pi$
$181$	−2.27777e6	−	3.94522e6i	−0.384127	−	0.665328i	−0.991648	+	0.128976i	$0.958831\pi$
$182$	563109.	−	99291.3i	0.0934067	−	0.0164701i
$183$	4.90084e6	+	4.38935e6i	0.799682	+	0.716221i
$184$	−648681.	+	236101.i	−0.104130	+	0.0379004i
$185$	−8.91613e6	−	1.57215e6i	−1.40819	−	0.248302i
$186$	−4.00362e6	+	9.98515e6i	−0.622177	+	1.55173i
$187$	−900170.	+	755332.i	−0.137657	+	0.115508i
$188$		−	1.53563e7i		−	2.31107i
$189$	360687.	−	247467.i	0.0534251	−	0.0366549i
$190$	3.09065e7			4.50598
$191$	4.23625e6	+	5.04856e6i	0.607969	+	0.724549i	0.978952	−	0.204091i	$-0.0654237\pi$
$191$	4.23625e6	+	5.04856e6i	0.607969	+	0.724549i	−0.370983	+	0.928640i	$0.620979\pi$
$192$	1.22148e6	+	8.52780e6i	0.172577	+	1.20485i
$193$	1.39515e6	−	7.91230e6i	0.194066	−	1.10060i	−0.719676	−	0.694310i	$-0.755710\pi$
$193$	1.39515e6	−	7.91230e6i	0.194066	−	1.10060i	0.913742	−	0.406294i	$-0.133179\pi$
$194$	176195.	+	484091.i	0.0241317	+	0.0663012i
$195$	−3.84857e6	−	1.17391e7i	−0.519034	−	1.58318i
$196$	2.49862e6	+	1.41704e7i	0.331842	+	1.88197i
$197$	8.89976e6	−	5.13828e6i	1.16407	−	0.672077i	0.211795	−	0.977314i	$-0.432069\pi$
$197$	8.89976e6	−	5.13828e6i	1.16407	−	0.672077i	0.952276	+	0.305237i	$0.0987357\pi$
$198$	−1.50512e6	−	1.36275e7i	−0.193899	−	1.75557i
$199$	−5.52156e6	+	9.56362e6i	−0.700652	+	1.21357i	0.267586	+	0.963534i	$0.413774\pi$
$199$	−5.52156e6	+	9.56362e6i	−0.700652	+	1.21357i	−0.968238	+	0.250031i	$0.919559\pi$
$200$	−1.19485e7	+	3.28284e7i	−1.49357	+	4.10354i
$201$	−7.61589e6	−	245817.i	−0.937848	−	0.0302707i
$202$	−1.67496e7	−	1.40546e7i	−2.03213	−	1.70516i
$203$	140282.	−	167181.i	0.0167692	−	0.0199848i
$204$	−91360.4	+	2.83053e6i	−0.0107614	+	0.333409i
$205$	−1.12816e7	−	4.10618e6i	−1.30952	−	0.476625i
$206$	−5.85778e6	−	3.38199e6i	−0.670087	−	0.386875i
$207$	−251572.	+	573169.i	−0.0283629	+	0.0646207i
$208$	−2.94437e6	−	5.09979e6i	−0.327191	−	0.566712i
$209$	1.26062e7	−	2.22281e6i	1.38084	−	0.243480i
$210$	−1.89422e6	+	621003.i	−0.204537	+	0.0670558i
$211$	300953.	−	109538.i	0.0320369	−	0.0116605i	−0.325952	−	0.945386i	$-0.605685\pi$
$211$	300953.	−	109538.i	0.0320369	−	0.0116605i	0.357989	+	0.933726i	$0.383463\pi$
$212$	2.79603e6	+	493015.i	0.293450	+	0.0517432i
$213$	7.48072e6	−	1.07150e6i	0.774113	−	0.110880i
$214$	−4.08250e6	+	3.42563e6i	−0.416567	+	0.349541i
$215$		−	2.84213e6i		−	0.285975i
$216$	−1.28755e7	−	9.19960e6i	−1.27762	−	0.912867i
$217$	647826.			0.0633985
$218$	−8.65657e6	−	1.03165e7i	−0.835558	−	0.995779i
$219$	6.60807e6	+	2.64955e6i	0.629132	+	0.252255i
$220$	−7.13285e6	+	4.04524e7i	−0.669877	+	3.79906i
$221$	549841.	+	1.51068e6i	0.0509401	+	0.139957i
$222$	−9.17102e6	+	1.02397e7i	−0.838222	+	0.935898i
$223$	2.73002e6	+	1.54827e7i	0.246179	+	1.39615i	0.817739	+	0.575589i	$0.195227\pi$
$223$	2.73002e6	+	1.54827e7i	0.246179	+	1.39615i	−0.571560	+	0.820560i	$0.693662\pi$
$224$	167366.	−	96628.6i	0.0148909	−	0.00859729i
$225$	1.40369e7	+	2.83981e7i	1.23232	+	2.49312i
$226$	3.55317e6	−	6.15427e6i	0.307816	−	0.533152i
$227$	919351.	−	2.52590e6i	0.0785966	−	0.215942i	−0.894171	−	0.447726i	$-0.852234\pi$
$227$	919351.	−	2.52590e6i	0.0785966	−	0.215942i	0.972767	+	0.231784i	$0.0744562\pi$
$228$	1.62788e7	−	2.62053e7i	1.37347	−	2.21098i
$229$	8.96676e6	+	7.52400e6i	0.746670	+	0.626531i	0.934620	−	0.355648i	$-0.115740\pi$
$229$	8.96676e6	+	7.52400e6i	0.746670	+	0.626531i	−0.187950	+	0.982179i	$0.560184\pi$
$230$	1.83360e6	−	2.18521e6i	0.150703	−	0.179601i
$231$	−727950.	+	389527.i	−0.0590562	+	0.0316011i
$232$	−7.41905e6	−	2.70031e6i	−0.594134	−	0.216247i
$233$	−3.92717e6	−	2.26735e6i	−0.310465	−	0.179247i	0.336670	−	0.941623i	$-0.390699\pi$
$233$	−3.92717e6	−	2.26735e6i	−0.310465	−	0.179247i	−0.647134	+	0.762376i	$0.724033\pi$
$234$	−1.82235e7	−	4.44152e6i	−1.42228	−	0.346645i
$235$	1.51951e7	+	2.63187e7i	1.17085	+	2.02797i
$236$	3.50046e7	−	6.17226e6i	2.66311	−	0.469578i
$237$	1.82813e6	−	8.71379e6i	0.137329	−	0.654579i
$238$	243762.	−	88722.0i	0.0180815	−	0.00658113i
$239$	7.09461e6	+	1.25097e6i	0.519679	+	0.0916334i	0.427334	−	0.904094i	$-0.359453\pi$
$239$	7.09461e6	+	1.25097e6i	0.519679	+	0.0916334i	0.0923445	+	0.995727i	$0.470564\pi$
$240$	1.26819e7	+	1.61440e7i	0.917383	+	1.16783i
$241$	2.10801e7	−	1.76883e7i	1.50599	−	1.26368i	0.634856	−	0.772630i	$-0.281059\pi$
$241$	2.10801e7	−	1.76883e7i	1.50599	−	1.26368i	0.871134	−	0.491045i	$-0.163385\pi$
$242$			1.66383e6i			0.117398i
$243$	−1.40968e7	+	2.67804e6i	−0.982429	+	0.186637i
$244$	−2.99276e7			−2.06016
$245$	−1.83040e7	−	2.18138e7i	−1.24465	−	1.48331i
$246$	−1.43344e7	+	1.12603e7i	−0.962884	+	0.756391i
$247$	3.04100e6	−	1.72464e7i	0.201802	−	1.14448i
$248$	−8.01564e6	−	2.20228e7i	−0.525513	−	1.44383i
$249$	4.29295e6	+	900652.i	0.278073	+	0.0583390i
$250$	−1.60544e7	−	9.10489e7i	−1.02748	−	5.82713i
$251$	1.77247e7	−	1.02334e7i	1.12088	−	0.647138i	0.179251	−	0.983803i	$-0.442632\pi$
$251$	1.77247e7	−	1.02334e7i	1.12088	−	0.647138i	0.941624	+	0.336665i	$0.109299\pi$
$252$	−471163.	+	1.93318e6i	−0.0294422	+	0.120801i
$253$	590730.	−	1.02318e6i	0.0364777	−	0.0631813i
$254$	−7.15378e6	+	1.96548e7i	−0.436550	+	1.19941i
$255$	−2.64424e6	−	4.94157e6i	−0.159471	−	0.298019i
$256$	−2.41922e7	−	2.02997e7i	−1.44197	−	1.20996i
$257$	−1.87237e7	+	2.23141e7i	−1.10304	+	1.31456i	−0.158064	+	0.987429i	$0.550525\pi$
$257$	−1.87237e7	+	2.23141e7i	−1.10304	+	1.31456i	−0.944980	+	0.327128i	$0.893919\pi$
$258$	−3.66554e6	−	2.27704e6i	−0.213441	−	0.132591i
$259$	777859.	+	283118.i	0.0447715	+	0.0162955i
$260$	4.86674e7	+	2.80982e7i	2.76897	+	1.59867i
$261$	−6.41785e6	+	3.17226e6i	−0.360967	+	0.178422i
$262$	−514651.	−	891402.i	−0.0286160	−	0.0495644i
$263$	−1.36198e7	+	2.40154e6i	−0.748694	+	0.132015i	−0.534960	−	0.844877i	$-0.679674\pi$
$263$	−1.36198e7	+	2.40154e6i	−0.748694	+	0.132015i	−0.213733	+	0.976892i	$0.568562\pi$
$264$	2.22490e7	+	1.99269e7i	1.20920	+	1.08300i
$265$	−5.27988e6	+	1.92172e6i	−0.283718	+	0.103265i
$266$	−2.78286e6	−	490694.i	−0.147859	−	0.0260715i
$267$	−4.99487e6	+	1.24574e7i	−0.262416	+	0.654474i
$268$	2.65525e7	−	2.22802e7i	1.37943	−	1.15748i
$269$			3.59968e7i			1.84930i	0.380818	+	0.924650i	$0.375642\pi$
$269$			3.59968e7i			1.84930i	−0.380818	+	0.924650i	$0.624358\pi$
$270$	6.50850e7	+	6.31977e6i	3.30666	+	0.321078i
$271$	5.12906e6			0.257709			0.128855	−	0.991664i	$-0.458870\pi$
$271$	5.12906e6			0.257709			0.128855	+	0.991664i	$0.458870\pi$
$272$	−1.71723e6	−	2.04651e6i	−0.0853338	−	0.101697i
$273$	160152.	+	1.11811e6i	0.00787126	+	0.0549535i
$274$	−4.38957e6	+	2.48945e7i	−0.213388	+	1.21018i
$275$	−2.04498e7	−	5.61854e7i	−0.983311	−	2.70162i
$276$	−887032.	−	2.70567e6i	−0.0421902	−	0.128691i
$277$	3.89983e6	+	2.21171e7i	0.183488	+	1.04061i	0.927883	+	0.372871i	$0.121627\pi$
$277$	3.89983e6	+	2.21171e7i	0.183488	+	1.04061i	−0.744395	+	0.667739i	$0.767262\pi$
$278$	−2.93740e7	+	1.69591e7i	−1.36719	+	0.789348i
$279$	−1.94591e7	−	8.54090e6i	−0.896006	−	0.393270i
$280$	2.17134e6	−	3.76086e6i	0.0989129	−	0.171322i
$281$	1.19189e7	−	3.27468e7i	0.537175	−	1.47588i	−0.313195	−	0.949689i	$-0.601399\pi$
$281$	1.19189e7	−	3.27468e7i	0.537175	−	1.47588i	0.850369	−	0.526186i	$-0.176379\pi$
$282$	4.61176e7	+	1.48853e6i	2.05646	+	0.0663758i
$283$	7.71534e6	+	6.47394e6i	0.340405	+	0.285634i	0.796924	−	0.604080i	$-0.206459\pi$
$283$	7.71534e6	+	6.47394e6i	0.340405	+	0.285634i	−0.456518	+	0.889714i	$0.650904\pi$
$284$	−2.20966e7	+	2.63337e7i	−0.964651	+	1.14963i
$285$	−1.96955e6	+	6.10206e7i	−0.0850810	+	2.63598i
$286$	3.32682e7	+	1.21086e7i	1.42210	+	0.517603i
$287$	950620.	+	548841.i	0.0402125	+	0.0232167i
$288$	−6.30121e6	+	695954.i	−0.263783	+	0.0291342i
$289$	−1.17041e7	−	2.02721e7i	−0.484892	−	0.839858i
$290$	3.21297e7	−	5.66534e6i	1.31739	−	0.232291i
$291$	−966997.	+	317022.i	−0.0392416	+	0.0128650i
$292$	−3.04325e7	+	1.10765e7i	−1.22233	+	0.444892i
$293$	−2.92238e7	−	5.15295e6i	−1.16181	−	0.204858i	−0.440683	−	0.897663i	$-0.645264\pi$
$293$	−2.92238e7	−	5.15295e6i	−1.16181	−	0.204858i	−0.721125	+	0.692805i	$0.756375\pi$
$294$	−4.27983e7	+	6.13021e6i	−1.68416	+	0.241231i
$295$	−5.38860e7	+	4.52157e7i	−2.09899	+	1.76126i
$296$		−	2.99463e7i		−	1.15470i
$297$	2.70014e7	−	2.10322e6i	1.03066	−	0.0802816i
$298$	−3.32174e7			−1.25521
$299$	−1.03897e6	−	1.23819e6i	−0.0388676	−	0.0463206i
$300$	−1.33748e8	−	5.36274e7i	−4.95364	−	1.98620i
$301$	−45123.6	+	255909.i	−0.00165464	+	0.00938395i
$302$	2.63594e7	+	7.24219e7i	0.957007	+	2.62935i
$303$	2.88163e7	−	3.21742e7i	1.03588	−	1.15659i
$304$	5.05349e6	+	2.86598e7i	0.179875	+	1.02012i
$305$	5.12920e7	−	2.96135e7i	1.80780	−	1.04373i
$306$	−8.49173e6	−	548743.i	−0.296368	−	0.0191516i
$307$	1.55162e7	−	2.68749e7i	0.536255	−	0.928821i	−0.462846	−	0.886439i	$-0.653172\pi$
$307$	1.55162e7	−	2.68749e7i	0.536255	−	0.928821i	0.999101	−	0.0423826i	$-0.0134948\pi$
$308$	1.28450e6	−	3.52914e6i	0.0439625	−	0.120786i
$309$	7.05056e6	−	1.13498e7i	0.238973	−	0.384693i
$310$	7.41880e7	+	6.22511e7i	2.49028	+	2.08959i
$311$	951753.	−	1.13425e6i	0.0316405	−	0.0377076i	−0.749992	−	0.661447i	$-0.769943\pi$
$311$	951753.	−	1.13425e6i	0.0316405	−	0.0377076i	0.781633	+	0.623739i	$0.214387\pi$
$312$	3.60284e7	−	1.92789e7i	1.18626	−	0.634772i
$313$	1.42046e6	+	517004.i	0.0463228	+	0.0168601i	0.365078	−	0.930977i	$-0.381042\pi$
$313$	1.42046e6	+	517004.i	0.0463228	+	0.0168601i	−0.318755	+	0.947837i	$0.603265\pi$
$314$	−6.83468e7	−	3.94600e7i	−2.20764	−	1.27458i
$315$	−1.10537e6	−	3.77944e6i	−0.0353653	−	0.120919i
$316$	2.02505e7	+	3.50748e7i	0.641761	+	1.11156i
$317$	−4.95629e6	+	873928.i	−0.155589	+	0.0274346i	−0.250900	−	0.968013i	$-0.580727\pi$
$317$	−4.95629e6	+	873928.i	−0.155589	+	0.0274346i	0.0953110	+	0.995448i	$0.469615\pi$
$318$	−1.75164e6	+	8.34918e6i	−0.0544708	+	0.259635i
$319$	1.26976e7	−	4.62156e6i	0.391156	−	0.142369i
$320$	7.63750e7	+	1.34670e7i	2.33078	+	0.410979i
$321$	−6.50326e6	−	8.27863e6i	−0.196615	−	0.250290i
$322$	−199794.	+	167647.i	−0.00598432	+	0.00502144i
$323$		−	7.94483e6i		−	0.235764i
$324$	3.96395e7	−	5.18562e7i	1.16545	−	1.52464i
$325$	−8.17998e7			−2.38288
$326$	−1.67031e7	−	1.99060e7i	−0.482108	−	0.574554i
$327$	2.09201e7	−	1.64338e7i	0.598303	−	0.469995i
$328$	6.89565e6	−	3.91072e7i	0.195413	−	1.10824i
$329$	−950332.	−	2.61102e6i	−0.0266863	−	0.0733199i
$330$	−1.20794e8	−	2.53424e7i	−3.36128	−	0.705189i
$331$	8.40635e6	+	4.76748e7i	0.231805	+	1.31463i	0.849238	+	0.528010i	$0.177062\pi$
$331$	8.40635e6	+	4.76748e7i	0.231805	+	1.31463i	−0.617433	+	0.786624i	$0.711827\pi$
$332$	−1.72800e7	+	9.97664e6i	−0.472205	+	0.272628i
$333$	−1.96324e7	−	1.87594e7i	−0.531669	−	0.508027i
$334$	4.59465e7	−	7.95817e7i	1.23314	−	2.13587i
$335$	−2.34612e7	+	6.44592e7i	−0.624046	+	1.71455i
$336$	−885580.	−	1.65498e6i	−0.0233459	−	0.0436288i
$337$	−8.12913e6	−	6.82115e6i	−0.212400	−	0.178225i	0.530381	−	0.847760i	$-0.322049\pi$
$337$	−8.12913e6	−	6.82115e6i	−0.212400	−	0.178225i	−0.742781	+	0.669535i	$0.766493\pi$
$338$	−1.12738e7	+	1.34356e7i	−0.291958	+	0.347942i
$339$	1.19243e7	+	7.40742e6i	0.306080	+	0.190138i
$340$	2.39570e7	+	8.71963e6i	0.609530	+	0.221851i
$341$	3.47369e7	+	2.00554e7i	0.876048	+	0.505787i
$342$	7.71213e7	+	5.14284e7i	1.92795	+	1.28566i
$343$	2.60905e6	+	4.51900e6i	0.0646546	+	0.111985i
$344$	9.25793e6	−	1.63242e6i	0.227425	−	0.0401012i
$345$	4.19753e6	+	3.75945e6i	0.102220	+	0.0915518i
$346$	4.80458e7	−	1.74872e7i	1.15992	−	0.422176i
$347$	−8.94324e6	−	1.57693e6i	−0.214046	−	0.0377420i	0.0655970	−	0.997846i	$-0.479105\pi$
$347$	−8.94324e6	−	1.57693e6i	−0.214046	−	0.0377420i	−0.279643	+	0.960104i	$0.590216\pi$
$348$	1.21195e7	−	3.02265e7i	0.287573	−	0.717216i
$349$	3.55204e7	−	2.98051e7i	0.835606	−	0.701156i	−0.120965	−	0.992657i	$-0.538599\pi$
$349$	3.55204e7	−	2.98051e7i	0.835606	−	0.701156i	0.956571	+	0.291500i	$0.0941545\pi$
$350$			1.31992e7i			0.307852i
$351$	9.93048e6	−	3.56967e7i	0.229641	−	0.825481i
$352$	1.19657e7			0.274353
$353$	2.71883e7	+	3.24018e7i	0.618100	+	0.736623i	0.980742	−	0.195306i	$-0.0625699\pi$
$353$	2.71883e7	+	3.24018e7i	0.618100	+	0.736623i	−0.362643	+	0.931928i	$0.618125\pi$
$354$	1.51433e7	+	1.05723e8i	0.341358	+	2.38320i
$355$	1.18134e7	−	6.69973e7i	0.264053	−	1.49752i
$356$	−2.08812e7	−	5.73705e7i	−0.462812	−	1.27157i
$357$	159635.	+	486927.i	0.00350852	+	0.0107019i
$358$	2.34828e6	+	1.33178e7i	0.0511800	+	0.290256i
$359$	−7.31689e7	+	4.22441e7i	−1.58140	+	0.913025i	−0.586750	+	0.809768i	$0.699593\pi$
$359$	−7.31689e7	+	4.22441e7i	−1.58140	+	0.913025i	−0.994655	+	0.103257i	$0.967074\pi$
$360$	−1.14805e8	+	8.43406e7i	−2.46067	+	1.80771i
$361$	−1.97499e7	+	3.42079e7i	−0.419801	+	0.727117i
$362$	−2.12963e7	+	5.85111e7i	−0.448929	+	1.23342i
$363$	−3.28499e6	−	106029.i	−0.0686775	−	0.00221669i
$364$	−3.93597e6	−	3.30267e6i	−0.0816108	−	0.0684796i
$365$	4.11971e7	−	4.90968e7i	0.847204	−	1.00966i
$366$	2.90096e6	−	8.98777e7i	0.0591697	−	1.83320i
$367$	−2.80213e7	−	1.01989e7i	−0.566879	−	0.206327i	0.0426513	−	0.999090i	$-0.486420\pi$
$367$	−2.80213e7	−	1.01989e7i	−0.566879	−	0.206327i	−0.609530	+	0.792763i	$0.708642\pi$
$368$	2.32616e6	+	1.34301e6i	0.0466763	+	0.0269486i
$369$	−2.13185e7	−	2.90188e7i	−0.424304	−	0.577565i
$370$	6.18738e7	+	1.07169e8i	1.22152	+	2.11574i
$371$	505917.	−	89206.9i	0.00990736	−	0.00174693i
$372$	9.18578e7	−	3.01148e7i	1.78438	−	0.584994i
$373$	−7.57366e7	+	2.75659e7i	−1.45942	+	0.531184i	−0.945204	−	0.326479i	$-0.894138\pi$
$373$	−7.57366e7	+	2.75659e7i	−1.45942	+	0.531184i	−0.514212	+	0.857663i	$0.671915\pi$
$374$	1.58173e7	+	2.78902e6i	0.302356	+	0.0533135i
$375$	1.80786e8	−	2.58949e7i	3.42825	−	0.491045i
$376$	−7.70027e7	+	6.46130e7i	−1.44858	+	1.21550i
$377$		−	1.84864e7i		−	0.345007i
$378$	−5.76000e6	−	1.60238e6i	−0.106647	−	0.0296680i
$379$	1.86866e7			0.343252			0.171626	−	0.985162i	$-0.445098\pi$
$379$	1.86866e7			0.343252			0.171626	+	0.985162i	$0.445098\pi$
$380$	−1.78515e8	−	2.12746e8i	−3.25330	−	3.87713i
$381$	−3.83499e7	−	1.53767e7i	−0.693408	−	0.278027i
$382$	1.56421e7	−	8.87109e7i	0.280611	−	1.59143i
$383$	1.79189e7	+	4.92317e7i	0.318944	+	0.876291i	0.990767	+	0.135579i	$0.0432895\pi$
$383$	1.79189e7	+	4.92317e7i	0.318944	+	0.876291i	−0.671823	+	0.740712i	$0.734488\pi$
$384$	6.85328e7	−	7.65188e7i	1.21033	−	1.35137i
$385$	1.29063e6	+	7.31952e6i	0.0226162	+	0.128263i
$386$	−9.51029e7	+	5.49077e7i	−1.65360	+	0.954709i
$387$	4.72929e6	−	7.09199e6i	0.0815950	−	0.122359i
$388$	2.31456e6	−	4.00893e6i	0.0396253	−	0.0686330i
$389$	−3.88114e6	+	1.06633e7i	−0.0659342	+	0.181153i	−0.968284	−	0.249851i	$-0.919618\pi$
$389$	−3.88114e6	+	1.06633e7i	−0.0659342	+	0.181153i	0.902350	+	0.431004i	$0.141841\pi$
$390$	−8.91012e7	+	1.43433e8i	−1.50207	+	2.41800i
$391$	−561729.	−	471346.i	−0.00939715	−	0.00788515i
$392$	6.05429e7	−	7.21523e7i	1.00509	−	1.19782i
$393$	1.79275e6	−	959301.i	0.0295353	−	0.0158044i
$394$	−1.31991e8	−	4.80409e7i	−2.15802	−	0.785457i
$395$	−6.94134e7	−	4.00758e7i	−1.12629	−	0.650266i
$396$	−8.51114e7	+	8.90722e7i	−1.37057	+	1.43435i
$397$	−3.07730e7	−	5.33004e7i	−0.491811	−	0.851842i	0.508144	−	0.861272i	$-0.330332\pi$
$397$	−3.07730e7	−	5.33004e7i	−0.491811	−	0.851842i	−0.999956	+	0.00942987i	$0.996998\pi$
$398$	1.48646e8	−	2.62104e7i	2.35779	−	0.415742i
$399$	1.14615e6	−	5.46310e6i	0.0180435	−	0.0860044i
$400$	1.27736e8	−	4.64921e7i	1.99587	−	0.726439i
$401$	−4.37946e6	−	772217.i	−0.0679184	−	0.0119759i	0.139586	−	0.990210i	$-0.455423\pi$
$401$	−4.37946e6	−	772217.i	−0.0679184	−	0.0119759i	−0.207504	+	0.978234i	$0.566534\pi$
$402$	6.43375e7	+	8.19015e7i	0.990344	+	1.26071i
$403$	4.20368e7	−	3.52730e7i	0.642265	−	0.538924i
$404$			1.96475e8i			2.97964i
$405$	−1.66251e7	+	1.28099e8i	−0.250265	+	1.92832i
$406$	−2.98295e6			−0.0445725
$407$	3.29447e7	+	3.92619e7i	0.488654	+	0.582356i
$408$	1.45779e7	−	1.14516e7i	0.214641	−	0.168611i
$409$	−6.24923e6	+	3.54411e7i	−0.0913390	+	0.518009i	0.904469	+	0.426540i	$0.140268\pi$
$409$	−6.24923e6	+	3.54411e7i	−0.0913390	+	0.518009i	−0.995808	+	0.0914696i	$0.970844\pi$
$410$	5.61241e7	+	1.54200e8i	0.814326	+	2.23734i
$411$	−4.88709e7	−	1.02530e7i	−0.703922	−	0.147681i
$412$	1.05543e7	+	5.98564e7i	0.150917	+	0.855892i
$413$	5.56983e6	−	3.21575e6i	0.0790664	−	0.0456490i
$414$	8.21158e6	−	2.40165e6i	0.115725	−	0.0338460i
$415$	1.97439e7	−	3.41974e7i	0.276241	−	0.478463i
$416$	5.59892e6	−	1.53829e7i	0.0777722	−	0.213677i
$417$	−3.16115e7	−	5.90756e7i	−0.435950	−	0.814705i
$418$	−1.34028e8	−	1.12463e8i	−1.83513	−	1.53986i
$419$	5.34011e7	−	6.36410e7i	0.725953	−	0.865157i	−0.269242	−	0.963073i	$-0.586773\pi$
$419$	5.34011e7	−	6.36410e7i	0.725953	−	0.865157i	0.995195	+	0.0979159i	$0.0312176\pi$
$420$	1.52156e7	+	9.45199e6i	0.205372	+	0.127578i
$421$	4.94704e7	+	1.80058e7i	0.662978	+	0.241304i	0.651522	−	0.758630i	$-0.274131\pi$
$421$	4.94704e7	+	1.80058e7i	0.662978	+	0.241304i	0.0114566	+	0.999934i	$0.496353\pi$
$422$	−3.79100e6	−	2.18874e6i	−0.0504449	−	0.0291244i
$423$	−5.87778e6	+	9.09579e7i	−0.0776590	+	1.20176i
$424$	−9.29237e6	−	1.60949e7i	−0.121907	−	0.211149i
$425$	−3.65462e7	+	6.44408e6i	−0.476075	+	0.0839448i
$426$	−7.69428e7	−	6.89126e7i	−0.995267	−	0.891394i
$427$	−5.08856e6	+	1.85208e6i	−0.0653599	+	0.0237891i
$428$	4.71608e7	+	8.31571e6i	0.601519	+	0.106064i
$429$	−2.60268e7	+	6.49118e7i	−0.329647	+	0.822151i
$430$	−2.97584e7	+	2.49702e7i	−0.374286	+	0.314063i
$431$		−	1.36978e8i		−	1.71088i	−0.517906	−	0.855438i	$-0.673288\pi$
$431$		−	1.36978e8i		−	1.71088i	0.517906	−	0.855438i	$-0.326712\pi$
$432$	4.78162e6	+	6.13870e7i	0.0593095	+	0.761421i
$433$	−1.02944e8			−1.26805			−0.634024	−	0.773314i	$-0.718598\pi$
$433$	−1.02944e8			−1.26805			−0.634024	+	0.773314i	$0.718598\pi$
$434$	−5.69163e6	−	6.78303e6i	−0.0696254	−	0.0829763i
$435$	9.13791e6	+	6.37967e7i	0.111014	+	0.775051i
$436$	−2.10138e7	+	1.19175e8i	−0.253540	+	1.43790i
$437$	2.73203e6	+	7.50619e6i	0.0327371	+	0.0899446i
$438$	−3.03148e7	−	9.24677e7i	−0.360772	−	1.10044i
$439$	−1.30923e7	−	7.42500e7i	−0.154747	−	0.877612i	−0.959017	−	0.283349i	$-0.908555\pi$
$439$	−1.30923e7	−	7.42500e7i	−0.154747	−	0.877612i	0.804270	−	0.594264i	$-0.202556\pi$
$440$	2.32857e8	−	1.34440e8i	2.73358	−	1.57823i
$441$	−9.37588e6	−	8.48899e7i	−0.109319	−	0.989783i
$442$	1.09867e7	−	1.90295e7i	0.127233	−	0.220374i
$443$	−5.54552e7	+	1.52362e8i	−0.637869	+	1.75253i	0.0204506	+	0.999791i	$0.493490\pi$
$443$	−5.54552e7	+	1.52362e8i	−0.637869	+	1.75253i	−0.658319	+	0.752739i	$0.728732\pi$
$444$	1.23457e8	+	3.98479e6i	1.41048	+	0.0455257i
$445$	9.25561e7	+	7.76638e7i	1.05033	+	0.881330i
$446$	1.38125e8	−	1.64612e8i	1.55693	−	1.85548i
$447$	2.11681e6	−	6.55831e7i	0.0237006	−	0.734294i
$448$	−6.66308e6	−	2.42516e6i	−0.0741039	−	0.0269716i
$449$	4.00320e7	+	2.31125e7i	0.442250	+	0.255333i	0.704552	−	0.709653i	$-0.251148\pi$
$449$	4.00320e7	+	2.31125e7i	0.442250	+	0.255333i	−0.262301	+	0.964986i	$0.584481\pi$
$450$	1.74017e8	−	3.96471e8i	1.90965	−	4.35085i
$451$	3.39820e7	+	5.88586e7i	0.370441	+	0.641623i
$452$	−6.28861e7	+	1.10885e7i	−0.680987	+	0.120076i
$453$	−1.44667e8	+	4.74278e7i	−1.55623	+	0.510198i
$454$	−3.45245e7	+	1.25659e7i	−0.368943	+	0.134284i
$455$	1.00138e7	+	1.76570e6i	0.106307	+	0.0187448i
$456$	−1.99899e8	+	2.86326e7i	−2.10822	+	0.301971i
$457$	−5.91638e7	+	4.96444e7i	−0.619880	+	0.520141i	−0.897766	−	0.440473i	$-0.854811\pi$
$457$	−5.91638e7	+	4.96444e7i	−0.619880	+	0.520141i	0.277886	+	0.960614i	$0.410366\pi$
$458$		−	1.59990e8i		−	1.66531i
$459$	1.62456e6	−	1.67308e7i	0.0167995	−	0.173012i
$460$	−2.56327e7			−0.263343
$461$	1.01846e8	+	1.21376e8i	1.03954	+	1.23888i	0.970458	+	0.241269i	$0.0775637\pi$
$461$	1.01846e8	+	1.21376e8i	1.03954	+	1.23888i	0.0690857	+	0.997611i	$0.477992\pi$
$462$	1.04741e7	+	4.19967e6i	0.106216	+	0.0425882i
$463$	7.92228e6	−	4.49295e7i	0.0798192	−	0.452677i	−0.918536	−	0.395338i	$-0.870627\pi$
$463$	7.92228e6	−	4.49295e7i	0.0798192	−	0.452677i	0.998355	−	0.0573387i	$-0.0182615\pi$
$464$	1.05070e7	+	2.88677e7i	0.105178	+	0.288974i
$465$	−1.27634e8	+	1.42507e8i	−1.26942	+	1.41735i
$466$	1.07629e7	+	6.10397e7i	0.106359	+	0.603190i
$467$	−6.35207e6	+	3.66737e6i	−0.0623684	+	0.0360084i	−0.530860	−	0.847460i	$-0.678131\pi$
$467$	−6.35207e6	+	3.66737e6i	−0.0623684	+	0.0360084i	0.468492	+	0.883468i	$0.344798\pi$
$468$	7.46850e7	+	1.51096e8i	0.728611	+	1.47406i
$469$	3.13588e6	−	5.43150e6i	0.0303977	−	0.0526504i
$470$	1.42068e8	−	3.90329e8i	1.36837	−	3.75956i
$471$	8.22638e7	−	1.32427e8i	0.787310	−	1.26740i
$472$	−1.78235e8	−	1.49557e8i	−1.69499	−	1.42227i
$473$	−1.03420e7	+	1.23251e7i	−0.0977283	+	0.116468i
$474$	−1.07299e8	+	5.74158e7i	−1.00753	+	0.539133i
$475$	3.79872e8	+	1.38262e8i	3.54451	+	1.29010i
$476$	−2.01868e6	−	1.16548e6i	−0.0187174	−	0.0108065i
$477$	−1.63727e7	−	3.99043e6i	−0.150857	−	0.0367675i
$478$	−4.92333e7	−	8.52745e7i	−0.450791	−	0.780792i
$479$	−8.89695e7	+	1.56877e7i	−0.809533	+	0.142743i	−0.563070	−	0.826409i	$-0.690380\pi$
$479$	−8.89695e7	+	1.56877e7i	−0.809533	+	0.142743i	−0.246464	+	0.969152i	$0.579269\pi$
$480$	−1.17181e7	+	5.58542e7i	−0.105958	+	0.505048i
$481$	6.58898e7	−	2.39819e7i	0.592084	−	0.215501i
$482$	−3.70410e8	−	6.53132e7i	−3.30781	−	0.583257i
$483$	−318263.	−	405148.i	−0.00282452	−	0.00359561i
$484$	1.14530e7	−	9.61020e6i	0.101014	−	0.0847610i
$485$			9.16106e6i			0.0803009i
$486$	1.51891e8	+	1.24071e8i	1.32319	+	1.08084i
$487$	−8.81098e7			−0.762846			−0.381423	−	0.924401i	$-0.624566\pi$
$487$	−8.81098e7			−0.762846			−0.381423	+	0.924401i	$0.624566\pi$
$488$	1.25923e8	+	1.50069e8i	1.08354	+	1.29132i
$489$	4.03660e7	−	3.17094e7i	0.345214	−	0.271182i
$490$	−6.75864e7	+	3.83301e8i	−0.574475	+	3.25801i
$491$	−3.80422e7	−	1.04520e8i	−0.321381	−	0.882988i	−0.990212	−	0.139573i	$-0.955427\pi$
$491$	−3.80422e7	−	1.04520e8i	−0.321381	−	0.882988i	0.668830	−	0.743415i	$-0.266795\pi$
$492$	1.60306e8	+	3.36318e7i	1.34603	+	0.282393i
$493$	−1.45633e6	−	8.25926e6i	−0.0121540	−	0.0689288i
$494$	−2.07295e8	+	1.19682e8i	−1.71952	+	0.992766i
$495$	5.77327e7	−	2.36877e8i	0.475999	−	1.95302i
$496$	−4.55953e7	+	7.89735e7i	−0.373659	+	0.647196i
$497$	−2.12739e6	+	5.84496e6i	−0.0173292	+	0.0476116i
$498$	−2.82866e7	−	5.28621e7i	−0.229030	−	0.428012i
$499$	1.57296e8	+	1.31987e8i	1.26595	+	1.06226i	0.995022	+	0.0996548i	$0.0317739\pi$
$499$	1.57296e8	+	1.31987e8i	1.26595	+	1.06226i	0.270925	+	0.962601i	$0.412671\pi$
$500$	−5.34008e8	+	6.36406e8i	−4.27206	+	5.09125i
$501$	1.54195e8	+	9.57864e7i	1.22619	+	0.761712i
$502$	−2.62873e8	−	9.56778e7i	−2.07795	−	0.756310i
$503$	1.24255e8	+	7.17388e7i	0.976362	+	0.563703i	0.901170	−	0.433466i	$-0.142710\pi$
$503$	1.24255e8	+	7.17388e7i	0.976362	+	0.563703i	0.0751925	+	0.997169i	$0.476043\pi$
$504$	1.16762e7	−	5.77141e6i	0.0912033	−	0.0450807i
$505$	−1.94413e8	−	3.36734e8i	−1.50957	−	2.61465i
$506$	−1.59031e7	+	2.80415e6i	−0.122753	+	0.0216446i
$507$	−2.58083e7	−	2.31147e7i	−0.198032	−	0.177364i
$508$	1.76615e8	−	6.42824e7i	1.34721	−	0.490344i
$509$	1.54818e8	+	2.72985e7i	1.17400	+	0.207007i	0.726428	−	0.687242i	$-0.241179\pi$
$509$	1.54818e8	+	2.72985e7i	1.17400	+	0.207007i	0.447569	+	0.894249i	$0.352290\pi$
$510$	−2.85088e7	+	7.11018e7i	−0.214916	+	0.536007i
$511$	−4.48893e6	+	3.76666e6i	−0.0336419	+	0.0282289i
$512$			1.88162e8i			1.40192i
$513$	−1.06453e8	+	1.48988e8i	−0.788506	+	1.10357i
$514$	3.98140e8			2.93188
$515$	−7.73170e7	−	9.21428e7i	−0.566048	−	0.674589i
$516$	5.49793e6	+	3.83839e7i	0.0400175	+	0.279383i
$517$	2.98742e7	−	1.69425e8i	0.216185	−	1.22604i
$518$	−3.86971e6	−	1.06319e7i	−0.0278413	−	0.0764932i
$519$	3.14643e7	+	9.59741e7i	0.225069	+	0.686518i
$520$	−6.38770e7	−	3.62264e8i	−0.454291	−	2.57641i
$521$	5.83335e7	−	3.36789e7i	0.412482	−	0.238147i	−0.279374	−	0.960182i	$-0.590127\pi$
$521$	5.83335e7	−	3.36789e7i	0.412482	−	0.238147i	0.691856	+	0.722036i	$0.256793\pi$
$522$	8.96006e7	+	3.93270e7i	0.629941	+	0.276490i
$523$	3.75177e6	−	6.49825e6i	0.0262259	−	0.0454247i	−0.852615	−	0.522540i	$-0.824984\pi$
$523$	3.75177e6	−	6.49825e6i	0.0262259	−	0.0454247i	0.878840	+	0.477116i	$0.158318\pi$
$524$	−3.16338e6	+	8.69132e6i	−0.0219866	+	0.0604076i
$525$	−2.60599e7	−	841129.i	−0.180092	−	0.00581279i
$526$	1.44806e8	+	1.21506e8i	0.995012	+	0.834914i
$527$	1.60023e7	−	1.90708e7i	0.109333	−	0.130297i
$528$	3.74917e6	−	1.16157e8i	0.0254703	−	0.789120i
$529$	−1.38415e8	−	5.03791e7i	−0.935013	−	0.340317i
$530$	6.65090e7	+	3.83990e7i	0.446738	+	0.257924i
$531$	−2.09701e8	+	2.31610e7i	−1.40061	+	0.154694i
$532$	1.26960e7	+	2.19901e7i	0.0843203	+	0.146047i
$533$	9.15683e7	−	1.61460e7i	0.604733	−	0.106631i
$534$	1.74318e8	−	5.71487e7i	1.14477	−	0.375304i
$535$	−8.90560e7	+	3.24137e7i	−0.581570	+	0.211674i
$536$	−2.23444e8	−	3.93993e7i	−1.45102	−	0.255855i
$537$	−2.64437e7	+	3.78766e6i	−0.170765	+	0.0244595i
$538$	3.76903e8	−	3.16259e8i	2.42038	−	2.03094i
$539$			1.61202e8i			1.02945i
$540$	−3.32426e8	−	4.84517e8i	−2.11113	−	3.07700i
$541$	2.28296e8			1.44181			0.720903	−	0.693036i	$-0.243727\pi$
$541$	2.28296e8			1.44181			0.720903	+	0.693036i	$0.243727\pi$
$542$	−4.50626e7	−	5.37036e7i	−0.283021	−	0.337291i
$543$	−1.14165e8	−	4.57752e7i	−0.713071	−	0.285911i
$544$	1.28962e6	−	7.31380e6i	0.00801060	−	0.0454304i
$545$	−8.19096e7	−	2.25045e8i	−0.505994	−	1.39021i
$546$	1.03000e7	−	1.15003e7i	0.0632791	−	0.0706529i
$547$	−835410.	−	4.73784e6i	−0.00510432	−	0.0289480i	0.982149	−	0.188103i	$-0.0602340\pi$
$547$	−835410.	−	4.73784e6i	−0.00510432	−	0.0289480i	−0.987254	+	0.159155i	$0.949123\pi$
$548$	1.96716e8	−	1.13574e8i	1.19536	−	0.690139i
$549$	1.77266e8	+	1.14551e7i	1.07129	+	0.0692280i
$550$	−4.08619e8	+	7.07749e8i	−2.45601	+	4.25394i
$551$	−3.12466e7	+	8.58493e7i	−0.186787	+	0.513194i
$552$	−9.83508e6	+	1.58323e7i	−0.0584737	+	0.0941298i
$553$	5.61379e6	+	4.71053e6i	0.0331956	+	0.0278545i
$554$	1.97313e8	−	2.35148e8i	1.16045	−	1.38297i
$555$	−2.15532e8	+	1.15332e8i	−1.26076	+	0.674636i
$556$	2.86402e8	+	1.04242e8i	1.66629	+	0.606481i
$557$	−1.16373e8	−	6.71882e7i	−0.673423	−	0.388801i	0.123950	−	0.992289i	$-0.460444\pi$
$557$	−1.16373e8	−	6.71882e7i	−0.673423	−	0.388801i	−0.797372	+	0.603488i	$0.793777\pi$
$558$	8.15361e7	+	2.78784e8i	0.469297	+	1.60460i
$559$	1.10058e7	+	1.90626e7i	0.0630065	+	0.109131i
$560$	−1.66407e7	+	2.93421e6i	−0.0947563	+	0.0167081i
$561$	−6.51451e6	+	3.10514e7i	−0.0368972	+	0.175870i
$562$	−4.47590e8	+	1.62909e8i	−2.52157	+	0.917777i
$563$	−1.72487e8	−	3.04142e7i	−0.966567	−	0.170432i	−0.331983	−	0.943286i	$-0.607718\pi$
$563$	−1.72487e8	−	3.04142e7i	−0.966567	−	0.170432i	−0.634584	+	0.772854i	$0.718829\pi$
$564$	−2.56127e8	−	3.26049e8i	−1.42764	−	1.81738i
$565$	9.68066e7	−	8.12303e7i	0.536734	−	0.450374i
$566$		−	1.37662e8i		−	0.759213i
$567$	3.53073e6	−	1.12702e7i	0.0193693	−	0.0618276i
$568$	2.25022e8			1.22795
$569$	−6.74556e7	−	8.03905e7i	−0.366169	−	0.436383i	0.551229	−	0.834354i	$-0.314159\pi$
$569$	−6.74556e7	−	8.03905e7i	−0.366169	−	0.436383i	−0.917398	+	0.397971i	$0.869715\pi$
$570$	6.56217e8	−	5.15490e8i	3.54342	−	2.78353i
$571$	−2.68331e7	+	1.52178e8i	−0.144133	+	0.817418i	0.823927	+	0.566697i	$0.191779\pi$
$571$	−2.68331e7	+	1.52178e8i	−0.144133	+	0.817418i	−0.968059	+	0.250721i	$0.919332\pi$
$572$	−1.08806e8	−	2.98941e8i	−0.581385	−	1.59734i
$573$	1.74150e8	+	3.65364e7i	0.925679	+	0.194205i
$574$	−2.60530e6	−	1.47754e7i	−0.0137760	−	0.0781275i
$575$	3.23125e7	−	1.86556e7i	0.169968	−	0.0981309i
$576$	1.68170e8	+	1.60692e8i	0.879997	+	0.840866i
$577$	−1.43294e7	+	2.48192e7i	−0.0745933	+	0.129199i	−0.900909	−	0.434007i	$-0.857099\pi$
$577$	−1.43294e7	+	2.48192e7i	−0.0745933	+	0.129199i	0.826316	+	0.563207i	$0.190433\pi$
$578$	−1.09429e8	+	3.00653e8i	−0.566694	+	1.55698i
$579$	−1.02347e8	−	1.91266e8i	−0.527277	−	0.985378i
$580$	−2.24578e8	−	1.88443e8i	−1.15102	−	0.965819i
$581$	−2.32070e6	+	2.76571e6i	−0.0118329	+	0.0141019i
$582$	1.18152e7	+	7.33962e6i	0.0599337	+	0.0372310i
$583$	2.98894e7	+	1.08788e7i	0.150838	+	0.0549006i
$584$	1.83590e8	+	1.05996e8i	0.921743	+	0.532168i
$585$	−2.77511e8	−	1.85058e8i	−1.38616	−	0.924359i
$586$	2.02800e8	+	3.51259e8i	1.00780	+	1.74556i
$587$	7.15805e7	−	1.26216e7i	0.353900	−	0.0624021i	0.00612788	−	0.999981i	$-0.498049\pi$
$587$	7.15805e7	−	1.26216e7i	0.353900	−	0.0624021i	0.347772	+	0.937579i	$0.386938\pi$
$588$	2.89399e8	+	2.59195e8i	1.42352	+	1.27496i
$589$	−2.54836e8	+	9.27527e7i	−1.24714	+	0.453921i
$590$	9.46857e8	+	1.66957e8i	4.61029	+	0.812919i
$591$	1.03261e8	−	2.57537e8i	0.500236	−	1.24760i
$592$	−8.92609e7	+	7.48988e7i	−0.430226	+	0.361002i
$593$			5.22381e7i			0.250509i	0.992125	+	0.125254i	$0.0399747\pi$
$593$			5.22381e7i			0.250509i	−0.992125	+	0.125254i	$0.960025\pi$
$594$	−2.59249e8	−	2.64239e8i	−1.23697	−	1.26077i
$595$	4.61301e6			0.0218995
$596$	1.91863e8	+	2.28653e8i	0.906257	+	1.08004i
$597$	4.22761e7	+	2.95152e8i	0.198688	+	1.38715i
$598$	−3.83633e6	+	2.17569e7i	−0.0179396	+	0.101740i
$599$	3.82205e7	+	1.05010e8i	0.177835	+	0.488597i	0.996298	−	0.0859614i	$-0.0273962\pi$
$599$	3.82205e7	+	1.05010e8i	0.177835	+	0.488597i	−0.818464	+	0.574558i	$0.805174\pi$
$600$	2.93849e8	+	8.96312e8i	1.36041	+	4.14959i
$601$	−6.18647e6	−	3.50852e7i	−0.0284983	−	0.161622i	0.967237	−	0.253874i	$-0.0817047\pi$
$601$	−6.18647e6	−	3.50852e7i	−0.0284983	−	0.161622i	−0.995736	+	0.0922516i	$0.970594\pi$
$602$	3.07592e6	−	1.77589e6i	0.0140989	−	0.00814002i
$603$	−1.65803e8	+	1.21806e8i	−0.756207	+	0.555543i
$604$	3.46267e8	−	5.99752e8i	1.57145	−	2.72183i
$605$	−1.01196e7	+	2.78034e7i	−0.0456981	+	0.125555i
$606$	−5.90050e8	−	1.90449e7i	−2.65138	−	0.0855779i
$607$	1.69472e8	+	1.42204e8i	0.757761	+	0.635837i	0.937543	−	0.347870i	$-0.113095\pi$
$607$	1.69472e8	+	1.42204e8i	0.757761	+	0.635837i	−0.179782	+	0.983706i	$0.557539\pi$
$608$	−5.20020e7	+	6.19735e7i	−0.231371	+	0.275737i
$609$	190091.	−	5.88941e6i	0.000841608	−	0.0260747i
$610$	−7.60705e8	−	2.76874e8i	−3.35141	−	1.21981i
$611$	−2.03832e8	−	1.17682e8i	−0.893610	−	0.515926i
$612$	4.52706e7	+	6.16225e7i	0.197498	+	0.268835i
$613$	1.05244e8	+	1.82288e8i	0.456894	+	0.791364i	0.998795	−	0.0490786i	$-0.0156285\pi$
$613$	1.05244e8	+	1.82288e8i	0.456894	+	0.791364i	−0.541901	+	0.840442i	$0.682295\pi$
$614$	−4.17714e8	+	7.36543e7i	−1.80457	+	0.318195i
$615$	−3.08022e8	+	1.00983e8i	−1.32421	+	0.434132i
$616$	−2.31012e7	+	8.40816e6i	−0.0988310	+	0.0359715i
$617$	5.43117e7	+	9.57661e6i	0.231227	+	0.0407715i	0.288061	−	0.957612i	$-0.406990\pi$
$617$	5.43117e7	+	9.57661e6i	0.231227	+	0.0407715i	−0.0568342	+	0.998384i	$0.518101\pi$
$618$	−1.80782e8	+	2.58944e7i	−0.765933	+	0.109708i
$619$	−2.70598e8	+	2.27059e8i	−1.14091	+	0.957339i	−0.999468	−	0.0326069i	$-0.989619\pi$
$619$	−2.70598e8	+	2.27059e8i	−1.14091	+	0.957339i	−0.141444	+	0.989946i	$0.545175\pi$
$620$		−	8.70235e8i		−	3.65142i
$621$	4.21842e6	+	1.63657e7i	0.0176147	+	0.0683375i
$622$	−2.02380e7			−0.0841002
$623$	−7.10082e6	−	8.46243e6i	−0.0293660	−	0.0349970i
$624$	−1.47575e8	−	5.91713e7i	−0.607379	−	0.243533i
$625$	1.67594e8	−	9.50470e8i	0.686463	−	3.89313i
$626$	−7.06652e6	−	1.94151e7i	−0.0288060	−	0.0791437i
$627$	2.30584e8	−	2.57453e8i	0.935462	−	1.04447i
$628$	1.23144e8	+	6.98386e8i	0.497205	+	2.81979i
$629$	2.75487e7	−	1.59053e7i	0.110701	−	0.0639130i
$630$	−2.98609e7	+	4.47789e7i	−0.119421	+	0.179082i
$631$	−3.08081e7	+	5.33612e7i	−0.122624	+	0.212391i	−0.920802	−	0.390031i	$-0.872464\pi$
$631$	−3.08081e7	+	5.33612e7i	−0.122624	+	0.212391i	0.798178	+	0.602422i	$0.205798\pi$
$632$	9.06740e7	−	2.49125e8i	0.359196	−	0.986883i
$633$	4.56294e6	−	7.34533e6i	0.0179901	−	0.0289601i
$634$	5.26952e7	+	4.42165e7i	0.206777	+	0.173507i
$635$	−2.39087e8	+	2.84933e8i	−0.933759	+	1.11281i
$636$	6.75892e7	−	3.61671e7i	0.262728	−	0.140586i
$637$	2.07239e8	+	7.54287e7i	0.801775	+	0.291822i
$638$	−1.59948e8	−	9.23460e7i	−0.615909	−	0.355595i
$639$	1.40961e8	−	1.47521e8i	0.540254	−	0.565395i
$640$	−4.62367e8	−	8.00844e8i	−1.76379	−	3.05498i
$641$	2.73050e8	−	4.81461e7i	1.03674	−	0.182804i	0.370722	−	0.928744i	$-0.379110\pi$
$641$	2.73050e8	−	4.81461e7i	1.03674	−	0.182804i	0.666014	+	0.745940i	$0.267999\pi$
$642$	−2.95450e7	+	1.40826e8i	−0.111655	+	0.532203i
$643$	−3.79620e8	+	1.38170e8i	−1.42796	+	0.519735i	−0.936346	−	0.351079i	$-0.885815\pi$
$643$	−3.79620e8	+	1.38170e8i	−1.42796	+	0.519735i	−0.491613	+	0.870814i	$0.663593\pi$
$644$	2.30800e6	+	406963.i	0.00864130	+	0.00152369i
$645$	−4.74038e7	−	6.03450e7i	−0.176658	−	0.224886i
$646$	−8.31860e7	+	6.98013e7i	−0.308569	+	0.258920i
$647$			2.15199e8i			0.794562i	0.917697	+	0.397281i	$0.130046\pi$
$647$			2.15199e8i			0.794562i	−0.917697	+	0.397281i	$0.869954\pi$
$648$	−4.26816e8	+	1.94210e7i	−1.56861	+	0.0713749i
$649$	3.98212e8			1.45673
$650$	7.18672e8	+	8.56480e8i	2.61692	+	3.11873i
$651$	1.37548e7	−	1.08051e7i	0.0498554	−	0.0391638i
$652$	−4.05468e7	+	2.29952e8i	−0.146290	+	0.829650i
$653$	9.41424e7	+	2.58654e8i	0.338100	+	0.928923i	0.985933	+	0.167141i	$0.0534534\pi$
$653$	9.41424e7	+	2.58654e8i	0.338100	+	0.928923i	−0.647833	+	0.761783i	$0.724324\pi$
$654$	−3.55868e8	−	7.46603e7i	−1.27220	−	0.266905i
$655$	−3.17847e6	−	1.80260e7i	−0.0113108	−	0.0641469i
$656$	−1.33813e8	+	7.72572e7i	−0.474011	+	0.273670i
$657$	1.84496e8	−	5.39597e7i	0.650567	−	0.190271i
$658$	−1.89891e7	+	3.28901e7i	−0.0666542	+	0.115448i
$659$	1.71111e8	−	4.70124e8i	0.597892	−	1.64269i	−0.157575	−	0.987507i	$-0.550368\pi$
$659$	1.71111e8	−	4.70124e8i	0.597892	−	1.64269i	0.755467	−	0.655187i	$-0.227410\pi$
$660$	5.23259e8	+	9.77867e8i	1.82006	+	3.40133i
$661$	−3.79848e8	−	3.18730e8i	−1.31524	−	1.10362i	−0.987291	−	0.158922i	$-0.949198\pi$
$661$	−3.79848e8	−	3.18730e8i	−1.31524	−	1.10362i	−0.327949	−	0.944695i	$-0.606357\pi$
$662$	4.25320e8	−	5.06877e8i	1.46603	−	1.74714i
$663$	3.68709e7	+	2.29043e7i	0.126515	+	0.0785918i
$664$	1.22734e8	+	4.46717e7i	0.419239	+	0.152591i
$665$	−4.35187e7	−	2.51255e7i	−0.147983	−	0.0854378i
$666$	−2.39340e7	+	3.70376e8i	−0.0810202	+	1.25378i
$667$	4.21608e6	+	7.30246e6i	0.0142079	+	0.0246089i
$668$	−8.13188e8	+	1.43387e8i	−2.72811	+	0.481039i
$669$	3.16200e8	+	2.83199e8i	1.05605	+	0.945832i
$670$	8.81042e8	−	3.20673e8i	2.92936	−	1.06620i
$671$	−3.30189e8	−	5.82213e7i	−1.09294	−	0.192715i
$672$	1.94189e6	−	4.84314e6i	0.00639907	−	0.0159595i
$673$	−2.66163e8	+	2.23337e8i	−0.873176	+	0.732682i	−0.964764	−	0.263115i	$-0.915250\pi$
$673$	−2.66163e8	+	2.23337e8i	−0.873176	+	0.732682i	0.0915884	+	0.995797i	$0.470806\pi$
$674$			1.45045e8i			0.473720i
$675$	7.71688e8	+	3.68838e8i	2.50917	+	1.19929i
$676$	1.57601e8			0.510176
$677$	2.68260e8	+	3.19700e8i	0.864550	+	1.03033i	0.999222	+	0.0394400i	$0.0125574\pi$
$677$	2.68260e8	+	3.19700e8i	0.864550	+	1.03033i	−0.134672	+	0.990890i	$0.542998\pi$
$678$	−2.72050e7	−	1.89933e8i	−0.0872891	−	0.609412i
$679$	145447.	−	824873.i	0.000464618	−	0.00263498i
$680$	−5.70774e7	−	1.56819e8i	−0.181526	−	0.498737i
$681$	−2.26094e7	−	6.89645e7i	−0.0715894	−	0.218365i
$682$	−9.52012e7	−	5.39913e8i	−0.300116	−	1.70204i
$683$	4.27935e8	−	2.47068e8i	1.34312	−	0.775452i	0.355858	−	0.934540i	$-0.384189\pi$
$683$	4.27935e8	−	2.47068e8i	1.34312	−	0.775452i	0.987264	+	0.159088i	$0.0508555\pi$
$684$	−9.14412e7	−	8.27915e8i	−0.285742	−	2.58712i
$685$	−2.24764e8	+	3.89302e8i	−0.699285	+	1.21120i
$686$	2.43935e7	−	6.70207e7i	0.0755618	−	0.207604i
$687$	3.15878e8	+	1.01955e7i	0.974201	+	0.0314441i
$688$	−2.80208e7	−	2.35122e7i	−0.0860429	−	0.0721985i
$689$	2.79713e7	−	3.33349e7i	0.0855176	−	0.101916i
$690$	2.48466e6	−	7.69796e7i	0.00756343	−	0.234330i
$691$	−3.97023e8	−	1.44505e8i	−1.20332	−	0.437973i	−0.338939	−	0.940808i	$-0.610068\pi$
$691$	−3.97023e8	−	1.44505e8i	−1.20332	−	0.437973i	−0.864382	+	0.502835i	$0.832290\pi$
$692$	−3.97885e8	−	2.29719e8i	−1.20071	−	0.693231i
$693$	−8.95914e6	+	2.04120e7i	−0.0269195	+	0.0613320i
$694$	6.20618e7	+	1.07494e8i	0.185672	+	0.321593i
$695$	−5.94004e8	+	1.04739e8i	−1.76944	+	0.311999i
$696$	−2.02562e8	+	6.64084e7i	−0.600801	+	0.196968i
$697$	3.96386e7	−	1.44273e7i	0.117063	−	0.0426075i
$698$	−6.24147e8	−	1.10054e8i	−1.83536	−	0.323623i
$699$	−1.21200e8	+	1.73601e7i	−0.354872	+	0.0508301i
$700$	9.08567e7	−	7.62378e7i	0.264888	−	0.222268i
$701$		−	1.31299e7i		−	0.0381159i	−0.999818	−	0.0190580i	$-0.993933\pi$
$701$		−	1.31299e7i		−	0.0381159i	0.999818	−	0.0190580i	$-0.00606671\pi$
$702$	−4.61007e8	+	2.09646e8i	−1.33259	+	0.606003i
$703$	−3.46523e8			−0.997392
$704$	−2.82202e8	−	3.36315e8i	−0.808801	−	0.963891i
$705$	7.61597e8	+	3.05368e8i	2.17349	+	0.871477i
$706$	1.00391e8	−	5.69348e8i	0.285287	−	1.61795i
$707$	1.21590e7	+	3.34066e7i	0.0344064	+	0.0945309i
$708$	6.40282e8	−	7.14893e8i	1.80415	−	2.01438i
$709$	−1.70404e7	−	9.66410e7i	−0.0478125	−	0.271158i	0.951524	−	0.307574i	$-0.0995171\pi$
$709$	−1.70404e7	−	9.66410e7i	−0.0478125	−	0.271158i	−0.999337	+	0.0364156i	$0.988406\pi$
$710$	−8.05282e8	+	4.64930e8i	−2.24995	+	1.29901i
$711$	−1.06522e8	−	2.15505e8i	−0.296367	−	0.599583i
$712$	−1.99820e8	+	3.46099e8i	−0.553604	+	0.958871i
$713$	−8.56080e6	+	2.35206e7i	−0.0236181	+	0.0648903i
$714$	3.69583e6	−	5.94947e6i	0.0101535	−	0.0163450i
$715$	4.82283e8	+	4.04684e8i	1.31942	+	1.10713i
$716$	7.81095e7	−	9.30873e7i	0.212797	−	0.253601i
$717$	1.71500e8	−	9.17700e7i	0.465272	−	0.248968i
$718$	1.08516e9	+	3.94965e8i	2.93170	+	1.06705i
$719$	1.83168e8	+	1.05752e8i	0.492792	+	0.284513i	0.725732	−	0.687978i	$-0.241501\pi$
$719$	1.83168e8	+	1.05752e8i	0.492792	+	0.284513i	−0.232940	+	0.972491i	$0.574835\pi$
$720$	5.38532e8	+	1.31254e8i	1.44283	+	0.351653i
$721$	5.49879e6	+	9.52418e6i	0.0146711	+	0.0254110i
$722$	5.31690e8	−	9.37512e7i	1.41269	−	0.249095i
$723$	1.52556e8	−	7.27159e8i	0.403660	−	1.92404i
$724$	5.25769e8	−	1.91364e8i	1.38541	−	0.504249i
$725$	4.20250e8	+	7.41015e7i	1.10279	+	0.194452i
$726$	2.77509e7	+	3.53269e7i	0.0725217	+	0.0923199i
$727$	7.23777e7	−	6.07321e7i	0.188365	−	0.158057i	−0.543728	−	0.839261i	$-0.682988\pi$
$727$	7.23777e7	−	6.07321e7i	0.188365	−	0.158057i	0.732094	+	0.681204i	$0.238543\pi$
$728$			3.36329e7i			0.0871706i
$729$	−2.54640e8	+	2.91981e8i	−0.657271	+	0.753654i
$730$	−8.76013e8			−2.25186
$731$	6.41885e6	+	7.64968e6i	0.0164325	+	0.0195835i
$732$	−6.35431e8	+	4.99162e8i	−1.62008	+	1.27265i
$733$	−7.01555e7	+	3.97871e8i	−0.178135	+	1.01025i	0.756327	+	0.654193i	$0.226992\pi$
$733$	−7.01555e7	+	3.97871e8i	−0.178135	+	1.01025i	−0.934463	+	0.356061i	$0.884119\pi$
$734$	1.39401e8	+	3.83001e8i	0.352515	+	0.968526i
$735$	−7.52468e8	−	1.57866e8i	−1.89507	−	0.397582i
$736$	1.29661e6	+	7.35346e6i	0.00325220	+	0.0184441i
$737$	3.36297e8	−	1.94161e8i	0.840079	−	0.485020i
$738$	−1.16541e8	+	4.78166e8i	−0.289941	+	1.18962i
$739$	3.38385e8	−	5.86100e8i	0.838451	−	1.45224i	−0.0527378	−	0.998608i	$-0.516795\pi$
$739$	3.38385e8	−	5.86100e8i	0.838451	−	1.45224i	0.891189	−	0.453632i	$-0.149872\pi$
$740$	3.80316e8	−	1.04491e9i	0.938534	−	2.57860i
$741$	−2.23085e8	−	4.16901e8i	−0.548296	−	1.02466i
$742$	−5.37890e6	−	4.51343e6i	−0.0131668	−	0.0110483i
$743$	−2.89177e7	+	3.44627e7i	−0.0705012	+	0.0840201i	−0.800142	−	0.599810i	$-0.795243\pi$
$743$	−2.89177e7	+	3.44627e7i	−0.0705012	+	0.0840201i	0.729641	+	0.683830i	$0.239687\pi$
$744$	−5.37509e8	−	3.33902e8i	−1.30517	−	0.810775i
$745$	−5.55081e8	−	2.02033e8i	−1.34242	−	0.488600i
$746$	9.54030e8	+	5.50809e8i	2.29798	+	1.32674i
$747$	1.06171e8	−	5.24792e7i	0.254710	−	0.125900i
$748$	−7.21620e7	−	1.24988e8i	−0.172427	−	0.298651i
$749$	8.53333e6	−	1.50466e6i	0.0203083	−	0.00358090i
$750$	−1.85948e9	−	1.66541e9i	−4.40765	−	3.94764i
$751$	5.83479e7	−	2.12369e7i	0.137754	−	0.0501385i	−0.272223	−	0.962234i	$-0.587759\pi$
$751$	5.83479e7	−	2.12369e7i	0.137754	−	0.0501385i	0.409977	+	0.912096i	$0.365537\pi$
$752$	3.85183e8	+	6.79182e7i	0.905762	+	0.159710i
$753$	2.05654e8	−	5.12908e8i	0.481673	−	1.20131i
$754$	−1.93560e8	+	1.62417e8i	−0.451547	+	0.378893i
$755$			1.37053e9i			3.18455i
$756$	2.22395e7	+	4.89043e7i	0.0514708	+	0.113183i
$757$	−2.81969e7			−0.0650001			−0.0325000	−	0.999472i	$-0.510347\pi$
$757$	−2.81969e7			−0.0650001			−0.0325000	+	0.999472i	$0.510347\pi$
$758$	−1.64176e8	−	1.95657e8i	−0.376966	−	0.449250i
$759$	−4.52296e6	−	3.15772e7i	−0.0103442	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.78575 - 10.4705i) q^{2} +(21.2323 - 16.6790i) q^{3} +(-21.3274 + 120.954i) q^{4} +(-83.1319 - 228.403i) q^{5} +(-361.178 - 75.7744i) q^{6} +(3.85901 + 21.8856i) q^{7} +(696.250 - 401.980i) q^{8} +(172.622 - 708.267i) q^{9} +O(q^{10})\)	\(q+(-8.78575 - 10.4705i) q^{2} +(21.2323 - 16.6790i) q^{3} +(-21.3274 + 120.954i) q^{4} +(-83.1319 - 228.403i) q^{5} +(-361.178 - 75.7744i) q^{6} +(3.85901 + 21.8856i) q^{7} +(696.250 - 401.980i) q^{8} +(172.622 - 708.267i) q^{9} +(-1661.11 + 2877.12i) q^{10} +(-470.609 + 1292.99i) q^{11} +(1564.56 + 2923.85i) q^{12} +(1442.04 + 1210.02i) q^{13} +(195.247 - 232.687i) q^{14} +(-5574.62 - 3462.97i) q^{15} +(-2939.57 - 1069.92i) q^{16} +(739.593 + 427.004i) q^{17} +(-8932.49 + 4415.23i) q^{18} +(-4651.50 - 8056.63i) q^{19} +(29399.2 - 5183.88i) q^{20} +(446.965 + 400.317i) q^{21} +(17672.8 - 6432.38i) q^{22} +(-845.594 - 149.101i) q^{23} +(8078.38 - 20147.7i) q^{24} +(-33287.6 + 27931.6i) q^{25} -25729.7i q^{26} +(-8148.01 - 17917.3i) q^{27} -2729.44 q^{28} +(-6312.41 - 7522.84i) q^{29} +(12718.3 + 88793.5i) q^{30} +(5062.00 - 28708.0i) q^{31} +(-2974.27 - 8171.75i) q^{32} +(11573.6 + 35302.4i) q^{33} +(-2026.95 - 11495.4i) q^{34} +(4677.92 - 2700.80i) q^{35} +(81986.1 + 35984.9i) q^{36} +(18624.3 - 32258.2i) q^{37} +(-43489.6 + 119487. i) q^{38} +(50799.7 + 1639.65i) q^{39} +(-149694. - 125608. i) q^{40} +(31749.6 - 37837.7i) q^{41} +(264.573 - 8197.00i) q^{42} +(10987.9 + 3999.26i) q^{43} +(-146355. - 84498.1i) q^{44} +(-176121. + 19452.1i) q^{45} +(5868.03 + 10163.7i) q^{46} +(-123131. + 21711.4i) q^{47} +(-80259.1 + 26312.3i) q^{48} +(110090. - 40069.4i) q^{49} +(584913. + 103136. i) q^{50} +(22825.3 - 3269.38i) q^{51} +(-177111. + 148614. i) q^{52} -23116.5i q^{53} +(-116016. + 242730. i) q^{54} +334445. q^{55} +(11484.4 + 13686.6i) q^{56} +(-233139. - 93478.6i) q^{57} +(-23308.2 + 132188. i) q^{58} +(-98982.2 - 271951. i) q^{59} +(537752. - 600415. i) q^{60} +(42313.0 + 239969. i) q^{61} +(-345060. + 199220. i) q^{62} +(16167.0 + 1044.72i) q^{63} +(-159534. + 276321. i) q^{64} +(156492. - 429957. i) q^{65} +(267949. - 431339. i) q^{66} +(-216191. - 181406. i) q^{67} +(-67421.4 + 80349.7i) q^{68} +(-20440.8 + 10937.9i) q^{69} +(-69377.6 - 25251.4i) q^{70} +(242393. + 139946. i) q^{71} +(-164521. - 562522. i) q^{72} +(131842. + 228357. i) q^{73} +(-501386. + 88407.8i) q^{74} +(-240902. + 1.14826e6i) q^{75} +(1.07368e6 - 390789. i) q^{76} +(-30113.8 - 5309.88i) q^{77} +(-429146. - 546301. i) q^{78} +(252610. - 211965. i) q^{79} +760352. i q^{80} +(-471844. - 244526. i) q^{81} -675121. q^{82} +(104427. + 124451. i) q^{83} +(-57952.4 + 45524.4i) q^{84} +(36045.3 - 204423. i) q^{85} +(-54662.7 - 150184. i) q^{86} +(-259501. - 54442.6i) q^{87} +(192094. + 1.08942e6i) q^{88} +(-430492. + 248545. i) q^{89} +(1.75103e6 + 1.67316e6i) q^{90} +(-20917.0 + 36229.3i) q^{91} +(36068.7 - 99098.0i) q^{92} +(-371343. - 693967. i) q^{93} +(1.30913e6 + 1.09849e6i) q^{94} +(-1.45347e6 + 1.73218e6i) q^{95} +(-199447. - 123897. i) q^{96} +(-35417.3 - 12890.8i) q^{97} +(-1.38677e6 - 800650. i) q^{98} +(834543. + 556516. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

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