LMFDB - Embedded newform 27.7.f.a.5.3

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			5.3
Character	$\chi$	$=$	27.5
Dual form			27.7.f.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.36754 - 9.97205i) q^{2} +(-20.7807 + 17.2384i) q^{3} +(-18.3125 + 103.855i) q^{4} +(-10.7822 - 29.6238i) q^{5} +(345.786 + 62.9829i) q^{6} +(45.8281 + 259.904i) q^{7} +(467.375 - 269.839i) q^{8} +(134.674 - 716.452i) q^{9} +O(q^{10})$	\(q+(-8.36754 - 9.97205i) q^{2} +(-20.7807 + 17.2384i) q^{3} +(-18.3125 + 103.855i) q^{4} +(-10.7822 - 29.6238i) q^{5} +(345.786 + 62.9829i) q^{6} +(45.8281 + 259.904i) q^{7} +(467.375 - 269.839i) q^{8} +(134.674 - 716.452i) q^{9} +(-205.189 + 355.398i) q^{10} +(556.762 - 1529.69i) q^{11} +(-1409.76 - 2473.87i) q^{12} +(-516.182 - 433.128i) q^{13} +(2208.31 - 2631.76i) q^{14} +(734.728 + 429.735i) q^{15} +(-259.372 - 94.4038i) q^{16} +(7224.90 + 4171.30i) q^{17} +(-8271.39 + 4651.97i) q^{18} +(2452.48 + 4247.82i) q^{19} +(3274.04 - 577.301i) q^{20} +(-5432.67 - 4610.98i) q^{21} +(-19912.9 + 7247.70i) q^{22} +(13427.7 + 2367.66i) q^{23} +(-5060.77 + 13664.2i) q^{24} +(11208.1 - 9404.74i) q^{25} +8771.60i q^{26} +(9551.88 + 17209.9i) q^{27} -27831.7 q^{28} +(-19605.3 - 23364.7i) q^{29} +(-1862.53 - 10922.6i) q^{30} +(-4183.58 + 23726.3i) q^{31} +(-10584.3 - 29080.0i) q^{32} +(14799.6 + 41385.7i) q^{33} +(-18858.3 - 106951. i) q^{34} +(7205.21 - 4159.93i) q^{35} +(71941.3 + 27106.7i) q^{36} +(6254.14 - 10832.5i) q^{37} +(21838.2 - 60000.1i) q^{38} +(18193.0 + 102.540i) q^{39} +(-13033.0 - 10935.9i) q^{40} +(-78828.2 + 93943.8i) q^{41} +(-522.803 + 92757.4i) q^{42} +(75854.4 + 27608.8i) q^{43} +(148671. + 85835.3i) q^{44} +(-22676.1 + 3735.36i) q^{45} +(-88746.1 - 153713. i) q^{46} +(123569. - 21788.6i) q^{47} +(7017.31 - 2509.39i) q^{48} +(45104.1 - 16416.5i) q^{49} +(-187569. - 33073.5i) q^{50} +(-222045. + 37863.4i) q^{51} +(54435.3 - 45676.6i) q^{52} -84492.8i q^{53} +(91692.6 - 239257. i) q^{54} -51318.3 q^{55} +(91551.1 + 109106. i) q^{56} +(-124190. - 45995.7i) q^{57} +(-68945.6 + 391010. i) q^{58} +(-92903.0 - 255249. i) q^{59} +(-58085.0 + 68435.9i) q^{60} +(24350.3 + 138097. i) q^{61} +(271606. - 156812. i) q^{62} +(192381. + 2168.67i) q^{63} +(-210256. + 364173. i) q^{64} +(-7265.32 + 19961.3i) q^{65} +(288865. - 493879. i) q^{66} +(316858. + 265876. i) q^{67} +(-565518. + 673958. i) q^{68} +(-319851. + 182270. i) q^{69} +(-101773. - 37042.3i) q^{70} +(-43295.7 - 24996.8i) q^{71} +(-130384. - 371192. i) q^{72} +(14823.6 + 25675.3i) q^{73} +(-160354. + 28274.7i) q^{74} +(-70789.9 + 388647. i) q^{75} +(-486070. + 176915. i) q^{76} +(423088. + 74601.8i) q^{77} +(-151209. - 182280. i) q^{78} +(720308. - 604410. i) q^{79} +8701.46i q^{80} +(-495167. - 192975. i) q^{81} +1.59641e6 q^{82} +(61772.9 + 73618.1i) q^{83} +(578361. - 479774. i) q^{84} +(45669.5 - 259004. i) q^{85} +(-359399. - 987442. i) q^{86} +(810181. + 147570. i) q^{87} +(-152554. - 865175. i) q^{88} +(-307049. + 177275. i) q^{89} +(226992. + 194871. i) q^{90} +(88916.0 - 154007. i) q^{91} +(-491789. + 1.35118e6i) q^{92} +(-322066. - 565167. i) q^{93} +(-1.25125e6 - 1.04992e6i) q^{94} +(99393.3 - 118452. i) q^{95} +(721241. + 421847. i) q^{96} +(-328801. - 119674. i) q^{97} +(-541117. - 312414. i) q^{98} +(-1.02097e6 - 604903. 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 $

$2$	−8.36754	−	9.97205i	−1.04594	−	1.24651i	−0.968370	−	0.249520i	$-0.919727\pi$
$2$	−8.36754	−	9.97205i	−1.04594	−	1.24651i	−0.0775733	−	0.996987i	$-0.524717\pi$
$3$	−20.7807	+	17.2384i	−0.769655	+	0.638460i
$3$	−20.7807	+	17.2384i	−0.769655	+	0.638460i
$4$	−18.3125	+	103.855i	−0.286133	+	1.62274i
$5$	−10.7822	−	29.6238i	−0.0862573	−	0.236990i	0.889063	−	0.457785i	$-0.151357\pi$
$5$	−10.7822	−	29.6238i	−0.0862573	−	0.236990i	−0.975320	+	0.220795i	$0.929135\pi$
$6$	345.786	+	62.9829i	1.60086	+	0.291587i
$7$	45.8281	+	259.904i	0.133610	+	0.757737i	0.975818	+	0.218585i	$0.0701441\pi$
$7$	45.8281	+	259.904i	0.133610	+	0.757737i	−0.842208	+	0.539152i	$0.818745\pi$
$8$	467.375	−	269.839i	0.912841	−	0.527029i
$9$	134.674	−	716.452i	0.184738	−	0.982788i
$10$	−205.189	+	355.398i	−0.205189	+	0.355398i
$11$	556.762	−	1529.69i	0.418304	−	1.14928i	−0.534361	−	0.845256i	$-0.679448\pi$
$11$	556.762	−	1529.69i	0.418304	−	1.14928i	0.952665	−	0.304023i	$-0.0983301\pi$
$12$	−1409.76	−	2473.87i	−0.815832	−	1.43164i
$13$	−516.182	−	433.128i	−0.234948	−	0.197145i	0.517710	−	0.855556i	$-0.326784\pi$
$13$	−516.182	−	433.128i	−0.234948	−	0.197145i	−0.752659	+	0.658411i	$0.771229\pi$
$14$	2208.31	−	2631.76i	0.804777	−	0.959095i
$15$	734.728	+	429.735i	0.217697	+	0.127329i
$16$	−259.372	−	94.4038i	−0.0633233	−	0.0230478i
$17$	7224.90	+	4171.30i	1.47057	+	0.849033i	0.999454	−	0.0330397i	$-0.0105188\pi$
$17$	7224.90	+	4171.30i	1.47057	+	0.849033i	0.471114	+	0.882072i	$0.343852\pi$
$18$	−8271.39	+	4651.97i	−1.41828	+	0.797663i
$19$	2452.48	+	4247.82i	0.357556	+	0.619306i	0.987552	−	0.157293i	$-0.0502767\pi$
$19$	2452.48	+	4247.82i	0.357556	+	0.619306i	−0.629996	+	0.776599i	$0.716943\pi$
$20$	3274.04	−	577.301i	0.409255	−	0.0721627i
$21$	−5432.67	−	4610.98i	−0.586618	−	0.497892i
$22$	−19912.9	+	7247.70i	−1.87011	+	0.680663i
$23$	13427.7	+	2367.66i	1.10361	+	0.194597i	0.695635	−	0.718395i	$-0.255123\pi$
$23$	13427.7	+	2367.66i	1.10361	+	0.194597i	0.407978	+	0.912992i	$0.366234\pi$
$24$	−5060.77	+	13664.2i	−0.366086	+	0.988443i
$25$	11208.1	−	9404.74i	0.717320	−	0.601903i
$26$			8771.60i			0.499067i
$27$	9551.88	+	17209.9i	0.485286	+	0.874355i
$28$	−27831.7			−1.26784
$29$	−19605.3	−	23364.7i	−0.803858	−	0.958000i	0.195886	−	0.980627i	$-0.437242\pi$
$29$	−19605.3	−	23364.7i	−0.803858	−	0.958000i	−0.999744	+	0.0226265i	$0.992797\pi$
$30$	−1862.53	−	10922.6i	−0.0689826	−	0.404539i
$31$	−4183.58	+	23726.3i	−0.140431	+	0.796424i	0.830492	+	0.557031i	$0.188060\pi$
$31$	−4183.58	+	23726.3i	−0.140431	+	0.796424i	−0.970923	+	0.239393i	$0.923051\pi$
$32$	−10584.3	−	29080.0i	−0.323006	−	0.887451i
$33$	14799.6	+	41385.7i	0.411819	+	1.15162i
$34$	−18858.3	−	106951.i	−0.479805	−	2.72111i
$35$	7205.21	−	4159.93i	0.168051	−	0.0970245i
$36$	71941.3	+	27106.7i	1.54195	+	0.580990i
$37$	6254.14	−	10832.5i	0.123470	−	0.213857i	−0.797664	−	0.603102i	$-0.793931\pi$
$37$	6254.14	−	10832.5i	0.123470	−	0.213857i	0.921134	+	0.389246i	$0.127264\pi$
$38$	21838.2	−	60000.1i	0.397985	−	1.09345i
$39$	18193.0	+	102.540i	0.306698	+	0.00172862i
$40$	−13033.0	−	10935.9i	−0.203640	−	0.170874i
$41$	−78828.2	+	93943.8i	−1.14375	+	1.36306i	−0.222105	+	0.975023i	$0.571293\pi$
$41$	−78828.2	+	93943.8i	−1.14375	+	1.36306i	−0.921642	+	0.388042i	$0.873152\pi$
$42$	−522.803	+	92757.4i	−0.00705651	+	1.25199i
$43$	75854.4	+	27608.8i	0.954060	+	0.347249i	0.771703	−	0.635983i	$-0.219405\pi$
$43$	75854.4	+	27608.8i	0.954060	+	0.347249i	0.182357	+	0.983232i	$0.441627\pi$
$44$	148671.	+	85835.3i	1.74529	+	1.00765i
$45$	−22676.1	+	3735.36i	−0.248846	+	0.0409916i
$46$	−88746.1	−	153713.i	−0.911750	−	1.57920i
$47$	123569.	−	21788.6i	1.19019	−	0.209863i	0.456737	−	0.889602i	$-0.349018\pi$
$47$	123569.	−	21788.6i	1.19019	−	0.209863i	0.733454	+	0.679739i	$0.237907\pi$
$48$	7017.31	−	2509.39i	0.0634522	−	0.0226905i
$49$	45104.1	−	16416.5i	0.383378	−	0.139538i
$50$	−187569.	−	33073.5i	−1.50055	−	0.264588i
$51$	−222045.	+	37863.4i	−1.67390	+	0.285436i
$52$	54435.3	−	45676.6i	0.387142	−	0.324851i
$53$		−	84492.8i		−	0.567535i	−0.958893	−	0.283767i	$-0.908416\pi$
$53$		−	84492.8i		−	0.567535i	0.958893	−	0.283767i	$-0.0915843\pi$
$54$	91692.6	−	239257.i	0.582308	−	1.51944i
$55$	−51318.3			−0.308450
$56$	91551.1	+	109106.i	0.521314	+	0.621278i
$57$	−124190.	−	45995.7i	−0.670597	−	0.248366i
$58$	−68945.6	+	391010.i	−0.353364	+	2.00403i
$59$	−92903.0	−	255249.i	−0.452349	−	1.24282i	−0.931066	−	0.364850i	$-0.881120\pi$
$59$	−92903.0	−	255249.i	−0.452349	−	1.24282i	0.478717	−	0.877969i	$-0.341102\pi$
$60$	−58085.0	+	68435.9i	−0.268912	+	0.316833i
$61$	24350.3	+	138097.i	0.107279	+	0.608408i	0.990286	+	0.139048i	$0.0444043\pi$
$61$	24350.3	+	138097.i	0.107279	+	0.608408i	−0.883007	+	0.469360i	$0.844485\pi$
$62$	271606.	−	156812.i	1.13963	−	0.657966i
$63$	192381.	+	2168.67i	0.769378	+	0.00867307i
$64$	−210256.	+	364173.i	−0.802062	+	1.38921i
$65$	−7265.32	+	19961.3i	−0.0264554	+	0.0726856i
$66$	288865.	−	493879.i	1.00476	−	1.71786i
$67$	316858.	+	265876.i	1.05352	+	0.884004i	0.993459	−	0.114191i	$-0.0364274\pi$
$67$	316858.	+	265876.i	1.05352	+	0.884004i	0.0600566	+	0.998195i	$0.480872\pi$
$68$	−565518.	+	673958.i	−1.79854	+	2.14342i
$69$	−319851.	+	182270.i	−0.973644	+	0.554840i
$70$	−101773.	−	37042.3i	−0.296714	−	0.107995i
$71$	−43295.7	−	24996.8i	−0.120968	−	0.0698408i	0.438295	−	0.898831i	$-0.355582\pi$
$71$	−43295.7	−	24996.8i	−0.120968	−	0.0698408i	−0.559263	+	0.828990i	$0.688916\pi$
$72$	−130384.	−	371192.i	−0.349321	−	0.994492i
$73$	14823.6	+	25675.3i	0.0381053	+	0.0660004i	0.884449	−	0.466637i	$-0.154534\pi$
$73$	14823.6	+	25675.3i	0.0381053	+	0.0660004i	−0.846344	+	0.532637i	$0.821201\pi$
$74$	−160354.	+	28274.7i	−0.395717	+	0.0697755i
$75$	−70789.9	+	388647.i	−0.167798	+	0.921238i
$76$	−486070.	+	176915.i	−1.10728	+	0.403018i
$77$	423088.	+	74601.8i	0.926742	+	0.163410i
$78$	−151209.	−	182280.i	−0.318634	−	0.384110i
$79$	720308.	−	604410.i	1.46095	−	1.22589i	0.536889	−	0.843653i	$-0.319599\pi$
$79$	720308.	−	604410.i	1.46095	−	1.22589i	0.924066	−	0.382233i	$-0.124845\pi$
$80$			8701.46i			0.0169950i
$81$	−495167.	−	192975.i	−0.931744	−	0.363117i
$82$	1.59641e6			2.89536
$83$	61772.9	+	73618.1i	0.108035	+	0.128751i	0.817352	−	0.576138i	$-0.195441\pi$
$83$	61772.9	+	73618.1i	0.108035	+	0.128751i	−0.709317	+	0.704889i	$0.750997\pi$
$84$	578361.	−	479774.i	0.975801	−	0.809466i
$85$	45669.5	−	259004.i	0.0743651	−	0.421745i
$86$	−359399.	−	987442.i	−0.565044	−	1.55245i
$87$	810181.	+	147570.i	1.23034	+	0.224099i
$88$	−152554.	−	865175.i	−0.223859	−	1.26957i
$89$	−307049.	+	177275.i	−0.435549	+	0.251464i	−0.701708	−	0.712465i	$-0.747579\pi$
$89$	−307049.	+	177275.i	−0.435549	+	0.251464i	0.266159	+	0.963929i	$0.414245\pi$
$90$	226992.	+	194871.i	0.311375	+	0.267313i
$91$	88916.0	−	154007.i	0.117993	−	0.204370i
$92$	−491789.	+	1.35118e6i	−0.631561	+	1.73520i
$93$	−322066.	−	565167.i	−0.400401	−	0.702632i
$94$	−1.25125e6	−	1.04992e6i	−1.50647	−	1.26408i
$95$	99393.3	−	118452.i	0.115927	−	0.138157i
$96$	721241.	+	421847.i	0.815205	+	0.476805i
$97$	−328801.	−	119674.i	−0.360262	−	0.131125i	0.155546	−	0.987829i	$-0.450286\pi$
$97$	−328801.	−	119674.i	−0.360262	−	0.131125i	−0.515808	+	0.856704i	$0.672508\pi$
$98$	−541117.	−	312414.i	−0.574927	−	0.331934i
$99$	−1.02097e6	−	604903.i	−1.05222	−	0.623419i
$100$	771484.	+	1.33625e6i	0.771484	+	1.33625i
$101$	−502522.	+	88608.2i	−0.487743	+	0.0860022i	−0.412111	−	0.911134i	$-0.635208\pi$
$101$	−502522.	+	88608.2i	−0.487743	+	0.0860022i	−0.0756317	+	0.997136i	$0.524097\pi$
$102$	2.23555e6	+	1.89742e6i	2.10661	+	1.78798i
$103$	−823407.	+	299696.i	−0.753534	+	0.274264i	−0.690092	−	0.723721i	$-0.742430\pi$
$103$	−823407.	+	299696.i	−0.753534	+	0.274264i	−0.0634422	+	0.997986i	$0.520208\pi$
$104$	−358125.	−	63147.1i	−0.318372	−	0.0561375i
$105$	−78018.6	+	210652.i	−0.0673954	+	0.181970i
$106$	−842567.	+	706998.i	−0.707435	+	0.593609i
$107$		−	400060.i		−	0.326568i	−0.986579	−	0.163284i	$-0.947791\pi$
$107$		−	400060.i		−	0.326568i	0.986579	−	0.163284i	$-0.0522087\pi$
$108$	−1.96227e6	+	676858.i	−1.55771	+	0.537312i
$109$	1.85549e6			1.43278			0.716388	−	0.697702i	$-0.245794\pi$
$109$	1.85549e6			1.43278			0.716388	+	0.697702i	$0.245794\pi$
$110$	429408.	+	511749.i	0.322621	+	0.384484i
$111$	56769.6	+	332918.i	0.0415094	+	0.243427i
$112$	12649.4	−	71738.2i	0.00900358	−	0.0510619i
$113$	−48658.0	−	133687.i	−0.0337224	−	0.0926516i	0.921689	−	0.387930i	$-0.126810\pi$
$113$	−48658.0	−	133687.i	−0.0337224	−	0.0926516i	−0.955411	+	0.295278i	$0.904588\pi$
$114$	580492.	+	1.62330e6i	0.391816	+	1.09568i
$115$	−74640.3	−	423306.i	−0.0490772	−	0.278331i
$116$	2.78557e6	−	1.60825e6i	1.78460	−	1.03034i
$117$	−379832.	+	311488.i	−0.237156	+	0.194484i
$118$	−1.76799e6	+	3.06224e6i	−1.07605	+	1.86377i
$119$	−753033.	+	2.06894e6i	−0.446862	+	1.22774i
$120$	459352.	+	2589.02i	0.265829	+	0.00149827i
$121$	−672877.	−	564611.i	−0.379822	−	0.318708i
$122$	1.17336e6	−	1.39836e6i	0.646177	−	0.770084i
$123$	18662.1	−	3.31109e6i	0.0100287	−	1.77933i
$124$	−2.38749e6	−	868976.i	−1.25221	−	0.455767i
$125$	−826036.	−	476912.i	−0.422931	−	0.244179i
$126$	−1.58813e6	−	1.93658e6i	−0.793914	−	0.968106i
$127$	−1.81059e6	−	3.13604e6i	−0.883914	−	1.53098i	−0.846953	−	0.531668i	$-0.821566\pi$
$127$	−1.81059e6	−	3.13604e6i	−0.883914	−	1.53098i	−0.0369611	−	0.999317i	$-0.511768\pi$
$128$	3.44041e6	−	606636.i	1.64051	−	0.289267i
$129$	−2.05224e6	+	733882.i	−0.956002	+	0.341867i
$130$	259848.	−	94576.9i	0.118274	−	0.0430482i
$131$	2.30745e6	+	406866.i	1.02640	+	0.180983i	0.661408	−	0.750026i	$-0.269959\pi$
$131$	2.30745e6	+	406866.i	1.02640	+	0.180983i	0.364997	+	0.931009i	$0.381070\pi$
$132$	−4.56915e6	+	779138.i	−1.98662	+	0.338760i
$133$	−991632.	+	832078.i	−0.421498	+	0.353679i
$134$		−	5.38446e6i		−	2.23783i
$135$	406833.	−	468523.i	0.165354	−	0.190428i
$136$	4.50231e6			1.78986
$137$	2.94238e6	+	3.50659e6i	1.14429	+	1.36372i	0.921280	+	0.388900i	$0.127145\pi$
$137$	2.94238e6	+	3.50659e6i	1.14429	+	1.36372i	0.223013	+	0.974815i	$0.428411\pi$
$138$	4.49397e6	+	1.66442e6i	1.70999	+	0.633322i
$139$	124034.	−	703431.i	0.0461845	−	0.261925i	−0.952969	−	0.303068i	$-0.901989\pi$
$139$	124034.	−	703431.i	0.0461845	−	0.261925i	0.999153	+	0.0411433i	$0.0131000\pi$
$140$	300086.	+	824479.i	0.109361	+	0.300466i
$141$	−2.19225e6	+	2.58292e6i	−0.782047	+	0.921411i
$142$	113009.	+	640909.i	0.0394684	+	0.223837i
$143$	−949942.	+	548449.i	−0.324855	+	0.187555i
$144$	−102567.	+	173114.i	−0.0343493	+	0.0579756i
$145$	−480762.	+	832704.i	−0.157698	+	0.273141i
$146$	131998.	−	362661.i	0.0424139	−	0.116531i
$147$	−654298.	+	1.11867e6i	−0.205979	+	0.352168i
$148$	1.01048e6	+	847896.i	0.311705	+	0.261552i
$149$	66552.2	−	79313.8i	0.0201189	−	0.0239767i	−0.755891	−	0.654697i	$-0.772796\pi$
$149$	66552.2	−	79313.8i	0.0201189	−	0.0239767i	0.776010	+	0.630721i	$0.217241\pi$
$150$	4.46795e6	−	2.54610e6i	1.32384	−	0.754401i
$151$	2.94820e6	+	1.07306e6i	0.856300	+	0.311668i	0.732606	−	0.680653i	$-0.238304\pi$
$151$	2.94820e6	+	1.07306e6i	0.856300	+	0.311668i	0.123694	+	0.992320i	$0.460526\pi$
$152$	2.29245e6	+	1.32355e6i	0.652784	+	0.376885i
$153$	3.96154e6	−	4.61453e6i	1.10609	−	1.28841i
$154$	−2.79628e6	−	4.84329e6i	−0.765628	−	1.32611i
$155$	747970.	−	131887.i	0.200858	−	0.0354167i
$156$	−343810.	+	1.88757e6i	−0.0905617	+	0.497198i
$157$	−2.65544e6	+	966502.i	−0.686180	+	0.249749i	−0.661499	−	0.749946i	$-0.730079\pi$
$157$	−2.65544e6	+	966502.i	−0.686180	+	0.249749i	−0.0246812	+	0.999695i	$0.507857\pi$
$158$	−1.20544e7	−	2.12552e6i	−3.05615	−	0.538882i
$159$	1.45652e6	+	1.75582e6i	0.362348	+	0.436806i
$160$	−747338.	+	627091.i	−0.182456	+	0.153098i
$161$			3.59841e6i			0.862249i
$162$	2.21897e6	+	6.55256e6i	0.521924	+	1.54122i
$163$	3.26286e6			0.753417			0.376708	−	0.926332i	$-0.377056\pi$
$163$	3.26286e6			0.753417			0.376708	+	0.926332i	$0.377056\pi$
$164$	−8.31303e6	−	9.90709e6i	−1.88464	−	2.24602i
$165$	1.06643e6	−	884646.i	0.237400	−	0.196933i
$166$	217236.	−	1.23201e6i	0.0474905	−	0.269332i
$167$	1.98834e6	+	5.46291e6i	0.426914	+	1.17294i	0.947676	+	0.319235i	$0.103426\pi$
$167$	1.98834e6	+	5.46291e6i	0.426914	+	1.17294i	−0.520762	+	0.853702i	$0.674352\pi$
$168$	−3.78332e6	−	689109.i	−0.797893	−	0.145332i
$169$	−759323.	−	4.30633e6i	−0.157314	−	0.892170i
$170$	−2.96495e6	+	1.71181e6i	−0.603490	+	0.348425i
$171$	3.37364e6	−	1.18501e6i	0.674700	−	0.236993i
$172$	−4.25641e6	+	7.37231e6i	−0.836484	+	1.44883i
$173$	−1.04575e6	+	2.87317e6i	−0.201971	+	0.554911i	−0.998783	−	0.0493164i	$-0.984296\pi$
$173$	−1.04575e6	+	2.87317e6i	−0.201971	+	0.554911i	0.796812	+	0.604227i	$0.206518\pi$
$174$	−5.30765e6	−	9.31396e6i	−1.00752	−	1.76802i
$175$	2.95798e6	+	2.48204e6i	0.551926	+	0.463121i
$176$	−288817.	+	344199.i	−0.0529767	+	0.0631352i
$177$	6.33068e6	+	3.70275e6i	1.14164	+	0.667735i
$178$	4.33704e6	+	1.57855e6i	0.769012	+	0.279897i
$179$	783189.	+	452174.i	0.136555	+	0.0788400i	0.566721	−	0.823910i	$-0.308212\pi$
$179$	783189.	+	452174.i	0.136555	+	0.0788400i	−0.430166	+	0.902750i	$0.641545\pi$
$180$	27319.0	−	2.42344e6i	0.00468433	−	0.415542i
$181$	−4.20949e6	−	7.29105e6i	−0.709894	−	1.22957i	−0.964896	−	0.262632i	$-0.915409\pi$
$181$	−4.20949e6	−	7.29105e6i	−0.709894	−	1.22957i	0.255002	−	0.966941i	$-0.417924\pi$
$182$	−2.27977e6	+	401986.i	−0.378162	+	0.0666801i
$183$	−2.88659e6	−	2.44999e6i	−0.471012	−	0.399771i
$184$	6.91464e6	−	2.51672e6i	1.10998	−	0.404000i
$185$	−388332.	−	68473.4i	−0.0613321	−	0.0108145i
$186$	−2.94097e6	+	7.94071e6i	−0.457038	+	1.23402i
$187$	1.04033e7	−	8.72945e6i	1.59092	−	1.33494i
$188$			1.32323e7i			1.99142i
$189$	−4.03519e6	+	3.27127e6i	−0.597693	+	0.484542i
$190$	−2.01289e6			−0.293467
$191$	−2.00538e6	−	2.38992e6i	−0.287804	−	0.342991i	0.602699	−	0.797968i	$-0.294092\pi$
$191$	−2.00538e6	−	2.38992e6i	−0.287804	−	0.342991i	−0.890503	+	0.454977i	$0.849647\pi$
$192$	−1.90852e6	−	1.11922e7i	−0.269645	−	1.58130i
$193$	−2.03900e6	+	1.15638e7i	−0.283626	+	1.60852i	0.426527	+	0.904475i	$0.359737\pi$
$193$	−2.03900e6	+	1.15638e7i	−0.283626	+	1.60852i	−0.710153	+	0.704048i	$0.751374\pi$
$194$	1.55787e6	+	4.28020e6i	0.213366	+	0.586218i
$195$	−193123.	−	540052.i	−0.0260453	−	0.0728336i
$196$	878978.	+	4.98493e6i	0.116737	+	0.662050i
$197$	−6.80635e6	+	3.92965e6i	−0.890258	+	0.513990i	−0.874027	−	0.485878i	$-0.838500\pi$
$197$	−6.80635e6	+	3.92965e6i	−0.890258	+	0.513990i	−0.0162308	+	0.999868i	$0.505167\pi$
$198$	2.51088e6	+	1.52427e7i	0.323468	+	1.96366i
$199$	−1.18535e6	+	2.05308e6i	−0.150413	+	0.260524i	−0.931379	−	0.364050i	$-0.881394\pi$
$199$	−1.18535e6	+	2.05308e6i	−0.150413	+	0.260524i	0.780966	+	0.624573i	$0.214727\pi$
$200$	2.70063e6	−	7.41993e6i	0.337579	−	0.927491i
$201$	−1.11678e7	−	62944.5i	−1.37524	−	0.00775121i
$202$	5.08848e6	+	4.26974e6i	0.617354	+	0.518021i
$203$	5.17410e6	−	6.16625e6i	0.618509	−	0.737111i
$204$	133883.	−	2.37540e7i	0.0157701	−	2.79799i
$205$	3.63291e6	+	1.32227e6i	0.421689	+	0.153482i
$206$	9.87848e6	+	5.70334e6i	1.13003	+	0.652421i
$207$	3.50467e6	−	9.30142e6i	0.395127	−	1.04867i
$208$	92994.3	+	161071.i	0.0103339	+	0.0178989i
$209$	7.86330e6	−	1.38651e6i	0.861323	−	0.151874i
$210$	2.75346e6	−	984639.i	0.297318	−	0.106321i
$211$	−6.08433e6	+	2.21451e6i	−0.647687	+	0.235739i	−0.644911	−	0.764257i	$-0.723106\pi$
$211$	−6.08433e6	+	2.21451e6i	−0.647687	+	0.235739i	−0.00277559	+	0.999996i	$0.500883\pi$
$212$	8.77504e6	+	1.54728e6i	0.920962	+	0.162390i
$213$	1.33062e6	−	226899.i	0.137694	−	0.0234798i
$214$	−3.98942e6	+	3.34752e6i	−0.407069	+	0.341572i
$215$		−	2.54478e6i		−	0.256056i
$216$	9.10822e6	+	5.46602e6i	0.903800	+	0.542388i
$217$	−6.35828e6			−0.622244
$218$	−1.55259e7	−	1.85030e7i	−1.49860	−	1.78596i
$219$	−750646.	−	278014.i	−0.0714666	−	0.0264688i
$220$	939768.	−	5.32969e6i	0.0882577	−	0.500534i
$221$	−1.92265e6	−	5.28245e6i	−0.178125	−	0.489394i
$222$	2.84485e6	−	3.35181e6i	0.260016	−	0.306352i
$223$	2.55047e6	+	1.44644e7i	0.229988	+	1.30433i	0.852915	+	0.522049i	$0.174832\pi$
$223$	2.55047e6	+	1.44644e7i	0.229988	+	1.30433i	−0.622927	+	0.782280i	$0.714057\pi$
$224$	7.07295e6	−	4.08357e6i	0.629298	−	0.363326i
$225$	−5.22860e6	−	9.29667e6i	−0.459027	−	0.816168i
$226$	−925983.	+	1.60385e6i	−0.0802191	+	0.138944i
$227$	1.42951e6	−	3.92756e6i	0.122211	−	0.335772i	−0.863468	−	0.504404i	$-0.831712\pi$
$227$	1.42951e6	−	3.92756e6i	0.122211	−	0.335772i	0.985679	+	0.168631i	$0.0539346\pi$
$228$	7.05114e6	−	1.20555e7i	0.594915	−	1.01714i
$229$	−2.67283e6	−	2.24277e6i	−0.222569	−	0.186758i	0.524684	−	0.851297i	$-0.324183\pi$
$229$	−2.67283e6	−	2.24277e6i	−0.222569	−	0.186758i	−0.747253	+	0.664539i	$0.768628\pi$
$230$	−3.59668e6	+	4.28635e6i	−0.295609	+	0.352293i
$231$	−1.00781e7	+	5.74309e6i	−0.817602	+	0.465918i
$232$	−1.54677e7	−	5.62979e6i	−1.23869	−	0.450846i
$233$	−1.87991e7	−	1.08537e7i	−1.48617	−	0.858041i	−0.486295	−	0.873795i	$-0.661652\pi$
$233$	−1.87991e7	−	1.08537e7i	−1.48617	−	0.858041i	−0.999876	+	0.0157535i	$0.994985\pi$
$234$	6.28444e6	+	1.18131e6i	0.490477	+	0.0921967i
$235$	−1.97780e6	−	3.42566e6i	−0.152398	−	0.263961i
$236$	2.82103e7	−	4.97423e6i	2.14621	−	0.378434i
$237$	−4.54942e6	+	2.49770e7i	−0.341752	+	1.87627i
$238$	2.69326e7	−	9.80268e6i	1.99778	−	0.727133i
$239$	1.00135e7	+	1.76565e6i	0.733486	+	0.129333i	0.527901	−	0.849306i	$-0.322979\pi$
$239$	1.00135e7	+	1.76565e6i	0.733486	+	0.129333i	0.205585	+	0.978639i	$0.434090\pi$
$240$	−149999.	−	180822.i	−0.0108507	−	0.0130803i
$241$	−5.41040e6	+	4.53987e6i	−0.386526	+	0.324334i	−0.815258	−	0.579098i	$-0.803405\pi$
$241$	−5.41040e6	+	4.53987e6i	−0.386526	+	0.324334i	0.428732	+	0.903432i	$0.358960\pi$
$242$			1.14344e7i			0.806800i
$243$	1.36165e7	−	4.52574e6i	0.948957	−	0.315406i
$244$	−1.47881e7			−1.01799
$245$	−972639.	−	1.15915e6i	−0.0661384	−	0.0788206i
$246$	−3.31745e7	+	2.75196e7i	−2.22843	+	1.84857i
$247$	573924.	−	3.25488e6i	0.0380858	−	0.215995i
$248$	4.44697e6	+	1.22180e7i	0.291548	+	0.801020i
$249$	−2.55274e6	−	464967.i	−0.165352	−	0.0301179i
$250$	2.15610e6	+	1.22279e7i	0.137990	+	0.782583i
$251$	−3.68851e6	+	2.12956e6i	−0.233255	+	0.134670i	−0.612073	−	0.790802i	$-0.709664\pi$
$251$	−3.68851e6	+	2.12956e6i	−0.233255	+	0.134670i	0.378818	+	0.925471i	$0.376331\pi$
$252$	−3.74820e6	+	1.99401e7i	−0.234219	+	1.24602i
$253$	1.10978e7	−	1.92220e7i	0.685292	−	1.18696i
$254$	−1.61225e7	+	4.42963e7i	−0.983858	+	2.70313i
$255$	3.51578e6	+	6.16956e6i	0.212032	+	0.372078i
$256$	−1.42208e7	−	1.19327e7i	−0.847627	−	0.711243i
$257$	−2.13551e6	+	2.54500e6i	−0.125806	+	0.149930i	−0.825271	−	0.564737i	$-0.808978\pi$
$257$	−2.13551e6	+	2.54500e6i	−0.125806	+	0.149930i	0.699464	+	0.714667i	$0.253422\pi$
$258$	2.44905e7	+	1.43242e7i	1.42606	+	0.834089i
$259$	3.10202e6	+	1.12904e6i	0.178544	+	0.0649847i
$260$	−1.94004e6	−	1.12008e6i	−0.110380	−	0.0637281i
$261$	−1.93800e7	+	1.08996e7i	−1.09001	+	0.613042i
$262$	−1.52504e7	−	2.64145e7i	−0.847965	−	1.46872i
$263$	−6.58354e6	+	1.16086e6i	−0.361903	+	0.0638133i	−0.351643	−	0.936134i	$-0.614377\pi$
$263$	−6.58354e6	+	1.16086e6i	−0.361903	+	0.0638133i	−0.0102599	+	0.999947i	$0.503266\pi$
$264$	1.80844e7	+	1.53492e7i	0.982863	+	0.834205i
$265$	−2.50300e6	+	911016.i	−0.134500	+	0.0489540i
$266$	1.65951e7	+	2.92616e6i	0.881726	+	0.155472i
$267$	3.32475e6	−	8.97692e6i	0.174673	−	0.471622i
$268$	−3.34151e7	+	2.80386e7i	−1.73596	+	1.45664i
$269$		−	2.98704e7i		−	1.53456i	−0.641313	−	0.767279i	$-0.721610\pi$
$269$		−	2.98704e7i		−	1.53456i	0.641313	−	0.767279i	$-0.278390\pi$
$270$	−8.07633e6	−	136572.i	−0.410320	−	0.00693857i
$271$	8.43453e6			0.423792			0.211896	−	0.977292i	$-0.432036\pi$
$271$	8.43453e6			0.423792			0.211896	+	0.977292i	$0.432036\pi$
$272$	−1.48015e6	−	1.76398e6i	−0.0735529	−	0.0876569i
$273$	807101.	+	4.73314e6i	0.0396680	+	0.232628i
$274$	1.03474e7	−	5.86832e7i	0.503015	−	2.85274i
$275$	−8.14609e6	−	2.23812e7i	−0.391698	−	1.07618i
$276$	−1.30725e7	−	3.65561e7i	−0.621771	−	1.73873i
$277$	−4.03918e6	−	2.29074e7i	−0.190044	−	1.07779i	−0.919301	−	0.393554i	$-0.871245\pi$
$277$	−4.03918e6	−	2.29074e7i	−0.190044	−	1.07779i	0.729257	−	0.684240i	$-0.239866\pi$
$278$	−8.05251e6	+	4.64912e6i	−0.374798	+	0.216390i
$279$	1.64353e7	+	6.19265e6i	0.756773	+	0.285144i
$280$	2.24502e6	−	3.88849e6i	0.102270	−	0.177136i
$281$	1.04610e6	−	2.87414e6i	0.0471471	−	0.129535i	−0.913884	−	0.405975i	$-0.866932\pi$
$281$	1.04610e6	−	2.87414e6i	0.0471471	−	0.129535i	0.961031	+	0.276439i	$0.0891544\pi$
$282$	4.41008e7	+	248562.i	1.96652	+	0.0110838i
$283$	1.22324e7	+	1.02642e7i	0.539699	+	0.452862i	0.871435	−	0.490511i	$-0.163190\pi$
$283$	1.22324e7	+	1.02642e7i	0.539699	+	0.452862i	−0.331736	+	0.943372i	$0.607634\pi$
$284$	3.38891e6	−	4.03874e6i	0.147946	−	0.176316i
$285$	−23530.8	+	4.17490e6i	−0.00101649	+	0.180348i
$286$	1.34178e7	+	4.88370e6i	0.573568	+	0.208762i
$287$	−2.80289e7	−	1.61825e7i	−1.18566	−	0.684541i
$288$	−2.22599e7	+	3.66679e6i	−0.931848	+	0.153500i
$289$	2.27307e7	+	3.93707e7i	0.941713	+	1.63109i
$290$	1.23266e7	−	2.17351e6i	0.505415	−	0.0891183i
$291$	8.89571e6	−	3.18111e6i	0.360995	−	0.129092i
$292$	−2.93797e6	+	1.06934e6i	−0.118005	+	0.0429502i
$293$	4.90077e7	+	8.64137e6i	1.94832	+	0.343542i	0.999626	+	0.0273578i	$0.00870935\pi$
$293$	4.90077e7	+	8.64137e6i	1.94832	+	0.343542i	0.948698	+	0.316184i	$0.102402\pi$
$294$	1.66303e7	−	2.83582e6i	0.654422	−	0.111593i
$295$	−6.55974e6	+	5.50427e6i	−0.255517	+	0.214405i
$296$		−	6.75044e6i		−	0.260290i
$297$	3.16440e7	−	5.02959e6i	1.20788	−	0.191983i
$298$	−1.34780e6			−0.0509304
$299$	−5.90561e6	−	7.03803e6i	−0.220928	−	0.263292i
$300$	−3.90668e7	−	1.44690e7i	−1.44692	−	0.535890i
$301$	−3.69936e6	+	2.09801e7i	−0.135652	+	0.769323i
$302$	−1.39686e7	−	3.83784e7i	−0.507145	−	1.39337i
$303$	8.91529e6	−	1.05040e7i	0.320485	−	0.377596i
$304$	−235095.	−	1.33329e6i	−0.00836802	−	0.0474574i
$305$	3.82841e6	−	2.21033e6i	0.134933	−	0.0779037i
$306$	−7.91647e7	−	892410.i	−2.76291	−	0.0311459i
$307$	−4.31226e6	+	7.46906e6i	−0.149036	+	0.258137i	−0.930871	−	0.365347i	$-0.880950\pi$
$307$	−4.31226e6	+	7.46906e6i	−0.149036	+	0.258137i	0.781836	+	0.623485i	$0.214284\pi$
$308$	−1.54956e7	+	4.25739e7i	−0.530343	+	1.45711i
$309$	1.19447e7	−	2.04221e7i	0.404855	−	0.692190i
$310$	−7.57386e6	−	6.35522e6i	−0.254233	−	0.213327i
$311$	2.63937e6	−	3.14548e6i	0.0877443	−	0.104570i	−0.720386	−	0.693573i	$-0.756035\pi$
$311$	2.63937e6	−	3.14548e6i	0.0877443	−	0.104570i	0.808130	+	0.589004i	$0.200480\pi$
$312$	8.53064e6	−	4.86127e6i	0.280878	−	0.160061i
$313$	−1.60441e7	−	5.83956e6i	−0.523216	−	0.190435i	0.0668906	−	0.997760i	$-0.478692\pi$
$313$	−1.60441e7	−	5.83956e6i	−0.523216	−	0.190435i	−0.590107	+	0.807325i	$0.700914\pi$
$314$	3.18575e7	+	1.83930e7i	1.02902	+	0.594104i
$315$	−2.01004e6	−	5.72242e6i	−0.0643091	−	0.183083i
$316$	4.95806e7	+	8.58761e7i	1.57127	+	2.72152i
$317$	4.55112e6	−	802486.i	0.142870	−	0.0251918i	−0.101756	−	0.994809i	$-0.532446\pi$
$317$	4.55112e6	−	802486.i	0.142870	−	0.0251918i	0.244626	+	0.969618i	$0.421335\pi$
$318$	5.32160e6	−	2.92164e7i	0.165486	−	0.908543i
$319$	−4.66562e7	+	1.69815e7i	−1.43727	+	0.523122i
$320$	1.30552e7	+	2.30198e6i	0.398413	+	0.0702510i
$321$	6.89640e6	+	8.31352e6i	0.208501	+	0.251345i
$322$	3.58835e7	−	3.01098e7i	1.07480	−	0.901863i
$323$			4.09201e7i			1.21431i
$324$	2.91093e7	−	4.78919e7i	0.855847	−	1.40808i
$325$	−9.85888e6			−0.287196
$326$	−2.73021e7	−	3.25374e7i	−0.788031	−	0.939139i
$327$	−3.85583e7	+	3.19857e7i	−1.10274	+	0.914770i
$328$	−1.14926e7	+	6.51779e7i	−0.325685	+	1.84705i
$329$	1.13259e7	+	3.11176e7i	0.318042	+	0.873812i
$330$	−1.77451e7	−	3.23217e6i	−0.493785	−	0.0899400i
$331$	125611.	+	712374.i	0.00346372	+	0.0196437i	0.986491	−	0.163818i	$-0.0523809\pi$
$331$	125611.	+	712374.i	0.00346372	+	0.0196437i	−0.983027	+	0.183461i	$0.941270\pi$
$332$	−8.77686e6	+	5.06732e6i	−0.239842	+	0.138473i
$333$	−6.91869e6	−	5.93965e6i	−0.187366	−	0.160853i
$334$	3.78389e7	−	6.55389e7i	1.01555	−	1.75898i
$335$	4.45982e6	−	1.22533e7i	0.118627	−	0.325925i
$336$	973791.	+	1.70883e6i	0.0256713	+	0.0450484i
$337$	−1.71172e7	−	1.43630e7i	−0.447242	−	0.375280i	0.391169	−	0.920319i	$-0.372071\pi$
$337$	−1.71172e7	−	1.43630e7i	−0.447242	−	0.375280i	−0.838411	+	0.545038i	$0.816515\pi$
$338$	−3.65893e7	+	4.36054e7i	−0.947554	+	1.12925i
$339$	3.31569e6	+	1.93932e6i	0.0851090	+	0.0497794i
$340$	2.60627e7	+	9.48604e6i	0.663105	+	0.241351i
$341$	3.39646e7	+	1.96095e7i	0.856572	+	0.494542i
$342$	−4.00461e7	−	2.37265e7i	−1.00111	−	0.593138i
$343$	2.18583e7	+	3.78597e7i	0.541670	+	0.938199i
$344$	4.29024e7	−	7.56485e6i	1.05392	−	0.185834i
$345$	8.84821e6	+	7.50992e6i	0.215476	+	0.182885i
$346$	3.74017e7	−	1.36131e7i	0.902950	−	0.328647i
$347$	−6.90272e7	−	1.21713e7i	−1.65208	−	0.291307i	−0.731496	−	0.681846i	$-0.761177\pi$
$347$	−6.90272e7	−	1.21713e7i	−1.65208	−	0.291307i	−0.920586	+	0.390540i	$0.872288\pi$
$348$	−3.01624e7	+	8.14394e7i	−0.715695	+	1.93240i
$349$	2.79575e7	−	2.34591e7i	0.657691	−	0.551868i	−0.251703	−	0.967805i	$-0.580990\pi$
$349$	2.79575e7	−	2.34591e7i	0.657691	−	0.551868i	0.909394	+	0.415936i	$0.136546\pi$
$350$		−	5.02656e7i		−	1.17238i
$351$	2.52360e6	−	1.30206e7i	0.0583577	−	0.301100i
$352$	−5.03763e7			−1.15504
$353$	−1.23251e7	−	1.46884e7i	−0.280198	−	0.333927i	0.607529	−	0.794298i	$-0.292161\pi$
$353$	−1.23251e7	−	1.46884e7i	−0.280198	−	0.333927i	−0.887727	+	0.460371i	$0.847716\pi$
$354$	−1.60482e7	−	9.41127e7i	−0.361757	−	2.12148i
$355$	−273677.	+	1.55210e6i	−0.00611721	+	0.0346924i
$356$	−1.27881e7	−	3.51350e7i	−0.283437	−	0.778736i
$357$	−2.00167e7	−	5.59751e7i	−0.439935	−	1.23024i
$358$	−2.04426e6	−	1.15936e7i	−0.0445541	−	0.252679i
$359$	−3.30945e7	+	1.91071e7i	−0.715275	+	0.412964i	−0.813011	−	0.582248i	$-0.802173\pi$
$359$	−3.30945e7	+	1.91071e7i	−0.715275	+	0.412964i	0.0977361	+	0.995212i	$0.468840\pi$
$360$	−9.59029e6	+	7.86470e6i	−0.205553	+	0.168568i
$361$	1.14936e7	−	1.99076e7i	0.244307	−	0.423152i
$362$	−3.74836e7	+	1.02985e8i	−0.790161	+	2.17095i
$363$	2.37158e7	+	133668.i	0.495814	+	0.00279452i
$364$	1.43662e7	+	1.20547e7i	0.297877	+	0.249949i
$365$	600767.	−	715967.i	0.0123546	−	0.0147236i
$366$	−277786.	+	4.92857e7i	−0.00566587	+	1.00526i
$367$	−6.53348e7	−	2.37799e7i	−1.32174	−	0.481074i	−0.417725	−	0.908573i	$-0.637172\pi$
$367$	−6.53348e7	−	2.37799e7i	−1.32174	−	0.481074i	−0.904016	+	0.427499i	$0.859395\pi$
$368$	−3.25925e6	−	1.88173e6i	−0.0653994	−	0.0377584i
$369$	5.66901e7	+	6.91284e7i	1.12831	+	1.37587i
$370$	2.56657e6	+	4.44542e6i	0.0506696	+	0.0877623i
$371$	2.19600e7	−	3.87214e6i	0.430042	−	0.0758280i
$372$	6.45935e7	−	2.30987e7i	1.25476	−	0.448702i
$373$	−5.31320e7	+	1.93385e7i	−1.02383	+	0.372645i	−0.798730	−	0.601689i	$-0.794494\pi$
$373$	−5.31320e7	+	1.93385e7i	−1.02383	+	0.372645i	−0.225104	+	0.974335i	$0.572272\pi$
$374$	−1.74101e8	−	3.06987e7i	−3.32802	−	0.586820i
$375$	2.53868e7	−	4.32899e6i	0.481409	−	0.0820905i
$376$	5.18737e7	−	4.35272e7i	0.975851	−	0.818837i
$377$			2.05520e7i			0.383557i
$378$	6.63859e7	+	1.28666e7i	1.22914	+	0.238225i
$379$	−3.47474e7			−0.638271			−0.319135	−	0.947709i	$-0.603393\pi$
$379$	−3.47474e7			−0.638271			−0.319135	+	0.947709i	$0.603393\pi$
$380$	1.04818e7	+	1.24917e7i	0.191022	+	0.227652i
$381$	9.16858e7	+	3.39573e7i	1.65778	+	0.613986i
$382$	−7.05228e6	+	3.99955e7i	−0.126514	+	0.717498i
$383$	2.83296e7	+	7.78348e7i	0.504247	+	1.38541i	0.887091	+	0.461594i	$0.152722\pi$
$383$	2.83296e7	+	7.78348e7i	0.504247	+	1.38541i	−0.382844	+	0.923813i	$0.625055\pi$
$384$	−6.10365e7	+	7.19135e7i	−1.07794	+	1.27004i
$385$	−2.35182e6	−	1.33378e7i	−0.0412118	−	0.233724i
$386$	1.32376e8	−	7.64272e7i	2.30169	−	1.32888i
$387$	2.99960e7	−	5.06279e7i	0.517524	−	0.873488i
$388$	1.84500e7	−	3.19563e7i	0.315864	−	0.547093i
$389$	1.37993e7	−	3.79132e7i	0.234427	−	0.644083i	−0.765573	−	0.643349i	$-0.777544\pi$
$389$	1.37993e7	−	3.79132e7i	0.234427	−	0.644083i	1.00000		0.000733713i	$-0.000233548\pi$
$390$	−3.76946e6	+	6.44474e6i	−0.0635456	+	0.108645i
$391$	8.71373e7	+	7.31169e7i	1.45772	+	1.22317i
$392$	1.66507e7	−	1.98435e7i	0.276423	−	0.329428i
$393$	−5.49642e7	+	3.13219e7i	−0.905528	+	0.516024i
$394$	9.61391e7	+	3.49918e7i	1.57185	+	0.572107i
$395$	−2.56714e7	−	1.48214e7i	−0.416541	−	0.240490i
$396$	8.15190e7	−	9.49560e7i	1.31272	−	1.52910i
$397$	−3.94861e7	−	6.83920e7i	−0.631063	−	1.09303i	−0.987335	−	0.158651i	$-0.949286\pi$
$397$	−3.94861e7	−	6.83920e7i	−0.631063	−	1.09303i	0.356272	−	0.934382i	$-0.384048\pi$
$398$	3.03919e7	−	5.35891e6i	0.482068	−	0.0850016i
$399$	6.26309e6	−	3.43853e7i	0.0985984	−	0.541321i
$400$	−3.79492e6	+	1.38124e6i	−0.0592957	+	0.0215819i
$401$	−3.22993e7	−	5.69524e6i	−0.500911	−	0.0883241i	−0.0825166	−	0.996590i	$-0.526296\pi$
$401$	−3.22993e7	−	5.69524e6i	−0.500911	−	0.0883241i	−0.418394	+	0.908266i	$0.637407\pi$
$402$	9.28195e7	+	1.11893e8i	1.42877	+	1.72236i
$403$	1.24360e7	−	1.04350e7i	0.190005	−	0.159433i
$404$		−	5.38123e7i		−	0.816089i
$405$	−377674.	+	1.67494e7i	−0.00568528	+	0.252135i
$406$	−1.04785e8			−1.56574
$407$	−1.30883e7	−	1.55980e7i	−0.194133	−	0.231359i
$408$	−9.35612e7	+	7.76128e7i	−1.37757	+	1.14275i
$409$	1.66999e7	−	9.47100e7i	0.244087	−	1.38429i	−0.578516	−	0.815671i	$-0.696368\pi$
$409$	1.66999e7	−	9.47100e7i	0.244087	−	1.38429i	0.822603	−	0.568616i	$-0.192521\pi$
$410$	−1.72128e7	−	4.72917e7i	−0.249746	−	0.686172i
$411$	−1.21593e8	−	2.21474e7i	−1.75139	−	0.319005i
$412$	−1.60464e7	−	9.10035e7i	−0.229449	−	1.30127i
$413$	6.20826e7	−	3.58434e7i	0.881292	−	0.508814i
$414$	−1.22080e8	+	4.28813e7i	−1.72045	+	0.604319i
$415$	1.51480e6	−	2.62371e6i	0.0211939	−	0.0367089i
$416$	−7.13196e6	+	1.95949e7i	−0.0990670	+	0.272184i
$417$	9.54853e6	+	1.67559e7i	0.131683	+	0.231079i
$418$	−7.96229e7	−	6.68115e7i	−1.09021	−	0.914792i
$419$	−6.33911e7	+	7.55466e7i	−0.861760	+	1.02701i	0.137573	+	0.990492i	$0.456070\pi$
$419$	−6.33911e7	+	7.55466e7i	−0.861760	+	1.02701i	−0.999333	+	0.0365139i	$0.988375\pi$
$420$	−2.04487e7	−	1.19602e7i	−0.276005	−	0.161433i
$421$	−4.71869e7	−	1.71746e7i	−0.632376	−	0.230166i	0.00588922	−	0.999983i	$-0.498125\pi$
$421$	−4.71869e7	−	1.71746e7i	−0.632376	−	0.230166i	−0.638265	+	0.769817i	$0.720348\pi$
$422$	7.29941e7	+	4.21432e7i	0.971294	+	0.560777i
$423$	1.03108e6	−	9.14658e7i	0.0136229	−	1.20847i
$424$	−2.27995e7	−	3.94898e7i	−0.299107	−	0.518069i
$425$	1.20208e8	−	2.11958e7i	1.56590	−	0.276111i
$426$	−1.33967e7	−	1.13704e7i	−0.173288	−	0.147078i
$427$	−3.47761e7	+	1.26575e7i	−0.446680	+	0.162578i
$428$	4.15484e7	+	7.32611e6i	0.529936	+	0.0934420i
$429$	1.02861e7	−	2.77726e7i	0.130280	−	0.351759i
$430$	−2.53766e7	+	2.12935e7i	−0.319175	+	0.267820i
$431$			2.33020e7i			0.291046i	0.989355	+	0.145523i	$0.0464865\pi$
$431$			2.33020e7i			0.291046i	−0.989355	+	0.145523i	$0.953513\pi$
$432$	−852811.	−	5.36552e6i	−0.0105779	−	0.0665519i
$433$	1.24609e8			1.53491			0.767457	−	0.641100i	$-0.221522\pi$
$433$	1.24609e8			1.53491			0.767457	+	0.641100i	$0.221522\pi$
$434$	5.32032e7	+	6.34051e7i	0.650831	+	0.775630i
$435$	−4.36393e6	−	2.55917e7i	−0.0530164	−	0.310908i
$436$	−3.39786e7	+	1.92702e8i	−0.409965	+	2.32503i
$437$	2.28737e7	+	6.28449e7i	0.274089	+	0.753053i
$438$	3.50869e6	+	9.81178e6i	0.0417564	+	0.116768i
$439$	−9.93258e6	−	5.63304e7i	−0.117400	−	0.665809i	−0.985534	−	0.169479i	$-0.945792\pi$
$439$	−9.93258e6	−	5.63304e7i	−0.117400	−	0.665809i	0.868134	−	0.496330i	$-0.165319\pi$
$440$	−2.39849e7	+	1.38477e7i	−0.281566	+	0.162562i
$441$	−5.68732e6	−	3.45258e7i	−0.0663120	−	0.402557i
$442$	−3.65890e7	+	6.33740e7i	−0.423724	+	0.733912i
$443$	2.33920e7	−	6.42689e7i	0.269064	−	0.739247i	−0.729413	−	0.684074i	$-0.760207\pi$
$443$	2.33920e7	−	6.42689e7i	0.269064	−	0.739247i	0.998477	−	0.0551732i	$-0.0175711\pi$
$444$	−3.56149e7	−	200734.i	−0.406896	−	0.00229336i
$445$	8.56219e6	+	7.18453e6i	0.0971639	+	0.0815302i
$446$	1.22899e8	−	1.46465e8i	1.38530	−	1.65094i
$447$	−15755.8	+	2.79545e6i	−0.000176408	+	0.0312989i
$448$	−1.04286e8	−	3.79569e7i	−1.15982	−	0.422140i
$449$	5.46408e7	+	3.15469e7i	0.603640	+	0.348511i	0.770472	−	0.637474i	$-0.220021\pi$
$449$	5.46408e7	+	3.15469e7i	0.603640	+	0.348511i	−0.166833	+	0.985985i	$0.553354\pi$
$450$	−4.89563e7	+	1.29930e8i	−0.537243	+	1.42585i
$451$	9.98164e7	+	1.72887e8i	1.08811	+	1.88466i
$452$	1.47751e7	−	2.60526e6i	0.159999	−	0.0282121i
$453$	−7.97634e7	+	2.85234e7i	−0.858043	+	0.306837i
$454$	−5.11273e7	+	1.86088e7i	−0.546368	+	0.198862i
$455$	−5.52097e6	−	973497.i	−0.0586113	−	0.0103348i
$456$	−7.04547e7	+	1.20140e7i	−0.743045	+	0.126705i
$457$	−9.44965e7	+	7.92920e7i	−0.990073	+	0.830770i	−0.985578	−	0.169220i	$-0.945875\pi$
$457$	−9.44965e7	+	7.92920e7i	−0.990073	+	0.830770i	−0.00449439	+	0.999990i	$0.501431\pi$
$458$			4.54201e7i			0.472772i
$459$	−2.77637e6	+	1.64184e8i	−0.0287104	+	1.69782i
$460$	4.53295e7			0.465702
$461$	−8.41198e7	−	1.00250e8i	−0.858609	−	1.02325i	−0.999448	−	0.0332182i	$-0.989424\pi$
$461$	−8.41198e7	−	1.00250e8i	−0.858609	−	1.02325i	0.140839	−	0.990033i	$-0.455020\pi$
$462$	1.41599e8	+	5.24436e7i	1.43594	+	0.531822i
$463$	2.05420e7	−	1.16499e8i	0.206966	−	1.17376i	−0.687350	−	0.726326i	$-0.741226\pi$
$463$	2.05420e7	−	1.16499e8i	0.206966	−	1.17376i	0.894316	−	0.447436i	$-0.147663\pi$
$464$	2.87935e6	+	7.91096e6i	0.0288231	+	0.0791909i
$465$	−1.32698e7	+	1.56345e7i	−0.131979	+	0.155498i
$466$	4.90689e7	+	2.78284e8i	0.484896	+	2.74998i
$467$	−6.21078e7	+	3.58580e7i	−0.609812	+	0.352075i	−0.772892	−	0.634538i	$-0.781190\pi$
$467$	−6.21078e7	+	3.58580e7i	−0.609812	+	0.352075i	0.163080	+	0.986613i	$0.447857\pi$
$468$	−2.53941e7	−	4.51517e7i	−0.247739	−	0.440491i
$469$	−5.45812e7	+	9.45373e7i	−0.529084	+	0.916400i
$470$	−1.76115e7	+	4.83871e7i	−0.169630	+	0.466054i
$471$	3.85210e7	−	6.58602e7i	0.368667	−	0.630319i
$472$	−1.12297e8	−	9.42281e7i	−1.06792	−	0.896095i
$473$	8.44658e7	−	1.00662e8i	0.798173	−	0.951226i
$474$	2.87140e8	−	1.63629e8i	2.69624	−	1.53648i
$475$	6.74373e7	+	2.45452e7i	0.629245	+	0.229026i
$476$	−2.01081e8	−	1.16094e8i	−1.86445	−	1.07644i
$477$	−6.05351e7	−	1.13790e7i	−0.557766	−	0.104845i
$478$	−6.61812e7	−	1.14629e8i	−0.605970	−	1.04957i
$479$	−1.54289e8	+	2.72053e7i	−1.40387	+	0.247541i	−0.823733	−	0.566977i	$-0.808113\pi$
$479$	−1.54289e8	+	2.72053e7i	−1.40387	+	0.247541i	−0.580139	+	0.814518i	$0.697002\pi$
$480$	4.72014e6	−	2.59143e7i	0.0426807	−	0.234323i
$481$	−7.92012e6	+	2.88269e6i	−0.0711699	+	0.0259037i
$482$	9.05436e7	+	1.59653e7i	0.808568	+	0.142572i
$483$	−6.20308e7	−	7.47774e7i	−0.550511	−	0.663634i
$484$	7.09600e7	−	5.95425e7i	0.625860	−	0.525159i
$485$			1.10307e7i			0.0966890i
$486$	−1.59067e8	−	9.79150e7i	−1.38571	−	0.852983i
$487$	1.36588e8			1.18256			0.591282	−	0.806465i	$-0.298622\pi$
$487$	1.36588e8			1.18256			0.591282	+	0.806465i	$0.298622\pi$
$488$	4.86447e7	+	5.79725e7i	0.418578	+	0.498841i
$489$	−6.78044e7	+	5.62465e7i	−0.579871	+	0.481026i
$490$	−3.42046e6	+	1.93984e7i	−0.0290735	+	0.164884i
$491$	1.97558e7	+	5.42787e7i	0.166898	+	0.458548i	0.994742	−	0.102410i	$-0.0326552\pi$
$491$	1.97558e7	+	5.42787e7i	0.166898	+	0.458548i	−0.827844	+	0.560958i	$0.810433\pi$
$492$	3.43533e8	+	6.25726e7i	2.88452	+	0.525398i
$493$	−4.41852e7	−	2.50587e8i	−0.368754	−	2.09131i
$494$	−3.72602e7	+	2.15122e7i	−0.309075	+	0.178445i
$495$	−6.91124e6	+	3.67671e7i	−0.0569824	+	0.303141i
$496$	3.32496e6	−	5.75899e6i	0.0272484	−	0.0471956i
$497$	4.51260e6	−	1.23983e7i	0.0367585	−	0.100993i
$498$	1.67235e7	+	2.93467e7i	0.135406	+	0.237614i
$499$	−3.84874e7	−	3.22948e7i	−0.309754	−	0.259915i	0.474636	−	0.880182i	$-0.342580\pi$
$499$	−3.84874e7	−	3.22948e7i	−0.309754	−	0.259915i	−0.784390	+	0.620268i	$0.787024\pi$
$500$	6.46567e7	−	7.70549e7i	0.517254	−	0.616439i
$501$	−1.35491e8	−	7.92472e7i	−1.07745	−	0.630189i
$502$	5.20999e7	+	1.89628e7i	0.411838	+	0.149897i
$503$	−6.05203e7	−	3.49414e7i	−0.475551	−	0.274559i	0.243010	−	0.970024i	$-0.421865\pi$
$503$	−6.05203e7	−	3.49414e7i	−0.475551	−	0.274559i	−0.718560	+	0.695465i	$0.755199\pi$
$504$	9.04990e7	−	5.08982e7i	0.706891	−	0.397567i
$505$	8.04318e6	+	1.39312e7i	0.0624531	+	0.108172i
$506$	−2.84544e8	+	5.01727e7i	−2.19633	+	0.387272i
$507$	9.00136e7	+	7.63991e7i	0.690692	+	0.586225i
$508$	3.58852e8	−	1.30611e8i	2.73731	−	0.996299i
$509$	8.56596e7	+	1.51041e7i	0.649565	+	0.114536i	0.488716	−	0.872443i	$-0.337466\pi$
$509$	8.56596e7	+	1.51041e7i	0.649565	+	0.114536i	0.160849	+	0.986979i	$0.448577\pi$
$510$	3.21047e7	−	8.66836e7i	0.242024	−	0.653471i
$511$	−5.99377e6	+	5.02937e6i	−0.0449197	+	0.0376921i
$512$			1.80752e7i			0.134671i
$513$	−4.96789e7	+	8.27817e7i	−0.367976	+	0.613172i
$514$	4.32479e7			0.318475
$515$	1.77562e7	+	2.11611e7i	0.129996	+	0.154923i
$516$	−3.86359e7	−	2.26575e8i	−0.281217	−	1.64916i
$517$	3.54688e7	−	2.01154e8i	0.256670	−	1.45565i
$518$	−1.46974e7	−	4.03808e7i	−0.105743	−	0.290527i
$519$	−2.77975e7	−	7.77335e7i	−0.198840	−	0.556040i
$520$	1.99071e6	+	1.12899e7i	0.0141579	+	0.0802932i
$521$	−5.91987e7	+	3.41784e7i	−0.418600	+	0.241679i	−0.694478	−	0.719514i	$-0.744365\pi$
$521$	−5.91987e7	+	3.41784e7i	−0.418600	+	0.241679i	0.275878	+	0.961193i	$0.411031\pi$
$522$	2.70855e8	+	1.02055e8i	1.90425	+	0.717502i
$523$	7.05914e7	−	1.22268e8i	0.493454	−	0.854687i	−0.506518	−	0.862230i	$-0.669068\pi$
$523$	7.05914e7	−	1.22268e8i	0.493454	−	0.854687i	0.999972	+	0.00754242i	$0.00240085\pi$
$524$	−8.45105e7	+	2.32191e8i	−0.587377	+	1.61380i
$525$	−1.04255e8	−	587607.i	−0.720476	−	0.00406077i
$526$	6.66642e7	+	5.59379e7i	0.458074	+	0.384370i
$527$	−1.29195e8	+	1.53969e8i	−0.882704	+	1.05197i
$528$	68375.7	−	1.21314e7i	0.000464515	−	0.0824159i
$529$	3.55881e7	+	1.29530e7i	0.240402	+	0.0874991i
$530$	3.00286e7	+	1.73370e7i	0.201701	+	0.116452i
$531$	−1.95385e8	+	3.21852e7i	−1.30499	+	0.214967i
$532$	−6.82566e7	−	1.18224e8i	−0.453325	−	0.785182i
$533$	8.13793e7	−	1.43494e7i	0.537443	−	0.0947657i
$534$	−1.17338e8	+	4.19602e7i	−0.770577	+	0.275559i
$535$	−1.18513e7	+	4.31351e6i	−0.0773934	+	0.0281689i
$536$	2.19835e8	+	3.87629e7i	1.42759	+	0.251722i
$537$	−2.40700e7	+	4.10444e6i	−0.155436	+	0.0265052i
$538$	−2.97869e8	+	2.49942e8i	−1.91284	+	1.60506i
$539$		−	7.81354e7i		−	0.498978i
$540$	4.12085e7	+	5.08317e7i	0.261701	+	0.322815i
$541$	1.14004e8			0.719996			0.359998	−	0.932953i	$-0.382777\pi$
$541$	1.14004e8			0.719996			0.359998	+	0.932953i	$0.382777\pi$
$542$	−7.05763e7	−	8.41095e7i	−0.443262	−	0.528260i
$543$	2.13162e8	+	7.89481e7i	1.33141	+	0.493108i
$544$	4.48312e7	−	2.54250e8i	0.278473	−	1.57930i
$545$	−2.00062e7	−	5.49665e7i	−0.123587	−	0.339554i
$546$	4.04457e7	−	4.76532e7i	0.248482	−	0.292762i
$547$	5.30861e7	+	3.01066e8i	0.324354	+	1.83950i	0.514178	+	0.857684i	$0.328097\pi$
$547$	5.30861e7	+	3.01066e8i	0.324354	+	1.83950i	−0.189824	+	0.981818i	$0.560792\pi$
$548$	−4.18061e8	+	2.41368e8i	−2.54038	+	1.46669i
$549$	1.02219e8	+	1.15230e6i	0.617755	+	0.00696385i
$550$	−1.55024e8	+	2.68509e8i	−0.931772	+	1.61388i
$551$	5.11673e7	−	1.40581e8i	0.305871	−	0.840373i
$552$	−1.00307e8	+	1.71497e8i	−0.596365	+	1.01962i
$553$	1.90099e8	+	1.59512e8i	1.12410	+	0.943230i
$554$	−1.94635e8	+	2.31957e8i	−1.14470	+	1.36420i
$555$	9.25018e6	−	5.27131e6i	0.0541092	−	0.0308347i
$556$	7.07838e7	+	2.57632e7i	0.411822	+	0.149891i
$557$	−4.51576e6	−	2.60718e6i	−0.0261316	−	0.0150871i	0.486877	−	0.873470i	$-0.338136\pi$
$557$	−4.51576e6	−	2.60718e6i	−0.0261316	−	0.0150871i	−0.513009	+	0.858383i	$0.671469\pi$
$558$	−7.57699e7	−	2.15711e8i	−0.436108	−	1.24157i
$559$	−2.71965e7	−	4.71058e7i	−0.155696	−	0.269674i
$560$	−2.26154e6	+	398771.i	−0.0128778	+	0.00227070i
$561$	−6.57069e7	+	3.60741e8i	−0.372154	+	2.04318i
$562$	−3.74143e7	+	1.36177e7i	−0.210780	+	0.0767176i
$563$	3.36062e7	+	5.92568e6i	0.188319	+	0.0332057i	0.267012	−	0.963693i	$-0.413964\pi$
$563$	3.36062e7	+	5.92568e6i	0.188319	+	0.0332057i	−0.0786932	+	0.996899i	$0.525075\pi$
$564$	−2.28105e8	−	2.74977e8i	−1.27144	−	1.53271i
$565$	−3.43567e6	+	2.88287e6i	−0.0190487	+	0.0159838i
$566$		−	2.07868e8i		−	1.14641i
$567$	2.74624e7	−	1.37539e8i	0.150657	−	0.754533i
$568$	−2.69804e7			−0.147233
$569$	1.60205e8	+	1.90925e8i	0.869640	+	1.03640i	0.998996	+	0.0447985i	$0.0142646\pi$
$569$	1.60205e8	+	1.90925e8i	0.869640	+	1.03640i	−0.129356	+	0.991598i	$0.541291\pi$
$570$	4.18293e7	−	3.46990e7i	0.225868	−	0.187367i
$571$	−4.37117e7	+	2.47901e8i	−0.234795	+	1.33159i	0.608249	+	0.793746i	$0.291872\pi$
$571$	−4.37117e7	+	2.47901e8i	−0.234795	+	1.33159i	−0.843045	+	0.537844i	$0.819239\pi$
$572$	−3.95636e7	−	1.08700e8i	−0.211401	−	0.580821i
$573$	8.28715e7	+	1.50946e7i	0.440495	+	0.0802337i
$574$	7.31604e7	+	4.14913e8i	0.386848	+	2.19392i
$575$	1.72766e8	−	9.97466e7i	0.908773	−	0.524680i
$576$	2.32597e8	+	1.99683e8i	1.21713	+	1.04490i
$577$	1.00060e7	−	1.73309e7i	0.0520873	−	0.0902179i	−0.838806	−	0.544430i	$-0.816746\pi$
$577$	1.00060e7	−	1.73309e7i	0.0520873	−	0.0902179i	0.890893	+	0.454212i	$0.150079\pi$
$578$	2.02406e8	−	5.56107e8i	1.04819	−	2.87988i
$579$	−1.56969e8	−	2.75452e8i	−0.808683	−	1.41909i
$580$	−7.76769e7	−	6.51786e7i	−0.398114	−	0.334058i
$581$	−1.63027e7	+	1.94288e7i	−0.0831249	+	0.0990644i
$582$	−1.06157e8	−	6.20904e7i	−0.538495	−	0.314960i
$583$	−1.29248e8	−	4.70424e7i	−0.652256	−	0.237402i
$584$	1.38564e7	+	7.99998e6i	0.0695683	+	0.0401653i
$585$	1.33229e7	+	7.89352e6i	0.0665472	+	0.0394279i
$586$	−3.23902e8	−	5.61014e8i	−1.60961	−	2.78792i
$587$	−1.71906e7	+	3.03116e6i	−0.0849916	+	0.0149863i	−0.215982	−	0.976397i	$-0.569295\pi$
$587$	−1.71906e7	+	3.03116e6i	−0.0849916	+	0.0149863i	0.130991	+	0.991384i	$0.458184\pi$
$588$	−1.04198e8	−	8.84381e7i	−0.512540	−	0.435018i
$589$	−1.11045e8	+	4.04171e7i	−0.543442	+	0.197797i
$590$	1.09778e8	+	1.93568e7i	0.534513	+	0.0942491i
$591$	7.36997e7	−	1.98992e8i	0.357029	−	0.963989i
$592$	−2.64478e6	+	2.21923e6i	−0.0127475	+	0.0106964i
$593$			3.72451e8i			1.78610i	0.449961	+	0.893048i	$0.351438\pi$
$593$			3.72451e8i			1.78610i	−0.449961	+	0.893048i	$0.648562\pi$
$594$	−3.14938e8	−	2.73470e8i	−1.50268	−	1.30482i
$595$	6.94092e7			0.329508
$596$	7.01844e6	+	8.36425e6i	0.0331514	+	0.0395083i
$597$	−1.07595e7	−	6.30979e7i	−0.0505674	−	0.296546i
$598$	−2.07682e7	+	1.17782e8i	−0.0971169	+	0.550777i
$599$	−2.50434e7	−	6.88061e7i	−0.116523	−	0.320145i	0.867697	−	0.497094i	$-0.165599\pi$
$599$	−2.50434e7	−	6.88061e7i	−0.116523	−	0.320145i	−0.984220	+	0.176949i	$0.943377\pi$
$600$	7.17868e7	+	2.00746e8i	0.332346	+	0.929379i
$601$	−2.31947e7	−	1.31544e8i	−0.106848	−	0.605965i	−0.990466	−	0.137756i	$-0.956011\pi$
$601$	−2.31947e7	−	1.31544e8i	−0.106848	−	0.605965i	0.883618	−	0.468208i	$-0.155100\pi$
$602$	2.40169e8	−	1.38662e8i	1.10085	−	0.635576i
$603$	2.33160e8	−	1.91207e8i	1.06341	−	0.872073i
$604$	−1.65432e8	+	2.86536e8i	−0.750772	+	1.30038i
$605$	−9.47082e6	+	2.60209e7i	−0.0427683	+	0.117505i
$606$	−1.79346e8	−	1.01083e6i	−0.805885	−	0.00454216i
$607$	2.45726e8	+	2.06189e8i	1.09871	+	0.921931i	0.997338	−	0.0729167i	$-0.0232307\pi$
$607$	2.45726e8	+	2.06189e8i	1.09871	+	0.921931i	0.101377	+	0.994848i	$0.467675\pi$
$608$	9.75689e7	−	1.16278e8i	0.434111	−	0.517353i
$609$	−1.22494e6	+	2.17332e8i	−0.00542327	+	0.962215i
$610$	−5.40759e7	−	1.96820e7i	−0.238240	−	0.0867122i
$611$	−7.32214e7	−	4.22744e7i	−0.321007	−	0.185333i
$612$	4.06698e8	+	4.95931e8i	1.77426	+	2.16355i
$613$	−5.07862e7	−	8.79642e7i	−0.220477	−	0.381878i	0.734476	−	0.678635i	$-0.237428\pi$
$613$	−5.07862e7	−	8.79642e7i	−0.220477	−	0.381878i	−0.954953	+	0.296757i	$0.904095\pi$
$614$	1.10565e8	−	1.94956e7i	0.477653	−	0.0842230i
$615$	−9.82881e7	+	3.51479e7i	−0.422548	+	0.151103i
$616$	2.17871e8	−	7.92986e7i	0.932090	−	0.339253i
$617$	1.91819e8	+	3.38229e7i	0.816652	+	0.143998i	0.566345	−	0.824169i	$-0.308357\pi$
$617$	1.91819e8	+	3.38229e7i	0.816652	+	0.143998i	0.250307	+	0.968166i	$0.419468\pi$
$618$	−3.03598e8	+	5.17700e7i	−1.28627	+	0.219337i
$619$	2.65930e8	−	2.23142e8i	1.12123	−	0.940825i	0.122565	−	0.992460i	$-0.460888\pi$
$619$	2.65930e8	−	2.23142e8i	1.12123	−	0.940825i	0.998666	+	0.0516358i	$0.0164435\pi$
$620$			8.00959e7i			0.336074i
$621$	8.75122e7	+	2.53705e8i	0.365421	+	1.05939i
$622$	−5.34519e7			−0.222122
$623$	−6.01458e7	−	7.16790e7i	−0.248738	−	0.296434i
$624$	−4.70909e6	−	1.74409e6i	−0.0193813	−	0.00717819i
$625$	3.44766e7	−	1.95527e8i	0.141216	−	0.800877i
$626$	7.60170e7	+	2.08855e8i	0.309876	+	0.851376i
$627$	−1.39503e8	+	1.64363e8i	−0.565956	+	0.666811i
$628$	−5.17487e7	−	2.93481e8i	−0.208939	−	1.18495i
$629$	9.03710e7	−	5.21757e7i	0.363143	−	0.209661i
$630$	−4.02452e7	+	6.79268e7i	−0.160951	+	0.271656i
$631$	−2.03645e8	+	3.52724e8i	−0.810561	+	1.40393i	0.101910	+	0.994794i	$0.467504\pi$
$631$	−2.03645e8	+	3.52724e8i	−0.810561	+	1.40393i	−0.912472	+	0.409140i	$0.865829\pi$
$632$	1.73560e8	−	4.76853e8i	0.687542	−	1.88901i
$633$	8.82618e7	−	1.50903e8i	0.347986	−	0.594960i
$634$	−4.60842e7	−	3.86692e7i	−0.180836	−	0.151739i
$635$	−7.33792e7	+	8.74500e7i	−0.286584	+	0.341538i
$636$	−2.09024e8	+	1.19114e8i	−0.812503	+	0.463013i
$637$	−3.03923e7	−	1.10619e7i	−0.117583	−	0.0427968i
$638$	5.59738e8	+	3.23165e8i	2.15537	+	1.24441i
$639$	−2.37398e7	+	2.76529e7i	−0.0909860	+	0.105983i
$640$	−5.50659e7	−	9.53769e7i	−0.210060	−	0.363834i
$641$	−8.69629e7	+	1.53339e7i	−0.330187	+	0.0582209i	−0.336284	−	0.941761i	$-0.609170\pi$
$641$	−8.69629e7	+	1.53339e7i	−0.330187	+	0.0582209i	0.00609723	+	0.999981i	$0.498059\pi$
$642$	2.51969e7	−	1.38335e8i	0.0952231	−	0.522790i
$643$	1.47014e7	−	5.35088e6i	0.0553001	−	0.0201276i	−0.314222	−	0.949350i	$-0.601744\pi$
$643$	1.47014e7	−	5.35088e6i	0.0553001	−	0.0201276i	0.369522	+	0.929222i	$0.379521\pi$
$644$	−3.73714e8	−	6.58959e7i	−1.39921	−	0.246718i
$645$	4.38679e7	+	5.28822e7i	0.163481	+	0.197074i
$646$	4.08057e8	−	3.42401e8i	1.51364	−	1.27010i
$647$			3.22521e7i			0.119082i	0.998226	+	0.0595409i	$0.0189637\pi$
$647$			3.22521e7i			0.119082i	−0.998226	+	0.0595409i	$0.981036\pi$
$648$	−2.83501e8	+	4.34236e7i	−1.04191	+	0.159588i
$649$	−4.42177e8			−1.61757
$650$	8.24946e7	+	9.83133e7i	0.300390	+	0.357991i
$651$	1.32129e8	−	1.09607e8i	0.478913	−	0.397278i
$652$	−5.97511e7	+	3.38866e8i	−0.215577	+	1.22260i
$653$	−7.29545e7	−	2.00441e8i	−0.262007	−	0.719858i	−0.999032	−	0.0439925i	$-0.985992\pi$
$653$	−7.29545e7	−	2.00441e8i	−0.262007	−	0.719858i	0.737025	−	0.675866i	$-0.236230\pi$
$654$	6.41601e8	+	1.16864e8i	2.29367	+	0.417779i
$655$	−1.28264e7	−	7.27423e7i	−0.0456438	−	0.258859i
$656$	2.93145e7	−	1.69247e7i	0.103842	−	0.0599529i
$657$	2.03915e7	−	7.16263e6i	0.0719039	−	0.0252567i
$658$	2.15536e8	−	3.73320e8i	0.756559	−	1.31040i
$659$	−3.92519e7	+	1.07844e8i	−0.137153	+	0.376824i	−0.989187	−	0.146663i	$-0.953147\pi$
$659$	−3.92519e7	+	1.07844e8i	−0.137153	+	0.376824i	0.852034	+	0.523487i	$0.175369\pi$
$660$	7.23463e7	+	1.26955e8i	0.251643	+	0.441588i
$661$	−2.65750e8	−	2.22991e8i	−0.920172	−	0.772116i	0.0538551	−	0.998549i	$-0.482849\pi$
$661$	−2.65750e8	−	2.22991e8i	−0.920172	−	0.772116i	−0.974027	+	0.226433i	$0.927294\pi$
$662$	6.05278e6	−	7.21342e6i	0.0208632	−	0.0248638i
$663$	1.31015e8	+	7.66294e7i	0.449553	+	0.262939i
$664$	4.87361e7	+	1.77385e7i	0.166474	+	0.0605916i
$665$	3.53412e7	+	2.04043e7i	0.120176	+	0.0693835i
$666$	−1.33801e6	+	1.18694e8i	−0.00452937	+	0.401796i
$667$	−2.07934e8	−	3.60151e8i	−0.700724	−	1.21369i
$668$	−6.03764e8	+	1.06460e8i	−2.02553	+	0.357155i
$669$	−3.02345e8	−	2.56615e8i	−1.00977	−	0.857045i
$670$	−1.59508e8	+	5.80561e7i	−0.530344	+	0.193029i
$671$	2.24803e8	+	3.96389e7i	0.744107	+	0.131206i
$672$	−7.65865e7	+	2.06786e8i	−0.252374	+	0.681417i
$673$	−6.39911e6	+	5.36949e6i	−0.0209930	+	0.0176152i	−0.653224	−	0.757165i	$-0.726584\pi$
$673$	−6.39911e6	+	5.36949e6i	−0.0209930	+	0.0176152i	0.632231	+	0.774780i	$0.282139\pi$
$674$			2.90877e8i			0.950012i
$675$	2.68914e8	+	1.03058e8i	0.874383	+	0.335098i
$676$	4.61141e8			1.49277
$677$	−2.17035e8	−	2.58653e8i	−0.699462	−	0.833587i	0.293003	−	0.956111i	$-0.405345\pi$
$677$	−2.17035e8	−	2.58653e8i	−0.699462	−	0.833587i	−0.992465	+	0.122525i	$0.960901\pi$
$678$	−8.40526e6	−	4.92916e7i	−0.0269688	−	0.158155i
$679$	1.60354e7	−	9.09412e7i	0.0512236	−	0.290504i
$680$	−4.85447e7	−	1.33375e8i	−0.154389	−	0.424179i
$681$	3.79986e7	+	1.06260e8i	0.120317	+	0.336456i
$682$	−8.86537e7	−	5.02780e8i	−0.279476	−	1.58498i
$683$	−2.88261e8	+	1.66427e8i	−0.904739	+	0.522351i	−0.878735	−	0.477311i	$-0.841612\pi$
$683$	−2.88261e8	+	1.66427e8i	−0.904739	+	0.522351i	−0.0260042	+	0.999662i	$0.508278\pi$
$684$	6.12902e7	+	3.72072e8i	0.191524	+	1.16268i
$685$	7.21533e7	−	1.24973e8i	0.224483	−	0.388817i
$686$	1.94639e8	−	5.34765e8i	0.602916	−	1.65650i
$687$	9.42051e7	+	530962.i	0.290539	+	0.00163755i
$688$	−1.70682e7	−	1.43219e7i	−0.0524109	−	0.0439780i
$689$	−3.65962e7	+	4.36136e7i	−0.111887	+	0.133341i
$690$	851491.	−	1.51074e8i	0.00259199	−	0.459879i
$691$	1.14246e8	+	4.15821e7i	0.346263	+	0.126030i	0.509297	−	0.860591i	$-0.329906\pi$
$691$	1.14246e8	+	4.15821e7i	0.346263	+	0.126030i	−0.163033	+	0.986621i	$0.552128\pi$
$692$	−2.79244e8	−	1.61222e8i	−0.842686	−	0.486525i
$693$	1.10428e8	−	2.93076e8i	0.331801	−	0.880602i
$694$	4.56214e8	+	7.90187e8i	1.36487	+	2.36402i
$695$	−2.21756e7	+	3.91016e6i	−0.0660574	+	0.0116477i
$696$	4.18478e8	−	1.49648e8i	1.24121	−	0.443857i
$697$	−9.61393e8	+	3.49919e8i	−2.83924	+	1.03340i
$698$	−4.67871e8	−	8.24983e7i	−1.37582	−	0.242593i
$699$	5.77758e8	−	9.85200e7i	1.69166	−	0.288465i
$700$	−3.11941e8	+	2.61750e8i	−0.909449	+	0.763118i
$701$		−	8.66600e7i		−	0.251573i	−0.992057	−	0.125787i	$-0.959855\pi$
$701$		−	8.66600e7i		−	0.251573i	0.992057	−	0.125787i	$-0.0401455\pi$
$702$	−1.50959e8	+	8.37853e7i	−0.436362	+	0.242190i
$703$	6.13526e7			0.176590
$704$	4.40011e8	+	5.24384e8i	1.26109	+	1.50291i
$705$	1.00153e8	+	3.70933e7i	0.285823	+	0.105859i
$706$	−4.33433e7	+	2.45812e8i	−0.123171	+	0.698537i
$707$	−4.60592e7	−	1.26547e8i	−0.130334	−	0.358090i
$708$	−5.00481e8	+	5.89669e8i	−1.41022	+	1.66153i
$709$	2.33917e7	+	1.32661e8i	0.0656330	+	0.372223i	0.999878	+	0.0155926i	$0.00496348\pi$
$709$	2.33917e7	+	1.32661e8i	0.0656330	+	0.372223i	−0.934245	+	0.356631i	$0.883925\pi$
$710$	1.77676e7	−	1.02582e7i	0.0496426	−	0.0286612i
$711$	−3.36024e8	−	5.97464e8i	−0.934892	−	1.66228i
$712$	−9.56712e7	+	1.65707e8i	−0.265058	+	0.459094i
$713$	−1.12351e8	+	3.08683e8i	−0.309963	+	0.851617i
$714$	−3.90696e8	+	6.67982e8i	−1.07336	+	1.83515i
$715$	2.64896e7	+	2.22274e7i	0.0724697	+	0.0608093i
$716$	−6.13029e7	+	7.30580e7i	−0.167010	+	0.199035i
$717$	−2.38524e8	+	1.35925e8i	−0.647105	+	0.368759i
$718$	4.67457e8	+	1.70141e8i	1.26290	+	0.459658i
$719$	−4.80053e8	−	2.77159e8i	−1.29152	−	0.745662i	−0.312600	−	0.949885i	$-0.601200\pi$
$719$	−4.80053e8	−	2.77159e8i	−1.29152	−	0.745662i	−0.978924	+	0.204223i	$0.934533\pi$
$720$	6.23418e6	+	1.17186e6i	0.0167025	+	0.00313963i
$721$	−1.15627e8	−	2.00272e8i	−0.308500	−	0.534337i
$722$	−2.94693e8	+	5.19623e7i	−0.782993	+	0.138063i
$723$	3.41718e7	−	1.87608e8i	0.0904175	−	0.496406i
$724$	8.34302e8	−	3.03661e8i	2.19840	−	0.800153i
$725$	−4.39477e8	−	7.74917e7i	−1.15325	−	0.203349i
$726$	−1.97110e8	−	2.37614e8i	−0.515110	−	0.620958i
$727$	−2.98975e8	+	2.50870e8i	−0.778094	+	0.652899i	−0.942768	−	0.333449i	$-0.891787\pi$
$727$	−2.98975e8	+	2.50870e8i	−0.778094	+	0.652899i	0.164674	+	0.986348i	$0.447343\pi$
$728$		−	9.59720e7i		−	0.248743i
$729$	−2.04943e8	+	3.28775e8i	−0.528995	+	0.848625i
$730$	−1.21666e7			−0.0312752
$731$	4.32876e8	+	5.15882e8i	1.10818	+	1.32068i
$732$	3.07306e8	−	2.54923e8i	0.783498	−	0.649943i
$733$	−2.68537e7	+	1.52295e8i	−0.0681854	+	0.386699i	0.931548	+	0.363618i	$0.118459\pi$
$733$	−2.68537e7	+	1.52295e8i	−0.0681854	+	0.386699i	−0.999734	+	0.0230809i	$0.992652\pi$
$734$	3.09557e8	+	8.50501e8i	0.782803	+	2.15073i
$735$	4.01939e7	+	7.32110e6i	0.101228	+	0.0184380i
$736$	−7.32703e7	−	4.15536e8i	−0.183778	−	1.04226i
$737$	5.83123e8	−	3.36666e8i	1.45666	−	0.841002i
$738$	2.14995e8	−	1.14375e9i	0.534884	−	2.84553i
$739$	6.62492e7	−	1.14747e8i	0.164152	−	0.284320i	−0.772202	−	0.635378i	$-0.780844\pi$
$739$	6.62492e7	−	1.14747e8i	0.164152	−	0.284320i	0.936354	+	0.351057i	$0.114178\pi$
$740$	1.42227e7	−	3.90765e7i	0.0350983	−	0.0964318i
$741$	4.41825e7	+	7.75322e7i	0.108591	+	0.190558i
$742$	−2.22365e8	−	1.86586e8i	−0.544320	−	0.456738i
$743$	4.65670e8	−	5.54964e8i	1.13530	−	1.35300i	0.208248	−	0.978076i	$-0.433224\pi$
$743$	4.65670e8	−	5.54964e8i	1.13530	−	1.35300i	0.927055	−	0.374925i	$-0.122332\pi$
$744$	−3.03029e8	−	1.77239e8i	−0.735810	−	0.430368i
$745$	−3.06715e6	−	1.11635e6i	−0.00741765	−	0.00269980i
$746$	6.37429e8	+	3.68020e8i	1.53538	+	0.886450i
$747$	6.10631e7	−	3.43429e7i	0.146493	−	0.0823901i
$748$	7.16089e8	+	1.24030e9i	1.71105	+	2.96362i
$749$	1.03977e8	−	1.83340e7i	0.247453	−	0.0436326i
$750$	−2.55594e8	−	2.16936e8i	−0.605853	−	0.514218i
$751$	1.73557e8	−	6.31696e7i	0.409753	−	0.149138i	−0.128916	−	0.991656i	$-0.541150\pi$
$751$	1.73557e8	−	6.31696e7i	0.409753	−	0.149138i	0.538669	+	0.842518i	$0.318927\pi$
$752$	−3.41073e7	−	6.01405e6i	−0.0802037	−	0.0141421i
$753$	3.99395e7	−	1.07838e8i	0.0935445	−	0.252573i
$754$	2.04946e8	−	1.71970e8i	0.478106	−	0.401179i
$755$		−	9.89066e7i		−	0.229818i
$756$	−2.65845e8	−	4.78981e8i	−0.615266	−	1.10854i
$757$	2.52056e6			0.00581044			0.00290522	−	0.999996i	$-0.499075\pi$
$757$	2.52056e6			0.00581044			0.00290522	+	0.999996i	$0.499075\pi$
$758$	2.90751e8	+	3.46503e8i	0.667595	+	0.795609i
$759$	1.00736e8	+	5.90754e8i	0.230388

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)

\(f(q)\)	\(=\)	\(q+(-8.36754 - 9.97205i) q^{2} +(-20.7807 + 17.2384i) q^{3} +(-18.3125 + 103.855i) q^{4} +(-10.7822 - 29.6238i) q^{5} +(345.786 + 62.9829i) q^{6} +(45.8281 + 259.904i) q^{7} +(467.375 - 269.839i) q^{8} +(134.674 - 716.452i) q^{9} +O(q^{10})\)	\(q+(-8.36754 - 9.97205i) q^{2} +(-20.7807 + 17.2384i) q^{3} +(-18.3125 + 103.855i) q^{4} +(-10.7822 - 29.6238i) q^{5} +(345.786 + 62.9829i) q^{6} +(45.8281 + 259.904i) q^{7} +(467.375 - 269.839i) q^{8} +(134.674 - 716.452i) q^{9} +(-205.189 + 355.398i) q^{10} +(556.762 - 1529.69i) q^{11} +(-1409.76 - 2473.87i) q^{12} +(-516.182 - 433.128i) q^{13} +(2208.31 - 2631.76i) q^{14} +(734.728 + 429.735i) q^{15} +(-259.372 - 94.4038i) q^{16} +(7224.90 + 4171.30i) q^{17} +(-8271.39 + 4651.97i) q^{18} +(2452.48 + 4247.82i) q^{19} +(3274.04 - 577.301i) q^{20} +(-5432.67 - 4610.98i) q^{21} +(-19912.9 + 7247.70i) q^{22} +(13427.7 + 2367.66i) q^{23} +(-5060.77 + 13664.2i) q^{24} +(11208.1 - 9404.74i) q^{25} +8771.60i q^{26} +(9551.88 + 17209.9i) q^{27} -27831.7 q^{28} +(-19605.3 - 23364.7i) q^{29} +(-1862.53 - 10922.6i) q^{30} +(-4183.58 + 23726.3i) q^{31} +(-10584.3 - 29080.0i) q^{32} +(14799.6 + 41385.7i) q^{33} +(-18858.3 - 106951. i) q^{34} +(7205.21 - 4159.93i) q^{35} +(71941.3 + 27106.7i) q^{36} +(6254.14 - 10832.5i) q^{37} +(21838.2 - 60000.1i) q^{38} +(18193.0 + 102.540i) q^{39} +(-13033.0 - 10935.9i) q^{40} +(-78828.2 + 93943.8i) q^{41} +(-522.803 + 92757.4i) q^{42} +(75854.4 + 27608.8i) q^{43} +(148671. + 85835.3i) q^{44} +(-22676.1 + 3735.36i) q^{45} +(-88746.1 - 153713. i) q^{46} +(123569. - 21788.6i) q^{47} +(7017.31 - 2509.39i) q^{48} +(45104.1 - 16416.5i) q^{49} +(-187569. - 33073.5i) q^{50} +(-222045. + 37863.4i) q^{51} +(54435.3 - 45676.6i) q^{52} -84492.8i q^{53} +(91692.6 - 239257. i) q^{54} -51318.3 q^{55} +(91551.1 + 109106. i) q^{56} +(-124190. - 45995.7i) q^{57} +(-68945.6 + 391010. i) q^{58} +(-92903.0 - 255249. i) q^{59} +(-58085.0 + 68435.9i) q^{60} +(24350.3 + 138097. i) q^{61} +(271606. - 156812. i) q^{62} +(192381. + 2168.67i) q^{63} +(-210256. + 364173. i) q^{64} +(-7265.32 + 19961.3i) q^{65} +(288865. - 493879. i) q^{66} +(316858. + 265876. i) q^{67} +(-565518. + 673958. i) q^{68} +(-319851. + 182270. i) q^{69} +(-101773. - 37042.3i) q^{70} +(-43295.7 - 24996.8i) q^{71} +(-130384. - 371192. i) q^{72} +(14823.6 + 25675.3i) q^{73} +(-160354. + 28274.7i) q^{74} +(-70789.9 + 388647. i) q^{75} +(-486070. + 176915. i) q^{76} +(423088. + 74601.8i) q^{77} +(-151209. - 182280. i) q^{78} +(720308. - 604410. i) q^{79} +8701.46i q^{80} +(-495167. - 192975. i) q^{81} +1.59641e6 q^{82} +(61772.9 + 73618.1i) q^{83} +(578361. - 479774. i) q^{84} +(45669.5 - 259004. i) q^{85} +(-359399. - 987442. i) q^{86} +(810181. + 147570. i) q^{87} +(-152554. - 865175. i) q^{88} +(-307049. + 177275. i) q^{89} +(226992. + 194871. i) q^{90} +(88916.0 - 154007. i) q^{91} +(-491789. + 1.35118e6i) q^{92} +(-322066. - 565167. i) q^{93} +(-1.25125e6 - 1.04992e6i) q^{94} +(99393.3 - 118452. i) q^{95} +(721241. + 421847. i) q^{96} +(-328801. - 119674. i) q^{97} +(-541117. - 312414. i) q^{98} +(-1.02097e6 - 604903. 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

Introduction

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