LMFDB - Embedded newform 135.3.n.a.74.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(14,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("135.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.n (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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			74.33
Character	$\chi$	$=$	135.74
Dual form			135.3.n.a.104.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.50983 - 1.27747i) q^{2} +(-2.46859 - 1.70472i) q^{3} +(7.62280 - 6.39629i) q^{4} +(-4.44069 - 2.29788i) q^{5} +(-10.8421 - 2.82972i) q^{6} +(-1.03030 + 1.22786i) q^{7} +(11.1135 - 19.2491i) q^{8} +(3.18787 + 8.41650i) q^{9} +(-18.5216 - 2.39229i) q^{10} +(11.9341 + 2.10430i) q^{11} +(-29.7214 + 2.79508i) q^{12} +(4.71168 - 12.9452i) q^{13} +(-2.04761 + 5.62576i) q^{14} +(7.04501 + 13.2427i) q^{15} +(7.50440 - 42.5596i) q^{16} +(8.93265 + 15.4718i) q^{17} +(21.9407 + 25.4681i) q^{18} +(-14.5705 + 25.2368i) q^{19} +(-48.5484 + 10.8877i) q^{20} +(4.63654 - 1.27472i) q^{21} +(44.5747 - 7.85972i) q^{22} +(22.0238 - 18.4801i) q^{23} +(-60.2489 + 28.5728i) q^{24} +(14.4395 + 20.4083i) q^{25} -51.4546i q^{26} +(6.47822 - 26.2113i) q^{27} +15.9498i q^{28} +(-6.96737 - 19.1427i) q^{29} +(41.6440 + 37.4796i) q^{30} +(-5.05373 + 4.24059i) q^{31} +(-12.5909 - 71.4065i) q^{32} +(-25.8730 - 25.5388i) q^{33} +(51.1169 + 42.8922i) q^{34} +(7.39671 - 3.08506i) q^{35} +(78.1349 + 43.7668i) q^{36} +(-33.0454 + 19.0788i) q^{37} +(-18.9005 + 107.190i) q^{38} +(-33.6992 + 23.9244i) q^{39} +(-93.5837 + 59.9420i) q^{40} +(-16.8042 + 46.1691i) q^{41} +(14.6451 - 10.3971i) q^{42} +(-23.8547 - 4.20622i) q^{43} +(104.431 - 60.2930i) q^{44} +(5.18374 - 44.7004i) q^{45} +(53.6918 - 92.9970i) q^{46} +(-5.12070 - 4.29678i) q^{47} +(-91.0774 + 92.2692i) q^{48} +(8.06263 + 45.7255i) q^{49} +(76.7514 + 53.1837i) q^{50} +(4.32402 - 53.4212i) q^{51} +(-46.8852 - 128.816i) q^{52} -35.3575 q^{53} +(-10.7468 - 100.273i) q^{54} +(-48.1601 - 36.7675i) q^{55} +(12.1850 + 33.4781i) q^{56} +(78.9901 - 37.4607i) q^{57} +(-48.9086 - 58.2870i) q^{58} +(81.0242 - 14.2868i) q^{59} +(138.407 + 55.8841i) q^{60} +(-42.3934 - 35.5723i) q^{61} +(-12.3205 + 21.3398i) q^{62} +(-13.6188 - 4.75724i) q^{63} +(-48.9797 - 84.8352i) q^{64} +(-50.6696 + 46.6589i) q^{65} +(-123.435 - 56.5849i) q^{66} +(-10.5187 + 28.8998i) q^{67} +(167.054 + 60.8026i) q^{68} +(-85.8711 + 8.07555i) q^{69} +(22.0201 - 20.2771i) q^{70} +(46.8725 - 27.0619i) q^{71} +(197.438 + 32.1729i) q^{72} +(-80.6986 - 46.5914i) q^{73} +(-91.6111 + 109.178i) q^{74} +(-0.854746 - 74.9951i) q^{75} +(50.3540 + 285.572i) q^{76} +(-14.8794 + 12.4853i) q^{77} +(-87.7156 + 127.020i) q^{78} +(27.1542 - 9.88334i) q^{79} +(-131.121 + 171.750i) q^{80} +(-60.6750 + 53.6614i) q^{81} +183.513i q^{82} +(25.7526 - 9.37318i) q^{83} +(27.1900 - 39.3736i) q^{84} +(-4.11484 - 89.2317i) q^{85} +(-89.0992 + 15.7106i) q^{86} +(-15.4333 + 59.1328i) q^{87} +(173.135 - 206.334i) q^{88} +(41.9166 + 24.2006i) q^{89} +(-38.9096 - 163.513i) q^{90} +(11.0405 + 19.1227i) q^{91} +(49.6785 - 281.741i) q^{92} +(19.7046 - 1.85307i) q^{93} +(-23.4618 - 8.53941i) q^{94} +(122.694 - 78.5876i) q^{95} +(-90.6463 + 197.737i) q^{96} +(-133.103 - 23.4697i) q^{97} +(86.7116 + 150.189i) q^{98} +(20.3334 + 107.151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31}+ \cdots + 792 q^{99}+O(q^{100}) $ 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	3.50983	−	1.27747i	1.75492	−	0.638737i	0.755059	−	0.655657i	$-0.227608\pi$
$2$	3.50983	−	1.27747i	1.75492	−	0.638737i	0.999857	+	0.0169199i	$0.00538603\pi$
$3$	−2.46859	−	1.70472i	−0.822863	−	0.568239i
$3$	−2.46859	−	1.70472i	−0.822863	−	0.568239i
$4$	7.62280	−	6.39629i	1.90570	−	1.59907i
$5$	−4.44069	−	2.29788i	−0.888139	−	0.459576i
$5$	−4.44069	−	2.29788i	−0.888139	−	0.459576i
$6$	−10.8421	−	2.82972i	−1.80701	−	0.471619i
$7$	−1.03030	+	1.22786i	−0.147185	+	0.175409i	−0.834600	−	0.550857i	$-0.814301\pi$
$7$	−1.03030	+	1.22786i	−0.147185	+	0.175409i	0.687415	+	0.726265i	$0.258746\pi$
$8$	11.1135	−	19.2491i	1.38918	−	2.40614i
$9$	3.18787	+	8.41650i	0.354208	+	0.935167i
$10$	−18.5216	−	2.39229i	−1.85216	−	0.239229i
$11$	11.9341	+	2.10430i	1.08491	+	0.191300i	0.687387	−	0.726291i	$-0.258758\pi$
$11$	11.9341	+	2.10430i	1.08491	+	0.191300i	0.397527	+	0.917591i	$0.369869\pi$
$12$	−29.7214	+	2.79508i	−2.47679	+	0.232924i
$13$	4.71168	−	12.9452i	0.362437	−	0.995786i	−0.615729	−	0.787958i	$-0.711138\pi$
$13$	4.71168	−	12.9452i	0.362437	−	0.995786i	0.978165	−	0.207828i	$-0.0666395\pi$
$14$	−2.04761	+	5.62576i	−0.146258	+	0.401840i
$15$	7.04501	+	13.2427i	0.469668	+	0.882843i
$16$	7.50440	−	42.5596i	0.469025	−	2.65997i
$17$	8.93265	+	15.4718i	0.525450	+	0.910106i	0.999561	+	0.0296407i	$0.00943630\pi$
$17$	8.93265	+	15.4718i	0.525450	+	0.910106i	−0.474111	+	0.880465i	$0.657230\pi$
$18$	21.9407	+	25.4681i	1.21893	+	1.41489i
$19$	−14.5705	+	25.2368i	−0.766866	+	1.32825i	0.172388	+	0.985029i	$0.444852\pi$
$19$	−14.5705	+	25.2368i	−0.766866	+	1.32825i	−0.939254	+	0.343222i	$0.888482\pi$
$20$	−48.5484	+	10.8877i	−2.42742	+	0.544384i
$21$	4.63654	−	1.27472i	0.220788	−	0.0607008i
$22$	44.5747	−	7.85972i	2.02612	−	0.357260i
$23$	22.0238	−	18.4801i	0.957555	−	0.803484i	−0.0229985	−	0.999735i	$-0.507321\pi$
$23$	22.0238	−	18.4801i	0.957555	−	0.803484i	0.980554	+	0.196251i	$0.0628769\pi$
$24$	−60.2489	+	28.5728i	−2.51037	+	1.19053i
$25$	14.4395	+	20.4083i	0.577580	+	0.816334i
$26$		−	51.4546i		−	1.97902i
$27$	6.47822	−	26.2113i	0.239934	−	0.970789i
$28$			15.9498i			0.569636i
$29$	−6.96737	−	19.1427i	−0.240254	−	0.660092i	−0.999952	−	0.00981620i	$-0.996875\pi$
$29$	−6.96737	−	19.1427i	−0.240254	−	0.660092i	0.759698	−	0.650276i	$-0.225347\pi$
$30$	41.6440	+	37.4796i	1.38813	+	1.24932i
$31$	−5.05373	+	4.24059i	−0.163024	+	0.136793i	−0.720650	−	0.693299i	$-0.756157\pi$
$31$	−5.05373	+	4.24059i	−0.163024	+	0.136793i	0.557626	+	0.830092i	$0.311712\pi$
$32$	−12.5909	−	71.4065i	−0.393466	−	2.23145i
$33$	−25.8730	−	25.5388i	−0.784032	−	0.773904i
$34$	51.1169	+	42.8922i	1.50344	+	1.26153i
$35$	7.39671	−	3.08506i	0.211335	−	0.0881444i
$36$	78.1349	+	43.7668i	2.17041	+	1.21574i
$37$	−33.0454	+	19.0788i	−0.893118	+	0.515642i	−0.874961	−	0.484193i	$-0.839113\pi$
$37$	−33.0454	+	19.0788i	−0.893118	+	0.515642i	−0.0181570	+	0.999835i	$0.505780\pi$
$38$	−18.9005	+	107.190i	−0.497382	+	2.82080i
$39$	−33.6992	+	23.9244i	−0.864081	+	0.613445i
$40$	−93.5837	+	59.9420i	−2.33959	+	1.49855i
$41$	−16.8042	+	46.1691i	−0.409858	+	1.12608i	0.547408	+	0.836866i	$0.315615\pi$
$41$	−16.8042	+	46.1691i	−0.409858	+	1.12608i	−0.957266	+	0.289210i	$0.906607\pi$
$42$	14.6451	−	10.3971i	0.348692	−	0.247550i
$43$	−23.8547	−	4.20622i	−0.554760	−	0.0978191i	−0.110762	−	0.993847i	$-0.535329\pi$
$43$	−23.8547	−	4.20622i	−0.554760	−	0.0978191i	−0.443998	+	0.896028i	$0.646440\pi$
$44$	104.431	−	60.2930i	2.37342	−	1.37030i
$45$	5.18374	−	44.7004i	0.115194	−	0.993343i
$46$	53.6918	−	92.9970i	1.16721	−	2.02167i
$47$	−5.12070	−	4.29678i	−0.108951	−	0.0914209i	0.586685	−	0.809815i	$-0.300433\pi$
$47$	−5.12070	−	4.29678i	−0.108951	−	0.0914209i	−0.695636	+	0.718395i	$0.744877\pi$
$48$	−91.0774	+	92.2692i	−1.89745	+	1.92228i
$49$	8.06263	+	45.7255i	0.164543	+	0.933173i
$50$	76.7514	+	53.1837i	1.53503	+	1.06367i
$51$	4.32402	−	53.4212i	0.0847847	−	1.04747i
$52$	−46.8852	−	128.816i	−0.901639	−	2.47723i
$53$	−35.3575			−0.667123			−0.333562	−	0.942728i	$-0.608251\pi$
$53$	−35.3575			−0.667123			−0.333562	+	0.942728i	$0.608251\pi$
$54$	−10.7468	−	100.273i	−0.199015	−	1.85691i
$55$	−48.1601	−	36.7675i	−0.875637	−	0.668501i
$56$	12.1850	+	33.4781i	0.217590	+	0.597824i
$57$	78.9901	−	37.4607i	1.38579	−	0.657206i
$58$	−48.9086	−	58.2870i	−0.843251	−	1.00495i
$59$	81.0242	−	14.2868i	1.37329	−	0.242148i	0.562168	−	0.827023i	$-0.309967\pi$
$59$	81.0242	−	14.2868i	1.37329	−	0.242148i	0.811124	+	0.584874i	$0.198856\pi$
$60$	138.407	+	55.8841i	2.30678	+	0.931402i
$61$	−42.3934	−	35.5723i	−0.694974	−	0.583153i	0.225365	−	0.974274i	$-0.427643\pi$
$61$	−42.3934	−	35.5723i	−0.694974	−	0.583153i	−0.920339	+	0.391122i	$0.872087\pi$
$62$	−12.3205	+	21.3398i	−0.198718	+	0.344190i
$63$	−13.6188	−	4.75724i	−0.216171	−	0.0755118i
$64$	−48.9797	−	84.8352i	−0.765307	−	1.32555i
$65$	−50.6696	+	46.6589i	−0.779533	+	0.717829i
$66$	−123.435	−	56.5849i	−1.87023	−	0.857347i
$67$	−10.5187	+	28.8998i	−0.156995	+	0.431340i	−0.993106	−	0.117220i	$-0.962602\pi$
$67$	−10.5187	+	28.8998i	−0.156995	+	0.431340i	0.836111	+	0.548560i	$0.184824\pi$
$68$	167.054	+	60.8026i	2.45667	+	0.894156i
$69$	−85.8711	+	8.07555i	−1.24451	+	0.117037i
$70$	22.0201	−	20.2771i	0.314573	−	0.289673i
$71$	46.8725	−	27.0619i	0.660176	−	0.381153i	−0.132168	−	0.991227i	$-0.542194\pi$
$71$	46.8725	−	27.0619i	0.660176	−	0.381153i	0.792344	+	0.610074i	$0.208860\pi$
$72$	197.438	+	32.1729i	2.74220	+	0.446846i
$73$	−80.6986	−	46.5914i	−1.10546	−	0.638238i	−0.167811	−	0.985819i	$-0.553670\pi$
$73$	−80.6986	−	46.5914i	−1.10546	−	0.638238i	−0.937650	+	0.347581i	$0.887003\pi$
$74$	−91.6111	+	109.178i	−1.23799	+	1.47538i
$75$	−0.854746	−	74.9951i	−0.0113966	−	0.999935i
$76$	50.3540	+	285.572i	0.662553	+	3.75752i
$77$	−14.8794	+	12.4853i	−0.193239	+	0.162147i
$78$	−87.7156	+	127.020i	−1.12456	+	1.62846i
$79$	27.1542	−	9.88334i	0.343725	−	0.125106i	−0.164389	−	0.986396i	$-0.552565\pi$
$79$	27.1542	−	9.88334i	0.343725	−	0.125106i	0.508114	+	0.861290i	$0.330343\pi$
$80$	−131.121	+	171.750i	−1.63902	+	2.14687i
$81$	−60.6750	+	53.6614i	−0.749074	+	0.662487i
$82$			183.513i			2.23796i
$83$	25.7526	−	9.37318i	0.310272	−	0.112930i	−0.182191	−	0.983263i	$-0.558319\pi$
$83$	25.7526	−	9.37318i	0.310272	−	0.112930i	0.492463	+	0.870333i	$0.336097\pi$
$84$	27.1900	−	39.3736i	0.323690	−	0.468733i
$85$	−4.11484	−	89.2317i	−0.0484098	−	1.04978i
$86$	−89.0992	+	15.7106i	−1.03604	+	0.182681i
$87$	−15.4333	+	59.1328i	−0.177394	+	0.679688i
$88$	173.135	−	206.334i	1.96744	−	2.34470i
$89$	41.9166	+	24.2006i	0.470973	+	0.271917i	0.716647	−	0.697436i	$-0.245676\pi$
$89$	41.9166	+	24.2006i	0.470973	+	0.271917i	−0.245674	+	0.969353i	$0.579009\pi$
$90$	−38.9096	−	163.513i	−0.432329	−	1.81681i
$91$	11.0405	+	19.1227i	0.121324	+	0.210140i
$92$	49.6785	−	281.741i	0.539984	−	3.06240i
$93$	19.7046	−	1.85307i	0.211877	−	0.0199255i
$94$	−23.4618	−	8.53941i	−0.249594	−	0.0908448i
$95$	122.694	−	78.5876i	1.29152	−	0.827238i
$96$	−90.6463	+	197.737i	−0.944232	+	2.05976i
$97$	−133.103	−	23.4697i	−1.37220	−	0.241956i	−0.561528	−	0.827458i	$-0.689786\pi$
$97$	−133.103	−	23.4697i	−1.37220	−	0.241956i	−0.810671	+	0.585502i	$0.800897\pi$
$98$	86.7116	+	150.189i	0.884812	+	1.53254i
$99$	20.3334	+	107.151i	0.205388	+	1.08234i
$100$	240.607	+	63.2094i	2.40607	+	0.632094i
$101$	93.6071	−	111.557i	0.926803	−	1.10452i	−0.0674781	−	0.997721i	$-0.521495\pi$
$101$	93.6071	−	111.557i	0.926803	−	1.10452i	0.994281	−	0.106799i	$-0.0340603\pi$
$102$	−53.0676	−	193.023i	−0.520270	−	1.89238i
$103$	13.4708	−	2.37526i	0.130784	−	0.0230608i	−0.107873	−	0.994165i	$-0.534404\pi$
$103$	13.4708	−	2.37526i	0.130784	−	0.0230608i	0.238657	+	0.971104i	$0.423293\pi$
$104$	−196.821	−	234.562i	−1.89251	−	2.25540i
$105$	−23.5186	−	4.99358i	−0.223987	−	0.0475579i
$106$	−124.099	+	45.1683i	−1.17075	+	0.426116i
$107$	−123.329			−1.15261			−0.576306	−	0.817234i	$-0.695506\pi$
$107$	−123.329			−1.15261			−0.576306	+	0.817234i	$0.695506\pi$
$108$	−118.273	−	241.240i	−1.09512	−	2.23370i
$109$	−135.797			−1.24584			−0.622920	−	0.782285i	$-0.714054\pi$
$109$	−135.797			−1.24584			−0.622920	+	0.782285i	$0.714054\pi$
$110$	−216.003	−	67.5246i	−1.96367	−	0.613860i
$111$	114.099	+	9.23544i	1.02792	+	0.0832022i
$112$	44.5255	+	53.0634i	0.397549	+	0.473780i
$113$	16.9029	+	95.8613i	0.149584	+	0.848330i	0.963572	+	0.267449i	$0.0861808\pi$
$113$	16.9029	+	95.8613i	0.149584	+	0.848330i	−0.813988	+	0.580881i	$0.802708\pi$
$114$	229.387	−	232.389i	2.01217	−	2.03850i
$115$	−140.266	+	31.4567i	−1.21970	+	0.273536i
$116$	−175.553	−	101.356i	−1.51339	−	0.873755i
$117$	123.974	−	1.61186i	1.05960	−	0.0137766i
$118$	266.130	−	153.650i	2.25534	−	1.30212i
$119$	−28.2005	−	4.97251i	−0.236979	−	0.0417858i
$120$	333.204	+	11.5617i	2.77670	+	0.0963472i
$121$	24.2908	+	8.84111i	0.200750	+	0.0730671i
$122$	−194.236	−	70.6963i	−1.59210	−	0.579478i
$123$	120.188	−	85.3262i	0.977138	−	0.693709i
$124$	−11.3996	+	64.6503i	−0.0919322	+	0.521373i
$125$	−17.2255	−	123.807i	−0.137804	−	0.990459i
$126$	−53.8768	+	0.700487i	−0.427593	+	0.00555942i
$127$	192.478	+	111.127i	1.51558	+	0.875019i	0.999833	+	0.0182767i	$0.00581798\pi$
$127$	192.478	+	111.127i	1.51558	+	0.875019i	0.515745	+	0.856742i	$0.327515\pi$
$128$	−58.1075	−	48.7580i	−0.453965	−	0.380922i
$129$	51.7169	+	51.0489i	0.400907	+	0.395728i
$130$	−118.236	+	228.494i	−0.909511	+	1.75765i
$131$	10.0305	+	11.9539i	0.0765690	+	0.0912514i	0.802969	−	0.596021i	$-0.203252\pi$
$131$	10.0305	+	11.9539i	0.0765690	+	0.0912514i	−0.726400	+	0.687272i	$0.758808\pi$
$132$	−360.579	−	29.1860i	−2.73166	−	0.221106i
$133$	−15.9753	−	43.8919i	−0.120115	−	0.330014i
$134$			114.871i			0.857245i
$135$	−88.9982	+	101.510i	−0.659246	+	0.751927i
$136$	397.091			2.91979
$137$	−6.93037	+	2.52245i	−0.0505867	+	0.0184120i	−0.367190	−	0.930146i	$-0.619680\pi$
$137$	−6.93037	+	2.52245i	−0.0505867	+	0.0184120i	0.316603	+	0.948558i	$0.397458\pi$
$138$	−291.077	+	138.042i	−2.10925	+	1.00030i
$139$	114.438	−	96.0245i	0.823292	−	0.690824i	−0.130449	−	0.991455i	$-0.541642\pi$
$139$	114.438	−	96.0245i	0.823292	−	0.690824i	0.953740	+	0.300631i	$0.0971974\pi$
$140$	36.6507	−	70.8283i	0.261791	−	0.505916i
$141$	5.31612	+	19.3363i	0.0377029	+	0.137137i
$142$	129.944	−	154.861i	0.915097	−	1.09057i
$143$	83.4700	−	144.574i	0.583706	−	1.01101i
$144$	382.126	−	72.5136i	2.65365	−	0.503567i
$145$	−13.0476	+	101.017i	−0.0899836	+	0.696669i
$146$	−342.758	−	60.4375i	−2.34766	−	0.413955i
$147$	58.0457	−	126.622i	0.394869	−	0.861373i
$148$	−129.865	+	356.801i	−0.877466	+	2.41082i
$149$	−74.0973	+	203.581i	−0.497297	+	1.36631i	0.396579	+	0.918000i	$0.370197\pi$
$149$	−74.0973	+	203.581i	−0.497297	+	1.36631i	−0.893877	+	0.448313i	$0.852025\pi$
$150$	−98.8044	−	262.128i	−0.658696	−	1.74752i
$151$	2.21211	−	12.5455i	0.0146497	−	0.0830828i	−0.976606	−	0.215035i	$-0.931013\pi$
$151$	2.21211	−	12.5455i	0.0146497	−	0.0830828i	0.991256	+	0.131952i	$0.0421245\pi$
$152$	323.857	+	560.937i	2.13064	+	3.69037i
$153$	−101.742	+	124.504i	−0.664982	+	0.813750i
$154$	−36.2746	+	62.8294i	−0.235549	+	0.407983i
$155$	32.1864	−	7.21828i	0.207654	−	0.0465695i
$156$	−103.855	+	397.920i	−0.665736	+	2.55077i
$157$	85.3324	−	15.0464i	0.543519	−	0.0958370i	0.104854	−	0.994488i	$-0.466563\pi$
$157$	85.3324	−	15.0464i	0.543519	−	0.0958370i	0.438665	+	0.898651i	$0.355451\pi$
$158$	82.6811	−	69.3777i	0.523298	−	0.439099i
$159$	87.2832	+	60.2746i	0.548951	+	0.379086i
$160$	−108.171	+	346.027i	−0.676070	+	2.16267i
$161$			46.0822i			0.286225i
$162$	−144.408	+	265.853i	−0.891406	+	1.64107i
$163$			44.5111i			0.273075i	0.990635	+	0.136537i	$0.0435973\pi$
$163$			44.5111i			0.273075i	−0.990635	+	0.136537i	$0.956403\pi$
$164$	167.216	+	459.422i	1.01961	+	2.80136i
$165$	56.2091	+	172.863i	0.340661	+	1.04766i
$166$	78.4133	−	65.7965i	0.472369	−	0.396365i
$167$	−11.7528	−	66.6535i	−0.0703761	−	0.399123i	−0.999564	−	0.0295159i	$-0.990603\pi$
$167$	−11.7528	−	66.6535i	−0.0703761	−	0.399123i	0.929188	−	0.369607i	$-0.120508\pi$
$168$	26.9909	−	103.416i	0.160660	−	0.615570i
$169$	−15.9174	−	13.3563i	−0.0941856	−	0.0790311i
$170$	−128.434	−	307.931i	−0.755491	−	1.81136i
$171$	−258.854	−	42.1807i	−1.51377	−	0.246671i
$172$	−208.743	+	120.518i	−1.21362	+	0.700687i
$173$	1.72745	−	9.79683i	0.00998523	−	0.0566291i	−0.979408	−	0.201891i	$-0.935291\pi$
$173$	1.72745	−	9.79683i	0.00998523	−	0.0566291i	0.989393	+	0.145262i	$0.0464025\pi$
$174$	21.3723	+	227.262i	0.122829	+	1.30610i
$175$	−39.9356	−	3.29696i	−0.228203	−	0.0188398i
$176$	179.116	−	492.117i	1.01770	−	2.79612i
$177$	−224.370	−	102.855i	−1.26763	−	0.581104i
$178$	178.036	+	31.3925i	1.00020	+	0.176363i
$179$	183.909	−	106.180i	1.02743	−	0.593184i	0.111179	−	0.993800i	$-0.464537\pi$
$179$	183.909	−	106.180i	1.02743	−	0.593184i	0.916246	+	0.400616i	$0.131204\pi$
$180$	−246.402	−	373.899i	−1.36890	−	2.07722i
$181$	−76.4143	+	132.353i	−0.422178	+	0.731234i	−0.996152	−	0.0876392i	$-0.972068\pi$
$181$	−76.4143	+	132.353i	−0.422178	+	0.731234i	0.573974	+	0.818874i	$0.305401\pi$
$182$	63.1791	+	53.0136i	0.347138	+	0.291283i
$183$	44.0112	+	160.082i	0.240498	+	0.874767i
$184$	−110.965	−	629.316i	−0.603073	−	3.42020i
$185$	190.585	−	8.78865i	1.03019	−	0.0475062i
$186$	66.7926	−	31.6761i	0.359100	−	0.170302i
$187$	74.0455	+	203.438i	0.395965	+	1.08790i
$188$	−66.5175			−0.353817
$189$	25.5093	+	34.9598i	0.134970	+	0.184973i
$190$	330.242	−	432.568i	1.73811	−	2.27667i
$191$	25.7878	+	70.8514i	0.135015	+	0.370950i	0.988714	−	0.149817i	$-0.0478684\pi$
$191$	25.7878	+	70.8514i	0.135015	+	0.370950i	−0.853699	+	0.520767i	$0.825646\pi$
$192$	−23.7095	+	292.920i	−0.123487	+	1.52562i
$193$	−86.3157	−	102.867i	−0.447231	−	0.532990i	0.494580	−	0.869132i	$-0.335322\pi$
$193$	−86.3157	−	102.867i	−0.447231	−	0.532990i	−0.941811	+	0.336143i	$0.890878\pi$
$194$	−497.152	+	87.6613i	−2.56264	+	0.451862i
$195$	204.623	−	28.8042i	1.04935	−	0.147714i
$196$	353.933	+	296.985i	1.80578	+	1.51523i
$197$	−34.3090	+	59.4249i	−0.174157	+	0.301649i	−0.939869	−	0.341534i	$-0.889053\pi$
$197$	−34.3090	+	59.4249i	−0.174157	+	0.301649i	0.765712	+	0.643184i	$0.222387\pi$
$198$	208.250	+	350.107i	1.05177	+	1.76822i
$199$	30.4787	+	52.7906i	0.153159	+	0.265279i	0.932387	−	0.361461i	$-0.117722\pi$
$199$	30.4787	+	52.7906i	0.153159	+	0.265279i	−0.779228	+	0.626740i	$0.784389\pi$
$200$	553.316	−	51.1400i	2.76658	−	0.255700i
$201$	75.2323	−	53.4104i	0.374290	−	0.265723i
$202$	186.034	−	511.125i	0.920962	−	2.53032i
$203$	30.6830	+	11.1677i	0.151148	+	0.0550133i
$204$	−308.736	−	434.877i	−1.51341	−	2.13175i
$205$	180.713	−	166.409i	0.881528	−	0.811751i
$206$	44.2458	−	25.5453i	0.214785	−	0.124006i
$207$	225.747	+	126.451i	1.09057	+	0.610873i
$208$	−515.585	−	297.673i	−2.47877	−	1.43112i
$209$	−226.990	+	270.517i	−1.08608	+	1.29434i
$210$	−88.9255	+	12.5178i	−0.423455	+	0.0596085i
$211$	−65.8918	−	373.691i	−0.312284	−	1.77105i	−0.587064	−	0.809541i	$-0.699716\pi$
$211$	−65.8918	−	373.691i	−0.312284	−	1.77105i	0.274780	−	0.961507i	$-0.411395\pi$
$212$	−269.523	+	226.157i	−1.27134	+	1.06678i
$213$	−161.842	−	13.0998i	−0.759821	−	0.0615015i
$214$	−432.866	+	157.550i	−2.02274	+	0.736216i
$215$	96.2659	+	73.4936i	0.447748	+	0.341831i
$216$	−432.549	−	415.999i	−2.00254	−	1.92592i
$217$		−	10.5744i		−	0.0487297i
$218$	−476.623	+	173.477i	−2.18634	+	0.795764i
$219$	119.787	+	252.583i	0.546971	+	1.15335i
$220$	−602.290	+	27.7741i	−2.73768	+	0.126246i
$221$	242.374	−	42.7370i	1.09671	−	0.193380i
$222$	412.268	−	113.344i	1.85706	−	0.510559i
$223$	−192.748	+	229.708i	−0.864339	+	1.03008i	0.134891	+	0.990860i	$0.456932\pi$
$223$	−192.748	+	229.708i	−0.864339	+	1.03008i	−0.999231	+	0.0392192i	$0.987513\pi$
$224$	100.650	+	58.1101i	0.449329	+	0.259420i
$225$	−125.736	+	186.589i	−0.558825	+	0.829286i
$226$	181.787	+	314.864i	0.804367	+	1.39320i
$227$	−20.9629	+	118.887i	−0.0923476	+	0.523729i	0.903180	+	0.429261i	$0.141226\pi$
$227$	−20.9629	+	118.887i	−0.0923476	+	0.523729i	−0.995528	+	0.0944679i	$0.969885\pi$
$228$	362.516	−	790.799i	1.58998	−	3.46842i
$229$	175.173	+	63.7578i	0.764948	+	0.278418i	0.694882	−	0.719124i	$-0.255457\pi$
$229$	175.173	+	63.7578i	0.764948	+	0.278418i	0.0700666	+	0.997542i	$0.477679\pi$
$230$	−452.125	+	289.594i	−1.96576	+	1.25910i
$231$	58.0151	−	5.45590i	0.251148	−	0.0236186i
$232$	−445.911	−	78.6262i	−1.92203	−	0.338906i
$233$	−73.0177	−	126.470i	−0.313381	−	0.542791i	0.665711	−	0.746209i	$-0.268128\pi$
$233$	−73.0177	−	126.470i	−0.313381	−	0.542791i	−0.979092	+	0.203418i	$0.934795\pi$
$234$	433.068	−	164.031i	1.85072	−	0.700985i
$235$	12.8660	+	30.8474i	0.0547489	+	0.131266i
$236$	526.249	−	627.159i	2.22987	−	2.65746i
$237$	−83.8810	−	21.8924i	−0.353928	−	0.0923732i
$238$	−105.331	+	18.5727i	−0.442568	+	0.0780368i
$239$	−135.434	−	161.404i	−0.566668	−	0.675329i	0.404275	−	0.914637i	$-0.367524\pi$
$239$	−135.434	−	161.404i	−0.566668	−	0.675329i	−0.970944	+	0.239308i	$0.923079\pi$
$240$	616.470	−	200.455i	2.56863	−	0.835228i
$241$	73.8445	−	26.8772i	0.306409	−	0.111524i	−0.184240	−	0.982881i	$-0.558982\pi$
$241$	73.8445	−	26.8772i	0.306409	−	0.111524i	0.490648	+	0.871358i	$0.336760\pi$
$242$	96.5508			0.398970
$243$	241.259	−	29.0343i	0.992836	−	0.119483i
$244$	−550.687			−2.25691
$245$	69.2679	−	221.580i	0.282726	−	0.904407i
$246$	312.838	−	453.018i	1.27170	−	1.84153i
$247$	258.044	+	307.525i	1.04471	+	1.24504i
$248$	25.4629	+	144.408i	0.102673	+	0.582288i
$249$	−79.5512	−	20.7624i	−0.319483	−	0.0833831i
$250$	−218.620	−	412.538i	−0.874478	−	1.65015i
$251$	−28.4525	−	16.4271i	−0.113357	−	0.0654465i	0.442250	−	0.896892i	$-0.354180\pi$
$251$	−28.4525	−	16.4271i	−0.113357	−	0.0654465i	−0.555606	+	0.831445i	$0.687514\pi$
$252$	−134.242	+	50.8460i	−0.532705	+	0.201770i
$253$	301.720	−	174.198i	1.19257	−	0.688531i
$254$	817.529	+	144.152i	3.21862	+	0.567529i
$255$	−141.957	+	227.291i	−0.556694	+	0.891337i
$256$	101.972	+	37.1147i	0.398328	+	0.144979i
$257$	−267.150	−	97.2345i	−1.03949	−	0.378344i	−0.234805	−	0.972043i	$-0.575445\pi$
$257$	−267.150	−	97.2345i	−1.03949	−	0.378344i	−0.804688	+	0.593698i	$0.797667\pi$
$258$	246.731	+	113.106i	0.956323	+	0.438395i
$259$	10.6205	−	60.2319i	0.0410058	−	0.232556i
$260$	−87.8008	+	679.769i	−0.337695	+	2.61450i
$261$	138.903	−	119.665i	0.532197	−	0.458487i
$262$	50.4763	+	29.1425i	0.192658	+	0.111231i
$263$	−219.036	−	183.793i	−0.832838	−	0.698834i	0.123102	−	0.992394i	$-0.460716\pi$
$263$	−219.036	−	183.793i	−0.832838	−	0.698834i	−0.955941	+	0.293560i	$0.905160\pi$
$264$	−779.140	+	214.208i	−2.95129	+	0.811393i
$265$	157.012	+	81.2473i	0.592498	+	0.306594i
$266$	−112.142	−	133.645i	−0.421585	−	0.502425i
$267$	−62.2198	−	131.197i	−0.233033	−	0.491376i
$268$	104.670	+	287.578i	0.390559	+	1.07305i
$269$		−	143.973i		−	0.535215i	−0.963528	−	0.267607i	$-0.913767\pi$
$269$		−	143.973i		−	0.535215i	0.963528	−	0.267607i	$-0.0862330\pi$
$270$	−182.692	+	469.977i	−0.676637	+	1.74065i
$271$	−386.716			−1.42699			−0.713497	−	0.700658i	$-0.752890\pi$
$271$	−386.716			−1.42699			−0.713497	+	0.700658i	$0.752890\pi$
$272$	725.508	−	264.063i	2.66731	−	0.970820i
$273$	5.34437	−	66.0271i	0.0195764	−	0.241857i
$274$	−21.1021	+	17.7068i	−0.0770149	+	0.0646232i
$275$	129.377	+	273.939i	0.470461	+	0.996143i
$276$	−602.924	+	610.814i	−2.18451	+	2.21310i
$277$	−132.179	+	157.524i	−0.477179	+	0.568680i	−0.949909	−	0.312528i	$-0.898824\pi$
$277$	−132.179	+	157.524i	−0.477179	+	0.568680i	0.472730	+	0.881208i	$0.343269\pi$
$278$	278.988	−	483.221i	1.00355	−	1.73820i
$279$	−51.8015	−	29.0163i	−0.185669	−	0.104001i
$280$	22.8186	−	176.666i	0.0814951	−	0.630949i
$281$	−498.789	−	87.9499i	−1.77505	−	0.312989i	−0.812271	−	0.583280i	$-0.801769\pi$
$281$	−498.789	−	87.9499i	−1.77505	−	0.312989i	−0.962779	+	0.270291i	$0.912880\pi$
$282$	43.3604	+	61.0761i	0.153760	+	0.216582i
$283$	146.487	−	402.471i	0.517623	−	1.42216i	−0.355508	−	0.934673i	$-0.615692\pi$
$283$	146.487	−	402.471i	0.517623	−	1.42216i	0.873131	−	0.487485i	$-0.162086\pi$
$284$	184.204	−	506.097i	0.648607	−	1.78203i
$285$	−436.851	−	15.1581i	−1.53281	−	0.0531862i
$286$	108.276	−	614.062i	0.378586	−	2.14707i
$287$	−39.3759	−	68.2011i	−0.137198	−	0.237635i
$288$	560.855	−	333.606i	1.94741	−	1.15835i
$289$	−15.0844	+	26.1269i	−0.0521952	+	0.0904047i
$290$	83.2516	+	371.220i	0.287074	+	1.28007i
$291$	288.568	+	284.841i	0.991643	+	0.978834i
$292$	−913.161	+	161.015i	−3.12726	+	0.551421i
$293$	258.409	−	216.831i	0.881942	−	0.740037i	−0.0846357	−	0.996412i	$-0.526973\pi$
$293$	258.409	−	216.831i	0.881942	−	0.740037i	0.966577	+	0.256375i	$0.0825282\pi$
$294$	41.9744	−	518.573i	0.142770	−	1.76386i
$295$	−392.633	−	122.741i	−1.33096	−	0.416070i
$296$			848.125i			2.86529i
$297$	132.468	−	299.175i	0.446019	−	1.00732i
$298$			809.191i			2.71541i
$299$	−135.461	−	372.175i	−0.453046	−	1.24473i
$300$	−486.206	−	566.206i	−1.62069	−	1.88735i
$301$	29.7421	−	24.9566i	0.0988108	−	0.0829121i
$302$	−8.26242	−	46.8585i	−0.0273590	−	0.155161i
$303$	−421.250	+	115.814i	−1.39026	+	0.382223i
$304$	964.724	+	809.500i	3.17343	+	2.66283i
$305$	106.515	+	255.381i	0.349231	+	0.837313i
$306$	−198.048	+	566.960i	−0.647216	+	1.85281i
$307$	−90.5911	+	52.3028i	−0.295085	+	0.170367i	−0.640233	−	0.768181i	$-0.721162\pi$
$307$	−90.5911	+	52.3028i	−0.295085	+	0.170367i	0.345148	+	0.938548i	$0.387829\pi$
$308$	−33.5631	+	190.346i	−0.108971	+	0.618007i
$309$	−37.3030	−	17.1003i	−0.120722	−	0.0553409i
$310$	103.748	−	66.4523i	0.334670	−	0.214362i
$311$	−124.512	+	342.094i	−0.400360	+	1.09998i	0.561748	+	0.827309i	$0.310129\pi$
$311$	−124.512	+	342.094i	−0.400360	+	1.09998i	−0.962107	+	0.272671i	$0.912093\pi$
$312$	86.0078	+	914.561i	0.275666	+	2.93129i
$313$	−259.852	−	45.8188i	−0.830197	−	0.146386i	−0.257629	−	0.966244i	$-0.582941\pi$
$313$	−259.852	−	45.8188i	−0.830197	−	0.146386i	−0.572567	+	0.819858i	$0.694052\pi$
$314$	280.281	−	161.820i	0.892615	−	0.515351i
$315$	49.5451	+	52.4197i	0.157286	+	0.166412i
$316$	143.775	−	249.025i	0.454983	−	0.788054i
$317$	−319.270	−	267.899i	−1.00716	−	0.845107i	−0.0191996	−	0.999816i	$-0.506112\pi$
$317$	−319.270	−	267.899i	−1.00716	−	0.845107i	−0.987960	+	0.154708i	$0.950556\pi$
$318$	383.349	+	100.052i	1.20550	+	0.314628i
$319$	−42.8671	−	243.111i	−0.134380	−	0.762104i
$320$	22.5625	+	489.277i	0.0705079	+	1.52899i
$321$	304.450	+	210.242i	0.948442	+	0.654959i
$322$	58.8688	+	161.741i	0.182822	+	0.502300i
$323$	−520.611			−1.61180
$324$	−119.279	+	797.145i	−0.368146	+	2.46032i
$325$	332.225	−	90.7652i	1.02223	−	0.279277i
$326$	56.8618	+	156.227i	0.174423	+	0.479223i
$327$	335.226	+	231.495i	1.02516	+	0.707936i
$328$	701.961	+	836.565i	2.14013	+	2.55050i
$329$	10.5517	−	1.86055i	0.0320720	−	0.00565517i
$330$	418.113	+	534.915i	1.26701	+	1.62096i
$331$	−55.6735	−	46.7156i	−0.168198	−	0.141135i	0.554803	−	0.831982i	$-0.312793\pi$
$331$	−55.6735	−	46.7156i	−0.168198	−	0.141135i	−0.723001	+	0.690847i	$0.757238\pi$
$332$	136.353	−	236.171i	0.410703	−	0.711358i
$333$	−265.921	−	217.306i	−0.798561	−	0.652570i
$334$	−126.399	−	218.929i	−0.378439	−	0.655475i
$335$	113.118	−	104.165i	0.337667	−	0.310939i
$336$	−19.4570	−	206.895i	−0.0579077	−	0.615760i
$337$	30.3392	−	83.3563i	0.0900273	−	0.247348i	−0.886505	−	0.462719i	$-0.846874\pi$
$337$	30.3392	−	83.3563i	0.0900273	−	0.247348i	0.976532	+	0.215371i	$0.0690961\pi$
$338$	−72.9296	−	26.5442i	−0.215768	−	0.0785331i
$339$	121.690	−	265.457i	0.358968	−	0.783059i
$340$	−602.118	−	653.875i	−1.77093	−	1.92316i
$341$	−69.2350	+	39.9728i	−0.203035	+	0.117222i
$342$	−962.419	+	182.632i	−2.81409	+	0.534012i
$343$	−132.469	−	76.4811i	−0.386207	−	0.222977i
$344$	−346.074	+	412.435i	−1.00603	+	1.19894i
$345$	399.884	+	161.460i	1.15908	+	0.468001i
$346$	−6.45215	−	36.5920i	−0.0186478	−	0.105757i
$347$	305.192	−	256.086i	0.879515	−	0.738001i	−0.0865644	−	0.996246i	$-0.527589\pi$
$347$	305.192	−	256.086i	0.879515	−	0.738001i	0.966079	+	0.258246i	$0.0831444\pi$
$348$	260.586	+	549.474i	0.748809	+	1.57895i
$349$	414.030	−	150.695i	1.18633	−	0.431790i	0.327899	−	0.944713i	$-0.393660\pi$
$349$	414.030	−	150.695i	1.18633	−	0.431790i	0.858435	+	0.512923i	$0.171437\pi$
$350$	−144.379	+	39.4449i	−0.412512	+	0.112700i
$351$	−308.788	−	207.361i	−0.879738	−	0.590773i
$352$		−	878.664i		−	2.49621i
$353$	361.633	−	131.624i	1.02446	−	0.372871i	0.225488	−	0.974246i	$-0.427602\pi$
$353$	361.633	−	131.624i	1.02446	−	0.372871i	0.798967	+	0.601375i	$0.205380\pi$
$354$	−918.898	−	74.3775i	−2.59576	−	0.210106i
$355$	−270.331	+	12.4661i	−0.761497	+	0.0351157i
$356$	474.316	−	83.6347i	1.33235	−	0.234929i
$357$	61.1388	+	60.3490i	0.171257	+	0.169045i
$358$	509.848	−	607.613i	1.42416	−	1.69724i
$359$	88.2741	+	50.9651i	0.245889	+	0.141964i	0.617880	−	0.786272i	$-0.287992\pi$
$359$	88.2741	+	50.9651i	0.245889	+	0.141964i	−0.371991	+	0.928236i	$0.621325\pi$
$360$	−802.834	−	596.560i	−2.23009	−	1.65711i
$361$	−244.097	−	422.788i	−0.676168	−	1.17116i
$362$	−99.1232	+	562.155i	−0.273821	+	1.55292i
$363$	−44.8923	−	63.2340i	−0.123670	−	0.174198i
$364$	206.474	+	75.1504i	0.567236	+	0.206457i
$365$	251.297	+	392.334i	0.688484	+	1.07489i
$366$	358.973	+	505.639i	0.980800	+	1.38153i
$367$	513.441	+	90.5336i	1.39902	+	0.246686i	0.821742	−	0.569860i	$-0.193003\pi$
$367$	513.441	+	90.5336i	1.39902	+	0.246686i	0.577281	+	0.816545i	$0.304114\pi$
$368$	−621.232	−	1076.00i	−1.68813	−	2.92393i
$369$	−442.152	+	5.74870i	−1.19824	+	0.0155791i
$370$	657.694	−	274.314i	1.77755	−	0.741389i
$371$	36.4288	−	43.4141i	0.0981908	−	0.117019i
$372$	138.351	−	140.162i	0.371912	−	0.376779i
$373$	−62.8021	+	11.0737i	−0.168370	+	0.0296882i	−0.257198	−	0.966359i	$-0.582799\pi$
$373$	−62.8021	+	11.0737i	−0.168370	+	0.0296882i	0.0888274	+	0.996047i	$0.471688\pi$
$374$	519.774	+	619.443i	1.38977	+	1.65626i
$375$	−168.534	+	334.994i	−0.449424	+	0.893319i
$376$	−139.618	+	50.8168i	−0.371325	+	0.135151i
$377$	−280.634			−0.744388
$378$	134.194	+	90.1155i	0.355010	+	0.238401i
$379$	270.107			0.712684			0.356342	−	0.934356i	$-0.384024\pi$
$379$	270.107			0.712684			0.356342	+	0.934356i	$0.384024\pi$
$380$	432.602	−	1383.84i	1.13843	−	3.64169i
$381$	−285.709	−	602.449i	−0.749893	−	1.58123i
$382$	181.022	+	215.733i	0.473879	+	0.564746i
$383$	5.06194	+	28.7077i	0.0132165	+	0.0749547i	0.990703	−	0.136045i	$-0.0434392\pi$
$383$	5.06194	+	28.7077i	0.0132165	+	0.0749547i	−0.977486	+	0.211000i	$0.932328\pi$
$384$	60.3250	+	219.420i	0.157096	+	0.571407i
$385$	94.7646	−	21.2523i	0.246142	−	0.0552009i
$386$	−434.363	−	250.780i	−1.12529	−	0.649689i
$387$	−40.6439	−	214.182i	−0.105023	−	0.553441i
$388$	−1164.74	+	672.462i	−3.00190	+	1.73315i
$389$	−497.062	−	87.6455i	−1.27780	−	0.225310i	−0.506752	−	0.862092i	$-0.669154\pi$
$389$	−497.062	−	87.6455i	−1.27780	−	0.225310i	−0.771044	+	0.636782i	$0.780265\pi$
$390$	681.395	−	362.498i	1.74717	−	0.929483i
$391$	482.652	+	175.671i	1.23440	+	0.449286i
$392$	969.778	+	352.970i	2.47392	+	0.900435i
$393$	−4.38320	−	46.6086i	−0.0111532	−	0.118597i
$394$	−44.5050	+	252.400i	−0.112957	+	0.640610i
$395$	−143.294	−	18.5083i	−0.362771	−	0.0468564i
$396$	840.367	+	686.734i	2.12214	+	1.73418i
$397$	172.126	+	99.3771i	0.433567	+	0.250320i	0.700865	−	0.713294i	$-0.252797\pi$
$397$	172.126	+	99.3771i	0.433567	+	0.250320i	−0.267298	+	0.963614i	$0.586131\pi$
$398$	174.414	+	146.350i	0.438225	+	0.367715i
$399$	−35.3868	+	135.585i	−0.0886886	+	0.339811i
$400$	976.930	−	461.387i	2.44233	−	1.15347i
$401$	243.584	+	290.292i	0.607440	+	0.723919i	0.978857	−	0.204547i	$-0.0655722\pi$
$401$	243.584	+	290.292i	0.607440	+	0.723919i	−0.371416	+	0.928466i	$0.621128\pi$
$402$	195.822	−	283.569i	0.487120	−	0.705395i
$403$	31.0838	+	85.4020i	0.0771310	+	0.211916i
$404$		−	1449.11i		−	3.58691i
$405$	392.746	−	98.8702i	0.969744	−	0.244124i
$406$	121.959			0.300391
$407$	−434.513	+	158.150i	−1.06760	+	0.388574i
$408$	−980.255	−	676.929i	−2.40259	−	1.65914i
$409$	126.040	−	105.760i	0.308167	−	0.258583i	−0.475567	−	0.879680i	$-0.657757\pi$
$409$	126.040	−	105.760i	0.308167	−	0.258583i	0.783734	+	0.621097i	$0.213313\pi$
$410$	421.690	−	814.924i	1.02851	−	1.98762i
$411$	21.4083	+	5.58744i	0.0520884	+	0.0135948i
$412$	87.4921	−	104.269i	0.212360	−	0.253080i
$413$	−65.9369	+	114.206i	−0.159654	+	0.276528i
$414$	953.871	+	155.435i	2.30404	+	0.375447i
$415$	−135.898	−	17.5529i	−0.327465	−	0.0422962i
$416$	−983.697	−	173.452i	−2.36466	−	0.416953i
$417$	−446.194	+	41.9613i	−1.07001	+	0.100627i
$418$	−451.120	+	1239.44i	−1.07923	+	2.96517i
$419$	166.490	−	457.429i	0.397352	−	1.09172i	−0.566217	−	0.824256i	$-0.691594\pi$
$419$	166.490	−	457.429i	0.397352	−	1.09172i	0.963569	−	0.267460i	$-0.0861842\pi$
$420$	−211.218	+	112.367i	−0.502900	+	0.267540i
$421$	−109.527	+	621.157i	−0.260159	+	1.47543i	0.522317	+	0.852751i	$0.325068\pi$
$421$	−109.527	+	621.157i	−0.260159	+	1.47543i	−0.782476	+	0.622681i	$0.786043\pi$
$422$	−708.650	−	1227.42i	−1.67927	−	2.90857i
$423$	19.8397	−	56.7960i	0.0469024	−	0.134269i
$424$	−392.945	+	680.601i	−0.926757	+	1.60519i
$425$	−186.771	+	405.706i	−0.439461	+	0.954602i
$426$	−584.772	+	160.771i	−1.37271	+	0.377396i
$427$	87.3557	−	15.4032i	0.204580	−	0.0360730i
$428$	−940.116	+	788.851i	−2.19653	+	1.84311i
$429$	−452.511	+	214.602i	−1.05481	+	0.500237i
$430$	431.763	+	134.973i	1.00410	+	0.313891i
$431$		−	538.952i		−	1.25047i	−0.780437	−	0.625235i	$-0.785003\pi$
$431$		−	538.952i		−	1.25047i	0.780437	−	0.625235i	$-0.214997\pi$
$432$	−1066.93	−	472.411i	−2.46974	−	1.09354i
$433$		−	142.952i		−	0.330144i	−0.986282	−	0.165072i	$-0.947214\pi$
$433$		−	142.952i		−	0.330144i	0.986282	−	0.165072i	$-0.0527856\pi$
$434$	−13.5085	−	37.1142i	−0.0311255	−	0.0855166i
$435$	204.415	−	227.127i	0.469919	−	0.522131i
$436$	−1035.15	+	868.594i	−2.37420	+	1.99219i
$437$	145.483	+	825.073i	0.332912	+	1.88804i
$438$	743.100	+	733.501i	1.69657	+	1.67466i
$439$	120.959	+	101.496i	0.275532	+	0.231199i	0.770074	−	0.637955i	$-0.220219\pi$
$439$	120.959	+	101.496i	0.275532	+	0.231199i	−0.494541	+	0.869154i	$0.664664\pi$
$440$	−1242.97	+	518.423i	−2.82493	+	1.17823i
$441$	−359.146	+	213.626i	−0.814389	+	0.484413i
$442$	796.095	−	459.626i	1.80112	−	1.03988i
$443$	33.6677	−	190.939i	0.0759993	−	0.431013i	−0.922939	−	0.384946i	$-0.874220\pi$
$443$	33.6677	−	190.939i	0.0759993	−	0.431013i	0.998938	−	0.0460672i	$-0.0146688\pi$
$444$	928.829	−	659.412i	2.09196	−	1.48516i
$445$	−130.529	−	203.787i	−0.293323	−	0.457947i
$446$	−383.066	+	1052.47i	−0.858893	+	2.35979i
$447$	529.964	−	376.242i	1.18560	−	0.841705i
$448$	154.630	+	27.2654i	0.345155	+	0.0608602i
$449$	−34.7894	+	20.0857i	−0.0774820	+	0.0447343i	−0.538240	−	0.842791i	$-0.680911\pi$
$449$	−34.7894	+	20.0857i	−0.0774820	+	0.0447343i	0.460758	+	0.887526i	$0.347577\pi$
$450$	−202.948	+	815.521i	−0.450995	+	1.81227i
$451$	−297.695	+	515.624i	−0.660079	+	1.14329i
$452$	742.004	+	622.616i	1.64160	+	1.37747i
$453$	−26.8474	+	27.1987i	−0.0592657	+	0.0600412i
$454$	78.2982	+	444.051i	0.172463	+	0.978087i
$455$	−5.08582	−	110.288i	−0.0111776	−	0.242391i
$456$	156.769	−	1936.81i	0.343792	−	4.24739i
$457$	75.2035	+	206.620i	0.164559	+	0.452122i	0.994375	−	0.105915i	$-0.0337770\pi$
$457$	75.2035	+	206.620i	0.164559	+	0.452122i	−0.829816	+	0.558037i	$0.811555\pi$
$458$	696.277			1.52026
$459$	463.404	−	133.907i	1.00959	−	0.291736i
$460$	−868.013	+	1136.97i	−1.88698	+	2.47167i
$461$	239.621	+	658.355i	0.519786	+	1.42810i	0.870757	+	0.491714i	$0.163630\pi$
$461$	239.621	+	658.355i	0.519786	+	1.42810i	−0.350970	+	0.936387i	$0.614148\pi$
$462$	196.653	−	93.2621i	0.425657	−	0.201866i
$463$	93.8008	+	111.787i	0.202593	+	0.241441i	0.857769	−	0.514035i	$-0.171850\pi$
$463$	93.8008	+	111.787i	0.202593	+	0.241441i	−0.655176	+	0.755477i	$0.727405\pi$
$464$	−866.990	+	152.874i	−1.86851	+	0.329469i
$465$	−91.7602	−	37.0498i	−0.197334	−	0.0796771i
$466$	−417.842	−	350.611i	−0.896658	−	0.752385i
$467$	−137.204	+	237.644i	−0.293798	+	0.508873i	−0.974705	−	0.223497i	$-0.928253\pi$
$467$	−137.204	+	237.644i	−0.293798	+	0.508873i	0.680907	+	0.732370i	$0.261586\pi$
$468$	934.716	−	805.258i	1.99726	−	1.72064i
$469$	−24.6476	−	42.6909i	−0.0525535	−	0.0910253i
$470$	84.5643	+	91.8333i	0.179924	+	0.195390i
$471$	−236.301	−	108.324i	−0.501700	−	0.229988i
$472$	625.454	−	1718.42i	1.32511	−	3.64072i
$473$	−275.832	−	100.395i	−0.583154	−	0.212251i
$474$	−322.375	+	30.3170i	−0.680116	+	0.0639600i
$475$	−725.431	+	67.0478i	−1.52722	+	0.141153i
$476$	−246.772	+	142.474i	−0.518429	+	0.299315i
$477$	−112.715	−	297.587i	−0.236300	−	0.623871i
$478$	−681.539	−	393.487i	−1.42581	−	0.823194i
$479$	68.8982	−	82.1097i	0.143838	−	0.171419i	−0.689316	−	0.724461i	$-0.742089\pi$
$479$	68.8982	−	82.1097i	0.143838	−	0.171419i	0.833153	+	0.553042i	$0.186533\pi$
$480$	856.909	−	669.797i	1.78523	−	1.39541i
$481$	91.2796	+	517.673i	0.189771	+	1.07624i
$482$	224.847	−	188.669i	0.466487	−	0.391429i
$483$	78.5571	−	113.758i	0.162644	−	0.235524i
$484$	241.714	−	87.9767i	0.499409	−	0.181770i
$485$	537.140	+	410.077i	1.10751	+	0.845519i
$486$	809.689	−	410.108i	1.66603	−	0.843843i
$487$		−	532.318i		−	1.09305i	−0.837441	−	0.546527i	$-0.815949\pi$
$487$		−	532.318i		−	1.09305i	0.837441	−	0.546527i	$-0.184051\pi$
$488$	−1155.87	+	420.704i	−2.36859	+	0.862097i
$489$	75.8790	−	109.880i	0.155172	−	0.224703i
$490$	−39.9438	−	866.195i	−0.0815179	−	1.76775i
$491$	−203.492	+	35.8811i	−0.414444	+	0.0730776i	−0.376982	−	0.926220i	$-0.623038\pi$
$491$	−203.492	+	35.8811i	−0.414444	+	0.0730776i	−0.0374614	+	0.999298i	$0.511927\pi$
$492$	370.398	−	1419.18i	0.752841	−	2.88451i
$493$	233.935	−	278.793i	0.474513	−	0.565502i
$494$	1298.55	+	749.717i	2.62864	+	1.51765i
$495$	155.926	−	522.549i	0.315002	−	1.05566i
$496$	142.552	+	246.908i	0.287404	+	0.497798i
$497$	−15.0644	+	85.4347i	−0.0303108	+	0.171901i
$498$	−305.735	+	28.7521i	−0.613925	+	0.0577352i
$499$	−554.526	−	201.831i	−1.11127	−	0.404471i	−0.279813	−	0.960054i	$-0.590273\pi$
$499$	−554.526	−	201.831i	−1.11127	−	0.404471i	−0.831461	+	0.555584i	$0.812495\pi$
$500$	−923.215	−	833.580i	−1.84643	−	1.66716i
$501$	−84.6126	+	184.575i	−0.168887	+	0.368414i
$502$	−120.849	−	21.3089i	−0.240734	−	0.0424480i
$503$	366.904	+	635.497i	0.729432	+	1.26341i	0.957123	+	0.289680i	$0.0935490\pi$
$503$	366.904	+	635.497i	0.729432	+	1.26341i	−0.227691	+	0.973733i	$0.573118\pi$
$504$	−242.924	+	209.279i	−0.481993	+	0.415237i
$505$	−672.024	+	280.291i	−1.33074	+	0.555031i
$506$	836.454	−	996.847i	1.65307	−	1.97005i
$507$	16.5248	+	60.1057i	0.0325933	+	0.118552i
$508$	2178.03	−	384.045i	4.28745	−	0.755994i
$509$	−572.292	−	682.031i	−1.12435	−	1.33994i	−0.933605	−	0.358303i	$-0.883355\pi$
$509$	−572.292	−	682.031i	−1.12435	−	1.33994i	−0.190741	−	0.981640i	$-0.561089\pi$
$510$	−207.887	+	979.099i	−0.407621	+	1.91980i
$511$	140.351	−	51.0837i	0.274660	−	0.0999681i
$512$	708.733			1.38424
$513$	567.098	+	545.400i	1.10545	+	1.06316i
$514$	−1061.86			−2.06588
$515$	−65.2776	−	20.4064i	−0.126753	−	0.0396241i
$516$	720.751	+	58.3391i	1.39681	+	0.113060i
$517$	−52.0691	−	62.0535i	−0.100714	−	0.120026i
$518$	−39.6685	−	224.971i	−0.0765802	−	0.434308i
$519$	−20.9652	+	21.2395i	−0.0403954	+	0.0409240i
$520$	335.026	+	1493.89i	0.644281	+	2.87286i
$521$	−173.520	−	100.182i	−0.333052	−	0.192288i	0.324143	−	0.946008i	$-0.394924\pi$
$521$	−173.520	−	100.182i	−0.333052	−	0.192288i	−0.657195	+	0.753720i	$0.728257\pi$
$522$	334.658	−	597.450i	0.641107	−	1.14454i
$523$	−514.780	+	297.208i	−0.984283	+	0.568276i	−0.903560	−	0.428461i	$-0.859056\pi$
$523$	−514.780	+	297.208i	−0.984283	+	0.568276i	−0.0807223	+	0.996737i	$0.525723\pi$
$524$	152.922	+	26.9642i	0.291835	+	0.0514584i
$525$	92.9643	+	76.2178i	0.177075	+	0.145177i
$526$	−1003.57	−	365.271i	−1.90793	−	0.694431i
$527$	−110.753	−	40.3107i	−0.210157	−	0.0764909i
$528$	−1281.08	+	909.492i	−2.42630	+	1.72252i
$529$	51.6711	−	293.041i	0.0976769	−	0.553953i
$530$	654.877	+	84.5856i	1.23562	+	0.159596i
$531$	378.539	+	636.396i	0.712880	+	1.19849i
$532$	−402.522	−	232.396i	−0.756621	−	0.436835i
$533$	518.494	+	435.068i	0.972783	+	0.816262i
$534$	−385.982	−	380.996i	−0.722813	−	0.713476i
$535$	547.668	+	283.396i	1.02368	+	0.529712i
$536$	439.396	+	523.652i	0.819770	+	0.976963i
$537$	−635.003	−	51.3985i	−1.18250	−	0.0957141i
$538$	−183.921	−	505.320i	−0.341861	−	0.939257i
$539$			562.656i			1.04389i
$540$	−29.1268	+	1343.05i	−0.0539385	+	2.48713i
$541$	446.693			0.825681			0.412840	−	0.910803i	$-0.364537\pi$
$541$	446.693			0.825681			0.412840	+	0.910803i	$0.364537\pi$
$542$	−1357.31	+	494.019i	−2.50426	+	0.911475i
$543$	414.261	−	196.461i	0.762911	−	0.361807i
$544$	992.317	−	832.653i	1.82411	−	1.53061i
$545$	603.031	+	312.044i	1.10648	+	0.572558i
$546$	−65.5901	−	238.571i	−0.120128	−	0.436944i
$547$	−341.647	+	407.160i	−0.624584	+	0.744350i	−0.981851	−	0.189652i	$-0.939264\pi$
$547$	−341.647	+	407.160i	−0.624584	+	0.744350i	0.357267	+	0.934002i	$0.383708\pi$
$548$	−36.6945	+	63.5568i	−0.0669608	+	0.115980i
$549$	164.250	−	470.204i	0.299180	−	0.856474i
$550$	804.041	+	796.205i	1.46189	+	1.44765i
$551$	584.617	+	103.084i	1.06101	+	0.187085i
$552$	−798.879	+	1742.69i	−1.44724	+	3.15705i
$553$	−15.8416	+	43.5244i	−0.0286466	+	0.0787060i
$554$	−262.691	+	721.738i	−0.474172	+	1.30278i
$555$	−485.458	−	303.198i	−0.874700	−	0.546303i
$556$	258.134	−	1463.95i	0.464270	−	2.63301i
$557$	−128.583	−	222.713i	−0.230850	−	0.399844i	0.727209	−	0.686417i	$-0.240817\pi$
$557$	−128.583	−	222.713i	−0.230850	−	0.399844i	−0.958058	+	0.286573i	$0.907484\pi$
$558$	−218.882	−	35.6673i	−0.392262	−	0.0639198i
$559$	−166.846	+	288.986i	−0.298472	+	0.516969i
$560$	−75.7908	−	337.952i	−0.135341	−	0.603487i
$561$	164.017	−	628.432i	0.292365	−	1.12020i
$562$	−1863.02	+	328.500i	−3.31498	+	0.584520i
$563$	361.325	−	303.188i	0.641786	−	0.538522i	−0.262780	−	0.964856i	$-0.584639\pi$
$563$	361.325	−	303.188i	0.641786	−	0.538522i	0.904566	+	0.426333i	$0.140195\pi$
$564$	164.205	+	113.394i	0.291143	+	0.201053i
$565$	145.217	−	464.532i	0.257021	−	0.822180i
$566$		−	1599.74i		−	2.82639i
$567$	−3.37548	−	129.788i	−0.00595322	−	0.228902i
$568$		−	1203.01i		−	2.11797i
$569$	−35.4016	−	97.2651i	−0.0622173	−	0.170941i	0.904689	−	0.426073i	$-0.140103\pi$
$569$	−35.4016	−	97.2651i	−0.0622173	−	0.170941i	−0.966906	+	0.255132i	$0.917881\pi$
$570$	−1552.64	+	504.864i	−2.72393	+	0.885726i
$571$	462.971	−	388.479i	0.810807	−	0.680348i	−0.139993	−	0.990153i	$-0.544708\pi$
$571$	462.971	−	388.479i	0.810807	−	0.680348i	0.950800	+	0.309804i	$0.100264\pi$
$572$	−288.464	−	1635.96i	−0.504307	−	2.86007i
$573$	57.1222	−	218.864i	0.0996897	−	0.381961i
$574$	−225.328	−	189.073i	−0.392558	−	0.329395i
$575$	695.161	+	182.625i	1.20898	+	0.317608i
$576$	557.875	−	682.681i	0.968533	−	1.18521i
$577$	219.729	−	126.861i	0.380813	−	0.219863i	−0.297359	−	0.954766i	$-0.596106\pi$
$577$	219.729	−	126.861i	0.380813	−	0.219863i	0.678172	+	0.734903i	$0.262772\pi$
$578$	−19.5672	+	110.971i	−0.0338533	+	0.191992i
$579$	37.7187	+	401.080i	0.0651445	+	0.692712i
$580$	546.674	+	853.488i	0.942541	+	1.47153i
$581$	−15.0239	+	41.2778i	−0.0258587	+	0.0710461i
$582$	1376.70	+	631.104i	2.36547	+	1.08437i
$583$	−421.959	−	74.4027i	−0.723771	−	0.127620i
$584$	−1793.68	+	1035.58i	−3.07138	+	1.77326i
$585$	−554.233	−	277.719i	−0.947407	−	0.474733i
$586$	629.976	−	1091.15i	1.07504	−	1.86203i
$587$	402.386	+	337.642i	0.685496	+	0.575199i	0.917606	−	0.397490i	$-0.130119\pi$
$587$	402.386	+	337.642i	0.685496	+	0.575199i	−0.232111	+	0.972689i	$0.574563\pi$
$588$	−367.439	−	1336.49i	−0.624897	−	2.27294i
$589$	−33.3835	−	189.327i	−0.0566783	−	0.321439i
$590$	−1534.87	+	70.7793i	−2.60148	+	0.119965i
$591$	185.998	−	88.2086i	0.314717	−	0.149253i
$592$	563.998	+	1549.57i	0.952699	+	2.61752i
$593$	841.771			1.41951			0.709757	−	0.704447i	$-0.248805\pi$
$593$	841.771			1.41951			0.709757	+	0.704447i	$0.248805\pi$
$594$	82.7512	−	1219.28i	0.139312	−	2.05266i
$595$	113.804	+	86.8827i	0.191267	+	0.146021i
$596$	737.332	+	2025.80i	1.23713	+	3.39900i
$597$	14.7538	−	182.276i	0.0247132	−	0.305320i
$598$	−950.888	−	1133.22i	−1.59011	−	1.89502i
$599$	607.717	−	107.157i	1.01455	−	0.178893i	0.358437	−	0.933554i	$-0.383310\pi$
$599$	607.717	−	107.157i	1.01455	−	0.178893i	0.656115	+	0.754661i	$0.272199\pi$
$600$	−1453.09	−	817.004i	−2.42181	−	1.36167i
$601$	687.872	+	577.193i	1.14455	+	0.960388i	0.999578	−	0.0290485i	$-0.00924772\pi$
$601$	687.872	+	577.193i	1.14455	+	0.960388i	0.144968	+	0.989436i	$0.453692\pi$
$602$	72.5083	−	125.588i	0.120446	−	0.208618i
$603$	−276.767	+	3.59843i	−0.458984	+	0.00596755i
$604$	−63.3822	−	109.781i	−0.104937	−	0.181757i
$605$	−87.5520	−	95.0779i	−0.144714	−	0.157154i
$606$	−1330.57	+	944.622i	−2.19566	+	1.55878i
$607$	−305.379	+	839.023i	−0.503096	+	1.38225i	0.385140	+	0.922858i	$0.374153\pi$
$607$	−305.379	+	839.023i	−0.503096	+	1.38225i	−0.888236	+	0.459388i	$0.848069\pi$
$608$	1985.53	+	722.672i	3.26567	+	1.18861i
$609$	−56.7060	−	79.8744i	−0.0931133	−	0.131157i
$610$	700.093	+	760.272i	1.14769	+	1.24635i
$611$	−79.7499	+	46.0436i	−0.130524	+	0.0753578i
$612$	20.8006	+	1599.84i	0.0339878	+	2.61412i
$613$	499.634	+	288.464i	0.815063	+	0.470577i	0.848711	−	0.528857i	$-0.177379\pi$
$613$	499.634	+	288.464i	0.815063	+	0.470577i	−0.0336481	+	0.999434i	$0.510713\pi$
$614$	−251.144	+	299.302i	−0.409029	+	0.487462i
$615$	−729.787	+	102.730i	−1.18665	+	0.167041i
$616$	74.9691	+	425.171i	0.121703	+	0.690212i
$617$	−235.192	+	197.349i	−0.381186	+	0.319853i	−0.813168	−	0.582029i	$-0.802259\pi$
$617$	−235.192	+	197.349i	−0.381186	+	0.319853i	0.431982	+	0.901882i	$0.357815\pi$
$618$	−152.772	−	12.3657i	−0.247204	−	0.0200092i
$619$	−278.964	+	101.535i	−0.450668	+	0.164030i	−0.557375	−	0.830261i	$-0.688192\pi$
$619$	−278.964	+	101.535i	−0.450668	+	0.164030i	0.106707	+	0.994291i	$0.465969\pi$
$620$	199.181	−	260.897i	0.321259	−	0.420802i
$621$	−341.714	−	696.990i	−0.550264	−	1.12237i
$622$			1359.75i			2.18610i
$623$	−72.9016	+	26.5340i	−0.117017	+	0.0425907i
$624$	765.319	+	1613.76i	1.22647	+	2.58615i
$625$	−208.001	+	589.373i	−0.332802	+	0.942997i
$626$	−970.567	+	171.137i	−1.55043	+	0.273382i
$627$	1021.50	−	280.840i	1.62919	−	0.447910i
$628$	554.231	−	660.507i	0.882533	−	1.05176i
$629$	−590.365	−	340.848i	−0.938578	−	0.541888i
$630$	240.860	+	120.692i	0.382317	+	0.191574i
$631$	−152.227	−	263.664i	−0.241247	−	0.417851i	0.719823	−	0.694158i	$-0.244223\pi$
$631$	−152.227	−	263.664i	−0.241247	−	0.417851i	−0.961070	+	0.276306i	$0.910890\pi$
$632$	111.533	−	632.533i	0.176476	−	1.00084i
$633$	−474.378	+	1034.82i	−0.749413	+	1.63478i
$634$	−1462.82	−	532.422i	−2.30728	−	0.839782i
$635$	−599.380	−	935.775i	−0.943905	−	1.47366i
$636$	1050.88	−	98.8273i	1.65232	−	0.155389i
$637$	629.915	+	111.071i	0.988877	+	0.174366i
$638$	−461.024	−	798.518i	−0.722609	−	1.25160i
$639$	377.190	+	308.233i	0.590281	+	0.482368i
$640$	145.998	+	350.043i	0.228121	+	0.546943i
$641$	710.009	−	846.156i	1.10766	−	1.32006i	0.165001	−	0.986293i	$-0.447237\pi$
$641$	710.009	−	846.156i	1.10766	−	1.32006i	0.942657	−	0.333762i	$-0.108318\pi$
$642$	1337.15	+	348.987i	2.08278	+	0.543594i
$643$	421.371	−	74.2990i	0.655320	−	0.115551i	0.163905	−	0.986476i	$-0.447591\pi$
$643$	421.371	−	74.2990i	0.655320	−	0.115551i	0.491415	+	0.870926i	$0.336480\pi$
$644$	294.755	+	351.275i	0.457694	+	0.545458i
$645$	−112.355	−	345.532i	−0.174194	−	0.535708i
$646$	−1827.26	+	665.067i	−2.82857	+	1.02952i
$647$	−839.214			−1.29709			−0.648543	−	0.761178i	$-0.724621\pi$
$647$	−839.214			−1.29709			−0.648543	+	0.761178i	$0.724621\pi$
$648$	358.624	+	1764.30i	0.553433	+	2.72269i
$649$	997.011			1.53623
$650$	1050.10	−	742.979i	1.61554	−	1.14304i
$651$	−18.0263	+	26.1037i	−0.0276902	+	0.0400979i
$652$	284.706	+	339.300i	0.436666	+	0.520398i
$653$	218.407	+	1238.65i	0.334468	+	1.89686i	0.432426	+	0.901670i	$0.357658\pi$
$653$	218.407	+	1238.65i	0.334468	+	1.89686i	−0.0979579	+	0.995191i	$0.531231\pi$
$654$	1472.32	+	384.266i	2.25125	+	0.587562i
$655$	−17.0739	−	76.1327i	−0.0260670	−	0.116233i
$656$	1838.83	+	1061.65i	2.80310	+	1.61837i
$657$	134.880	−	827.727i	0.205296	−	1.25986i
$658$	34.6579	−	20.0097i	0.0526716	−	0.0304099i
$659$	102.328	+	18.0433i	0.155278	+	0.0273798i	0.250747	−	0.968053i	$-0.419324\pi$
$659$	102.328	+	18.0433i	0.155278	+	0.0273798i	−0.0954686	+	0.995432i	$0.530435\pi$
$660$	1534.15	+	958.172i	2.32448	+	1.45178i
$661$	−528.130	−	192.224i	−0.798986	−	0.290807i	−0.0899200	−	0.995949i	$-0.528661\pi$
$661$	−528.130	−	192.224i	−0.798986	−	0.290807i	−0.709066	+	0.705142i	$0.750883\pi$
$662$	−255.083	−	92.8425i	−0.385321	−	0.140245i
$663$	−671.176	−	307.679i	−1.01233	−	0.464070i
$664$	105.776	−	599.883i	0.159301	−	0.903438i
$665$	−29.9166	+	231.620i	−0.0449874	+	0.348301i
$666$	−1210.94	−	423.000i	−1.81823	−	0.635135i
$667$	−507.207	−	292.836i	−0.760430	−	0.439035i
$668$	−515.924	−	432.912i	−0.772342	−	0.648072i
$669$	867.402	−	238.474i	1.29657	−	0.356463i
$670$	263.959	−	510.106i	0.393969	−	0.761352i
$671$	−431.071	−	513.730i	−0.642430	−	0.765619i
$672$	−149.401	−	315.029i	−0.222323	−	0.468794i
$673$	83.8135	+	230.276i	0.124537	+	0.342163i	0.986256	−	0.165222i	$-0.0528342\pi$
$673$	83.8135	+	230.276i	0.124537	+	0.342163i	−0.861719	+	0.507386i	$0.830612\pi$
$674$		−	331.324i		−	0.491579i
$675$	628.472	−	246.269i	0.931069	−	0.364842i
$676$	−206.765			−0.305866
$677$	1015.64	−	369.663i	1.50021	−	0.546031i	0.544094	−	0.839024i	$-0.316873\pi$
$677$	1015.64	−	369.663i	1.50021	−	0.546031i	0.956115	+	0.292992i	$0.0946511\pi$
$678$	87.9975	−	1087.17i	0.129790	−	1.60349i
$679$	165.953	−	139.252i	0.244409	−	0.205083i
$680$	−1763.36	−	912.467i	−2.59318	−	1.34186i
$681$	254.417	−	257.746i	0.373593	−	0.378482i
$682$	−191.939	+	228.744i	−0.281435	+	0.335401i
$683$	−428.494	+	742.173i	−0.627370	+	1.08664i	0.360707	+	0.932679i	$0.382535\pi$
$683$	−428.494	+	742.173i	−0.627370	+	1.08664i	−0.988077	+	0.153958i	$0.950798\pi$
$684$	−2242.99	+	1334.17i	−3.27923	+	1.95054i
$685$	36.5720	+	4.72373i	0.0533897	+	0.00689596i
$686$	−562.647	−	99.2098i	−0.820185	−	0.144621i
$687$	−323.742	−	456.013i	−0.471240	−	0.663774i
$688$	−358.030	+	983.679i	−0.520392	+	1.42977i
$689$	−166.593	+	457.711i	−0.241790	+	0.664312i
$690$	1609.79	+	55.8571i	2.33302	+	0.0809524i
$691$	−214.349	+	1215.63i	−0.310201	+	1.75924i	0.287749	+	0.957706i	$0.407093\pi$
$691$	−214.349	+	1215.63i	−0.310201	+	1.75924i	−0.597951	+	0.801533i	$0.704018\pi$
$692$	−49.4954	−	85.7285i	−0.0715251	−	0.123885i
$693$	−152.516	−	85.4310i	−0.220081	−	0.123277i
$694$	744.028	−	1288.69i	1.07209	−	1.85691i
$695$	−728.835	+	163.452i	−1.04868	+	0.235182i
$696$	966.736	+	954.249i	1.38899	+	1.37105i
$697$	−864.425	+	152.421i	−1.24021	+	0.218682i
$698$	1260.67	−	1057.83i	1.80611	−	1.51551i
$699$	−35.3456	+	436.678i	−0.0505660	+	0.624718i
$700$	−325.509	+	230.308i	−0.465013	+	0.329011i
$701$			691.765i			0.986826i	0.869795	+	0.493413i	$0.164251\pi$
$701$			691.765i			0.986826i	−0.869795	+	0.493413i	$0.835749\pi$
$702$	−1348.69	−	333.334i	−1.92121	−	0.474835i
$703$		−	1111.95i		−	1.58171i
$704$	−406.007	−	1115.50i	−0.576715	−	1.58451i
$705$	20.8253	−	98.0826i	0.0295395	−	0.139124i
$706$	1101.12	−	923.953i	1.55967	−	1.30871i
$707$	40.5328	+	229.873i	0.0573307	+	0.325139i
$708$	−2368.22	+	651.092i	−3.34495	+	0.919622i
$709$	199.020	+	166.998i	0.280705	+	0.235540i	0.772259	−	0.635307i	$-0.219127\pi$
$709$	199.020	+	166.998i	0.280705	+	0.235540i	−0.491554	+	0.870847i	$0.663571\pi$
$710$	−932.892	+	389.095i	−1.31393	+	0.548021i
$711$	169.747	+	197.037i	0.238744	+	0.277126i
$712$	931.679	−	537.905i	1.30854	−	0.755485i
$713$	−32.9357	+	186.787i	−0.0461931	+	0.261974i
$714$	291.681	+	133.712i	0.408517	+	0.187271i
$715$	−702.878	+	450.206i	−0.983047	+	0.629659i
$716$	722.744	−	1985.72i	1.00942	−	2.77336i
$717$	59.1826	+	629.316i	0.0825419	+	0.877707i
$718$	374.934	+	66.1110i	0.522192	+	0.0920765i
$719$	−687.917	+	397.169i	−0.956769	+	0.552391i	−0.895177	−	0.445711i	$-0.852951\pi$
$719$	−687.917	+	397.169i	−0.956769	+	0.552391i	−0.0615920	+	0.998101i	$0.519618\pi$
$720$	−1863.53	−	556.068i	−2.58824	−	0.772317i
$721$	−10.9624	+	18.9875i	−0.0152045	+	0.0263349i
$722$	−1396.84	−	1172.09i	−1.93468	−	1.62339i
$723$	−228.110	−	59.5353i	−0.315504	−	0.0823448i
$724$	264.080	+	1497.67i	0.364751	+	2.06861i
$725$	290.065	−	418.603i	0.400090	−	0.577384i
$726$	−238.344	−	164.592i	−0.328298	−	0.226711i
$727$	−29.4405	−	80.8871i	−0.0404959	−	0.111261i	0.917797	−	0.397051i	$-0.129966\pi$
$727$	−29.4405	−	80.8871i	−0.0404959	−	0.111261i	−0.958292	+	0.285790i	$0.907744\pi$
$728$	490.794			0.674167
$729$	−645.065	−	339.605i	−0.884863	−	0.465851i
$730$	1383.20	+	1056.00i	1.89480	+	1.44658i
$731$	−148.007	−	406.647i	−0.202473	−	0.556289i
$732$	1359.42	+	938.767i	1.85713	+	1.28247i
$733$	−166.327	−	198.220i	−0.226912	−	0.270423i	0.640561	−	0.767907i	$-0.278702\pi$
$733$	−166.327	−	198.220i	−0.226912	−	0.270423i	−0.867473	+	0.497484i	$0.834257\pi$
$734$	1917.75	−	338.151i	2.61273	−	0.460696i
$735$	−548.725	+	428.907i	−0.746564	+	0.583547i
$736$	−1596.90	−	1339.96i	−2.16970	−	1.82060i
$737$	−186.344	+	322.757i	−0.252841	+	0.437934i
$738$	−1544.53	+	585.015i	−2.09287	+	0.792703i
$739$	−157.730	−	273.197i	−0.213438	−	0.369685i	0.739350	−	0.673321i	$-0.235133\pi$
$739$	−157.730	−	273.197i	−0.213438	−	0.369685i	−0.952788	+	0.303636i	$0.901799\pi$
$740$	1396.58	−	1286.03i	1.88727	−	1.73788i
$741$	−112.762	−	1199.05i	−0.152175	−	1.61815i
$742$	72.3985	−	198.913i	0.0975721	−	0.268077i
$743$	−219.384	−	79.8494i	−0.295268	−	0.107469i	0.190139	−	0.981757i	$-0.439106\pi$
$743$	−219.384	−	79.8494i	−0.295268	−	0.107469i	−0.485407	+	0.874288i	$0.661328\pi$
$744$	183.317	−	399.890i	0.246393	−	0.537487i
$745$	796.847	−	733.773i	1.06959	−	0.984930i
$746$	−206.278	+	119.095i	−0.276513	+	0.159645i
$747$	160.985	+	186.866i	0.215509	+	0.250156i
$748$	1865.68	+	1077.15i	2.49423	+	1.44004i
$749$	127.066	−	151.431i	0.169648	−	0.202178i
$750$	−163.579	+	1391.07i	−0.218106	+	1.85476i
$751$	−163.837	−	929.165i	−0.218158	−	1.23724i	−0.875341	−	0.483506i	$-0.839363\pi$
$751$	−163.837	−	929.165i	−0.218158	−	1.23724i	0.657183	−	0.753731i	$-0.271748\pi$
$752$	−221.297	+	185.690i	−0.294278	+	0.246929i
$753$	42.2341	+	89.0552i	0.0560877	+	0.118267i
$754$	−984.979	+	358.503i	−1.30634	+	0.475468i
$755$	−38.6514	+	50.6276i	−0.0511939	+	0.0670564i
$756$	418.066	+	103.326i	0.552997	+	0.136675i
$757$		−	197.402i		−	0.260769i	−0.991464	−	0.130384i	$-0.958379\pi$
$757$		−	197.402i		−	0.260769i	0.991464	−	0.130384i	$-0.0416211\pi$
$758$	948.031	−	345.055i	1.25070	−	0.455218i
$759$	−1041.78	−	84.3241i	−1.37257	−	0.111099i
$760$	−149.185	−	3235.13i	−0.196296	−	4.25675i
$761$	7.30341	−	1.28779i	0.00959713	−	0.00169223i	−0.168848	−	0.985642i	$-0.554005\pi$
$761$	7.30341	−	1.28779i	0.00959713	−	0.00169223i	0.178445	+	0.983950i	$0.442893\pi$
$762$	−1772.40	−	1749.51i	−2.32599	−	2.29594i
$763$	139.911	−	166.739i	0.183369	−	0.218531i
$764$	649.761	+	375.140i	0.850472	+	0.491020i
$765$	737.901	−	319.091i	0.964576	−	0.417113i
$766$	54.4398	+	94.2926i	0.0710703	+	0.123097i
$767$	196.815	−	1116.19i	0.256603	−	1.45527i
$768$	−188.457	−	265.454i	−0.245386	−	0.345644i
$769$	1240.22	+	451.405i	1.61278	+	0.587003i	0.981986	−	0.188951i	$-0.0605088\pi$
$769$	1240.22	+	451.405i	1.61278	+	0.587003i	0.630790	+	0.775954i	$0.282731\pi$
$770$	305.459	−	195.652i	0.396699	−	0.254093i
$771$	493.725	+	695.447i	0.640370	+	0.902006i
$772$	−1315.93	−	232.035i	−1.70458	−	0.300563i
$773$	−238.322	−	412.785i	−0.308307	−	0.534004i	0.669685	−	0.742645i	$-0.266429\pi$
$773$	−238.322	−	412.785i	−0.308307	−	0.534004i	−0.977992	+	0.208641i	$0.933096\pi$
$774$	−416.265	−	699.820i	−0.537810	−	0.904160i
$775$	−159.517	−	41.9064i	−0.205828	−	0.0540727i
$776$	−1931.01	+	2301.29i	−2.48842	+	2.96558i
$777$	−128.896	+	130.583i	−0.165890	+	0.168060i
$778$	−1856.57	+	327.363i	−2.38634	+	0.420776i
$779$	−920.315	−	1096.79i	−1.18141	−	1.40794i
$780$	1375.56	−	1528.40i	1.76354	−	1.95948i
$781$	616.325	−	224.324i	0.789149	−	0.287227i
$782$	1918.44			2.45325
$783$	−546.891	+	58.6132i	−0.698456	+	0.0748573i
$784$	2006.56			2.55939
$785$	−413.510	−	129.267i	−0.526764	−	0.164671i
$786$	−74.9256	−	157.989i	−0.0953251	−	0.201004i
$787$	470.940	+	561.245i	0.598400	+	0.713145i	0.977197	−	0.212335i	$-0.0681067\pi$
$787$	470.940	+	561.245i	0.598400	+	0.713145i	−0.378797	+	0.925480i	$0.623662\pi$
$788$	118.568	+	672.434i	0.150467	+	0.853343i
$789$	227.395	+	827.106i	0.288207	+	1.04830i
$790$	−526.583	+	118.094i	−0.666561	+	0.149486i
$791$	−135.119	−	78.0113i	−0.170821	−	0.0986236i
$792$	2288.54	+	799.422i	2.88957	+	1.00937i
$793$	−660.235	+	381.187i	−0.832579	+	0.480690i
$794$	731.086	+	128.910i	0.920763	+	0.162355i
$795$	−249.094	−	468.227i	−0.313326	−	0.588965i
$796$	569.997	+	207.462i	0.716076	+	0.260630i
$797$	−545.314	−	198.478i	−0.684209	−	0.249032i	−0.0235551	−	0.999723i	$-0.507498\pi$
$797$	−545.314	−	198.478i	−0.684209	−	0.249032i	−0.660653	+	0.750691i	$0.729721\pi$
$798$	49.0042	+	521.085i	0.0614088	+	0.652988i
$799$	20.7375	−	117.608i	0.0259543	−	0.147194i
$800$	1275.48	−	1288.03i	1.59435	−	1.61004i
$801$	−70.0594	+	429.940i	−0.0874649	+	0.536754i
$802$	1225.78	+	707.703i	1.52840	+	0.882423i
$803$	−865.020	−	725.838i	−1.07723	−	0.903907i
$804$	231.853	−	888.344i	0.288374	−	1.10491i
$805$	105.891	−	204.637i	0.131542	−	0.254207i
$806$	218.198	+	260.038i	0.270717	+	0.322628i
$807$	−245.433	+	355.410i	−0.304130	+	0.440409i
$808$	−1107.06	−	3041.63i	−1.37013	−	3.76440i
$809$			459.833i			0.568397i	0.958765	+	0.284199i	$0.0917275\pi$
$809$			459.833i			0.568397i	−0.958765	+	0.284199i	$0.908272\pi$
$810$	1252.17	−	848.741i	1.54589	−	1.04783i
$811$	−1419.14			−1.74986			−0.874931	−	0.484248i	$-0.839093\pi$
$811$	−1419.14			−1.74986			−0.874931	+	0.484248i	$0.839093\pi$
$812$	305.322	−	111.128i	0.376013	−	0.136857i
$813$	954.642	+	659.241i	1.17422	+	0.810875i
$814$	−1323.03	+	1110.16i	−1.62535	+	1.36383i
$815$	102.281	−	197.660i	0.125498	−	0.242528i
$816$	−2241.13	−	584.923i	−2.74649	−	0.716817i
$817$	453.725	−	540.728i	0.555355	−	0.661846i
$818$	307.274	−	532.215i	0.375641	−	0.650629i
$819$	−125.751	+	153.883i	−0.153542	+	0.187892i
$820$	313.141	−	2424.40i	0.381880	−	2.95658i
$821$	1297.62	+	228.805i	1.58053	+	0.278691i	0.893884	−	0.448299i	$-0.147970\pi$
$821$	1297.62	+	228.805i	1.58053	+	0.278691i	0.686649	+	0.726989i	$0.259081\pi$
$822$	82.2774	−	7.73759i	0.100094	−	0.00941313i
$823$	−49.4573	+	135.883i	−0.0600940	+	0.165107i	−0.966106	−	0.258144i	$-0.916889\pi$
$823$	−49.4573	+	135.883i	−0.0600940	+	0.165107i	0.906012	+	0.423251i	$0.139111\pi$
$824$	103.985	−	285.698i	0.126196	−	0.346721i
$825$	147.611	−	896.795i	0.178923	−	1.08702i
$826$	−85.5322	+	485.077i	−0.103550	+	0.587260i
$827$	548.614	+	950.226i	0.663378	+	1.14900i	0.979722	+	0.200360i	$0.0642111\pi$
$827$	548.614	+	950.226i	0.663378	+	1.14900i	−0.316345	+	0.948644i	$0.602456\pi$
$828$	2529.64	−	480.034i	3.05512	−	0.579751i
$829$	562.861	−	974.904i	0.678964	−	1.17600i	−0.296329	−	0.955086i	$-0.595763\pi$
$829$	562.861	−	974.904i	0.678964	−	1.17600i	0.975293	−	0.220914i	$-0.0709041\pi$
$830$	−499.402	+	111.998i	−0.601689	+	0.134937i
$831$	594.829	−	163.536i	0.715799	−	0.196794i
$832$	−1328.99	+	234.336i	−1.59734	+	0.281654i
$833$	−635.434	+	533.193i	−0.762826	+	0.640087i
$834$	−1512.46	+	717.278i	−1.81350	+	0.860046i
$835$	−100.971	+	322.994i	−0.120923	+	0.386820i
$836$			3513.99i			4.20334i
$837$	78.4121	+	159.936i	0.0936823	+	0.191083i
$838$		−	1818.19i		−	2.16967i
$839$	204.373	+	561.510i	0.243591	+	0.669261i	0.999887	+	0.0150315i	$0.00478486\pi$
$839$	204.373	+	561.510i	0.243591	+	0.669261i	−0.756296	+	0.654230i	$0.772993\pi$
$840$	−357.495	+	397.216i	−0.425590	+	0.472876i
$841$	326.345	−	273.836i	0.388044	−	0.325608i
$842$	409.092	+	2320.07i	0.485857	+	2.75543i
$843$	1081.38	+	1067.41i	1.28277	+	1.26620i
$844$	−2892.52	−	2427.11i	−3.42715	−	2.87572i
$845$	39.9931	+	95.8872i	0.0473291	+	0.113476i
$846$	−2.92133	−	224.689i	−0.00345311	−	0.265590i
$847$	−35.8824	+	20.7167i	−0.0423641	+	0.0244589i
$848$	−265.337	+	1504.80i	−0.312898	+	1.77453i
$849$	−1047.72	+	743.815i	−1.23406	+	0.876108i
$850$	−137.255	+	1662.55i	−0.161477	+	1.95595i
$851$	−375.206	+	1030.87i	−0.440900	+	1.21136i
$852$	−1317.48	+	935.330i	−1.54634	+	1.09781i
$853$	53.6769	+	9.46469i	0.0629272	+	0.0110958i	0.205023	−	0.978757i	$-0.434273\pi$
$853$	53.6769	+	9.46469i	0.0629272	+	0.0110958i	−0.142096	+	0.989853i	$0.545384\pi$
$854$	286.927	−	165.657i	0.335980	−	0.193978i
$855$	1052.57	+	782.127i	1.23107	+	0.914768i
$856$	−1370.62	+	2373.98i	−1.60119	+	2.77334i
$857$	−218.563	−	183.396i	−0.255033	−	0.213998i	0.506303	−	0.862356i	$-0.331012\pi$
$857$	−218.563	−	183.396i	−0.255033	−	0.213998i	−0.761336	+	0.648358i	$0.775456\pi$
$858$	−1314.09	+	1331.29i	−1.53157	+	1.55162i
$859$	177.600	+	1007.22i	0.206752	+	1.17255i	0.894659	+	0.446749i	$0.147418\pi$
$859$	177.600	+	1007.22i	0.206752	+	1.17255i	−0.687908	+	0.725798i	$0.741471\pi$
$860$	1203.90	−	55.5168i	1.39989	−	0.0645544i
$861$	−19.0607	+	235.486i	−0.0221379	+	0.273502i
$862$	−688.498	−	1891.63i	−0.798721	−	2.19447i
$863$	649.495			0.752601			0.376300	−	0.926498i	$-0.377196\pi$
$863$	649.495			0.752601			0.376300	+	0.926498i	$0.377196\pi$
$864$	−1953.22	−	132.563i	−2.26068	−	0.153430i
$865$	−30.1830	+	39.5353i	−0.0348936	+	0.0457055i
$866$	−182.618	−	501.739i	−0.210875	−	0.579375i
$867$	81.7763	−	38.7821i	0.0943210	−	0.0447313i
$868$	−67.6366	−	80.6062i	−0.0779223	−	0.0928642i
$869$	344.858	−	60.8077i	0.396844	−	0.0699744i
$870$	427.312	−	1058.31i	0.491164	−	1.21645i
$871$	324.554	+	272.333i	0.372622	+	0.312667i
$872$	−1509.17	+	2613.96i	−1.73070	+	2.99766i
$873$	−226.783	−	1195.08i	−0.259774	−	1.36894i
$874$	1564.63	+	2710.02i	1.79019	+	3.10071i
$875$	169.766	+	106.408i	0.194018	+	0.121609i
$876$	2528.71	+	1159.20i	2.88665	+	1.32329i
$877$	551.626	−	1515.58i	0.628992	−	1.72814i	−0.0548340	−	0.998495i	$-0.517463\pi$
$877$	551.626	−	1515.58i	0.628992	−	1.72814i	0.683826	−	0.729645i	$-0.260315\pi$
$878$	554.204	+	201.714i	0.631212	+	0.229742i
$879$	−1007.54	+	94.7519i	−1.14624	+	0.107795i
$880$	−1926.22	+	1773.75i	−2.18889	+	2.01563i
$881$	−969.613	+	559.806i	−1.10058	+	0.635421i	−0.936374	−	0.351004i	$-0.885840\pi$
$881$	−969.613	+	559.806i	−1.10058	+	0.635421i	−0.164208	+	0.986426i	$0.552507\pi$
$882$	−987.639	+	1208.59i	−1.11977	+	1.37028i
$883$	328.990	+	189.942i	0.372582	+	0.215110i	0.674586	−	0.738196i	$-0.264322\pi$
$883$	328.990	+	189.942i	0.372582	+	0.215110i	−0.302004	+	0.953307i	$0.597656\pi$
$884$	1574.21	−	1876.07i	1.78078	−	2.12225i
$885$	760.011	+	972.325i	0.858770	+	1.09867i
$886$	−125.752	−	713.173i	−0.141932	−	0.804936i
$887$	321.634	−	269.883i	0.362609	−	0.304265i	−0.443221	−	0.896413i	$-0.646164\pi$
$887$	321.634	−	269.883i	0.362609	−	0.304265i	0.805830	+	0.592148i	$0.201720\pi$
$888$	1445.81	−	2093.67i	1.62817	−	2.35774i
$889$	−334.759	+	121.842i	−0.376557	+	0.137056i
$890$	−718.467	−	548.509i	−0.807266	−	0.616303i
$891$	−837.018	+	512.720i	−0.939414	+	0.575443i
$892$			2983.89i			3.34516i
$893$	183.048	−	66.6240i	0.204981	−	0.0746069i
$894$	1379.44	−	1997.56i	1.54300	−	2.23441i
$895$	−1060.67	+	48.9119i	−1.18511	+	0.0546502i
$896$	119.736	−	21.1127i	0.133634	−	0.0235633i
$897$	−300.057	+	1149.67i	−0.334512	+	1.28168i
$898$	−96.4460	+	114.940i	−0.107401	+	0.127995i
$899$	116.387	+	67.1963i	0.129463	+	0.0747456i
$900$	235.022	+	2226.57i	0.261135	+	2.47397i
$901$	−315.836	−	547.045i	−0.350540	−	0.607153i
$902$	−386.165	+	2190.05i	−0.428121	+	2.42799i
$903$	−115.965	+	10.9056i	−0.128422	+	0.0120771i
$904$	2033.10	+	739.986i	2.24900	+	0.818569i
$905$	643.464	−	412.150i	0.711010	−	0.455415i
$906$	−59.4841	+	129.760i	−0.0656557	+	0.143223i
$907$	816.196	+	143.917i	0.899885	+	0.158674i	0.604407	−	0.796675i	$-0.293410\pi$
$907$	816.196	+	143.917i	0.899885	+	0.158674i	0.295478	+	0.955350i	$0.404521\pi$
$908$	600.637	+	1040.33i	0.661494	+	1.14574i
$909$	1237.32	+	432.216i	1.36119	+	0.475485i
$910$	−158.740	−	380.595i	−0.174440	−	0.418236i
$911$	−240.268	+	286.340i	−0.263740	+	0.314314i	−0.881621	−	0.471959i	$-0.843547\pi$
$911$	−240.268	+	286.340i	−0.263740	+	0.314314i	0.617880	+	0.786272i	$0.287992\pi$
$912$	−1001.54	−	3642.91i	−1.09818	−	3.99441i
$913$	327.057	−	57.6689i	0.358222	−	0.0631642i
$914$	527.903	+	629.130i	0.577574	+	0.688326i
$915$	172.409	−	812.009i	0.188426	−	0.887441i
$916$	1743.12	−	634.445i	1.90297	−	0.692626i
$917$	−25.0122			−0.0272761
$918$	1455.41	−	1061.98i	1.58541	−	1.15684i
$919$	670.084			0.729144			0.364572	−	0.931175i	$-0.381215\pi$
$919$	670.084			0.729144			0.364572	+	0.931175i	$0.381215\pi$
$920$	−953.329	+	3049.59i	−1.03623	+	3.31477i
$921$	312.794	+	25.3182i	0.339624	+	0.0274899i
$922$	1682.06	+	2004.60i	1.82436	+	2.17419i
$923$	−129.474	−	734.282i	−0.140275	−	0.795538i
$924$	407.340	−	412.670i	0.440844	−	0.446613i
$925$	−866.525	−	398.913i	−0.936784	−	0.431258i
$926$	472.030	+	272.527i	0.509752	+	0.294305i
$927$	62.9344	+	105.805i	0.0678904	+	0.114137i
$928$	−1279.19	+	738.539i	−1.37843	+	0.795839i
$929$	−254.515	−	44.8778i	−0.273966	−	0.0483076i	0.0349770	−	0.999388i	$-0.488864\pi$
$929$	−254.515	−	44.8778i	−0.273966	−	0.0483076i	−0.308943	+	0.951080i	$0.599975\pi$
$930$	−369.393	−	12.8174i	−0.397197	−	0.0137821i
$931$	−1271.44	−	462.766i	−1.36567	−	0.497064i
$932$	−1365.54	−	497.016i	−1.46517	−	0.533279i
$933$	890.542	−	632.231i	0.954493	−	0.677632i
$934$	−177.978	+	1009.36i	−0.190555	+	1.08069i
$935$	138.663	−	1073.55i	0.148303	−	1.14819i
$936$	1346.75	−	2404.30i	1.43884	−	2.56869i
$937$	−1183.51	−	683.299i	−1.26308	−	0.729241i	−0.289413	−	0.957204i	$-0.593460\pi$
$937$	−1183.51	−	683.299i	−1.26308	−	0.729241i	−0.973670	+	0.227963i	$0.926794\pi$
$938$	−141.045	−	118.351i	−0.150368	−	0.126174i
$939$	563.359	+	556.082i	0.599956	+	0.592206i
$940$	295.384	+	152.849i	0.314238	+	0.162606i
$941$	−404.676	−	482.275i	−0.430049	−	0.512513i	0.506887	−	0.862012i	$-0.330796\pi$
$941$	−404.676	−	482.275i	−0.430049	−	0.512513i	−0.936937	+	0.349500i	$0.886352\pi$
$942$	−967.757	−	78.3323i	−1.02734	−	0.0831553i
$943$	483.120	+	1327.36i	0.512322	+	1.40759i
$944$		−	3555.57i		−	3.76649i
$945$	−32.9458	−	213.863i	−0.0348633	−	0.226310i
$946$	−1096.37			−1.15896
$947$	449.992	−	163.784i	0.475177	−	0.172950i	−0.0933193	−	0.995636i	$-0.529748\pi$
$947$	449.992	−	163.784i	0.475177	−	0.172950i	0.568496	+	0.822686i	$0.307526\pi$
$948$	−779.438	+	369.645i	−0.822192	+	0.389921i
$949$	−983.361	+	825.138i	−1.03621	+	0.869482i
$950$	−2460.49	+	1162.05i	−2.58999	+	1.22321i
$951$	331.453	+	1205.60i	0.348531	+	1.26772i
$952$	−409.122	+	487.573i	−0.429750	+	0.512156i
$953$	243.506	−	421.765i	0.255516	−	0.442566i	−0.709520	−	0.704685i	$-0.751088\pi$
$953$	243.506	−	421.765i	0.255516	−	0.442566i	0.965035	+	0.262120i	$0.0844215\pi$
$954$	−775.771	−	900.488i	−0.813177	−	0.943908i
$955$	48.2922	−	373.886i	0.0505677	−	0.391504i
$956$	−2064.77	−	364.074i	−2.15980	−	0.380831i
$957$	−308.615	+	673.218i	−0.322482	+	0.703467i
$958$	136.928	−	376.207i	0.142931	−	0.392700i
$959$	4.04313	−	11.1084i	0.00421599	−	0.0115833i
$960$	778.381	−	1246.29i	0.810814	−	1.29821i
$961$	−159.318	+	903.539i	−0.165784	+	0.940207i
$962$	981.689	+	1700.34i	1.02047	+	1.76750i
$963$	−393.158	−	1038.00i	−0.408264	−	1.07788i
$964$	390.987	−	677.210i	0.405588	−	0.702500i
$965$	146.926	+	655.144i	0.152254	+	0.678905i
$966$	130.399	−	499.626i	0.134989	−	0.517211i
$967$	159.464	−	28.1178i	0.164906	−	0.0290774i	−0.0905855	−	0.995889i	$-0.528874\pi$
$967$	159.464	−	28.1178i	0.164906	−	0.0290774i	0.255491	+	0.966811i	$0.417763\pi$
$968$	440.138	−	369.320i	0.454688	−	0.381529i
$969$	1285.18	+	887.496i	1.32629	+	0.915888i
$970$	2409.13	+	753.118i	2.48364	+	0.776410i
$971$		−	1357.14i		−	1.39768i	−0.715280	−	0.698838i	$-0.753701\pi$
$971$		−	1357.14i		−	1.39768i	0.715280	−	0.698838i	$-0.246299\pi$
$972$	1653.36	−	1764.49i	1.70099	−	1.81531i
$973$			239.447i			0.246092i
$974$	−680.022	−	1868.34i	−0.698174	−	1.91822i
$975$	−974.856	−	342.288i	−0.999852	−	0.351064i
$976$	−1832.08	+	1537.30i	−1.87713	+	1.57510i
$977$	−244.318	−	1385.60i	−0.250070	−	1.41822i	−0.808418	−	0.588609i	$-0.799676\pi$
$977$	−244.318	−	1385.60i	−0.250070	−	1.41822i	0.558348	−	0.829607i	$-0.311435\pi$
$978$	125.954	−	482.593i	0.128787	−	0.493449i
$979$	449.310	+	377.016i	0.458948	+	0.385103i
$980$	−889.272	−	2132.11i	−0.907421	−	2.17563i
$981$	−432.902	−	1142.93i	−0.441286	−	1.16507i
$982$	−668.385	+	385.892i	−0.680636	+	0.392966i
$983$	147.248	−	835.086i	0.149795	−	0.849528i	−0.813597	−	0.581430i	$-0.802494\pi$
$983$	147.248	−	835.086i	0.149795	−	0.849528i	0.963391	−	0.268099i	$-0.0863953\pi$
$984$	−306.747	−	3261.78i	−0.311735	−	3.31482i
$985$	288.907	−	185.050i	0.293307	−	0.187868i
$986$	464.921	−	1277.36i	0.471522	−	1.29550i
$987$	−29.2195	−	13.3947i	−0.0296044	−	0.0135712i
$988$	3934.04	+	693.678i	3.98182	+	0.702103i
$989$	−603.101	+	348.201i	−0.609809	+	0.352073i
$990$	−120.269	−	2033.25i	−0.121484	−	2.05379i
$991$	161.951	−	280.507i	0.163422	−	0.283055i	−0.772672	−	0.634805i	$-0.781080\pi$
$991$	161.951	−	280.507i	0.163422	−	0.283055i	0.936094	+	0.351751i	$0.114414\pi$
$992$	366.437	+	307.477i	0.369392	+	0.309956i
$993$	57.7981	+	210.229i	0.0582055	+	0.211711i
$994$	56.2670	+	319.106i	0.0566066	+	0.321032i
$995$	−14.0400	−	304.463i	−0.0141106	−	0.305993i
$996$	−739.205	+	350.565i	−0.742174	+	0.351973i
$997$	−148.115	−	406.943i	−0.148561	−	0.408168i	0.842983	−	0.537940i	$-0.180797\pi$
$997$	−148.115	−	406.943i	−0.148561	−	0.408168i	−0.991544	+	0.129773i	$0.958575\pi$
$998$	−2204.13			−2.20854
$999$	286.004	+	989.759i	0.286290	+	0.990750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.n.a.74.33	yes	204
3.2	odd	2		405.3.n.a.224.2		204
5.4	even	2	inner	135.3.n.a.74.2	✓	204
15.14	odd	2		405.3.n.a.224.33		204
27.4	even	9		405.3.n.a.179.33		204
27.23	odd	18	inner	135.3.n.a.104.2	yes	204
135.4	even	18		405.3.n.a.179.2		204
135.104	odd	18	inner	135.3.n.a.104.33	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.2	✓	204	5.4	even	2	inner
135.3.n.a.74.33	yes	204	1.1	even	1	trivial
135.3.n.a.104.2	yes	204	27.23	odd	18	inner
135.3.n.a.104.33	yes	204	135.104	odd	18	inner
405.3.n.a.179.2		204	135.4	even	18
405.3.n.a.179.33		204	27.4	even	9
405.3.n.a.224.2		204	3.2	odd	2
405.3.n.a.224.33		204	15.14	odd	2

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.n (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.50983 - 1.27747i) q^{2} +(-2.46859 - 1.70472i) q^{3} +(7.62280 - 6.39629i) q^{4} +(-4.44069 - 2.29788i) q^{5} +(-10.8421 - 2.82972i) q^{6} +(-1.03030 + 1.22786i) q^{7} +(11.1135 - 19.2491i) q^{8} +(3.18787 + 8.41650i) q^{9} +(-18.5216 - 2.39229i) q^{10} +(11.9341 + 2.10430i) q^{11} +(-29.7214 + 2.79508i) q^{12} +(4.71168 - 12.9452i) q^{13} +(-2.04761 + 5.62576i) q^{14} +(7.04501 + 13.2427i) q^{15} +(7.50440 - 42.5596i) q^{16} +(8.93265 + 15.4718i) q^{17} +(21.9407 + 25.4681i) q^{18} +(-14.5705 + 25.2368i) q^{19} +(-48.5484 + 10.8877i) q^{20} +(4.63654 - 1.27472i) q^{21} +(44.5747 - 7.85972i) q^{22} +(22.0238 - 18.4801i) q^{23} +(-60.2489 + 28.5728i) q^{24} +(14.4395 + 20.4083i) q^{25} -51.4546i q^{26} +(6.47822 - 26.2113i) q^{27} +15.9498i q^{28} +(-6.96737 - 19.1427i) q^{29} +(41.6440 + 37.4796i) q^{30} +(-5.05373 + 4.24059i) q^{31} +(-12.5909 - 71.4065i) q^{32} +(-25.8730 - 25.5388i) q^{33} +(51.1169 + 42.8922i) q^{34} +(7.39671 - 3.08506i) q^{35} +(78.1349 + 43.7668i) q^{36} +(-33.0454 + 19.0788i) q^{37} +(-18.9005 + 107.190i) q^{38} +(-33.6992 + 23.9244i) q^{39} +(-93.5837 + 59.9420i) q^{40} +(-16.8042 + 46.1691i) q^{41} +(14.6451 - 10.3971i) q^{42} +(-23.8547 - 4.20622i) q^{43} +(104.431 - 60.2930i) q^{44} +(5.18374 - 44.7004i) q^{45} +(53.6918 - 92.9970i) q^{46} +(-5.12070 - 4.29678i) q^{47} +(-91.0774 + 92.2692i) q^{48} +(8.06263 + 45.7255i) q^{49} +(76.7514 + 53.1837i) q^{50} +(4.32402 - 53.4212i) q^{51} +(-46.8852 - 128.816i) q^{52} -35.3575 q^{53} +(-10.7468 - 100.273i) q^{54} +(-48.1601 - 36.7675i) q^{55} +(12.1850 + 33.4781i) q^{56} +(78.9901 - 37.4607i) q^{57} +(-48.9086 - 58.2870i) q^{58} +(81.0242 - 14.2868i) q^{59} +(138.407 + 55.8841i) q^{60} +(-42.3934 - 35.5723i) q^{61} +(-12.3205 + 21.3398i) q^{62} +(-13.6188 - 4.75724i) q^{63} +(-48.9797 - 84.8352i) q^{64} +(-50.6696 + 46.6589i) q^{65} +(-123.435 - 56.5849i) q^{66} +(-10.5187 + 28.8998i) q^{67} +(167.054 + 60.8026i) q^{68} +(-85.8711 + 8.07555i) q^{69} +(22.0201 - 20.2771i) q^{70} +(46.8725 - 27.0619i) q^{71} +(197.438 + 32.1729i) q^{72} +(-80.6986 - 46.5914i) q^{73} +(-91.6111 + 109.178i) q^{74} +(-0.854746 - 74.9951i) q^{75} +(50.3540 + 285.572i) q^{76} +(-14.8794 + 12.4853i) q^{77} +(-87.7156 + 127.020i) q^{78} +(27.1542 - 9.88334i) q^{79} +(-131.121 + 171.750i) q^{80} +(-60.6750 + 53.6614i) q^{81} +183.513i q^{82} +(25.7526 - 9.37318i) q^{83} +(27.1900 - 39.3736i) q^{84} +(-4.11484 - 89.2317i) q^{85} +(-89.0992 + 15.7106i) q^{86} +(-15.4333 + 59.1328i) q^{87} +(173.135 - 206.334i) q^{88} +(41.9166 + 24.2006i) q^{89} +(-38.9096 - 163.513i) q^{90} +(11.0405 + 19.1227i) q^{91} +(49.6785 - 281.741i) q^{92} +(19.7046 - 1.85307i) q^{93} +(-23.4618 - 8.53941i) q^{94} +(122.694 - 78.5876i) q^{95} +(-90.6463 + 197.737i) q^{96} +(-133.103 - 23.4697i) q^{97} +(86.7116 + 150.189i) q^{98} +(20.3334 + 107.151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31}+ \cdots + 792 q^{99}+O(q^{100}) \) 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

Introduction

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