LMFDB - Embedded newform 180.3.t.a.149.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(29,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("180.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.9
Character	$\chi$	$=$	180.149
Dual form			180.3.t.a.29.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56781 + 2.55773i) q^{3} +(-3.59000 - 3.48021i) q^{5} +(-9.96186 + 5.75148i) q^{7} +(-4.08395 + 8.02006i) q^{9} +O(q^{10})$	\(q+(1.56781 + 2.55773i) q^{3} +(-3.59000 - 3.48021i) q^{5} +(-9.96186 + 5.75148i) q^{7} +(-4.08395 + 8.02006i) q^{9} +(-13.2043 + 7.62351i) q^{11} +(14.7585 + 8.52085i) q^{13} +(3.27299 - 14.6386i) q^{15} +10.4260 q^{17} -23.1507 q^{19} +(-30.3290 - 16.4625i) q^{21} +(6.98060 - 12.0908i) q^{23} +(0.776254 + 24.9879i) q^{25} +(-26.9160 + 2.12830i) q^{27} +(38.8276 - 22.4171i) q^{29} +(-2.72391 + 4.71796i) q^{31} +(-40.2007 - 21.8208i) q^{33} +(55.7795 + 14.0215i) q^{35} +50.7314i q^{37} +(1.34456 + 51.1074i) q^{39} +(-36.9497 - 21.3329i) q^{41} +(-5.32518 + 3.07449i) q^{43} +(42.5729 - 14.5790i) q^{45} +(16.0466 + 27.7935i) q^{47} +(41.6591 - 72.1557i) q^{49} +(16.3460 + 26.6669i) q^{51} +16.7365 q^{53} +(73.9350 + 18.5854i) q^{55} +(-36.2958 - 59.2131i) q^{57} +(16.9286 + 9.77374i) q^{59} +(-3.29969 - 5.71522i) q^{61} +(-5.44352 - 103.383i) q^{63} +(-23.3289 - 81.9527i) q^{65} +(-30.7981 - 17.7813i) q^{67} +(41.8691 - 1.10152i) q^{69} -65.5016i q^{71} +104.118i q^{73} +(-62.6954 + 41.1618i) q^{75} +(87.6930 - 151.889i) q^{77} +(75.2628 + 130.359i) q^{79} +(-47.6427 - 65.5070i) q^{81} +(40.7295 + 70.5455i) q^{83} +(-37.4294 - 36.2847i) q^{85} +(118.211 + 64.1646i) q^{87} +14.3858i q^{89} -196.030 q^{91} +(-16.3378 + 0.429826i) q^{93} +(83.1110 + 80.5693i) q^{95} +(23.2672 - 13.4333i) q^{97} +(-7.21531 - 137.033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{5} + 2 q^{9}+O(q^{10}) $ 24 * q - 9 * q^5 + 2 * q^9	$ 24 q - 9 q^{5} + 2 q^{9} - 18 q^{11} + 25 q^{15} - 26 q^{21} + 3 q^{25} + 36 q^{29} + 30 q^{31} + 6 q^{39} - 36 q^{41} - 31 q^{45} + 108 q^{49} + 124 q^{51} + 42 q^{55} - 306 q^{59} + 48 q^{61} - 225 q^{65} - 268 q^{69} - 217 q^{75} + 114 q^{79} - 14 q^{81} + 48 q^{85} - 84 q^{91} + 324 q^{95} + 418 q^{99}+O(q^{100}) $ 24 * q - 9 * q^5 + 2 * q^9 - 18 * q^11 + 25 * q^15 - 26 * q^21 + 3 * q^25 + 36 * q^29 + 30 * q^31 + 6 * q^39 - 36 * q^41 - 31 * q^45 + 108 * q^49 + 124 * q^51 + 42 * q^55 - 306 * q^59 + 48 * q^61 - 225 * q^65 - 268 * q^69 - 217 * q^75 + 114 * q^79 - 14 * q^81 + 48 * q^85 - 84 * q^91 + 324 * q^95 + 418 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.56781	+	2.55773i	0.522603	+	0.852576i
$3$	1.56781	+	2.55773i	0.522603	+	0.852576i
$4$		0			0
$5$	−3.59000	−	3.48021i	−0.718001	−	0.696042i
$5$	−3.59000	−	3.48021i	−0.718001	−	0.696042i
$6$		0			0
$7$	−9.96186	+	5.75148i	−1.42312	+	0.821641i	−0.996565	−	0.0828194i	$-0.973608\pi$
$7$	−9.96186	+	5.75148i	−1.42312	+	0.821641i	−0.426559	+	0.904460i	$0.640274\pi$
$8$		0			0
$9$	−4.08395	+	8.02006i	−0.453772	+	0.891118i
$10$		0			0
$11$	−13.2043	+	7.62351i	−1.20039	+	0.693047i	−0.960642	−	0.277788i	$-0.910399\pi$
$11$	−13.2043	+	7.62351i	−1.20039	+	0.693047i	−0.239750	+	0.970835i	$0.577065\pi$
$12$		0			0
$13$	14.7585	+	8.52085i	1.13527	+	0.655450i	0.945256	−	0.326331i	$-0.105812\pi$
$13$	14.7585	+	8.52085i	1.13527	+	0.655450i	0.190017	+	0.981781i	$0.439146\pi$
$14$		0			0
$15$	3.27299	−	14.6386i	0.218200	−	0.975904i
$16$		0			0
$17$	10.4260			0.613294			0.306647	−	0.951823i	$-0.400793\pi$
$17$	10.4260			0.613294			0.306647	+	0.951823i	$0.400793\pi$
$18$		0			0
$19$	−23.1507			−1.21846			−0.609228	−	0.792995i	$-0.708521\pi$
$19$	−23.1507			−1.21846			−0.609228	+	0.792995i	$0.708521\pi$
$20$		0			0
$21$	−30.3290	−	16.4625i	−1.44424	−	0.783929i
$22$		0			0
$23$	6.98060	−	12.0908i	0.303504	−	0.525685i	−0.673423	−	0.739258i	$-0.735177\pi$
$23$	6.98060	−	12.0908i	0.303504	−	0.525685i	0.976927	+	0.213572i	$0.0685099\pi$
$24$		0			0
$25$	0.776254	+	24.9879i	0.0310502	+	0.999518i
$26$		0			0
$27$	−26.9160	+	2.12830i	−0.996888	+	0.0788258i
$28$		0			0
$29$	38.8276	−	22.4171i	1.33888	−	0.773004i	0.352240	−	0.935910i	$-0.385420\pi$
$29$	38.8276	−	22.4171i	1.33888	−	0.773004i	0.986642	+	0.162906i	$0.0520867\pi$
$30$		0			0
$31$	−2.72391	+	4.71796i	−0.0878682	+	0.152192i	−0.906610	−	0.421970i	$-0.861339\pi$
$31$	−2.72391	+	4.71796i	−0.0878682	+	0.152192i	0.818742	+	0.574162i	$0.194672\pi$
$32$		0			0
$33$	−40.2007	−	21.8208i	−1.21820	−	0.661237i
$34$		0			0
$35$	55.7795	+	14.0215i	1.59370	+	0.400615i
$36$		0			0
$37$			50.7314i			1.37112i	0.728017	+	0.685559i	$0.240442\pi$
$37$			50.7314i			1.37112i	−0.728017	+	0.685559i	$0.759558\pi$
$38$		0			0
$39$	1.34456	+	51.1074i	0.0344760	+	1.31045i
$40$		0			0
$41$	−36.9497	−	21.3329i	−0.901211	−	0.520315i	−0.0236184	−	0.999721i	$-0.507519\pi$
$41$	−36.9497	−	21.3329i	−0.901211	−	0.520315i	−0.877593	+	0.479406i	$0.840852\pi$
$42$		0			0
$43$	−5.32518	+	3.07449i	−0.123841	+	0.0714998i	−0.560641	−	0.828059i	$-0.689445\pi$
$43$	−5.32518	+	3.07449i	−0.123841	+	0.0714998i	0.436800	+	0.899559i	$0.356112\pi$
$44$		0			0
$45$	42.5729	−	14.5790i	0.946064	−	0.323979i
$46$		0			0
$47$	16.0466	+	27.7935i	0.341417	+	0.591351i	0.984696	−	0.174280i	$-0.0557599\pi$
$47$	16.0466	+	27.7935i	0.341417	+	0.591351i	−0.643279	+	0.765632i	$0.722427\pi$
$48$		0			0
$49$	41.6591	−	72.1557i	0.850186	−	1.47257i
$50$		0			0
$51$	16.3460	+	26.6669i	0.320509	+	0.522880i
$52$		0			0
$53$	16.7365			0.315783			0.157892	−	0.987456i	$-0.449530\pi$
$53$	16.7365			0.315783			0.157892	+	0.987456i	$0.449530\pi$
$54$		0			0
$55$	73.9350	+	18.5854i	1.34427	+	0.337916i
$56$		0			0
$57$	−36.2958	−	59.2131i	−0.636769	−	1.03883i
$58$		0			0
$59$	16.9286	+	9.77374i	0.286926	+	0.165657i	0.636555	−	0.771232i	$-0.280359\pi$
$59$	16.9286	+	9.77374i	0.286926	+	0.165657i	−0.349629	+	0.936888i	$0.613692\pi$
$60$		0			0
$61$	−3.29969	−	5.71522i	−0.0540932	−	0.0936922i	0.837711	−	0.546114i	$-0.183893\pi$
$61$	−3.29969	−	5.71522i	−0.0540932	−	0.0936922i	−0.891804	+	0.452422i	$0.850560\pi$
$62$		0			0
$63$	−5.44352	−	103.383i	−0.0864051	−	1.64101i
$64$		0			0
$65$	−23.3289	−	81.9527i	−0.358906	−	1.26081i
$66$		0			0
$67$	−30.7981	−	17.7813i	−0.459673	−	0.265392i	0.252234	−	0.967666i	$-0.418835\pi$
$67$	−30.7981	−	17.7813i	−0.459673	−	0.265392i	−0.711907	+	0.702274i	$0.752168\pi$
$68$		0			0
$69$	41.8691	−	1.10152i	0.606799	−	0.0159640i
$70$		0			0
$71$		−	65.5016i		−	0.922557i	−0.887255	−	0.461279i	$-0.847391\pi$
$71$		−	65.5016i		−	0.922557i	0.887255	−	0.461279i	$-0.152609\pi$
$72$		0			0
$73$			104.118i			1.42628i	0.701023	+	0.713139i	$0.252727\pi$
$73$			104.118i			1.42628i	−0.701023	+	0.713139i	$0.747273\pi$
$74$		0			0
$75$	−62.6954	+	41.1618i	−0.835938	+	0.548824i
$76$		0			0
$77$	87.6930	−	151.889i	1.13887	−	1.97258i
$78$		0			0
$79$	75.2628	+	130.359i	0.952694	+	1.65011i	0.739560	+	0.673091i	$0.235034\pi$
$79$	75.2628	+	130.359i	0.952694	+	1.65011i	0.213133	+	0.977023i	$0.431633\pi$
$80$		0			0
$81$	−47.6427	−	65.5070i	−0.588182	−	0.808729i
$82$		0			0
$83$	40.7295	+	70.5455i	0.490716	+	0.849946i	0.999943	−	0.0106869i	$-0.00340181\pi$
$83$	40.7295	+	70.5455i	0.490716	+	0.849946i	−0.509227	+	0.860633i	$0.670068\pi$
$84$		0			0
$85$	−37.4294	−	36.2847i	−0.440346	−	0.426879i
$86$		0			0
$87$	118.211	+	64.1646i	1.35875	+	0.737525i
$88$		0			0
$89$			14.3858i			0.161638i	0.996729	+	0.0808189i	$0.0257536\pi$
$89$			14.3858i			0.161638i	−0.996729	+	0.0808189i	$0.974246\pi$
$90$		0			0
$91$	−196.030			−2.15418
$92$		0			0
$93$	−16.3378	+	0.429826i	−0.175676	+	0.00462178i
$94$		0			0
$95$	83.1110	+	80.5693i	0.874853	+	0.848097i
$96$		0			0
$97$	23.2672	−	13.4333i	0.239868	−	0.138488i	−0.375248	−	0.926924i	$-0.622443\pi$
$97$	23.2672	−	13.4333i	0.239868	−	0.138488i	0.615116	+	0.788437i	$0.289109\pi$
$98$		0			0
$99$	−7.21531	−	137.033i	−0.0728819	−	1.38418i
$100$		0			0
$101$	−82.7052	+	47.7499i	−0.818863	+	0.472771i	−0.850024	−	0.526743i	$-0.823413\pi$
$101$	−82.7052	+	47.7499i	−0.818863	+	0.472771i	0.0311610	+	0.999514i	$0.490080\pi$
$102$		0			0
$103$	50.0428	+	28.8922i	0.485852	+	0.280507i	0.722852	−	0.691003i	$-0.242831\pi$
$103$	50.0428	+	28.8922i	0.485852	+	0.280507i	−0.237000	+	0.971510i	$0.576164\pi$
$104$		0			0
$105$	51.5883	+	164.652i	0.491317	+	1.56811i
$106$		0			0
$107$	−64.8388			−0.605970			−0.302985	−	0.952995i	$-0.597983\pi$
$107$	−64.8388			−0.605970			−0.302985	+	0.952995i	$0.597983\pi$
$108$		0			0
$109$	−40.9173			−0.375388			−0.187694	−	0.982228i	$-0.560101\pi$
$109$	−40.9173			−0.375388			−0.187694	+	0.982228i	$0.560101\pi$
$110$		0			0
$111$	−129.757	+	79.5371i	−1.16898	+	0.716550i
$112$		0			0
$113$	−108.221	+	187.445i	−0.957709	+	1.65880i	−0.229667	+	0.973269i	$0.573764\pi$
$113$	−108.221	+	187.445i	−0.957709	+	1.65880i	−0.728043	+	0.685532i	$0.759570\pi$
$114$		0			0
$115$	−67.1388	+	19.1119i	−0.583816	+	0.166190i
$116$		0			0
$117$	−128.611	+	83.5657i	−1.09924	+	0.714237i
$118$		0			0
$119$	−103.862	+	59.9650i	−0.872793	+	0.503907i
$120$		0			0
$121$	55.7359	−	96.5374i	0.460627	−	0.797830i
$122$		0			0
$123$	−3.36627	−	127.953i	−0.0273680	−	1.04027i
$124$		0			0
$125$	84.1766	−	92.4083i	0.673413	−	0.739267i
$126$		0			0
$127$		−	128.534i		−	1.01208i	−0.862510	−	0.506041i	$-0.831109\pi$
$127$		−	128.534i		−	1.01208i	0.862510	−	0.506041i	$-0.168891\pi$
$128$		0			0
$129$	−16.2126	−	8.80014i	−0.125679	−	0.0682181i
$130$		0			0
$131$	−23.1907	−	13.3892i	−0.177028	−	0.102207i	0.408867	−	0.912594i	$-0.365924\pi$
$131$	−23.1907	−	13.3892i	−0.177028	−	0.102207i	−0.585896	+	0.810386i	$0.699257\pi$
$132$		0			0
$133$	230.624	−	133.151i	1.73401	−	1.00113i
$134$		0			0
$135$	104.035	+	86.0327i	0.770633	+	0.637280i
$136$		0			0
$137$	49.9236	+	86.4703i	0.364406	+	0.631170i	0.988681	−	0.150035i	$-0.0479387\pi$
$137$	49.9236	+	86.4703i	0.364406	+	0.631170i	−0.624275	+	0.781205i	$0.714605\pi$
$138$		0			0
$139$	7.69396	−	13.3263i	0.0553522	−	0.0958729i	−0.837022	−	0.547170i	$-0.815705\pi$
$139$	7.69396	−	13.3263i	0.0553522	−	0.0958729i	0.892374	+	0.451297i	$0.149038\pi$
$140$		0			0
$141$	−45.9302	+	84.6177i	−0.325746	+	0.600126i
$142$		0			0
$143$	−259.835			−1.81703
$144$		0			0
$145$	−217.407	−	54.6507i	−1.49936	−	0.376901i
$146$		0			0
$147$	249.868	−	6.57369i	1.69978	−	0.0447190i
$148$		0			0
$149$	−104.146	−	60.1287i	−0.698966	−	0.403548i	0.107996	−	0.994151i	$-0.465557\pi$
$149$	−104.146	−	60.1287i	−0.698966	−	0.403548i	−0.806962	+	0.590603i	$0.798890\pi$
$150$		0			0
$151$	22.1568	+	38.3766i	0.146733	+	0.254150i	0.930018	−	0.367513i	$-0.119791\pi$
$151$	22.1568	+	38.3766i	0.146733	+	0.254150i	−0.783285	+	0.621663i	$0.786457\pi$
$152$		0			0
$153$	−42.5792	+	83.6171i	−0.278296	+	0.546517i
$154$		0			0
$155$	26.1984	−	7.45769i	0.169022	−	0.0481141i
$156$		0			0
$157$	−51.5673	−	29.7724i	−0.328454	−	0.189633i	0.326701	−	0.945128i	$-0.394063\pi$
$157$	−51.5673	−	29.7724i	−0.328454	−	0.189633i	−0.655154	+	0.755495i	$0.727396\pi$
$158$		0			0
$159$	26.2396	+	42.8074i	0.165029	+	0.269229i
$160$		0			0
$161$			160.595i			0.997486i
$162$		0			0
$163$		−	200.140i		−	1.22785i	−0.789363	−	0.613927i	$-0.789589\pi$
$163$		−	200.140i		−	1.22785i	0.789363	−	0.613927i	$-0.210411\pi$
$164$		0			0
$165$	68.3796	+	218.244i	0.414422	+	1.32269i
$166$		0			0
$167$	−38.5630	+	66.7931i	−0.230916	+	0.399959i	−0.958078	−	0.286508i	$-0.907506\pi$
$167$	−38.5630	+	66.7931i	−0.230916	+	0.399959i	0.727162	+	0.686466i	$0.240839\pi$
$168$		0			0
$169$	60.7097	+	105.152i	0.359229	+	0.622203i
$170$		0			0
$171$	94.5462	−	185.670i	0.552902	−	1.08579i
$172$		0			0
$173$	−129.355	−	224.050i	−0.747718	−	1.29509i	−0.948914	−	0.315535i	$-0.897816\pi$
$173$	−129.355	−	224.050i	−0.747718	−	1.29509i	0.201195	−	0.979551i	$-0.435517\pi$
$174$		0			0
$175$	−151.451	−	244.462i	−0.865433	−	1.39692i
$176$		0			0
$177$	1.54227	+	58.6222i	0.00871338	+	0.331199i
$178$		0			0
$179$			174.572i			0.975261i	0.873050	+	0.487630i	$0.162139\pi$
$179$			174.572i			0.975261i	−0.873050	+	0.487630i	$0.837861\pi$
$180$		0			0
$181$	−22.3291			−0.123365			−0.0616825	−	0.998096i	$-0.519647\pi$
$181$	−22.3291			−0.123365			−0.0616825	+	0.998096i	$0.519647\pi$
$182$		0			0
$183$	9.44471	−	17.4001i	0.0516104	−	0.0950824i
$184$		0			0
$185$	176.556	−	182.126i	0.954356	−	0.984464i
$186$		0			0
$187$	−137.668	+	79.4827i	−0.736193	+	0.425041i
$188$		0			0
$189$	255.892	−	176.009i	1.35393	−	0.931263i
$190$		0			0
$191$	190.213	−	109.819i	0.995879	−	0.574971i	0.0888528	−	0.996045i	$-0.471680\pi$
$191$	190.213	−	109.819i	0.995879	−	0.574971i	0.907026	+	0.421074i	$0.138347\pi$
$192$		0			0
$193$	295.702	+	170.724i	1.53214	+	0.884579i	0.999263	+	0.0383835i	$0.0122209\pi$
$193$	295.702	+	170.724i	1.53214	+	0.884579i	0.532873	+	0.846195i	$0.321112\pi$
$194$		0			0
$195$	173.038	−	188.155i	0.887372	−	0.964898i
$196$		0			0
$197$	−200.719			−1.01888			−0.509439	−	0.860507i	$-0.670147\pi$
$197$	−200.719			−1.01888			−0.509439	+	0.860507i	$0.670147\pi$
$198$		0			0
$199$	−79.9313			−0.401665			−0.200833	−	0.979626i	$-0.564365\pi$
$199$	−79.9313			−0.401665			−0.200833	+	0.979626i	$0.564365\pi$
$200$		0			0
$201$	−2.80584	−	106.651i	−0.0139594	−	0.530601i
$202$		0			0
$203$	−257.863	+	446.632i	−1.27026	+	2.20016i
$204$		0			0
$205$	58.4064	+	205.178i	0.284909	+	1.00087i
$206$		0			0
$207$	68.4602	+	105.363i	0.330726	+	0.508999i
$208$		0			0
$209$	305.689	−	176.489i	1.46263	−	0.844447i
$210$		0			0
$211$	35.9481	−	62.2639i	0.170370	−	0.295089i	−0.768179	−	0.640235i	$-0.778837\pi$
$211$	35.9481	−	62.2639i	0.170370	−	0.295089i	0.938549	+	0.345145i	$0.112170\pi$
$212$		0			0
$213$	167.535	−	102.694i	0.786550	−	0.482131i
$214$		0			0
$215$	29.8173	+	7.49531i	0.138685	+	0.0348619i
$216$		0			0
$217$		−	62.6662i		−	0.288784i
$218$		0			0
$219$	−266.306	+	163.238i	−1.21601	+	0.745377i
$220$		0			0
$221$	153.873	+	88.8383i	0.696256	+	0.401983i
$222$		0			0
$223$	305.820	−	176.565i	1.37139	−	0.791773i	0.380288	−	0.924868i	$-0.375825\pi$
$223$	305.820	−	176.565i	1.37139	−	0.791773i	0.991103	+	0.133095i	$0.0424916\pi$
$224$		0			0
$225$	−203.575	−	95.8239i	−0.904778	−	0.425884i
$226$		0			0
$227$	−85.7010	−	148.439i	−0.377538	−	0.653914i	0.613166	−	0.789954i	$-0.289896\pi$
$227$	−85.7010	−	148.439i	−0.377538	−	0.653914i	−0.990703	+	0.136040i	$0.956562\pi$
$228$		0			0
$229$	82.9005	−	143.588i	0.362011	−	0.627021i	−0.626281	−	0.779597i	$-0.715424\pi$
$229$	82.9005	−	143.588i	0.362011	−	0.627021i	0.988292	+	0.152576i	$0.0487570\pi$
$230$		0			0
$231$	525.976	−	13.8377i	2.27695	−	0.0599035i
$232$		0			0
$233$	6.09276			0.0261492			0.0130746	−	0.999915i	$-0.495838\pi$
$233$	6.09276			0.0261492			0.0130746	+	0.999915i	$0.495838\pi$
$234$		0			0
$235$	39.1200	−	155.624i	0.166468	−	0.662231i
$236$		0			0
$237$	−215.425	+	396.880i	−0.908967	+	1.67460i
$238$		0			0
$239$	−30.7721	−	17.7663i	−0.128754	−	0.0743360i	0.434240	−	0.900797i	$-0.357017\pi$
$239$	−30.7721	−	17.7663i	−0.128754	−	0.0743360i	−0.562994	+	0.826461i	$0.690350\pi$
$240$		0			0
$241$	150.152	+	260.071i	0.623038	+	1.07913i	0.988917	+	0.148471i	$0.0474352\pi$
$241$	150.152	+	260.071i	0.623038	+	1.07913i	−0.365879	+	0.930663i	$0.619232\pi$
$242$		0			0
$243$	92.8544	−	224.560i	0.382117	−	0.924114i
$244$		0			0
$245$	−400.674	+	114.057i	−1.63540	+	0.465538i
$246$		0			0
$247$	−341.670	−	197.263i	−1.38328	−	0.798637i
$248$		0			0
$249$	−116.580	+	214.777i	−0.468193	+	0.862557i
$250$		0			0
$251$		−	240.776i		−	0.959268i	−0.877469	−	0.479634i	$-0.840770\pi$
$251$		−	240.776i		−	0.959268i	0.877469	−	0.479634i	$-0.159230\pi$
$252$		0			0
$253$			212.867i			0.841371i
$254$		0			0
$255$	34.1242	−	152.622i	0.133821	−	0.598516i
$256$		0			0
$257$	67.0253	−	116.091i	0.260799	−	0.451717i	−0.705656	−	0.708555i	$-0.749347\pi$
$257$	67.0253	−	116.091i	0.260799	−	0.451717i	0.966454	+	0.256838i	$0.0826807\pi$
$258$		0			0
$259$	−291.781	−	505.379i	−1.12657	−	1.95127i
$260$		0			0
$261$	21.2168	+	402.950i	0.0812903	+	1.54387i
$262$		0			0
$263$	218.575	+	378.584i	0.831085	+	1.43948i	0.897178	+	0.441668i	$0.145613\pi$
$263$	218.575	+	378.584i	0.831085	+	1.43948i	−0.0660933	+	0.997813i	$0.521053\pi$
$264$		0			0
$265$	−60.0841	−	58.2466i	−0.226732	−	0.219798i
$266$		0			0
$267$	−36.7949	+	22.5541i	−0.137809	+	0.0844725i
$268$		0			0
$269$			39.0128i			0.145029i	0.997367	+	0.0725146i	$0.0231024\pi$
$269$			39.0128i			0.145029i	−0.997367	+	0.0725146i	$0.976898\pi$
$270$		0			0
$271$	225.452			0.831925			0.415963	−	0.909382i	$-0.363445\pi$
$271$	225.452			0.831925			0.415963	+	0.909382i	$0.363445\pi$
$272$		0			0
$273$	−307.338	−	501.392i	−1.12578	−	1.83660i
$274$		0			0
$275$	−200.746	−	324.031i	−0.729985	−	1.17829i
$276$		0			0
$277$	197.530	−	114.044i	0.713106	−	0.411712i	−0.0991038	−	0.995077i	$-0.531598\pi$
$277$	197.530	−	114.044i	0.713106	−	0.411712i	0.812210	+	0.583365i	$0.198264\pi$
$278$		0			0
$279$	−26.7140	−	41.1138i	−0.0957490	−	0.147361i
$280$		0			0
$281$	−208.527	+	120.393i	−0.742089	+	0.428445i	−0.822828	−	0.568290i	$-0.807605\pi$
$281$	−208.527	+	120.393i	−0.742089	+	0.428445i	0.0807396	+	0.996735i	$0.474272\pi$
$282$		0			0
$283$	40.2490	+	23.2378i	0.142223	+	0.0821123i	0.569423	−	0.822045i	$-0.307167\pi$
$283$	40.2490	+	23.2378i	0.142223	+	0.0821123i	−0.427200	+	0.904157i	$0.640500\pi$
$284$		0			0
$285$	−75.7720	+	338.893i	−0.265867	+	1.18910i
$286$		0			0
$287$	490.783			1.71005
$288$		0			0
$289$	−180.299			−0.623871
$290$		0			0
$291$	70.8372	+	38.4502i	0.243427	+	0.132131i
$292$		0			0
$293$	−48.2701	+	83.6062i	−0.164744	+	0.285345i	−0.936564	−	0.350495i	$-0.886013\pi$
$293$	−48.2701	+	83.6062i	−0.164744	+	0.285345i	0.771820	+	0.635841i	$0.219347\pi$
$294$		0			0
$295$	−26.7591	−	94.0029i	−0.0907089	−	0.318654i
$296$		0			0
$297$	339.182	−	233.297i	1.14203	−	0.785512i
$298$		0			0
$299$	206.047	−	118.961i	0.689120	−	0.397864i
$300$		0			0
$301$	35.3658	−	61.2554i	0.117494	−	0.203506i
$302$		0			0
$303$	−251.797	−	136.675i	−0.831014	−	0.451072i
$304$		0			0
$305$	−8.04430	+	32.0013i	−0.0263748	+	0.104922i
$306$		0			0
$307$			398.954i			1.29952i	0.760138	+	0.649762i	$0.225131\pi$
$307$			398.954i			1.29952i	−0.760138	+	0.649762i	$0.774869\pi$
$308$		0			0
$309$	4.55910	+	173.293i	0.0147544	+	0.560820i
$310$		0			0
$311$	346.600	+	200.110i	1.11447	+	0.643440i	0.939984	−	0.341220i	$-0.110840\pi$
$311$	346.600	+	200.110i	1.11447	+	0.643440i	0.174487	+	0.984659i	$0.444173\pi$
$312$		0			0
$313$	−179.093	+	103.400i	−0.572183	+	0.330350i	−0.758021	−	0.652230i	$-0.773833\pi$
$313$	−179.093	+	103.400i	−0.572183	+	0.330350i	0.185838	+	0.982580i	$0.440500\pi$
$314$		0			0
$315$	−340.254	+	390.092i	−1.08017	+	1.23839i
$316$		0			0
$317$	−31.3986	−	54.3839i	−0.0990491	−	0.171558i	0.812242	−	0.583320i	$-0.198247\pi$
$317$	−31.3986	−	54.3839i	−0.0990491	−	0.171558i	−0.911291	+	0.411762i	$0.864913\pi$
$318$		0			0
$319$	−341.794	+	592.005i	−1.07146	+	1.85582i
$320$		0			0
$321$	−101.655	−	165.840i	−0.316682	−	0.516636i
$322$		0			0
$323$	−241.369			−0.747272
$324$		0			0
$325$	−201.462	+	375.400i	−0.619883	+	1.15508i
$326$		0			0
$327$	−64.1505	−	104.655i	−0.196179	−	0.320047i
$328$		0			0
$329$	−319.708	−	184.583i	−0.971756	−	0.561044i
$330$		0			0
$331$	120.382	+	208.509i	0.363693	+	0.629935i	0.988566	−	0.150792i	$-0.0481823\pi$
$331$	120.382	+	208.509i	0.363693	+	0.629935i	−0.624872	+	0.780727i	$0.714849\pi$
$332$		0			0
$333$	−406.869	−	207.184i	−1.22183	−	0.622175i
$334$		0			0
$335$	48.6826	+	171.019i	0.145321	+	0.510504i
$336$		0			0
$337$	296.941	+	171.439i	0.881130	+	0.508720i	0.871031	−	0.491229i	$-0.163452\pi$
$337$	296.941	+	171.439i	0.881130	+	0.508720i	0.0100989	+	0.999949i	$0.496785\pi$
$338$		0			0
$339$	−649.102	+	17.0770i	−1.91476	+	0.0503746i
$340$		0			0
$341$		−	83.0632i		−	0.243587i
$342$		0			0
$343$			394.762i			1.15091i
$344$		0			0
$345$	−154.144	−	141.759i	−0.446794	−	0.410896i
$346$		0			0
$347$	45.6812	−	79.1222i	0.131646	−	0.228018i	−0.792665	−	0.609657i	$-0.791307\pi$
$347$	45.6812	−	79.1222i	0.131646	−	0.228018i	0.924311	+	0.381639i	$0.124640\pi$
$348$		0			0
$349$	31.0445	+	53.7706i	0.0889526	+	0.154070i	0.907069	−	0.420983i	$-0.138315\pi$
$349$	31.0445	+	53.7706i	0.0889526	+	0.154070i	−0.818116	+	0.575053i	$0.804981\pi$
$350$		0			0
$351$	−415.376	−	197.936i	−1.18341	−	0.563922i
$352$		0			0
$353$	66.0940	+	114.478i	0.187235	+	0.324301i	0.944327	−	0.329007i	$-0.106714\pi$
$353$	66.0940	+	114.478i	0.187235	+	0.324301i	−0.757092	+	0.653308i	$0.773381\pi$
$354$		0			0
$355$	−227.959	+	235.151i	−0.642139	+	0.662397i
$356$		0			0
$357$	−316.210	−	171.638i	−0.885743	−	0.480779i
$358$		0			0
$359$			299.807i			0.835118i	0.908650	+	0.417559i	$0.137114\pi$
$359$			299.807i			0.835118i	−0.908650	+	0.417559i	$0.862886\pi$
$360$		0			0
$361$	174.954			0.484637
$362$		0			0
$363$	334.300	−	8.79496i	0.920936	−	0.0242285i
$364$		0			0
$365$	362.354	−	373.785i	0.992750	−	1.02407i
$366$		0			0
$367$	−371.066	+	214.235i	−1.01108	+	0.583747i	−0.911508	−	0.411283i	$-0.865081\pi$
$367$	−371.066	+	214.235i	−1.01108	+	0.583747i	−0.0995722	+	0.995030i	$0.531747\pi$
$368$		0			0
$369$	321.992	−	209.216i	0.872606	−	0.566981i
$370$		0			0
$371$	−166.727	+	96.2597i	−0.449398	+	0.259460i
$372$		0			0
$373$	362.959	+	209.555i	0.973081	+	0.561809i	0.900174	−	0.435530i	$-0.143439\pi$
$373$	362.959	+	209.555i	0.973081	+	0.561809i	0.0729068	+	0.997339i	$0.476772\pi$
$374$		0			0
$375$	368.328	+	70.4222i	0.982209	+	0.187792i
$376$		0			0
$377$	764.051			2.02666
$378$		0			0
$379$	394.789			1.04166			0.520830	−	0.853660i	$-0.325622\pi$
$379$	394.789			1.04166			0.520830	+	0.853660i	$0.325622\pi$
$380$		0			0
$381$	328.756	−	201.517i	0.862876	−	0.528917i
$382$		0			0
$383$	257.876	−	446.655i	0.673307	−	1.16620i	−0.303654	−	0.952782i	$-0.598207\pi$
$383$	257.876	−	446.655i	0.673307	−	1.16620i	0.976961	−	0.213419i	$-0.0684599\pi$
$384$		0			0
$385$	−843.423	+	240.091i	−2.19071	+	0.623613i
$386$		0			0
$387$	−2.90987	−	55.2643i	−0.00751904	−	0.142802i
$388$		0			0
$389$	−94.1463	+	54.3554i	−0.242021	+	0.139731i	−0.616105	−	0.787664i	$-0.711290\pi$
$389$	−94.1463	+	54.3554i	−0.242021	+	0.139731i	0.374084	+	0.927395i	$0.377957\pi$
$390$		0			0
$391$	72.7797	−	126.058i	0.186137	−	0.322400i
$392$		0			0
$393$	−2.11277	−	80.3071i	−0.00537600	−	0.204344i
$394$		0			0
$395$	183.483	−	729.920i	0.464514	−	1.84790i
$396$		0			0
$397$		−	319.633i		−	0.805121i	−0.915393	−	0.402560i	$-0.868120\pi$
$397$		−	319.633i		−	0.805121i	0.915393	−	0.402560i	$-0.131880\pi$
$398$		0			0
$399$	702.138	+	381.118i	1.75974	+	0.955183i
$400$		0			0
$401$	74.7066	+	43.1319i	0.186301	+	0.107561i	0.590250	−	0.807221i	$-0.299029\pi$
$401$	74.7066	+	43.1319i	0.186301	+	0.107561i	−0.403949	+	0.914782i	$0.632363\pi$
$402$		0			0
$403$	−80.4020	+	46.4201i	−0.199509	+	0.115186i
$404$		0			0
$405$	−56.9407	+	400.977i	−0.140594	+	0.990067i
$406$		0			0
$407$	−386.751	−	669.873i	−0.950249	−	1.64588i
$408$		0			0
$409$	335.486	−	581.079i	0.820260	−	1.42073i	−0.0852283	−	0.996361i	$-0.527162\pi$
$409$	335.486	−	581.079i	0.820260	−	1.42073i	0.905488	−	0.424371i	$-0.139505\pi$
$410$		0			0
$411$	−142.897	+	263.260i	−0.347681	+	0.640535i
$412$		0			0
$413$	−224.854			−0.544441
$414$		0			0
$415$	99.2943	−	395.006i	0.239263	−	0.951821i
$416$		0			0
$417$	46.1478	−	1.21408i	0.110666	−	0.00291147i
$418$		0			0
$419$	−617.394	−	356.453i	−1.47349	−	0.850723i	−0.473940	−	0.880557i	$-0.657169\pi$
$419$	−617.394	−	356.453i	−1.47349	−	0.850723i	−0.999555	+	0.0298344i	$0.990502\pi$
$420$		0			0
$421$	−205.862	−	356.564i	−0.488983	−	0.846944i	0.510936	−	0.859619i	$-0.329299\pi$
$421$	−205.862	−	356.564i	−0.488983	−	0.846944i	−0.999920	+	0.0126744i	$0.995966\pi$
$422$		0			0
$423$	−288.439	+	15.1874i	−0.681889	+	0.0359039i
$424$		0			0
$425$	8.09322	+	260.524i	0.0190429	+	0.612998i
$426$		0			0
$427$	65.7420	+	37.9562i	0.153963	+	0.0888903i
$428$		0			0
$429$	−407.372	−	664.588i	−0.949585	−	1.54916i
$430$		0			0
$431$			165.609i			0.384243i	0.981371	+	0.192122i	$0.0615368\pi$
$431$			165.609i			0.384243i	−0.981371	+	0.192122i	$0.938463\pi$
$432$		0			0
$433$		−	227.973i		−	0.526497i	−0.964728	−	0.263248i	$-0.915206\pi$
$433$		−	227.973i		−	0.526497i	0.964728	−	0.263248i	$-0.0847938\pi$
$434$		0			0
$435$	−201.072	−	641.751i	−0.462234	−	1.47529i
$436$		0			0
$437$	−161.606	+	279.909i	−0.369807	+	0.640525i
$438$		0			0
$439$	238.105	+	412.410i	0.542380	+	0.939430i	0.998767	+	0.0496487i	$0.0158102\pi$
$439$	238.105	+	412.410i	0.542380	+	0.939430i	−0.456386	+	0.889782i	$0.650856\pi$
$440$		0			0
$441$	408.560	+	628.789i	0.926439	+	1.42583i
$442$		0			0
$443$	270.526	+	468.565i	0.610669	+	1.05771i	0.991128	+	0.132912i	$0.0424327\pi$
$443$	270.526	+	468.565i	0.610669	+	1.05771i	−0.380459	+	0.924798i	$0.624234\pi$
$444$		0			0
$445$	50.0655	−	51.6450i	0.112507	−	0.116056i
$446$		0			0
$447$	−9.48813	−	360.648i	−0.0212262	−	0.806818i
$448$		0			0
$449$		−	98.6418i		−	0.219692i	−0.993949	−	0.109846i	$-0.964964\pi$
$449$		−	98.6418i		−	0.219692i	0.993949	−	0.109846i	$-0.0350358\pi$
$450$		0			0
$451$	650.527			1.44241
$452$		0			0
$453$	−63.4194	+	116.838i	−0.139999	+	0.257921i
$454$		0			0
$455$	703.749	+	682.226i	1.54670	+	1.49940i
$456$		0			0
$457$	−238.948	+	137.957i	−0.522862	+	0.301874i	−0.738105	−	0.674686i	$-0.764279\pi$
$457$	−238.948	+	137.957i	−0.522862	+	0.301874i	0.215243	+	0.976561i	$0.430946\pi$
$458$		0			0
$459$	−280.626	+	22.1896i	−0.611386	+	0.0483434i
$460$		0			0
$461$	686.984	−	396.631i	1.49020	−	0.860370i	0.490267	−	0.871572i	$-0.336899\pi$
$461$	686.984	−	396.631i	1.49020	−	0.860370i	0.999937	+	0.0112022i	$0.00356585\pi$
$462$		0			0
$463$	674.806	+	389.599i	1.45746	+	0.841468i	0.998886	−	0.0471863i	$-0.0150254\pi$
$463$	674.806	+	389.599i	1.45746	+	0.841468i	0.458579	+	0.888654i	$0.348359\pi$
$464$		0			0
$465$	60.1488	+	55.3160i	0.129352	+	0.118959i
$466$		0			0
$467$	233.839			0.500726			0.250363	−	0.968152i	$-0.419450\pi$
$467$	233.839			0.500726			0.250363	+	0.968152i	$0.419450\pi$
$468$		0			0
$469$	409.075			0.872229
$470$		0			0
$471$	−4.69799	−	178.572i	−0.00997450	−	0.379135i
$472$		0			0
$473$	46.8769	−	81.1931i	0.0991054	−	0.171656i
$474$		0			0
$475$	−17.9708	−	578.488i	−0.0378333	−	1.21787i
$476$		0			0
$477$	−68.3510	+	134.228i	−0.143294	+	0.281400i
$478$		0			0
$479$	83.5159	−	48.2179i	0.174355	−	0.100664i	−0.410283	−	0.911958i	$-0.634570\pi$
$479$	83.5159	−	48.2179i	0.174355	−	0.100664i	0.584638	+	0.811295i	$0.301237\pi$
$480$		0			0
$481$	−432.274	+	748.721i	−0.898699	+	1.55659i
$482$		0			0
$483$	−410.759	+	251.783i	−0.850433	+	0.521289i
$484$		0			0
$485$	−130.280	−	32.7491i	−0.268618	−	0.0675238i
$486$		0			0
$487$			171.674i			0.352513i	0.984344	+	0.176256i	$0.0563988\pi$
$487$			171.674i			0.352513i	−0.984344	+	0.176256i	$0.943601\pi$
$488$		0			0
$489$	511.905	−	313.782i	1.04684	−	0.641681i
$490$		0			0
$491$	18.7250	+	10.8109i	0.0381364	+	0.0220181i	0.518947	−	0.854806i	$-0.326324\pi$
$491$	18.7250	+	10.8109i	0.0381364	+	0.0220181i	−0.480811	+	0.876824i	$0.659658\pi$
$492$		0			0
$493$	404.816	−	233.721i	0.821128	−	0.474079i
$494$		0			0
$495$	−451.002	+	517.061i	−0.911116	+	1.04457i
$496$		0			0
$497$	376.731	+	652.518i	0.758010	+	1.31291i
$498$		0			0
$499$	−259.979	+	450.298i	−0.521001	+	0.902400i	0.478701	+	0.877978i	$0.341108\pi$
$499$	−259.979	+	450.298i	−0.521001	+	0.902400i	−0.999702	+	0.0244219i	$0.992226\pi$
$500$		0			0
$501$	−231.298	+	6.08513i	−0.461673	+	0.0121460i
$502$		0			0
$503$	−362.526			−0.720727			−0.360363	−	0.932812i	$-0.617347\pi$
$503$	−362.526			−0.720727			−0.360363	+	0.932812i	$0.617347\pi$
$504$		0			0
$505$	463.092	+	116.409i	0.917013	+	0.230514i
$506$		0			0
$507$	−173.770	+	320.138i	−0.342741	+	0.631435i
$508$		0			0
$509$	391.066	+	225.782i	0.768303	+	0.443580i	0.832269	−	0.554372i	$-0.187042\pi$
$509$	391.066	+	225.782i	0.768303	+	0.443580i	−0.0639662	+	0.997952i	$0.520375\pi$
$510$		0			0
$511$	−598.835	−	1037.21i	−1.17189	−	2.02977i
$512$		0			0
$513$	623.123	−	49.2715i	1.21467	−	0.0960458i
$514$		0			0
$515$	−79.1027	−	277.883i	−0.153598	−	0.539578i
$516$		0			0
$517$	−423.768	−	244.663i	−0.819668	−	0.473235i
$518$		0			0
$519$	370.254	−	682.123i	0.713400	−	1.31430i
$520$		0			0
$521$		−	901.613i		−	1.73054i	−0.501303	−	0.865272i	$-0.667146\pi$
$521$		−	901.613i		−	1.73054i	0.501303	−	0.865272i	$-0.332854\pi$
$522$		0			0
$523$		−	292.527i		−	0.559326i	−0.960098	−	0.279663i	$-0.909777\pi$
$523$		−	292.527i		−	0.559326i	0.960098	−	0.279663i	$-0.0902227\pi$
$524$		0			0
$525$	387.821	−	770.639i	0.738707	−	1.46788i
$526$		0			0
$527$	−28.3995	+	49.1894i	−0.0538890	+	0.0933385i
$528$		0			0
$529$	167.042	+	289.326i	0.315770	+	0.546930i
$530$		0			0
$531$	−147.522	+	95.8531i	−0.277818	+	0.180514i
$532$		0			0
$533$	−363.549	−	629.685i	−0.682080	−	1.18140i
$534$		0			0
$535$	232.772	+	225.653i	0.435087	+	0.421781i
$536$		0			0
$537$	−446.507	+	273.695i	−0.831484	+	0.509674i
$538$		0			0
$539$			1270.36i			2.35688i
$540$		0			0
$541$	−790.789			−1.46172			−0.730858	−	0.682529i	$-0.760880\pi$
$541$	−790.789			−1.46172			−0.730858	+	0.682529i	$0.760880\pi$
$542$		0			0
$543$	−35.0077	−	57.1117i	−0.0644710	−	0.105178i
$544$		0			0
$545$	146.893	+	142.401i	0.269529	+	0.261286i
$546$		0			0
$547$	−137.027	+	79.1123i	−0.250506	+	0.144629i	−0.619996	−	0.784605i	$-0.712866\pi$
$547$	−137.027	+	79.1123i	−0.250506	+	0.144629i	0.369490	+	0.929235i	$0.379532\pi$
$548$		0			0
$549$	59.3122	−	3.12300i	0.108037	−	0.00568853i
$550$		0			0
$551$	−898.885	+	518.971i	−1.63137	+	0.941872i
$552$		0			0
$553$	−1499.52	−	865.745i	−2.71160	−	1.56554i
$554$		0			0
$555$	742.634	+	166.043i	1.33808	+	0.299177i
$556$		0			0
$557$	−1011.82			−1.81655			−0.908273	−	0.418378i	$-0.862599\pi$
$557$	−1011.82			−1.81655			−0.908273	+	0.418378i	$0.862599\pi$
$558$		0			0
$559$	−104.789			−0.187458
$560$		0			0
$561$	−419.133	−	227.504i	−0.747117	−	0.405533i
$562$		0			0
$563$	40.4851	−	70.1223i	0.0719096	−	0.124551i	−0.827829	−	0.560981i	$-0.810424\pi$
$563$	40.4851	−	70.1223i	0.0719096	−	0.124551i	0.899738	+	0.436430i	$0.143757\pi$
$564$		0			0
$565$	1040.86	−	296.294i	1.84223	−	0.524414i
$566$		0			0
$567$	851.373	+	378.555i	1.50154	+	0.667646i
$568$		0			0
$569$	668.982	−	386.237i	1.17572	−	0.678800i	0.220696	−	0.975343i	$-0.429167\pi$
$569$	668.982	−	386.237i	1.17572	−	0.678800i	0.955020	+	0.296543i	$0.0958337\pi$
$570$		0			0
$571$	−384.389	+	665.781i	−0.673185	+	1.16599i	0.303811	+	0.952732i	$0.401741\pi$
$571$	−384.389	+	665.781i	−0.673185	+	1.16599i	−0.976996	+	0.213258i	$0.931592\pi$
$572$		0			0
$573$	579.106	+	314.337i	1.01066	+	0.548581i
$574$		0			0
$575$	307.542	+	165.045i	0.534856	+	0.287036i
$576$		0			0
$577$		−	188.653i		−	0.326955i	−0.986547	−	0.163477i	$-0.947729\pi$
$577$		−	188.653i		−	0.326955i	0.986547	−	0.163477i	$-0.0522710\pi$
$578$		0			0
$579$	26.9397	+	1023.99i	0.0465280	+	1.76855i
$580$		0			0
$581$	−811.482	−	468.510i	−1.39670	−	0.806385i
$582$		0			0
$583$	−220.994	+	127.591i	−0.379063	+	0.218852i
$584$		0			0
$585$	752.540	+	147.592i	1.28639	+	0.252294i
$586$		0			0
$587$	−278.328	−	482.078i	−0.474153	−	0.821258i	0.525409	−	0.850850i	$-0.323912\pi$
$587$	−278.328	−	482.078i	−0.474153	−	0.821258i	−0.999562	+	0.0295923i	$0.990579\pi$
$588$		0			0
$589$	63.0604	−	109.224i	0.107064	−	0.185440i
$590$		0			0
$591$	−314.689	−	513.385i	−0.532469	−	0.868671i
$592$		0			0
$593$	715.570			1.20670			0.603348	−	0.797478i	$-0.293833\pi$
$593$	715.570			1.20670			0.603348	+	0.797478i	$0.293833\pi$
$594$		0			0
$595$	581.557	+	146.189i	0.977407	+	0.245695i
$596$		0			0
$597$	−125.317	−	204.443i	−0.209911	−	0.342450i
$598$		0			0
$599$	−1014.24	−	585.573i	−1.69323	−	0.977585i	−0.951884	−	0.306458i	$-0.900856\pi$
$599$	−1014.24	−	585.573i	−1.69323	−	0.977585i	−0.741343	−	0.671127i	$-0.765811\pi$
$600$		0			0
$601$	−114.910	−	199.030i	−0.191198	−	0.331164i	0.754450	−	0.656358i	$-0.227904\pi$
$601$	−114.910	−	199.030i	−0.191198	−	0.331164i	−0.945647	+	0.325194i	$0.894571\pi$
$602$		0			0
$603$	268.385	−	174.385i	0.445083	−	0.289195i
$604$		0			0
$605$	−536.063	+	152.597i	−0.886054	+	0.252226i
$606$		0			0
$607$	895.835	+	517.211i	1.47584	+	0.852077i	0.999629	−	0.0272535i	$-0.00867613\pi$
$607$	895.835	+	517.211i	1.47584	+	0.852077i	0.476212	+	0.879330i	$0.342009\pi$
$608$		0			0
$609$	−1546.64	+	40.6901i	−2.53965	+	0.0668146i
$610$		0			0
$611$			546.922i			0.895126i
$612$		0			0
$613$			69.5129i			0.113398i	0.998391	+	0.0566989i	$0.0180575\pi$
$613$			69.5129i			0.113398i	−0.998391	+	0.0566989i	$0.981942\pi$
$614$		0			0
$615$	−433.219	+	471.068i	−0.704421	+	0.765963i
$616$		0			0
$617$	−517.335	+	896.050i	−0.838468	+	1.45227i	0.0527077	+	0.998610i	$0.483215\pi$
$617$	−517.335	+	896.050i	−0.838468	+	1.45227i	−0.891175	+	0.453659i	$0.850118\pi$
$618$		0			0
$619$	−488.346	−	845.840i	−0.788927	−	1.36646i	−0.926625	−	0.375987i	$-0.877304\pi$
$619$	−488.346	−	845.840i	−0.788927	−	1.36646i	0.137698	−	0.990474i	$-0.456030\pi$
$620$		0			0
$621$	−162.157	+	340.292i	−0.261123	+	0.547973i
$622$		0			0
$623$	−82.7395	−	143.309i	−0.132808	−	0.230031i
$624$		0			0
$625$	−623.795	+	38.7940i	−0.998072	+	0.0620704i
$626$		0			0
$627$	930.674	+	505.167i	1.48433	+	0.805689i
$628$		0			0
$629$			528.925i			0.840898i
$630$		0			0
$631$	257.928			0.408761			0.204380	−	0.978892i	$-0.434482\pi$
$631$	257.928			0.408761			0.204380	+	0.978892i	$0.434482\pi$
$632$		0			0
$633$	215.614	−	5.67250i	0.340622	−	0.00896129i
$634$		0			0
$635$	−447.327	+	461.439i	−0.704451	+	0.726675i
$636$		0			0
$637$	1229.66	−	709.942i	1.93039	−	1.11451i
$638$		0			0
$639$	525.327	+	267.505i	0.822107	+	0.418631i
$640$		0			0
$641$	−654.916	+	378.116i	−1.02171	+	0.589885i	−0.914599	−	0.404362i	$-0.867494\pi$
$641$	−654.916	+	378.116i	−1.02171	+	0.589885i	−0.107111	+	0.994247i	$0.534160\pi$
$642$		0			0
$643$	−216.133	−	124.784i	−0.336132	−	0.194066i	0.322428	−	0.946594i	$-0.395501\pi$
$643$	−216.133	−	124.784i	−0.336132	−	0.194066i	−0.658560	+	0.752528i	$0.728834\pi$
$644$		0			0
$645$	27.5769	+	88.0158i	0.0427549	+	0.136459i
$646$		0			0
$647$	−1210.85			−1.87149			−0.935743	−	0.352682i	$-0.885270\pi$
$647$	−1210.85			−1.87149			−0.935743	+	0.352682i	$0.885270\pi$
$648$		0			0
$649$	−298.041			−0.459231
$650$		0			0
$651$	160.283	−	98.2486i	0.246211	−	0.150920i
$652$		0			0
$653$	−414.612	+	718.130i	−0.634935	+	1.09974i	0.351594	+	0.936153i	$0.385640\pi$
$653$	−414.612	+	718.130i	−0.634935	+	1.09974i	−0.986529	+	0.163587i	$0.947694\pi$
$654$		0			0
$655$	36.6576	+	128.776i	0.0559658	+	0.196604i
$656$		0			0
$657$	−835.035	−	425.214i	−1.27098	−	0.647205i
$658$		0			0
$659$	1048.49	−	605.347i	1.59104	−	0.918585i	0.597905	−	0.801567i	$-0.296000\pi$
$659$	1048.49	−	605.347i	1.59104	−	0.918585i	0.993130	−	0.117018i	$-0.0373335\pi$
$660$		0			0
$661$	122.502	−	212.180i	0.185329	−	0.320999i	−0.758358	−	0.651838i	$-0.773998\pi$
$661$	122.502	−	212.180i	0.185329	−	0.320999i	0.943687	+	0.330839i	$0.107332\pi$
$662$		0			0
$663$	14.0184	+	532.846i	0.0211439	+	0.803689i
$664$		0			0
$665$	−1291.33	−	324.608i	−1.94185	−	0.488133i
$666$		0			0
$667$		−	625.940i		−	0.938440i
$668$		0			0
$669$	931.074	+	505.384i	1.39174	+	0.755432i
$670$		0			0
$671$	87.1402	+	50.3104i	0.129866	+	0.0749782i
$672$		0			0
$673$	−1019.13	+	588.395i	−1.51431	+	0.874287i	−0.514451	+	0.857520i	$0.672004\pi$
$673$	−1019.13	+	588.395i	−1.51431	+	0.874287i	−0.999859	+	0.0167673i	$0.994663\pi$
$674$		0			0
$675$	−74.0754	−	670.923i	−0.109741	−	0.993960i
$676$		0			0
$677$	366.583	+	634.940i	0.541481	+	0.937873i	0.998819	+	0.0485799i	$0.0154695\pi$
$677$	366.583	+	634.940i	0.541481	+	0.937873i	−0.457338	+	0.889293i	$0.651197\pi$
$678$		0			0
$679$	−154.523	+	267.641i	−0.227574	+	0.394170i
$680$		0			0
$681$	245.303	−	451.923i	0.360209	−	0.663617i
$682$		0			0
$683$	770.725			1.12844			0.564221	−	0.825624i	$-0.309177\pi$
$683$	770.725			1.12844			0.564221	+	0.825624i	$0.309177\pi$
$684$		0			0
$685$	121.709	−	484.174i	0.177677	−	0.706823i
$686$		0			0
$687$	497.231	−	13.0814i	0.723771	−	0.0190414i
$688$		0			0
$689$	247.006	+	142.609i	0.358500	+	0.206980i
$690$		0			0
$691$	83.3176	+	144.310i	0.120575	+	0.208843i	0.919995	−	0.391931i	$-0.128193\pi$
$691$	83.3176	+	144.310i	0.120575	+	0.208843i	−0.799419	+	0.600773i	$0.794859\pi$
$692$		0			0
$693$	860.023	+	1323.61i	1.24101	+	1.90997i
$694$		0			0
$695$	−73.9998	+	21.0650i	−0.106475	+	0.0303093i
$696$		0			0
$697$	−385.237	−	222.417i	−0.552708	−	0.319106i
$698$		0			0
$699$	9.55228	+	15.5836i	0.0136656	+	0.0222942i
$700$		0			0
$701$			857.331i			1.22301i	0.791240	+	0.611506i	$0.209436\pi$
$701$			857.331i			1.22301i	−0.791240	+	0.611506i	$0.790564\pi$
$702$		0			0
$703$		−	1174.47i		−	1.67065i
$704$		0			0
$705$	459.377	−	143.931i	0.651599	−	0.204157i
$706$		0			0
$707$	549.265	−	951.355i	0.776896	−	1.34562i
$708$		0			0
$709$	−562.074	−	973.541i	−0.792770	−	1.37312i	−0.924245	−	0.381799i	$-0.875305\pi$
$709$	−562.074	−	973.541i	−0.792770	−	1.37312i	0.131475	−	0.991319i	$-0.458029\pi$
$710$		0			0
$711$	−1352.86	+	71.2328i	−1.90275	+	0.100187i
$712$		0			0
$713$	38.0291	+	65.8684i	0.0533368	+	0.0923820i
$714$		0			0
$715$	932.809	+	904.281i	1.30463	+	1.26473i
$716$		0			0
$717$	−2.80347	−	106.561i	−0.00391000	−	0.148621i
$718$		0			0
$719$		−	772.421i		−	1.07430i	−0.843487	−	0.537150i	$-0.819501\pi$
$719$		−	772.421i		−	1.07430i	0.843487	−	0.537150i	$-0.180499\pi$
$720$		0			0
$721$	−664.692			−0.921903
$722$		0			0
$723$	−429.781	+	791.790i	−0.594442	+	1.09515i
$724$		0			0
$725$	590.298	+	952.820i	0.814204	+	1.31423i
$726$		0			0
$727$	−226.144	+	130.564i	−0.311065	+	0.179593i	−0.647403	−	0.762148i	$-0.724145\pi$
$727$	−226.144	+	130.564i	−0.311065	+	0.179593i	0.336338	+	0.941741i	$0.390811\pi$
$728$		0			0
$729$	719.941	−	114.570i	0.987573	−	0.157161i
$730$		0			0
$731$	−55.5203	+	32.0547i	−0.0759512	+	0.0438504i
$732$		0			0
$733$	448.068	+	258.692i	0.611280	+	0.352923i	0.773466	−	0.633838i	$-0.218521\pi$
$733$	448.068	+	258.692i	0.611280	+	0.352923i	−0.162186	+	0.986760i	$0.551855\pi$
$734$		0			0
$735$	−919.906	−	845.995i	−1.25157	−	1.15101i
$736$		0			0
$737$	542.224			0.735717
$738$		0			0
$739$	396.875			0.537044			0.268522	−	0.963274i	$-0.413465\pi$
$739$	396.875			0.537044			0.268522	+	0.963274i	$0.413465\pi$
$740$		0			0
$741$	−31.1276	−	1183.17i	−0.0420075	−	1.59672i
$742$		0			0
$743$	388.518	−	672.933i	0.522905	−	0.905698i	−0.476740	−	0.879044i	$-0.658182\pi$
$743$	388.518	−	672.933i	0.522905	−	0.905698i	0.999645	−	0.0266533i	$-0.00848502\pi$
$744$		0			0
$745$	164.624	+	578.312i	0.220972	+	0.776258i
$746$		0			0
$747$	−732.116	+	38.5486i	−0.980075	+	0.0516045i
$748$		0			0
$749$	645.915	−	372.919i	0.862370	−	0.497890i
$750$		0			0
$751$	234.632	−	406.395i	0.312426	−	0.541138i	−0.666461	−	0.745540i	$-0.732192\pi$
$751$	234.632	−	406.395i	0.312426	−	0.541138i	0.978887	+	0.204402i	$0.0655250\pi$
$752$		0			0
$753$	615.840	−	377.491i	0.817849	−	0.501316i
$754$		0			0
$755$	54.0160	−	214.882i	0.0715443	−	0.284613i
$756$		0			0
$757$		−	578.062i		−	0.763622i	−0.924240	−	0.381811i	$-0.875301\pi$
$757$		−	578.062i		−	0.763622i	0.924240	−	0.381811i	$-0.124699\pi$
$758$		0			0
$759$	−544.456	+	333.735i	−0.717333	+	0.439703i
$760$		0			0
$761$	693.715	+	400.517i	0.911584	+	0.526303i	0.880940	−	0.473227i	$-0.156911\pi$
$761$	693.715	+	400.517i	0.911584	+	0.526303i	0.0306434	+	0.999530i	$0.490244\pi$
$762$		0			0
$763$	407.612	−	235.335i	0.534223	−	0.308434i
$764$		0			0
$765$	443.865	−	152.001i	0.580216	−	0.198694i
$766$		0			0
$767$	166.561	+	288.492i	0.217159	+	0.376131i
$768$		0			0
$769$	−310.124	+	537.150i	−0.403282	+	0.698504i	−0.994120	−	0.108286i	$-0.965464\pi$
$769$	−310.124	+	537.150i	−0.403282	+	0.698504i	0.590838	+	0.806790i	$0.298797\pi$
$770$		0			0
$771$	402.013	−	10.5764i	0.521417	−	0.0137178i
$772$		0			0
$773$	−261.647			−0.338483			−0.169241	−	0.985575i	$-0.554132\pi$
$773$	−261.647			−0.338483			−0.169241	+	0.985575i	$0.554132\pi$
$774$		0			0
$775$	−120.007	−	64.4027i	−0.154847	−	0.0831002i
$776$		0			0
$777$	835.165	−	1538.63i	1.07486	−	1.98022i
$778$		0			0
$779$	855.410	+	493.871i	1.09809	+	0.633981i
$780$		0			0
$781$	499.352	+	864.903i	0.639375	+	1.10743i
$782$		0			0
$783$	−997.372	+	686.015i	−1.27378	+	0.876137i
$784$		0			0
$785$	81.5125	+	286.348i	0.103838	+	0.364774i
$786$		0			0
$787$	6.51512	+	3.76150i	0.00827842	+	0.00477955i	0.504133	−	0.863626i	$-0.331812\pi$
$787$	6.51512	+	3.76150i	0.00827842	+	0.00477955i	−0.495855	+	0.868405i	$0.665145\pi$
$788$		0			0
$789$	−625.630	+	1152.60i	−0.792940	+	1.46084i
$790$		0			0
$791$		−	2489.73i		−	3.14757i
$792$		0			0
$793$		−	112.464i		−	0.141822i
$794$		0			0
$795$	54.7785	−	244.998i	0.0689037	−	0.308174i
$796$		0			0
$797$	169.355	−	293.332i	0.212491	−	0.368045i	−0.740002	−	0.672604i	$-0.765176\pi$
$797$	169.355	−	293.332i	0.212491	−	0.368045i	0.952494	+	0.304559i	$0.0985090\pi$
$798$		0			0
$799$	167.302	+	289.775i	0.209389	+	0.362672i
$800$		0			0
$801$	−115.375	−	58.7507i	−0.144038	−	0.0733468i
$802$		0			0
$803$	−793.747	−	1374.81i	−0.988477	−	1.71209i
$804$		0			0
$805$	558.906	−	576.538i	0.694293	−	0.716196i
$806$		0			0
$807$	−99.7842	+	61.1647i	−0.123648	+	0.0757927i
$808$		0			0
$809$			1370.18i			1.69367i	0.531857	+	0.846834i	$0.321494\pi$
$809$			1370.18i			1.69367i	−0.531857	+	0.846834i	$0.678506\pi$
$810$		0			0
$811$	395.829			0.488075			0.244037	−	0.969766i	$-0.421528\pi$
$811$	395.829			0.488075			0.244037	+	0.969766i	$0.421528\pi$
$812$		0			0
$813$	353.465	+	576.644i	0.434767	+	0.709279i
$814$		0			0
$815$	−696.531	+	718.504i	−0.854639	+	0.881601i
$816$		0			0
$817$	123.281	−	71.1766i	0.150895	−	0.0871195i
$818$		0			0
$819$	800.577	−	1572.17i	0.977505	−	1.91962i
$820$		0			0
$821$	−828.903	+	478.567i	−1.00963	+	0.582908i	−0.911082	−	0.412225i	$-0.864752\pi$
$821$	−828.903	+	478.567i	−1.00963	+	0.582908i	−0.0985439	+	0.995133i	$0.531418\pi$
$822$		0			0
$823$	−1123.17	−	648.461i	−1.36472	−	0.787923i	−0.374475	−	0.927237i	$-0.622177\pi$
$823$	−1123.17	−	648.461i	−1.36472	−	0.787923i	−0.990248	+	0.139314i	$0.955510\pi$
$824$		0			0
$825$	514.052	−	1021.47i	0.623093	−	1.23815i
$826$		0			0
$827$	−1097.08			−1.32658			−0.663291	−	0.748361i	$-0.730841\pi$
$827$	−1097.08			−1.32658			−0.663291	+	0.748361i	$0.730841\pi$
$828$		0			0
$829$	286.317			0.345376			0.172688	−	0.984977i	$-0.444755\pi$
$829$	286.317			0.345376			0.172688	+	0.984977i	$0.444755\pi$
$830$		0			0
$831$	601.384	+	326.430i	0.723688	+	0.392815i
$832$		0			0
$833$	434.338	−	752.295i	0.521414	−	0.903116i
$834$		0			0
$835$	370.895	−	105.580i	0.444186	−	0.126443i
$836$		0			0
$837$	63.2756	−	132.786i	0.0755981	−	0.158645i
$838$		0			0
$839$	291.527	−	168.313i	0.347470	−	0.200612i	−0.316100	−	0.948726i	$-0.602374\pi$
$839$	291.527	−	168.313i	0.347470	−	0.200612i	0.663570	+	0.748114i	$0.269040\pi$
$840$		0			0
$841$	584.554	−	1012.48i	0.695070	−	1.20390i
$842$		0			0
$843$	−634.863	−	344.602i	−0.753100	−	0.408780i
$844$		0			0
$845$	148.004	−	588.779i	0.175153	−	0.696780i
$846$		0			0
$847$			1282.26i			1.51388i
$848$		0			0
$849$	3.66685	+	139.379i	0.00431903	+	0.164168i
$850$		0			0
$851$	613.381	+	354.135i	0.720776	+	0.416140i
$852$		0			0
$853$	−1054.83	+	609.006i	−1.23661	+	0.713958i	−0.968400	−	0.249402i	$-0.919766\pi$
$853$	−1054.83	+	609.006i	−1.23661	+	0.713958i	−0.268212	+	0.963360i	$0.586433\pi$
$854$		0			0
$855$	−985.591	+	337.515i	−1.15274	+	0.394754i
$856$		0			0
$857$	603.121	+	1044.64i	0.703758	+	1.21894i	0.967138	+	0.254252i	$0.0818294\pi$
$857$	603.121	+	1044.64i	0.703758	+	1.21894i	−0.263380	+	0.964692i	$0.584837\pi$
$858$		0			0
$859$	779.669	−	1350.43i	0.907647	−	1.57209i	0.0903231	−	0.995913i	$-0.471210\pi$
$859$	779.669	−	1350.43i	0.907647	−	1.57209i	0.817324	−	0.576178i	$-0.195457\pi$
$860$		0			0
$861$	769.455	+	1255.29i	0.893676	+	1.45794i
$862$		0			0
$863$	1124.20			1.30266			0.651332	−	0.758793i	$-0.274211\pi$
$863$	1124.20			1.30266			0.651332	+	0.758793i	$0.274211\pi$
$864$		0			0
$865$	−315.355	+	1254.52i	−0.364573	+	1.45032i
$866$		0			0
$867$	−282.674	−	461.155i	−0.326037	−	0.531897i
$868$		0			0
$869$	−1987.59	−	1147.53i	−2.28721	−	1.32052i
$870$		0			0
$871$	−303.023	−	524.852i	−0.347903	−	0.602585i
$872$		0			0
$873$	12.7140	+	241.465i	0.0145636	+	0.276592i
$874$		0			0
$875$	−307.070	+	1404.70i	−0.350938	+	1.60537i
$876$		0			0
$877$	996.604	+	575.390i	1.13638	+	0.656088i	0.945531	−	0.325531i	$-0.105543\pi$
$877$	996.604	+	575.390i	1.13638	+	0.656088i	0.190847	+	0.981620i	$0.438876\pi$
$878$		0			0
$879$	−289.520	+	7.61687i	−0.329375	+	0.00866539i
$880$		0			0
$881$		−	234.506i		−	0.266181i	−0.991104	−	0.133091i	$-0.957510\pi$
$881$		−	234.506i		−	0.266181i	0.991104	−	0.133091i	$-0.0424902\pi$
$882$		0			0
$883$			1211.86i			1.37243i	0.727399	+	0.686215i	$0.240729\pi$
$883$			1211.86i			1.37243i	−0.727399	+	0.686215i	$0.759271\pi$
$884$		0			0
$885$	198.481	−	215.821i	0.224272	−	0.243866i
$886$		0			0
$887$	661.516	−	1145.78i	0.745790	−	1.29175i	−0.204034	−	0.978964i	$-0.565405\pi$
$887$	661.516	−	1145.78i	0.745790	−	1.29175i	0.949825	−	0.312783i	$-0.101261\pi$
$888$		0			0
$889$	739.263	+	1280.44i	0.831567	+	1.44032i
$890$		0			0
$891$	1128.48	+	501.770i	1.26654	+	0.563154i
$892$		0			0
$893$	−371.489	−	643.438i	−0.416001	−	0.720536i
$894$		0			0
$895$	607.546	−	626.713i	0.678823	−	0.700238i
$896$		0			0
$897$	627.313	+	340.504i	0.699346	+	0.379603i
$898$		0			0
$899$			244.249i			0.271690i
$900$		0			0
$901$	174.495			0.193668
$902$		0			0
$903$	212.121	−	5.58062i	0.234907	−	0.00618009i
$904$		0			0
$905$	80.1615	+	77.7099i	0.0885762	+	0.0858673i
$906$		0			0
$907$	−428.451	+	247.366i	−0.472383	+	0.272730i	−0.717237	−	0.696830i	$-0.754593\pi$
$907$	−428.451	+	247.366i	−0.472383	+	0.272730i	0.244854	+	0.969560i	$0.421260\pi$
$908$		0			0
$909$	−45.1931	−	858.309i	−0.0497174	−	0.944234i
$910$		0			0
$911$	149.606	−	86.3753i	0.164222	−	0.0948137i	−0.415636	−	0.909531i	$-0.636441\pi$
$911$	149.606	−	86.3753i	0.164222	−	0.0948137i	0.579859	+	0.814717i	$0.303108\pi$
$912$		0			0
$913$	−1075.61	−	621.003i	−1.17810	−	0.680179i
$914$		0			0
$915$	−94.4625	+	29.5968i	−0.103238	+	0.0323462i
$916$		0			0
$917$	308.030			0.335911
$918$		0			0
$919$	414.019			0.450510			0.225255	−	0.974300i	$-0.427679\pi$
$919$	414.019			0.450510			0.225255	+	0.974300i	$0.427679\pi$
$920$		0			0
$921$	−1020.42	+	625.483i	−1.10794	+	0.679135i
$922$		0			0
$923$	558.129	−	966.708i	0.604690	−	1.04735i
$924$		0			0
$925$	−1267.67	+	39.3804i	−1.37046	+	0.0425734i
$926$		0			0
$927$	−436.089	+	283.352i	−0.470431	+	0.305665i
$928$		0			0
$929$	−1148.49	+	663.083i	−1.23627	+	0.713760i	−0.968330	−	0.249676i	$-0.919676\pi$
$929$	−1148.49	+	663.083i	−1.23627	+	0.713760i	−0.267939	+	0.963436i	$0.586343\pi$
$930$		0			0
$931$	−964.437	+	1670.45i	−1.03592	+	1.79426i
$932$		0			0
$933$	31.5767	+	1200.24i	0.0338443	+	1.28643i
$934$		0			0
$935$	770.846	+	193.771i	0.824434	+	0.207242i
$936$		0			0
$937$			419.126i			0.447306i	0.974669	+	0.223653i	$0.0717982\pi$
$937$			419.126i			0.447306i	−0.974669	+	0.223653i	$0.928202\pi$
$938$		0			0
$939$	−545.252	−	295.961i	−0.580673	−	0.315188i
$940$		0			0
$941$	579.729	+	334.707i	0.616077	+	0.355692i	0.775340	−	0.631544i	$-0.217578\pi$
$941$	579.729	+	334.707i	0.616077	+	0.355692i	−0.159263	+	0.987236i	$0.550912\pi$
$942$		0			0
$943$	−515.862	+	297.833i	−0.547043	+	0.315836i
$944$		0			0
$945$	−1531.20	−	258.688i	−1.62032	−	0.273744i
$946$		0			0
$947$	151.790	+	262.908i	0.160285	+	0.277622i	0.934971	−	0.354724i	$-0.115425\pi$
$947$	151.790	+	262.908i	0.160285	+	0.277622i	−0.774686	+	0.632346i	$0.782092\pi$
$948$		0			0
$949$	−887.176	+	1536.63i	−0.934854	+	1.61921i
$950$		0			0
$951$	89.8723	−	165.573i	0.0945029	−	0.174104i
$952$		0			0
$953$	1452.57			1.52421			0.762103	−	0.647455i	$-0.224167\pi$
$953$	1452.57			1.52421			0.762103	+	0.647455i	$0.224167\pi$
$954$		0			0
$955$	−1065.06	−	267.729i	−1.11525	−	0.280344i
$956$		0			0
$957$	−2050.06	+	53.9341i	−2.14217	+	0.0563575i
$958$		0			0
$959$	−994.665	−	574.270i	−1.03719	−	0.598822i
$960$		0			0
$961$	465.661	+	806.548i	0.484558	+	0.839280i
$962$		0			0
$963$	264.798	−	520.011i	0.274972	−	0.539991i
$964$		0			0
$965$	−467.417	−	1642.01i	−0.484370	−	1.70156i
$966$		0			0
$967$	−36.2742	−	20.9429i	−0.0375121	−	0.0216576i	0.481127	−	0.876651i	$-0.340228\pi$
$967$	−36.2742	−	20.9429i	−0.0375121	−	0.0216576i	−0.518639	+	0.854993i	$0.673561\pi$
$968$		0			0
$969$	−378.420	−	617.356i	−0.390527	−	0.637106i
$970$		0			0
$971$			513.822i			0.529168i	0.964363	+	0.264584i	$0.0852346\pi$
$971$			513.822i			0.529168i	−0.964363	+	0.264584i	$0.914765\pi$
$972$		0			0
$973$			177.007i			0.181919i
$974$		0			0
$975$	−1276.03	+	73.2702i	−1.30874	+	0.0751490i
$976$		0			0
$977$	−861.680	+	1492.47i	−0.881965	+	1.52761i	−0.0328124	+	0.999462i	$0.510446\pi$
$977$	−861.680	+	1492.47i	−0.881965	+	1.52761i	−0.849153	+	0.528147i	$0.822887\pi$
$978$		0			0
$979$	−109.670	−	189.954i	−0.112023	−	0.194029i
$980$		0			0
$981$	167.104	−	328.159i	0.170340	−	0.334515i
$982$		0			0
$983$	398.946	+	690.994i	0.405845	+	0.702944i	0.994419	−	0.105499i	$-0.0336439\pi$
$983$	398.946	+	690.994i	0.405845	+	0.702944i	−0.588574	+	0.808443i	$0.700311\pi$
$984$		0			0
$985$	720.582	+	698.545i	0.731556	+	0.709183i
$986$		0			0
$987$	−29.1267	−	1107.12i	−0.0295103	−	1.12170i
$988$		0			0
$989$			85.8473i			0.0868021i
$990$		0			0
$991$	−920.998			−0.929363			−0.464681	−	0.885478i	$-0.653831\pi$
$991$	−920.998			−0.929363			−0.464681	+	0.885478i	$0.653831\pi$
$992$		0			0
$993$	−344.572	+	634.807i	−0.347001	+	0.639282i
$994$		0			0
$995$	286.954	+	278.178i	0.288396	+	0.279576i
$996$		0			0
$997$	776.671	−	448.411i	0.779008	−	0.449761i	−0.0570705	−	0.998370i	$-0.518176\pi$
$997$	776.671	−	448.411i	0.779008	−	0.449761i	0.836079	+	0.548610i	$0.184843\pi$
$998$		0			0
$999$	−107.971	−	1365.48i	−0.108079	−	1.36685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.t.a.149.9	yes	24
3.2	odd	2		540.3.t.a.449.9		24
5.2	odd	4		900.3.p.f.401.10		24
5.3	odd	4		900.3.p.f.401.3		24
5.4	even	2	inner	180.3.t.a.149.4	yes	24
9.2	odd	6	inner	180.3.t.a.29.4	✓	24
9.4	even	3		1620.3.b.b.809.12		24
9.5	odd	6		1620.3.b.b.809.13		24
9.7	even	3		540.3.t.a.89.11		24
15.2	even	4		2700.3.p.f.2501.2		24
15.8	even	4		2700.3.p.f.2501.11		24
15.14	odd	2		540.3.t.a.449.11		24
45.2	even	12		900.3.p.f.101.10		24
45.4	even	6		1620.3.b.b.809.14		24
45.7	odd	12		2700.3.p.f.1601.2		24
45.14	odd	6		1620.3.b.b.809.11		24
45.29	odd	6	inner	180.3.t.a.29.9	yes	24
45.34	even	6		540.3.t.a.89.9		24
45.38	even	12		900.3.p.f.101.3		24
45.43	odd	12		2700.3.p.f.1601.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.4	✓	24	9.2	odd	6	inner
180.3.t.a.29.9	yes	24	45.29	odd	6	inner
180.3.t.a.149.4	yes	24	5.4	even	2	inner
180.3.t.a.149.9	yes	24	1.1	even	1	trivial
540.3.t.a.89.9		24	45.34	even	6
540.3.t.a.89.11		24	9.7	even	3
540.3.t.a.449.9		24	3.2	odd	2
540.3.t.a.449.11		24	15.14	odd	2
900.3.p.f.101.3		24	45.38	even	12
900.3.p.f.101.10		24	45.2	even	12
900.3.p.f.401.3		24	5.3	odd	4
900.3.p.f.401.10		24	5.2	odd	4
1620.3.b.b.809.11		24	45.14	odd	6
1620.3.b.b.809.12		24	9.4	even	3
1620.3.b.b.809.13		24	9.5	odd	6
1620.3.b.b.809.14		24	45.4	even	6
2700.3.p.f.1601.2		24	45.7	odd	12
2700.3.p.f.1601.11		24	45.43	odd	12
2700.3.p.f.2501.2		24	15.2	even	4
2700.3.p.f.2501.11		24	15.8	even	4

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56781 + 2.55773i) q^{3} +(-3.59000 - 3.48021i) q^{5} +(-9.96186 + 5.75148i) q^{7} +(-4.08395 + 8.02006i) q^{9} +O(q^{10})\)	\(q+(1.56781 + 2.55773i) q^{3} +(-3.59000 - 3.48021i) q^{5} +(-9.96186 + 5.75148i) q^{7} +(-4.08395 + 8.02006i) q^{9} +(-13.2043 + 7.62351i) q^{11} +(14.7585 + 8.52085i) q^{13} +(3.27299 - 14.6386i) q^{15} +10.4260 q^{17} -23.1507 q^{19} +(-30.3290 - 16.4625i) q^{21} +(6.98060 - 12.0908i) q^{23} +(0.776254 + 24.9879i) q^{25} +(-26.9160 + 2.12830i) q^{27} +(38.8276 - 22.4171i) q^{29} +(-2.72391 + 4.71796i) q^{31} +(-40.2007 - 21.8208i) q^{33} +(55.7795 + 14.0215i) q^{35} +50.7314i q^{37} +(1.34456 + 51.1074i) q^{39} +(-36.9497 - 21.3329i) q^{41} +(-5.32518 + 3.07449i) q^{43} +(42.5729 - 14.5790i) q^{45} +(16.0466 + 27.7935i) q^{47} +(41.6591 - 72.1557i) q^{49} +(16.3460 + 26.6669i) q^{51} +16.7365 q^{53} +(73.9350 + 18.5854i) q^{55} +(-36.2958 - 59.2131i) q^{57} +(16.9286 + 9.77374i) q^{59} +(-3.29969 - 5.71522i) q^{61} +(-5.44352 - 103.383i) q^{63} +(-23.3289 - 81.9527i) q^{65} +(-30.7981 - 17.7813i) q^{67} +(41.8691 - 1.10152i) q^{69} -65.5016i q^{71} +104.118i q^{73} +(-62.6954 + 41.1618i) q^{75} +(87.6930 - 151.889i) q^{77} +(75.2628 + 130.359i) q^{79} +(-47.6427 - 65.5070i) q^{81} +(40.7295 + 70.5455i) q^{83} +(-37.4294 - 36.2847i) q^{85} +(118.211 + 64.1646i) q^{87} +14.3858i q^{89} -196.030 q^{91} +(-16.3378 + 0.429826i) q^{93} +(83.1110 + 80.5693i) q^{95} +(23.2672 - 13.4333i) q^{97} +(-7.21531 - 137.033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{5} + 2 q^{9}+O(q^{10}) \) 24 * q - 9 * q^5 + 2 * q^9	\( 24 q - 9 q^{5} + 2 q^{9} - 18 q^{11} + 25 q^{15} - 26 q^{21} + 3 q^{25} + 36 q^{29} + 30 q^{31} + 6 q^{39} - 36 q^{41} - 31 q^{45} + 108 q^{49} + 124 q^{51} + 42 q^{55} - 306 q^{59} + 48 q^{61} - 225 q^{65} - 268 q^{69} - 217 q^{75} + 114 q^{79} - 14 q^{81} + 48 q^{85} - 84 q^{91} + 324 q^{95} + 418 q^{99}+O(q^{100}) \) 24 * q - 9 * q^5 + 2 * q^9 - 18 * q^11 + 25 * q^15 - 26 * q^21 + 3 * q^25 + 36 * q^29 + 30 * q^31 + 6 * q^39 - 36 * q^41 - 31 * q^45 + 108 * q^49 + 124 * q^51 + 42 * q^55 - 306 * q^59 + 48 * q^61 - 225 * q^65 - 268 * q^69 - 217 * q^75 + 114 * q^79 - 14 * q^81 + 48 * q^85 - 84 * q^91 + 324 * q^95 + 418 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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