LMFDB - Embedded newform 432.3.bc.b.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, not 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.2
Character	$\chi$	$=$	432.257
Dual form			432.3.bc.b.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49775 - 2.59937i) q^{3} +(-5.00278 + 5.96208i) q^{5} +(3.39388 + 1.23527i) q^{7} +(-4.51349 + 7.78642i) q^{9} +O(q^{10})$	\(q+(-1.49775 - 2.59937i) q^{3} +(-5.00278 + 5.96208i) q^{5} +(3.39388 + 1.23527i) q^{7} +(-4.51349 + 7.78642i) q^{9} +(-2.59766 - 3.09577i) q^{11} +(2.31163 - 13.1099i) q^{13} +(22.9906 + 4.07439i) q^{15} +(20.7679 + 11.9904i) q^{17} +(-13.5983 - 23.5530i) q^{19} +(-1.87225 - 10.6721i) q^{21} +(-3.97128 - 10.9110i) q^{23} +(-6.17739 - 35.0337i) q^{25} +(26.9999 + 0.0701370i) q^{27} +(22.8656 - 4.03181i) q^{29} +(3.81297 - 1.38781i) q^{31} +(-4.15642 + 11.3890i) q^{33} +(-24.3436 + 14.0548i) q^{35} +(35.3735 - 61.2687i) q^{37} +(-37.5399 + 13.6266i) q^{39} +(-43.0852 - 7.59708i) q^{41} +(-35.3804 + 29.6877i) q^{43} +(-23.8433 - 65.8635i) q^{45} +(28.3557 - 77.9066i) q^{47} +(-27.5437 - 23.1119i) q^{49} +(0.0622940 - 71.9422i) q^{51} -28.9765i q^{53} +31.4528 q^{55} +(-40.8561 + 70.6236i) q^{57} +(-33.8272 + 40.3136i) q^{59} +(4.08794 + 1.48789i) q^{61} +(-24.9366 + 20.8508i) q^{63} +(66.5978 + 79.3682i) q^{65} +(22.7477 - 129.009i) q^{67} +(-22.4138 + 26.6648i) q^{69} +(60.4484 + 34.8999i) q^{71} +(65.4584 + 113.377i) q^{73} +(-81.8135 + 68.5291i) q^{75} +(-4.99203 - 13.7155i) q^{77} +(4.20918 + 23.8714i) q^{79} +(-40.2568 - 70.2879i) q^{81} +(41.0021 - 7.22978i) q^{83} +(-175.385 + 63.8349i) q^{85} +(-44.7271 - 53.3975i) q^{87} +(84.1989 - 48.6122i) q^{89} +(24.0397 - 41.6380i) q^{91} +(-9.31831 - 7.83275i) q^{93} +(208.454 + 36.7561i) q^{95} +(37.2772 - 31.2793i) q^{97} +(35.8295 - 6.25375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

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

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

$2$		0			0
$2$		0			0
$3$	−1.49775	−	2.59937i	−0.499250	−	0.866458i
$3$	−1.49775	−	2.59937i	−0.499250	−	0.866458i
$4$		0			0
$5$	−5.00278	+	5.96208i	−1.00056	+	1.19242i	−0.0192785	+	0.999814i	$0.506137\pi$
$5$	−5.00278	+	5.96208i	−1.00056	+	1.19242i	−0.981277	+	0.192602i	$0.938308\pi$
$6$		0			0
$7$	3.39388	+	1.23527i	0.484840	+	0.176467i	0.572863	−	0.819651i	$-0.305833\pi$
$7$	3.39388	+	1.23527i	0.484840	+	0.176467i	−0.0880231	+	0.996118i	$0.528055\pi$
$8$		0			0
$9$	−4.51349	+	7.78642i	−0.501499	+	0.865158i
$10$		0			0
$11$	−2.59766	−	3.09577i	−0.236151	−	0.281434i	0.634934	−	0.772567i	$-0.281027\pi$
$11$	−2.59766	−	3.09577i	−0.236151	−	0.281434i	−0.871085	+	0.491133i	$0.836583\pi$
$12$		0			0
$13$	2.31163	−	13.1099i	0.177818	−	1.00846i	−0.757023	−	0.653389i	$-0.773347\pi$
$13$	2.31163	−	13.1099i	0.177818	−	1.00846i	0.934841	−	0.355067i	$-0.115542\pi$
$14$		0			0
$15$	22.9906	+	4.07439i	1.53271	+	0.271626i
$16$		0			0
$17$	20.7679	+	11.9904i	1.22164	+	0.705316i	0.965268	−	0.261262i	$-0.0841385\pi$
$17$	20.7679	+	11.9904i	1.22164	+	0.705316i	0.256375	+	0.966577i	$0.417472\pi$
$18$		0			0
$19$	−13.5983	−	23.5530i	−0.715701	−	1.23963i	−0.962688	−	0.270612i	$-0.912774\pi$
$19$	−13.5983	−	23.5530i	−0.715701	−	1.23963i	0.246987	−	0.969019i	$-0.420559\pi$
$20$		0			0
$21$	−1.87225	−	10.6721i	−0.0891548	−	0.508195i
$22$		0			0
$23$	−3.97128	−	10.9110i	−0.172665	−	0.474392i	0.822931	−	0.568141i	$-0.192337\pi$
$23$	−3.97128	−	10.9110i	−0.172665	−	0.474392i	−0.995596	+	0.0937489i	$0.970115\pi$
$24$		0			0
$25$	−6.17739	−	35.0337i	−0.247096	−	1.40135i
$26$		0			0
$27$	26.9999	+	0.0701370i	0.999997	+	0.00259767i
$28$		0			0
$29$	22.8656	−	4.03181i	0.788467	−	0.139028i	0.235106	−	0.971970i	$-0.424456\pi$
$29$	22.8656	−	4.03181i	0.788467	−	0.139028i	0.553361	+	0.832942i	$0.313345\pi$
$30$		0			0
$31$	3.81297	−	1.38781i	0.122999	−	0.0447680i	−0.279787	−	0.960062i	$-0.590264\pi$
$31$	3.81297	−	1.38781i	0.122999	−	0.0447680i	0.402786	+	0.915294i	$0.368042\pi$
$32$		0			0
$33$	−4.15642	+	11.3890i	−0.125952	+	0.345121i
$34$		0			0
$35$	−24.3436	+	14.0548i	−0.695532	+	0.401565i
$36$		0			0
$37$	35.3735	−	61.2687i	0.956041	−	1.65591i	0.224074	−	0.974572i	$-0.428064\pi$
$37$	35.3735	−	61.2687i	0.956041	−	1.65591i	0.731967	−	0.681340i	$-0.238602\pi$
$38$		0			0
$39$	−37.5399	+	13.6266i	−0.962560	+	0.349400i
$40$		0			0
$41$	−43.0852	−	7.59708i	−1.05086	−	0.185295i	−0.378561	−	0.925576i	$-0.623581\pi$
$41$	−43.0852	−	7.59708i	−1.05086	−	0.185295i	−0.672297	+	0.740282i	$0.734692\pi$
$42$		0			0
$43$	−35.3804	+	29.6877i	−0.822801	+	0.690412i	−0.953626	−	0.300994i	$-0.902682\pi$
$43$	−35.3804	+	29.6877i	−0.822801	+	0.690412i	0.130825	+	0.991405i	$0.458237\pi$
$44$		0			0
$45$	−23.8433	−	65.8635i	−0.529851	−	1.46363i
$46$		0			0
$47$	28.3557	−	77.9066i	0.603312	−	1.65759i	−0.141203	−	0.989981i	$-0.545097\pi$
$47$	28.3557	−	77.9066i	0.603312	−	1.65759i	0.744515	−	0.667606i	$-0.232681\pi$
$48$		0			0
$49$	−27.5437	−	23.1119i	−0.562115	−	0.471671i
$50$		0			0
$51$	0.0622940	−	71.9422i	0.00122145	−	1.41063i
$52$		0			0
$53$		−	28.9765i		−	0.546726i	−0.961911	−	0.273363i	$-0.911864\pi$
$53$		−	28.9765i		−	0.546726i	0.961911	−	0.273363i	$-0.0881361\pi$
$54$		0			0
$55$	31.4528			0.571868
$56$		0			0
$57$	−40.8561	+	70.6236i	−0.716774	+	1.23901i
$58$		0			0
$59$	−33.8272	+	40.3136i	−0.573342	+	0.683282i	−0.972313	−	0.233681i	$-0.924923\pi$
$59$	−33.8272	+	40.3136i	−0.573342	+	0.683282i	0.398972	+	0.916963i	$0.369367\pi$
$60$		0			0
$61$	4.08794	+	1.48789i	0.0670155	+	0.0243916i	0.375310	−	0.926899i	$-0.377536\pi$
$61$	4.08794	+	1.48789i	0.0670155	+	0.0243916i	−0.308295	+	0.951291i	$0.599758\pi$
$62$		0			0
$63$	−24.9366	+	20.8508i	−0.395819	+	0.330965i
$64$		0			0
$65$	66.5978	+	79.3682i	1.02458	+	1.22105i
$66$		0			0
$67$	22.7477	−	129.009i	0.339518	−	1.92550i	−0.0374978	−	0.999297i	$-0.511939\pi$
$67$	22.7477	−	129.009i	0.339518	−	1.92550i	0.377016	−	0.926207i	$-0.376950\pi$
$68$		0			0
$69$	−22.4138	+	26.6648i	−0.324838	+	0.386447i
$70$		0			0
$71$	60.4484	+	34.8999i	0.851386	+	0.491548i	0.861118	−	0.508405i	$-0.169765\pi$
$71$	60.4484	+	34.8999i	0.851386	+	0.491548i	−0.00973220	+	0.999953i	$0.503098\pi$
$72$		0			0
$73$	65.4584	+	113.377i	0.896690	+	1.55311i	0.831699	+	0.555226i	$0.187368\pi$
$73$	65.4584	+	113.377i	0.896690	+	1.55311i	0.0649905	+	0.997886i	$0.479298\pi$
$74$		0			0
$75$	−81.8135	+	68.5291i	−1.09085	+	0.913721i
$76$		0			0
$77$	−4.99203	−	13.7155i	−0.0648316	−	0.178123i
$78$		0			0
$79$	4.20918	+	23.8714i	0.0532807	+	0.302170i	0.999790	−	0.0205075i	$-0.00652821\pi$
$79$	4.20918	+	23.8714i	0.0532807	+	0.302170i	−0.946509	+	0.322677i	$0.895417\pi$
$80$		0			0
$81$	−40.2568	−	70.2879i	−0.496997	−	0.867752i
$82$		0			0
$83$	41.0021	−	7.22978i	0.494002	−	0.0871058i	0.0789031	−	0.996882i	$-0.474858\pi$
$83$	41.0021	−	7.22978i	0.494002	−	0.0871058i	0.415098	+	0.909776i	$0.363747\pi$
$84$		0			0
$85$	−175.385	+	63.8349i	−2.06335	+	0.750998i
$86$		0			0
$87$	−44.7271	−	53.3975i	−0.514104	−	0.613764i
$88$		0			0
$89$	84.1989	−	48.6122i	0.946055	−	0.546205i	0.0542015	−	0.998530i	$-0.482739\pi$
$89$	84.1989	−	48.6122i	0.946055	−	0.546205i	0.891853	+	0.452325i	$0.149405\pi$
$90$		0			0
$91$	24.0397	−	41.6380i	0.264173	−	0.457561i
$92$		0			0
$93$	−9.31831	−	7.83275i	−0.100197	−	0.0842231i
$94$		0			0
$95$	208.454	+	36.7561i	2.19425	+	0.386906i
$96$		0			0
$97$	37.2772	−	31.2793i	0.384301	−	0.322467i	−0.430087	−	0.902787i	$-0.641517\pi$
$97$	37.2772	−	31.2793i	0.384301	−	0.322467i	0.814388	+	0.580320i	$0.197073\pi$
$98$		0			0
$99$	35.8295	−	6.25375i	0.361914	−	0.0631692i
$100$		0			0
$101$	12.9628	−	35.6149i	0.128344	−	0.352623i	−0.858832	−	0.512257i	$-0.828809\pi$
$101$	12.9628	−	35.6149i	0.128344	−	0.352623i	0.987176	+	0.159635i	$0.0510316\pi$
$102$		0			0
$103$	−11.7726	−	9.87837i	−0.114297	−	0.0959065i	0.583848	−	0.811863i	$-0.301546\pi$
$103$	−11.7726	−	9.87837i	−0.114297	−	0.0959065i	−0.698145	+	0.715957i	$0.745991\pi$
$104$		0			0
$105$	72.9943	+	42.2276i	0.695184	+	0.402168i
$106$		0			0
$107$			116.068i			1.08475i	0.840138	+	0.542373i	$0.182474\pi$
$107$			116.068i			1.08475i	−0.840138	+	0.542373i	$0.817526\pi$
$108$		0			0
$109$	108.821			0.998362			0.499181	−	0.866498i	$-0.333634\pi$
$109$	108.821			0.998362			0.499181	+	0.866498i	$0.333634\pi$
$110$		0			0
$111$	−212.241	−	0.183778i	−1.91208	−	0.00165565i
$112$		0			0
$113$	−31.7762	+	37.8694i	−0.281205	+	0.335127i	−0.888096	−	0.459658i	$-0.847972\pi$
$113$	−31.7762	+	37.8694i	−0.281205	+	0.335127i	0.606891	+	0.794785i	$0.292416\pi$
$114$		0			0
$115$	84.9198	+	30.9083i	0.738433	+	0.268768i
$116$		0			0
$117$	91.6459	+	77.1709i	0.783298	+	0.659580i
$118$		0			0
$119$	55.6725	+	66.3479i	0.467836	+	0.557545i
$120$		0			0
$121$	18.1755	−	103.078i	0.150210	−	0.851886i
$122$		0			0
$123$	44.7832	+	123.373i	0.364091	+	1.00303i
$124$		0			0
$125$	71.2723	+	41.1491i	0.570178	+	0.329192i
$126$		0			0
$127$	−32.6359	−	56.5270i	−0.256975	−	0.445095i	0.708455	−	0.705756i	$-0.249393\pi$
$127$	−32.6359	−	56.5270i	−0.256975	−	0.445095i	−0.965430	+	0.260662i	$0.916059\pi$
$128$		0			0
$129$	130.160	+	47.5022i	1.00900	+	0.368234i
$130$		0			0
$131$	6.91556	+	19.0003i	0.0527905	+	0.145041i	0.963285	−	0.268480i	$-0.0865212\pi$
$131$	6.91556	+	19.0003i	0.0527905	+	0.145041i	−0.910495	+	0.413520i	$0.864299\pi$
$132$		0			0
$133$	−17.0567	−	96.7336i	−0.128246	−	0.727320i
$134$		0			0
$135$	−135.493	+	160.625i	−1.00365	+	1.18981i
$136$		0			0
$137$	41.6540	−	7.34472i	0.304044	−	0.0536111i	−0.0195449	−	0.999809i	$-0.506222\pi$
$137$	41.6540	−	7.34472i	0.304044	−	0.0536111i	0.323589	+	0.946198i	$0.395111\pi$
$138$		0			0
$139$	−82.7509	+	30.1189i	−0.595330	+	0.216682i	−0.622072	−	0.782960i	$-0.713709\pi$
$139$	−82.7509	+	30.1189i	−0.595330	+	0.216682i	0.0267421	+	0.999642i	$0.491487\pi$
$140$		0			0
$141$	−244.978	+	42.9775i	−1.73743	+	0.304805i
$142$		0			0
$143$	−46.5902	+	26.8989i	−0.325805	+	0.188104i
$144$		0			0
$145$	−90.3533	+	156.497i	−0.623126	+	1.07929i
$146$		0			0
$147$	−18.8229	+	106.212i	−0.128047	+	0.722531i
$148$		0			0
$149$	−208.714	−	36.8019i	−1.40077	−	0.246993i	−0.578308	−	0.815818i	$-0.696287\pi$
$149$	−208.714	−	36.8019i	−1.40077	−	0.246993i	−0.822458	+	0.568826i	$0.807398\pi$
$150$		0			0
$151$	135.180	−	113.429i	0.895229	−	0.751186i	−0.0740229	−	0.997257i	$-0.523584\pi$
$151$	135.180	−	113.429i	0.895229	−	0.751186i	0.969252	+	0.246070i	$0.0791393\pi$
$152$		0			0
$153$	−187.098	+	107.589i	−1.22286	+	0.703199i
$154$		0			0
$155$	−10.8012	+	29.6761i	−0.0696854	+	0.191459i
$156$		0			0
$157$	−4.29582	−	3.60462i	−0.0273619	−	0.0229594i	0.629004	−	0.777402i	$-0.283463\pi$
$157$	−4.29582	−	3.60462i	−0.0273619	−	0.0229594i	−0.656366	+	0.754443i	$0.727907\pi$
$158$		0			0
$159$	−75.3208	+	43.3995i	−0.473715	+	0.272953i
$160$		0			0
$161$		−	41.9363i		−	0.260474i
$162$		0			0
$163$	−176.753			−1.08437			−0.542186	−	0.840258i	$-0.682403\pi$
$163$	−176.753			−1.08437			−0.542186	+	0.840258i	$0.682403\pi$
$164$		0			0
$165$	−47.1084	−	81.7575i	−0.285505	−	0.495500i
$166$		0			0
$167$	−191.020	+	227.649i	−1.14383	+	1.36317i	−0.222249	+	0.974990i	$0.571340\pi$
$167$	−191.020	+	227.649i	−1.14383	+	1.36317i	−0.921585	+	0.388178i	$0.873105\pi$
$168$		0			0
$169$	−7.71852	−	2.80931i	−0.0456717	−	0.0166232i
$170$		0			0
$171$	244.769	+	0.423887i	1.43140	+	0.00247887i
$172$		0			0
$173$	90.8233	+	108.239i	0.524990	+	0.625659i	0.961753	−	0.273918i	$-0.0883197\pi$
$173$	90.8233	+	108.239i	0.524990	+	0.625659i	−0.436763	+	0.899577i	$0.643875\pi$
$174$		0			0
$175$	22.3108	−	126.531i	0.127490	−	0.723034i
$176$		0			0
$177$	155.455	+	27.5497i	0.878276	+	0.155648i
$178$		0			0
$179$	−152.323	−	87.9435i	−0.850964	−	0.491304i	0.0100121	−	0.999950i	$-0.496813\pi$
$179$	−152.323	−	87.9435i	−0.850964	−	0.491304i	−0.860976	+	0.508646i	$0.830146\pi$
$180$		0			0
$181$	−120.554	−	208.805i	−0.666042	−	1.15362i	−0.979002	−	0.203853i	$-0.934654\pi$
$181$	−120.554	−	208.805i	−0.666042	−	1.15362i	0.312959	−	0.949767i	$-0.398680\pi$
$182$		0			0
$183$	−2.25513	−	12.8546i	−0.0123231	−	0.0702436i
$184$		0			0
$185$	188.323	+	517.414i	1.01796	+	2.79683i
$186$		0			0
$187$	−16.8286	−	95.4397i	−0.0899925	−	0.510373i
$188$		0			0
$189$	91.5478	+	33.5902i	0.484380	+	0.177726i
$190$		0			0
$191$	159.627	−	28.1466i	0.835745	−	0.147364i	0.260632	−	0.965438i	$-0.416069\pi$
$191$	159.627	−	28.1466i	0.835745	−	0.147364i	0.575113	+	0.818074i	$0.304958\pi$
$192$		0			0
$193$	−13.5380	+	4.92744i	−0.0701452	+	0.0255308i	−0.376854	−	0.926272i	$-0.622994\pi$
$193$	−13.5380	+	4.92744i	−0.0701452	+	0.0255308i	0.306709	+	0.951803i	$0.400772\pi$
$194$		0			0
$195$	106.561	−	291.986i	0.546465	−	1.49737i
$196$		0			0
$197$	−188.497	+	108.829i	−0.956838	+	0.552431i	−0.895199	−	0.445668i	$-0.852966\pi$
$197$	−188.497	+	108.829i	−0.956838	+	0.552431i	−0.0616399	+	0.998098i	$0.519633\pi$
$198$		0			0
$199$	−20.5152	+	35.5335i	−0.103092	+	0.178560i	−0.912957	−	0.408056i	$-0.866207\pi$
$199$	−20.5152	+	35.5335i	−0.103092	+	0.178560i	0.809865	+	0.586616i	$0.199540\pi$
$200$		0			0
$201$	−369.412	+	134.093i	−1.83787	+	0.667129i
$202$		0			0
$203$	82.5833	+	14.5617i	0.406814	+	0.0717324i
$204$		0			0
$205$	260.840	−	218.871i	1.27239	−	1.06766i
$206$		0			0
$207$	102.882	+	18.3247i	0.497015	+	0.0885249i
$208$		0			0
$209$	−37.5908	+	103.280i	−0.179860	+	0.494163i
$210$		0			0
$211$	94.7998	+	79.5465i	0.449288	+	0.376998i	0.839172	−	0.543867i	$-0.183040\pi$
$211$	94.7998	+	79.5465i	0.449288	+	0.376998i	−0.389883	+	0.920864i	$0.627485\pi$
$212$		0			0
$213$	0.181317	−	209.399i	0.000851253	−	0.983096i
$214$		0			0
$215$		−	359.462i		−	1.67192i
$216$		0			0
$217$	14.6551			0.0675350
$218$		0			0
$219$	196.670	−	339.961i	0.898034	−	1.55234i
$220$		0			0
$221$	205.201	−	244.549i	0.928510	−	1.10656i
$222$		0			0
$223$	−245.799	−	89.4634i	−1.10224	−	0.401181i	−0.274096	−	0.961702i	$-0.588379\pi$
$223$	−245.799	−	89.4634i	−1.10224	−	0.401181i	−0.828140	+	0.560521i	$0.810601\pi$
$224$		0			0
$225$	300.669	+	110.025i	1.33631	+	0.488998i
$226$		0			0
$227$	−53.1278	−	63.3153i	−0.234043	−	0.278922i	0.636221	−	0.771507i	$-0.280497\pi$
$227$	−53.1278	−	63.3153i	−0.234043	−	0.278922i	−0.870264	+	0.492585i	$0.836052\pi$
$228$		0			0
$229$	23.0046	−	130.466i	0.100457	−	0.569719i	−0.892481	−	0.451084i	$-0.851037\pi$
$229$	23.0046	−	130.466i	0.100457	−	0.569719i	0.992938	−	0.118634i	$-0.0378516\pi$
$230$		0			0
$231$	−28.1749	+	33.5185i	−0.121969	+	0.145102i
$232$		0			0
$233$	−355.363	−	205.169i	−1.52516	−	0.880553i	−0.999555	−	0.0298260i	$-0.990505\pi$
$233$	−355.363	−	205.169i	−1.52516	−	0.880553i	−0.525608	−	0.850727i	$-0.676162\pi$
$234$		0			0
$235$	322.628	+	558.808i	1.37288	+	2.37791i
$236$		0			0
$237$	55.7465	−	46.6946i	0.235217	−	0.197024i
$238$		0			0
$239$	−38.7508	−	106.467i	−0.162137	−	0.445469i	0.831845	−	0.555008i	$-0.187285\pi$
$239$	−38.7508	−	106.467i	−0.162137	−	0.445469i	−0.993982	+	0.109539i	$0.965063\pi$
$240$		0			0
$241$	−18.3989	−	104.345i	−0.0763439	−	0.432968i	−0.998891	−	0.0470832i	$-0.985007\pi$
$241$	−18.3989	−	104.345i	−0.0763439	−	0.432968i	0.922547	−	0.385885i	$-0.126104\pi$
$242$		0			0
$243$	−122.410	+	209.916i	−0.503745	+	0.863853i
$244$		0			0
$245$	275.590	−	48.5939i	1.12486	−	0.198342i
$246$		0			0
$247$	−340.212	+	123.827i	−1.37738	+	0.501324i
$248$		0			0
$249$	−80.2038	−	95.7515i	−0.322104	−	0.384544i
$250$		0			0
$251$	13.6611	−	7.88725i	0.0544267	−	0.0314233i	−0.472540	−	0.881309i	$-0.656663\pi$
$251$	13.6611	−	7.88725i	0.0544267	−	0.0314233i	0.526966	+	0.849886i	$0.323329\pi$
$252$		0			0
$253$	−23.4620	+	40.6373i	−0.0927350	+	0.160622i
$254$		0			0
$255$	428.613	+	360.282i	1.68084	+	1.41287i
$256$		0			0
$257$	290.609	+	51.2422i	1.13077	+	0.199386i	0.707566	−	0.706647i	$-0.249793\pi$
$257$	290.609	+	51.2422i	1.13077	+	0.199386i	0.423207	+	0.906033i	$0.360904\pi$
$258$		0			0
$259$	195.737	−	164.243i	0.755741	−	0.634142i
$260$		0			0
$261$	−71.8101	+	196.238i	−0.275134	+	0.751871i
$262$		0			0
$263$	6.57712	−	18.0705i	0.0250080	−	0.0687090i	−0.926560	−	0.376146i	$-0.877249\pi$
$263$	6.57712	−	18.0705i	0.0250080	−	0.0687090i	0.951568	+	0.307437i	$0.0994713\pi$
$264$		0			0
$265$	172.760	+	144.963i	0.651925	+	0.547030i
$266$		0			0
$267$	−252.470	−	146.055i	−0.945581	−	0.547024i
$268$		0			0
$269$		−	190.266i		−	0.707309i	−0.935376	−	0.353654i	$-0.884939\pi$
$269$		−	190.266i		−	0.707309i	0.935376	−	0.353654i	$-0.115061\pi$
$270$		0			0
$271$	121.179			0.447154			0.223577	−	0.974686i	$-0.428227\pi$
$271$	121.179			0.447154			0.223577	+	0.974686i	$0.428227\pi$
$272$		0			0
$273$	−144.238	−	0.124895i	−0.528345	−	0.000457489i
$274$		0			0
$275$	−92.4096	+	110.129i	−0.336035	+	0.400471i
$276$		0			0
$277$	58.6745	+	21.3558i	0.211821	+	0.0770966i	0.445751	−	0.895157i	$-0.352937\pi$
$277$	58.6745	+	21.3558i	0.211821	+	0.0770966i	−0.233930	+	0.972253i	$0.575159\pi$
$278$		0			0
$279$	−6.40375	+	35.9533i	−0.0229525	+	0.128865i
$280$		0			0
$281$	−163.665	−	195.048i	−0.582437	−	0.694122i	0.391696	−	0.920095i	$-0.371888\pi$
$281$	−163.665	−	195.048i	−0.582437	−	0.694122i	−0.974134	+	0.225973i	$0.927444\pi$
$282$		0			0
$283$	−37.8599	+	214.714i	−0.133781	+	0.758707i	0.841921	+	0.539602i	$0.181425\pi$
$283$	−37.8599	+	214.714i	−0.133781	+	0.758707i	−0.975701	+	0.219106i	$0.929686\pi$
$284$		0			0
$285$	−216.669	−	596.902i	−0.760243	−	2.09439i
$286$		0			0
$287$	−136.841	−	79.0055i	−0.476800	−	0.275280i
$288$		0			0
$289$	143.038	+	247.749i	0.494941	+	0.857262i
$290$		0			0
$291$	−137.139	−	50.0489i	−0.471267	−	0.171989i
$292$		0			0
$293$	87.5538	+	240.552i	0.298818	+	0.820997i	0.994698	+	0.102838i	$0.0327924\pi$
$293$	87.5538	+	240.552i	0.298818	+	0.820997i	−0.695880	+	0.718158i	$0.744985\pi$
$294$		0			0
$295$	−71.1233	−	403.360i	−0.241096	−	1.36732i
$296$		0			0
$297$	−69.9195	−	83.7677i	−0.235419	−	0.282046i
$298$		0			0
$299$	−152.223	+	26.8410i	−0.509106	+	0.0897692i
$300$		0			0
$301$	−156.749	+	57.0521i	−0.520762	+	0.189542i
$302$		0			0
$303$	−111.991	+	19.6471i	−0.369609	+	0.0648421i
$304$		0			0
$305$	−29.3220	+	16.9291i	−0.0961377	+	0.0555051i
$306$		0			0
$307$	−176.673	+	306.006i	−0.575480	+	0.996761i	0.420509	+	0.907288i	$0.361852\pi$
$307$	−176.673	+	306.006i	−0.575480	+	0.996761i	−0.995989	+	0.0894730i	$0.971482\pi$
$308$		0			0
$309$	−8.04520	+	45.3967i	−0.0260362	+	0.146915i
$310$		0			0
$311$	47.8256	+	8.43294i	0.153780	+	0.0271156i	0.250008	−	0.968244i	$-0.419567\pi$
$311$	47.8256	+	8.43294i	0.153780	+	0.0271156i	−0.0962281	+	0.995359i	$0.530678\pi$
$312$		0			0
$313$	−50.3641	+	42.2605i	−0.160908	+	0.135018i	−0.719687	−	0.694299i	$-0.755714\pi$
$313$	−50.3641	+	42.2605i	−0.160908	+	0.135018i	0.558779	+	0.829317i	$0.311270\pi$
$314$		0			0
$315$	0.438116	−	252.986i	0.00139085	−	0.803130i
$316$		0			0
$317$	174.159	−	478.499i	0.549398	−	1.50946i	−0.285127	−	0.958490i	$-0.592036\pi$
$317$	174.159	−	478.499i	0.549398	−	1.50946i	0.834525	−	0.550970i	$-0.185742\pi$
$318$		0			0
$319$	−71.8785	−	60.3132i	−0.225325	−	0.189070i
$320$		0			0
$321$	301.703	−	173.840i	0.939886	−	0.541559i
$322$		0			0
$323$		−	652.196i		−	2.01918i
$324$		0			0
$325$	−473.569			−1.45714
$326$		0			0
$327$	−162.987	−	282.868i	−0.498432	−	0.865038i
$328$		0			0
$329$	192.471	−	229.379i	0.585020	−	0.697199i
$330$		0			0
$331$	417.785	+	152.061i	1.26219	+	0.459400i	0.884504	−	0.466534i	$-0.154497\pi$
$331$	417.785	+	152.061i	1.26219	+	0.459400i	0.377687	+	0.925933i	$0.376720\pi$
$332$		0			0
$333$	317.406	+	551.969i	0.953172	+	1.65757i
$334$		0			0
$335$	655.358	+	781.026i	1.95629	+	2.33142i
$336$		0			0
$337$	61.5963	−	349.330i	0.182778	−	1.03659i	−0.745999	−	0.665948i	$-0.768027\pi$
$337$	61.5963	−	349.330i	0.182778	−	1.03659i	0.928777	−	0.370639i	$-0.120861\pi$
$338$		0			0
$339$	146.029	+	25.8793i	0.430765	+	0.0763402i
$340$		0			0
$341$	−14.2011	−	8.19903i	−0.0416456	−	0.0240441i
$342$		0			0
$343$	−153.417	−	265.726i	−0.447279	−	0.774711i
$344$		0			0
$345$	−46.8464	−	267.031i	−0.135787	−	0.774003i
$346$		0			0
$347$	−156.901	−	431.082i	−0.452164	−	1.24231i	−0.931198	−	0.364514i	$-0.881235\pi$
$347$	−156.901	−	431.082i	−0.452164	−	1.24231i	0.479034	−	0.877797i	$-0.340987\pi$
$348$		0			0
$349$	72.6326	+	411.920i	0.208116	+	1.18029i	0.892460	+	0.451127i	$0.148978\pi$
$349$	72.6326	+	411.920i	0.208116	+	1.18029i	−0.684343	+	0.729160i	$0.739911\pi$
$350$		0			0
$351$	63.3334	−	353.805i	0.180437	−	1.00799i
$352$		0			0
$353$	−625.536	+	110.299i	−1.77206	+	0.312462i	−0.961829	−	0.273652i	$-0.911768\pi$
$353$	−625.536	+	110.299i	−1.77206	+	0.312462i	−0.810229	+	0.586114i	$0.800657\pi$
$354$		0			0
$355$	−510.486	+	185.802i	−1.43799	+	0.523385i
$356$		0			0
$357$	89.0795	−	244.086i	0.249522	−	0.683715i
$358$		0			0
$359$	387.565	−	223.761i	1.07957	−	0.623290i	0.148789	−	0.988869i	$-0.452462\pi$
$359$	387.565	−	223.761i	1.07957	−	0.623290i	0.930780	+	0.365579i	$0.119129\pi$
$360$		0			0
$361$	−189.329	+	327.927i	−0.524456	+	0.908385i
$362$		0			0
$363$	−295.161	+	107.141i	−0.813116	+	0.295153i
$364$		0			0
$365$	−1003.44	−	176.933i	−2.74914	−	0.484748i
$366$		0			0
$367$	437.316	−	366.952i	1.19160	−	0.999869i	0.191767	−	0.981440i	$-0.438578\pi$
$367$	437.316	−	366.952i	1.19160	−	0.999869i	0.999830	−	0.0184287i	$-0.00586638\pi$
$368$		0			0
$369$	253.619	−	301.190i	0.687314	−	0.816234i
$370$		0			0
$371$	35.7938	−	98.3427i	0.0964793	−	0.265075i
$372$		0			0
$373$	169.879	+	142.546i	0.455440	+	0.382160i	0.841450	−	0.540335i	$-0.181702\pi$
$373$	169.879	+	142.546i	0.455440	+	0.382160i	−0.386010	+	0.922495i	$0.626147\pi$
$374$		0			0
$375$	0.213783	−	246.894i	0.000570089	−	0.658385i
$376$		0			0
$377$		−	309.086i		−	0.819856i
$378$		0			0
$379$	523.969			1.38250			0.691252	−	0.722614i	$-0.257059\pi$
$379$	523.969			1.38250			0.691252	+	0.722614i	$0.257059\pi$
$380$		0			0
$381$	−98.0545	+	169.496i	−0.257361	+	0.444872i
$382$		0			0
$383$	−262.803	+	313.197i	−0.686171	+	0.817746i	−0.990887	−	0.134697i	$-0.956994\pi$
$383$	−262.803	+	313.197i	−0.686171	+	0.817746i	0.304716	+	0.952443i	$0.401438\pi$
$384$		0			0
$385$	106.747	+	38.8527i	0.277265	+	0.100916i
$386$		0			0
$387$	−71.4718	−	409.482i	−0.184682	−	1.05809i
$388$		0			0
$389$	256.377	+	305.538i	0.659066	+	0.785445i	0.987251	−	0.159169i	$-0.0508814\pi$
$389$	256.377	+	305.538i	0.659066	+	0.785445i	−0.328185	+	0.944613i	$0.606437\pi$
$390$		0			0
$391$	48.3517	−	274.216i	0.123662	−	0.701320i
$392$		0			0
$393$	39.0312	−	46.4339i	0.0993160	−	0.118152i
$394$		0			0
$395$	−163.381	−	94.3280i	−0.413622	−	0.238805i
$396$		0			0
$397$	138.738	+	240.302i	0.349467	+	0.605295i	0.986155	−	0.165827i	$-0.0530293\pi$
$397$	138.738	+	240.302i	0.349467	+	0.605295i	−0.636688	+	0.771122i	$0.719696\pi$
$398$		0			0
$399$	−225.900	+	189.220i	−0.566166	+	0.474235i
$400$		0			0
$401$	49.8939	+	137.082i	0.124424	+	0.341851i	0.986228	−	0.165389i	$-0.0528880\pi$
$401$	49.8939	+	137.082i	0.124424	+	0.341851i	−0.861805	+	0.507240i	$0.830666\pi$
$402$		0			0
$403$	−9.37987	−	53.1959i	−0.0232751	−	0.132000i
$404$		0			0
$405$	620.458	+	111.621i	1.53199	+	0.275606i
$406$		0			0
$407$	−281.562	+	49.6471i	−0.691800	+	0.121983i
$408$		0			0
$409$	−107.110	+	38.9847i	−0.261882	+	0.0953171i	−0.469624	−	0.882866i	$-0.655611\pi$
$409$	−107.110	+	38.9847i	−0.261882	+	0.0953171i	0.207743	+	0.978184i	$0.433388\pi$
$410$		0			0
$411$	−81.4789	−	97.2738i	−0.198246	−	0.236676i
$412$		0			0
$413$	−164.604	+	95.0339i	−0.398556	+	0.230106i
$414$		0			0
$415$	−162.020	+	280.627i	−0.390410	+	0.676209i
$416$		0			0
$417$	202.230	+	169.990i	0.484965	+	0.407650i
$418$		0			0
$419$	−514.237	−	90.6739i	−1.22730	−	0.216406i	−0.477833	−	0.878451i	$-0.658578\pi$
$419$	−514.237	−	90.6739i	−1.22730	−	0.216406i	−0.749464	+	0.662045i	$0.769689\pi$
$420$		0			0
$421$	−302.908	+	254.170i	−0.719495	+	0.603728i	−0.927246	−	0.374454i	$-0.877830\pi$
$421$	−302.908	+	254.170i	−0.719495	+	0.603728i	0.207750	+	0.978182i	$0.433386\pi$
$422$		0			0
$423$	478.630	+	572.420i	1.13151	+	1.35324i
$424$		0			0
$425$	291.776	−	801.647i	0.686531	−	1.88623i
$426$		0			0
$427$	12.0360	+	10.0994i	0.0281874	+	0.0236521i
$428$		0			0
$429$	139.701	+	80.8176i	0.325642	+	0.188386i
$430$		0			0
$431$			555.362i			1.28854i	0.764797	+	0.644272i	$0.222839\pi$
$431$			555.362i			1.28854i	−0.764797	+	0.644272i	$0.777161\pi$
$432$		0			0
$433$	13.3027			0.0307222			0.0153611	−	0.999882i	$-0.495110\pi$
$433$	13.3027			0.0307222			0.0153611	+	0.999882i	$0.495110\pi$
$434$		0			0
$435$	542.120	+	0.469416i	1.24625	+	0.00107912i
$436$		0			0
$437$	−202.984	+	241.907i	−0.464495	+	0.553563i
$438$		0			0
$439$	−279.612	−	101.770i	−0.636929	−	0.231823i	0.00331548	−	0.999995i	$-0.498945\pi$
$439$	−279.612	−	101.770i	−0.636929	−	0.231823i	−0.640244	+	0.768171i	$0.721167\pi$
$440$		0			0
$441$	304.277	−	110.151i	0.689970	−	0.249776i
$442$		0			0
$443$	−64.0510	−	76.3330i	−0.144585	−	0.172309i	0.688892	−	0.724864i	$-0.258097\pi$
$443$	−64.0510	−	76.3330i	−0.144585	−	0.172309i	−0.833477	+	0.552555i	$0.813653\pi$
$444$		0			0
$445$	−131.398	+	745.196i	−0.295277	+	1.67460i
$446$		0			0
$447$	216.940	+	597.646i	0.485324	+	1.33702i
$448$		0			0
$449$	−425.171	−	245.473i	−0.946929	−	0.546710i	−0.0548032	−	0.998497i	$-0.517453\pi$
$449$	−425.171	−	245.473i	−0.946929	−	0.546710i	−0.892126	+	0.451788i	$0.850786\pi$
$450$		0			0
$451$	88.4019	+	153.117i	0.196013	+	0.339505i
$452$		0			0
$453$	−497.310	−	181.494i	−1.09781	−	0.400649i
$454$		0			0
$455$	127.984	+	351.633i	0.281283	+	0.772819i
$456$		0			0
$457$	−20.0616	−	113.775i	−0.0438984	−	0.248960i	0.954960	−	0.296736i	$-0.0958980\pi$
$457$	−20.0616	−	113.775i	−0.0438984	−	0.248960i	−0.998858	+	0.0477752i	$0.984787\pi$
$458$		0			0
$459$	559.891	+	325.195i	1.21981	+	0.708487i
$460$		0			0
$461$	−113.395	+	19.9947i	−0.245977	+	0.0433724i	−0.295277	−	0.955412i	$-0.595412\pi$
$461$	−113.395	+	19.9947i	−0.245977	+	0.0433724i	0.0493001	+	0.998784i	$0.484301\pi$
$462$		0			0
$463$	42.9280	−	15.6245i	0.0927171	−	0.0337463i	−0.295245	−	0.955422i	$-0.595401\pi$
$463$	42.9280	−	15.6245i	0.0927171	−	0.0337463i	0.387962	+	0.921675i	$0.373179\pi$
$464$		0			0
$465$	93.3169	−	16.3710i	0.200682	−	0.0352064i
$466$		0			0
$467$	−343.979	+	198.596i	−0.736571	+	0.425259i	−0.820821	−	0.571185i	$-0.806484\pi$
$467$	−343.979	+	198.596i	−0.736571	+	0.425259i	0.0842504	+	0.996445i	$0.473150\pi$
$468$		0			0
$469$	236.564	−	409.740i	0.504400	−	0.873647i
$470$		0			0
$471$	−2.93569	+	16.5653i	−0.00623289	+	0.0351704i
$472$		0			0
$473$	183.813	+	32.4111i	0.388610	+	0.0685225i
$474$		0			0
$475$	−741.146	+	621.896i	−1.56031	+	1.30925i
$476$		0			0
$477$	225.623	+	130.785i	0.473005	+	0.274183i
$478$		0			0
$479$	267.653	−	735.372i	0.558775	−	1.53522i	−0.262641	−	0.964894i	$-0.584594\pi$
$479$	267.653	−	735.372i	0.558775	−	1.53522i	0.821416	−	0.570329i	$-0.193184\pi$
$480$		0			0
$481$	−721.458	−	605.375i	−1.49991	−	1.25858i
$482$		0			0
$483$	−109.008	+	62.8101i	−0.225690	+	0.130042i
$484$		0			0
$485$			378.733i			0.780893i
$486$		0			0
$487$	505.750			1.03850			0.519250	−	0.854622i	$-0.326211\pi$
$487$	505.750			1.03850			0.519250	+	0.854622i	$0.326211\pi$
$488$		0			0
$489$	264.731	+	459.446i	0.541373	+	0.939563i
$490$		0			0
$491$	−592.619	+	706.256i	−1.20696	+	1.43840i	−0.339714	+	0.940529i	$0.610330\pi$
$491$	−592.619	+	706.256i	−1.20696	+	1.43840i	−0.867250	+	0.497874i	$0.834114\pi$
$492$		0			0
$493$	523.213	+	190.434i	1.06128	+	0.386276i
$494$		0			0
$495$	−141.962	+	244.904i	−0.286791	+	0.494757i
$496$		0			0
$497$	162.044	+	193.116i	0.326044	+	0.388564i
$498$		0			0
$499$	−107.632	+	610.414i	−0.215696	+	1.22327i	0.663998	+	0.747734i	$0.268858\pi$
$499$	−107.632	+	610.414i	−0.215696	+	1.22327i	−0.879694	+	0.475540i	$0.842253\pi$
$500$		0			0
$501$	877.845	+	155.572i	1.75219	+	0.310522i
$502$		0			0
$503$	−1.70660	−	0.985304i	−0.00339284	−	0.00195885i	0.498303	−	0.867003i	$-0.333957\pi$
$503$	−1.70660	−	0.985304i	−0.00339284	−	0.00195885i	−0.501695	+	0.865044i	$0.667290\pi$
$504$		0			0
$505$	147.489	+	255.459i	0.292058	+	0.505859i
$506$		0			0
$507$	4.25796	+	24.2710i	0.00839835	+	0.0478718i
$508$		0			0
$509$	−4.31115	−	11.8448i	−0.00846985	−	0.0232707i	0.935386	−	0.353629i	$-0.115053\pi$
$509$	−4.31115	−	11.8448i	−0.00846985	−	0.0232707i	−0.943856	+	0.330359i	$0.892830\pi$
$510$		0			0
$511$	82.1062	+	465.647i	0.160677	+	0.911247i
$512$		0			0
$513$	−365.502	−	636.882i	−0.712479	−	1.24149i
$514$		0			0
$515$	117.791	−	20.7698i	0.228721	−	0.0403297i
$516$		0			0
$517$	−314.839	+	114.592i	−0.608974	+	0.221648i
$518$		0			0
$519$	145.323	−	398.198i	0.280006	−	0.767242i
$520$		0			0
$521$	−227.658	+	131.438i	−0.436964	+	0.252281i	−0.702309	−	0.711872i	$-0.747847\pi$
$521$	−227.658	+	131.438i	−0.436964	+	0.252281i	0.265345	+	0.964154i	$0.414514\pi$
$522$		0			0
$523$	−134.833	+	233.537i	−0.257807	+	0.446534i	−0.965654	−	0.259831i	$-0.916333\pi$
$523$	−134.833	+	233.537i	−0.257807	+	0.446534i	0.707847	+	0.706365i	$0.249666\pi$
$524$		0			0
$525$	−362.317	+	131.518i	−0.690128	+	0.250510i
$526$		0			0
$527$	95.8279	+	16.8970i	0.181837	+	0.0320627i
$528$		0			0
$529$	301.958	−	253.373i	0.570810	−	0.478966i
$530$		0			0
$531$	−161.220	−	445.348i	−0.303617	−	0.838696i
$532$		0			0
$533$	−199.194	+	547.282i	−0.373723	+	1.02680i
$534$		0			0
$535$	−692.005	−	580.661i	−1.29347	−	1.08535i
$536$		0			0
$537$	−0.456896	+	527.661i	−0.000850831	+	0.982608i
$538$		0			0
$539$			145.306i			0.269584i
$540$		0			0
$541$	986.273			1.82306			0.911528	−	0.411238i	$-0.134903\pi$
$541$	986.273			1.82306			0.911528	+	0.411238i	$0.134903\pi$
$542$		0			0
$543$	−362.203	+	626.102i	−0.667041	+	1.15304i
$544$		0			0
$545$	−544.409	+	648.802i	−0.998916	+	1.19046i
$546$		0			0
$547$	632.979	+	230.385i	1.15718	+	0.421180i	0.848090	−	0.529852i	$-0.177753\pi$
$547$	632.979	+	230.385i	1.15718	+	0.421180i	0.309092	+	0.951032i	$0.399975\pi$
$548$		0			0
$549$	−30.0362	+	25.1149i	−0.0547108	+	0.0457466i
$550$		0			0
$551$	−405.894	−	483.726i	−0.736651	−	0.877906i
$552$		0			0
$553$	−15.2022	+	86.2162i	−0.0274905	+	0.155906i
$554$		0			0
$555$	1062.89	−	1264.48i	1.91512	−	2.27834i
$556$		0			0
$557$	−192.011	−	110.858i	−0.344723	−	0.199026i	0.317635	−	0.948213i	$-0.397111\pi$
$557$	−192.011	−	110.858i	−0.344723	−	0.199026i	−0.662359	+	0.749187i	$0.730445\pi$
$558$		0			0
$559$	307.417	+	532.462i	0.549941	+	0.952526i
$560$		0			0
$561$	−222.878	+	186.689i	−0.397288	+	0.332778i
$562$		0			0
$563$	−34.1283	−	93.7667i	−0.0606187	−	0.166548i	0.905686	−	0.423949i	$-0.139356\pi$
$563$	−34.1283	−	93.7667i	−0.0606187	−	0.166548i	−0.966305	+	0.257400i	$0.917134\pi$
$564$		0			0
$565$	−66.8110	−	378.904i	−0.118250	−	0.670627i
$566$		0			0
$567$	−49.8021	−	288.277i	−0.0878344	−	0.508425i
$568$		0			0
$569$	601.483	−	106.058i	1.05709	−	0.186393i	0.382024	−	0.924153i	$-0.375227\pi$
$569$	601.483	−	106.058i	1.05709	−	0.186393i	0.675064	+	0.737760i	$0.264116\pi$
$570$		0			0
$571$	557.549	−	202.931i	0.976444	−	0.355397i	0.195987	−	0.980606i	$-0.437209\pi$
$571$	557.549	−	202.931i	0.976444	−	0.355397i	0.780457	+	0.625210i	$0.214987\pi$
$572$		0			0
$573$	−312.245	−	372.774i	−0.544931	−	0.650566i
$574$		0			0
$575$	−357.721	+	206.530i	−0.622124	+	0.359183i
$576$		0			0
$577$	−200.969	+	348.089i	−0.348300	+	0.603273i	−0.985948	−	0.167055i	$-0.946574\pi$
$577$	−200.969	+	348.089i	−0.348300	+	0.603273i	0.637648	+	0.770328i	$0.279908\pi$
$578$		0			0
$579$	33.0848	+	27.8103i	0.0571413	+	0.0480316i
$580$		0			0
$581$	148.087	+	26.1117i	0.254883	+	0.0449428i
$582$		0			0
$583$	−89.7046	+	75.2711i	−0.153867	+	0.129110i
$584$		0			0
$585$	−918.583	+	160.331i	−1.57023	+	0.274071i
$586$		0			0
$587$	138.391	−	380.226i	0.235759	−	0.647744i	−0.764237	−	0.644936i	$-0.776884\pi$
$587$	138.391	−	380.226i	0.235759	−	0.647744i	0.999996	−	0.00280774i	$-0.000893734\pi$
$588$		0			0
$589$	−84.5370	−	70.9350i	−0.143526	−	0.120433i
$590$		0			0
$591$	565.209	+	326.976i	0.956360	+	0.553259i
$592$		0			0
$593$			397.833i			0.670882i	0.942061	+	0.335441i	$0.108885\pi$
$593$			397.833i			0.670882i	−0.942061	+	0.335441i	$0.891115\pi$
$594$		0			0
$595$	−674.088			−1.13292
$596$		0			0
$597$	123.091	+	0.106584i	0.206183	+	0.000178532i
$598$		0			0
$599$	628.912	−	749.508i	1.04994	−	1.25127i	0.0829193	−	0.996556i	$-0.473576\pi$
$599$	628.912	−	749.508i	1.04994	−	1.25127i	0.967018	−	0.254710i	$-0.0819799\pi$
$600$		0			0
$601$	−289.500	−	105.369i	−0.481698	−	0.175324i	0.0897464	−	0.995965i	$-0.471394\pi$
$601$	−289.500	−	105.369i	−0.481698	−	0.175324i	−0.571444	+	0.820641i	$0.693617\pi$
$602$		0			0
$603$	901.845	+	759.403i	1.49560	+	1.25938i
$604$		0			0
$605$	523.633	+	624.041i	0.865508	+	1.03147i
$606$		0			0
$607$	−23.7810	+	134.869i	−0.0391779	+	0.222189i	−0.998110	−	0.0614454i	$-0.980429\pi$
$607$	−23.7810	+	134.869i	−0.0391779	+	0.222189i	0.958933	+	0.283634i	$0.0915401\pi$
$608$		0			0
$609$	−85.8379	−	236.475i	−0.140949	−	0.388300i
$610$		0			0
$611$	−955.801	−	551.832i	−1.56432	−	0.903162i
$612$		0			0
$613$	165.591	+	286.811i	0.270132	+	0.467882i	0.968895	−	0.247471i	$-0.0795995\pi$
$613$	165.591	+	286.811i	0.270132	+	0.467882i	−0.698764	+	0.715352i	$0.746266\pi$
$614$		0			0
$615$	−959.600	−	350.207i	−1.56033	−	0.569443i
$616$		0			0
$617$	−167.681	−	460.699i	−0.271768	−	0.746676i	−0.998230	−	0.0594697i	$-0.981059\pi$
$617$	−167.681	−	460.699i	−0.271768	−	0.746676i	0.726462	−	0.687206i	$-0.241163\pi$
$618$		0			0
$619$	44.5940	+	252.905i	0.0720420	+	0.408571i	0.999408	+	0.0344143i	$0.0109566\pi$
$619$	44.5940	+	252.905i	0.0720420	+	0.408571i	−0.927366	+	0.374156i	$0.877932\pi$
$620$		0			0
$621$	−106.459	−	294.875i	−0.171432	−	0.474839i
$622$		0			0
$623$	345.810	−	60.9756i	0.555072	−	0.0978742i
$624$		0			0
$625$	233.826	−	85.1058i	0.374122	−	0.136169i
$626$		0			0
$627$	324.765	−	56.9749i	0.517966	−	0.0908691i
$628$		0			0
$629$	1469.27	−	848.283i	2.33588	−	1.34862i
$630$		0			0
$631$	320.656	−	555.392i	0.508171	−	0.880177i	−0.491785	−	0.870717i	$-0.663655\pi$
$631$	320.656	−	555.392i	0.508171	−	0.880177i	0.999955	−	0.00946046i	$-0.00301140\pi$
$632$		0			0
$633$	64.7847	−	365.561i	0.102345	−	0.577506i
$634$		0			0
$635$	500.289	+	88.2144i	0.787856	+	0.138920i
$636$		0			0
$637$	−366.666	+	307.669i	−0.575614	+	0.482997i
$638$		0			0
$639$	−544.579	+	313.157i	−0.852236	+	0.490073i
$640$		0			0
$641$	296.689	−	815.145i	0.462853	−	1.27168i	−0.460478	−	0.887671i	$-0.652322\pi$
$641$	296.689	−	815.145i	0.462853	−	1.27168i	0.923330	−	0.384006i	$-0.125456\pi$
$642$		0			0
$643$	12.8197	+	10.7570i	0.0199373	+	0.0167294i	0.652702	−	0.757615i	$-0.273635\pi$
$643$	12.8197	+	10.7570i	0.0199373	+	0.0167294i	−0.632765	+	0.774344i	$0.718080\pi$
$644$		0			0
$645$	−934.376	+	538.384i	−1.44864	+	0.834704i
$646$		0			0
$647$		−	96.9735i		−	0.149882i	−0.997188	−	0.0749409i	$-0.976123\pi$
$647$		−	96.9735i		−	0.149882i	0.997188	−	0.0749409i	$-0.0238768\pi$
$648$		0			0
$649$	212.673			0.327694
$650$		0			0
$651$	−21.9497	−	38.0941i	−0.0337168	−	0.0585162i
$652$		0			0
$653$	−233.975	+	278.841i	−0.358309	+	0.427015i	−0.914843	−	0.403809i	$-0.867686\pi$
$653$	−233.975	+	278.841i	−0.358309	+	0.427015i	0.556535	+	0.830824i	$0.312131\pi$
$654$		0			0
$655$	−147.878	−	53.8234i	−0.225769	−	0.0821731i
$656$		0			0
$657$	−1178.25	−	2.04047i	−1.79338	−	0.00310574i
$658$		0			0
$659$	246.864	+	294.201i	0.374604	+	0.446436i	0.920104	−	0.391675i	$-0.128104\pi$
$659$	246.864	+	294.201i	0.374604	+	0.446436i	−0.545499	+	0.838111i	$0.683660\pi$
$660$		0			0
$661$	46.2263	−	262.162i	0.0699338	−	0.396614i	−0.929668	−	0.368398i	$-0.879906\pi$
$661$	46.2263	−	262.162i	0.0699338	−	0.396614i	0.999602	−	0.0282161i	$-0.00898265\pi$
$662$		0			0
$663$	−943.013	−	167.121i	−1.42234	−	0.252067i
$664$		0			0
$665$	662.064	+	382.243i	0.995586	+	0.574802i
$666$		0			0
$667$	−134.797	−	233.475i	−0.202094	−	0.350037i
$668$		0			0
$669$	135.596	+	772.917i	0.202685	+	1.15533i
$670$		0			0
$671$	−6.01292	−	16.5204i	−0.00896114	−	0.0246205i
$672$		0			0
$673$	−15.4024	−	87.3511i	−0.0228861	−	0.129794i	0.971224	−	0.238168i	$-0.0765467\pi$
$673$	−15.4024	−	87.3511i	−0.0228861	−	0.129794i	−0.994110	+	0.108374i	$0.965436\pi$
$674$		0			0
$675$	−164.332	−	946.340i	−0.243454	−	1.40199i
$676$		0			0
$677$	−440.545	+	77.6799i	−0.650731	+	0.114741i	−0.489262	−	0.872137i	$-0.662734\pi$
$677$	−440.545	+	77.6799i	−0.650731	+	0.114741i	−0.161468	+	0.986878i	$0.551623\pi$
$678$		0			0
$679$	165.153	−	60.1107i	0.243230	−	0.0885283i
$680$		0			0
$681$	−85.0079	+	232.929i	−0.124828	+	0.342040i
$682$		0			0
$683$	289.821	−	167.328i	0.424335	−	0.244990i	−0.272595	−	0.962129i	$-0.587882\pi$
$683$	289.821	−	167.328i	0.424335	−	0.244990i	0.696930	+	0.717139i	$0.254549\pi$
$684$		0			0
$685$	−164.596	+	285.088i	−0.240286	+	0.416187i
$686$		0			0
$687$	−373.584	+	135.607i	−0.543790	+	0.197390i
$688$		0			0
$689$	−379.880	−	66.9831i	−0.551349	−	0.0972178i
$690$		0			0
$691$	−319.613	+	268.187i	−0.462537	+	0.388115i	−0.844064	−	0.536243i	$-0.819843\pi$
$691$	−319.613	+	268.187i	−0.462537	+	0.388115i	0.381526	+	0.924358i	$0.375399\pi$
$692$		0			0
$693$	129.326	+	23.0347i	0.186618	+	0.0332391i
$694$		0			0
$695$	234.413	−	644.045i	0.337285	−	0.926684i
$696$		0			0
$697$	−803.698	−	674.383i	−1.15308	−	0.967551i
$698$		0			0
$699$	−1.06592	+	1231.01i	−0.00152492	+	1.76111i
$700$		0			0
$701$		−	613.675i		−	0.875428i	−0.899114	−	0.437714i	$-0.855788\pi$
$701$		−	613.675i		−	0.875428i	0.899114	−	0.437714i	$-0.144212\pi$
$702$		0			0
$703$	−1924.08			−2.73696
$704$		0			0
$705$	969.335	−	1675.59i	1.37494	−	2.37672i
$706$		0			0
$707$	87.9882	−	104.860i	0.124453	−	0.148317i
$708$		0			0
$709$	−788.773	−	287.090i	−1.11252	−	0.404923i	−0.280600	−	0.959825i	$-0.590533\pi$
$709$	−788.773	−	287.090i	−1.11252	−	0.404923i	−0.831916	+	0.554902i	$0.812756\pi$
$710$		0			0
$711$	−204.871	−	74.9690i	−0.288145	−	0.105442i
$712$		0			0
$713$	−30.2848	−	36.0920i	−0.0424752	−	0.0506199i
$714$		0			0
$715$	72.7073	−	412.343i	0.101688	−	0.576704i
$716$		0			0
$717$	−218.709	+	260.189i	−0.305033	+	0.362885i
$718$		0			0
$719$	866.895	+	500.502i	1.20570	+	0.696108i	0.961816	−	0.273697i	$-0.0882466\pi$
$719$	866.895	+	500.502i	1.20570	+	0.696108i	0.243879	+	0.969806i	$0.421580\pi$
$720$		0			0
$721$	−27.7523	−	48.0683i	−0.0384914	−	0.0666690i
$722$		0			0
$723$	−243.675	+	204.109i	−0.337034	+	0.282308i
$724$		0			0
$725$	−282.499	−	776.159i	−0.389654	−	1.07056i
$726$		0			0
$727$	184.123	+	1044.22i	0.253264	+	1.43633i	0.800488	+	0.599348i	$0.204573\pi$
$727$	184.123	+	1044.22i	0.253264	+	1.43633i	−0.547224	+	0.836986i	$0.684315\pi$
$728$		0			0
$729$	728.990	+	3.78739i	0.999987	+	0.00519532i
$730$		0			0
$731$	−1090.74	+	192.328i	−1.49213	+	0.263102i
$732$		0			0
$733$	330.701	−	120.365i	0.451161	−	0.164209i	−0.106438	−	0.994319i	$-0.533945\pi$
$733$	330.701	−	120.365i	0.451161	−	0.164209i	0.557600	+	0.830110i	$0.311723\pi$
$734$		0			0
$735$	−539.078	−	643.579i	−0.733439	−	0.875618i
$736$		0			0
$737$	−458.472	+	264.699i	−0.622079	+	0.359158i
$738$		0			0
$739$	417.279	−	722.749i	0.564654	−	0.978010i	−0.432428	−	0.901669i	$-0.642343\pi$
$739$	417.279	−	722.749i	0.564654	−	0.978010i	0.997082	−	0.0763410i	$-0.0243238\pi$
$740$		0			0
$741$	831.426	+	698.877i	1.12203	+	0.943154i
$742$		0			0
$743$	132.230	+	23.3158i	0.177968	+	0.0313806i	0.261922	−	0.965089i	$-0.415644\pi$
$743$	132.230	+	23.3158i	0.177968	+	0.0313806i	−0.0839538	+	0.996470i	$0.526755\pi$
$744$		0			0
$745$	1263.57	−	1060.26i	1.69606	−	1.42317i
$746$		0			0
$747$	−128.769	+	351.892i	−0.172381	+	0.471073i
$748$		0			0
$749$	−143.375	+	393.920i	−0.191422	+	0.525928i
$750$		0			0
$751$	234.728	+	196.960i	0.312554	+	0.262264i	0.785547	−	0.618802i	$-0.212382\pi$
$751$	234.728	+	196.960i	0.312554	+	0.262264i	−0.472992	+	0.881066i	$0.656826\pi$
$752$		0			0
$753$	−40.9628	−	23.6972i	−0.0543995	−	0.0314704i
$754$		0			0
$755$			1373.41i			1.81909i
$756$		0			0
$757$	248.812			0.328682			0.164341	−	0.986404i	$-0.447450\pi$
$757$	248.812			0.328682			0.164341	+	0.986404i	$0.447450\pi$
$758$		0			0
$759$	140.772	+	0.121893i	0.185470	+	0.000160597i
$760$		0			0
$761$	−80.5249	+	95.9658i	−0.105815	+	0.126105i	−0.816352	−	0.577554i	$-0.804007\pi$
$761$	−80.5249	+	95.9658i	−0.105815	+	0.126105i	0.710538	+	0.703659i	$0.248452\pi$
$762$		0			0
$763$	369.327	+	134.424i	0.484046	+	0.176178i
$764$		0			0
$765$	294.553	−	1653.74i	0.385036	−	2.16175i
$766$		0			0
$767$	450.313	+	536.662i	0.587109	+	0.699690i
$768$		0			0
$769$	−160.957	+	912.832i	−0.209307	+	1.18704i	0.681210	+	0.732088i	$0.261454\pi$
$769$	−160.957	+	912.832i	−0.209307	+	1.18704i	−0.890517	+	0.454950i	$0.849657\pi$
$770$		0			0
$771$	−302.062	−	832.149i	−0.391779	−	1.07931i
$772$		0			0
$773$	202.681	+	117.018i	0.262200	+	0.151381i	0.625338	−	0.780354i	$-0.284961\pi$
$773$	202.681	+	117.018i	0.262200	+	0.151381i	−0.363138	+	0.931736i	$0.618295\pi$
$774$		0			0
$775$	−72.1743	−	125.010i	−0.0931281	−	0.161303i
$776$		0			0
$777$	−720.094	−	262.799i	−0.926761	−	0.338223i
$778$		0			0
$779$	406.952	+	1118.09i	0.522404	+	1.43529i
$780$		0			0
$781$	−48.9823	−	277.793i	−0.0627175	−	0.355688i
$782$		0			0
$783$	617.651	−	107.255i	0.788826	−	0.136979i
$784$		0			0
$785$	42.9820	−	7.57889i	0.0547542	−	0.00965464i
$786$		0			0
$787$	1136.84	−	413.777i	1.44453	−	0.525765i	0.503470	−	0.864013i	$-0.332057\pi$
$787$	1136.84	−	413.777i	1.44453	−	0.525765i	0.941057	+	0.338248i	$0.109834\pi$
$788$		0			0
$789$	−56.8228	+	9.96867i	−0.0720188	+	0.0126346i
$790$		0			0
$791$	−154.623	+	89.2719i	−0.195478	+	0.112860i
$792$		0			0
$793$	28.9560	−	50.1532i	0.0365144	−	0.0632449i
$794$		0			0
$795$	118.062	−	666.186i	0.148505	−	0.837970i
$796$		0			0
$797$	812.196	+	143.212i	1.01907	+	0.179689i	0.658132	−	0.752903i	$-0.271347\pi$
$797$	812.196	+	143.212i	1.01907	+	0.179689i	0.360934	+	0.932591i	$0.382458\pi$
$798$		0			0
$799$	1523.02	−	1277.96i	1.90615	−	1.59945i
$800$		0			0
$801$	−1.51534	+	875.019i	−0.00189181	+	1.09241i
$802$		0			0
$803$	180.951	−	497.160i	0.225344	−	0.619128i
$804$		0			0
$805$	250.027	+	209.798i	0.310593	+	0.260618i
$806$		0			0
$807$	−494.573	+	284.971i	−0.612853	+	0.353124i
$808$		0			0
$809$		−	786.815i		−	0.972577i	−0.873798	−	0.486289i	$-0.838350\pi$
$809$		−	786.815i		−	0.972577i	0.873798	−	0.486289i	$-0.161650\pi$
$810$		0			0
$811$	935.082			1.15300			0.576500	−	0.817097i	$-0.304418\pi$
$811$	935.082			1.15300			0.576500	+	0.817097i	$0.304418\pi$
$812$		0			0
$813$	−181.496	−	314.989i	−0.223242	−	0.387440i
$814$		0			0
$815$	884.254	−	1053.81i	1.08497	−	1.29302i
$816$		0			0
$817$	1180.35	+	429.612i	1.44473	+	0.525841i
$818$		0			0
$819$	215.708	+	375.116i	0.263380	+	0.458018i
$820$		0			0
$821$	451.494	+	538.070i	0.549932	+	0.655383i	0.967384	−	0.253316i	$-0.0815211\pi$
$821$	451.494	+	538.070i	0.549932	+	0.655383i	−0.417452	+	0.908699i	$0.637077\pi$
$822$		0			0
$823$	102.126	−	579.184i	0.124090	−	0.703748i	−0.857755	−	0.514059i	$-0.828141\pi$
$823$	102.126	−	579.184i	0.124090	−	0.703748i	0.981844	−	0.189688i	$-0.0607478\pi$
$824$		0			0
$825$	424.674	+	75.2607i	0.514757	+	0.0912251i
$826$		0			0
$827$	428.539	+	247.417i	0.518184	+	0.299174i	0.736192	−	0.676773i	$-0.236622\pi$
$827$	428.539	+	247.417i	0.518184	+	0.299174i	−0.218007	+	0.975947i	$0.569956\pi$
$828$		0			0
$829$	−381.333	−	660.489i	−0.459992	−	0.796729i	0.538968	−	0.842326i	$-0.318814\pi$
$829$	−381.333	−	660.489i	−0.459992	−	0.796729i	−0.998960	+	0.0455969i	$0.985481\pi$
$830$		0			0
$831$	−32.3681	−	184.503i	−0.0389508	−	0.222025i
$832$		0			0
$833$	−294.905	−	810.244i	−0.354027	−	0.972682i
$834$		0			0
$835$	−401.630	−	2277.75i	−0.480994	−	2.72785i
$836$		0			0
$837$	103.047	−	37.2033i	0.123115	−	0.0444483i
$838$		0			0
$839$	−627.512	+	110.647i	−0.747929	+	0.131880i	−0.534606	−	0.845102i	$-0.679540\pi$
$839$	−627.512	+	110.647i	−0.747929	+	0.131880i	−0.213323	+	0.976982i	$0.568429\pi$
$840$		0			0
$841$	−283.703	+	103.260i	−0.337341	+	0.122782i
$842$		0			0
$843$	−261.874	+	717.559i	−0.310646	+	0.851198i
$844$		0			0
$845$	55.3634	−	31.9641i	0.0655188	−	0.0378273i
$846$		0			0
$847$	189.015	−	327.383i	0.223158	−	0.386521i
$848$		0			0
$849$	614.827	−	223.176i	0.724178	−	0.262869i
$850$		0			0
$851$	−808.982	−	142.645i	−0.950626	−	0.167621i
$852$		0			0
$853$	280.961	−	235.754i	0.329379	−	0.276382i	−0.463068	−	0.886323i	$-0.653251\pi$
$853$	280.961	−	235.754i	0.329379	−	0.276382i	0.792447	+	0.609941i	$0.208807\pi$
$854$		0			0
$855$	−1227.05	+	1457.21i	−1.43515	+	1.70434i
$856$		0			0
$857$	−57.0894	+	156.852i	−0.0666154	+	0.183024i	−0.968534	−	0.248882i	$-0.919937\pi$
$857$	−57.0894	+	156.852i	−0.0666154	+	0.183024i	0.901918	+	0.431907i	$0.142159\pi$
$858$		0			0
$859$	−834.077	−	699.873i	−0.970986	−	0.814754i	0.0117195	−	0.999931i	$-0.496269\pi$
$859$	−834.077	−	699.873i	−0.970986	−	0.814754i	−0.982705	+	0.185178i	$0.940714\pi$
$860$		0			0
$861$	−0.410460	+	474.033i	−0.000476725	+	0.550561i
$862$		0			0
$863$		−	1151.23i		−	1.33399i	−0.745062	−	0.666995i	$-0.767580\pi$
$863$		−	1151.23i		−	1.33399i	0.745062	−	0.666995i	$-0.232420\pi$
$864$		0			0
$865$	−1099.70			−1.27133
$866$		0			0
$867$	429.757	−	742.875i	0.495683	−	0.856834i
$868$		0			0
$869$	62.9665	−	75.0405i	0.0724585	−	0.0863527i
$870$		0			0
$871$	−1638.71	−	596.442i	−1.88141	−	0.684778i
$872$		0			0
$873$	75.3035	+	431.435i	0.0862583	+	0.494198i
$874$		0			0
$875$	191.059	+	227.695i	0.218353	+	0.260223i
$876$		0			0
$877$	−184.425	+	1045.93i	−0.210291	+	1.19262i	0.678602	+	0.734506i	$0.262586\pi$
$877$	−184.425	+	1045.93i	−0.210291	+	1.19262i	−0.888893	+	0.458115i	$0.848525\pi$
$878$		0			0
$879$	494.151	−	587.872i	0.562174	−	0.668796i
$880$		0			0
$881$	−457.133	−	263.926i	−0.518879	−	0.299575i	0.217597	−	0.976039i	$-0.430178\pi$
$881$	−457.133	−	263.926i	−0.518879	−	0.299575i	−0.736476	+	0.676464i	$0.763512\pi$
$882$		0			0
$883$	−498.266	−	863.022i	−0.564288	−	0.977375i	−0.997116	−	0.0758982i	$-0.975818\pi$
$883$	−498.266	−	863.022i	−0.564288	−	0.977375i	0.432828	−	0.901476i	$-0.357516\pi$
$884$		0			0
$885$	−941.959	+	789.009i	−1.06436	+	0.891536i
$886$		0			0
$887$	555.650	+	1526.63i	0.626437	+	1.72112i	0.690654	+	0.723185i	$0.257323\pi$
$887$	555.650	+	1526.63i	0.626437	+	1.72112i	−0.0642172	+	0.997936i	$0.520455\pi$
$888$		0			0
$889$	−40.9361	−	232.160i	−0.0460473	−	0.261147i
$890$		0			0
$891$	−113.022	+	307.210i	−0.126848	+	0.344792i
$892$		0			0
$893$	−2220.52	+	391.538i	−2.48659	+	0.438452i
$894$		0			0
$895$	1286.36	−	468.197i	1.43728	−	0.523125i
$896$		0			0
$897$	297.761	+	355.483i	0.331952	+	0.396302i
$898$		0			0
$899$	81.5903	−	47.1062i	0.0907568	−	0.0523984i
$900$		0			0
$901$	347.439	−	601.782i	0.385615	−	0.667904i
$902$		0			0
$903$	383.071	+	322.000i	0.424220	+	0.356589i
$904$		0			0
$905$	1848.02	+	325.855i	2.04201	+	0.360061i
$906$		0			0
$907$	−169.282	+	142.045i	−0.186640	+	0.156609i	−0.731320	−	0.682034i	$-0.761095\pi$
$907$	−169.282	+	142.045i	−0.186640	+	0.156609i	0.544680	+	0.838644i	$0.316651\pi$
$908$		0			0
$909$	218.805	+	261.681i	0.240710	+	0.287878i
$910$		0			0
$911$	−272.443	+	748.530i	−0.299059	+	0.821657i	0.695599	+	0.718430i	$0.255139\pi$
$911$	−272.443	+	748.530i	−0.299059	+	0.821657i	−0.994658	+	0.103227i	$0.967083\pi$
$912$		0			0
$913$	−128.891	−	108.153i	−0.141173	−	0.118459i
$914$		0			0
$915$	87.9220	+	50.8633i	0.0960896	+	0.0555883i
$916$		0			0
$917$			73.0274i			0.0796373i
$918$		0			0
$919$	445.659			0.484939			0.242469	−	0.970159i	$-0.422043\pi$
$919$	445.659			0.484939			0.242469	+	0.970159i	$0.422043\pi$
$920$		0			0
$921$	1060.03	+	0.917874i	1.15096	+	0.000996606i
$922$		0			0
$923$	597.270	−	711.799i	0.647096	−	0.771179i
$924$		0			0
$925$	−2364.99	−	860.785i	−2.55674	−	0.930579i
$926$		0			0
$927$	130.053	−	47.0804i	0.140294	−	0.0507879i
$928$		0			0
$929$	415.980	+	495.746i	0.447772	+	0.533634i	0.941962	−	0.335720i	$-0.108980\pi$
$929$	415.980	+	495.746i	0.447772	+	0.533634i	−0.494190	+	0.869354i	$0.664535\pi$
$930$		0			0
$931$	−169.806	+	963.018i	−0.182391	+	1.03439i
$932$		0			0
$933$	−49.7104	−	136.947i	−0.0532801	−	0.146781i
$934$		0			0
$935$	653.208	+	377.130i	0.698619	+	0.403348i
$936$		0			0
$937$	−332.215	−	575.414i	−0.354552	−	0.614103i	0.632489	−	0.774569i	$-0.282033\pi$
$937$	−332.215	−	575.414i	−0.354552	−	0.614103i	−0.987041	+	0.160467i	$0.948700\pi$
$938$		0			0
$939$	185.284	+	67.6195i	0.197320	+	0.0720123i
$940$		0			0
$941$	104.076	+	285.947i	0.110602	+	0.303876i	0.982629	−	0.185582i	$-0.0594170\pi$
$941$	104.076	+	285.947i	0.110602	+	0.303876i	−0.872027	+	0.489458i	$0.837195\pi$
$942$		0			0
$943$	88.2117	+	500.273i	0.0935437	+	0.530512i
$944$		0			0
$945$	−658.261	+	377.771i	−0.696572	+	0.399757i
$946$		0			0
$947$	−361.382	+	63.7214i	−0.381607	+	0.0672876i	−0.361161	−	0.932503i	$-0.617620\pi$
$947$	−361.382	+	63.7214i	−0.381607	+	0.0672876i	−0.0204457	+	0.999791i	$0.506509\pi$
$948$		0			0
$949$	1637.68	−	596.068i	1.72569	−	0.628101i
$950$		0			0
$951$	−1504.64	+	263.966i	−1.58217	+	0.277567i
$952$		0			0
$953$	−1322.97	+	763.814i	−1.38821	+	0.801484i	−0.993114	−	0.117155i	$-0.962623\pi$
$953$	−1322.97	+	763.814i	−1.38821	+	0.801484i	−0.395098	+	0.918639i	$0.629289\pi$
$954$		0			0
$955$	−630.767	+	1092.52i	−0.660489	+	1.14400i
$956$		0			0
$957$	−49.1206	+	277.173i	−0.0513277	+	0.289627i
$958$		0			0
$959$	150.441	+	26.5269i	0.156873	+	0.0276610i
$960$		0			0
$961$	−723.556	+	607.136i	−0.752920	+	0.631775i
$962$		0			0
$963$	−903.753	−	523.871i	−0.938476	−	0.543999i
$964$		0			0
$965$	38.3499	−	105.366i	0.0397409	−	0.109187i
$966$		0			0
$967$	335.855	+	281.816i	0.347317	+	0.291433i	0.799711	−	0.600384i	$-0.204986\pi$
$967$	335.855	+	281.816i	0.347317	+	0.291433i	−0.452395	+	0.891818i	$0.649430\pi$
$968$		0			0
$969$	−1695.30	+	976.826i	−1.74954	+	1.00808i
$970$		0			0
$971$		−	447.249i		−	0.460607i	−0.973119	−	0.230303i	$-0.926028\pi$
$971$		−	447.249i		−	0.460607i	0.973119	−	0.230303i	$-0.0739718\pi$
$972$		0			0
$973$	−318.051			−0.326877
$974$		0			0
$975$	709.288	+	1230.98i	0.727475	+	1.26255i
$976$		0			0
$977$	160.495	−	191.270i	0.164273	−	0.195773i	−0.677628	−	0.735405i	$-0.736992\pi$
$977$	160.495	−	191.270i	0.164273	−	0.195773i	0.841901	+	0.539632i	$0.181437\pi$
$978$		0			0
$979$	−369.212	−	134.382i	−0.377132	−	0.137265i
$980$		0			0
$981$	−491.165	+	847.330i	−0.500677	+	0.863741i
$982$		0			0
$983$	556.245	+	662.907i	0.565865	+	0.674372i	0.970777	−	0.239984i	$-0.0771422\pi$
$983$	556.245	+	662.907i	0.565865	+	0.674372i	−0.404912	+	0.914356i	$0.632698\pi$
$984$		0			0
$985$	294.163	−	1668.28i	0.298643	−	1.69369i
$986$		0			0
$987$	−884.515	−	156.754i	−0.896165	−	0.158818i
$988$		0			0
$989$	464.429	+	268.138i	0.469594	+	0.271120i
$990$		0			0
$991$	−686.111	−	1188.38i	−0.692342	−	1.19917i	−0.971068	−	0.238801i	$-0.923246\pi$
$991$	−686.111	−	1188.38i	−0.692342	−	1.19917i	0.278726	−	0.960371i	$-0.410088\pi$
$992$		0			0
$993$	−230.473	−	1313.73i	−0.232098	−	1.32299i
$994$		0			0
$995$	−109.220	−	300.079i	−0.109769	−	0.301587i
$996$		0			0
$997$	−65.6896	−	372.544i	−0.0658873	−	0.373665i	−0.999867	−	0.0163381i	$-0.994799\pi$
$997$	−65.6896	−	372.544i	−0.0658873	−	0.373665i	0.933979	−	0.357327i	$-0.116312\pi$
$998$		0			0
$999$	959.379	−	1651.77i	0.960340	−	1.65342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.b.257.2		36
4.3	odd	2		108.3.k.a.41.5	yes	36
12.11	even	2		324.3.k.a.233.6		36
27.2	odd	18	inner	432.3.bc.b.353.2		36
108.59	even	18		2916.3.c.b.1457.3		36
108.79	odd	18		324.3.k.a.89.6		36
108.83	even	18		108.3.k.a.29.5	✓	36
108.103	odd	18		2916.3.c.b.1457.34		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.5	✓	36	108.83	even	18
108.3.k.a.41.5	yes	36	4.3	odd	2
324.3.k.a.89.6		36	108.79	odd	18
324.3.k.a.233.6		36	12.11	even	2
432.3.bc.b.257.2		36	1.1	even	1	trivial
432.3.bc.b.353.2		36	27.2	odd	18	inner
2916.3.c.b.1457.3		36	108.59	even	18
2916.3.c.b.1457.34		36	108.103	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.49775 - 2.59937i) q^{3} +(-5.00278 + 5.96208i) q^{5} +(3.39388 + 1.23527i) q^{7} +(-4.51349 + 7.78642i) q^{9} +O(q^{10})\)	\(q+(-1.49775 - 2.59937i) q^{3} +(-5.00278 + 5.96208i) q^{5} +(3.39388 + 1.23527i) q^{7} +(-4.51349 + 7.78642i) q^{9} +(-2.59766 - 3.09577i) q^{11} +(2.31163 - 13.1099i) q^{13} +(22.9906 + 4.07439i) q^{15} +(20.7679 + 11.9904i) q^{17} +(-13.5983 - 23.5530i) q^{19} +(-1.87225 - 10.6721i) q^{21} +(-3.97128 - 10.9110i) q^{23} +(-6.17739 - 35.0337i) q^{25} +(26.9999 + 0.0701370i) q^{27} +(22.8656 - 4.03181i) q^{29} +(3.81297 - 1.38781i) q^{31} +(-4.15642 + 11.3890i) q^{33} +(-24.3436 + 14.0548i) q^{35} +(35.3735 - 61.2687i) q^{37} +(-37.5399 + 13.6266i) q^{39} +(-43.0852 - 7.59708i) q^{41} +(-35.3804 + 29.6877i) q^{43} +(-23.8433 - 65.8635i) q^{45} +(28.3557 - 77.9066i) q^{47} +(-27.5437 - 23.1119i) q^{49} +(0.0622940 - 71.9422i) q^{51} -28.9765i q^{53} +31.4528 q^{55} +(-40.8561 + 70.6236i) q^{57} +(-33.8272 + 40.3136i) q^{59} +(4.08794 + 1.48789i) q^{61} +(-24.9366 + 20.8508i) q^{63} +(66.5978 + 79.3682i) q^{65} +(22.7477 - 129.009i) q^{67} +(-22.4138 + 26.6648i) q^{69} +(60.4484 + 34.8999i) q^{71} +(65.4584 + 113.377i) q^{73} +(-81.8135 + 68.5291i) q^{75} +(-4.99203 - 13.7155i) q^{77} +(4.20918 + 23.8714i) q^{79} +(-40.2568 - 70.2879i) q^{81} +(41.0021 - 7.22978i) q^{83} +(-175.385 + 63.8349i) q^{85} +(-44.7271 - 53.3975i) q^{87} +(84.1989 - 48.6122i) q^{89} +(24.0397 - 41.6380i) q^{91} +(-9.31831 - 7.83275i) q^{93} +(208.454 + 36.7561i) q^{95} +(37.2772 - 31.2793i) q^{97} +(35.8295 - 6.25375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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