LMFDB - Embedded newform 108.3.k.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	108.41
Dual form			108.3.k.a.29.5

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		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	0.0880231	−	0.996118i	$-0.471945\pi$
$7$	−3.39388	−	1.23527i	−0.484840	−	0.176467i	−0.572863	+	0.819651i	$0.694167\pi$
$8$		0			0
$9$	−4.51349	+	7.78642i	−0.501499	+	0.865158i
$10$		0			0
$11$	2.59766	+	3.09577i	0.236151	+	0.281434i	0.871085	−	0.491133i	$-0.163417\pi$
$11$	2.59766	+	3.09577i	0.236151	+	0.281434i	−0.634934	+	0.772567i	$0.718973\pi$
$12$		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	$0.0872261\pi$
$19$	13.5983	+	23.5530i	0.715701	+	1.23963i	−0.246987	+	0.969019i	$0.579441\pi$
$20$		0			0
$21$	−1.87225	−	10.6721i	−0.0891548	−	0.508195i
$22$		0			0
$23$	3.97128	+	10.9110i	0.172665	+	0.474392i	0.995596	−	0.0937489i	$-0.0298851\pi$
$23$	3.97128	+	10.9110i	0.172665	+	0.474392i	−0.822931	+	0.568141i	$0.807663\pi$
$24$		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	−0.402786	−	0.915294i	$-0.631958\pi$
$31$	−3.81297	+	1.38781i	−0.122999	+	0.0447680i	0.279787	+	0.960062i	$0.409736\pi$
$32$		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	−0.130825	−	0.991405i	$-0.541763\pi$
$43$	35.3804	−	29.6877i	0.822801	−	0.690412i	0.953626	+	0.300994i	$0.0973183\pi$
$44$		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	$0.454903\pi$
$47$	−28.3557	+	77.9066i	−0.603312	+	1.65759i	−0.744515	+	0.667606i	$0.767319\pi$
$48$		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	−0.398972	−	0.916963i	$-0.630633\pi$
$59$	33.8272	−	40.3136i	0.573342	−	0.683282i	0.972313	+	0.233681i	$0.0750772\pi$
$60$		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	$0.488061\pi$
$67$	−22.7477	+	129.009i	−0.339518	+	1.92550i	−0.377016	+	0.926207i	$0.623050\pi$
$68$		0			0
$69$	−22.4138	+	26.6648i	−0.324838	+	0.386447i
$70$		0			0
$71$	−60.4484	−	34.8999i	−0.851386	−	0.491548i	0.00973220	−	0.999953i	$-0.496902\pi$
$71$	−60.4484	−	34.8999i	−0.851386	−	0.491548i	−0.861118	+	0.508405i	$0.830235\pi$
$72$		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	0.946509	−	0.322677i	$-0.104583\pi$
$79$	−4.20918	−	23.8714i	−0.0532807	−	0.302170i	−0.999790	+	0.0205075i	$0.993472\pi$
$80$		0			0
$81$	−40.2568	−	70.2879i	−0.496997	−	0.867752i
$82$		0			0
$83$	−41.0021	+	7.22978i	−0.494002	+	0.0871058i	−0.415098	−	0.909776i	$-0.636253\pi$
$83$	−41.0021	+	7.22978i	−0.494002	+	0.0871058i	−0.0789031	+	0.996882i	$0.525142\pi$
$84$		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	0.698145	−	0.715957i	$-0.254009\pi$
$103$	11.7726	+	9.87837i	0.114297	+	0.0959065i	−0.583848	+	0.811863i	$0.698454\pi$
$104$		0			0
$105$	72.9943	+	42.2276i	0.695184	+	0.402168i
$106$		0			0
$107$		−	116.068i		−	1.08475i	−0.840138	−	0.542373i	$-0.817526\pi$
$107$		−	116.068i		−	1.08475i	0.840138	−	0.542373i	$-0.182474\pi$
$108$		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	0.965430	−	0.260662i	$-0.0839407\pi$
$127$	32.6359	+	56.5270i	0.256975	+	0.445095i	−0.708455	+	0.705756i	$0.750607\pi$
$128$		0			0
$129$	130.160	+	47.5022i	1.00900	+	0.368234i
$130$		0			0
$131$	−6.91556	−	19.0003i	−0.0527905	−	0.145041i	0.910495	−	0.413520i	$-0.135701\pi$
$131$	−6.91556	−	19.0003i	−0.0527905	−	0.145041i	−0.963285	+	0.268480i	$0.913479\pi$
$132$		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	−0.0267421	−	0.999642i	$-0.508513\pi$
$139$	82.7509	−	30.1189i	0.595330	−	0.216682i	0.622072	+	0.782960i	$0.286291\pi$
$140$		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	−0.969252	−	0.246070i	$-0.920861\pi$
$151$	−135.180	+	113.429i	−0.895229	+	0.751186i	0.0740229	+	0.997257i	$0.476416\pi$
$152$		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	$-0.317597\pi$
$163$	176.753			1.08437			0.542186	+	0.840258i	$0.317597\pi$
$164$		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	$-0.428660\pi$
$167$	191.020	−	227.649i	1.14383	−	1.36317i	0.921585	−	0.388178i	$-0.126895\pi$
$168$		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	0.860976	−	0.508646i	$-0.169854\pi$
$179$	152.323	+	87.9435i	0.850964	+	0.491304i	−0.0100121	+	0.999950i	$0.503187\pi$
$180$		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	−0.575113	−	0.818074i	$-0.695042\pi$
$191$	−159.627	+	28.1466i	−0.835745	+	0.147364i	−0.260632	+	0.965438i	$0.583931\pi$
$192$		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	−0.809865	−	0.586616i	$-0.800460\pi$
$199$	20.5152	−	35.5335i	0.103092	−	0.178560i	0.912957	+	0.408056i	$0.133793\pi$
$200$		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	0.389883	−	0.920864i	$-0.372515\pi$
$211$	−94.7998	−	79.5465i	−0.449288	−	0.376998i	−0.839172	+	0.543867i	$0.816960\pi$
$212$		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	0.828140	−	0.560521i	$-0.189399\pi$
$223$	245.799	+	89.4634i	1.10224	+	0.401181i	0.274096	+	0.961702i	$0.411621\pi$
$224$		0			0
$225$	300.669	+	110.025i	1.33631	+	0.488998i
$226$		0			0
$227$	53.1278	+	63.3153i	0.234043	+	0.278922i	0.870264	−	0.492585i	$-0.163948\pi$
$227$	53.1278	+	63.3153i	0.234043	+	0.278922i	−0.636221	+	0.771507i	$0.719503\pi$
$228$		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	0.993982	−	0.109539i	$-0.0349375\pi$
$239$	38.7508	+	106.467i	0.162137	+	0.445469i	−0.831845	+	0.555008i	$0.812715\pi$
$240$		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	−0.526966	−	0.849886i	$-0.676671\pi$
$251$	−13.6611	+	7.88725i	−0.0544267	+	0.0314233i	0.472540	+	0.881309i	$0.343337\pi$
$252$		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	−0.951568	−	0.307437i	$-0.900529\pi$
$263$	−6.57712	+	18.0705i	−0.0250080	+	0.0687090i	0.926560	+	0.376146i	$0.122751\pi$
$264$		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	$-0.571773\pi$
$271$	−121.179			−0.447154			−0.223577	+	0.974686i	$0.571773\pi$
$272$		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	$-0.818575\pi$
$283$	37.8599	−	214.714i	0.133781	−	0.758707i	0.975701	−	0.219106i	$-0.0703140\pi$
$284$		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	$-0.638148\pi$
$307$	176.673	−	306.006i	0.575480	−	0.996761i	0.995989	−	0.0894730i	$-0.0285183\pi$
$308$		0			0
$309$	−8.04520	+	45.3967i	−0.0260362	+	0.146915i
$310$		0			0
$311$	−47.8256	−	8.43294i	−0.153780	−	0.0271156i	0.0962281	−	0.995359i	$-0.469322\pi$
$311$	−47.8256	−	8.43294i	−0.153780	−	0.0271156i	−0.250008	+	0.968244i	$0.580433\pi$
$312$		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	−0.377687	−	0.925933i	$-0.623280\pi$
$331$	−417.785	−	152.061i	−1.26219	−	0.459400i	−0.884504	+	0.466534i	$0.845503\pi$
$332$		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	$0.118765\pi$
$347$	156.901	+	431.082i	0.452164	+	1.24231i	−0.479034	+	0.877797i	$0.659013\pi$
$348$		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	−0.930780	−	0.365579i	$-0.880871\pi$
$359$	−387.565	+	223.761i	−1.07957	+	0.623290i	−0.148789	+	0.988869i	$0.547538\pi$
$360$		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	$0.561422\pi$
$367$	−437.316	+	366.952i	−1.19160	+	0.999869i	−0.999830	+	0.0184287i	$0.994134\pi$
$368$		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	$-0.742941\pi$
$379$	−523.969			−1.38250			−0.691252	+	0.722614i	$0.742941\pi$
$380$		0			0
$381$	−98.0545	+	169.496i	−0.257361	+	0.444872i
$382$		0			0
$383$	262.803	−	313.197i	0.686171	−	0.817746i	−0.304716	−	0.952443i	$-0.598562\pi$
$383$	262.803	−	313.197i	0.686171	−	0.817746i	0.990887	+	0.134697i	$0.0430060\pi$
$384$		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	0.749464	−	0.662045i	$-0.230311\pi$
$419$	514.237	+	90.6739i	1.22730	+	0.216406i	0.477833	+	0.878451i	$0.341422\pi$
$420$		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	$-0.777161\pi$
$431$		−	555.362i		−	1.28854i	0.764797	−	0.644272i	$-0.222839\pi$
$432$		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	0.640244	−	0.768171i	$-0.278833\pi$
$439$	279.612	+	101.770i	0.636929	+	0.231823i	−0.00331548	+	0.999995i	$0.501055\pi$
$440$		0			0
$441$	304.277	−	110.151i	0.689970	−	0.249776i
$442$		0			0
$443$	64.0510	+	76.3330i	0.144585	+	0.172309i	0.833477	−	0.552555i	$-0.186347\pi$
$443$	64.0510	+	76.3330i	0.144585	+	0.172309i	−0.688892	+	0.724864i	$0.741903\pi$
$444$		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	−0.387962	−	0.921675i	$-0.626821\pi$
$463$	−42.9280	+	15.6245i	−0.0927171	+	0.0337463i	0.295245	+	0.955422i	$0.404599\pi$
$464$		0			0
$465$	93.3169	−	16.3710i	0.200682	−	0.0352064i
$466$		0			0
$467$	343.979	−	198.596i	0.736571	−	0.425259i	−0.0842504	−	0.996445i	$-0.526850\pi$
$467$	343.979	−	198.596i	0.736571	−	0.425259i	0.820821	+	0.571185i	$0.193516\pi$
$468$		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	$0.415406\pi$
$479$	−267.653	+	735.372i	−0.558775	+	1.53522i	−0.821416	+	0.570329i	$0.806816\pi$
$480$		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	$-0.673789\pi$
$487$	−505.750			−1.03850			−0.519250	+	0.854622i	$0.673789\pi$
$488$		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	$-0.389670\pi$
$491$	592.619	−	706.256i	1.20696	−	1.43840i	0.867250	−	0.497874i	$-0.165886\pi$
$492$		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	$-0.731142\pi$
$499$	107.632	−	610.414i	0.215696	−	1.22327i	0.879694	−	0.475540i	$-0.157747\pi$
$500$		0			0
$501$	877.845	+	155.572i	1.75219	+	0.310522i
$502$		0			0
$503$	1.70660	+	0.985304i	0.00339284	+	0.00195885i	0.501695	−	0.865044i	$-0.332710\pi$
$503$	1.70660	+	0.985304i	0.00339284	+	0.00195885i	−0.498303	+	0.867003i	$0.666043\pi$
$504$		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	−0.707847	−	0.706365i	$-0.750334\pi$
$523$	134.833	−	233.537i	0.257807	−	0.446534i	0.965654	+	0.259831i	$0.0836669\pi$
$524$		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	−0.309092	−	0.951032i	$-0.600025\pi$
$547$	−632.979	−	230.385i	−1.15718	−	0.421180i	−0.848090	+	0.529852i	$0.822247\pi$
$548$		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	0.966305	−	0.257400i	$-0.0828659\pi$
$563$	34.1283	+	93.7667i	0.0606187	+	0.166548i	−0.905686	+	0.423949i	$0.860644\pi$
$564$		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	−0.780457	−	0.625210i	$-0.785013\pi$
$571$	−557.549	+	202.931i	−0.976444	+	0.355397i	−0.195987	+	0.980606i	$0.562791\pi$
$572$		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	$0.223116\pi$
$587$	−138.391	+	380.226i	−0.235759	+	0.647744i	−0.999996	+	0.00280774i	$0.999106\pi$
$588$		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	$0.526424\pi$
$599$	−628.912	+	749.508i	−1.04994	+	1.25127i	−0.967018	+	0.254710i	$0.918020\pi$
$600$		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	−0.958933	−	0.283634i	$-0.908460\pi$
$607$	23.7810	−	134.869i	0.0391779	−	0.222189i	0.998110	+	0.0614454i	$0.0195710\pi$
$608$		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	$-0.989043\pi$
$619$	−44.5940	−	252.905i	−0.0720420	−	0.408571i	0.927366	−	0.374156i	$-0.122068\pi$
$620$		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	$0.336345\pi$
$631$	−320.656	+	555.392i	−0.508171	+	0.880177i	−0.999955	+	0.00946046i	$0.996989\pi$
$632$		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	0.632765	−	0.774344i	$-0.281920\pi$
$643$	−12.8197	−	10.7570i	−0.0199373	−	0.0167294i	−0.652702	+	0.757615i	$0.726365\pi$
$644$		0			0
$645$	−934.376	+	538.384i	−1.44864	+	0.834704i
$646$		0			0
$647$			96.9735i			0.149882i	0.997188	+	0.0749409i	$0.0238768\pi$
$647$			96.9735i			0.149882i	−0.997188	+	0.0749409i	$0.976123\pi$
$648$		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	0.545499	−	0.838111i	$-0.316340\pi$
$659$	−246.864	−	294.201i	−0.374604	−	0.446436i	−0.920104	+	0.391675i	$0.871896\pi$
$660$		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	−0.696930	−	0.717139i	$-0.745451\pi$
$683$	−289.821	+	167.328i	−0.424335	+	0.244990i	0.272595	+	0.962129i	$0.412118\pi$
$684$		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	−0.381526	−	0.924358i	$-0.624601\pi$
$691$	319.613	−	268.187i	0.462537	−	0.388115i	0.844064	+	0.536243i	$0.180157\pi$
$692$		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	−0.243879	−	0.969806i	$-0.578420\pi$
$719$	−866.895	−	500.502i	−1.20570	−	0.696108i	−0.961816	+	0.273697i	$0.911753\pi$
$720$		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	$-0.795427\pi$
$727$	−184.123	−	1044.22i	−0.253264	−	1.43633i	0.547224	−	0.836986i	$-0.315685\pi$
$728$		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	$0.357657\pi$
$739$	−417.279	+	722.749i	−0.564654	+	0.978010i	−0.997082	+	0.0763410i	$0.975676\pi$
$740$		0			0
$741$	831.426	+	698.877i	1.12203	+	0.943154i
$742$		0			0
$743$	−132.230	−	23.3158i	−0.177968	−	0.0313806i	0.0839538	−	0.996470i	$-0.473245\pi$
$743$	−132.230	−	23.3158i	−0.177968	−	0.0313806i	−0.261922	+	0.965089i	$0.584356\pi$
$744$		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	0.472992	−	0.881066i	$-0.343174\pi$
$751$	−234.728	−	196.960i	−0.312554	−	0.262264i	−0.785547	+	0.618802i	$0.787618\pi$
$752$		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	−0.941057	−	0.338248i	$-0.890166\pi$
$787$	−1136.84	+	413.777i	−1.44453	+	0.525765i	−0.503470	+	0.864013i	$0.667943\pi$
$788$		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	$-0.695582\pi$
$811$	−935.082			−1.15300			−0.576500	+	0.817097i	$0.695582\pi$
$812$		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	$0.171859\pi$
$823$	−102.126	+	579.184i	−0.124090	+	0.703748i	−0.981844	+	0.189688i	$0.939252\pi$
$824$		0			0
$825$	424.674	+	75.2607i	0.514757	+	0.0912251i
$826$		0			0
$827$	−428.539	−	247.417i	−0.518184	−	0.299174i	0.218007	−	0.975947i	$-0.430044\pi$
$827$	−428.539	−	247.417i	−0.518184	−	0.299174i	−0.736192	+	0.676773i	$0.763378\pi$
$828$		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	0.213323	−	0.976982i	$-0.431571\pi$
$839$	627.512	−	110.647i	0.747929	−	0.131880i	0.534606	+	0.845102i	$0.320460\pi$
$840$		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	0.982705	−	0.185178i	$-0.0592861\pi$
$859$	834.077	+	699.873i	0.970986	+	0.814754i	−0.0117195	+	0.999931i	$0.503731\pi$
$860$		0			0
$861$	−0.410460	+	474.033i	−0.000476725	+	0.550561i
$862$		0			0
$863$			1151.23i			1.33399i	0.745062	+	0.666995i	$0.232420\pi$
$863$			1151.23i			1.33399i	−0.745062	+	0.666995i	$0.767580\pi$
$864$		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	$0.0241824\pi$
$883$	498.266	+	863.022i	0.564288	+	0.977375i	−0.432828	+	0.901476i	$0.642484\pi$
$884$		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	$-0.742677\pi$
$887$	−555.650	−	1526.63i	−0.626437	−	1.72112i	0.0642172	−	0.997936i	$-0.479545\pi$
$888$		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	−0.544680	−	0.838644i	$-0.683349\pi$
$907$	169.282	−	142.045i	0.186640	−	0.156609i	0.731320	+	0.682034i	$0.238905\pi$
$908$		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	$-0.744861\pi$
$911$	272.443	−	748.530i	0.299059	−	0.821657i	0.994658	−	0.103227i	$-0.0329168\pi$
$912$		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	$-0.577957\pi$
$919$	−445.659			−0.484939			−0.242469	+	0.970159i	$0.577957\pi$
$920$		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	0.0204457	−	0.999791i	$-0.493491\pi$
$947$	361.382	−	63.7214i	0.381607	−	0.0672876i	0.361161	+	0.932503i	$0.382380\pi$
$948$		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	0.452395	−	0.891818i	$-0.350570\pi$
$967$	−335.855	−	281.816i	−0.347317	−	0.291433i	−0.799711	+	0.600384i	$0.795014\pi$
$968$		0			0
$969$	−1695.30	+	976.826i	−1.74954	+	1.00808i
$970$		0			0
$971$			447.249i			0.460607i	0.973119	+	0.230303i	$0.0739718\pi$
$971$			447.249i			0.460607i	−0.973119	+	0.230303i	$0.926028\pi$
$972$		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	0.404912	−	0.914356i	$-0.367302\pi$
$983$	−556.245	−	662.907i	−0.565865	−	0.674372i	−0.970777	+	0.239984i	$0.922858\pi$
$984$		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	$0.0767545\pi$
$991$	686.111	+	1188.38i	0.692342	+	1.19917i	−0.278726	+	0.960371i	$0.589912\pi$
$992$		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	108.3.k.a.41.5	yes	36
3.2	odd	2		324.3.k.a.233.6		36
4.3	odd	2		432.3.bc.b.257.2		36
27.2	odd	18	inner	108.3.k.a.29.5	✓	36
27.5	odd	18		2916.3.c.b.1457.3		36
27.22	even	9		2916.3.c.b.1457.34		36
27.25	even	9		324.3.k.a.89.6		36
108.83	even	18		432.3.bc.b.353.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.5	✓	36	27.2	odd	18	inner
108.3.k.a.41.5	yes	36	1.1	even	1	trivial
324.3.k.a.89.6		36	27.25	even	9
324.3.k.a.233.6		36	3.2	odd	2
432.3.bc.b.257.2		36	4.3	odd	2
432.3.bc.b.353.2		36	108.83	even	18
2916.3.c.b.1457.3		36	27.5	odd	18
2916.3.c.b.1457.34		36	27.22	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), 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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