LMFDB - Embedded newform 220.3.i.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96707 + 0.361417i) q^{2} +(-2.82785 + 2.82785i) q^{3} +(3.73876 - 1.42187i) q^{4} +(3.27930 - 3.77442i) q^{5} +(4.54056 - 6.58463i) q^{6} +(-1.01424 + 1.01424i) q^{7} +(-6.84052 + 4.14816i) q^{8} -6.99351i q^{9} +(-5.08648 + 8.60974i) q^{10} +(-9.38106 + 5.74419i) q^{11} +(-6.55182 + 14.5935i) q^{12} +(-6.58788 + 6.58788i) q^{13} +(1.62853 - 2.36166i) q^{14} +(1.40012 + 19.9469i) q^{15} +(11.9566 - 10.6320i) q^{16} +(-4.97600 - 4.97600i) q^{17} +(2.52757 + 13.7567i) q^{18} -28.5444i q^{19} +(6.89378 - 18.7743i) q^{20} -5.73627i q^{21} +(16.3772 - 14.6897i) q^{22} +(-6.64492 + 6.64492i) q^{23} +(7.61359 - 31.0744i) q^{24} +(-3.49242 - 24.7549i) q^{25} +(10.5779 - 15.3398i) q^{26} +(-5.67406 - 5.67406i) q^{27} +(-2.34989 + 5.23413i) q^{28} -9.10097 q^{29} +(-9.96327 - 38.7309i) q^{30} -34.1714i q^{31} +(-19.6769 + 25.2353i) q^{32} +(10.2846 - 42.7720i) q^{33} +(11.5866 + 7.98975i) q^{34} +(0.502170 + 7.15418i) q^{35} +(-9.94383 - 26.1470i) q^{36} +(0.442813 - 0.442813i) q^{37} +(10.3164 + 56.1489i) q^{38} -37.2591i q^{39} +(-6.77521 + 39.4220i) q^{40} -37.1634i q^{41} +(2.07318 + 11.2837i) q^{42} +(24.3777 + 24.3777i) q^{43} +(-26.9060 + 34.8147i) q^{44} +(-26.3964 - 22.9338i) q^{45} +(10.6695 - 15.4726i) q^{46} +(-38.0953 - 38.0953i) q^{47} +(-3.74569 + 63.8773i) q^{48} +46.9426i q^{49} +(15.8167 + 47.4324i) q^{50} +28.1428 q^{51} +(-15.2634 + 33.9975i) q^{52} +(-66.2966 - 66.2966i) q^{53} +(13.2120 + 9.11060i) q^{54} +(-9.08235 + 54.2449i) q^{55} +(2.73071 - 11.1452i) q^{56} +(80.7193 + 80.7193i) q^{57} +(17.9023 - 3.28924i) q^{58} -83.9109 q^{59} +(33.5965 + 72.5857i) q^{60} -8.08430i q^{61} +(12.3501 + 67.2177i) q^{62} +(7.09312 + 7.09312i) q^{63} +(29.5855 - 56.7512i) q^{64} +(3.26177 + 46.4690i) q^{65} +(-4.77196 + 87.8526i) q^{66} +(-3.95289 - 3.95289i) q^{67} +(-25.6793 - 11.5288i) q^{68} -37.5817i q^{69} +(-3.57345 - 13.8913i) q^{70} +42.6559i q^{71} +(29.0102 + 47.8392i) q^{72} +(93.4981 - 93.4981i) q^{73} +(-0.711006 + 1.03109i) q^{74} +(79.8792 + 60.1271i) q^{75} +(-40.5863 - 106.720i) q^{76} +(3.68868 - 15.3407i) q^{77} +(13.4661 + 73.2914i) q^{78} +41.4724i q^{79} +(-0.920447 - 79.9947i) q^{80} +95.0324 q^{81} +(13.4315 + 73.1032i) q^{82} +(-65.0178 - 65.0178i) q^{83} +(-8.15620 - 21.4465i) q^{84} +(-35.0993 + 2.46371i) q^{85} +(-56.7632 - 39.1422i) q^{86} +(25.7362 - 25.7362i) q^{87} +(40.3435 - 78.2074i) q^{88} +125.157i q^{89} +(60.2123 + 35.5724i) q^{90} -13.3634i q^{91} +(-15.3956 + 34.2919i) q^{92} +(96.6318 + 96.6318i) q^{93} +(88.7045 + 61.1680i) q^{94} +(-107.738 - 93.6055i) q^{95} +(-15.7183 - 127.005i) q^{96} +(-62.8186 + 62.8186i) q^{97} +(-16.9658 - 92.3396i) q^{98} +(40.1720 + 65.6065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.96707	+	0.361417i	−0.983537	+	0.180708i
$2$	−1.96707	+	0.361417i	−0.983537	+	0.180708i
$3$	−2.82785	+	2.82785i	−0.942618	+	0.942618i	−0.998441	−	0.0558229i	$-0.982222\pi$
$3$	−2.82785	+	2.82785i	−0.942618	+	0.942618i	0.0558229	+	0.998441i	$0.482222\pi$
$4$	3.73876	−	1.42187i	0.934689	−	0.355467i
$5$	3.27930	−	3.77442i	0.655859	−	0.754883i
$5$	3.27930	−	3.77442i	0.655859	−	0.754883i
$6$	4.54056	−	6.58463i	0.756760	−	1.09744i
$7$	−1.01424	+	1.01424i	−0.144892	+	0.144892i	−0.775832	−	0.630940i	$-0.782669\pi$
$7$	−1.01424	+	1.01424i	−0.144892	+	0.144892i	0.630940	+	0.775832i	$0.282669\pi$
$8$	−6.84052	+	4.14816i	−0.855065	+	0.518521i
$9$		−	6.99351i		−	0.777057i
$10$	−5.08648	+	8.60974i	−0.508648	+	0.860974i
$11$	−9.38106	+	5.74419i	−0.852824	+	0.522199i
$11$	−9.38106	+	5.74419i	−0.852824	+	0.522199i
$12$	−6.55182	+	14.5935i	−0.545985	+	1.21612i
$13$	−6.58788	+	6.58788i	−0.506760	+	0.506760i	−0.913530	−	0.406771i	$-0.866655\pi$
$13$	−6.58788	+	6.58788i	−0.506760	+	0.506760i	0.406771	+	0.913530i	$0.366655\pi$
$14$	1.62853	−	2.36166i	0.116323	−	0.168690i
$15$	1.40012	+	19.9469i	0.0933414	+	1.32979i
$16$	11.9566	−	10.6320i	0.747287	−	0.664501i
$17$	−4.97600	−	4.97600i	−0.292706	−	0.292706i	0.545442	−	0.838148i	$-0.316362\pi$
$17$	−4.97600	−	4.97600i	−0.292706	−	0.292706i	−0.838148	+	0.545442i	$0.816362\pi$
$18$	2.52757	+	13.7567i	0.140421	+	0.764264i
$19$		−	28.5444i		−	1.50234i	−0.660111	−	0.751168i	$-0.729491\pi$
$19$		−	28.5444i		−	1.50234i	0.660111	−	0.751168i	$-0.270509\pi$
$20$	6.89378	−	18.7743i	0.344689	−	0.938717i
$21$		−	5.73627i		−	0.273155i
$22$	16.3772	−	14.6897i	0.744418	−	0.667714i
$23$	−6.64492	+	6.64492i	−0.288910	+	0.288910i	−0.836649	−	0.547739i	$-0.815489\pi$
$23$	−6.64492	+	6.64492i	−0.288910	+	0.288910i	0.547739	+	0.836649i	$0.315489\pi$
$24$	7.61359	−	31.0744i	0.317233	−	1.29477i
$25$	−3.49242	−	24.7549i	−0.139697	−	0.990194i
$26$	10.5779	−	15.3398i	0.406841	−	0.589993i
$27$	−5.67406	−	5.67406i	−0.210150	−	0.210150i
$28$	−2.34989	+	5.23413i	−0.0839247	+	0.186933i
$29$	−9.10097			−0.313826			−0.156913	−	0.987612i	$-0.550154\pi$
$29$	−9.10097			−0.313826			−0.156913	+	0.987612i	$0.550154\pi$
$30$	−9.96327	−	38.7309i	−0.332109	−	1.29103i
$31$		−	34.1714i		−	1.10230i	−0.834405	−	0.551152i	$-0.814188\pi$
$31$		−	34.1714i		−	1.10230i	0.834405	−	0.551152i	$-0.185812\pi$
$32$	−19.6769	+	25.2353i	−0.614903	+	0.788603i
$33$	10.2846	−	42.7720i	0.311653	−	1.29612i
$34$	11.5866	+	7.98975i	0.340781	+	0.234993i
$35$	0.502170	+	7.15418i	0.0143477	+	0.204405i
$36$	−9.94383	−	26.1470i	−0.276218	−	0.726306i
$37$	0.442813	−	0.442813i	0.0119679	−	0.0119679i	−0.701098	−	0.713065i	$-0.747306\pi$
$37$	0.442813	−	0.442813i	0.0119679	−	0.0119679i	0.713065	+	0.701098i	$0.247306\pi$
$38$	10.3164	+	56.1489i	0.271485	+	1.47760i
$39$		−	37.2591i		−	0.955361i
$40$	−6.77521	+	39.4220i	−0.169380	+	0.985551i
$41$		−	37.1634i		−	0.906425i	−0.891403	−	0.453212i	$-0.850278\pi$
$41$		−	37.1634i		−	0.906425i	0.891403	−	0.453212i	$-0.149722\pi$
$42$	2.07318	+	11.2837i	0.0493615	+	0.268658i
$43$	24.3777	+	24.3777i	0.566923	+	0.566923i	0.931265	−	0.364342i	$-0.118706\pi$
$43$	24.3777	+	24.3777i	0.566923	+	0.566923i	−0.364342	+	0.931265i	$0.618706\pi$
$44$	−26.9060	+	34.8147i	−0.611501	+	0.791244i
$45$	−26.3964	−	22.9338i	−0.586587	−	0.509640i
$46$	10.6695	−	15.4726i	0.231945	−	0.336362i
$47$	−38.0953	−	38.0953i	−0.810538	−	0.810538i	0.174176	−	0.984714i	$-0.444274\pi$
$47$	−38.0953	−	38.0953i	−0.810538	−	0.810538i	−0.984714	+	0.174176i	$0.944274\pi$
$48$	−3.74569	+	63.8773i	−0.0780352	+	1.33078i
$49$			46.9426i			0.958013i
$50$	15.8167	+	47.4324i	0.316333	+	0.948648i
$51$	28.1428			0.551820
$52$	−15.2634	+	33.9975i	−0.293527	+	0.653799i
$53$	−66.2966	−	66.2966i	−1.25088	−	1.25088i	−0.955326	−	0.295553i	$-0.904496\pi$
$53$	−66.2966	−	66.2966i	−1.25088	−	1.25088i	−0.295553	−	0.955326i	$-0.595504\pi$
$54$	13.2120	+	9.11060i	0.244667	+	0.168715i
$55$	−9.08235	+	54.2449i	−0.165134	+	0.986271i
$56$	2.73071	−	11.1452i	0.0487626	−	0.199022i
$57$	80.7193	+	80.7193i	1.41613	+	1.41613i
$58$	17.9023	−	3.28924i	0.308660	−	0.0567111i
$59$	−83.9109			−1.42222			−0.711109	−	0.703081i	$-0.751807\pi$
$59$	−83.9109			−1.42222			−0.711109	+	0.703081i	$0.751807\pi$
$60$	33.5965	+	72.5857i	0.559941	+	1.20976i
$61$		−	8.08430i		−	0.132530i	−0.997802	−	0.0662648i	$-0.978892\pi$
$61$		−	8.08430i		−	0.132530i	0.997802	−	0.0662648i	$-0.0211082\pi$
$62$	12.3501	+	67.2177i	0.199196	+	1.08416i
$63$	7.09312	+	7.09312i	0.112589	+	0.112589i
$64$	29.5855	−	56.7512i	0.462273	−	0.886738i
$65$	3.26177	+	46.4690i	0.0501812	+	0.714907i
$66$	−4.77196	+	87.8526i	−0.0723025	+	1.33110i
$67$	−3.95289	−	3.95289i	−0.0589984	−	0.0589984i	0.676992	−	0.735990i	$-0.263283\pi$
$67$	−3.95289	−	3.95289i	−0.0589984	−	0.0589984i	−0.735990	+	0.676992i	$0.763283\pi$
$68$	−25.6793	−	11.5288i	−0.377636	−	0.169542i
$69$		−	37.5817i		−	0.544663i
$70$	−3.57345	−	13.8913i	−0.0510492	−	0.198447i
$71$			42.6559i			0.600787i	0.953815	+	0.300394i	$0.0971180\pi$
$71$			42.6559i			0.600787i	−0.953815	+	0.300394i	$0.902882\pi$
$72$	29.0102	+	47.8392i	0.402920	+	0.664434i
$73$	93.4981	−	93.4981i	1.28080	−	1.28080i	0.340580	−	0.940215i	$-0.389376\pi$
$73$	93.4981	−	93.4981i	1.28080	−	1.28080i	0.940215	−	0.340580i	$-0.110624\pi$
$74$	−0.711006	+	1.03109i	−0.00960818	+	0.0139336i
$75$	79.8792	+	60.1271i	1.06506	+	0.801694i
$76$	−40.5863	−	106.720i	−0.534030	−	1.40422i
$77$	3.68868	−	15.3407i	0.0479049	−	0.199230i
$78$	13.4661	+	73.2914i	0.172642	+	0.939633i
$79$			41.4724i			0.524968i	0.964936	+	0.262484i	$0.0845416\pi$
$79$			41.4724i			0.524968i	−0.964936	+	0.262484i	$0.915458\pi$
$80$	−0.920447	−	79.9947i	−0.0115056	−	0.999934i
$81$	95.0324			1.17324
$82$	13.4315	+	73.1032i	0.163799	+	0.891502i
$83$	−65.0178	−	65.0178i	−0.783347	−	0.783347i	0.197047	−	0.980394i	$-0.436865\pi$
$83$	−65.0178	−	65.0178i	−0.783347	−	0.783347i	−0.980394	+	0.197047i	$0.936865\pi$
$84$	−8.15620	−	21.4465i	−0.0970977	−	0.255315i
$85$	−35.0993	+	2.46371i	−0.412933	+	0.0289848i
$86$	−56.7632	−	39.1422i	−0.660037	−	0.455142i
$87$	25.7362	−	25.7362i	0.295818	−	0.295818i
$88$	40.3435	−	78.2074i	0.458449	−	0.888721i
$89$			125.157i			1.40626i	0.711063	+	0.703128i	$0.248214\pi$
$89$			125.157i			1.40626i	−0.711063	+	0.703128i	$0.751786\pi$
$90$	60.2123	+	35.5724i	0.669026	+	0.395248i
$91$		−	13.3634i		−	0.146851i
$92$	−15.3956	+	34.2919i	−0.167343	+	0.372738i
$93$	96.6318	+	96.6318i	1.03905	+	1.03905i
$94$	88.7045	+	61.1680i	0.943665	+	0.650723i
$95$	−107.738	−	93.6055i	−1.13409	−	0.985321i
$96$	−15.7183	−	127.005i	−0.163732	−	1.32297i
$97$	−62.8186	+	62.8186i	−0.647614	+	0.647614i	−0.952416	−	0.304802i	$-0.901410\pi$
$97$	−62.8186	+	62.8186i	−0.647614	+	0.647614i	0.304802	+	0.952416i	$0.401410\pi$
$98$	−16.9658	−	92.3396i	−0.173121	−	0.942241i
$99$	40.1720	+	65.6065i	0.405778	+	0.662692i
$100$	−48.2554	−	87.5866i	−0.482554	−	0.875866i
$101$			162.543i			1.60933i	0.593728	+	0.804666i	$0.297656\pi$
$101$			162.543i			1.60933i	−0.593728	+	0.804666i	$0.702344\pi$
$102$	−55.3589	+	10.1713i	−0.542735	+	0.0997184i
$103$	16.6743	−	16.6743i	0.161887	−	0.161887i	−0.621515	−	0.783402i	$-0.713483\pi$
$103$	16.6743	−	16.6743i	0.161887	−	0.161887i	0.783402	+	0.621515i	$0.213483\pi$
$104$	17.7369	−	72.3921i	0.170547	−	0.696078i
$105$	−21.6510	−	18.8109i	−0.206200	−	0.179152i
$106$	154.371	+	106.450i	1.45633	+	1.00424i
$107$	−92.0951	+	92.0951i	−0.860702	+	0.860702i	−0.991420	−	0.130718i	$-0.958272\pi$
$107$	−92.0951	+	92.0951i	−0.860702	+	0.860702i	0.130718	+	0.991420i	$0.458272\pi$
$108$	−29.2817	−	13.1462i	−0.271127	−	0.121724i
$109$	−145.701			−1.33671			−0.668354	−	0.743844i	$-0.733001\pi$
$109$	−145.701			−1.33671			−0.668354	+	0.743844i	$0.733001\pi$
$110$	−1.73937	−	109.986i	−0.0158124	−	0.999875i
$111$			2.50442i			0.0225623i
$112$	−1.34344	+	22.9104i	−0.0119950	+	0.204557i
$113$	−3.96020	−	3.96020i	−0.0350460	−	0.0350460i	0.689367	−	0.724413i	$-0.257889\pi$
$113$	−3.96020	−	3.96020i	−0.0350460	−	0.0350460i	−0.724413	+	0.689367i	$0.757889\pi$
$114$	−187.954	−	129.608i	−1.64872	−	1.13691i
$115$	3.29002	+	46.8714i	0.0286089	+	0.407577i
$116$	−34.0263	+	12.9404i	−0.293330	+	0.111555i
$117$	46.0724	+	46.0724i	0.393781	+	0.393781i
$118$	165.059	−	30.3268i	1.39880	−	0.257007i
$119$	10.0938			0.0848215
$120$	−92.3204	−	130.639i	−0.769337	−	1.08866i
$121$	55.0087	−	107.773i	0.454617	−	0.890687i
$122$	2.92180	+	15.9024i	0.0239492	+	0.130348i
$123$	105.093	+	105.093i	0.854412	+	0.854412i
$124$	−48.5872	−	127.759i	−0.391832	−	1.03031i
$125$	−104.888	−	67.9967i	−0.839102	−	0.543974i
$126$	−16.5163	−	11.3891i	−0.131081	−	0.0903898i
$127$	70.4189	−	70.4189i	0.554479	−	0.554479i	−0.373251	−	0.927730i	$-0.621757\pi$
$127$	70.4189	−	70.4189i	0.554479	−	0.554479i	0.927730	+	0.373251i	$0.121757\pi$
$128$	−37.6859	+	122.326i	−0.294421	+	0.955676i
$129$	−137.873			−1.06878
$130$	−23.2108	−	90.2290i	−0.178545	−	0.694070i
$131$	241.083			1.84033			0.920163	−	0.391535i	$-0.128056\pi$
$131$	241.083			1.84033			0.920163	+	0.391535i	$0.128056\pi$
$132$	−22.3646	−	174.537i	−0.169429	−	1.32225i
$133$	28.9510	+	28.9510i	0.217676	+	0.217676i
$134$	9.20427	+	6.34699i	0.0686886	+	0.0473656i
$135$	−40.0232	+	2.80933i	−0.296468	+	0.0208099i
$136$	54.6797	+	13.3972i	0.402057	+	0.0985086i
$137$	−20.2524	+	20.2524i	−0.147828	+	0.147828i	−0.777147	−	0.629319i	$-0.783334\pi$
$137$	−20.2524	+	20.2524i	−0.147828	+	0.147828i	0.629319	+	0.777147i	$0.283334\pi$
$138$	13.5827	+	73.9260i	0.0984251	+	0.535696i
$139$			82.7488i			0.595315i	0.954673	+	0.297658i	$0.0962054\pi$
$139$			82.7488i			0.595315i	−0.954673	+	0.297658i	$0.903795\pi$
$140$	12.0498	+	26.0337i	0.0860699	+	0.185955i
$141$	215.456			1.52806
$142$	−15.4165	−	83.9072i	−0.108567	−	0.590896i
$143$	23.9593	−	99.6433i	0.167548	−	0.696806i
$144$	−74.3551	−	83.6185i	−0.516355	−	0.580684i
$145$	−29.8448	+	34.3508i	−0.205826	+	0.236902i
$146$	−150.126	+	217.709i	−1.02826	+	1.49116i
$147$	−132.747	−	132.747i	−0.903040	−	0.903040i
$148$	1.02595	−	2.28519i	0.00693209	−	0.0154405i
$149$	−163.982			−1.10055			−0.550274	−	0.834984i	$-0.685477\pi$
$149$	−163.982			−1.10055			−0.550274	+	0.834984i	$0.685477\pi$
$150$	−178.859	−	89.4047i	−1.19239	−	0.596031i
$151$	21.7413			0.143982			0.0719910	−	0.997405i	$-0.477065\pi$
$151$	21.7413			0.143982			0.0719910	+	0.997405i	$0.477065\pi$
$152$	118.407	+	195.258i	0.778992	+	1.28459i
$153$	−34.7997	+	34.7997i	−0.227449	+	0.227449i
$154$	−1.71152	+	31.5094i	−0.0111138	+	0.204607i
$155$	−128.977	−	112.058i	−0.832111	−	0.722957i
$156$	−52.9775	−	139.303i	−0.339599	−	0.892966i
$157$	−26.3279	+	26.3279i	−0.167694	+	0.167694i	−0.785965	−	0.618271i	$-0.787833\pi$
$157$	−26.3279	+	26.3279i	−0.167694	+	0.167694i	0.618271	+	0.785965i	$0.287833\pi$
$158$	−14.9888	−	81.5794i	−0.0948660	−	0.516325i
$159$	374.954			2.35820
$160$	30.7220	+	157.023i	0.192013	+	0.981392i
$161$		−	13.4791i		−	0.0837214i
$162$	−186.936	+	34.3463i	−1.15392	+	0.212014i
$163$	50.1844	−	50.1844i	0.307879	−	0.307879i	−0.536207	−	0.844086i	$-0.680143\pi$
$163$	50.1844	−	50.1844i	0.307879	−	0.307879i	0.844086	+	0.536207i	$0.180143\pi$
$164$	−52.8414	−	138.945i	−0.322204	−	0.847225i
$165$	−127.713	−	179.080i	−0.774019	−	1.08533i
$166$	151.393	+	104.396i	0.912008	+	0.628894i
$167$	141.192	−	141.192i	0.845459	−	0.845459i	−0.144103	−	0.989563i	$-0.546030\pi$
$167$	141.192	−	141.192i	0.845459	−	0.845459i	0.989563	+	0.144103i	$0.0460298\pi$
$168$	23.7950	+	39.2390i	0.141637	+	0.233566i
$169$			82.1998i			0.486389i
$170$	68.1524	−	17.5318i	0.400897	−	0.103128i
$171$	−199.625			−1.16740
$172$	125.804	+	56.4804i	0.731419	+	0.328375i
$173$	−85.8584	+	85.8584i	−0.496291	+	0.496291i	−0.910281	−	0.413990i	$-0.864135\pi$
$173$	−85.8584	+	85.8584i	−0.496291	+	0.496291i	0.413990	+	0.910281i	$0.364135\pi$
$174$	−41.3235	+	59.9265i	−0.237491	+	0.344405i
$175$	28.6496	+	21.5653i	0.163712	+	0.123230i
$176$	−51.0932	+	168.421i	−0.290302	+	0.956935i
$177$	237.288	−	237.288i	1.34061	−	1.34061i
$178$	−45.2337	−	246.193i	−0.254122	−	1.38310i
$179$	80.6220			0.450402			0.225201	−	0.974312i	$-0.427696\pi$
$179$	80.6220			0.450402			0.225201	+	0.974312i	$0.427696\pi$
$180$	−131.299	−	48.2117i	−0.729436	−	0.267843i
$181$	−156.229			−0.863145			−0.431573	−	0.902078i	$-0.642041\pi$
$181$	−156.229			−0.863145			−0.431573	+	0.902078i	$0.642041\pi$
$182$	4.82977	+	26.2868i	0.0265372	+	0.144433i
$183$	22.8612	+	22.8612i	0.124925	+	0.124925i
$184$	17.8905	−	73.0190i	0.0972310	−	0.396842i
$185$	−0.219245	−	3.12348i	−0.00118511	−	0.0168837i
$186$	−225.006	−	155.158i	−1.20971	−	0.834180i
$187$	75.2632	+	18.0971i	0.402477	+	0.0967759i
$188$	−196.595	−	88.2626i	−1.04572	−	0.469482i
$189$	11.5098			0.0608982
$190$	245.760	+	145.190i	1.29347	+	0.764160i
$191$		−	140.417i		−	0.735166i	−0.929991	−	0.367583i	$-0.880185\pi$
$191$		−	140.417i		−	0.735166i	0.929991	−	0.367583i	$-0.119815\pi$
$192$	76.8208	+	244.147i	0.400108	+	1.27160i
$193$	137.765	−	137.765i	0.713808	−	0.713808i	−0.253522	−	0.967330i	$-0.581589\pi$
$193$	137.765	−	137.765i	0.713808	−	0.713808i	0.967330	+	0.253522i	$0.0815890\pi$
$194$	100.865	−	146.272i	0.519923	−	0.753982i
$195$	−140.631	−	122.184i	−0.721186	−	0.626583i
$196$	66.7461	+	175.507i	0.340541	+	0.895444i
$197$	189.233	+	189.233i	0.960575	+	0.960575i	0.999252	−	0.0386771i	$-0.0123144\pi$
$197$	189.233	+	189.233i	0.960575	+	0.960575i	−0.0386771	+	0.999252i	$0.512314\pi$
$198$	−102.733	−	114.534i	−0.518851	−	0.578455i
$199$	209.413			1.05232			0.526162	−	0.850384i	$-0.323630\pi$
$199$	209.413			1.05232			0.526162	+	0.850384i	$0.323630\pi$
$200$	126.577	+	154.849i	0.632886	+	0.774245i
$201$	22.3564			0.111226
$202$	−58.7456	−	319.733i	−0.290820	−	1.58284i
$203$	9.23060	−	9.23060i	0.0454709	−	0.0454709i
$204$	105.219	−	40.0153i	0.515780	−	0.196153i
$205$	−140.270	−	121.870i	−0.684245	−	0.594487i
$206$	−26.7733	+	38.8260i	−0.129967	+	0.188476i
$207$	46.4713	+	46.4713i	0.224499	+	0.224499i
$208$	−8.72610	+	148.811i	−0.0419524	+	0.715438i
$209$	163.964	+	267.777i	0.784518	+	1.28123i
$210$	49.3878	+	29.1774i	0.235180	+	0.138940i
$211$	−171.000			−0.810425			−0.405213	−	0.914223i	$-0.632802\pi$
$211$	−171.000			−0.810425			−0.405213	+	0.914223i	$0.632802\pi$
$212$	−342.132	−	153.602i	−1.61383	−	0.724537i
$213$	−120.625	−	120.625i	−0.566313	−	0.566313i
$214$	147.873	−	214.443i	0.690996	−	1.00207i
$215$	171.953	−	12.0698i	0.799782	−	0.0561387i
$216$	62.3505	+	15.2766i	0.288660	+	0.0707250i
$217$	34.6582	+	34.6582i	0.159715	+	0.159715i
$218$	286.605	−	52.6588i	1.31470	−	0.241554i
$219$			528.798i			2.41460i
$220$	43.1723	+	215.722i	0.196238	+	0.980556i
$221$	65.5625			0.296663
$222$	−0.905139	−	4.92638i	−0.00407720	−	0.0221909i
$223$	−279.031	+	279.031i	−1.25126	+	1.25126i	−0.296104	+	0.955156i	$0.595687\pi$
$223$	−279.031	+	279.031i	−1.25126	+	1.25126i	−0.955156	+	0.296104i	$0.904313\pi$
$224$	−5.63755	−	45.5519i	−0.0251676	−	0.203357i
$225$	−173.123	+	24.4243i	−0.769437	+	0.108552i
$226$	9.22128	+	6.35872i	0.0408021	+	0.0281359i
$227$	−201.011	+	201.011i	−0.885513	+	0.885513i	−0.994088	−	0.108575i	$-0.965371\pi$
$227$	−201.011	+	201.011i	−0.885513	+	0.885513i	0.108575	+	0.994088i	$0.465371\pi$
$228$	416.562	+	187.018i	1.82703	+	0.820253i
$229$			313.536i			1.36915i	0.728940	+	0.684577i	$0.240013\pi$
$229$			313.536i			1.36915i	−0.728940	+	0.684577i	$0.759987\pi$
$230$	−23.4118	−	91.0104i	−0.101790	−	0.395697i
$231$	32.9502	+	53.8123i	0.142641	+	0.232954i
$232$	62.2554	−	37.7523i	0.268342	−	0.162725i
$233$	−267.874	+	267.874i	−1.14967	+	1.14967i	−0.163056	+	0.986617i	$0.552135\pi$
$233$	−267.874	+	267.874i	−1.14967	+	1.14967i	−0.986617	+	0.163056i	$0.947865\pi$
$234$	−107.279	−	73.9764i	−0.458458	−	0.316139i
$235$	−268.713	+	18.8617i	−1.14346	+	0.0802624i
$236$	−313.722	+	119.310i	−1.32933	+	0.505551i
$237$	−117.278	−	117.278i	−0.494844	−	0.494844i
$238$	−19.8552	+	3.64805i	−0.0834250	+	0.0153279i
$239$		−	435.146i		−	1.82069i	−0.413847	−	0.910347i	$-0.635815\pi$
$239$		−	435.146i		−	1.82069i	0.413847	−	0.910347i	$-0.364185\pi$
$240$	228.816	+	223.610i	0.953401	+	0.931710i
$241$		−	40.2443i		−	0.166989i	−0.996508	−	0.0834944i	$-0.973392\pi$
$241$		−	40.2443i		−	0.166989i	0.996508	−	0.0834944i	$-0.0266081\pi$
$242$	−69.2551	+	231.879i	−0.286178	+	0.958176i
$243$	−217.671	+	217.671i	−0.895766	+	0.895766i
$244$	−11.4948	−	30.2252i	−0.0471098	−	0.123874i
$245$	177.181	+	153.939i	0.723187	+	0.628322i
$246$	−244.707	−	168.743i	−0.994745	−	0.685946i
$247$	188.047	+	188.047i	0.761323	+	0.761323i
$248$	141.749	+	233.750i	0.571567	+	0.942542i
$249$	367.722			1.47679
$250$	230.897	+	95.8463i	0.923589	+	0.383385i
$251$			65.1380i			0.259514i	0.991546	+	0.129757i	$0.0414197\pi$
$251$			65.1380i			0.259514i	−0.991546	+	0.129757i	$0.958580\pi$
$252$	36.6049	+	16.4340i	0.145258	+	0.0652142i
$253$	24.1668	−	100.506i	0.0955208	−	0.397257i
$254$	−113.069	+	163.970i	−0.445152	+	0.645550i
$255$	92.2886	−	106.223i	0.361916	−	0.416559i
$256$	29.9202	−	254.246i	0.116876	−	0.993147i
$257$	284.539	−	284.539i	1.10716	−	1.10716i	0.113633	−	0.993523i	$-0.463751\pi$
$257$	284.539	−	284.539i	1.10716	−	1.10716i	0.993523	−	0.113633i	$-0.0362489\pi$
$258$	271.206	−	49.8296i	1.05119	−	0.193138i
$259$			0.898241i			0.00346811i
$260$	78.2677	+	169.098i	0.301029	+	0.650378i
$261$			63.6477i			0.243861i
$262$	−474.227	+	87.1313i	−1.81003	+	0.332562i
$263$	136.916	+	136.916i	0.520592	+	0.520592i	0.917750	−	0.397158i	$-0.130003\pi$
$263$	136.916	+	136.916i	0.520592	+	0.520592i	−0.397158	+	0.917750i	$0.630003\pi$
$264$	107.074	+	335.245i	0.405581	+	1.26987i
$265$	−467.637	+	32.8246i	−1.76467	+	0.123867i
$266$	−67.4120	−	46.4853i	−0.253429	−	0.174757i
$267$	−353.925	−	353.925i	−1.32556	−	1.32556i
$268$	−20.3994	−	9.15841i	−0.0761171	−	0.0341732i
$269$		−	436.064i		−	1.62106i	−0.585700	−	0.810528i	$-0.699180\pi$
$269$		−	436.064i		−	1.62106i	0.585700	−	0.810528i	$-0.300820\pi$
$270$	77.7133	−	19.9912i	0.287827	−	0.0740415i
$271$	154.250			0.569189			0.284594	−	0.958648i	$-0.408141\pi$
$271$	154.250			0.569189			0.284594	+	0.958648i	$0.408141\pi$
$272$	−112.401	−	6.59106i	−0.413239	−	0.0242318i
$273$	37.7898	+	37.7898i	0.138424	+	0.138424i
$274$	32.5184	−	47.1575i	0.118680	−	0.172108i
$275$	174.959	+	212.166i	0.636215	+	0.771512i
$276$	−53.4362	−	140.509i	−0.193609	−	0.509090i
$277$	−0.735422	−	0.735422i	−0.00265495	−	0.00265495i	0.705778	−	0.708433i	$-0.250598\pi$
$277$	−0.735422	−	0.735422i	−0.00265495	−	0.00265495i	−0.708433	+	0.705778i	$0.750598\pi$
$278$	−29.9068	−	162.773i	−0.107578	−	0.585514i
$279$	−238.978			−0.856553
$280$	−33.1118	−	46.8553i	−0.118257	−	0.167340i
$281$			466.090i			1.65869i	0.558741	+	0.829343i	$0.311285\pi$
$281$			466.090i			1.65869i	−0.558741	+	0.829343i	$0.688715\pi$
$282$	−423.817	+	77.8693i	−1.50290	+	0.276132i
$283$	−310.695	−	310.695i	−1.09786	−	1.09786i	−0.994660	−	0.103203i	$-0.967091\pi$
$283$	−310.695	−	310.695i	−1.09786	−	1.09786i	−0.103203	−	0.994660i	$-0.532909\pi$
$284$	60.6510	+	159.480i	0.213560	+	0.561549i
$285$	569.371	−	39.9656i	1.99779	−	0.140230i
$286$	−11.1170	+	204.665i	−0.0388705	+	0.715612i
$287$	37.6928	+	37.6928i	0.131334	+	0.131334i
$288$	176.483	+	137.611i	0.612789	+	0.477815i
$289$		−	239.479i		−	0.828647i
$290$	46.2919	−	78.3570i	0.159627	−	0.270197i
$291$		−	355.283i		−	1.22091i
$292$	216.625	−	482.508i	0.741866	−	1.65243i
$293$	250.373	−	250.373i	0.854515	−	0.854515i	−0.136170	−	0.990685i	$-0.543479\pi$
$293$	250.373	−	250.373i	0.854515	−	0.854515i	0.990685	+	0.136170i	$0.0434795\pi$
$294$	309.100	+	213.146i	1.05136	+	0.724986i
$295$	−275.169	+	316.715i	−0.932776	+	1.07361i
$296$	−1.19221	+	4.86593i	−0.00402774	+	0.0164390i
$297$	85.8216	+	20.6359i	0.288962	+	0.0694810i
$298$	322.564	−	59.2657i	1.08243	−	0.198878i
$299$		−	87.5519i		−	0.292816i
$300$	384.141	+	111.223i	1.28047	+	0.370743i
$301$	−49.4498			−0.164285
$302$	−42.7667	+	7.85766i	−0.141612	+	0.0260187i
$303$	−459.647	−	459.647i	−1.51699	−	1.51699i
$304$	−303.484	−	341.293i	−0.998304	−	1.12268i
$305$	−30.5135	−	26.5108i	−0.100044	−	0.0869208i
$306$	55.8764	−	81.0308i	0.182603	−	0.264806i
$307$	−182.250	+	182.250i	−0.593647	+	0.593647i	−0.938615	−	0.344967i	$-0.887890\pi$
$307$	−182.250	+	182.250i	−0.593647	+	0.593647i	0.344967	+	0.938615i	$0.387890\pi$
$308$	−8.02134	−	62.5999i	−0.0260433	−	0.203246i
$309$			94.3052i			0.305195i
$310$	294.207	+	173.812i	0.949056	+	0.560685i
$311$		−	176.904i		−	0.568824i	−0.958702	−	0.284412i	$-0.908202\pi$
$311$		−	176.904i		−	0.568824i	0.958702	−	0.284412i	$-0.0917984\pi$
$312$	154.557	+	254.872i	0.495375	+	0.816896i
$313$	2.62455	+	2.62455i	0.00838513	+	0.00838513i	0.711287	−	0.702902i	$-0.248113\pi$
$313$	2.62455	+	2.62455i	0.00838513	+	0.00838513i	−0.702902	+	0.711287i	$0.748113\pi$
$314$	42.2736	−	61.3043i	0.134629	−	0.195237i
$315$	50.0328	−	3.51193i	0.158834	−	0.0111490i
$316$	58.9683	+	155.055i	0.186608	+	0.490682i
$317$	27.4855	−	27.4855i	0.0867050	−	0.0867050i	−0.662424	−	0.749129i	$-0.730472\pi$
$317$	27.4855	−	27.4855i	0.0867050	−	0.0867050i	0.749129	+	0.662424i	$0.230472\pi$
$318$	−737.562	+	135.515i	−2.31938	+	0.426147i
$319$	85.3767	−	52.2776i	0.267639	−	0.163880i
$320$	−117.183	−	297.772i	−0.366197	−	0.930537i
$321$		−	520.863i		−	1.62263i
$322$	4.87159	+	26.5145i	0.0151292	+	0.0823431i
$323$	−142.037	+	142.037i	−0.439742	+	0.439742i
$324$	355.303	−	135.123i	1.09661	−	0.417048i
$325$	186.090	+	140.074i	0.572583	+	0.430998i
$326$	−80.5788	+	116.854i	−0.247174	+	0.358447i
$327$	412.021	−	412.021i	1.26000	−	1.26000i
$328$	154.160	+	254.217i	0.470000	+	0.775052i
$329$	77.2758			0.234881
$330$	315.944	+	306.106i	0.957405	+	0.927595i
$331$		−	20.1934i		−	0.0610072i	−0.999535	−	0.0305036i	$-0.990289\pi$
$331$		−	20.1934i		−	0.0610072i	0.999535	−	0.0305036i	$-0.00971110\pi$
$332$	−335.533	−	150.639i	−1.01064	−	0.453732i
$333$	−3.09682	−	3.09682i	−0.00929975	−	0.00929975i
$334$	−226.705	+	328.763i	−0.678759	+	0.984322i
$335$	−27.8826	+	1.95715i	−0.0832315	+	0.00584223i
$336$	−60.9881	−	68.5862i	−0.181512	−	0.204126i
$337$	−378.683	−	378.683i	−1.12369	−	1.12369i	−0.991182	−	0.132508i	$-0.957697\pi$
$337$	−378.683	−	378.683i	−1.12369	−	1.12369i	−0.132508	−	0.991182i	$-0.542303\pi$
$338$	−29.7084	−	161.693i	−0.0878946	−	0.478382i
$339$	22.3977			0.0660700
$340$	−127.725	+	59.1177i	−0.375660	+	0.173876i
$341$	196.287	+	320.564i	0.575622	+	0.940071i
$342$	392.678	−	72.1479i	1.14818	−	0.210959i
$343$	−97.3092	−	97.3092i	−0.283700	−	0.283700i
$344$	−267.879	−	65.6334i	−0.778717	−	0.190795i
$345$	−141.849	−	123.242i	−0.411157	−	0.357222i
$346$	137.859	−	199.920i	0.398437	−	0.577805i
$347$	−235.055	+	235.055i	−0.677391	+	0.677391i	−0.959409	−	0.282018i	$-0.908996\pi$
$347$	−235.055	+	235.055i	−0.677391	+	0.677391i	0.282018	+	0.959409i	$0.408996\pi$
$348$	59.6279	−	132.815i	0.171345	−	0.381652i
$349$	−235.716			−0.675404			−0.337702	−	0.941253i	$-0.609650\pi$
$349$	−235.716			−0.675404			−0.337702	+	0.941253i	$0.609650\pi$
$350$	−64.1500	−	32.0661i	−0.183286	−	0.0916173i
$351$	74.7601			0.212992
$352$	39.6341	−	349.762i	0.112597	−	0.993641i
$353$	−367.715	−	367.715i	−1.04168	−	1.04168i	−0.999093	−	0.0425925i	$-0.986438\pi$
$353$	−367.715	−	367.715i	−1.04168	−	1.04168i	−0.0425925	−	0.999093i	$-0.513562\pi$
$354$	−381.003	+	552.522i	−1.07628	+	1.56080i
$355$	161.001	+	139.881i	0.453524	+	0.394032i
$356$	177.956	+	467.931i	0.499877	+	1.31441i
$357$	−28.5437	+	28.5437i	−0.0799542	+	0.0799542i
$358$	−158.589	+	29.1381i	−0.442987	+	0.0813915i
$359$			235.587i			0.656230i	0.944638	+	0.328115i	$0.106413\pi$
$359$			235.587i			0.656230i	−0.944638	+	0.328115i	$0.893587\pi$
$360$	275.698	+	47.3825i	0.765829	+	0.131618i
$361$	−453.781			−1.25701
$362$	307.314	−	56.4639i	0.848935	−	0.155978i
$363$	149.210	+	460.323i	0.411047	+	1.26811i
$364$	−19.0010	−	49.9626i	−0.0522006	−	0.137260i
$365$	−46.2926	−	659.509i	−0.126829	−	1.80687i
$366$	−53.2321	−	36.7073i	−0.145443	−	0.100293i
$367$	225.118	+	225.118i	0.613401	+	0.613401i	0.943831	−	0.330429i	$-0.107194\pi$
$367$	225.118	+	225.118i	0.613401	+	0.613401i	−0.330429	+	0.943831i	$0.607194\pi$
$368$	−8.80166	+	150.100i	−0.0239176	+	0.407879i
$369$	−259.903			−0.704343
$370$	1.56015	+	6.06487i	0.00421661	+	0.0163915i
$371$	134.482			0.362485
$372$	498.680	+	223.885i	1.34054	+	0.601842i
$373$	273.487	−	273.487i	0.733209	−	0.733209i	−0.238045	−	0.971254i	$-0.576507\pi$
$373$	273.487	−	273.487i	0.733209	−	0.733209i	0.971254	+	0.238045i	$0.0765066\pi$
$374$	−154.589	−	8.39693i	−0.413339	−	0.0224517i
$375$	488.892	−	104.323i	1.30371	−	0.278194i
$376$	418.617	+	102.566i	1.11334	+	0.272782i
$377$	59.9560	−	59.9560i	0.159035	−	0.159035i
$378$	−22.6406	+	4.15982i	−0.0598957	+	0.0110048i
$379$	72.4143			0.191067			0.0955334	−	0.995426i	$-0.469544\pi$
$379$	72.4143			0.191067			0.0955334	+	0.995426i	$0.469544\pi$
$380$	−535.902	−	196.779i	−1.41027	−	0.517838i
$381$			398.269i			1.04532i
$382$	50.7490	+	276.210i	0.132851	+	0.723063i
$383$	451.049	−	451.049i	1.17767	−	1.17767i	0.197338	−	0.980336i	$-0.436770\pi$
$383$	451.049	−	451.049i	1.17767	−	1.17767i	0.980336	−	0.197338i	$-0.0632295\pi$
$384$	−239.351	−	452.492i	−0.623310	−	1.17836i
$385$	−45.8058	−	64.2293i	−0.118976	−	0.166829i
$386$	−221.203	+	320.784i	−0.573065	+	0.831047i
$387$	170.486	−	170.486i	0.440531	−	0.440531i
$388$	−145.544	+	324.183i	−0.375113	+	0.835523i
$389$			49.7514i			0.127896i	0.997953	+	0.0639478i	$0.0203691\pi$
$389$			49.7514i			0.127896i	−0.997953	+	0.0639478i	$0.979631\pi$
$390$	320.791	+	189.518i	0.822542	+	0.485943i
$391$	66.1303			0.169131
$392$	−194.726	−	321.112i	−0.496749	−	0.819163i
$393$	−681.747	+	681.747i	−1.73472	+	1.73472i
$394$	−440.628	−	303.844i	−1.11834	−	0.771177i
$395$	156.534	+	136.000i	0.396289	+	0.344305i
$396$	243.477	+	188.168i	0.614841	+	0.475171i
$397$	195.266	−	195.266i	0.491855	−	0.491855i	−0.417036	−	0.908890i	$-0.636931\pi$
$397$	195.266	−	195.266i	0.491855	−	0.491855i	0.908890	+	0.417036i	$0.136931\pi$
$398$	−411.930	+	75.6852i	−1.03500	+	0.190164i
$399$	−163.738			−0.410371
$400$	−304.952	−	258.852i	−0.762379	−	0.647131i
$401$	29.4592			0.0734643			0.0367322	−	0.999325i	$-0.488305\pi$
$401$	29.4592			0.0734643			0.0367322	+	0.999325i	$0.488305\pi$
$402$	−43.9767	+	8.07997i	−0.109395	+	0.0200994i
$403$	225.117	+	225.117i	0.558603	+	0.558603i
$404$	231.114	+	607.707i	0.572064	+	1.50423i
$405$	311.640	−	358.692i	0.769480	−	0.885659i
$406$	−14.8212	+	21.4934i	−0.0365054	+	0.0529393i
$407$	−1.61046	+	6.69766i	−0.00395689	+	0.0164562i
$408$	−192.511	+	116.741i	−0.471842	+	0.286130i
$409$	−123.288			−0.301437			−0.150719	−	0.988577i	$-0.548159\pi$
$409$	−123.288			−0.301437			−0.150719	+	0.988577i	$0.548159\pi$
$410$	319.968	+	189.031i	0.780409	+	0.461051i
$411$		−	114.542i		−	0.278690i
$412$	38.6326	−	86.0500i	0.0937685	−	0.208859i
$413$	85.1061	−	85.1061i	0.206068	−	0.206068i
$414$	−108.208	−	74.6170i	−0.261372	−	0.180234i
$415$	−458.617	+	32.1915i	−1.10510	+	0.0775699i
$416$	−36.6179	−	295.876i	−0.0880238	−	0.711240i
$417$	−234.001	−	234.001i	−0.561155	−	0.561155i
$418$	−419.309	−	467.477i	−1.00313	−	1.11837i
$419$	−610.564			−1.45719			−0.728596	−	0.684943i	$-0.759827\pi$
$419$	−610.564			−1.45719			−0.728596	+	0.684943i	$0.759827\pi$
$420$	−107.695	−	39.5445i	−0.256416	−	0.0941537i
$421$	−668.258			−1.58731			−0.793656	−	0.608367i	$-0.791825\pi$
$421$	−668.258			−1.58731			−0.793656	+	0.608367i	$0.791825\pi$
$422$	336.369	−	61.8021i	0.797083	−	0.146451i
$423$	−266.420	+	266.420i	−0.629834	+	0.629834i
$424$	728.512	+	178.494i	1.71819	+	0.420977i
$425$	−105.802	+	140.558i	−0.248946	+	0.330726i
$426$	280.873	+	193.682i	0.659327	+	0.454652i
$427$	8.19945	+	8.19945i	0.0192025	+	0.0192025i
$428$	−213.374	+	475.268i	−0.498538	+	1.11044i
$429$	214.023	+	349.530i	0.498888	+	0.814755i
$430$	−333.882	+	85.8890i	−0.776471	+	0.199742i
$431$	−457.041			−1.06042			−0.530210	−	0.847867i	$-0.677887\pi$
$431$	−457.041			−1.06042			−0.530210	+	0.847867i	$0.677887\pi$
$432$	−128.169	−	7.51569i	−0.296688	−	0.0173974i
$433$	228.327	+	228.327i	0.527314	+	0.527314i	0.919770	−	0.392457i	$-0.128375\pi$
$433$	228.327	+	228.327i	0.527314	+	0.527314i	−0.392457	+	0.919770i	$0.628375\pi$
$434$	−80.7012	−	55.6491i	−0.185947	−	0.128224i
$435$	−12.7425	−	181.536i	−0.0292930	−	0.417324i
$436$	−544.741	+	207.168i	−1.24941	+	0.475155i
$437$	189.675	+	189.675i	0.434039	+	0.434039i
$438$	−191.116	−	1040.18i	−0.436339	−	2.37485i
$439$			114.601i			0.261051i	0.991445	+	0.130525i	$0.0416664\pi$
$439$			114.601i			0.261051i	−0.991445	+	0.130525i	$0.958334\pi$
$440$	−162.889	−	408.739i	−0.370202	−	0.928951i
$441$	328.294			0.744430
$442$	−128.966	+	23.6954i	−0.291779	+	0.0536095i
$443$	315.936	−	315.936i	0.713173	−	0.713173i	−0.254025	−	0.967198i	$-0.581754\pi$
$443$	315.936	−	315.936i	0.713173	−	0.713173i	0.967198	+	0.254025i	$0.0817545\pi$
$444$	3.56095	+	9.36342i	0.00802016	+	0.0210888i
$445$	472.394	+	410.426i	1.06156	+	0.922306i
$446$	448.028	−	649.721i	1.00455	−	1.45677i
$447$	463.716	−	463.716i	1.03740	−	1.03740i
$448$	27.5527	+	87.5664i	0.0615015	+	0.195461i
$449$		−	27.7842i		−	0.0618802i	−0.999521	−	0.0309401i	$-0.990150\pi$
$449$		−	27.7842i		−	0.0618802i	0.999521	−	0.0309401i	$-0.00985012\pi$
$450$	331.719	−	110.614i	0.737153	−	0.245809i
$451$	213.474	+	348.632i	0.473334	+	0.773021i
$452$	−20.4371	−	9.17534i	−0.0452148	−	0.0202994i
$453$	−61.4811	+	61.4811i	−0.135720	+	0.135720i
$454$	322.755	−	468.053i	0.710915	−	1.03095i
$455$	−50.4391	−	43.8226i	−0.110855	−	0.0963135i
$456$	−886.999	−	217.325i	−1.94517	−	0.476590i
$457$	−286.988	−	286.988i	−0.627981	−	0.627981i	0.319578	−	0.947560i	$-0.396459\pi$
$457$	−286.988	−	286.988i	−0.627981	−	0.627981i	−0.947560	+	0.319578i	$0.896459\pi$
$458$	−113.317	−	616.749i	−0.247418	−	1.34661i
$459$			56.4683i			0.123025i
$460$	78.9454	+	170.563i	0.171620	+	0.370788i
$461$		−	740.355i		−	1.60598i	−0.595995	−	0.802988i	$-0.703242\pi$
$461$		−	740.355i		−	1.60598i	0.595995	−	0.802988i	$-0.296758\pi$
$462$	−84.2641	−	93.9439i	−0.182390	−	0.203342i
$463$	304.330	−	304.330i	0.657299	−	0.657299i	−0.297441	−	0.954740i	$-0.596133\pi$
$463$	304.330	−	304.330i	0.657299	−	0.657299i	0.954740	+	0.297441i	$0.0961331\pi$
$464$	−108.817	+	96.7617i	−0.234518	+	0.208538i
$465$	681.613	−	47.8441i	1.46583	−	0.102891i
$466$	430.113	−	623.741i	0.922990	−	1.33850i
$467$	190.747	+	190.747i	0.408451	+	0.408451i	0.881198	−	0.472747i	$-0.156738\pi$
$467$	190.747	+	190.747i	0.408451	+	0.408451i	−0.472747	+	0.881198i	$0.656738\pi$
$468$	237.762	+	106.745i	0.508039	+	0.228087i
$469$	8.01839			0.0170968
$470$	521.762	−	134.220i	1.11013	−	0.285574i
$471$		−	148.903i		−	0.316142i
$472$	573.994	−	348.076i	1.21609	−	0.737450i
$473$	−368.719	−	88.6587i	−0.779532	−	0.187439i
$474$	273.081	+	188.308i	0.576120	+	0.397275i
$475$	−706.612	+	99.6889i	−1.48760	+	0.209871i
$476$	37.7381	−	14.3520i	0.0792817	−	0.0301512i
$477$	−463.646	+	463.646i	−0.972004	+	0.972004i
$478$	157.269	+	855.964i	0.329014	+	1.79072i
$479$		−	51.0809i		−	0.106641i	−0.998577	−	0.0533203i	$-0.983020\pi$
$479$		−	51.0809i		−	0.106641i	0.998577	−	0.0533203i	$-0.0169804\pi$
$480$	−530.915	−	357.160i	−1.10607	−	0.744084i
$481$			5.83439i			0.0121297i
$482$	14.5450	+	79.1635i	0.0301763	+	0.164240i
$483$	38.1170	+	38.1170i	0.0789173	+	0.0789173i
$484$	52.4250	−	481.152i	0.108316	−	0.994117i
$485$	31.1026	+	443.104i	0.0641291	+	0.913617i
$486$	349.505	−	506.845i	0.719146	−	1.04289i
$487$	−80.6865	−	80.6865i	−0.165681	−	0.165681i	0.619397	−	0.785078i	$-0.287377\pi$
$487$	−80.6865	−	80.6865i	−0.165681	−	0.165681i	−0.785078	+	0.619397i	$0.787377\pi$
$488$	33.5350	+	55.3008i	0.0687193	+	0.113321i
$489$			283.828i			0.580425i
$490$	−404.164	−	238.773i	−0.824824	−	0.487291i
$491$	292.286			0.595287			0.297643	−	0.954677i	$-0.403799\pi$
$491$	292.286			0.595287			0.297643	+	0.954677i	$0.403799\pi$
$492$	542.344	+	243.488i	1.10232	+	0.494895i
$493$	45.2864	+	45.2864i	0.0918588	+	0.0918588i
$494$	−437.865	−	301.939i	−0.886367	−	0.611212i
$495$	379.362	+	63.5175i	0.766388	+	0.128318i
$496$	−363.311	−	408.574i	−0.732483	−	0.823738i
$497$	−43.2635	−	43.2635i	−0.0870492	−	0.0870492i
$498$	−723.336	+	132.901i	−1.45248	+	0.266869i
$499$	80.9534			0.162231			0.0811156	−	0.996705i	$-0.474152\pi$
$499$	80.9534			0.162231			0.0811156	+	0.996705i	$0.474152\pi$
$500$	−488.832	−	105.087i	−0.977664	−	0.210173i
$501$			798.539i			1.59389i
$502$	−23.5420	−	128.131i	−0.0468963	−	0.255241i
$503$	−341.197	−	341.197i	−0.678323	−	0.678323i	0.281297	−	0.959621i	$-0.409235\pi$
$503$	−341.197	−	341.197i	−0.678323	−	0.678323i	−0.959621	+	0.281297i	$0.909235\pi$
$504$	−77.9441	−	19.0972i	−0.154651	−	0.0378913i
$505$	613.503	+	533.025i	1.21486	+	1.05550i
$506$	−11.2132	+	206.437i	−0.0221605	+	0.407979i
$507$	−232.449	−	232.449i	−0.458479	−	0.458479i
$508$	163.153	−	363.405i	0.321167	−	0.715365i
$509$		−	108.383i		−	0.212933i	−0.994316	−	0.106467i	$-0.966046\pi$
$509$		−	108.383i		−	0.212933i	0.994316	−	0.106467i	$-0.0339538\pi$
$510$	−143.148	+	242.302i	−0.280682	+	0.475103i
$511$			189.660i			0.371154i
$512$	33.0334	+	510.933i	0.0645183	+	0.997917i
$513$	−161.963	+	161.963i	−0.315717	+	0.315717i
$514$	−456.872	+	662.547i	−0.888856	+	1.28900i
$515$	−8.25577	−	117.616i	−0.0160306	−	0.228381i
$516$	−515.474	+	196.037i	−0.998980	+	0.379917i
$517$	576.201	+	138.548i	1.11451	+	0.267984i
$518$	−0.324639	−	1.76691i	−0.000626717	−	0.00341101i
$519$		−	485.590i		−	0.935626i
$520$	−215.073	−	304.342i	−0.413602	−	0.585273i
$521$	781.573			1.50014			0.750070	−	0.661359i	$-0.230020\pi$
$521$	781.573			1.50014			0.750070	+	0.661359i	$0.230020\pi$
$522$	−23.0033	−	125.200i	−0.0440677	−	0.239846i
$523$	117.827	+	117.827i	0.225291	+	0.225291i	0.810722	−	0.585431i	$-0.199075\pi$
$523$	117.827	+	117.827i	0.225291	+	0.225291i	−0.585431	+	0.810722i	$0.699075\pi$
$524$	901.350	−	342.787i	1.72013	−	0.654175i
$525$	−142.000	+	20.0334i	−0.270477	+	0.0381589i
$526$	−318.807	−	219.840i	−0.606097	−	0.417946i
$527$	−170.037	+	170.037i	−0.322651	+	0.322651i
$528$	−331.784	−	620.753i	−0.628380	−	1.17567i
$529$			440.690i			0.833062i
$530$	908.013	−	233.580i	1.71323	−	0.440718i
$531$			586.832i			1.10514i
$532$	149.405	+	67.0762i	0.280836	+	0.126083i
$533$	244.828	+	244.828i	0.459340	+	0.459340i
$534$	824.111	+	568.282i	1.54328	+	1.06420i
$535$	45.5979	+	649.612i	0.0852298	+	1.21423i
$536$	43.4371	+	10.6426i	0.0810393	+	0.0198556i
$537$	−227.987	+	227.987i	−0.424557	+	0.424557i
$538$	157.601	+	857.770i	0.292938	+	1.59437i
$539$	−269.647	−	440.372i	−0.500273	−	0.817016i
$540$	−145.643	+	67.4111i	−0.269708	+	0.124835i
$541$		−	546.734i		−	1.01060i	−0.862944	−	0.505299i	$-0.831382\pi$
$541$		−	546.734i		−	1.01060i	0.862944	−	0.505299i	$-0.168618\pi$
$542$	−303.421	+	55.7486i	−0.559818	+	0.102857i
$543$	441.793	−	441.793i	0.813616	−	0.813616i
$544$	223.483	−	27.6585i	0.410814	−	0.0508428i
$545$	−477.797	+	549.937i	−0.876692	+	1.00906i
$546$	−87.9932	−	60.6775i	−0.161160	−	0.111131i
$547$	178.497	−	178.497i	0.326320	−	0.326320i	−0.524865	−	0.851185i	$-0.675884\pi$
$547$	178.497	−	178.497i	0.326320	−	0.326320i	0.851185	+	0.524865i	$0.175884\pi$
$548$	−46.9226	+	104.515i	−0.0856251	+	0.190721i
$549$	−56.5376			−0.102983
$550$	−420.838	−	354.113i	−0.765159	−	0.643841i
$551$			259.781i			0.471473i
$552$	155.895	+	257.079i	0.282419	+	0.465722i
$553$	−42.0632	−	42.0632i	−0.0760636	−	0.0760636i
$554$	1.71242	+	1.18084i	0.00309102	+	0.00213147i
$555$	9.45272	+	8.21274i	0.0170319	+	0.0147977i
$556$	117.658	+	309.378i	0.211615	+	0.556434i
$557$	22.5628	+	22.5628i	0.0405076	+	0.0405076i	0.727070	−	0.686563i	$-0.240881\pi$
$557$	22.5628	+	22.5628i	0.0405076	+	0.0405076i	−0.686563	+	0.727070i	$0.740881\pi$
$558$	470.088	−	86.3707i	0.842451	−	0.154786i
$559$	−321.194			−0.574588
$560$	82.0677	+	80.2006i	0.146549	+	0.143215i
$561$	−264.009	+	161.657i	−0.470605	+	0.288159i
$562$	−168.453	−	916.834i	−0.299738	−	1.63138i
$563$	631.928	+	631.928i	1.12243	+	1.12243i	0.991375	+	0.131055i	$0.0418364\pi$
$563$	631.928	+	631.928i	1.12243	+	1.12243i	0.131055	+	0.991375i	$0.458164\pi$
$564$	805.537	−	306.349i	1.42826	−	0.543173i
$565$	−27.9341	+	1.96076i	−0.0494409	+	0.00347038i
$566$	723.451	+	498.870i	1.27818	+	0.881396i
$567$	−96.3860	+	96.3860i	−0.169993	+	0.169993i
$568$	−176.944	−	291.788i	−0.311520	−	0.513712i
$569$	891.102			1.56608			0.783042	−	0.621968i	$-0.213667\pi$
$569$	891.102			1.56608			0.783042	+	0.621968i	$0.213667\pi$
$570$	−1105.55	+	284.395i	−1.93956	+	0.498939i
$571$	−558.409			−0.977949			−0.488975	−	0.872298i	$-0.662629\pi$
$571$	−558.409			−0.977949			−0.488975	+	0.872298i	$0.662629\pi$
$572$	−52.1015	−	406.609i	−0.0910865	−	0.710854i
$573$	397.078	+	397.078i	0.692981	+	0.692981i
$574$	−87.7672	−	60.5217i	−0.152905	−	0.105438i
$575$	187.701	+	141.287i	0.326436	+	0.245717i
$576$	−396.890	−	206.906i	−0.689045	−	0.359212i
$577$	−336.069	+	336.069i	−0.582442	+	0.582442i	−0.935574	−	0.353131i	$-0.885117\pi$
$577$	−336.069	+	336.069i	−0.582442	+	0.582442i	0.353131	+	0.935574i	$0.385117\pi$
$578$	86.5517	+	471.072i	0.149743	+	0.815004i
$579$			779.158i			1.34570i
$580$	−62.7400	+	170.865i	−0.108172	+	0.294594i
$581$	131.888			0.227002
$582$	128.405	+	698.869i	0.220628	+	1.20081i
$583$	1002.75	+	241.113i	1.71999	+	0.413572i
$584$	−251.730	+	1027.42i	−0.431045	+	1.75928i
$585$	324.981	−	22.8113i	0.555524	−	0.0389936i
$586$	−402.013	+	582.991i	−0.686029	+	0.994865i
$587$	471.198	+	471.198i	0.802723	+	0.802723i	0.983520	−	0.180798i	$-0.0578679\pi$
$587$	471.198	+	471.198i	0.802723	+	0.802723i	−0.180798	+	0.983520i	$0.557868\pi$
$588$	−685.056	−	307.560i	−1.16506	−	0.523061i
$589$	−975.402			−1.65603
$590$	426.811	−	722.451i	0.723409	−	1.22449i
$591$	−1070.25			−1.81091
$592$	0.586536	−	10.0025i	0.000990771	−	0.0168962i
$593$	744.232	−	744.232i	1.25503	−	1.25503i	0.301591	−	0.953438i	$-0.402482\pi$
$593$	744.232	−	744.232i	1.25503	−	1.25503i	0.953438	−	0.301591i	$-0.0975176\pi$
$594$	−176.276	−	9.57491i	−0.296760	−	0.0161194i
$595$	33.1004	−	38.0980i	0.0556310	−	0.0640303i
$596$	−613.087	+	233.160i	−1.02867	+	0.391208i
$597$	−592.188	+	592.188i	−0.991940	+	0.991940i
$598$	31.6427	+	172.221i	0.0529142	+	0.287995i
$599$	−812.447			−1.35634			−0.678169	−	0.734906i	$-0.737226\pi$
$599$	−812.447			−1.35634			−0.678169	+	0.734906i	$0.737226\pi$
$600$	−795.832	−	79.9486i	−1.32639	−	0.133248i
$601$			609.203i			1.01365i	0.862049	+	0.506825i	$0.169181\pi$
$601$			609.203i			1.01365i	−0.862049	+	0.506825i	$0.830819\pi$
$602$	97.2715	−	17.8720i	0.161581	−	0.0296877i
$603$	−27.6446	+	27.6446i	−0.0458451	+	0.0458451i
$604$	81.2853	−	30.9132i	0.134578	−	0.0511808i
$605$	−226.391	−	561.046i	−0.374200	−	0.927348i
$606$	1070.28	+	738.035i	1.76614	+	1.21788i
$607$	−442.748	+	442.748i	−0.729403	+	0.729403i	−0.970501	−	0.241098i	$-0.922493\pi$
$607$	−442.748	+	442.748i	−0.729403	+	0.729403i	0.241098	+	0.970501i	$0.422493\pi$
$608$	720.325	+	561.665i	1.18475	+	0.923791i
$609$			52.2056i			0.0857234i
$610$	69.6038	+	41.1207i	0.114105	+	0.0674109i
$611$	501.934			0.821496
$612$	−80.6271	+	179.588i	−0.131744	+	0.293445i
$613$	−167.994	+	167.994i	−0.274052	+	0.274052i	−0.830729	−	0.556677i	$-0.812076\pi$
$613$	−167.994	+	167.994i	−0.274052	+	0.274052i	0.556677	+	0.830729i	$0.312076\pi$
$614$	292.630	−	424.367i	0.476597	−	0.691151i
$615$	741.294	−	52.0333i	1.20536	−	0.0846070i
$616$	38.4032	+	120.240i	0.0623429	+	0.195194i
$617$	−237.555	+	237.555i	−0.385016	+	0.385016i	−0.872906	−	0.487889i	$-0.837767\pi$
$617$	−237.555	+	237.555i	−0.385016	+	0.385016i	0.487889	+	0.872906i	$0.337767\pi$
$618$	−34.0835	−	185.505i	−0.0551513	−	0.300170i
$619$	1135.27			1.83404			0.917019	−	0.398845i	$-0.130589\pi$
$619$	1135.27			1.83404			0.917019	+	0.398845i	$0.130589\pi$
$620$	−641.546	−	235.570i	−1.03475	−	0.379952i
$621$	75.4074			0.121429
$622$	63.9362	+	347.984i	0.102791	+	0.559460i
$623$	−126.939	−	126.939i	−0.203755	−	0.203755i
$624$	−396.140	−	445.492i	−0.634839	−	0.713929i
$625$	−600.606	+	172.909i	−0.960970	+	0.276654i
$626$	−6.11123	−	4.21412i	−0.00976235	−	0.00673182i
$627$	−1220.90	−	293.566i	−1.94721	−	0.468208i
$628$	−60.9989	+	135.869i	−0.0971320	+	0.216351i
$629$	−4.40687			−0.00700616
$630$	−97.1490	+	24.9909i	−0.154205	+	0.0396681i
$631$		−	149.150i		−	0.236371i	−0.992992	−	0.118186i	$-0.962292\pi$
$631$		−	149.150i		−	0.236371i	0.992992	−	0.118186i	$-0.0377078\pi$
$632$	−172.035	−	283.693i	−0.272207	−	0.448882i
$633$	483.562	−	483.562i	0.763921	−	0.763921i
$634$	−44.1322	+	63.9997i	−0.0696092	+	0.100946i
$635$	−34.8656	−	496.715i	−0.0549065	−	0.782228i
$636$	1401.86	−	533.135i	2.20419	−	0.838262i
$637$	−309.252	−	309.252i	−0.485482	−	0.485482i
$638$	−149.048	+	133.691i	−0.233618	+	0.209546i
$639$	298.314			0.466845
$640$	338.128	+	543.387i	0.528324	+	0.849043i
$641$	9.33545			0.0145639			0.00728194	−	0.999973i	$-0.497682\pi$
$641$	9.33545			0.0145639			0.00728194	+	0.999973i	$0.497682\pi$
$642$	188.249	+	1024.58i	0.293222	+	1.59591i
$643$	288.014	−	288.014i	0.447923	−	0.447923i	−0.446741	−	0.894663i	$-0.647415\pi$
$643$	288.014	−	288.014i	0.447923	−	0.447923i	0.894663	+	0.446741i	$0.147415\pi$
$644$	−19.1655	−	50.3952i	−0.0297602	−	0.0782535i
$645$	−452.127	+	520.390i	−0.700972	+	0.806807i
$646$	228.062	−	330.731i	0.353038	−	0.511968i
$647$	812.608	+	812.608i	1.25596	+	1.25596i	0.953003	+	0.302960i	$0.0979749\pi$
$647$	812.608	+	812.608i	1.25596	+	1.25596i	0.302960	+	0.953003i	$0.402025\pi$
$648$	−650.071	+	394.210i	−1.00320	+	0.608349i
$649$	787.173	−	482.000i	1.21290	−	0.742681i
$650$	−416.677	−	208.281i	−0.641042	−	0.320432i
$651$	−196.016			−0.301100
$652$	116.272	−	258.982i	0.178331	−	0.397212i
$653$	−100.863	−	100.863i	−0.154460	−	0.154460i	0.625646	−	0.780107i	$-0.284835\pi$
$653$	−100.863	−	100.863i	−0.154460	−	0.154460i	−0.780107	+	0.625646i	$0.784835\pi$
$654$	−661.565	+	959.388i	−1.01157	+	1.46695i
$655$	790.582	−	909.946i	1.20700	−	1.38923i
$656$	−395.122	−	444.348i	−0.602321	−	0.677360i
$657$	−653.880	−	653.880i	−0.995251	−	0.995251i
$658$	−152.007	+	27.9288i	−0.231014	+	0.0424449i
$659$			71.8407i			0.109015i	0.998513	+	0.0545073i	$0.0173588\pi$
$659$			71.8407i			0.109015i	−0.998513	+	0.0545073i	$0.982641\pi$
$660$	−732.116	−	487.946i	−1.10927	−	0.739313i
$661$	−243.935			−0.369039			−0.184520	−	0.982829i	$-0.559073\pi$
$661$	−243.935			−0.369039			−0.184520	+	0.982829i	$0.559073\pi$
$662$	7.29822	+	39.7219i	0.0110245	+	0.0600028i
$663$	−185.401	+	185.401i	−0.279640	+	0.279640i
$664$	714.461	+	175.051i	1.07599	+	0.263631i
$665$	204.212	−	14.3341i	0.307085	−	0.0215551i
$666$	7.21091	+	4.97242i	0.0108272	+	0.00746610i
$667$	60.4752	−	60.4752i	0.0906675	−	0.0906675i
$668$	327.126	−	728.637i	0.489709	−	1.09077i
$669$		−	1578.12i		−	2.35892i
$670$	54.1397	−	13.9271i	0.0808055	−	0.0207867i
$671$	46.4377	+	75.8393i	0.0692068	+	0.113024i
$672$	144.756	+	112.872i	0.215411	+	0.167964i
$673$	−599.461	+	599.461i	−0.890730	+	0.890730i	−0.994592	−	0.103862i	$-0.966880\pi$
$673$	−599.461	+	599.461i	−0.890730	+	0.890730i	0.103862	+	0.994592i	$0.466880\pi$
$674$	881.761	+	608.036i	1.30825	+	0.902130i
$675$	−120.644	+	160.277i	−0.178732	+	0.237447i
$676$	116.877	+	307.325i	0.172895	+	0.454623i
$677$	−204.115	−	204.115i	−0.301500	−	0.301500i	0.540101	−	0.841600i	$-0.318386\pi$
$677$	−204.115	−	204.115i	−0.301500	−	0.301500i	−0.841600	+	0.540101i	$0.818386\pi$
$678$	−44.0579	+	8.09491i	−0.0649822	+	0.0119394i
$679$		−	127.427i		−	0.187668i
$680$	229.877	−	162.451i	0.338055	−	0.238898i
$681$		−	1136.86i		−	1.66940i
$682$	−501.968	−	559.632i	−0.736024	−	0.820575i
$683$	−247.722	+	247.722i	−0.362697	+	0.362697i	−0.864805	−	0.502108i	$-0.832558\pi$
$683$	−247.722	+	247.722i	−0.362697	+	0.362697i	0.502108	+	0.864805i	$0.332558\pi$
$684$	−746.350	+	283.841i	−1.09116	+	0.414972i
$685$	10.0273	+	142.855i	0.0146384	+	0.208547i
$686$	226.584	+	156.245i	0.330297	+	0.227763i
$687$	−886.635	−	886.635i	−1.29059	−	1.29059i
$688$	550.658	+	32.2899i	0.800375	+	0.0469331i
$689$	873.508			1.26779
$690$	323.569	+	191.159i	0.468941	+	0.277042i
$691$		−	758.275i		−	1.09736i	−0.836033	−	0.548679i	$-0.815131\pi$
$691$		−	758.275i		−	1.09736i	0.836033	−	0.548679i	$-0.184869\pi$
$692$	−198.924	+	443.083i	−0.287463	+	0.640293i
$693$	−107.285	−	25.7968i	−0.154813	−	0.0372248i
$694$	377.417	−	547.322i	0.543829	−	0.788649i
$695$	312.328	+	271.358i	0.449393	+	0.390443i
$696$	−69.2910	+	282.807i	−0.0995561	+	0.406332i
$697$	−184.925	+	184.925i	−0.265316	+	0.265316i
$698$	463.671	−	85.1917i	0.664285	−	0.122051i
$699$		−	1515.02i		−	2.16740i
$700$	137.777	+	39.8914i	0.196824	+	0.0569878i
$701$		−	357.402i		−	0.509845i	−0.966961	−	0.254923i	$-0.917950\pi$
$701$		−	357.402i		−	0.509845i	0.966961	−	0.254923i	$-0.0820500\pi$
$702$	−147.059	+	27.0195i	−0.209485	+	0.0384894i
$703$	−12.6398	−	12.6398i	−0.0179798	−	0.0179798i
$704$	48.4464	+	702.331i	0.0688159	+	0.997629i
$705$	706.544	−	813.220i	1.00219	−	1.15350i
$706$	856.220	+	590.424i	1.21278	+	0.836294i
$707$	−164.858	−	164.858i	−0.233179	−	0.233179i
$708$	549.769	−	1224.55i	0.776511	−	1.72959i
$709$		−	1138.96i		−	1.60643i	−0.595687	−	0.803217i	$-0.703120\pi$
$709$		−	1138.96i		−	1.60643i	0.595687	−	0.803217i	$-0.296880\pi$
$710$	−367.256	−	216.968i	−0.517262	−	0.305589i
$711$	290.038			0.407930
$712$	−519.171	−	856.138i	−0.729173	−	1.20244i
$713$	227.067	+	227.067i	0.318466	+	0.318466i
$714$	45.8313	−	66.4636i	0.0641895	−	0.0930863i
$715$	−297.525	−	417.192i	−0.416119	−	0.583486i
$716$	301.426	−	114.634i	0.420986	−	0.160103i
$717$	1230.53	+	1230.53i	1.71622	+	1.71622i
$718$	−85.1449	−	463.416i	−0.118586	−	0.645426i
$719$	212.648			0.295755			0.147877	−	0.989006i	$-0.452756\pi$
$719$	212.648			0.295755			0.147877	+	0.989006i	$0.452756\pi$
$720$	−559.444	+	6.43716i	−0.777005	+	0.00894050i
$721$			33.8237i			0.0469122i
$722$	892.621	−	164.004i	1.23632	−	0.227153i
$723$	113.805	+	113.805i	0.157407	+	0.157407i
$724$	−584.103	+	222.137i	−0.806772	+	0.306819i
$725$	31.7844	+	225.293i	0.0438405	+	0.310749i
$726$	−459.876	−	851.562i	−0.633438	−	1.17295i
$727$	−224.546	−	224.546i	−0.308867	−	0.308867i	0.535603	−	0.844470i	$-0.320084\pi$
$727$	−224.546	−	224.546i	−0.308867	−	0.308867i	−0.844470	+	0.535603i	$0.820084\pi$
$728$	55.4337	+	91.4128i	0.0761452	+	0.125567i
$729$		−	375.792i		−	0.515490i
$730$	329.418	+	1280.57i	0.451258	+	1.75421i
$731$		−	242.607i		−	0.331883i
$732$	117.978	+	52.9669i	0.161172	+	0.0723592i
$733$	239.656	−	239.656i	0.326952	−	0.326952i	−0.524474	−	0.851426i	$-0.675738\pi$
$733$	239.656	−	239.656i	0.326952	−	0.326952i	0.851426	+	0.524474i	$0.175738\pi$
$734$	−524.186	−	361.463i	−0.714149	−	0.492456i
$735$	−936.358	+	65.7253i	−1.27396	+	0.0894222i
$736$	−36.9350	−	298.438i	−0.0501834	−	0.405486i
$737$	59.7885	+	14.3762i	0.0811241	+	0.0195064i
$738$	511.248	−	93.9332i	0.692748	−	0.127281i
$739$		−	1042.68i		−	1.41093i	−0.708746	−	0.705464i	$-0.750739\pi$
$739$		−	1042.68i		−	1.41093i	0.708746	−	0.705464i	$-0.249261\pi$
$740$	−5.26087	−	11.3662i	−0.00710928	−	0.0153597i
$741$	−1063.54			−1.43527
$742$	−264.536	+	48.6040i	−0.356517	+	0.0655040i
$743$	−700.774	−	700.774i	−0.943168	−	0.943168i	0.0553017	−	0.998470i	$-0.482388\pi$
$743$	−700.774	−	700.774i	−0.943168	−	0.943168i	−0.998470	+	0.0553017i	$0.982388\pi$
$744$	−1061.86	−	260.167i	−1.42723	−	0.349687i
$745$	−537.744	+	618.935i	−0.721805	+	0.830785i
$746$	−439.126	+	636.812i	−0.588641	+	0.853635i
$747$	−454.703	+	454.703i	−0.608705	+	0.608705i
$748$	307.123	−	39.3536i	0.410592	−	0.0526118i
$749$		−	186.814i		−	0.249418i
$750$	−923.983	+	381.904i	−1.23198	+	0.509205i
$751$			1246.38i			1.65962i	0.558043	+	0.829812i	$0.311552\pi$
$751$			1246.38i			1.65962i	−0.558043	+	0.829812i	$0.688448\pi$
$752$	−860.520	−	50.4599i	−1.14431	−	0.0671009i
$753$	−184.201	−	184.201i	−0.244622	−	0.244622i
$754$	−96.2688	+	139.607i	−0.127677	+	0.185155i
$755$	71.2961	−	82.0606i	0.0944319	−	0.108690i
$756$	43.0322	−	16.3654i	0.0569209	−	0.0216473i
$757$	−8.03843	+	8.03843i	−0.0106188	+	0.0106188i	−0.712396	−	0.701777i	$-0.752390\pi$
$757$	−8.03843	+	8.03843i	−0.0106188	+	0.0106188i	0.701777	+	0.712396i	$0.252390\pi$
$758$	−142.444	+	26.1718i	−0.187921	+	0.0345274i
$759$	215.876	+	352.557i	0.284422	+	0.464501i
$760$	1125.28	+	193.394i	1.48063	+	0.254466i
$761$		−	1214.85i		−	1.59639i	−0.602402	−	0.798193i	$-0.705790\pi$
$761$		−	1214.85i		−	1.59639i	0.602402	−	0.798193i	$-0.294210\pi$
$762$	−143.941	−	783.424i	−0.188899	−	1.02811i
$763$	147.776	−	147.776i	0.193678	−	0.193678i
$764$	−199.654	−	524.984i	−0.261327	−	0.687152i
$765$	17.2300	+	245.467i	0.0225228	+	0.320872i
$766$	−724.230	+	1050.26i	−0.945469	+	1.37110i
$767$	552.795	−	552.795i	0.720723	−	0.720723i
$768$	634.359	+	803.579i	0.825988	+	1.04633i
$769$	−538.046			−0.699670			−0.349835	−	0.936811i	$-0.613762\pi$
$769$	−538.046			−0.699670			−0.349835	+	0.936811i	$0.613762\pi$
$770$	113.317	+	109.789i	0.147165	+	0.142583i
$771$			1609.27i			2.08725i
$772$	319.186	−	710.953i	0.413454	−	0.920923i

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96707 + 0.361417i) q^{2} +(-2.82785 + 2.82785i) q^{3} +(3.73876 - 1.42187i) q^{4} +(3.27930 - 3.77442i) q^{5} +(4.54056 - 6.58463i) q^{6} +(-1.01424 + 1.01424i) q^{7} +(-6.84052 + 4.14816i) q^{8} -6.99351i q^{9} +(-5.08648 + 8.60974i) q^{10} +(-9.38106 + 5.74419i) q^{11} +(-6.55182 + 14.5935i) q^{12} +(-6.58788 + 6.58788i) q^{13} +(1.62853 - 2.36166i) q^{14} +(1.40012 + 19.9469i) q^{15} +(11.9566 - 10.6320i) q^{16} +(-4.97600 - 4.97600i) q^{17} +(2.52757 + 13.7567i) q^{18} -28.5444i q^{19} +(6.89378 - 18.7743i) q^{20} -5.73627i q^{21} +(16.3772 - 14.6897i) q^{22} +(-6.64492 + 6.64492i) q^{23} +(7.61359 - 31.0744i) q^{24} +(-3.49242 - 24.7549i) q^{25} +(10.5779 - 15.3398i) q^{26} +(-5.67406 - 5.67406i) q^{27} +(-2.34989 + 5.23413i) q^{28} -9.10097 q^{29} +(-9.96327 - 38.7309i) q^{30} -34.1714i q^{31} +(-19.6769 + 25.2353i) q^{32} +(10.2846 - 42.7720i) q^{33} +(11.5866 + 7.98975i) q^{34} +(0.502170 + 7.15418i) q^{35} +(-9.94383 - 26.1470i) q^{36} +(0.442813 - 0.442813i) q^{37} +(10.3164 + 56.1489i) q^{38} -37.2591i q^{39} +(-6.77521 + 39.4220i) q^{40} -37.1634i q^{41} +(2.07318 + 11.2837i) q^{42} +(24.3777 + 24.3777i) q^{43} +(-26.9060 + 34.8147i) q^{44} +(-26.3964 - 22.9338i) q^{45} +(10.6695 - 15.4726i) q^{46} +(-38.0953 - 38.0953i) q^{47} +(-3.74569 + 63.8773i) q^{48} +46.9426i q^{49} +(15.8167 + 47.4324i) q^{50} +28.1428 q^{51} +(-15.2634 + 33.9975i) q^{52} +(-66.2966 - 66.2966i) q^{53} +(13.2120 + 9.11060i) q^{54} +(-9.08235 + 54.2449i) q^{55} +(2.73071 - 11.1452i) q^{56} +(80.7193 + 80.7193i) q^{57} +(17.9023 - 3.28924i) q^{58} -83.9109 q^{59} +(33.5965 + 72.5857i) q^{60} -8.08430i q^{61} +(12.3501 + 67.2177i) q^{62} +(7.09312 + 7.09312i) q^{63} +(29.5855 - 56.7512i) q^{64} +(3.26177 + 46.4690i) q^{65} +(-4.77196 + 87.8526i) q^{66} +(-3.95289 - 3.95289i) q^{67} +(-25.6793 - 11.5288i) q^{68} -37.5817i q^{69} +(-3.57345 - 13.8913i) q^{70} +42.6559i q^{71} +(29.0102 + 47.8392i) q^{72} +(93.4981 - 93.4981i) q^{73} +(-0.711006 + 1.03109i) q^{74} +(79.8792 + 60.1271i) q^{75} +(-40.5863 - 106.720i) q^{76} +(3.68868 - 15.3407i) q^{77} +(13.4661 + 73.2914i) q^{78} +41.4724i q^{79} +(-0.920447 - 79.9947i) q^{80} +95.0324 q^{81} +(13.4315 + 73.1032i) q^{82} +(-65.0178 - 65.0178i) q^{83} +(-8.15620 - 21.4465i) q^{84} +(-35.0993 + 2.46371i) q^{85} +(-56.7632 - 39.1422i) q^{86} +(25.7362 - 25.7362i) q^{87} +(40.3435 - 78.2074i) q^{88} +125.157i q^{89} +(60.2123 + 35.5724i) q^{90} -13.3634i q^{91} +(-15.3956 + 34.2919i) q^{92} +(96.6318 + 96.6318i) q^{93} +(88.7045 + 61.1680i) q^{94} +(-107.738 - 93.6055i) q^{95} +(-15.7183 - 127.005i) q^{96} +(-62.8186 + 62.8186i) q^{97} +(-16.9658 - 92.3396i) q^{98} +(40.1720 + 65.6065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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