LMFDB - Embedded newform 560.2.cp.a.221.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(221,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 0, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("560.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cp (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			221.35
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0501251 + 1.41332i) q^{2} +(-1.30306 + 0.349155i) q^{3} +(-1.99497 + 0.141686i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-0.558786 - 1.82415i) q^{6} +(-2.53265 - 0.765294i) q^{7} +(-0.300247 - 2.81245i) q^{8} +(-1.02201 + 0.590057i) q^{9} +(0.317378 - 1.37814i) q^{10} +(0.0713321 + 0.266215i) q^{11} +(2.55011 - 0.881182i) q^{12} +(3.65921 + 3.65921i) q^{13} +(0.954660 - 3.61782i) q^{14} +1.34903 q^{15} +(3.95985 - 0.565321i) q^{16} +(-0.198682 + 0.344128i) q^{17} +(-0.885170 - 1.41485i) q^{18} +(2.16124 - 8.06586i) q^{19} +(1.96367 + 0.379479i) q^{20} +(3.56741 + 0.112939i) q^{21} +(-0.372673 + 0.114160i) q^{22} +(6.57451 - 3.79580i) q^{23} +(1.37322 + 3.55997i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-4.98824 + 5.35507i) q^{26} +(3.98745 - 3.98745i) q^{27} +(5.16101 + 1.16790i) q^{28} +(-3.37606 - 3.37606i) q^{29} +(0.0676204 + 1.90662i) q^{30} +(1.64452 - 2.84839i) q^{31} +(0.997470 + 5.56822i) q^{32} +(-0.185901 - 0.321989i) q^{33} +(-0.496324 - 0.263553i) q^{34} +(2.24828 + 1.39472i) q^{35} +(1.95528 - 1.32195i) q^{36} +(-5.36615 - 1.43786i) q^{37} +(11.5080 + 2.65023i) q^{38} +(-6.04582 - 3.49056i) q^{39} +(-0.437898 + 2.79432i) q^{40} +2.43623i q^{41} +(0.0191971 + 5.04758i) q^{42} +(-7.54379 + 7.54379i) q^{43} +(-0.180025 - 0.520986i) q^{44} +(1.13990 - 0.305436i) q^{45} +(5.69424 + 9.10166i) q^{46} +(1.76492 + 3.05693i) q^{47} +(-4.96256 + 2.11925i) q^{48} +(5.82865 + 3.87645i) q^{49} +(-0.663253 + 1.24904i) q^{50} +(0.138742 - 0.517792i) q^{51} +(-7.81850 - 6.78158i) q^{52} +(-1.62746 - 6.07377i) q^{53} +(5.83543 + 5.43569i) q^{54} -0.275606i q^{55} +(-1.39193 + 7.35272i) q^{56} +11.2650i q^{57} +(4.60225 - 4.94070i) q^{58} +(-3.44989 - 12.8752i) q^{59} +(-2.69128 + 0.191139i) q^{60} +(3.04696 - 11.3714i) q^{61} +(4.10813 + 2.18146i) q^{62} +(3.03996 - 0.712271i) q^{63} +(-7.81970 + 1.68886i) q^{64} +(-2.58745 - 4.48160i) q^{65} +(0.445757 - 0.278878i) q^{66} +(-5.09314 + 1.36470i) q^{67} +(0.347608 - 0.714677i) q^{68} +(-7.24169 + 7.24169i) q^{69} +(-1.85849 + 3.24746i) q^{70} -16.2287i q^{71} +(1.96636 + 2.69718i) q^{72} +(12.2350 + 7.06390i) q^{73} +(1.76318 - 7.65619i) q^{74} +(-1.30306 - 0.349155i) q^{75} +(-3.16880 + 16.3974i) q^{76} +(0.0230734 - 0.728820i) q^{77} +(4.63024 - 8.71967i) q^{78} +(-0.230789 - 0.399739i) q^{79} +(-3.97124 - 0.478827i) q^{80} +(-2.03350 + 3.52212i) q^{81} +(-3.44318 + 0.122116i) q^{82} +(4.17682 + 4.17682i) q^{83} +(-7.13291 + 0.280142i) q^{84} +(0.280979 - 0.280979i) q^{85} +(-11.0400 - 10.2837i) q^{86} +(5.57800 + 3.22046i) q^{87} +(0.727298 - 0.280548i) q^{88} +(-9.76496 + 5.63780i) q^{89} +(0.488818 + 1.59574i) q^{90} +(-6.46714 - 12.0679i) q^{91} +(-12.5782 + 8.50404i) q^{92} +(-1.14838 + 4.28583i) q^{93} +(-4.23197 + 2.64764i) q^{94} +(-4.17520 + 7.23166i) q^{95} +(-3.24394 - 6.90748i) q^{96} +11.6863 q^{97} +(-5.18652 + 8.43208i) q^{98} +(-0.229984 - 0.229984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.0501251	+	1.41332i	0.0354438	+	0.999372i
$2$	0.0501251	+	1.41332i	0.0354438	+	0.999372i
$3$	−1.30306	+	0.349155i	−0.752325	+	0.201585i	−0.614549	−	0.788879i	$-0.710662\pi$
$3$	−1.30306	+	0.349155i	−0.752325	+	0.201585i	−0.137776	+	0.990463i	$0.543995\pi$
$4$	−1.99497	+	0.141686i	−0.997487	+	0.0708431i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	−0.558786	−	1.82415i	−0.228123	−	0.744707i
$7$	−2.53265	−	0.765294i	−0.957252	−	0.289254i
$7$	−2.53265	−	0.765294i	−0.957252	−	0.289254i
$8$	−0.300247	−	2.81245i	−0.106153	−	0.994350i
$9$	−1.02201	+	0.590057i	−0.340669	+	0.196686i
$10$	0.317378	−	1.37814i	0.100364	−	0.435806i
$11$	0.0713321	+	0.266215i	0.0215074	+	0.0802669i	0.975845	−	0.218462i	$-0.0701040\pi$
$11$	0.0713321	+	0.266215i	0.0215074	+	0.0802669i	−0.954338	+	0.298729i	$0.903437\pi$
$12$	2.55011	−	0.881182i	0.736154	−	0.254375i
$13$	3.65921	+	3.65921i	1.01488	+	1.01488i	0.999888	+	0.0149951i	$0.00477328\pi$
$13$	3.65921	+	3.65921i	1.01488	+	1.01488i	0.0149951	+	0.999888i	$0.495227\pi$
$14$	0.954660	−	3.61782i	0.255144	−	0.966903i
$15$	1.34903			0.348318
$16$	3.95985	−	0.565321i	0.989963	−	0.141330i
$17$	−0.198682	+	0.344128i	−0.0481876	+	0.0834633i	−0.889113	−	0.457687i	$-0.848678\pi$
$17$	−0.198682	+	0.344128i	−0.0481876	+	0.0834633i	0.840926	+	0.541151i	$0.182011\pi$
$18$	−0.885170	−	1.41485i	−0.208637	−	0.333484i
$19$	2.16124	−	8.06586i	0.495823	−	1.85044i	−0.0295487	−	0.999563i	$-0.509407\pi$
$19$	2.16124	−	8.06586i	0.495823	−	1.85044i	0.525372	−	0.850873i	$-0.323926\pi$
$20$	1.96367	+	0.379479i	0.439090	+	0.0848541i
$21$	3.56741	+	0.112939i	0.778474	+	0.0246454i
$22$	−0.372673	+	0.114160i	−0.0794541	+	0.0243389i
$23$	6.57451	−	3.79580i	1.37088	−	0.791478i	0.379842	−	0.925051i	$-0.375978\pi$
$23$	6.57451	−	3.79580i	1.37088	−	0.791478i	0.991039	+	0.133573i	$0.0426451\pi$
$24$	1.37322	+	3.55997i	0.280308	+	0.726675i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−4.98824	+	5.35507i	−0.978274	+	1.05022i
$27$	3.98745	−	3.98745i	0.767385	−	0.767385i
$28$	5.16101	+	1.16790i	0.975339	+	0.220712i
$29$	−3.37606	−	3.37606i	−0.626919	−	0.626919i	0.320372	−	0.947292i	$-0.396192\pi$
$29$	−3.37606	−	3.37606i	−0.626919	−	0.626919i	−0.947292	+	0.320372i	$0.896192\pi$
$30$	0.0676204	+	1.90662i	0.0123457	+	0.348100i
$31$	1.64452	−	2.84839i	0.295364	−	0.511586i	−0.679705	−	0.733485i	$-0.737892\pi$
$31$	1.64452	−	2.84839i	0.295364	−	0.511586i	0.975070	+	0.221899i	$0.0712257\pi$
$32$	0.997470	+	5.56822i	0.176329	+	0.984331i
$33$	−0.185901	−	0.321989i	−0.0323612	−	0.0560512i
$34$	−0.496324	−	0.263553i	−0.0851188	−	0.0451990i
$35$	2.24828	+	1.39472i	0.380029	+	0.235750i
$36$	1.95528	−	1.32195i	0.325880	−	0.220326i
$37$	−5.36615	−	1.43786i	−0.882190	−	0.236382i	−0.210838	−	0.977521i	$-0.567619\pi$
$37$	−5.36615	−	1.43786i	−0.882190	−	0.236382i	−0.671352	+	0.741139i	$0.734286\pi$
$38$	11.5080	+	2.65023i	1.86685	+	0.429925i
$39$	−6.04582	−	3.49056i	−0.968106	−	0.558936i
$40$	−0.437898	+	2.79432i	−0.0692378	+	0.441821i
$41$			2.43623i			0.380475i	0.981738	+	0.190238i	$0.0609258\pi$
$41$			2.43623i			0.380475i	−0.981738	+	0.190238i	$0.939074\pi$
$42$	0.0191971	+	5.04758i	0.00296218	+	0.778858i
$43$	−7.54379	+	7.54379i	−1.15042	+	1.15042i	−0.163948	+	0.986469i	$0.552423\pi$
$43$	−7.54379	+	7.54379i	−1.15042	+	1.15042i	−0.986469	+	0.163948i	$0.947577\pi$
$44$	−0.180025	−	0.520986i	−0.0271398	−	0.0785415i
$45$	1.13990	−	0.305436i	0.169927	−	0.0455317i
$46$	5.69424	+	9.10166i	0.839570	+	1.34197i
$47$	1.76492	+	3.05693i	0.257440	+	0.445899i	0.965555	−	0.260197i	$-0.0837877\pi$
$47$	1.76492	+	3.05693i	0.257440	+	0.445899i	−0.708115	+	0.706097i	$0.750454\pi$
$48$	−4.96256	+	2.11925i	−0.716283	+	0.305888i
$49$	5.82865	+	3.87645i	0.832664	+	0.553778i
$50$	−0.663253	+	1.24904i	−0.0937981	+	0.176641i
$51$	0.138742	−	0.517792i	0.0194278	−	0.0725054i
$52$	−7.81850	−	6.78158i	−1.08423	−	0.940435i
$53$	−1.62746	−	6.07377i	−0.223549	−	0.834296i	−0.982981	−	0.183709i	$-0.941190\pi$
$53$	−1.62746	−	6.07377i	−0.223549	−	0.834296i	0.759432	−	0.650587i	$-0.225477\pi$
$54$	5.83543	+	5.43569i	0.794102	+	0.739704i
$55$		−	0.275606i		−	0.0371627i
$56$	−1.39193	+	7.35272i	−0.186004	+	0.982549i
$57$			11.2650i			1.49208i
$58$	4.60225	−	4.94070i	0.604305	−	0.648746i
$59$	−3.44989	−	12.8752i	−0.449138	−	1.67621i	−0.704774	−	0.709432i	$-0.748951\pi$
$59$	−3.44989	−	12.8752i	−0.449138	−	1.67621i	0.255636	−	0.966773i	$-0.417715\pi$
$60$	−2.69128	+	0.191139i	−0.347443	+	0.0246760i
$61$	3.04696	−	11.3714i	0.390124	−	1.45596i	−0.439805	−	0.898093i	$-0.644953\pi$
$61$	3.04696	−	11.3714i	0.390124	−	1.45596i	0.829929	−	0.557869i	$-0.188381\pi$
$62$	4.10813	+	2.18146i	0.521733	+	0.277046i
$63$	3.03996	−	0.712271i	0.382999	−	0.0897378i
$64$	−7.81970	+	1.68886i	−0.977463	+	0.211107i
$65$	−2.58745	−	4.48160i	−0.320934	−	0.555874i
$66$	0.445757	−	0.278878i	0.0548690	−	0.0343275i
$67$	−5.09314	+	1.36470i	−0.622226	+	0.166725i	−0.556140	−	0.831089i	$-0.687718\pi$
$67$	−5.09314	+	1.36470i	−0.622226	+	0.166725i	−0.0660865	+	0.997814i	$0.521051\pi$
$68$	0.347608	−	0.714677i	0.0421537	−	0.0866674i
$69$	−7.24169	+	7.24169i	−0.871797	+	0.871797i
$70$	−1.85849	+	3.24746i	−0.222132	+	0.388146i
$71$		−	16.2287i		−	1.92600i	−0.269506	−	0.962999i	$-0.586860\pi$
$71$		−	16.2287i		−	1.92600i	0.269506	−	0.962999i	$-0.413140\pi$
$72$	1.96636	+	2.69718i	0.231737	+	0.317866i
$73$	12.2350	+	7.06390i	1.43200	+	0.826767i	0.997273	−	0.0737948i	$-0.0235110\pi$
$73$	12.2350	+	7.06390i	1.43200	+	0.826767i	0.434729	+	0.900562i	$0.356844\pi$
$74$	1.76318	−	7.65619i	0.204965	−	0.890014i
$75$	−1.30306	−	0.349155i	−0.150465	−	0.0403170i
$76$	−3.16880	+	16.3974i	−0.363486	+	1.88091i
$77$	0.0230734	−	0.728820i	0.00262946	−	0.0830568i
$78$	4.63024	−	8.71967i	0.524272	−	0.987309i
$79$	−0.230789	−	0.399739i	−0.0259658	−	0.0449741i	0.852750	−	0.522318i	$-0.174933\pi$
$79$	−0.230789	−	0.399739i	−0.0259658	−	0.0449741i	−0.878716	+	0.477344i	$0.841599\pi$
$80$	−3.97124	−	0.478827i	−0.443998	−	0.0535344i
$81$	−2.03350	+	3.52212i	−0.225944	+	0.391346i
$82$	−3.44318	+	0.122116i	−0.380236	+	0.0134855i
$83$	4.17682	+	4.17682i	0.458465	+	0.458465i	0.898151	−	0.439686i	$-0.144910\pi$
$83$	4.17682	+	4.17682i	0.458465	+	0.458465i	−0.439686	+	0.898151i	$0.644910\pi$
$84$	−7.13291	+	0.280142i	−0.778264	+	0.0305660i
$85$	0.280979	−	0.280979i	0.0304765	−	0.0304765i
$86$	−11.0400	−	10.2837i	−1.19047	−	1.10892i
$87$	5.57800	+	3.22046i	0.598024	+	0.345269i
$88$	0.727298	−	0.280548i	0.0775303	−	0.0299065i
$89$	−9.76496	+	5.63780i	−1.03508	+	0.597606i	−0.918437	−	0.395568i	$-0.870548\pi$
$89$	−9.76496	+	5.63780i	−1.03508	+	0.597606i	−0.116647	+	0.993173i	$0.537214\pi$
$90$	0.488818	+	1.59574i	0.0515259	+	0.168206i
$91$	−6.46714	−	12.0679i	−0.677940	−	1.26506i
$92$	−12.5782	+	8.50404i	−1.31137	+	0.886607i
$93$	−1.14838	+	4.28583i	−0.119082	+	0.444420i
$94$	−4.23197	+	2.64764i	−0.436495	+	0.273083i
$95$	−4.17520	+	7.23166i	−0.428366	+	0.741952i
$96$	−3.24394	−	6.90748i	−0.331083	−	0.704991i
$97$	11.6863			1.18656			0.593282	−	0.804995i	$-0.297832\pi$
$97$	11.6863			1.18656			0.593282	+	0.804995i	$0.297832\pi$
$98$	−5.18652	+	8.43208i	−0.523917	+	0.851769i
$99$	−0.229984	−	0.229984i	−0.0231143	−	0.0231143i
$100$	−1.79854	−	0.874784i	−0.179854	−	0.0874784i
$101$	−1.16881	−	4.36207i	−0.116301	−	0.434042i	0.883080	−	0.469223i	$-0.155466\pi$
$101$	−1.16881	−	4.36207i	−0.116301	−	0.434042i	−0.999381	+	0.0351809i	$0.988799\pi$
$102$	0.738763	+	0.170133i	0.0731484	+	0.0168457i
$103$	4.86363	−	2.80802i	0.479228	−	0.276682i	−0.240867	−	0.970558i	$-0.577432\pi$
$103$	4.86363	−	2.80802i	0.479228	−	0.276682i	0.720095	+	0.693876i	$0.244098\pi$
$104$	9.19267	−	11.3900i	0.901415	−	1.11688i
$105$	−3.41663	−	1.03241i	−0.333429	−	0.100753i
$106$	8.50263	−	2.60458i	0.825848	−	0.252979i
$107$	−14.4951	−	3.88394i	−1.40129	−	0.375475i	−0.522483	−	0.852650i	$-0.674994\pi$
$107$	−14.4951	−	3.88394i	−1.40129	−	0.375475i	−0.878808	+	0.477175i	$0.841661\pi$
$108$	−7.38990	+	8.51983i	−0.711093	+	0.819821i
$109$	−6.67256	+	1.78791i	−0.639115	+	0.171250i	−0.563803	−	0.825910i	$-0.690662\pi$
$109$	−6.67256	+	1.78791i	−0.639115	+	0.171250i	−0.0753126	+	0.997160i	$0.523995\pi$
$110$	0.389521	−	0.0138148i	0.0371394	−	0.00131719i
$111$	7.49448			0.711344
$112$	−10.4616	−	1.59869i	−0.988524	−	0.151062i
$113$	−5.02096			−0.472332			−0.236166	−	0.971713i	$-0.575891\pi$
$113$	−5.02096			−0.472332			−0.236166	+	0.971713i	$0.575891\pi$
$114$	−15.9210	+	0.564657i	−1.49114	+	0.0528850i
$115$	−7.33292	+	1.96485i	−0.683798	+	0.183223i
$116$	7.21350	+	6.25682i	0.669757	+	0.580931i
$117$	−5.89889	−	1.58060i	−0.545352	−	0.146127i
$118$	18.0239	−	5.52119i	1.65923	−	0.508267i
$119$	0.766553	−	0.719506i	0.0702698	−	0.0659570i
$120$	−0.405043	−	3.79408i	−0.0369752	−	0.346350i
$121$	9.46050	−	5.46202i	0.860045	−	0.496547i
$122$	16.2243	+	3.73636i	1.46887	+	0.338274i
$123$	−0.850622	−	3.17456i	−0.0766980	−	0.286241i
$124$	−2.87720	+	5.91547i	−0.258380	+	0.531225i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	1.15905	+	4.26075i	0.103256	+	0.379577i
$127$	4.87757			0.432814			0.216407	−	0.976303i	$-0.430566\pi$
$127$	4.87757			0.432814			0.216407	+	0.976303i	$0.430566\pi$
$128$	−2.77887	−	10.9671i	−0.245619	−	0.969366i
$129$	7.19609	−	12.4640i	0.633581	−	1.09739i
$130$	6.20426	−	3.88155i	0.544150	−	0.340435i
$131$	0.0512852	−	0.191399i	0.00448081	−	0.0167226i	−0.963649	−	0.267171i	$-0.913911\pi$
$131$	0.0512852	−	0.191399i	0.00448081	−	0.0167226i	0.968130	+	0.250448i	$0.0805779\pi$
$132$	0.416489	+	0.616021i	0.0362507	+	0.0536178i
$133$	−11.6464	+	18.7740i	−1.00987	+	1.62792i
$134$	−2.18406	−	7.12986i	−0.188674	−	0.615926i
$135$	−4.88361	+	2.81955i	−0.420314	+	0.242668i
$136$	1.02750	+	0.455460i	0.0881070	+	0.0390554i
$137$	−4.83556	−	2.79181i	−0.413129	−	0.238520i	0.279004	−	0.960290i	$-0.409996\pi$
$137$	−4.83556	−	2.79181i	−0.413129	−	0.238520i	−0.692133	+	0.721770i	$0.743329\pi$
$138$	−10.5979	−	9.87187i	−0.902149	−	0.840350i
$139$	2.27521	−	2.27521i	0.192980	−	0.192980i	−0.604002	−	0.796983i	$-0.706428\pi$
$139$	2.27521	−	2.27521i	0.192980	−	0.192980i	0.796983	+	0.604002i	$0.206428\pi$
$140$	−4.68288	−	2.46387i	−0.395775	−	0.208235i
$141$	−3.36715	−	3.36715i	−0.283565	−	0.283565i
$142$	22.9365	−	0.813468i	1.92479	−	0.0682647i
$143$	−0.713118	+	1.23516i	−0.0596339	+	0.103289i
$144$	−3.71343	+	2.91430i	−0.309452	+	0.242858i
$145$	2.38724	+	4.13482i	0.198249	+	0.343378i
$146$	−9.37030	+	17.6462i	−0.775492	+	1.46041i
$147$	−8.94859	−	3.01616i	−0.738067	−	0.248768i
$148$	10.9091	+	2.10818i	0.896719	+	0.173291i
$149$	14.4340	+	3.86757i	1.18248	+	0.316843i	0.795908	−	0.605418i	$-0.206994\pi$
$149$	14.4340	+	3.86757i	1.18248	+	0.316843i	0.386568	+	0.922261i	$0.373661\pi$
$150$	0.428153	−	1.85916i	0.0349586	−	0.151799i
$151$	−5.73152	−	3.30910i	−0.466425	−	0.269290i	0.248317	−	0.968679i	$-0.420122\pi$
$151$	−5.73152	−	3.30910i	−0.466425	−	0.269290i	−0.714742	+	0.699388i	$0.753456\pi$
$152$	−23.3337	−	3.65662i	−1.89261	−	0.296591i
$153$		−	0.468936i		−	0.0379112i
$154$	1.03122	−	0.00392196i	0.0830978	−	0.000316041i
$155$	−2.32570	+	2.32570i	−0.186805	+	0.186805i
$156$	12.5558	+	6.10696i	1.00527	+	0.488948i
$157$	12.0001	−	3.21543i	0.957715	−	0.256619i	0.254082	−	0.967183i	$-0.418227\pi$
$157$	12.0001	−	3.21543i	0.957715	−	0.256619i	0.703633	+	0.710564i	$0.251560\pi$
$158$	0.553392	−	0.346217i	0.0440255	−	0.0275436i
$159$	4.24137	+	7.34627i	0.336363	+	0.582597i
$160$	0.477679	−	5.63665i	0.0377638	−	0.445616i
$161$	−19.5559	+	4.58200i	−1.54122	+	0.361112i
$162$	−5.07983	−	2.69744i	−0.399109	−	0.211931i
$163$	5.00838	−	18.6915i	0.392287	−	1.46403i	−0.434066	−	0.900881i	$-0.642921\pi$
$163$	5.00838	−	18.6915i	0.392287	−	1.46403i	0.826352	−	0.563153i	$-0.190412\pi$
$164$	−0.345180	−	4.86022i	−0.0269540	−	0.379519i
$165$	0.0962293	+	0.359133i	0.00749144	+	0.0279584i
$166$	−5.69384	+	6.11256i	−0.441928	+	0.474427i
$167$		−	6.28773i		−	0.486559i	−0.969956	−	0.243280i	$-0.921777\pi$
$167$		−	6.28773i		−	0.486559i	0.969956	−	0.243280i	$-0.0782233\pi$
$168$	−0.753470	−	10.0671i	−0.0581315	−	0.776691i
$169$			13.7797i			1.05997i
$170$	0.411199	+	0.383031i	0.0315375	+	0.0293771i
$171$	2.55051	+	9.51864i	0.195042	+	0.727908i
$172$	13.9808	−	16.1185i	1.06603	−	1.22903i
$173$	5.78427	−	21.5872i	0.439770	−	1.64124i	−0.289618	−	0.957142i	$-0.593528\pi$
$173$	5.78427	−	21.5872i	0.439770	−	1.64124i	0.729388	−	0.684100i	$-0.239805\pi$
$174$	−4.27196	+	8.04495i	−0.323856	+	0.609886i
$175$	−1.81069	−	1.92909i	−0.136876	−	0.145825i
$176$	0.432961	+	1.01385i	0.0326357	+	0.0764215i
$177$	8.99087	+	15.5726i	0.675795	+	1.17051i
$178$	−8.45751	−	13.5185i	−0.633917	−	1.01325i
$179$	−6.88430	+	1.84464i	−0.514557	+	0.137875i	−0.506748	−	0.862094i	$-0.669152\pi$
$179$	−6.88430	+	1.84464i	−0.514557	+	0.137875i	−0.00780923	+	0.999970i	$0.502486\pi$
$180$	−2.23080	+	0.770845i	−0.166274	+	0.0574554i
$181$	8.19934	−	8.19934i	0.609452	−	0.609452i	−0.333351	−	0.942803i	$-0.608179\pi$
$181$	8.19934	−	8.19934i	0.609452	−	0.609452i	0.942803	+	0.333351i	$0.108179\pi$
$182$	16.7317	−	9.74507i	1.24023	−	0.722353i
$183$			15.8816i			1.17400i
$184$	−12.6495	−	17.3508i	−0.932530	−	1.27912i
$185$	4.81116	+	2.77772i	0.353724	+	0.204222i
$186$	−6.11483	−	1.40821i	−0.448361	−	0.103255i
$187$	−0.105785	−	0.0283449i	−0.00773573	−	0.00207278i
$188$	−3.95410	−	5.84844i	−0.288382	−	0.426541i
$189$	−13.1504	+	7.04725i	−0.956550	+	0.512612i
$190$	−10.4300	−	5.53842i	−0.756669	−	0.401800i
$191$	5.89951	+	10.2182i	0.426873	+	0.739366i	0.996593	−	0.0824725i	$-0.0262817\pi$
$191$	5.89951	+	10.2182i	0.426873	+	0.739366i	−0.569720	+	0.821839i	$0.692948\pi$
$192$	9.59991	−	4.93098i	0.692813	−	0.355863i
$193$	−4.34770	+	7.53044i	−0.312954	+	0.542053i	−0.979001	−	0.203858i	$-0.934652\pi$
$193$	−4.34770	+	7.53044i	−0.312954	+	0.542053i	0.666046	+	0.745911i	$0.267985\pi$
$194$	0.585777	+	16.5165i	0.0420563	+	1.18582i
$195$	4.93639	+	4.93639i	0.353502	+	0.353502i
$196$	−12.1772	−	6.90758i	−0.869804	−	0.493398i
$197$	1.87206	−	1.87206i	0.133379	−	0.133379i	−0.637265	−	0.770644i	$-0.719935\pi$
$197$	1.87206	−	1.87206i	0.133379	−	0.133379i	0.770644	+	0.637265i	$0.219935\pi$
$198$	0.313514	−	0.336570i	0.0222805	−	0.0239190i
$199$	−2.24100	−	1.29384i	−0.158861	−	0.0917182i	0.418462	−	0.908234i	$-0.362569\pi$
$199$	−2.24100	−	1.29384i	−0.158861	−	0.0917182i	−0.577323	+	0.816516i	$0.695903\pi$
$200$	1.14620	−	2.58577i	0.0810487	−	0.182842i
$201$	6.16020	−	3.55659i	0.434507	−	0.250863i
$202$	6.10643	−	1.87056i	0.429647	−	0.131612i
$203$	5.96671	+	11.1341i	0.418781	+	0.781459i
$204$	−0.203423	+	1.05264i	−0.0142424	+	0.0736995i
$205$	0.630542	−	2.35322i	0.0440390	−	0.164356i
$206$	4.21244	+	6.73314i	0.293494	+	0.469120i
$207$	−4.47947	+	7.75867i	−0.311345	+	0.539265i
$208$	16.5586	+	12.4213i	1.14813	+	0.861262i
$209$	2.30142			0.159193
$210$	1.28787	−	4.88055i	0.0888712	−	0.336790i
$211$	17.2689	+	17.2689i	1.18884	+	1.18884i	0.977389	+	0.211451i	$0.0678188\pi$
$211$	17.2689	+	17.2689i	1.18884	+	1.18884i	0.211451	+	0.977389i	$0.432181\pi$
$212$	4.10731	+	11.8864i	0.282091	+	0.816363i
$213$	5.66635	+	21.1471i	0.388252	+	1.44898i
$214$	4.76271	−	20.6809i	0.325572	−	1.41372i
$215$	9.23922	−	5.33426i	0.630109	−	0.363794i
$216$	−12.4117	−	10.0173i	−0.844510	−	0.681589i
$217$	−6.34485	+	5.95544i	−0.430716	+	0.404282i
$218$	−2.86136	−	9.34087i	−0.193795	−	0.632644i
$219$	−18.4094	−	4.93279i	−1.24399	−	0.333327i
$220$	0.0390496	+	0.549827i	0.00263272	+	0.0370694i
$221$	−1.98626	+	0.532216i	−0.133610	+	0.0358007i
$222$	0.375662	+	10.5921i	0.0252128	+	0.710897i
$223$	−4.81139			−0.322195			−0.161097	−	0.986939i	$-0.551503\pi$
$223$	−4.81139			−0.322195			−0.161097	+	0.986939i	$0.551503\pi$
$224$	1.73508	−	14.8657i	0.115930	−	0.993257i
$225$	−1.18011			−0.0786742
$226$	−0.251676	−	7.09625i	−0.0167413	−	0.472035i
$227$	−8.16376	+	2.18747i	−0.541848	+	0.145188i	−0.519354	−	0.854559i	$-0.673827\pi$
$227$	−8.16376	+	2.18747i	−0.541848	+	0.145188i	−0.0224939	+	0.999747i	$0.507161\pi$
$228$	−1.59609	−	22.4733i	−0.105704	−	1.48833i
$229$	−1.44440	−	0.387026i	−0.0954487	−	0.0255754i	0.210779	−	0.977534i	$-0.432400\pi$
$229$	−1.44440	−	0.387026i	−0.0954487	−	0.0255754i	−0.306227	+	0.951958i	$0.599067\pi$
$230$	−3.14453	−	10.2653i	−0.207344	−	0.676874i
$231$	0.224405	+	0.957756i	0.0147648	+	0.0630157i
$232$	−8.48134	+	10.5086i	−0.556827	+	0.689927i
$233$	−14.3497	+	8.28480i	−0.940079	+	0.542755i	−0.889985	−	0.455989i	$-0.849285\pi$
$233$	−14.3497	+	8.28480i	−0.940079	+	0.542755i	−0.0500941	+	0.998745i	$0.515952\pi$
$234$	1.93822	−	8.41627i	0.126706	−	0.550189i
$235$	−0.913590	−	3.40956i	−0.0595960	−	0.222415i
$236$	8.70669	+	25.1969i	0.566757	+	1.64018i
$237$	0.440304	+	0.440304i	0.0286008	+	0.0286008i
$238$	1.05532	+	1.04732i	0.0684062	+	0.0678878i
$239$	−10.3360			−0.668580			−0.334290	−	0.942470i	$-0.608497\pi$
$239$	−10.3360			−0.668580			−0.334290	+	0.942470i	$0.608497\pi$
$240$	5.34196	−	0.762636i	0.344822	−	0.0492279i
$241$	6.56919	−	11.3782i	0.423158	−	0.732932i	−0.573088	−	0.819494i	$-0.694255\pi$
$241$	6.56919	−	11.3782i	0.423158	−	0.732932i	0.996246	+	0.0865619i	$0.0275880\pi$
$242$	8.19382	+	13.0970i	0.526719	+	0.841905i
$243$	−2.95851	+	11.0413i	−0.189789	+	0.708301i
$244$	−4.46744	+	23.1174i	−0.285999	+	1.47994i
$245$	−4.62675	−	5.25293i	−0.295592	−	0.335597i
$246$	4.44405	−	1.36133i	0.283342	−	0.0867953i
$247$	37.4231	−	21.6063i	2.38118	−	1.37477i
$248$	−8.50470	−	3.76990i	−0.540049	−	0.239389i
$249$	−6.90102	−	3.98431i	−0.437334	−	0.252495i
$250$	0.963928	−	1.03482i	0.0609642	−	0.0654475i
$251$	−13.0296	+	13.0296i	−0.822423	+	0.822423i	−0.986455	−	0.164032i	$-0.947550\pi$
$251$	−13.0296	+	13.0296i	−0.822423	+	0.822423i	0.164032	+	0.986455i	$0.447550\pi$
$252$	−5.96372	+	1.85168i	−0.375679	+	0.116645i
$253$	1.47947	+	1.47947i	0.0930136	+	0.0930136i
$254$	0.244489	+	6.89359i	0.0153406	+	0.432542i
$255$	−0.268029	+	0.464240i	−0.0167846	+	0.0290718i
$256$	15.3608	−	4.47717i	0.960052	−	0.279823i
$257$	1.99198	+	3.45021i	0.124256	+	0.215218i	0.921442	−	0.388516i	$-0.127012\pi$
$257$	1.99198	+	3.45021i	0.124256	+	0.215218i	−0.797186	+	0.603734i	$0.793679\pi$
$258$	17.9764	+	9.54566i	1.11916	+	0.594287i
$259$	12.4902	+	7.74827i	0.776104	+	0.481454i
$260$	5.79689	+	8.57407i	0.359508	+	0.531742i
$261$	5.44243	+	1.45830i	0.336878	+	0.0902663i
$262$	0.273080	+	0.0628888i	0.0168709	+	0.00388528i
$263$	−11.4479	−	6.60945i	−0.705908	−	0.407556i	0.103636	−	0.994615i	$-0.466952\pi$
$263$	−11.4479	−	6.60945i	−0.705908	−	0.407556i	−0.809544	+	0.587059i	$0.800286\pi$
$264$	−0.849762	+	0.619512i	−0.0522992	+	0.0381283i
$265$			6.28803i			0.386270i
$266$	−27.1176	−	15.5191i	−1.66269	−	0.951540i
$267$	10.7559	−	10.7559i	0.658250	−	0.658250i
$268$	9.96733	−	3.44418i	0.608851	−	0.210386i
$269$	−10.2466	+	2.74556i	−0.624745	+	0.167400i	−0.557284	−	0.830322i	$-0.688157\pi$
$269$	−10.2466	+	2.74556i	−0.624745	+	0.167400i	−0.0674610	+	0.997722i	$0.521490\pi$
$270$	−4.22974	−	6.76080i	−0.257414	−	0.411449i
$271$	6.70982	+	11.6217i	0.407592	+	0.705971i	0.994619	−	0.103597i	$-0.0330351\pi$
$271$	6.70982	+	11.6217i	0.407592	+	0.705971i	−0.587027	+	0.809567i	$0.699702\pi$
$272$	−0.592210	+	1.47501i	−0.0359080	+	0.0894359i
$273$	12.6407	+	13.4672i	0.765047	+	0.815072i
$274$	3.70335	−	6.97415i	0.223728	−	0.421324i
$275$	−0.0713321	+	0.266215i	−0.00430149	+	0.0160534i
$276$	13.4209	−	15.4730i	0.807846	−	0.931368i
$277$	0.951227	+	3.55003i	0.0571537	+	0.213300i	0.988597	−	0.150586i	$-0.0481162\pi$
$277$	0.951227	+	3.55003i	0.0571537	+	0.213300i	−0.931443	+	0.363887i	$0.881449\pi$
$278$	3.32965	+	3.10156i	0.199699	+	0.186019i
$279$			3.88144i			0.232376i
$280$	3.24752	−	6.74193i	0.194077	−	0.402907i
$281$		−	12.2399i		−	0.730169i	−0.930974	−	0.365085i	$-0.881040\pi$
$281$		−	12.2399i		−	0.730169i	0.930974	−	0.365085i	$-0.118960\pi$
$282$	4.59010	−	4.92765i	0.273336	−	0.293438i
$283$	6.41907	+	23.9563i	0.381574	+	1.42405i	0.843497	+	0.537133i	$0.180493\pi$
$283$	6.41907	+	23.9563i	0.381574	+	1.42405i	−0.461923	+	0.886920i	$0.652840\pi$
$284$	2.29939	+	32.3759i	0.136444	+	1.92116i
$285$	2.91558	−	10.8811i	0.172704	−	0.644541i
$286$	−1.78142	−	0.945955i	−0.105338	−	0.0559355i
$287$	1.86443	−	6.17012i	0.110054	−	0.364211i
$288$	−4.30499	−	5.10220i	−0.253674	−	0.300650i
$289$	8.42105	+	14.5857i	0.495356	+	0.857982i
$290$	−5.72418	+	3.58120i	−0.336135	+	0.210295i
$291$	−15.2280	+	4.08033i	−0.892681	+	0.239193i
$292$	−25.4094	−	12.3588i	−1.48697	−	0.723242i
$293$	1.48974	−	1.48974i	0.0870315	−	0.0870315i	−0.662251	−	0.749282i	$-0.730399\pi$
$293$	1.48974	−	1.48974i	0.0870315	−	0.0870315i	0.749282	+	0.662251i	$0.230399\pi$
$294$	3.81426	−	12.7984i	0.222452	−	0.746421i
$295$			13.3294i			0.776066i
$296$	−2.43272	+	15.5237i	−0.141399	+	0.902298i
$297$	1.34595	+	0.777086i	0.0781001	+	0.0450911i
$298$	−4.74263	+	20.5937i	−0.274733	+	1.19296i
$299$	37.9472	+	10.1679i	2.19454	+	0.588025i
$300$	2.64905	+	0.511929i	0.152943	+	0.0295563i
$301$	24.8790	−	13.3326i	1.43400	−	0.768477i
$302$	4.38953	−	8.26637i	0.252589	−	0.475676i
$303$	3.04608	+	5.27596i	0.174993	+	0.303096i
$304$	3.99839	−	33.1614i	0.229324	−	1.90194i
$305$	−5.88628	+	10.1953i	−0.337048	+	0.583784i
$306$	0.662758	−	0.0235055i	0.0378874	−	0.00134372i
$307$	−15.4771	−	15.4771i	−0.883322	−	0.883322i	0.110548	−	0.993871i	$-0.464739\pi$
$307$	−15.4771	−	15.4771i	−0.883322	−	0.883322i	−0.993871	+	0.110548i	$0.964739\pi$
$308$	0.0572329	+	1.45725i	0.00326114	+	0.0830344i
$309$	−5.35719	+	5.35719i	−0.304760	+	0.304760i
$310$	−3.40355	−	3.17039i	−0.193308	−	0.180066i
$311$	−3.73505	−	2.15643i	−0.211795	−	0.122280i	0.390350	−	0.920666i	$-0.372354\pi$
$311$	−3.73505	−	2.15643i	−0.211795	−	0.122280i	−0.602145	+	0.798386i	$0.705687\pi$
$312$	−8.00176	+	18.0516i	−0.453011	+	1.02197i
$313$	−10.6513	+	6.14950i	−0.602045	+	0.347591i	−0.769845	−	0.638230i	$-0.779667\pi$
$313$	−10.6513	+	6.14950i	−0.602045	+	0.347591i	0.167801	+	0.985821i	$0.446333\pi$
$314$	5.14595	+	16.7989i	0.290403	+	0.948018i
$315$	−3.12072	−	0.0987977i	−0.175833	−	0.00556662i
$316$	0.517056	+	0.764769i	0.0290867	+	0.0430216i
$317$	6.44637	−	24.0582i	0.362064	−	1.35124i	−0.509294	−	0.860593i	$-0.670093\pi$
$317$	6.44637	−	24.0582i	0.362064	−	1.35124i	0.871358	−	0.490649i	$-0.163240\pi$
$318$	−10.1701	+	6.36267i	−0.570309	+	0.356801i
$319$	0.657937	−	1.13958i	0.0368374	−	0.0638043i
$320$	7.99036	+	0.392578i	0.446675	+	0.0219458i
$321$	20.2441			1.12992
$322$	−7.45609	−	27.4091i	−0.415512	−	1.52745i
$323$	2.34629	+	2.34629i	0.130551	+	0.130551i
$324$	3.55774	−	7.31465i	0.197652	−	0.406370i
$325$	1.33936	+	4.99858i	0.0742946	+	0.277271i
$326$	26.6683	+	6.14156i	1.47702	+	0.340149i
$327$	8.07052	−	4.65952i	0.446301	−	0.257672i
$328$	6.85176	−	0.731470i	0.378325	−	0.0403887i
$329$	−2.13048	−	9.09283i	−0.117457	−	0.501304i
$330$	−0.502748	+	0.154005i	−0.0276753	+	0.00847769i
$331$	−10.4614	−	2.80312i	−0.575011	−	0.154074i	−0.0404170	−	0.999183i	$-0.512869\pi$
$331$	−10.4614	−	2.80312i	−0.575011	−	0.154074i	−0.534594	+	0.845109i	$0.679535\pi$
$332$	−8.92444	−	7.74085i	−0.489793	−	0.424834i
$333$	6.33267	−	1.69683i	0.347028	−	0.0929859i
$334$	8.88661	−	0.315173i	0.486254	−	0.0172455i
$335$	5.27281			0.288084
$336$	14.1903	−	1.56951i	0.774143	−	0.0856238i
$337$	−1.31103			−0.0714166			−0.0357083	−	0.999362i	$-0.511369\pi$
$337$	−1.31103			−0.0714166			−0.0357083	+	0.999362i	$0.511369\pi$
$338$	−19.4751	+	0.690707i	−1.05931	+	0.0375695i
$339$	6.54263	−	1.75309i	0.355347	−	0.0952150i
$340$	−0.520736	+	0.600358i	−0.0282409	+	0.0325590i
$341$	0.875591	+	0.234614i	0.0474159	+	0.0127051i
$342$	−13.3251	+	4.08182i	−0.720538	+	0.220720i
$343$	−11.7953	−	14.2783i	−0.636887	−	0.770957i
$344$	23.4815	+	18.9515i	1.26604	+	1.02180i
$345$	8.86923	−	5.12065i	0.477503	−	0.275687i
$346$	30.7996	+	7.09299i	1.65580	+	0.381321i
$347$	1.11479	+	4.16045i	0.0598450	+	0.223345i	0.989371	−	0.145411i	$-0.0464505\pi$
$347$	1.11479	+	4.16045i	0.0598450	+	0.223345i	−0.929526	+	0.368756i	$0.879784\pi$
$348$	−11.5843	−	5.63441i	−0.620982	−	0.302036i
$349$	−3.78662	−	3.78662i	−0.202693	−	0.202693i	0.598460	−	0.801153i	$-0.295780\pi$
$349$	−3.78662	−	3.78662i	−0.202693	−	0.202693i	−0.801153	+	0.598460i	$0.795780\pi$
$350$	2.63567	−	2.65579i	0.140882	−	0.141958i
$351$	29.1818			1.55761
$352$	−1.41119	+	0.662734i	−0.0752168	+	0.0353239i
$353$	−6.46138	+	11.1914i	−0.343905	+	0.595660i	−0.985154	−	0.171672i	$-0.945083\pi$
$353$	−6.46138	+	11.1914i	−0.343905	+	0.595660i	0.641250	+	0.767332i	$0.278416\pi$
$354$	−21.5585	+	13.4876i	−1.14582	+	0.716858i
$355$	−4.20031	+	15.6758i	−0.222929	+	0.831983i
$356$	18.6820	−	12.6308i	0.990146	−	0.669433i
$357$	−0.747648	+	1.20521i	−0.0395697	+	0.0637864i
$358$	−2.95216	−	9.63729i	−0.156026	−	0.509347i
$359$	3.90293	−	2.25336i	0.205989	−	0.118928i	−0.393457	−	0.919343i	$-0.628721\pi$
$359$	3.90293	−	2.25336i	0.205989	−	0.118928i	0.599446	+	0.800415i	$0.295388\pi$
$360$	−1.20127	−	3.11421i	−0.0633127	−	0.164133i
$361$	−43.9327	−	25.3646i	−2.31225	−	1.33498i
$362$	11.9993	+	11.1773i	0.630670	+	0.587468i
$363$	−10.4205	+	10.4205i	−0.546937	+	0.546937i
$364$	14.6116	+	23.1588i	0.765857	+	1.21385i
$365$	−9.98986	−	9.98986i	−0.522893	−	0.522893i
$366$	−22.4458	+	0.796066i	−1.17326	+	0.0416110i
$367$	3.66129	−	6.34154i	0.191118	−	0.331026i	−0.754503	−	0.656296i	$-0.772122\pi$
$367$	3.66129	−	6.34154i	0.191118	−	0.331026i	0.945621	+	0.325271i	$0.105455\pi$
$368$	23.8882	−	18.7475i	1.24526	−	0.977281i
$369$	−1.43751	−	2.48985i	−0.0748340	−	0.129616i
$370$	−3.68467	+	6.93897i	−0.191557	+	0.360740i
$371$	−0.526426	+	16.6282i	−0.0273307	+	0.863294i
$372$	1.68375	−	8.71283i	0.0872986	−	0.451739i
$373$	18.6280	+	4.99135i	0.964520	+	0.258442i	0.706512	−	0.707701i	$-0.250267\pi$
$373$	18.6280	+	4.99135i	0.964520	+	0.258442i	0.258007	+	0.966143i	$0.416934\pi$
$374$	0.0347581	−	0.150929i	0.00179730	−	0.00780434i
$375$	1.16830	+	0.674516i	0.0603305	+	0.0348318i
$376$	8.06754	−	5.88158i	0.416052	−	0.303319i
$377$		−	24.7075i		−	1.27250i
$378$	−10.6192	−	18.2325i	−0.546194	−	0.937780i
$379$	−8.45939	+	8.45939i	−0.434530	+	0.434530i	−0.890166	−	0.455636i	$-0.849412\pi$
$379$	−8.45939	+	8.45939i	−0.434530	+	0.434530i	0.455636	+	0.890166i	$0.349412\pi$
$380$	7.30479	−	15.0185i	0.374728	−	0.770435i
$381$	−6.35578	+	1.70303i	−0.325617	+	0.0872487i
$382$	−14.1460	+	8.85011i	−0.723772	+	0.452811i
$383$	−9.68886	−	16.7816i	−0.495077	−	0.857499i	0.504906	−	0.863174i	$-0.331527\pi$
$383$	−9.68886	−	16.7816i	−0.495077	−	0.857499i	−0.999984	+	0.00567474i	$0.998194\pi$
$384$	7.45027	+	13.3206i	0.380195	+	0.679765i
$385$	−0.210920	+	0.698014i	−0.0107495	+	0.0355741i
$386$	−10.8609	−	5.76725i	−0.552805	−	0.293545i
$387$	3.25855	−	12.1611i	0.165641	−	0.618182i
$388$	−23.3139	+	1.65579i	−1.18358	+	0.0840598i
$389$	−2.99390	−	11.1734i	−0.151797	−	0.566513i	−0.999358	−	0.0358162i	$-0.988597\pi$
$389$	−2.99390	−	11.1734i	−0.151797	−	0.566513i	0.847562	−	0.530697i	$-0.178070\pi$
$390$	−6.72929	+	7.22416i	−0.340751	+	0.365810i
$391$			3.01663i			0.152558i
$392$	9.15226	−	17.5567i	0.462259	−	0.886745i
$393$			0.267312i			0.0134841i
$394$	2.73967	+	2.55199i	0.138023	+	0.128568i
$395$	0.119465	+	0.445851i	0.00601095	+	0.0224332i
$396$	0.491398	+	0.426227i	0.0246937	+	0.0214187i
$397$	−2.78459	+	10.3922i	−0.139755	+	0.521571i	0.860178	+	0.509993i	$0.170352\pi$
$397$	−2.78459	+	10.3922i	−0.139755	+	0.521571i	−0.999933	+	0.0115778i	$0.996315\pi$
$398$	1.71629	−	3.23212i	0.0860299	−	0.162012i
$399$	8.62100	−	28.5302i	0.431590	−	1.42830i
$400$	3.71199	+	1.49034i	0.185600	+	0.0745171i
$401$	−1.54184	−	2.67055i	−0.0769960	−	0.133361i	0.824957	−	0.565196i	$-0.191200\pi$
$401$	−1.54184	−	2.67055i	−0.0769960	−	0.133361i	−0.901953	+	0.431835i	$0.857866\pi$
$402$	5.33540	+	8.52809i	0.266106	+	0.425342i
$403$	16.4405	−	4.40522i	0.818960	−	0.219440i
$404$	2.94980	+	8.53661i	0.146758	+	0.424712i
$405$	2.87580	−	2.87580i	0.142899	−	0.142899i
$406$	−15.4370	+	8.99100i	−0.766125	+	0.446216i
$407$		−	1.53112i		−	0.0758946i
$408$	−1.49792	−	0.234739i	−0.0741580	−	0.0116213i
$409$	12.2154	+	7.05258i	0.604014	+	0.348728i	0.770619	−	0.637296i	$-0.219947\pi$
$409$	12.2154	+	7.05258i	0.604014	+	0.348728i	−0.166605	+	0.986024i	$0.553280\pi$
$410$	3.35747	+	0.773206i	0.165813	+	0.0381859i
$411$	7.27582	+	1.94955i	0.358890	+	0.0961642i
$412$	−9.30497	+	6.29104i	−0.458423	+	0.309937i
$413$	−1.11592	+	35.2485i	−0.0549108	+	1.73447i
$414$	−11.1901	−	5.94204i	−0.549961	−	0.292036i
$415$	−2.95346	−	5.11554i	−0.144979	−	0.251112i
$416$	−16.7253	+	24.0252i	−0.820027	+	1.17793i
$417$	−2.17034	+	3.75914i	−0.106282	+	0.184086i
$418$	0.115359	+	3.25266i	0.00564239	+	0.159093i
$419$	−18.2841	−	18.2841i	−0.893235	−	0.893235i	0.101591	−	0.994826i	$-0.467607\pi$
$419$	−18.2841	−	18.2841i	−0.893235	−	0.893235i	−0.994826	+	0.101591i	$0.967607\pi$
$420$	6.96236	+	1.57554i	0.339729	+	0.0768782i
$421$	7.28032	−	7.28032i	0.354821	−	0.354821i	−0.507079	−	0.861900i	$-0.669275\pi$
$421$	7.28032	−	7.28032i	0.354821	−	0.354821i	0.861900	+	0.507079i	$0.169275\pi$
$422$	−23.5409	+	25.2722i	−1.14596	+	1.23023i
$423$	−3.60753	−	2.08281i	−0.175404	−	0.101270i
$424$	−16.5935	+	6.40078i	−0.805852	+	0.310849i
$425$	−0.344128	+	0.198682i	−0.0166927	+	0.00963751i
$426$	−29.6037	+	9.06839i	−1.43430	+	0.439365i
$427$	−16.4194	+	26.4680i	−0.794590	+	1.28088i
$428$	29.4676	+	5.69462i	1.42437	+	0.275260i
$429$	0.497978	−	1.85848i	0.0240426	−	0.0897281i
$430$	8.00217	+	12.7906i	0.385899	+	0.616819i
$431$	−5.12410	+	8.87521i	−0.246819	+	0.427504i	−0.962642	−	0.270779i	$-0.912719\pi$
$431$	−5.12410	+	8.87521i	−0.246819	+	0.427504i	0.715822	+	0.698283i	$0.246052\pi$
$432$	13.5355	−	18.0439i	0.651228	−	0.868137i
$433$	5.78867			0.278186			0.139093	−	0.990279i	$-0.455581\pi$
$433$	5.78867			0.278186			0.139093	+	0.990279i	$0.455581\pi$
$434$	−8.73501	−	8.66882i	−0.419294	−	0.416117i
$435$	−4.55442	−	4.55442i	−0.218368	−	0.218368i
$436$	13.0583	−	4.51224i	0.625377	−	0.216097i
$437$	−16.4073	−	61.2328i	−0.784866	−	2.92916i
$438$	6.04886	−	26.2658i	0.289026	−	1.25503i
$439$	12.8142	−	7.39826i	0.611586	−	0.353100i	−0.162000	−	0.986791i	$-0.551794\pi$
$439$	12.8142	−	7.39826i	0.611586	−	0.353100i	0.773586	+	0.633691i	$0.218461\pi$
$440$	−0.775127	+	0.0827499i	−0.0369527	+	0.00394495i
$441$	−8.24425	−	0.522527i	−0.392583	−	0.0248822i
$442$	−0.851756	−	2.78055i	−0.0405139	−	0.132257i
$443$	−22.7453	−	6.09458i	−1.08066	−	0.289562i	−0.325794	−	0.945441i	$-0.605632\pi$
$443$	−22.7453	−	6.09458i	−1.08066	−	0.289562i	−0.754866	+	0.655879i	$0.772298\pi$
$444$	−14.9513	+	1.06186i	−0.709557	+	0.0503938i
$445$	10.8914	−	2.91834i	0.516302	−	0.138343i
$446$	−0.241172	−	6.80006i	−0.0114198	−	0.321992i
$447$	−20.1588			−0.953477
$448$	21.0971	+	1.70709i	0.996742	+	0.0806523i
$449$	18.8147			0.887921			0.443960	−	0.896046i	$-0.353573\pi$
$449$	18.8147			0.887921			0.443960	+	0.896046i	$0.353573\pi$
$450$	−0.0591533	−	1.66788i	−0.00278852	−	0.0786248i
$451$	−0.648561	+	0.173781i	−0.0305395	+	0.00818305i
$452$	10.0167	−	0.711401i	0.471145	−	0.0334615i
$453$	8.62393	+	2.31077i	0.405188	+	0.108570i
$454$	−3.50082	−	11.4284i	−0.164302	−	0.536361i
$455$	3.12338	+	13.3305i	0.146426	+	0.624943i
$456$	31.6821	−	3.38227i	1.48365	−	0.158389i
$457$	−21.1062	+	12.1856i	−0.987304	+	0.570020i	−0.904467	−	0.426543i	$-0.859731\pi$
$457$	−21.1062	+	12.1856i	−0.987304	+	0.570020i	−0.0828367	+	0.996563i	$0.526398\pi$
$458$	0.474593	−	2.06081i	0.0221763	−	0.0962952i
$459$	0.579957	+	2.16443i	0.0270701	+	0.101027i
$460$	14.3506	−	4.95880i	0.669100	−	0.231205i
$461$	−27.0021	−	27.0021i	−1.25761	−	1.25761i	−0.952229	−	0.305384i	$-0.901215\pi$
$461$	−27.0021	−	27.0021i	−1.25761	−	1.25761i	−0.305384	−	0.952229i	$-0.598785\pi$
$462$	−1.34237	+	0.365165i	−0.0624528	+	0.0169890i
$463$	29.9564			1.39219			0.696095	−	0.717949i	$-0.254919\pi$
$463$	29.9564			1.39219			0.696095	+	0.717949i	$0.254919\pi$
$464$	−15.2773	−	11.4601i	−0.709229	−	0.532024i
$465$	2.21851	−	3.84257i	0.102881	−	0.178195i
$466$	−12.4284	−	19.8655i	−0.575734	−	0.920251i
$467$	−0.848877	+	3.16805i	−0.0392814	+	0.146600i	−0.982781	−	0.184773i	$-0.940845\pi$
$467$	−0.848877	+	3.16805i	−0.0392814	+	0.146600i	0.943500	+	0.331373i	$0.107512\pi$
$468$	11.9921	+	2.31747i	0.554334	+	0.107125i
$469$	13.9435	+	0.441433i	0.643853	+	0.0203835i
$470$	4.77303	−	1.46210i	0.220163	−	0.0674419i
$471$	−14.5143	+	8.37982i	−0.668782	+	0.386122i
$472$	−35.1749	+	13.5684i	−1.61906	+	0.624535i
$473$	−2.54639	−	1.47016i	−0.117083	−	0.0675978i
$474$	−0.600222	+	0.644363i	−0.0275691	+	0.0295966i
$475$	5.90462	−	5.90462i	0.270923	−	0.270923i
$476$	−1.42731	+	1.54401i	−0.0654206	+	0.0707694i
$477$	5.24715	+	5.24715i	0.240250	+	0.240250i
$478$	−0.518093	−	14.6081i	−0.0236970	−	0.668160i
$479$	−1.10537	+	1.91455i	−0.0505055	+	0.0874781i	−0.890173	−	0.455623i	$-0.849417\pi$
$479$	−1.10537	+	1.91455i	−0.0505055	+	0.0874781i	0.839667	+	0.543101i	$0.182750\pi$
$480$	1.34562	+	7.51170i	0.0614188	+	0.342861i
$481$	−14.3745	−	24.8973i	−0.655419	−	1.13522i
$482$	16.4103	+	8.71406i	0.747470	+	0.396915i
$483$	23.8827	−	12.7987i	1.08670	−	0.582359i
$484$	−18.0996	+	12.2370i	−0.822707	+	0.556228i
$485$	−11.2881	−	3.02464i	−0.512566	−	0.137342i
$486$	−15.7533	−	3.62789i	−0.714583	−	0.164565i
$487$	8.29773	+	4.79070i	0.376006	+	0.217087i	0.676079	−	0.736829i	$-0.263678\pi$
$487$	8.29773	+	4.79070i	0.376006	+	0.217087i	−0.300073	+	0.953916i	$0.597011\pi$
$488$	−32.8964	−	5.15519i	−1.48915	−	0.233364i
$489$			26.1050i			1.18051i
$490$	7.19217	−	6.80240i	0.324909	−	0.307301i
$491$	6.52132	−	6.52132i	0.294303	−	0.294303i	−0.544474	−	0.838778i	$-0.683271\pi$
$491$	6.52132	−	6.52132i	0.294303	−	0.294303i	0.838778	+	0.544474i	$0.183271\pi$
$492$	2.14676	+	6.21265i	0.0967835	+	0.280088i
$493$	1.83256	−	0.491034i	0.0825345	−	0.0221150i
$494$	32.4125	+	51.8081i	1.45831	+	2.33095i
$495$	0.162623	+	0.281672i	0.00730937	+	0.0126602i
$496$	4.90179	−	12.2089i	0.220097	−	0.548195i
$497$	−12.4198	+	41.1018i	−0.557102	+	1.84367i
$498$	5.28520	−	9.95310i	0.236836	−	0.446009i
$499$	9.58563	−	35.7740i	0.429112	−	1.60147i	−0.325666	−	0.945485i	$-0.605588\pi$
$499$	9.58563	−	35.7740i	0.429112	−	1.60147i	0.754777	−	0.655981i	$-0.227745\pi$
$500$	1.51085	+	1.31047i	0.0675672	+	0.0586061i
$501$	2.19539	+	8.19332i	0.0980829	+	0.366051i
$502$	−19.0682	−	17.7620i	−0.851056	−	0.792757i
$503$			18.2208i			0.812427i	0.913778	+	0.406213i	$0.133151\pi$
$503$			18.2208i			0.812427i	−0.913778	+	0.406213i	$0.866849\pi$
$504$	−2.91596	−	8.33586i	−0.129887	−	0.371309i
$505$			4.51595i			0.200957i
$506$	−2.01682	+	2.16513i	−0.0896584	+	0.0962519i
$507$	−4.81124	−	17.9558i	−0.213675	−	0.797444i
$508$	−9.73062	+	0.691084i	−0.431727	+	0.0306619i
$509$	−2.10897	+	7.87078i	−0.0934784	+	0.348866i	−0.996784	−	0.0801307i	$-0.974466\pi$
$509$	−2.10897	+	7.87078i	−0.0934784	+	0.348866i	0.903306	+	0.428997i	$0.141133\pi$
$510$	−0.669556	−	0.355542i	−0.0296485	−	0.0157437i
$511$	−25.5811	−	27.2538i	−1.13164	−	1.20564i
$512$	7.09766	+	21.4854i	0.313675	+	0.949530i
$513$	−23.5444	−	40.7801i	−1.03951	−	1.80048i
$514$	−4.77642	+	2.98825i	−0.210679	+	0.131806i
$515$	−5.42468	+	1.45354i	−0.239040	+	0.0640505i
$516$	−12.5900	+	25.8849i	−0.554246	+	1.13952i
$517$	−0.687906	+	0.687906i	−0.0302541	+	0.0302541i
$518$	−10.3248	+	18.0411i	−0.453644	+	0.792681i
$519$			30.1491i			1.32340i
$520$	−11.8274	+	8.62266i	−0.518665	+	0.378129i
$521$	34.4463	+	19.8876i	1.50912	+	0.871290i	0.999944	+	0.0106264i	$0.00338255\pi$
$521$	34.4463	+	19.8876i	1.50912	+	0.871290i	0.509174	+	0.860663i	$0.329951\pi$
$522$	−1.78824	+	7.76503i	−0.0782693	+	0.339866i
$523$	−30.2794	−	8.11335i	−1.32403	−	0.354772i	−0.473542	−	0.880771i	$-0.657025\pi$
$523$	−30.2794	−	8.11335i	−1.32403	−	0.354772i	−0.850485	+	0.526000i	$0.823691\pi$
$524$	−0.0751941	+	0.389103i	−0.00328487	+	0.0169980i
$525$	3.03300	+	1.88152i	0.132371	+	0.0821161i
$526$	8.76747	−	16.5109i	0.382280	−	0.719910i
$527$	0.653474	+	1.13185i	0.0284658	+	0.0493042i
$528$	−0.918166	−	1.16994i	−0.0399581	−	0.0509150i
$529$	17.3161	−	29.9924i	0.752876	−	1.30402i
$530$	−8.88702	+	0.315188i	−0.386028	+	0.0136909i
$531$	11.1229	+	11.1229i	0.482693	+	0.482693i
$532$	20.5743	−	39.1039i	0.892010	−	1.69537i
$533$	−8.91468	+	8.91468i	−0.386138	+	0.386138i
$534$	15.7407	+	14.6624i	0.681168	+	0.634506i
$535$	12.9959	+	7.50320i	0.561863	+	0.324392i
$536$	5.36735	+	13.9144i	0.231834	+	0.601012i
$537$	8.32662	−	4.80738i	0.359320	−	0.207454i
$538$	−4.39398	−	14.3441i	−0.189438	−	0.618419i
$539$	−0.616199	+	1.82819i	−0.0265416	+	0.0787457i
$540$	9.34319	−	6.31688i	0.402067	−	0.271835i
$541$	−10.5831	+	39.4968i	−0.455005	+	1.69810i	0.233068	+	0.972460i	$0.425124\pi$
$541$	−10.5831	+	39.4968i	−0.455005	+	1.69810i	−0.688073	+	0.725641i	$0.741543\pi$
$542$	−16.0890	+	10.0657i	−0.691081	+	0.432359i
$543$	−7.82142	+	13.5471i	−0.335649	+	0.581362i
$544$	−2.11436	−	0.763050i	−0.0906524	−	0.0327155i
$545$	6.90794			0.295904
$546$	−18.3999	+	18.5404i	−0.787443	+	0.793456i
$547$	15.2310	+	15.2310i	0.651229	+	0.651229i	0.953289	−	0.302060i	$-0.0976744\pi$
$547$	15.2310	+	15.2310i	0.651229	+	0.651229i	−0.302060	+	0.953289i	$0.597674\pi$
$548$	10.0424	+	4.88446i	0.428989	+	0.208654i
$549$	3.59576	+	13.4196i	0.153463	+	0.572734i
$550$	−0.379824	−	0.0874714i	−0.0161957	−	0.00372979i
$551$	−34.5274	+	19.9344i	−1.47092	+	0.849233i
$552$	22.5412	+	18.1926i	0.959416	+	0.774327i
$553$	0.278591	+	1.18902i	0.0118469	+	0.0505623i
$554$	−4.96966	+	1.52234i	−0.211141	+	0.0646780i
$555$	−7.23911	−	1.93971i	−0.307283	−	0.0823362i
$556$	−4.21661	+	4.86134i	−0.178824	+	0.206167i
$557$	−0.692221	+	0.185480i	−0.0293303	+	0.00785904i	−0.273454	−	0.961885i	$-0.588166\pi$
$557$	−0.692221	+	0.185480i	−0.0293303	+	0.00785904i	0.244124	+	0.969744i	$0.421500\pi$
$558$	−5.48573	+	0.194558i	−0.232230	+	0.00823628i
$559$	−55.2086			−2.33508
$560$	9.69132	+	4.25187i	0.409533	+	0.179674i
$561$	0.147741			0.00623762
$562$	17.2989	−	0.613525i	0.729711	−	0.0258800i
$563$	−18.4115	+	4.93335i	−0.775952	+	0.207916i	−0.625000	−	0.780625i	$-0.714901\pi$
$563$	−18.4115	+	4.93335i	−0.775952	+	0.207916i	−0.150953	+	0.988541i	$0.548234\pi$
$564$	7.19446	+	6.24030i	0.302941	+	0.262764i
$565$	4.84987	+	1.29952i	0.204036	+	0.0546712i
$566$	−33.5363	+	10.2730i	−1.40963	+	0.431808i
$567$	7.84559	−	7.36408i	0.329484	−	0.309262i
$568$	−45.6425	+	4.87263i	−1.91512	+	0.204451i
$569$	9.86875	−	5.69772i	0.413719	−	0.238861i	−0.278667	−	0.960388i	$-0.589893\pi$
$569$	9.86875	−	5.69772i	0.413719	−	0.238861i	0.692387	+	0.721527i	$0.256559\pi$
$570$	15.5247	+	3.57525i	0.650257	+	0.149751i
$571$	1.82084	+	6.79546i	0.0761997	+	0.284381i	0.993503	−	0.113809i	$-0.0363052\pi$
$571$	1.82084	+	6.79546i	0.0761997	+	0.284381i	−0.917303	+	0.398190i	$0.869639\pi$
$572$	1.24765	−	2.56515i	0.0521668	−	0.107254i
$573$	−11.2552	−	11.2552i	−0.470192	−	0.470192i
$574$	8.81384	+	2.32577i	0.367883	+	0.0970758i
$575$	7.59159			0.316591
$576$	6.99528	−	6.34010i	0.291470	−	0.264171i
$577$	1.16050	−	2.01005i	0.0483124	−	0.0836795i	−0.840858	−	0.541256i	$-0.817949\pi$
$577$	1.16050	−	2.01005i	0.0483124	−	0.0836795i	0.889170	+	0.457576i	$0.151282\pi$
$578$	−20.1922	+	12.6328i	−0.839885	+	0.525455i
$579$	3.03604	−	11.3307i	0.126174	−	0.470887i
$580$	−5.34833	−	7.91062i	−0.222077	−	0.328471i
$581$	−7.38193	−	13.7749i	−0.306254	−	0.571480i
$582$	−6.53014	−	21.3176i	−0.270683	−	0.883642i
$583$	1.50084	−	0.866509i	0.0621584	−	0.0358871i
$584$	16.1933	−	36.5313i	0.670084	−	1.51167i
$585$	5.28880	+	3.05349i	0.218665	+	0.126246i
$586$	2.18016	+	2.03081i	0.0900616	+	0.0838921i
$587$	25.2051	−	25.2051i	1.04032	−	1.04032i	0.0411725	−	0.999152i	$-0.486891\pi$
$587$	25.2051	−	25.2051i	1.04032	−	1.04032i	0.999152	−	0.0411725i	$-0.0131093\pi$
$588$	18.2796	+	4.74927i	0.753836	+	0.195856i
$589$	−19.4205	−	19.4205i	−0.800209	−	0.800209i
$590$	−18.8387	+	0.668136i	−0.775578	+	0.0275067i
$591$	−1.78578	+	3.09306i	−0.0734571	+	0.127231i
$592$	−22.0620	−	2.66010i	−0.906743	−	0.109329i
$593$	−15.6571	−	27.1190i	−0.642962	−	1.11364i	−0.984768	−	0.173872i	$-0.944372\pi$
$593$	−15.6571	−	27.1190i	−0.642962	−	1.11364i	0.341806	−	0.939770i	$-0.388961\pi$
$594$	−1.03081	+	1.94122i	−0.0422946	+	0.0796492i
$595$	−0.926655	+	0.496591i	−0.0379891	+	0.0203582i
$596$	−29.3434	−	5.67061i	−1.20195	−	0.232277i
$597$	3.37192	+	0.903504i	0.138004	+	0.0369780i
$598$	−12.4685	+	54.1413i	−0.509873	+	2.21400i
$599$	−8.10097	−	4.67709i	−0.330996	−	0.191101i	0.325287	−	0.945615i	$-0.394539\pi$
$599$	−8.10097	−	4.67709i	−0.330996	−	0.191101i	−0.656283	+	0.754514i	$0.727872\pi$
$600$	−0.590739	+	3.76963i	−0.0241168	+	0.153895i
$601$		−	31.0302i		−	1.26575i	−0.774255	−	0.632874i	$-0.781875\pi$
$601$		−	31.0302i		−	1.26575i	0.774255	−	0.632874i	$-0.218125\pi$
$602$	20.0903	+	34.4938i	0.818820	+	1.40586i
$603$	4.39998	−	4.39998i	0.179181	−	0.179181i
$604$	11.9031	+	5.78948i	0.484330	+	0.235571i
$605$	−10.5518	+	2.82735i	−0.428992	+	0.114948i
$606$	−7.30396	+	4.56956i	−0.296703	+	0.185625i
$607$	−10.5761	−	18.3183i	−0.429270	−	0.743517i	0.567539	−	0.823347i	$-0.307896\pi$
$607$	−10.5761	−	18.3183i	−0.429270	−	0.743517i	−0.996809	+	0.0798296i	$0.974562\pi$
$608$	47.0683	+	3.98881i	1.90887	+	0.161768i
$609$	−11.6625	−	12.4251i	−0.472590	−	0.503491i
$610$	−14.7044	−	7.80819i	−0.595363	−	0.316144i
$611$	−4.72774	+	17.6442i	−0.191264	+	0.713807i
$612$	0.0664417	+	0.935515i	0.00268575	+	0.0378159i
$613$	−11.0398	−	41.2011i	−0.445894	−	1.66410i	−0.713566	−	0.700588i	$-0.752921\pi$
$613$	−11.0398	−	41.2011i	−0.445894	−	1.66410i	0.267672	−	0.963510i	$-0.413746\pi$
$614$	21.0983	−	22.6499i	0.851459	−	0.914076i
$615$			3.28655i			0.132526i
$616$	−2.05670	+	0.153933i	−0.0828666	+	0.00620215i
$617$			16.9739i			0.683343i	0.939819	+	0.341671i	$0.110993\pi$
$617$			16.9739i			0.683343i	−0.939819	+	0.341671i	$0.889007\pi$
$618$	−7.83999	−	7.30293i	−0.315370	−	0.293767i
$619$	6.73025	+	25.1176i	0.270512	+	1.00956i	0.958790	+	0.284116i	$0.0917002\pi$
$619$	6.73025	+	25.1176i	0.270512	+	1.00956i	−0.688278	+	0.725447i	$0.741633\pi$
$620$	4.31019	−	4.96923i	0.173102	−	0.199569i
$621$	11.0800	−	41.3511i	0.444625	−	1.65936i
$622$	2.86052	−	5.38693i	0.114696	−	0.215996i
$623$	29.0458	−	6.80552i	1.16370	−	0.272657i
$624$	−25.9138	−	10.4043i	−1.03738	−	0.416503i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−9.22514	−	14.7454i	−0.368711	−	0.589346i
$627$	−2.99890	+	0.803553i	−0.119765	+	0.0320908i
$628$	−23.4844	+	8.11495i	−0.937129	+	0.323822i
$629$	1.56097	−	1.56097i	0.0622398	−	0.0622398i
$630$	−0.0167934	−	4.41555i	−0.000669064	−	0.175920i
$631$			50.1212i			1.99529i	0.0685766	+	0.997646i	$0.478154\pi$
$631$			50.1212i			1.99529i	−0.0685766	+	0.997646i	$0.521846\pi$
$632$	−1.05495	+	0.769103i	−0.0419636	+	0.0305933i
$633$	−28.5320	−	16.4730i	−1.13405	−	0.654741i
$634$	34.3251	+	7.90489i	1.36323	+	0.313943i
$635$	−4.71137	−	1.26241i	−0.186965	−	0.0500971i
$636$	−9.50230	−	14.0547i	−0.376791	−	0.557305i
$637$	7.14352	+	35.5130i	0.283037	+	1.40708i
$638$	1.64358	+	0.872758i	0.0650699	+	0.0345528i
$639$	9.57588	+	16.5859i	0.378816	+	0.656129i
$640$	−0.154322	+	11.3127i	−0.00610011	+	0.447172i
$641$	0.180672	−	0.312933i	0.00713610	−	0.0123601i	−0.862435	−	0.506167i	$-0.831062\pi$
$641$	0.180672	−	0.312933i	0.00713610	−	0.0123601i	0.869571	+	0.493807i	$0.164395\pi$
$642$	1.01474	+	28.6115i	0.0400485	+	1.12921i
$643$	−0.231419	−	0.231419i	−0.00912626	−	0.00912626i	0.702529	−	0.711655i	$-0.252054\pi$
$643$	−0.231419	−	0.231419i	−0.00912626	−	0.00912626i	−0.711655	+	0.702529i	$0.752054\pi$
$644$	38.3642	−	11.9118i	1.51176	−	0.469389i
$645$	−10.1768	+	10.1768i	−0.400712	+	0.400712i
$646$	−3.19846	+	3.43368i	−0.125842	+	0.135096i
$647$	28.1005	+	16.2238i	1.10474	+	0.637824i	0.937463	−	0.348085i	$-0.113168\pi$
$647$	28.1005	+	16.2238i	1.10474	+	0.637824i	0.167281	+	0.985909i	$0.446501\pi$
$648$	10.5163	+	4.66159i	0.413120	+	0.183125i
$649$	3.18148	−	1.83683i	0.124884	−	0.0721018i
$650$	−6.99748	+	2.14351i	−0.274464	+	0.0840754i
$651$	6.18838	−	9.97566i	0.242542	−	0.390977i
$652$	−7.34327	+	37.9988i	−0.287585	+	1.48815i
$653$	−7.07087	+	26.3888i	−0.276704	+	1.03267i	0.677986	+	0.735075i	$0.262853\pi$
$653$	−7.07087	+	26.3888i	−0.276704	+	1.03267i	−0.954691	+	0.297600i	$0.903814\pi$
$654$	6.98995	+	11.1727i	0.273328	+	0.436887i
$655$	−0.0990755	+	0.171604i	−0.00387120	+	0.00670511i
$656$	1.37725	+	9.64710i	0.0537726	+	0.376656i
$657$	−16.6724			−0.650452
$658$	12.7443	−	3.46684i	0.496826	−	0.135151i
$659$	22.3415	+	22.3415i	0.870302	+	0.870302i	0.992505	−	0.122203i	$-0.0389960\pi$
$659$	22.3415	+	22.3415i	0.870302	+	0.870302i	−0.122203	+	0.992505i	$0.538996\pi$
$660$	−0.242859	−	0.702826i	−0.00945328	−	0.0273575i
$661$	−5.47555	−	20.4350i	−0.212974	−	0.794830i	−0.986870	−	0.161517i	$-0.948361\pi$
$661$	−5.47555	−	20.4350i	−0.212974	−	0.794830i	0.773896	−	0.633313i	$-0.218305\pi$
$662$	3.43735	−	14.9259i	0.133596	−	0.580110i
$663$	2.40240	−	1.38702i	0.0933014	−	0.0538676i
$664$	10.4930	−	13.0012i	0.407207	−	0.504543i
$665$	16.1087	−	15.1200i	0.624667	−	0.586329i
$666$	2.71560	+	8.86507i	0.105227	+	0.343514i
$667$	−35.0108	−	9.38112i	−1.35562	−	0.363239i
$668$	0.890885	+	12.5439i	0.0344694	+	0.485337i
$669$	6.26955	−	1.67992i	0.242395	−	0.0649495i
$670$	0.264300	+	7.45219i	0.0102108	+	0.287903i
$671$	3.24459			0.125256
$672$	2.92952	+	19.9768i	0.113009	+	0.770622i
$673$	10.0867			0.388815			0.194408	−	0.980921i	$-0.437722\pi$
$673$	10.0867			0.388815			0.194408	+	0.980921i	$0.437722\pi$
$674$	−0.0657158	−	1.85292i	−0.00253128	−	0.0713717i
$675$	5.44696	−	1.45951i	0.209653	−	0.0561765i
$676$	−1.95239	−	27.4901i	−0.0750918	−	1.05731i
$677$	−3.78848	−	1.01512i	−0.145603	−	0.0390143i	0.185281	−	0.982686i	$-0.440680\pi$
$677$	−3.78848	−	1.01512i	−0.145603	−	0.0390143i	−0.330884	+	0.943671i	$0.607347\pi$
$678$	2.80564	+	9.15899i	0.107750	+	0.351749i
$679$	−29.5973	−	8.94345i	−1.13584	−	0.343218i
$680$	−0.874602	−	0.705876i	−0.0335395	−	0.0270691i
$681$	9.87414	−	5.70084i	0.378378	−	0.218457i
$682$	−0.287697	+	1.24926i	−0.0110165	+	0.0478365i
$683$	6.61155	+	24.6746i	0.252984	+	0.944149i	0.969201	+	0.246271i	$0.0792054\pi$
$683$	6.61155	+	24.6746i	0.252984	+	0.944149i	−0.716217	+	0.697878i	$0.754128\pi$
$684$	−6.43686	−	18.6281i	−0.246120	−	0.712262i
$685$	3.94822	+	3.94822i	0.150854	+	0.150854i
$686$	19.5887	−	17.3863i	0.747899	−	0.663813i
$687$	2.01728			0.0769640
$688$	−25.6076	+	34.1369i	−0.976281	+	1.30146i
$689$	16.2700	−	28.1804i	0.619837	−	1.07359i
$690$	7.68171	+	12.2784i	0.292438	+	0.467432i
$691$	2.82402	−	10.5394i	0.107431	−	0.400937i	−0.891179	−	0.453652i	$-0.850121\pi$
$691$	2.82402	−	10.5394i	0.107431	−	0.400937i	0.998610	+	0.0527150i	$0.0167875\pi$
$692$	−8.48086	+	43.8854i	−0.322394	+	1.66827i
$693$	0.406464	+	0.758475i	0.0154403	+	0.0288121i
$694$	−5.82419	+	1.78410i	−0.221083	+	0.0677236i
$695$	−2.78655	+	1.60881i	−0.105700	+	0.0610258i
$696$	7.38259	−	16.6548i	0.279836	−	0.631297i
$697$	−0.838375	−	0.484036i	−0.0317557	−	0.0183342i
$698$	5.16192	−	5.54153i	0.195381	−	0.209750i
$699$	15.8059	−	15.8059i	0.597834	−	0.597834i
$700$	3.88561	+	3.59194i	0.146862	+	0.135762i
$701$	−22.1463	−	22.1463i	−0.836454	−	0.836454i	0.151936	−	0.988390i	$-0.451449\pi$
$701$	−22.1463	−	22.1463i	−0.836454	−	0.836454i	−0.988390	+	0.151936i	$0.951449\pi$
$702$	1.46274	+	41.2434i	0.0552077	+	1.55663i
$703$	−23.1951	+	40.1751i	−0.874820	+	1.51523i
$704$	−1.00740	−	1.96125i	−0.0379676	−	0.0739175i
$705$	2.38093	+	4.12390i	0.0896711	+	0.155315i
$706$	−16.1410	−	8.57106i	−0.607475	−	0.322576i
$707$	−0.378070	+	11.9421i	−0.0142188	+	0.449128i
$708$	−20.1430	−	29.7931i	−0.757020	−	1.11970i
$709$	0.458675	+	0.122902i	0.0172259	+	0.00461567i	0.267422	−	0.963580i	$-0.413828\pi$
$709$	0.458675	+	0.122902i	0.0172259	+	0.00461567i	−0.250196	+	0.968195i	$0.580495\pi$
$710$	−22.3655	−	5.15065i	−0.839362	−	0.193300i
$711$	0.471737	+	0.272358i	0.0176915	+	0.0102142i
$712$	18.7879	+	25.7707i	0.704107	+	0.965797i
$713$		−	24.9690i		−	0.935098i
$714$	−1.74083	−	0.996259i	−0.0651488	−	0.0372840i
$715$	1.00850	−	1.00850i	0.0377158	−	0.0377158i
$716$	13.4727	−	4.65543i	0.503497	−	0.173982i
$717$	13.4685	−	3.60887i	0.502989	−	0.134776i
$718$	3.38037	+	5.40317i	0.126154	+	0.201644i
$719$	18.8290	+	32.6127i	0.702202	+	1.21625i	0.967692	+	0.252135i	$0.0811328\pi$
$719$	18.8290	+	32.6127i	0.702202	+	1.21625i	−0.265490	+	0.964114i	$0.585534\pi$
$720$	4.34117	−	1.85389i	0.161786	−	0.0690904i
$721$	−14.4669	+	3.38963i	−0.538774	+	0.126236i
$722$	33.6462	−	63.3626i	1.25218	−	2.35811i
$723$	−4.58733	+	17.1201i	−0.170605	+	0.636705i
$724$	−15.1957	+	17.5192i	−0.564745	+	0.651096i
$725$	−1.23573	−	4.61179i	−0.0458937	−	0.171278i
$726$	−15.2499	−	14.2053i	−0.565979	−	0.527208i
$727$			6.76489i			0.250896i	0.992100	+	0.125448i	$0.0400368\pi$
$727$			6.76489i			0.250896i	−0.992100	+	0.125448i	$0.959963\pi$
$728$	−31.9985	+	21.8118i	−1.18594	+	0.808400i
$729$		−	27.6215i		−	1.02302i
$730$	13.6182	−	14.6197i	0.504031	−	0.541098i
$731$	−1.09721	−	4.09485i	−0.0405818	−	0.151453i
$732$	−2.25020	−	31.6833i	−0.0831697	−	1.17105i
$733$	−3.40403	+	12.7040i	−0.125731	+	0.469234i	−0.999865	−	0.0164513i	$-0.994763\pi$
$733$	−3.40403	+	12.7040i	−0.125731	+	0.469234i	0.874134	+	0.485685i	$0.161430\pi$
$734$	9.14618	+	4.85672i	0.337592	+	0.179265i
$735$	7.86303	+	5.22945i	0.290032	+	0.192891i
$736$	27.6937	+	32.8221i	1.02080	+	1.20984i
$737$	−0.726609	−	1.25852i	−0.0267650	−	0.0463583i
$738$	3.44691	−	2.15648i	0.126882	−	0.0793810i
$739$	45.8794	−	12.2934i	1.68770	−	0.452218i	0.717907	−	0.696139i	$-0.245100\pi$
$739$	45.8794	−	12.2934i	1.68770	−	0.452218i	0.969795	+	0.243921i	$0.0784336\pi$
$740$	−9.99171	−	4.85982i	−0.367303	−	0.178650i
$741$	−41.2208	+	41.2208i	−1.51429	+	1.51429i
$742$	−23.5275	+	0.0894805i	−0.863721	+	0.00328493i
$743$		−	41.3118i		−	1.51558i	−0.652498	−	0.757791i	$-0.726279\pi$
$743$		−	41.3118i		−	1.51558i	0.652498	−	0.757791i	$-0.273721\pi$
$744$	12.3985	+	1.94296i	0.454550	+	0.0712324i
$745$	−12.9411	−	7.47157i	−0.474126	−	0.273737i
$746$	−6.12067	+	26.5776i	−0.224094	+	0.973074i
$747$	−6.73330	−	1.80418i	−0.246359	−	0.0660116i
$748$	0.215054	+	0.0415591i	0.00786314	+	0.00151955i
$749$	33.7386	+	20.9297i	1.23278	+	0.764753i
$750$	−0.894749	+	1.68499i	−0.0326716	+	0.0615272i
$751$	9.50189	+	16.4578i	0.346729	+	0.600552i	0.985666	−	0.168707i	$-0.0539590\pi$
$751$	9.50189	+	16.4578i	0.346729	+	0.600552i	−0.638937	+	0.769259i	$0.720626\pi$
$752$	8.71697	+	11.1072i	0.317875	+	0.405040i
$753$	12.4291	−	21.5278i	0.452941	−	0.784517i
$754$	34.9197	−	1.23846i	1.27170	−	0.0451022i
$755$	4.67977	+	4.67977i	0.170314	+	0.170314i
$756$	25.2362	−	15.9223i	0.917832	−	0.579089i
$757$	−8.84848	+	8.84848i	−0.321603	+	0.321603i	−0.849382	−	0.527779i	$-0.823025\pi$
$757$	−8.84848	+	8.84848i	−0.321603	+	0.321603i	0.527779	+	0.849382i	$0.323025\pi$
$758$	−12.3799	−	11.5318i	−0.449658	−	0.418855i
$759$	−2.44441	−	1.41128i	−0.0887266	−	0.0512263i
$760$	21.5922	+	9.57124i	0.783233	+	0.347185i
$761$	29.4564	−	17.0067i	1.06779	−	0.616491i	0.140216	−	0.990121i	$-0.455220\pi$
$761$	29.4564	−	17.0067i	1.06779	−	0.616491i	0.927578	+	0.373629i	$0.121887\pi$
$762$	−2.72552	−	8.89742i	−0.0987350	−	0.322320i
$763$	18.2675	+	0.578325i	0.661329	+	0.0209368i
$764$	−13.2172	−	19.5493i	−0.478180	−	0.707268i
$765$	−0.121369	+	0.452957i	−0.00438812	+	0.0163767i
$766$	23.2322	−	14.5347i	0.839413	−	0.525159i
$767$	34.4891	−	59.7369i	1.24533	−	2.15697i
$768$	−18.4529	+	11.1974i	−0.665862	+	0.404050i
$769$	−20.5789			−0.742092			−0.371046	−	0.928614i	$-0.621001\pi$
$769$	−20.5789			−0.742092			−0.371046	+	0.928614i	$0.621001\pi$
$770$	−0.997094	−	0.263110i	−0.0359328	−	0.00948183i
$771$	−3.80033	−	3.80033i	−0.136866	−	0.136866i
$772$	7.60660	−	15.6390i	0.273767	−	0.562862i
$773$	−3.73941	−	13.9557i	−0.134497	−	0.501950i	−0.999999	−	0.00104516i	$-0.999667\pi$
$773$	−3.73941	−	13.9557i	−0.134497	−	0.501950i	0.865502	−	0.500905i	$-0.166999\pi$
$774$	17.3509	+	3.99582i	0.623665	+	0.143627i
$775$	2.84839	−	1.64452i	0.102317	−	0.0590729i
$776$	−3.50877	−	32.8671i	−0.125958	−	1.17986i
$777$	−18.9809	−	5.73548i	−0.680936	−	0.205759i
$778$	15.6416	−	4.79142i	0.560777	−	0.171781i
$779$	19.6503	+	5.26528i	0.704045	+	0.188648i
$780$	−10.5474	−	9.14856i	−0.377657	−	0.327571i
$781$	4.32034	−	1.15763i	0.154594	−	0.0414233i
$782$	−4.26348	+	0.151209i	−0.152462	+	0.00540723i
$783$	−26.9238			−0.962177
$784$	25.2720	+	12.0551i	0.902572	+	0.430539i
$785$	−12.4235			−0.443412
$786$	−0.377799	+	0.0133990i	−0.0134756	+	0.000477928i
$787$	−11.7839	+	3.15748i	−0.420050	+	0.112552i	−0.462652	−	0.886540i	$-0.653102\pi$
$787$	−11.7839	+	3.15748i	−0.420050	+	0.112552i	0.0426019	+	0.999092i	$0.486435\pi$
$788$	−3.46947	+	3.99996i	−0.123595	+	0.142493i
$789$	17.2251	+	4.61544i	0.613229	+	0.164314i
$790$	−0.624144	+	0.191192i	−0.0222060	+	0.00680229i
$791$	12.7163	+	3.84251i	0.452141	+	0.136624i
$792$	−0.577766	+	0.715870i	−0.0205300	+	0.0254373i
$793$	52.7599	−	30.4610i	1.87356	−	1.08170i
$794$	−14.8272	−	3.41462i	−0.526197	−	0.121180i
$795$	−2.19550	−	8.19370i	−0.0778662	−	0.290601i
$796$	4.65407	+	2.26367i	0.164959	+	0.0802336i
$797$	17.4265	+	17.4265i	0.617278	+	0.617278i	0.944832	−	0.327554i	$-0.106224\pi$
$797$	17.4265	+	17.4265i	0.617278	+	0.617278i	−0.327554	+	0.944832i	$0.606224\pi$
$798$	40.7546	+	10.7542i	1.44270	+	0.380694i
$799$	−1.40263			−0.0496216
$800$	−1.92027	+	5.32095i	−0.0678920	+	0.188124i
$801$	6.65324	−	11.5238i	0.235081	−	0.407172i
$802$	3.69707	−	2.31299i	0.130548	−	0.0816744i
$803$	−1.00777	+	3.76103i	−0.0355633	+	0.132724i
$804$	−11.7855	+	7.96813i	−0.415643	+	0.281014i
$805$	20.0754	+	0.635559i	0.707565	+	0.0224005i
$806$	7.05009	+	23.0150i	0.248329	+	0.810667i
$807$	12.3933	−	7.15529i	0.436266	−	0.251878i
$808$	−11.9172	+	4.59692i	−0.419244	+	0.161719i
$809$	23.3114	+	13.4589i	0.819586	+	0.473188i	0.850274	−	0.526341i	$-0.176436\pi$
$809$	23.3114	+	13.4589i	0.819586	+	0.473188i	−0.0306878	+	0.999529i	$0.509770\pi$
$810$	4.20859	+	3.92029i	0.147875	+	0.137745i
$811$	15.0306	−	15.0306i	0.527795	−	0.527795i	−0.392120	−	0.919914i	$-0.628258\pi$
$811$	15.0306	−	15.0306i	0.527795	−	0.527795i	0.919914	+	0.392120i	$0.128258\pi$
$812$	−13.4810	−	21.3668i	−0.473090	−	0.749828i
$813$	−12.8011	−	12.8011i	−0.448955	−	0.448955i
$814$	2.16396	−	0.0767474i	0.0758469	−	0.00268999i
$815$	−9.67545	+	16.7584i	−0.338916	+	0.587020i
$816$	0.256679	−	2.12881i	0.00898555	−	0.0745233i
$817$	44.5432	+	77.1511i	1.55837	+	2.69918i
$818$	−9.35529	+	17.6179i	−0.327100	+	0.615995i
$819$	13.7302	+	8.51750i	0.479772	+	0.297625i
$820$	−0.924498	+	4.78395i	−0.0322849	+	0.167063i
$821$	26.8813	+	7.20283i	0.938165	+	0.251380i	0.695333	−	0.718688i	$-0.255257\pi$
$821$	26.8813	+	7.20283i	0.938165	+	0.251380i	0.242832	+	0.970068i	$0.421924\pi$
$822$	−2.39065	+	10.3808i	−0.0833833	+	0.362072i
$823$	−15.3299	−	8.85074i	−0.534368	−	0.308517i	0.208425	−	0.978038i	$-0.433166\pi$
$823$	−15.3299	−	8.85074i	−0.534368	−	0.308517i	−0.742793	+	0.669521i	$0.766499\pi$
$824$	−9.35770	−	12.8356i	−0.325991	−	0.447150i
$825$		−	0.371801i		−	0.0129445i
$826$	−49.8736	+	0.189681i	−1.73532	+	0.00659985i
$827$	8.65865	−	8.65865i	0.301091	−	0.301091i	−0.540350	−	0.841441i	$-0.681708\pi$
$827$	8.65865	−	8.65865i	0.301091	−	0.301091i	0.841441	+	0.540350i	$0.181708\pi$
$828$	7.83714	−	16.1130i	0.272359	−	0.559967i
$829$	−18.1230	+	4.85605i	−0.629438	+	0.168658i	−0.559415	−	0.828888i	$-0.688974\pi$
$829$	−18.1230	+	4.85605i	−0.629438	+	0.168658i	−0.0700236	+	0.997545i	$0.522307\pi$
$830$	7.08187	−	4.43061i	0.245815	−	0.153789i
$831$	−2.47902	−	4.29379i	−0.0859963	−	0.148950i
$832$	−34.7938	−	22.4341i	−1.20626	−	0.777761i
$833$	−2.49204	+	1.23562i	−0.0863442	+	0.0428117i
$834$	−5.42167	−	2.87897i	−0.187737	−	0.0996905i
$835$	−1.62738	+	6.07348i	−0.0563180	+	0.210182i
$836$	−4.59128	+	0.326080i	−0.158793	+	0.0112777i
$837$	−4.80038	−	17.9152i	−0.165925	−	0.619242i
$838$	24.9248	−	26.7578i	0.861014	−	0.924334i
$839$		−	42.0851i		−	1.45294i	−0.687199	−	0.726469i	$-0.741160\pi$
$839$		−	42.0851i		−	1.45294i	0.687199	−	0.726469i	$-0.258840\pi$
$840$	−1.87775	+	9.91906i	−0.0647887	+	0.342240i
$841$		−	6.20439i		−	0.213944i
$842$	10.6544	+	9.92453i	0.367174	+	0.342022i
$843$	4.27361	+	15.9493i	0.147191	+	0.549324i
$844$	−36.8978	−	32.0042i	−1.27007	−	1.10163i
$845$	3.56644	−	13.3101i	0.122689	−	0.457882i
$846$	2.76286	−	5.20301i	0.0949889	−	0.178883i
$847$	−28.1402	+	6.59333i	−0.966909	+	0.226550i
$848$	−9.87813	−	23.1312i	−0.339216	−	0.794328i
$849$	−16.7289	−	28.9753i	−0.574135	−	0.994431i
$850$	−0.298052	−	0.476406i	−0.0102231	−	0.0163406i
$851$	−40.7376	+	10.9156i	−1.39647	+	0.374183i
$852$	−14.3005	−	41.3851i	−0.489926	−	1.41783i
$853$	24.5255	−	24.5255i	0.839736	−	0.839736i	−0.149088	−	0.988824i	$-0.547634\pi$
$853$	24.5255	−	24.5255i	0.839736	−	0.839736i	0.988824	+	0.149088i	$0.0476338\pi$
$854$	−38.2310	−	21.8792i	−1.30824	−	0.748691i
$855$		−	9.85442i		−	0.337014i
$856$	−6.57128	+	41.9327i	−0.224602	+	1.43323i
$857$	25.0777	+	14.4786i	0.856637	+	0.494580i	0.862885	−	0.505401i	$-0.168655\pi$
$857$	25.0777	+	14.4786i	0.856637	+	0.494580i	−0.00624767	+	0.999980i	$0.501989\pi$
$858$	2.65159	+	0.610648i	0.0905239	+	0.0208472i
$859$	28.0188	+	7.50761i	0.955989	+	0.256156i	0.702902	−	0.711287i	$-0.251887\pi$
$859$	28.0188	+	7.50761i	0.955989	+	0.256156i	0.253087	+	0.967443i	$0.418554\pi$
$860$	−17.6762	+	11.9508i	−0.602754	+	0.407519i
$861$	−0.275146	+	8.69104i	−0.00937695	+	0.296190i
$862$	−12.8004	−	6.79715i	−0.435983	−	0.231512i
$863$	−21.6002	−	37.4127i	−0.735281	−	1.27354i	−0.954600	−	0.297891i	$-0.903717\pi$
$863$	−21.6002	−	37.4127i	−0.735281	−	1.27354i	0.219319	−	0.975653i	$-0.429616\pi$
$864$	26.1804	+	18.2256i	0.890674	+	0.620048i
$865$	−11.1743	+	19.3545i	−0.379939	+	0.658074i
$866$	0.290158	+	8.18128i	0.00985997	+	0.278011i
$867$	−16.0658	−	16.0658i	−0.545625	−	0.545625i
$868$	11.8140	−	12.7799i	0.400994	−	0.433779i
$869$	0.0899538	−	0.0899538i	0.00305147	−	0.00305147i
$870$	6.20858	−	6.66516i	0.210491	−	0.225970i
$871$	−23.6306	−	13.6431i	−0.800693	−	0.462280i
$872$	7.03181	+	18.2294i	0.238127	+	0.617325i
$873$	−11.9435	+	6.89558i	−0.404226	+	0.233380i
$874$	85.7194	−	26.2581i	2.89950	−	0.888194i
$875$	1.24971	+	2.33200i	0.0422479	+	0.0788360i
$876$	37.4253	+	7.23243i	1.26448	+	0.244361i
$877$	−14.6993	+	54.8586i	−0.496361	+	1.85244i	0.0259105	+	0.999664i	$0.491752\pi$
$877$	−14.6993	+	54.8586i	−0.496361	+	1.85244i	−0.522271	+	0.852779i	$0.674915\pi$
$878$	11.0985	+	17.7397i	0.374555	+	0.598687i
$879$	−1.42108	+	2.46138i	−0.0479317	+	0.0830202i
$880$	−0.155806	−	1.09136i	−0.00525222	−	0.0367897i
$881$	31.4930			1.06102			0.530512	−	0.847677i	$-0.322000\pi$
$881$	31.4930			1.06102			0.530512	+	0.847677i	$0.322000\pi$
$882$	0.325256	−	11.6780i	0.0109519	−	0.393219i
$883$	−27.9719	−	27.9719i	−0.941328	−	0.941328i	0.0570436	−	0.998372i	$-0.481833\pi$
$883$	−27.9719	−	27.9719i	−0.941328	−	0.941328i	−0.998372	+	0.0570436i	$0.981833\pi$
$884$	3.88713	−	1.34318i	0.130738	−	0.0451762i
$885$	−4.65402	−	17.3690i	−0.156443	−	0.583853i
$886$	7.47351	−	32.4519i	0.251077	−	1.09024i
$887$	−2.30013	+	1.32798i	−0.0772307	+	0.0445892i	−0.538118	−	0.842869i	$-0.680865\pi$
$887$	−2.30013	+	1.32798i	−0.0772307	+	0.0445892i	0.460887	+	0.887459i	$0.347531\pi$
$888$	−2.25019	−	21.0778i	−0.0755116	−	0.707325i
$889$	−12.3532	−	3.73277i	−0.414312	−	0.125193i
$890$	4.67050	+	15.2468i	0.156555	+	0.511074i
$891$	−1.08269	−	0.290107i	−0.0362716	−	0.00971895i
$892$	9.59860	−	0.681708i	0.321385	−	0.0228253i
$893$	28.4712	−	7.62884i	0.952753	−	0.255289i
$894$	−1.01046	−	28.4909i	−0.0337949	−	0.952877i
$895$	7.12716			0.238235
$896$	−1.35518	+	29.9026i	−0.0452732	+	0.998975i
$897$	−52.9978			−1.76954
$898$	0.943090	+	26.5913i	0.0314713	+	0.887363i
$899$	−15.1683	+	4.06435i	−0.505893	+	0.135554i
$900$	2.35430	−	0.167206i	0.0784766	−	0.00557353i
$901$	2.41350	+	0.646696i	0.0804054	+	0.0215446i
$902$	−0.278119	−	0.907917i	−0.00926034	−	0.0302303i
$903$	−27.7638	+	26.0598i	−0.923922	+	0.867217i
$904$	1.50753	+	14.1212i	0.0501396	+	0.469663i
$905$	−10.0421	+	5.79781i	−0.333811	+	0.192726i
$906$	−2.83360	+	12.3042i	−0.0941401	+	0.408781i
$907$	−6.59383	−	24.6085i	−0.218945	−	0.817113i	−0.984741	−	0.174029i	$-0.944321\pi$
$907$	−6.59383	−	24.6085i	−0.218945	−	0.817113i	0.765796	−	0.643084i	$-0.222345\pi$
$908$	15.9766	−	5.52065i	0.530201	−	0.183209i
$909$	3.76841	+	3.76841i	0.124990	+	0.124990i
$910$	−18.6838	+	5.08254i	−0.619361	+	0.168484i
$911$	−13.6975			−0.453820			−0.226910	−	0.973916i	$-0.572862\pi$
$911$	−13.6975			−0.453820			−0.226910	+	0.973916i	$0.572862\pi$
$912$	6.36831	+	44.6075i	0.210876	+	1.47710i
$913$	−0.813991	+	1.40987i	−0.0269392	+	0.0466600i
$914$	−18.2802	−	29.2190i	−0.604656	−	0.966480i
$915$	4.11045	−	15.3404i	0.135887	−	0.507139i
$916$	2.93638	+	0.567456i	0.0970207	+	0.0187493i
$917$	−0.276364	+	0.445499i	−0.00912635	+	0.0147117i
$918$	−3.02997	+	0.928160i	−0.100004	+	0.0306338i
$919$	−16.9270	+	9.77278i	−0.558369	+	0.322374i	−0.752491	−	0.658603i	$-0.771148\pi$
$919$	−16.9270	+	9.77278i	−0.558369	+	0.322374i	0.194122	+	0.980977i	$0.437814\pi$
$920$	7.72772	+	20.0335i	0.254775	+	0.660485i
$921$	25.5715	+	14.7637i	0.842610	+	0.486481i
$922$	36.8093	−	39.5162i	1.21225	−	1.30140i
$923$	59.3844	−	59.3844i	1.95466	−	1.95466i
$924$	−0.583383	−	1.87890i	−0.0191919	−	0.0618114i
$925$	−3.92830	−	3.92830i	−0.129162	−	0.129162i
$926$	1.50157	+	42.3381i	0.0493446	+	1.39132i
$927$	−3.31378	+	5.73964i	−0.108839	+	0.188515i
$928$	15.4311	−	22.1662i	0.506552	−	0.727641i
$929$	−25.6859	−	44.4893i	−0.842727	−	1.45965i	−0.887580	−	0.460653i	$-0.847615\pi$
$929$	−25.6859	−	44.4893i	−0.842727	−	1.45965i	0.0448529	−	0.998994i	$-0.485718\pi$
$930$	5.54200	+	2.94286i	0.181729	+	0.0965003i
$931$	43.8640	−	38.6352i	1.43759	−	1.26622i
$932$	27.4534	−	18.5611i	0.899267	−	0.607989i
$933$	5.61994	+	1.50586i	0.183989	+	0.0492996i
$934$	−4.52004	−	1.04094i	−0.147900	−	0.0340606i
$935$	0.0948438	+	0.0547581i	0.00310172	+	0.00179078i
$936$	−2.67423	+	17.0649i	−0.0874101	+	0.557783i
$937$			37.1760i			1.21449i	0.794515	+	0.607244i	$0.207725\pi$
$937$			37.1760i			1.21449i	−0.794515	+	0.607244i	$0.792275\pi$
$938$	0.0750337	+	19.7289i	0.00244994	+	0.644171i
$939$	11.7321	−	11.7321i	0.382864	−	0.382864i
$940$	2.30568	+	6.67255i	0.0752029	+	0.217635i
$941$	−4.34462	+	1.16414i	−0.141631	+	0.0379498i	−0.328938	−	0.944352i	$-0.606691\pi$
$941$	−4.34462	+	1.16414i	−0.141631	+	0.0379498i	0.187307	+	0.982301i	$0.440024\pi$
$942$	−12.5709	−	20.0933i	−0.409583	−	0.654676i
$943$	9.24743	+	16.0170i	0.301138	+	0.521586i
$944$	−20.9397	−	49.0335i	−0.681528	−	1.59590i
$945$	14.5263	−	3.40355i	0.472540	−	0.110717i
$946$	1.95017	−	3.67256i	0.0634055	−	0.119405i
$947$	−2.11111	+	7.87878i	−0.0686019	+	0.256026i	−0.991707	−	0.128523i	$-0.958976\pi$
$947$	−2.11111	+	7.87878i	−0.0686019	+	0.256026i	0.923105	+	0.384549i	$0.125643\pi$
$948$	−0.940781	−	0.816011i	−0.0305551	−	0.0265028i
$949$	18.9223	+	70.6189i	0.614243	+	2.29239i
$950$	8.64112	+	8.04918i	0.280355	+	0.261150i
$951$			33.6001i			1.08956i
$952$	−2.25373	−	1.93986i	−0.0730437	−	0.0628712i
$953$			29.8848i			0.968064i	0.875050	+	0.484032i	$0.160828\pi$
$953$			29.8848i			0.968064i	−0.875050	+	0.484032i	$0.839172\pi$
$954$	−7.15291	+	7.67894i	−0.231584	+	0.248615i
$955$	−3.05381	−	11.3970i	−0.0988190	−	0.368797i
$956$	20.6201	−	1.46447i	0.666900	−	0.0473643i
$957$	−0.459444	+	1.71467i	−0.0148517	+	0.0554274i
$958$	−2.76129	−	1.46628i	−0.0892133	−	0.0473732i
$959$	10.1102	+	10.7713i	0.326476	+	0.347824i
$960$	−10.5490	+	2.27832i	−0.340468	+	0.0735325i
$961$	10.0911	+	17.4783i	0.325520	+	0.563817i
$962$	34.4675	−	21.5638i	1.11128	−	0.695244i
$963$	17.1058	−	4.58349i	0.551228	−	0.147701i
$964$	−11.4932	+	23.6299i	−0.370172	+	0.761068i
$965$	6.14858	−	6.14858i	0.197930	−	0.197930i
$966$	19.2858	+	33.1125i	0.620510	+	1.06538i
$967$			3.55646i			0.114368i	0.998364	+	0.0571840i	$0.0182122\pi$
$967$			3.55646i			0.114368i	−0.998364	+	0.0571840i	$0.981788\pi$
$968$	−18.2021	−	24.9672i	−0.585038	−	0.802476i
$969$	−3.87659	−	2.23815i	−0.124534	−	0.0718997i
$970$	3.70898	−	16.1054i	0.119088	−	0.517112i
$971$	9.62126	+	2.57801i	0.308761	+	0.0827322i	0.409872	−	0.912143i	$-0.365573\pi$
$971$	9.62126	+	2.57801i	0.308761	+	0.0827322i	−0.101112	+	0.994875i	$0.532240\pi$
$972$	4.33776	−	22.4463i	0.139134	−	0.719967i
$973$	−7.50351	+	4.02110i	−0.240551	+	0.128911i
$974$	−6.35489	+	11.9675i	−0.203624	+	0.383464i
$975$	−3.49056	−	6.04582i	−0.111787	−	0.193621i
$976$	5.63702	−	46.7517i	0.180437	−	1.49648i
$977$	−24.8692	+	43.0747i	−0.795636	+	1.37808i	0.126799	+	0.991928i	$0.459530\pi$
$977$	−24.8692	+	43.0747i	−0.795636	+	1.37808i	−0.922435	+	0.386153i	$0.873804\pi$
$978$	−36.8948	+	1.30852i	−1.17977	+	0.0418417i
$979$	−2.19742	−	2.19742i	−0.0702299	−	0.0702299i
$980$	9.97451	+	9.82391i	0.318624	+	0.313813i
$981$	5.76444	−	5.76444i	0.184045	−	0.184045i
$982$	9.54363	+	8.88987i	0.304550	+	0.283687i
$983$	−21.2421	−	12.2641i	−0.677517	−	0.391165i	0.121402	−	0.992603i	$-0.461261\pi$
$983$	−21.2421	−	12.2641i	−0.677517	−	0.391165i	−0.798919	+	0.601439i	$0.794594\pi$
$984$	−8.67289	+	3.34548i	−0.276482	+	0.106650i
$985$	−2.29280	+	1.32375i	−0.0730546	+	0.0421781i
$986$	0.785848	+	2.56539i	0.0250265	+	0.0816988i
$987$	5.95096	+	11.1047i	0.189421	+	0.353466i
$988$	−71.5969	+	48.4063i	−2.27780	+	1.54001i
$989$	−20.9620	+	78.2314i	−0.666554	+	2.48761i
$990$	−0.389942	+	0.243958i	−0.0123932	+	0.00775351i
$991$	1.70839	−	2.95902i	0.0542688	−	0.0939964i	−0.837615	−	0.546261i	$-0.816051\pi$
$991$	1.70839	−	2.95902i	0.0542688	−	0.0939964i	0.891884	+	0.452265i	$0.149384\pi$
$992$	17.5008	+	6.31586i	0.555651	+	0.200529i
$993$	14.6106			0.463653
$994$	−58.7127	−	15.4929i	−1.86225	−	0.491406i
$995$	1.82977	+	1.82977i	0.0580077	+	0.0580077i
$996$	14.3319	+	6.97081i	0.454123	+	0.220879i
$997$	2.24652	+	8.38412i	0.0711479	+	0.265528i	0.992332	−	0.123599i	$-0.0394436\pi$
$997$	2.24652	+	8.38412i	0.0711479	+	0.265528i	−0.921184	+	0.389126i	$0.872777\pi$
$998$	51.0408	+	11.7544i	1.61567	+	0.372080i
$999$	−27.1306	+	15.6639i	−0.858375	+	0.495583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.221.35	✓	256
7.2	even	3	inner	560.2.cp.a.541.51	yes	256
16.5	even	4	inner	560.2.cp.a.501.51	yes	256
112.37	even	12	inner	560.2.cp.a.261.35	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.35	✓	256	1.1	even	1	trivial
560.2.cp.a.261.35	yes	256	112.37	even	12	inner
560.2.cp.a.501.51	yes	256	16.5	even	4	inner
560.2.cp.a.541.51	yes	256	7.2	even	3	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0501251 + 1.41332i) q^{2} +(-1.30306 + 0.349155i) q^{3} +(-1.99497 + 0.141686i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-0.558786 - 1.82415i) q^{6} +(-2.53265 - 0.765294i) q^{7} +(-0.300247 - 2.81245i) q^{8} +(-1.02201 + 0.590057i) q^{9} +(0.317378 - 1.37814i) q^{10} +(0.0713321 + 0.266215i) q^{11} +(2.55011 - 0.881182i) q^{12} +(3.65921 + 3.65921i) q^{13} +(0.954660 - 3.61782i) q^{14} +1.34903 q^{15} +(3.95985 - 0.565321i) q^{16} +(-0.198682 + 0.344128i) q^{17} +(-0.885170 - 1.41485i) q^{18} +(2.16124 - 8.06586i) q^{19} +(1.96367 + 0.379479i) q^{20} +(3.56741 + 0.112939i) q^{21} +(-0.372673 + 0.114160i) q^{22} +(6.57451 - 3.79580i) q^{23} +(1.37322 + 3.55997i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-4.98824 + 5.35507i) q^{26} +(3.98745 - 3.98745i) q^{27} +(5.16101 + 1.16790i) q^{28} +(-3.37606 - 3.37606i) q^{29} +(0.0676204 + 1.90662i) q^{30} +(1.64452 - 2.84839i) q^{31} +(0.997470 + 5.56822i) q^{32} +(-0.185901 - 0.321989i) q^{33} +(-0.496324 - 0.263553i) q^{34} +(2.24828 + 1.39472i) q^{35} +(1.95528 - 1.32195i) q^{36} +(-5.36615 - 1.43786i) q^{37} +(11.5080 + 2.65023i) q^{38} +(-6.04582 - 3.49056i) q^{39} +(-0.437898 + 2.79432i) q^{40} +2.43623i q^{41} +(0.0191971 + 5.04758i) q^{42} +(-7.54379 + 7.54379i) q^{43} +(-0.180025 - 0.520986i) q^{44} +(1.13990 - 0.305436i) q^{45} +(5.69424 + 9.10166i) q^{46} +(1.76492 + 3.05693i) q^{47} +(-4.96256 + 2.11925i) q^{48} +(5.82865 + 3.87645i) q^{49} +(-0.663253 + 1.24904i) q^{50} +(0.138742 - 0.517792i) q^{51} +(-7.81850 - 6.78158i) q^{52} +(-1.62746 - 6.07377i) q^{53} +(5.83543 + 5.43569i) q^{54} -0.275606i q^{55} +(-1.39193 + 7.35272i) q^{56} +11.2650i q^{57} +(4.60225 - 4.94070i) q^{58} +(-3.44989 - 12.8752i) q^{59} +(-2.69128 + 0.191139i) q^{60} +(3.04696 - 11.3714i) q^{61} +(4.10813 + 2.18146i) q^{62} +(3.03996 - 0.712271i) q^{63} +(-7.81970 + 1.68886i) q^{64} +(-2.58745 - 4.48160i) q^{65} +(0.445757 - 0.278878i) q^{66} +(-5.09314 + 1.36470i) q^{67} +(0.347608 - 0.714677i) q^{68} +(-7.24169 + 7.24169i) q^{69} +(-1.85849 + 3.24746i) q^{70} -16.2287i q^{71} +(1.96636 + 2.69718i) q^{72} +(12.2350 + 7.06390i) q^{73} +(1.76318 - 7.65619i) q^{74} +(-1.30306 - 0.349155i) q^{75} +(-3.16880 + 16.3974i) q^{76} +(0.0230734 - 0.728820i) q^{77} +(4.63024 - 8.71967i) q^{78} +(-0.230789 - 0.399739i) q^{79} +(-3.97124 - 0.478827i) q^{80} +(-2.03350 + 3.52212i) q^{81} +(-3.44318 + 0.122116i) q^{82} +(4.17682 + 4.17682i) q^{83} +(-7.13291 + 0.280142i) q^{84} +(0.280979 - 0.280979i) q^{85} +(-11.0400 - 10.2837i) q^{86} +(5.57800 + 3.22046i) q^{87} +(0.727298 - 0.280548i) q^{88} +(-9.76496 + 5.63780i) q^{89} +(0.488818 + 1.59574i) q^{90} +(-6.46714 - 12.0679i) q^{91} +(-12.5782 + 8.50404i) q^{92} +(-1.14838 + 4.28583i) q^{93} +(-4.23197 + 2.64764i) q^{94} +(-4.17520 + 7.23166i) q^{95} +(-3.24394 - 6.90748i) q^{96} +11.6863 q^{97} +(-5.18652 + 8.43208i) q^{98} +(-0.229984 - 0.229984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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