LMFDB - Embedded newform 961.2.g.k.732.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6,3,-14,-3,11,-13] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.1
Root			$1.03739i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.k.235.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02470 - 0.744490i) q^{2} +(1.35599 + 0.603725i) q^{3} +(-0.122284 - 0.376353i) q^{4} +(1.90016 - 3.29117i) q^{5} +(-0.940018 - 1.62816i) q^{6} +(1.46472 - 1.62674i) q^{7} +(-0.937688 + 2.88591i) q^{8} +(-0.533169 - 0.592145i) q^{9} +(-4.39734 + 1.95782i) q^{10} +(0.929823 + 0.197640i) q^{11} +(0.0613973 - 0.584156i) q^{12} +(-0.0175757 - 0.167221i) q^{13} +(-2.71199 + 0.576451i) q^{14} +(4.56356 - 3.31562i) q^{15} +(2.46909 - 1.79390i) q^{16} +(6.43294 - 1.36736i) q^{17} +(0.105494 + 1.00371i) q^{18} +(0.120505 - 1.14653i) q^{19} +(-1.47100 - 0.312671i) q^{20} +(2.96825 - 1.32155i) q^{21} +(-0.805651 - 0.894766i) q^{22} +(-1.43029 + 4.40197i) q^{23} +(-3.01379 + 3.34715i) q^{24} +(-4.72122 - 8.17739i) q^{25} +(-0.106485 + 0.184437i) q^{26} +(-1.74151 - 5.35983i) q^{27} +(-0.791339 - 0.352327i) q^{28} +(-1.08143 - 0.785701i) q^{29} -7.14474 q^{30} +2.20322 q^{32} +(1.14151 + 0.829355i) q^{33} +(-7.60983 - 3.38812i) q^{34} +(-2.57067 - 7.91171i) q^{35} +(-0.157657 + 0.273070i) q^{36} +(1.93582 + 3.35295i) q^{37} +(-0.977059 + 1.08513i) q^{38} +(0.0771233 - 0.237361i) q^{39} +(7.71627 + 8.56978i) q^{40} +(0.299828 - 0.133492i) q^{41} +(-4.02545 - 0.855635i) q^{42} +(-1.00667 + 9.57782i) q^{43} +(-0.0393205 - 0.374110i) q^{44} +(-2.96196 + 0.629584i) q^{45} +(4.74283 - 3.44587i) q^{46} +(-4.56170 + 3.31427i) q^{47} +(4.43108 - 0.941856i) q^{48} +(0.230833 + 2.19623i) q^{49} +(-1.25014 + 11.8943i) q^{50} +(9.54851 + 2.02960i) q^{51} +(-0.0607850 + 0.0270632i) q^{52} +(-4.90670 - 5.44944i) q^{53} +(-2.20581 + 6.78877i) q^{54} +(2.41728 - 2.68466i) q^{55} +(3.32116 + 5.75242i) q^{56} +(0.855590 - 1.48193i) q^{57} +(0.523192 + 1.61022i) q^{58} +(-2.42375 - 1.07912i) q^{59} +(-1.80590 - 1.31206i) q^{60} -1.74967 q^{61} -1.74421 q^{63} +(-7.19583 - 5.22808i) q^{64} +(-0.583751 - 0.259903i) q^{65} +(-0.552261 - 1.69968i) q^{66} +(-0.276003 + 0.478052i) q^{67} +(-1.30126 - 2.25385i) q^{68} +(-4.59703 + 5.10552i) q^{69} +(-3.25601 + 10.0210i) q^{70} +(0.760794 + 0.844947i) q^{71} +(2.20882 - 0.983431i) q^{72} +(7.74947 + 1.64720i) q^{73} +(0.512590 - 4.87697i) q^{74} +(-1.46502 - 13.9388i) q^{75} +(-0.446234 + 0.0948500i) q^{76} +(1.68344 - 1.22309i) q^{77} +(-0.255741 + 0.185807i) q^{78} +(-4.44302 + 0.944393i) q^{79} +(-1.21237 - 11.5349i) q^{80} +(0.624523 - 5.94194i) q^{81} +(-0.406618 - 0.0864293i) q^{82} +(0.298177 - 0.132757i) q^{83} +(-0.860338 - 0.955503i) q^{84} +(7.72338 - 23.7701i) q^{85} +(8.16212 - 9.06495i) q^{86} +(-0.992053 - 1.71829i) q^{87} +(-1.44225 + 2.49806i) q^{88} +(-4.54569 - 13.9902i) q^{89} +(3.50384 + 1.56001i) q^{90} +(-0.297768 - 0.216341i) q^{91} +1.83159 q^{92} +7.14183 q^{94} +(-3.54444 - 2.57519i) q^{95} +(2.98755 + 1.33014i) q^{96} +(4.79569 + 14.7596i) q^{97} +(1.39853 - 2.42233i) q^{98} +(-0.378722 - 0.655965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−1.02470	−	0.744490i	−0.724574	−	0.526434i	0.163268	−	0.986582i	$-0.447796\pi$
$2$	−1.02470	−	0.744490i	−0.724574	−	0.526434i	−0.887842	+	0.460148i	$0.847796\pi$
$3$	1.35599	+	0.603725i	0.782881	+	0.348561i	0.758947	−	0.651153i	$-0.225714\pi$
$3$	1.35599	+	0.603725i	0.782881	+	0.348561i	0.0239339	+	0.999714i	$0.492381\pi$
$4$	−0.122284	−	0.376353i	−0.0611422	−	0.188176i
$5$	1.90016	−	3.29117i	0.849778	−	1.47186i	−0.0316291	−	0.999500i	$-0.510070\pi$
$5$	1.90016	−	3.29117i	0.849778	−	1.47186i	0.881407	−	0.472358i	$-0.156597\pi$
$6$	−0.940018	−	1.62816i	−0.383761	−	0.664693i
$7$	1.46472	−	1.62674i	0.553612	−	0.614849i	−0.399770	−	0.916616i	$-0.630910\pi$
$7$	1.46472	−	1.62674i	0.553612	−	0.614849i	0.953382	+	0.301767i	$0.0975765\pi$
$8$	−0.937688	+	2.88591i	−0.331523	+	1.02032i
$9$	−0.533169	−	0.592145i	−0.177723	−	0.197382i
$10$	−4.39734	+	1.95782i	−1.39056	+	0.619118i
$11$	0.929823	+	0.197640i	0.280352	+	0.0595907i	0.345942	−	0.938256i	$-0.387559\pi$
$11$	0.929823	+	0.197640i	0.280352	+	0.0595907i	−0.0655896	+	0.997847i	$0.520893\pi$
$12$	0.0613973	−	0.584156i	0.0177239	−	0.168631i
$13$	−0.0175757	−	0.167221i	−0.00487461	−	0.0463788i	0.991814	−	0.127689i	$-0.0407561\pi$
$13$	−0.0175757	−	0.167221i	−0.00487461	−	0.0463788i	−0.996689	+	0.0813106i	$0.974089\pi$
$14$	−2.71199	+	0.576451i	−0.724810	+	0.154063i
$15$	4.56356	−	3.31562i	1.17831	−	0.856090i
$16$	2.46909	−	1.79390i	0.617273	−	0.448475i
$17$	6.43294	−	1.36736i	1.56022	−	0.331634i	0.654681	−	0.755905i	$-0.272803\pi$
$17$	6.43294	−	1.36736i	1.56022	−	0.331634i	0.905535	+	0.424271i	$0.139469\pi$
$18$	0.105494	+	1.00371i	0.0248652	+	0.236577i
$19$	0.120505	−	1.14653i	0.0276457	−	0.263031i	−0.971965	−	0.235126i	$-0.924450\pi$
$19$	0.120505	−	1.14653i	0.0276457	−	0.263031i	0.999611	−	0.0279051i	$-0.00888363\pi$
$20$	−1.47100	−	0.312671i	−0.328926	−	0.0699154i
$21$	2.96825	−	1.32155i	0.647724	−	0.288385i
$22$	−0.805651	−	0.894766i	−0.171765	−	0.190765i
$23$	−1.43029	+	4.40197i	−0.298235	+	0.917873i	0.683880	+	0.729594i	$0.260291\pi$
$23$	−1.43029	+	4.40197i	−0.298235	+	0.917873i	−0.982116	+	0.188279i	$0.939709\pi$
$24$	−3.01379	+	3.34715i	−0.615187	+	0.683235i
$25$	−4.72122	−	8.17739i	−0.944244	−	1.63548i
$26$	−0.106485	+	0.184437i	−0.0208834	+	0.0361711i
$27$	−1.74151	−	5.35983i	−0.335155	−	1.03150i
$28$	−0.791339	−	0.352327i	−0.149549	−	0.0665835i
$29$	−1.08143	−	0.785701i	−0.200816	−	0.145901i	0.482833	−	0.875713i	$-0.339608\pi$
$29$	−1.08143	−	0.785701i	−0.200816	−	0.145901i	−0.683649	+	0.729811i	$0.739608\pi$
$30$	−7.14474			−1.30444
$31$		0			0
$31$		0			0
$32$	2.20322			0.389479
$33$	1.14151	+	0.829355i	0.198711	+	0.144372i
$34$	−7.60983	−	3.38812i	−1.30508	−	0.581057i
$35$	−2.57067	−	7.91171i	−0.434523	−	1.33732i
$36$	−0.157657	+	0.273070i	−0.0262762	+	0.0455116i
$37$	1.93582	+	3.35295i	0.318248	+	0.551221i	0.980122	−	0.198393i	$-0.0635723\pi$
$37$	1.93582	+	3.35295i	0.318248	+	0.551221i	−0.661875	+	0.749614i	$0.730239\pi$
$38$	−0.977059	+	1.08513i	−0.158500	+	0.176032i
$39$	0.0771233	−	0.237361i	0.0123496	−	0.0380082i
$40$	7.71627	+	8.56978i	1.22005	+	1.35500i
$41$	0.299828	−	0.133492i	0.0468253	−	0.0208480i	−0.383190	−	0.923669i	$-0.625175\pi$
$41$	0.299828	−	0.133492i	0.0468253	−	0.0208480i	0.430016	+	0.902821i	$0.358508\pi$
$42$	−4.02545	−	0.855635i	−0.621140	−	0.132027i
$43$	−1.00667	+	9.57782i	−0.153516	+	1.46060i	0.598323	+	0.801255i	$0.295834\pi$
$43$	−1.00667	+	9.57782i	−0.153516	+	1.46060i	−0.751838	+	0.659348i	$0.770833\pi$
$44$	−0.0393205	−	0.374110i	−0.00592779	−	0.0563991i
$45$	−2.96196	+	0.629584i	−0.441543	+	0.0938528i
$46$	4.74283	−	3.44587i	0.699293	−	0.508066i
$47$	−4.56170	+	3.31427i	−0.665393	+	0.483436i	−0.868480	−	0.495725i	$-0.834903\pi$
$47$	−4.56170	+	3.31427i	−0.665393	+	0.483436i	0.203087	+	0.979161i	$0.434903\pi$
$48$	4.43108	−	0.941856i	0.639572	−	0.135945i
$49$	0.230833	+	2.19623i	0.0329761	+	0.313747i
$50$	−1.25014	+	11.8943i	−0.176797	+	1.68211i
$51$	9.54851	+	2.02960i	1.33706	+	0.284201i
$52$	−0.0607850	+	0.0270632i	−0.00842936	+	0.00375299i
$53$	−4.90670	−	5.44944i	−0.673987	−	0.748538i	0.305024	−	0.952345i	$-0.401335\pi$
$53$	−4.90670	−	5.44944i	−0.673987	−	0.748538i	−0.979011	+	0.203806i	$0.934669\pi$
$54$	−2.20581	+	6.78877i	−0.300172	+	0.923835i
$55$	2.41728	−	2.68466i	0.325946	−	0.362000i
$56$	3.32116	+	5.75242i	0.443809	+	0.768699i
$57$	0.855590	−	1.48193i	0.113326	−	0.196286i
$58$	0.523192	+	1.61022i	0.0686985	+	0.211432i
$59$	−2.42375	−	1.07912i	−0.315545	−	0.140490i	0.242853	−	0.970063i	$-0.421917\pi$
$59$	−2.42375	−	1.07912i	−0.315545	−	0.140490i	−0.558397	+	0.829574i	$0.688584\pi$
$60$	−1.80590	−	1.31206i	−0.233140	−	0.169386i
$61$	−1.74967			−0.224023			−0.112011	−	0.993707i	$-0.535729\pi$
$61$	−1.74967			−0.224023			−0.112011	+	0.993707i	$0.535729\pi$
$62$		0			0
$63$	−1.74421			−0.219749
$64$	−7.19583	−	5.22808i	−0.899479	−	0.653510i
$65$	−0.583751	−	0.259903i	−0.0724054	−	0.0322370i
$66$	−0.552261	−	1.69968i	−0.0679786	−	0.209217i
$67$	−0.276003	+	0.478052i	−0.0337192	+	0.0584033i	−0.882393	−	0.470514i	$-0.844069\pi$
$67$	−0.276003	+	0.478052i	−0.0337192	+	0.0584033i	0.848673	+	0.528917i	$0.177402\pi$
$68$	−1.30126	−	2.25385i	−0.157801	−	0.273319i
$69$	−4.59703	+	5.10552i	−0.553417	+	0.614632i
$70$	−3.25601	+	10.0210i	−0.389168	+	1.19774i
$71$	0.760794	+	0.844947i	0.0902896	+	0.100277i	0.786596	−	0.617468i	$-0.211841\pi$
$71$	0.760794	+	0.844947i	0.0902896	+	0.100277i	−0.696307	+	0.717744i	$0.745175\pi$
$72$	2.20882	−	0.983431i	0.260312	−	0.115898i
$73$	7.74947	+	1.64720i	0.907007	+	0.192790i	0.637719	−	0.770269i	$-0.279878\pi$
$73$	7.74947	+	1.64720i	0.907007	+	0.192790i	0.269288	+	0.963060i	$0.413212\pi$
$74$	0.512590	−	4.87697i	0.0595874	−	0.566937i
$75$	−1.46502	−	13.9388i	−0.169166	−	1.60951i
$76$	−0.446234	+	0.0948500i	−0.0511866	+	0.0108800i
$77$	1.68344	−	1.22309i	0.191846	−	0.139384i
$78$	−0.255741	+	0.185807i	−0.0289570	+	0.0210385i
$79$	−4.44302	+	0.944393i	−0.499879	+	0.106253i	−0.450949	−	0.892550i	$-0.648914\pi$
$79$	−4.44302	+	0.944393i	−0.499879	+	0.106253i	−0.0489298	+	0.998802i	$0.515581\pi$
$80$	−1.21237	−	11.5349i	−0.135547	−	1.28964i
$81$	0.624523	−	5.94194i	0.0693914	−	0.660215i
$82$	−0.406618	−	0.0864293i	−0.0449034	−	0.00954452i
$83$	0.298177	−	0.132757i	0.0327292	−	0.0145720i	−0.390307	−	0.920685i	$-0.627631\pi$
$83$	0.298177	−	0.132757i	0.0327292	−	0.0145720i	0.423036	+	0.906113i	$0.360964\pi$
$84$	−0.860338	−	0.955503i	−0.0938706	−	0.104254i
$85$	7.72338	−	23.7701i	0.837719	−	2.57823i
$86$	8.16212	−	9.06495i	0.880144	−	0.977499i
$87$	−0.992053	−	1.71829i	−0.106359	−	0.184220i
$88$	−1.44225	+	2.49806i	−0.153745	+	0.266294i
$89$	−4.54569	−	13.9902i	−0.481842	−	1.48296i	−0.836503	−	0.547962i	$-0.815404\pi$
$89$	−4.54569	−	13.9902i	−0.481842	−	1.48296i	0.354661	−	0.934995i	$-0.384596\pi$
$90$	3.50384	+	1.56001i	0.369338	+	0.164440i
$91$	−0.297768	−	0.216341i	−0.0312146	−	0.0226787i
$92$	1.83159			0.190957
$93$		0			0
$94$	7.14183			0.736623
$95$	−3.54444	−	2.57519i	−0.363652	−	0.264209i
$96$	2.98755	+	1.33014i	0.304915	+	0.135757i
$97$	4.79569	+	14.7596i	0.486929	+	1.49861i	0.829168	+	0.559000i	$0.188815\pi$
$97$	4.79569	+	14.7596i	0.486929	+	1.49861i	−0.342239	+	0.939613i	$0.611185\pi$
$98$	1.39853	−	2.42233i	0.141273	−	0.244692i
$99$	−0.378722	−	0.655965i	−0.0380630	−	0.0659270i
$100$	−2.50025	+	2.77681i	−0.250025	+	0.277681i
$101$	1.50602	−	4.63507i	0.149855	−	0.461206i	−0.847748	−	0.530399i	$-0.822042\pi$
$101$	1.50602	−	4.63507i	0.149855	−	0.461206i	0.997603	+	0.0691923i	$0.0220422\pi$
$102$	−8.27336	−	9.18850i	−0.819185	−	0.909797i
$103$	1.76371	−	0.785254i	0.173783	−	0.0773733i	−0.318001	−	0.948090i	$-0.603012\pi$
$103$	1.76371	−	0.785254i	0.173783	−	0.0773733i	0.491784	+	0.870717i	$0.336345\pi$
$104$	0.499066	+	0.106080i	0.0489374	+	0.0104020i
$105$	1.29070	−	12.2802i	0.125959	−	1.19842i
$106$	0.970852	+	9.23704i	0.0942975	+	0.897181i
$107$	−12.2538	+	2.60462i	−1.18462	+	0.251798i	−0.757767	−	0.652525i	$-0.773710\pi$
$107$	−12.2538	+	2.60462i	−1.18462	+	0.251798i	−0.426849	+	0.904323i	$0.640376\pi$
$108$	−1.80423	+	1.31085i	−0.173612	+	0.126136i
$109$	8.30253	−	6.03214i	0.795238	−	0.577774i	−0.114275	−	0.993449i	$-0.536455\pi$
$109$	8.30253	−	6.03214i	0.795238	−	0.577774i	0.909513	+	0.415675i	$0.136455\pi$
$110$	−4.47570	+	0.951338i	−0.426741	+	0.0907066i
$111$	0.600699	+	5.71526i	0.0570158	+	0.542469i
$112$	0.698325	−	6.64412i	0.0659855	−	0.627810i
$113$	3.75896	+	0.798993i	0.353614	+	0.0751629i	0.381294	−	0.924454i	$-0.375479\pi$
$113$	3.75896	+	0.798993i	0.353614	+	0.0751629i	−0.0276801	+	0.999617i	$0.508812\pi$
$114$	−1.98000	+	0.881554i	−0.185444	+	0.0825651i
$115$	11.7699	+	13.0718i	1.09755	+	1.21895i
$116$	−0.163459	+	0.503076i	−0.0151768	+	0.0467095i
$117$	−0.0896484	+	0.0995646i	−0.00828800	+	0.00920475i
$118$	1.68022	+	2.91023i	0.154677	+	0.267908i
$119$	7.19811	−	12.4675i	0.659850	−	1.14289i
$120$	5.28938	+	16.2790i	0.482852	+	1.48607i
$121$	−9.22349	−	4.10656i	−0.838499	−	0.373324i
$122$	1.79289	+	1.30261i	0.162321	+	0.117933i
$123$	0.487156			0.0439254
$124$		0			0
$125$	−16.8827			−1.51003
$126$	1.78729	+	1.29854i	0.159225	+	0.115684i
$127$	6.70897	+	2.98703i	0.595325	+	0.265056i	0.682203	−	0.731163i	$-0.261022\pi$
$127$	6.70897	+	2.98703i	0.595325	+	0.265056i	−0.0868775	+	0.996219i	$0.527689\pi$
$128$	2.11967	+	6.52366i	0.187354	+	0.576616i
$129$	−7.14740	+	12.3797i	−0.629294	+	1.08997i
$130$	0.404676	+	0.700920i	0.0354924	+	0.0614747i
$131$	8.72123	−	9.68591i	0.761977	−	0.846262i	−0.229932	−	0.973207i	$-0.573851\pi$
$131$	8.72123	−	9.68591i	0.761977	−	0.846262i	0.991910	+	0.126945i	$0.0405172\pi$
$132$	0.172541	−	0.531027i	0.0150178	−	0.0462200i
$133$	−1.68859	−	1.87537i	−0.146419	−	0.162615i
$134$	0.638726	−	0.284379i	0.0551775	−	0.0245666i
$135$	−20.9493	−	4.45291i	−1.80303	−	0.383246i
$136$	−2.08601	+	19.8470i	−0.178874	+	1.70187i
$137$	0.0140381	+	0.133564i	0.00119936	+	0.0114111i	0.995105	−	0.0988212i	$-0.0315072\pi$
$137$	0.0140381	+	0.133564i	0.00119936	+	0.0114111i	−0.993906	+	0.110232i	$0.964841\pi$
$138$	8.51159	−	1.80919i	0.724555	−	0.154009i
$139$	−9.32593	+	6.77569i	−0.791015	+	0.574706i	−0.908265	−	0.418396i	$-0.862592\pi$
$139$	−9.32593	+	6.77569i	−0.791015	+	0.574706i	0.117249	+	0.993103i	$0.462592\pi$
$140$	−2.66324	+	1.93496i	−0.225085	+	0.163534i
$141$	−8.18653	+	1.74010i	−0.689430	+	0.146543i
$142$	−0.150533	−	1.43222i	−0.0126324	−	0.120189i
$143$	0.0167074	−	0.158960i	0.00139714	−	0.0132929i
$144$	−2.37869	−	0.505607i	−0.198224	−	0.0421339i
$145$	−4.64076	+	2.06620i	−0.385394	+	0.171589i
$146$	−6.71457	−	7.45729i	−0.555702	−	0.617170i
$147$	−1.01291	+	3.11742i	−0.0835435	+	0.257120i
$148$	1.02517	−	1.13857i	0.0842684	−	0.0935895i
$149$	2.72054	+	4.71211i	0.222875	+	0.386031i	0.955680	−	0.294408i	$-0.0951224\pi$
$149$	2.72054	+	4.71211i	0.222875	+	0.386031i	−0.732805	+	0.680439i	$0.761789\pi$
$150$	−8.87606	+	15.3738i	−0.724727	+	1.25526i
$151$	4.23019	+	13.0192i	0.344248	+	1.05949i	0.961985	+	0.273102i	$0.0880496\pi$
$151$	4.23019	+	13.0192i	0.344248	+	1.05949i	−0.617737	+	0.786385i	$0.711950\pi$
$152$	3.19577	+	1.42285i	0.259211	+	0.115408i
$153$	−4.23952	−	3.08019i	−0.342745	−	0.249019i
$154$	−2.63560			−0.212383
$155$		0			0
$156$	−0.0987625			−0.00790733
$157$	12.1800	+	8.84931i	0.972072	+	0.706252i	0.955923	−	0.293618i	$-0.0948593\pi$
$157$	12.1800	+	8.84931i	0.972072	+	0.706252i	0.0161493	+	0.999870i	$0.494859\pi$
$158$	5.25586	+	2.34006i	0.418134	+	0.186165i
$159$	−3.36346	−	10.3517i	−0.266740	−	0.820942i
$160$	4.18648	−	7.25120i	0.330970	−	0.573257i
$161$	5.06587	+	8.77434i	0.399246	+	0.691515i
$162$	−5.06366	+	5.62377i	−0.397839	+	0.441845i
$163$	5.26506	−	16.2042i	0.412391	−	1.26921i	−0.502172	−	0.864768i	$-0.667466\pi$
$163$	5.26506	−	16.2042i	0.412391	−	1.26921i	0.914563	−	0.404443i	$-0.132534\pi$
$164$	−0.0869044	−	0.0965171i	−0.00678609	−	0.00753672i
$165$	4.89860	−	2.18100i	0.381356	−	0.169791i
$166$	−0.404379	−	0.0859535i	−0.0313859	−	0.00667129i
$167$	1.69318	−	16.1095i	0.131022	−	1.24659i	−0.709458	−	0.704748i	$-0.751060\pi$
$167$	1.69318	−	16.1095i	0.131022	−	1.24659i	0.840480	−	0.541843i	$-0.182273\pi$
$168$	1.03058	+	9.80529i	0.0795107	+	0.756494i
$169$	12.6883	−	2.69697i	0.976020	−	0.207460i
$170$	−25.6108	+	18.6073i	−1.96426	+	1.42712i
$171$	−0.743159	+	0.539937i	−0.0568308	+	0.0412900i
$172$	3.72774	−	0.792355i	0.284237	−	0.0604165i
$173$	0.243679	+	2.31845i	0.0185265	+	0.176268i	0.999872	−	0.0159831i	$-0.00508779\pi$
$173$	0.243679	+	2.31845i	0.0185265	+	0.176268i	−0.981346	+	0.192251i	$0.938421\pi$
$174$	−0.262688	+	2.49930i	−0.0199143	+	0.189472i
$175$	−20.2177	−	4.29741i	−1.52832	−	0.324854i
$176$	2.65036	−	1.18002i	0.199779	−	0.0889472i
$177$	−2.63508	−	2.92655i	−0.198065	−	0.219973i
$178$	−5.75758	+	17.7200i	−0.431549	+	1.32817i
$179$	−11.3556	+	12.6116i	−0.848755	+	0.942638i	−0.998941	−	0.0460201i	$-0.985346\pi$
$179$	−11.3556	+	12.6116i	−0.848755	+	0.942638i	0.150186	+	0.988658i	$0.452013\pi$
$180$	0.599147	+	1.03775i	0.0446578	+	0.0773495i
$181$	3.66788	−	6.35296i	0.272631	−	0.472211i	−0.696903	−	0.717165i	$-0.745439\pi$
$181$	3.66788	−	6.35296i	0.272631	−	0.472211i	0.969535	+	0.244954i	$0.0787727\pi$
$182$	0.144060	+	0.443371i	0.0106784	+	0.0328648i
$183$	−2.37254	−	1.05632i	−0.175383	−	0.0780856i
$184$	−11.3625	−	8.25534i	−0.837655	−	0.608592i
$185$	14.7135			1.08176
$186$		0			0
$187$	6.25174			0.457173
$188$	1.80516	+	1.31153i	0.131655	+	0.0956528i
$189$	−11.2699	−	5.01767i	−0.819762	−	0.364982i
$190$	1.71480	+	5.27760i	0.124404	+	0.382877i
$191$	−3.91138	+	6.77471i	−0.283018	+	0.490201i	−0.972127	−	0.234457i	$-0.924669\pi$
$191$	−3.91138	+	6.77471i	−0.283018	+	0.490201i	0.689109	+	0.724658i	$0.258002\pi$
$192$	−6.60115	−	11.4335i	−0.476397	−	0.825143i
$193$	−3.09908	+	3.44188i	−0.223077	+	0.247752i	−0.844286	−	0.535893i	$-0.819975\pi$
$193$	−3.09908	+	3.44188i	−0.223077	+	0.247752i	0.621209	+	0.783645i	$0.286642\pi$
$194$	6.07423	−	18.6946i	0.436104	−	1.34219i
$195$	−0.634650	−	0.704851i	−0.0454483	−	0.0504754i
$196$	0.798329	−	0.355439i	0.0570235	−	0.0253885i
$197$	21.8952	+	4.65397i	1.55997	+	0.331582i	0.905447	−	0.424460i	$-0.139536\pi$
$197$	21.8952	+	4.65397i	1.55997	+	0.331582i	0.654524	+	0.756042i	$0.272869\pi$
$198$	−0.100282	+	0.954123i	−0.00712676	+	0.0678066i
$199$	2.78085	+	26.4580i	0.197129	+	1.87556i	0.429689	+	0.902977i	$0.358623\pi$
$199$	2.78085	+	26.4580i	0.197129	+	1.87556i	−0.232560	+	0.972582i	$0.574710\pi$
$200$	28.0262	−	5.95716i	1.98175	−	0.421235i
$201$	−0.662869	+	0.481603i	−0.0467552	+	0.0339696i
$202$	−4.99399	+	3.62834i	−0.351376	+	0.255289i
$203$	−2.86211	+	0.608361i	−0.200881	+	0.0426986i
$204$	−0.403789	−	3.84179i	−0.0282709	−	0.268979i
$205$	0.130376	−	1.24044i	0.00910584	−	0.0866363i
$206$	−2.39189	−	0.508412i	−0.166651	−	0.0354227i
$207$	3.36918	−	1.50006i	0.234175	−	0.104261i
$208$	−0.343374	−	0.381356i	−0.0238087	−	0.0264423i
$209$	0.338648	−	1.04225i	0.0234247	−	0.0720939i
$210$	−10.4650	+	11.6226i	−0.722156	+	0.802036i
$211$	−0.663069	−	1.14847i	−0.0456476	−	0.0790639i	0.842299	−	0.539011i	$-0.181202\pi$
$211$	−0.663069	−	1.14847i	−0.0456476	−	0.0790639i	−0.887946	+	0.459947i	$0.847868\pi$
$212$	−1.45090	+	2.51303i	−0.0996481	+	0.172596i
$213$	0.521512	+	1.60505i	0.0357334	+	0.109976i
$214$	14.4956	+	6.45384i	0.990896	+	0.441175i
$215$	29.6094	+	21.5125i	2.01935	+	1.46714i
$216$	17.1010			1.16357
$217$		0			0
$218$	−12.9985			−0.880368
$219$	9.51374	+	6.91214i	0.642879	+	0.467079i
$220$	−1.30598	−	0.581458i	−0.0880488	−	0.0392019i
$221$	−0.341716	−	1.05169i	−0.0229863	−	0.0707445i
$222$	3.63942	−	6.30366i	0.244262	−	0.423074i
$223$	6.05997	+	10.4962i	0.405806	+	0.702876i	0.994415	−	0.105542i	$-0.0336576\pi$
$223$	6.05997	+	10.4962i	0.405806	+	0.702876i	−0.588609	+	0.808418i	$0.700324\pi$
$224$	3.22711	−	3.58407i	0.215620	−	0.239470i
$225$	−2.32499	+	7.15558i	−0.154999	+	0.477039i
$226$	−3.25698	−	3.61724i	−0.216651	−	0.240615i
$227$	−14.5273	+	6.46799i	−0.964213	+	0.429296i	−0.827593	−	0.561328i	$-0.810291\pi$
$227$	−14.5273	+	6.46799i	−0.964213	+	0.429296i	−0.136620	+	0.990624i	$0.543624\pi$
$228$	−0.662352	−	0.140787i	−0.0438653	−	0.00932386i
$229$	1.70367	−	16.2093i	0.112582	−	1.07114i	−0.781705	−	0.623648i	$-0.785650\pi$
$229$	1.70367	−	16.2093i	0.112582	−	1.07114i	0.894287	−	0.447494i	$-0.147683\pi$
$230$	−2.32882	−	22.1572i	−0.153558	−	1.46100i
$231$	3.02113	−	0.642162i	0.198776	−	0.0422511i
$232$	3.28150	−	2.38415i	0.215441	−	0.156527i
$233$	4.14456	−	3.01120i	0.271519	−	0.197270i	−0.443691	−	0.896180i	$-0.646331\pi$
$233$	4.14456	−	3.01120i	0.271519	−	0.197270i	0.715210	+	0.698910i	$0.246331\pi$
$234$	0.165988	−	0.0352818i	0.0108510	−	0.00230644i
$235$	2.23988	+	21.3110i	0.146113	+	1.39018i
$236$	−0.109744	+	1.04414i	−0.00714371	+	0.0679679i
$237$	−6.59484	−	1.40178i	−0.428381	−	0.0910552i
$238$	−16.6578	+	7.41655i	−1.07977	+	0.480744i
$239$	5.73311	+	6.36726i	0.370844	+	0.411864i	0.899464	−	0.436994i	$-0.143957\pi$
$239$	5.73311	+	6.36726i	0.370844	+	0.411864i	−0.528620	+	0.848858i	$0.677290\pi$
$240$	5.31996	−	16.3731i	0.343402	−	1.05688i
$241$	−4.58138	+	5.08814i	−0.295113	+	0.327756i	−0.872407	−	0.488781i	$-0.837442\pi$
$241$	−4.58138	+	5.08814i	−0.295113	+	0.327756i	0.577294	+	0.816536i	$0.304109\pi$
$242$	6.39404	+	11.0748i	0.411024	+	0.711915i
$243$	−4.01935	+	6.96171i	−0.257841	+	0.446594i
$244$	0.213958	+	0.658494i	0.0136972	+	0.0421558i
$245$	7.66679	+	3.41347i	0.489813	+	0.218079i
$246$	−0.499190	−	0.362683i	−0.0318272	−	0.0231238i
$247$	−0.193842			−0.0123338
$248$		0			0
$249$	0.484474			0.0307023
$250$	17.2997	+	12.5690i	1.09413	+	0.794933i
$251$	20.7065	+	9.21913i	1.30698	+	0.581906i	0.937712	−	0.347415i	$-0.112940\pi$
$251$	20.7065	+	9.21913i	1.30698	+	0.581906i	0.369272	+	0.929321i	$0.379607\pi$
$252$	0.213289	+	0.656437i	0.0134360	+	0.0413516i
$253$	−2.19992	+	3.81037i	−0.138308	+	0.239556i
$254$	−4.65089	−	8.05558i	−0.291823	−	0.505452i
$255$	24.8235	−	27.5692i	1.55451	−	1.72645i
$256$	−2.81235	+	8.65553i	−0.175772	+	0.540971i
$257$	−11.1466	−	12.3796i	−0.695307	−	0.772217i	0.287315	−	0.957836i	$-0.407237\pi$
$257$	−11.1466	−	12.3796i	−0.695307	−	0.772217i	−0.982622	+	0.185620i	$0.940571\pi$
$258$	16.5405	−	7.36430i	1.02977	−	0.458481i
$259$	8.28980	+	1.76205i	0.515103	+	0.109489i
$260$	−0.0264314	+	0.251478i	−0.00163921	+	0.0155960i
$261$	0.111334	+	1.05927i	0.00689140	+	0.0655673i
$262$	−16.1477	+	3.43230i	−0.997609	+	0.212048i
$263$	19.8908	−	14.4515i	1.22652	−	0.891118i	0.229894	−	0.973216i	$-0.426162\pi$
$263$	19.8908	−	14.4515i	1.22652	−	0.891118i	0.996624	+	0.0820979i	$0.0261620\pi$
$264$	−3.46382	+	2.51661i	−0.213184	+	0.154887i
$265$	−27.2586	+	5.79399i	−1.67448	+	0.355922i
$266$	0.334109	+	3.17883i	0.0204855	+	0.194907i
$267$	2.28233	−	21.7149i	0.139676	−	1.32893i
$268$	0.213667	+	0.0454163i	0.0130518	+	0.00277424i
$269$	11.4322	−	5.08996i	0.697036	−	0.310340i	−0.0274565	−	0.999623i	$-0.508741\pi$
$269$	11.4322	−	5.08996i	0.697036	−	0.310340i	0.724493	+	0.689283i	$0.242074\pi$
$270$	18.1516	+	20.1594i	1.10467	+	1.22686i
$271$	−8.39516	+	25.8376i	−0.509969	+	1.56952i	0.282283	+	0.959331i	$0.408908\pi$
$271$	−8.39516	+	25.8376i	−0.509969	+	1.56952i	−0.792252	+	0.610194i	$0.791092\pi$
$272$	13.4306	−	14.9162i	0.814350	−	0.904427i
$273$	−0.273160	−	0.473127i	−0.0165324	−	0.0286349i
$274$	0.0850519	−	0.147314i	0.00513817	−	0.00889957i
$275$	−2.77372	−	8.53663i	−0.167261	−	0.514778i
$276$	2.48362	+	1.10578i	0.149496	+	0.0665601i
$277$	12.2625	+	8.90926i	0.736785	+	0.535305i	0.891703	−	0.452622i	$-0.149511\pi$
$277$	12.2625	+	8.90926i	0.736785	+	0.535305i	−0.154918	+	0.987927i	$0.549511\pi$
$278$	14.6007			0.875694
$279$		0			0
$280$	25.2430			1.50855
$281$	−24.4709	−	17.7792i	−1.45981	−	1.06062i	−0.983412	−	0.181387i	$-0.941941\pi$
$281$	−24.4709	−	17.7792i	−1.45981	−	1.06062i	−0.476401	−	0.879228i	$-0.658059\pi$
$282$	9.68424	+	4.31170i	0.576688	+	0.256758i
$283$	0.971958	+	2.99138i	0.0577769	+	0.177819i	0.975780	−	0.218754i	$-0.0701993\pi$
$283$	0.971958	+	2.99138i	0.0577769	+	0.177819i	−0.918003	+	0.396573i	$0.870199\pi$
$284$	0.224965	−	0.389651i	0.0133492	−	0.0231215i
$285$	−3.25152	−	5.63179i	−0.192603	−	0.333599i
$286$	−0.135464	+	0.150448i	−0.00801016	+	0.00889618i
$287$	0.222008	−	0.683269i	0.0131047	−	0.0403321i
$288$	−1.17469	−	1.30463i	−0.0692194	−	0.0768759i
$289$	23.9828	−	10.6778i	1.41075	−	0.628106i
$290$	6.29366	+	1.33776i	0.369577	+	0.0785559i
$291$	−2.40785	+	22.9092i	−0.141151	+	1.34296i
$292$	−0.327711	−	3.11796i	−0.0191778	−	0.182465i
$293$	−1.85856	+	0.395049i	−0.108578	+	0.0230790i	−0.261880	−	0.965100i	$-0.584343\pi$
$293$	−1.85856	+	0.395049i	−0.108578	+	0.0230790i	0.153302	+	0.988179i	$0.451009\pi$
$294$	3.35882	−	2.44033i	0.195890	−	0.142323i
$295$	−8.15708	+	5.92647i	−0.474924	+	0.345052i
$296$	−11.4915	+	2.44259i	−0.667930	+	0.141973i
$297$	−0.559984	−	5.32789i	−0.0324935	−	0.309155i
$298$	0.720377	−	6.85393i	0.0417303	−	0.397037i
$299$	0.761241	+	0.161807i	0.0440237	+	0.00935752i
$300$	−5.06674	+	2.25586i	−0.292529	+	0.130242i
$301$	14.1061	+	15.6664i	0.813062	+	0.902996i
$302$	5.35797	−	16.4901i	0.308316	−	0.948900i
$303$	4.84046	−	5.37588i	0.278077	−	0.308836i
$304$	−1.75922	−	3.04705i	−0.100898	−	0.174760i
$305$	−3.32466	+	5.75848i	−0.190370	+	0.329730i
$306$	2.05108	+	6.31256i	0.117252	+	0.360865i
$307$	20.7631	+	9.24435i	1.18502	+	0.527603i	0.902094	−	0.431540i	$-0.142030\pi$
$307$	20.7631	+	9.24435i	1.18502	+	0.527603i	0.282922	+	0.959143i	$0.408696\pi$
$308$	−0.666171	−	0.484002i	−0.0379586	−	0.0275786i
$309$	2.86565			0.163021
$310$		0			0
$311$	15.8754			0.900213			0.450106	−	0.892975i	$-0.351386\pi$
$311$	15.8754			0.900213			0.450106	+	0.892975i	$0.351386\pi$
$312$	0.612685	+	0.445142i	0.0346865	+	0.0252012i
$313$	5.80042	+	2.58251i	0.327859	+	0.145972i	0.564064	−	0.825731i	$-0.309237\pi$
$313$	5.80042	+	2.58251i	0.327859	+	0.145972i	−0.236205	+	0.971703i	$0.575904\pi$
$314$	−5.89268	−	18.1358i	−0.332543	−	1.02346i
$315$	−3.31427	+	5.74049i	−0.186738	+	0.323440i
$316$	0.898737	+	1.55666i	0.0505579	+	0.0875689i
$317$	−10.2384	+	11.3709i	−0.575044	+	0.638651i	−0.958563	−	0.284882i	$-0.908046\pi$
$317$	−10.2384	+	11.3709i	−0.575044	+	0.638651i	0.383518	+	0.923533i	$0.374712\pi$
$318$	−4.26017	+	13.1115i	−0.238898	+	0.735254i
$319$	−0.850248	−	0.944296i	−0.0476047	−	0.0528704i
$320$	−30.8797	+	13.7485i	−1.72623	+	0.768567i
$321$	−18.1884	−	3.86607i	−1.01518	−	0.215783i
$322$	1.34140	−	12.7626i	0.0747533	−	0.711231i
$323$	−0.792518	−	7.54031i	−0.0440969	−	0.419554i
$324$	−2.31263	+	0.491565i	−0.128480	+	0.0273092i
$325$	−1.28446	+	0.933212i	−0.0712488	+	0.0517653i
$326$	−17.4590	+	12.6847i	−0.966963	+	0.702540i
$327$	14.8999	−	3.16707i	0.823966	−	0.175139i
$328$	0.104100	+	0.990450i	0.00574799	+	0.0546884i
$329$	−1.29017	+	12.2752i	−0.0711295	+	0.676752i
$330$	−6.64334	−	1.41209i	−0.365704	−	0.0777328i
$331$	−8.19263	+	3.64760i	−0.450308	+	0.200490i	−0.619344	−	0.785120i	$-0.712601\pi$
$331$	−8.19263	+	3.64760i	−0.450308	+	0.200490i	0.169036	+	0.985610i	$0.445935\pi$
$332$	−0.0864260	−	0.0959858i	−0.00474324	−	0.00526790i
$333$	0.953307	−	2.93398i	0.0522409	−	0.160781i
$334$	−13.7284	+	15.2469i	−0.751182	+	0.834273i
$335$	1.04890	+	1.81675i	0.0573076	+	0.0992597i
$336$	4.95814	−	8.58776i	0.270489	−	0.468501i
$337$	−1.35002	−	4.15495i	−0.0735405	−	0.226334i	0.907529	−	0.419989i	$-0.137966\pi$
$337$	−1.35002	−	4.15495i	−0.0735405	−	0.226334i	−0.981070	+	0.193654i	$0.937966\pi$
$338$	−15.0096	−	6.68269i	−0.816413	−	0.363490i
$339$	4.61474	+	3.35281i	0.250638	+	0.182100i
$340$	−9.89040			−0.536382
$341$		0			0
$342$	1.16349			0.0629145
$343$	16.3073	+	11.8479i	0.880511	+	0.639729i
$344$	−26.6968	−	11.8862i	−1.43939	−	0.640859i
$345$	8.06806	+	24.8309i	0.434370	+	1.33685i
$346$	1.47636	−	2.55713i	0.0793697	−	0.137472i
$347$	−12.2026	−	21.1356i	−0.655073	−	1.13462i	−0.981876	−	0.189526i	$-0.939305\pi$
$347$	−12.2026	−	21.1356i	−0.655073	−	1.13462i	0.326803	−	0.945092i	$-0.394029\pi$
$348$	−0.525369	+	0.583481i	−0.0281627	+	0.0312779i
$349$	4.03079	−	12.4055i	0.215763	−	0.664051i	−0.783335	−	0.621599i	$-0.786483\pi$
$349$	4.03079	−	12.4055i	0.215763	−	0.664051i	0.999099	−	0.0424515i	$-0.0135168\pi$
$350$	17.5178	+	19.4554i	0.936364	+	1.03994i
$351$	−0.865670	+	0.385421i	−0.0462060	+	0.0205723i
$352$	2.04861	+	0.435445i	0.109191	+	0.0232093i
$353$	−1.13150	+	10.7655i	−0.0602237	+	0.572990i	0.922251	+	0.386592i	$0.126348\pi$
$353$	−1.13150	+	10.7655i	−0.0602237	+	0.572990i	−0.982474	+	0.186398i	$0.940319\pi$
$354$	0.521384	+	4.96063i	0.0277112	+	0.263655i
$355$	4.22650	−	0.898370i	0.224319	−	0.0476805i
$356$	−4.70938	+	3.42156i	−0.249597	+	0.181343i
$357$	17.2875	−	12.5601i	0.914952	−	0.664752i
$358$	21.0253	−	4.46907i	1.11122	−	0.236197i
$359$	−3.53133	−	33.5983i	−0.186376	−	1.77325i	−0.543708	−	0.839275i	$-0.682980\pi$
$359$	−3.53133	−	33.5983i	−0.186376	−	1.77325i	0.357331	−	0.933978i	$-0.383687\pi$
$360$	0.960473	−	9.13829i	0.0506214	−	0.481630i
$361$	17.2848	+	3.67400i	0.909726	+	0.193368i
$362$	−8.48819	+	3.77919i	−0.446130	+	0.198630i
$363$	−10.0277	−	11.1369i	−0.526319	−	0.584536i
$364$	−0.0450082	+	0.138521i	−0.00235907	+	0.00726048i
$365$	20.1465	−	22.3749i	1.05451	−	1.17116i
$366$	1.64472	+	2.84875i	0.0859711	+	0.148906i
$367$	−11.3157	+	19.5993i	−0.590673	+	1.02308i	0.403469	+	0.914993i	$0.367804\pi$
$367$	−11.3157	+	19.5993i	−0.590673	+	1.02308i	−0.994142	+	0.108082i	$0.965529\pi$
$368$	4.36518	+	13.4346i	0.227551	+	0.700329i
$369$	−0.238906	−	0.106368i	−0.0124369	−	0.00553728i
$370$	−15.0770	−	10.9541i	−0.783814	−	0.569474i
$371$	−16.0517			−0.833365
$372$		0			0
$373$	−32.9720			−1.70723			−0.853613	−	0.520908i	$-0.825593\pi$
$373$	−32.9720			−1.70723			−0.853613	+	0.520908i	$0.825593\pi$
$374$	−6.40617	−	4.65436i	−0.331255	−	0.240671i
$375$	−22.8927	−	10.1925i	−1.18218	−	0.526339i
$376$	−5.28723	−	16.2724i	−0.272668	−	0.839185i
$377$	−0.112379	+	0.194647i	−0.00578783	+	0.0100248i
$378$	7.81265	+	13.5319i	0.401840	+	0.696006i
$379$	−21.7413	+	24.1462i	−1.11678	+	1.24031i	−0.148906	+	0.988851i	$0.547575\pi$
$379$	−21.7413	+	24.1462i	−1.11678	+	1.24031i	−0.967869	+	0.251454i	$0.919091\pi$
$380$	−0.535748	+	1.64886i	−0.0274833	+	0.0845850i
$381$	7.29395	+	8.10075i	0.373680	+	0.415014i
$382$	9.05170	−	4.03008i	0.463125	−	0.206197i
$383$	26.1952	+	5.56796i	1.33851	+	0.284510i	0.820884	−	0.571095i	$-0.193481\pi$
$383$	26.1952	+	5.56796i	1.33851	+	0.284510i	0.517629	+	0.855605i	$0.326815\pi$
$384$	−1.06425	+	10.1257i	−0.0543100	+	0.516725i
$385$	−0.826598	−	7.86455i	−0.0421273	−	0.400815i
$386$	5.73808	−	1.21967i	0.292061	−	0.0620794i
$387$	6.20818	−	4.51050i	0.315579	−	0.229282i
$388$	4.96838	−	3.60974i	0.252232	−	0.183257i
$389$	17.3499	−	3.68783i	0.879675	−	0.186981i	0.254131	−	0.967170i	$-0.418211\pi$
$389$	17.3499	−	3.68783i	0.879675	−	0.186981i	0.625544	+	0.780189i	$0.284877\pi$
$390$	0.125574	+	1.19475i	0.00635866	+	0.0604986i
$391$	−3.18185	+	30.2733i	−0.160913	+	1.53099i
$392$	−6.55456	−	1.39321i	−0.331055	−	0.0703680i
$393$	17.6735	−	7.86876i	0.891511	−	0.396926i
$394$	−18.9713	−	21.0697i	−0.955758	−	1.06148i
$395$	−5.33429	+	16.4173i	−0.268397	+	0.826042i
$396$	−0.200563	+	0.222747i	−0.0100786	+	0.0111935i
$397$	−4.97476	−	8.61654i	−0.249676	−	0.432452i	0.713760	−	0.700391i	$-0.246991\pi$
$397$	−4.97476	−	8.61654i	−0.249676	−	0.432452i	−0.963436	+	0.267939i	$0.913658\pi$
$398$	16.8482	−	29.1819i	0.844523	−	1.46276i
$399$	−1.15750	−	3.56243i	−0.0579476	−	0.178344i
$400$	−26.3265	−	11.7213i	−1.31633	−	0.586066i
$401$	−16.0959	−	11.6943i	−0.803789	−	0.583987i	0.108234	−	0.994125i	$-0.465480\pi$
$401$	−16.0959	−	11.6943i	−0.803789	−	0.583987i	−0.912023	+	0.410138i	$0.865480\pi$
$402$	1.03779			0.0517604
$403$		0			0
$404$	−1.92858			−0.0959506
$405$	−18.3693	−	13.3460i	−0.912776	−	0.663170i
$406$	3.38573	+	1.50743i	0.168031	+	0.0748123i
$407$	1.13730	+	3.50024i	0.0563738	+	0.173501i
$408$	−14.8108	+	25.6530i	−0.733242	+	1.27001i
$409$	12.1628	+	21.0665i	0.601410	+	1.04167i	0.992608	+	0.121365i	$0.0387273\pi$
$409$	12.1628	+	21.0665i	0.601410	+	1.04167i	−0.391198	+	0.920306i	$0.627939\pi$
$410$	−1.05709	+	1.17402i	−0.0522061	+	0.0579807i
$411$	−0.0616002	+	0.189586i	−0.00303851	+	0.00935159i
$412$	−0.511206	−	0.567752i	−0.0251853	−	0.0279711i
$413$	−5.30555	+	2.36218i	−0.261069	+	0.116235i
$414$	−4.56919	−	0.971211i	−0.224563	−	0.0477324i
$415$	0.129658	−	1.23361i	0.00636466	−	0.0605557i
$416$	−0.0387231	−	0.368426i	−0.00189856	−	0.0180636i
$417$	−16.7365	+	3.55746i	−0.819591	+	0.174209i
$418$	−1.12296	+	0.815876i	−0.0549256	+	0.0399058i
$419$	3.56513	−	2.59022i	0.174168	−	0.126541i	−0.497286	−	0.867587i	$-0.665670\pi$
$419$	3.56513	−	2.59022i	0.174168	−	0.126541i	0.671454	+	0.741046i	$0.265670\pi$
$420$	−4.77951	+	1.01592i	−0.233216	+	0.0495716i
$421$	1.29863	+	12.3556i	0.0632912	+	0.602176i	0.979496	+	0.201465i	$0.0645702\pi$
$421$	1.29863	+	12.3556i	0.0632912	+	0.602176i	−0.916204	+	0.400711i	$0.868763\pi$
$422$	−0.175575	+	1.67049i	−0.00854687	+	0.0813181i
$423$	4.39469	+	0.934120i	0.213677	+	0.0454185i
$424$	20.3275	−	9.05040i	0.987192	−	0.439526i
$425$	−41.5528	−	46.1490i	−2.01561	−	2.23856i
$426$	0.660548	−	2.03296i	0.0320037	−	0.0984972i
$427$	−2.56278	+	2.84626i	−0.124022	+	0.137740i
$428$	2.47870	+	4.29323i	0.119812	+	0.207521i
$429$	0.118623	−	0.205461i	0.00572718	−	0.00991976i
$430$	−14.3250	−	44.0878i	−0.690813	−	2.12610i
$431$	−16.9602	−	7.55119i	−0.816946	−	0.363728i	−0.0446597	−	0.999002i	$-0.514220\pi$
$431$	−16.9602	−	7.55119i	−0.816946	−	0.363728i	−0.772287	+	0.635274i	$0.780887\pi$
$432$	−13.9150	−	10.1098i	−0.669484	−	0.486408i
$433$	−36.1204			−1.73584			−0.867918	−	0.496708i	$-0.834542\pi$
$433$	−36.1204			−1.73584			−0.867918	+	0.496708i	$0.834542\pi$
$434$		0			0
$435$	−7.54024			−0.361527
$436$	−3.28548	−	2.38704i	−0.157346	−	0.114319i
$437$	4.87461	+	2.17032i	0.233184	+	0.103820i
$438$	−4.60274	−	14.1658i	−0.219927	−	0.676866i
$439$	9.50469	−	16.4626i	0.453634	−	0.785718i	−0.544974	−	0.838453i	$-0.683461\pi$
$439$	9.50469	−	16.4626i	0.453634	−	0.785718i	0.998609	+	0.0527352i	$0.0167939\pi$
$440$	5.48103	+	9.49342i	0.261298	+	0.452581i
$441$	1.17741	−	1.30765i	0.0560672	−	0.0622689i
$442$	−0.432817	+	1.33208i	−0.0205870	+	0.0633603i
$443$	8.33337	+	9.25515i	0.395931	+	0.439725i	0.907842	−	0.419313i	$-0.137729\pi$
$443$	8.33337	+	9.25515i	0.395931	+	0.439725i	−0.511911	+	0.859038i	$0.671062\pi$
$444$	2.07750	−	0.924962i	0.0985937	−	0.0438968i
$445$	−54.6817	−	11.6230i	−2.59216	−	0.550981i
$446$	1.60463	−	15.2670i	0.0759815	−	0.722916i
$447$	0.844201	+	8.03203i	0.0399293	+	0.379902i
$448$	−19.0446	+	4.04805i	−0.899772	+	0.191252i
$449$	−20.5786	+	14.9513i	−0.971166	+	0.705593i	−0.955717	−	0.294287i	$-0.904918\pi$
$449$	−20.5786	+	14.9513i	−0.971166	+	0.705593i	−0.0154490	+	0.999881i	$0.504918\pi$
$450$	7.70968	−	5.60141i	0.363438	−	0.264053i
$451$	0.305170	−	0.0648659i	0.0143699	−	0.00305442i
$452$	−0.158960	−	1.51240i	−0.00747684	−	0.0711373i
$453$	−2.12392	+	20.2078i	−0.0997905	+	0.949443i
$454$	19.7015	+	4.18769i	0.924640	+	0.196538i
$455$	−1.27783	+	0.568924i	−0.0599054	+	0.0266716i
$456$	3.47442	+	3.85874i	0.162705	+	0.180702i
$457$	9.88049	−	30.4090i	0.462190	−	1.42247i	−0.400292	−	0.916388i	$-0.631091\pi$
$457$	9.88049	−	30.4090i	0.462190	−	1.42247i	0.862482	−	0.506087i	$-0.168909\pi$
$458$	−13.8134	+	15.3414i	−0.645459	+	0.716855i
$459$	−18.5319	−	32.0982i	−0.864995	−	1.49822i
$460$	3.48032	−	6.02809i	0.162271	−	0.281061i
$461$	5.97950	+	18.4030i	0.278493	+	0.857114i	0.988274	+	0.152691i	$0.0487940\pi$
$461$	5.97950	+	18.4030i	0.278493	+	0.857114i	−0.709781	+	0.704423i	$0.751206\pi$
$462$	−3.57385	−	1.59118i	−0.166270	−	0.0740283i
$463$	−0.0335439	−	0.0243710i	−0.00155892	−	0.00113262i	0.587006	−	0.809583i	$-0.300307\pi$
$463$	−0.0335439	−	0.0243710i	−0.00155892	−	0.00113262i	−0.588564	+	0.808450i	$0.700307\pi$
$464$	−4.07961			−0.189391
$465$		0			0
$466$	−6.48875			−0.300586
$467$	−20.4748	−	14.8758i	−0.947462	−	0.688372i	0.00274297	−	0.999996i	$-0.499127\pi$
$467$	−20.4748	−	14.8758i	−0.947462	−	0.688372i	−0.950205	+	0.311625i	$0.899127\pi$
$468$	0.0484340	+	0.0215642i	0.00223886	+	0.000996806i
$469$	0.373397	+	1.14920i	0.0172419	+	0.0530650i
$470$	13.5706	−	23.5050i	0.625966	−	1.08420i
$471$	11.1734	+	19.3530i	0.514845	+	0.891737i
$472$	5.38696	−	5.98283i	0.247955	−	0.275382i
$473$	−2.82898	+	8.70671i	−0.130077	+	0.400335i
$474$	5.71414	+	6.34620i	0.262459	+	0.291490i
$475$	−9.94452	+	4.42759i	−0.456286	+	0.203152i
$476$	−5.57239	−	1.18445i	−0.255410	−	0.0542891i
$477$	−0.610755	+	5.81095i	−0.0279646	+	0.266065i
$478$	−1.13437	−	10.7928i	−0.0518848	−	0.493651i
$479$	20.7770	−	4.41628i	0.949324	−	0.201785i	0.292871	−	0.956152i	$-0.405389\pi$
$479$	20.7770	−	4.41628i	0.949324	−	0.201785i	0.656453	+	0.754367i	$0.272056\pi$
$480$	10.0546	−	7.30506i	0.458925	−	0.333429i
$481$	0.526661	−	0.382641i	0.0240137	−	0.0174469i
$482$	8.48261	−	1.80304i	0.386372	−	0.0821260i
$483$	1.57197	+	14.9563i	0.0715272	+	0.680536i
$484$	−0.417627	+	3.97345i	−0.0189830	+	0.180612i
$485$	57.6891	+	12.2622i	2.61953	+	0.556797i
$486$	9.30156	−	4.14132i	0.421927	−	0.187854i
$487$	17.9073	+	19.8880i	0.811455	+	0.901212i	0.996675	−	0.0814851i	$-0.0259663\pi$
$487$	17.9073	+	19.8880i	0.811455	+	0.901212i	−0.185220	+	0.982697i	$0.559300\pi$
$488$	1.64065	−	5.04940i	0.0742687	−	0.228575i
$489$	16.9222	−	18.7941i	0.765250	−	0.849897i
$490$	−5.31488	−	9.20564i	−0.240102	−	0.415868i
$491$	6.28320	−	10.8828i	0.283557	−	0.491135i	−0.688701	−	0.725045i	$-0.741819\pi$
$491$	6.28320	−	10.8828i	0.283557	−	0.491135i	0.972258	+	0.233910i	$0.0751522\pi$
$492$	−0.0595716	−	0.183342i	−0.00268569	−	0.00826572i
$493$	−8.03108	−	3.57567i	−0.361702	−	0.161040i
$494$	0.198630	+	0.144313i	0.00893678	+	0.00649295i
$495$	−2.87853			−0.129380
$496$		0			0
$497$	2.48886			0.111640
$498$	−0.496442	−	0.360686i	−0.0222461	−	0.0161627i
$499$	−21.0393	−	9.36729i	−0.941848	−	0.419338i	−0.122393	−	0.992482i	$-0.539057\pi$
$499$	−21.0393	−	9.36729i	−0.941848	−	0.419338i	−0.819455	+	0.573144i	$0.805724\pi$
$500$	2.06449	+	6.35384i	0.0923268	+	0.284153i
$501$	12.0216	−	20.8221i	0.537087	−	0.930263i
$502$	−14.3545	−	24.8626i	−0.640671	−	1.10967i
$503$	0.442682	−	0.491648i	0.0197382	−	0.0219215i	−0.733195	−	0.680019i	$-0.761972\pi$
$503$	0.442682	−	0.491648i	0.0197382	−	0.0219215i	0.752933	+	0.658097i	$0.228638\pi$
$504$	1.63552	−	5.03362i	0.0728520	−	0.224215i
$505$	−12.3931	−	13.7640i	−0.551487	−	0.612488i
$506$	5.09104	−	2.26668i	0.226324	−	0.100766i
$507$	18.8334	+	4.00316i	0.836420	+	0.177787i
$508$	0.303773	−	2.89021i	0.0134777	−	0.128232i
$509$	1.21958	+	11.6035i	0.0540568	+	0.514316i	0.987728	+	0.156184i	$0.0499194\pi$
$509$	1.21958	+	11.6035i	0.0540568	+	0.514316i	−0.933671	+	0.358131i	$0.883414\pi$
$510$	−45.9617	+	9.76945i	−2.03522	+	0.432599i
$511$	14.0304	−	10.1937i	0.620667	−	0.450941i
$512$	20.4245	−	14.8393i	0.902644	−	0.655809i
$513$	−6.35505	+	1.35081i	−0.280582	+	0.0596396i
$514$	2.20550	+	20.9839i	0.0972804	+	0.925561i
$515$	0.766922	−	7.29678i	0.0337946	−	0.321535i
$516$	5.53313	+	1.17610i	0.243583	+	0.0517751i
$517$	−4.89661	+	2.18011i	−0.215353	+	0.0958812i
$518$	−7.18275	−	7.97725i	−0.315592	−	0.350500i
$519$	−1.06928	+	3.29090i	−0.0469362	+	0.144455i
$520$	1.29743	−	1.44094i	0.0568962	−	0.0631896i
$521$	15.9592	+	27.6422i	0.699186	+	1.21103i	0.968749	+	0.248043i	$0.0797874\pi$
$521$	15.9592	+	27.6422i	0.699186	+	1.21103i	−0.269563	+	0.962983i	$0.586879\pi$
$522$	0.674533	−	1.16833i	0.0295235	−	0.0511362i
$523$	−0.00128254	−	0.00394726i	−5.60817e−5	−	0.000172602i	0.951028	−	0.309103i	$-0.100029\pi$
$523$	−0.00128254	−	0.00394726i	−5.60817e−5	−	0.000172602i	−0.951085	+	0.308931i	$0.900029\pi$
$524$	−4.71179	−	2.09782i	−0.205835	−	0.0916438i
$525$	−24.8206	−	18.0332i	−1.08326	−	0.787033i
$526$	−31.1411			−1.35782
$527$		0			0
$528$	4.30627			0.187406
$529$	1.27581	+	0.926929i	0.0554699	+	0.0403013i
$530$	32.2455	+	14.3566i	1.40065	+	0.623611i
$531$	0.653271	+	2.01056i	0.0283496	+	0.0872510i
$532$	−0.499312	+	0.864834i	−0.0216479	+	0.0374953i
$533$	−0.0275924	−	0.0477914i	−0.00119516	−	0.00207008i
$534$	−18.5052	+	20.5521i	−0.800799	+	0.889378i
$535$	−14.7119	+	45.2784i	−0.636049	+	1.95756i
$536$	−1.12081	−	1.24478i	−0.0484115	−	0.0537665i
$537$	−23.0120	+	10.2456i	−0.993040	+	0.442130i
$538$	−15.5041	−	3.29549i	−0.668428	−	0.142079i
$539$	−0.219429	+	2.08772i	−0.00945146	+	0.0899246i
$540$	0.885907	+	8.42885i	0.0381234	+	0.362720i
$541$	−28.6353	+	6.08662i	−1.23113	+	0.261684i	−0.777142	−	0.629325i	$-0.783332\pi$
$541$	−28.6353	+	6.08662i	−1.23113	+	0.261684i	−0.453985	+	0.891009i	$0.649998\pi$
$542$	27.8384	−	20.2258i	1.19576	−	0.868771i
$543$	8.80905	−	6.40015i	0.378032	−	0.274657i
$544$	14.1732	−	3.01261i	0.607671	−	0.129165i
$545$	−4.07669	−	38.7871i	−0.174626	−	1.66146i
$546$	−0.0723305	+	0.688179i	−0.00309546	+	0.0294513i
$547$	−40.2657	−	8.55875i	−1.72164	−	0.365946i	−0.762086	−	0.647476i	$-0.775825\pi$
$547$	−40.2657	−	8.55875i	−1.72164	−	0.365946i	−0.959552	+	0.281530i	$0.909158\pi$
$548$	0.0485504	−	0.0216160i	0.00207397	−	0.000923391i
$549$	0.932873	+	1.03606i	0.0398140	+	0.0442180i
$550$	−3.51320	+	10.8125i	−0.149803	+	0.461047i
$551$	−1.03114	+	1.14520i	−0.0439282	+	0.0487872i
$552$	−10.4235	−	18.0540i	−0.443653	−	0.768429i
$553$	−4.97150	+	8.61089i	−0.211410	+	0.366172i
$554$	−5.93260	−	18.2587i	−0.252052	−	0.775737i
$555$	19.9514	+	8.88292i	0.846888	+	0.377059i
$556$	3.69046	+	2.68128i	0.156511	+	0.113712i
$557$	−5.73810			−0.243131			−0.121566	−	0.992583i	$-0.538791\pi$
$557$	−5.73810			−0.243131			−0.121566	+	0.992583i	$0.538791\pi$
$558$		0			0
$559$	1.61931			0.0684894
$560$	−20.5400	−	14.9232i	−0.867975	−	0.630620i
$561$	8.47729	+	3.77433i	0.357912	+	0.159352i
$562$	11.8390	+	36.4367i	0.499398	+	1.53699i
$563$	7.14710	−	12.3791i	0.301214	−	0.521718i	−0.675197	−	0.737637i	$-0.735941\pi$
$563$	7.14710	−	12.3791i	0.301214	−	0.521718i	0.976411	+	0.215919i	$0.0692748\pi$
$564$	1.65598	+	2.86823i	0.0697292	+	0.120774i
$565$	9.77226	−	10.8532i	0.411122	−	0.456597i
$566$	1.23108	−	3.78889i	0.0517463	−	0.159259i
$567$	−8.75121	−	9.71921i	−0.367516	−	0.408168i
$568$	−3.15183	+	1.40328i	−0.132248	+	0.0588805i
$569$	−14.0480	−	2.98598i	−0.588921	−	0.125179i	−0.0961933	−	0.995363i	$-0.530667\pi$
$569$	−14.0480	−	2.98598i	−0.588921	−	0.125179i	−0.492727	+	0.870184i	$0.664000\pi$
$570$	−0.860975	+	8.19163i	−0.0360623	+	0.343110i
$571$	−3.48906	−	33.1962i	−0.146012	−	1.38922i	−0.784760	−	0.619800i	$-0.787214\pi$
$571$	−3.48906	−	33.1962i	−0.146012	−	1.38922i	0.638748	−	0.769416i	$-0.279453\pi$
$572$	−0.0618680	+	0.0131505i	−0.00258683	+	0.000549848i
$573$	−9.39385	+	6.82503i	−0.392434	+	0.285120i
$574$	−0.736179	+	0.534865i	−0.0307275	+	0.0223248i
$575$	42.7493	−	9.08664i	1.78277	−	0.378939i
$576$	0.740819	+	7.04842i	0.0308675	+	0.293684i
$577$	2.34976	−	22.3565i	0.0978217	−	0.930712i	−0.830019	−	0.557735i	$-0.811670\pi$
$577$	2.34976	−	22.3565i	0.0978217	−	0.930712i	0.927841	−	0.372977i	$-0.121663\pi$
$578$	−32.5247	−	6.91334i	−1.35285	−	0.287557i
$579$	−6.28027	+	2.79616i	−0.260999	+	0.116204i
$580$	1.34511	+	1.49390i	0.0558528	+	0.0620308i
$581$	0.220786	−	0.679508i	0.00915973	−	0.0281908i
$582$	19.5230	−	21.6825i	0.809253	−	0.898767i
$583$	−3.48533	−	6.03677i	−0.144348	−	0.250018i
$584$	−12.0203	+	20.8197i	−0.497402	+	0.861525i
$585$	0.157338	+	0.484237i	0.00650514	+	0.0200207i
$586$	2.19858	+	0.978871i	0.0908225	+	0.0404368i
$587$	5.19079	+	3.77133i	0.214247	+	0.155659i	0.689733	−	0.724064i	$-0.257728\pi$
$587$	5.19079	+	3.77133i	0.214247	+	0.155659i	−0.475486	+	0.879723i	$0.657728\pi$
$588$	1.29711			0.0534920
$589$		0			0
$590$	12.7708			0.525764
$591$	26.8800	+	19.5294i	1.10569	+	0.803334i
$592$	10.7946	+	4.80605i	0.443654	+	0.197528i
$593$	−6.44614	−	19.8392i	−0.264711	−	0.814697i	−0.991760	−	0.128111i	$-0.959109\pi$
$593$	−6.44614	−	19.8392i	−0.264711	−	0.814697i	0.727049	−	0.686586i	$-0.240891\pi$
$594$	−3.39274	+	5.87640i	−0.139206	+	0.241112i
$595$	−27.3551	−	47.3805i	−1.12145	−	1.94241i
$596$	1.44074	−	1.60010i	0.0590149	−	0.0655427i
$597$	−12.2026	+	37.5557i	−0.499418	+	1.53705i
$598$	−0.659582	−	0.732539i	−0.0269723	−	0.0299558i
$599$	−10.5591	+	4.70122i	−0.431434	+	0.192087i	−0.610951	−	0.791668i	$-0.709213\pi$
$599$	−10.5591	+	4.70122i	−0.431434	+	0.192087i	0.179518	+	0.983755i	$0.442546\pi$
$600$	41.5998	+	8.84230i	1.69830	+	0.360985i
$601$	−0.451293	+	4.29377i	−0.0184086	+	0.175146i	−0.999863	−	0.0165493i	$-0.994732\pi$
$601$	−0.451293	+	4.29377i	−0.0184086	+	0.175146i	0.981454	+	0.191696i	$0.0613986\pi$
$602$	−2.79107	−	26.5552i	−0.113755	−	1.08231i
$603$	0.430232	−	0.0914487i	0.0175204	−	0.00372408i
$604$	4.38252	−	3.18409i	0.178322	−	0.129559i
$605$	−31.0415	+	22.5530i	−1.26202	+	0.916909i
$606$	−8.96231	+	1.90500i	−0.364069	+	0.0773853i
$607$	−4.69429	−	44.6632i	−0.190536	−	1.81282i	−0.504524	−	0.863398i	$-0.668332\pi$
$607$	−4.69429	−	44.6632i	−0.190536	−	1.81282i	0.313988	−	0.949427i	$-0.398335\pi$
$608$	0.265499	−	2.52605i	0.0107674	−	0.102445i
$609$	−4.24828	−	0.902999i	−0.172149	−	0.0365914i
$610$	7.69392	−	3.42555i	0.311518	−	0.138697i
$611$	0.634392	+	0.704563i	0.0256647	+	0.0285036i
$612$	−0.640812	+	1.97222i	−0.0259033	+	0.0797221i
$613$	−1.74319	+	1.93601i	−0.0704070	+	0.0781949i	−0.777319	−	0.629106i	$-0.783421\pi$
$613$	−1.74319	+	1.93601i	−0.0704070	+	0.0781949i	0.706912	+	0.707301i	$0.250088\pi$
$614$	−14.3937	−	24.9306i	−0.580883	−	1.00612i
$615$	0.925674	−	1.60332i	0.0373268	−	0.0646519i
$616$	1.95118	+	6.00512i	0.0786154	+	0.241953i
$617$	−22.8266	−	10.1630i	−0.918963	−	0.409149i	−0.107936	−	0.994158i	$-0.534424\pi$
$617$	−22.8266	−	10.1630i	−0.918963	−	0.409149i	−0.811027	+	0.585009i	$0.801091\pi$
$618$	−2.93643	−	2.13344i	−0.118121	−	0.0858197i
$619$	31.9083			1.28250			0.641252	−	0.767330i	$-0.278415\pi$
$619$	31.9083			1.28250			0.641252	+	0.767330i	$0.278415\pi$
$620$		0			0
$621$	26.0847			1.04674
$622$	−16.2676	−	11.8191i	−0.652271	−	0.473902i
$623$	−29.4165	−	13.0971i	−1.17855	−	0.524723i
$624$	−0.235378	−	0.724418i	−0.00942264	−	0.0289999i
$625$	−8.47372	+	14.6769i	−0.338949	+	0.587077i
$626$	−4.02105	−	6.96466i	−0.160713	−	0.278364i
$627$	1.08843	−	1.20883i	0.0434679	−	0.0482760i
$628$	1.84103	−	5.66612i	0.0734652	−	0.226103i
$629$	17.0377	+	18.9223i	0.679339	+	0.754482i
$630$	7.66988	−	3.41485i	0.305575	−	0.136051i
$631$	0.351890	+	0.0747965i	0.0140085	+	0.00297760i	0.214911	−	0.976634i	$-0.431054\pi$
$631$	0.351890	+	0.0747965i	0.0140085	+	0.00297760i	−0.200902	+	0.979611i	$0.564387\pi$
$632$	1.44074	−	13.7077i	0.0573094	−	0.545263i
$633$	−0.205755	−	1.95762i	−0.00817801	−	0.0778086i
$634$	18.9568	−	4.02939i	0.752869	−	0.160027i
$635$	22.5790	−	16.4046i	0.896019	−	0.650996i
$636$	−3.48458	+	2.53170i	−0.138173	+	0.100388i
$637$	0.363199	−	0.0772003i	0.0143905	−	0.00305879i
$638$	0.168232	+	1.60062i	0.00666038	+	0.0633693i
$639$	0.0946989	−	0.901000i	0.00374623	−	0.0356430i
$640$	25.4982	+	5.41981i	1.00791	+	0.214237i
$641$	−28.1435	+	12.5303i	−1.11160	+	0.494917i	−0.878600	−	0.477559i	$-0.841522\pi$
$641$	−28.1435	+	12.5303i	−1.11160	+	0.494917i	−0.233003	+	0.972476i	$0.574855\pi$
$642$	15.7595	+	17.5027i	0.621977	+	0.690775i
$643$	−0.541347	+	1.66609i	−0.0213486	+	0.0657044i	−0.961163	−	0.275980i	$-0.910998\pi$
$643$	−0.541347	+	1.66609i	−0.0213486	+	0.0657044i	0.939815	+	0.341685i	$0.110998\pi$
$644$	2.68277	−	2.97952i	0.105716	−	0.117409i
$645$	27.1624	+	47.0467i	1.06952	+	1.85246i
$646$	−4.80159	+	8.31659i	−0.188916	+	0.327212i
$647$	−7.61739	−	23.4439i	−0.299470	−	0.921675i	−0.981683	−	0.190521i	$-0.938982\pi$
$647$	−7.61739	−	23.4439i	−0.299470	−	0.921675i	0.682213	−	0.731154i	$-0.261018\pi$
$648$	16.5623	+	7.37400i	0.650628	+	0.289678i
$649$	−2.04038	−	1.48242i	−0.0800918	−	0.0581901i
$650$	2.01095			0.0788760
$651$		0			0
$652$	−6.74233			−0.264050
$653$	0.231107	+	0.167909i	0.00904393	+	0.00657080i	0.592298	−	0.805719i	$-0.298221\pi$
$653$	0.231107	+	0.167909i	0.00904393	+	0.00657080i	−0.583254	+	0.812290i	$0.698221\pi$
$654$	−17.6258	−	7.84751i	−0.689223	−	0.306862i
$655$	−15.3063	−	47.1079i	−0.598065	−	1.84066i
$656$	0.500831	−	0.867465i	0.0195542	−	0.0338688i
$657$	−3.15640	−	5.46704i	−0.123143	−	0.213290i
$658$	10.4608	−	11.6179i	0.407804	−	0.452912i
$659$	11.5649	−	35.5930i	0.450503	−	1.38651i	−0.425832	−	0.904802i	$-0.640018\pi$
$659$	11.5649	−	35.5930i	0.450503	−	1.38651i	0.876335	−	0.481703i	$-0.159982\pi$
$660$	−1.41985	−	1.57690i	−0.0552675	−	0.0613808i
$661$	3.82919	−	1.70487i	0.148938	−	0.0663116i	−0.330914	−	0.943661i	$-0.607357\pi$
$661$	3.82919	−	1.70487i	0.148938	−	0.0663116i	0.479852	+	0.877349i	$0.340690\pi$
$662$	11.1106	+	2.36163i	0.431826	+	0.0917875i
$663$	0.171571	−	1.63239i	0.00666325	−	0.0633966i
$664$	0.103527	+	0.984998i	0.00401764	+	0.0382253i
$665$	−9.38076	+	1.99394i	−0.363770	+	0.0773218i
$666$	−3.16117	+	2.29673i	−0.122493	+	0.0889963i
$667$	5.00538	−	3.63662i	0.193809	−	0.140810i
$668$	−6.26990	+	1.33271i	−0.242590	+	0.0515641i
$669$	1.88045	+	17.8913i	0.0727023	+	0.691716i
$670$	0.277740	−	2.64252i	0.0107300	−	0.102090i
$671$	−1.62689	−	0.345805i	−0.0628053	−	0.0133497i
$672$	6.53971	−	2.91167i	0.252275	−	0.112320i
$673$	6.67302	+	7.41114i	0.257226	+	0.285678i	0.857901	−	0.513815i	$-0.171768\pi$
$673$	6.67302	+	7.41114i	0.257226	+	0.285678i	−0.600675	+	0.799493i	$0.705101\pi$
$674$	−1.70994	+	5.26266i	−0.0658645	+	0.202710i
$675$	−35.6074	+	39.5460i	−1.37053	+	1.52213i
$676$	−2.56659	−	4.44546i	−0.0987150	−	0.170979i
$677$	23.8788	−	41.3594i	0.917738	−	1.58957i	0.114896	−	0.993377i	$-0.463346\pi$
$677$	23.8788	−	41.3594i	0.917738	−	1.58957i	0.802842	−	0.596192i	$-0.203320\pi$
$678$	−2.23261	−	6.87126i	−0.0857428	−	0.263889i
$679$	31.0344	+	13.8174i	1.19099	+	0.530263i
$680$	61.3563	+	44.5780i	2.35291	+	1.70949i
$681$	−23.6038			−0.904500
$682$		0			0
$683$	27.7600			1.06221			0.531104	−	0.847307i	$-0.321777\pi$
$683$	27.7600			1.06221			0.531104	+	0.847307i	$0.321777\pi$
$684$	0.294083	+	0.213664i	0.0112446	+	0.00816965i
$685$	0.466256	+	0.207590i	0.0178147	+	0.00793162i
$686$	−7.88945	−	24.2812i	−0.301221	−	0.927062i
$687$	12.0961	−	20.9511i	0.461496	−	0.799335i
$688$	14.6961	+	25.4544i	0.560283	+	0.970438i
$689$	−0.825024	+	0.916282i	−0.0314309	+	0.0349076i
$690$	10.2190	−	31.4509i	0.389031	−	1.19731i
$691$	25.4477	+	28.2625i	0.968075	+	1.07516i	0.997140	+	0.0755790i	$0.0240805\pi$
$691$	25.4477	+	28.2625i	0.968075	+	1.07516i	−0.0290645	+	0.999578i	$0.509253\pi$
$692$	0.842756	−	0.375219i	0.0320368	−	0.0142637i
$693$	−1.62180	−	0.344725i	−0.0616072	−	0.0130950i
$694$	−3.23116	+	30.7425i	−0.122653	+	1.16697i
$695$	4.57920	+	43.5682i	0.173699	+	1.65263i
$696$	5.88905	−	1.25176i	0.223224	−	0.0474477i
$697$	1.74624	−	1.26872i	0.0661437	−	0.0480562i
$698$	−13.3661	+	9.71106i	−0.505915	+	0.367569i
$699$	7.43792	−	1.58098i	0.281328	−	0.0597981i
$700$	0.854970	+	8.13450i	0.0323148	+	0.307455i
$701$	−4.29155	+	40.8313i	−0.162089	+	1.54218i	0.547044	+	0.837104i	$0.315753\pi$
$701$	−4.29155	+	40.8313i	−0.162089	+	1.54218i	−0.709133	+	0.705074i	$0.750914\pi$
$702$	1.17400	+	0.249541i	0.0443096	+	0.00941830i
$703$	4.07752	−	1.81543i	0.153786	−	0.0684701i
$704$	−5.65757	−	6.28337i	−0.213228	−	0.236813i
$705$	−9.82874	+	30.2498i	−0.370172	+	1.13927i
$706$	9.17426	−	10.1891i	0.345278	−	0.383470i
$707$	−5.33413	−	9.23898i	−0.200611	−	0.347468i
$708$	−0.779187	+	1.34959i	−0.0292836	+	0.0507207i
$709$	12.9990	+	40.0069i	0.488188	+	1.50249i	0.827309	+	0.561747i	$0.189870\pi$
$709$	12.9990	+	40.0069i	0.488188	+	1.50249i	−0.339121	+	0.940743i	$0.610130\pi$
$710$	−4.99973	−	2.22602i	−0.187637	−	0.0835412i
$711$	2.92810	+	2.12739i	0.109812	+	0.0797833i
$712$	44.6368			1.67284
$713$		0			0
$714$	−27.0654			−1.01290
$715$	−0.491418	−	0.357036i	−0.0183780	−	0.0133524i
$716$	6.13503	+	2.73149i	0.229277	+	0.102081i
$717$	3.92996	+	12.0952i	0.146767	+	0.451702i
$718$	−21.3951	+	37.0573i	−0.798456	+	1.38297i
$719$	16.6345	+	28.8118i	0.620362	+	1.07450i	0.989418	+	0.145092i	$0.0463477\pi$
$719$	16.6345	+	28.8118i	0.620362	+	1.07450i	−0.369056	+	0.929407i	$0.620319\pi$
$720$	−6.18394	+	6.86796i	−0.230462	+	0.255954i
$721$	1.30594	−	4.01926i	0.0486357	−	0.149685i
$722$	−14.9765	−	16.6331i	−0.557368	−	0.619020i
$723$	−9.28414	+	4.13356i	−0.345281	+	0.153729i
$724$	−2.83948	−	0.603549i	−0.105528	−	0.0224307i
$725$	−1.31934	+	12.5527i	−0.0489991	+	0.466196i
$726$	1.98411	+	18.8775i	0.0736372	+	0.700611i
$727$	32.0078	−	6.80347i	1.18710	−	0.252327i	0.428295	−	0.903639i	$-0.359115\pi$
$727$	32.0078	−	6.80347i	1.18710	−	0.252327i	0.758810	+	0.651312i	$0.225781\pi$
$728$	0.903555	−	0.656471i	0.0334880	−	0.0243305i
$729$	−24.1540	+	17.5489i	−0.894592	+	0.649959i
$730$	−37.3020	+	7.92879i	−1.38061	+	0.293458i
$731$	6.62051	+	62.9900i	0.244869	+	2.32977i
$732$	−0.107425	+	1.02208i	−0.00397055	+	0.0377773i
$733$	9.74617	+	2.07161i	0.359983	+	0.0765168i	0.384353	−	0.923186i	$-0.374425\pi$
$733$	9.74617	+	2.07161i	0.359983	+	0.0765168i	−0.0243699	+	0.999703i	$0.507758\pi$
$734$	26.1867	−	11.6591i	0.966567	−	0.430343i
$735$	8.33528	+	9.25726i	0.307451	+	0.341459i
$736$	−3.15124	+	9.69852i	−0.116156	+	0.357492i
$737$	−0.351116	+	0.389954i	−0.0129335	+	0.0143641i
$738$	0.165618	+	0.286858i	0.00609647	+	0.0105594i
$739$	−15.4792	+	26.8108i	−0.569412	+	0.986251i	0.427212	+	0.904152i	$0.359496\pi$
$739$	−15.4792	+	26.8108i	−0.569412	+	0.986251i	−0.996624	+	0.0820995i	$0.973837\pi$
$740$	−1.79923	−	5.53747i	−0.0661411	−	0.203561i
$741$	−0.262847	−	0.117027i	−0.00965593	−	0.00429910i
$742$	16.4483	+	11.9504i	0.603834	+	0.438711i
$743$	1.11003			0.0407231			0.0203615	−	0.999793i	$-0.493518\pi$
$743$	1.11003			0.0407231			0.0203615	+	0.999793i	$0.493518\pi$
$744$		0			0
$745$	20.6778			0.757578
$746$	33.7865	+	24.5473i	1.23701	+	0.898741i
$747$	−0.237591	−	0.105782i	−0.00869299	−	0.00387037i
$748$	−0.764490	−	2.35286i	−0.0279525	−	0.0860290i
$749$	−13.7113	+	23.7487i	−0.501000	+	0.867757i
$750$	15.8700	+	27.4877i	0.579491	+	1.00371i
$751$	18.8396	−	20.9235i	0.687466	−	0.763508i	−0.293863	−	0.955848i	$-0.594941\pi$
$751$	18.8396	−	20.9235i	0.687466	−	0.763508i	0.981328	+	0.192339i	$0.0616075\pi$
$752$	−5.31779	+	16.3665i	−0.193920	+	0.596824i
$753$	22.5120	+	25.0021i	0.820382	+	0.911127i
$754$	0.260068	−	0.115790i	0.00947110	−	0.00421681i
$755$	50.8865	+	10.8163i	1.85195	+	0.393644i
$756$	−0.510284	+	4.85503i	−0.0185588	+	0.176576i
$757$	−4.04758	−	38.5102i	−0.147112	−	1.39968i	−0.780168	−	0.625570i	$-0.784866\pi$
$757$	−4.04758	−	38.5102i	−0.147112	−	1.39968i	0.633056	−	0.774106i	$-0.281800\pi$
$758$	40.2549	−	8.55645i	1.46212	−	0.310784i
$759$	−5.28348	+	3.83867i	−0.191778	+	0.139335i
$760$	10.7553	−	7.81420i	0.390137	−	0.283451i
$761$	−42.4877	+	9.03103i	−1.54018	+	0.327375i	−0.898282	−	0.439419i	$-0.855185\pi$
$761$	−42.4877	+	9.03103i	−1.54018	+	0.327375i	−0.641894	+	0.766793i	$0.721851\pi$
$762$	−1.44320	−	13.7311i	−0.0522816	−	0.497426i
$763$	2.34818	−	22.3414i	0.0850097	−	0.808814i
$764$	3.02798	+	0.643617i	0.109549	+	0.0232853i
$765$	−18.1932	+	8.10015i	−0.657778	+	0.292861i
$766$	−22.6970	−	25.2076i	−0.820076	−	0.910786i
$767$	−0.137853	+	0.424268i	−0.00497759	+	0.0153194i
$768$	−9.03908	+	10.0389i	−0.326170	+	0.362248i
$769$	1.55509	+	2.69350i	0.0560781	+	0.0971302i	0.892702	−	0.450648i	$-0.148807\pi$
$769$	1.55509	+	2.69350i	0.0560781	+	0.0971302i	−0.836624	+	0.547778i	$0.815474\pi$
$770$	−5.00806	+	8.67422i	−0.180478	+	0.312597i
$771$	−7.64083	−	23.5161i	−0.275178	−	0.846910i
$772$	1.67433	+	0.745460i	0.0602604	+	0.0268297i
$773$	−17.5073	−	12.7198i	−0.629693	−	0.457499i	0.226601	−	0.973988i	$-0.427239\pi$
$773$	−17.5073	−	12.7198i	−0.629693	−	0.457499i	−0.856294	+	0.516489i	$0.827239\pi$
$774$	−9.71956			−0.349362
$775$		0			0
$776$	−47.0918			−1.69050
$777$	10.1771	+	7.39408i	0.365101	+	0.265261i
$778$	−20.5240	−	9.13789i	−0.735822	−	0.327609i
$779$	−0.116921	−	0.359847i	−0.00418914	−	0.0128929i
$780$	−0.187665	+	0.325045i	−0.00671947	+	0.0116385i
$781$	0.540408	+	0.936015i	0.0193373	+	0.0334932i
$782$	25.7986	−	28.6523i	0.922556	−	1.02460i
$783$	−2.32791	+	7.16457i	−0.0831927	+	0.256041i
$784$	4.50976	+	5.00859i	0.161063	+	0.178878i
$785$	52.2686	−	23.2715i	1.86555	−	0.830595i
$786$	−23.9683	−	5.09462i	−0.854921	−	0.181719i
$787$	0.823322	−	7.83339i	0.0293483	−	0.279230i	−0.969999	−	0.243108i	$-0.921833\pi$
$787$	0.823322	−	7.83339i	0.0293483	−	0.279230i	0.999347	−	0.0361217i	$-0.0115004\pi$
$788$	−0.925909	−	8.80944i	−0.0329841	−	0.313823i
$789$	35.6964	−	7.58751i	1.27083	−	0.270122i
$790$	17.6885	−	12.8515i	0.629330	−	0.457235i
$791$	6.80558	−	4.94454i	0.241979	−	0.175808i
$792$	2.24818	−	0.477865i	0.0798855	−	0.0169802i
$793$	0.0307517	+	0.292583i	0.00109202	+	0.0103899i
$794$	−1.31728	+	12.5330i	−0.0467484	+	0.444781i
$795$	−40.4603	−	8.60010i	−1.43498	−	0.305014i
$796$	9.61749	−	4.28198i	0.340883	−	0.151771i
$797$	19.7515	+	21.9363i	0.699634	+	0.777022i	0.983318	−	0.181896i	$-0.0582233\pi$
$797$	19.7515	+	21.9363i	0.699634	+	0.777022i	−0.283684	+	0.958918i	$0.591557\pi$
$798$	−1.46609	+	4.51217i	−0.0518992	+	0.159729i
$799$	−24.8133	+	27.5580i	−0.877833	+	0.974932i
$800$	−10.4019	−	18.0166i	−0.367763	−	0.636984i
$801$	−5.86059	+	10.1508i	−0.207074	+	0.358663i
$802$	7.78716	+	23.9664i	0.274974	+	0.846283i
$803$	6.88008	+	3.06321i	0.242793	+	0.108098i
$804$	0.262311	+	0.190580i	0.00925100	+	0.00672124i
$805$	38.5039			1.35708
$806$		0			0
$807$	18.5749			0.653869
$808$	11.9642	+	8.69250i	0.420899	+	0.305801i
$809$	−1.94359	−	0.865343i	−0.0683331	−	0.0304238i	0.372286	−	0.928118i	$-0.378574\pi$
$809$	−1.94359	−	0.865343i	−0.0683331	−	0.0304238i	−0.440619	+	0.897694i	$0.645241\pi$
$810$	8.88702	+	27.3514i	0.312258	+	0.961032i
$811$	−3.60252	+	6.23975i	−0.126502	+	0.219107i	−0.922319	−	0.386430i	$-0.873708\pi$
$811$	−3.60252	+	6.23975i	−0.126502	+	0.219107i	0.795817	+	0.605537i	$0.207042\pi$
$812$	0.578950	+	1.00277i	0.0203172	+	0.0351904i
$813$	−26.9826	+	29.9672i	−0.946320	+	1.05100i
$814$	1.44050	−	4.43341i	0.0504896	−	0.155391i
$815$	−43.3264	−	48.1188i	−1.51766	−	1.68553i
$816$	27.2170	−	12.1178i	0.952787	−	0.424208i
$817$	10.8599	+	2.30834i	0.379940	+	0.0807588i
$818$	3.22060	−	30.6419i	0.112606	−	1.07137i
$819$	0.0306556	+	0.291669i	0.00107119	+	0.0101917i
$820$	−0.482787	+	0.102619i	−0.0168596	+	0.00358363i
$821$	−34.0270	+	24.7221i	−1.18755	+	0.862807i	−0.993003	−	0.118086i	$-0.962324\pi$
$821$	−34.0270	+	24.7221i	−1.18755	+	0.862807i	−0.194548	+	0.980893i	$0.562324\pi$
$822$	0.204267	−	0.148408i	0.00712462	−	0.00517634i
$823$	29.5136	−	6.27331i	1.02878	−	0.218674i	0.337549	−	0.941308i	$-0.390402\pi$
$823$	29.5136	−	6.27331i	1.02878	−	0.218674i	0.691231	+	0.722634i	$0.257069\pi$
$824$	0.612361	+	5.82622i	0.0213326	+	0.202966i
$825$	1.39265	−	13.2501i	0.0484857	−	0.461311i
$826$	7.19523	+	1.52939i	0.250354	+	0.0532144i
$827$	−3.53584	+	1.57426i	−0.122953	+	0.0547423i	−0.467291	−	0.884103i	$-0.654770\pi$
$827$	−3.53584	+	1.57426i	−0.122953	+	0.0547423i	0.344338	+	0.938846i	$0.388103\pi$
$828$	−0.976549	−	1.08457i	−0.0339374	−	0.0376913i
$829$	4.07025	−	12.5269i	0.141366	−	0.435079i	−0.855160	−	0.518364i	$-0.826541\pi$
$829$	4.07025	−	12.5269i	0.141366	−	0.435079i	0.996526	+	0.0832851i	$0.0265412\pi$
$830$	−1.05127	+	1.16756i	−0.0364902	+	0.0405265i
$831$	11.2491	+	19.4841i	0.390228	+	0.675895i
$832$	−0.747774	+	1.29518i	−0.0259244	+	0.0449024i
$833$	4.48797	+	13.8126i	0.155499	+	0.478577i
$834$	19.7984	+	8.81483i	0.685564	+	0.305233i
$835$	−49.8019	−	36.1832i	−1.72346	−	1.25217i
$836$	−0.433665			−0.0149986
$837$		0			0
$838$	−5.58159			−0.192813
$839$	27.7080	+	20.1311i	0.956588	+	0.695002i	0.952356	−	0.304989i	$-0.0986530\pi$
$839$	27.7080	+	20.1311i	0.956588	+	0.695002i	0.00423187	+	0.999991i	$0.498653\pi$
$840$	34.2292	+	15.2398i	1.18102	+	0.525823i
$841$	−8.40934	−	25.8813i	−0.289977	−	0.892458i
$842$	7.86792	−	13.6276i	0.271147	−	0.469640i
$843$	−22.4486	−	38.8821i	−0.773170	−	1.33917i
$844$	−0.351147	+	0.389988i	−0.0120870	+	0.0134239i
$845$	15.2335	−	46.8840i	0.524049	−	1.61286i
$846$	−3.80780	−	4.22900i	−0.130915	−	0.145396i
$847$	−20.1901	+	8.98922i	−0.693741	+	0.308873i
$848$	−21.8908	−	4.65304i	−0.751734	−	0.159786i
$849$	−0.488007	+	4.64307i	−0.0167483	+	0.159350i
$850$	8.22174	+	78.2246i	0.282003	+	2.68308i
$851$	−17.5283	+	3.72576i	−0.600864	+	0.127717i
$852$	0.540292	−	0.392545i	0.0185101	−	0.0134484i
$853$	11.6886	−	8.49225i	0.400209	−	0.290769i	−0.369417	−	0.929264i	$-0.620443\pi$
$853$	11.6886	−	8.49225i	0.400209	−	0.290769i	0.769626	+	0.638495i	$0.220443\pi$
$854$	4.74510	−	1.00860i	0.162374	−	0.0345136i
$855$	0.364904	+	3.47183i	0.0124795	+	0.118734i
$856$	3.97352	−	37.8055i	0.135812	−	1.29217i
$857$	−27.2248	−	5.78682i	−0.929983	−	0.197674i	−0.282075	−	0.959392i	$-0.591023\pi$
$857$	−27.2248	−	5.78682i	−0.929983	−	0.197674i	−0.647908	+	0.761719i	$0.724356\pi$
$858$	−0.274517	+	0.122223i	−0.00937186	+	0.00417262i
$859$	−31.6634	−	35.1657i	−1.08034	−	1.19984i	−0.978759	−	0.205012i	$-0.934277\pi$
$859$	−31.6634	−	35.1657i	−1.08034	−	1.19984i	−0.101581	−	0.994827i	$-0.532390\pi$
$860$	4.47552	−	13.7742i	0.152614	−	0.469697i
$861$	0.713547	−	0.792474i	0.0243176	−	0.0270075i
$862$	11.7574	+	20.3644i	0.400459	+	0.693616i
$863$	−13.0267	+	22.5629i	−0.443434	+	0.768049i	−0.997942	−	0.0641289i	$-0.979573\pi$
$863$	−13.0267	+	22.5629i	−0.443434	+	0.768049i	0.554508	+	0.832178i	$0.312906\pi$
$864$	−3.83695	−	11.8089i	−0.130536	−	0.401747i
$865$	8.09344	+	3.60343i	0.275185	+	0.122520i
$866$	37.0127	+	26.8913i	1.25774	+	0.913802i
$867$	38.9668			1.32338
$868$		0			0
$869$	−4.31787			−0.146474
$870$	7.72650	+	5.61363i	0.261953	+	0.190320i
$871$	0.0847914	+	0.0377516i	0.00287305	+	0.00127916i
$872$	9.62302	+	29.6166i	0.325876	+	1.00294i
$873$	6.18291	−	10.7091i	0.209260	−	0.362449i
$874$	−3.37925	−	5.85303i	−0.114305	−	0.197982i
$875$	−24.7284	+	27.4637i	−0.835973	+	0.928442i
$876$	1.43802	−	4.42577i	0.0485862	−	0.149533i
$877$	−22.9655	−	25.5058i	−0.775491	−	0.861271i	0.217909	−	0.975969i	$-0.430076\pi$
$877$	−22.9655	−	25.5058i	−0.775491	−	0.861271i	−0.993400	+	0.114699i	$0.963410\pi$
$878$	−21.9957	+	9.79313i	−0.742320	+	0.330502i
$879$	−2.75869	−	0.586377i	−0.0930483	−	0.0197780i
$880$	1.15247	−	10.9650i	0.0388498	−	0.369631i
$881$	0.379927	+	3.61476i	0.0128001	+	0.121784i	0.999056	−	0.0434401i	$-0.0138318\pi$
$881$	0.379927	+	3.61476i	0.0128001	+	0.121784i	−0.986256	+	0.165225i	$0.947165\pi$
$882$	−2.18003	+	0.463379i	−0.0734053	+	0.0156028i
$883$	−31.9217	+	23.1925i	−1.07425	+	0.780489i	−0.976671	−	0.214739i	$-0.931110\pi$
$883$	−31.9217	+	23.1925i	−1.07425	+	0.780489i	−0.0975789	+	0.995228i	$0.531110\pi$
$884$	−0.354021	+	0.257211i	−0.0119070	+	0.00865095i
$885$	−14.6389	+	3.11159i	−0.492080	+	0.104595i
$886$	−1.64886	−	15.6879i	−0.0553946	−	0.527045i
$887$	4.42184	−	42.0710i	0.148471	−	1.41261i	−0.625914	−	0.779892i	$-0.715274\pi$
$887$	4.42184	−	42.0710i	0.148471	−	1.41261i	0.774385	−	0.632714i	$-0.218059\pi$
$888$	−17.0570	−	3.62558i	−0.572395	−	0.121666i
$889$	14.6859	−	6.53857i	0.492548	−	0.219297i
$890$	47.3793	+	52.6200i	1.58816	+	1.76383i
$891$	1.75506	−	5.40152i	0.0587967	−	0.180958i
$892$	3.20923	−	3.56421i	0.107453	−	0.119338i
$893$	3.25019	+	5.62950i	0.108764	+	0.188384i
$894$	5.11471	−	8.85894i	0.171062	−	0.296287i
$895$	19.9297	+	61.3373i	0.666176	+	2.05028i
$896$	13.7170	+	6.10720i	0.458253	+	0.204027i
$897$	0.934547	+	0.678988i	0.0312036	+	0.0226708i
$898$	32.2180			1.07513
$899$		0			0
$900$	2.97733			0.0992444
$901$	−39.0159	−	28.3467i	−1.29981	−	0.944365i
$902$	−0.361001	−	0.160728i	−0.0120200	−	0.00535165i
$903$	9.66950	+	29.7597i	0.321781	+	0.990340i
$904$	−5.83056	+	10.0988i	−0.193921	+	0.335882i
$905$	−13.9391	−	24.1433i	−0.463352	−	0.802549i
$906$	17.2208	−	19.1257i	0.572124	−	0.635409i
$907$	−10.0023	+	30.7838i	−0.332120	+	1.02216i	0.636003	+	0.771686i	$0.280586\pi$
$907$	−10.0023	+	30.7838i	−0.332120	+	1.02216i	−0.968123	+	0.250474i	$0.919414\pi$
$908$	4.21071	+	4.67647i	0.139737	+	0.155194i
$909$	−3.54760	+	1.57949i	−0.117666	+	0.0523884i
$910$	1.73295	+	0.368350i	0.0574467	+	0.0122107i
$911$	2.82862	−	26.9125i	0.0937163	−	0.891651i	−0.842138	−	0.539263i	$-0.818703\pi$
$911$	2.82862	−	26.9125i	0.0937163	−	0.891651i	0.935854	−	0.352388i	$-0.114630\pi$
$912$	−0.545896	−	5.19385i	−0.0180764	−	0.171986i
$913$	0.303490	−	0.0645089i	0.0100441	−	0.00213493i
$914$	−32.7638	+	23.8043i	−1.08373	+	0.787376i
$915$	−7.98474	+	5.80126i	−0.263968	+	0.191784i
$916$	−6.30875	+	1.34097i	−0.208447	+	0.0443068i
$917$	−2.98226	−	28.3743i	−0.0984828	−	0.937001i
$918$	−4.90709	+	46.6879i	−0.161958	+	1.54093i
$919$	−20.3112	−	4.31727i	−0.670004	−	0.142414i	−0.139664	−	0.990199i	$-0.544602\pi$
$919$	−20.3112	−	4.31727i	−0.670004	−	0.142414i	−0.530340	+	0.847785i	$0.677936\pi$
$920$	−48.7604	+	21.7095i	−1.60758	+	0.715741i
$921$	22.5736	+	25.0705i	0.743824	+	0.826100i
$922$	7.57365	−	23.3093i	0.249425	−	0.767651i
$923$	0.127922	−	0.142071i	0.00421060	−	0.00467634i
$924$	−0.611117	−	1.05849i	−0.0201043	−	0.0348216i
$925$	18.2789	−	31.6600i	0.601007	−	1.04097i
$926$	0.0162285	+	0.0499461i	0.000533301	+	0.00164133i
$927$	−1.40534	−	0.625697i	−0.0461574	−	0.0205506i
$928$	−2.38262	−	1.73108i	−0.0782134	−	0.0568254i
$929$	−20.6589			−0.677798			−0.338899	−	0.940823i	$-0.610055\pi$
$929$	−20.6589			−0.677798			−0.338899	+	0.940823i	$0.610055\pi$
$930$		0			0
$931$	2.54585			0.0834368
$932$	−1.64009	−	1.19159i	−0.0537229	−	0.0390320i
$933$	21.5269	+	9.58440i	0.704759	+	0.313779i
$934$	9.90570	+	30.4866i	0.324124	+	0.997552i
$935$	11.8793	−	20.5756i	0.388495	−	0.672893i
$936$	−0.203272	−	0.352078i	−0.00664416	−	0.0115080i
$937$	1.95426	−	2.17043i	0.0638430	−	0.0709048i	−0.710377	−	0.703821i	$-0.751476\pi$
$937$	1.95426	−	2.17043i	0.0638430	−	0.0709048i	0.774220	+	0.632916i	$0.218142\pi$
$938$	0.472945	−	1.45557i	0.0154422	−	0.0475262i
$939$	6.30618	+	7.00372i	0.205794	+	0.228558i
$940$	7.74655	−	3.44899i	0.252665	−	0.112494i
$941$	−32.1322	−	6.82992i	−1.04748	−	0.222649i	−0.348144	−	0.937441i	$-0.613188\pi$
$941$	−32.1322	−	6.82992i	−1.04748	−	0.222649i	−0.699337	+	0.714792i	$0.746521\pi$
$942$	2.95863	−	28.1495i	0.0963975	−	0.917161i
$943$	0.158788	+	1.51076i	0.00517084	+	0.0491972i
$944$	−7.92028	+	1.68351i	−0.257783	+	0.0547935i
$945$	−37.9286	+	27.5567i	−1.23382	+	0.896420i
$946$	9.38092	−	6.81564i	0.305000	−	0.221596i
$947$	−38.2698	+	8.13449i	−1.24360	+	0.264335i	−0.782296	−	0.622907i	$-0.785952\pi$
$947$	−38.2698	+	8.13449i	−1.24360	+	0.264335i	−0.461304	+	0.887242i	$0.652618\pi$
$948$	0.278884	+	2.65340i	0.00905772	+	0.0861785i
$949$	0.139245	−	1.32483i	0.00452008	−	0.0430057i
$950$	13.4865	+	2.86664i	0.437559	+	0.0930060i
$951$	−20.7480	+	9.23760i	−0.672800	+	0.299550i
$952$	29.2305	+	32.4637i	0.947365	+	1.05216i
$953$	1.86020	−	5.72512i	0.0602579	−	0.185455i	−0.916396	−	0.400272i	$-0.868916\pi$
$953$	1.86020	−	5.72512i	0.0602579	−	0.185455i	0.976654	+	0.214817i	$0.0689156\pi$
$954$	4.95203	−	5.49979i	0.160328	−	0.178062i
$955$	14.8645	+	25.7461i	0.481004	+	0.833123i
$956$	1.69527	−	2.93629i	0.0548288	−	0.0949663i
$957$	−0.582832	−	1.79377i	−0.0188403	−	0.0579844i
$958$	−24.5781	−	10.9429i	−0.794082	−	0.353548i
$959$	0.237835	+	0.172797i	0.00768008	+	0.00557991i
$960$	−50.1729			−1.61932
$961$		0			0
$962$	−0.824543			−0.0265843
$963$	8.07564	+	5.86729i	0.260234	+	0.189071i
$964$	2.47516	+	1.10201i	0.0797197	+	0.0354935i
$965$	5.43907	+	16.7397i	0.175090	+	0.538871i
$966$	9.52401	−	16.4961i	0.306430	−	0.530753i
$967$	−13.1552	−	22.7854i	−0.423042	−	0.732730i	0.573194	−	0.819420i	$-0.305704\pi$
$967$	−13.1552	−	22.7854i	−0.423042	−	0.732730i	−0.996235	+	0.0866903i	$0.972371\pi$
$968$	20.4999	−	22.7675i	0.658892	−	0.731774i
$969$	3.47763	−	10.7030i	0.111718	−	0.343831i
$970$	−49.9850	−	55.5140i	−1.60492	−	1.78245i
$971$	−4.32643	+	1.92625i	−0.138842	+	0.0618164i	−0.474981	−	0.879996i	$-0.657545\pi$
$971$	−4.32643	+	1.92625i	−0.138842	+	0.0618164i	0.336140	+	0.941812i	$0.390879\pi$
$972$	3.11156	+	0.661383i	0.0998034	+	0.0212139i
$973$	−2.63762	+	25.0953i	−0.0845584	+	0.804519i
$974$	−3.54318	−	33.7111i	−0.113531	−	1.08017i
$975$	−2.30511	+	0.489966i	−0.0738226	+	0.0156915i
$976$	−4.32010	+	3.13874i	−0.138283	+	0.100469i
$977$	13.9798	−	10.1569i	0.447255	−	0.324950i	−0.341256	−	0.939970i	$-0.610852\pi$
$977$	13.9798	−	10.1569i	0.447255	−	0.324950i	0.788511	+	0.615021i	$0.210852\pi$
$978$	−31.3322	+	6.65987i	−1.00189	+	0.212959i
$979$	−1.46166	−	13.9068i	−0.0467150	−	0.444464i
$980$	0.347141	−	3.30283i	0.0110890	−	0.105505i
$981$	−7.99855	−	1.70014i	−0.255374	−	0.0542814i
$982$	−14.5406	+	6.47387i	−0.464008	+	0.206589i
$983$	−27.4120	−	30.4441i	−0.874306	−	0.971015i	0.125472	−	0.992097i	$-0.459955\pi$
$983$	−27.4120	−	30.4441i	−0.874306	−	0.971015i	−0.999778	+	0.0210824i	$0.993289\pi$
$984$	−0.456801	+	1.40589i	−0.0145623	+	0.0448181i
$985$	56.9215	−	63.2177i	1.81367	−	2.01428i
$986$	5.56742	+	9.64305i	0.177303	+	0.307097i
$987$	−9.16029	+	15.8661i	−0.291575	+	0.505023i
$988$	0.0237038	+	0.0729528i	0.000754118	+	0.00232094i
$989$	−40.7214	−	18.1303i	−1.29486	−	0.576511i
$990$	2.94963	+	2.14303i	0.0937455	+	0.0681101i
$991$	14.1338			0.448975			0.224487	−	0.974477i	$-0.427929\pi$
$991$	14.1338			0.448975			0.224487	+	0.974477i	$0.427929\pi$
$992$		0			0
$993$	−13.3113			−0.422420
$994$	−2.55034	−	1.85293i	−0.0808918	−	0.0587713i
$995$	92.3620	+	41.1222i	2.92807	+	1.30366i
$996$	−0.0592436	−	0.182333i	−0.00187721	−	0.00577745i
$997$	−7.72692	+	13.3834i	−0.244714	+	0.423857i	−0.962051	−	0.272869i	$-0.912027\pi$
$997$	−7.72692	+	13.3834i	−0.244714	+	0.423857i	0.717337	+	0.696726i	$0.245361\pi$
$998$	14.5852	+	25.2622i	0.461685	+	0.799662i
$999$	14.6000	−	16.2149i	0.461922	−	0.513017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.k.732.1		16
31.2	even	5		961.2.g.s.448.2		16
31.3	odd	30		961.2.d.n.388.2		16
31.4	even	5		961.2.c.j.521.6		16
31.5	even	3		31.2.g.a.10.1	✓	16
31.6	odd	6		961.2.d.n.374.2		16
31.7	even	15		961.2.a.i.1.6		8
31.8	even	5		961.2.g.t.844.2		16
31.9	even	15		961.2.g.s.547.2		16
31.10	even	15		961.2.g.t.846.2		16
31.11	odd	30		961.2.c.i.439.6		16
31.12	odd	30		961.2.d.q.628.3		16
31.13	odd	30		961.2.g.j.235.1		16
31.14	even	15		961.2.d.p.531.3		16
31.15	odd	10		961.2.g.l.338.1		16
31.16	even	5		31.2.g.a.28.1	yes	16
31.17	odd	30		961.2.d.q.531.3		16
31.18	even	15	inner	961.2.g.k.235.1		16
31.19	even	15		961.2.d.p.628.3		16
31.20	even	15		961.2.c.j.439.6		16
31.21	odd	30		961.2.g.n.846.2		16
31.22	odd	30		961.2.g.m.547.2		16
31.23	odd	10		961.2.g.n.844.2		16
31.24	odd	30		961.2.a.j.1.6		8
31.25	even	3		961.2.d.o.374.2		16
31.26	odd	6		961.2.g.l.816.1		16
31.27	odd	10		961.2.c.i.521.6		16
31.28	even	15		961.2.d.o.388.2		16
31.29	odd	10		961.2.g.m.448.2		16
31.30	odd	2		961.2.g.j.732.1		16
93.5	odd	6		279.2.y.c.10.2		16
93.38	odd	30		8649.2.a.bf.1.3		8
93.47	odd	10		279.2.y.c.28.2		16
93.86	even	30		8649.2.a.be.1.3		8
124.47	odd	10		496.2.bg.c.369.2		16
124.67	odd	6		496.2.bg.c.289.2		16
155.47	odd	20		775.2.ck.a.524.1		32
155.67	odd	12		775.2.ck.a.599.4		32
155.78	odd	20		775.2.ck.a.524.4		32
155.98	odd	12		775.2.ck.a.599.1		32
155.109	even	10		775.2.bl.a.276.2		16
155.129	even	6		775.2.bl.a.351.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.1	✓	16	31.5	even	3
31.2.g.a.28.1	yes	16	31.16	even	5
279.2.y.c.10.2		16	93.5	odd	6
279.2.y.c.28.2		16	93.47	odd	10
496.2.bg.c.289.2		16	124.67	odd	6
496.2.bg.c.369.2		16	124.47	odd	10
775.2.bl.a.276.2		16	155.109	even	10
775.2.bl.a.351.2		16	155.129	even	6
775.2.ck.a.524.1		32	155.47	odd	20
775.2.ck.a.524.4		32	155.78	odd	20
775.2.ck.a.599.1		32	155.98	odd	12
775.2.ck.a.599.4		32	155.67	odd	12
961.2.a.i.1.6		8	31.7	even	15
961.2.a.j.1.6		8	31.24	odd	30
961.2.c.i.439.6		16	31.11	odd	30
961.2.c.i.521.6		16	31.27	odd	10
961.2.c.j.439.6		16	31.20	even	15
961.2.c.j.521.6		16	31.4	even	5
961.2.d.n.374.2		16	31.6	odd	6
961.2.d.n.388.2		16	31.3	odd	30
961.2.d.o.374.2		16	31.25	even	3
961.2.d.o.388.2		16	31.28	even	15
961.2.d.p.531.3		16	31.14	even	15
961.2.d.p.628.3		16	31.19	even	15
961.2.d.q.531.3		16	31.17	odd	30
961.2.d.q.628.3		16	31.12	odd	30
961.2.g.j.235.1		16	31.13	odd	30
961.2.g.j.732.1		16	31.30	odd	2
961.2.g.k.235.1		16	31.18	even	15	inner
961.2.g.k.732.1		16	1.1	even	1	trivial
961.2.g.l.338.1		16	31.15	odd	10
961.2.g.l.816.1		16	31.26	odd	6
961.2.g.m.448.2		16	31.29	odd	10
961.2.g.m.547.2		16	31.22	odd	30
961.2.g.n.844.2		16	31.23	odd	10
961.2.g.n.846.2		16	31.21	odd	30
961.2.g.s.448.2		16	31.2	even	5
961.2.g.s.547.2		16	31.9	even	15
961.2.g.t.844.2		16	31.8	even	5
961.2.g.t.846.2		16	31.10	even	15
8649.2.a.be.1.3		8	93.86	even	30
8649.2.a.bf.1.3		8	93.38	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02470 - 0.744490i) q^{2} +(1.35599 + 0.603725i) q^{3} +(-0.122284 - 0.376353i) q^{4} +(1.90016 - 3.29117i) q^{5} +(-0.940018 - 1.62816i) q^{6} +(1.46472 - 1.62674i) q^{7} +(-0.937688 + 2.88591i) q^{8} +(-0.533169 - 0.592145i) q^{9} +(-4.39734 + 1.95782i) q^{10} +(0.929823 + 0.197640i) q^{11} +(0.0613973 - 0.584156i) q^{12} +(-0.0175757 - 0.167221i) q^{13} +(-2.71199 + 0.576451i) q^{14} +(4.56356 - 3.31562i) q^{15} +(2.46909 - 1.79390i) q^{16} +(6.43294 - 1.36736i) q^{17} +(0.105494 + 1.00371i) q^{18} +(0.120505 - 1.14653i) q^{19} +(-1.47100 - 0.312671i) q^{20} +(2.96825 - 1.32155i) q^{21} +(-0.805651 - 0.894766i) q^{22} +(-1.43029 + 4.40197i) q^{23} +(-3.01379 + 3.34715i) q^{24} +(-4.72122 - 8.17739i) q^{25} +(-0.106485 + 0.184437i) q^{26} +(-1.74151 - 5.35983i) q^{27} +(-0.791339 - 0.352327i) q^{28} +(-1.08143 - 0.785701i) q^{29} -7.14474 q^{30} +2.20322 q^{32} +(1.14151 + 0.829355i) q^{33} +(-7.60983 - 3.38812i) q^{34} +(-2.57067 - 7.91171i) q^{35} +(-0.157657 + 0.273070i) q^{36} +(1.93582 + 3.35295i) q^{37} +(-0.977059 + 1.08513i) q^{38} +(0.0771233 - 0.237361i) q^{39} +(7.71627 + 8.56978i) q^{40} +(0.299828 - 0.133492i) q^{41} +(-4.02545 - 0.855635i) q^{42} +(-1.00667 + 9.57782i) q^{43} +(-0.0393205 - 0.374110i) q^{44} +(-2.96196 + 0.629584i) q^{45} +(4.74283 - 3.44587i) q^{46} +(-4.56170 + 3.31427i) q^{47} +(4.43108 - 0.941856i) q^{48} +(0.230833 + 2.19623i) q^{49} +(-1.25014 + 11.8943i) q^{50} +(9.54851 + 2.02960i) q^{51} +(-0.0607850 + 0.0270632i) q^{52} +(-4.90670 - 5.44944i) q^{53} +(-2.20581 + 6.78877i) q^{54} +(2.41728 - 2.68466i) q^{55} +(3.32116 + 5.75242i) q^{56} +(0.855590 - 1.48193i) q^{57} +(0.523192 + 1.61022i) q^{58} +(-2.42375 - 1.07912i) q^{59} +(-1.80590 - 1.31206i) q^{60} -1.74967 q^{61} -1.74421 q^{63} +(-7.19583 - 5.22808i) q^{64} +(-0.583751 - 0.259903i) q^{65} +(-0.552261 - 1.69968i) q^{66} +(-0.276003 + 0.478052i) q^{67} +(-1.30126 - 2.25385i) q^{68} +(-4.59703 + 5.10552i) q^{69} +(-3.25601 + 10.0210i) q^{70} +(0.760794 + 0.844947i) q^{71} +(2.20882 - 0.983431i) q^{72} +(7.74947 + 1.64720i) q^{73} +(0.512590 - 4.87697i) q^{74} +(-1.46502 - 13.9388i) q^{75} +(-0.446234 + 0.0948500i) q^{76} +(1.68344 - 1.22309i) q^{77} +(-0.255741 + 0.185807i) q^{78} +(-4.44302 + 0.944393i) q^{79} +(-1.21237 - 11.5349i) q^{80} +(0.624523 - 5.94194i) q^{81} +(-0.406618 - 0.0864293i) q^{82} +(0.298177 - 0.132757i) q^{83} +(-0.860338 - 0.955503i) q^{84} +(7.72338 - 23.7701i) q^{85} +(8.16212 - 9.06495i) q^{86} +(-0.992053 - 1.71829i) q^{87} +(-1.44225 + 2.49806i) q^{88} +(-4.54569 - 13.9902i) q^{89} +(3.50384 + 1.56001i) q^{90} +(-0.297768 - 0.216341i) q^{91} +1.83159 q^{92} +7.14183 q^{94} +(-3.54444 - 2.57519i) q^{95} +(2.98755 + 1.33014i) q^{96} +(4.79569 + 14.7596i) q^{97} +(1.39853 - 2.42233i) q^{98} +(-0.378722 - 0.655965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

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Database

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