LMFDB - Embedded newform 29.2.e.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,2,Mod(4,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.231566165862$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	12.0.7877952219361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 $ x^12 - 3x^11 + 13x^9 - 18x^8 - 14x^7 + 57x^6 - 28x^5 - 72x^4 + 104x^3 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			4.2
Root			$1.38491 - 0.286410i$ of defining polynomial
Character	$\chi$	$=$	29.4
Dual form			29.2.e.a.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.536089 - 0.122359i) q^{2} +(0.855966 + 1.77743i) q^{3} +(-1.52952 - 0.736577i) q^{4} +(0.610610 - 2.67526i) q^{5} +(-0.241390 - 1.05760i) q^{6} +(-4.03077 + 1.94112i) q^{7} +(1.58965 + 1.26771i) q^{8} +(-0.556117 + 0.697349i) q^{9} +O(q^{10})$	\(q+(-0.536089 - 0.122359i) q^{2} +(0.855966 + 1.77743i) q^{3} +(-1.52952 - 0.736577i) q^{4} +(0.610610 - 2.67526i) q^{5} +(-0.241390 - 1.05760i) q^{6} +(-4.03077 + 1.94112i) q^{7} +(1.58965 + 1.26771i) q^{8} +(-0.556117 + 0.697349i) q^{9} +(-0.654683 + 1.35946i) q^{10} +(1.16531 - 0.929305i) q^{11} -3.34910i q^{12} +(0.906494 + 1.13671i) q^{13} +(2.39836 - 0.547411i) q^{14} +(5.27775 - 1.20461i) q^{15} +(1.41984 + 1.78042i) q^{16} +2.07293i q^{17} +(0.383455 - 0.305796i) q^{18} +(-0.236123 + 0.490315i) q^{19} +(-2.90447 + 3.64209i) q^{20} +(-6.90040 - 5.50289i) q^{21} +(-0.738420 + 0.355604i) q^{22} +(-0.382936 - 1.67775i) q^{23} +(-0.892571 + 3.91061i) q^{24} +(-2.27930 - 1.09766i) q^{25} +(-0.346875 - 0.720294i) q^{26} +(4.05451 + 0.925415i) q^{27} +7.59491 q^{28} +(-3.78014 - 3.83543i) q^{29} -2.97674 q^{30} +(-4.54177 - 1.03663i) q^{31} +(-2.30769 - 4.79197i) q^{32} +(2.64924 + 1.27581i) q^{33} +(0.253641 - 1.11128i) q^{34} +(2.73175 + 11.9686i) q^{35} +(1.36424 - 0.656985i) q^{36} +(-2.37655 - 1.89524i) q^{37} +(0.186578 - 0.233961i) q^{38} +(-1.24449 + 2.58421i) q^{39} +(4.36209 - 3.47865i) q^{40} -0.595175i q^{41} +(3.02590 + 3.79436i) q^{42} +(0.321297 - 0.0733340i) q^{43} +(-2.46687 + 0.563047i) q^{44} +(1.52602 + 1.91356i) q^{45} +0.946280i q^{46} +(8.97652 - 7.15853i) q^{47} +(-1.94924 + 4.04764i) q^{48} +(8.11473 - 10.1755i) q^{49} +(1.08760 + 0.867335i) q^{50} +(-3.68449 + 1.77436i) q^{51} +(-0.549226 - 2.40632i) q^{52} +(-2.28813 + 10.0249i) q^{53} +(-2.06035 - 0.992210i) q^{54} +(-1.77458 - 3.68495i) q^{55} +(-8.86828 - 2.02413i) q^{56} -1.07362 q^{57} +(1.55719 + 2.51867i) q^{58} -4.03359 q^{59} +(-8.95970 - 2.04499i) q^{60} +(5.18352 + 10.7637i) q^{61} +(2.30795 + 1.11145i) q^{62} +(0.887945 - 3.89034i) q^{63} +(-0.362680 - 1.58901i) q^{64} +(3.59450 - 1.73102i) q^{65} +(-1.26412 - 1.00811i) q^{66} +(-5.20630 + 6.52849i) q^{67} +(1.52687 - 3.17058i) q^{68} +(2.65431 - 2.11674i) q^{69} -6.75049i q^{70} +(-5.78348 - 7.25226i) q^{71} +(-1.76807 + 0.403550i) q^{72} +(-3.37292 + 0.769848i) q^{73} +(1.04215 + 1.30681i) q^{74} -4.99087i q^{75} +(0.722310 - 0.576023i) q^{76} +(-2.89321 + 6.00781i) q^{77} +(0.983360 - 1.23309i) q^{78} +(6.50888 + 5.19066i) q^{79} +(5.63005 - 2.71129i) q^{80} +(2.42109 + 10.6075i) q^{81} +(-0.0728249 + 0.319067i) q^{82} +(-0.955764 - 0.460272i) q^{83} +(6.50099 + 13.4994i) q^{84} +(5.54562 + 1.26575i) q^{85} -0.181217 q^{86} +(3.58155 - 10.0019i) q^{87} +3.03052 q^{88} +(4.68343 + 1.06896i) q^{89} +(-0.583940 - 1.21256i) q^{90} +(-5.86034 - 2.82219i) q^{91} +(-0.650086 + 2.84821i) q^{92} +(-2.04506 - 8.96001i) q^{93} +(-5.68812 + 2.73926i) q^{94} +(1.16754 + 0.931082i) q^{95} +(6.54209 - 8.20353i) q^{96} +(2.09615 - 4.35270i) q^{97} +(-5.59529 + 4.46209i) q^{98} +1.32943i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−0.536089	−	0.122359i	−0.379072	−	0.0865208i	0.0287391	−	0.999587i	$-0.490851\pi$
$2$	−0.536089	−	0.122359i	−0.379072	−	0.0865208i	−0.407811	+	0.913066i	$0.633708\pi$
$3$	0.855966	+	1.77743i	0.494192	+	1.02620i	0.987686	+	0.156451i	$0.0500054\pi$
$3$	0.855966	+	1.77743i	0.494192	+	1.02620i	−0.493493	+	0.869750i	$0.664280\pi$
$4$	−1.52952	−	0.736577i	−0.764759	−	0.368288i
$5$	0.610610	−	2.67526i	0.273073	−	1.19641i	−0.633291	−	0.773914i	$-0.718296\pi$
$5$	0.610610	−	2.67526i	0.273073	−	1.19641i	0.906364	−	0.422497i	$-0.138846\pi$
$6$	−0.241390	−	1.05760i	−0.0985469	−	0.431762i
$7$	−4.03077	+	1.94112i	−1.52349	+	0.733673i	−0.993446	−	0.114300i	$-0.963538\pi$
$7$	−4.03077	+	1.94112i	−1.52349	+	0.733673i	−0.530040	+	0.847972i	$0.677823\pi$
$8$	1.58965	+	1.26771i	0.562027	+	0.448201i
$9$	−0.556117	+	0.697349i	−0.185372	+	0.232450i
$10$	−0.654683	+	1.35946i	−0.207029	+	0.429900i
$11$	1.16531	−	0.929305i	0.351355	−	0.280196i	−0.431869	−	0.901937i	$-0.642146\pi$
$11$	1.16531	−	0.929305i	0.351355	−	0.280196i	0.783223	+	0.621741i	$0.213574\pi$
$12$		−	3.34910i		−	0.966802i
$13$	0.906494	+	1.13671i	0.251416	+	0.315266i	0.891484	−	0.453053i	$-0.149665\pi$
$13$	0.906494	+	1.13671i	0.251416	+	0.315266i	−0.640068	+	0.768319i	$0.721094\pi$
$14$	2.39836	−	0.547411i	0.640990	−	0.146302i
$15$	5.27775	−	1.20461i	1.36271	−	0.311029i
$16$	1.41984	+	1.78042i	0.354959	+	0.445105i
$17$			2.07293i			0.502759i	0.967889	+	0.251380i	$0.0808843\pi$
$17$			2.07293i			0.502759i	−0.967889	+	0.251380i	$0.919116\pi$
$18$	0.383455	−	0.305796i	0.0903813	−	0.0720767i
$19$	−0.236123	+	0.490315i	−0.0541704	+	0.112486i	−0.926297	−	0.376794i	$-0.877026\pi$
$19$	−0.236123	+	0.490315i	−0.0541704	+	0.112486i	0.872126	+	0.489281i	$0.162741\pi$
$20$	−2.90447	+	3.64209i	−0.649459	+	0.814396i
$21$	−6.90040	−	5.50289i	−1.50579	−	1.20083i
$22$	−0.738420	+	0.355604i	−0.157432	+	0.0758151i
$23$	−0.382936	−	1.67775i	−0.0798476	−	0.349835i	0.919184	−	0.393828i	$-0.128849\pi$
$23$	−0.382936	−	1.67775i	−0.0798476	−	0.349835i	−0.999032	+	0.0439925i	$0.985992\pi$
$24$	−0.892571	+	3.91061i	−0.182195	+	0.798250i
$25$	−2.27930	−	1.09766i	−0.455861	−	0.219531i
$26$	−0.346875	−	0.720294i	−0.0680279	−	0.141261i
$27$	4.05451	+	0.925415i	0.780290	+	0.178096i
$28$	7.59491			1.43530
$29$	−3.78014	−	3.83543i	−0.701954	−	0.712222i
$29$	−3.78014	−	3.83543i	−0.701954	−	0.712222i
$30$	−2.97674			−0.543476
$31$	−4.54177	−	1.03663i	−0.815726	−	0.186184i	−0.205750	−	0.978604i	$-0.565964\pi$
$31$	−4.54177	−	1.03663i	−0.815726	−	0.186184i	−0.609975	+	0.792420i	$0.708821\pi$
$32$	−2.30769	−	4.79197i	−0.407946	−	0.847108i
$33$	2.64924	+	1.27581i	0.461174	+	0.222090i
$34$	0.253641	−	1.11128i	0.0434992	−	0.190582i
$35$	2.73175	+	11.9686i	0.461751	+	2.02306i
$36$	1.36424	−	0.656985i	0.227374	−	0.109497i
$37$	−2.37655	−	1.89524i	−0.390703	−	0.311575i	0.408362	−	0.912820i	$-0.366100\pi$
$37$	−2.37655	−	1.89524i	−0.390703	−	0.311575i	−0.799065	+	0.601245i	$0.794672\pi$
$38$	0.186578	−	0.233961i	0.0302669	−	0.0379535i
$39$	−1.24449	+	2.58421i	−0.199278	+	0.413805i
$40$	4.36209	−	3.47865i	0.689707	−	0.550023i
$41$		−	0.595175i		−	0.0929507i	−0.998919	−	0.0464753i	$-0.985201\pi$
$41$		−	0.595175i		−	0.0929507i	0.998919	−	0.0464753i	$-0.0147989\pi$
$42$	3.02590	+	3.79436i	0.466907	+	0.585483i
$43$	0.321297	−	0.0733340i	0.0489974	−	0.0111833i	−0.197952	−	0.980212i	$-0.563429\pi$
$43$	0.321297	−	0.0733340i	0.0489974	−	0.0111833i	0.246949	+	0.969028i	$0.420572\pi$
$44$	−2.46687	+	0.563047i	−0.371894	+	0.0848825i
$45$	1.52602	+	1.91356i	0.227485	+	0.285257i
$46$			0.946280i			0.139521i
$47$	8.97652	−	7.15853i	1.30936	−	1.04418i	0.313854	−	0.949471i	$-0.398380\pi$
$47$	8.97652	−	7.15853i	1.30936	−	1.04418i	0.995505	−	0.0947081i	$-0.0301918\pi$
$48$	−1.94924	+	4.04764i	−0.281349	+	0.584227i
$49$	8.11473	−	10.1755i	1.15925	−	1.45365i
$50$	1.08760	+	0.867335i	0.153810	+	0.122660i
$51$	−3.68449	+	1.77436i	−0.515932	+	0.248460i
$52$	−0.549226	−	2.40632i	−0.0761639	−	0.333696i
$53$	−2.28813	+	10.0249i	−0.314299	+	1.37703i	0.533090	+	0.846059i	$0.321031\pi$
$53$	−2.28813	+	10.0249i	−0.314299	+	1.37703i	−0.847389	+	0.530973i	$0.821826\pi$
$54$	−2.06035	−	0.992210i	−0.280377	−	0.135023i
$55$	−1.77458	−	3.68495i	−0.239284	−	0.496878i
$56$	−8.86828	−	2.02413i	−1.18507	−	0.270485i
$57$	−1.07362			−0.142204
$58$	1.55719	+	2.51867i	0.204470	+	0.330717i
$59$	−4.03359			−0.525129			−0.262564	−	0.964914i	$-0.584568\pi$
$59$	−4.03359			−0.525129			−0.262564	+	0.964914i	$0.584568\pi$
$60$	−8.95970	−	2.04499i	−1.15669	−	0.264007i
$61$	5.18352	+	10.7637i	0.663682	+	1.37815i	0.912290	+	0.409545i	$0.134313\pi$
$61$	5.18352	+	10.7637i	0.663682	+	1.37815i	−0.248608	+	0.968604i	$0.579973\pi$
$62$	2.30795	+	1.11145i	0.293110	+	0.141155i
$63$	0.887945	−	3.89034i	0.111871	−	0.490137i
$64$	−0.362680	−	1.58901i	−0.0453350	−	0.198626i
$65$	3.59450	−	1.73102i	0.445842	−	0.214706i
$66$	−1.26412	−	1.00811i	−0.155603	−	0.124089i
$67$	−5.20630	+	6.52849i	−0.636050	+	0.797582i	−0.990503	−	0.137492i	$-0.956096\pi$
$67$	−5.20630	+	6.52849i	−0.636050	+	0.797582i	0.354453	+	0.935074i	$0.384667\pi$
$68$	1.52687	−	3.17058i	0.185161	−	0.384490i
$69$	2.65431	−	2.11674i	0.319541	−	0.254826i
$70$		−	6.75049i		−	0.806838i
$71$	−5.78348	−	7.25226i	−0.686373	−	0.860685i	0.309551	−	0.950883i	$-0.399821\pi$
$71$	−5.78348	−	7.25226i	−0.686373	−	0.860685i	−0.995924	+	0.0901983i	$0.971250\pi$
$72$	−1.76807	+	0.403550i	−0.208369	+	0.0475588i
$73$	−3.37292	+	0.769848i	−0.394771	+	0.0901039i	−0.415298	−	0.909685i	$-0.636323\pi$
$73$	−3.37292	+	0.769848i	−0.394771	+	0.0901039i	0.0205272	+	0.999789i	$0.493466\pi$
$74$	1.04215	+	1.30681i	0.121147	+	0.151913i
$75$		−	4.99087i		−	0.576295i
$76$	0.722310	−	0.576023i	0.0828546	−	0.0660744i
$77$	−2.89321	+	6.00781i	−0.329712	+	0.684654i
$78$	0.983360	−	1.23309i	0.111344	−	0.139621i
$79$	6.50888	+	5.19066i	0.732307	+	0.583995i	0.917041	−	0.398794i	$-0.130571\pi$
$79$	6.50888	+	5.19066i	0.732307	+	0.583995i	−0.184734	+	0.982789i	$0.559142\pi$
$80$	5.63005	−	2.71129i	0.629458	−	0.303131i
$81$	2.42109	+	10.6075i	0.269010	+	1.17861i
$82$	−0.0728249	+	0.319067i	−0.00804217	+	0.0352350i
$83$	−0.955764	−	0.460272i	−0.104909	−	0.0505214i	0.380693	−	0.924701i	$-0.375685\pi$
$83$	−0.955764	−	0.460272i	−0.104909	−	0.0505214i	−0.485602	+	0.874180i	$0.661400\pi$
$84$	6.50099	+	13.4994i	0.709316	+	1.47291i
$85$	5.54562	+	1.26575i	0.601507	+	0.137290i
$86$	−0.181217			−0.0195411
$87$	3.58155	−	10.0019i	0.383982	−	1.07232i
$88$	3.03052			0.323055
$89$	4.68343	+	1.06896i	0.496442	+	0.113310i	0.463409	−	0.886145i	$-0.346626\pi$
$89$	4.68343	+	1.06896i	0.496442	+	0.113310i	0.0330334	+	0.999454i	$0.489483\pi$
$90$	−0.583940	−	1.21256i	−0.0615526	−	0.127815i
$91$	−5.86034	−	2.82219i	−0.614331	−	0.295846i
$92$	−0.650086	+	2.84821i	−0.0677761	+	0.296947i
$93$	−2.04506	−	8.96001i	−0.212063	−	0.929109i
$94$	−5.68812	+	2.73926i	−0.586685	+	0.282533i
$95$	1.16754	+	0.931082i	0.119787	+	0.0955270i
$96$	6.54209	−	8.20353i	0.667700	−	0.837269i
$97$	2.09615	−	4.35270i	0.212832	−	0.441950i	−0.767034	−	0.641606i	$-0.778268\pi$
$97$	2.09615	−	4.35270i	0.212832	−	0.441950i	0.979866	+	0.199656i	$0.0639826\pi$
$98$	−5.59529	+	4.46209i	−0.565209	+	0.450739i
$99$			1.32943i			0.133613i
$100$	2.67773	+	3.35777i	0.267773	+	0.335777i
$101$	11.7217	−	2.67540i	1.16635	−	0.266212i	0.404856	−	0.914381i	$-0.367322\pi$
$101$	11.7217	−	2.67540i	1.16635	−	0.266212i	0.761497	+	0.648168i	$0.224465\pi$
$102$	2.19233	−	0.500384i	0.217073	−	0.0495454i
$103$	−4.21214	−	5.28185i	−0.415034	−	0.520436i	0.529739	−	0.848160i	$-0.322290\pi$
$103$	−4.21214	−	5.28185i	−0.415034	−	0.520436i	−0.944773	+	0.327724i	$0.893718\pi$
$104$			2.95614i			0.289873i
$105$	−18.9351	+	15.1002i	−1.84787	+	1.47363i
$106$	2.45328	−	5.09429i	0.238284	−	0.494801i
$107$	−8.52897	+	10.6950i	−0.824527	+	1.03392i	0.174261	+	0.984700i	$0.444246\pi$
$107$	−8.52897	+	10.6950i	−0.824527	+	1.03392i	−0.998788	+	0.0492247i	$0.984325\pi$
$108$	−5.51980	−	4.40189i	−0.531143	−	0.423573i
$109$	0.850324	−	0.409495i	0.0814463	−	0.0392225i	−0.392717	−	0.919659i	$-0.628465\pi$
$109$	0.850324	−	0.409495i	0.0814463	−	0.0392225i	0.474163	+	0.880437i	$0.342751\pi$
$110$	0.500446	+	2.19260i	0.0477156	+	0.209056i
$111$	1.33441	−	5.84642i	0.126656	−	0.554918i
$112$	−9.17904	−	4.42039i	−0.867337	−	0.417688i
$113$	−7.26684	−	15.0897i	−0.683606	−	1.41952i	−0.896766	−	0.442506i	$-0.854090\pi$
$113$	−7.26684	−	15.0897i	−0.683606	−	1.41952i	0.213159	−	0.977017i	$-0.431625\pi$
$114$	0.575554	+	0.131366i	0.0539056	+	0.0123036i
$115$	−4.72224			−0.440351
$116$	2.95670	+	8.65072i	0.274523	+	0.803200i
$117$	−1.29680			−0.119889
$118$	2.16236	+	0.493546i	0.199062	+	0.0454346i
$119$	−4.02380	−	8.35550i	−0.368861	−	0.765947i
$120$	9.91687	+	4.77571i	0.905282	+	0.435961i
$121$	−1.95339	+	8.55835i	−0.177581	+	0.778032i
$122$	−1.46180	−	6.40455i	−0.132345	−	0.579841i
$123$	1.05788	−	0.509450i	0.0953861	−	0.0459355i
$124$	6.18316	+	4.93091i	0.555264	+	0.442808i
$125$	4.22618	−	5.29946i	0.378001	−	0.473998i
$126$	−0.952035	+	1.97692i	−0.0848141	+	0.176118i
$127$	−9.64469	+	7.69138i	−0.855828	+	0.682500i	−0.949726	−	0.313082i	$-0.898639\pi$
$127$	−9.64469	+	7.69138i	−0.855828	+	0.682500i	0.0938983	+	0.995582i	$0.470067\pi$
$128$			11.5336i			1.01944i
$129$	0.405366	+	0.508313i	0.0356905	+	0.0447544i
$130$	−2.13878	+	0.488162i	−0.187583	+	0.0428146i
$131$	12.2846	−	2.80387i	1.07331	−	0.244975i	0.350878	−	0.936421i	$-0.385883\pi$
$131$	12.2846	−	2.80387i	1.07331	−	0.244975i	0.722428	+	0.691446i	$0.243026\pi$
$132$	−3.11233	−	3.90274i	−0.270894	−	0.339690i
$133$		−	2.43469i		−	0.211114i
$134$	3.58986	−	2.86282i	0.310116	−	0.247310i
$135$	4.95144	−	10.2818i	0.426152	−	0.884914i
$136$	−2.62786	+	3.29524i	−0.225338	+	0.282564i
$137$	5.06920	+	4.04255i	0.433091	+	0.345378i	0.815643	−	0.578555i	$-0.196383\pi$
$137$	5.06920	+	4.04255i	0.433091	+	0.345378i	−0.382552	+	0.923934i	$0.624955\pi$
$138$	−1.68195	+	0.809984i	−0.143177	+	0.0689504i
$139$	−1.85332	−	8.11994i	−0.157197	−	0.688724i	−0.990683	−	0.136185i	$-0.956516\pi$
$139$	−1.85332	−	8.11994i	−0.157197	−	0.688724i	0.833487	−	0.552540i	$-0.186341\pi$
$140$	4.63753	−	20.3183i	0.391942	−	1.71721i
$141$	20.4074	+	9.82769i	1.71861	+	0.827640i
$142$	2.21309	+	4.59552i	0.185718	+	0.385647i
$143$	2.11269	+	0.482209i	0.176672	+	0.0403243i
$144$	−2.03117			−0.169264
$145$	−12.5690	+	7.77089i	−1.04379	+	0.645337i
$146$	1.90239			0.157443
$147$	25.0323	+	5.71345i	2.06463	+	0.471238i
$148$	2.23899	+	4.64931i	0.184044	+	0.382171i
$149$	−14.5448	−	7.00441i	−1.19156	−	0.573824i	−0.270300	−	0.962776i	$-0.587123\pi$
$149$	−14.5448	−	7.00441i	−1.19156	−	0.573824i	−0.921258	+	0.388953i	$0.872837\pi$
$150$	−0.610677	+	2.67555i	−0.0498615	+	0.218458i
$151$	−0.708124	−	3.10249i	−0.0576263	−	0.252477i	0.937907	−	0.346886i	$-0.112761\pi$
$151$	−0.708124	−	3.10249i	−0.0576263	−	0.252477i	−0.995533	+	0.0944090i	$0.969904\pi$
$152$	−0.996929	+	0.480096i	−0.0808616	+	0.0389409i
$153$	−1.44556	−	1.15279i	−0.116866	−	0.0931978i
$154$	2.28613	−	2.86672i	0.184222	−	0.231007i
$155$	−5.54650	+	11.5174i	−0.445505	+	0.925101i
$156$	3.80694	−	3.03594i	0.304800	−	0.243069i
$157$			17.6378i			1.40765i	0.710375	+	0.703824i	$0.248526\pi$
$157$			17.6378i			1.40765i	−0.710375	+	0.703824i	$0.751474\pi$
$158$	−2.85422	−	3.57908i	−0.227070	−	0.284736i
$159$	−19.7772	+	4.51402i	−1.56844	+	0.357985i
$160$	−14.2288	+	3.24764i	−1.12489	+	0.256748i
$161$	4.80023	+	6.01930i	0.378311	+	0.474387i
$162$		−	5.98280i		−	0.470053i
$163$	−1.98183	+	1.58046i	−0.155229	+	0.123791i	−0.698024	−	0.716074i	$-0.745937\pi$
$163$	−1.98183	+	1.58046i	−0.155229	+	0.123791i	0.542795	+	0.839865i	$0.317366\pi$
$164$	−0.438392	+	0.910330i	−0.0342327	+	0.0710849i
$165$	5.03077	−	6.30838i	0.391645	−	0.491107i
$166$	0.456057	+	0.363693i	0.0353969	+	0.0282281i
$167$	12.3660	−	5.95514i	0.956908	−	0.460823i	0.110805	−	0.993842i	$-0.464657\pi$
$167$	12.3660	−	5.95514i	0.956908	−	0.460823i	0.846103	+	0.533020i	$0.178943\pi$
$168$	−3.99320	−	17.4953i	−0.308082	−	1.34980i
$169$	2.42240	−	10.6132i	0.186338	−	0.816402i
$170$	−2.81807	−	1.35711i	−0.216136	−	0.104086i
$171$	−0.210609	−	0.437333i	−0.0161056	−	0.0334437i
$172$	−0.545446	−	0.124494i	−0.0415899	−	0.00949262i
$173$	−7.05351			−0.536268			−0.268134	−	0.963382i	$-0.586407\pi$
$173$	−7.05351			−0.536268			−0.268134	+	0.963382i	$0.586407\pi$
$174$	−3.14386	+	4.92370i	−0.238335	+	0.373265i
$175$	11.3180			0.855562
$176$	3.30911	+	0.755282i	0.249433	+	0.0569315i
$177$	−3.45262	−	7.16943i	−0.259515	−	0.538887i
$178$	−2.37994	−	1.14612i	−0.178384	−	0.0859052i
$179$	1.19772	−	5.24757i	0.0895222	−	0.392222i	−0.910239	−	0.414084i	$-0.864102\pi$
$179$	1.19772	−	5.24757i	0.0895222	−	0.392222i	0.999761	+	0.0218614i	$0.00695926\pi$
$180$	−0.924582	−	4.05086i	−0.0689143	−	0.301933i
$181$	14.1408	−	6.80987i	1.05108	−	0.506174i	0.173117	−	0.984901i	$-0.444616\pi$
$181$	14.1408	−	6.80987i	1.05108	−	0.506174i	0.877964	+	0.478727i	$0.158902\pi$
$182$	2.79635	+	2.23001i	0.207279	+	0.165300i
$183$	−14.6948	+	18.4267i	−1.08627	+	1.36214i
$184$	1.51816	−	3.15249i	0.111920	−	0.232405i
$185$	−6.52139	+	5.20063i	−0.479462	+	0.382358i
$186$			5.05360i			0.370548i
$187$	1.92638	+	2.41561i	0.140871	+	0.176647i
$188$	−19.0025	+	4.33721i	−1.38590	+	0.316323i
$189$	−18.1391	+	4.14013i	−1.31943	+	0.301150i
$190$	−0.511979	−	0.642002i	−0.0371429	−	0.0465757i
$191$			4.28271i			0.309886i	0.987923	+	0.154943i	$0.0495194\pi$
$191$			4.28271i			0.309886i	−0.987923	+	0.154943i	$0.950481\pi$
$192$	2.51391	−	2.00477i	0.181426	−	0.144682i
$193$	10.2525	−	21.2896i	0.737994	−	1.53246i	−0.104961	−	0.994476i	$-0.533472\pi$
$193$	10.2525	−	21.2896i	0.737994	−	1.53246i	0.842955	−	0.537984i	$-0.180814\pi$
$194$	−1.65632	+	2.07695i	−0.118917	+	0.149117i
$195$	6.15353	+	4.90728i	0.440664	+	0.351418i
$196$	−19.9067	+	9.58656i	−1.42191	+	0.684754i
$197$	1.12719	+	4.93853i	0.0803088	+	0.351856i	0.999078	−	0.0429401i	$-0.0136725\pi$
$197$	1.12719	+	4.93853i	0.0803088	+	0.351856i	−0.918769	+	0.394796i	$0.870815\pi$
$198$	0.162668	−	0.712694i	0.0115603	−	0.0506490i
$199$	21.1994	+	10.2091i	1.50279	+	0.723703i	0.990806	−	0.135294i	$-0.0431978\pi$
$199$	21.1994	+	10.2091i	1.50279	+	0.723703i	0.511980	+	0.858997i	$0.328912\pi$
$200$	−2.23180	−	4.63438i	−0.157812	−	0.327700i
$201$	−16.0604	−	3.66567i	−1.13281	−	0.258557i
$202$	−6.61124			−0.465165
$203$	22.6819	+	8.12204i	1.59196	+	0.570056i
$204$	6.94245			0.486069
$205$	−1.59224	−	0.363419i	−0.111207	−	0.0253823i
$206$	1.61180	+	3.34694i	0.112299	+	0.233192i
$207$	1.38294	+	0.665987i	0.0961207	+	0.0462893i
$208$	−0.736742	+	3.22788i	−0.0510839	+	0.223813i
$209$	0.180495	+	0.790801i	0.0124851	+	0.0547008i
$210$	11.9985	−	5.77819i	0.827978	−	0.398733i
$211$	−14.3321	−	11.4295i	−0.986663	−	0.786838i	−0.00963631	−	0.999954i	$-0.503067\pi$
$211$	−14.3321	−	11.4295i	−0.986663	−	0.786838i	−0.977027	+	0.213116i	$0.931639\pi$
$212$	10.8839	−	13.6479i	0.747508	−	0.937345i
$213$	7.93993	−	16.4874i	0.544035	−	1.12970i
$214$	5.88092	−	4.68988i	0.402011	−	0.320593i
$215$		−	0.904331i		−	0.0616749i
$216$	5.27210	+	6.61101i	0.358721	+	0.449822i
$217$	20.3190	−	4.63769i	1.37935	−	0.314827i
$218$	−0.505955	+	0.115481i	−0.0342676	+	0.00782136i
$219$	−4.25546	−	5.33618i	−0.287557	−	0.360586i
$220$			6.94331i			0.468118i
$221$	−2.35631	+	1.87910i	−0.158503	+	0.126402i
$222$	−1.43072	+	2.97093i	−0.0960238	+	0.199396i
$223$	−2.98934	+	3.74852i	−0.200181	+	0.251019i	−0.871782	−	0.489894i	$-0.837036\pi$
$223$	−2.98934	+	3.74852i	−0.200181	+	0.251019i	0.671601	+	0.740913i	$0.265607\pi$
$224$	18.6035	+	14.8358i	1.24300	+	0.991260i
$225$	2.03301	−	0.979046i	0.135534	−	0.0652697i
$226$	2.04931	+	8.97861i	0.136318	+	0.597248i
$227$	−0.759662	+	3.32830i	−0.0504206	+	0.220907i	−0.993861	−	0.110635i	$-0.964712\pi$
$227$	−0.759662	+	3.32830i	−0.0504206	+	0.220907i	0.943441	+	0.331542i	$0.107569\pi$
$228$	1.64211	+	0.790801i	0.108752	+	0.0523720i
$229$	8.66379	+	17.9906i	0.572520	+	1.18885i	0.963315	+	0.268372i	$0.0864855\pi$
$229$	8.66379	+	17.9906i	0.572520	+	1.18885i	−0.390796	+	0.920477i	$0.627800\pi$
$230$	2.53154	+	0.577808i	0.166925	+	0.0380995i
$231$	−13.1550			−0.865534
$232$	−1.14691	−	10.8891i	−0.0752984	−	0.714905i
$233$	−4.14336			−0.271440			−0.135720	−	0.990747i	$-0.543335\pi$
$233$	−4.14336			−0.271440			−0.135720	+	0.990747i	$0.543335\pi$
$234$	0.695200	+	0.158675i	0.0454466	+	0.0103729i
$235$	−13.6698	−	28.3855i	−0.891717	−	1.85167i
$236$	6.16945	+	2.97105i	0.401597	+	0.193399i
$237$	−3.65466	+	16.0121i	−0.237396	+	1.04010i
$238$	1.13474	+	4.97164i	0.0735546	+	0.322264i
$239$	−18.8278	+	9.06700i	−1.21787	+	0.586495i	−0.928718	−	0.370788i	$-0.879088\pi$
$239$	−18.8278	+	9.06700i	−1.21787	+	0.586495i	−0.289152	+	0.957283i	$0.593373\pi$
$240$	9.63826	+	7.68625i	0.622147	+	0.496146i
$241$	−2.28011	+	2.85917i	−0.146875	+	0.184176i	−0.849827	−	0.527062i	$-0.823294\pi$
$241$	−2.28011	+	2.85917i	−0.146875	+	0.184176i	0.702952	+	0.711238i	$0.251865\pi$
$242$	2.09438	−	4.34902i	0.134632	−	0.279566i
$243$	−7.02731	+	5.60409i	−0.450802	+	0.359503i
$244$		−	20.2813i		−	1.29838i
$245$	−22.2673	−	27.9223i	−1.42260	−	1.78389i
$246$	−0.629455	+	0.143669i	−0.0401326	+	0.00916001i
$247$	−0.771389	+	0.176065i	−0.0490823	+	0.0112027i
$248$	−5.90569	−	7.40550i	−0.375012	−	0.470250i
$249$		−	2.09278i		−	0.132625i
$250$	−2.91404	+	2.32387i	−0.184300	+	0.146975i
$251$	−6.00009	+	12.4593i	−0.378722	+	0.786425i	0.621274	+	0.783594i	$0.286616\pi$
$251$	−6.00009	+	12.4593i	−0.378722	+	0.786425i	−0.999996	+	0.00283143i	$0.999099\pi$
$252$	−4.22366	+	5.29630i	−0.266066	+	0.333636i
$253$	−2.00538	−	1.59924i	−0.126077	−	0.100543i
$254$	6.11152	−	2.94316i	0.383471	−	0.184670i
$255$	2.49708	+	10.9404i	0.156373	+	0.685115i
$256$	0.685877	−	3.00502i	0.0428673	−	0.187814i
$257$	−15.1065	−	7.27489i	−0.942315	−	0.453795i	−0.101330	−	0.994853i	$-0.532310\pi$
$257$	−15.1065	−	7.27489i	−0.942315	−	0.453795i	−0.840985	+	0.541058i	$0.818024\pi$
$258$	−0.155116	−	0.322101i	−0.00965708	−	0.0200531i
$259$	13.2582	+	3.02610i	0.823825	+	0.188033i
$260$	−6.77287			−0.420036
$261$	4.77684	−	0.503127i	0.295679	−	0.0311428i
$262$	−6.92870			−0.428056
$263$	−3.43964	−	0.785076i	−0.212097	−	0.0484099i	0.115152	−	0.993348i	$-0.463265\pi$
$263$	−3.43964	−	0.785076i	−0.212097	−	0.0484099i	−0.327249	+	0.944938i	$0.606122\pi$
$264$	2.59403	+	5.38655i	0.159651	+	0.331519i
$265$	25.4221	+	12.2427i	1.56167	+	0.752060i
$266$	−0.297906	+	1.30521i	−0.0182658	+	0.0800276i
$267$	2.10885	+	9.23947i	0.129059	+	0.565446i
$268$	12.7719	−	6.15060i	0.780165	−	0.375708i
$269$	−18.7417	−	14.9460i	−1.14270	−	0.911274i	−0.145751	−	0.989321i	$-0.546560\pi$
$269$	−18.7417	−	14.9460i	−1.14270	−	0.911274i	−0.996950	+	0.0780476i	$0.975131\pi$
$270$	−3.91248	+	4.90610i	−0.238106	+	0.298576i
$271$	9.85146	−	20.4568i	0.598434	−	1.24266i	−0.353235	−	0.935535i	$-0.614918\pi$
$271$	9.85146	−	20.4568i	0.598434	−	1.24266i	0.951669	−	0.307126i	$-0.0993673\pi$
$272$	−3.69069	+	2.94322i	−0.223781	+	0.178459i
$273$		−	12.8321i		−	0.776632i
$274$	−2.22290	−	2.78743i	−0.134290	−	0.168395i
$275$	−3.67616	+	0.839059i	−0.221681	+	0.0505971i
$276$	−5.61895	+	1.28249i	−0.338221	+	0.0771968i
$277$	−12.7570	−	15.9968i	−0.766495	−	0.961154i	0.233442	−	0.972371i	$-0.425001\pi$
$277$	−12.7570	−	15.9968i	−0.766495	−	0.961154i	−0.999937	+	0.0112168i	$0.996430\pi$
$278$			4.57978i			0.274677i
$279$	3.24865	−	2.59071i	0.194492	−	0.155102i
$280$	−10.8301	+	22.4890i	−0.647223	+	1.34397i
$281$	1.78761	−	2.24159i	0.106640	−	0.133722i	−0.725647	−	0.688067i	$-0.758460\pi$
$281$	1.78761	−	2.24159i	0.106640	−	0.133722i	0.832287	+	0.554345i	$0.187031\pi$
$282$	−9.73768	−	7.76554i	−0.579871	−	0.462431i
$283$	4.70357	−	2.26512i	0.279598	−	0.134647i	−0.288830	−	0.957380i	$-0.593266\pi$
$283$	4.70357	−	2.26512i	0.279598	−	0.134647i	0.568428	+	0.822733i	$0.307552\pi$
$284$	3.50409	+	15.3524i	0.207930	+	0.910999i
$285$	−0.655560	+	2.87220i	−0.0388320	+	0.170134i
$286$	−1.07359	−	0.517014i	−0.0634827	−	0.0305717i
$287$	1.15530	+	2.39901i	0.0681954	+	0.141609i
$288$	4.62502	+	1.05563i	0.272532	+	0.0622037i
$289$	12.7030			0.747233
$290$	7.68892	−	2.62797i	0.451509	−	0.154320i
$291$	9.53087			0.558709
$292$	5.72600	+	1.30692i	0.335089	+	0.0764818i
$293$	11.8669	+	24.6418i	0.693271	+	1.43959i	0.888520	+	0.458838i	$0.151734\pi$
$293$	11.8669	+	24.6418i	0.693271	+	1.43959i	−0.195249	+	0.980754i	$0.562552\pi$
$294$	−12.7204	−	6.12584i	−0.741871	−	0.357266i
$295$	−2.46295	+	10.7909i	−0.143398	+	0.628270i
$296$	−1.37529	−	6.02553i	−0.0799370	−	0.350227i
$297$	5.58476	−	2.68948i	0.324060	−	0.156059i
$298$	6.94027	+	5.53468i	0.402039	+	0.320615i
$299$	1.55998	−	1.95616i	0.0902162	−	0.113127i
$300$	−3.67616	+	7.63362i	−0.212243	+	0.440727i
$301$	−1.15272	+	0.919267i	−0.0664420	+	0.0529857i
$302$			1.74986i			0.100693i
$303$	14.7887	+	18.5445i	0.849590	+	1.06535i
$304$	−1.20822	+	0.275769i	−0.0692964	+	0.0158165i
$305$	31.9607	−	7.29483i	1.83007	−	0.417701i
$306$	0.633893	+	0.794877i	0.0362372	+	0.0454401i
$307$		−	5.31763i		−	0.303493i	−0.988419	−	0.151746i	$-0.951510\pi$
$307$		−	5.31763i		−	0.303493i	0.988419	−	0.151746i	$-0.0484897\pi$
$308$	8.85043	−	7.05799i	0.504300	−	0.402166i
$309$	5.78269	−	12.0079i	0.328965	−	0.683104i
$310$	4.38268	−	5.49570i	0.248919	−	0.312135i
$311$	5.17845	+	4.12968i	0.293643	+	0.234173i	0.759219	−	0.650835i	$-0.225581\pi$
$311$	5.17845	+	4.12968i	0.293643	+	0.234173i	−0.465576	+	0.885008i	$0.654153\pi$
$312$	−5.25433	+	2.53035i	−0.297468	+	0.143253i
$313$	0.329444	+	1.44339i	0.0186213	+	0.0815852i	0.983385	−	0.181533i	$-0.0581061\pi$
$313$	0.329444	+	1.44339i	0.0186213	+	0.0815852i	−0.964763	+	0.263119i	$0.915249\pi$
$314$	2.15814	−	9.45542i	0.121791	−	0.533600i
$315$	−9.86547	−	4.75096i	−0.555856	−	0.267686i
$316$	−6.13213	−	12.7335i	−0.344959	−	0.716315i
$317$	−4.49826	−	1.02670i	−0.252648	−	0.0576652i	0.0943212	−	0.995542i	$-0.469932\pi$
$317$	−4.49826	−	1.02670i	−0.252648	−	0.0576652i	−0.346969	+	0.937877i	$0.612789\pi$
$318$	11.1547			0.625524
$319$	−7.96933	−	0.956570i	−0.446197	−	0.0535576i
$320$	−4.47245			−0.250018
$321$	−26.3101	−	6.00512i	−1.46849	−	0.335173i
$322$	−1.83684	−	3.81424i	−0.102363	−	0.212559i
$323$	−1.01639	−	0.489467i	−0.0565534	−	0.0272347i
$324$	4.11013	−	18.0076i	0.228340	−	1.00042i
$325$	−0.818463	−	3.58592i	−0.0454001	−	0.198911i
$326$	1.25582	−	0.604771i	0.0695535	−	0.0334952i
$327$	1.45570	+	1.16088i	0.0805003	+	0.0641968i
$328$	0.754506	−	0.946121i	0.0416606	−	0.0522408i
$329$	−22.2867	+	46.2788i	−1.22871	+	2.55143i
$330$	−3.46883	+	2.76630i	−0.190953	+	0.152280i
$331$		−	1.65763i		−	0.0911116i	−0.998962	−	0.0455558i	$-0.985494\pi$
$331$		−	1.65763i		−	0.0911116i	0.998962	−	0.0455558i	$-0.0145059\pi$
$332$	1.12283	+	1.40799i	0.0616235	+	0.0772734i
$333$	2.64328	−	0.603312i	0.144851	−	0.0330613i
$334$	−7.35793	+	1.67940i	−0.402608	+	0.0918927i
$335$	14.2864	+	17.9145i	0.780547	+	0.978775i
$336$		−	20.0988i		−	1.09648i
$337$	−13.9220	+	11.1024i	−0.758378	+	0.604786i	−0.924439	−	0.381329i	$-0.875466\pi$
$337$	−13.9220	+	11.1024i	−0.758378	+	0.604786i	0.166061	+	0.986115i	$0.446895\pi$
$338$	−2.59725	+	5.39324i	−0.141272	+	0.293353i
$339$	20.6008	−	25.8326i	1.11888	−	1.40304i
$340$	−7.54980	−	6.02076i	−0.409445	−	0.326522i
$341$	−6.25592	+	3.01269i	−0.338777	+	0.163146i
$342$	0.0593934	+	0.260220i	0.00321163	+	0.0140711i
$343$	−5.98805	+	26.2354i	−0.323324	+	1.41658i
$344$	0.603717	+	0.290735i	0.0325502	+	0.0156754i
$345$	−4.04208	−	8.39346i	−0.217618	−	0.451889i
$346$	3.78131	+	0.863060i	0.203285	+	0.0463984i
$347$	3.69857			0.198550			0.0992748	−	0.995060i	$-0.468348\pi$
$347$	3.69857			0.198550			0.0992748	+	0.995060i	$0.468348\pi$
$348$	−12.8452	+	12.6601i	−0.688577	+	0.678651i
$349$	−22.2918			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$349$	−22.2918			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$350$	−6.06747	−	1.38486i	−0.324320	−	0.0740239i
$351$	2.62346	+	5.44767i	0.140030	+	0.290775i
$352$	−7.14238	−	3.43959i	−0.380690	−	0.183331i
$353$	5.28701	−	23.1639i	0.281399	−	1.23289i	−0.614601	−	0.788838i	$-0.710683\pi$
$353$	5.28701	−	23.1639i	0.281399	−	1.23289i	0.896001	−	0.444053i	$-0.146460\pi$
$354$	0.973667	+	4.26591i	0.0517498	+	0.226731i
$355$	−22.9331	+	11.0440i	−1.21716	+	0.586154i
$356$	−6.37601	−	5.08470i	−0.337928	−	0.269489i
$357$	11.4071	−	14.3041i	0.603728	−	0.757051i
$358$	−1.28417	+	2.66662i	−0.0678708	+	0.140935i
$359$	27.9498	−	22.2893i	1.47514	−	1.17638i	0.530757	−	0.847524i	$-0.321908\pi$
$359$	27.9498	−	22.2893i	1.47514	−	1.17638i	0.944380	−	0.328857i	$-0.106664\pi$
$360$			4.97644i			0.262281i
$361$	11.6617	+	14.6232i	0.613771	+	0.769645i
$362$	−8.41400	+	1.92044i	−0.442230	+	0.100936i
$363$	−16.8839	+	3.85364i	−0.886176	+	0.202264i
$364$	6.88474	+	8.63319i	0.360858	+	0.452502i
$365$			9.49351i			0.496913i
$366$	10.1324	−	8.08032i	0.529629	−	0.422365i
$367$	0.613081	−	1.27308i	0.0320026	−	0.0664540i	−0.884355	−	0.466816i	$-0.845401\pi$
$367$	0.613081	−	1.27308i	0.0320026	−	0.0664540i	0.916357	+	0.400362i	$0.131115\pi$
$368$	2.44340	−	3.06392i	0.127371	−	0.159718i
$369$	0.415045	+	0.330987i	0.0216064	+	0.0172305i
$370$	4.13239	−	1.99005i	0.214833	−	0.103458i
$371$	−10.2367	−	44.8497i	−0.531461	−	2.32848i
$372$	−3.47177	+	15.2108i	−0.180003	+	0.788645i
$373$	−3.25539	−	1.56771i	−0.168557	−	0.0811730i	0.347703	−	0.937605i	$-0.386962\pi$
$373$	−3.25539	−	1.56771i	−0.168557	−	0.0811730i	−0.516260	+	0.856432i	$0.672676\pi$
$374$	−0.737143	−	1.53069i	−0.0381167	−	0.0791502i
$375$	13.0369	+	2.97559i	0.673222	+	0.153659i
$376$	23.3444			1.20390
$377$	0.933089	−	7.77371i	0.0480565	−	0.400366i
$378$	10.2308			0.526214
$379$	5.57574	+	1.27263i	0.286407	+	0.0653704i	0.363311	−	0.931668i	$-0.381646\pi$
$379$	5.57574	+	1.27263i	0.286407	+	0.0653704i	−0.0769040	+	0.997038i	$0.524504\pi$
$380$	−1.09996	−	2.28409i	−0.0564267	−	0.117171i
$381$	−21.9264	−	10.5592i	−1.12333	−	0.540965i
$382$	0.524028	−	2.29592i	0.0268116	−	0.117469i
$383$	−2.41813	−	10.5945i	−0.123561	−	0.541354i	−0.998380	−	0.0569044i	$-0.981877\pi$
$383$	−2.41813	−	10.5945i	−0.123561	−	0.541354i	0.874819	−	0.484450i	$-0.160980\pi$
$384$	−20.5002	+	9.87237i	−1.04615	+	0.503797i
$385$	14.3058	+	11.4085i	0.729092	+	0.581431i
$386$	−8.10125	+	10.1586i	−0.412343	+	0.517062i
$387$	−0.127540	+	0.264839i	−0.00648320	+	0.0134625i
$388$	−6.41220	+	5.11356i	−0.325530	+	0.259602i
$389$			27.0337i			1.37066i	0.728232	+	0.685331i	$0.240342\pi$
$389$			27.0337i			1.37066i	−0.728232	+	0.685331i	$0.759658\pi$
$390$	−2.69839	−	3.38368i	−0.136639	−	0.171339i
$391$	3.47786	−	0.793799i	0.175883	−	0.0401442i
$392$	25.7992	−	5.88850i	1.30306	−	0.297414i
$393$	15.4989	+	19.4350i	0.781814	+	0.980364i
$394$		−	2.78541i		−	0.140327i
$395$	17.8607	−	14.2435i	0.898671	−	0.716666i
$396$	0.979228	−	2.03339i	0.0492081	−	0.102182i
$397$	−18.3457	+	23.0047i	−0.920742	+	1.15457i	0.0668862	+	0.997761i	$0.478694\pi$
$397$	−18.3457	+	23.0047i	−0.920742	+	1.15457i	−0.987628	+	0.156813i	$0.949878\pi$
$398$	−10.1156	−	8.06692i	−0.507049	−	0.404358i
$399$	4.32750	−	2.08401i	0.216646	−	0.104331i
$400$	−1.28196	−	5.61661i	−0.0640978	−	0.280831i
$401$	−1.76229	+	7.72111i	−0.0880047	+	0.385574i	−0.999679	−	0.0253400i	$-0.991933\pi$
$401$	−1.76229	+	7.72111i	−0.0880047	+	0.385574i	0.911674	+	0.410914i	$0.134790\pi$
$402$	8.16126	+	3.93025i	0.407047	+	0.196023i
$403$	−2.93874	−	6.10236i	−0.146389	−	0.303980i
$404$	−19.8992	−	4.54186i	−0.990022	−	0.225966i
$405$	29.8560			1.48356
$406$	−11.1657	−	7.12947i	−0.554145	−	0.353830i
$407$	−4.53068			−0.224577
$408$	−8.10642	−	1.85024i	−0.401328	−	0.0916005i
$409$	11.1814	+	23.2184i	0.552883	+	1.14807i	0.970867	+	0.239619i	$0.0770226\pi$
$409$	11.1814	+	23.2184i	0.552883	+	1.14807i	−0.417984	+	0.908454i	$0.637263\pi$
$410$	0.809118	+	0.389651i	0.0399595	+	0.0192435i
$411$	−2.84630	+	12.4704i	−0.140397	+	0.615122i
$412$	2.55205	+	11.1812i	0.125730	+	0.550860i
$413$	16.2585	−	7.82966i	0.800027	−	0.385272i
$414$	−0.659888	−	0.526243i	−0.0324317	−	0.0258634i
$415$	−1.81494	+	2.27587i	−0.0890921	+	0.111718i
$416$	3.35516	−	6.96706i	0.164500	−	0.341588i
$417$	12.8463	−	10.2446i	0.629084	−	0.501678i
$418$		−	0.446025i		−	0.0218158i
$419$	0.231745	+	0.290599i	0.0113215	+	0.0141967i	0.787460	−	0.616366i	$-0.211396\pi$
$419$	0.231745	+	0.290599i	0.0113215	+	0.0141967i	−0.776139	+	0.630562i	$0.782824\pi$
$420$	40.0840	−	9.14891i	1.95590	−	0.446421i
$421$	21.8509	−	4.98733i	1.06495	−	0.243068i	0.346074	−	0.938207i	$-0.387515\pi$
$421$	21.8509	−	4.98733i	1.06495	−	0.243068i	0.718875	+	0.695139i	$0.244657\pi$
$422$	6.28479	+	7.88088i	0.305939	+	0.383635i
$423$			10.2408i			0.497922i
$424$	−16.3460	+	13.0355i	−0.793832	+	0.633060i
$425$	2.27536	−	4.72484i	0.110371	−	0.229188i
$426$	−6.27390	+	7.86722i	−0.303971	+	0.381168i
$427$	−41.7871	−	33.3241i	−2.02222	−	1.61267i
$428$	20.9229	−	10.0759i	1.01135	−	0.487039i
$429$	0.951302	+	4.16793i	0.0459293	+	0.201229i
$430$	−0.110653	+	0.484802i	−0.00533616	+	0.0233792i
$431$	−31.3909	−	15.1171i	−1.51205	−	0.728164i	−0.520016	−	0.854156i	$-0.674074\pi$
$431$	−31.3909	−	15.1171i	−1.51205	−	0.728164i	−0.992031	+	0.125992i	$0.959788\pi$
$432$	4.10911	+	8.53266i	0.197700	+	0.410528i
$433$	−21.0132	−	4.79613i	−1.00983	−	0.230488i	−0.314562	−	0.949237i	$-0.601858\pi$
$433$	−21.0132	−	4.79613i	−1.00983	−	0.230488i	−0.695269	+	0.718749i	$0.744715\pi$
$434$	−11.4603			−0.550111
$435$	−24.5708	−	15.6888i	−1.17808	−	0.752222i
$436$	−1.60221			−0.0767319
$437$	0.913047	+	0.208397i	0.0436770	+	0.00996898i
$438$	1.62838	+	3.38136i	0.0778069	+	0.161568i
$439$	1.48009	+	0.712776i	0.0706411	+	0.0340189i	0.468871	−	0.883267i	$-0.344661\pi$
$439$	1.48009	+	0.712776i	0.0706411	+	0.0340189i	−0.398230	+	0.917286i	$0.630375\pi$
$440$	1.85047	−	8.10743i	0.0882176	−	0.386506i
$441$	2.58317	+	11.3176i	0.123008	+	0.538933i
$442$	1.49312	−	0.719049i	0.0710205	−	0.0342017i
$443$	27.6581	+	22.0566i	1.31407	+	1.04794i	0.994965	+	0.100221i	$0.0319549\pi$
$443$	27.6581	+	22.0566i	1.31407	+	1.04794i	0.319109	+	0.947718i	$0.396616\pi$
$444$	−6.34734	+	7.95931i	−0.301231	+	0.377732i
$445$	5.71949	−	11.8766i	0.271130	−	0.563007i
$446$	2.06122	−	1.64377i	0.0976016	−	0.0778347i
$447$		−	31.8480i		−	1.50636i
$448$	4.54632	+	5.70091i	0.214794	+	0.269343i
$449$	12.0435	−	2.74885i	0.568367	−	0.129726i	0.0713260	−	0.997453i	$-0.477277\pi$
$449$	12.0435	−	2.74885i	0.568367	−	0.129726i	0.497041	+	0.867727i	$0.334420\pi$
$450$	−1.20967	+	0.276099i	−0.0570244	+	0.0130154i
$451$	−0.553099	−	0.693564i	−0.0260444	−	0.0326587i
$452$			28.4326i			1.33736i
$453$	4.90834	−	3.91427i	0.230614	−	0.183909i
$454$	0.814494	−	1.69131i	0.0382261	−	0.0793773i
$455$	−11.1285	+	13.9547i	−0.521711	+	0.654205i
$456$	−1.70668	−	1.36103i	−0.0799224	−	0.0637360i
$457$	−28.2167	+	13.5884i	−1.31992	+	0.635640i	−0.955334	−	0.295530i	$-0.904504\pi$
$457$	−28.2167	+	13.5884i	−1.31992	+	0.635640i	−0.364586	+	0.931170i	$0.618790\pi$
$458$	−2.44326	−	10.7046i	−0.114166	−	0.500195i
$459$	−1.91832	+	8.40471i	−0.0895395	+	0.392298i
$460$	7.22275	+	3.47829i	0.336762	+	0.162176i
$461$	2.80526	+	5.82519i	0.130654	+	0.271306i	0.956025	−	0.293285i	$-0.0947484\pi$
$461$	2.80526	+	5.82519i	0.130654	+	0.271306i	−0.825371	+	0.564591i	$0.809034\pi$
$462$	7.05224	+	1.60963i	0.328100	+	0.0748867i
$463$	−14.5214			−0.674867			−0.337434	−	0.941349i	$-0.609559\pi$
$463$	−14.5214			−0.674867			−0.337434	+	0.941349i	$0.609559\pi$
$464$	1.46149	−	12.1759i	0.0678482	−	0.565253i
$465$	−25.2190			−1.16951
$466$	2.22121	+	0.506977i	0.102896	+	0.0234852i
$467$	−11.3476	−	23.5636i	−0.525105	−	1.09039i	−0.979843	−	0.199767i	$-0.935981\pi$
$467$	−11.3476	−	23.5636i	−0.525105	−	1.09039i	0.454738	−	0.890625i	$-0.349733\pi$
$468$	1.98348	+	0.955192i	0.0916862	+	0.0441538i
$469$	8.31282	−	36.4208i	0.383850	−	1.68176i
$470$	3.85499	+	16.8898i	0.177817	+	0.779069i
$471$	−31.3499	+	15.0973i	−1.44453	+	0.695649i
$472$	−6.41200	−	5.11340i	−0.295136	−	0.235363i
$473$	0.306262	−	0.384040i	0.0140819	−	0.0176582i
$474$	3.91845	−	8.13675i	0.179980	−	0.373733i
$475$	1.07639	−	0.858396i	0.0493884	−	0.0393859i
$476$			15.7437i			0.721612i
$477$	−5.71842	−	7.17067i	−0.261828	−	0.328322i
$478$	11.2028	−	2.55697i	0.512405	−	0.116953i
$479$	−24.5946	+	5.61357i	−1.12376	+	0.256490i	−0.743727	−	0.668483i	$-0.766944\pi$
$479$	−24.5946	+	5.61357i	−1.12376	+	0.256490i	−0.380031	+	0.924974i	$0.624087\pi$
$480$	−17.9519	−	22.5109i	−0.819387	−	1.02748i
$481$		−	4.41946i		−	0.201510i
$482$	1.57219	−	1.25378i	0.0716113	−	0.0571081i
$483$	−6.59006	+	13.6844i	−0.299858	+	0.622662i
$484$	9.29162	−	11.6513i	0.422346	−	0.529606i
$485$	−10.3647	−	8.26554i	−0.470635	−	0.375319i
$486$	4.45298	−	2.14444i	0.201991	−	0.0972738i
$487$	8.92818	+	39.1169i	0.404575	+	1.77256i	0.608483	+	0.793567i	$0.291778\pi$
$487$	8.92818	+	39.1169i	0.404575	+	1.77256i	−0.203909	+	0.978990i	$0.565365\pi$
$488$	−5.40519	+	23.6817i	−0.244682	+	1.07202i
$489$	−4.50553	−	2.16975i	−0.203747	−	0.0981195i
$490$	8.52070	+	17.6934i	0.384926	+	0.799307i
$491$	9.91823	+	2.26377i	0.447604	+	0.102163i	0.440380	−	0.897811i	$-0.354844\pi$
$491$	9.91823	+	2.26377i	0.447604	+	0.102163i	0.00722326	+	0.999974i	$0.497701\pi$
$492$	−1.99330			−0.0898649
$493$	7.95058	−	7.83597i	0.358076	−	0.352914i
$494$	0.435077			0.0195750
$495$	3.55657	+	0.811764i	0.159856	+	0.0364861i
$496$	−4.60294	−	9.55810i	−0.206678	−	0.429171i
$497$	37.3893	+	18.0058i	1.67714	+	0.807669i
$498$	−0.256071	+	1.12192i	−0.0114748	+	0.0502744i
$499$	−1.83329	−	8.03215i	−0.0820691	−	0.359568i	0.917173	−	0.398489i	$-0.130465\pi$
$499$	−1.83329	−	8.03215i	−0.0820691	−	0.359568i	−0.999242	+	0.0389205i	$0.987608\pi$
$500$	−10.3675	+	4.99271i	−0.463647	+	0.223281i
$501$	21.1697	+	16.8823i	0.945793	+	0.754245i
$502$	4.74109	−	5.94514i	0.211605	−	0.265345i
$503$	1.18362	−	2.45782i	0.0527751	−	0.109589i	−0.872914	−	0.487875i	$-0.837772\pi$
$503$	1.18362	−	2.45782i	0.0527751	−	0.109589i	0.925689	+	0.378286i	$0.123487\pi$
$504$	6.34333	−	5.05863i	0.282554	−	0.225329i
$505$		−	32.9922i		−	1.46813i
$506$	0.879383	+	1.10271i	0.0390933	+	0.0490215i
$507$	20.9378	−	4.77891i	0.929880	−	0.212239i
$508$	20.4170	−	4.66005i	0.905859	−	0.206756i
$509$	21.3596	+	26.7840i	0.946746	+	1.18718i	0.982205	+	0.187810i	$0.0601390\pi$
$509$	21.3596	+	26.7840i	0.946746	+	1.18718i	−0.0354598	+	0.999371i	$0.511290\pi$
$510$		−	6.17057i		−	0.273238i
$511$	12.1011	−	9.65031i	0.535321	−	0.426905i
$512$	9.27309	−	19.2558i	0.409817	−	0.850993i
$513$	−1.41111	+	1.76947i	−0.0623020	+	0.0781242i
$514$	7.20827	+	5.74840i	0.317943	+	0.253551i
$515$	−16.7023	+	8.04339i	−0.735990	+	0.354434i
$516$	−0.245603	−	1.07606i	−0.0108121	−	0.0473707i
$517$	3.80798	−	16.6838i	0.167475	−	0.733754i
$518$	−6.73731	−	3.24452i	−0.296020	−	0.142556i
$519$	−6.03757	−	12.5371i	−0.265020	−	0.550319i
$520$	7.90842	+	1.80504i	0.346807	+	0.0791565i
$521$	−30.8597			−1.35199			−0.675994	−	0.736907i	$-0.736285\pi$
$521$	−30.8597			−1.35199			−0.675994	+	0.736907i	$0.736285\pi$
$522$	−2.62237	−	0.314767i	−0.114778	−	0.0137770i
$523$	31.8103			1.39097			0.695484	−	0.718542i	$-0.255190\pi$
$523$	31.8103			1.39097			0.695484	+	0.718542i	$0.255190\pi$
$524$	−20.8547	−	4.75995i	−0.911042	−	0.207939i
$525$	9.68784	+	20.1170i	0.422812	+	0.877979i
$526$	1.74789	+	0.841742i	0.0762118	+	0.0367017i
$527$	2.14886	−	9.41477i	0.0936058	−	0.410114i
$528$	1.49002	+	6.52821i	0.0648448	+	0.284104i
$529$	18.0541	−	8.69438i	0.784960	−	0.378017i
$530$	−12.1305	−	9.67378i	−0.526917	−	0.420202i
$531$	2.24315	−	2.81282i	0.0973444	−	0.122066i
$532$	−1.79334	+	3.72390i	−0.0777510	+	0.161452i
$533$	0.676539	−	0.539522i	0.0293042	−	0.0233693i
$534$		−	5.21122i		−	0.225511i
$535$	23.4040	+	29.3477i	1.01184	+	1.26881i
$536$	−16.5524	+	3.77798i	−0.714955	+	0.163184i
$537$	10.3524	−	2.36287i	0.446740	−	0.101965i
$538$	8.21844	+	10.3056i	0.354322	+	0.444306i
$539$		−	19.3987i		−	0.835563i
$540$	−15.1466	+	12.0790i	−0.651808	+	0.519799i
$541$	−15.2290	+	31.6234i	−0.654747	+	1.35960i	0.263913	+	0.964546i	$0.414987\pi$
$541$	−15.2290	+	31.6234i	−0.654747	+	1.35960i	−0.918660	+	0.395049i	$0.870727\pi$
$542$	−7.78433	+	9.76124i	−0.334366	+	0.419281i
$543$	24.2082	+	19.3054i	1.03887	+	0.828473i
$544$	9.93342	−	4.78368i	0.425892	−	0.205099i
$545$	−0.576286	−	2.52488i	−0.0246854	−	0.108154i
$546$	−1.57012	+	6.87913i	−0.0671948	+	0.294400i
$547$	−2.77683	−	1.33725i	−0.118729	−	0.0571768i	0.373576	−	0.927599i	$-0.378131\pi$
$547$	−2.77683	−	1.33725i	−0.118729	−	0.0571768i	−0.492305	+	0.870423i	$0.663846\pi$
$548$	−4.77578	−	9.91701i	−0.204011	−	0.423634i
$549$	−10.3887	−	2.37115i	−0.443379	−	0.101198i
$550$	2.07341			0.0884107
$551$	2.77315	−	0.947826i	0.118140	−	0.0403787i
$552$	6.90283			0.293804
$553$	−36.3115	−	8.28785i	−1.54412	−	0.352435i
$554$	4.88155	+	10.1366i	0.207397	+	0.430665i
$555$	−14.8259	−	7.13976i	−0.629323	−	0.303066i
$556$	−3.14627	+	13.7847i	−0.133432	+	0.584602i
$557$	4.85165	+	21.2565i	0.205571	+	0.900666i	0.967473	+	0.252974i	$0.0814087\pi$
$557$	4.85165	+	21.2565i	0.205571	+	0.900666i	−0.761902	+	0.647692i	$0.775734\pi$
$558$	−2.05856	+	0.991352i	−0.0871459	+	0.0419673i
$559$	0.374613	+	0.298744i	0.0158445	+	0.0126355i
$560$	−17.4305	+	21.8571i	−0.736572	+	0.923632i
$561$	−2.64466	+	5.49170i	−0.111658	+	0.231860i
$562$	−1.23260	+	0.982965i	−0.0519940	+	0.0414639i
$563$		−	5.22049i		−	0.220017i	−0.993931	−	0.110009i	$-0.964912\pi$
$563$		−	5.22049i		−	0.220017i	0.993931	−	0.110009i	$-0.0350879\pi$
$564$	−23.9746	−	30.0632i	−1.00951	−	1.26589i
$565$	−44.8061	+	10.2267i	−1.88501	+	0.430241i
$566$	−2.79869	+	0.638783i	−0.117638	+	0.0268500i
$567$	−30.3492	−	38.0567i	−1.27455	−	1.59823i
$568$		−	18.8603i		−	0.791361i
$569$	20.0881	−	16.0197i	0.842138	−	0.671583i	−0.104272	−	0.994549i	$-0.533251\pi$
$569$	20.0881	−	16.0197i	0.842138	−	0.671583i	0.946411	+	0.322966i	$0.104680\pi$
$570$	0.702878	−	1.45954i	0.0294403	−	0.0611334i
$571$	26.2637	−	32.9337i	1.09910	−	1.37823i	0.180254	−	0.983620i	$-0.442308\pi$
$571$	26.2637	−	32.9337i	1.09910	−	1.37823i	0.918848	−	0.394611i	$-0.129121\pi$
$572$	−2.87622	−	2.29371i	−0.120261	−	0.0959048i
$573$	−7.61223	+	3.66586i	−0.318006	+	0.153143i
$574$	−0.325805	−	1.42745i	−0.0135988	−	0.0595804i
$575$	−0.968765	+	4.24444i	−0.0404003	+	0.177005i
$576$	1.30978	+	0.630759i	0.0545744	+	0.0262816i
$577$	−3.03601	−	6.30433i	−0.126391	−	0.262453i	0.828166	−	0.560483i	$-0.189385\pi$
$577$	−3.03601	−	6.30433i	−0.126391	−	0.262453i	−0.954556	+	0.298030i	$0.903670\pi$
$578$	−6.80992	−	1.55432i	−0.283255	−	0.0646512i
$579$	46.6167			1.93732
$580$	24.9483	−	2.62772i	1.03592	−	0.109110i
$581$	4.74590			0.196893
$582$	−5.10940	−	1.16619i	−0.211791	−	0.0483400i
$583$	6.64985	+	13.8085i	0.275409	+	0.571892i
$584$	−6.33771	−	3.05208i	−0.262256	−	0.126296i
$585$	−0.791838	+	3.46927i	−0.0327385	+	0.143437i
$586$	−3.34656	−	14.6622i	−0.138245	−	0.605692i
$587$	27.7213	−	13.3499i	1.14418	−	0.551009i	0.236900	−	0.971534i	$-0.423869\pi$
$587$	27.7213	−	13.3499i	1.14418	−	0.551009i	0.907281	+	0.420525i	$0.138154\pi$
$588$	−34.0789	−	27.1770i	−1.40539	−	1.12076i
$589$	1.58069	−	1.98213i	0.0651313	−	0.0816721i
$590$	2.64072	−	5.48351i	0.108717	−	0.225753i
$591$	−7.81307	+	6.23071i	−0.321387	+	0.256297i
$592$		−	6.92219i		−	0.284500i
$593$	−17.5078	−	21.9541i	−0.718961	−	0.901549i	0.279317	−	0.960199i	$-0.409892\pi$
$593$	−17.5078	−	21.9541i	−0.718961	−	0.901549i	−0.998279	+	0.0586500i	$0.981320\pi$
$594$	−3.32301	+	0.758455i	−0.136345	+	0.0311198i
$595$	−24.8101	+	5.66274i	−1.01711	+	0.232150i
$596$	17.0873	+	21.4267i	0.699921	+	0.877674i
$597$			46.4191i			1.89981i
$598$	−1.07564	+	0.857797i	−0.0439863	+	0.0350779i
$599$	−15.9299	+	33.0787i	−0.650877	+	1.35156i	0.270436	+	0.962738i	$0.412832\pi$
$599$	−15.9299	+	33.0787i	−0.650877	+	1.35156i	−0.921313	+	0.388822i	$0.872882\pi$
$600$	6.32695	−	7.93374i	0.258296	−	0.323894i
$601$	16.6833	+	13.3045i	0.680525	+	0.542701i	0.901608	−	0.432554i	$-0.142388\pi$
$601$	16.6833	+	13.3045i	0.680525	+	0.542701i	−0.221083	+	0.975255i	$0.570959\pi$
$602$	0.730444	−	0.351763i	0.0297707	−	0.0143368i
$603$	−1.65732	−	7.26121i	−0.0674915	−	0.295699i
$604$	−1.20214	+	5.26691i	−0.0489143	+	0.214307i
$605$	21.7030	+	10.4516i	0.882353	+	0.424919i
$606$	−5.65900	−	11.7510i	−0.229881	−	0.477353i
$607$	10.2345	+	2.33595i	0.415405	+	0.0948134i	0.425115	−	0.905139i	$-0.360234\pi$
$607$	10.2345	+	2.33595i	0.415405	+	0.0948134i	−0.00971006	+	0.999953i	$0.503091\pi$
$608$	2.89447			0.117386
$609$	4.97854	+	47.2677i	0.201741	+	1.91538i
$610$	−18.0264			−0.729867
$611$	16.2743	+	3.71451i	0.658388	+	0.150273i
$612$	1.36188	+	2.82798i	0.0550509	+	0.114314i
$613$	−22.5656	−	10.8670i	−0.911417	−	0.438915i	−0.0814179	−	0.996680i	$-0.525945\pi$
$613$	−22.5656	−	10.8670i	−0.911417	−	0.438915i	−0.829999	+	0.557765i	$0.811659\pi$
$614$	−0.650659	+	2.85072i	−0.0262585	+	0.115046i
$615$	−0.716954	−	3.14118i	−0.0289104	−	0.126665i
$616$	−12.2153	+	5.88260i	−0.492170	+	0.237017i
$617$	−26.2440	−	20.9289i	−1.05654	−	0.842565i	−0.0686411	−	0.997641i	$-0.521866\pi$
$617$	−26.2440	−	20.9289i	−1.05654	−	0.842565i	−0.987903	+	0.155076i	$0.950438\pi$
$618$	−4.56931	+	5.72973i	−0.183804	+	0.230483i
$619$	−16.7105	+	34.6998i	−0.671653	+	1.39470i	0.234654	+	0.972079i	$0.424604\pi$
$619$	−16.7105	+	34.6998i	−0.671653	+	1.39470i	−0.906306	+	0.422622i	$0.861110\pi$
$620$	16.9669	−	13.5307i	0.681408	−	0.543405i
$621$		−	7.15683i		−	0.287194i
$622$	−2.27081	−	2.84751i	−0.0910512	−	0.114175i
$623$	−20.9528	+	4.78234i	−0.839456	+	0.191600i
$624$	−6.36796	+	1.45345i	−0.254923	+	0.0581844i
$625$	−19.4835	−	24.4315i	−0.779340	−	0.977262i
$626$		−	0.814096i		−	0.0325378i
$627$	−1.25110	+	0.997716i	−0.0499640	+	0.0398450i
$628$	12.9916	−	26.9773i	0.518420	−	1.07651i
$629$	3.92869	−	4.92643i	0.156647	−	0.196430i
$630$	4.70745	+	3.75407i	0.187549	+	0.149566i
$631$	35.2889	−	16.9943i	1.40483	−	0.676531i	0.430696	−	0.902497i	$-0.358268\pi$
$631$	35.2889	−	16.9943i	1.40483	−	0.676531i	0.974135	+	0.225967i	$0.0725540\pi$
$632$	3.76663	+	16.5027i	0.149829	+	0.656442i
$633$	8.04732	−	35.2576i	0.319852	−	1.40136i
$634$	2.28585	+	1.10081i	0.0907825	+	0.0437186i
$635$	14.6873	+	30.4984i	0.582847	+	1.21029i
$636$	33.5745	+	7.66317i	1.33132	+	0.303864i
$637$	18.9226			0.749739
$638$	4.15523	+	1.48792i	0.164507	+	0.0589075i
$639$	8.27365			0.327301
$640$	30.8553	+	7.04252i	1.21966	+	0.278380i
$641$	−18.3563	−	38.1173i	−0.725032	−	1.50554i	−0.857571	−	0.514366i	$-0.828027\pi$
$641$	−18.3563	−	38.1173i	−0.725032	−	1.50554i	0.132539	−	0.991178i	$-0.457687\pi$
$642$	13.3698	+	6.43856i	0.527664	+	0.254110i
$643$	−5.21491	+	22.8480i	−0.205656	+	0.901038i	0.761763	+	0.647856i	$0.224334\pi$
$643$	−5.21491	+	22.8480i	−0.205656	+	0.901038i	−0.967419	+	0.253182i	$0.918523\pi$
$644$	−2.90836	−	12.7424i	−0.114606	−	0.502120i
$645$	1.60739	−	0.774077i	0.0632908	−	0.0304792i
$646$	0.484985	+	0.386763i	0.0190815	+	0.0152170i
$647$	10.5713	−	13.2560i	0.415602	−	0.521149i	−0.529329	−	0.848416i	$-0.677556\pi$
$647$	10.5713	−	13.2560i	0.415602	−	0.521149i	0.944932	+	0.327268i	$0.106128\pi$
$648$	−9.59847	+	19.9314i	−0.377063	+	0.782980i
$649$	−4.70039	+	3.74843i	−0.184506	+	0.147139i
$650$			2.02252i			0.0793297i
$651$	25.6356	+	32.1460i	1.00474	+	1.25990i
$652$	4.19537	−	0.957566i	0.164303	−	0.0375012i
$653$	6.30263	−	1.43853i	0.246641	−	0.0562942i	−0.0974130	−	0.995244i	$-0.531057\pi$
$653$	6.30263	−	1.43853i	0.246641	−	0.0562942i	0.344054	+	0.938950i	$0.388200\pi$
$654$	−0.638340	−	0.800453i	−0.0249611	−	0.0313002i
$655$		−	34.5764i		−	1.35101i
$656$	1.05966	−	0.845052i	0.0413728	−	0.0329937i
$657$	1.33889	−	2.78023i	0.0522350	−	0.108467i
$658$	17.6103	−	22.0826i	0.686521	−	0.860870i
$659$	16.1927	+	12.9133i	0.630780	+	0.503030i	0.885898	−	0.463880i	$-0.153543\pi$
$659$	16.1927	+	12.9133i	0.630780	+	0.503030i	−0.255119	+	0.966910i	$0.582115\pi$
$660$	−12.3413	+	5.94324i	−0.480383	+	0.231340i
$661$	−1.12801	−	4.94211i	−0.0438743	−	0.192226i	0.948242	−	0.317550i	$-0.102860\pi$
$661$	−1.12801	−	4.94211i	−0.0438743	−	0.192226i	−0.992116	+	0.125324i	$0.960003\pi$
$662$	−0.202826	+	0.888638i	−0.00788305	+	0.0345379i
$663$	−5.35690	−	2.57975i	−0.208045	−	0.100189i
$664$	−0.935844	−	1.94330i	−0.0363178	−	0.0754147i
$665$	−6.51342	−	1.48664i	−0.252579	−	0.0576496i
$666$	−1.49086			−0.0577695
$667$	−4.98735	+	7.81086i	−0.193111	+	0.302438i
$668$	−23.3004			−0.901519
$669$	−9.22152	−	2.10475i	−0.356524	−	0.0813744i
$670$	−5.46676	−	11.3519i	−0.211199	−	0.438560i
$671$	16.0432	+	7.72598i	0.619339	+	0.298258i
$672$	−10.4457	+	45.7655i	−0.402950	+	1.76544i
$673$	−1.39139	−	6.09608i	−0.0536342	−	0.234987i	0.941005	−	0.338392i	$-0.109883\pi$
$673$	−1.39139	−	6.09608i	−0.0536342	−	0.234987i	−0.994639	+	0.103406i	$0.967026\pi$
$674$	8.82190	−	4.24840i	0.339807	−	0.163642i
$675$	−8.22567	−	6.55975i	−0.316606	−	0.252485i
$676$	−11.5226	+	14.4488i	−0.443175	+	0.555724i
$677$	14.3011	−	29.6966i	0.549637	−	1.14133i	−0.422379	−	0.906419i	$-0.638805\pi$
$677$	14.3011	−	29.6966i	0.549637	−	1.14133i	0.972016	−	0.234914i	$-0.0754809\pi$
$678$	−14.2047	+	11.3279i	−0.545529	+	0.435045i
$679$			21.6136i			0.829454i
$680$	7.21100	+	9.04231i	0.276529	+	0.346757i
$681$	−6.56607	+	1.49866i	−0.251612	+	0.0574289i
$682$	3.72236	−	0.849605i	0.142537	−	0.0325330i
$683$	−19.6682	−	24.6631i	−0.752582	−	0.943708i	0.247098	−	0.968990i	$-0.420523\pi$
$683$	−19.6682	−	24.6631i	−0.752582	−	0.943708i	−0.999680	+	0.0252824i	$0.991951\pi$
$684$			0.824039i			0.0315079i
$685$	13.9102	−	11.0930i	0.531480	−	0.423841i
$686$	6.42026	−	13.3318i	0.245127	−	0.509011i
$687$	−24.5611	+	30.7986i	−0.937063	+	1.17504i
$688$	0.586755	+	0.467922i	0.0223698	+	0.0178393i
$689$	−13.4696	+	6.48662i	−0.513151	+	0.247120i
$690$	1.13990	+	4.99423i	0.0433952	+	0.190127i
$691$	−2.32737	+	10.1969i	−0.0885372	+	0.387907i	−0.999709	−	0.0241197i	$-0.992322\pi$
$691$	−2.32737	+	10.1969i	−0.0885372	+	0.387907i	0.911172	+	0.412026i	$0.135179\pi$
$692$	10.7885	+	5.19545i	0.410116	+	0.197501i
$693$	−2.58058	−	5.35863i	−0.0980281	−	0.203557i
$694$	−1.98276	−	0.452553i	−0.0752646	−	0.0171787i
$695$	−22.8546			−0.866923
$696$	18.3729	−	11.3593i	0.696424	−	0.430572i
$697$	1.23376			0.0467318
$698$	11.9504	+	2.72760i	0.452329	+	0.103241i
$699$	−3.54657	−	7.36454i	−0.134144	−	0.278552i
$700$	−17.3111	−	8.33659i	−0.654299	−	0.315094i
$701$	1.34313	−	5.88465i	0.0507294	−	0.222260i	−0.943209	−	0.332201i	$-0.892209\pi$
$701$	1.34313	−	5.88465i	0.0507294	−	0.222260i	0.993938	+	0.109940i	$0.0350660\pi$
$702$	−0.739838	−	3.24144i	−0.0279234	−	0.122340i
$703$	1.49042	−	0.717750i	0.0562124	−	0.0270705i
$704$	−1.89931	−	1.51465i	−0.0715828	−	0.0570854i
$705$	38.7525	−	48.5941i	1.45950	−	1.83016i
$706$	−5.66862	+	11.7710i	−0.213341	+	0.443008i
$707$	−42.0542	+	33.5371i	−1.58161	+	1.26129i
$708$			13.5089i			0.507695i
$709$	−11.4416	−	14.3473i	−0.429698	−	0.538824i	0.519097	−	0.854715i	$-0.326268\pi$
$709$	−11.4416	−	14.3473i	−0.429698	−	0.538824i	−0.948796	+	0.315891i	$0.897697\pi$
$710$	13.6455	−	3.11450i	0.512107	−	0.116885i
$711$	−7.23941	+	1.65235i	−0.271499	+	0.0619679i
$712$	6.08989	+	7.63648i	0.228228	+	0.286189i
$713$			8.01692i			0.300236i
$714$	−7.86545	+	6.27249i	−0.294357	+	0.234742i
$715$	2.58006	−	5.35756i	0.0964889	−	0.200361i
$716$	−5.69718	+	7.14404i	−0.212914	+	0.266985i
$717$	−32.2319	−	25.7041i	−1.20372	−	0.959938i
$718$	−17.7109	+	8.52912i	−0.660965	+	0.318304i
$719$	−2.01071	−	8.80950i	−0.0749868	−	0.328539i	0.923496	−	0.383609i	$-0.125319\pi$
$719$	−2.01071	−	8.80950i	−0.0749868	−	0.328539i	−0.998482	+	0.0550701i	$0.982462\pi$
$720$	−1.24025	+	5.43390i	−0.0462215	+	0.202510i
$721$	27.2308	+	13.1137i	1.01413	+	0.488379i
$722$	−4.46240	−	9.26627i	−0.166073	−	0.344855i
$723$	−7.03369	−	1.60539i	−0.261586	−	0.0597052i
$724$	−26.6447			−0.990241
$725$	4.40611	+	12.8914i	0.163639	+	0.478775i
$726$	9.52282			0.353425
$727$	5.64989	+	1.28955i	0.209543	+	0.0478268i	0.326004	−	0.945368i	$-0.394298\pi$
$727$	5.64989	+	1.28955i	0.209543	+	0.0478268i	−0.116461	+	0.993195i	$0.537155\pi$
$728$	−5.73820	−	11.9155i	−0.212672	−	0.441618i
$729$	13.4323	+	6.46866i	0.497493	+	0.239580i
$730$	1.16162	−	5.08937i	0.0429933	−	0.188366i
$731$	0.152016	+	0.666027i	0.00562253	+	0.0246339i
$732$	36.0487	−	17.3601i	1.33240	−	0.641648i
$733$	−5.33969	−	4.25826i	−0.197226	−	0.157282i	0.519897	−	0.854229i	$-0.325970\pi$
$733$	−5.33969	−	4.25826i	−0.197226	−	0.157282i	−0.717123	+	0.696946i	$0.754542\pi$
$734$	−0.484438	+	0.607466i	−0.0178809	+	0.0224220i
$735$	30.5699	−	63.4790i	1.12759	−	2.34146i
$736$	−7.15603	+	5.70675i	−0.263775	+	0.210353i
$737$			12.4460i			0.458453i
$738$	−0.182002	−	0.228223i	−0.00669958	−	0.00840101i
$739$	−33.0680	+	7.54755i	−1.21643	+	0.277641i	−0.782122	−	0.623125i	$-0.785863\pi$
$739$	−33.0680	+	7.54755i	−1.21643	+	0.277641i	−0.434304	+	0.900767i	$0.643005\pi$
$740$	13.8052	−	3.15096i	0.507491	−	0.115832i
$741$	−0.973226	−	1.22039i	−0.0357524	−	0.0448320i
$742$			25.2960i			0.928646i
$743$	−24.7299	+	19.7214i	−0.907252	+	0.723509i	−0.961438	−	0.275021i	$-0.911315\pi$
$743$	−24.7299	+	19.7214i	−0.907252	+	0.723509i	0.0541860	+	0.998531i	$0.482744\pi$
$744$	8.10771	−	16.8358i	0.297243	−	0.617231i
$745$	−27.6198	+	34.6341i	−1.01191	+	1.26890i
$746$	1.55335	+	1.23876i	0.0568723	+	0.0453542i
$747$	0.852488	−	0.410536i	0.0311909	−	0.0150207i
$748$	−1.16716	−	5.11365i	−0.0426755	−	0.186973i
$749$	13.6181	−	59.6648i	0.497594	−	2.18010i
$750$	−6.62485	−	3.19036i	−0.241905	−	0.116495i
$751$	10.0485	+	20.8659i	0.366675	+	0.761408i	0.999921	−	0.0125423i	$-0.00399245\pi$
$751$	10.0485	+	20.8659i	0.366675	+	0.761408i	−0.633247	+	0.773950i	$0.718278\pi$
$752$	25.4904	+	5.81802i	0.929539	+	0.212161i
$753$	−27.2815			−0.994192
$754$	−1.45140	+	4.05323i	−0.0528569	+	0.147610i
$755$	−8.73235			−0.317803
$756$	30.7936	+	7.02844i	1.11995	+	0.255622i
$757$	0.873631	+	1.81411i	0.0317527	+	0.0659351i	0.916242	−	0.400626i	$-0.131207\pi$
$757$	0.873631	+	1.81411i	0.0317527	+	0.0659351i	−0.884489	+	0.466561i	$0.845493\pi$
$758$	−2.83338	−	1.36448i	−0.102913	−	0.0495603i
$759$	1.12600	−	4.93332i	0.0408712	−	0.179068i
$760$	0.675644	+	2.96019i	0.0245082	+	0.107377i
$761$	−6.54560	+	3.15220i	−0.237278	+	0.114267i	−0.548745	−	0.835990i	$-0.684894\pi$
$761$	−6.54560	+	3.15220i	−0.237278	+	0.114267i	0.311467	+	0.950257i	$0.399180\pi$
$762$	10.4625	+	8.34358i	0.379017	+	0.302256i
$763$	−2.63258	+	3.30115i	−0.0953059	+	0.119510i
$764$	3.15455	−	6.55048i	0.114128	−	0.236988i
$765$	−3.96669	+	3.16333i	−0.143416	+	0.114370i
$766$			5.97548i			0.215903i
$767$	−3.65642	−	4.58501i	−0.132026	−	0.165555i
$768$	5.92831	−	1.35310i	0.213920	−	0.0488258i
$769$	−25.9802	+	5.92981i	−0.936869	+	0.213834i	−0.663587	−	0.748099i	$-0.730967\pi$
$769$	−25.9802	+	5.92981i	−0.936869	+	0.213834i	−0.273283	+	0.961934i	$0.588109\pi$
$770$	−6.27326	−	7.86642i	−0.226073	−	0.283486i
$771$		−	33.0778i		−	1.19127i
$772$	−31.3629	+	25.0111i	−1.12877	+	0.900168i
$773$	−7.26841	+	15.0930i	−0.261427	+	0.542858i	−0.989824	−	0.142297i	$-0.954551\pi$
$773$	−7.26841	+	15.0930i	−0.261427	+	0.542858i	0.728397	+	0.685155i	$0.240266\pi$
$774$	0.100778	−	0.126372i	0.00362239	−	0.00454233i
$775$	9.21422	+	7.34809i	0.330984	+	0.263951i
$776$	8.85009	−	4.26198i	0.317700	−	0.152996i
$777$	5.96989	+	26.1558i	0.214169	+	0.938334i
$778$	3.30781	−	14.4925i	0.118591	−	0.519580i
$779$	0.291823	+	0.140535i	0.0104557	+	0.00503518i
$780$	−5.79735	−	12.0383i	−0.207578	−	0.431041i
$781$	−13.4791	−	3.07652i	−0.482321	−	0.110087i
$782$	−1.96157			−0.0701457
$783$	−11.7772	−	19.0490i	−0.420884	−	0.680755i
$784$	29.6383			1.05851
$785$	47.1856	+	10.7698i	1.68412	+	0.384391i
$786$	−5.93073	−	12.3153i	−0.211542	−	0.439272i
$787$	21.2463	+	10.2317i	0.757349	+	0.364720i	0.772375	−	0.635167i	$-0.219069\pi$
$787$	21.2463	+	10.2317i	0.757349	+	0.364720i	−0.0150260	+	0.999887i	$0.504783\pi$
$788$	1.91355	−	8.38383i	0.0681675	−	0.298662i
$789$	−1.54880	−	6.78573i	−0.0551387	−	0.241578i
$790$	−11.3178	+	5.45035i	−0.402668	+	0.193915i
$791$	58.5818	+	46.7175i	2.08293	+	1.66108i
$792$	−1.68533	+	2.11333i	−0.0598855	+	0.0750940i
$793$	−7.53634	+	15.6494i	−0.267623	+	0.555725i
$794$	12.6497	−	10.0878i	0.448923	−	0.358004i
$795$			55.6654i			1.97425i
$796$	−24.9051	−	31.2300i	−0.882737	−	1.10692i
$797$	27.8945	−	6.36673i	0.988073	−	0.225521i	0.302202	−	0.953244i	$-0.402278\pi$
$797$	27.8945	−	6.36673i	0.988073	−	0.225521i	0.685871	+	0.727723i	$0.259421\pi$
$798$	−2.57492	+	0.587709i	−0.0911512	+	0.0208047i
$799$	14.8391	+	18.6077i	0.524971	+	0.658293i
$800$			13.4554i			0.475720i
$801$	−3.34998	+	2.67152i	−0.118366	+	0.0943934i
$802$	1.88949	−	3.92357i	0.0667203	−	0.138546i
$803$	−3.21508	+	4.03159i	−0.113458	+	0.142272i
$804$	21.8645	+	17.4364i	0.771103	+	0.614934i
$805$	19.0342	−	9.16641i	0.670869	−	0.323073i
$806$	0.828750	+	3.63099i	0.0291915	+	0.127896i
$807$	10.5232	−	46.1054i	0.370436	−	1.62299i
$808$	22.0250	+	10.6067i	0.774838	+	0.373142i
$809$	4.98171	+	10.3446i	0.175148	+	0.363698i	0.970000	−	0.243105i	$-0.0781660\pi$
$809$	4.98171	+	10.3446i	0.175148	+	0.363698i	−0.794852	+	0.606803i	$0.792452\pi$
$810$	−16.0055	−	3.65315i	−0.562376	−	0.128359i
$811$	−26.3454			−0.925111			−0.462555	−	0.886590i	$-0.653067\pi$
$811$	−26.3454			−0.925111			−0.462555	+	0.886590i	$0.653067\pi$
$812$	−28.7098	−	29.1298i	−1.00752	−	1.02225i
$813$	44.7930			1.57096
$814$	2.42885	+	0.554368i	0.0851310	+	0.0194306i
$815$	3.01800	+	6.26694i	0.105716	+	0.219521i
$816$	−8.39049	−	4.04064i	−0.293726	−	0.141451i
$817$	−0.0399090	+	0.174853i	−0.00139624	+	0.00611733i
$818$	−3.15324	−	13.8153i	−0.110250	−	0.483039i
$819$	5.22709	−	2.51724i	0.182649	−	0.0879593i
$820$	2.16768	+	1.72867i	0.0756987	+	0.0603677i
$821$	−7.84675	+	9.83951i	−0.273853	+	0.343401i	−0.899671	−	0.436568i	$-0.856194\pi$
$821$	−7.84675	+	9.83951i	−0.273853	+	0.343401i	0.625818	+	0.779969i	$0.284765\pi$
$822$	3.05174	−	6.33700i	0.106442	−	0.221028i
$823$	37.3908	−	29.8182i	1.30336	−	1.03940i	0.307221	−	0.951638i	$-0.400601\pi$
$823$	37.3908	−	29.8182i	1.30336	−	1.03940i	0.996142	−	0.0877587i	$-0.0279704\pi$
$824$		−	13.7360i		−	0.478518i
$825$	−4.63804	−	5.81591i	−0.161476	−	0.202484i
$826$	−9.67402	+	2.20803i	−0.336602	+	0.0768272i
$827$	−9.20610	+	2.10123i	−0.320128	+	0.0730670i	−0.379565	−	0.925165i	$-0.623926\pi$
$827$	−9.20610	+	2.10123i	−0.320128	+	0.0730670i	0.0594376	+	0.998232i	$0.481069\pi$
$828$	−1.62467	−	2.03728i	−0.0564613	−	0.0708003i
$829$			22.2232i			0.771843i	0.922532	+	0.385921i	$0.126116\pi$
$829$			22.2232i			0.771843i	−0.922532	+	0.385921i	$0.873884\pi$
$830$	1.25144	−	0.997994i	0.0434383	−	0.0346409i
$831$	17.5136	−	36.3674i	0.607541	−	1.26157i
$832$	1.47747	−	1.85268i	0.0512220	−	0.0642303i
$833$	21.0932	+	16.8213i	0.730836	+	0.582822i
$834$	−8.14025	+	3.92014i	−0.281874	+	0.135743i
$835$	−8.38074	−	36.7184i	−0.290027	−	1.27069i
$836$	0.306415	−	1.34249i	0.0105976	−	0.0464311i
$837$	−17.4553	−	8.40604i	−0.603344	−	0.290555i
$838$	−0.0886786	−	0.184143i	−0.00306335	−	0.00636112i
$839$	−40.5091	−	9.24594i	−1.39853	−	0.319205i	−0.544208	−	0.838950i	$-0.683170\pi$
$839$	−40.5091	−	9.24594i	−1.39853	−	0.319205i	−0.854321	+	0.519745i	$0.826027\pi$
$840$	−49.2428			−1.69904
$841$	−0.421076	+	28.9969i	−0.0145198	+	0.999895i
$842$	−12.3243			−0.424723
$843$	5.51442	+	1.25863i	0.189927	+	0.0433495i
$844$	13.5025	+	28.0383i	0.464776	+	0.965118i
$845$	−26.9140	−	12.9611i	−0.925868	−	0.445875i
$846$	1.25305	−	5.48996i	0.0430806	−	0.188749i
$847$	−8.73909	−	38.2885i	−0.300279	−	1.31561i
$848$	−21.0974	+	10.1600i	−0.724487	+	0.348895i
$849$	8.05219	+	6.42141i	0.276350	+	0.220382i
$850$	−1.79792	+	2.25453i	−0.0616683	+	0.0773296i
$851$	−2.26967	+	4.71302i	−0.0778033	+	0.161560i
$852$	−24.2885	+	19.3695i	−0.832111	+	0.663587i
$853$		−	1.76038i		−	0.0602743i	−0.999546	−	0.0301371i	$-0.990406\pi$
$853$		−	1.76038i		−	0.0602743i	0.999546	−	0.0301371i	$-0.00959440\pi$
$854$	18.3241	+	22.9777i	0.627039	+	0.786282i
$855$	−1.29858	+	0.296392i	−0.0444104	+	0.0101364i
$856$	−27.1162	+	6.18910i	−0.926813	+	0.211539i
$857$	−8.71902	−	10.9333i	−0.297836	−	0.373474i	0.610285	−	0.792182i	$-0.291055\pi$
$857$	−8.71902	−	10.9333i	−0.297836	−	0.373474i	−0.908121	+	0.418707i	$0.862483\pi$
$858$		−	2.35078i		−	0.0802543i
$859$	0.625735	−	0.499007i	0.0213498	−	0.0170259i	−0.612757	−	0.790272i	$-0.709939\pi$
$859$	0.625735	−	0.499007i	0.0213498	−	0.0170259i	0.634107	+	0.773246i	$0.281368\pi$
$860$	−0.666109	+	1.38319i	−0.0227141	+	0.0471664i
$861$	−3.27518	+	4.10694i	−0.111618	+	0.139964i
$862$	14.9786	+	11.9451i	0.510174	+	0.406850i
$863$	9.60543	−	4.62573i	0.326973	−	0.157462i	−0.263194	−	0.964743i	$-0.584776\pi$
$863$	9.60543	−	4.62573i	0.326973	−	0.157462i	0.590167	+	0.807281i	$0.299062\pi$
$864$	−4.92199	−	21.5646i	−0.167449	−	0.733644i
$865$	−4.30694	+	18.8699i	−0.146440	+	0.641597i
$866$	10.6781	+	5.14231i	0.362857	+	0.174743i
$867$	10.8733	+	22.5786i	0.369277	+	0.766811i
$868$	−34.4943	−	7.87311i	−1.17081	−	0.267231i
$869$	12.4086			0.420932
$870$	11.2525	+	11.4171i	0.381495	+	0.387075i
$871$	−12.1405			−0.411364
$872$	1.87084	+	0.427007i	0.0633546	+	0.0144603i
$873$	1.86965	+	3.88236i	0.0632780	+	0.131398i
$874$	−0.463976	−	0.223439i	−0.0156942	−	0.00755793i
$875$	−6.74788	+	29.5644i	−0.228120	+	0.999458i
$876$	2.57830	+	11.2963i	0.0871126	+	0.381665i
$877$	14.6169	−	7.03914i	0.493578	−	0.237695i	−0.170500	−	0.985358i	$-0.554538\pi$
$877$	14.6169	−	7.03914i	0.493578	−	0.237695i	0.664078	+	0.747663i	$0.268824\pi$
$878$	−0.706248	−	0.563214i	−0.0238347	−	0.0190076i
$879$	−33.6415	+	42.1852i	−1.13470	+	1.42287i
$880$	4.04114	−	8.39152i	0.136227	−	0.282878i
$881$	−17.6471	+	14.0731i	−0.594545	+	0.474134i	−0.873934	−	0.486044i	$-0.838439\pi$
$881$	−17.6471	+	14.0731i	−0.594545	+	0.474134i	0.279389	+	0.960178i	$0.409868\pi$
$882$		−	6.38332i		−	0.214937i
$883$	−6.36666	−	7.98354i	−0.214255	−	0.268668i	0.663077	−	0.748551i	$-0.269250\pi$
$883$	−6.36666	−	7.98354i	−0.214255	−	0.268668i	−0.877332	+	0.479884i	$0.840679\pi$
$884$	4.98813	−	1.13851i	0.167769	−	0.0382921i
$885$	−21.2883	+	4.85891i	−0.715597	+	0.163330i
$886$	−12.1284	−	15.2085i	−0.407461	−	0.510939i
$887$		−	45.7130i		−	1.53489i	−0.641113	−	0.767447i	$-0.721527\pi$
$887$		−	45.7130i		−	1.53489i	0.641113	−	0.767447i	$-0.278473\pi$
$888$	9.53278	−	7.60214i	0.319899	−	0.255111i
$889$	23.9456	−	49.7236i	0.803111	−	1.66768i
$890$	−4.51937	+	5.66711i	−0.151490	+	0.189962i
$891$	12.6789	+	10.1111i	0.424759	+	0.338734i
$892$	7.33333	−	3.53154i	0.245538	−	0.118245i
$893$	1.39037	+	6.09162i	0.0465270	+	0.203848i
$894$	−3.89688	+	17.0733i	−0.130331	+	0.571018i
$895$	−13.3073	−	6.40844i	−0.444813	−	0.214211i
$896$	−22.3880	−	46.4892i	−0.747932	−	1.55310i
$897$	4.81223	+	1.09836i	0.160676	+	0.0366732i
$898$	−6.79273			−0.226676
$899$	13.1926	+	21.3383i	0.439998	+	0.711671i
$900$	−3.83067			−0.127689
$901$	−20.7810	−	4.74313i	−0.692316	−	0.158017i
$902$	0.211647	+	0.439489i	0.00704706	+	0.0146334i
$903$	−2.62063	−	1.26203i	−0.0872091	−	0.0419977i
$904$	7.57760	−	33.1996i	0.252027	−	1.10420i
$905$	−9.58361	−	41.9886i	−0.318570	−	1.39575i
$906$	−3.11026	+	1.49782i	−0.103331	+	0.0497617i
$907$	25.2645	+	20.1478i	0.838894	+	0.668996i	0.945613	−	0.325293i	$-0.105463\pi$
$907$	25.2645	+	20.1478i	0.838894	+	0.668996i	−0.106719	+	0.994289i	$0.534035\pi$
$908$	3.61346	−	4.53114i	0.119917	−	0.150371i
$909$	−4.65295	+	9.66196i	−0.154329	+	0.320467i
$910$	7.67333	−	6.11928i	0.254368	−	0.202852i
$911$		−	10.6165i		−	0.351739i	−0.984413	−	0.175870i	$-0.943726\pi$
$911$		−	10.6165i		−	0.351739i	0.984413	−	0.175870i	$-0.0562737\pi$
$912$	−1.52436	−	1.91149i	−0.0504766	−	0.0632957i
$913$	−1.54150	+	0.351836i	−0.0510161	+	0.0116441i
$914$	16.7893	−	3.83205i	0.555341	−	0.126753i
$915$	40.3234	+	50.5639i	1.33305	+	1.67159i
$916$		−	33.8984i		−	1.12004i
$917$	−44.0736	+	35.1475i	−1.45544	+	1.16067i
$918$	2.05678	−	4.27095i	0.0678839	−	0.140962i
$919$	11.4579	−	14.3678i	0.377962	−	0.473949i	−0.556072	−	0.831134i	$-0.687692\pi$
$919$	11.4579	−	14.3678i	0.377962	−	0.473949i	0.934034	+	0.357185i	$0.116263\pi$
$920$	−7.50672	−	5.98641i	−0.247489	−	0.197366i
$921$	9.45172	−	4.55171i	0.311445	−	0.149984i
$922$	−0.791108	−	3.46607i	−0.0260537	−	0.114149i
$923$	3.00100	−	13.1483i	0.0987792	−	0.432780i
$924$	20.1208	+	9.68965i	0.661925	+	0.318766i
$925$	3.33657	+	6.92846i	0.109706	+	0.227806i
$926$	7.78478	+	1.77682i	0.255824	+	0.0583901i
$927$	6.02574			0.197911
$928$	−9.65587	+	26.9653i	−0.316970	+	0.885179i
$929$	56.4863			1.85325			0.926627	−	0.375981i	$-0.122694\pi$
$929$	56.4863			1.85325			0.926627	+	0.375981i	$0.122694\pi$
$930$	13.5197	+	3.08577i	0.443327	+	0.101187i
$931$	3.07315	+	6.38146i	0.100718	+	0.209144i
$932$	6.33734	+	3.05190i	0.207586	+	0.0999684i
$933$	−2.90764	+	12.7392i	−0.0951920	+	0.417063i
$934$	3.20013	+	14.0207i	0.104711	+	0.458770i
$935$	7.63864	−	3.67858i	0.249810	−	0.120302i
$936$	−2.06146	−	1.64396i	−0.0673809	−	0.0537345i
$937$	18.0257	−	22.6035i	0.588874	−	0.738425i	−0.394724	−	0.918800i	$-0.629160\pi$
$937$	18.0257	−	22.6035i	0.588874	−	0.738425i	0.983598	+	0.180375i	$0.0577312\pi$
$938$	−8.91283	+	18.5077i	−0.291014	+	0.604297i
$939$	−2.28353	+	1.82106i	−0.0745203	+	0.0594280i
$940$			53.4850i			1.74449i
$941$	−1.55635	−	1.95160i	−0.0507355	−	0.0636202i	0.755816	−	0.654784i	$-0.227240\pi$
$941$	−1.55635	−	1.95160i	−0.0507355	−	0.0636202i	−0.806552	+	0.591163i	$0.798669\pi$
$942$	18.6537	−	4.25758i	0.607769	−	0.138719i
$943$	−0.998555	+	0.227914i	−0.0325174	+	0.00742189i
$944$	−5.72704	−	7.18148i	−0.186399	−	0.233737i
$945$			51.0548i			1.66081i
$946$	−0.211174	+	0.168406i	−0.00686587	+	0.00547535i
$947$	−4.44526	+	9.23068i	−0.144452	+	0.299957i	−0.960624	−	0.277852i	$-0.910378\pi$
$947$	−4.44526	+	9.23068i	−0.144452	+	0.299957i	0.816172	+	0.577808i	$0.196092\pi$
$948$	17.3840	−	21.7989i	0.564607	−	0.707995i
$949$	−3.93263	−	3.13616i	−0.127658	−	0.101804i
$950$	−0.682076	+	0.328470i	−0.0221295	+	0.0106570i
$951$	−2.02547	−	8.87418i	−0.0656805	−	0.287765i
$952$	4.19587	−	18.3833i	0.135989	−	0.595807i
$953$	3.97726	+	1.91535i	0.128836	+	0.0620442i	0.497191	−	0.867641i	$-0.334365\pi$
$953$	3.97726	+	1.91535i	0.128836	+	0.0620442i	−0.368355	+	0.929685i	$0.620079\pi$
$954$	2.18819	+	4.54382i	0.0708452	+	0.147112i
$955$	11.4574	+	2.61507i	0.370751	+	0.0846215i
$956$	35.4760			1.14738
$957$	−5.12124	−	14.9837i	−0.165546	−	0.484355i
$958$	13.8718			0.448177
$959$	−28.2798	−	6.45468i	−0.913203	−	0.208433i
$960$	−3.82827	−	7.94948i	−0.123557	−	0.256568i
$961$	−8.37697	−	4.03413i	−0.270225	−	0.130133i
$962$	−0.540761	+	2.36923i	−0.0174348	+	0.0763870i
$963$	−2.71504	−	11.8953i	−0.0874908	−	0.383322i
$964$	5.59348	−	2.69368i	0.180154	−	0.0867575i
$965$	−50.6949	−	40.4278i	−1.63193	−	1.30142i
$966$	5.20727	−	6.52971i	0.167541	−	0.210090i
$967$	7.82186	−	16.2423i	0.251534	−	0.522316i	−0.736521	−	0.676414i	$-0.763533\pi$
$967$	7.82186	−	16.2423i	0.251534	−	0.522316i	0.988056	+	0.154098i	$0.0492473\pi$
$968$	−13.9547	+	11.1285i	−0.448520	+	0.357683i
$969$		−	2.22553i		−	0.0714944i
$970$	4.54502	+	5.69928i	0.145932	+	0.182993i
$971$	−23.6230	+	5.39179i	−0.758097	+	0.173031i	−0.584062	−	0.811709i	$-0.698538\pi$
$971$	−23.6230	+	5.39179i	−0.758097	+	0.173031i	−0.174035	+	0.984739i	$0.555681\pi$
$972$	14.8762	−	3.39541i	0.477156	−	0.108908i
$973$	23.2321	+	29.1321i	0.744785	+	0.933931i
$974$		−	22.0626i		−	0.706931i
$975$	5.67315	−	4.52419i	0.181686	−	0.144890i
$976$	−11.8041	+	24.5115i	−0.377841	+	0.784595i
$977$	3.03471	−	3.80541i	0.0970890	−	0.121746i	−0.730914	−	0.682470i	$-0.760906\pi$
$977$	3.03471	−	3.80541i	0.0970890	−	0.121746i	0.828003	+	0.560724i	$0.189477\pi$
$978$	2.14988	+	1.71447i	0.0687456	+	0.0548228i
$979$	6.45104	−	3.10666i	0.206176	−	0.0992892i
$980$	13.4913	+	59.1091i	0.430963	+	1.88817i
$981$	−0.187319	+	0.820700i	−0.00598065	+	0.0262029i
$982$	−5.04007	−	2.42717i	−0.160835	−	0.0774540i
$983$	10.0684	+	20.9073i	0.321133	+	0.666840i	0.997571	−	0.0696600i	$-0.0221914\pi$
$983$	10.0684	+	20.9073i	0.321133	+	0.666840i	−0.676438	+	0.736500i	$0.736477\pi$
$984$	2.32750	+	0.531236i	0.0741979	+	0.0169352i
$985$	13.9001			0.442894
$986$	−5.22102	+	3.22795i	−0.166271	+	0.102799i
$987$	−101.334			−3.22550
$988$	1.30954	+	0.298894i	0.0416620	+	0.00950907i
$989$	−0.246072	−	0.510975i	−0.00782465	−	0.0162481i
$990$	−1.80731	−	0.870356i	−0.0574402	−	0.0276617i
$991$	−5.94679	+	26.0546i	−0.188906	+	0.827651i	0.788289	+	0.615306i	$0.210967\pi$
$991$	−5.94679	+	26.0546i	−0.188906	+	0.827651i	−0.977195	+	0.212346i	$0.931890\pi$
$992$	5.51350	+	24.1562i	0.175054	+	0.766961i
$993$	2.94633	−	1.41888i	0.0934988	−	0.0450267i
$994$	−17.8409	−	14.2276i	−0.565878	−	0.451272i
$995$	40.2565	−	50.4801i	1.27622	−	1.60033i
$996$	−1.54150	+	3.20095i	−0.0488442	+	0.101426i
$997$	23.2732	−	18.5597i	0.737069	−	0.587793i	−0.181342	−	0.983420i	$-0.558044\pi$
$997$	23.2732	−	18.5597i	0.737069	−	0.587793i	0.918411	+	0.395627i	$0.129473\pi$
$998$			4.53027i			0.143403i
$999$	−7.88187	−	9.88355i	−0.249371	−	0.312702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.2.e.a.4.2	✓	12
3.2	odd	2		261.2.o.a.91.1		12
4.3	odd	2		464.2.y.d.33.1		12
5.2	odd	4		725.2.p.a.149.3		24
5.3	odd	4		725.2.p.a.149.2		24
5.4	even	2		725.2.q.a.526.1		12
29.2	odd	28		841.2.d.l.190.2		24
29.3	odd	28		841.2.d.m.645.2		24
29.4	even	14		841.2.e.f.267.2		12
29.5	even	14		841.2.e.a.651.2		12
29.6	even	14		841.2.b.e.840.5		12
29.7	even	7		841.2.e.i.196.1		12
29.8	odd	28		841.2.d.k.778.2		24
29.9	even	14		841.2.e.e.63.1		12
29.10	odd	28		841.2.d.k.574.2		24
29.11	odd	28		841.2.d.l.571.2		24
29.12	odd	4		841.2.d.m.605.3		24
29.13	even	14		841.2.e.h.270.1		12
29.14	odd	28		841.2.a.k.1.8		12
29.15	odd	28		841.2.a.k.1.5		12
29.16	even	7		841.2.e.a.270.2		12
29.17	odd	4		841.2.d.m.605.2		24
29.18	odd	28		841.2.d.l.571.3		24
29.19	odd	28		841.2.d.k.574.3		24
29.20	even	7		841.2.e.f.63.2		12
29.21	odd	28		841.2.d.k.778.3		24
29.22	even	14	inner	29.2.e.a.22.2	yes	12
29.23	even	7		841.2.b.e.840.8		12
29.24	even	7		841.2.e.h.651.1		12
29.25	even	7		841.2.e.e.267.1		12
29.26	odd	28		841.2.d.m.645.3		24
29.27	odd	28		841.2.d.l.190.3		24
29.28	even	2		841.2.e.i.236.1		12
87.14	even	28		7569.2.a.bp.1.5		12
87.44	even	28		7569.2.a.bp.1.8		12
87.80	odd	14		261.2.o.a.109.1		12
116.51	odd	14		464.2.y.d.225.1		12
145.22	odd	28		725.2.p.a.399.2		24
145.109	even	14		725.2.q.a.51.1		12
145.138	odd	28		725.2.p.a.399.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.4.2	✓	12	1.1	even	1	trivial
29.2.e.a.22.2	yes	12	29.22	even	14	inner
261.2.o.a.91.1		12	3.2	odd	2
261.2.o.a.109.1		12	87.80	odd	14
464.2.y.d.33.1		12	4.3	odd	2
464.2.y.d.225.1		12	116.51	odd	14
725.2.p.a.149.2		24	5.3	odd	4
725.2.p.a.149.3		24	5.2	odd	4
725.2.p.a.399.2		24	145.22	odd	28
725.2.p.a.399.3		24	145.138	odd	28
725.2.q.a.51.1		12	145.109	even	14
725.2.q.a.526.1		12	5.4	even	2
841.2.a.k.1.5		12	29.15	odd	28
841.2.a.k.1.8		12	29.14	odd	28
841.2.b.e.840.5		12	29.6	even	14
841.2.b.e.840.8		12	29.23	even	7
841.2.d.k.574.2		24	29.10	odd	28
841.2.d.k.574.3		24	29.19	odd	28
841.2.d.k.778.2		24	29.8	odd	28
841.2.d.k.778.3		24	29.21	odd	28
841.2.d.l.190.2		24	29.2	odd	28
841.2.d.l.190.3		24	29.27	odd	28
841.2.d.l.571.2		24	29.11	odd	28
841.2.d.l.571.3		24	29.18	odd	28
841.2.d.m.605.2		24	29.17	odd	4
841.2.d.m.605.3		24	29.12	odd	4
841.2.d.m.645.2		24	29.3	odd	28
841.2.d.m.645.3		24	29.26	odd	28
841.2.e.a.270.2		12	29.16	even	7
841.2.e.a.651.2		12	29.5	even	14
841.2.e.e.63.1		12	29.9	even	14
841.2.e.e.267.1		12	29.25	even	7
841.2.e.f.63.2		12	29.20	even	7
841.2.e.f.267.2		12	29.4	even	14
841.2.e.h.270.1		12	29.13	even	14
841.2.e.h.651.1		12	29.24	even	7
841.2.e.i.196.1		12	29.7	even	7
841.2.e.i.236.1		12	29.28	even	2
7569.2.a.bp.1.5		12	87.14	even	28
7569.2.a.bp.1.8		12	87.44	even	28

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.536089 - 0.122359i) q^{2} +(0.855966 + 1.77743i) q^{3} +(-1.52952 - 0.736577i) q^{4} +(0.610610 - 2.67526i) q^{5} +(-0.241390 - 1.05760i) q^{6} +(-4.03077 + 1.94112i) q^{7} +(1.58965 + 1.26771i) q^{8} +(-0.556117 + 0.697349i) q^{9} +O(q^{10})\)	\(q+(-0.536089 - 0.122359i) q^{2} +(0.855966 + 1.77743i) q^{3} +(-1.52952 - 0.736577i) q^{4} +(0.610610 - 2.67526i) q^{5} +(-0.241390 - 1.05760i) q^{6} +(-4.03077 + 1.94112i) q^{7} +(1.58965 + 1.26771i) q^{8} +(-0.556117 + 0.697349i) q^{9} +(-0.654683 + 1.35946i) q^{10} +(1.16531 - 0.929305i) q^{11} -3.34910i q^{12} +(0.906494 + 1.13671i) q^{13} +(2.39836 - 0.547411i) q^{14} +(5.27775 - 1.20461i) q^{15} +(1.41984 + 1.78042i) q^{16} +2.07293i q^{17} +(0.383455 - 0.305796i) q^{18} +(-0.236123 + 0.490315i) q^{19} +(-2.90447 + 3.64209i) q^{20} +(-6.90040 - 5.50289i) q^{21} +(-0.738420 + 0.355604i) q^{22} +(-0.382936 - 1.67775i) q^{23} +(-0.892571 + 3.91061i) q^{24} +(-2.27930 - 1.09766i) q^{25} +(-0.346875 - 0.720294i) q^{26} +(4.05451 + 0.925415i) q^{27} +7.59491 q^{28} +(-3.78014 - 3.83543i) q^{29} -2.97674 q^{30} +(-4.54177 - 1.03663i) q^{31} +(-2.30769 - 4.79197i) q^{32} +(2.64924 + 1.27581i) q^{33} +(0.253641 - 1.11128i) q^{34} +(2.73175 + 11.9686i) q^{35} +(1.36424 - 0.656985i) q^{36} +(-2.37655 - 1.89524i) q^{37} +(0.186578 - 0.233961i) q^{38} +(-1.24449 + 2.58421i) q^{39} +(4.36209 - 3.47865i) q^{40} -0.595175i q^{41} +(3.02590 + 3.79436i) q^{42} +(0.321297 - 0.0733340i) q^{43} +(-2.46687 + 0.563047i) q^{44} +(1.52602 + 1.91356i) q^{45} +0.946280i q^{46} +(8.97652 - 7.15853i) q^{47} +(-1.94924 + 4.04764i) q^{48} +(8.11473 - 10.1755i) q^{49} +(1.08760 + 0.867335i) q^{50} +(-3.68449 + 1.77436i) q^{51} +(-0.549226 - 2.40632i) q^{52} +(-2.28813 + 10.0249i) q^{53} +(-2.06035 - 0.992210i) q^{54} +(-1.77458 - 3.68495i) q^{55} +(-8.86828 - 2.02413i) q^{56} -1.07362 q^{57} +(1.55719 + 2.51867i) q^{58} -4.03359 q^{59} +(-8.95970 - 2.04499i) q^{60} +(5.18352 + 10.7637i) q^{61} +(2.30795 + 1.11145i) q^{62} +(0.887945 - 3.89034i) q^{63} +(-0.362680 - 1.58901i) q^{64} +(3.59450 - 1.73102i) q^{65} +(-1.26412 - 1.00811i) q^{66} +(-5.20630 + 6.52849i) q^{67} +(1.52687 - 3.17058i) q^{68} +(2.65431 - 2.11674i) q^{69} -6.75049i q^{70} +(-5.78348 - 7.25226i) q^{71} +(-1.76807 + 0.403550i) q^{72} +(-3.37292 + 0.769848i) q^{73} +(1.04215 + 1.30681i) q^{74} -4.99087i q^{75} +(0.722310 - 0.576023i) q^{76} +(-2.89321 + 6.00781i) q^{77} +(0.983360 - 1.23309i) q^{78} +(6.50888 + 5.19066i) q^{79} +(5.63005 - 2.71129i) q^{80} +(2.42109 + 10.6075i) q^{81} +(-0.0728249 + 0.319067i) q^{82} +(-0.955764 - 0.460272i) q^{83} +(6.50099 + 13.4994i) q^{84} +(5.54562 + 1.26575i) q^{85} -0.181217 q^{86} +(3.58155 - 10.0019i) q^{87} +3.03052 q^{88} +(4.68343 + 1.06896i) q^{89} +(-0.583940 - 1.21256i) q^{90} +(-5.86034 - 2.82219i) q^{91} +(-0.650086 + 2.84821i) q^{92} +(-2.04506 - 8.96001i) q^{93} +(-5.68812 + 2.73926i) q^{94} +(1.16754 + 0.931082i) q^{95} +(6.54209 - 8.20353i) q^{96} +(2.09615 - 4.35270i) q^{97} +(-5.59529 + 4.46209i) q^{98} +1.32943i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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