LMFDB - Embedded newform 74.2.f.b.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, 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:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			71.2
Root			$2.20976 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	74.71
Dual form			74.2.f.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.972925 - 0.816381i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{5} +1.27006 q^{6} +(-1.82850 - 0.665520i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.240839 + 1.36587i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.972925 - 0.816381i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{5} +1.27006 q^{6} +(-1.82850 - 0.665520i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.240839 + 1.36587i) q^{9} +(-0.766044 - 1.32683i) q^{10} +(-0.220544 + 0.381994i) q^{11} +(0.972925 + 0.816381i) q^{12} +(-0.367592 - 2.08472i) q^{13} +(-0.972925 - 1.68516i) q^{14} +(-1.82850 + 0.665520i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.664245 + 3.76712i) q^{17} +(-1.06246 + 0.891507i) q^{18} +(4.55479 - 3.82192i) q^{19} +(0.266044 - 1.50881i) q^{20} +(-2.32231 + 0.845253i) q^{21} +(-0.414488 + 0.150861i) q^{22} +(-2.85558 - 4.94600i) q^{23} +(0.220544 + 1.25077i) q^{24} +(-2.03209 - 1.70513i) q^{25} +(1.05844 - 1.83327i) q^{26} +(2.78585 + 4.82523i) q^{27} +(0.337893 - 1.91629i) q^{28} +(-1.36712 + 2.36792i) q^{29} +(-1.82850 - 0.665520i) q^{30} +9.87516 q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.0972795 + 0.551699i) q^{33} +(-2.93030 + 2.45881i) q^{34} +(2.28374 + 1.91629i) q^{35} -1.38694 q^{36} +(2.18831 + 5.67550i) q^{37} +5.94585 q^{38} +(-2.05956 - 1.72818i) q^{39} +(1.17365 - 0.984808i) q^{40} +(1.80615 + 10.2432i) q^{41} +(-2.32231 - 0.845253i) q^{42} +3.84681 q^{43} +(-0.414488 - 0.150861i) q^{44} +(1.06246 - 1.84023i) q^{45} +(0.991731 - 5.62439i) q^{46} +(-3.84316 - 6.65655i) q^{47} +(-0.635032 + 1.09991i) q^{48} +(-2.46181 - 2.06571i) q^{49} +(-0.460637 - 2.61240i) q^{50} +(2.42915 + 4.20740i) q^{51} +(1.98921 - 0.724014i) q^{52} +(-1.62561 + 0.591673i) q^{53} +(-0.967514 + 5.48704i) q^{54} +(0.517683 - 0.434387i) q^{55} +(1.49061 - 1.25077i) q^{56} +(1.31132 - 7.43688i) q^{57} +(-2.56934 + 0.935163i) q^{58} +(-1.93027 + 0.702561i) q^{59} +(-0.972925 - 1.68516i) q^{60} +(-1.89894 - 10.7694i) q^{61} +(7.56481 + 6.34763i) q^{62} +(1.34939 - 2.33721i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.563183 + 3.19397i) q^{65} +(-0.280105 + 0.485156i) q^{66} +(1.57261 + 0.572384i) q^{67} -3.82524 q^{68} +(-6.81608 - 2.48085i) q^{69} +(0.517683 + 2.93592i) q^{70} +(-7.70462 + 6.46494i) q^{71} +(-1.06246 - 0.891507i) q^{72} -9.88570 q^{73} +(-1.97180 + 5.75430i) q^{74} -3.36910 q^{75} +(4.55479 + 3.82192i) q^{76} +(0.657490 - 0.551699i) q^{77} +(-0.466865 - 2.64772i) q^{78} +(-12.5395 - 4.56401i) q^{79} +1.53209 q^{80} +(2.73975 + 0.997189i) q^{81} +(-5.20061 + 9.00771i) q^{82} +(0.617999 - 3.50484i) q^{83} +(-1.23568 - 2.14025i) q^{84} +(2.93030 - 5.07543i) q^{85} +(2.94683 + 2.47268i) q^{86} +(0.603020 + 3.41989i) q^{87} +(-0.220544 - 0.381994i) q^{88} +(11.1543 - 4.05982i) q^{89} +(1.99677 - 0.726763i) q^{90} +(-0.715278 + 4.05654i) q^{91} +(4.37500 - 3.67106i) q^{92} +(9.60779 - 8.06190i) q^{93} +(1.33472 - 7.56955i) q^{94} +(-8.56020 + 3.11566i) q^{95} +(-1.19347 + 0.434387i) q^{96} +(0.296748 + 0.513983i) q^{97} +(-0.558047 - 3.16484i) q^{98} +(-0.468637 - 0.393233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.972925	−	0.816381i	0.561719	−	0.471338i	−0.317168	−	0.948370i	$-0.602732\pi$
$3$	0.972925	−	0.816381i	0.561719	−	0.471338i	0.878886	+	0.477032i	$0.158287\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−1.43969	−	0.524005i	−0.643850	−	0.234342i	−0.000601695	−	1.00000i	$-0.500192\pi$
$5$	−1.43969	−	0.524005i	−0.643850	−	0.234342i	−0.643248	+	0.765658i	$0.722414\pi$
$6$	1.27006			0.518501
$7$	−1.82850	−	0.665520i	−0.691108	−	0.251543i	−0.0274987	−	0.999622i	$-0.508754\pi$
$7$	−1.82850	−	0.665520i	−0.691108	−	0.251543i	−0.663610	+	0.748079i	$0.730976\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.240839	+	1.36587i	−0.0802798	+	0.455289i
$10$	−0.766044	−	1.32683i	−0.242245	−	0.419580i
$11$	−0.220544	+	0.381994i	−0.0664966	+	0.115175i	−0.897357	−	0.441306i	$-0.854515\pi$
$11$	−0.220544	+	0.381994i	−0.0664966	+	0.115175i	0.830860	+	0.556481i	$0.187849\pi$
$12$	0.972925	+	0.816381i	0.280859	+	0.235669i
$13$	−0.367592	−	2.08472i	−0.101952	−	0.578196i	−0.992394	−	0.123100i	$-0.960716\pi$
$13$	−0.367592	−	2.08472i	−0.101952	−	0.578196i	0.890443	−	0.455095i	$-0.150395\pi$
$14$	−0.972925	−	1.68516i	−0.260025	−	0.450377i
$15$	−1.82850	+	0.665520i	−0.472117	+	0.171837i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.664245	+	3.76712i	−0.161103	+	0.913661i	0.791889	+	0.610665i	$0.209098\pi$
$17$	−0.664245	+	3.76712i	−0.161103	+	0.913661i	−0.952992	+	0.302996i	$0.902013\pi$
$18$	−1.06246	+	0.891507i	−0.250423	+	0.210130i
$19$	4.55479	−	3.82192i	1.04494	−	0.876808i	0.0523871	−	0.998627i	$-0.483317\pi$
$19$	4.55479	−	3.82192i	1.04494	−	0.876808i	0.992552	+	0.121819i	$0.0388726\pi$
$20$	0.266044	−	1.50881i	0.0594893	−	0.337381i
$21$	−2.32231	+	0.845253i	−0.506770	+	0.184449i
$22$	−0.414488	+	0.150861i	−0.0883690	+	0.0321637i
$23$	−2.85558	−	4.94600i	−0.595429	−	1.03131i	−0.993486	−	0.113952i	$-0.963649\pi$
$23$	−2.85558	−	4.94600i	−0.595429	−	1.03131i	0.398057	−	0.917360i	$-0.369684\pi$
$24$	0.220544	+	1.25077i	0.0450184	+	0.255312i
$25$	−2.03209	−	1.70513i	−0.406418	−	0.341025i
$26$	1.05844	−	1.83327i	0.207577	−	0.359533i
$27$	2.78585	+	4.82523i	0.536136	+	0.928615i
$28$	0.337893	−	1.91629i	0.0638558	−	0.362144i
$29$	−1.36712	+	2.36792i	−0.253867	+	0.439711i	−0.964587	−	0.263764i	$-0.915036\pi$
$29$	−1.36712	+	2.36792i	−0.253867	+	0.439711i	0.710720	+	0.703475i	$0.248369\pi$
$30$	−1.82850	−	0.665520i	−0.333837	−	0.121507i
$31$	9.87516			1.77363			0.886816	−	0.462123i	$-0.152912\pi$
$31$	9.87516			1.77363			0.886816	+	0.462123i	$0.152912\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.0972795	+	0.551699i	0.0169342	+	0.0960386i
$34$	−2.93030	+	2.45881i	−0.502542	+	0.421683i
$35$	2.28374	+	1.91629i	0.386023	+	0.323912i
$36$	−1.38694			−0.231156
$37$	2.18831	+	5.67550i	0.359755	+	0.933047i
$37$	2.18831	+	5.67550i	0.359755	+	0.933047i
$38$	5.94585			0.964544
$39$	−2.05956	−	1.72818i	−0.329794	−	0.276730i
$40$	1.17365	−	0.984808i	0.185570	−	0.155712i
$41$	1.80615	+	10.2432i	0.282073	+	1.59972i	0.715556	+	0.698556i	$0.246174\pi$
$41$	1.80615	+	10.2432i	0.282073	+	1.59972i	−0.433482	+	0.901162i	$0.642715\pi$
$42$	−2.32231	−	0.845253i	−0.358341	−	0.130425i
$43$	3.84681			0.586633			0.293317	−	0.956015i	$-0.405241\pi$
$43$	3.84681			0.586633			0.293317	+	0.956015i	$0.405241\pi$
$44$	−0.414488	−	0.150861i	−0.0624863	−	0.0227432i
$45$	1.06246	−	1.84023i	0.158382	−	0.274325i
$46$	0.991731	−	5.62439i	0.146223	−	0.829271i
$47$	−3.84316	−	6.65655i	−0.560582	−	0.970957i	−0.997446	−	0.0714293i	$-0.977244\pi$
$47$	−3.84316	−	6.65655i	−0.560582	−	0.970957i	0.436863	−	0.899528i	$-0.356089\pi$
$48$	−0.635032	+	1.09991i	−0.0916589	+	0.158758i
$49$	−2.46181	−	2.06571i	−0.351687	−	0.295101i
$50$	−0.460637	−	2.61240i	−0.0651439	−	0.369450i
$51$	2.42915	+	4.20740i	0.340148	+	0.589154i
$52$	1.98921	−	0.724014i	0.275854	−	0.100403i
$53$	−1.62561	+	0.591673i	−0.223295	+	0.0812726i	−0.451245	−	0.892400i	$-0.649020\pi$
$53$	−1.62561	+	0.591673i	−0.223295	+	0.0812726i	0.227950	+	0.973673i	$0.426798\pi$
$54$	−0.967514	+	5.48704i	−0.131662	+	0.746692i
$55$	0.517683	−	0.434387i	0.0698043	−	0.0585728i
$56$	1.49061	−	1.25077i	0.199191	−	0.167141i
$57$	1.31132	−	7.43688i	0.173689	−	0.985039i
$58$	−2.56934	+	0.935163i	−0.337371	+	0.122793i
$59$	−1.93027	+	0.702561i	−0.251300	+	0.0914656i	−0.464599	−	0.885521i	$-0.653801\pi$
$59$	−1.93027	+	0.702561i	−0.251300	+	0.0914656i	0.213299	+	0.976987i	$0.431579\pi$
$60$	−0.972925	−	1.68516i	−0.125604	−	0.217553i
$61$	−1.89894	−	10.7694i	−0.243134	−	1.37888i	−0.824786	−	0.565444i	$-0.808705\pi$
$61$	−1.89894	−	10.7694i	−0.243134	−	1.37888i	0.581652	−	0.813437i	$-0.302406\pi$
$62$	7.56481	+	6.34763i	0.960732	+	0.806150i
$63$	1.34939	−	2.33721i	0.170007	−	0.294460i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.563183	+	3.19397i	−0.0698542	+	0.396163i
$66$	−0.280105	+	0.485156i	−0.0344786	+	0.0597186i
$67$	1.57261	+	0.572384i	0.192125	+	0.0699279i	0.436291	−	0.899806i	$-0.356292\pi$
$67$	1.57261	+	0.572384i	0.192125	+	0.0699279i	−0.244166	+	0.969734i	$0.578514\pi$
$68$	−3.82524			−0.463878
$69$	−6.81608	−	2.48085i	−0.820560	−	0.298659i
$70$	0.517683	+	2.93592i	0.0618749	+	0.350910i
$71$	−7.70462	+	6.46494i	−0.914370	+	0.767248i	−0.972945	−	0.231035i	$-0.925789\pi$
$71$	−7.70462	+	6.46494i	−0.914370	+	0.767248i	0.0585751	+	0.998283i	$0.481344\pi$
$72$	−1.06246	−	0.891507i	−0.125212	−	0.105065i
$73$	−9.88570			−1.15703			−0.578517	−	0.815671i	$-0.696368\pi$
$73$	−9.88570			−1.15703			−0.578517	+	0.815671i	$0.696368\pi$
$74$	−1.97180	+	5.75430i	−0.229217	+	0.668924i
$75$	−3.36910			−0.389030
$76$	4.55479	+	3.82192i	0.522470	+	0.438404i
$77$	0.657490	−	0.551699i	0.0749279	−	0.0628720i
$78$	−0.466865	−	2.64772i	−0.0528620	−	0.299795i
$79$	−12.5395	−	4.56401i	−1.41081	−	0.513491i	−0.479439	−	0.877575i	$-0.659160\pi$
$79$	−12.5395	−	4.56401i	−1.41081	−	0.513491i	−0.931366	+	0.364084i	$0.881382\pi$
$80$	1.53209			0.171293
$81$	2.73975	+	0.997189i	0.304417	+	0.110799i
$82$	−5.20061	+	9.00771i	−0.574311	+	0.994735i
$83$	0.617999	−	3.50484i	0.0678341	−	0.384707i	−0.931923	−	0.362657i	$-0.881870\pi$
$83$	0.617999	−	3.50484i	0.0678341	−	0.384707i	0.999757	−	0.0220497i	$-0.00701920\pi$
$84$	−1.23568	−	2.14025i	−0.134823	−	0.233521i
$85$	2.93030	−	5.07543i	0.317836	−	0.550508i
$86$	2.94683	+	2.47268i	0.317765	+	0.266636i
$87$	0.603020	+	3.41989i	0.0646505	+	0.366651i
$88$	−0.220544	−	0.381994i	−0.0235101	−	0.0407207i
$89$	11.1543	−	4.05982i	1.18235	−	0.430340i	0.325319	−	0.945604i	$-0.394528\pi$
$89$	11.1543	−	4.05982i	1.18235	−	0.430340i	0.857031	+	0.515264i	$0.172306\pi$
$90$	1.99677	−	0.726763i	0.210478	−	0.0766076i
$91$	−0.715278	+	4.05654i	−0.0749815	+	0.425241i
$92$	4.37500	−	3.67106i	0.456125	−	0.382734i
$93$	9.60779	−	8.06190i	0.996282	−	0.835980i
$94$	1.33472	−	7.56955i	0.137665	−	0.780739i
$95$	−8.56020	+	3.11566i	−0.878258	+	0.319660i
$96$	−1.19347	+	0.434387i	−0.121808	+	0.0443345i
$97$	0.296748	+	0.513983i	0.0301302	+	0.0521871i	0.880697	−	0.473679i	$-0.157074\pi$
$97$	0.296748	+	0.513983i	0.0301302	+	0.0521871i	−0.850567	+	0.525867i	$0.823741\pi$
$98$	−0.558047	−	3.16484i	−0.0563713	−	0.319698i
$99$	−0.468637	−	0.393233i	−0.0470998	−	0.0395214i
$100$	1.32635	−	2.29731i	0.132635	−	0.229731i
$101$	6.61396	+	11.4557i	0.658113	+	1.13989i	0.981104	+	0.193483i	$0.0619785\pi$
$101$	6.61396	+	11.4557i	0.658113	+	1.13989i	−0.322990	+	0.946402i	$0.604688\pi$
$102$	−0.843634	+	4.78448i	−0.0835322	+	0.473734i
$103$	1.57500	−	2.72797i	0.155189	−	0.268795i	−0.777939	−	0.628340i	$-0.783735\pi$
$103$	1.57500	−	2.72797i	0.155189	−	0.268795i	0.933128	+	0.359545i	$0.117068\pi$
$104$	1.98921	+	0.724014i	0.195058	+	0.0709954i
$105$	3.78633			0.369508
$106$	−1.62561	−	0.591673i	−0.157893	−	0.0574684i
$107$	−0.643654	−	3.65035i	−0.0622244	−	0.352892i	−0.999984	−	0.00560785i	$-0.998215\pi$
$107$	−0.643654	−	3.65035i	−0.0622244	−	0.352892i	0.937760	−	0.347284i	$-0.112896\pi$
$108$	−4.26816	+	3.58141i	−0.410704	+	0.344622i
$109$	11.4667	+	9.62169i	1.09831	+	0.921591i	0.997310	−	0.0732954i	$-0.0233516\pi$
$109$	11.4667	+	9.62169i	1.09831	+	0.921591i	0.100999	+	0.994887i	$0.467796\pi$
$110$	0.675787			0.0644337
$111$	6.76243	+	3.73535i	0.641861	+	0.354543i
$112$	1.94585			0.183866
$113$	−15.2648	−	12.8087i	−1.43599	−	1.20494i	−0.942062	−	0.335438i	$-0.891116\pi$
$113$	−15.2648	−	12.8087i	−1.43599	−	1.20494i	−0.493929	−	0.869502i	$-0.664440\pi$
$114$	5.78487	−	4.85408i	0.541802	−	0.454626i
$115$	1.51942	+	8.61706i	0.141687	+	0.803545i
$116$	−2.56934	−	0.935163i	−0.238557	−	0.0868277i
$117$	2.93598			0.271431
$118$	−1.93027	−	0.702561i	−0.177696	−	0.0646759i
$119$	3.72167	−	6.44612i	0.341165	−	0.590915i
$120$	0.337893	−	1.91629i	0.0308453	−	0.174932i
$121$	5.40272	+	9.35779i	0.491156	+	0.850708i
$122$	5.46777	−	9.47046i	0.495029	−	0.857415i
$123$	10.1196	+	8.49135i	0.912454	+	0.765639i
$124$	1.71480	+	9.72514i	0.153994	+	0.873343i
$125$	5.86231	+	10.1538i	0.524341	+	0.908185i
$126$	2.53602	−	0.923035i	0.225927	−	0.0822305i
$127$	−4.60748	+	1.67699i	−0.408848	+	0.148808i	−0.538253	−	0.842783i	$-0.680916\pi$
$127$	−4.60748	+	1.67699i	−0.408848	+	0.148808i	0.129405	+	0.991592i	$0.458693\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	3.74266	−	3.14046i	0.329523	−	0.276502i
$130$	−2.48447	+	2.08472i	−0.217902	+	0.182842i
$131$	0.0536454	−	0.304238i	0.00468702	−	0.0265814i	−0.982375	−	0.186923i	$-0.940148\pi$
$131$	0.0536454	−	0.304238i	0.00468702	−	0.0265814i	0.987062	+	0.160342i	$0.0512596\pi$
$132$	−0.526426	+	0.191603i	−0.0458195	+	0.0166769i
$133$	−10.8720	+	3.95708i	−0.942721	+	0.343123i
$134$	0.836770	+	1.44933i	0.0722859	+	0.125203i
$135$	−1.48232	−	8.40664i	−0.127578	−	0.723528i
$136$	−2.93030	−	2.45881i	−0.251271	−	0.210842i
$137$	10.1508	−	17.5818i	0.867245	−	1.50211i	0.00244359	−	0.999997i	$-0.499222\pi$
$137$	10.1508	−	17.5818i	0.867245	−	1.50211i	0.864801	−	0.502115i	$-0.167444\pi$
$138$	−3.62676	−	6.28174i	−0.308731	−	0.534737i
$139$	−2.28137	+	12.9383i	−0.193503	+	1.09741i	0.721031	+	0.692903i	$0.243668\pi$
$139$	−2.28137	+	12.9383i	−0.193503	+	1.09741i	−0.914534	+	0.404508i	$0.867443\pi$
$140$	−1.49061	+	2.58181i	−0.125979	+	0.218203i
$141$	−9.17339	−	3.33884i	−0.772538	−	0.281181i
$142$	−10.0577			−0.844021
$143$	0.877418	+	0.319354i	0.0733734	+	0.0267057i
$144$	−0.240839	−	1.36587i	−0.0200699	−	0.113822i
$145$	3.20903	−	2.69270i	0.266495	−	0.223616i
$146$	−7.57288	−	6.35440i	−0.626736	−	0.525894i
$147$	−4.08156			−0.336641
$148$	−5.20928	+	3.14060i	−0.428200	+	0.258156i
$149$	−3.98826			−0.326731			−0.163366	−	0.986566i	$-0.552235\pi$
$149$	−3.98826			−0.326731			−0.163366	+	0.986566i	$0.552235\pi$
$150$	−2.58088	−	2.16562i	−0.210728	−	0.176822i
$151$	−15.0525	+	12.6306i	−1.22496	+	1.02786i	−0.226408	+	0.974032i	$0.572698\pi$
$151$	−15.0525	+	12.6306i	−1.22496	+	1.02786i	−0.998550	+	0.0538298i	$0.982857\pi$
$152$	1.03249	+	5.85552i	0.0837457	+	0.474945i
$153$	−4.98541	−	1.81454i	−0.403047	−	0.146697i
$154$	0.858292			0.0691631
$155$	−14.2172	−	5.17464i	−1.14195	−	0.415637i
$156$	1.34428	−	2.32837i	0.107629	−	0.186419i
$157$	1.58561	−	8.99242i	0.126545	−	0.717674i	−0.853833	−	0.520547i	$-0.825728\pi$
$157$	1.58561	−	8.99242i	0.126545	−	0.717674i	0.980378	−	0.197126i	$-0.0631609\pi$
$158$	−6.67213	−	11.5565i	−0.530807	−	0.919384i
$159$	−1.09856	+	1.90277i	−0.0871218	+	0.150899i
$160$	1.17365	+	0.984808i	0.0927850	+	0.0778559i
$161$	1.92976	+	10.9442i	0.152086	+	0.862525i
$162$	1.45779	+	2.52497i	0.114535	+	0.198380i
$163$	1.76208	−	0.641343i	0.138016	−	0.0502339i	−0.272088	−	0.962272i	$-0.587714\pi$
$163$	1.76208	−	0.641343i	0.138016	−	0.0502339i	0.410105	+	0.912038i	$0.365492\pi$
$164$	−9.77394	+	3.55742i	−0.763217	+	0.277788i
$165$	0.149041	−	0.845253i	0.0116028	−	0.0658028i
$166$	2.72628	−	2.28762i	0.211601	−	0.177554i
$167$	3.52918	−	2.96133i	0.273096	−	0.229155i	−0.495945	−	0.868354i	$-0.665178\pi$
$167$	3.52918	−	2.96133i	0.273096	−	0.229155i	0.769041	+	0.639199i	$0.220734\pi$
$168$	0.429146	−	2.43381i	0.0331093	−	0.187772i
$169$	8.00509	−	2.91361i	0.615776	−	0.224124i
$170$	5.50716	−	2.00444i	0.422380	−	0.153734i
$171$	4.12326	+	7.14170i	0.315314	+	0.546140i
$172$	0.667992	+	3.78837i	0.0509339	+	0.288860i
$173$	−11.5656	−	9.70473i	−0.879320	−	0.737837i	0.0867194	−	0.996233i	$-0.472362\pi$
$173$	−11.5656	−	9.70473i	−0.879320	−	0.737837i	−0.966039	+	0.258396i	$0.916806\pi$
$174$	−1.73633	+	3.00740i	−0.131631	+	0.227991i
$175$	2.58088	+	4.47022i	0.195096	+	0.337917i
$176$	0.0765942	−	0.434387i	0.00577351	−	0.0327432i
$177$	−1.30445	+	2.25937i	−0.0980485	+	0.169825i
$178$	11.1543	+	4.05982i	0.836048	+	0.304296i
$179$	20.1143			1.50342			0.751708	−	0.659496i	$-0.229230\pi$
$179$	20.1143			1.50342			0.751708	+	0.659496i	$0.229230\pi$
$180$	1.99677	+	0.726763i	0.148830	+	0.0541697i
$181$	1.61762	+	9.17397i	0.120237	+	0.681896i	0.984024	+	0.178038i	$0.0569751\pi$
$181$	1.61762	+	9.17397i	0.120237	+	0.681896i	−0.863787	+	0.503857i	$0.831914\pi$
$182$	−3.15543	+	2.64772i	−0.233896	+	0.196262i
$183$	−10.6395	−	8.92757i	−0.786492	−	0.659945i
$184$	5.71115			0.421032
$185$	−0.176496	−	9.31766i	−0.0129763	−	0.685048i
$186$	12.5421			0.919630
$187$	−1.29252	−	1.08455i	−0.0945185	−	0.0793105i
$188$	5.88806	−	4.94067i	0.429431	−	0.360335i
$189$	−1.88264	−	10.6770i	−0.136942	−	0.776635i
$190$	−8.56020	−	3.11566i	−0.621022	−	0.226034i
$191$	−10.6491			−0.770541			−0.385271	−	0.922804i	$-0.625892\pi$
$191$	−10.6491			−0.770541			−0.385271	+	0.922804i	$0.625892\pi$
$192$	−1.19347	−	0.434387i	−0.0861312	−	0.0313492i
$193$	−6.12636	+	10.6112i	−0.440985	+	0.763809i	−0.997763	−	0.0668528i	$-0.978704\pi$
$193$	−6.12636	+	10.6112i	−0.440985	+	0.763809i	0.556778	+	0.830662i	$0.312038\pi$
$194$	−0.103060	+	0.584480i	−0.00739925	+	0.0419632i
$195$	2.05956	+	3.56726i	0.147488	+	0.255457i
$196$	1.60683	−	2.78312i	0.114774	−	0.198794i
$197$	12.3511	+	10.3638i	0.879978	+	0.738389i	0.966175	−	0.257889i	$-0.0830269\pi$
$197$	12.3511	+	10.3638i	0.879978	+	0.738389i	−0.0861968	+	0.996278i	$0.527471\pi$
$198$	−0.106231	−	0.602469i	−0.00754954	−	0.0428156i
$199$	0.995370	+	1.72403i	0.0705599	+	0.122213i	0.899147	−	0.437647i	$-0.144188\pi$
$199$	0.995370	+	1.72403i	0.0705599	+	0.122213i	−0.828587	+	0.559860i	$0.810855\pi$
$200$	2.49273	−	0.907278i	0.176262	−	0.0641542i
$201$	1.99732	−	0.726964i	0.140880	−	0.0512761i
$202$	−2.29700	+	13.0270i	−0.161617	+	0.916573i
$203$	4.07567	−	3.41989i	0.286056	−	0.240030i
$204$	−3.72167	+	3.12285i	−0.260569	+	0.218643i
$205$	2.76718	−	15.6935i	0.193269	−	1.09608i
$206$	2.96003	−	1.07736i	0.206235	−	0.0750633i
$207$	7.44332	−	2.70915i	0.517347	−	0.188299i
$208$	1.05844	+	1.83327i	0.0733894	+	0.127114i
$209$	0.455418	+	2.58280i	0.0315019	+	0.178656i
$210$	2.90050	+	2.43381i	0.200153	+	0.167949i
$211$	6.30255	−	10.9163i	0.433885	−	0.751512i	−0.563319	−	0.826240i	$-0.690476\pi$
$211$	6.30255	−	10.9163i	0.433885	−	0.751512i	0.997204	+	0.0747282i	$0.0238089\pi$
$212$	−0.864968	−	1.49817i	−0.0594063	−	0.102895i
$213$	−2.21816	+	12.5798i	−0.151986	+	0.861955i
$214$	1.85333	−	3.21006i	0.126691	−	0.219435i
$215$	−5.53823	−	2.01575i	−0.377704	−	0.137473i
$216$	−5.57169			−0.379106
$217$	−18.0567	−	6.57212i	−1.22577	−	0.446144i
$218$	2.59929	+	14.7413i	0.176046	+	0.998406i
$219$	−9.61804	+	8.07049i	−0.649927	+	0.545353i
$220$	0.517683	+	0.434387i	0.0349022	+	0.0292864i
$221$	8.09755			0.544700
$222$	2.77929	+	7.20825i	0.186534	+	0.483786i
$223$	20.3949			1.36575			0.682873	−	0.730538i	$-0.260730\pi$
$223$	20.3949			1.36575			0.682873	+	0.730538i	$0.260730\pi$
$224$	1.49061	+	1.25077i	0.0995954	+	0.0835705i
$225$	2.81838	−	2.36490i	0.187892	−	0.157660i
$226$	−3.46025	−	19.6240i	−0.230172	−	1.30537i
$227$	7.11595	+	2.58999i	0.472302	+	0.171904i	0.567195	−	0.823584i	$-0.308029\pi$
$227$	7.11595	+	2.58999i	0.472302	+	0.171904i	−0.0948927	+	0.995488i	$0.530251\pi$
$228$	7.55161			0.500117
$229$	0.294030	+	0.107018i	0.0194301	+	0.00707197i	0.351717	−	0.936106i	$-0.385598\pi$
$229$	0.294030	+	0.107018i	0.0194301	+	0.00707197i	−0.332287	+	0.943178i	$0.607820\pi$
$230$	−4.37500	+	7.57772i	−0.288479	+	0.499660i
$231$	0.189291	−	1.07352i	0.0124545	−	0.0706327i
$232$	−1.36712	−	2.36792i	−0.0897557	−	0.155461i
$233$	0.341583	−	0.591640i	0.0223779	−	0.0387596i	−0.854620	−	0.519255i	$-0.826210\pi$
$233$	0.341583	−	0.591640i	0.0223779	−	0.0387596i	0.876997	+	0.480495i	$0.159543\pi$
$234$	2.24909	+	1.88721i	0.147027	+	0.123371i
$235$	2.04490	+	11.5972i	0.133395	+	0.756519i
$236$	−1.02707	−	1.77895i	−0.0668569	−	0.115800i
$237$	−15.9260	+	5.79658i	−1.03450	+	0.376528i
$238$	6.99445	−	2.54577i	0.453383	−	0.165018i
$239$	1.94597	−	11.0361i	0.125874	−	0.713869i	−0.854910	−	0.518776i	$-0.826388\pi$
$239$	1.94597	−	11.0361i	0.125874	−	0.713869i	0.980785	−	0.195093i	$-0.0625009\pi$
$240$	1.49061	−	1.25077i	0.0962183	−	0.0807368i
$241$	−3.96856	+	3.33002i	−0.255638	+	0.214505i	−0.761595	−	0.648053i	$-0.775584\pi$
$241$	−3.96856	+	3.33002i	−0.255638	+	0.214505i	0.505958	+	0.862558i	$0.331139\pi$
$242$	−1.87635	+	10.6413i	−0.120616	+	0.684048i
$243$	−12.2274	+	4.45040i	−0.784386	+	0.285493i
$244$	10.2761	−	3.74018i	0.657857	−	0.239440i
$245$	2.46181	+	4.26398i	0.157279	+	0.272416i
$246$	2.29393	+	13.0095i	0.146255	+	0.829456i
$247$	−9.64191	−	8.09052i	−0.613500	−	0.514788i
$248$	−4.93758	+	8.55214i	−0.313537	+	0.543062i
$249$	−2.26002	−	3.91447i	−0.143223	−	0.248070i
$250$	−2.03596	+	11.5465i	−0.128765	+	0.730265i
$251$	15.2460	−	26.4069i	0.962321	−	1.66679i	0.245675	−	0.969352i	$-0.420991\pi$
$251$	15.2460	−	26.4069i	0.962321	−	1.66679i	0.716646	−	0.697437i	$-0.245676\pi$
$252$	2.53602	+	0.923035i	0.159754	+	0.0581458i
$253$	2.51912			0.158376
$254$	−4.60748	−	1.67699i	−0.289099	−	0.105223i
$255$	−1.29252	−	7.33025i	−0.0809408	−	0.459038i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	4.49488	+	3.77165i	0.280383	+	0.235269i	0.772123	−	0.635473i	$-0.219195\pi$
$257$	4.49488	+	3.77165i	0.280383	+	0.235269i	−0.491741	+	0.870742i	$0.663639\pi$
$258$	4.88570			0.304170
$259$	−0.224162	−	11.8340i	−0.0139287	−	0.735330i
$260$	−3.24324			−0.201137
$261$	−2.90501	−	2.43759i	−0.179815	−	0.150883i
$262$	0.236655	−	0.198577i	0.0146206	−	0.0122681i
$263$	2.83262	+	16.0646i	0.174667	+	0.990586i	0.938528	+	0.345204i	$0.112190\pi$
$263$	2.83262	+	16.0646i	0.174667	+	0.990586i	−0.763861	+	0.645381i	$0.776698\pi$
$264$	−0.526426	−	0.191603i	−0.0323993	−	0.0117924i
$265$	2.65042			0.162814
$266$	−10.8720	−	3.95708i	−0.666605	−	0.242624i
$267$	7.53791	−	13.0560i	0.461312	−	0.799016i
$268$	−0.290607	+	1.64812i	−0.0177517	+	0.100675i
$269$	5.00302	+	8.66548i	0.305039	+	0.528344i	0.977270	−	0.211998i	$-0.0679970\pi$
$269$	5.00302	+	8.66548i	0.305039	+	0.528344i	−0.672231	+	0.740342i	$0.734664\pi$
$270$	4.26816	−	7.39267i	0.259752	−	0.449904i
$271$	−9.47356	−	7.94926i	−0.575478	−	0.482883i	0.307981	−	0.951393i	$-0.400347\pi$
$271$	−9.47356	−	7.94926i	−0.575478	−	0.482883i	−0.883459	+	0.468509i	$0.844791\pi$
$272$	−0.664245	−	3.76712i	−0.0402758	−	0.228415i
$273$	2.61577	+	4.53065i	0.158314	+	0.274208i
$274$	19.0773	−	6.94358i	1.15250	−	0.419477i
$275$	1.09951	−	0.400190i	0.0663031	−	0.0241324i
$276$	1.25956	−	7.14333i	0.0758167	−	0.429978i
$277$	−16.2756	+	13.6568i	−0.977905	+	0.820559i	−0.983772	−	0.179423i	$-0.942577\pi$
$277$	−16.2756	+	13.6568i	−0.977905	+	0.820559i	0.00586739	+	0.999983i	$0.498132\pi$
$278$	−10.0642	+	8.44487i	−0.603611	+	0.506489i
$279$	−2.37833	+	13.4882i	−0.142387	+	0.807515i
$280$	−2.80143	+	1.01964i	−0.167417	+	0.0609349i
$281$	−15.2217	+	5.54025i	−0.908052	+	0.330504i	−0.753475	−	0.657477i	$-0.771624\pi$
$281$	−15.2217	+	5.54025i	−0.908052	+	0.330504i	−0.154577	+	0.987981i	$0.549401\pi$
$282$	−4.88106	−	8.45424i	−0.290663	−	0.503443i
$283$	−0.866198	−	4.91245i	−0.0514901	−	0.292015i	0.948179	−	0.317737i	$-0.102923\pi$
$283$	−0.866198	−	4.91245i	−0.0514901	−	0.292015i	−0.999669	+	0.0257216i	$0.991812\pi$
$284$	−7.70462	−	6.46494i	−0.457185	−	0.383624i
$285$	−5.78487	+	10.0197i	−0.342666	+	0.593515i
$286$	0.466865	+	0.808633i	0.0276063	+	0.0478155i
$287$	3.51450	−	19.9317i	0.207454	−	1.17653i
$288$	0.693469	−	1.20112i	0.0408631	−	0.0707769i
$289$	2.22479	+	0.809758i	0.130870	+	0.0476328i
$290$	4.18909			0.245992
$291$	0.708320	+	0.257807i	0.0415224	+	0.0151129i
$292$	−1.71663	−	9.73551i	−0.100458	−	0.569728i
$293$	4.25093	−	3.56696i	0.248342	−	0.208384i	−0.510116	−	0.860106i	$-0.670397\pi$
$293$	4.25093	−	3.56696i	0.248342	−	0.208384i	0.758458	+	0.651722i	$0.225953\pi$
$294$	−3.12666	−	2.62358i	−0.182350	−	0.153010i
$295$	3.14714			0.183234
$296$	−6.00928	−	0.942621i	−0.349282	−	0.0547888i
$297$	−2.45761			−0.142605
$298$	−3.05519	−	2.56361i	−0.176982	−	0.148506i
$299$	−9.26132	+	7.77117i	−0.535596	+	0.449418i
$300$	−0.585038	−	3.31792i	−0.0337772	−	0.191560i
$301$	−7.03390	−	2.56013i	−0.405427	−	0.147563i
$302$	−19.6497			−1.13071
$303$	15.7871	+	5.74604i	0.906946	+	0.330101i
$304$	−2.97293	+	5.14926i	−0.170509	+	0.295330i
$305$	−2.90934	+	16.4997i	−0.166588	+	0.944770i
$306$	−2.65268	−	4.59458i	−0.151644	−	0.262655i
$307$	−7.58074	+	13.1302i	−0.432656	+	0.749382i	−0.997101	−	0.0760888i	$-0.975757\pi$
$307$	−7.58074	+	13.1302i	−0.432656	+	0.749382i	0.564445	+	0.825470i	$0.309090\pi$
$308$	0.657490	+	0.551699i	0.0374640	+	0.0314360i
$309$	−0.694713	−	3.93991i	−0.0395208	−	0.224134i
$310$	−7.56481	−	13.1026i	−0.429653	−	0.744180i
$311$	−14.2914	+	5.20165i	−0.810392	+	0.294959i	−0.713786	−	0.700364i	$-0.753021\pi$
$311$	−14.2914	+	5.20165i	−0.810392	+	0.294959i	−0.0966062	+	0.995323i	$0.530799\pi$
$312$	2.52643	−	0.919544i	0.143031	−	0.0520589i
$313$	5.06559	−	28.7284i	0.286324	−	1.62382i	−0.414193	−	0.910189i	$-0.635936\pi$
$313$	5.06559	−	28.7284i	0.286324	−	1.62382i	0.700517	−	0.713636i	$-0.252953\pi$
$314$	6.99486	−	5.86939i	0.394743	−	0.331229i
$315$	−3.16741	+	2.65777i	−0.178463	+	0.149749i
$316$	2.31721	−	13.1415i	0.130353	−	0.739269i
$317$	18.0323	−	6.56322i	1.01279	−	0.368627i	0.218289	−	0.975884i	$-0.429952\pi$
$317$	18.0323	−	6.56322i	1.01279	−	0.368627i	0.794505	+	0.607257i	$0.207730\pi$
$318$	−2.06463	+	0.751462i	−0.115778	+	0.0421399i
$319$	−0.603020	−	1.04446i	−0.0337626	−	0.0584786i
$320$	0.266044	+	1.50881i	0.0148723	+	0.0843452i
$321$	−3.60630	−	3.02605i	−0.201284	−	0.168897i
$322$	−5.55652	+	9.62418i	−0.309653	+	0.536335i
$323$	11.3721	+	19.6971i	0.632763	+	1.09598i
$324$	−0.506286	+	2.87129i	−0.0281270	+	0.159516i
$325$	−2.80772	+	4.86312i	−0.155744	+	0.269757i
$326$	1.76208	+	0.641343i	0.0975924	+	0.0355207i
$327$	19.0112			1.05132
$328$	−9.77394	−	3.55742i	−0.539676	−	0.196426i
$329$	2.59716	+	14.7292i	0.143186	+	0.812047i
$330$	0.657490	−	0.551699i	0.0361936	−	0.0303701i
$331$	−6.00049	−	5.03501i	−0.329817	−	0.276749i	0.462808	−	0.886458i	$-0.346842\pi$
$331$	−6.00049	−	5.03501i	−0.329817	−	0.276749i	−0.792625	+	0.609709i	$0.791286\pi$
$332$	3.55891			0.195321
$333$	−8.27902	+	1.62205i	−0.453687	+	0.0888880i
$334$	4.60701			0.252085
$335$	−1.96415	−	1.64812i	−0.107313	−	0.0900461i
$336$	1.89317	−	1.58856i	0.103281	−	0.0866628i
$337$	3.41476	+	19.3661i	0.186014	+	1.05494i	0.924646	+	0.380828i	$0.124361\pi$
$337$	3.41476	+	19.3661i	0.186014	+	1.05494i	−0.738632	+	0.674109i	$0.764528\pi$
$338$	8.00509	+	2.91361i	0.435420	+	0.158480i
$339$	−25.3083			−1.37456
$340$	5.50716	+	2.00444i	0.298668	+	0.108706i
$341$	−2.17791	+	3.77225i	−0.117940	+	0.204279i
$342$	−1.43199	+	8.12125i	−0.0774334	+	0.439147i
$343$	9.93713	+	17.2116i	0.536555	+	0.929340i
$344$	−1.92341	+	3.33144i	−0.103703	+	0.179619i
$345$	8.51309	+	7.14333i	0.458329	+	0.384584i
$346$	−2.62172	−	14.8685i	−0.140944	−	0.799336i
$347$	−10.7822	−	18.6753i	−0.578817	−	1.00254i	−0.995615	−	0.0935416i	$-0.970181\pi$
$347$	−10.7822	−	18.6753i	−0.578817	−	1.00254i	0.416798	−	0.908999i	$-0.363152\pi$
$348$	−3.26323	+	1.18772i	−0.174927	+	0.0636683i
$349$	25.2549	−	9.19201i	1.35186	−	0.492037i	0.438333	−	0.898813i	$-0.355569\pi$
$349$	25.2549	−	9.19201i	1.35186	−	0.492037i	0.913528	+	0.406775i	$0.133347\pi$
$350$	−0.896331	+	5.08335i	−0.0479109	+	0.271716i
$351$	9.03517	−	7.58141i	0.482262	−	0.404666i
$352$	0.337893	−	0.283526i	0.0180098	−	0.0151120i
$353$	−2.28842	+	12.9783i	−0.121800	+	0.690763i	0.861357	+	0.508000i	$0.169615\pi$
$353$	−2.28842	+	12.9783i	−0.121800	+	0.690763i	−0.983157	+	0.182763i	$0.941496\pi$
$354$	−2.45156	+	0.892297i	−0.130299	+	0.0474250i
$355$	14.4800	−	5.27027i	0.768516	−	0.279717i
$356$	5.93506	+	10.2798i	0.314558	+	0.544830i
$357$	−1.64158	−	9.30989i	−0.0868819	−	0.492732i
$358$	15.4085	+	12.9293i	0.814364	+	0.683332i
$359$	−1.69284	+	2.93209i	−0.0893448	+	0.154750i	−0.907234	−	0.420626i	$-0.861811\pi$
$359$	−1.69284	+	2.93209i	−0.0893448	+	0.154750i	0.817890	+	0.575375i	$0.195144\pi$
$360$	1.06246	+	1.84023i	0.0559964	+	0.0969886i
$361$	2.83969	−	16.1047i	0.149457	−	0.847615i
$362$	−4.65774	+	8.06745i	−0.244806	+	0.424016i
$363$	12.8960	+	4.69375i	0.676862	+	0.246358i
$364$	−4.11912			−0.215901
$365$	14.2324	+	5.18016i	0.744956	+	0.271142i
$366$	−2.41177	−	13.6778i	−0.126065	−	0.714952i
$367$	5.05350	−	4.24039i	0.263790	−	0.221347i	−0.501293	−	0.865278i	$-0.667142\pi$
$367$	5.05350	−	4.24039i	0.263790	−	0.221347i	0.765083	+	0.643931i	$0.222698\pi$
$368$	4.37500	+	3.67106i	0.228062	+	0.191367i
$369$	−14.4258			−0.750979
$370$	5.85407	−	7.25119i	0.304339	−	0.376972i
$371$	3.36620			0.174764
$372$	9.60779	+	8.06190i	0.498141	+	0.417990i
$373$	0.809650	−	0.679377i	0.0419221	−	0.0351768i	−0.621586	−	0.783346i	$-0.713511\pi$
$373$	0.809650	−	0.679377i	0.0419221	−	0.0351768i	0.663508	+	0.748169i	$0.269067\pi$
$374$	−0.292991	−	1.66163i	−0.0151502	−	0.0859210i
$375$	13.9930	+	5.09303i	0.722594	+	0.263003i
$376$	7.68632			0.396392
$377$	5.43897	+	1.97962i	0.280121	+	0.101956i
$378$	5.42084	−	9.38917i	0.278818	−	0.482927i
$379$	3.85749	−	21.8769i	0.198146	−	1.12374i	−0.709721	−	0.704482i	$-0.751179\pi$
$379$	3.85749	−	21.8769i	0.198146	−	1.12374i	0.907867	−	0.419258i	$-0.137710\pi$
$380$	−4.55479	−	7.88912i	−0.233656	−	0.404703i
$381$	−3.11368	+	5.39304i	−0.159518	+	0.276294i
$382$	−8.15768	−	6.84510i	−0.417383	−	0.350226i
$383$	1.62312	+	9.20517i	0.0829375	+	0.470362i	0.997783	+	0.0665572i	$0.0212015\pi$
$383$	1.62312	+	9.20517i	0.0829375	+	0.470362i	−0.914845	+	0.403805i	$0.867687\pi$
$384$	−0.635032	−	1.09991i	−0.0324063	−	0.0561294i
$385$	−1.23568	+	0.449750i	−0.0629759	+	0.0229214i
$386$	−11.5138	+	4.19068i	−0.586037	+	0.213300i
$387$	−0.926464	+	5.25424i	−0.0470948	+	0.267088i
$388$	−0.454645	+	0.381492i	−0.0230811	+	0.0193673i
$389$	1.85358	−	1.55534i	0.0939804	−	0.0788589i	−0.594587	−	0.804031i	$-0.702684\pi$
$389$	1.85358	−	1.55534i	0.0939804	−	0.0788589i	0.688567	+	0.725172i	$0.258240\pi$
$390$	−0.715278	+	4.05654i	−0.0362195	+	0.205411i
$391$	20.5290	−	7.47194i	1.03820	−	0.377872i
$392$	3.01986	−	1.09914i	0.152526	−	0.0555149i
$393$	−0.196181	−	0.339796i	−0.00989603	−	0.0171404i
$394$	2.79976	+	15.8782i	0.141050	+	0.799934i
$395$	15.6615	+	13.1415i	0.788014	+	0.661223i
$396$	0.305881	−	0.529802i	0.0153711	−	0.0266235i
$397$	−9.85205	−	17.0643i	−0.494460	−	0.856430i	0.505519	−	0.862815i	$-0.331301\pi$
$397$	−9.85205	−	17.0643i	−0.494460	−	0.856430i	−0.999980	+	0.00638497i	$0.997968\pi$
$398$	−0.345688	+	1.96050i	−0.0173278	+	0.0982707i
$399$	−7.34715	+	12.7256i	−0.367817	+	0.637079i
$400$	2.49273	+	0.907278i	0.124636	+	0.0453639i
$401$	−29.2178			−1.45907			−0.729534	−	0.683944i	$-0.760263\pi$
$401$	−29.2178			−1.45907			−0.729534	+	0.683944i	$0.760263\pi$
$402$	1.99732	+	0.726964i	0.0996172	+	0.0362577i
$403$	−3.63003	−	20.5869i	−0.180824	−	1.02551i
$404$	−10.1332	+	8.50274i	−0.504144	+	0.423027i
$405$	−3.42187	−	2.87129i	−0.170034	−	0.142676i
$406$	5.32041			0.264048
$407$	−2.65062	−	0.415779i	−0.131387	−	0.0206094i
$408$	−4.85829			−0.240521
$409$	−2.89098	−	2.42582i	−0.142950	−	0.119949i	0.568509	−	0.822677i	$-0.307521\pi$
$409$	−2.89098	−	2.42582i	−0.142950	−	0.119949i	−0.711458	+	0.702728i	$0.751965\pi$
$410$	12.2074	−	10.2432i	0.602879	−	0.505875i
$411$	−4.47742	−	25.3927i	−0.220855	−	1.25253i
$412$	2.96003	+	1.07736i	0.145830	+	0.0530778i
$413$	3.99707			0.196683
$414$	7.44332	+	2.70915i	0.365819	+	0.133147i
$415$	−2.72628	+	4.72206i	−0.133828	+	0.231797i
$416$	−0.367592	+	2.08472i	−0.0180227	+	0.102212i
$417$	8.34297	+	14.4504i	0.408557	+	0.707642i
$418$	−1.31132	+	2.27128i	−0.0641389	+	0.111092i
$419$	−27.7696	−	23.3015i	−1.35663	−	1.13835i	−0.977006	−	0.213213i	$-0.931607\pi$
$419$	−27.7696	−	23.3015i	−1.35663	−	1.13835i	−0.379629	−	0.925139i	$-0.623948\pi$
$420$	0.657490	+	3.72881i	0.0320822	+	0.181947i
$421$	−8.08913	−	14.0108i	−0.394240	−	0.682844i	0.598764	−	0.800926i	$-0.295659\pi$
$421$	−8.08913	−	14.0108i	−0.394240	−	0.682844i	−0.993004	+	0.118082i	$0.962325\pi$
$422$	11.8449	−	4.31120i	0.576602	−	0.209866i
$423$	10.0175	−	3.64609i	0.487070	−	0.177279i
$424$	0.300400	−	1.70365i	0.0145887	−	0.0827368i
$425$	7.77322	−	6.52250i	0.377056	−	0.316388i
$426$	−9.78536	+	8.21089i	−0.474102	+	0.397819i
$427$	−3.69505	+	20.9557i	−0.178816	+	1.01412i
$428$	3.48312	−	1.26775i	0.168363	−	0.0612791i
$429$	1.11438	−	0.405600i	0.0538026	−	0.0195826i
$430$	−2.94683	−	5.10406i	−0.142109	−	0.246139i
$431$	3.59966	+	20.4147i	0.173390	+	0.983342i	0.939986	+	0.341213i	$0.110838\pi$
$431$	3.59966	+	20.4147i	0.173390	+	0.983342i	−0.766596	+	0.642129i	$0.778051\pi$
$432$	−4.26816	−	3.58141i	−0.205352	−	0.172311i
$433$	−13.3927	+	23.1968i	−0.643611	+	1.11477i	0.341010	+	0.940060i	$0.389231\pi$
$433$	−13.3927	+	23.1968i	−0.643611	+	1.11477i	−0.984621	+	0.174707i	$0.944102\pi$
$434$	−9.60779	−	16.6412i	−0.461189	−	0.798803i
$435$	0.923880	−	5.23958i	0.0442966	−	0.251219i
$436$	−7.48435	+	12.9633i	−0.358435	+	0.620828i
$437$	−31.9098	−	11.6142i	−1.52645	−	0.555583i
$438$	−12.5555			−0.599923
$439$	7.88952	+	2.87155i	0.376546	+	0.137052i	0.523358	−	0.852113i	$-0.324679\pi$
$439$	7.88952	+	2.87155i	0.376546	+	0.137052i	−0.146812	+	0.989164i	$0.546901\pi$
$440$	0.117349	+	0.665520i	0.00559440	+	0.0317274i
$441$	3.41438	−	2.86501i	0.162590	−	0.136429i
$442$	6.20308	+	5.20500i	0.295050	+	0.247577i
$443$	−19.6599			−0.934068			−0.467034	−	0.884239i	$-0.654677\pi$
$443$	−19.6599			−0.934068			−0.467034	+	0.884239i	$0.654677\pi$
$444$	−2.50431	+	7.30833i	−0.118849	+	0.346838i
$445$	−18.1861			−0.862103
$446$	15.6234	+	13.1096i	0.739790	+	0.620758i
$447$	−3.88028	+	3.25594i	−0.183531	+	0.154001i
$448$	0.337893	+	1.91629i	0.0159640	+	0.0905361i
$449$	25.5337	+	9.29349i	1.20501	+	0.438587i	0.864970	−	0.501824i	$-0.167338\pi$
$449$	25.5337	+	9.29349i	1.20501	+	0.438587i	0.340039	+	0.940411i	$0.389560\pi$
$450$	3.67914			0.173436
$451$	−4.31117	−	1.56914i	−0.203005	−	0.0738878i
$452$	9.96339	−	17.2571i	0.468639	−	0.811706i
$453$	−4.33363	+	24.5772i	−0.203612	+	1.15474i
$454$	3.78632	+	6.55810i	0.177701	+	0.307787i
$455$	3.15543	−	5.46537i	0.147929	−	0.256220i
$456$	5.78487	+	4.85408i	0.270901	+	0.227313i
$457$	−3.46724	−	19.6637i	−0.162191	−	0.919829i	−0.951914	−	0.306366i	$-0.900887\pi$
$457$	−3.46724	−	19.6637i	−0.162191	−	0.919829i	0.789723	−	0.613463i	$-0.210224\pi$
$458$	0.156450	+	0.270980i	0.00731044	+	0.0126621i
$459$	−20.0277	+	7.28949i	−0.934813	+	0.340244i
$460$	−8.22230	+	2.99267i	−0.383367	+	0.139534i
$461$	1.36552	−	7.74427i	0.0635987	−	0.360686i	−0.936355	−	0.351055i	$-0.885823\pi$
$461$	1.36552	−	7.74427i	0.0635987	−	0.360686i	0.999954	−	0.00963149i	$-0.00306585\pi$
$462$	0.835054	−	0.700693i	0.0388502	−	0.0325992i
$463$	−4.62851	+	3.88378i	−0.215105	+	0.180495i	−0.743973	−	0.668209i	$-0.767061\pi$
$463$	−4.62851	+	3.88378i	−0.215105	+	0.180495i	0.528868	+	0.848704i	$0.322617\pi$
$464$	0.474795	−	2.69270i	0.0220418	−	0.125005i
$465$	−18.0567	+	6.57212i	−0.837362	+	0.304775i
$466$	0.641967	−	0.233657i	0.0297385	−	0.0108239i
$467$	−14.6623	−	25.3958i	−0.678489	−	1.17518i	−0.975436	−	0.220283i	$-0.929302\pi$
$467$	−14.6623	−	25.3958i	−0.678489	−	1.17518i	0.296947	−	0.954894i	$-0.404032\pi$
$468$	0.509827	+	2.89137i	0.0235668	+	0.133654i
$469$	−2.49459	−	2.09321i	−0.115190	−	0.0966555i
$470$	−5.88806	+	10.1984i	−0.271596	+	0.470418i
$471$	−5.79857	−	10.0434i	−0.267184	−	0.462776i
$472$	0.356699	−	2.02294i	0.0164184	−	0.0931135i
$473$	−0.848392	+	1.46946i	−0.0390091	+	0.0675658i
$474$	−15.9260	−	5.79658i	−0.731504	−	0.266246i
$475$	−15.7726			−0.723696
$476$	6.99445	+	2.54577i	0.320590	+	0.116685i
$477$	−0.416637	−	2.36286i	−0.0190765	−	0.108188i
$478$	8.58460	−	7.20333i	0.392650	−	0.329473i
$479$	−3.16884	−	2.65897i	−0.144788	−	0.121492i	0.567517	−	0.823362i	$-0.307904\pi$
$479$	−3.16884	−	2.65897i	−0.144788	−	0.121492i	−0.712305	+	0.701870i	$0.752349\pi$
$480$	1.94585			0.0888155
$481$	11.0274	−	6.64826i	0.502806	−	0.303135i
$482$	−5.18059			−0.235969
$483$	10.8122	+	9.07248i	0.491970	+	0.412812i
$484$	−8.27745	+	6.94560i	−0.376248	+	0.315709i
$485$	−0.157896	−	0.895475i	−0.00716971	−	0.0406614i
$486$	−12.2274	−	4.45040i	−0.554645	−	0.201874i
$487$	28.9347			1.31116			0.655579	−	0.755126i	$-0.272425\pi$
$487$	28.9347			1.31116			0.655579	+	0.755126i	$0.272425\pi$
$488$	10.2761	+	3.74018i	0.465175	+	0.169310i
$489$	1.19079	−	2.06251i	0.0538493	−	0.0932697i
$490$	−0.854978	+	4.84882i	−0.0386240	+	0.219047i
$491$	−9.77117	−	16.9242i	−0.440967	−	0.763776i	0.556795	−	0.830650i	$-0.312031\pi$
$491$	−9.77117	−	16.9242i	−0.440967	−	0.763776i	−0.997761	+	0.0668736i	$0.978698\pi$
$492$	−6.60510	+	11.4404i	−0.297781	+	0.515772i
$493$	−8.01213	−	6.72298i	−0.360848	−	0.302788i
$494$	−2.18564	−	12.3954i	−0.0983368	−	0.557696i
$495$	0.468637	+	0.811704i	0.0210637	+	0.0364834i
$496$	−9.27962	+	3.37750i	−0.416667	+	0.151654i
$497$	18.3905	−	6.69358i	0.824925	−	0.300248i
$498$	0.784897	−	4.45137i	0.0351721	−	0.199471i
$499$	−32.3469	+	27.1423i	−1.44805	+	1.21505i	−0.514056	+	0.857757i	$0.671858\pi$
$499$	−32.3469	+	27.1423i	−1.44805	+	1.21505i	−0.933990	+	0.357298i	$0.883698\pi$
$500$	−8.98158	+	7.53644i	−0.401669	+	0.337040i
$501$	1.01605	−	5.76231i	0.0453938	−	0.257441i
$502$	28.6532	−	10.4289i	1.27885	−	0.465465i
$503$	12.5255	−	4.55890i	0.558483	−	0.203271i	−0.0473286	−	0.998879i	$-0.515071\pi$
$503$	12.5255	−	4.55890i	0.558483	−	0.203271i	0.605811	+	0.795608i	$0.292849\pi$
$504$	1.34939	+	2.33721i	0.0601065	+	0.104108i
$505$	−3.51921	−	19.9584i	−0.156603	−	0.888139i
$506$	1.92976	+	1.61926i	0.0857883	+	0.0719849i
$507$	5.40973	−	9.36993i	0.240255	−	0.416133i
$508$	−2.45159	−	4.24628i	−0.108772	−	0.188398i
$509$	4.74665	−	26.9196i	0.210392	−	1.19319i	−0.678335	−	0.734753i	$-0.737298\pi$
$509$	4.74665	−	26.9196i	0.210392	−	1.19319i	0.888727	−	0.458438i	$-0.151591\pi$
$510$	3.72167	−	6.44612i	0.164798	−	0.285439i
$511$	18.0760	+	6.57913i	0.799635	+	0.291043i
$512$	1.00000			0.0441942
$513$	31.1305	+	11.3306i	1.37445	+	0.500258i
$514$	1.01891	+	5.77851i	0.0449420	+	0.254879i
$515$	−3.69698	+	3.10214i	−0.162909	+	0.136697i
$516$	3.74266	+	3.14046i	0.164761	+	0.138251i
$517$	3.39035			0.149107
$518$	7.43504	−	9.20948i	0.326677	−	0.404641i
$519$	−19.1753			−0.841701
$520$	−2.48447	−	2.08472i	−0.108951	−	0.0914208i
$521$	16.9953	−	14.2607i	0.744576	−	0.624773i	−0.189487	−	0.981883i	$-0.560682\pi$
$521$	16.9953	−	14.2607i	0.744576	−	0.624773i	0.934062	+	0.357110i	$0.116238\pi$
$522$	−0.658511	−	3.73460i	−0.0288223	−	0.163459i
$523$	36.0869	+	13.1346i	1.57797	+	0.574335i	0.974762	−	0.223247i	$-0.0716658\pi$
$523$	36.0869	+	13.1346i	1.57797	+	0.574335i	0.603210	+	0.797582i	$0.293888\pi$
$524$	0.308931			0.0134957
$525$	6.16041	+	2.24220i	0.268862	+	0.0978578i
$526$	−8.15621	+	14.1270i	−0.355628	+	0.615965i
$527$	−6.55953	+	37.2009i	−0.285738	+	1.62050i
$528$	−0.280105	−	0.485156i	−0.0121900	−	0.0211137i
$529$	−4.80863	+	8.32879i	−0.209071	+	0.362121i
$530$	2.03034	+	1.70365i	0.0881922	+	0.0740020i
$531$	−0.494720	−	2.80570i	−0.0214690	−	0.121757i
$532$	−5.78487	−	10.0197i	−0.250806	−	0.434408i
$533$	20.6902	−	7.53062i	0.896193	−	0.326187i
$534$	14.1666	−	5.15623i	0.613050	−	0.223132i
$535$	−0.986136	+	5.59265i	−0.0426344	+	0.241792i
$536$	−1.28201	+	1.07573i	−0.0553742	+	0.0464645i
$537$	19.5698	−	16.4210i	0.844497	−	0.708617i
$538$	−1.73753	+	9.85402i	−0.0749103	+	0.424837i
$539$	1.33202	−	0.484817i	0.0573744	−	0.0208826i
$540$	8.02152	−	2.91960i	0.345191	−	0.125639i
$541$	17.7662	+	30.7719i	0.763827	+	1.32299i	0.940865	+	0.338783i	$0.110015\pi$
$541$	17.7662	+	30.7719i	0.763827	+	1.32299i	−0.177038	+	0.984204i	$0.556651\pi$
$542$	−2.14748	−	12.1790i	−0.0922422	−	0.523132i
$543$	9.06327	+	7.60499i	0.388942	+	0.326361i
$544$	1.91262	−	3.31275i	0.0820028	−	0.142033i
$545$	−11.4667	−	19.8609i	−0.491179	−	0.850747i
$546$	−0.908449	+	5.15207i	−0.0388780	+	0.220488i
$547$	−19.9167	+	34.4968i	−0.851579	+	1.47498i	0.0282043	+	0.999602i	$0.491021\pi$
$547$	−19.9167	+	34.4968i	−0.851579	+	1.47498i	−0.879783	+	0.475375i	$0.842312\pi$
$548$	19.0773	+	6.94358i	0.814943	+	0.296615i
$549$	15.1669			0.647309
$550$	1.09951	+	0.400190i	0.0468834	+	0.0170642i
$551$	2.82306	+	16.0104i	0.120266	+	0.682065i
$552$	5.55652	−	4.66248i	0.236501	−	0.198448i
$553$	19.8911	+	16.6906i	0.845854	+	0.709756i
$554$	−21.2463			−0.902667
$555$	−7.77848	−	8.92130i	−0.330178	−	0.378688i
$556$	−13.1379			−0.557170
$557$	−5.98445	−	5.02155i	−0.253569	−	0.212770i	0.507138	−	0.861865i	$-0.330703\pi$
$557$	−5.98445	−	5.02155i	−0.253569	−	0.212770i	−0.760708	+	0.649095i	$0.775148\pi$
$558$	−10.4919	+	8.80378i	−0.444159	+	0.372694i
$559$	−1.41406	−	8.01951i	−0.0598082	−	0.339189i
$560$	−2.80143	−	1.01964i	−0.118382	−	0.0430875i
$561$	−2.14294			−0.0904748
$562$	−15.2217	−	5.54025i	−0.642089	−	0.233701i
$563$	17.5698	−	30.4318i	0.740479	−	1.28255i	−0.211799	−	0.977313i	$-0.567932\pi$
$563$	17.5698	−	30.4318i	0.740479	−	1.28255i	0.952278	−	0.305233i	$-0.0987345\pi$
$564$	1.69517	−	9.61381i	0.0713797	−	0.404814i
$565$	15.2648	+	26.4394i	0.642195	+	1.11231i
$566$	2.49412	−	4.31994i	0.104836	−	0.181581i
$567$	−4.34599	−	3.64672i	−0.182515	−	0.153148i
$568$	−1.74650	−	9.90487i	−0.0732813	−	0.415599i
$569$	13.4402	+	23.2792i	0.563444	+	0.975913i	0.997193	+	0.0748791i	$0.0238571\pi$
$569$	13.4402	+	23.2792i	0.563444	+	0.975913i	−0.433749	+	0.901034i	$0.642810\pi$
$570$	−10.8720	+	3.95708i	−0.455378	+	0.165744i
$571$	−37.5779	+	13.6772i	−1.57259	+	0.572375i	−0.973575	−	0.228366i	$-0.926662\pi$
$571$	−37.5779	+	13.6772i	−1.57259	+	0.572375i	−0.599011	+	0.800741i	$0.704440\pi$
$572$	−0.162140	+	0.919544i	−0.00677943	+	0.0384481i
$573$	−10.3608	+	8.69372i	−0.432827	+	0.363185i
$574$	15.5041	−	13.0095i	0.647130	−	0.543006i
$575$	−2.63077	+	14.9198i	−0.109711	+	0.622200i
$576$	1.30330	−	0.474361i	0.0543040	−	0.0197650i
$577$	−15.5041	+	5.64304i	−0.645445	+	0.234923i	−0.643940	−	0.765076i	$-0.722701\pi$
$577$	−15.5041	+	5.64304i	−0.645445	+	0.234923i	−0.00150512	+	0.999999i	$0.500479\pi$
$578$	1.18379	+	2.05038i	0.0492390	+	0.0852845i
$579$	2.70227	+	15.3253i	0.112302	+	0.636899i
$580$	3.20903	+	2.69270i	0.133248	+	0.111808i
$581$	−3.46255	+	5.99732i	−0.143651	+	0.248811i
$582$	0.376889	+	0.652791i	0.0156226	+	0.0270591i
$583$	0.132503	−	0.751462i	0.00548772	−	0.0311224i
$584$	4.94285	−	8.56126i	0.204536	−	0.354268i
$585$	−4.22690	−	1.53847i	−0.174761	−	0.0636078i
$586$	5.54920			0.229235
$587$	26.0305	+	9.47432i	1.07439	+	0.391047i	0.817818	−	0.575477i	$-0.195184\pi$
$587$	26.0305	+	9.47432i	1.07439	+	0.391047i	0.256575	+	0.966524i	$0.417406\pi$
$588$	−0.708756	−	4.01955i	−0.0292286	−	0.165764i
$589$	44.9792	−	37.7421i	1.85334	−	1.55513i
$590$	2.41085	+	2.02294i	0.0992531	+	0.0832832i
$591$	20.4775			0.842331
$592$	−3.99747	−	4.58478i	−0.164295	−	0.188433i
$593$	−43.2875			−1.77760			−0.888802	−	0.458292i	$-0.848461\pi$
$593$	−43.2875			−1.77760			−0.888802	+	0.458292i	$0.848461\pi$
$594$	−1.88264	−	1.57972i	−0.0772455	−	0.0648167i
$595$	−8.73586	+	7.33025i	−0.358135	+	0.300511i
$596$	−0.692555	−	3.92767i	−0.0283681	−	0.160884i
$597$	2.37589	+	0.864752i	0.0972385	+	0.0353919i
$598$	−12.0898			−0.494389
$599$	−2.17628	−	0.792102i	−0.0889205	−	0.0323644i	0.297177	−	0.954822i	$-0.403955\pi$
$599$	−2.17628	−	0.792102i	−0.0889205	−	0.0323644i	−0.386097	+	0.922458i	$0.626177\pi$
$600$	1.68455	−	2.91773i	0.0687715	−	0.119116i
$601$	2.32161	−	13.1665i	0.0947005	−	0.537073i	−0.900138	−	0.435604i	$-0.856535\pi$
$601$	2.32161	−	13.1665i	0.0947005	−	0.537073i	0.994839	−	0.101469i	$-0.0323542\pi$
$602$	−3.74266	−	6.48248i	−0.152539	−	0.264206i
$603$	−1.16055	+	2.01013i	−0.0472612	+	0.0818588i
$604$	−15.0525	−	12.6306i	−0.612479	−	0.513931i
$605$	−2.87473	−	16.3034i	−0.116874	−	0.662827i
$606$	8.40014	+	14.5495i	0.341233	+	0.591032i
$607$	−33.6174	+	12.2357i	−1.36449	+	0.496633i	−0.917439	−	0.397877i	$-0.869747\pi$
$607$	−33.6174	+	12.2357i	−1.36449	+	0.496633i	−0.447048	+	0.894510i	$0.647525\pi$
$608$	−5.58727	+	2.03360i	−0.226594	+	0.0824734i
$609$	1.17339	−	6.65460i	0.0475480	−	0.269658i
$610$	−12.8345	+	10.7694i	−0.519653	+	0.436041i
$611$	−12.4643	+	10.4588i	−0.504251	+	0.423117i
$612$	0.921267	−	5.22477i	0.0372400	−	0.211199i
$613$	−4.73396	+	1.72302i	−0.191203	+	0.0695921i	−0.435847	−	0.900021i	$-0.643551\pi$
$613$	−4.73396	+	1.72302i	−0.191203	+	0.0695921i	0.244644	+	0.969613i	$0.421329\pi$
$614$	−14.2471	+	5.18553i	−0.574967	+	0.209271i
$615$	−10.1196	−	17.5277i	−0.408062	−	0.706783i
$616$	0.149041	+	0.845253i	0.00600503	+	0.0340562i
$617$	22.8182	+	19.1467i	0.918625	+	0.770818i	0.973740	−	0.227662i	$-0.0731082\pi$
$617$	22.8182	+	19.1467i	0.918625	+	0.770818i	−0.0551152	+	0.998480i	$0.517553\pi$
$618$	2.00035	−	3.46470i	0.0804657	−	0.139371i
$619$	−5.82105	−	10.0823i	−0.233968	−	0.405244i	0.725005	−	0.688744i	$-0.241838\pi$
$619$	−5.82105	−	10.0823i	−0.233968	−	0.405244i	−0.958972	+	0.283500i	$0.908504\pi$
$620$	2.62723	−	14.8998i	0.105512	−	0.598389i
$621$	15.9104	−	27.5576i	0.638462	−	1.10585i
$622$	−14.2914	−	5.20165i	−0.573034	−	0.208567i
$623$	−23.0975			−0.925381
$624$	2.52643	+	0.919544i	0.101138	+	0.0368112i
$625$	−0.816085	−	4.62825i	−0.0326434	−	0.185130i
$626$	22.3467	−	18.7511i	0.893155	−	0.749446i
$627$	2.55164	+	2.14108i	0.101903	+	0.0855064i
$628$	9.13115			0.364372
$629$	−22.8339	+	4.47369i	−0.910446	+	0.178378i
$630$	−4.13476			−0.164733
$631$	25.1488	+	21.1023i	1.00116	+	0.840070i	0.987144	−	0.159832i	$-0.0510952\pi$
$631$	25.1488	+	21.1023i	1.00116	+	0.840070i	0.0140121	+	0.999902i	$0.495540\pi$
$632$	10.2223	−	8.57753i	0.406621	−	0.341196i
$633$	−2.77998	−	15.7661i	−0.110494	−	0.626645i
$634$	18.0323	+	6.56322i	0.716154	+	0.260659i
$635$	7.51211			0.298109
$636$	−2.06463	−	0.751462i	−0.0818678	−	0.0297974i
$637$	−3.40147	+	5.89151i	−0.134771	+	0.233430i
$638$	0.209427	−	1.18772i	0.00829128	−	0.0470222i
$639$	−6.97468	−	12.0805i	−0.275914	−	0.477897i
$640$	−0.766044	+	1.32683i	−0.0302806	+	0.0524475i
$641$	−7.75179	−	6.50452i	−0.306177	−	0.256913i	0.476733	−	0.879048i	$-0.341821\pi$
$641$	−7.75179	−	6.50452i	−0.306177	−	0.256913i	−0.782910	+	0.622135i	$0.786265\pi$
$642$	−0.817482	−	4.63617i	−0.0322634	−	0.182975i
$643$	−9.94109	−	17.2185i	−0.392038	−	0.679030i	0.600680	−	0.799490i	$-0.294897\pi$
$643$	−9.94109	−	17.2185i	−0.392038	−	0.679030i	−0.992718	+	0.120459i	$0.961563\pi$
$644$	−10.4428	+	3.80089i	−0.411506	+	0.149776i
$645$	−7.03390	+	2.56013i	−0.276960	+	0.100805i
$646$	−3.94950	+	22.3987i	−0.155391	+	0.881267i
$647$	−6.83200	+	5.73273i	−0.268594	+	0.225377i	−0.767129	−	0.641492i	$-0.778316\pi$
$647$	−6.83200	+	5.73273i	−0.268594	+	0.225377i	0.498536	+	0.866869i	$0.333871\pi$
$648$	−2.23347	+	1.87410i	−0.0877389	+	0.0736217i
$649$	0.157336	−	0.892297i	0.00617598	−	0.0350257i
$650$	−5.27679	+	1.92059i	−0.206973	+	0.0753319i
$651$	−22.9332	+	8.34701i	−0.898824	+	0.327145i
$652$	0.937581	+	1.62394i	0.0367185	+	0.0635983i
$653$	6.58685	+	37.3559i	0.257763	+	1.46185i	0.788879	+	0.614549i	$0.210662\pi$
$653$	6.58685	+	37.3559i	0.257763	+	1.46185i	−0.531115	+	0.847300i	$0.678227\pi$
$654$	14.5634	+	12.2202i	0.569475	+	0.477846i
$655$	−0.236655	+	0.409899i	−0.00924688	+	0.0160161i
$656$	−5.20061	−	9.00771i	−0.203050	−	0.351692i
$657$	2.38086	−	13.5026i	0.0928864	−	0.526785i
$658$	−7.47821	+	12.9526i	−0.291531	+	0.504947i
$659$	−6.16662	−	2.24447i	−0.240217	−	0.0874320i	0.219106	−	0.975701i	$-0.429686\pi$
$659$	−6.16662	−	2.24447i	−0.240217	−	0.0874320i	−0.459324	+	0.888269i	$0.651908\pi$
$660$	0.858292			0.0334090
$661$	−15.8047	−	5.75246i	−0.614733	−	0.223745i	0.0158397	−	0.999875i	$-0.494958\pi$
$661$	−15.8047	−	5.75246i	−0.614733	−	0.223745i	−0.630573	+	0.776130i	$0.717180\pi$
$662$	−1.36020	−	7.71408i	−0.0528657	−	0.299816i
$663$	7.87831	−	6.61068i	0.305968	−	0.256738i
$664$	2.72628	+	2.28762i	0.105800	+	0.0887770i
$665$	17.7259			0.687379
$666$	−7.38473	−	4.07908i	−0.286152	−	0.158061i
$667$	15.6156			0.604640
$668$	3.52918	+	2.96133i	0.136548	+	0.114577i
$669$	19.8427	−	16.6500i	0.767164	−	0.643727i
$670$	−0.445236	−	2.52506i	−0.0172010	−	0.0975515i
$671$	4.53265	+	1.64975i	0.174981	+	0.0636878i
$672$	2.47135			0.0953345
$673$	7.68493	+	2.79709i	0.296232	+	0.107820i	0.485861	−	0.874036i	$-0.338506\pi$
$673$	7.68493	+	2.79709i	0.296232	+	0.107820i	−0.189629	+	0.981856i	$0.560728\pi$
$674$	−9.83241	+	17.0302i	−0.378730	+	0.655980i
$675$	2.56653	−	14.5555i	0.0987857	−	0.560242i
$676$	4.25942	+	7.37753i	0.163824	+	0.283751i
$677$	−13.2217	+	22.9007i	−0.508152	+	0.880145i	0.491804	+	0.870706i	$0.336338\pi$
$677$	−13.2217	+	22.9007i	−0.508152	+	0.880145i	−0.999955	+	0.00943859i	$0.996996\pi$
$678$	−19.3873	−	16.2678i	−0.744563	−	0.624763i
$679$	−0.200539	−	1.13731i	−0.00769596	−	0.0436460i
$680$	2.93030	+	5.07543i	0.112372	+	0.194634i
$681$	9.03771	−	3.28946i	0.346326	−	0.126052i
$682$	−4.09313	+	1.48978i	−0.156734	+	0.0570466i
$683$	2.15766	−	12.2367i	0.0825604	−	0.468223i	−0.915296	−	0.402782i	$-0.868043\pi$
$683$	2.15766	−	12.2367i	0.0825604	−	0.468223i	0.997856	−	0.0654415i	$-0.0208456\pi$
$684$	−6.31721	+	5.30077i	−0.241544	+	0.202680i
$685$	−23.8270	+	19.9932i	−0.910384	+	0.763903i
$686$	−3.45113	+	19.5723i	−0.131765	+	0.747275i
$687$	0.373437	−	0.135920i	0.0142475	−	0.00518567i
$688$	−3.61482	+	1.31569i	−0.137814	+	0.0501601i
$689$	1.83103	+	3.17144i	0.0697567	+	0.120822i
$690$	1.92976	+	10.9442i	0.0734647	+	0.416639i
$691$	−21.0501	−	17.6632i	−0.800785	−	0.671938i	0.147605	−	0.989046i	$-0.452844\pi$
$691$	−21.0501	−	17.6632i	−0.800785	−	0.671938i	−0.948389	+	0.317108i	$0.897288\pi$
$692$	7.54894	−	13.0751i	0.286968	−	0.497042i
$693$	0.595199	+	1.03092i	0.0226097	+	0.0391612i
$694$	3.74461	−	21.2367i	0.142143	−	0.806135i
$695$	10.0642	−	17.4317i	0.381757	−	0.661222i
$696$	−3.26323	−	1.18772i	−0.123692	−	0.0450203i
$697$	−39.7871			−1.50704
$698$	25.2549	+	9.19201i	0.955910	+	0.347923i
$699$	−0.150668	−	0.854483i	−0.00569881	−	0.0323195i
$700$	−3.95414	+	3.31792i	−0.149452	+	0.125406i
$701$	−15.0052	−	12.5909i	−0.566739	−	0.475551i	0.313823	−	0.949482i	$-0.398390\pi$
$701$	−15.0052	−	12.5909i	−0.566739	−	0.475551i	−0.880562	+	0.473931i	$0.842835\pi$
$702$	11.7946			0.445157
$703$	31.6586	+	17.4872i	1.19403	+	0.659541i
$704$	0.441088			0.0166241
$705$	11.4573	+	9.61381i	0.431506	+	0.362077i
$706$	−10.0953	+	8.47096i	−0.379941	+	0.318809i
$707$	−4.46962	−	25.3485i	−0.168097	−	0.953328i
$708$	−2.45156	−	0.892297i	−0.0921354	−	0.0335346i
$709$	18.8660			0.708528			0.354264	−	0.935145i	$-0.384731\pi$
$709$	18.8660			0.708528			0.354264	+	0.935145i	$0.384731\pi$
$710$	14.4800	+	5.27027i	0.543423	+	0.197790i
$711$	9.25384	−	16.0281i	0.347046	−	0.601102i
$712$	−2.06123	+	11.6898i	−0.0772477	+	0.438093i
$713$	−28.1993	−	48.8426i	−1.05607	−	1.82917i
$714$	4.72675	−	8.18698i	0.176894	−	0.306390i
$715$	−1.09587	−	0.919544i	−0.0409832	−	0.0343890i
$716$	3.49282	+	19.8088i	0.130533	+	0.740288i
$717$	−7.11642	−	12.3260i	−0.265767	−	0.460323i
$718$	−3.18150	+	1.15797i	−0.118733	+	0.0432151i
$719$	−15.2536	+	5.55186i	−0.568863	+	0.207049i	−0.610408	−	0.792087i	$-0.708994\pi$
$719$	−15.2536	+	5.55186i	−0.568863	+	0.207049i	0.0415444	+	0.999137i	$0.486772\pi$
$720$	−0.368987	+	2.09263i	−0.0137513	+	0.0779878i
$721$	−4.69540	+	3.93991i	−0.174866	+	0.146730i
$722$	12.5272	−	10.5116i	0.466215	−	0.391201i
$723$	−1.14255	+	6.47972i	−0.0424919	+	0.240983i
$724$	−8.75370	+	3.18609i	−0.325329	+	0.118410i
$725$	6.81570	−	2.48071i	0.253129	−	0.0921313i
$726$	6.86180	+	11.8850i	0.254665	+	0.441093i
$727$	−2.94600	−	16.7076i	−0.109261	−	0.619650i	−0.989433	−	0.144994i	$-0.953684\pi$
$727$	−2.94600	−	16.7076i	−0.109261	−	0.619650i	0.880172	−	0.474656i	$-0.157427\pi$
$728$	−3.15543	−	2.64772i	−0.116948	−	0.0981311i
$729$	−12.6365	+	21.8870i	−0.468017	+	0.810630i
$730$	7.57288	+	13.1166i	0.280285	+	0.485468i
$731$	−2.55523	+	14.4914i	−0.0945084	+	0.535984i
$732$	6.94442	−	12.0281i	0.256673	−	0.444571i
$733$	31.7060	+	11.5400i	1.17109	+	0.426241i	0.853046	−	0.521835i	$-0.174753\pi$
$733$	31.7060	+	11.5400i	1.17109	+	0.426241i	0.318042	+	0.948077i	$0.396975\pi$
$734$	6.59687			0.243495
$735$	5.87619	+	2.13876i	0.216747	+	0.0788893i
$736$	0.991731	+	5.62439i	0.0365557	+	0.207318i
$737$	−0.565478	+	0.474492i	−0.0208296	+	0.0174782i
$738$	−11.0508	−	9.27275i	−0.406787	−	0.341335i
$739$	15.5694			0.572730			0.286365	−	0.958121i	$-0.407553\pi$
$739$	15.5694			0.572730			0.286365	+	0.958121i	$0.407553\pi$
$740$	9.14546	−	1.79181i	0.336194	−	0.0658682i
$741$	−15.9858			−0.587253
$742$	2.57866	+	2.16375i	0.0946655	+	0.0794338i
$743$	−36.6033	+	30.7138i	−1.34285	+	1.12678i	−0.361961	+	0.932193i	$0.617893\pi$
$743$	−36.6033	+	30.7138i	−1.34285	+	1.12678i	−0.980885	+	0.194588i	$0.937663\pi$
$744$	2.17791	+	12.3515i	0.0798461	+	0.452829i
$745$	5.74187	+	2.08987i	0.210366	+	0.0765669i
$746$	1.05692			0.0386967
$747$	4.63832	+	1.68821i	0.169707	+	0.0617683i
$748$	0.843634	−	1.46122i	0.0308463	−	0.0534274i
$749$	−1.25246	+	7.10303i	−0.0457637	+	0.259539i
$750$	7.44551	+	12.8960i	0.271871	+	0.470895i
$751$	13.6489	−	23.6406i	0.498055	−	0.862657i	−0.501942	−	0.864901i	$-0.667381\pi$
$751$	13.6489	−	23.6406i	0.498055	−	0.862657i	0.999997	+	0.00224411i	$0.000714323\pi$
$752$	5.88806	+	4.94067i	0.214716	+	0.180168i
$753$	−6.72485	−	38.1385i	−0.245067	−	1.38984i
$754$	2.89402	+	5.01258i	0.105394	+	0.182548i
$755$	28.2895	−	10.2965i	1.02956	−	0.374730i
$756$	10.1878	−	3.70807i	0.370528	−	0.134861i
$757$	−8.23710	+	46.7149i	−0.299383	+	1.69788i	0.349453	+	0.936954i	$0.386367\pi$
$757$	−8.23710	+	46.7149i	−0.299383	+	1.69788i	−0.648835	+	0.760929i	$0.724744\pi$
$758$	17.0172	−	14.2791i	0.618092	−	0.518641i
$759$	2.45092	−	2.05656i	0.0889627	−	0.0746486i
$760$	1.58186	−	8.97118i	0.0573801	−	0.325419i
$761$	−8.81599	+	3.20876i	−0.319579	+	0.116317i	−0.496829	−	0.867849i	$-0.665502\pi$
$761$	−8.81599	+	3.20876i	−0.319579	+	0.116317i	0.177249	+	0.984166i	$0.443280\pi$
$762$	−5.85180	+	2.12988i	−0.211988	+	0.0771574i
$763$	−14.5634	−	25.2246i	−0.527231	−	0.913191i
$764$	−1.84920	−	10.4873i	−0.0669015	−	0.379417i
$765$	6.22663	+	5.22477i	0.225124	+	0.188902i
$766$	−4.67359	+	8.09489i	−0.168864	+	0.292480i
$767$	2.17419	+	3.76581i	0.0785054	+	0.135975i
$768$	0.220544	−	1.25077i	0.00795820	−	0.0451332i
$769$	−1.14862	+	1.98947i	−0.0414203	+	0.0717420i	−0.885992	−	0.463700i	$-0.846522\pi$
$769$	−1.14862	+	1.98947i	−0.0414203	+	0.0717420i	0.844572	+	0.535442i	$0.179855\pi$
$770$	−1.23568	−	0.449750i	−0.0445307	−	0.0162078i
$771$	7.45229			0.268388
$772$	−11.5138	−	4.19068i	−0.414391	−	0.150826i
$773$	−3.65406	−	20.7232i	−0.131427	−	0.745361i	−0.977281	−	0.211947i	$-0.932020\pi$
$773$	−3.65406	−	20.7232i	−0.131427	−	0.745361i	0.845854	−	0.533414i	$-0.179091\pi$
$774$	−4.08707	+	3.42946i	−0.146907	+	0.123269i
$775$	−20.0672	−	16.8384i	−0.720835	−	0.604853i
$776$	−0.593497			−0.0213053
$777$	−9.87916	−	11.3306i	−0.354413	−	0.406484i
$778$	2.41968			0.0867497
$779$	47.3753	+	39.7526i	1.69740	+	1.42428i
$780$	−3.15543	+	2.64772i	−0.112983	+	0.0948036i
$781$	−0.770359	−	4.36892i	−0.0275656	−	0.156332i
$782$	20.5290	+	7.47194i	0.734115	+	0.267196i
$783$	−15.2343			−0.544430
$784$	3.01986	+	1.09914i	0.107852	+	0.0392550i
$785$	−6.99486	+	12.1155i	−0.249657	+	0.432419i
$786$	0.0681330	−	0.386402i	0.00243022	−	0.0137825i
$787$	9.94650	+	17.2278i	0.354555	+	0.614106i	0.987042	−	0.160464i	$-0.0512992\pi$
$787$	9.94650	+	17.2278i	0.354555	+	0.614106i	−0.632487	+	0.774571i	$0.717966\pi$
$788$	−8.06159	+	13.9631i	−0.287182	+	0.497414i
$789$	15.8708	+	13.3172i	0.565014	+	0.474103i
$790$	3.55017	+	20.1340i	0.126309	+	0.716336i
$791$	19.3873	+	33.5797i	0.689332	+	1.19396i
$792$	0.574869	−	0.209235i	0.0204271	−	0.00743485i
$793$	−21.7531	+	7.91749i	−0.772476	+	0.281158i
$794$	3.42158	−	19.4048i	0.121427	−	0.688649i
$795$	2.57866	−	2.16375i	0.0914555	−	0.0767403i
$796$	−1.52499	+	1.27962i	−0.0540520	+	0.0453550i
$797$	−3.96311	+	22.4759i	−0.140380	+	0.796137i	0.830580	+	0.556899i	$0.188009\pi$
$797$	−3.96311	+	22.4759i	−0.140380	+	0.796137i	−0.970961	+	0.239238i	$0.923102\pi$
$798$	−13.8081	+	5.02575i	−0.488802	+	0.177909i
$799$	27.6288	−	10.0561i	0.977438	−	0.355758i
$800$	1.32635	+	2.29731i	0.0468936	+	0.0812221i
$801$	2.85879	+	16.2130i	0.101010	+	0.572859i
$802$	−22.3822	−	18.7809i	−0.790341	−	0.663175i
$803$	2.18023	−	3.77627i	0.0769387	−	0.133262i
$804$	1.06275	+	1.84074i	0.0374803	+	0.0649178i
$805$	2.95656	−	16.7675i	0.104205	−	0.590977i
$806$	10.4522	−	18.1038i	0.368165	−	0.637680i
$807$	11.9419	+	4.34650i	0.420375	+	0.153004i
$808$	−13.2279			−0.465356
$809$	−8.00473	−	2.91348i	−0.281431	−	0.102433i	0.197448	−	0.980313i	$-0.436735\pi$
$809$	−8.00473	−	2.91348i	−0.281431	−	0.102433i	−0.478879	+	0.877881i	$0.658957\pi$
$810$	−0.775675	−	4.39907i	−0.0272545	−	0.154568i
$811$	42.0356	−	35.2721i	1.47607	−	1.23857i	0.565807	−	0.824538i	$-0.308565\pi$
$811$	42.0356	−	35.2721i	1.47607	−	1.23857i	0.910263	−	0.414031i	$-0.135880\pi$
$812$	4.07567	+	3.41989i	0.143028	+	0.120015i
$813$	−15.7067			−0.550858
$814$	−1.76324	−	2.02229i	−0.0618015	−	0.0708814i
$815$	−2.87292			−0.100634
$816$	−3.72167	−	3.12285i	−0.130284	−	0.109322i
$817$	17.5214	−	14.7022i	0.612996	−	0.514365i
$818$	−0.655331	−	3.71657i	−0.0229131	−	0.129947i
$819$	−5.36844	−	1.95395i	−0.187588	−	0.0682766i
$820$	15.9356			0.556495
$821$	23.4205	+	8.52435i	0.817380	+	0.297502i	0.716669	−	0.697414i	$-0.245666\pi$
$821$	23.4205	+	8.52435i	0.817380	+	0.297502i	0.100711	+	0.994916i	$0.467888\pi$
$822$	12.8922	−	22.3300i	0.449667	−	0.778847i
$823$	6.03516	−	34.2271i	0.210373	−	1.19308i	−0.678386	−	0.734706i	$-0.737320\pi$
$823$	6.03516	−	34.2271i	0.210373	−	1.19308i	0.888758	−	0.458376i	$-0.151569\pi$
$824$	1.57500	+	2.72797i	0.0548676	+	0.0950335i
$825$	0.743036	−	1.28698i	0.0258692	−	0.0448068i
$826$	3.06193	+	2.56927i	0.106538	+	0.0893962i
$827$	2.07962	+	11.7941i	0.0723156	+	0.410122i	0.999380	+	0.0352192i	$0.0112129\pi$
$827$	2.07962	+	11.7941i	0.0723156	+	0.410122i	−0.927064	+	0.374903i	$0.877676\pi$
$828$	3.96051	+	6.85980i	0.137637	+	0.238395i
$829$	6.74182	−	2.45382i	0.234153	−	0.0852248i	−0.222279	−	0.974983i	$-0.571349\pi$
$829$	6.74182	−	2.45382i	0.234153	−	0.0852248i	0.456432	+	0.889758i	$0.349127\pi$
$830$	−5.12374	+	1.86489i	−0.177848	+	0.0647312i
$831$	−4.68574	+	26.5741i	−0.162546	+	0.921847i
$832$	−1.62162	+	1.36070i	−0.0562196	+	0.0471738i
$833$	9.41701	−	7.90181i	0.326280	−	0.273781i
$834$	−2.89748	+	16.4324i	−0.100332	+	0.569009i
$835$	−6.63268	+	2.41410i	−0.229533	+	0.0835433i
$836$	−2.46448	+	0.896998i	−0.0852359	+	0.0310233i
$837$	27.5107	+	47.6499i	0.950908	+	1.64702i
$838$	−6.29486	−	35.6999i	−0.217452	−	1.23323i
$839$	16.6124	+	13.9395i	0.573525	+	0.481244i	0.882813	−	0.469724i	$-0.155647\pi$
$839$	16.6124	+	13.9395i	0.573525	+	0.481244i	−0.309289	+	0.950968i	$0.600091\pi$
$840$	−1.89317	+	3.27906i	−0.0653205	+	0.113138i
$841$	10.7620	+	18.6403i	0.371103	+	0.642769i
$842$	2.80932	−	15.9325i	0.0968157	−	0.549069i
$843$	−10.2866	+	17.8170i	−0.354291	+	0.613649i
$844$	11.8449	+	4.31120i	0.407719	+	0.148398i
$845$	−13.0516			−0.448989
$846$	10.0175	+	3.64609i	0.344410	+	0.125355i
$847$	−3.65109	−	20.7063i	−0.125453	−	0.711478i
$848$	1.32521	−	1.11198i	0.0455078	−	0.0381856i
$849$	−4.85318	−	4.07230i	−0.166561	−	0.139761i
$850$	10.1472			0.348047
$851$	21.8222	−	27.0302i	0.748054	−	0.926583i
$852$	−12.7739			−0.437626
$853$	−27.4605	−	23.0421i	−0.940231	−	0.788948i	0.0373944	−	0.999301i	$-0.488094\pi$
$853$	−27.4605	−	23.0421i	−0.940231	−	0.788948i	−0.977625	+	0.210353i	$0.932539\pi$
$854$	−16.3006	+	13.6778i	−0.557795	+	0.468046i
$855$	−2.19394	−	12.4425i	−0.0750313	−	0.425524i
$856$	3.48312	+	1.26775i	0.119051	+	0.0433309i
$857$	−16.3281			−0.557757			−0.278879	−	0.960326i	$-0.589963\pi$
$857$	−16.3281			−0.557757			−0.278879	+	0.960326i	$0.589963\pi$
$858$	1.11438	+	0.405600i	0.0380442	+	0.0138470i
$859$	−6.97836	+	12.0869i	−0.238099	+	0.412399i	−0.960169	−	0.279421i	$-0.909857\pi$
$859$	−6.97836	+	12.0869i	−0.238099	+	0.412399i	0.722070	+	0.691820i	$0.243191\pi$
$860$	1.02342	−	5.80412i	0.0348984	−	0.197919i
$861$	−12.8525	−	22.2612i	−0.438013	−	0.758661i
$862$	−10.3648	+	17.9524i	−0.353027	+	0.611461i
$863$	−37.6158	−	31.5634i	−1.28046	−	1.07443i	−0.993181	−	0.116583i	$-0.962806\pi$
$863$	−37.6158	−	31.5634i	−1.28046	−	1.07443i	−0.287276	−	0.957848i	$-0.592750\pi$
$864$	−0.967514	−	5.48704i	−0.0329155	−	0.186673i
$865$	11.5656	+	20.0323i	0.393244	+	0.681118i
$866$	−25.1700	+	9.16113i	−0.855311	+	0.311308i
$867$	2.82563	−	1.02844i	0.0959633	−	0.0349278i
$868$	3.33675	−	18.9237i	0.113257	−	0.642311i
$869$	4.50894	−	3.78345i	0.152955	−	0.128345i
$870$	4.07567	−	3.41989i	0.138178	−	0.115945i
$871$	0.615179	−	3.48885i	0.0208445	−	0.118215i
$872$	−14.0660	+	5.11960i	−0.476334	+	0.173371i
$873$	−0.773502	+	0.281532i	−0.0261791	+	0.00952840i
$874$	−16.9788	−	29.4082i	−0.574317	−	0.994747i
$875$	−3.96167	−	22.4678i	−0.133929	−	0.759549i
$876$	−9.61804	−	8.07049i	−0.324963	−	0.272677i
$877$	−17.0002	+	29.4453i	−0.574057	+	0.994297i	0.422086	+	0.906556i	$0.361298\pi$
$877$	−17.0002	+	29.4453i	−0.574057	+	0.994297i	−0.996143	+	0.0877408i	$0.972035\pi$
$878$	4.19793	+	7.27102i	0.141673	+	0.245385i
$879$	1.22384	−	6.94076i	0.0412792	−	0.234106i
$880$	−0.337893	+	0.585248i	−0.0113904	+	0.0197287i
$881$	−49.9500	−	18.1803i	−1.68286	−	0.612510i	−0.689161	−	0.724609i	$-0.742021\pi$
$881$	−49.9500	−	18.1803i	−1.68286	−	0.612510i	−0.993697	+	0.112098i	$0.964243\pi$
$882$	4.45716			0.150080
$883$	−14.5551	−	5.29763i	−0.489819	−	0.178279i	0.0852904	−	0.996356i	$-0.472818\pi$
$883$	−14.5551	−	5.29763i	−0.489819	−	0.178279i	−0.575109	+	0.818077i	$0.695040\pi$
$884$	1.40612	+	7.97453i	0.0472931	+	0.268212i
$885$	3.06193	−	2.56927i	0.102926	−	0.0863649i
$886$	−15.0603	−	12.6371i	−0.505961	−	0.424552i
$887$	17.6841			0.593774			0.296887	−	0.954913i	$-0.404052\pi$
$887$	17.6841			0.593774			0.296887	+	0.954913i	$0.404052\pi$
$888$	−6.61612	+	3.98876i	−0.222022	+	0.133854i
$889$	9.54086			0.319990
$890$	−13.9313	−	11.6898i	−0.466980	−	0.391843i
$891$	−0.985157	+	0.826645i	−0.0330040	+	0.0276936i
$892$	3.54154	+	20.0851i	0.118580	+	0.672498i
$893$	−42.9456	−	15.6309i	−1.43712	−	0.523068i
$894$	−5.06535			−0.169411
$895$	−28.9585	−	10.5400i	−0.967975	−	0.352314i
$896$	−0.972925	+	1.68516i	−0.0325031	+	0.0562971i
$897$	−2.66633	+	15.1215i	−0.0890263	+	0.504893i
$898$	13.5862	+	23.5320i	0.453377	+	0.785271i
$899$	−13.5005	+	23.3836i	−0.450267	+	0.779886i
$900$	2.81838	+	2.36490i	0.0939461	+	0.0788301i
$901$	−1.14910	−	6.51688i	−0.0382821	−	0.217109i
$902$	−2.29393	−	3.97320i	−0.0763794	−	0.132293i
$903$	−8.93350	+	3.25153i	−0.297288	+	0.108204i
$904$	18.7251	−	6.81536i	0.622786	−	0.226676i
$905$	2.47833	−	14.0553i	0.0823826	−	0.467215i
$906$	−19.1177	+	16.0416i	−0.635143	+	0.532948i
$907$	−27.9435	+	23.4474i	−0.927850	+	0.778558i	−0.975430	−	0.220309i	$-0.929293\pi$
$907$	−27.9435	+	23.4474i	−0.927850	+	0.778558i	0.0475804	+	0.998867i	$0.484849\pi$
$908$	−1.31497	+	7.45759i	−0.0436390	+	0.247489i
$909$	−17.2399	+	6.27481i	−0.571811	+	0.208122i
$910$	5.93027	−	2.15844i	0.196587	−	0.0715516i
$911$	3.84129	+	6.65330i	0.127267	+	0.220434i	0.922617	−	0.385717i	$-0.126046\pi$
$911$	3.84129	+	6.65330i	0.127267	+	0.220434i	−0.795350	+	0.606151i	$0.792713\pi$
$912$	1.31132	+	7.43688i	0.0434222	+	0.246260i
$913$	1.20253	+	1.00904i	0.0397980	+	0.0333945i
$914$	9.98352	−	17.2920i	0.330225	−	0.571967i
$915$	10.6395	+	18.4281i	0.351730	+	0.609214i
$916$	−0.0543346	+	0.308147i	−0.00179527	+	0.0101815i
$917$	−0.300567	+	0.520597i	−0.00992560	+	0.0171916i
$918$	−20.0277	−	7.28949i	−0.661012	−	0.240589i
$919$	−0.166200			−0.00548242			−0.00274121	−	0.999996i	$-0.500873\pi$
$919$	−0.166200			−0.00548242			−0.00274121	+	0.999996i	$0.500873\pi$
$920$	−8.22230	−	2.99267i	−0.271081	−	0.0986655i
$921$	3.34378	+	18.9635i	0.110181	+	0.624869i
$922$	6.02397	−	5.05471i	0.198389	−	0.166468i
$923$	16.3097	+	13.6855i	0.536841	+	0.450463i
$924$	1.09009			0.0358612
$925$	5.23061	−	15.2645i	0.171981	−	0.501892i
$926$	−6.04210			−0.198556
$927$	3.34673	+	2.80824i	0.109921	+	0.0922347i
$928$	2.09455	−	1.75753i	0.0687568	−	0.0576938i
$929$	6.14457	+	34.8476i	0.201597	+	1.14331i	0.902706	+	0.430258i	$0.141577\pi$
$929$	6.14457	+	34.8476i	0.201597	+	1.14331i	−0.701109	+	0.713054i	$0.747311\pi$
$930$	−18.0567	−	6.57212i	−0.592104	−	0.215508i
$931$	−19.1080			−0.626239
$932$	0.641967	+	0.233657i	0.0210283	+	0.00765368i
$933$	−9.65795	+	16.7281i	−0.316187	+	0.547652i
$934$	5.09215	−	28.8790i	0.166620	−	0.944951i
$935$	1.29252	+	2.23871i	0.0422700	+	0.0732137i
$936$	−1.46799	+	2.54263i	−0.0479827	+	0.0831085i
$937$	11.8267	+	9.92376i	0.386361	+	0.324195i	0.815193	−	0.579189i	$-0.196631\pi$
$937$	11.8267	+	9.92376i	0.386361	+	0.324195i	−0.428833	+	0.903384i	$0.641075\pi$
$938$	−0.565478	−	3.20699i	−0.0184635	−	0.104712i
$939$	−18.5249	−	32.0860i	−0.604537	−	1.04709i
$940$	−11.0659	+	4.02767i	−0.360931	+	0.131368i
$941$	21.9764	−	7.99875i	0.716410	−	0.260752i	0.0420089	−	0.999117i	$-0.486624\pi$
$941$	21.9764	−	7.99875i	0.716410	−	0.260752i	0.674401	+	0.738365i	$0.264402\pi$
$942$	2.01382	−	11.4210i	0.0656139	−	0.372115i
$943$	45.5053	−	38.1834i	1.48186	−	1.24342i
$944$	1.57357	−	1.32038i	0.0512153	−	0.0429748i
$945$	−2.88437	+	16.3581i	−0.0938285	+	0.532128i
$946$	−1.59446	+	0.580334i	−0.0518402	+	0.0188683i
$947$	25.1514	−	9.15437i	0.817311	−	0.297477i	0.100671	−	0.994920i	$-0.467901\pi$
$947$	25.1514	−	9.15437i	0.817311	−	0.297477i	0.716640	+	0.697443i	$0.245679\pi$
$948$	−8.47403	−	14.6775i	−0.275224	−	0.476702i
$949$	3.63390	+	20.6089i	0.117961	+	0.668992i
$950$	−12.0825	−	10.1384i	−0.392008	−	0.328934i
$951$	12.1860	−	21.1067i	0.395158	−	0.684433i
$952$	3.72167	+	6.44612i	0.120620	+	0.208920i
$953$	−7.42555	+	42.1124i	−0.240537	+	1.36415i	0.590095	+	0.807334i	$0.299090\pi$
$953$	−7.42555	+	42.1124i	−0.240537	+	1.36415i	−0.830632	+	0.556821i	$0.812021\pi$
$954$	1.19966	−	2.07787i	0.0388404	−	0.0672735i
$955$	15.3314	+	5.58018i	0.496113	+	0.180570i
$956$	11.2064			0.362441
$957$	−1.43937	−	0.523888i	−0.0465283	−	0.0169349i
$958$	−0.718317	−	4.07378i	−0.0232078	−	0.131618i
$959$	−30.2618	+	25.3927i	−0.977206	+	0.819973i
$960$	1.49061	+	1.25077i	0.0481092	+	0.0403684i
$961$	66.5188			2.14577
$962$	12.7209	+	1.99541i	0.410138	+	0.0643347i
$963$	5.14091			0.165663
$964$	−3.96856	−	3.33002i	−0.127819	−	0.107253i
$965$	14.3804	−	12.0666i	0.462921	−	0.388437i
$966$	2.45092	+	13.8998i	0.0788570	+	0.447220i
$967$	3.28122	+	1.19426i	0.105517	+	0.0384050i	0.394239	−	0.919008i	$-0.371008\pi$
$967$	3.28122	+	1.19426i	0.105517	+	0.0384050i	−0.288722	+	0.957413i	$0.593230\pi$
$968$	−10.8054			−0.347300
$969$	27.1446	+	9.87983i	0.872010	+	0.317386i
$970$	0.454645	−	0.787468i	0.0145978	−	0.0252841i
$971$	1.07928	−	6.12087i	0.0346356	−	0.196428i	−0.962580	−	0.270997i	$-0.912647\pi$
$971$	1.07928	−	6.12087i	0.0346356	−	0.196428i	0.997216	+	0.0745684i	$0.0237579\pi$
$972$	−6.50605	−	11.2688i	−0.208682	−	0.361447i
$973$	12.7822	−	22.1394i	0.409778	−	0.709756i
$974$	22.1653	+	18.5989i	0.710222	+	0.595947i
$975$	1.23845	+	7.02362i	0.0396622	+	0.224936i
$976$	5.46777	+	9.47046i	0.175019	+	0.303142i
$977$	0.127278	−	0.0463253i	0.00407198	−	0.00148208i	−0.339983	−	0.940431i	$-0.610421\pi$
$977$	0.127278	−	0.0463253i	0.00407198	−	0.00148208i	0.344055	+	0.938949i	$0.388199\pi$
$978$	2.23795	−	0.814547i	0.0715617	−	0.0260463i
$979$	−0.909183	+	5.15623i	−0.0290576	+	0.164794i
$980$	−3.77171	+	3.16484i	−0.120483	+	0.101097i
$981$	−15.9036	+	13.3447i	−0.507763	+	0.426063i
$982$	3.39349	−	19.2454i	0.108291	−	0.614147i
$983$	1.92791	−	0.701702i	0.0614908	−	0.0223808i	−0.311092	−	0.950380i	$-0.600695\pi$
$983$	1.92791	−	0.701702i	0.0614908	−	0.0223808i	0.372582	+	0.927999i	$0.378472\pi$
$984$	−12.4135	+	4.51815i	−0.395729	+	0.144033i
$985$	−12.3511	−	21.3927i	−0.393538	−	0.681628i
$986$	−1.81620	−	10.3002i	−0.0578397	−	0.328025i
$987$	14.5515	+	12.2101i	0.463179	+	0.388653i
$988$	6.29331	−	10.9003i	0.200217	−	0.346786i
$989$	−10.9849	−	19.0263i	−0.349298	−	0.605002i
$990$	−0.162756	+	0.923035i	−0.00517273	+	0.0293360i
$991$	−8.69906	+	15.0672i	−0.276335	+	0.478626i	−0.970471	−	0.241218i	$-0.922453\pi$
$991$	−8.69906	+	15.0672i	−0.276335	+	0.478626i	0.694136	+	0.719844i	$0.255787\pi$
$992$	−9.27962	−	3.37750i	−0.294628	−	0.107236i
$993$	−9.94851			−0.315707
$994$	18.3905	+	6.69358i	0.583310	+	0.212307i
$995$	−0.529625	−	3.00365i	−0.0167902	−	0.0952222i
$996$	3.46255	−	2.90543i	0.109715	−	0.0920620i
$997$	5.44281	+	4.56706i	0.172376	+	0.144640i	0.724894	−	0.688860i	$-0.241889\pi$
$997$	5.44281	+	4.56706i	0.172376	+	0.144640i	−0.552518	+	0.833501i	$0.686333\pi$
$998$	−42.2259			−1.33664
$999$	−21.2893	+	26.3701i	−0.673563	+	0.834314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.b.71.2	yes	12
3.2	odd	2		666.2.x.g.145.1		12
4.3	odd	2		592.2.bc.d.145.1		12
37.7	even	9		2738.2.a.t.1.4		6
37.12	even	9	inner	74.2.f.b.49.2	✓	12
37.30	even	18		2738.2.a.q.1.4		6
111.86	odd	18		666.2.x.g.271.1		12
148.123	odd	18		592.2.bc.d.49.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.49.2	✓	12	37.12	even	9	inner
74.2.f.b.71.2	yes	12	1.1	even	1	trivial
592.2.bc.d.49.1		12	148.123	odd	18
592.2.bc.d.145.1		12	4.3	odd	2
666.2.x.g.145.1		12	3.2	odd	2
666.2.x.g.271.1		12	111.86	odd	18
2738.2.a.q.1.4		6	37.30	even	18
2738.2.a.t.1.4		6	37.7	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.972925 - 0.816381i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{5} +1.27006 q^{6} +(-1.82850 - 0.665520i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.240839 + 1.36587i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.972925 - 0.816381i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{5} +1.27006 q^{6} +(-1.82850 - 0.665520i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.240839 + 1.36587i) q^{9} +(-0.766044 - 1.32683i) q^{10} +(-0.220544 + 0.381994i) q^{11} +(0.972925 + 0.816381i) q^{12} +(-0.367592 - 2.08472i) q^{13} +(-0.972925 - 1.68516i) q^{14} +(-1.82850 + 0.665520i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.664245 + 3.76712i) q^{17} +(-1.06246 + 0.891507i) q^{18} +(4.55479 - 3.82192i) q^{19} +(0.266044 - 1.50881i) q^{20} +(-2.32231 + 0.845253i) q^{21} +(-0.414488 + 0.150861i) q^{22} +(-2.85558 - 4.94600i) q^{23} +(0.220544 + 1.25077i) q^{24} +(-2.03209 - 1.70513i) q^{25} +(1.05844 - 1.83327i) q^{26} +(2.78585 + 4.82523i) q^{27} +(0.337893 - 1.91629i) q^{28} +(-1.36712 + 2.36792i) q^{29} +(-1.82850 - 0.665520i) q^{30} +9.87516 q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.0972795 + 0.551699i) q^{33} +(-2.93030 + 2.45881i) q^{34} +(2.28374 + 1.91629i) q^{35} -1.38694 q^{36} +(2.18831 + 5.67550i) q^{37} +5.94585 q^{38} +(-2.05956 - 1.72818i) q^{39} +(1.17365 - 0.984808i) q^{40} +(1.80615 + 10.2432i) q^{41} +(-2.32231 - 0.845253i) q^{42} +3.84681 q^{43} +(-0.414488 - 0.150861i) q^{44} +(1.06246 - 1.84023i) q^{45} +(0.991731 - 5.62439i) q^{46} +(-3.84316 - 6.65655i) q^{47} +(-0.635032 + 1.09991i) q^{48} +(-2.46181 - 2.06571i) q^{49} +(-0.460637 - 2.61240i) q^{50} +(2.42915 + 4.20740i) q^{51} +(1.98921 - 0.724014i) q^{52} +(-1.62561 + 0.591673i) q^{53} +(-0.967514 + 5.48704i) q^{54} +(0.517683 - 0.434387i) q^{55} +(1.49061 - 1.25077i) q^{56} +(1.31132 - 7.43688i) q^{57} +(-2.56934 + 0.935163i) q^{58} +(-1.93027 + 0.702561i) q^{59} +(-0.972925 - 1.68516i) q^{60} +(-1.89894 - 10.7694i) q^{61} +(7.56481 + 6.34763i) q^{62} +(1.34939 - 2.33721i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.563183 + 3.19397i) q^{65} +(-0.280105 + 0.485156i) q^{66} +(1.57261 + 0.572384i) q^{67} -3.82524 q^{68} +(-6.81608 - 2.48085i) q^{69} +(0.517683 + 2.93592i) q^{70} +(-7.70462 + 6.46494i) q^{71} +(-1.06246 - 0.891507i) q^{72} -9.88570 q^{73} +(-1.97180 + 5.75430i) q^{74} -3.36910 q^{75} +(4.55479 + 3.82192i) q^{76} +(0.657490 - 0.551699i) q^{77} +(-0.466865 - 2.64772i) q^{78} +(-12.5395 - 4.56401i) q^{79} +1.53209 q^{80} +(2.73975 + 0.997189i) q^{81} +(-5.20061 + 9.00771i) q^{82} +(0.617999 - 3.50484i) q^{83} +(-1.23568 - 2.14025i) q^{84} +(2.93030 - 5.07543i) q^{85} +(2.94683 + 2.47268i) q^{86} +(0.603020 + 3.41989i) q^{87} +(-0.220544 - 0.381994i) q^{88} +(11.1543 - 4.05982i) q^{89} +(1.99677 - 0.726763i) q^{90} +(-0.715278 + 4.05654i) q^{91} +(4.37500 - 3.67106i) q^{92} +(9.60779 - 8.06190i) q^{93} +(1.33472 - 7.56955i) q^{94} +(-8.56020 + 3.11566i) q^{95} +(-1.19347 + 0.434387i) q^{96} +(0.296748 + 0.513983i) q^{97} +(-0.558047 - 3.16484i) q^{98} +(-0.468637 - 0.393233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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