LMFDB - Embedded newform 592.2.bc.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.1
Root			$-2.20976 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	592.49
Dual form			592.2.bc.d.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.972925 - 0.816381i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(1.82850 - 0.665520i) q^{7} +(-0.240839 - 1.36587i) q^{9} +O(q^{10})$	\(q+(-0.972925 - 0.816381i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(1.82850 - 0.665520i) q^{7} +(-0.240839 - 1.36587i) q^{9} +(0.220544 + 0.381994i) q^{11} +(-0.367592 + 2.08472i) q^{13} +(1.82850 + 0.665520i) q^{15} +(-0.664245 - 3.76712i) q^{17} +(-4.55479 - 3.82192i) q^{19} +(-2.32231 - 0.845253i) q^{21} +(2.85558 - 4.94600i) q^{23} +(-2.03209 + 1.70513i) q^{25} +(-2.78585 + 4.82523i) q^{27} +(-1.36712 - 2.36792i) q^{29} -9.87516 q^{31} +(0.0972795 - 0.551699i) q^{33} +(-2.28374 + 1.91629i) q^{35} +(2.18831 - 5.67550i) q^{37} +(2.05956 - 1.72818i) q^{39} +(1.80615 - 10.2432i) q^{41} -3.84681 q^{43} +(1.06246 + 1.84023i) q^{45} +(3.84316 - 6.65655i) q^{47} +(-2.46181 + 2.06571i) q^{49} +(-2.42915 + 4.20740i) q^{51} +(-1.62561 - 0.591673i) q^{53} +(-0.517683 - 0.434387i) q^{55} +(1.31132 + 7.43688i) q^{57} +(1.93027 + 0.702561i) q^{59} +(-1.89894 + 10.7694i) q^{61} +(-1.34939 - 2.33721i) q^{63} +(-0.563183 - 3.19397i) q^{65} +(-1.57261 + 0.572384i) q^{67} +(-6.81608 + 2.48085i) q^{69} +(7.70462 + 6.46494i) q^{71} -9.88570 q^{73} +3.36910 q^{75} +(0.657490 + 0.551699i) q^{77} +(12.5395 - 4.56401i) q^{79} +(2.73975 - 0.997189i) q^{81} +(-0.617999 - 3.50484i) q^{83} +(2.93030 + 5.07543i) q^{85} +(-0.603020 + 3.41989i) q^{87} +(11.1543 + 4.05982i) q^{89} +(0.715278 + 4.05654i) q^{91} +(9.60779 + 8.06190i) q^{93} +(8.56020 + 3.11566i) q^{95} +(0.296748 - 0.513983i) q^{97} +(0.468637 - 0.393233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.972925	−	0.816381i	−0.561719	−	0.471338i	0.317168	−	0.948370i	$-0.397268\pi$
$3$	−0.972925	−	0.816381i	−0.561719	−	0.471338i	−0.878886	+	0.477032i	$0.841713\pi$
$4$		0			0
$5$	−1.43969	+	0.524005i	−0.643850	+	0.234342i	−0.643248	−	0.765658i	$-0.722414\pi$
$5$	−1.43969	+	0.524005i	−0.643850	+	0.234342i	−0.000601695		1.00000i	$0.500192\pi$
$6$		0			0
$7$	1.82850	−	0.665520i	0.691108	−	0.251543i	0.0274987	−	0.999622i	$-0.491246\pi$
$7$	1.82850	−	0.665520i	0.691108	−	0.251543i	0.663610	+	0.748079i	$0.269024\pi$
$8$		0			0
$9$	−0.240839	−	1.36587i	−0.0802798	−	0.455289i
$10$		0			0
$11$	0.220544	+	0.381994i	0.0664966	+	0.115175i	0.897357	−	0.441306i	$-0.145485\pi$
$11$	0.220544	+	0.381994i	0.0664966	+	0.115175i	−0.830860	+	0.556481i	$0.812151\pi$
$12$		0			0
$13$	−0.367592	+	2.08472i	−0.101952	+	0.578196i	0.890443	+	0.455095i	$0.150395\pi$
$13$	−0.367592	+	2.08472i	−0.101952	+	0.578196i	−0.992394	+	0.123100i	$0.960716\pi$
$14$		0			0
$15$	1.82850	+	0.665520i	0.472117	+	0.171837i
$16$		0			0
$17$	−0.664245	−	3.76712i	−0.161103	−	0.913661i	−0.952992	−	0.302996i	$-0.902013\pi$
$17$	−0.664245	−	3.76712i	−0.161103	−	0.913661i	0.791889	−	0.610665i	$-0.209098\pi$
$18$		0			0
$19$	−4.55479	−	3.82192i	−1.04494	−	0.876808i	−0.0523871	−	0.998627i	$-0.516683\pi$
$19$	−4.55479	−	3.82192i	−1.04494	−	0.876808i	−0.992552	+	0.121819i	$0.961127\pi$
$20$		0			0
$21$	−2.32231	−	0.845253i	−0.506770	−	0.184449i
$22$		0			0
$23$	2.85558	−	4.94600i	0.595429	−	1.03131i	−0.398057	−	0.917360i	$-0.630316\pi$
$23$	2.85558	−	4.94600i	0.595429	−	1.03131i	0.993486	−	0.113952i	$-0.0363511\pi$
$24$		0			0
$25$	−2.03209	+	1.70513i	−0.406418	+	0.341025i
$26$		0			0
$27$	−2.78585	+	4.82523i	−0.536136	+	0.928615i
$28$		0			0
$29$	−1.36712	−	2.36792i	−0.253867	−	0.439711i	0.710720	−	0.703475i	$-0.248369\pi$
$29$	−1.36712	−	2.36792i	−0.253867	−	0.439711i	−0.964587	+	0.263764i	$0.915036\pi$
$30$		0			0
$31$	−9.87516			−1.77363			−0.886816	−	0.462123i	$-0.847088\pi$
$31$	−9.87516			−1.77363			−0.886816	+	0.462123i	$0.847088\pi$
$32$		0			0
$33$	0.0972795	−	0.551699i	0.0169342	−	0.0960386i
$34$		0			0
$35$	−2.28374	+	1.91629i	−0.386023	+	0.323912i
$36$		0			0
$37$	2.18831	−	5.67550i	0.359755	−	0.933047i
$37$	2.18831	−	5.67550i	0.359755	−	0.933047i
$38$		0			0
$39$	2.05956	−	1.72818i	0.329794	−	0.276730i
$40$		0			0
$41$	1.80615	−	10.2432i	0.282073	−	1.59972i	−0.433482	−	0.901162i	$-0.642715\pi$
$41$	1.80615	−	10.2432i	0.282073	−	1.59972i	0.715556	−	0.698556i	$-0.246174\pi$
$42$		0			0
$43$	−3.84681			−0.586633			−0.293317	−	0.956015i	$-0.594759\pi$
$43$	−3.84681			−0.586633			−0.293317	+	0.956015i	$0.594759\pi$
$44$		0			0
$45$	1.06246	+	1.84023i	0.158382	+	0.274325i
$46$		0			0
$47$	3.84316	−	6.65655i	0.560582	−	0.970957i	−0.436863	−	0.899528i	$-0.643911\pi$
$47$	3.84316	−	6.65655i	0.560582	−	0.970957i	0.997446	−	0.0714293i	$-0.0227560\pi$
$48$		0			0
$49$	−2.46181	+	2.06571i	−0.351687	+	0.295101i
$50$		0			0
$51$	−2.42915	+	4.20740i	−0.340148	+	0.589154i
$52$		0			0
$53$	−1.62561	−	0.591673i	−0.223295	−	0.0812726i	0.227950	−	0.973673i	$-0.426798\pi$
$53$	−1.62561	−	0.591673i	−0.223295	−	0.0812726i	−0.451245	+	0.892400i	$0.649020\pi$
$54$		0			0
$55$	−0.517683	−	0.434387i	−0.0698043	−	0.0585728i
$56$		0			0
$57$	1.31132	+	7.43688i	0.173689	+	0.985039i
$58$		0			0
$59$	1.93027	+	0.702561i	0.251300	+	0.0914656i	0.464599	−	0.885521i	$-0.346199\pi$
$59$	1.93027	+	0.702561i	0.251300	+	0.0914656i	−0.213299	+	0.976987i	$0.568421\pi$
$60$		0			0
$61$	−1.89894	+	10.7694i	−0.243134	+	1.37888i	0.581652	+	0.813437i	$0.302406\pi$
$61$	−1.89894	+	10.7694i	−0.243134	+	1.37888i	−0.824786	+	0.565444i	$0.808705\pi$
$62$		0			0
$63$	−1.34939	−	2.33721i	−0.170007	−	0.294460i
$64$		0			0
$65$	−0.563183	−	3.19397i	−0.0698542	−	0.396163i
$66$		0			0
$67$	−1.57261	+	0.572384i	−0.192125	+	0.0699279i	−0.436291	−	0.899806i	$-0.643708\pi$
$67$	−1.57261	+	0.572384i	−0.192125	+	0.0699279i	0.244166	+	0.969734i	$0.421486\pi$
$68$		0			0
$69$	−6.81608	+	2.48085i	−0.820560	+	0.298659i
$70$		0			0
$71$	7.70462	+	6.46494i	0.914370	+	0.767248i	0.972945	−	0.231035i	$-0.0742113\pi$
$71$	7.70462	+	6.46494i	0.914370	+	0.767248i	−0.0585751	+	0.998283i	$0.518656\pi$
$72$		0			0
$73$	−9.88570			−1.15703			−0.578517	−	0.815671i	$-0.696368\pi$
$73$	−9.88570			−1.15703			−0.578517	+	0.815671i	$0.696368\pi$
$74$		0			0
$75$	3.36910			0.389030
$76$		0			0
$77$	0.657490	+	0.551699i	0.0749279	+	0.0628720i
$78$		0			0
$79$	12.5395	−	4.56401i	1.41081	−	0.513491i	0.479439	−	0.877575i	$-0.340840\pi$
$79$	12.5395	−	4.56401i	1.41081	−	0.513491i	0.931366	+	0.364084i	$0.118618\pi$
$80$		0			0
$81$	2.73975	−	0.997189i	0.304417	−	0.110799i
$82$		0			0
$83$	−0.617999	−	3.50484i	−0.0678341	−	0.384707i	−0.999757	−	0.0220497i	$-0.992981\pi$
$83$	−0.617999	−	3.50484i	−0.0678341	−	0.384707i	0.931923	−	0.362657i	$-0.118130\pi$
$84$		0			0
$85$	2.93030	+	5.07543i	0.317836	+	0.550508i
$86$		0			0
$87$	−0.603020	+	3.41989i	−0.0646505	+	0.366651i
$88$		0			0
$89$	11.1543	+	4.05982i	1.18235	+	0.430340i	0.857031	−	0.515264i	$-0.172306\pi$
$89$	11.1543	+	4.05982i	1.18235	+	0.430340i	0.325319	+	0.945604i	$0.394528\pi$
$90$		0			0
$91$	0.715278	+	4.05654i	0.0749815	+	0.425241i
$92$		0			0
$93$	9.60779	+	8.06190i	0.996282	+	0.835980i
$94$		0			0
$95$	8.56020	+	3.11566i	0.878258	+	0.319660i
$96$		0			0
$97$	0.296748	−	0.513983i	0.0301302	−	0.0521871i	−0.850567	−	0.525867i	$-0.823741\pi$
$97$	0.296748	−	0.513983i	0.0301302	−	0.0521871i	0.880697	+	0.473679i	$0.157074\pi$
$98$		0			0
$99$	0.468637	−	0.393233i	0.0470998	−	0.0395214i
$100$		0			0
$101$	6.61396	−	11.4557i	0.658113	−	1.13989i	−0.322990	−	0.946402i	$-0.604688\pi$
$101$	6.61396	−	11.4557i	0.658113	−	1.13989i	0.981104	−	0.193483i	$-0.0619785\pi$
$102$		0			0
$103$	−1.57500	−	2.72797i	−0.155189	−	0.268795i	0.777939	−	0.628340i	$-0.216265\pi$
$103$	−1.57500	−	2.72797i	−0.155189	−	0.268795i	−0.933128	+	0.359545i	$0.882932\pi$
$104$		0			0
$105$	3.78633			0.369508
$106$		0			0
$107$	0.643654	−	3.65035i	0.0622244	−	0.352892i	−0.937760	−	0.347284i	$-0.887104\pi$
$107$	0.643654	−	3.65035i	0.0622244	−	0.352892i	0.999984	−	0.00560785i	$-0.00178504\pi$
$108$		0			0
$109$	11.4667	−	9.62169i	1.09831	−	0.921591i	0.100999	−	0.994887i	$-0.467796\pi$
$109$	11.4667	−	9.62169i	1.09831	−	0.921591i	0.997310	+	0.0732954i	$0.0233516\pi$
$110$		0			0
$111$	−6.76243	+	3.73535i	−0.641861	+	0.354543i
$112$		0			0
$113$	−15.2648	+	12.8087i	−1.43599	+	1.20494i	−0.493929	+	0.869502i	$0.664440\pi$
$113$	−15.2648	+	12.8087i	−1.43599	+	1.20494i	−0.942062	+	0.335438i	$0.891116\pi$
$114$		0			0
$115$	−1.51942	+	8.61706i	−0.141687	+	0.803545i
$116$		0			0
$117$	2.93598			0.271431
$118$		0			0
$119$	−3.72167	−	6.44612i	−0.341165	−	0.590915i
$120$		0			0
$121$	5.40272	−	9.35779i	0.491156	−	0.850708i
$122$		0			0
$123$	−10.1196	+	8.49135i	−0.912454	+	0.765639i
$124$		0			0
$125$	5.86231	−	10.1538i	0.524341	−	0.908185i
$126$		0			0
$127$	4.60748	+	1.67699i	0.408848	+	0.148808i	0.538253	−	0.842783i	$-0.319084\pi$
$127$	4.60748	+	1.67699i	0.408848	+	0.148808i	−0.129405	+	0.991592i	$0.541307\pi$
$128$		0			0
$129$	3.74266	+	3.14046i	0.329523	+	0.276502i
$130$		0			0
$131$	−0.0536454	−	0.304238i	−0.00468702	−	0.0265814i	0.982375	−	0.186923i	$-0.0598515\pi$
$131$	−0.0536454	−	0.304238i	−0.00468702	−	0.0265814i	−0.987062	+	0.160342i	$0.948740\pi$
$132$		0			0
$133$	−10.8720	−	3.95708i	−0.942721	−	0.343123i
$134$		0			0
$135$	1.48232	−	8.40664i	0.127578	−	0.723528i
$136$		0			0
$137$	10.1508	+	17.5818i	0.867245	+	1.50211i	0.864801	+	0.502115i	$0.167444\pi$
$137$	10.1508	+	17.5818i	0.867245	+	1.50211i	0.00244359	+	0.999997i	$0.499222\pi$
$138$		0			0
$139$	2.28137	+	12.9383i	0.193503	+	1.09741i	0.914534	+	0.404508i	$0.132557\pi$
$139$	2.28137	+	12.9383i	0.193503	+	1.09741i	−0.721031	+	0.692903i	$0.756332\pi$
$140$		0			0
$141$	−9.17339	+	3.33884i	−0.772538	+	0.281181i
$142$		0			0
$143$	−0.877418	+	0.319354i	−0.0733734	+	0.0267057i
$144$		0			0
$145$	3.20903	+	2.69270i	0.266495	+	0.223616i
$146$		0			0
$147$	4.08156			0.336641
$148$		0			0
$149$	−3.98826			−0.326731			−0.163366	−	0.986566i	$-0.552235\pi$
$149$	−3.98826			−0.326731			−0.163366	+	0.986566i	$0.552235\pi$
$150$		0			0
$151$	15.0525	+	12.6306i	1.22496	+	1.02786i	0.998550	+	0.0538298i	$0.0171428\pi$
$151$	15.0525	+	12.6306i	1.22496	+	1.02786i	0.226408	+	0.974032i	$0.427302\pi$
$152$		0			0
$153$	−4.98541	+	1.81454i	−0.403047	+	0.146697i
$154$		0			0
$155$	14.2172	−	5.17464i	1.14195	−	0.415637i
$156$		0			0
$157$	1.58561	+	8.99242i	0.126545	+	0.717674i	0.980378	+	0.197126i	$0.0631609\pi$
$157$	1.58561	+	8.99242i	0.126545	+	0.717674i	−0.853833	+	0.520547i	$0.825728\pi$
$158$		0			0
$159$	1.09856	+	1.90277i	0.0871218	+	0.150899i
$160$		0			0
$161$	1.92976	−	10.9442i	0.152086	−	0.862525i
$162$		0			0
$163$	−1.76208	−	0.641343i	−0.138016	−	0.0502339i	0.272088	−	0.962272i	$-0.412286\pi$
$163$	−1.76208	−	0.641343i	−0.138016	−	0.0502339i	−0.410105	+	0.912038i	$0.634508\pi$
$164$		0			0
$165$	0.149041	+	0.845253i	0.0116028	+	0.0658028i
$166$		0			0
$167$	−3.52918	−	2.96133i	−0.273096	−	0.229155i	0.495945	−	0.868354i	$-0.334822\pi$
$167$	−3.52918	−	2.96133i	−0.273096	−	0.229155i	−0.769041	+	0.639199i	$0.779266\pi$
$168$		0			0
$169$	8.00509	+	2.91361i	0.615776	+	0.224124i
$170$		0			0
$171$	−4.12326	+	7.14170i	−0.315314	+	0.546140i
$172$		0			0
$173$	−11.5656	+	9.70473i	−0.879320	+	0.737837i	−0.966039	−	0.258396i	$-0.916806\pi$
$173$	−11.5656	+	9.70473i	−0.879320	+	0.737837i	0.0867194	+	0.996233i	$0.472362\pi$
$174$		0			0
$175$	−2.58088	+	4.47022i	−0.195096	+	0.337917i
$176$		0			0
$177$	−1.30445	−	2.25937i	−0.0980485	−	0.169825i
$178$		0			0
$179$	−20.1143			−1.50342			−0.751708	−	0.659496i	$-0.770770\pi$
$179$	−20.1143			−1.50342			−0.751708	+	0.659496i	$0.770770\pi$
$180$		0			0
$181$	1.61762	−	9.17397i	0.120237	−	0.681896i	−0.863787	−	0.503857i	$-0.831914\pi$
$181$	1.61762	−	9.17397i	0.120237	−	0.681896i	0.984024	−	0.178038i	$-0.0569751\pi$
$182$		0			0
$183$	10.6395	−	8.92757i	0.786492	−	0.659945i
$184$		0			0
$185$	−0.176496	+	9.31766i	−0.0129763	+	0.685048i
$186$		0			0
$187$	1.29252	−	1.08455i	0.0945185	−	0.0793105i
$188$		0			0
$189$	−1.88264	+	10.6770i	−0.136942	+	0.776635i
$190$		0			0
$191$	10.6491			0.770541			0.385271	−	0.922804i	$-0.374108\pi$
$191$	10.6491			0.770541			0.385271	+	0.922804i	$0.374108\pi$
$192$		0			0
$193$	−6.12636	−	10.6112i	−0.440985	−	0.763809i	0.556778	−	0.830662i	$-0.312038\pi$
$193$	−6.12636	−	10.6112i	−0.440985	−	0.763809i	−0.997763	+	0.0668528i	$0.978704\pi$
$194$		0			0
$195$	−2.05956	+	3.56726i	−0.147488	+	0.255457i
$196$		0			0
$197$	12.3511	−	10.3638i	0.879978	−	0.738389i	−0.0861968	−	0.996278i	$-0.527471\pi$
$197$	12.3511	−	10.3638i	0.879978	−	0.738389i	0.966175	+	0.257889i	$0.0830269\pi$
$198$		0			0
$199$	−0.995370	+	1.72403i	−0.0705599	+	0.122213i	−0.899147	−	0.437647i	$-0.855812\pi$
$199$	−0.995370	+	1.72403i	−0.0705599	+	0.122213i	0.828587	+	0.559860i	$0.189145\pi$
$200$		0			0
$201$	1.99732	+	0.726964i	0.140880	+	0.0512761i
$202$		0			0
$203$	−4.07567	−	3.41989i	−0.286056	−	0.240030i
$204$		0			0
$205$	2.76718	+	15.6935i	0.193269	+	1.09608i
$206$		0			0
$207$	−7.44332	−	2.70915i	−0.517347	−	0.188299i
$208$		0			0
$209$	0.455418	−	2.58280i	0.0315019	−	0.178656i
$210$		0			0
$211$	−6.30255	−	10.9163i	−0.433885	−	0.751512i	0.563319	−	0.826240i	$-0.309524\pi$
$211$	−6.30255	−	10.9163i	−0.433885	−	0.751512i	−0.997204	+	0.0747282i	$0.976191\pi$
$212$		0			0
$213$	−2.21816	−	12.5798i	−0.151986	−	0.861955i
$214$		0			0
$215$	5.53823	−	2.01575i	0.377704	−	0.137473i
$216$		0			0
$217$	−18.0567	+	6.57212i	−1.22577	+	0.446144i
$218$		0			0
$219$	9.61804	+	8.07049i	0.649927	+	0.545353i
$220$		0			0
$221$	8.09755			0.544700
$222$		0			0
$223$	−20.3949			−1.36575			−0.682873	−	0.730538i	$-0.739270\pi$
$223$	−20.3949			−1.36575			−0.682873	+	0.730538i	$0.739270\pi$
$224$		0			0
$225$	2.81838	+	2.36490i	0.187892	+	0.157660i
$226$		0			0
$227$	−7.11595	+	2.58999i	−0.472302	+	0.171904i	−0.567195	−	0.823584i	$-0.691971\pi$
$227$	−7.11595	+	2.58999i	−0.472302	+	0.171904i	0.0948927	+	0.995488i	$0.469749\pi$
$228$		0			0
$229$	0.294030	−	0.107018i	0.0194301	−	0.00707197i	−0.332287	−	0.943178i	$-0.607820\pi$
$229$	0.294030	−	0.107018i	0.0194301	−	0.00707197i	0.351717	+	0.936106i	$0.385598\pi$
$230$		0			0
$231$	−0.189291	−	1.07352i	−0.0124545	−	0.0706327i
$232$		0			0
$233$	0.341583	+	0.591640i	0.0223779	+	0.0387596i	0.876997	−	0.480495i	$-0.159543\pi$
$233$	0.341583	+	0.591640i	0.0223779	+	0.0387596i	−0.854620	+	0.519255i	$0.826210\pi$
$234$		0			0
$235$	−2.04490	+	11.5972i	−0.133395	+	0.756519i
$236$		0			0
$237$	−15.9260	−	5.79658i	−1.03450	−	0.376528i
$238$		0			0
$239$	−1.94597	−	11.0361i	−0.125874	−	0.713869i	−0.980785	−	0.195093i	$-0.937499\pi$
$239$	−1.94597	−	11.0361i	−0.125874	−	0.713869i	0.854910	−	0.518776i	$-0.173612\pi$
$240$		0			0
$241$	−3.96856	−	3.33002i	−0.255638	−	0.214505i	0.505958	−	0.862558i	$-0.331139\pi$
$241$	−3.96856	−	3.33002i	−0.255638	−	0.214505i	−0.761595	+	0.648053i	$0.775584\pi$
$242$		0			0
$243$	12.2274	+	4.45040i	0.784386	+	0.285493i
$244$		0			0
$245$	2.46181	−	4.26398i	0.157279	−	0.272416i
$246$		0			0
$247$	9.64191	−	8.09052i	0.613500	−	0.514788i
$248$		0			0
$249$	−2.26002	+	3.91447i	−0.143223	+	0.248070i
$250$		0			0
$251$	−15.2460	−	26.4069i	−0.962321	−	1.66679i	−0.716646	−	0.697437i	$-0.754324\pi$
$251$	−15.2460	−	26.4069i	−0.962321	−	1.66679i	−0.245675	−	0.969352i	$-0.579009\pi$
$252$		0			0
$253$	2.51912			0.158376
$254$		0			0
$255$	1.29252	−	7.33025i	0.0809408	−	0.459038i
$256$		0			0
$257$	4.49488	−	3.77165i	0.280383	−	0.235269i	−0.491741	−	0.870742i	$-0.663639\pi$
$257$	4.49488	−	3.77165i	0.280383	−	0.235269i	0.772123	+	0.635473i	$0.219195\pi$
$258$		0			0
$259$	0.224162	−	11.8340i	0.0139287	−	0.735330i
$260$		0			0
$261$	−2.90501	+	2.43759i	−0.179815	+	0.150883i
$262$		0			0
$263$	−2.83262	+	16.0646i	−0.174667	+	0.990586i	0.763861	+	0.645381i	$0.223302\pi$
$263$	−2.83262	+	16.0646i	−0.174667	+	0.990586i	−0.938528	+	0.345204i	$0.887810\pi$
$264$		0			0
$265$	2.65042			0.162814
$266$		0			0
$267$	−7.53791	−	13.0560i	−0.461312	−	0.799016i
$268$		0			0
$269$	5.00302	−	8.66548i	0.305039	−	0.528344i	−0.672231	−	0.740342i	$-0.734664\pi$
$269$	5.00302	−	8.66548i	0.305039	−	0.528344i	0.977270	+	0.211998i	$0.0679970\pi$
$270$		0			0
$271$	9.47356	−	7.94926i	0.575478	−	0.482883i	−0.307981	−	0.951393i	$-0.599653\pi$
$271$	9.47356	−	7.94926i	0.575478	−	0.482883i	0.883459	+	0.468509i	$0.155209\pi$
$272$		0			0
$273$	2.61577	−	4.53065i	0.158314	−	0.274208i
$274$		0			0
$275$	−1.09951	−	0.400190i	−0.0663031	−	0.0241324i
$276$		0			0
$277$	−16.2756	−	13.6568i	−0.977905	−	0.820559i	0.00586739	−	0.999983i	$-0.498132\pi$
$277$	−16.2756	−	13.6568i	−0.977905	−	0.820559i	−0.983772	+	0.179423i	$0.942577\pi$
$278$		0			0
$279$	2.37833	+	13.4882i	0.142387	+	0.807515i
$280$		0			0
$281$	−15.2217	−	5.54025i	−0.908052	−	0.330504i	−0.154577	−	0.987981i	$-0.549401\pi$
$281$	−15.2217	−	5.54025i	−0.908052	−	0.330504i	−0.753475	+	0.657477i	$0.771624\pi$
$282$		0			0
$283$	0.866198	−	4.91245i	0.0514901	−	0.292015i	−0.948179	−	0.317737i	$-0.897077\pi$
$283$	0.866198	−	4.91245i	0.0514901	−	0.292015i	0.999669	+	0.0257216i	$0.00818833\pi$
$284$		0			0
$285$	−5.78487	−	10.0197i	−0.342666	−	0.593515i
$286$		0			0
$287$	−3.51450	−	19.9317i	−0.207454	−	1.17653i
$288$		0			0
$289$	2.22479	−	0.809758i	0.130870	−	0.0476328i
$290$		0			0
$291$	−0.708320	+	0.257807i	−0.0415224	+	0.0151129i
$292$		0			0
$293$	4.25093	+	3.56696i	0.248342	+	0.208384i	0.758458	−	0.651722i	$-0.225953\pi$
$293$	4.25093	+	3.56696i	0.248342	+	0.208384i	−0.510116	+	0.860106i	$0.670397\pi$
$294$		0			0
$295$	−3.14714			−0.183234
$296$		0			0
$297$	−2.45761			−0.142605
$298$		0			0
$299$	9.26132	+	7.77117i	0.535596	+	0.449418i
$300$		0			0
$301$	−7.03390	+	2.56013i	−0.405427	+	0.147563i
$302$		0			0
$303$	−15.7871	+	5.74604i	−0.906946	+	0.330101i
$304$		0			0
$305$	−2.90934	−	16.4997i	−0.166588	−	0.944770i
$306$		0			0
$307$	7.58074	+	13.1302i	0.432656	+	0.749382i	0.997101	−	0.0760888i	$-0.0242432\pi$
$307$	7.58074	+	13.1302i	0.432656	+	0.749382i	−0.564445	+	0.825470i	$0.690910\pi$
$308$		0			0
$309$	−0.694713	+	3.93991i	−0.0395208	+	0.224134i
$310$		0			0
$311$	14.2914	+	5.20165i	0.810392	+	0.294959i	0.713786	−	0.700364i	$-0.246979\pi$
$311$	14.2914	+	5.20165i	0.810392	+	0.294959i	0.0966062	+	0.995323i	$0.469201\pi$
$312$		0			0
$313$	5.06559	+	28.7284i	0.286324	+	1.62382i	0.700517	+	0.713636i	$0.252953\pi$
$313$	5.06559	+	28.7284i	0.286324	+	1.62382i	−0.414193	+	0.910189i	$0.635936\pi$
$314$		0			0
$315$	3.16741	+	2.65777i	0.178463	+	0.149749i
$316$		0			0
$317$	18.0323	+	6.56322i	1.01279	+	0.368627i	0.794505	−	0.607257i	$-0.207730\pi$
$317$	18.0323	+	6.56322i	1.01279	+	0.368627i	0.218289	+	0.975884i	$0.429952\pi$
$318$		0			0
$319$	0.603020	−	1.04446i	0.0337626	−	0.0584786i
$320$		0			0
$321$	−3.60630	+	3.02605i	−0.201284	+	0.168897i
$322$		0			0
$323$	−11.3721	+	19.6971i	−0.632763	+	1.09598i
$324$		0			0
$325$	−2.80772	−	4.86312i	−0.155744	−	0.269757i
$326$		0			0
$327$	−19.0112			−1.05132
$328$		0			0
$329$	2.59716	−	14.7292i	0.143186	−	0.812047i
$330$		0			0
$331$	6.00049	−	5.03501i	0.329817	−	0.276749i	−0.462808	−	0.886458i	$-0.653158\pi$
$331$	6.00049	−	5.03501i	0.329817	−	0.276749i	0.792625	+	0.609709i	$0.208714\pi$
$332$		0			0
$333$	−8.27902	−	1.62205i	−0.453687	−	0.0888880i
$334$		0			0
$335$	1.96415	−	1.64812i	0.107313	−	0.0900461i
$336$		0			0
$337$	3.41476	−	19.3661i	0.186014	−	1.05494i	−0.738632	−	0.674109i	$-0.764528\pi$
$337$	3.41476	−	19.3661i	0.186014	−	1.05494i	0.924646	−	0.380828i	$-0.124361\pi$
$338$		0			0
$339$	25.3083			1.37456
$340$		0			0
$341$	−2.17791	−	3.77225i	−0.117940	−	0.204279i
$342$		0			0
$343$	−9.93713	+	17.2116i	−0.536555	+	0.929340i
$344$		0			0
$345$	8.51309	−	7.14333i	0.458329	−	0.384584i
$346$		0			0
$347$	10.7822	−	18.6753i	0.578817	−	1.00254i	−0.416798	−	0.908999i	$-0.636848\pi$
$347$	10.7822	−	18.6753i	0.578817	−	1.00254i	0.995615	−	0.0935416i	$-0.0298188\pi$
$348$		0			0
$349$	25.2549	+	9.19201i	1.35186	+	0.492037i	0.913528	−	0.406775i	$-0.133347\pi$
$349$	25.2549	+	9.19201i	1.35186	+	0.492037i	0.438333	+	0.898813i	$0.355569\pi$
$350$		0			0
$351$	−9.03517	−	7.58141i	−0.482262	−	0.404666i
$352$		0			0
$353$	−2.28842	−	12.9783i	−0.121800	−	0.690763i	−0.983157	−	0.182763i	$-0.941496\pi$
$353$	−2.28842	−	12.9783i	−0.121800	−	0.690763i	0.861357	−	0.508000i	$-0.169615\pi$
$354$		0			0
$355$	−14.4800	−	5.27027i	−0.768516	−	0.279717i
$356$		0			0
$357$	−1.64158	+	9.30989i	−0.0868819	+	0.492732i
$358$		0			0
$359$	1.69284	+	2.93209i	0.0893448	+	0.154750i	0.907234	−	0.420626i	$-0.138189\pi$
$359$	1.69284	+	2.93209i	0.0893448	+	0.154750i	−0.817890	+	0.575375i	$0.804856\pi$
$360$		0			0
$361$	2.83969	+	16.1047i	0.149457	+	0.847615i
$362$		0			0
$363$	−12.8960	+	4.69375i	−0.676862	+	0.246358i
$364$		0			0
$365$	14.2324	−	5.18016i	0.744956	−	0.271142i
$366$		0			0
$367$	−5.05350	−	4.24039i	−0.263790	−	0.221347i	0.501293	−	0.865278i	$-0.332858\pi$
$367$	−5.05350	−	4.24039i	−0.263790	−	0.221347i	−0.765083	+	0.643931i	$0.777302\pi$
$368$		0			0
$369$	−14.4258			−0.750979
$370$		0			0
$371$	−3.36620			−0.174764
$372$		0			0
$373$	0.809650	+	0.679377i	0.0419221	+	0.0351768i	0.663508	−	0.748169i	$-0.269067\pi$
$373$	0.809650	+	0.679377i	0.0419221	+	0.0351768i	−0.621586	+	0.783346i	$0.713511\pi$
$374$		0			0
$375$	−13.9930	+	5.09303i	−0.722594	+	0.263003i
$376$		0			0
$377$	5.43897	−	1.97962i	0.280121	−	0.101956i
$378$		0			0
$379$	−3.85749	−	21.8769i	−0.198146	−	1.12374i	−0.907867	−	0.419258i	$-0.862290\pi$
$379$	−3.85749	−	21.8769i	−0.198146	−	1.12374i	0.709721	−	0.704482i	$-0.248821\pi$
$380$		0			0
$381$	−3.11368	−	5.39304i	−0.159518	−	0.276294i
$382$		0			0
$383$	−1.62312	+	9.20517i	−0.0829375	+	0.470362i	0.914845	+	0.403805i	$0.132313\pi$
$383$	−1.62312	+	9.20517i	−0.0829375	+	0.470362i	−0.997783	+	0.0665572i	$0.978799\pi$
$384$		0			0
$385$	−1.23568	−	0.449750i	−0.0629759	−	0.0229214i
$386$		0			0
$387$	0.926464	+	5.25424i	0.0470948	+	0.267088i
$388$		0			0
$389$	1.85358	+	1.55534i	0.0939804	+	0.0788589i	0.688567	−	0.725172i	$-0.258240\pi$
$389$	1.85358	+	1.55534i	0.0939804	+	0.0788589i	−0.594587	+	0.804031i	$0.702684\pi$
$390$		0			0
$391$	−20.5290	−	7.47194i	−1.03820	−	0.377872i
$392$		0			0
$393$	−0.196181	+	0.339796i	−0.00989603	+	0.0171404i
$394$		0			0
$395$	−15.6615	+	13.1415i	−0.788014	+	0.661223i
$396$		0			0
$397$	−9.85205	+	17.0643i	−0.494460	+	0.856430i	−0.999980	−	0.00638497i	$-0.997968\pi$
$397$	−9.85205	+	17.0643i	−0.494460	+	0.856430i	0.505519	+	0.862815i	$0.331301\pi$
$398$		0			0
$399$	7.34715	+	12.7256i	0.367817	+	0.637079i
$400$		0			0
$401$	−29.2178			−1.45907			−0.729534	−	0.683944i	$-0.760263\pi$
$401$	−29.2178			−1.45907			−0.729534	+	0.683944i	$0.760263\pi$
$402$		0			0
$403$	3.63003	−	20.5869i	0.180824	−	1.02551i
$404$		0			0
$405$	−3.42187	+	2.87129i	−0.170034	+	0.142676i
$406$		0			0
$407$	2.65062	−	0.415779i	0.131387	−	0.0206094i
$408$		0			0
$409$	−2.89098	+	2.42582i	−0.142950	+	0.119949i	−0.711458	−	0.702728i	$-0.751965\pi$
$409$	−2.89098	+	2.42582i	−0.142950	+	0.119949i	0.568509	+	0.822677i	$0.307521\pi$
$410$		0			0
$411$	4.47742	−	25.3927i	0.220855	−	1.25253i
$412$		0			0
$413$	3.99707			0.196683
$414$		0			0
$415$	2.72628	+	4.72206i	0.133828	+	0.231797i
$416$		0			0
$417$	8.34297	−	14.4504i	0.408557	−	0.707642i
$418$		0			0
$419$	27.7696	−	23.3015i	1.35663	−	1.13835i	0.379629	−	0.925139i	$-0.376052\pi$
$419$	27.7696	−	23.3015i	1.35663	−	1.13835i	0.977006	−	0.213213i	$-0.0683927\pi$
$420$		0			0
$421$	−8.08913	+	14.0108i	−0.394240	+	0.682844i	−0.993004	−	0.118082i	$-0.962325\pi$
$421$	−8.08913	+	14.0108i	−0.394240	+	0.682844i	0.598764	+	0.800926i	$0.295659\pi$
$422$		0			0
$423$	−10.0175	−	3.64609i	−0.487070	−	0.177279i
$424$		0			0
$425$	7.77322	+	6.52250i	0.377056	+	0.316388i
$426$		0			0
$427$	3.69505	+	20.9557i	0.178816	+	1.01412i
$428$		0			0
$429$	1.11438	+	0.405600i	0.0538026	+	0.0195826i
$430$		0			0
$431$	−3.59966	+	20.4147i	−0.173390	+	0.983342i	0.766596	+	0.642129i	$0.221949\pi$
$431$	−3.59966	+	20.4147i	−0.173390	+	0.983342i	−0.939986	+	0.341213i	$0.889162\pi$
$432$		0			0
$433$	−13.3927	−	23.1968i	−0.643611	−	1.11477i	−0.984621	−	0.174707i	$-0.944102\pi$
$433$	−13.3927	−	23.1968i	−0.643611	−	1.11477i	0.341010	−	0.940060i	$-0.389231\pi$
$434$		0			0
$435$	−0.923880	−	5.23958i	−0.0442966	−	0.251219i
$436$		0			0
$437$	−31.9098	+	11.6142i	−1.52645	+	0.555583i
$438$		0			0
$439$	−7.88952	+	2.87155i	−0.376546	+	0.137052i	−0.523358	−	0.852113i	$-0.675321\pi$
$439$	−7.88952	+	2.87155i	−0.376546	+	0.137052i	0.146812	+	0.989164i	$0.453099\pi$
$440$		0			0
$441$	3.41438	+	2.86501i	0.162590	+	0.136429i
$442$		0			0
$443$	19.6599			0.934068			0.467034	−	0.884239i	$-0.345323\pi$
$443$	19.6599			0.934068			0.467034	+	0.884239i	$0.345323\pi$
$444$		0			0
$445$	−18.1861			−0.862103
$446$		0			0
$447$	3.88028	+	3.25594i	0.183531	+	0.154001i
$448$		0			0
$449$	25.5337	−	9.29349i	1.20501	−	0.438587i	0.340039	−	0.940411i	$-0.389560\pi$
$449$	25.5337	−	9.29349i	1.20501	−	0.438587i	0.864970	+	0.501824i	$0.167338\pi$
$450$		0			0
$451$	4.31117	−	1.56914i	0.203005	−	0.0738878i
$452$		0			0
$453$	−4.33363	−	24.5772i	−0.203612	−	1.15474i
$454$		0			0
$455$	−3.15543	−	5.46537i	−0.147929	−	0.256220i
$456$		0			0
$457$	−3.46724	+	19.6637i	−0.162191	+	0.919829i	0.789723	+	0.613463i	$0.210224\pi$
$457$	−3.46724	+	19.6637i	−0.162191	+	0.919829i	−0.951914	+	0.306366i	$0.900887\pi$
$458$		0			0
$459$	20.0277	+	7.28949i	0.934813	+	0.340244i
$460$		0			0
$461$	1.36552	+	7.74427i	0.0635987	+	0.360686i	0.999954	+	0.00963149i	$0.00306585\pi$
$461$	1.36552	+	7.74427i	0.0635987	+	0.360686i	−0.936355	+	0.351055i	$0.885823\pi$
$462$		0			0
$463$	4.62851	+	3.88378i	0.215105	+	0.180495i	0.743973	−	0.668209i	$-0.232939\pi$
$463$	4.62851	+	3.88378i	0.215105	+	0.180495i	−0.528868	+	0.848704i	$0.677383\pi$
$464$		0			0
$465$	−18.0567	−	6.57212i	−0.837362	−	0.304775i
$466$		0			0
$467$	14.6623	−	25.3958i	0.678489	−	1.17518i	−0.296947	−	0.954894i	$-0.595968\pi$
$467$	14.6623	−	25.3958i	0.678489	−	1.17518i	0.975436	−	0.220283i	$-0.0706982\pi$
$468$		0			0
$469$	−2.49459	+	2.09321i	−0.115190	+	0.0966555i
$470$		0			0
$471$	5.79857	−	10.0434i	0.267184	−	0.462776i
$472$		0			0
$473$	−0.848392	−	1.46946i	−0.0390091	−	0.0675658i
$474$		0			0
$475$	15.7726			0.723696
$476$		0			0
$477$	−0.416637	+	2.36286i	−0.0190765	+	0.108188i
$478$		0			0
$479$	3.16884	−	2.65897i	0.144788	−	0.121492i	−0.567517	−	0.823362i	$-0.692096\pi$
$479$	3.16884	−	2.65897i	0.144788	−	0.121492i	0.712305	+	0.701870i	$0.247651\pi$
$480$		0			0
$481$	11.0274	+	6.64826i	0.502806	+	0.303135i
$482$		0			0
$483$	−10.8122	+	9.07248i	−0.491970	+	0.412812i
$484$		0			0
$485$	−0.157896	+	0.895475i	−0.00716971	+	0.0406614i
$486$		0			0
$487$	−28.9347			−1.31116			−0.655579	−	0.755126i	$-0.727575\pi$
$487$	−28.9347			−1.31116			−0.655579	+	0.755126i	$0.727575\pi$
$488$		0			0
$489$	1.19079	+	2.06251i	0.0538493	+	0.0932697i
$490$		0			0
$491$	9.77117	−	16.9242i	0.440967	−	0.763776i	−0.556795	−	0.830650i	$-0.687969\pi$
$491$	9.77117	−	16.9242i	0.440967	−	0.763776i	0.997761	+	0.0668736i	$0.0213024\pi$
$492$		0			0
$493$	−8.01213	+	6.72298i	−0.360848	+	0.302788i
$494$		0			0
$495$	−0.468637	+	0.811704i	−0.0210637	+	0.0364834i
$496$		0			0
$497$	18.3905	+	6.69358i	0.824925	+	0.300248i
$498$		0			0
$499$	32.3469	+	27.1423i	1.44805	+	1.21505i	0.933990	+	0.357298i	$0.116302\pi$
$499$	32.3469	+	27.1423i	1.44805	+	1.21505i	0.514056	+	0.857757i	$0.328142\pi$
$500$		0			0
$501$	1.01605	+	5.76231i	0.0453938	+	0.257441i
$502$		0			0
$503$	−12.5255	−	4.55890i	−0.558483	−	0.203271i	0.0473286	−	0.998879i	$-0.484929\pi$
$503$	−12.5255	−	4.55890i	−0.558483	−	0.203271i	−0.605811	+	0.795608i	$0.707151\pi$
$504$		0			0
$505$	−3.51921	+	19.9584i	−0.156603	+	0.888139i
$506$		0			0
$507$	−5.40973	−	9.36993i	−0.240255	−	0.416133i
$508$		0			0
$509$	4.74665	+	26.9196i	0.210392	+	1.19319i	0.888727	+	0.458438i	$0.151591\pi$
$509$	4.74665	+	26.9196i	0.210392	+	1.19319i	−0.678335	+	0.734753i	$0.737298\pi$
$510$		0			0
$511$	−18.0760	+	6.57913i	−0.799635	+	0.291043i
$512$		0			0
$513$	31.1305	−	11.3306i	1.37445	−	0.500258i
$514$		0			0
$515$	3.69698	+	3.10214i	0.162909	+	0.136697i
$516$		0			0
$517$	3.39035			0.149107
$518$		0			0
$519$	19.1753			0.841701
$520$		0			0
$521$	16.9953	+	14.2607i	0.744576	+	0.624773i	0.934062	−	0.357110i	$-0.116238\pi$
$521$	16.9953	+	14.2607i	0.744576	+	0.624773i	−0.189487	+	0.981883i	$0.560682\pi$
$522$		0			0
$523$	−36.0869	+	13.1346i	−1.57797	+	0.574335i	−0.974762	−	0.223247i	$-0.928334\pi$
$523$	−36.0869	+	13.1346i	−1.57797	+	0.574335i	−0.603210	+	0.797582i	$0.706112\pi$
$524$		0			0
$525$	6.16041	−	2.24220i	0.268862	−	0.0978578i
$526$		0			0
$527$	6.55953	+	37.2009i	0.285738	+	1.62050i
$528$		0			0
$529$	−4.80863	−	8.32879i	−0.209071	−	0.362121i
$530$		0			0
$531$	0.494720	−	2.80570i	0.0214690	−	0.121757i
$532$		0			0
$533$	20.6902	+	7.53062i	0.896193	+	0.326187i
$534$		0			0
$535$	0.986136	+	5.59265i	0.0426344	+	0.241792i
$536$		0			0
$537$	19.5698	+	16.4210i	0.844497	+	0.708617i
$538$		0			0
$539$	−1.33202	−	0.484817i	−0.0573744	−	0.0208826i
$540$		0			0
$541$	17.7662	−	30.7719i	0.763827	−	1.32299i	−0.177038	−	0.984204i	$-0.556651\pi$
$541$	17.7662	−	30.7719i	0.763827	−	1.32299i	0.940865	−	0.338783i	$-0.110015\pi$
$542$		0			0
$543$	−9.06327	+	7.60499i	−0.388942	+	0.326361i
$544$		0			0
$545$	−11.4667	+	19.8609i	−0.491179	+	0.850747i
$546$		0			0
$547$	19.9167	+	34.4968i	0.851579	+	1.47498i	0.879783	+	0.475375i	$0.157688\pi$
$547$	19.9167	+	34.4968i	0.851579	+	1.47498i	−0.0282043	+	0.999602i	$0.508979\pi$
$548$		0			0
$549$	15.1669			0.647309
$550$		0			0
$551$	−2.82306	+	16.0104i	−0.120266	+	0.682065i
$552$		0			0
$553$	19.8911	−	16.6906i	0.845854	−	0.709756i
$554$		0			0
$555$	7.77848	−	8.92130i	0.330178	−	0.378688i
$556$		0			0
$557$	−5.98445	+	5.02155i	−0.253569	+	0.212770i	−0.760708	−	0.649095i	$-0.775148\pi$
$557$	−5.98445	+	5.02155i	−0.253569	+	0.212770i	0.507138	+	0.861865i	$0.330703\pi$
$558$		0			0
$559$	1.41406	−	8.01951i	0.0598082	−	0.339189i
$560$		0			0
$561$	−2.14294			−0.0904748
$562$		0			0
$563$	−17.5698	−	30.4318i	−0.740479	−	1.28255i	−0.952278	−	0.305233i	$-0.901266\pi$
$563$	−17.5698	−	30.4318i	−0.740479	−	1.28255i	0.211799	−	0.977313i	$-0.432068\pi$
$564$		0			0
$565$	15.2648	−	26.4394i	0.642195	−	1.11231i
$566$		0			0
$567$	4.34599	−	3.64672i	0.182515	−	0.153148i
$568$		0			0
$569$	13.4402	−	23.2792i	0.563444	−	0.975913i	−0.433749	−	0.901034i	$-0.642810\pi$
$569$	13.4402	−	23.2792i	0.563444	−	0.975913i	0.997193	−	0.0748791i	$-0.0238571\pi$
$570$		0			0
$571$	37.5779	+	13.6772i	1.57259	+	0.572375i	0.973575	−	0.228366i	$-0.0733383\pi$
$571$	37.5779	+	13.6772i	1.57259	+	0.572375i	0.599011	+	0.800741i	$0.295560\pi$
$572$		0			0
$573$	−10.3608	−	8.69372i	−0.432827	−	0.363185i
$574$		0			0
$575$	2.63077	+	14.9198i	0.109711	+	0.622200i
$576$		0			0
$577$	−15.5041	−	5.64304i	−0.645445	−	0.234923i	−0.00150512	−	0.999999i	$-0.500479\pi$
$577$	−15.5041	−	5.64304i	−0.645445	−	0.234923i	−0.643940	+	0.765076i	$0.722701\pi$
$578$		0			0
$579$	−2.70227	+	15.3253i	−0.112302	+	0.636899i
$580$		0			0
$581$	−3.46255	−	5.99732i	−0.143651	−	0.248811i
$582$		0			0
$583$	−0.132503	−	0.751462i	−0.00548772	−	0.0311224i
$584$		0			0
$585$	−4.22690	+	1.53847i	−0.174761	+	0.0636078i
$586$		0			0
$587$	−26.0305	+	9.47432i	−1.07439	+	0.391047i	−0.817818	−	0.575477i	$-0.804816\pi$
$587$	−26.0305	+	9.47432i	−1.07439	+	0.391047i	−0.256575	+	0.966524i	$0.582594\pi$
$588$		0			0
$589$	44.9792	+	37.7421i	1.85334	+	1.55513i
$590$		0			0
$591$	−20.4775			−0.842331
$592$		0			0
$593$	−43.2875			−1.77760			−0.888802	−	0.458292i	$-0.848461\pi$
$593$	−43.2875			−1.77760			−0.888802	+	0.458292i	$0.848461\pi$
$594$		0			0
$595$	8.73586	+	7.33025i	0.358135	+	0.300511i
$596$		0			0
$597$	2.37589	−	0.864752i	0.0972385	−	0.0353919i
$598$		0			0
$599$	2.17628	−	0.792102i	0.0889205	−	0.0323644i	−0.297177	−	0.954822i	$-0.596045\pi$
$599$	2.17628	−	0.792102i	0.0889205	−	0.0323644i	0.386097	+	0.922458i	$0.373823\pi$
$600$		0			0
$601$	2.32161	+	13.1665i	0.0947005	+	0.537073i	0.994839	+	0.101469i	$0.0323542\pi$
$601$	2.32161	+	13.1665i	0.0947005	+	0.537073i	−0.900138	+	0.435604i	$0.856535\pi$
$602$		0			0
$603$	1.16055	+	2.01013i	0.0472612	+	0.0818588i
$604$		0			0
$605$	−2.87473	+	16.3034i	−0.116874	+	0.662827i
$606$		0			0
$607$	33.6174	+	12.2357i	1.36449	+	0.496633i	0.917439	−	0.397877i	$-0.130253\pi$
$607$	33.6174	+	12.2357i	1.36449	+	0.496633i	0.447048	+	0.894510i	$0.352475\pi$
$608$		0			0
$609$	1.17339	+	6.65460i	0.0475480	+	0.269658i
$610$		0			0
$611$	12.4643	+	10.4588i	0.504251	+	0.423117i
$612$		0			0
$613$	−4.73396	−	1.72302i	−0.191203	−	0.0695921i	0.244644	−	0.969613i	$-0.421329\pi$
$613$	−4.73396	−	1.72302i	−0.191203	−	0.0695921i	−0.435847	+	0.900021i	$0.643551\pi$
$614$		0			0
$615$	10.1196	−	17.5277i	0.408062	−	0.706783i
$616$		0			0
$617$	22.8182	−	19.1467i	0.918625	−	0.770818i	−0.0551152	−	0.998480i	$-0.517553\pi$
$617$	22.8182	−	19.1467i	0.918625	−	0.770818i	0.973740	+	0.227662i	$0.0731082\pi$
$618$		0			0
$619$	5.82105	−	10.0823i	0.233968	−	0.405244i	−0.725005	−	0.688744i	$-0.758162\pi$
$619$	5.82105	−	10.0823i	0.233968	−	0.405244i	0.958972	+	0.283500i	$0.0914957\pi$
$620$		0			0
$621$	15.9104	+	27.5576i	0.638462	+	1.10585i
$622$		0			0
$623$	23.0975			0.925381
$624$		0			0
$625$	−0.816085	+	4.62825i	−0.0326434	+	0.185130i
$626$		0			0
$627$	−2.55164	+	2.14108i	−0.101903	+	0.0855064i
$628$		0			0
$629$	−22.8339	−	4.47369i	−0.910446	−	0.178378i
$630$		0			0
$631$	−25.1488	+	21.1023i	−1.00116	+	0.840070i	−0.987144	−	0.159832i	$-0.948905\pi$
$631$	−25.1488	+	21.1023i	−1.00116	+	0.840070i	−0.0140121	+	0.999902i	$0.504460\pi$
$632$		0			0
$633$	−2.77998	+	15.7661i	−0.110494	+	0.626645i
$634$		0			0
$635$	−7.51211			−0.298109
$636$		0			0
$637$	−3.40147	−	5.89151i	−0.134771	−	0.233430i
$638$		0			0
$639$	6.97468	−	12.0805i	0.275914	−	0.477897i
$640$		0			0
$641$	−7.75179	+	6.50452i	−0.306177	+	0.256913i	−0.782910	−	0.622135i	$-0.786265\pi$
$641$	−7.75179	+	6.50452i	−0.306177	+	0.256913i	0.476733	+	0.879048i	$0.341821\pi$
$642$		0			0
$643$	9.94109	−	17.2185i	0.392038	−	0.679030i	−0.600680	−	0.799490i	$-0.705103\pi$
$643$	9.94109	−	17.2185i	0.392038	−	0.679030i	0.992718	+	0.120459i	$0.0384367\pi$
$644$		0			0
$645$	−7.03390	−	2.56013i	−0.276960	−	0.100805i
$646$		0			0
$647$	6.83200	+	5.73273i	0.268594	+	0.225377i	0.767129	−	0.641492i	$-0.221684\pi$
$647$	6.83200	+	5.73273i	0.268594	+	0.225377i	−0.498536	+	0.866869i	$0.666129\pi$
$648$		0			0
$649$	0.157336	+	0.892297i	0.00617598	+	0.0350257i
$650$		0			0
$651$	22.9332	+	8.34701i	0.898824	+	0.327145i
$652$		0			0
$653$	6.58685	−	37.3559i	0.257763	−	1.46185i	−0.531115	−	0.847300i	$-0.678227\pi$
$653$	6.58685	−	37.3559i	0.257763	−	1.46185i	0.788879	−	0.614549i	$-0.210662\pi$
$654$		0			0
$655$	0.236655	+	0.409899i	0.00924688	+	0.0160161i
$656$		0			0
$657$	2.38086	+	13.5026i	0.0928864	+	0.526785i
$658$		0			0
$659$	6.16662	−	2.24447i	0.240217	−	0.0874320i	−0.219106	−	0.975701i	$-0.570314\pi$
$659$	6.16662	−	2.24447i	0.240217	−	0.0874320i	0.459324	+	0.888269i	$0.348092\pi$
$660$		0			0
$661$	−15.8047	+	5.75246i	−0.614733	+	0.223745i	−0.630573	−	0.776130i	$-0.717180\pi$
$661$	−15.8047	+	5.75246i	−0.614733	+	0.223745i	0.0158397	+	0.999875i	$0.494958\pi$
$662$		0			0
$663$	−7.87831	−	6.61068i	−0.305968	−	0.256738i
$664$		0			0
$665$	17.7259			0.687379
$666$		0			0
$667$	−15.6156			−0.604640
$668$		0			0
$669$	19.8427	+	16.6500i	0.767164	+	0.643727i
$670$		0			0
$671$	−4.53265	+	1.64975i	−0.174981	+	0.0636878i
$672$		0			0
$673$	7.68493	−	2.79709i	0.296232	−	0.107820i	−0.189629	−	0.981856i	$-0.560728\pi$
$673$	7.68493	−	2.79709i	0.296232	−	0.107820i	0.485861	+	0.874036i	$0.338506\pi$
$674$		0			0
$675$	−2.56653	−	14.5555i	−0.0987857	−	0.560242i
$676$		0			0
$677$	−13.2217	−	22.9007i	−0.508152	−	0.880145i	−0.999955	−	0.00943859i	$-0.996996\pi$
$677$	−13.2217	−	22.9007i	−0.508152	−	0.880145i	0.491804	−	0.870706i	$-0.336338\pi$
$678$		0			0
$679$	0.200539	−	1.13731i	0.00769596	−	0.0436460i
$680$		0			0
$681$	9.03771	+	3.28946i	0.346326	+	0.126052i
$682$		0			0
$683$	−2.15766	−	12.2367i	−0.0825604	−	0.468223i	−0.997856	−	0.0654415i	$-0.979154\pi$
$683$	−2.15766	−	12.2367i	−0.0825604	−	0.468223i	0.915296	−	0.402782i	$-0.131957\pi$
$684$		0			0
$685$	−23.8270	−	19.9932i	−0.910384	−	0.763903i
$686$		0			0
$687$	−0.373437	−	0.135920i	−0.0142475	−	0.00518567i
$688$		0			0
$689$	1.83103	−	3.17144i	0.0697567	−	0.120822i
$690$		0			0
$691$	21.0501	−	17.6632i	0.800785	−	0.671938i	−0.147605	−	0.989046i	$-0.547156\pi$
$691$	21.0501	−	17.6632i	0.800785	−	0.671938i	0.948389	+	0.317108i	$0.102712\pi$
$692$		0			0
$693$	0.595199	−	1.03092i	0.0226097	−	0.0391612i
$694$		0			0
$695$	−10.0642	−	17.4317i	−0.381757	−	0.661222i
$696$		0			0
$697$	−39.7871			−1.50704
$698$		0			0
$699$	0.150668	−	0.854483i	0.00569881	−	0.0323195i
$700$		0			0
$701$	−15.0052	+	12.5909i	−0.566739	+	0.475551i	−0.880562	−	0.473931i	$-0.842835\pi$
$701$	−15.0052	+	12.5909i	−0.566739	+	0.475551i	0.313823	+	0.949482i	$0.398390\pi$
$702$		0			0
$703$	−31.6586	+	17.4872i	−1.19403	+	0.659541i
$704$		0			0
$705$	11.4573	−	9.61381i	0.431506	−	0.362077i
$706$		0			0
$707$	4.46962	−	25.3485i	0.168097	−	0.953328i
$708$		0			0
$709$	18.8660			0.708528			0.354264	−	0.935145i	$-0.384731\pi$
$709$	18.8660			0.708528			0.354264	+	0.935145i	$0.384731\pi$
$710$		0			0
$711$	−9.25384	−	16.0281i	−0.347046	−	0.601102i
$712$		0			0
$713$	−28.1993	+	48.8426i	−1.05607	+	1.82917i
$714$		0			0
$715$	1.09587	−	0.919544i	0.0409832	−	0.0343890i
$716$		0			0
$717$	−7.11642	+	12.3260i	−0.265767	+	0.460323i
$718$		0			0
$719$	15.2536	+	5.55186i	0.568863	+	0.207049i	0.610408	−	0.792087i	$-0.291006\pi$
$719$	15.2536	+	5.55186i	0.568863	+	0.207049i	−0.0415444	+	0.999137i	$0.513228\pi$
$720$		0			0
$721$	−4.69540	−	3.93991i	−0.174866	−	0.146730i
$722$		0			0
$723$	1.14255	+	6.47972i	0.0424919	+	0.240983i
$724$		0			0
$725$	6.81570	+	2.48071i	0.253129	+	0.0921313i
$726$		0			0
$727$	2.94600	−	16.7076i	0.109261	−	0.619650i	−0.880172	−	0.474656i	$-0.842573\pi$
$727$	2.94600	−	16.7076i	0.109261	−	0.619650i	0.989433	−	0.144994i	$-0.0463163\pi$
$728$		0			0
$729$	−12.6365	−	21.8870i	−0.468017	−	0.810630i
$730$		0			0
$731$	2.55523	+	14.4914i	0.0945084	+	0.535984i
$732$		0			0
$733$	31.7060	−	11.5400i	1.17109	−	0.426241i	0.318042	−	0.948077i	$-0.396975\pi$
$733$	31.7060	−	11.5400i	1.17109	−	0.426241i	0.853046	+	0.521835i	$0.174753\pi$
$734$		0			0
$735$	−5.87619	+	2.13876i	−0.216747	+	0.0788893i
$736$		0			0
$737$	−0.565478	−	0.474492i	−0.0208296	−	0.0174782i
$738$		0			0
$739$	−15.5694			−0.572730			−0.286365	−	0.958121i	$-0.592447\pi$
$739$	−15.5694			−0.572730			−0.286365	+	0.958121i	$0.592447\pi$
$740$		0			0
$741$	−15.9858			−0.587253
$742$		0			0
$743$	36.6033	+	30.7138i	1.34285	+	1.12678i	0.980885	+	0.194588i	$0.0623371\pi$
$743$	36.6033	+	30.7138i	1.34285	+	1.12678i	0.361961	+	0.932193i	$0.382107\pi$
$744$		0			0
$745$	5.74187	−	2.08987i	0.210366	−	0.0765669i
$746$		0			0
$747$	−4.63832	+	1.68821i	−0.169707	+	0.0617683i
$748$		0			0
$749$	−1.25246	−	7.10303i	−0.0457637	−	0.259539i
$750$		0			0
$751$	−13.6489	−	23.6406i	−0.498055	−	0.862657i	0.501942	−	0.864901i	$-0.332619\pi$
$751$	−13.6489	−	23.6406i	−0.498055	−	0.862657i	−0.999997	+	0.00224411i	$0.999286\pi$
$752$		0			0
$753$	−6.72485	+	38.1385i	−0.245067	+	1.38984i
$754$		0			0
$755$	−28.2895	−	10.2965i	−1.02956	−	0.374730i
$756$		0			0
$757$	−8.23710	−	46.7149i	−0.299383	−	1.69788i	−0.648835	−	0.760929i	$-0.724744\pi$
$757$	−8.23710	−	46.7149i	−0.299383	−	1.69788i	0.349453	−	0.936954i	$-0.386367\pi$
$758$		0			0
$759$	−2.45092	−	2.05656i	−0.0889627	−	0.0746486i
$760$		0			0
$761$	−8.81599	−	3.20876i	−0.319579	−	0.116317i	0.177249	−	0.984166i	$-0.443280\pi$
$761$	−8.81599	−	3.20876i	−0.319579	−	0.116317i	−0.496829	+	0.867849i	$0.665502\pi$
$762$		0			0
$763$	14.5634	−	25.2246i	0.527231	−	0.913191i
$764$		0			0
$765$	6.22663	−	5.22477i	0.225124	−	0.188902i
$766$		0			0
$767$	−2.17419	+	3.76581i	−0.0785054	+	0.135975i
$768$		0			0
$769$	−1.14862	−	1.98947i	−0.0414203	−	0.0717420i	0.844572	−	0.535442i	$-0.179855\pi$
$769$	−1.14862	−	1.98947i	−0.0414203	−	0.0717420i	−0.885992	+	0.463700i	$0.846522\pi$
$770$		0			0
$771$	−7.45229			−0.268388
$772$		0			0
$773$	−3.65406	+	20.7232i	−0.131427	+	0.745361i	0.845854	+	0.533414i	$0.179091\pi$
$773$	−3.65406	+	20.7232i	−0.131427	+	0.745361i	−0.977281	+	0.211947i	$0.932020\pi$
$774$		0			0
$775$	20.0672	−	16.8384i	0.720835	−	0.604853i
$776$		0			0
$777$	−9.87916	+	11.3306i	−0.354413	+	0.406484i
$778$		0			0
$779$	−47.3753	+	39.7526i	−1.69740	+	1.42428i
$780$		0			0
$781$	−0.770359	+	4.36892i	−0.0275656	+	0.156332i
$782$		0			0
$783$	15.2343			0.544430
$784$		0			0
$785$	−6.99486	−	12.1155i	−0.249657	−	0.432419i
$786$		0			0
$787$	−9.94650	+	17.2278i	−0.354555	+	0.614106i	−0.987042	−	0.160464i	$-0.948701\pi$
$787$	−9.94650	+	17.2278i	−0.354555	+	0.614106i	0.632487	+	0.774571i	$0.282034\pi$
$788$		0			0
$789$	15.8708	−	13.3172i	0.565014	−	0.474103i
$790$		0			0
$791$	−19.3873	+	33.5797i	−0.689332	+	1.19396i
$792$		0			0
$793$	−21.7531	−	7.91749i	−0.772476	−	0.281158i
$794$		0			0
$795$	−2.57866	−	2.16375i	−0.0914555	−	0.0767403i
$796$		0			0
$797$	−3.96311	−	22.4759i	−0.140380	−	0.796137i	−0.970961	−	0.239238i	$-0.923102\pi$
$797$	−3.96311	−	22.4759i	−0.140380	−	0.796137i	0.830580	−	0.556899i	$-0.188009\pi$
$798$		0			0
$799$	−27.6288	−	10.0561i	−0.977438	−	0.355758i
$800$		0			0
$801$	2.85879	−	16.2130i	0.101010	−	0.572859i
$802$		0			0
$803$	−2.18023	−	3.77627i	−0.0769387	−	0.133262i
$804$		0			0
$805$	2.95656	+	16.7675i	0.104205	+	0.590977i
$806$		0			0
$807$	−11.9419	+	4.34650i	−0.420375	+	0.153004i
$808$		0			0
$809$	−8.00473	+	2.91348i	−0.281431	+	0.102433i	−0.478879	−	0.877881i	$-0.658957\pi$
$809$	−8.00473	+	2.91348i	−0.281431	+	0.102433i	0.197448	+	0.980313i	$0.436735\pi$
$810$		0			0
$811$	−42.0356	−	35.2721i	−1.47607	−	1.23857i	−0.910263	−	0.414031i	$-0.864120\pi$
$811$	−42.0356	−	35.2721i	−1.47607	−	1.23857i	−0.565807	−	0.824538i	$-0.691435\pi$
$812$		0			0
$813$	−15.7067			−0.550858
$814$		0			0
$815$	2.87292			0.100634
$816$		0			0
$817$	17.5214	+	14.7022i	0.612996	+	0.514365i
$818$		0			0
$819$	5.36844	−	1.95395i	0.187588	−	0.0682766i
$820$		0			0
$821$	23.4205	−	8.52435i	0.817380	−	0.297502i	0.100711	−	0.994916i	$-0.467888\pi$
$821$	23.4205	−	8.52435i	0.817380	−	0.297502i	0.716669	+	0.697414i	$0.245666\pi$
$822$		0			0
$823$	−6.03516	−	34.2271i	−0.210373	−	1.19308i	−0.888758	−	0.458376i	$-0.848431\pi$
$823$	−6.03516	−	34.2271i	−0.210373	−	1.19308i	0.678386	−	0.734706i	$-0.262680\pi$
$824$		0			0
$825$	0.743036	+	1.28698i	0.0258692	+	0.0448068i
$826$		0			0
$827$	−2.07962	+	11.7941i	−0.0723156	+	0.410122i	0.927064	+	0.374903i	$0.122324\pi$
$827$	−2.07962	+	11.7941i	−0.0723156	+	0.410122i	−0.999380	+	0.0352192i	$0.988787\pi$
$828$		0			0
$829$	6.74182	+	2.45382i	0.234153	+	0.0852248i	0.456432	−	0.889758i	$-0.349127\pi$
$829$	6.74182	+	2.45382i	0.234153	+	0.0852248i	−0.222279	+	0.974983i	$0.571349\pi$
$830$		0			0
$831$	4.68574	+	26.5741i	0.162546	+	0.921847i
$832$		0			0
$833$	9.41701	+	7.90181i	0.326280	+	0.273781i
$834$		0			0
$835$	6.63268	+	2.41410i	0.229533	+	0.0835433i
$836$		0			0
$837$	27.5107	−	47.6499i	0.950908	−	1.64702i
$838$		0			0
$839$	−16.6124	+	13.9395i	−0.573525	+	0.481244i	−0.882813	−	0.469724i	$-0.844353\pi$
$839$	−16.6124	+	13.9395i	−0.573525	+	0.481244i	0.309289	+	0.950968i	$0.399909\pi$
$840$		0			0
$841$	10.7620	−	18.6403i	0.371103	−	0.642769i
$842$		0			0
$843$	10.2866	+	17.8170i	0.354291	+	0.613649i
$844$		0			0
$845$	−13.0516			−0.448989
$846$		0			0
$847$	3.65109	−	20.7063i	0.125453	−	0.711478i
$848$		0			0
$849$	−4.85318	+	4.07230i	−0.166561	+	0.139761i
$850$		0			0
$851$	−21.8222	−	27.0302i	−0.748054	−	0.926583i
$852$		0			0
$853$	−27.4605	+	23.0421i	−0.940231	+	0.788948i	−0.977625	−	0.210353i	$-0.932539\pi$
$853$	−27.4605	+	23.0421i	−0.940231	+	0.788948i	0.0373944	+	0.999301i	$0.488094\pi$
$854$		0			0
$855$	2.19394	−	12.4425i	0.0750313	−	0.425524i
$856$		0			0
$857$	−16.3281			−0.557757			−0.278879	−	0.960326i	$-0.589963\pi$
$857$	−16.3281			−0.557757			−0.278879	+	0.960326i	$0.589963\pi$
$858$		0			0
$859$	6.97836	+	12.0869i	0.238099	+	0.412399i	0.960169	−	0.279421i	$-0.0901425\pi$
$859$	6.97836	+	12.0869i	0.238099	+	0.412399i	−0.722070	+	0.691820i	$0.756809\pi$
$860$		0			0
$861$	−12.8525	+	22.2612i	−0.438013	+	0.758661i
$862$		0			0
$863$	37.6158	−	31.5634i	1.28046	−	1.07443i	0.287276	−	0.957848i	$-0.407250\pi$
$863$	37.6158	−	31.5634i	1.28046	−	1.07443i	0.993181	−	0.116583i	$-0.0371941\pi$
$864$		0			0
$865$	11.5656	−	20.0323i	0.393244	−	0.681118i
$866$		0			0
$867$	−2.82563	−	1.02844i	−0.0959633	−	0.0349278i
$868$		0			0
$869$	4.50894	+	3.78345i	0.152955	+	0.128345i
$870$		0			0
$871$	−0.615179	−	3.48885i	−0.0208445	−	0.118215i
$872$		0			0
$873$	−0.773502	−	0.281532i	−0.0261791	−	0.00952840i
$874$		0			0
$875$	3.96167	−	22.4678i	0.133929	−	0.759549i
$876$		0			0
$877$	−17.0002	−	29.4453i	−0.574057	−	0.994297i	−0.996143	−	0.0877408i	$-0.972035\pi$
$877$	−17.0002	−	29.4453i	−0.574057	−	0.994297i	0.422086	−	0.906556i	$-0.361298\pi$
$878$		0			0
$879$	−1.22384	−	6.94076i	−0.0412792	−	0.234106i
$880$		0			0
$881$	−49.9500	+	18.1803i	−1.68286	+	0.612510i	−0.993697	−	0.112098i	$-0.964243\pi$
$881$	−49.9500	+	18.1803i	−1.68286	+	0.612510i	−0.689161	+	0.724609i	$0.742021\pi$
$882$		0			0
$883$	14.5551	−	5.29763i	0.489819	−	0.178279i	−0.0852904	−	0.996356i	$-0.527182\pi$
$883$	14.5551	−	5.29763i	0.489819	−	0.178279i	0.575109	+	0.818077i	$0.304960\pi$
$884$		0			0
$885$	3.06193	+	2.56927i	0.102926	+	0.0863649i
$886$		0			0
$887$	−17.6841			−0.593774			−0.296887	−	0.954913i	$-0.595948\pi$
$887$	−17.6841			−0.593774			−0.296887	+	0.954913i	$0.595948\pi$
$888$		0			0
$889$	9.54086			0.319990
$890$		0			0
$891$	0.985157	+	0.826645i	0.0330040	+	0.0276936i
$892$		0			0
$893$	−42.9456	+	15.6309i	−1.43712	+	0.523068i
$894$		0			0
$895$	28.9585	−	10.5400i	0.967975	−	0.352314i
$896$		0			0
$897$	−2.66633	−	15.1215i	−0.0890263	−	0.504893i
$898$		0			0
$899$	13.5005	+	23.3836i	0.450267	+	0.779886i
$900$		0			0
$901$	−1.14910	+	6.51688i	−0.0382821	+	0.217109i
$902$		0			0
$903$	8.93350	+	3.25153i	0.297288	+	0.108204i
$904$		0			0
$905$	2.47833	+	14.0553i	0.0823826	+	0.467215i
$906$		0			0
$907$	27.9435	+	23.4474i	0.927850	+	0.778558i	0.975430	−	0.220309i	$-0.0707066\pi$
$907$	27.9435	+	23.4474i	0.927850	+	0.778558i	−0.0475804	+	0.998867i	$0.515151\pi$
$908$		0			0
$909$	−17.2399	−	6.27481i	−0.571811	−	0.208122i
$910$		0			0
$911$	−3.84129	+	6.65330i	−0.127267	+	0.220434i	−0.922617	−	0.385717i	$-0.873954\pi$
$911$	−3.84129	+	6.65330i	−0.127267	+	0.220434i	0.795350	+	0.606151i	$0.207287\pi$
$912$		0			0
$913$	1.20253	−	1.00904i	0.0397980	−	0.0333945i
$914$		0			0
$915$	−10.6395	+	18.4281i	−0.351730	+	0.609214i
$916$		0			0
$917$	−0.300567	−	0.520597i	−0.00992560	−	0.0171916i
$918$		0			0
$919$	0.166200			0.00548242			0.00274121	−	0.999996i	$-0.499127\pi$
$919$	0.166200			0.00548242			0.00274121	+	0.999996i	$0.499127\pi$
$920$		0			0
$921$	3.34378	−	18.9635i	0.110181	−	0.624869i
$922$		0			0
$923$	−16.3097	+	13.6855i	−0.536841	+	0.450463i
$924$		0			0
$925$	5.23061	+	15.2645i	0.171981	+	0.501892i
$926$		0			0
$927$	−3.34673	+	2.80824i	−0.109921	+	0.0922347i
$928$		0			0
$929$	6.14457	−	34.8476i	0.201597	−	1.14331i	−0.701109	−	0.713054i	$-0.747311\pi$
$929$	6.14457	−	34.8476i	0.201597	−	1.14331i	0.902706	−	0.430258i	$-0.141577\pi$
$930$		0			0
$931$	19.1080			0.626239
$932$		0			0
$933$	−9.65795	−	16.7281i	−0.316187	−	0.547652i
$934$		0			0
$935$	−1.29252	+	2.23871i	−0.0422700	+	0.0732137i
$936$		0			0
$937$	11.8267	−	9.92376i	0.386361	−	0.324195i	−0.428833	−	0.903384i	$-0.641075\pi$
$937$	11.8267	−	9.92376i	0.386361	−	0.324195i	0.815193	+	0.579189i	$0.196631\pi$
$938$		0			0
$939$	18.5249	−	32.0860i	0.604537	−	1.04709i
$940$		0			0
$941$	21.9764	+	7.99875i	0.716410	+	0.260752i	0.674401	−	0.738365i	$-0.264402\pi$
$941$	21.9764	+	7.99875i	0.716410	+	0.260752i	0.0420089	+	0.999117i	$0.486624\pi$
$942$		0			0
$943$	−45.5053	−	38.1834i	−1.48186	−	1.24342i
$944$		0			0
$945$	−2.88437	−	16.3581i	−0.0938285	−	0.532128i
$946$		0			0
$947$	−25.1514	−	9.15437i	−0.817311	−	0.297477i	−0.100671	−	0.994920i	$-0.532099\pi$
$947$	−25.1514	−	9.15437i	−0.817311	−	0.297477i	−0.716640	+	0.697443i	$0.754321\pi$
$948$		0			0
$949$	3.63390	−	20.6089i	0.117961	−	0.668992i
$950$		0			0
$951$	−12.1860	−	21.1067i	−0.395158	−	0.684433i
$952$		0			0
$953$	−7.42555	−	42.1124i	−0.240537	−	1.36415i	−0.830632	−	0.556821i	$-0.812021\pi$
$953$	−7.42555	−	42.1124i	−0.240537	−	1.36415i	0.590095	−	0.807334i	$-0.299090\pi$
$954$		0			0
$955$	−15.3314	+	5.58018i	−0.496113	+	0.180570i
$956$		0			0
$957$	−1.43937	+	0.523888i	−0.0465283	+	0.0169349i
$958$		0			0
$959$	30.2618	+	25.3927i	0.977206	+	0.819973i
$960$		0			0
$961$	66.5188			2.14577
$962$		0			0
$963$	−5.14091			−0.165663
$964$		0			0
$965$	14.3804	+	12.0666i	0.462921	+	0.388437i
$966$		0			0
$967$	−3.28122	+	1.19426i	−0.105517	+	0.0384050i	−0.394239	−	0.919008i	$-0.628992\pi$
$967$	−3.28122	+	1.19426i	−0.105517	+	0.0384050i	0.288722	+	0.957413i	$0.406770\pi$
$968$		0			0
$969$	27.1446	−	9.87983i	0.872010	−	0.317386i
$970$		0			0
$971$	−1.07928	−	6.12087i	−0.0346356	−	0.196428i	0.962580	−	0.270997i	$-0.0873532\pi$
$971$	−1.07928	−	6.12087i	−0.0346356	−	0.196428i	−0.997216	+	0.0745684i	$0.976242\pi$
$972$		0			0
$973$	12.7822	+	22.1394i	0.409778	+	0.709756i
$974$		0			0
$975$	−1.23845	+	7.02362i	−0.0396622	+	0.224936i
$976$		0			0
$977$	0.127278	+	0.0463253i	0.00407198	+	0.00148208i	0.344055	−	0.938949i	$-0.388199\pi$
$977$	0.127278	+	0.0463253i	0.00407198	+	0.00148208i	−0.339983	+	0.940431i	$0.610421\pi$
$978$		0			0
$979$	0.909183	+	5.15623i	0.0290576	+	0.164794i
$980$		0			0
$981$	−15.9036	−	13.3447i	−0.507763	−	0.426063i
$982$		0			0
$983$	−1.92791	−	0.701702i	−0.0614908	−	0.0223808i	0.311092	−	0.950380i	$-0.399305\pi$
$983$	−1.92791	−	0.701702i	−0.0614908	−	0.0223808i	−0.372582	+	0.927999i	$0.621528\pi$
$984$		0			0
$985$	−12.3511	+	21.3927i	−0.393538	+	0.681628i
$986$		0			0
$987$	−14.5515	+	12.2101i	−0.463179	+	0.388653i
$988$		0			0
$989$	−10.9849	+	19.0263i	−0.349298	+	0.605002i
$990$		0			0
$991$	8.69906	+	15.0672i	0.276335	+	0.478626i	0.970471	−	0.241218i	$-0.0775468\pi$
$991$	8.69906	+	15.0672i	0.276335	+	0.478626i	−0.694136	+	0.719844i	$0.744213\pi$
$992$		0			0
$993$	−9.94851			−0.315707
$994$		0			0
$995$	0.529625	−	3.00365i	0.0167902	−	0.0952222i
$996$		0			0
$997$	5.44281	−	4.56706i	0.172376	−	0.144640i	−0.552518	−	0.833501i	$-0.686333\pi$
$997$	5.44281	−	4.56706i	0.172376	−	0.144640i	0.724894	+	0.688860i	$0.241889\pi$
$998$		0			0
$999$	21.2893	+	26.3701i	0.673563	+	0.834314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.d.49.1		12
4.3	odd	2		74.2.f.b.49.2	✓	12
12.11	even	2		666.2.x.g.271.1		12
37.34	even	9	inner	592.2.bc.d.145.1		12
148.71	odd	18		74.2.f.b.71.2	yes	12
148.95	odd	18		2738.2.a.q.1.4		6
148.127	odd	18		2738.2.a.t.1.4		6
444.71	even	18		666.2.x.g.145.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.49.2	✓	12	4.3	odd	2
74.2.f.b.71.2	yes	12	148.71	odd	18
592.2.bc.d.49.1		12	1.1	even	1	trivial
592.2.bc.d.145.1		12	37.34	even	9	inner
666.2.x.g.145.1		12	444.71	even	18
666.2.x.g.271.1		12	12.11	even	2
2738.2.a.q.1.4		6	148.95	odd	18
2738.2.a.t.1.4		6	148.127	odd	18

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bc (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.972925 - 0.816381i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(1.82850 - 0.665520i) q^{7} +(-0.240839 - 1.36587i) q^{9} +O(q^{10})\)	\(q+(-0.972925 - 0.816381i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(1.82850 - 0.665520i) q^{7} +(-0.240839 - 1.36587i) q^{9} +(0.220544 + 0.381994i) q^{11} +(-0.367592 + 2.08472i) q^{13} +(1.82850 + 0.665520i) q^{15} +(-0.664245 - 3.76712i) q^{17} +(-4.55479 - 3.82192i) q^{19} +(-2.32231 - 0.845253i) q^{21} +(2.85558 - 4.94600i) q^{23} +(-2.03209 + 1.70513i) q^{25} +(-2.78585 + 4.82523i) q^{27} +(-1.36712 - 2.36792i) q^{29} -9.87516 q^{31} +(0.0972795 - 0.551699i) q^{33} +(-2.28374 + 1.91629i) q^{35} +(2.18831 - 5.67550i) q^{37} +(2.05956 - 1.72818i) q^{39} +(1.80615 - 10.2432i) q^{41} -3.84681 q^{43} +(1.06246 + 1.84023i) q^{45} +(3.84316 - 6.65655i) q^{47} +(-2.46181 + 2.06571i) q^{49} +(-2.42915 + 4.20740i) q^{51} +(-1.62561 - 0.591673i) q^{53} +(-0.517683 - 0.434387i) q^{55} +(1.31132 + 7.43688i) q^{57} +(1.93027 + 0.702561i) q^{59} +(-1.89894 + 10.7694i) q^{61} +(-1.34939 - 2.33721i) q^{63} +(-0.563183 - 3.19397i) q^{65} +(-1.57261 + 0.572384i) q^{67} +(-6.81608 + 2.48085i) q^{69} +(7.70462 + 6.46494i) q^{71} -9.88570 q^{73} +3.36910 q^{75} +(0.657490 + 0.551699i) q^{77} +(12.5395 - 4.56401i) q^{79} +(2.73975 - 0.997189i) q^{81} +(-0.617999 - 3.50484i) q^{83} +(2.93030 + 5.07543i) q^{85} +(-0.603020 + 3.41989i) q^{87} +(11.1543 + 4.05982i) q^{89} +(0.715278 + 4.05654i) q^{91} +(9.60779 + 8.06190i) q^{93} +(8.56020 + 3.11566i) q^{95} +(0.296748 - 0.513983i) q^{97} +(0.468637 - 0.393233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Introduction

L-functions

Modular forms

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Database

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