LMFDB - Embedded newform 1734.2.b.j.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(577,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1734.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.b (of order $2$, degree $1$, 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:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.419904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 9x^{2} + 1 $ x^6 + 6x^4 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			577.1
Root			$-1.53209i$ of defining polynomial
Character	$\chi$	$=$	1734.577
Dual form			1734.2.b.j.577.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.53209i q^{5} -1.00000i q^{6} -2.75877i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.53209i q^{5} -1.00000i q^{6} -2.75877i q^{7} +1.00000 q^{8} -1.00000 q^{9} -3.53209i q^{10} -2.94356i q^{11} -1.00000i q^{12} +5.06418 q^{13} -2.75877i q^{14} -3.53209 q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.36959 q^{19} -3.53209i q^{20} -2.75877 q^{21} -2.94356i q^{22} +6.00000i q^{23} -1.00000i q^{24} -7.47565 q^{25} +5.06418 q^{26} +1.00000i q^{27} -2.75877i q^{28} +4.80066i q^{29} -3.53209 q^{30} -0.716881i q^{31} +1.00000 q^{32} -2.94356 q^{33} -9.74422 q^{35} -1.00000 q^{36} -10.2121i q^{37} +4.36959 q^{38} -5.06418i q^{39} -3.53209i q^{40} +12.5817i q^{41} -2.75877 q^{42} -10.9067 q^{43} -2.94356i q^{44} +3.53209i q^{45} +6.00000i q^{46} +5.14796 q^{47} -1.00000i q^{48} -0.610815 q^{49} -7.47565 q^{50} +5.06418 q^{52} -4.57398 q^{53} +1.00000i q^{54} -10.3969 q^{55} -2.75877i q^{56} -4.36959i q^{57} +4.80066i q^{58} -5.53209 q^{59} -3.53209 q^{60} -6.24123i q^{61} -0.716881i q^{62} +2.75877i q^{63} +1.00000 q^{64} -17.8871i q^{65} -2.94356 q^{66} +5.67499 q^{67} +6.00000 q^{69} -9.74422 q^{70} +9.80335i q^{71} -1.00000 q^{72} +9.04189i q^{73} -10.2121i q^{74} +7.47565i q^{75} +4.36959 q^{76} -8.12061 q^{77} -5.06418i q^{78} -6.61856i q^{79} -3.53209i q^{80} +1.00000 q^{81} +12.5817i q^{82} +3.32501 q^{83} -2.75877 q^{84} -10.9067 q^{86} +4.80066 q^{87} -2.94356i q^{88} +13.8425 q^{89} +3.53209i q^{90} -13.9709i q^{91} +6.00000i q^{92} -0.716881 q^{93} +5.14796 q^{94} -15.4338i q^{95} -1.00000i q^{96} +11.0273i q^{97} -0.610815 q^{98} +2.94356i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 + 6 * q^8 - 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} + 6 q^{8} - 6 q^{9} + 12 q^{13} - 12 q^{15} + 6 q^{16} - 6 q^{18} + 12 q^{19} + 6 q^{21} - 6 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{32} + 12 q^{33} - 6 q^{36} + 12 q^{38} + 6 q^{42} - 12 q^{43} - 12 q^{49} - 6 q^{50} + 12 q^{52} - 12 q^{53} - 6 q^{55} - 24 q^{59} - 12 q^{60} + 6 q^{64} + 12 q^{66} + 24 q^{67} + 36 q^{69} - 6 q^{72} + 12 q^{76} - 60 q^{77} + 6 q^{81} + 30 q^{83} + 6 q^{84} - 12 q^{86} + 48 q^{89} + 12 q^{93} - 12 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + 6 * q^8 - 6 * q^9 + 12 * q^13 - 12 * q^15 + 6 * q^16 - 6 * q^18 + 12 * q^19 + 6 * q^21 - 6 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^32 + 12 * q^33 - 6 * q^36 + 12 * q^38 + 6 * q^42 - 12 * q^43 - 12 * q^49 - 6 * q^50 + 12 * q^52 - 12 * q^53 - 6 * q^55 - 24 * q^59 - 12 * q^60 + 6 * q^64 + 12 * q^66 + 24 * q^67 + 36 * q^69 - 6 * q^72 + 12 * q^76 - 60 * q^77 + 6 * q^81 + 30 * q^83 + 6 * q^84 - 12 * q^86 + 48 * q^89 + 12 * q^93 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	1.00000	0.500000
$5$	− 3.53209i	− 1.57960i	−0.613366	−	0.789799i	$-0.710185\pi$
$5$	− 3.53209i	− 1.57960i	0.613366	−	0.789799i	$-0.289815\pi$
$6$	− 1.00000i	− 0.408248i
$7$	− 2.75877i	− 1.04272i	−0.853338	−	0.521359i	$-0.825425\pi$
$7$	− 2.75877i	− 1.04272i	0.853338	−	0.521359i	$-0.174575\pi$
$8$	1.00000	0.353553
$9$	−1.00000	−0.333333
$10$	− 3.53209i	− 1.11694i
$11$	− 2.94356i	− 0.887518i	−0.896146	−	0.443759i	$-0.853645\pi$
$11$	− 2.94356i	− 0.887518i	0.896146	−	0.443759i	$-0.146355\pi$
$12$	− 1.00000i	− 0.288675i
$13$	5.06418	1.40455	0.702275	−	0.711906i	$-0.252168\pi$
$13$	5.06418	1.40455	0.702275	+	0.711906i	$0.252168\pi$
$14$	− 2.75877i	− 0.737312i
$15$	−3.53209	−0.911981
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−1.00000	−0.235702
$19$	4.36959	1.00245	0.501226	−	0.865317i	$-0.332883\pi$
$19$	4.36959	1.00245	0.501226	+	0.865317i	$0.332883\pi$
$20$	− 3.53209i	− 0.789799i
$21$	−2.75877	−0.602013
$22$	− 2.94356i	− 0.627570i
$23$	6.00000i	1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$	6.00000i	1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	− 1.00000i	− 0.204124i
$25$	−7.47565	−1.49513
$26$	5.06418	0.993167
$27$	1.00000i	0.192450i
$28$	− 2.75877i	− 0.521359i
$29$	4.80066i	0.891460i	0.895167	+	0.445730i	$0.147056\pi$
$29$	4.80066i	0.891460i	−0.895167	+	0.445730i	$0.852944\pi$
$30$	−3.53209	−0.644868
$31$	− 0.716881i	− 0.128756i	−0.997926	−	0.0643779i	$-0.979494\pi$
$31$	− 0.716881i	− 0.128756i	0.997926	−	0.0643779i	$-0.0205063\pi$
$32$	1.00000	0.176777
$33$	−2.94356	−0.512409
$34$	0	0
$35$	−9.74422	−1.64707
$36$	−1.00000	−0.166667
$37$	− 10.2121i	− 1.67886i	−0.543464	−	0.839432i	$-0.682888\pi$
$37$	− 10.2121i	− 1.67886i	0.543464	−	0.839432i	$-0.317112\pi$
$38$	4.36959	0.708840
$39$	− 5.06418i	− 0.810917i
$40$	− 3.53209i	− 0.558472i
$41$	12.5817i	1.96493i	0.186436	+	0.982467i	$0.440306\pi$
$41$	12.5817i	1.96493i	−0.186436	+	0.982467i	$0.559694\pi$
$42$	−2.75877	−0.425688
$43$	−10.9067	−1.66326	−0.831630	−	0.555330i	$-0.812592\pi$
$43$	−10.9067	−1.66326	−0.831630	+	0.555330i	$0.812592\pi$
$44$	− 2.94356i	− 0.443759i
$45$	3.53209i	0.526533i
$46$	6.00000i	0.884652i
$47$	5.14796	0.750907	0.375453	−	0.926841i	$-0.377487\pi$
$47$	5.14796	0.750907	0.375453	+	0.926841i	$0.377487\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−0.610815	−0.0872592
$50$	−7.47565	−1.05722
$51$	0	0
$52$	5.06418	0.702275
$53$	−4.57398	−0.628284	−0.314142	−	0.949376i	$-0.601717\pi$
$53$	−4.57398	−0.628284	−0.314142	+	0.949376i	$0.601717\pi$
$54$	1.00000i	0.136083i
$55$	−10.3969	−1.40192
$56$	− 2.75877i	− 0.368656i
$57$	− 4.36959i	− 0.578766i
$58$	4.80066i	0.630357i
$59$	−5.53209	−0.720217	−0.360108	−	0.932911i	$-0.617260\pi$
$59$	−5.53209	−0.720217	−0.360108	+	0.932911i	$0.617260\pi$
$60$	−3.53209	−0.455991
$61$	− 6.24123i	− 0.799108i	−0.916710	−	0.399554i	$-0.869165\pi$
$61$	− 6.24123i	− 0.799108i	0.916710	−	0.399554i	$-0.130835\pi$
$62$	− 0.716881i	− 0.0910440i
$63$	2.75877i	0.347572i
$64$	1.00000	0.125000
$65$	− 17.8871i	− 2.21862i
$66$	−2.94356	−0.362328
$67$	5.67499	0.693311	0.346655	−	0.937993i	$-0.387317\pi$
$67$	5.67499	0.693311	0.346655	+	0.937993i	$0.387317\pi$
$68$	0	0
$69$	6.00000	0.722315
$70$	−9.74422	−1.16466
$71$	9.80335i	1.16344i	0.813388	+	0.581722i	$0.197621\pi$
$71$	9.80335i	1.16344i	−0.813388	+	0.581722i	$0.802379\pi$
$72$	−1.00000	−0.117851
$73$	9.04189i	1.05827i	0.848537	+	0.529137i	$0.177484\pi$
$73$	9.04189i	1.05827i	−0.848537	+	0.529137i	$0.822516\pi$
$74$	− 10.2121i	− 1.18714i
$75$	7.47565i	0.863214i
$76$	4.36959	0.501226
$77$	−8.12061	−0.925430
$78$	− 5.06418i	− 0.573405i
$79$	− 6.61856i	− 0.744646i	−0.928103	−	0.372323i	$-0.878561\pi$
$79$	− 6.61856i	− 0.744646i	0.928103	−	0.372323i	$-0.121439\pi$
$80$	− 3.53209i	− 0.394900i
$81$	1.00000	0.111111
$82$	12.5817i	1.38942i
$83$	3.32501	0.364967	0.182484	−	0.983209i	$-0.441586\pi$
$83$	3.32501	0.364967	0.182484	+	0.983209i	$0.441586\pi$
$84$	−2.75877	−0.301007
$85$	0	0
$86$	−10.9067	−1.17610
$87$	4.80066	0.514685
$88$	− 2.94356i	− 0.313785i
$89$	13.8425	1.46731	0.733654	−	0.679524i	$-0.237814\pi$
$89$	13.8425	1.46731	0.733654	+	0.679524i	$0.237814\pi$
$90$	3.53209i	0.372315i
$91$	− 13.9709i	− 1.46455i
$92$	6.00000i	0.625543i
$93$	−0.716881	−0.0743371
$94$	5.14796	0.530971
$95$	− 15.4338i	− 1.58347i
$96$	− 1.00000i	− 0.102062i
$97$	11.0273i	1.11966i	0.828609	+	0.559828i	$0.189133\pi$
$97$	11.0273i	1.11966i	−0.828609	+	0.559828i	$0.810867\pi$
$98$	−0.610815	−0.0617016
$99$	2.94356i	0.295839i
$100$	−7.47565	−0.747565
$101$	0.921274	0.0916702	0.0458351	−	0.998949i	$-0.485405\pi$
$101$	0.921274	0.0916702	0.0458351	+	0.998949i	$0.485405\pi$
$102$	0	0
$103$	−16.9736	−1.67246	−0.836229	−	0.548381i	$-0.815245\pi$
$103$	−16.9736	−1.67246	−0.836229	+	0.548381i	$0.815245\pi$
$104$	5.06418	0.496583
$105$	9.74422i	0.950939i
$106$	−4.57398	−0.444264
$107$	3.08647i	0.298380i	0.988809	+	0.149190i	$0.0476666\pi$
$107$	3.08647i	0.298380i	−0.988809	+	0.149190i	$0.952333\pi$
$108$	1.00000i	0.0962250i
$109$	− 2.24123i	− 0.214671i	−0.994223	−	0.107335i	$-0.965768\pi$
$109$	− 2.24123i	− 0.214671i	0.994223	−	0.107335i	$-0.0342319\pi$
$110$	−10.3969	−0.991308
$111$	−10.2121	−0.969293
$112$	− 2.75877i	− 0.260679i
$113$	11.4338i	1.07560i	0.843073	+	0.537799i	$0.180744\pi$
$113$	11.4338i	1.07560i	−0.843073	+	0.537799i	$0.819256\pi$
$114$	− 4.36959i	− 0.409249i
$115$	21.1925	1.97621
$116$	4.80066i	0.445730i
$117$	−5.06418	−0.468183
$118$	−5.53209	−0.509270
$119$	0	0
$120$	−3.53209	−0.322434
$121$	2.33544	0.212312
$122$	− 6.24123i	− 0.565054i
$123$	12.5817	1.13446
$124$	− 0.716881i	− 0.0643779i
$125$	8.74422i	0.782107i
$126$	2.75877i	0.245771i
$127$	8.75877	0.777215	0.388608	−	0.921403i	$-0.372956\pi$
$127$	8.75877	0.777215	0.388608	+	0.921403i	$0.372956\pi$
$128$	1.00000	0.0883883
$129$	10.9067i	0.960284i
$130$	− 17.8871i	− 1.56880i
$131$	− 1.28581i	− 0.112341i	−0.998421	−	0.0561707i	$-0.982111\pi$
$131$	− 1.28581i	− 0.112341i	0.998421	−	0.0561707i	$-0.0178891\pi$
$132$	−2.94356	−0.256204
$133$	− 12.0547i	− 1.04527i
$134$	5.67499	0.490245
$135$	3.53209	0.303994
$136$	0	0
$137$	2.36959	0.202447	0.101224	−	0.994864i	$-0.467724\pi$
$137$	2.36959	0.202447	0.101224	+	0.994864i	$0.467724\pi$
$138$	6.00000	0.510754
$139$	− 5.64590i	− 0.478879i	−0.970911	−	0.239439i	$-0.923036\pi$
$139$	− 5.64590i	− 0.478879i	0.970911	−	0.239439i	$-0.0769636\pi$
$140$	−9.74422	−0.823537
$141$	− 5.14796i	− 0.433536i
$142$	9.80335i	0.822679i
$143$	− 14.9067i	− 1.24656i
$144$	−1.00000	−0.0833333
$145$	16.9564	1.40815
$146$	9.04189i	0.748312i
$147$	0.610815i	0.0503791i
$148$	− 10.2121i	− 0.839432i
$149$	11.4260	0.936056	0.468028	−	0.883714i	$-0.344965\pi$
$149$	11.4260	0.936056	0.468028	+	0.883714i	$0.344965\pi$
$150$	7.47565i	0.610384i
$151$	−11.7510	−0.956285	−0.478143	−	0.878282i	$-0.658690\pi$
$151$	−11.7510	−0.956285	−0.478143	+	0.878282i	$0.658690\pi$
$152$	4.36959	0.354420
$153$	0	0
$154$	−8.12061	−0.654378
$155$	−2.53209	−0.203382
$156$	− 5.06418i	− 0.405459i
$157$	−3.51754	−0.280730	−0.140365	−	0.990100i	$-0.544828\pi$
$157$	−3.51754	−0.280730	−0.140365	+	0.990100i	$0.544828\pi$
$158$	− 6.61856i	− 0.526544i
$159$	4.57398i	0.362740i
$160$	− 3.53209i	− 0.279236i
$161$	16.5526	1.30453
$162$	1.00000	0.0785674
$163$	− 6.32501i	− 0.495413i	−0.968835	−	0.247706i	$-0.920323\pi$
$163$	− 6.32501i	− 0.495413i	0.968835	−	0.247706i	$-0.0796768\pi$
$164$	12.5817i	0.982467i
$165$	10.3969i	0.809400i
$166$	3.32501	0.258071
$167$	14.3405i	1.10970i	0.831950	+	0.554850i	$0.187224\pi$
$167$	14.3405i	1.10970i	−0.831950	+	0.554850i	$0.812776\pi$
$168$	−2.75877	−0.212844
$169$	12.6459	0.972761
$170$	0	0
$171$	−4.36959	−0.334151
$172$	−10.9067	−0.831630
$173$	0.815207i	0.0619791i	0.999520	+	0.0309895i	$0.00986586\pi$
$173$	0.815207i	0.0619791i	−0.999520	+	0.0309895i	$0.990134\pi$
$174$	4.80066	0.363937
$175$	20.6236i	1.55900i
$176$	− 2.94356i	− 0.221879i
$177$	5.53209i	0.415817i
$178$	13.8425	1.03754
$179$	−14.0642	−1.05121	−0.525603	−	0.850730i	$-0.676160\pi$
$179$	−14.0642	−1.05121	−0.525603	+	0.850730i	$0.676160\pi$
$180$	3.53209i	0.263266i
$181$	− 20.3405i	− 1.51190i	−0.654631	−	0.755948i	$-0.727176\pi$
$181$	− 20.3405i	− 1.51190i	0.654631	−	0.755948i	$-0.272824\pi$
$182$	− 13.9709i	− 1.03559i
$183$	−6.24123	−0.461365
$184$	6.00000i	0.442326i
$185$	−36.0702	−2.65193
$186$	−0.716881	−0.0525643
$187$	0	0
$188$	5.14796	0.375453
$189$	2.75877	0.200671
$190$	− 15.4338i	− 1.11968i
$191$	15.6459	1.13210	0.566049	−	0.824372i	$-0.308471\pi$
$191$	15.6459	1.13210	0.566049	+	0.824372i	$0.308471\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	10.2713i	0.739341i	0.929163	+	0.369671i	$0.120529\pi$
$193$	10.2713i	0.739341i	−0.929163	+	0.369671i	$0.879471\pi$
$194$	11.0273i	0.791717i
$195$	−17.8871	−1.28092
$196$	−0.610815	−0.0436296
$197$	− 8.72967i	− 0.621964i	−0.950416	−	0.310982i	$-0.899342\pi$
$197$	− 8.72967i	− 0.621964i	0.950416	−	0.310982i	$-0.100658\pi$
$198$	2.94356i	0.209190i
$199$	− 16.8922i	− 1.19745i	−0.800953	−	0.598727i	$-0.795673\pi$
$199$	− 16.8922i	− 1.19745i	0.800953	−	0.598727i	$-0.204327\pi$
$200$	−7.47565	−0.528608
$201$	− 5.67499i	− 0.400283i
$202$	0.921274	0.0648206
$203$	13.2439	0.929541
$204$	0	0
$205$	44.4397	3.10381
$206$	−16.9736	−1.18261
$207$	− 6.00000i	− 0.417029i
$208$	5.06418	0.351138
$209$	− 12.8621i	− 0.889693i
$210$	9.74422i	0.672415i
$211$	− 14.0993i	− 0.970633i	−0.874339	−	0.485317i	$-0.838704\pi$
$211$	− 14.0993i	− 0.970633i	0.874339	−	0.485317i	$-0.161296\pi$
$212$	−4.57398	−0.314142
$213$	9.80335	0.671714
$214$	3.08647i	0.210987i
$215$	38.5235i	2.62728i
$216$	1.00000i	0.0680414i
$217$	−1.97771	−0.134256
$218$	− 2.24123i	− 0.151795i
$219$	9.04189	0.610994
$220$	−10.3969	−0.700961
$221$	0	0
$222$	−10.2121	−0.685394
$223$	26.3037	1.76142	0.880711	−	0.473653i	$-0.157065\pi$
$223$	26.3037	1.76142	0.880711	+	0.473653i	$0.157065\pi$
$224$	− 2.75877i	− 0.184328i
$225$	7.47565	0.498377
$226$	11.4338i	0.760563i
$227$	− 6.06418i	− 0.402494i	−0.979541	−	0.201247i	$-0.935501\pi$
$227$	− 6.06418i	− 0.402494i	0.979541	−	0.201247i	$-0.0644993\pi$
$228$	− 4.36959i	− 0.289383i
$229$	−8.56624	−0.566073	−0.283036	−	0.959109i	$-0.591342\pi$
$229$	−8.56624	−0.566073	−0.283036	+	0.959109i	$0.591342\pi$
$230$	21.1925	1.39739
$231$	8.12061i	0.534297i
$232$	4.80066i	0.315179i
$233$	− 12.2121i	− 0.800043i	−0.916506	−	0.400022i	$-0.869003\pi$
$233$	− 12.2121i	− 0.800043i	0.916506	−	0.400022i	$-0.130997\pi$
$234$	−5.06418	−0.331056
$235$	− 18.1830i	− 1.18613i
$236$	−5.53209	−0.360108
$237$	−6.61856	−0.429921
$238$	0	0
$239$	11.8716	0.767913	0.383956	−	0.923351i	$-0.374561\pi$
$239$	11.8716	0.767913	0.383956	+	0.923351i	$0.374561\pi$
$240$	−3.53209	−0.227995
$241$	23.9172i	1.54064i	0.637658	+	0.770320i	$0.279903\pi$
$241$	23.9172i	1.54064i	−0.637658	+	0.770320i	$0.720097\pi$
$242$	2.33544	0.150128
$243$	− 1.00000i	− 0.0641500i
$244$	− 6.24123i	− 0.399554i
$245$	2.15745i	0.137835i
$246$	12.5817	0.802181
$247$	22.1284	1.40799
$248$	− 0.716881i	− 0.0455220i
$249$	− 3.32501i	− 0.210714i
$250$	8.74422i	0.553033i
$251$	−18.6040	−1.17427	−0.587137	−	0.809487i	$-0.699745\pi$
$251$	−18.6040	−1.17427	−0.587137	+	0.809487i	$0.699745\pi$
$252$	2.75877i	0.173786i
$253$	17.6614	1.11036
$254$	8.75877	0.549574
$255$	0	0
$256$	1.00000	0.0625000
$257$	4.16756	0.259965	0.129983	−	0.991516i	$-0.458508\pi$
$257$	4.16756	0.259965	0.129983	+	0.991516i	$0.458508\pi$
$258$	10.9067i	0.679023i
$259$	−28.1729	−1.75058
$260$	− 17.8871i	− 1.10931i
$261$	− 4.80066i	− 0.297153i
$262$	− 1.28581i	− 0.0794374i
$263$	−7.97090	−0.491507	−0.245754	−	0.969332i	$-0.579035\pi$
$263$	−7.97090	−0.491507	−0.245754	+	0.969332i	$0.579035\pi$
$264$	−2.94356	−0.181164
$265$	16.1557i	0.992437i
$266$	− 12.0547i	− 0.739120i
$267$	− 13.8425i	− 0.847150i
$268$	5.67499	0.346655
$269$	5.96316i	0.363580i	0.983337	+	0.181790i	$0.0581892\pi$
$269$	5.96316i	0.363580i	−0.983337	+	0.181790i	$0.941811\pi$
$270$	3.53209	0.214956
$271$	−3.07098	−0.186549	−0.0932745	−	0.995640i	$-0.529733\pi$
$271$	−3.07098	−0.186549	−0.0932745	+	0.995640i	$0.529733\pi$
$272$	0	0
$273$	−13.9709	−0.845558
$274$	2.36959	0.143152
$275$	22.0051i	1.32695i
$276$	6.00000	0.361158
$277$	23.2472i	1.39679i	0.715713	+	0.698395i	$0.246102\pi$
$277$	23.2472i	1.39679i	−0.715713	+	0.698395i	$0.753898\pi$
$278$	− 5.64590i	− 0.338618i
$279$	0.716881i	0.0429186i
$280$	−9.74422	−0.582329
$281$	−21.7297	−1.29628	−0.648142	−	0.761520i	$-0.724454\pi$
$281$	−21.7297	−1.29628	−0.648142	+	0.761520i	$0.724454\pi$
$282$	− 5.14796i	− 0.306556i
$283$	− 17.1925i	− 1.02199i	−0.859584	−	0.510995i	$-0.829277\pi$
$283$	− 17.1925i	− 1.02199i	0.859584	−	0.510995i	$-0.170723\pi$
$284$	9.80335i	0.581722i
$285$	−15.4338	−0.914217
$286$	− 14.9067i	− 0.881453i
$287$	34.7101	2.04887
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	16.9564	0.995712
$291$	11.0273	0.646434
$292$	9.04189i	0.529137i
$293$	−9.20708	−0.537883	−0.268942	−	0.963156i	$-0.586674\pi$
$293$	−9.20708	−0.537883	−0.268942	+	0.963156i	$0.586674\pi$
$294$	0.610815i	0.0356234i
$295$	19.5398i	1.13765i
$296$	− 10.2121i	− 0.593568i
$297$	2.94356	0.170803
$298$	11.4260	0.661892
$299$	30.3851i	1.75721i
$300$	7.47565i	0.431607i
$301$	30.0892i	1.73431i
$302$	−11.7510	−0.676196
$303$	− 0.921274i	− 0.0529258i
$304$	4.36959	0.250613
$305$	−22.0446	−1.26227
$306$	0	0
$307$	2.90673	0.165896	0.0829478	−	0.996554i	$-0.473567\pi$
$307$	2.90673	0.165896	0.0829478	+	0.996554i	$0.473567\pi$
$308$	−8.12061	−0.462715
$309$	16.9736i	0.965594i
$310$	−2.53209	−0.143813
$311$	13.0351i	0.739152i	0.929201	+	0.369576i	$0.120497\pi$
$311$	13.0351i	0.739152i	−0.929201	+	0.369576i	$0.879503\pi$
$312$	− 5.06418i	− 0.286703i
$313$	3.22163i	0.182097i	0.995846	+	0.0910486i	$0.0290219\pi$
$313$	3.22163i	0.182097i	−0.995846	+	0.0910486i	$0.970978\pi$
$314$	−3.51754	−0.198506
$315$	9.74422	0.549025
$316$	− 6.61856i	− 0.372323i
$317$	− 19.0838i	− 1.07185i	−0.844265	−	0.535926i	$-0.819963\pi$
$317$	− 19.0838i	− 1.07185i	0.844265	−	0.535926i	$-0.180037\pi$
$318$	4.57398i	0.256496i
$319$	14.1310	0.791187
$320$	− 3.53209i	− 0.197450i
$321$	3.08647	0.172270
$322$	16.5526	0.922442
$323$	0	0
$324$	1.00000	0.0555556
$325$	−37.8580	−2.09999
$326$	− 6.32501i	− 0.350310i
$327$	−2.24123	−0.123940
$328$	12.5817i	0.694709i
$329$	− 14.2020i	− 0.782983i
$330$	10.3969i	0.572332i
$331$	−3.43376	−0.188737	−0.0943683	−	0.995537i	$-0.530083\pi$
$331$	−3.43376	−0.188737	−0.0943683	+	0.995537i	$0.530083\pi$
$332$	3.32501	0.182484
$333$	10.2121i	0.559621i
$334$	14.3405i	0.784677i
$335$	− 20.0446i	− 1.09515i
$336$	−2.75877	−0.150503
$337$	35.7202i	1.94580i	0.231222	+	0.972901i	$0.425728\pi$
$337$	35.7202i	1.94580i	−0.231222	+	0.972901i	$0.574272\pi$
$338$	12.6459	0.687846
$339$	11.4338	0.620997
$340$	0	0
$341$	−2.11019	−0.114273
$342$	−4.36959	−0.236280
$343$	− 17.6263i	− 0.951731i
$344$	−10.9067	−0.588051
$345$	− 21.1925i	− 1.14097i
$346$	0.815207i	0.0438258i
$347$	− 1.10782i	− 0.0594710i	−0.999558	−	0.0297355i	$-0.990534\pi$
$347$	− 1.10782i	− 0.0594710i	0.999558	−	0.0297355i	$-0.00946650\pi$
$348$	4.80066	0.257342
$349$	−11.2371	−0.601509	−0.300754	−	0.953702i	$-0.597238\pi$
$349$	−11.2371	−0.601509	−0.300754	+	0.953702i	$0.597238\pi$
$350$	20.6236i	1.10238i
$351$	5.06418i	0.270306i
$352$	− 2.94356i	− 0.156892i
$353$	−11.2608	−0.599353	−0.299677	−	0.954041i	$-0.596879\pi$
$353$	−11.2608	−0.599353	−0.299677	+	0.954041i	$0.596879\pi$
$354$	5.53209i	0.294027i
$355$	34.6263	1.83777
$356$	13.8425	0.733654
$357$	0	0
$358$	−14.0642	−0.743315
$359$	−2.04458	−0.107909	−0.0539543	−	0.998543i	$-0.517183\pi$
$359$	−2.04458	−0.107909	−0.0539543	+	0.998543i	$0.517183\pi$
$360$	3.53209i	0.186157i
$361$	0.0932736	0.00490914
$362$	− 20.3405i	− 1.06907i
$363$	− 2.33544i	− 0.122579i
$364$	− 13.9709i	− 0.732274i
$365$	31.9368	1.67165
$366$	−6.24123	−0.326234
$367$	24.4097i	1.27418i	0.770791	+	0.637088i	$0.219861\pi$
$367$	24.4097i	1.27418i	−0.770791	+	0.637088i	$0.780139\pi$
$368$	6.00000i	0.312772i
$369$	− 12.5817i	− 0.654978i
$370$	−36.0702	−1.87520
$371$	12.6186i	0.655123i
$372$	−0.716881	−0.0371686
$373$	27.3756	1.41745	0.708727	−	0.705483i	$-0.249270\pi$
$373$	27.3756	1.41745	0.708727	+	0.705483i	$0.249270\pi$
$374$	0	0
$375$	8.74422	0.451550
$376$	5.14796	0.265486
$377$	24.3114i	1.25210i
$378$	2.75877	0.141896
$379$	− 22.4979i	− 1.15564i	−0.816164	−	0.577821i	$-0.803903\pi$
$379$	− 22.4979i	− 1.15564i	0.816164	−	0.577821i	$-0.196097\pi$
$380$	− 15.4338i	− 0.791735i
$381$	− 8.75877i	− 0.448725i
$382$	15.6459	0.800514
$383$	−16.5972	−0.848077	−0.424039	−	0.905644i	$-0.639388\pi$
$383$	−16.5972	−0.848077	−0.424039	+	0.905644i	$0.639388\pi$
$384$	− 1.00000i	− 0.0510310i
$385$	28.6827i	1.46181i
$386$	10.2713i	0.522793i
$387$	10.9067	0.554420
$388$	11.0273i	0.559828i
$389$	17.2249	0.873338	0.436669	−	0.899622i	$-0.356158\pi$
$389$	17.2249	0.873338	0.436669	+	0.899622i	$0.356158\pi$
$390$	−17.8871	−0.905750
$391$	0	0
$392$	−0.610815	−0.0308508
$393$	−1.28581	−0.0648604
$394$	− 8.72967i	− 0.439795i
$395$	−23.3773	−1.17624
$396$	2.94356i	0.147920i
$397$	4.49794i	0.225745i	0.993609	+	0.112873i	$0.0360052\pi$
$397$	4.49794i	0.225745i	−0.993609	+	0.112873i	$0.963995\pi$
$398$	− 16.8922i	− 0.846728i
$399$	−12.0547	−0.603489
$400$	−7.47565	−0.373783
$401$	2.04458i	0.102101i	0.998696	+	0.0510507i	$0.0162570\pi$
$401$	2.04458i	0.102101i	−0.998696	+	0.0510507i	$0.983743\pi$
$402$	− 5.67499i	− 0.283043i
$403$	− 3.63041i	− 0.180844i
$404$	0.921274	0.0458351
$405$	− 3.53209i	− 0.175511i
$406$	13.2439	0.657285
$407$	−30.0601	−1.49002
$408$	0	0
$409$	23.2841	1.15132	0.575661	−	0.817688i	$-0.304745\pi$
$409$	23.2841	1.15132	0.575661	+	0.817688i	$0.304745\pi$
$410$	44.4397	2.19472
$411$	− 2.36959i	− 0.116883i
$412$	−16.9736	−0.836229
$413$	15.2618i	0.750982i
$414$	− 6.00000i	− 0.294884i
$415$	− 11.7442i	− 0.576501i
$416$	5.06418	0.248292
$417$	−5.64590	−0.276481
$418$	− 12.8621i	− 0.629108i
$419$	1.50299i	0.0734260i	0.999326	+	0.0367130i	$0.0116887\pi$
$419$	1.50299i	0.0734260i	−0.999326	+	0.0367130i	$0.988311\pi$
$420$	9.74422i	0.475469i
$421$	18.1438	0.884277	0.442138	−	0.896947i	$-0.354220\pi$
$421$	18.1438	0.884277	0.442138	+	0.896947i	$0.354220\pi$
$422$	− 14.0993i	− 0.686341i
$423$	−5.14796	−0.250302
$424$	−4.57398	−0.222132
$425$	0	0
$426$	9.80335	0.474974
$427$	−17.2181	−0.833243
$428$	3.08647i	0.149190i
$429$	−14.9067	−0.719704
$430$	38.5235i	1.85777i
$431$	26.2276i	1.26334i	0.775237	+	0.631670i	$0.217630\pi$
$431$	26.2276i	1.26334i	−0.775237	+	0.631670i	$0.782370\pi$
$432$	1.00000i	0.0481125i
$433$	27.6604	1.32928	0.664638	−	0.747165i	$-0.268586\pi$
$433$	27.6604	1.32928	0.664638	+	0.747165i	$0.268586\pi$
$434$	−1.97771	−0.0949332
$435$	− 16.9564i	− 0.812995i
$436$	− 2.24123i	− 0.107335i
$437$	26.2175i	1.25415i
$438$	9.04189	0.432038
$439$	− 29.6459i	− 1.41492i	−0.706753	−	0.707461i	$-0.749841\pi$
$439$	− 29.6459i	− 1.41492i	0.706753	−	0.707461i	$-0.250159\pi$
$440$	−10.3969	−0.495654
$441$	0.610815	0.0290864
$442$	0	0
$443$	−34.3209	−1.63063	−0.815317	−	0.579014i	$-0.803437\pi$
$443$	−34.3209	−1.63063	−0.815317	+	0.579014i	$0.803437\pi$
$444$	−10.2121	−0.484646
$445$	− 48.8931i	− 2.31776i
$446$	26.3037	1.24551
$447$	− 11.4260i	− 0.540432i
$448$	− 2.75877i	− 0.130340i
$449$	− 23.8188i	− 1.12408i	−0.827110	−	0.562040i	$-0.810017\pi$
$449$	− 23.8188i	− 1.12408i	0.827110	−	0.562040i	$-0.189983\pi$
$450$	7.47565	0.352406
$451$	37.0351	1.74391
$452$	11.4338i	0.537799i
$453$	11.7510i	0.552112i
$454$	− 6.06418i	− 0.284606i
$455$	−49.3465	−2.31340
$456$	− 4.36959i	− 0.204625i
$457$	21.4662	1.00414	0.502072	−	0.864826i	$-0.332571\pi$
$457$	21.4662	1.00414	0.502072	+	0.864826i	$0.332571\pi$
$458$	−8.56624	−0.400274
$459$	0	0
$460$	21.1925	0.988107
$461$	16.8898	0.786637	0.393319	−	0.919402i	$-0.371327\pi$
$461$	16.8898	0.786637	0.393319	+	0.919402i	$0.371327\pi$
$462$	8.12061i	0.377805i
$463$	−3.75784	−0.174641	−0.0873207	−	0.996180i	$-0.527831\pi$
$463$	−3.75784	−0.174641	−0.0873207	+	0.996180i	$0.527831\pi$
$464$	4.80066i	0.222865i
$465$	2.53209i	0.117423i
$466$	− 12.2121i	− 0.565716i
$467$	−12.4311	−0.575242	−0.287621	−	0.957744i	$-0.592864\pi$
$467$	−12.4311	−0.575242	−0.287621	+	0.957744i	$0.592864\pi$
$468$	−5.06418	−0.234092
$469$	− 15.6560i	− 0.722927i
$470$	− 18.1830i	− 0.838721i
$471$	3.51754i	0.162080i
$472$	−5.53209	−0.254635
$473$	32.1046i	1.47617i
$474$	−6.61856	−0.304000
$475$	−32.6655	−1.49880
$476$	0	0
$477$	4.57398	0.209428
$478$	11.8716	0.542996
$479$	− 11.6905i	− 0.534151i	−0.963676	−	0.267076i	$-0.913943\pi$
$479$	− 11.6905i	− 0.534151i	0.963676	−	0.267076i	$-0.0860574\pi$
$480$	−3.53209	−0.161217
$481$	− 51.7161i	− 2.35805i
$482$	23.9172i	1.08940i
$483$	− 16.5526i	− 0.753170i
$484$	2.33544	0.106156
$485$	38.9495	1.76861
$486$	− 1.00000i	− 0.0453609i
$487$	− 7.33544i	− 0.332400i	−0.986092	−	0.166200i	$-0.946850\pi$
$487$	− 7.33544i	− 0.332400i	0.986092	−	0.166200i	$-0.0531498\pi$
$488$	− 6.24123i	− 0.282527i
$489$	−6.32501	−0.286027
$490$	2.15745i	0.0974637i
$491$	−2.27126	−0.102500	−0.0512502	−	0.998686i	$-0.516321\pi$
$491$	−2.27126	−0.102500	−0.0512502	+	0.998686i	$0.516321\pi$
$492$	12.5817	0.567228
$493$	0	0
$494$	22.1284	0.995602
$495$	10.3969	0.467307
$496$	− 0.716881i	− 0.0321889i
$497$	27.0452	1.21314
$498$	− 3.32501i	− 0.148997i
$499$	− 9.71957i	− 0.435108i	−0.976048	−	0.217554i	$-0.930192\pi$
$499$	− 9.71957i	− 0.435108i	0.976048	−	0.217554i	$-0.0698078\pi$
$500$	8.74422i	0.391054i
$501$	14.3405	0.640686
$502$	−18.6040	−0.830337
$503$	− 17.7588i	− 0.791824i	−0.918288	−	0.395912i	$-0.870428\pi$
$503$	− 17.7588i	− 0.791824i	0.918288	−	0.395912i	$-0.129572\pi$
$504$	2.75877i	0.122885i
$505$	− 3.25402i	− 0.144802i
$506$	17.6614	0.785144
$507$	− 12.6459i	− 0.561624i
$508$	8.75877	0.388608
$509$	−7.39786	−0.327904	−0.163952	−	0.986468i	$-0.552424\pi$
$509$	−7.39786	−0.327904	−0.163952	+	0.986468i	$0.552424\pi$
$510$	0	0
$511$	24.9445	1.10348
$512$	1.00000	0.0441942
$513$	4.36959i	0.192922i
$514$	4.16756	0.183823
$515$	59.9522i	2.64181i
$516$	10.9067i	0.480142i
$517$	− 15.1533i	− 0.666443i
$518$	−28.1729	−1.23785
$519$	0.815207	0.0357836
$520$	− 17.8871i	− 0.784402i
$521$	− 4.12298i	− 0.180631i	−0.995913	−	0.0903155i	$-0.971212\pi$
$521$	− 4.12298i	− 0.180631i	0.995913	−	0.0903155i	$-0.0287875\pi$
$522$	− 4.80066i	− 0.210119i
$523$	−36.5134	−1.59662	−0.798310	−	0.602246i	$-0.794272\pi$
$523$	−36.5134	−1.59662	−0.798310	+	0.602246i	$0.794272\pi$
$524$	− 1.28581i	− 0.0561707i
$525$	20.6236	0.900088
$526$	−7.97090	−0.347548
$527$	0	0
$528$	−2.94356	−0.128102
$529$	−13.0000	−0.565217
$530$	16.1557i	0.701759i
$531$	5.53209	0.240072
$532$	− 12.0547i	− 0.522637i
$533$	63.7161i	2.75985i
$534$	− 13.8425i	− 0.599026i
$535$	10.9017	0.471320
$536$	5.67499	0.245122
$537$	14.0642i	0.606914i
$538$	5.96316i	0.257090i
$539$	1.79797i	0.0774441i
$540$	3.53209	0.151997
$541$	44.7939i	1.92584i	0.269790	+	0.962919i	$0.413046\pi$
$541$	44.7939i	1.92584i	−0.269790	+	0.962919i	$0.586954\pi$
$542$	−3.07098	−0.131910
$543$	−20.3405	−0.872894
$544$	0	0
$545$	−7.91622	−0.339094
$546$	−13.9709	−0.597900
$547$	22.0993i	0.944896i	0.881359	+	0.472448i	$0.156630\pi$
$547$	22.0993i	0.944896i	−0.881359	+	0.472448i	$0.843370\pi$
$548$	2.36959	0.101224
$549$	6.24123i	0.266369i
$550$	22.0051i	0.938299i
$551$	20.9769i	0.893646i
$552$	6.00000	0.255377
$553$	−18.2591	−0.776455
$554$	23.2472i	0.987680i
$555$	36.0702i	1.53109i
$556$	− 5.64590i	− 0.239439i
$557$	21.9905	0.931768	0.465884	−	0.884846i	$-0.345736\pi$
$557$	21.9905	0.931768	0.465884	+	0.884846i	$0.345736\pi$
$558$	0.716881i	0.0303480i
$559$	−55.2336	−2.33613
$560$	−9.74422	−0.411769
$561$	0	0
$562$	−21.7297	−0.916611
$563$	31.9486	1.34647	0.673237	−	0.739427i	$-0.264903\pi$
$563$	31.9486	1.34647	0.673237	+	0.739427i	$0.264903\pi$
$564$	− 5.14796i	− 0.216768i
$565$	40.3851	1.69901
$566$	− 17.1925i	− 0.722656i
$567$	− 2.75877i	− 0.115857i
$568$	9.80335i	0.411339i
$569$	30.9614	1.29797	0.648985	−	0.760801i	$-0.275194\pi$
$569$	30.9614	1.29797	0.648985	+	0.760801i	$0.275194\pi$
$570$	−15.4338	−0.646449
$571$	− 16.5080i	− 0.690840i	−0.938448	−	0.345420i	$-0.887736\pi$
$571$	− 16.5080i	− 0.690840i	0.938448	−	0.345420i	$-0.112264\pi$
$572$	− 14.9067i	− 0.623282i
$573$	− 15.6459i	− 0.653617i
$574$	34.7101	1.44877
$575$	− 44.8539i	− 1.87054i
$576$	−1.00000	−0.0416667
$577$	−18.9026	−0.786926	−0.393463	−	0.919340i	$-0.628723\pi$
$577$	−18.9026	−0.786926	−0.393463	+	0.919340i	$0.628723\pi$
$578$	0	0
$579$	10.2713	0.426859
$580$	16.9564	0.704074
$581$	− 9.17293i	− 0.380557i
$582$	11.0273	0.457098
$583$	13.4638i	0.557613i
$584$	9.04189i	0.374156i
$585$	17.8871i	0.739542i
$586$	−9.20708	−0.380341
$587$	−7.17799	−0.296267	−0.148134	−	0.988967i	$-0.547327\pi$
$587$	−7.17799	−0.296267	−0.148134	+	0.988967i	$0.547327\pi$
$588$	0.610815i	0.0251896i
$589$	− 3.13247i	− 0.129071i
$590$	19.5398i	0.804442i
$591$	−8.72967	−0.359091
$592$	− 10.2121i	− 0.419716i
$593$	−26.2823	−1.07928	−0.539642	−	0.841894i	$-0.681441\pi$
$593$	−26.2823	−1.07928	−0.539642	+	0.841894i	$0.681441\pi$
$594$	2.94356	0.120776
$595$	0	0
$596$	11.4260	0.468028
$597$	−16.8922	−0.691351
$598$	30.3851i	1.24254i
$599$	−28.3114	−1.15677	−0.578386	−	0.815763i	$-0.696317\pi$
$599$	−28.3114	−1.15677	−0.578386	+	0.815763i	$0.696317\pi$
$600$	7.47565i	0.305192i
$601$	− 11.4406i	− 0.466671i	−0.972396	−	0.233335i	$-0.925036\pi$
$601$	− 11.4406i	− 0.466671i	0.972396	−	0.233335i	$-0.0749640\pi$
$602$	30.0892i	1.22634i
$603$	−5.67499	−0.231104
$604$	−11.7510	−0.478143
$605$	− 8.24897i	− 0.335368i
$606$	− 0.921274i	− 0.0374242i
$607$	− 32.4911i	− 1.31877i	−0.751804	−	0.659387i	$-0.770816\pi$
$607$	− 32.4911i	− 1.31877i	0.751804	−	0.659387i	$-0.229184\pi$
$608$	4.36959	0.177210
$609$	− 13.2439i	− 0.536671i
$610$	−22.0446	−0.892559
$611$	26.0702	1.05469
$612$	0	0
$613$	−14.2959	−0.577406	−0.288703	−	0.957419i	$-0.593224\pi$
$613$	−14.2959	−0.577406	−0.288703	+	0.957419i	$0.593224\pi$
$614$	2.90673	0.117306
$615$	− 44.4397i	− 1.79198i
$616$	−8.12061	−0.327189
$617$	− 41.4356i	− 1.66814i	−0.551662	−	0.834068i	$-0.686006\pi$
$617$	− 41.4356i	− 1.66814i	0.551662	−	0.834068i	$-0.313994\pi$
$618$	16.9736i	0.682778i
$619$	− 8.05468i	− 0.323745i	−0.986812	−	0.161873i	$-0.948247\pi$
$619$	− 8.05468i	− 0.323745i	0.986812	−	0.161873i	$-0.0517533\pi$
$620$	−2.53209	−0.101691
$621$	−6.00000	−0.240772
$622$	13.0351i	0.522659i
$623$	− 38.1884i	− 1.52999i
$624$	− 5.06418i	− 0.202729i
$625$	−6.49289	−0.259716
$626$	3.22163i	0.128762i
$627$	−12.8621	−0.513665
$628$	−3.51754	−0.140365
$629$	0	0
$630$	9.74422	0.388219
$631$	−10.5885	−0.421523	−0.210761	−	0.977538i	$-0.567594\pi$
$631$	−10.5885	−0.421523	−0.210761	+	0.977538i	$0.567594\pi$
$632$	− 6.61856i	− 0.263272i
$633$	−14.0993	−0.560395
$634$	− 19.0838i	− 0.757914i
$635$	− 30.9368i	− 1.22769i
$636$	4.57398i	0.181370i
$637$	−3.09327	−0.122560
$638$	14.1310	0.559453
$639$	− 9.80335i	− 0.387814i
$640$	− 3.53209i	− 0.139618i
$641$	32.5526i	1.28575i	0.765971	+	0.642876i	$0.222259\pi$
$641$	32.5526i	1.28575i	−0.765971	+	0.642876i	$0.777741\pi$
$642$	3.08647	0.121813
$643$	− 10.5817i	− 0.417302i	−0.977990	−	0.208651i	$-0.933093\pi$
$643$	− 10.5817i	− 0.417302i	0.977990	−	0.208651i	$-0.0669073\pi$
$644$	16.5526	0.652265
$645$	38.5235	1.51686
$646$	0	0
$647$	−25.4884	−1.00205	−0.501027	−	0.865432i	$-0.667044\pi$
$647$	−25.4884	−1.00205	−0.501027	+	0.865432i	$0.667044\pi$
$648$	1.00000	0.0392837
$649$	16.2841i	0.639205i
$650$	−37.8580	−1.48491
$651$	1.97771i	0.0775126i
$652$	− 6.32501i	− 0.247706i
$653$	− 20.6108i	− 0.806564i	−0.915076	−	0.403282i	$-0.867869\pi$
$653$	− 20.6108i	− 0.806564i	0.915076	−	0.403282i	$-0.132131\pi$
$654$	−2.24123	−0.0876390
$655$	−4.54158	−0.177454
$656$	12.5817i	0.491234i
$657$	− 9.04189i	− 0.352758i
$658$	− 14.2020i	− 0.553653i
$659$	−41.5117	−1.61706	−0.808532	−	0.588452i	$-0.799738\pi$
$659$	−41.5117	−1.61706	−0.808532	+	0.588452i	$0.799738\pi$
$660$	10.3969i	0.404700i
$661$	17.0060	0.661456	0.330728	−	0.943726i	$-0.392706\pi$
$661$	17.0060	0.661456	0.330728	+	0.943726i	$0.392706\pi$
$662$	−3.43376	−0.133457
$663$	0	0
$664$	3.32501	0.129035
$665$	−42.5782	−1.65111
$666$	10.2121i	0.395712i
$667$	−28.8040	−1.11529
$668$	14.3405i	0.554850i
$669$	− 26.3037i	− 1.01696i
$670$	− 20.0446i	− 0.774390i
$671$	−18.3715	−0.709222
$672$	−2.75877	−0.106422
$673$	20.0392i	0.772454i	0.922404	+	0.386227i	$0.126222\pi$
$673$	20.0392i	0.772454i	−0.922404	+	0.386227i	$0.873778\pi$
$674$	35.7202i	1.37589i
$675$	− 7.47565i	− 0.287738i
$676$	12.6459	0.486381
$677$	47.9823i	1.84411i	0.387061	+	0.922054i	$0.373490\pi$
$677$	47.9823i	1.84411i	−0.387061	+	0.922054i	$0.626510\pi$
$678$	11.4338	0.439111
$679$	30.4219	1.16749
$680$	0	0
$681$	−6.06418	−0.232380
$682$	−2.11019	−0.0808032
$683$	− 33.4739i	− 1.28084i	−0.768024	−	0.640422i	$-0.778760\pi$
$683$	− 33.4739i	− 1.28084i	0.768024	−	0.640422i	$-0.221240\pi$
$684$	−4.36959	−0.167075
$685$	− 8.36959i	− 0.319785i
$686$	− 17.6263i	− 0.672975i
$687$	8.56624i	0.326822i
$688$	−10.9067	−0.415815
$689$	−23.1634	−0.882457
$690$	− 21.1925i	− 0.806786i
$691$	20.4979i	0.779778i	0.920862	+	0.389889i	$0.127487\pi$
$691$	20.4979i	0.779778i	−0.920862	+	0.389889i	$0.872513\pi$
$692$	0.815207i	0.0309895i
$693$	8.12061	0.308477
$694$	− 1.10782i	− 0.0420523i
$695$	−19.9418	−0.756436
$696$	4.80066	0.181969
$697$	0	0
$698$	−11.2371	−0.425331
$699$	−12.2121	−0.461905
$700$	20.6236i	0.779499i
$701$	51.4415	1.94292	0.971459	−	0.237206i	$-0.0762316\pi$
$701$	51.4415	1.94292	0.971459	+	0.237206i	$0.0762316\pi$
$702$	5.06418i	0.191135i
$703$	− 44.6228i	− 1.68298i
$704$	− 2.94356i	− 0.110940i
$705$	−18.1830	−0.684813
$706$	−11.2608	−0.423807
$707$	− 2.54158i	− 0.0955861i
$708$	5.53209i	0.207909i
$709$	10.1438i	0.380960i	0.981691	+	0.190480i	$0.0610044\pi$
$709$	10.1438i	0.380960i	−0.981691	+	0.190480i	$0.938996\pi$
$710$	34.6263	1.29950
$711$	6.61856i	0.248215i
$712$	13.8425	0.518771
$713$	4.30129	0.161085
$714$	0	0
$715$	−52.6519	−1.96907
$716$	−14.0642	−0.525603
$717$	− 11.8716i	− 0.443355i
$718$	−2.04458	−0.0763030
$719$	15.4047i	0.574497i	0.957856	+	0.287249i	$0.0927406\pi$
$719$	15.4047i	0.574497i	−0.957856	+	0.287249i	$0.907259\pi$
$720$	3.53209i	0.131633i
$721$	46.8262i	1.74390i
$722$	0.0932736	0.00347128
$723$	23.9172	0.889489
$724$	− 20.3405i	− 0.755948i
$725$	− 35.8881i	− 1.33285i
$726$	− 2.33544i	− 0.0866762i
$727$	−23.1097	−0.857091	−0.428545	−	0.903520i	$-0.640974\pi$
$727$	−23.1097	−0.857091	−0.428545	+	0.903520i	$0.640974\pi$
$728$	− 13.9709i	− 0.517796i
$729$	−1.00000	−0.0370370
$730$	31.9368	1.18203
$731$	0	0
$732$	−6.24123	−0.230682
$733$	4.20676	0.155380	0.0776901	−	0.996978i	$-0.475246\pi$
$733$	4.20676	0.155380	0.0776901	+	0.996978i	$0.475246\pi$
$734$	24.4097i	0.900979i
$735$	2.15745	0.0795788
$736$	6.00000i	0.221163i
$737$	− 16.7047i	− 0.615325i
$738$	− 12.5817i	− 0.463139i
$739$	−7.79797	−0.286853	−0.143427	−	0.989661i	$-0.545812\pi$
$739$	−7.79797	−0.286853	−0.143427	+	0.989661i	$0.545812\pi$
$740$	−36.0702	−1.32597
$741$	− 22.1284i	− 0.812905i
$742$	12.6186i	0.463242i
$743$	11.5567i	0.423976i	0.977272	+	0.211988i	$0.0679937\pi$
$743$	11.5567i	0.423976i	−0.977272	+	0.211988i	$0.932006\pi$
$744$	−0.716881	−0.0262821
$745$	− 40.3577i	− 1.47859i
$746$	27.3756	1.00229
$747$	−3.32501	−0.121656
$748$	0	0
$749$	8.51485	0.311126
$750$	8.74422	0.319294
$751$	13.9172i	0.507844i	0.967225	+	0.253922i	$0.0817207\pi$
$751$	13.9172i	0.507844i	−0.967225	+	0.253922i	$0.918279\pi$
$752$	5.14796	0.187727
$753$	18.6040i	0.677968i
$754$	24.3114i	0.885369i
$755$	41.5057i	1.51055i
$756$	2.75877	0.100336
$757$	18.0702	0.656771	0.328386	−	0.944544i	$-0.393495\pi$
$757$	18.0702	0.656771	0.328386	+	0.944544i	$0.393495\pi$
$758$	− 22.4979i	− 0.817162i
$759$	− 17.6614i	− 0.641067i
$760$	− 15.4338i	− 0.559841i
$761$	−0.241230	−0.00874456	−0.00437228	−	0.999990i	$-0.501392\pi$
$761$	−0.241230	−0.00874456	−0.00437228	+	0.999990i	$0.501392\pi$
$762$	− 8.75877i	− 0.317297i
$763$	−6.18304	−0.223841
$764$	15.6459	0.566049
$765$	0	0
$766$	−16.5972	−0.599681
$767$	−28.0155	−1.01158
$768$	− 1.00000i	− 0.0360844i
$769$	12.5963	0.454233	0.227116	−	0.973868i	$-0.427070\pi$
$769$	12.5963	0.454233	0.227116	+	0.973868i	$0.427070\pi$
$770$	28.6827i	1.03365i
$771$	− 4.16756i	− 0.150091i
$772$	10.2713i	0.369671i
$773$	−33.4807	−1.20422	−0.602109	−	0.798414i	$-0.705673\pi$
$773$	−33.4807	−1.20422	−0.602109	+	0.798414i	$0.705673\pi$
$774$	10.9067	0.392034
$775$	5.35916i	0.192507i
$776$	11.0273i	0.395858i
$777$	28.1729i	1.01070i
$778$	17.2249	0.617544
$779$	54.9769i	1.96975i
$780$	−17.8871	−0.640462
$781$	28.8568	1.03258
$782$	0	0
$783$	−4.80066	−0.171562
$784$	−0.610815	−0.0218148
$785$	12.4243i	0.443441i
$786$	−1.28581	−0.0458632
$787$	− 25.9181i	− 0.923880i	−0.886911	−	0.461940i	$-0.847154\pi$
$787$	− 25.9181i	− 0.923880i	0.886911	−	0.461940i	$-0.152846\pi$
$788$	− 8.72967i	− 0.310982i
$789$	7.97090i	0.283772i
$790$	−23.3773	−0.831728
$791$	31.5431	1.12154
$792$	2.94356i	0.104595i
$793$	− 31.6067i	− 1.12239i
$794$	4.49794i	0.159626i
$795$	16.1557	0.572984
$796$	− 16.8922i	− 0.598727i
$797$	−55.5580	−1.96797	−0.983983	−	0.178264i	$-0.942952\pi$
$797$	−55.5580	−1.96797	−0.983983	+	0.178264i	$0.942952\pi$
$798$	−12.0547	−0.426731
$799$	0	0
$800$	−7.47565	−0.264304
$801$	−13.8425	−0.489102
$802$	2.04458i	0.0721965i
$803$	26.6154	0.939236
$804$	− 5.67499i	− 0.200142i
$805$	− 58.4653i	− 2.06063i
$806$	− 3.63041i	− 0.127876i
$807$	5.96316	0.209913
$808$	0.921274	0.0324103
$809$	− 17.9317i	− 0.630445i	−0.949018	−	0.315223i	$-0.897921\pi$
$809$	− 17.9317i	− 0.630445i	0.949018	−	0.315223i	$-0.102079\pi$
$810$	− 3.53209i	− 0.124105i
$811$	25.2472i	0.886550i	0.896386	+	0.443275i	$0.146183\pi$
$811$	25.2472i	0.886550i	−0.896386	+	0.443275i	$0.853817\pi$
$812$	13.2439	0.464770
$813$	3.07098i	0.107704i
$814$	−30.0601	−1.05360
$815$	−22.3405	−0.782553
$816$	0	0
$817$	−47.6579	−1.66734
$818$	23.2841	0.814108
$819$	13.9709i	0.488183i
$820$	44.4397	1.55190
$821$	− 2.68098i	− 0.0935668i	−0.998905	−	0.0467834i	$-0.985103\pi$
$821$	− 2.68098i	− 0.0935668i	0.998905	−	0.0467834i	$-0.0148971\pi$
$822$	− 2.36959i	− 0.0826488i
$823$	25.1712i	0.877412i	0.898631	+	0.438706i	$0.144563\pi$
$823$	25.1712i	0.877412i	−0.898631	+	0.438706i	$0.855437\pi$
$824$	−16.9736	−0.591303
$825$	22.0051	0.766118
$826$	15.2618i	0.531025i
$827$	− 11.4638i	− 0.398635i	−0.979935	−	0.199318i	$-0.936127\pi$
$827$	− 11.4638i	− 0.398635i	0.979935	−	0.199318i	$-0.0638725\pi$
$828$	− 6.00000i	− 0.208514i
$829$	49.4593	1.71779	0.858897	−	0.512148i	$-0.171150\pi$
$829$	49.4593	1.71779	0.858897	+	0.512148i	$0.171150\pi$
$830$	− 11.7442i	− 0.407648i
$831$	23.2472	0.806437
$832$	5.06418	0.175569
$833$	0	0
$834$	−5.64590	−0.195501
$835$	50.6519	1.75288
$836$	− 12.8621i	− 0.444847i
$837$	0.716881	0.0247790
$838$	1.50299i	0.0519200i
$839$	− 33.6560i	− 1.16193i	−0.813927	−	0.580967i	$-0.802674\pi$
$839$	− 33.6560i	− 1.16193i	0.813927	−	0.580967i	$-0.197326\pi$
$840$	9.74422i	0.336208i
$841$	5.95367	0.205299
$842$	18.1438	0.625278
$843$	21.7297i	0.748410i
$844$	− 14.0993i	− 0.485317i
$845$	− 44.6664i	− 1.53657i
$846$	−5.14796	−0.176990
$847$	− 6.44293i	− 0.221382i
$848$	−4.57398	−0.157071
$849$	−17.1925	−0.590046
$850$	0	0
$851$	61.2728	2.10040
$852$	9.80335	0.335857
$853$	2.42427i	0.0830053i	0.999138	+	0.0415027i	$0.0132145\pi$
$853$	2.42427i	0.0830053i	−0.999138	+	0.0415027i	$0.986785\pi$
$854$	−17.2181	−0.589192
$855$	15.4338i	0.527824i
$856$	3.08647i	0.105493i
$857$	3.21625i	0.109865i	0.998490	+	0.0549325i	$0.0174944\pi$
$857$	3.21625i	0.109865i	−0.998490	+	0.0549325i	$0.982506\pi$
$858$	−14.9067	−0.508907
$859$	−23.4831	−0.801232	−0.400616	−	0.916246i	$-0.631204\pi$
$859$	−23.4831	−0.801232	−0.400616	+	0.916246i	$0.631204\pi$
$860$	38.5235i	1.31364i
$861$	− 34.7101i	− 1.18292i
$862$	26.2276i	0.893316i
$863$	44.4344	1.51256	0.756282	−	0.654246i	$-0.227014\pi$
$863$	44.4344	1.51256	0.756282	+	0.654246i	$0.227014\pi$
$864$	1.00000i	0.0340207i
$865$	2.87939	0.0979020
$866$	27.6604	0.939940
$867$	0	0
$868$	−1.97771	−0.0671279
$869$	−19.4821	−0.660886
$870$	− 16.9564i	− 0.574874i
$871$	28.7392	0.973790
$872$	− 2.24123i	− 0.0758976i
$873$	− 11.0273i	− 0.373219i
$874$	26.2175i	0.886821i
$875$	24.1233	0.815516
$876$	9.04189	0.305497
$877$	9.07966i	0.306598i	0.988180	+	0.153299i	$0.0489898\pi$
$877$	9.07966i	0.306598i	−0.988180	+	0.153299i	$0.951010\pi$
$878$	− 29.6459i	− 1.00050i
$879$	9.20708i	0.310547i
$880$	−10.3969	−0.350480
$881$	− 25.5912i	− 0.862190i	−0.902307	−	0.431095i	$-0.858127\pi$
$881$	− 25.5912i	− 0.862190i	0.902307	−	0.431095i	$-0.141873\pi$
$882$	0.610815	0.0205672
$883$	−22.3506	−0.752157	−0.376079	−	0.926588i	$-0.622728\pi$
$883$	−22.3506	−0.752157	−0.376079	+	0.926588i	$0.622728\pi$
$884$	0	0
$885$	19.5398	0.656824
$886$	−34.3209	−1.15303
$887$	− 26.4688i	− 0.888737i	−0.895844	−	0.444368i	$-0.853428\pi$
$887$	− 26.4688i	− 0.888737i	0.895844	−	0.444368i	$-0.146572\pi$
$888$	−10.2121	−0.342697
$889$	− 24.1634i	− 0.810416i
$890$	− 48.8931i	− 1.63890i
$891$	− 2.94356i	− 0.0986131i
$892$	26.3037	0.880711
$893$	22.4944	0.752747
$894$	− 11.4260i	− 0.382143i
$895$	49.6759i	1.66048i
$896$	− 2.75877i	− 0.0921641i
$897$	30.3851	1.01453
$898$	− 23.8188i	− 0.794845i
$899$	3.44150	0.114781
$900$	7.47565	0.249188
$901$	0	0
$902$	37.0351	1.23313
$903$	30.0892	1.00130
$904$	11.4338i	0.380281i
$905$	−71.8444	−2.38819
$906$	11.7510i	0.390402i
$907$	55.5722i	1.84525i	0.385704	+	0.922623i	$0.373959\pi$
$907$	55.5722i	1.84525i	−0.385704	+	0.922623i	$0.626041\pi$
$908$	− 6.06418i	− 0.201247i
$909$	−0.921274	−0.0305567
$910$	−49.3465	−1.63582
$911$	− 49.0506i	− 1.62512i	−0.582879	−	0.812559i	$-0.698074\pi$
$911$	− 49.0506i	− 1.62512i	0.582879	−	0.812559i	$-0.301926\pi$
$912$	− 4.36959i	− 0.144691i
$913$	− 9.78737i	− 0.323915i
$914$	21.4662	0.710037
$915$	22.0446i	0.728771i
$916$	−8.56624	−0.283036
$917$	−3.54725	−0.117140
$918$	0	0
$919$	−15.2020	−0.501469	−0.250734	−	0.968056i	$-0.580672\pi$
$919$	−15.2020	−0.501469	−0.250734	+	0.968056i	$0.580672\pi$
$920$	21.1925	0.698697
$921$	− 2.90673i	− 0.0957799i
$922$	16.8898	0.556236
$923$	49.6459i	1.63411i
$924$	8.12061i	0.267149i
$925$	76.3424i	2.51012i
$926$	−3.75784	−0.123490
$927$	16.9736	0.557486
$928$	4.80066i	0.157589i
$929$	22.8966i	0.751214i	0.926779	+	0.375607i	$0.122566\pi$
$929$	22.8966i	0.751214i	−0.926779	+	0.375607i	$0.877434\pi$
$930$	2.53209i	0.0830305i
$931$	−2.66901	−0.0874731
$932$	− 12.2121i	− 0.400022i
$933$	13.0351	0.426749
$934$	−12.4311	−0.406757
$935$	0	0
$936$	−5.06418	−0.165528
$937$	−3.34554	−0.109294	−0.0546470	−	0.998506i	$-0.517403\pi$
$937$	−3.34554	−0.109294	−0.0546470	+	0.998506i	$0.517403\pi$
$938$	− 15.6560i	− 0.511187i
$939$	3.22163	0.105134
$940$	− 18.1830i	− 0.593065i
$941$	11.5877i	0.377748i	0.982001	+	0.188874i	$0.0604838\pi$
$941$	11.5877i	0.377748i	−0.982001	+	0.188874i	$0.939516\pi$
$942$	3.51754i	0.114608i
$943$	−75.4903	−2.45830
$944$	−5.53209	−0.180054
$945$	− 9.74422i	− 0.316980i
$946$	32.1046i	1.04381i
$947$	− 33.6792i	− 1.09443i	−0.836993	−	0.547214i	$-0.815688\pi$
$947$	− 33.6792i	− 1.09443i	0.836993	−	0.547214i	$-0.184312\pi$
$948$	−6.61856	−0.214961
$949$	45.7897i	1.48640i
$950$	−32.6655	−1.05981
$951$	−19.0838	−0.618834
$952$	0	0
$953$	−13.9655	−0.452388	−0.226194	−	0.974082i	$-0.572628\pi$
$953$	−13.9655	−0.452388	−0.226194	+	0.974082i	$0.572628\pi$
$954$	4.57398	0.148088
$955$	− 55.2627i	− 1.78826i
$956$	11.8716	0.383956
$957$	− 14.1310i	− 0.456792i
$958$	− 11.6905i	− 0.377702i
$959$	− 6.53714i	− 0.211095i
$960$	−3.53209	−0.113998
$961$	30.4861	0.983422
$962$	− 51.7161i	− 1.66739i
$963$	− 3.08647i	− 0.0994600i
$964$	23.9172i	0.770320i
$965$	36.2790	1.16786
$966$	− 16.5526i	− 0.532572i
$967$	−47.0515	−1.51307	−0.756537	−	0.653951i	$-0.773110\pi$
$967$	−47.0515	−1.51307	−0.756537	+	0.653951i	$0.773110\pi$
$968$	2.33544	0.0750638
$969$	0	0
$970$	38.9495	1.25059
$971$	−30.2044	−0.969305	−0.484653	−	0.874707i	$-0.661054\pi$
$971$	−30.2044	−0.969305	−0.484653	+	0.874707i	$0.661054\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	−15.5757	−0.499335
$974$	− 7.33544i	− 0.235043i
$975$	37.8580i	1.21243i
$976$	− 6.24123i	− 0.199777i
$977$	−12.4534	−0.398418	−0.199209	−	0.979957i	$-0.563837\pi$
$977$	−12.4534	−0.398418	−0.199209	+	0.979957i	$0.563837\pi$
$978$	−6.32501	−0.202251
$979$	− 40.7464i	− 1.30226i
$980$	2.15745i	0.0689173i
$981$	2.24123i	0.0715570i
$982$	−2.27126	−0.0724788
$983$	− 42.9769i	− 1.37075i	−0.728190	−	0.685375i	$-0.759638\pi$
$983$	− 42.9769i	− 1.37075i	0.728190	−	0.685375i	$-0.240362\pi$
$984$	12.5817	0.401091
$985$	−30.8340	−0.982453
$986$	0	0
$987$	−14.2020	−0.452056
$988$	22.1284	0.703997
$989$	− 65.4404i	− 2.08088i
$990$	10.3969	0.330436
$991$	9.24123i	0.293557i	0.989169	+	0.146779i	$0.0468905\pi$
$991$	9.24123i	0.293557i	−0.989169	+	0.146779i	$0.953109\pi$
$992$	− 0.716881i	− 0.0227610i
$993$	3.43376i	0.108967i
$994$	27.0452	0.857821
$995$	−59.6647	−1.89150
$996$	− 3.32501i	− 0.105357i
$997$	28.2567i	0.894899i	0.894309	+	0.447450i	$0.147668\pi$
$997$	28.2567i	0.894899i	−0.894309	+	0.447450i	$0.852332\pi$
$998$	− 9.71957i	− 0.307668i
$999$	10.2121	0.323098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.b.j.577.1		6
17.2	even	8		1734.2.f.n.829.3		12
17.4	even	4		1734.2.a.p.1.1	✓	3
17.8	even	8		1734.2.f.n.1483.3		12
17.9	even	8		1734.2.f.n.1483.4		12
17.13	even	4		1734.2.a.q.1.3	yes	3
17.15	even	8		1734.2.f.n.829.4		12
17.16	even	2	inner	1734.2.b.j.577.6		6
51.38	odd	4		5202.2.a.bp.1.3		3
51.47	odd	4		5202.2.a.bm.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1734.2.a.p.1.1	✓	3	17.4	even	4
1734.2.a.q.1.3	yes	3	17.13	even	4
1734.2.b.j.577.1		6	1.1	even	1	trivial
1734.2.b.j.577.6		6	17.16	even	2	inner
1734.2.f.n.829.3		12	17.2	even	8
1734.2.f.n.829.4		12	17.15	even	8
1734.2.f.n.1483.3		12	17.8	even	8
1734.2.f.n.1483.4		12	17.9	even	8
5202.2.a.bm.1.1		3	51.47	odd	4
5202.2.a.bp.1.3		3	51.38	odd	4

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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.53209i q^{5} -1.00000i q^{6} -2.75877i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.53209i q^{5} -1.00000i q^{6} -2.75877i q^{7} +1.00000 q^{8} -1.00000 q^{9} -3.53209i q^{10} -2.94356i q^{11} -1.00000i q^{12} +5.06418 q^{13} -2.75877i q^{14} -3.53209 q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.36959 q^{19} -3.53209i q^{20} -2.75877 q^{21} -2.94356i q^{22} +6.00000i q^{23} -1.00000i q^{24} -7.47565 q^{25} +5.06418 q^{26} +1.00000i q^{27} -2.75877i q^{28} +4.80066i q^{29} -3.53209 q^{30} -0.716881i q^{31} +1.00000 q^{32} -2.94356 q^{33} -9.74422 q^{35} -1.00000 q^{36} -10.2121i q^{37} +4.36959 q^{38} -5.06418i q^{39} -3.53209i q^{40} +12.5817i q^{41} -2.75877 q^{42} -10.9067 q^{43} -2.94356i q^{44} +3.53209i q^{45} +6.00000i q^{46} +5.14796 q^{47} -1.00000i q^{48} -0.610815 q^{49} -7.47565 q^{50} +5.06418 q^{52} -4.57398 q^{53} +1.00000i q^{54} -10.3969 q^{55} -2.75877i q^{56} -4.36959i q^{57} +4.80066i q^{58} -5.53209 q^{59} -3.53209 q^{60} -6.24123i q^{61} -0.716881i q^{62} +2.75877i q^{63} +1.00000 q^{64} -17.8871i q^{65} -2.94356 q^{66} +5.67499 q^{67} +6.00000 q^{69} -9.74422 q^{70} +9.80335i q^{71} -1.00000 q^{72} +9.04189i q^{73} -10.2121i q^{74} +7.47565i q^{75} +4.36959 q^{76} -8.12061 q^{77} -5.06418i q^{78} -6.61856i q^{79} -3.53209i q^{80} +1.00000 q^{81} +12.5817i q^{82} +3.32501 q^{83} -2.75877 q^{84} -10.9067 q^{86} +4.80066 q^{87} -2.94356i q^{88} +13.8425 q^{89} +3.53209i q^{90} -13.9709i q^{91} +6.00000i q^{92} -0.716881 q^{93} +5.14796 q^{94} -15.4338i q^{95} -1.00000i q^{96} +11.0273i q^{97} -0.610815 q^{98} +2.94356i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 + 6 * q^8 - 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} + 6 q^{8} - 6 q^{9} + 12 q^{13} - 12 q^{15} + 6 q^{16} - 6 q^{18} + 12 q^{19} + 6 q^{21} - 6 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{32} + 12 q^{33} - 6 q^{36} + 12 q^{38} + 6 q^{42} - 12 q^{43} - 12 q^{49} - 6 q^{50} + 12 q^{52} - 12 q^{53} - 6 q^{55} - 24 q^{59} - 12 q^{60} + 6 q^{64} + 12 q^{66} + 24 q^{67} + 36 q^{69} - 6 q^{72} + 12 q^{76} - 60 q^{77} + 6 q^{81} + 30 q^{83} + 6 q^{84} - 12 q^{86} + 48 q^{89} + 12 q^{93} - 12 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + 6 * q^8 - 6 * q^9 + 12 * q^13 - 12 * q^15 + 6 * q^16 - 6 * q^18 + 12 * q^19 + 6 * q^21 - 6 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^32 + 12 * q^33 - 6 * q^36 + 12 * q^38 + 6 * q^42 - 12 * q^43 - 12 * q^49 - 6 * q^50 + 12 * q^52 - 12 * q^53 - 6 * q^55 - 24 * q^59 - 12 * q^60 + 6 * q^64 + 12 * q^66 + 24 * q^67 + 36 * q^69 - 6 * q^72 + 12 * q^76 - 60 * q^77 + 6 * q^81 + 30 * q^83 + 6 * q^84 - 12 * q^86 + 48 * q^89 + 12 * q^93 - 12 * q^98

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