LMFDB - Embedded newform 867.2.d.e.577.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(577,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, 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("867.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.d (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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			577.6
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	867.577
Dual form			867.2.d.e.577.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.765367 q^{2} +1.00000i q^{3} -1.41421 q^{4} -2.08239i q^{5} +0.765367i q^{6} +1.23463i q^{7} -2.61313 q^{8} -1.00000 q^{9} -1.59379i q^{10} -1.49661i q^{11} -1.41421i q^{12} +4.10973 q^{13} +0.944947i q^{14} +2.08239 q^{15} +0.828427 q^{16} -0.765367 q^{18} +6.81204 q^{19} +2.94495i q^{20} -1.23463 q^{21} -1.14545i q^{22} -3.30864i q^{23} -2.61313i q^{24} +0.663643 q^{25} +3.14545 q^{26} -1.00000i q^{27} -1.74603i q^{28} -6.24264i q^{29} +1.59379 q^{30} -10.2700i q^{31} +5.86030 q^{32} +1.49661 q^{33} +2.57099 q^{35} +1.41421 q^{36} -3.93694i q^{37} +5.21371 q^{38} +4.10973i q^{39} +5.44155i q^{40} +12.1371i q^{41} -0.944947 q^{42} +3.44609 q^{43} +2.11652i q^{44} +2.08239i q^{45} -2.53233i q^{46} +1.56940 q^{47} +0.828427i q^{48} +5.47568 q^{49} +0.507930 q^{50} -5.81204 q^{52} -3.96134 q^{53} -0.765367i q^{54} -3.11652 q^{55} -3.22625i q^{56} +6.81204i q^{57} -4.77791i q^{58} -8.06306 q^{59} -2.94495 q^{60} +3.27330i q^{61} -7.86030i q^{62} -1.23463i q^{63} +2.82843 q^{64} -8.55807i q^{65} +1.14545 q^{66} +2.11652 q^{67} +3.30864 q^{69} +1.96775 q^{70} +0.226626i q^{71} +2.61313 q^{72} +0.368233i q^{73} -3.01320i q^{74} +0.663643i q^{75} -9.63368 q^{76} +1.84776 q^{77} +3.14545i q^{78} +2.71485i q^{79} -1.72511i q^{80} +1.00000 q^{81} +9.28931i q^{82} -14.4138 q^{83} +1.74603 q^{84} +2.63752 q^{86} +6.24264 q^{87} +3.91082i q^{88} +13.6694 q^{89} +1.59379i q^{90} +5.07401i q^{91} +4.67913i q^{92} +10.2700 q^{93} +1.20116 q^{94} -14.1853i q^{95} +5.86030i q^{96} +2.68457i q^{97} +4.19090 q^{98} +1.49661i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{9} - 8 q^{13} + 8 q^{15} - 16 q^{16} + 24 q^{19} - 16 q^{21} - 16 q^{30} - 8 q^{33} + 32 q^{35} + 32 q^{38} + 16 q^{42} - 8 q^{43} + 16 q^{47} + 8 q^{49} + 32 q^{50} - 16 q^{52} - 16 q^{53} - 24 q^{55}+ \cdots + 64 q^{98}+O(q^{100}) $ 8 * q - 8 * q^9 - 8 * q^13 + 8 * q^15 - 16 * q^16 + 24 * q^19 - 16 * q^21 - 16 * q^30 - 8 * q^33 + 32 * q^35 + 32 * q^38 + 16 * q^42 - 8 * q^43 + 16 * q^47 + 8 * q^49 + 32 * q^50 - 16 * q^52 - 16 * q^53 - 24 * q^55 - 48 * q^59 - 16 * q^66 + 16 * q^67 - 24 * q^69 - 48 * q^70 + 16 * q^76 + 8 * q^81 - 16 * q^83 - 32 * q^86 + 16 * q^87 + 32 * q^89 + 16 * q^93 + 32 * q^94 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$-1$

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 $

$2$	0.765367	0.541196	0.270598	−	0.962692i	$-0.412779\pi$
$2$	0.765367	0.541196	0.270598	+	0.962692i	$0.412779\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.41421	−0.707107
$5$	− 2.08239i	− 0.931274i	−0.884976	−	0.465637i	$-0.845825\pi$
$5$	− 2.08239i	− 0.931274i	0.884976	−	0.465637i	$-0.154175\pi$
$6$	0.765367i	0.312460i
$7$	1.23463i	0.466647i	0.972399	+	0.233324i	$0.0749602\pi$
$7$	1.23463i	0.466647i	−0.972399	+	0.233324i	$0.925040\pi$
$8$	−2.61313	−0.923880
$9$	−1.00000	−0.333333
$10$	− 1.59379i	− 0.504002i
$11$	− 1.49661i	− 0.451244i	−0.974215	−	0.225622i	$-0.927559\pi$
$11$	− 1.49661i	− 0.451244i	0.974215	−	0.225622i	$-0.0724414\pi$
$12$	− 1.41421i	− 0.408248i
$13$	4.10973	1.13983	0.569917	−	0.821702i	$-0.306975\pi$
$13$	4.10973	1.13983	0.569917	+	0.821702i	$0.306975\pi$
$14$	0.944947i	0.252548i
$15$	2.08239	0.537671
$16$	0.828427	0.207107
$17$	0	0
$17$	0	0
$18$	−0.765367	−0.180399
$19$	6.81204	1.56279	0.781394	−	0.624038i	$-0.214509\pi$
$19$	6.81204	1.56279	0.781394	+	0.624038i	$0.214509\pi$
$20$	2.94495i	0.658510i
$21$	−1.23463	−0.269419
$22$	− 1.14545i	− 0.244211i
$23$	− 3.30864i	− 0.689900i	−0.938621	−	0.344950i	$-0.887896\pi$
$23$	− 3.30864i	− 0.689900i	0.938621	−	0.344950i	$-0.112104\pi$
$24$	− 2.61313i	− 0.533402i
$25$	0.663643	0.132729
$26$	3.14545	0.616874
$27$	− 1.00000i	− 0.192450i
$28$	− 1.74603i	− 0.329970i
$29$	− 6.24264i	− 1.15923i	−0.814891	−	0.579615i	$-0.803203\pi$
$29$	− 6.24264i	− 1.15923i	0.814891	−	0.579615i	$-0.196797\pi$
$30$	1.59379	0.290986
$31$	− 10.2700i	− 1.84454i	−0.386543	−	0.922271i	$-0.626331\pi$
$31$	− 10.2700i	− 1.84454i	0.386543	−	0.922271i	$-0.373669\pi$
$32$	5.86030	1.03596
$33$	1.49661	0.260526
$34$	0	0
$35$	2.57099	0.434577
$36$	1.41421	0.235702
$37$	− 3.93694i	− 0.647229i	−0.946189	−	0.323614i	$-0.895102\pi$
$37$	− 3.93694i	− 0.647229i	0.946189	−	0.323614i	$-0.104898\pi$
$38$	5.21371	0.845775
$39$	4.10973i	0.658084i
$40$	5.44155i	0.860385i
$41$	12.1371i	1.89549i	0.319026	+	0.947746i	$0.396644\pi$
$41$	12.1371i	1.89549i	−0.319026	+	0.947746i	$0.603356\pi$
$42$	−0.944947	−0.145809
$43$	3.44609	0.525524	0.262762	−	0.964861i	$-0.415367\pi$
$43$	3.44609	0.525524	0.262762	+	0.964861i	$0.415367\pi$
$44$	2.11652i	0.319077i
$45$	2.08239i	0.310425i
$46$	− 2.53233i	− 0.373371i
$47$	1.56940	0.228920	0.114460	−	0.993428i	$-0.463486\pi$
$47$	1.56940	0.228920	0.114460	+	0.993428i	$0.463486\pi$
$48$	0.828427i	0.119573i
$49$	5.47568	0.782240
$50$	0.507930	0.0718322
$51$	0	0
$52$	−5.81204	−0.805985
$53$	−3.96134	−0.544131	−0.272066	−	0.962279i	$-0.587707\pi$
$53$	−3.96134	−0.544131	−0.272066	+	0.962279i	$0.587707\pi$
$54$	− 0.765367i	− 0.104153i
$55$	−3.11652	−0.420231
$56$	− 3.22625i	− 0.431126i
$57$	6.81204i	0.902277i
$58$	− 4.77791i	− 0.627370i
$59$	−8.06306	−1.04972	−0.524861	−	0.851188i	$-0.675883\pi$
$59$	−8.06306	−1.04972	−0.524861	+	0.851188i	$0.675883\pi$
$60$	−2.94495	−0.380191
$61$	3.27330i	0.419103i	0.977798	+	0.209551i	$0.0672003\pi$
$61$	3.27330i	0.419103i	−0.977798	+	0.209551i	$0.932800\pi$
$62$	− 7.86030i	− 0.998259i
$63$	− 1.23463i	− 0.155549i
$64$	2.82843	0.353553
$65$	− 8.55807i	− 1.06150i
$66$	1.14545	0.140995
$67$	2.11652	0.258574	0.129287	−	0.991607i	$-0.458731\pi$
$67$	2.11652	0.258574	0.129287	+	0.991607i	$0.458731\pi$
$68$	0	0
$69$	3.30864	0.398314
$70$	1.96775	0.235191
$71$	0.226626i	0.0268955i	0.999910	+	0.0134478i	$0.00428068\pi$
$71$	0.226626i	0.0268955i	−0.999910	+	0.0134478i	$0.995719\pi$
$72$	2.61313	0.307960
$73$	0.368233i	0.0430984i	0.999768	+	0.0215492i	$0.00685985\pi$
$73$	0.368233i	0.0430984i	−0.999768	+	0.0215492i	$0.993140\pi$
$74$	− 3.01320i	− 0.350278i
$75$	0.663643i	0.0766309i
$76$	−9.63368	−1.10506
$77$	1.84776	0.210572
$78$	3.14545i	0.356152i
$79$	2.71485i	0.305444i	0.988269	+	0.152722i	$0.0488040\pi$
$79$	2.71485i	0.305444i	−0.988269	+	0.152722i	$0.951196\pi$
$80$	− 1.72511i	− 0.192873i
$81$	1.00000	0.111111
$82$	9.28931i	1.02583i
$83$	−14.4138	−1.58212	−0.791062	−	0.611736i	$-0.790472\pi$
$83$	−14.4138	−1.58212	−0.791062	+	0.611736i	$0.790472\pi$
$84$	1.74603	0.190508
$85$	0	0
$86$	2.63752	0.284411
$87$	6.24264	0.669281
$88$	3.91082i	0.416895i
$89$	13.6694	1.44895	0.724477	−	0.689299i	$-0.242082\pi$
$89$	13.6694	1.44895	0.724477	+	0.689299i	$0.242082\pi$
$90$	1.59379i	0.168001i
$91$	5.07401i	0.531901i
$92$	4.67913i	0.487833i
$93$	10.2700	1.06495
$94$	1.20116	0.123891
$95$	− 14.1853i	− 1.45538i
$96$	5.86030i	0.598115i
$97$	2.68457i	0.272577i	0.990669	+	0.136288i	$0.0435173\pi$
$97$	2.68457i	0.272577i	−0.990669	+	0.136288i	$0.956483\pi$
$98$	4.19090	0.423345
$99$	1.49661i	0.150415i
$100$	−0.938533	−0.0938533
$101$	−2.38009	−0.236827	−0.118414	−	0.992964i	$-0.537781\pi$
$101$	−2.38009	−0.236827	−0.118414	+	0.992964i	$0.537781\pi$
$102$	0	0
$103$	−13.2909	−1.30959	−0.654796	−	0.755806i	$-0.727245\pi$
$103$	−13.2909	−1.30959	−0.654796	+	0.755806i	$0.727245\pi$
$104$	−10.7392	−1.05307
$105$	2.57099i	0.250903i
$106$	−3.03188	−0.294482
$107$	− 13.0724i	− 1.26376i	−0.775067	−	0.631879i	$-0.782284\pi$
$107$	− 13.0724i	− 1.26376i	0.775067	−	0.631879i	$-0.217716\pi$
$108$	1.41421i	0.136083i
$109$	0.956272i	0.0915942i	0.998951	+	0.0457971i	$0.0145828\pi$
$109$	0.956272i	0.0915942i	−0.998951	+	0.0457971i	$0.985417\pi$
$110$	−2.38528	−0.227428
$111$	3.93694	0.373678
$112$	1.02280i	0.0966459i
$113$	8.62951i	0.811796i	0.913918	+	0.405898i	$0.133041\pi$
$113$	8.62951i	0.811796i	−0.913918	+	0.405898i	$0.866959\pi$
$114$	5.21371i	0.488309i
$115$	−6.88989	−0.642486
$116$	8.82843i	0.819699i
$117$	−4.10973	−0.379945
$118$	−6.17120	−0.568105
$119$	0	0
$120$	−5.44155	−0.496744
$121$	8.76017	0.796379
$122$	2.50527i	0.226817i
$123$	−12.1371	−1.09436
$124$	14.5239i	1.30429i
$125$	− 11.7939i	− 1.05488i
$126$	− 0.944947i	− 0.0841826i
$127$	14.1484	1.25547	0.627734	−	0.778428i	$-0.283983\pi$
$127$	14.1484	1.25547	0.627734	+	0.778428i	$0.283983\pi$
$128$	−9.55582	−0.844623
$129$	3.44609i	0.303411i
$130$	− 6.55007i	− 0.574479i
$131$	2.59085i	0.226364i	0.993574	+	0.113182i	$0.0361043\pi$
$131$	2.59085i	0.226364i	−0.993574	+	0.113182i	$0.963896\pi$
$132$	−2.11652	−0.184219
$133$	8.41037i	0.729271i
$134$	1.61991	0.139939
$135$	−2.08239	−0.179224
$136$	0	0
$137$	15.2684	1.30447	0.652233	−	0.758018i	$-0.273832\pi$
$137$	15.2684	1.30447	0.652233	+	0.758018i	$0.273832\pi$
$138$	2.53233	0.215566
$139$	− 4.04214i	− 0.342849i	−0.985197	−	0.171425i	$-0.945163\pi$
$139$	− 4.04214i	− 0.342849i	0.985197	−	0.171425i	$-0.0548370\pi$
$140$	−3.63593	−0.307292
$141$	1.56940i	0.132167i
$142$	0.173452i	0.0145557i
$143$	− 6.15065i	− 0.514343i
$144$	−0.828427	−0.0690356
$145$	−12.9996	−1.07956
$146$	0.281833i	0.0233247i
$147$	5.47568i	0.451627i
$148$	5.56767i	0.457660i
$149$	−18.1219	−1.48460	−0.742302	−	0.670065i	$-0.766266\pi$
$149$	−18.1219	−1.48460	−0.742302	+	0.670065i	$0.766266\pi$
$150$	0.507930i	0.0414723i
$151$	−5.27133	−0.428975	−0.214487	−	0.976727i	$-0.568808\pi$
$151$	−5.27133	−0.428975	−0.214487	+	0.976727i	$0.568808\pi$
$152$	−17.8007	−1.44383
$153$	0	0
$154$	1.41421	0.113961
$155$	−21.3861	−1.71778
$156$	− 5.81204i	− 0.465335i
$157$	−3.80334	−0.303540	−0.151770	−	0.988416i	$-0.548497\pi$
$157$	−3.80334	−0.303540	−0.151770	+	0.988416i	$0.548497\pi$
$158$	2.07786i	0.165305i
$159$	− 3.96134i	− 0.314154i
$160$	− 12.2034i	− 0.964767i
$161$	4.08496	0.321940
$162$	0.765367	0.0601329
$163$	9.06882i	0.710324i	0.934805	+	0.355162i	$0.115574\pi$
$163$	9.06882i	0.710324i	−0.934805	+	0.355162i	$0.884426\pi$
$164$	− 17.1644i	− 1.34032i
$165$	− 3.11652i	− 0.242621i
$166$	−11.0319	−0.856240
$167$	− 8.88764i	− 0.687746i	−0.939016	−	0.343873i	$-0.888261\pi$
$167$	− 8.88764i	− 0.687746i	0.939016	−	0.343873i	$-0.111739\pi$
$168$	3.22625	0.248911
$169$	3.88989	0.299223
$170$	0	0
$171$	−6.81204	−0.520930
$172$	−4.87351	−0.371601
$173$	− 12.2472i	− 0.931136i	−0.885012	−	0.465568i	$-0.845850\pi$
$173$	− 12.2472i	− 0.931136i	0.885012	−	0.465568i	$-0.154150\pi$
$174$	4.77791	0.362212
$175$	0.819355i	0.0619374i
$176$	− 1.23983i	− 0.0934556i
$177$	− 8.06306i	− 0.606057i
$178$	10.4621	0.784168
$179$	10.6173	0.793573	0.396787	−	0.917911i	$-0.370125\pi$
$179$	10.6173	0.793573	0.396787	+	0.917911i	$0.370125\pi$
$180$	− 2.94495i	− 0.219503i
$181$	16.5274i	1.22847i	0.789122	+	0.614237i	$0.210536\pi$
$181$	16.5274i	1.22847i	−0.789122	+	0.614237i	$0.789464\pi$
$182$	3.88348i	0.287863i
$183$	−3.27330	−0.241969
$184$	8.64590i	0.637384i
$185$	−8.19825	−0.602748
$186$	7.86030	0.576345
$187$	0	0
$188$	−2.21946	−0.161871
$189$	1.23463	0.0898063
$190$	− 10.8570i	− 0.787649i
$191$	−12.0167	−0.869498	−0.434749	−	0.900552i	$-0.643163\pi$
$191$	−12.0167	−0.869498	−0.434749	+	0.900552i	$0.643163\pi$
$192$	2.82843i	0.204124i
$193$	− 10.7183i	− 0.771522i	−0.922599	−	0.385761i	$-0.873939\pi$
$193$	− 10.7183i	− 0.771522i	0.922599	−	0.385761i	$-0.126061\pi$
$194$	2.05468i	0.147517i
$195$	8.55807	0.612856
$196$	−7.74378	−0.553127
$197$	− 3.16895i	− 0.225778i	−0.993608	−	0.112889i	$-0.963990\pi$
$197$	− 3.16895i	− 0.225778i	0.993608	−	0.112889i	$-0.0360105\pi$
$198$	1.14545i	0.0814038i
$199$	13.6746i	0.969366i	0.874690	+	0.484683i	$0.161065\pi$
$199$	13.6746i	0.969366i	−0.874690	+	0.484683i	$0.838935\pi$
$200$	−1.73418	−0.122625
$201$	2.11652i	0.149288i
$202$	−1.82164	−0.128170
$203$	7.70737	0.540951
$204$	0	0
$205$	25.2741	1.76522
$206$	−10.1724	−0.708746
$207$	3.30864i	0.229967i
$208$	3.40461	0.236067
$209$	− 10.1949i	− 0.705198i
$210$	1.96775i	0.135788i
$211$	− 5.92856i	− 0.408139i	−0.978956	−	0.204069i	$-0.934583\pi$
$211$	− 5.92856i	− 0.408139i	0.978956	−	0.204069i	$-0.0654168\pi$
$212$	5.60218	0.384759
$213$	−0.226626	−0.0155281
$214$	− 10.0052i	− 0.683941i
$215$	− 7.17611i	− 0.489407i
$216$	2.61313i	0.177801i
$217$	12.6797	0.860751
$218$	0.731899i	0.0495704i
$219$	−0.368233	−0.0248829
$220$	4.40743	0.297149
$221$	0	0
$222$	3.01320	0.202233
$223$	−26.1476	−1.75098	−0.875488	−	0.483240i	$-0.839460\pi$
$223$	−26.1476	−1.75098	−0.875488	+	0.483240i	$0.839460\pi$
$224$	7.23532i	0.483430i
$225$	−0.663643	−0.0442428
$226$	6.60474i	0.439341i
$227$	− 10.9746i	− 0.728408i	−0.931319	−	0.364204i	$-0.881341\pi$
$227$	− 10.9746i	− 0.728408i	0.931319	−	0.364204i	$-0.118659\pi$
$228$	− 9.63368i	− 0.638006i
$229$	14.4872	0.957341	0.478670	−	0.877995i	$-0.341119\pi$
$229$	14.4872	0.957341	0.478670	+	0.877995i	$0.341119\pi$
$230$	−5.27330	−0.347711
$231$	1.84776i	0.121574i
$232$	16.3128i	1.07099i
$233$	19.0980i	1.25115i	0.780163	+	0.625577i	$0.215136\pi$
$233$	19.0980i	1.25115i	−0.780163	+	0.625577i	$0.784864\pi$
$234$	−3.14545	−0.205625
$235$	− 3.26810i	− 0.213187i
$236$	11.4029	0.742265
$237$	−2.71485	−0.176348
$238$	0	0
$239$	0.740970	0.0479294	0.0239647	−	0.999713i	$-0.492371\pi$
$239$	0.740970	0.0479294	0.0239647	+	0.999713i	$0.492371\pi$
$240$	1.72511	0.111355
$241$	21.3617i	1.37603i	0.725696	+	0.688015i	$0.241518\pi$
$241$	21.3617i	1.37603i	−0.725696	+	0.688015i	$0.758482\pi$
$242$	6.70474	0.430997
$243$	1.00000i	0.0641500i
$244$	− 4.62914i	− 0.296350i
$245$	− 11.4025i	− 0.728480i
$246$	−9.28931	−0.592265
$247$	27.9956	1.78132
$248$	26.8368i	1.70414i
$249$	− 14.4138i	− 0.913440i
$250$	− 9.02668i	− 0.570897i
$251$	−0.938819	−0.0592577	−0.0296289	−	0.999561i	$-0.509433\pi$
$251$	−0.938819	−0.0592577	−0.0296289	+	0.999561i	$0.509433\pi$
$252$	1.74603i	0.109990i
$253$	−4.95174	−0.311313
$254$	10.8287	0.679454
$255$	0	0
$256$	−12.9706	−0.810660
$257$	15.8293	0.987403	0.493701	−	0.869631i	$-0.335644\pi$
$257$	15.8293	0.987403	0.493701	+	0.869631i	$0.335644\pi$
$258$	2.63752i	0.164205i
$259$	4.86068	0.302028
$260$	12.1029i	0.750593i
$261$	6.24264i	0.386410i
$262$	1.98295i	0.122507i
$263$	−11.4573	−0.706486	−0.353243	−	0.935532i	$-0.614921\pi$
$263$	−11.4573	−0.706486	−0.353243	+	0.935532i	$0.614921\pi$
$264$	−3.91082	−0.240694
$265$	8.24906i	0.506735i
$266$	6.43702i	0.394679i
$267$	13.6694i	0.836554i
$268$	−2.99321	−0.182839
$269$	19.1689i	1.16875i	0.811483	+	0.584376i	$0.198661\pi$
$269$	19.1689i	1.16875i	−0.811483	+	0.584376i	$0.801339\pi$
$270$	−1.59379	−0.0969952
$271$	6.82805	0.414775	0.207387	−	0.978259i	$-0.433504\pi$
$271$	6.82805	0.414775	0.207387	+	0.978259i	$0.433504\pi$
$272$	0	0
$273$	−5.07401	−0.307093
$274$	11.6859	0.705972
$275$	− 0.993212i	− 0.0598929i
$276$	−4.67913	−0.281650
$277$	− 8.12784i	− 0.488355i	−0.969731	−	0.244177i	$-0.921482\pi$
$277$	− 8.12784i	− 0.488355i	0.969731	−	0.244177i	$-0.0785179\pi$
$278$	− 3.09372i	− 0.185549i
$279$	10.2700i	0.614848i
$280$	−6.71832	−0.401497
$281$	−11.6070	−0.692417	−0.346209	−	0.938158i	$-0.612531\pi$
$281$	−11.6070	−0.692417	−0.346209	+	0.938158i	$0.612531\pi$
$282$	1.20116i	0.0715283i
$283$	− 6.06404i	− 0.360470i	−0.983624	−	0.180235i	$-0.942314\pi$
$283$	− 6.06404i	− 0.360470i	0.983624	−	0.180235i	$-0.0576858\pi$
$284$	− 0.320497i	− 0.0190180i
$285$	14.1853	0.840267
$286$	− 4.70750i	− 0.278360i
$287$	−14.9848	−0.884527
$288$	−5.86030	−0.345322
$289$	0	0
$290$	−9.94948	−0.584254
$291$	−2.68457	−0.157372
$292$	− 0.520760i	− 0.0304752i
$293$	6.87547	0.401669	0.200835	−	0.979625i	$-0.435635\pi$
$293$	6.87547	0.401669	0.200835	+	0.979625i	$0.435635\pi$
$294$	4.19090i	0.244419i
$295$	16.7905i	0.977578i
$296$	10.2877i	0.597962i
$297$	−1.49661	−0.0868419
$298$	−13.8699	−0.803462
$299$	− 13.5976i	− 0.786372i
$300$	− 0.938533i	− 0.0541862i
$301$	4.25466i	0.245234i
$302$	−4.03450	−0.232159
$303$	− 2.38009i	− 0.136732i
$304$	5.64328	0.323664
$305$	6.81629	0.390300
$306$	0	0
$307$	22.2451	1.26959	0.634797	−	0.772679i	$-0.281084\pi$
$307$	22.2451	1.26959	0.634797	+	0.772679i	$0.281084\pi$
$308$	−2.61313	−0.148897
$309$	− 13.2909i	− 0.756093i
$310$	−16.3682	−0.929653
$311$	5.41421i	0.307012i	0.988148	+	0.153506i	$0.0490564\pi$
$311$	5.41421i	0.307012i	−0.988148	+	0.153506i	$0.950944\pi$
$312$	− 10.7392i	− 0.607990i
$313$	11.2945i	0.638403i	0.947687	+	0.319202i	$0.103415\pi$
$313$	11.2945i	0.638403i	−0.947687	+	0.319202i	$0.896585\pi$
$314$	−2.91095	−0.164274
$315$	−2.57099	−0.144859
$316$	− 3.83938i	− 0.215982i
$317$	18.4520i	1.03637i	0.855270	+	0.518183i	$0.173391\pi$
$317$	18.4520i	1.03637i	−0.855270	+	0.518183i	$0.826609\pi$
$318$	− 3.03188i	− 0.170019i
$319$	−9.34277	−0.523095
$320$	− 5.88989i	− 0.329255i
$321$	13.0724	0.729631
$322$	3.12649	0.174233
$323$	0	0
$324$	−1.41421	−0.0785674
$325$	2.72739	0.151289
$326$	6.94097i	0.384425i
$327$	−0.956272	−0.0528819
$328$	− 31.7157i	− 1.75121i
$329$	1.93763i	0.106825i
$330$	− 2.38528i	− 0.131305i
$331$	−5.76606	−0.316931	−0.158466	−	0.987365i	$-0.550655\pi$
$331$	−5.76606	−0.316931	−0.158466	+	0.987365i	$0.550655\pi$
$332$	20.3842	1.11873
$333$	3.93694i	0.215743i
$334$	− 6.80231i	− 0.372206i
$335$	− 4.40743i	− 0.240803i
$336$	−1.02280	−0.0557985
$337$	− 16.2707i	− 0.886320i	−0.896443	−	0.443160i	$-0.853857\pi$
$337$	− 16.2707i	− 0.886320i	0.896443	−	0.443160i	$-0.146143\pi$
$338$	2.97720	0.161938
$339$	−8.62951	−0.468691
$340$	0	0
$341$	−15.3701	−0.832338
$342$	−5.21371	−0.281925
$343$	15.4029i	0.831678i
$344$	−9.00506	−0.485521
$345$	− 6.88989i	− 0.370939i
$346$	− 9.37358i	− 0.503927i
$347$	− 4.29038i	− 0.230319i	−0.993347	−	0.115160i	$-0.963262\pi$
$347$	− 4.29038i	− 0.230319i	0.993347	−	0.115160i	$-0.0367380\pi$
$348$	−8.82843	−0.473253
$349$	−14.1553	−0.757718	−0.378859	−	0.925454i	$-0.623683\pi$
$349$	−14.1553	−0.757718	−0.378859	+	0.925454i	$0.623683\pi$
$350$	0.627107i	0.0335203i
$351$	− 4.10973i	− 0.219361i
$352$	− 8.77056i	− 0.467473i
$353$	23.8142	1.26750	0.633752	−	0.773536i	$-0.281514\pi$
$353$	23.8142	1.26750	0.633752	+	0.773536i	$0.281514\pi$
$354$	− 6.17120i	− 0.327996i
$355$	0.471923	0.0250471
$356$	−19.3314	−1.02456
$357$	0	0
$358$	8.12612	0.429479
$359$	35.2676	1.86135	0.930677	−	0.365841i	$-0.119219\pi$
$359$	35.2676	1.86135	0.930677	+	0.365841i	$0.119219\pi$
$360$	− 5.44155i	− 0.286795i
$361$	27.4039	1.44231
$362$	12.6495i	0.664845i
$363$	8.76017i	0.459790i
$364$	− 7.17574i	− 0.376111i
$365$	0.766805	0.0401364
$366$	−2.50527	−0.130953
$367$	− 16.3212i	− 0.851959i	−0.904733	−	0.425980i	$-0.859930\pi$
$367$	− 16.3212i	− 0.851959i	0.904733	−	0.425980i	$-0.140070\pi$
$368$	− 2.74097i	− 0.142883i
$369$	− 12.1371i	− 0.631831i
$370$	−6.27467	−0.326205
$371$	− 4.89080i	− 0.253918i
$372$	−14.5239	−0.753031
$373$	−25.0156	−1.29526	−0.647630	−	0.761955i	$-0.724240\pi$
$373$	−25.0156	−1.29526	−0.647630	+	0.761955i	$0.724240\pi$
$374$	0	0
$375$	11.7939	0.609036
$376$	−4.10103	−0.211495
$377$	− 25.6556i	− 1.32133i
$378$	0.944947	0.0486028
$379$	32.6281i	1.67599i	0.545675	+	0.837997i	$0.316273\pi$
$379$	32.6281i	1.67599i	−0.545675	+	0.837997i	$0.683727\pi$
$380$	20.0611i	1.02911i
$381$	14.1484i	0.724844i
$382$	−9.19719	−0.470569
$383$	0.585258	0.0299053	0.0149526	−	0.999888i	$-0.495240\pi$
$383$	0.585258	0.0299053	0.0149526	+	0.999888i	$0.495240\pi$
$384$	− 9.55582i	− 0.487643i
$385$	− 3.84776i	− 0.196100i
$386$	− 8.20345i	− 0.417545i
$387$	−3.44609	−0.175175
$388$	− 3.79655i	− 0.192741i
$389$	22.1261	1.12184	0.560918	−	0.827871i	$-0.310448\pi$
$389$	22.1261	1.12184	0.560918	+	0.827871i	$0.310448\pi$
$390$	6.55007	0.331675
$391$	0	0
$392$	−14.3086	−0.722696
$393$	−2.59085	−0.130691
$394$	− 2.42541i	− 0.122190i
$395$	5.65338	0.284453
$396$	− 2.11652i	− 0.106359i
$397$	5.83031i	0.292615i	0.989239	+	0.146307i	$0.0467388\pi$
$397$	5.83031i	0.292615i	−0.989239	+	0.146307i	$0.953261\pi$
$398$	10.4661i	0.524617i
$399$	−8.41037	−0.421045
$400$	0.549780	0.0274890
$401$	5.19021i	0.259187i	0.991567	+	0.129593i	$0.0413672\pi$
$401$	5.19021i	0.259187i	−0.991567	+	0.129593i	$0.958633\pi$
$402$	1.61991i	0.0807940i
$403$	− 42.2069i	− 2.10247i
$404$	3.36595	0.167462
$405$	− 2.08239i	− 0.103475i
$406$	5.89897	0.292761
$407$	−5.89205	−0.292058
$408$	0	0
$409$	−27.2400	−1.34693	−0.673465	−	0.739219i	$-0.735195\pi$
$409$	−27.2400	−1.34693	−0.673465	+	0.739219i	$0.735195\pi$
$410$	19.3440	0.955332
$411$	15.2684i	0.753134i
$412$	18.7962	0.926021
$413$	− 9.95492i	− 0.489850i
$414$	2.53233i	0.124457i
$415$	30.0153i	1.47339i
$416$	24.0843	1.18083
$417$	4.04214	0.197944
$418$	− 7.80287i	− 0.381651i
$419$	− 14.0301i	− 0.685416i	−0.939442	−	0.342708i	$-0.888656\pi$
$419$	− 14.0301i	− 0.685416i	0.939442	−	0.342708i	$-0.111344\pi$
$420$	− 3.63593i	− 0.177415i
$421$	15.3811	0.749627	0.374814	−	0.927100i	$-0.377707\pi$
$421$	15.3811	0.749627	0.374814	+	0.927100i	$0.377707\pi$
$422$	− 4.53752i	− 0.220883i
$423$	−1.56940	−0.0763067
$424$	10.3515	0.502712
$425$	0	0
$426$	−0.173452	−0.00840376
$427$	−4.04132	−0.195573
$428$	18.4872i	0.893612i
$429$	6.15065	0.296956
$430$	− 5.49236i	− 0.264865i
$431$	16.3907i	0.789510i	0.918786	+	0.394755i	$0.129171\pi$
$431$	16.3907i	0.789510i	−0.918786	+	0.394755i	$0.870829\pi$
$432$	− 0.828427i	− 0.0398577i
$433$	−21.7106	−1.04335	−0.521673	−	0.853145i	$-0.674692\pi$
$433$	−21.7106	−1.04335	−0.521673	+	0.853145i	$0.674692\pi$
$434$	9.70459	0.465835
$435$	− 12.9996i	− 0.623284i
$436$	− 1.35237i	− 0.0647669i
$437$	− 22.5386i	− 1.07817i
$438$	−0.281833	−0.0134665
$439$	23.5304i	1.12304i	0.827462	+	0.561522i	$0.189784\pi$
$439$	23.5304i	1.12304i	−0.827462	+	0.561522i	$0.810216\pi$
$440$	8.14386	0.388243
$441$	−5.47568	−0.260747
$442$	0	0
$443$	−15.4238	−0.732808	−0.366404	−	0.930456i	$-0.619411\pi$
$443$	−15.4238	−0.732808	−0.366404	+	0.930456i	$0.619411\pi$
$444$	−5.56767	−0.264230
$445$	− 28.4650i	− 1.34937i
$446$	−20.0125	−0.947621
$447$	− 18.1219i	− 0.857137i
$448$	3.49207i	0.164985i
$449$	− 13.5494i	− 0.639438i	−0.947512	−	0.319719i	$-0.896411\pi$
$449$	− 13.5494i	− 0.639438i	0.947512	−	0.319719i	$-0.103589\pi$
$450$	−0.507930	−0.0239441
$451$	18.1644	0.855329
$452$	− 12.2040i	− 0.574027i
$453$	− 5.27133i	− 0.247669i
$454$	− 8.39957i	− 0.394211i
$455$	10.5661	0.495346
$456$	− 17.8007i	− 0.833595i
$457$	15.3875	0.719796	0.359898	−	0.932992i	$-0.382812\pi$
$457$	15.3875	0.719796	0.359898	+	0.932992i	$0.382812\pi$
$458$	11.0880	0.518109
$459$	0	0
$460$	9.74378	0.454306
$461$	20.8006	0.968780	0.484390	−	0.874852i	$-0.339042\pi$
$461$	20.8006	0.968780	0.484390	+	0.874852i	$0.339042\pi$
$462$	1.41421i	0.0657952i
$463$	−26.4325	−1.22842	−0.614212	−	0.789141i	$-0.710526\pi$
$463$	−26.4325	−1.22842	−0.614212	+	0.789141i	$0.710526\pi$
$464$	− 5.17157i	− 0.240084i
$465$	− 21.3861i	− 0.991758i
$466$	14.6170i	0.677120i
$467$	7.17088	0.331829	0.165914	−	0.986140i	$-0.446942\pi$
$467$	7.17088	0.331829	0.165914	+	0.986140i	$0.446942\pi$
$468$	5.81204	0.268662
$469$	2.61313i	0.120663i
$470$	− 2.50130i	− 0.115376i
$471$	− 3.80334i	− 0.175249i
$472$	21.0698	0.969816
$473$	− 5.15744i	− 0.237139i
$474$	−2.07786	−0.0954391
$475$	4.52076	0.207427
$476$	0	0
$477$	3.96134	0.181377
$478$	0.567114	0.0259392
$479$	2.93400i	0.134058i	0.997751	+	0.0670289i	$0.0213520\pi$
$479$	2.93400i	0.134058i	−0.997751	+	0.0670289i	$0.978648\pi$
$480$	12.2034	0.557009
$481$	− 16.1798i	− 0.737734i
$482$	16.3496i	0.744702i
$483$	4.08496i	0.185872i
$484$	−12.3888	−0.563125
$485$	5.59032	0.253843
$486$	0.765367i	0.0347177i
$487$	− 23.2420i	− 1.05319i	−0.850115	−	0.526597i	$-0.823468\pi$
$487$	− 23.2420i	− 1.05319i	0.850115	−	0.526597i	$-0.176532\pi$
$488$	− 8.55354i	− 0.387200i
$489$	−9.06882	−0.410106
$490$	− 8.72711i	− 0.394251i
$491$	−13.6586	−0.616403	−0.308202	−	0.951321i	$-0.599727\pi$
$491$	−13.6586	−0.616403	−0.308202	+	0.951321i	$0.599727\pi$
$492$	17.1644	0.773831
$493$	0	0
$494$	21.4269	0.964044
$495$	3.11652	0.140077
$496$	− 8.50793i	− 0.382017i
$497$	−0.279799	−0.0125507
$498$	− 11.0319i	− 0.494350i
$499$	7.53220i	0.337187i	0.985686	+	0.168594i	$0.0539226\pi$
$499$	7.53220i	0.337187i	−0.985686	+	0.168594i	$0.946077\pi$
$500$	16.6791i	0.745913i
$501$	8.88764	0.397071
$502$	−0.718541	−0.0320700
$503$	25.7161i	1.14662i	0.819338	+	0.573311i	$0.194341\pi$
$503$	25.7161i	1.14662i	−0.819338	+	0.573311i	$0.805659\pi$
$504$	3.22625i	0.143709i
$505$	4.95627i	0.220551i
$506$	−3.78989	−0.168481
$507$	3.88989i	0.172756i
$508$	−20.0089	−0.887749
$509$	34.7796	1.54158	0.770789	−	0.637090i	$-0.219862\pi$
$509$	34.7796	1.54158	0.770789	+	0.637090i	$0.219862\pi$
$510$	0	0
$511$	−0.454632	−0.0201117
$512$	9.18440	0.405897
$513$	− 6.81204i	− 0.300759i
$514$	12.1152	0.534379
$515$	27.6769i	1.21959i
$516$	− 4.87351i	− 0.214544i
$517$	− 2.34877i	− 0.103299i
$518$	3.72020	0.163456
$519$	12.2472	0.537591
$520$	22.3633i	0.980697i
$521$	44.5784i	1.95302i	0.215479	+	0.976508i	$0.430869\pi$
$521$	44.5784i	1.95302i	−0.215479	+	0.976508i	$0.569131\pi$
$522$	4.77791i	0.209123i
$523$	19.8918	0.869808	0.434904	−	0.900477i	$-0.356782\pi$
$523$	19.8918	0.869808	0.434904	+	0.900477i	$0.356782\pi$
$524$	− 3.66402i	− 0.160063i
$525$	−0.819355	−0.0357596
$526$	−8.76902	−0.382348
$527$	0	0
$528$	1.23983	0.0539566
$529$	12.0529	0.524038
$530$	6.31355i	0.274243i
$531$	8.06306	0.349907
$532$	− 11.8941i	− 0.515673i
$533$	49.8801i	2.16055i
$534$	10.4621i	0.452740i
$535$	−27.2219	−1.17691
$536$	−5.53073	−0.238891
$537$	10.6173i	0.458170i
$538$	14.6713i	0.632524i
$539$	− 8.19494i	− 0.352981i
$540$	2.94495	0.126730
$541$	0.781382i	0.0335942i	0.999859	+	0.0167971i	$0.00534694\pi$
$541$	0.781382i	0.0335942i	−0.999859	+	0.0167971i	$0.994653\pi$
$542$	5.22597	0.224474
$543$	−16.5274	−0.709259
$544$	0	0
$545$	1.99133	0.0852993
$546$	−3.88348	−0.166198
$547$	39.0565i	1.66994i	0.550299	+	0.834968i	$0.314514\pi$
$547$	39.0565i	1.66994i	−0.550299	+	0.834968i	$0.685486\pi$
$548$	−21.5928	−0.922397
$549$	− 3.27330i	− 0.139701i
$550$	− 0.760171i	− 0.0324138i
$551$	− 42.5251i	− 1.81163i
$552$	−8.64590	−0.367994
$553$	−3.35184	−0.142535
$554$	− 6.22078i	− 0.264296i
$555$	− 8.19825i	− 0.347996i
$556$	5.71644i	0.242431i
$557$	−13.0371	−0.552398	−0.276199	−	0.961100i	$-0.589075\pi$
$557$	−13.0371	−0.552398	−0.276199	+	0.961100i	$0.589075\pi$
$558$	7.86030i	0.332753i
$559$	14.1625	0.599010
$560$	2.12988	0.0900038
$561$	0	0
$562$	−8.88363	−0.374734
$563$	−11.2168	−0.472733	−0.236367	−	0.971664i	$-0.575957\pi$
$563$	−11.2168	−0.472733	−0.236367	+	0.971664i	$0.575957\pi$
$564$	− 2.21946i	− 0.0934563i
$565$	17.9700	0.756005
$566$	− 4.64121i	− 0.195085i
$567$	1.23463i	0.0518497i
$568$	− 0.592201i	− 0.0248482i
$569$	−36.4695	−1.52888	−0.764440	−	0.644694i	$-0.776985\pi$
$569$	−36.4695	−1.52888	−0.764440	+	0.644694i	$0.776985\pi$
$570$	10.8570	0.454749
$571$	− 13.5450i	− 0.566842i	−0.958996	−	0.283421i	$-0.908531\pi$
$571$	− 13.5450i	− 0.566842i	0.958996	−	0.283421i	$-0.0914693\pi$
$572$	8.69833i	0.363695i
$573$	− 12.0167i	− 0.502005i
$574$	−11.4689	−0.478702
$575$	− 2.19576i	− 0.0915694i
$576$	−2.82843	−0.117851
$577$	−7.10617	−0.295834	−0.147917	−	0.989000i	$-0.547257\pi$
$577$	−7.10617	−0.295834	−0.147917	+	0.989000i	$0.547257\pi$
$578$	0	0
$579$	10.7183	0.445438
$580$	18.3842	0.763364
$581$	− 17.7958i	− 0.738294i
$582$	−2.05468	−0.0851692
$583$	5.92856i	0.245536i
$584$	− 0.962238i	− 0.0398177i
$585$	8.55807i	0.353833i
$586$	5.26226	0.217382
$587$	−40.2951	−1.66316	−0.831578	−	0.555408i	$-0.812562\pi$
$587$	−40.2951	−1.66316	−0.831578	+	0.555408i	$0.812562\pi$
$588$	− 7.74378i	− 0.319348i
$589$	− 69.9595i	− 2.88263i
$590$	12.8509i	0.529061i
$591$	3.16895	0.130353
$592$	− 3.26147i	− 0.134045i
$593$	37.8418	1.55398	0.776989	−	0.629515i	$-0.216746\pi$
$593$	37.8418	1.55398	0.776989	+	0.629515i	$0.216746\pi$
$594$	−1.14545	−0.0469985
$595$	0	0
$596$	25.6282	1.04977
$597$	−13.6746	−0.559664
$598$	− 10.4072i	− 0.425581i
$599$	−10.1505	−0.414739	−0.207369	−	0.978263i	$-0.566490\pi$
$599$	−10.1505	−0.414739	−0.207369	+	0.978263i	$0.566490\pi$
$600$	− 1.73418i	− 0.0707977i
$601$	− 35.2538i	− 1.43803i	−0.694994	−	0.719016i	$-0.744593\pi$
$601$	− 35.2538i	− 1.43803i	0.694994	−	0.719016i	$-0.255407\pi$
$602$	3.25637i	0.132720i
$603$	−2.11652	−0.0861914
$604$	7.45479	0.303331
$605$	− 18.2421i	− 0.741647i
$606$	− 1.82164i	− 0.0739990i
$607$	47.5878i	1.93153i	0.259420	+	0.965764i	$0.416468\pi$
$607$	47.5878i	1.93153i	−0.259420	+	0.965764i	$0.583532\pi$
$608$	39.9206	1.61899
$609$	7.70737i	0.312318i
$610$	5.21696	0.211229
$611$	6.44980	0.260931
$612$	0	0
$613$	−26.9812	−1.08976	−0.544880	−	0.838514i	$-0.683425\pi$
$613$	−26.9812	−1.08976	−0.544880	+	0.838514i	$0.683425\pi$
$614$	17.0256	0.687099
$615$	25.2741i	1.01915i
$616$	−4.82843	−0.194543
$617$	14.9919i	0.603553i	0.953379	+	0.301776i	$0.0975796\pi$
$617$	14.9919i	0.603553i	−0.953379	+	0.301776i	$0.902420\pi$
$618$	− 10.1724i	− 0.409195i
$619$	2.20241i	0.0885225i	0.999020	+	0.0442613i	$0.0140934\pi$
$619$	2.20241i	0.0885225i	−0.999020	+	0.0442613i	$0.985907\pi$
$620$	30.2446	1.21465
$621$	−3.30864	−0.132771
$622$	4.14386i	0.166154i
$623$	16.8767i	0.676150i
$624$	3.40461i	0.136294i
$625$	−21.2414	−0.849655
$626$	8.64444i	0.345501i
$627$	10.1949	0.407147
$628$	5.37874	0.214635
$629$	0	0
$630$	−1.96775	−0.0783971
$631$	−34.7230	−1.38230	−0.691151	−	0.722710i	$-0.742896\pi$
$631$	−34.7230	−1.38230	−0.691151	+	0.722710i	$0.742896\pi$
$632$	− 7.09425i	− 0.282194i
$633$	5.92856	0.235639
$634$	14.1225i	0.560877i
$635$	− 29.4625i	− 1.16918i
$636$	5.60218i	0.222141i
$637$	22.5036	0.891624
$638$	−7.15065	−0.283097
$639$	− 0.226626i	− 0.00896517i
$640$	19.8990i	0.786576i
$641$	24.9301i	0.984678i	0.870403	+	0.492339i	$0.163858\pi$
$641$	24.9301i	0.984678i	−0.870403	+	0.492339i	$0.836142\pi$
$642$	10.0052	0.394874
$643$	− 35.1614i	− 1.38663i	−0.720634	−	0.693315i	$-0.756149\pi$
$643$	− 35.1614i	− 1.38663i	0.720634	−	0.693315i	$-0.243851\pi$
$644$	−5.77701	−0.227646
$645$	7.17611	0.282559
$646$	0	0
$647$	−28.0142	−1.10135	−0.550677	−	0.834719i	$-0.685630\pi$
$647$	−28.0142	−1.10135	−0.550677	+	0.834719i	$0.685630\pi$
$648$	−2.61313	−0.102653
$649$	12.0672i	0.473680i
$650$	2.08746	0.0818768
$651$	12.6797i	0.496955i
$652$	− 12.8252i	− 0.502275i
$653$	− 37.6735i	− 1.47428i	−0.675742	−	0.737138i	$-0.736177\pi$
$653$	− 37.6735i	− 1.47428i	0.675742	−	0.737138i	$-0.263823\pi$
$654$	−0.731899	−0.0286195
$655$	5.39517	0.210807
$656$	10.0547i	0.392569i
$657$	− 0.368233i	− 0.0143661i
$658$	1.48300i	0.0578133i
$659$	−13.5356	−0.527272	−0.263636	−	0.964622i	$-0.584922\pi$
$659$	−13.5356	−0.527272	−0.263636	+	0.964622i	$0.584922\pi$
$660$	4.40743i	0.171559i
$661$	2.00626	0.0780345	0.0390172	−	0.999239i	$-0.487577\pi$
$661$	2.00626	0.0780345	0.0390172	+	0.999239i	$0.487577\pi$
$662$	−4.41315	−0.171522
$663$	0	0
$664$	37.6652	1.46169
$665$	17.5137	0.679152
$666$	3.01320i	0.116759i
$667$	−20.6547	−0.799752
$668$	12.5690i	0.486310i
$669$	− 26.1476i	− 1.01093i
$670$	− 3.37330i	− 0.130322i
$671$	4.89884	0.189117
$672$	−7.23532	−0.279109
$673$	16.7634i	0.646180i	0.946368	+	0.323090i	$0.104722\pi$
$673$	16.7634i	0.646180i	−0.946368	+	0.323090i	$0.895278\pi$
$674$	− 12.4530i	− 0.479673i
$675$	− 0.663643i	− 0.0255436i
$676$	−5.50114	−0.211582
$677$	− 23.0647i	− 0.886449i	−0.896411	−	0.443225i	$-0.853834\pi$
$677$	− 23.0647i	− 0.886449i	0.896411	−	0.443225i	$-0.146166\pi$
$678$	−6.60474	−0.253654
$679$	−3.31446	−0.127197
$680$	0	0
$681$	10.9746	0.420546
$682$	−11.7638	−0.450458
$683$	28.0179i	1.07207i	0.844194	+	0.536037i	$0.180079\pi$
$683$	28.0179i	1.07207i	−0.844194	+	0.536037i	$0.819921\pi$
$684$	9.63368	0.368353
$685$	− 31.7948i	− 1.21482i
$686$	11.7889i	0.450101i
$687$	14.4872i	0.552721i
$688$	2.85483	0.108840
$689$	−16.2800	−0.620220
$690$	− 5.27330i	− 0.200751i
$691$	26.6761i	1.01481i	0.861708	+	0.507404i	$0.169395\pi$
$691$	26.6761i	1.01481i	−0.861708	+	0.507404i	$0.830605\pi$
$692$	17.3201i	0.658412i
$693$	−1.84776	−0.0701906
$694$	− 3.28371i	− 0.124648i
$695$	−8.41731	−0.319287
$696$	−16.3128	−0.618335
$697$	0	0
$698$	−10.8340	−0.410074
$699$	−19.0980	−0.722354
$700$	− 1.15874i	− 0.0437964i
$701$	−9.75054	−0.368273	−0.184136	−	0.982901i	$-0.558949\pi$
$701$	−9.75054	−0.368273	−0.184136	+	0.982901i	$0.558949\pi$
$702$	− 3.14545i	− 0.118717i
$703$	− 26.8186i	− 1.01148i
$704$	− 4.23304i	− 0.159539i
$705$	3.26810	0.123084
$706$	18.2266	0.685968
$707$	− 2.93853i	− 0.110515i
$708$	11.4029i	0.428547i
$709$	− 28.7535i	− 1.07986i	−0.841710	−	0.539929i	$-0.818451\pi$
$709$	− 28.7535i	− 1.07986i	0.841710	−	0.539929i	$-0.181549\pi$
$710$	0.361194	0.0135554
$711$	− 2.71485i	− 0.101815i
$712$	−35.7199	−1.33866
$713$	−33.9797	−1.27255
$714$	0	0
$715$	−12.8081	−0.478994
$716$	−15.0151	−0.561141
$717$	0.740970i	0.0276720i
$718$	26.9927	1.00736
$719$	47.2247i	1.76118i	0.473876	+	0.880592i	$0.342855\pi$
$719$	47.2247i	1.76118i	−0.473876	+	0.880592i	$0.657145\pi$
$720$	1.72511i	0.0642911i
$721$	− 16.4094i	− 0.611118i
$722$	20.9740	0.780572
$723$	−21.3617	−0.794451
$724$	− 23.3733i	− 0.868662i
$725$	− 4.14288i	− 0.153863i
$726$	6.70474i	0.248836i
$727$	−27.7790	−1.03027	−0.515134	−	0.857110i	$-0.672258\pi$
$727$	−27.7790	−1.03027	−0.515134	+	0.857110i	$0.672258\pi$
$728$	− 13.2590i	− 0.491412i
$729$	−1.00000	−0.0370370
$730$	0.586887	0.0217217
$731$	0	0
$732$	4.62914	0.171098
$733$	5.38987	0.199080	0.0995398	−	0.995034i	$-0.468263\pi$
$733$	5.38987	0.199080	0.0995398	+	0.995034i	$0.468263\pi$
$734$	− 12.4917i	− 0.461077i
$735$	11.4025	0.420588
$736$	− 19.3897i	− 0.714712i
$737$	− 3.16760i	− 0.116680i
$738$	− 9.28931i	− 0.341944i
$739$	3.61782	0.133084	0.0665418	−	0.997784i	$-0.478803\pi$
$739$	3.61782	0.133084	0.0665418	+	0.997784i	$0.478803\pi$
$740$	11.5941	0.426207
$741$	27.9956i	1.02845i
$742$	− 3.74325i	− 0.137419i
$743$	6.18399i	0.226868i	0.993546	+	0.113434i	$0.0361851\pi$
$743$	6.18399i	0.226868i	−0.993546	+	0.113434i	$0.963815\pi$
$744$	−26.8368	−0.983883
$745$	37.7369i	1.38257i
$746$	−19.1461	−0.700990
$747$	14.4138	0.527375
$748$	0	0
$749$	16.1396	0.589730
$750$	9.02668	0.329608
$751$	− 51.3317i	− 1.87312i	−0.350508	−	0.936560i	$-0.613991\pi$
$751$	− 51.3317i	− 1.87312i	0.350508	−	0.936560i	$-0.386009\pi$
$752$	1.30013	0.0474109
$753$	− 0.938819i	− 0.0342125i
$754$	− 19.6359i	− 0.715098i
$755$	10.9770i	0.399493i
$756$	−1.74603	−0.0635027
$757$	−3.83750	−0.139476	−0.0697381	−	0.997565i	$-0.522216\pi$
$757$	−3.83750	−0.139476	−0.0697381	+	0.997565i	$0.522216\pi$
$758$	24.9725i	0.907041i
$759$	− 4.95174i	− 0.179737i
$760$	37.0681i	1.34460i
$761$	−16.5850	−0.601206	−0.300603	−	0.953749i	$-0.597188\pi$
$761$	−16.5850	−0.601206	−0.300603	+	0.953749i	$0.597188\pi$
$762$	10.8287i	0.392283i
$763$	−1.18064	−0.0427422
$764$	16.9942	0.614828
$765$	0	0
$766$	0.447937	0.0161846
$767$	−33.1370	−1.19651
$768$	− 12.9706i	− 0.468035i
$769$	−27.7826	−1.00187	−0.500933	−	0.865486i	$-0.667010\pi$
$769$	−27.7826	−1.00187	−0.500933	+	0.865486i	$0.667010\pi$
$770$	− 2.94495i	− 0.106129i
$771$	15.8293i	0.570077i
$772$	15.1580i	0.545548i
$773$	13.9509	0.501778	0.250889	−	0.968016i	$-0.419277\pi$
$773$	13.9509	0.501778	0.250889	+	0.968016i	$0.419277\pi$
$774$	−2.63752	−0.0948038
$775$	− 6.81560i	− 0.244823i
$776$	− 7.01511i	− 0.251828i
$777$	4.86068i	0.174376i
$778$	16.9346	0.607133
$779$	82.6782i	2.96225i
$780$	−12.1029	−0.433355
$781$	0.339169	0.0121364
$782$	0	0
$783$	−6.24264	−0.223094
$784$	4.53620	0.162007
$785$	7.92005i	0.282679i
$786$	−1.98295	−0.0707295
$787$	4.23206i	0.150857i	0.997151	+	0.0754284i	$0.0240324\pi$
$787$	4.23206i	0.150857i	−0.997151	+	0.0754284i	$0.975968\pi$
$788$	4.48157i	0.159649i
$789$	− 11.4573i	− 0.407890i
$790$	4.32691	0.153945
$791$	−10.6543	−0.378823
$792$	− 3.91082i	− 0.138965i
$793$	13.4524i	0.477708i
$794$	4.46232i	0.158362i
$795$	−8.24906	−0.292564
$796$	− 19.3388i	− 0.685445i
$797$	27.7502	0.982962	0.491481	−	0.870888i	$-0.336456\pi$
$797$	27.7502	0.982962	0.491481	+	0.870888i	$0.336456\pi$
$798$	−6.43702	−0.227868
$799$	0	0
$800$	3.88915	0.137502
$801$	−13.6694	−0.482984
$802$	3.97242i	0.140271i
$803$	0.551099	0.0194479
$804$	− 2.99321i	− 0.105562i
$805$	− 8.50649i	− 0.299814i
$806$	− 32.3037i	− 1.13785i
$807$	−19.1689	−0.674779
$808$	6.21946	0.218800
$809$	− 4.07279i	− 0.143192i	−0.997434	−	0.0715959i	$-0.977191\pi$
$809$	− 4.07279i	− 0.143192i	0.997434	−	0.0715959i	$-0.0228092\pi$
$810$	− 1.59379i	− 0.0560002i
$811$	6.28674i	0.220757i	0.993890	+	0.110379i	$0.0352064\pi$
$811$	6.28674i	0.220757i	−0.993890	+	0.110379i	$0.964794\pi$
$812$	−10.8999	−0.382510
$813$	6.82805i	0.239470i
$814$	−4.50958	−0.158061
$815$	18.8848	0.661507
$816$	0	0
$817$	23.4749	0.821282
$818$	−20.8486	−0.728954
$819$	− 5.07401i	− 0.177300i
$820$	−35.7430	−1.24820
$821$	− 19.7998i	− 0.691018i	−0.938415	−	0.345509i	$-0.887706\pi$
$821$	− 19.7998i	− 0.691018i	0.938415	−	0.345509i	$-0.112294\pi$
$822$	11.6859i	0.407593i
$823$	− 11.6739i	− 0.406927i	−0.979083	−	0.203463i	$-0.934780\pi$
$823$	− 11.6739i	− 0.406927i	0.979083	−	0.203463i	$-0.0652198\pi$
$824$	34.7308	1.20991
$825$	0.993212	0.0345792
$826$	− 7.61917i	− 0.265105i
$827$	13.8910i	0.483037i	0.970396	+	0.241518i	$0.0776454\pi$
$827$	13.8910i	0.483037i	−0.970396	+	0.241518i	$0.922355\pi$
$828$	− 4.67913i	− 0.162611i
$829$	−34.2670	−1.19014	−0.595071	−	0.803673i	$-0.702876\pi$
$829$	−34.2670	−1.19014	−0.595071	+	0.803673i	$0.702876\pi$
$830$	22.9727i	0.797394i
$831$	8.12784	0.281952
$832$	11.6241	0.402992
$833$	0	0
$834$	3.09372	0.107127
$835$	−18.5076	−0.640480
$836$	14.4178i	0.498651i
$837$	−10.2700	−0.354982
$838$	− 10.7382i	− 0.370945i
$839$	24.2470i	0.837098i	0.908194	+	0.418549i	$0.137461\pi$
$839$	24.2470i	0.837098i	−0.908194	+	0.418549i	$0.862539\pi$
$840$	− 6.71832i	− 0.231804i
$841$	−9.97056	−0.343813
$842$	11.7722	0.405695
$843$	− 11.6070i	− 0.399767i
$844$	8.38425i	0.288598i
$845$	− 8.10029i	− 0.278658i
$846$	−1.20116	−0.0412969
$847$	10.8156i	0.371628i
$848$	−3.28168	−0.112693
$849$	6.06404	0.208117
$850$	0	0
$851$	−13.0259	−0.446523
$852$	0.320497	0.0109800
$853$	− 7.38937i	− 0.253007i	−0.991966	−	0.126504i	$-0.959624\pi$
$853$	− 7.38937i	− 0.253007i	0.991966	−	0.126504i	$-0.0403755\pi$
$854$	−3.09309	−0.105843
$855$	14.1853i	0.485128i
$856$	34.1599i	1.16756i
$857$	− 8.03331i	− 0.274413i	−0.990542	−	0.137206i	$-0.956188\pi$
$857$	− 8.03331i	− 0.274413i	0.990542	−	0.137206i	$-0.0438123\pi$
$858$	4.70750	0.160711
$859$	7.66672	0.261585	0.130793	−	0.991410i	$-0.458248\pi$
$859$	7.66672	0.261585	0.130793	+	0.991410i	$0.458248\pi$
$860$	10.1486i	0.346063i
$861$	− 14.9848i	− 0.510682i
$862$	12.5449i	0.427280i
$863$	−14.4183	−0.490804	−0.245402	−	0.969421i	$-0.578920\pi$
$863$	−14.4183	−0.490804	−0.245402	+	0.969421i	$0.578920\pi$
$864$	− 5.86030i	− 0.199372i
$865$	−25.5034	−0.867142
$866$	−16.6166	−0.564655
$867$	0	0
$868$	−17.9317	−0.608643
$869$	4.06306	0.137830
$870$	− 9.94948i	− 0.337319i
$871$	8.69833	0.294732
$872$	− 2.49886i	− 0.0846220i
$873$	− 2.68457i	− 0.0908588i
$874$	− 17.2503i	− 0.583500i
$875$	14.5612	0.492257
$876$	0.520760	0.0175948
$877$	53.8226i	1.81746i	0.417383	+	0.908731i	$0.362947\pi$
$877$	53.8226i	1.81746i	−0.417383	+	0.908731i	$0.637053\pi$
$878$	18.0094i	0.607787i
$879$	6.87547i	0.231904i
$880$	−2.58181	−0.0870328
$881$	29.7945i	1.00380i	0.864925	+	0.501901i	$0.167366\pi$
$881$	29.7945i	1.00380i	−0.864925	+	0.501901i	$0.832634\pi$
$882$	−4.19090	−0.141115
$883$	−28.2666	−0.951247	−0.475624	−	0.879649i	$-0.657778\pi$
$883$	−28.2666	−0.951247	−0.475624	+	0.879649i	$0.657778\pi$
$884$	0	0
$885$	−16.7905	−0.564405
$886$	−11.8049	−0.396593
$887$	− 25.1167i	− 0.843338i	−0.906750	−	0.421669i	$-0.861444\pi$
$887$	− 25.1167i	− 0.843338i	0.906750	−	0.421669i	$-0.138556\pi$
$888$	−10.2877	−0.345233
$889$	17.4681i	0.585861i
$890$	− 21.7862i	− 0.730275i
$891$	− 1.49661i	− 0.0501382i
$892$	36.9784	1.23813
$893$	10.6908	0.357754
$894$	− 13.8699i	− 0.463879i
$895$	− 22.1094i	− 0.739034i
$896$	− 11.7979i	− 0.394141i
$897$	13.5976	0.454012
$898$	− 10.3703i	− 0.346061i
$899$	−64.1118	−2.13825
$900$	0.938533	0.0312844
$901$	0	0
$902$	13.9024	0.462901
$903$	−4.25466	−0.141586
$904$	− 22.5500i	− 0.750002i
$905$	34.4166	1.14405
$906$	− 4.03450i	− 0.134037i
$907$	49.0993i	1.63032i	0.579238	+	0.815158i	$0.303350\pi$
$907$	49.0993i	1.63032i	−0.579238	+	0.815158i	$0.696650\pi$
$908$	15.5204i	0.515062i
$909$	2.38009	0.0789425
$910$	8.08693	0.268079
$911$	− 7.97626i	− 0.264265i	−0.991232	−	0.132133i	$-0.957817\pi$
$911$	− 7.97626i	− 0.264265i	0.991232	−	0.132133i	$-0.0421825\pi$
$912$	5.64328i	0.186868i
$913$	21.5718i	0.713924i
$914$	11.7771	0.389551
$915$	6.81629i	0.225340i
$916$	−20.4880	−0.676942
$917$	−3.19875	−0.105632
$918$	0	0
$919$	19.8027	0.653229	0.326615	−	0.945158i	$-0.394092\pi$
$919$	19.8027	0.653229	0.326615	+	0.945158i	$0.394092\pi$
$920$	18.0042	0.593580
$921$	22.2451i	0.733000i
$922$	15.9201	0.524300
$923$	0.931370i	0.0306564i
$924$	− 2.61313i	− 0.0859655i
$925$	− 2.61272i	− 0.0859058i
$926$	−20.2306	−0.664818
$927$	13.2909	0.436531
$928$	− 36.5838i	− 1.20092i
$929$	5.57451i	0.182894i	0.995810	+	0.0914468i	$0.0291491\pi$
$929$	5.57451i	0.182894i	−0.995810	+	0.0914468i	$0.970851\pi$
$930$	− 16.3682i	− 0.536735i
$931$	37.3005	1.22248
$932$	− 27.0087i	− 0.884699i
$933$	−5.41421	−0.177253
$934$	5.48836	0.179584
$935$	0	0
$936$	10.7392	0.351023
$937$	−0.398572	−0.0130208	−0.00651039	−	0.999979i	$-0.502072\pi$
$937$	−0.398572	−0.0130208	−0.00651039	+	0.999979i	$0.502072\pi$
$938$	2.00000i	0.0653023i
$939$	−11.2945	−0.368582
$940$	4.62179i	0.150746i
$941$	− 4.30846i	− 0.140452i	−0.997531	−	0.0702259i	$-0.977628\pi$
$941$	− 4.30846i	− 0.140452i	0.997531	−	0.0702259i	$-0.0223720\pi$
$942$	− 2.91095i	− 0.0948439i
$943$	40.1572	1.30770
$944$	−6.67966	−0.217404
$945$	− 2.57099i	− 0.0836343i
$946$	− 3.94733i	− 0.128339i
$947$	− 11.4156i	− 0.370957i	−0.982648	−	0.185478i	$-0.940616\pi$
$947$	− 11.4156i	− 0.370957i	0.982648	−	0.185478i	$-0.0593835\pi$
$948$	3.83938	0.124697
$949$	1.51334i	0.0491250i
$950$	3.46004	0.112259
$951$	−18.4520	−0.598346
$952$	0	0
$953$	−40.8932	−1.32466	−0.662330	−	0.749213i	$-0.730432\pi$
$953$	−40.8932	−1.32466	−0.662330	+	0.749213i	$0.730432\pi$
$954$	3.03188	0.0981606
$955$	25.0235i	0.809741i
$956$	−1.04789	−0.0338912
$957$	− 9.34277i	− 0.302009i
$958$	2.24558i	0.0725515i
$959$	18.8509i	0.608726i
$960$	5.88989	0.190096
$961$	−74.4725	−2.40234
$962$	− 12.3835i	− 0.399259i
$963$	13.0724i	0.421253i
$964$	− 30.2100i	− 0.973000i
$965$	−22.3197	−0.718498
$966$	3.12649i	0.100593i
$967$	−23.5335	−0.756788	−0.378394	−	0.925645i	$-0.623524\pi$
$967$	−23.5335	−0.756788	−0.378394	+	0.925645i	$0.623524\pi$
$968$	−22.8914	−0.735758
$969$	0	0
$970$	4.27865	0.137379
$971$	−6.44140	−0.206714	−0.103357	−	0.994644i	$-0.532958\pi$
$971$	−6.44140	−0.206714	−0.103357	+	0.994644i	$0.532958\pi$
$972$	− 1.41421i	− 0.0453609i
$973$	4.99055	0.159990
$974$	− 17.7886i	− 0.569985i
$975$	2.72739i	0.0873465i
$976$	2.71169i	0.0867990i
$977$	−17.8474	−0.570989	−0.285495	−	0.958380i	$-0.592158\pi$
$977$	−17.8474	−0.570989	−0.285495	+	0.958380i	$0.592158\pi$
$978$	−6.94097	−0.221948
$979$	− 20.4577i	− 0.653831i
$980$	16.1256i	0.515113i
$981$	− 0.956272i	− 0.0305314i
$982$	−10.4538	−0.333595
$983$	− 24.1176i	− 0.769232i	−0.923077	−	0.384616i	$-0.874334\pi$
$983$	− 24.1176i	− 0.769232i	0.923077	−	0.384616i	$-0.125666\pi$
$984$	31.7157	1.01106
$985$	−6.59899	−0.210261
$986$	0	0
$987$	−1.93763	−0.0616755
$988$	−39.5918	−1.25958
$989$	− 11.4019i	− 0.362559i
$990$	2.38528	0.0758092
$991$	24.2059i	0.768925i	0.923141	+	0.384463i	$0.125613\pi$
$991$	24.2059i	0.768925i	−0.923141	+	0.384463i	$0.874387\pi$
$992$	− 60.1852i	− 1.91088i
$993$	− 5.76606i	− 0.182980i
$994$	−0.214149	−0.00679240
$995$	28.4759	0.902746
$996$	20.3842i	0.645900i
$997$	36.9151i	1.16911i	0.811353	+	0.584557i	$0.198732\pi$
$997$	36.9151i	1.16911i	−0.811353	+	0.584557i	$0.801268\pi$
$998$	5.76489i	0.182484i
$999$	−3.93694	−0.124559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.d.e.577.6		8
17.2	even	8		867.2.e.h.829.3		8
17.3	odd	16		867.2.h.g.688.2		8
17.4	even	4		867.2.a.n.1.2		4
17.5	odd	16		867.2.h.f.757.1		8
17.6	odd	16		51.2.h.a.49.2	yes	8
17.7	odd	16		867.2.h.b.733.1		8
17.8	even	8		867.2.e.h.616.2		8
17.9	even	8		867.2.e.i.616.2		8
17.10	odd	16		867.2.h.f.733.1		8
17.11	odd	16		867.2.h.g.712.2		8
17.12	odd	16		867.2.h.b.757.1		8
17.13	even	4		867.2.a.m.1.2		4
17.14	odd	16		51.2.h.a.25.2	✓	8
17.15	even	8		867.2.e.i.829.3		8
17.16	even	2	inner	867.2.d.e.577.5		8
51.14	even	16		153.2.l.e.127.1		8
51.23	even	16		153.2.l.e.100.1		8
51.38	odd	4		2601.2.a.bd.1.3		4
51.47	odd	4		2601.2.a.bc.1.3		4
68.23	even	16		816.2.bq.a.49.1		8
68.31	even	16		816.2.bq.a.433.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.25.2	✓	8	17.14	odd	16
51.2.h.a.49.2	yes	8	17.6	odd	16
153.2.l.e.100.1		8	51.23	even	16
153.2.l.e.127.1		8	51.14	even	16
816.2.bq.a.49.1		8	68.23	even	16
816.2.bq.a.433.1		8	68.31	even	16
867.2.a.m.1.2		4	17.13	even	4
867.2.a.n.1.2		4	17.4	even	4
867.2.d.e.577.5		8	17.16	even	2	inner
867.2.d.e.577.6		8	1.1	even	1	trivial
867.2.e.h.616.2		8	17.8	even	8
867.2.e.h.829.3		8	17.2	even	8
867.2.e.i.616.2		8	17.9	even	8
867.2.e.i.829.3		8	17.15	even	8
867.2.h.b.733.1		8	17.7	odd	16
867.2.h.b.757.1		8	17.12	odd	16
867.2.h.f.733.1		8	17.10	odd	16
867.2.h.f.757.1		8	17.5	odd	16
867.2.h.g.688.2		8	17.3	odd	16
867.2.h.g.712.2		8	17.11	odd	16
2601.2.a.bc.1.3		4	51.47	odd	4
2601.2.a.bd.1.3		4	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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.765367 q^{2} +1.00000i q^{3} -1.41421 q^{4} -2.08239i q^{5} +0.765367i q^{6} +1.23463i q^{7} -2.61313 q^{8} -1.00000 q^{9} -1.59379i q^{10} -1.49661i q^{11} -1.41421i q^{12} +4.10973 q^{13} +0.944947i q^{14} +2.08239 q^{15} +0.828427 q^{16} -0.765367 q^{18} +6.81204 q^{19} +2.94495i q^{20} -1.23463 q^{21} -1.14545i q^{22} -3.30864i q^{23} -2.61313i q^{24} +0.663643 q^{25} +3.14545 q^{26} -1.00000i q^{27} -1.74603i q^{28} -6.24264i q^{29} +1.59379 q^{30} -10.2700i q^{31} +5.86030 q^{32} +1.49661 q^{33} +2.57099 q^{35} +1.41421 q^{36} -3.93694i q^{37} +5.21371 q^{38} +4.10973i q^{39} +5.44155i q^{40} +12.1371i q^{41} -0.944947 q^{42} +3.44609 q^{43} +2.11652i q^{44} +2.08239i q^{45} -2.53233i q^{46} +1.56940 q^{47} +0.828427i q^{48} +5.47568 q^{49} +0.507930 q^{50} -5.81204 q^{52} -3.96134 q^{53} -0.765367i q^{54} -3.11652 q^{55} -3.22625i q^{56} +6.81204i q^{57} -4.77791i q^{58} -8.06306 q^{59} -2.94495 q^{60} +3.27330i q^{61} -7.86030i q^{62} -1.23463i q^{63} +2.82843 q^{64} -8.55807i q^{65} +1.14545 q^{66} +2.11652 q^{67} +3.30864 q^{69} +1.96775 q^{70} +0.226626i q^{71} +2.61313 q^{72} +0.368233i q^{73} -3.01320i q^{74} +0.663643i q^{75} -9.63368 q^{76} +1.84776 q^{77} +3.14545i q^{78} +2.71485i q^{79} -1.72511i q^{80} +1.00000 q^{81} +9.28931i q^{82} -14.4138 q^{83} +1.74603 q^{84} +2.63752 q^{86} +6.24264 q^{87} +3.91082i q^{88} +13.6694 q^{89} +1.59379i q^{90} +5.07401i q^{91} +4.67913i q^{92} +10.2700 q^{93} +1.20116 q^{94} -14.1853i q^{95} +5.86030i q^{96} +2.68457i q^{97} +4.19090 q^{98} +1.49661i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9} - 8 q^{13} + 8 q^{15} - 16 q^{16} + 24 q^{19} - 16 q^{21} - 16 q^{30} - 8 q^{33} + 32 q^{35} + 32 q^{38} + 16 q^{42} - 8 q^{43} + 16 q^{47} + 8 q^{49} + 32 q^{50} - 16 q^{52} - 16 q^{53} - 24 q^{55}+ \cdots + 64 q^{98}+O(q^{100}) \) 8 * q - 8 * q^9 - 8 * q^13 + 8 * q^15 - 16 * q^16 + 24 * q^19 - 16 * q^21 - 16 * q^30 - 8 * q^33 + 32 * q^35 + 32 * q^38 + 16 * q^42 - 8 * q^43 + 16 * q^47 + 8 * q^49 + 32 * q^50 - 16 * q^52 - 16 * q^53 - 24 * q^55 - 48 * q^59 - 16 * q^66 + 16 * q^67 - 24 * q^69 - 48 * q^70 + 16 * q^76 + 8 * q^81 - 16 * q^83 - 32 * q^86 + 16 * q^87 + 32 * q^89 + 16 * q^93 + 32 * q^94 + 64 * q^98

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