LMFDB - Embedded newform 867.2.d.e.577.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(577,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			577.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	867.577
Dual form			867.2.d.e.577.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.84776 q^{2} -1.00000i q^{3} +1.41421 q^{4} +3.61313i q^{5} +1.84776i q^{6} -3.84776i q^{7} +1.08239 q^{8} -1.00000 q^{9} -6.67619i q^{10} +0.198912i q^{11} -1.41421i q^{12} -0.883480 q^{13} +7.10973i q^{14} +3.61313 q^{15} -4.82843 q^{16} +1.84776 q^{18} +2.24943 q^{19} +5.10973i q^{20} -3.84776 q^{21} -0.367542i q^{22} -2.55166i q^{23} -1.08239i q^{24} -8.05468 q^{25} +1.63246 q^{26} +1.00000i q^{27} -5.44155i q^{28} -2.24264i q^{29} -6.67619 q^{30} -4.73925i q^{31} +6.75699 q^{32} +0.198912 q^{33} +13.9024 q^{35} -1.41421 q^{36} +6.98067i q^{37} -4.15640 q^{38} +0.883480i q^{39} +3.91082i q^{40} -0.619914i q^{41} +7.10973 q^{42} +7.17120 q^{43} +0.281305i q^{44} -3.61313i q^{45} +4.71485i q^{46} +5.49207 q^{47} +4.82843i q^{48} -7.80525 q^{49} +14.8831 q^{50} -1.24943 q^{52} +5.18759 q^{53} -1.84776i q^{54} -0.718695 q^{55} -4.16478i q^{56} -2.24943i q^{57} +4.14386i q^{58} -5.01933 q^{59} +5.10973 q^{60} -15.0353i q^{61} +8.75699i q^{62} +3.84776i q^{63} -2.82843 q^{64} -3.19212i q^{65} -0.367542 q^{66} -0.281305 q^{67} -2.55166 q^{69} -25.6884 q^{70} -13.9382i q^{71} -1.08239 q^{72} -15.6401i q^{73} -12.8986i q^{74} +8.05468i q^{75} +3.18117 q^{76} +0.765367 q^{77} -1.63246i q^{78} -5.12453i q^{79} -17.4457i q^{80} +1.00000 q^{81} +1.14545i q^{82} +9.51716 q^{83} -5.44155 q^{84} -13.2506 q^{86} -2.24264 q^{87} +0.215301i q^{88} +4.33476 q^{89} +6.67619i q^{90} +3.39942i q^{91} -3.60859i q^{92} -4.73925 q^{93} -10.1480 q^{94} +8.12747i q^{95} -6.75699i q^{96} -5.94948i q^{97} +14.4222 q^{98} -0.198912i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.84776	−1.30656	−0.653281	−	0.757115i	$-0.726608\pi$
$2$	−1.84776	−1.30656	−0.653281	+	0.757115i	$0.726608\pi$
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	1.41421	0.707107
$5$	3.61313i	1.61584i	0.589293	+	0.807920i	$0.299406\pi$
$5$	3.61313i	1.61584i	−0.589293	+	0.807920i	$0.700594\pi$
$6$	1.84776i	0.754344i
$7$	− 3.84776i	− 1.45432i	−0.686470	−	0.727158i	$-0.740841\pi$
$7$	− 3.84776i	− 1.45432i	0.686470	−	0.727158i	$-0.259159\pi$
$8$	1.08239	0.382683
$9$	−1.00000	−0.333333
$10$	− 6.67619i	− 2.11120i
$11$	0.198912i	0.0599743i	0.999550	+	0.0299872i	$0.00954664\pi$
$11$	0.198912i	0.0599743i	−0.999550	+	0.0299872i	$0.990453\pi$
$12$	− 1.41421i	− 0.408248i
$13$	−0.883480	−0.245033	−0.122517	−	0.992466i	$-0.539096\pi$
$13$	−0.883480	−0.245033	−0.122517	+	0.992466i	$0.539096\pi$
$14$	7.10973i	1.90016i
$15$	3.61313	0.932905
$16$	−4.82843	−1.20711
$17$	0	0
$17$	0	0
$18$	1.84776	0.435521
$19$	2.24943	0.516054	0.258027	−	0.966138i	$-0.416928\pi$
$19$	2.24943	0.516054	0.258027	+	0.966138i	$0.416928\pi$
$20$	5.10973i	1.14257i
$21$	−3.84776	−0.839650
$22$	− 0.367542i	− 0.0783602i
$23$	− 2.55166i	− 0.532058i	−0.963965	−	0.266029i	$-0.914288\pi$
$23$	− 2.55166i	− 0.532058i	0.963965	−	0.266029i	$-0.0857116\pi$
$24$	− 1.08239i	− 0.220942i
$25$	−8.05468	−1.61094
$26$	1.63246	0.320151
$27$	1.00000i	0.192450i
$28$	− 5.44155i	− 1.02836i
$29$	− 2.24264i	− 0.416448i	−0.978081	−	0.208224i	$-0.933232\pi$
$29$	− 2.24264i	− 0.416448i	0.978081	−	0.208224i	$-0.0667683\pi$
$30$	−6.67619	−1.21890
$31$	− 4.73925i	− 0.851194i	−0.904913	−	0.425597i	$-0.860064\pi$
$31$	− 4.73925i	− 0.851194i	0.904913	−	0.425597i	$-0.139936\pi$
$32$	6.75699	1.19448
$33$	0.198912	0.0346262
$34$	0	0
$35$	13.9024	2.34994
$36$	−1.41421	−0.235702
$37$	6.98067i	1.14761i	0.818990	+	0.573807i	$0.194534\pi$
$37$	6.98067i	1.14761i	−0.818990	+	0.573807i	$0.805466\pi$
$38$	−4.15640	−0.674258
$39$	0.883480i	0.141470i
$40$	3.91082i	0.618355i
$41$	− 0.619914i	− 0.0968144i	−0.998828	−	0.0484072i	$-0.984585\pi$
$41$	− 0.619914i	− 0.0968144i	0.998828	−	0.0484072i	$-0.0154145\pi$
$42$	7.10973	1.09706
$43$	7.17120	1.09360	0.546799	−	0.837264i	$-0.315846\pi$
$43$	7.17120	1.09360	0.546799	+	0.837264i	$0.315846\pi$
$44$	0.281305i	0.0424083i
$45$	− 3.61313i	− 0.538613i
$46$	4.71485i	0.695167i
$47$	5.49207	0.801101	0.400550	−	0.916275i	$-0.368819\pi$
$47$	5.49207	0.801101	0.400550	+	0.916275i	$0.368819\pi$
$48$	4.82843i	0.696923i
$49$	−7.80525	−1.11504
$50$	14.8831	2.10479
$51$	0	0
$52$	−1.24943	−0.173265
$53$	5.18759	0.712570	0.356285	−	0.934377i	$-0.384043\pi$
$53$	5.18759	0.712570	0.356285	+	0.934377i	$0.384043\pi$
$54$	− 1.84776i	− 0.251448i
$55$	−0.718695	−0.0969089
$56$	− 4.16478i	− 0.556543i
$57$	− 2.24943i	− 0.297944i
$58$	4.14386i	0.544115i
$59$	−5.01933	−0.653461	−0.326731	−	0.945117i	$-0.605947\pi$
$59$	−5.01933	−0.653461	−0.326731	+	0.945117i	$0.605947\pi$
$60$	5.10973	0.659664
$61$	− 15.0353i	− 1.92508i	−0.271142	−	0.962539i	$-0.587401\pi$
$61$	− 15.0353i	− 1.92508i	0.271142	−	0.962539i	$-0.412599\pi$
$62$	8.75699i	1.11214i
$63$	3.84776i	0.484772i
$64$	−2.82843	−0.353553
$65$	− 3.19212i	− 0.395934i
$66$	−0.367542	−0.0452413
$67$	−0.281305	−0.0343668	−0.0171834	−	0.999852i	$-0.505470\pi$
$67$	−0.281305	−0.0343668	−0.0171834	+	0.999852i	$0.505470\pi$
$68$	0	0
$69$	−2.55166	−0.307184
$70$	−25.6884	−3.07035
$71$	− 13.9382i	− 1.65416i	−0.562088	−	0.827078i	$-0.690002\pi$
$71$	− 13.9382i	− 1.65416i	0.562088	−	0.827078i	$-0.309998\pi$
$72$	−1.08239	−0.127561
$73$	− 15.6401i	− 1.83053i	−0.402847	−	0.915267i	$-0.631979\pi$
$73$	− 15.6401i	− 1.83053i	0.402847	−	0.915267i	$-0.368021\pi$
$74$	− 12.8986i	− 1.49943i
$75$	8.05468i	0.930074i
$76$	3.18117	0.364906
$77$	0.765367	0.0872216
$78$	− 1.63246i	− 0.184839i
$79$	− 5.12453i	− 0.576554i	−0.957547	−	0.288277i	$-0.906918\pi$
$79$	− 5.12453i	− 0.576554i	0.957547	−	0.288277i	$-0.0930825\pi$
$80$	− 17.4457i	− 1.95049i
$81$	1.00000	0.111111
$82$	1.14545i	0.126494i
$83$	9.51716	1.04464	0.522322	−	0.852748i	$-0.325066\pi$
$83$	9.51716	1.04464	0.522322	+	0.852748i	$0.325066\pi$
$84$	−5.44155	−0.593722
$85$	0	0
$86$	−13.2506	−1.42885
$87$	−2.24264	−0.240436
$88$	0.215301i	0.0229512i
$89$	4.33476	0.459484	0.229742	−	0.973252i	$-0.426212\pi$
$89$	4.33476	0.459484	0.229742	+	0.973252i	$0.426212\pi$
$90$	6.67619i	0.703732i
$91$	3.39942i	0.356356i
$92$	− 3.60859i	− 0.376222i
$93$	−4.73925	−0.491437
$94$	−10.1480	−1.04669
$95$	8.12747i	0.833861i
$96$	− 6.75699i	− 0.689632i
$97$	− 5.94948i	− 0.604078i	−0.953295	−	0.302039i	$-0.902333\pi$
$97$	− 5.94948i	− 0.604078i	0.953295	−	0.302039i	$-0.0976674\pi$
$98$	14.4222	1.45686
$99$	− 0.198912i	− 0.0199914i
$100$	−11.3910	−1.13910
$101$	−3.48022	−0.346295	−0.173147	−	0.984896i	$-0.555394\pi$
$101$	−3.48022	−0.346295	−0.173147	+	0.984896i	$0.555394\pi$
$102$	0	0
$103$	−10.2649	−1.01143	−0.505716	−	0.862700i	$-0.668772\pi$
$103$	−10.2649	−1.01143	−0.505716	+	0.862700i	$0.668772\pi$
$104$	−0.956272	−0.0937702
$105$	− 13.9024i	− 1.35674i
$106$	−9.58541	−0.931018
$107$	− 2.80979i	− 0.271632i	−0.990734	−	0.135816i	$-0.956634\pi$
$107$	− 2.80979i	− 0.271632i	0.990734	−	0.135816i	$-0.0433656\pi$
$108$	1.41421i	0.136083i
$109$	− 8.57446i	− 0.821285i	−0.911797	−	0.410642i	$-0.865305\pi$
$109$	− 8.57446i	− 0.821285i	0.911797	−	0.410642i	$-0.134695\pi$
$110$	1.32798	0.126618
$111$	6.98067	0.662576
$112$	18.5786i	1.75551i
$113$	− 3.83975i	− 0.361213i	−0.983555	−	0.180607i	$-0.942194\pi$
$113$	− 3.83975i	− 0.361213i	0.983555	−	0.180607i	$-0.0578061\pi$
$114$	4.15640i	0.389283i
$115$	9.21946	0.859719
$116$	− 3.17157i	− 0.294473i
$117$	0.883480	0.0816777
$118$	9.27452	0.853788
$119$	0	0
$120$	3.91082	0.357007
$121$	10.9604	0.996403
$122$	27.7817i	2.51524i
$123$	−0.619914	−0.0558958
$124$	− 6.70231i	− 0.601885i
$125$	− 11.0369i	− 0.987174i
$126$	− 7.10973i	− 0.633385i
$127$	18.3041	1.62423	0.812113	−	0.583500i	$-0.198317\pi$
$127$	18.3041	1.62423	0.812113	+	0.583500i	$0.198317\pi$
$128$	−8.28772	−0.732538
$129$	− 7.17120i	− 0.631389i
$130$	5.89828i	0.517313i
$131$	11.3478i	0.991465i	0.868475	+	0.495733i	$0.165100\pi$
$131$	11.3478i	0.991465i	−0.868475	+	0.495733i	$0.834900\pi$
$132$	0.281305	0.0244844
$133$	− 8.65526i	− 0.750506i
$134$	0.519783	0.0449024
$135$	−3.61313	−0.310968
$136$	0	0
$137$	−7.14961	−0.610833	−0.305416	−	0.952219i	$-0.598796\pi$
$137$	−7.14961	−0.610833	−0.305416	+	0.952219i	$0.598796\pi$
$138$	4.71485	0.401355
$139$	− 10.9848i	− 0.931721i	−0.884858	−	0.465861i	$-0.845745\pi$
$139$	− 10.9848i	− 0.931721i	0.884858	−	0.465861i	$-0.154255\pi$
$140$	19.6610	1.66166
$141$	− 5.49207i	− 0.462516i
$142$	25.7544i	2.16126i
$143$	− 0.175735i	− 0.0146957i
$144$	4.82843	0.402369
$145$	8.10294	0.672913
$146$	28.8991i	2.39171i
$147$	7.80525i	0.643766i
$148$	9.87216i	0.811486i
$149$	5.99480	0.491114	0.245557	−	0.969382i	$-0.421029\pi$
$149$	5.99480	0.491114	0.245557	+	0.969382i	$0.421029\pi$
$150$	− 14.8831i	− 1.21520i
$151$	11.4780	0.934063	0.467032	−	0.884241i	$-0.345323\pi$
$151$	11.4780	0.934063	0.467032	+	0.884241i	$0.345323\pi$
$152$	2.43476	0.197485
$153$	0	0
$154$	−1.41421	−0.113961
$155$	17.1235	1.37539
$156$	1.24943i	0.100034i
$157$	5.81166	0.463821	0.231911	−	0.972737i	$-0.425502\pi$
$157$	5.81166	0.463821	0.231911	+	0.972737i	$0.425502\pi$
$158$	9.46889i	0.753305i
$159$	− 5.18759i	− 0.411402i
$160$	24.4138i	1.93008i
$161$	−9.81817	−0.773780
$162$	−1.84776	−0.145174
$163$	− 5.40878i	− 0.423648i	−0.977308	−	0.211824i	$-0.932060\pi$
$163$	− 5.40878i	− 0.423648i	0.977308	−	0.211824i	$-0.0679404\pi$
$164$	− 0.876691i	− 0.0684581i
$165$	0.718695i	0.0559504i
$166$	−17.5854	−1.36489
$167$	3.26038i	0.252296i	0.992011	+	0.126148i	$0.0402614\pi$
$167$	3.26038i	0.252296i	−0.992011	+	0.126148i	$0.959739\pi$
$168$	−4.16478	−0.321320
$169$	−12.2195	−0.939959
$170$	0	0
$171$	−2.24943	−0.172018
$172$	10.1416	0.773290
$173$	16.8394i	1.28027i	0.768261	+	0.640137i	$0.221122\pi$
$173$	16.8394i	1.28027i	−0.768261	+	0.640137i	$0.778878\pi$
$174$	4.14386	0.314145
$175$	30.9925i	2.34281i
$176$	− 0.960434i	− 0.0723954i
$177$	5.01933i	0.377276i
$178$	−8.00960	−0.600345
$179$	−1.10332	−0.0824658	−0.0412329	−	0.999150i	$-0.513129\pi$
$179$	−1.10332	−0.0824658	−0.0412329	+	0.999150i	$0.513129\pi$
$180$	− 5.10973i	− 0.380857i
$181$	15.4701i	1.14988i	0.818194	+	0.574942i	$0.194975\pi$
$181$	15.4701i	1.14988i	−0.818194	+	0.574942i	$0.805025\pi$
$182$	− 6.28130i	− 0.465601i
$183$	−15.0353	−1.11144
$184$	− 2.76190i	− 0.203610i
$185$	−25.2220	−1.85436
$186$	8.75699	0.642093
$187$	0	0
$188$	7.76696	0.566464
$189$	3.84776	0.279883
$190$	− 15.0176i	− 1.08949i
$191$	−5.97069	−0.432024	−0.216012	−	0.976391i	$-0.569305\pi$
$191$	−5.97069	−0.432024	−0.216012	+	0.976391i	$0.569305\pi$
$192$	2.82843i	0.204124i
$193$	− 11.0479i	− 0.795245i	−0.917549	−	0.397622i	$-0.869835\pi$
$193$	− 11.0479i	− 0.795245i	0.917549	−	0.397622i	$-0.130165\pi$
$194$	10.9932i	0.789267i
$195$	−3.19212	−0.228593
$196$	−11.0383	−0.788449
$197$	− 1.79467i	− 0.127865i	−0.997954	−	0.0639326i	$-0.979636\pi$
$197$	− 1.79467i	− 0.127865i	0.997954	−	0.0639326i	$-0.0203643\pi$
$198$	0.367542i	0.0261201i
$199$	0.473428i	0.0335605i	0.999859	+	0.0167802i	$0.00534156\pi$
$199$	0.473428i	0.0335605i	−0.999859	+	0.0167802i	$0.994658\pi$
$200$	−8.71832	−0.616478
$201$	0.281305i	0.0198417i
$202$	6.43060	0.452456
$203$	−8.62914	−0.605647
$204$	0	0
$205$	2.23983	0.156436
$206$	18.9671	1.32150
$207$	2.55166i	0.177353i
$208$	4.26582	0.295781
$209$	0.447439i	0.0309500i
$210$	25.6884i	1.77266i
$211$	− 1.03188i	− 0.0710372i	−0.999369	−	0.0355186i	$-0.988692\pi$
$211$	− 1.03188i	− 0.0710372i	0.999369	−	0.0355186i	$-0.0113083\pi$
$212$	7.33636	0.503863
$213$	−13.9382	−0.955027
$214$	5.19181i	0.354905i
$215$	25.9104i	1.76708i
$216$	1.08239i	0.0736475i
$217$	−18.2355	−1.23790
$218$	15.8435i	1.07306i
$219$	−15.6401	−1.05686
$220$	−1.01639	−0.0685249
$221$	0	0
$222$	−12.8986	−0.865697
$223$	11.9018	0.797002	0.398501	−	0.917168i	$-0.369531\pi$
$223$	11.9018	0.797002	0.398501	+	0.917168i	$0.369531\pi$
$224$	− 25.9993i	− 1.73715i
$225$	8.05468	0.536979
$226$	7.09494i	0.471948i
$227$	19.9555i	1.32449i	0.749285	+	0.662247i	$0.230397\pi$
$227$	19.9555i	1.32449i	−0.749285	+	0.662247i	$0.769603\pi$
$228$	− 3.18117i	− 0.210678i
$229$	−0.0263629	−0.00174211	−0.000871055	−	1.00000i	$-0.500277\pi$
$229$	−0.0263629	−0.00174211	−0.000871055		1.00000i	$0.500277\pi$
$230$	−17.0353	−1.12328
$231$	− 0.765367i	− 0.0503574i
$232$	− 2.42742i	− 0.159368i
$233$	22.6706i	1.48520i	0.669734	+	0.742601i	$0.266408\pi$
$233$	22.6706i	1.48520i	−0.669734	+	0.742601i	$0.733592\pi$
$234$	−1.63246	−0.106717
$235$	19.8435i	1.29445i
$236$	−7.09841	−0.462067
$237$	−5.12453	−0.332874
$238$	0	0
$239$	10.3205	0.667577	0.333789	−	0.942648i	$-0.391673\pi$
$239$	10.3205	0.667577	0.333789	+	0.942648i	$0.391673\pi$
$240$	−17.4457	−1.12612
$241$	4.95524i	0.319195i	0.987182	+	0.159597i	$0.0510196\pi$
$241$	4.95524i	0.319195i	−0.987182	+	0.159597i	$0.948980\pi$
$242$	−20.2522	−1.30186
$243$	− 1.00000i	− 0.0641500i
$244$	− 21.2632i	− 1.36124i
$245$	− 28.2014i	− 1.80172i
$246$	1.14545	0.0730314
$247$	−1.98733	−0.126450
$248$	− 5.12972i	− 0.325738i
$249$	− 9.51716i	− 0.603125i
$250$	20.3936i	1.28980i
$251$	27.6021	1.74223	0.871115	−	0.491079i	$-0.163397\pi$
$251$	27.6021	1.74223	0.871115	+	0.491079i	$0.163397\pi$
$252$	5.44155i	0.342786i
$253$	0.507556	0.0319098
$254$	−33.8216	−2.12215
$255$	0	0
$256$	20.9706	1.31066
$257$	−24.6239	−1.53600	−0.768000	−	0.640450i	$-0.778748\pi$
$257$	−24.6239	−1.53600	−0.768000	+	0.640450i	$0.778748\pi$
$258$	13.2506i	0.824949i
$259$	26.8599	1.66899
$260$	− 4.51434i	− 0.279968i
$261$	2.24264i	0.138816i
$262$	− 20.9681i	− 1.29541i
$263$	−18.9015	−1.16552	−0.582759	−	0.812645i	$-0.698027\pi$
$263$	−18.9015	−1.16552	−0.582759	+	0.812645i	$0.698027\pi$
$264$	0.215301	0.0132509
$265$	18.7434i	1.15140i
$266$	15.9928i	0.980584i
$267$	− 4.33476i	− 0.265283i
$268$	−0.397825	−0.0243010
$269$	− 14.2053i	− 0.866114i	−0.901367	−	0.433057i	$-0.857435\pi$
$269$	− 14.2053i	− 0.866114i	0.901367	−	0.433057i	$-0.142565\pi$
$270$	6.67619	0.406300
$271$	−19.9314	−1.21074	−0.605372	−	0.795942i	$-0.706976\pi$
$271$	−19.9314	−1.21074	−0.605372	+	0.795942i	$0.706976\pi$
$272$	0	0
$273$	3.39942	0.205742
$274$	13.2108	0.798092
$275$	− 1.60218i	− 0.0966148i
$276$	−3.60859	−0.217212
$277$	21.4029i	1.28597i	0.765877	+	0.642987i	$0.222305\pi$
$277$	21.4029i	1.28597i	−0.765877	+	0.642987i	$0.777695\pi$
$278$	20.2973i	1.21735i
$279$	4.73925i	0.283731i
$280$	15.0479	0.899283
$281$	−21.4669	−1.28061	−0.640305	−	0.768121i	$-0.721192\pi$
$281$	−21.4669	−1.28061	−0.640305	+	0.768121i	$0.721192\pi$
$282$	10.1480i	0.604306i
$283$	− 19.8223i	− 1.17832i	−0.808018	−	0.589158i	$-0.799460\pi$
$283$	− 19.8223i	− 1.17832i	0.808018	−	0.589158i	$-0.200540\pi$
$284$	− 19.7115i	− 1.16966i
$285$	8.12747	0.481430
$286$	0.324716i	0.0192009i
$287$	−2.38528	−0.140799
$288$	−6.75699	−0.398159
$289$	0	0
$290$	−14.9723	−0.879203
$291$	−5.94948	−0.348765
$292$	− 22.1184i	− 1.29438i
$293$	20.3717	1.19013	0.595064	−	0.803678i	$-0.297127\pi$
$293$	20.3717	1.19013	0.595064	+	0.803678i	$0.297127\pi$
$294$	− 14.4222i	− 0.841121i
$295$	− 18.1355i	− 1.05589i
$296$	7.55582i	0.439173i
$297$	−0.198912	−0.0115421
$298$	−11.0770	−0.641671
$299$	2.25434i	0.130372i
$300$	11.3910i	0.657662i
$301$	− 27.5930i	− 1.59044i
$302$	−21.2085	−1.22041
$303$	3.48022i	0.199933i
$304$	−10.8612	−0.622933
$305$	54.3246	3.11062
$306$	0	0
$307$	−13.6278	−0.777779	−0.388890	−	0.921284i	$-0.627141\pi$
$307$	−13.6278	−0.777779	−0.388890	+	0.921284i	$0.627141\pi$
$308$	1.08239	0.0616750
$309$	10.2649i	0.583951i
$310$	−31.6401	−1.79704
$311$	− 2.58579i	− 0.146626i	−0.997309	−	0.0733132i	$-0.976643\pi$
$311$	− 2.58579i	− 0.146626i	0.997309	−	0.0733132i	$-0.0233573\pi$
$312$	0.956272i	0.0541382i
$313$	3.95365i	0.223473i	0.993738	+	0.111737i	$0.0356413\pi$
$313$	3.95365i	0.223473i	−0.993738	+	0.111737i	$0.964359\pi$
$314$	−10.7386	−0.606012
$315$	−13.9024	−0.783314
$316$	− 7.24718i	− 0.407686i
$317$	− 33.5145i	− 1.88236i	−0.337903	−	0.941181i	$-0.609718\pi$
$317$	− 33.5145i	− 1.88236i	0.337903	−	0.941181i	$-0.390282\pi$
$318$	9.58541i	0.537523i
$319$	0.446089	0.0249762
$320$	− 10.2195i	− 0.571285i
$321$	−2.80979	−0.156827
$322$	18.1416	1.01099
$323$	0	0
$324$	1.41421	0.0785674
$325$	7.11615	0.394733
$326$	9.99411i	0.553523i
$327$	−8.57446	−0.474169
$328$	− 0.670991i	− 0.0370493i
$329$	− 21.1322i	− 1.16505i
$330$	− 1.32798i	− 0.0731027i
$331$	−19.3037	−1.06103	−0.530515	−	0.847676i	$-0.678001\pi$
$331$	−19.3037	−1.06103	−0.530515	+	0.847676i	$0.678001\pi$
$332$	13.4593	0.738675
$333$	− 6.98067i	− 0.382538i
$334$	− 6.02440i	− 0.329640i
$335$	− 1.01639i	− 0.0555313i
$336$	18.5786	1.01355
$337$	17.4122i	0.948506i	0.880389	+	0.474253i	$0.157282\pi$
$337$	17.4122i	0.948506i	−0.880389	+	0.474253i	$0.842718\pi$
$338$	22.5786	1.22812
$339$	−3.83975	−0.208547
$340$	0	0
$341$	0.942695	0.0510498
$342$	4.15640	0.224753
$343$	3.09841i	0.167298i
$344$	7.76205	0.418502
$345$	− 9.21946i	− 0.496359i
$346$	− 31.1151i	− 1.67276i
$347$	31.1090i	1.67002i	0.550236	+	0.835009i	$0.314538\pi$
$347$	31.1090i	1.67002i	−0.550236	+	0.835009i	$0.685462\pi$
$348$	−3.17157	−0.170014
$349$	30.0407	1.60804	0.804022	−	0.594600i	$-0.202690\pi$
$349$	30.0407	1.60804	0.804022	+	0.594600i	$0.202690\pi$
$350$	− 57.2666i	− 3.06103i
$351$	− 0.883480i	− 0.0471567i
$352$	1.34405i	0.0716380i
$353$	−17.2848	−0.919977	−0.459989	−	0.887925i	$-0.652147\pi$
$353$	−17.2848	−0.919977	−0.459989	+	0.887925i	$0.652147\pi$
$354$	− 9.27452i	− 0.492935i
$355$	50.3603	2.67285
$356$	6.13028	0.324904
$357$	0	0
$358$	2.03866	0.107747
$359$	−29.3555	−1.54932	−0.774662	−	0.632375i	$-0.782080\pi$
$359$	−29.3555	−1.54932	−0.774662	+	0.632375i	$0.782080\pi$
$360$	− 3.91082i	− 0.206118i
$361$	−13.9401	−0.733688
$362$	− 28.5850i	− 1.50240i
$363$	− 10.9604i	− 0.575274i
$364$	4.80750i	0.251982i
$365$	56.5096	2.95785
$366$	27.7817	1.45217
$367$	12.4400i	0.649361i	0.945824	+	0.324680i	$0.105257\pi$
$367$	12.4400i	0.649361i	−0.945824	+	0.324680i	$0.894743\pi$
$368$	12.3205i	0.642250i
$369$	0.619914i	0.0322715i
$370$	46.6042	2.42284
$371$	− 19.9606i	− 1.03630i
$372$	−6.70231	−0.347498
$373$	18.2837	0.946696	0.473348	−	0.880875i	$-0.343045\pi$
$373$	18.2837	0.946696	0.473348	+	0.880875i	$0.343045\pi$
$374$	0	0
$375$	−11.0369	−0.569945
$376$	5.94457	0.306568
$377$	1.98133i	0.102044i
$378$	−7.10973	−0.365685
$379$	− 3.52408i	− 0.181020i	−0.995896	−	0.0905098i	$-0.971150\pi$
$379$	− 3.52408i	− 0.181020i	0.995896	−	0.0905098i	$-0.0288497\pi$
$380$	11.4940i	0.589629i
$381$	− 18.3041i	− 0.937748i
$382$	11.0324	0.564467
$383$	33.2583	1.69942	0.849709	−	0.527251i	$-0.176777\pi$
$383$	33.2583	1.69942	0.849709	+	0.527251i	$0.176777\pi$
$384$	8.28772i	0.422931i
$385$	2.76537i	0.140936i
$386$	20.4138i	1.03904i
$387$	−7.17120	−0.364533
$388$	− 8.41384i	− 0.427148i
$389$	−10.0157	−0.507818	−0.253909	−	0.967228i	$-0.581716\pi$
$389$	−10.0157	−0.507818	−0.253909	+	0.967228i	$0.581716\pi$
$390$	5.89828	0.298671
$391$	0	0
$392$	−8.44834	−0.426706
$393$	11.3478	0.572423
$394$	3.31612i	0.167064i
$395$	18.5156	0.931619
$396$	− 0.281305i	− 0.0141361i
$397$	31.4112i	1.57648i	0.615366	+	0.788242i	$0.289008\pi$
$397$	31.4112i	1.57648i	−0.615366	+	0.788242i	$0.710992\pi$
$398$	− 0.874782i	− 0.0438488i
$399$	−8.65526	−0.433305
$400$	38.8914	1.94457
$401$	0.729272i	0.0364181i	0.999834	+	0.0182091i	$0.00579644\pi$
$401$	0.729272i	0.0364181i	−0.999834	+	0.0182091i	$0.994204\pi$
$402$	− 0.519783i	− 0.0259244i
$403$	4.18703i	0.208571i
$404$	−4.92177	−0.244867
$405$	3.61313i	0.179538i
$406$	15.9446	0.791316
$407$	−1.38854	−0.0688274
$408$	0	0
$409$	25.9074	1.28104	0.640520	−	0.767941i	$-0.278719\pi$
$409$	25.9074	1.28104	0.640520	+	0.767941i	$0.278719\pi$
$410$	−4.13866	−0.204394
$411$	7.14961i	0.352664i
$412$	−14.5168	−0.715191
$413$	19.3132i	0.950339i
$414$	− 4.71485i	− 0.231722i
$415$	34.3867i	1.68798i
$416$	−5.96966	−0.292687
$417$	−10.9848	−0.537929
$418$	− 0.826760i	− 0.0404382i
$419$	− 32.8205i	− 1.60339i	−0.597735	−	0.801694i	$-0.703933\pi$
$419$	− 32.8205i	− 1.60339i	0.597735	−	0.801694i	$-0.296067\pi$
$420$	− 19.6610i	− 0.959359i
$421$	−6.36144	−0.310038	−0.155019	−	0.987912i	$-0.549544\pi$
$421$	−6.36144	−0.310038	−0.155019	+	0.987912i	$0.549544\pi$
$422$	1.90666i	0.0928146i
$423$	−5.49207	−0.267034
$424$	5.61500	0.272689
$425$	0	0
$426$	25.7544	1.24780
$427$	−57.8524	−2.79967
$428$	− 3.97364i	− 0.192073i
$429$	−0.175735	−0.00848457
$430$	− 47.8763i	− 2.30880i
$431$	9.04148i	0.435513i	0.976003	+	0.217756i	$0.0698738\pi$
$431$	9.04148i	0.435513i	−0.976003	+	0.217756i	$0.930126\pi$
$432$	− 4.82843i	− 0.232308i
$433$	−6.09106	−0.292718	−0.146359	−	0.989232i	$-0.546755\pi$
$433$	−6.09106	−0.292718	−0.146359	+	0.989232i	$0.546755\pi$
$434$	33.6948	1.61740
$435$	− 8.10294i	− 0.388506i
$436$	− 12.1261i	− 0.580736i
$437$	− 5.73977i	− 0.274571i
$438$	28.8991	1.38085
$439$	− 31.2432i	− 1.49116i	−0.666417	−	0.745579i	$-0.732173\pi$
$439$	− 31.2432i	− 1.49116i	0.666417	−	0.745579i	$-0.267827\pi$
$440$	−0.777910	−0.0370854
$441$	7.80525	0.371679
$442$	0	0
$443$	−8.90575	−0.423125	−0.211563	−	0.977364i	$-0.567855\pi$
$443$	−8.90575	−0.423125	−0.211563	+	0.977364i	$0.567855\pi$
$444$	9.87216	0.468512
$445$	15.6620i	0.742452i
$446$	−21.9916	−1.04133
$447$	− 5.99480i	− 0.283545i
$448$	10.8831i	0.514178i
$449$	− 17.3538i	− 0.818974i	−0.912316	−	0.409487i	$-0.865708\pi$
$449$	− 17.3538i	− 0.818974i	0.912316	−	0.409487i	$-0.134292\pi$
$450$	−14.8831	−0.701596
$451$	0.123309	0.00580638
$452$	− 5.43023i	− 0.255416i
$453$	− 11.4780i	− 0.539282i
$454$	− 36.8730i	− 1.73054i
$455$	−12.2825	−0.575814
$456$	− 2.43476i	− 0.114018i
$457$	−24.8622	−1.16301	−0.581503	−	0.813545i	$-0.697535\pi$
$457$	−24.8622	−1.16301	−0.581503	+	0.813545i	$0.697535\pi$
$458$	0.0487123	0.00227618
$459$	0	0
$460$	13.0383	0.607913
$461$	−11.3886	−0.530421	−0.265210	−	0.964191i	$-0.585441\pi$
$461$	−11.3886	−0.530421	−0.265210	+	0.964191i	$0.585441\pi$
$462$	1.41421i	0.0657952i
$463$	−24.9668	−1.16031	−0.580154	−	0.814507i	$-0.697008\pi$
$463$	−24.9668	−1.16031	−0.580154	+	0.814507i	$0.697008\pi$
$464$	10.8284i	0.502697i
$465$	− 17.1235i	− 0.794083i
$466$	− 41.8898i	− 1.94051i
$467$	−3.32307	−0.153773	−0.0768866	−	0.997040i	$-0.524498\pi$
$467$	−3.32307	−0.153773	−0.0768866	+	0.997040i	$0.524498\pi$
$468$	1.24943	0.0577549
$469$	1.08239i	0.0499802i
$470$	− 36.6661i	− 1.69128i
$471$	− 5.81166i	− 0.267787i
$472$	−5.43289	−0.250069
$473$	1.42644i	0.0655878i
$474$	9.46889	0.434921
$475$	−18.1184	−0.831331
$476$	0	0
$477$	−5.18759	−0.237523
$478$	−19.0698	−0.872232
$479$	− 0.309018i	− 0.0141194i	−0.999975	−	0.00705969i	$-0.997753\pi$
$479$	− 0.309018i	− 0.0141194i	0.999975	−	0.00705969i	$-0.00224719\pi$
$480$	24.4138	1.11433
$481$	− 6.16728i	− 0.281204i
$482$	− 9.15609i	− 0.417048i
$483$	9.81817i	0.446742i
$484$	15.5004	0.704563
$485$	21.4962	0.976094
$486$	1.84776i	0.0838161i
$487$	32.6476i	1.47940i	0.672935	+	0.739701i	$0.265033\pi$
$487$	32.6476i	1.47940i	−0.672935	+	0.739701i	$0.734967\pi$
$488$	− 16.2741i	− 0.736696i
$489$	−5.40878	−0.244593
$490$	52.1093i	2.35406i
$491$	−21.7074	−0.979640	−0.489820	−	0.871824i	$-0.662937\pi$
$491$	−21.7074	−0.979640	−0.489820	+	0.871824i	$0.662937\pi$
$492$	−0.876691	−0.0395243
$493$	0	0
$494$	3.67210	0.165216
$495$	0.718695	0.0323030
$496$	22.8831i	1.02748i
$497$	−53.6307	−2.40566
$498$	17.5854i	0.788021i
$499$	2.23901i	0.100232i	0.998743	+	0.0501159i	$0.0159591\pi$
$499$	2.23901i	0.100232i	−0.998743	+	0.0501159i	$0.984041\pi$
$500$	− 15.6086i	− 0.698037i
$501$	3.26038	0.145663
$502$	−51.0021	−2.27633
$503$	− 14.4320i	− 0.643489i	−0.946827	−	0.321744i	$-0.895731\pi$
$503$	− 14.4320i	− 0.643489i	0.946827	−	0.321744i	$-0.104269\pi$
$504$	4.16478i	0.185514i
$505$	− 12.5745i	− 0.559556i
$506$	−0.937842	−0.0416922
$507$	12.2195i	0.542685i
$508$	25.8859	1.14850
$509$	−35.4472	−1.57117	−0.785584	−	0.618755i	$-0.787637\pi$
$509$	−35.4472	−1.57117	−0.785584	+	0.618755i	$0.787637\pi$
$510$	0	0
$511$	−60.1793	−2.66218
$512$	−22.1731	−0.979922
$513$	2.24943i	0.0993147i
$514$	45.4991	2.00688
$515$	− 37.0884i	− 1.63431i
$516$	− 10.1416i	− 0.446459i
$517$	1.09244i	0.0480455i
$518$	−49.6307	−2.18065
$519$	16.8394	0.739167
$520$	− 3.45513i	− 0.151517i
$521$	14.2992i	0.626457i	0.949678	+	0.313229i	$0.101411\pi$
$521$	14.2992i	0.626457i	−0.949678	+	0.313229i	$0.898589\pi$
$522$	− 4.14386i	− 0.181372i
$523$	6.23946	0.272832	0.136416	−	0.990652i	$-0.456442\pi$
$523$	6.23946	0.272832	0.136416	+	0.990652i	$0.456442\pi$
$524$	16.0483i	0.701072i
$525$	30.9925	1.35262
$526$	34.9255	1.52282
$527$	0	0
$528$	−0.960434	−0.0417975
$529$	16.4890	0.716915
$530$	− 34.6333i	− 1.50437i
$531$	5.01933	0.217820
$532$	− 12.2404i	− 0.530688i
$533$	0.547682i	0.0237227i
$534$	8.00960i	0.346609i
$535$	10.1521	0.438914
$536$	−0.304482	−0.0131516
$537$	1.10332i	0.0476116i
$538$	26.2480i	1.13163i
$539$	− 1.55256i	− 0.0668735i
$540$	−5.10973	−0.219888
$541$	24.0286i	1.03307i	0.856267	+	0.516534i	$0.172778\pi$
$541$	24.0286i	1.03307i	−0.856267	+	0.516534i	$0.827222\pi$
$542$	36.8284	1.58191
$543$	15.4701	0.663886
$544$	0	0
$545$	30.9806	1.32706
$546$	−6.28130	−0.268815
$547$	31.6304i	1.35242i	0.736710	+	0.676209i	$0.236378\pi$
$547$	31.6304i	1.35242i	−0.736710	+	0.676209i	$0.763622\pi$
$548$	−10.1111	−0.431924
$549$	15.0353i	0.641693i
$550$	2.96043i	0.126233i
$551$	− 5.04466i	− 0.214910i
$552$	−2.76190	−0.117554
$553$	−19.7179	−0.838492
$554$	− 39.5474i	− 1.68021i
$555$	25.2220i	1.07062i
$556$	− 15.5349i	− 0.658826i
$557$	−14.7772	−0.626131	−0.313065	−	0.949732i	$-0.601356\pi$
$557$	−14.7772	−0.626131	−0.313065	+	0.949732i	$0.601356\pi$
$558$	− 8.75699i	− 0.370713i
$559$	−6.33561	−0.267968
$560$	−67.1269	−2.83663
$561$	0	0
$562$	39.6657	1.67320
$563$	9.39006	0.395744	0.197872	−	0.980228i	$-0.436597\pi$
$563$	9.39006	0.395744	0.197872	+	0.980228i	$0.436597\pi$
$564$	− 7.76696i	− 0.327048i
$565$	13.8735	0.583663
$566$	36.6269i	1.53954i
$567$	− 3.84776i	− 0.161591i
$568$	− 15.0866i	− 0.633018i
$569$	23.3520	0.978968	0.489484	−	0.872012i	$-0.337185\pi$
$569$	23.3520	0.978968	0.489484	+	0.872012i	$0.337185\pi$
$570$	−15.0176	−0.629018
$571$	− 33.2405i	− 1.39107i	−0.718491	−	0.695537i	$-0.755167\pi$
$571$	− 33.2405i	− 1.39107i	0.718491	−	0.695537i	$-0.244833\pi$
$572$	− 0.248527i	− 0.0103914i
$573$	5.97069i	0.249429i
$574$	4.40743	0.183962
$575$	20.5528i	0.857111i
$576$	2.82843	0.117851
$577$	33.8072	1.40741	0.703705	−	0.710492i	$-0.251528\pi$
$577$	33.8072	1.40741	0.703705	+	0.710492i	$0.251528\pi$
$578$	0	0
$579$	−11.0479	−0.459135
$580$	11.4593	0.475821
$581$	− 36.6197i	− 1.51924i
$582$	10.9932	0.455683
$583$	1.03188i	0.0427359i
$584$	− 16.9287i	− 0.700515i
$585$	3.19212i	0.131978i
$586$	−37.6420	−1.55498
$587$	−29.2440	−1.20703	−0.603514	−	0.797352i	$-0.706233\pi$
$587$	−29.2440	−1.20703	−0.603514	+	0.797352i	$0.706233\pi$
$588$	11.0383i	0.455211i
$589$	− 10.6606i	− 0.439262i
$590$	33.5100i	1.37958i
$591$	−1.79467	−0.0738230
$592$	− 33.7056i	− 1.38529i
$593$	−0.632327	−0.0259665	−0.0129833	−	0.999916i	$-0.504133\pi$
$593$	−0.632327	−0.0259665	−0.0129833	+	0.999916i	$0.504133\pi$
$594$	0.367542	0.0150804
$595$	0	0
$596$	8.47793	0.347270
$597$	0.473428	0.0193761
$598$	− 4.16547i	− 0.170339i
$599$	8.12959	0.332166	0.166083	−	0.986112i	$-0.446888\pi$
$599$	8.12959	0.332166	0.166083	+	0.986112i	$0.446888\pi$
$600$	8.71832i	0.355924i
$601$	4.43330i	0.180838i	0.995904	+	0.0904191i	$0.0288207\pi$
$601$	4.43330i	0.180838i	−0.995904	+	0.0904191i	$0.971179\pi$
$602$	50.9853i	2.07801i
$603$	0.281305	0.0114556
$604$	16.2323	0.660483
$605$	39.6014i	1.61003i
$606$	− 6.43060i	− 0.261225i
$607$	24.1283i	0.979336i	0.871909	+	0.489668i	$0.162882\pi$
$607$	24.1283i	0.979336i	−0.871909	+	0.489668i	$0.837118\pi$
$608$	15.1994	0.616415
$609$	8.62914i	0.349670i
$610$	−100.379	−4.06422
$611$	−4.85213	−0.196296
$612$	0	0
$613$	−0.549449	−0.0221921	−0.0110960	−	0.999938i	$-0.503532\pi$
$613$	−0.549449	−0.0221921	−0.0110960	+	0.999938i	$0.503532\pi$
$614$	25.1809	1.01622
$615$	− 2.23983i	− 0.0903186i
$616$	0.828427	0.0333783
$617$	− 0.0360068i	− 0.00144958i	−1.00000		0.000724790i	$-0.999769\pi$
$617$	− 0.0360068i	− 0.00144958i	1.00000		0.000724790i	$-0.000230708\pi$
$618$	− 18.9671i	− 0.762968i
$619$	− 11.2011i	− 0.450211i	−0.974334	−	0.225105i	$-0.927727\pi$
$619$	− 11.2011i	− 0.450211i	0.974334	−	0.225105i	$-0.0722726\pi$
$620$	24.2163	0.972549
$621$	2.55166	0.102395
$622$	4.77791i	0.191577i
$623$	− 16.6791i	− 0.668235i
$624$	− 4.26582i	− 0.170769i
$625$	−0.395541	−0.0158217
$626$	− 7.30538i	− 0.291982i
$627$	0.447439	0.0178690
$628$	8.21893	0.327971
$629$	0	0
$630$	25.6884	1.02345
$631$	−9.12882	−0.363413	−0.181706	−	0.983353i	$-0.558162\pi$
$631$	−9.12882	−0.363413	−0.181706	+	0.983353i	$0.558162\pi$
$632$	− 5.54675i	− 0.220638i
$633$	−1.03188	−0.0410134
$634$	61.9267i	2.45942i
$635$	66.1350i	2.62449i
$636$	− 7.33636i	− 0.290905i
$637$	6.89578	0.273221
$638$	−0.824265	−0.0326330
$639$	13.9382i	0.551385i
$640$	− 29.9446i	− 1.18366i
$641$	34.7176i	1.37126i	0.727949	+	0.685631i	$0.240474\pi$
$641$	34.7176i	1.37126i	−0.727949	+	0.685631i	$0.759526\pi$
$642$	5.19181	0.204904
$643$	− 14.6027i	− 0.575876i	−0.957649	−	0.287938i	$-0.907030\pi$
$643$	− 14.6027i	− 0.575876i	0.957649	−	0.287938i	$-0.0929696\pi$
$644$	−13.8850	−0.547145
$645$	25.9104	1.02022
$646$	0	0
$647$	39.5994	1.55681	0.778407	−	0.627760i	$-0.216028\pi$
$647$	39.5994	1.55681	0.778407	+	0.627760i	$0.216028\pi$
$648$	1.08239	0.0425204
$649$	− 0.998407i	− 0.0391909i
$650$	−13.1489	−0.515743
$651$	18.2355i	0.714705i
$652$	− 7.64916i	− 0.299564i
$653$	− 39.7823i	− 1.55680i	−0.627769	−	0.778400i	$-0.716032\pi$
$653$	− 39.7823i	− 1.55680i	0.627769	−	0.778400i	$-0.283968\pi$
$654$	15.8435	0.619531
$655$	−41.0012	−1.60205
$656$	2.99321i	0.116865i
$657$	15.6401i	0.610178i
$658$	39.0471i	1.52222i
$659$	−16.4351	−0.640219	−0.320109	−	0.947381i	$-0.603720\pi$
$659$	−16.4351	−0.640219	−0.320109	+	0.947381i	$0.603720\pi$
$660$	1.01639i	0.0395629i
$661$	34.4462	1.33980	0.669902	−	0.742450i	$-0.266336\pi$
$661$	34.4462	1.33980	0.669902	+	0.742450i	$0.266336\pi$
$662$	35.6687	1.38630
$663$	0	0
$664$	10.3013	0.399768
$665$	31.2725	1.21270
$666$	12.8986i	0.499810i
$667$	−5.72245	−0.221574
$668$	4.61087i	0.178400i
$669$	− 11.9018i	− 0.460149i
$670$	1.87804i	0.0725551i
$671$	2.99072	0.115455
$672$	−25.9993	−1.00294
$673$	− 33.7812i	− 1.30217i	−0.759006	−	0.651084i	$-0.774314\pi$
$673$	− 33.7812i	− 1.30217i	0.759006	−	0.651084i	$-0.225686\pi$
$674$	− 32.1736i	− 1.23928i
$675$	− 8.05468i	− 0.310025i
$676$	−17.2809	−0.664651
$677$	13.3292i	0.512281i	0.966640	+	0.256141i	$0.0824510\pi$
$677$	13.3292i	0.512281i	−0.966640	+	0.256141i	$0.917549\pi$
$678$	7.09494	0.272479
$679$	−22.8922	−0.878521
$680$	0	0
$681$	19.9555	0.764697
$682$	−1.74187	−0.0666998
$683$	25.7636i	0.985816i	0.870081	+	0.492908i	$0.164066\pi$
$683$	25.7636i	0.985816i	−0.870081	+	0.492908i	$0.835934\pi$
$684$	−3.18117	−0.121635
$685$	− 25.8325i	− 0.987007i
$686$	− 5.72511i	− 0.218586i
$687$	0.0263629i	0.00100581i
$688$	−34.6256	−1.32009
$689$	−4.58313	−0.174603
$690$	17.0353i	0.648525i
$691$	6.11745i	0.232719i	0.993207	+	0.116359i	$0.0371225\pi$
$691$	6.11745i	0.232719i	−0.993207	+	0.116359i	$0.962878\pi$
$692$	23.8145i	0.905291i
$693$	−0.765367	−0.0290739
$694$	− 57.4819i	− 2.18198i
$695$	39.6896	1.50551
$696$	−2.42742	−0.0920110
$697$	0	0
$698$	−55.5080	−2.10101
$699$	22.6706	0.857481
$700$	43.8300i	1.65662i
$701$	18.4012	0.695005	0.347503	−	0.937679i	$-0.387030\pi$
$701$	18.4012	0.695005	0.347503	+	0.937679i	$0.387030\pi$
$702$	1.63246i	0.0616132i
$703$	15.7025i	0.592232i
$704$	− 0.562609i	− 0.0212041i
$705$	19.8435	0.747351
$706$	31.9382	1.20201
$707$	13.3910i	0.503622i
$708$	7.09841i	0.266774i
$709$	14.2577i	0.535460i	0.963494	+	0.267730i	$0.0862735\pi$
$709$	14.2577i	0.535460i	−0.963494	+	0.267730i	$0.913726\pi$
$710$	−93.0537	−3.49224
$711$	5.12453i	0.192185i
$712$	4.69192	0.175837
$713$	−12.0929	−0.452884
$714$	0	0
$715$	0.634953	0.0237459
$716$	−1.56033	−0.0583121
$717$	− 10.3205i	− 0.385426i
$718$	54.2419	2.02429
$719$	30.4760i	1.13656i	0.822834	+	0.568282i	$0.192392\pi$
$719$	30.4760i	1.13656i	−0.822834	+	0.568282i	$0.807608\pi$
$720$	17.4457i	0.650163i
$721$	39.4969i	1.47094i
$722$	25.7579	0.958609
$723$	4.95524	0.184287
$724$	21.8780i	0.813091i
$725$	18.0638i	0.670871i
$726$	20.2522i	0.751631i
$727$	46.6448	1.72996	0.864980	−	0.501806i	$-0.167331\pi$
$727$	46.6448	1.72996	0.864980	+	0.501806i	$0.167331\pi$
$728$	3.67950i	0.136371i
$729$	−1.00000	−0.0370370
$730$	−104.416	−3.86462
$731$	0	0
$732$	−21.2632	−0.785910
$733$	40.8084	1.50729	0.753647	−	0.657279i	$-0.228293\pi$
$733$	40.8084	1.50729	0.753647	+	0.657279i	$0.228293\pi$
$734$	− 22.9860i	− 0.848431i
$735$	−28.2014	−1.04022
$736$	− 17.2415i	− 0.635531i
$737$	− 0.0559550i	− 0.00206113i
$738$	− 1.14545i	− 0.0421647i
$739$	−37.9474	−1.39592	−0.697959	−	0.716138i	$-0.745908\pi$
$739$	−37.9474	−1.39592	−0.697959	+	0.716138i	$0.745908\pi$
$740$	−35.6693	−1.31123
$741$	1.98733i	0.0730062i
$742$	36.8824i	1.35399i
$743$	− 1.86619i	− 0.0684638i	−0.999414	−	0.0342319i	$-0.989102\pi$
$743$	− 1.86619i	− 0.0684638i	0.999414	−	0.0342319i	$-0.0108985\pi$
$744$	−5.12972	−0.188065
$745$	21.6600i	0.793560i
$746$	−33.7840	−1.23692
$747$	−9.51716	−0.348215
$748$	0	0
$749$	−10.8114	−0.395039
$750$	20.3936	0.744669
$751$	− 39.1778i	− 1.42962i	−0.699319	−	0.714810i	$-0.746513\pi$
$751$	− 39.1778i	− 1.42962i	0.699319	−	0.714810i	$-0.253487\pi$
$752$	−26.5181	−0.967014
$753$	− 27.6021i	− 1.00588i
$754$	− 3.66102i	− 0.133326i
$755$	41.4713i	1.50930i
$756$	5.44155	0.197907
$757$	−24.3356	−0.884493	−0.442246	−	0.896894i	$-0.645818\pi$
$757$	−24.3356	−0.884493	−0.442246	+	0.896894i	$0.645818\pi$
$758$	6.51164i	0.236514i
$759$	− 0.507556i	− 0.0184231i
$760$	8.79711i	0.319105i
$761$	−25.3506	−0.918957	−0.459479	−	0.888189i	$-0.651964\pi$
$761$	−25.3506	−0.918957	−0.459479	+	0.888189i	$0.651964\pi$
$762$	33.8216i	1.22523i
$763$	−32.9925	−1.19441
$764$	−8.44384	−0.305487
$765$	0	0
$766$	−61.4533	−2.22040
$767$	4.43448	0.160120
$768$	− 20.9706i	− 0.756710i
$769$	10.7211	0.386614	0.193307	−	0.981138i	$-0.438079\pi$
$769$	10.7211	0.386614	0.193307	+	0.981138i	$0.438079\pi$
$770$	− 5.10973i	− 0.184142i
$771$	24.6239i	0.886810i
$772$	− 15.6241i	− 0.562323i
$773$	51.2753	1.84424	0.922122	−	0.386900i	$-0.126454\pi$
$773$	51.2753	1.84424	0.922122	+	0.386900i	$0.126454\pi$
$774$	13.2506	0.476285
$775$	38.1731i	1.37122i
$776$	− 6.43967i	− 0.231171i
$777$	− 26.8599i	− 0.963595i
$778$	18.5067	0.663496
$779$	− 1.39445i	− 0.0499615i
$780$	−4.51434	−0.161639
$781$	2.77247	0.0992069
$782$	0	0
$783$	2.24264	0.0801454
$784$	37.6871	1.34597
$785$	20.9983i	0.749461i
$786$	−20.9681	−0.747906
$787$	− 22.2791i	− 0.794162i	−0.917783	−	0.397081i	$-0.870023\pi$
$787$	− 22.2791i	− 0.794162i	0.917783	−	0.397081i	$-0.129977\pi$
$788$	− 2.53805i	− 0.0904143i
$789$	18.9015i	0.672912i
$790$	−34.2123	−1.21722
$791$	−14.7744	−0.525319
$792$	− 0.215301i	− 0.00765039i
$793$	13.2834i	0.471708i
$794$	− 58.0404i	− 2.05978i
$795$	18.7434	0.664760
$796$	0.669529i	0.0237308i
$797$	12.5375	0.444102	0.222051	−	0.975035i	$-0.428725\pi$
$797$	12.5375	0.444102	0.222051	+	0.975035i	$0.428725\pi$
$798$	15.9928	0.566140
$799$	0	0
$800$	−54.4253	−1.92423
$801$	−4.33476	−0.153161
$802$	− 1.34752i	− 0.0475826i
$803$	3.11101	0.109785
$804$	0.397825i	0.0140302i
$805$	− 35.4743i	− 1.25030i
$806$	− 7.73662i	− 0.272511i
$807$	−14.2053	−0.500051
$808$	−3.76696	−0.132521
$809$	9.29316i	0.326730i	0.986566	+	0.163365i	$0.0522348\pi$
$809$	9.29316i	0.326730i	−0.986566	+	0.163365i	$0.947765\pi$
$810$	− 6.67619i	− 0.234577i
$811$	− 11.2858i	− 0.396299i	−0.980172	−	0.198150i	$-0.936507\pi$
$811$	− 11.2858i	− 0.396299i	0.980172	−	0.198150i	$-0.0634932\pi$
$812$	−12.2034	−0.428257
$813$	19.9314i	0.699024i
$814$	2.56569	0.0899274
$815$	19.5426	0.684547
$816$	0	0
$817$	16.1311	0.564356
$818$	−47.8707	−1.67376
$819$	− 3.39942i	− 0.118785i
$820$	3.16760	0.110617
$821$	8.30636i	0.289894i	0.989439	+	0.144947i	$0.0463012\pi$
$821$	8.30636i	0.289894i	−0.989439	+	0.144947i	$0.953699\pi$
$822$	− 13.2108i	− 0.460778i
$823$	− 18.6249i	− 0.649224i	−0.945847	−	0.324612i	$-0.894766\pi$
$823$	− 18.6249i	− 0.649224i	0.945847	−	0.324612i	$-0.105234\pi$
$824$	−11.1107	−0.387058
$825$	−1.60218	−0.0557806
$826$	− 35.6861i	− 1.24168i
$827$	27.8659i	0.968992i	0.874793	+	0.484496i	$0.160997\pi$
$827$	27.8659i	0.968992i	−0.874793	+	0.484496i	$0.839003\pi$
$828$	3.60859i	0.125407i
$829$	12.4653	0.432937	0.216469	−	0.976290i	$-0.430546\pi$
$829$	12.4653	0.432937	0.216469	+	0.976290i	$0.430546\pi$
$830$	− 63.5383i	− 2.20545i
$831$	21.4029	0.742458
$832$	2.49886	0.0866323
$833$	0	0
$834$	20.2973	0.702839
$835$	−11.7802	−0.407669
$836$	0.632775i	0.0218850i
$837$	4.73925	0.163812
$838$	60.6444i	2.09493i
$839$	43.2106i	1.49179i	0.666061	+	0.745897i	$0.267979\pi$
$839$	43.2106i	1.49179i	−0.666061	+	0.745897i	$0.732021\pi$
$840$	− 15.0479i	− 0.519202i
$841$	23.9706	0.826571
$842$	11.7544	0.405084
$843$	21.4669i	0.739360i
$844$	− 1.45929i	− 0.0502309i
$845$	− 44.1505i	− 1.51882i
$846$	10.1480	0.348896
$847$	− 42.1731i	− 1.44909i
$848$	−25.0479	−0.860148
$849$	−19.8223	−0.680301
$850$	0	0
$851$	17.8123	0.610597
$852$	−19.7115	−0.675306
$853$	9.75164i	0.333890i	0.985966	+	0.166945i	$0.0533902\pi$
$853$	9.75164i	0.333890i	−0.985966	+	0.166945i	$0.946610\pi$
$854$	106.897	3.65795
$855$	− 8.12747i	− 0.277954i
$856$	− 3.04129i	− 0.103949i
$857$	− 23.9998i	− 0.819817i	−0.912127	−	0.409908i	$-0.865561\pi$
$857$	− 23.9998i	− 0.819817i	0.912127	−	0.409908i	$-0.134439\pi$
$858$	0.324716	0.0110856
$859$	16.5708	0.565389	0.282695	−	0.959210i	$-0.408772\pi$
$859$	16.5708	0.565389	0.282695	+	0.959210i	$0.408772\pi$
$860$	36.6429i	1.24951i
$861$	2.38528i	0.0812902i
$862$	− 16.7065i	− 0.569025i
$863$	56.5312	1.92435	0.962173	−	0.272440i	$-0.0878306\pi$
$863$	56.5312	1.92435	0.962173	+	0.272440i	$0.0878306\pi$
$864$	6.75699i	0.229877i
$865$	−60.8428	−2.06872
$866$	11.2548	0.382454
$867$	0	0
$868$	−25.7889	−0.875331
$869$	1.01933	0.0345785
$870$	14.9723i	0.507608i
$871$	0.248527	0.00842101
$872$	− 9.28093i	− 0.314292i
$873$	5.94948i	0.201359i
$874$	10.6057i	0.358744i
$875$	−42.4675	−1.43566
$876$	−22.1184	−0.747312
$877$	40.1731i	1.35655i	0.734808	+	0.678275i	$0.237272\pi$
$877$	40.1731i	1.35655i	−0.734808	+	0.678275i	$0.762728\pi$
$878$	57.7300i	1.94829i
$879$	− 20.3717i	− 0.687121i
$880$	3.47017	0.116979
$881$	− 11.1607i	− 0.376013i	−0.982168	−	0.188007i	$-0.939797\pi$
$881$	− 11.1607i	− 0.376013i	0.982168	−	0.188007i	$-0.0602027\pi$
$882$	−14.4222	−0.485621
$883$	39.5682	1.33158	0.665789	−	0.746140i	$-0.268095\pi$
$883$	39.5682	1.33158	0.665789	+	0.746140i	$0.268095\pi$
$884$	0	0
$885$	−18.1355	−0.609617
$886$	16.4557	0.552840
$887$	− 42.3289i	− 1.42126i	−0.703564	−	0.710632i	$-0.748409\pi$
$887$	− 42.3289i	− 1.42126i	0.703564	−	0.710632i	$-0.251591\pi$
$888$	7.55582	0.253557
$889$	− 70.4298i	− 2.36214i
$890$	− 28.9397i	− 0.970061i
$891$	0.198912i	0.00666382i
$892$	16.8317	0.563566
$893$	12.3540	0.413412
$894$	11.0770i	0.370469i
$895$	− 3.98642i	− 0.133251i
$896$	31.8891i	1.06534i
$897$	2.25434	0.0752702
$898$	32.0656i	1.07004i
$899$	−10.6284	−0.354478
$900$	11.3910	0.379701
$901$	0	0
$902$	−0.227845	−0.00758640
$903$	−27.5930	−0.918239
$904$	− 4.15612i	− 0.138230i
$905$	−55.8955	−1.85803
$906$	21.2085i	0.704606i
$907$	20.4637i	0.679487i	0.940518	+	0.339743i	$0.110340\pi$
$907$	20.4637i	0.679487i	−0.940518	+	0.339743i	$0.889660\pi$
$908$	28.2214i	0.936559i
$909$	3.48022	0.115432
$910$	22.6951	0.752337
$911$	2.27804i	0.0754750i	0.999288	+	0.0377375i	$0.0120151\pi$
$911$	2.27804i	0.0754750i	−0.999288	+	0.0377375i	$0.987985\pi$
$912$	10.8612i	0.359650i
$913$	1.89308i	0.0626518i
$914$	45.9394	1.51954
$915$	− 54.3246i	− 1.79592i
$916$	−0.0372828	−0.00123186
$917$	43.6637	1.44190
$918$	0	0
$919$	36.0659	1.18970	0.594851	−	0.803836i	$-0.297211\pi$
$919$	36.0659	1.18970	0.594851	+	0.803836i	$0.297211\pi$
$920$	9.97908	0.329000
$921$	13.6278i	0.449051i
$922$	21.0434	0.693028
$923$	12.3141i	0.405323i
$924$	− 1.08239i	− 0.0356081i
$925$	− 56.2270i	− 1.84873i
$926$	46.1327	1.51602
$927$	10.2649	0.337144
$928$	− 15.1535i	− 0.497438i
$929$	55.4122i	1.81802i	0.416779	+	0.909008i	$0.363159\pi$
$929$	55.4122i	1.81802i	−0.416779	+	0.909008i	$0.636841\pi$
$930$	31.6401i	1.03752i
$931$	−17.5574	−0.575419
$932$	32.0611i	1.05020i
$933$	−2.58579	−0.0846548
$934$	6.14023	0.200914
$935$	0	0
$936$	0.956272	0.0312567
$937$	−40.8695	−1.33515	−0.667575	−	0.744543i	$-0.732668\pi$
$937$	−40.8695	−1.33515	−0.667575	+	0.744543i	$0.732668\pi$
$938$	− 2.00000i	− 0.0653023i
$939$	3.95365	0.129022
$940$	28.0630i	0.915314i
$941$	15.3536i	0.500515i	0.968179	+	0.250257i	$0.0805152\pi$
$941$	15.3536i	0.500515i	−0.968179	+	0.250257i	$0.919485\pi$
$942$	10.7386i	0.349881i
$943$	−1.58181	−0.0515108
$944$	24.2355	0.788798
$945$	13.9024i	0.452246i
$946$	− 2.63572i	− 0.0856946i
$947$	40.8888i	1.32871i	0.747419	+	0.664353i	$0.231293\pi$
$947$	40.8888i	1.32871i	−0.747419	+	0.664353i	$0.768707\pi$
$948$	−7.24718	−0.235377
$949$	13.8177i	0.448542i
$950$	33.4785	1.08619
$951$	−33.5145	−1.08678
$952$	0	0
$953$	−25.5007	−0.826050	−0.413025	−	0.910720i	$-0.635528\pi$
$953$	−25.5007	−0.826050	−0.413025	+	0.910720i	$0.635528\pi$
$954$	9.58541	0.310339
$955$	− 21.5729i	− 0.698082i
$956$	14.5954	0.472049
$957$	− 0.446089i	− 0.0144200i
$958$	0.570990i	0.0184479i
$959$	27.5100i	0.888344i
$960$	−10.2195	−0.329832
$961$	8.53954	0.275469
$962$	11.3956i	0.367410i
$963$	2.80979i	0.0905441i
$964$	7.00777i	0.225705i
$965$	39.9174	1.28499
$966$	− 18.1416i	− 0.583697i
$967$	−12.0223	−0.386610	−0.193305	−	0.981139i	$-0.561921\pi$
$967$	−12.0223	−0.386610	−0.193305	+	0.981139i	$0.561921\pi$
$968$	11.8635	0.381307
$969$	0	0
$970$	−39.7199	−1.27533
$971$	−48.0362	−1.54155	−0.770777	−	0.637105i	$-0.780132\pi$
$971$	−48.0362	−1.54155	−0.770777	+	0.637105i	$0.780132\pi$
$972$	− 1.41421i	− 0.0453609i
$973$	−42.2670	−1.35502
$974$	− 60.3248i	− 1.93293i
$975$	− 7.11615i	− 0.227899i
$976$	72.5971i	2.32378i
$977$	−29.7041	−0.950319	−0.475160	−	0.879900i	$-0.657610\pi$
$977$	−29.7041	−0.950319	−0.475160	+	0.879900i	$0.657610\pi$
$978$	9.99411	0.319577
$979$	0.862238i	0.0275573i
$980$	− 39.8827i	− 1.27401i
$981$	8.57446i	0.273762i
$982$	40.1100	1.27996
$983$	− 3.92774i	− 0.125275i	−0.998036	−	0.0626377i	$-0.980049\pi$
$983$	− 3.92774i	− 0.125275i	0.998036	−	0.0626377i	$-0.0199513\pi$
$984$	−0.670991	−0.0213904
$985$	6.48438	0.206609
$986$	0	0
$987$	−21.1322	−0.672644
$988$	−2.81050	−0.0894140
$989$	− 18.2985i	− 0.581857i
$990$	−1.32798	−0.0422058
$991$	− 9.02869i	− 0.286806i	−0.989664	−	0.143403i	$-0.954196\pi$
$991$	− 9.02869i	− 0.286806i	0.989664	−	0.143403i	$-0.0458045\pi$
$992$	− 32.0230i	− 1.01673i
$993$	19.3037i	0.612585i
$994$	99.0966	3.14315
$995$	−1.71056	−0.0542283
$996$	− 13.4593i	− 0.426474i
$997$	− 36.7176i	− 1.16286i	−0.813597	−	0.581430i	$-0.802494\pi$
$997$	− 36.7176i	− 1.16286i	0.813597	−	0.581430i	$-0.197506\pi$
$998$	− 4.13715i	− 0.130959i
$999$	−6.98067	−0.220859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.d.e.577.1		8
17.2	even	8		867.2.e.h.829.1		8
17.3	odd	16		867.2.h.b.688.1		8
17.4	even	4		867.2.a.m.1.4		4
17.5	odd	16		867.2.h.g.757.2		8
17.6	odd	16		867.2.h.f.712.1		8
17.7	odd	16		51.2.h.a.19.2	✓	8
17.8	even	8		867.2.e.h.616.4		8
17.9	even	8		867.2.e.i.616.4		8
17.10	odd	16		867.2.h.g.733.2		8
17.11	odd	16		867.2.h.b.712.1		8
17.12	odd	16		51.2.h.a.43.2	yes	8
17.13	even	4		867.2.a.n.1.4		4
17.14	odd	16		867.2.h.f.688.1		8
17.15	even	8		867.2.e.i.829.1		8
17.16	even	2	inner	867.2.d.e.577.2		8
51.29	even	16		153.2.l.e.145.1		8
51.38	odd	4		2601.2.a.bc.1.1		4
51.41	even	16		153.2.l.e.19.1		8
51.47	odd	4		2601.2.a.bd.1.1		4
68.7	even	16		816.2.bq.a.529.2		8
68.63	even	16		816.2.bq.a.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.2	✓	8	17.7	odd	16
51.2.h.a.43.2	yes	8	17.12	odd	16
153.2.l.e.19.1		8	51.41	even	16
153.2.l.e.145.1		8	51.29	even	16
816.2.bq.a.145.2		8	68.63	even	16
816.2.bq.a.529.2		8	68.7	even	16
867.2.a.m.1.4		4	17.4	even	4
867.2.a.n.1.4		4	17.13	even	4
867.2.d.e.577.1		8	1.1	even	1	trivial
867.2.d.e.577.2		8	17.16	even	2	inner
867.2.e.h.616.4		8	17.8	even	8
867.2.e.h.829.1		8	17.2	even	8
867.2.e.i.616.4		8	17.9	even	8
867.2.e.i.829.1		8	17.15	even	8
867.2.h.b.688.1		8	17.3	odd	16
867.2.h.b.712.1		8	17.11	odd	16
867.2.h.f.688.1		8	17.14	odd	16
867.2.h.f.712.1		8	17.6	odd	16
867.2.h.g.733.2		8	17.10	odd	16
867.2.h.g.757.2		8	17.5	odd	16
2601.2.a.bc.1.1		4	51.38	odd	4
2601.2.a.bd.1.1		4	51.47	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.84776 q^{2} -1.00000i q^{3} +1.41421 q^{4} +3.61313i q^{5} +1.84776i q^{6} -3.84776i q^{7} +1.08239 q^{8} -1.00000 q^{9} -6.67619i q^{10} +0.198912i q^{11} -1.41421i q^{12} -0.883480 q^{13} +7.10973i q^{14} +3.61313 q^{15} -4.82843 q^{16} +1.84776 q^{18} +2.24943 q^{19} +5.10973i q^{20} -3.84776 q^{21} -0.367542i q^{22} -2.55166i q^{23} -1.08239i q^{24} -8.05468 q^{25} +1.63246 q^{26} +1.00000i q^{27} -5.44155i q^{28} -2.24264i q^{29} -6.67619 q^{30} -4.73925i q^{31} +6.75699 q^{32} +0.198912 q^{33} +13.9024 q^{35} -1.41421 q^{36} +6.98067i q^{37} -4.15640 q^{38} +0.883480i q^{39} +3.91082i q^{40} -0.619914i q^{41} +7.10973 q^{42} +7.17120 q^{43} +0.281305i q^{44} -3.61313i q^{45} +4.71485i q^{46} +5.49207 q^{47} +4.82843i q^{48} -7.80525 q^{49} +14.8831 q^{50} -1.24943 q^{52} +5.18759 q^{53} -1.84776i q^{54} -0.718695 q^{55} -4.16478i q^{56} -2.24943i q^{57} +4.14386i q^{58} -5.01933 q^{59} +5.10973 q^{60} -15.0353i q^{61} +8.75699i q^{62} +3.84776i q^{63} -2.82843 q^{64} -3.19212i q^{65} -0.367542 q^{66} -0.281305 q^{67} -2.55166 q^{69} -25.6884 q^{70} -13.9382i q^{71} -1.08239 q^{72} -15.6401i q^{73} -12.8986i q^{74} +8.05468i q^{75} +3.18117 q^{76} +0.765367 q^{77} -1.63246i q^{78} -5.12453i q^{79} -17.4457i q^{80} +1.00000 q^{81} +1.14545i q^{82} +9.51716 q^{83} -5.44155 q^{84} -13.2506 q^{86} -2.24264 q^{87} +0.215301i q^{88} +4.33476 q^{89} +6.67619i q^{90} +3.39942i q^{91} -3.60859i q^{92} -4.73925 q^{93} -10.1480 q^{94} +8.12747i q^{95} -6.75699i q^{96} -5.94948i q^{97} +14.4222 q^{98} -0.198912i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9} - 8 q^{13} + 8 q^{15} - 16 q^{16} + 24 q^{19} - 16 q^{21} - 16 q^{30} - 8 q^{33} + 32 q^{35} + 32 q^{38} + 16 q^{42} - 8 q^{43} + 16 q^{47} + 8 q^{49} + 32 q^{50} - 16 q^{52} - 16 q^{53} - 24 q^{55}+ \cdots + 64 q^{98}+O(q^{100}) \) 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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