LMFDB - Embedded newform 867.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(1,867)]

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, 0]))

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

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

chi := DirichletCharacter("867.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.a (trivial)

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:	yes
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{16})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 2 $ x^4 - 4*x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.84776$ of defining polynomial
Character	$\chi$	$=$	867.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.84776 q^{2} -1.00000 q^{3} +1.41421 q^{4} -1.61313 q^{5} +1.84776 q^{6} +0.152241 q^{7} +1.08239 q^{8} +1.00000 q^{9} +2.98067 q^{10} +5.02734 q^{11} -1.41421 q^{12} -3.94495 q^{13} -0.281305 q^{14} +1.61313 q^{15} -4.82843 q^{16} -1.84776 q^{18} -6.57900 q^{19} -2.28130 q^{20} -0.152241 q^{21} -9.28931 q^{22} +3.44834 q^{23} -1.08239 q^{24} -2.39782 q^{25} +7.28931 q^{26} -1.00000 q^{27} +0.215301 q^{28} -2.24264 q^{29} -2.98067 q^{30} -2.57446 q^{31} +6.75699 q^{32} -5.02734 q^{33} -0.245584 q^{35} +1.41421 q^{36} +10.6762 q^{37} +12.1564 q^{38} +3.94495 q^{39} -1.74603 q^{40} -0.276769 q^{41} +0.281305 q^{42} +6.34277 q^{43} +7.10973 q^{44} -1.61313 q^{45} -6.37170 q^{46} +9.82164 q^{47} +4.82843 q^{48} -6.97682 q^{49} +4.43060 q^{50} -5.57900 q^{52} -2.12612 q^{53} +1.84776 q^{54} -8.10973 q^{55} +0.164784 q^{56} +6.57900 q^{57} +4.14386 q^{58} +1.32381 q^{59} +2.28130 q^{60} +8.27836 q^{61} +4.75699 q^{62} +0.152241 q^{63} -2.82843 q^{64} +6.36370 q^{65} +9.28931 q^{66} +7.10973 q^{67} -3.44834 q^{69} +0.453780 q^{70} -6.54712 q^{71} +1.08239 q^{72} +8.32638 q^{73} -19.7270 q^{74} +2.39782 q^{75} -9.30411 q^{76} +0.765367 q^{77} -7.28931 q^{78} +0.532327 q^{79} +7.78886 q^{80} +1.00000 q^{81} +0.511402 q^{82} +2.20345 q^{83} -0.215301 q^{84} -11.7199 q^{86} +2.24264 q^{87} +5.44155 q^{88} -7.64847 q^{89} +2.98067 q^{90} -0.600582 q^{91} +4.87669 q^{92} +2.57446 q^{93} -18.1480 q^{94} +10.6128 q^{95} -6.75699 q^{96} +3.60634 q^{97} +12.8915 q^{98} +5.02734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{5} + 8 q^{7} + 4 q^{9} + 8 q^{10} + 4 q^{11} - 4 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 12 q^{23} - 4 q^{27} + 8 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{33}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^5 + 8 * q^7 + 4 * q^9 + 8 * q^10 + 4 * q^11 - 4 * q^13 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 12 * q^23 - 4 * q^27 + 8 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^33 + 16 * q^35 + 24 * q^37 + 16 * q^38 + 4 * q^39 + 12 * q^41 - 8 * q^42 + 4 * q^43 + 8 * q^44 + 4 * q^45 + 8 * q^46 + 8 * q^47 + 8 * q^48 - 4 * q^49 + 16 * q^50 - 8 * q^52 + 8 * q^53 - 12 * q^55 - 8 * q^56 + 12 * q^57 + 24 * q^59 + 24 * q^61 - 8 * q^62 + 8 * q^63 + 12 * q^65 + 8 * q^66 + 8 * q^67 - 12 * q^69 + 24 * q^70 - 24 * q^71 + 8 * q^73 - 8 * q^74 - 8 * q^76 - 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 - 16 * q^86 - 8 * q^87 + 16 * q^89 + 8 * q^90 - 8 * q^91 - 8 * q^93 - 16 * q^94 - 12 * q^95 - 16 * q^97 + 32 * q^98 + 4 * q^99

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	$0.726608\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.41421	0.707107
$5$	−1.61313	−0.721412	−0.360706	−	0.932680i	$-0.617464\pi$
$5$	−1.61313	−0.721412	−0.360706	+	0.932680i	$0.617464\pi$
$6$	1.84776	0.754344
$7$	0.152241	0.0575417	0.0287708	−	0.999586i	$-0.490841\pi$
$7$	0.152241	0.0575417	0.0287708	+	0.999586i	$0.490841\pi$
$8$	1.08239	0.382683
$9$	1.00000	0.333333
$10$	2.98067	0.942570
$11$	5.02734	1.51580	0.757900	−	0.652371i	$-0.226226\pi$
$11$	5.02734	1.51580	0.757900	+	0.652371i	$0.226226\pi$
$12$	−1.41421	−0.408248
$13$	−3.94495	−1.09413	−0.547066	−	0.837090i	$-0.684255\pi$
$13$	−3.94495	−1.09413	−0.547066	+	0.837090i	$0.684255\pi$
$14$	−0.281305	−0.0751818
$15$	1.61313	0.416507
$16$	−4.82843	−1.20711
$17$	0	0
$17$	0	0
$18$	−1.84776	−0.435521
$19$	−6.57900	−1.50933	−0.754663	−	0.656113i	$-0.772200\pi$
$19$	−6.57900	−1.50933	−0.754663	+	0.656113i	$0.772200\pi$
$20$	−2.28130	−0.510115
$21$	−0.152241	−0.0332217
$22$	−9.28931	−1.98049
$23$	3.44834	0.719029	0.359514	−	0.933140i	$-0.382942\pi$
$23$	3.44834	0.719029	0.359514	+	0.933140i	$0.382942\pi$
$24$	−1.08239	−0.220942
$25$	−2.39782	−0.479565
$26$	7.28931	1.42955
$27$	−1.00000	−0.192450
$28$	0.215301	0.0406881
$29$	−2.24264	−0.416448	−0.208224	−	0.978081i	$-0.566768\pi$
$29$	−2.24264	−0.416448	−0.208224	+	0.978081i	$0.566768\pi$
$30$	−2.98067	−0.544193
$31$	−2.57446	−0.462387	−0.231194	−	0.972908i	$-0.574263\pi$
$31$	−2.57446	−0.462387	−0.231194	+	0.972908i	$0.574263\pi$
$32$	6.75699	1.19448
$33$	−5.02734	−0.875147
$34$	0	0
$35$	−0.245584	−0.0415112
$36$	1.41421	0.235702
$37$	10.6762	1.75515	0.877577	−	0.479436i	$-0.159159\pi$
$37$	10.6762	1.75515	0.877577	+	0.479436i	$0.159159\pi$
$38$	12.1564	1.97203
$39$	3.94495	0.631697
$40$	−1.74603	−0.276072
$41$	−0.276769	−0.0432240	−0.0216120	−	0.999766i	$-0.506880\pi$
$41$	−0.276769	−0.0432240	−0.0216120	+	0.999766i	$0.506880\pi$
$42$	0.281305	0.0434062
$43$	6.34277	0.967264	0.483632	−	0.875272i	$-0.339317\pi$
$43$	6.34277	0.967264	0.483632	+	0.875272i	$0.339317\pi$
$44$	7.10973	1.07183
$45$	−1.61313	−0.240471
$46$	−6.37170	−0.939457
$47$	9.82164	1.43263	0.716317	−	0.697775i	$-0.245827\pi$
$47$	9.82164	1.43263	0.716317	+	0.697775i	$0.245827\pi$
$48$	4.82843	0.696923
$49$	−6.97682	−0.996689
$50$	4.43060	0.626582
$51$	0	0
$52$	−5.57900	−0.773668
$53$	−2.12612	−0.292045	−0.146023	−	0.989281i	$-0.546647\pi$
$53$	−2.12612	−0.292045	−0.146023	+	0.989281i	$0.546647\pi$
$54$	1.84776	0.251448
$55$	−8.10973	−1.09352
$56$	0.164784	0.0220202
$57$	6.57900	0.871410
$58$	4.14386	0.544115
$59$	1.32381	0.172346	0.0861729	−	0.996280i	$-0.472536\pi$
$59$	1.32381	0.172346	0.0861729	+	0.996280i	$0.472536\pi$
$60$	2.28130	0.294515
$61$	8.27836	1.05994	0.529968	−	0.848018i	$-0.322204\pi$
$61$	8.27836	1.05994	0.529968	+	0.848018i	$0.322204\pi$
$62$	4.75699	0.604138
$63$	0.152241	0.0191806
$64$	−2.82843	−0.353553
$65$	6.36370	0.789319
$66$	9.28931	1.14344
$67$	7.10973	0.868592	0.434296	−	0.900770i	$-0.356997\pi$
$67$	7.10973	0.868592	0.434296	+	0.900770i	$0.356997\pi$
$68$	0	0
$69$	−3.44834	−0.415132
$70$	0.453780	0.0542370
$71$	−6.54712	−0.777000	−0.388500	−	0.921449i	$-0.627007\pi$
$71$	−6.54712	−0.777000	−0.388500	+	0.921449i	$0.627007\pi$
$72$	1.08239	0.127561
$73$	8.32638	0.974529	0.487265	−	0.873254i	$-0.337995\pi$
$73$	8.32638	0.974529	0.487265	+	0.873254i	$0.337995\pi$
$74$	−19.7270	−2.29322
$75$	2.39782	0.276877
$76$	−9.30411	−1.06725
$77$	0.765367	0.0872216
$78$	−7.28931	−0.825352
$79$	0.532327	0.0598914	0.0299457	−	0.999552i	$-0.490467\pi$
$79$	0.532327	0.0598914	0.0299457	+	0.999552i	$0.490467\pi$
$80$	7.78886	0.870821
$81$	1.00000	0.111111
$82$	0.511402	0.0564749
$83$	2.20345	0.241860	0.120930	−	0.992661i	$-0.461412\pi$
$83$	2.20345	0.241860	0.120930	+	0.992661i	$0.461412\pi$
$84$	−0.215301	−0.0234913
$85$	0	0
$86$	−11.7199	−1.26379
$87$	2.24264	0.240436
$88$	5.44155	0.580072
$89$	−7.64847	−0.810737	−0.405368	−	0.914153i	$-0.632857\pi$
$89$	−7.64847	−0.810737	−0.405368	+	0.914153i	$0.632857\pi$
$90$	2.98067	0.314190
$91$	−0.600582	−0.0629581
$92$	4.87669	0.508430
$93$	2.57446	0.266959
$94$	−18.1480	−1.87183
$95$	10.6128	1.08885
$96$	−6.75699	−0.689632
$97$	3.60634	0.366168	0.183084	−	0.983097i	$-0.441392\pi$
$97$	3.60634	0.366168	0.183084	+	0.983097i	$0.441392\pi$
$98$	12.8915	1.30224
$99$	5.02734	0.505267
$100$	−3.39104	−0.339104
$101$	9.13707	0.909173	0.454586	−	0.890703i	$-0.349787\pi$
$101$	9.13707	0.909173	0.454586	+	0.890703i	$0.349787\pi$
$102$	0	0
$103$	7.57862	0.746744	0.373372	−	0.927682i	$-0.378202\pi$
$103$	7.57862	0.746744	0.373372	+	0.927682i	$0.378202\pi$
$104$	−4.26998	−0.418706
$105$	0.245584	0.0239665
$106$	3.92856	0.381575
$107$	18.4666	1.78524	0.892619	−	0.450812i	$-0.148866\pi$
$107$	18.4666	1.78524	0.892619	+	0.450812i	$0.148866\pi$
$108$	−1.41421	−0.136083
$109$	10.7392	1.02863	0.514317	−	0.857600i	$-0.328046\pi$
$109$	10.7392	1.02863	0.514317	+	0.857600i	$0.328046\pi$
$110$	14.9848	1.42875
$111$	−10.6762	−1.01334
$112$	−0.735084	−0.0694589
$113$	1.67497	0.157568	0.0787838	−	0.996892i	$-0.474896\pi$
$113$	1.67497	0.157568	0.0787838	+	0.996892i	$0.474896\pi$
$114$	−12.1564	−1.13855
$115$	−5.56261	−0.518716
$116$	−3.17157	−0.294473
$117$	−3.94495	−0.364711
$118$	−2.44609	−0.225181
$119$	0	0
$120$	1.74603	0.159390
$121$	14.2741	1.29765
$122$	−15.2964	−1.38487
$123$	0.276769	0.0249554
$124$	−3.64084	−0.326957
$125$	11.9336	1.06738
$126$	−0.281305	−0.0250606
$127$	−12.1812	−1.08090	−0.540452	−	0.841375i	$-0.681747\pi$
$127$	−12.1812	−1.08090	−0.540452	+	0.841375i	$0.681747\pi$
$128$	−8.28772	−0.732538
$129$	−6.34277	−0.558450
$130$	−11.7586	−1.03130
$131$	10.4512	0.913122	0.456561	−	0.889692i	$-0.349081\pi$
$131$	10.4512	0.913122	0.456561	+	0.889692i	$0.349081\pi$
$132$	−7.10973	−0.618823
$133$	−1.00159	−0.0868491
$134$	−13.1371	−1.13487
$135$	1.61313	0.138836
$136$	0	0
$137$	13.4928	1.15276	0.576382	−	0.817180i	$-0.304464\pi$
$137$	13.4928	1.15276	0.576382	+	0.817180i	$0.304464\pi$
$138$	6.37170	0.542395
$139$	5.32798	0.451913	0.225957	−	0.974137i	$-0.427449\pi$
$139$	5.32798	0.451913	0.225957	+	0.974137i	$0.427449\pi$
$140$	−0.347308	−0.0293529
$141$	−9.82164	−0.827131
$142$	12.0975	1.01520
$143$	−19.8326	−1.65848
$144$	−4.82843	−0.402369
$145$	3.61766	0.300430
$146$	−15.3852	−1.27328
$147$	6.97682	0.575439
$148$	15.0984	1.24108
$149$	9.31890	0.763434	0.381717	−	0.924279i	$-0.375333\pi$
$149$	9.31890	0.763434	0.381717	+	0.924279i	$0.375333\pi$
$150$	−4.43060	−0.361757
$151$	11.9632	0.973555	0.486778	−	0.873526i	$-0.338172\pi$
$151$	11.9632	0.973555	0.486778	+	0.873526i	$0.338172\pi$
$152$	−7.12106	−0.577594
$153$	0	0
$154$	−1.41421	−0.113961
$155$	4.15293	0.333571
$156$	5.57900	0.446677
$157$	−18.1548	−1.44891	−0.724456	−	0.689321i	$-0.757909\pi$
$157$	−18.1548	−1.44891	−0.724456	+	0.689321i	$0.757909\pi$
$158$	−0.983611	−0.0782519
$159$	2.12612	0.168612
$160$	−10.8999	−0.861710
$161$	0.524979	0.0413741
$162$	−1.84776	−0.145174
$163$	−20.7225	−1.62311	−0.811555	−	0.584276i	$-0.801379\pi$
$163$	−20.7225	−1.62311	−0.811555	+	0.584276i	$0.801379\pi$
$164$	−0.391410	−0.0305640
$165$	8.10973	0.631342
$166$	−4.07144	−0.316005
$167$	−8.08881	−0.625931	−0.312965	−	0.949765i	$-0.601322\pi$
$167$	−8.08881	−0.625931	−0.312965	+	0.949765i	$0.601322\pi$
$168$	−0.164784	−0.0127134
$169$	2.56261	0.197124
$170$	0	0
$171$	−6.57900	−0.503109
$172$	8.97003	0.683959
$173$	1.16062	0.0882405	0.0441202	−	0.999026i	$-0.485952\pi$
$173$	1.16062	0.0882405	0.0441202	+	0.999026i	$0.485952\pi$
$174$	−4.14386	−0.314145
$175$	−0.365047	−0.0275950
$176$	−24.2741	−1.82973
$177$	−1.32381	−0.0995039
$178$	14.1325	1.05928
$179$	2.89668	0.216508	0.108254	−	0.994123i	$-0.465474\pi$
$179$	2.89668	0.216508	0.108254	+	0.994123i	$0.465474\pi$
$180$	−2.28130	−0.170038
$181$	0.842695	0.0626370	0.0313185	−	0.999509i	$-0.490029\pi$
$181$	0.842695	0.0626370	0.0313185	+	0.999509i	$0.490029\pi$
$182$	1.10973	0.0822588
$183$	−8.27836	−0.611954
$184$	3.73246	0.275160
$185$	−17.2220	−1.26619
$186$	−4.75699	−0.348799
$187$	0	0
$188$	13.8899	1.01302
$189$	−0.152241	−0.0110739
$190$	−19.6098	−1.42265
$191$	9.97069	0.721454	0.360727	−	0.932671i	$-0.382529\pi$
$191$	9.97069	0.721454	0.360727	+	0.932671i	$0.382529\pi$
$192$	2.82843	0.204124
$193$	−3.73418	−0.268792	−0.134396	−	0.990928i	$-0.542909\pi$
$193$	−3.73418	−0.268792	−0.134396	+	0.990928i	$0.542909\pi$
$194$	−6.66364	−0.478422
$195$	−6.36370	−0.455714
$196$	−9.86672	−0.704766
$197$	16.2053	1.15458	0.577291	−	0.816539i	$-0.304110\pi$
$197$	16.2053	1.15458	0.577291	+	0.816539i	$0.304110\pi$
$198$	−9.28931	−0.660163
$199$	−16.4734	−1.16777	−0.583885	−	0.811836i	$-0.698468\pi$
$199$	−16.4734	−1.16777	−0.583885	+	0.811836i	$0.698468\pi$
$200$	−2.59539	−0.183522
$201$	−7.10973	−0.501482
$202$	−16.8831	−1.18789
$203$	−0.341422	−0.0239631
$204$	0	0
$205$	0.446463	0.0311823
$206$	−14.0035	−0.975668
$207$	3.44834	0.239676
$208$	19.0479	1.32073
$209$	−33.0749	−2.28784
$210$	−0.453780	−0.0313138
$211$	−10.6887	−0.735842	−0.367921	−	0.929857i	$-0.619930\pi$
$211$	−10.6887	−0.735842	−0.367921	+	0.929857i	$0.619930\pi$
$212$	−3.00679	−0.206507
$213$	6.54712	0.448601
$214$	−34.1219	−2.33253
$215$	−10.2317	−0.697795
$216$	−1.08239	−0.0736475
$217$	−0.391939	−0.0266065
$218$	−19.8435	−1.34397
$219$	−8.32638	−0.562645
$220$	−11.4689	−0.773233
$221$	0	0
$222$	19.7270	1.32399
$223$	5.41650	0.362715	0.181358	−	0.983417i	$-0.441951\pi$
$223$	5.41650	0.362715	0.181358	+	0.983417i	$0.441951\pi$
$224$	1.02869	0.0687322
$225$	−2.39782	−0.159855
$226$	−3.09494	−0.205872
$227$	12.2987	0.816291	0.408146	−	0.912917i	$-0.366176\pi$
$227$	12.2987	0.816291	0.408146	+	0.912917i	$0.366176\pi$
$228$	9.30411	0.616180
$229$	30.1158	1.99011	0.995053	−	0.0993441i	$-0.0316745\pi$
$229$	30.1158	1.99011	0.995053	+	0.0993441i	$0.0316745\pi$
$230$	10.2784	0.677735
$231$	−0.765367	−0.0503574
$232$	−2.42742	−0.159368
$233$	8.78523	0.575539	0.287770	−	0.957700i	$-0.407086\pi$
$233$	8.78523	0.575539	0.287770	+	0.957700i	$0.407086\pi$
$234$	7.28931	0.476517
$235$	−15.8435	−1.03352
$236$	1.87216	0.121867
$237$	−0.532327	−0.0345783
$238$	0	0
$239$	14.6501	0.947634	0.473817	−	0.880623i	$-0.342876\pi$
$239$	14.6501	0.947634	0.473817	+	0.880623i	$0.342876\pi$
$240$	−7.78886	−0.502769
$241$	−16.9552	−1.09218	−0.546091	−	0.837726i	$-0.683885\pi$
$241$	−16.9552	−1.09218	−0.546091	+	0.837726i	$0.683885\pi$
$242$	−26.3752	−1.69546
$243$	−1.00000	−0.0641500
$244$	11.7074	0.749488
$245$	11.2545	0.719023
$246$	−0.511402	−0.0326058
$247$	25.9538	1.65140
$248$	−2.78658	−0.176948
$249$	−2.20345	−0.139638
$250$	−22.0505	−1.39459
$251$	−13.9453	−0.880217	−0.440109	−	0.897945i	$-0.645060\pi$
$251$	−13.9453	−0.880217	−0.440109	+	0.897945i	$0.645060\pi$
$252$	0.215301	0.0135627
$253$	17.3360	1.08990
$254$	22.5079	1.41227
$255$	0	0
$256$	20.9706	1.31066
$257$	19.6603	1.22638	0.613189	−	0.789936i	$-0.289887\pi$
$257$	19.6603	1.22638	0.613189	+	0.789936i	$0.289887\pi$
$258$	11.7199	0.729650
$259$	1.62535	0.100994
$260$	8.99963	0.558133
$261$	−2.24264	−0.138816
$262$	−19.3112	−1.19305
$263$	−27.8721	−1.71867	−0.859334	−	0.511415i	$-0.829121\pi$
$263$	−27.8721	−1.71867	−0.859334	+	0.511415i	$0.829121\pi$
$264$	−5.44155	−0.334904
$265$	3.42970	0.210685
$266$	1.85070	0.113474
$267$	7.64847	0.468079
$268$	10.0547	0.614187
$269$	0.205327	0.0125190	0.00625951	−	0.999980i	$-0.498008\pi$
$269$	0.205327	0.0125190	0.00625951	+	0.999980i	$0.498008\pi$
$270$	−2.98067	−0.181398
$271$	−8.21077	−0.498768	−0.249384	−	0.968405i	$-0.580228\pi$
$271$	−8.21077	−0.498768	−0.249384	+	0.968405i	$0.580228\pi$
$272$	0	0
$273$	0.600582	0.0363489
$274$	−24.9314	−1.50616
$275$	−12.0547	−0.726924
$276$	−4.87669	−0.293542
$277$	23.5677	1.41604	0.708022	−	0.706190i	$-0.249588\pi$
$277$	23.5677	1.41604	0.708022	+	0.706190i	$0.249588\pi$
$278$	−9.84482	−0.590453
$279$	−2.57446	−0.154129
$280$	−0.265818	−0.0158857
$281$	−10.1532	−0.605690	−0.302845	−	0.953040i	$-0.597936\pi$
$281$	−10.1532	−0.605690	−0.302845	+	0.953040i	$0.597936\pi$
$282$	18.1480	1.08070
$283$	−9.47918	−0.563479	−0.281739	−	0.959491i	$-0.590911\pi$
$283$	−9.47918	−0.563479	−0.281739	+	0.959491i	$0.590911\pi$
$284$	−9.25903	−0.549422
$285$	−10.6128	−0.628645
$286$	36.6458	2.16691
$287$	−0.0421355	−0.00248718
$288$	6.75699	0.398159
$289$	0	0
$290$	−6.68457	−0.392531
$291$	−3.60634	−0.211407
$292$	11.7753	0.689096
$293$	9.28515	0.542444	0.271222	−	0.962517i	$-0.412572\pi$
$293$	9.28515	0.542444	0.271222	+	0.962517i	$0.412572\pi$
$294$	−12.8915	−0.751847
$295$	−2.13548	−0.124332
$296$	11.5558	0.671668
$297$	−5.02734	−0.291716
$298$	−17.2191	−0.997475
$299$	−13.6035	−0.786712
$300$	3.39104	0.195782
$301$	0.965630	0.0556580
$302$	−22.1052	−1.27201
$303$	−9.13707	−0.524911
$304$	31.7662	1.82192
$305$	−13.3540	−0.764650
$306$	0	0
$307$	−27.1418	−1.54906	−0.774531	−	0.632536i	$-0.782014\pi$
$307$	−27.1418	−1.54906	−0.774531	+	0.632536i	$0.782014\pi$
$308$	1.08239	0.0616750
$309$	−7.57862	−0.431133
$310$	−7.67362	−0.435832
$311$	−2.58579	−0.146626	−0.0733132	−	0.997309i	$-0.523357\pi$
$311$	−2.58579	−0.146626	−0.0733132	+	0.997309i	$0.523357\pi$
$312$	4.26998	0.241740
$313$	25.6105	1.44759	0.723796	−	0.690015i	$-0.242396\pi$
$313$	25.6105	1.44759	0.723796	+	0.690015i	$0.242396\pi$
$314$	33.5457	1.89309
$315$	−0.245584	−0.0138371
$316$	0.752823	0.0423496
$317$	25.5982	1.43774	0.718869	−	0.695146i	$-0.244660\pi$
$317$	25.5982	1.43774	0.718869	+	0.695146i	$0.244660\pi$
$318$	−3.92856	−0.220303
$319$	−11.2745	−0.631252
$320$	4.56261	0.255058
$321$	−18.4666	−1.03071
$322$	−0.970034	−0.0540579
$323$	0	0
$324$	1.41421	0.0785674
$325$	9.45929	0.524707
$326$	38.2902	2.12070
$327$	−10.7392	−0.593882
$328$	−0.299572	−0.0165411
$329$	1.49526	0.0824361
$330$	−14.9848	−0.824888
$331$	−0.333172	−0.0183128	−0.00915639	−	0.999958i	$-0.502915\pi$
$331$	−0.333172	−0.0183128	−0.00915639	+	0.999958i	$0.502915\pi$
$332$	3.11615	0.171021
$333$	10.6762	0.585051
$334$	14.9462	0.817818
$335$	−11.4689	−0.626613
$336$	0.735084	0.0401021
$337$	−3.75539	−0.204569	−0.102285	−	0.994755i	$-0.532615\pi$
$337$	−3.75539	−0.204569	−0.102285	+	0.994755i	$0.532615\pi$
$338$	−4.73508	−0.257555
$339$	−1.67497	−0.0909717
$340$	0	0
$341$	−12.9427	−0.700886
$342$	12.1564	0.657343
$343$	−2.12784	−0.114893
$344$	6.86537	0.370156
$345$	5.56261	0.299481
$346$	−2.14455	−0.115292
$347$	3.30999	0.177690	0.0888449	−	0.996045i	$-0.471682\pi$
$347$	3.30999	0.177690	0.0888449	+	0.996045i	$0.471682\pi$
$348$	3.17157	0.170014
$349$	2.58488	0.138366	0.0691828	−	0.997604i	$-0.477961\pi$
$349$	2.58488	0.138366	0.0691828	+	0.997604i	$0.477961\pi$
$350$	0.674519	0.0360546
$351$	3.94495	0.210566
$352$	33.9697	1.81059
$353$	13.2848	0.707079	0.353539	−	0.935420i	$-0.384978\pi$
$353$	13.2848	0.707079	0.353539	+	0.935420i	$0.384978\pi$
$354$	2.44609	0.130008
$355$	10.5613	0.560537
$356$	−10.8166	−0.573277
$357$	0	0
$358$	−5.35237	−0.282882
$359$	−14.7281	−0.777319	−0.388659	−	0.921382i	$-0.627062\pi$
$359$	−14.7281	−0.777319	−0.388659	+	0.921382i	$0.627062\pi$
$360$	−1.74603	−0.0920241
$361$	24.2832	1.27806
$362$	−1.55710	−0.0818392
$363$	−14.2741	−0.749198
$364$	−0.849352	−0.0445181
$365$	−13.4315	−0.703037
$366$	15.2964	0.799557
$367$	0.439960	0.0229657	0.0114829	−	0.999934i	$-0.496345\pi$
$367$	0.439960	0.0229657	0.0114829	+	0.999934i	$0.496345\pi$
$368$	−16.6501	−0.867945
$369$	−0.276769	−0.0144080
$370$	31.8222	1.65436
$371$	−0.323683	−0.0168048
$372$	3.64084	0.188769
$373$	−0.827899	−0.0428670	−0.0214335	−	0.999770i	$-0.506823\pi$
$373$	−0.827899	−0.0428670	−0.0214335	+	0.999770i	$0.506823\pi$
$374$	0	0
$375$	−11.9336	−0.616250
$376$	10.6309	0.548245
$377$	8.84710	0.455649
$378$	0.281305	0.0144687
$379$	19.8083	1.01749	0.508743	−	0.860918i	$-0.330110\pi$
$379$	19.8083	1.01749	0.508743	+	0.860918i	$0.330110\pi$
$380$	15.0087	0.769930
$381$	12.1812	0.624060
$382$	−18.4234	−0.942625
$383$	−16.6828	−0.852453	−0.426227	−	0.904616i	$-0.640157\pi$
$383$	−16.6828	−0.852453	−0.426227	+	0.904616i	$0.640157\pi$
$384$	8.28772	0.422931
$385$	−1.23463	−0.0629227
$386$	6.89987	0.351194
$387$	6.34277	0.322421
$388$	5.10013	0.258920
$389$	17.2980	0.877042	0.438521	−	0.898721i	$-0.355502\pi$
$389$	17.2980	0.877042	0.438521	+	0.898721i	$0.355502\pi$
$390$	11.7586	0.595419
$391$	0	0
$392$	−7.55166	−0.381416
$393$	−10.4512	−0.527191
$394$	−29.9435	−1.50853
$395$	−0.858710	−0.0432064
$396$	7.10973	0.357277
$397$	6.44065	0.323247	0.161623	−	0.986852i	$-0.448327\pi$
$397$	6.44065	0.323247	0.161623	+	0.986852i	$0.448327\pi$
$398$	30.4389	1.52577
$399$	1.00159	0.0501424
$400$	11.5777	0.578886
$401$	21.0724	1.05231	0.526153	−	0.850390i	$-0.323634\pi$
$401$	21.0724	1.05231	0.526153	+	0.850390i	$0.323634\pi$
$402$	13.1371	0.655218
$403$	10.1561	0.505912
$404$	12.9218	0.642882
$405$	−1.61313	−0.0801569
$406$	0.630865	0.0313093
$407$	53.6728	2.66046
$408$	0	0
$409$	−27.6232	−1.36588	−0.682939	−	0.730475i	$-0.739299\pi$
$409$	−27.6232	−1.36588	−0.682939	+	0.730475i	$0.739299\pi$
$410$	−0.824955	−0.0407416
$411$	−13.4928	−0.665549
$412$	10.7178	0.528028
$413$	0.201539	0.00991707
$414$	−6.37170	−0.313152
$415$	−3.55444	−0.174481
$416$	−26.6560	−1.30692
$417$	−5.32798	−0.260912
$418$	61.1144	2.98920
$419$	−12.0510	−0.588728	−0.294364	−	0.955693i	$-0.595108\pi$
$419$	−12.0510	−0.588728	−0.294364	+	0.955693i	$0.595108\pi$
$420$	0.347308	0.0169469
$421$	14.0183	0.683210	0.341605	−	0.939844i	$-0.389029\pi$
$421$	14.0183	0.683210	0.341605	+	0.939844i	$0.389029\pi$
$422$	19.7502	0.961425
$423$	9.82164	0.477544
$424$	−2.30130	−0.111761
$425$	0	0
$426$	−12.0975	−0.586126
$427$	1.26031	0.0609905
$428$	26.1158	1.26235
$429$	19.8326	0.957526
$430$	18.9057	0.911714
$431$	−3.44381	−0.165882	−0.0829411	−	0.996554i	$-0.526431\pi$
$431$	−3.44381	−0.165882	−0.0829411	+	0.996554i	$0.526431\pi$
$432$	4.82843	0.232308
$433$	5.56579	0.267475	0.133738	−	0.991017i	$-0.457302\pi$
$433$	5.56579	0.267475	0.133738	+	0.991017i	$0.457302\pi$
$434$	0.724208	0.0347631
$435$	−3.61766	−0.173454
$436$	15.1876	0.727354
$437$	−22.6866	−1.08525
$438$	15.3852	0.735131
$439$	17.5864	0.839353	0.419676	−	0.907674i	$-0.362144\pi$
$439$	17.5864	0.839353	0.419676	+	0.907674i	$0.362144\pi$
$440$	−8.77791	−0.418470
$441$	−6.97682	−0.332230
$442$	0	0
$443$	5.87632	0.279192	0.139596	−	0.990209i	$-0.455420\pi$
$443$	5.87632	0.279192	0.139596	+	0.990209i	$0.455420\pi$
$444$	−15.0984	−0.716539
$445$	12.3380	0.584875
$446$	−10.0084	−0.473911
$447$	−9.31890	−0.440769
$448$	−0.430602	−0.0203441
$449$	−39.9812	−1.88683	−0.943414	−	0.331617i	$-0.892406\pi$
$449$	−39.9812	−1.88683	−0.943414	+	0.331617i	$0.892406\pi$
$450$	4.43060	0.208861
$451$	−1.39141	−0.0655189
$452$	2.36876	0.111417
$453$	−11.9632	−0.562082
$454$	−22.7250	−1.06654
$455$	0.968815	0.0454188
$456$	7.12106	0.333474
$457$	−17.6906	−0.827533	−0.413767	−	0.910383i	$-0.635787\pi$
$457$	−17.6906	−0.827533	−0.413767	+	0.910383i	$0.635787\pi$
$458$	−55.6467	−2.60020
$459$	0	0
$460$	−7.86672	−0.366788
$461$	29.8662	1.39101	0.695504	−	0.718522i	$-0.255181\pi$
$461$	29.8662	1.39101	0.695504	+	0.718522i	$0.255181\pi$
$462$	1.41421	0.0657952
$463$	9.45213	0.439278	0.219639	−	0.975581i	$-0.429512\pi$
$463$	9.45213	0.439278	0.219639	+	0.975581i	$0.429512\pi$
$464$	10.8284	0.502697
$465$	−4.15293	−0.192588
$466$	−16.2330	−0.751978
$467$	−20.0094	−0.925923	−0.462961	−	0.886378i	$-0.653213\pi$
$467$	−20.0094	−0.925923	−0.462961	+	0.886378i	$0.653213\pi$
$468$	−5.57900	−0.257889
$469$	1.08239	0.0499802
$470$	29.2750	1.35036
$471$	18.1548	0.836530
$472$	1.43289	0.0659539
$473$	31.8873	1.46618
$474$	0.983611	0.0451788
$475$	15.7753	0.723820
$476$	0	0
$477$	−2.12612	−0.0973484
$478$	−27.0698	−1.23814
$479$	−1.20570	−0.0550899	−0.0275449	−	0.999621i	$-0.508769\pi$
$479$	−1.20570	−0.0550899	−0.0275449	+	0.999621i	$0.508769\pi$
$480$	10.8999	0.497509
$481$	−42.1170	−1.92037
$482$	31.3292	1.42701
$483$	−0.524979	−0.0238874
$484$	20.1867	0.917577
$485$	−5.81748	−0.264158
$486$	1.84776	0.0838161
$487$	11.9613	0.542017	0.271009	−	0.962577i	$-0.412643\pi$
$487$	11.9613	0.542017	0.271009	+	0.962577i	$0.412643\pi$
$488$	8.96043	0.405620
$489$	20.7225	0.937103
$490$	−20.7956	−0.939449
$491$	31.2632	1.41089	0.705444	−	0.708766i	$-0.250748\pi$
$491$	31.2632	1.41089	0.705444	+	0.708766i	$0.250748\pi$
$492$	0.391410	0.0176461
$493$	0	0
$494$	−47.9564	−2.15766
$495$	−8.10973	−0.364505
$496$	12.4306	0.558151
$497$	−0.996740	−0.0447099
$498$	4.07144	0.182446
$499$	−41.3590	−1.85148	−0.925741	−	0.378158i	$-0.876558\pi$
$499$	−41.3590	−1.85148	−0.925741	+	0.378158i	$0.876558\pi$
$500$	16.8767	0.754749
$501$	8.08881	0.361381
$502$	25.7675	1.15006
$503$	3.08277	0.137454	0.0687269	−	0.997636i	$-0.478106\pi$
$503$	3.08277	0.137454	0.0687269	+	0.997636i	$0.478106\pi$
$504$	0.164784	0.00734008
$505$	−14.7392	−0.655888
$506$	−32.0327	−1.42403
$507$	−2.56261	−0.113809
$508$	−17.2268	−0.764315
$509$	−33.8077	−1.49850	−0.749249	−	0.662288i	$-0.769585\pi$
$509$	−33.8077	−1.49850	−0.749249	+	0.662288i	$0.769585\pi$
$510$	0	0
$511$	1.26762	0.0560760
$512$	−22.1731	−0.979922
$513$	6.57900	0.290470
$514$	−36.3275	−1.60234
$515$	−12.2253	−0.538710
$516$	−8.97003	−0.394884
$517$	49.3767	2.17159
$518$	−3.00326	−0.131956
$519$	−1.16062	−0.0509457
$520$	6.88802	0.302059
$521$	−40.9557	−1.79430	−0.897150	−	0.441725i	$-0.854367\pi$
$521$	−40.9557	−1.79430	−0.897150	+	0.441725i	$0.854367\pi$
$522$	4.14386	0.181372
$523$	−9.06788	−0.396511	−0.198255	−	0.980150i	$-0.563528\pi$
$523$	−9.06788	−0.396511	−0.198255	+	0.980150i	$0.563528\pi$
$524$	14.7802	0.645674
$525$	0.365047	0.0159320
$526$	51.5009	2.24555
$527$	0	0
$528$	24.2741	1.05640
$529$	−11.1089	−0.482997
$530$	−6.33726	−0.275273
$531$	1.32381	0.0574486
$532$	−1.41647	−0.0614116
$533$	1.09184	0.0472927
$534$	−14.1325	−0.611575
$535$	−29.7890	−1.28789
$536$	7.69552	0.332396
$537$	−2.89668	−0.125001
$538$	−0.379395	−0.0163569
$539$	−35.0749	−1.51078
$540$	2.28130	0.0981717
$541$	12.9420	0.556420	0.278210	−	0.960520i	$-0.410259\pi$
$541$	12.9420	0.556420	0.278210	+	0.960520i	$0.410259\pi$
$542$	15.1715	0.651672
$543$	−0.842695	−0.0361635
$544$	0	0
$545$	−17.3238	−0.742068
$546$	−1.10973	−0.0474921
$547$	−10.6598	−0.455781	−0.227891	−	0.973687i	$-0.573183\pi$
$547$	−10.6598	−0.455781	−0.227891	+	0.973687i	$0.573183\pi$
$548$	19.0816	0.815127
$549$	8.27836	0.353312
$550$	22.2741	0.949773
$551$	14.7543	0.628556
$552$	−3.73246	−0.158864
$553$	0.0810419	0.00344625
$554$	−43.5474	−1.85015
$555$	17.2220	0.731035
$556$	7.53490	0.319551
$557$	−30.1933	−1.27933	−0.639667	−	0.768653i	$-0.720928\pi$
$557$	−30.1933	−1.27933	−0.639667	+	0.768653i	$0.720928\pi$
$558$	4.75699	0.201379
$559$	−25.0219	−1.05831
$560$	1.18578	0.0501085
$561$	0	0
$562$	18.7607	0.791372
$563$	−29.9236	−1.26113	−0.630566	−	0.776136i	$-0.717177\pi$
$563$	−29.9236	−1.26113	−0.630566	+	0.776136i	$0.717177\pi$
$564$	−13.8899	−0.584870
$565$	−2.70193	−0.113671
$566$	17.5152	0.736221
$567$	0.152241	0.00639352
$568$	−7.08655	−0.297345
$569$	25.6952	1.07720	0.538599	−	0.842562i	$-0.318954\pi$
$569$	25.6952	1.07720	0.538599	+	0.842562i	$0.318954\pi$
$570$	19.6098	0.821365
$571$	28.0143	1.17236	0.586181	−	0.810180i	$-0.300631\pi$
$571$	28.0143	1.17236	0.586181	+	0.810180i	$0.300631\pi$
$572$	−28.0475	−1.17273
$573$	−9.97069	−0.416532
$574$	0.0778563	0.00324966
$575$	−8.26852	−0.344821
$576$	−2.82843	−0.117851
$577$	−11.8072	−0.491538	−0.245769	−	0.969328i	$-0.579041\pi$
$577$	−11.8072	−0.491538	−0.245769	+	0.969328i	$0.579041\pi$
$578$	0	0
$579$	3.73418	0.155187
$580$	5.11615	0.212436
$581$	0.335455	0.0139170
$582$	6.66364	0.276217
$583$	−10.6887	−0.442682
$584$	9.01241	0.372936
$585$	6.36370	0.263106
$586$	−17.1567	−0.708738
$587$	7.44230	0.307177	0.153588	−	0.988135i	$-0.450917\pi$
$587$	7.44230	0.307177	0.153588	+	0.988135i	$0.450917\pi$
$588$	9.86672	0.406897
$589$	16.9374	0.697893
$590$	3.94585	0.162448
$591$	−16.2053	−0.666598
$592$	−51.5492	−2.11866
$593$	7.65194	0.314228	0.157114	−	0.987580i	$-0.449781\pi$
$593$	7.65194	0.314228	0.157114	+	0.987580i	$0.449781\pi$
$594$	9.28931	0.381145
$595$	0	0
$596$	13.1789	0.539830
$597$	16.4734	0.674213
$598$	25.1360	1.02789
$599$	16.1547	0.660062	0.330031	−	0.943970i	$-0.392941\pi$
$599$	16.1547	0.660062	0.330031	+	0.943970i	$0.392941\pi$
$600$	2.59539	0.105956
$601$	28.7176	1.17141	0.585707	−	0.810523i	$-0.300817\pi$
$601$	28.7176	1.17141	0.585707	+	0.810523i	$0.300817\pi$
$602$	−1.78425	−0.0727206
$603$	7.10973	0.289531
$604$	16.9186	0.688407
$605$	−23.0260	−0.936140
$606$	16.8831	0.685829
$607$	25.8129	1.04771	0.523856	−	0.851807i	$-0.324493\pi$
$607$	25.8129	1.04771	0.523856	+	0.851807i	$0.324493\pi$
$608$	−44.4542	−1.80286
$609$	0.341422	0.0138351
$610$	24.6750	0.999063
$611$	−38.7458	−1.56749
$612$	0	0
$613$	49.1769	1.98623	0.993117	−	0.117123i	$-0.0373670\pi$
$613$	49.1769	1.98623	0.993117	+	0.117123i	$0.0373670\pi$
$614$	50.1514	2.02395
$615$	−0.446463	−0.0180031
$616$	0.828427	0.0333783
$617$	3.55073	0.142947	0.0714734	−	0.997443i	$-0.477230\pi$
$617$	3.55073	0.142947	0.0714734	+	0.997443i	$0.477230\pi$
$618$	14.0035	0.563302
$619$	−35.2011	−1.41485	−0.707426	−	0.706787i	$-0.750144\pi$
$619$	−35.2011	−1.41485	−0.707426	+	0.706787i	$0.750144\pi$
$620$	5.87313	0.235871
$621$	−3.44834	−0.138377
$622$	4.77791	0.191577
$623$	−1.16441	−0.0466511
$624$	−19.0479	−0.762526
$625$	−7.26131	−0.290453
$626$	−47.3220	−1.89137
$627$	33.0749	1.32088
$628$	−25.6748	−1.02454
$629$	0	0
$630$	0.453780	0.0180790
$631$	−31.4131	−1.25054	−0.625268	−	0.780410i	$-0.715010\pi$
$631$	−31.4131	−1.25054	−0.625268	+	0.780410i	$0.715010\pi$
$632$	0.576186	0.0229195
$633$	10.6887	0.424839
$634$	−47.2993	−1.87850
$635$	19.6498	0.779777
$636$	3.00679	0.119227
$637$	27.5232	1.09051
$638$	20.8326	0.824770
$639$	−6.54712	−0.259000
$640$	13.3691	0.528461
$641$	−26.5755	−1.04967	−0.524834	−	0.851205i	$-0.675873\pi$
$641$	−26.5755	−1.04967	−0.524834	+	0.851205i	$0.675873\pi$
$642$	34.1219	1.34668
$643$	−16.0247	−0.631952	−0.315976	−	0.948767i	$-0.602332\pi$
$643$	−16.0247	−0.631952	−0.315976	+	0.948767i	$0.602332\pi$
$644$	0.742432	0.0292559
$645$	10.2317	0.402872
$646$	0	0
$647$	41.6554	1.63764	0.818822	−	0.574048i	$-0.194628\pi$
$647$	41.6554	1.63764	0.818822	+	0.574048i	$0.194628\pi$
$648$	1.08239	0.0425204
$649$	6.65526	0.261242
$650$	−17.4785	−0.685563
$651$	0.391939	0.0153613
$652$	−29.3060	−1.14771
$653$	−12.3264	−0.482370	−0.241185	−	0.970479i	$-0.577536\pi$
$653$	−12.3264	−0.482370	−0.241185	+	0.970479i	$0.577536\pi$
$654$	19.8435	0.775944
$655$	−16.8590	−0.658737
$656$	1.33636	0.0521760
$657$	8.32638	0.324843
$658$	−2.76287	−0.107708
$659$	3.46449	0.134957	0.0674786	−	0.997721i	$-0.478505\pi$
$659$	3.46449	0.134957	0.0674786	+	0.997721i	$0.478505\pi$
$660$	11.4689	0.446426
$661$	−28.3233	−1.10165	−0.550825	−	0.834621i	$-0.685687\pi$
$661$	−28.3233	−1.10165	−0.550825	+	0.834621i	$0.685687\pi$
$662$	0.615621	0.0239268
$663$	0	0
$664$	2.38500	0.0925558
$665$	1.61570	0.0626540
$666$	−19.7270	−0.764406
$667$	−7.73339	−0.299438
$668$	−11.4393	−0.442600
$669$	−5.41650	−0.209414
$670$	21.1918	0.818709
$671$	41.6181	1.60665
$672$	−1.02869	−0.0396826
$673$	−28.4086	−1.09507	−0.547535	−	0.836783i	$-0.684434\pi$
$673$	−28.4086	−1.09507	−0.547535	+	0.836783i	$0.684434\pi$
$674$	6.93906	0.267283
$675$	2.39782	0.0922923
$676$	3.62408	0.139388
$677$	19.2983	0.741692	0.370846	−	0.928694i	$-0.379068\pi$
$677$	19.2983	0.741692	0.370846	+	0.928694i	$0.379068\pi$
$678$	3.09494	0.118860
$679$	0.549032	0.0210699
$680$	0	0
$681$	−12.2987	−0.471286
$682$	23.9150	0.915752
$683$	−19.4793	−0.745355	−0.372678	−	0.927961i	$-0.621560\pi$
$683$	−19.4793	−0.745355	−0.372678	+	0.927961i	$0.621560\pi$
$684$	−9.30411	−0.355751
$685$	−21.7655	−0.831618
$686$	3.93174	0.150115
$687$	−30.1158	−1.14899
$688$	−30.6256	−1.16759
$689$	8.38743	0.319536
$690$	−10.2784	−0.391291
$691$	−7.53940	−0.286812	−0.143406	−	0.989664i	$-0.545806\pi$
$691$	−7.53940	−0.286812	−0.143406	+	0.989664i	$0.545806\pi$
$692$	1.64137	0.0623954
$693$	0.765367	0.0290739
$694$	−6.11607	−0.232163
$695$	−8.59470	−0.326015
$696$	2.42742	0.0920110
$697$	0	0
$698$	−4.77624	−0.180783
$699$	−8.78523	−0.332288
$700$	−0.516255	−0.0195126
$701$	−39.0875	−1.47632	−0.738158	−	0.674628i	$-0.764304\pi$
$701$	−39.0875	−1.47632	−0.738158	+	0.674628i	$0.764304\pi$
$702$	−7.28931	−0.275117
$703$	−70.2386	−2.64910
$704$	−14.2195	−0.535916
$705$	15.8435	0.596702
$706$	−24.5471	−0.923843
$707$	1.39104	0.0523153
$708$	−1.87216	−0.0703599
$709$	6.71284	0.252106	0.126053	−	0.992024i	$-0.459769\pi$
$709$	6.71284	0.252106	0.126053	+	0.992024i	$0.459769\pi$
$710$	−19.5148	−0.732377
$711$	0.532327	0.0199638
$712$	−8.27865	−0.310255
$713$	−8.87762	−0.332470
$714$	0	0
$715$	31.9925	1.19645
$716$	4.09653	0.153094
$717$	−14.6501	−0.547117
$718$	27.2140	1.01562
$719$	7.40623	0.276206	0.138103	−	0.990418i	$-0.455900\pi$
$719$	7.40623	0.276206	0.138103	+	0.990418i	$0.455900\pi$
$720$	7.78886	0.290274
$721$	1.15378	0.0429689
$722$	−44.8695	−1.66987
$723$	16.9552	0.630572
$724$	1.19175	0.0442910
$725$	5.37746	0.199714
$726$	26.3752	0.978875
$727$	−6.36054	−0.235899	−0.117950	−	0.993020i	$-0.537632\pi$
$727$	−6.36054	−0.235899	−0.117950	+	0.993020i	$0.537632\pi$
$728$	−0.650066	−0.0240930
$729$	1.00000	0.0370370
$730$	24.8182	0.918562
$731$	0	0
$732$	−11.7074	−0.432717
$733$	−41.3337	−1.52670	−0.763348	−	0.645988i	$-0.776446\pi$
$733$	−41.3337	−1.52670	−0.763348	+	0.645988i	$0.776446\pi$
$734$	−0.812941	−0.0300062
$735$	−11.2545	−0.415128
$736$	23.3004	0.858864
$737$	35.7430	1.31661
$738$	0.511402	0.0188250
$739$	23.1653	0.852150	0.426075	−	0.904688i	$-0.359896\pi$
$739$	23.1653	0.852150	0.426075	+	0.904688i	$0.359896\pi$
$740$	−24.3556	−0.895331
$741$	−25.9538	−0.953437
$742$	0.598087	0.0219565
$743$	38.1505	1.39960	0.699802	−	0.714337i	$-0.253271\pi$
$743$	38.1505	1.39960	0.699802	+	0.714337i	$0.253271\pi$
$744$	2.78658	0.102161
$745$	−15.0326	−0.550751
$746$	1.52976	0.0560084
$747$	2.20345	0.0806200
$748$	0	0
$749$	2.81138	0.102726
$750$	22.0505	0.805169
$751$	34.2073	1.24824	0.624120	−	0.781328i	$-0.285457\pi$
$751$	34.2073	1.24824	0.624120	+	0.781328i	$0.285457\pi$
$752$	−47.4231	−1.72934
$753$	13.9453	0.508194
$754$	−16.3473	−0.595334
$755$	−19.2982	−0.702334
$756$	−0.215301	−0.00783043
$757$	−7.02190	−0.255215	−0.127608	−	0.991825i	$-0.540730\pi$
$757$	−7.02190	−0.255215	−0.127608	+	0.991825i	$0.540730\pi$
$758$	−36.6011	−1.32941
$759$	−17.3360	−0.629256
$760$	11.4872	0.416683
$761$	47.2917	1.71432	0.857161	−	0.515048i	$-0.172226\pi$
$761$	47.2917	1.71432	0.857161	+	0.515048i	$0.172226\pi$
$762$	−22.5079	−0.815374
$763$	1.63495	0.0591893
$764$	14.1007	0.510145
$765$	0	0
$766$	30.8259	1.11378
$767$	−5.22238	−0.188569
$768$	−20.9706	−0.756710
$769$	6.39156	0.230486	0.115243	−	0.993337i	$-0.463235\pi$
$769$	6.39156	0.230486	0.115243	+	0.993337i	$0.463235\pi$
$770$	2.28130	0.0822125
$771$	−19.6603	−0.708049
$772$	−5.28093	−0.190065
$773$	3.67729	0.132263	0.0661315	−	0.997811i	$-0.478934\pi$
$773$	3.67729	0.132263	0.0661315	+	0.997811i	$0.478934\pi$
$774$	−11.7199	−0.421264
$775$	6.17311	0.221745
$776$	3.90347	0.140126
$777$	−1.62535	−0.0583092
$778$	−31.9625	−1.14591
$779$	1.82086	0.0652391
$780$	−8.99963	−0.322238
$781$	−32.9146	−1.17778
$782$	0	0
$783$	2.24264	0.0801454
$784$	33.6871	1.20311
$785$	29.2860	1.04526
$786$	19.3112	0.688808
$787$	−4.06409	−0.144869	−0.0724346	−	0.997373i	$-0.523077\pi$
$787$	−4.06409	−0.144869	−0.0724346	+	0.997373i	$0.523077\pi$
$788$	22.9178	0.816413
$789$	27.8721	0.992273
$790$	1.58669	0.0564519
$791$	0.254999	0.00906670
$792$	5.44155	0.193357
$793$	−32.6577	−1.15971
$794$	−11.9008	−0.422343
$795$	−3.42970	−0.121639
$796$	−23.2969	−0.825738
$797$	−13.8056	−0.489020	−0.244510	−	0.969647i	$-0.578627\pi$
$797$	−13.8056	−0.489020	−0.244510	+	0.969647i	$0.578627\pi$
$798$	−1.85070	−0.0655141
$799$	0	0
$800$	−16.2021	−0.572830
$801$	−7.64847	−0.270246
$802$	−38.9368	−1.37490
$803$	41.8596	1.47719
$804$	−10.0547	−0.354601
$805$	−0.846857	−0.0298478
$806$	−18.7661	−0.661006
$807$	−0.205327	−0.00722786
$808$	9.88989	0.347925
$809$	−18.8490	−0.662695	−0.331347	−	0.943509i	$-0.607503\pi$
$809$	−18.8490	−0.662695	−0.331347	+	0.943509i	$0.607503\pi$
$810$	2.98067	0.104730
$811$	2.59955	0.0912825	0.0456413	−	0.998958i	$-0.485467\pi$
$811$	2.59955	0.0912825	0.0456413	+	0.998958i	$0.485467\pi$
$812$	−0.482843	−0.0169445
$813$	8.21077	0.287964
$814$	−99.1744	−3.47606
$815$	33.4280	1.17093
$816$	0	0
$817$	−41.7291	−1.45992
$818$	51.0410	1.78461
$819$	−0.600582	−0.0209860
$820$	0.631394	0.0220492
$821$	13.0073	0.453960	0.226980	−	0.973899i	$-0.427115\pi$
$821$	13.0073	0.453960	0.226980	+	0.973899i	$0.427115\pi$
$822$	24.9314	0.869581
$823$	−21.6544	−0.754824	−0.377412	−	0.926046i	$-0.623186\pi$
$823$	−21.6544	−0.754824	−0.377412	+	0.926046i	$0.623186\pi$
$824$	8.20304	0.285767
$825$	12.0547	0.419690
$826$	−0.372395	−0.0129573
$827$	−47.8742	−1.66475	−0.832375	−	0.554213i	$-0.813019\pi$
$827$	−47.8742	−1.66475	−0.832375	+	0.554213i	$0.813019\pi$
$828$	4.87669	0.169477
$829$	12.9906	0.451181	0.225590	−	0.974222i	$-0.427569\pi$
$829$	12.9906	0.451181	0.225590	+	0.974222i	$0.427569\pi$
$830$	6.56775	0.227970
$831$	−23.5677	−0.817554
$832$	11.1580	0.386834
$833$	0	0
$834$	9.84482	0.340898
$835$	13.0483	0.451554
$836$	−46.7749	−1.61774
$837$	2.57446	0.0889864
$838$	22.2673	0.769210
$839$	−18.8727	−0.651557	−0.325779	−	0.945446i	$-0.605626\pi$
$839$	−18.8727	−0.651557	−0.325779	+	0.945446i	$0.605626\pi$
$840$	0.265818	0.00917159
$841$	−23.9706	−0.826571
$842$	−25.9024	−0.892657
$843$	10.1532	0.349695
$844$	−15.1161	−0.520319
$845$	−4.13381	−0.142207
$846$	−18.1480	−0.623942
$847$	2.17311	0.0746689
$848$	10.2658	0.352530
$849$	9.47918	0.325325
$850$	0	0
$851$	36.8151	1.26201
$852$	9.25903	0.317209
$853$	−6.03591	−0.206665	−0.103333	−	0.994647i	$-0.532951\pi$
$853$	−6.03591	−0.206665	−0.103333	+	0.994647i	$0.532951\pi$
$854$	−2.32874	−0.0796879
$855$	10.6128	0.362948
$856$	19.9881	0.683181
$857$	16.0835	0.549401	0.274701	−	0.961530i	$-0.411421\pi$
$857$	16.0835	0.549401	0.274701	+	0.961530i	$0.411421\pi$
$858$	−36.6458	−1.25107
$859$	−57.8556	−1.97401	−0.987003	−	0.160699i	$-0.948625\pi$
$859$	−57.8556	−1.97401	−0.987003	+	0.160699i	$0.948625\pi$
$860$	−14.4698	−0.493416
$861$	0.0421355	0.00143597
$862$	6.36332	0.216736
$863$	−7.56067	−0.257368	−0.128684	−	0.991686i	$-0.541075\pi$
$863$	−7.56067	−0.257368	−0.128684	+	0.991686i	$0.541075\pi$
$864$	−6.75699	−0.229877
$865$	−1.87223	−0.0636577
$866$	−10.2842	−0.349473
$867$	0	0
$868$	−0.554285	−0.0188137
$869$	2.67619	0.0907834
$870$	6.68457	0.226628
$871$	−28.0475	−0.950354
$872$	11.6241	0.393641
$873$	3.60634	0.122056
$874$	41.9194	1.41795
$875$	1.81679	0.0614186
$876$	−11.7753	−0.397850
$877$	−17.3660	−0.586407	−0.293204	−	0.956050i	$-0.594721\pi$
$877$	−17.3660	−0.586407	−0.293204	+	0.956050i	$0.594721\pi$
$878$	−32.4954	−1.09667
$879$	−9.28515	−0.313180
$880$	39.1572	1.31999
$881$	41.1018	1.38476	0.692378	−	0.721535i	$-0.256563\pi$
$881$	41.1018	1.38476	0.692378	+	0.721535i	$0.256563\pi$
$882$	12.8915	0.434079
$883$	28.3729	0.954824	0.477412	−	0.878680i	$-0.341575\pi$
$883$	28.3729	0.954824	0.477412	+	0.878680i	$0.341575\pi$
$884$	0	0
$885$	2.13548	0.0717833
$886$	−10.8580	−0.364782
$887$	21.5004	0.721914	0.360957	−	0.932583i	$-0.382450\pi$
$887$	21.5004	0.721914	0.360957	+	0.932583i	$0.382450\pi$
$888$	−11.5558	−0.387788
$889$	−1.85447	−0.0621970
$890$	−22.7976	−0.764176
$891$	5.02734	0.168422
$892$	7.66008	0.256479
$893$	−64.6165	−2.16231
$894$	17.2191	0.575893
$895$	−4.67271	−0.156192
$896$	−1.26173	−0.0421514
$897$	13.6035	0.454208
$898$	73.8756	2.46526
$899$	5.77359	0.192560
$900$	−3.39104	−0.113035
$901$	0	0
$902$	2.57099	0.0856046
$903$	−0.965630	−0.0321341
$904$	1.81297	0.0602985
$905$	−1.35937	−0.0451871
$906$	22.1052	0.734396
$907$	14.8069	0.491654	0.245827	−	0.969314i	$-0.420940\pi$
$907$	14.8069	0.491654	0.245827	+	0.969314i	$0.420940\pi$
$908$	17.3929	0.577205
$909$	9.13707	0.303058
$910$	−1.79014	−0.0593425
$911$	−47.5209	−1.57444	−0.787220	−	0.616673i	$-0.788480\pi$
$911$	−47.5209	−1.57444	−0.787220	+	0.616673i	$0.788480\pi$
$912$	−31.7662	−1.05188
$913$	11.0775	0.366611
$914$	32.6880	1.08122
$915$	13.3540	0.441471
$916$	42.5901	1.40722
$917$	1.59109	0.0525425
$918$	0	0
$919$	−52.4090	−1.72881	−0.864407	−	0.502793i	$-0.832306\pi$
$919$	−52.4090	−1.72881	−0.864407	+	0.502793i	$0.832306\pi$
$920$	−6.02092	−0.198504
$921$	27.1418	0.894351
$922$	−55.1856	−1.81744
$923$	25.8281	0.850141
$924$	−1.08239	−0.0356081
$925$	−25.5996	−0.841710
$926$	−17.4653	−0.573944
$927$	7.57862	0.248915
$928$	−15.1535	−0.497438
$929$	45.8975	1.50585	0.752924	−	0.658107i	$-0.228643\pi$
$929$	45.8975	1.50585	0.752924	+	0.658107i	$0.228643\pi$
$930$	7.67362	0.251628
$931$	45.9005	1.50433
$932$	12.4242	0.406968
$933$	2.58579	0.0846548
$934$	36.9725	1.20978
$935$	0	0
$936$	−4.26998	−0.139569
$937$	21.7579	0.710799	0.355400	−	0.934714i	$-0.384345\pi$
$937$	21.7579	0.710799	0.355400	+	0.934714i	$0.384345\pi$
$938$	−2.00000	−0.0653023
$939$	−25.6105	−0.835767
$940$	−22.4061	−0.730808
$941$	−54.1022	−1.76368	−0.881841	−	0.471548i	$-0.843696\pi$
$941$	−54.1022	−1.76368	−0.881841	+	0.471548i	$0.843696\pi$
$942$	−33.5457	−1.09298
$943$	−0.954393	−0.0310793
$944$	−6.39194	−0.208040
$945$	0.245584	0.00798884
$946$	−58.9200	−1.91565
$947$	−5.77608	−0.187697	−0.0938486	−	0.995586i	$-0.529917\pi$
$947$	−5.77608	−0.187697	−0.0938486	+	0.995586i	$0.529917\pi$
$948$	−0.752823	−0.0244506
$949$	−32.8471	−1.06626
$950$	−29.1489	−0.945716
$951$	−25.5982	−0.830078
$952$	0	0
$953$	−31.4698	−1.01941	−0.509704	−	0.860350i	$-0.670245\pi$
$953$	−31.4698	−1.01941	−0.509704	+	0.860350i	$0.670245\pi$
$954$	3.92856	0.127192
$955$	−16.0840	−0.520466
$956$	20.7183	0.670078
$957$	11.2745	0.364453
$958$	2.22784	0.0719784
$959$	2.05415	0.0663320
$960$	−4.56261	−0.147258
$961$	−24.3721	−0.786198
$962$	77.8221	2.50908
$963$	18.4666	0.595079
$964$	−23.9783	−0.772290
$965$	6.02371	0.193910
$966$	0.970034	0.0312103
$967$	−5.82126	−0.187199	−0.0935996	−	0.995610i	$-0.529837\pi$
$967$	−5.82126	−0.187199	−0.0935996	+	0.995610i	$0.529837\pi$
$968$	15.4502	0.496589
$969$	0	0
$970$	10.7493	0.345139
$971$	21.9049	0.702963	0.351481	−	0.936195i	$-0.385678\pi$
$971$	21.9049	0.702963	0.351481	+	0.936195i	$0.385678\pi$
$972$	−1.41421	−0.0453609
$973$	0.811136	0.0260038
$974$	−22.1016	−0.708180
$975$	−9.45929	−0.302940
$976$	−39.9715	−1.27946
$977$	−28.0473	−0.897312	−0.448656	−	0.893705i	$-0.648097\pi$
$977$	−28.0473	−0.897312	−0.448656	+	0.893705i	$0.648097\pi$
$978$	−38.2902	−1.22438
$979$	−38.4515	−1.22891
$980$	15.9163	0.508426
$981$	10.7392	0.342878
$982$	−57.7668	−1.84341
$983$	−31.3271	−0.999179	−0.499590	−	0.866262i	$-0.666516\pi$
$983$	−31.3271	−0.999179	−0.499590	+	0.866262i	$0.666516\pi$
$984$	0.299572	0.00955001
$985$	−26.1412	−0.832929
$986$	0	0
$987$	−1.49526	−0.0475945
$988$	36.7042	1.16772
$989$	21.8720	0.695491
$990$	14.9848	0.476249
$991$	17.9993	0.571765	0.285883	−	0.958265i	$-0.407713\pi$
$991$	17.9993	0.571765	0.285883	+	0.958265i	$0.407713\pi$
$992$	−17.3956	−0.552311
$993$	0.333172	0.0105729
$994$	1.84174	0.0584163
$995$	26.5737	0.842443
$996$	−3.11615	−0.0987389
$997$	55.5666	1.75981	0.879907	−	0.475147i	$-0.157605\pi$
$997$	55.5666	1.75981	0.879907	+	0.475147i	$0.157605\pi$
$998$	76.4214	2.41908
$999$	−10.6762	−0.337780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.a.m.1.1		4
3.2	odd	2		2601.2.a.bc.1.4		4
17.2	even	8		867.2.e.h.616.1		8
17.3	odd	16		867.2.h.g.757.1		8
17.4	even	4		867.2.d.e.577.8		8
17.5	odd	16		867.2.h.f.688.2		8
17.6	odd	16		867.2.h.g.733.1		8
17.7	odd	16		867.2.h.f.712.2		8
17.8	even	8		867.2.e.i.829.4		8
17.9	even	8		867.2.e.h.829.4		8
17.10	odd	16		867.2.h.b.712.2		8
17.11	odd	16		51.2.h.a.19.1	✓	8
17.12	odd	16		867.2.h.b.688.2		8
17.13	even	4		867.2.d.e.577.7		8
17.14	odd	16		51.2.h.a.43.1	yes	8
17.15	even	8		867.2.e.i.616.1		8
17.16	even	2		867.2.a.n.1.1		4
51.11	even	16		153.2.l.e.19.2		8
51.14	even	16		153.2.l.e.145.2		8
51.50	odd	2		2601.2.a.bd.1.4		4
68.11	even	16		816.2.bq.a.529.1		8
68.31	even	16		816.2.bq.a.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.1	✓	8	17.11	odd	16
51.2.h.a.43.1	yes	8	17.14	odd	16
153.2.l.e.19.2		8	51.11	even	16
153.2.l.e.145.2		8	51.14	even	16
816.2.bq.a.145.1		8	68.31	even	16
816.2.bq.a.529.1		8	68.11	even	16
867.2.a.m.1.1		4	1.1	even	1	trivial
867.2.a.n.1.1		4	17.16	even	2
867.2.d.e.577.7		8	17.13	even	4
867.2.d.e.577.8		8	17.4	even	4
867.2.e.h.616.1		8	17.2	even	8
867.2.e.h.829.4		8	17.9	even	8
867.2.e.i.616.1		8	17.15	even	8
867.2.e.i.829.4		8	17.8	even	8
867.2.h.b.688.2		8	17.12	odd	16
867.2.h.b.712.2		8	17.10	odd	16
867.2.h.f.688.2		8	17.5	odd	16
867.2.h.f.712.2		8	17.7	odd	16
867.2.h.g.733.1		8	17.6	odd	16
867.2.h.g.757.1		8	17.3	odd	16
2601.2.a.bc.1.4		4	3.2	odd	2
2601.2.a.bd.1.4		4	51.50	odd	2

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.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84776 q^{2} -1.00000 q^{3} +1.41421 q^{4} -1.61313 q^{5} +1.84776 q^{6} +0.152241 q^{7} +1.08239 q^{8} +1.00000 q^{9} +2.98067 q^{10} +5.02734 q^{11} -1.41421 q^{12} -3.94495 q^{13} -0.281305 q^{14} +1.61313 q^{15} -4.82843 q^{16} -1.84776 q^{18} -6.57900 q^{19} -2.28130 q^{20} -0.152241 q^{21} -9.28931 q^{22} +3.44834 q^{23} -1.08239 q^{24} -2.39782 q^{25} +7.28931 q^{26} -1.00000 q^{27} +0.215301 q^{28} -2.24264 q^{29} -2.98067 q^{30} -2.57446 q^{31} +6.75699 q^{32} -5.02734 q^{33} -0.245584 q^{35} +1.41421 q^{36} +10.6762 q^{37} +12.1564 q^{38} +3.94495 q^{39} -1.74603 q^{40} -0.276769 q^{41} +0.281305 q^{42} +6.34277 q^{43} +7.10973 q^{44} -1.61313 q^{45} -6.37170 q^{46} +9.82164 q^{47} +4.82843 q^{48} -6.97682 q^{49} +4.43060 q^{50} -5.57900 q^{52} -2.12612 q^{53} +1.84776 q^{54} -8.10973 q^{55} +0.164784 q^{56} +6.57900 q^{57} +4.14386 q^{58} +1.32381 q^{59} +2.28130 q^{60} +8.27836 q^{61} +4.75699 q^{62} +0.152241 q^{63} -2.82843 q^{64} +6.36370 q^{65} +9.28931 q^{66} +7.10973 q^{67} -3.44834 q^{69} +0.453780 q^{70} -6.54712 q^{71} +1.08239 q^{72} +8.32638 q^{73} -19.7270 q^{74} +2.39782 q^{75} -9.30411 q^{76} +0.765367 q^{77} -7.28931 q^{78} +0.532327 q^{79} +7.78886 q^{80} +1.00000 q^{81} +0.511402 q^{82} +2.20345 q^{83} -0.215301 q^{84} -11.7199 q^{86} +2.24264 q^{87} +5.44155 q^{88} -7.64847 q^{89} +2.98067 q^{90} -0.600582 q^{91} +4.87669 q^{92} +2.57446 q^{93} -18.1480 q^{94} +10.6128 q^{95} -6.75699 q^{96} +3.60634 q^{97} +12.8915 q^{98} +5.02734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{5} + 8 q^{7} + 4 q^{9} + 8 q^{10} + 4 q^{11} - 4 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 12 q^{23} - 4 q^{27} + 8 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{33}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^5 + 8 * q^7 + 4 * q^9 + 8 * q^10 + 4 * q^11 - 4 * q^13 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 12 * q^23 - 4 * q^27 + 8 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^33 + 16 * q^35 + 24 * q^37 + 16 * q^38 + 4 * q^39 + 12 * q^41 - 8 * q^42 + 4 * q^43 + 8 * q^44 + 4 * q^45 + 8 * q^46 + 8 * q^47 + 8 * q^48 - 4 * q^49 + 16 * q^50 - 8 * q^52 + 8 * q^53 - 12 * q^55 - 8 * q^56 + 12 * q^57 + 24 * q^59 + 24 * q^61 - 8 * q^62 + 8 * q^63 + 12 * q^65 + 8 * q^66 + 8 * q^67 - 12 * q^69 + 24 * q^70 - 24 * q^71 + 8 * q^73 - 8 * q^74 - 8 * q^76 - 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 - 16 * q^86 - 8 * q^87 + 16 * q^89 + 8 * q^90 - 8 * q^91 - 8 * q^93 - 16 * q^94 - 12 * q^95 - 16 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

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Database

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