LMFDB - Embedded newform 2325.2.c.l.1024.3

Error: no document with id 226758600 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2325,2,Mod(1024,2325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2325.1024"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2325 = 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2325.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-10,0,6,0,0,-6,0,4,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$18.5652184699$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 465)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1024.3
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	2325.1024
Dual form			2325.2.c.l.1024.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.21432i q^{2} -1.00000i q^{3} +0.525428 q^{4} -1.21432 q^{6} -1.59210i q^{7} -3.06668i q^{8} -1.00000 q^{9} +0.622216 q^{11} -0.525428i q^{12} -0.214320i q^{13} -1.93332 q^{14} -2.67307 q^{16} +3.52543i q^{17} +1.21432i q^{18} -1.80642 q^{19} -1.59210 q^{21} -0.755569i q^{22} -6.90321i q^{23} -3.06668 q^{24} -0.260253 q^{26} +1.00000i q^{27} -0.836535i q^{28} -9.73975 q^{29} -1.00000 q^{31} -2.88739i q^{32} -0.622216i q^{33} +4.28100 q^{34} -0.525428 q^{36} -4.83654i q^{37} +2.19358i q^{38} -0.214320 q^{39} -7.47949 q^{41} +1.93332i q^{42} -8.23506i q^{43} +0.326929 q^{44} -8.38271 q^{46} +11.4652i q^{47} +2.67307i q^{48} +4.46520 q^{49} +3.52543 q^{51} -0.112610i q^{52} -13.7605i q^{53} +1.21432 q^{54} -4.88247 q^{56} +1.80642i q^{57} +11.8272i q^{58} +4.26025 q^{59} +2.85728 q^{61} +1.21432i q^{62} +1.59210i q^{63} -8.85236 q^{64} -0.755569 q^{66} -2.08097i q^{67} +1.85236i q^{68} -6.90321 q^{69} +1.31111 q^{71} +3.06668i q^{72} +1.65233i q^{73} -5.87310 q^{74} -0.949145 q^{76} -0.990632i q^{77} +0.260253i q^{78} +5.19850 q^{79} +1.00000 q^{81} +9.08250i q^{82} +5.65878i q^{83} -0.836535 q^{84} -10.0000 q^{86} +9.73975i q^{87} -1.90813i q^{88} +1.93332 q^{89} -0.341219 q^{91} -3.62714i q^{92} +1.00000i q^{93} +13.9224 q^{94} -2.88739 q^{96} +6.91750i q^{97} -5.42219i q^{98} -0.622216 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 6 q^{6} - 6 q^{9} + 4 q^{11} - 12 q^{14} + 10 q^{16} + 16 q^{19} + 4 q^{21} - 18 q^{24} - 28 q^{26} - 32 q^{29} - 6 q^{31} + 12 q^{34} + 10 q^{36} + 12 q^{39} + 8 q^{41} + 28 q^{44} + 16 q^{46}+ \cdots - 4 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 6 * q^6 - 6 * q^9 + 4 * q^11 - 12 * q^14 + 10 * q^16 + 16 * q^19 + 4 * q^21 - 18 * q^24 - 28 * q^26 - 32 * q^29 - 6 * q^31 + 12 * q^34 + 10 * q^36 + 12 * q^39 + 8 * q^41 + 28 * q^44 + 16 * q^46 - 14 * q^49 + 8 * q^51 - 6 * q^54 - 56 * q^56 + 52 * q^59 - 36 * q^61 - 66 * q^64 - 4 * q^66 - 28 * q^69 + 8 * q^71 - 8 * q^74 - 32 * q^76 - 8 * q^79 + 6 * q^81 + 8 * q^84 - 60 * q^86 + 12 * q^89 - 16 * q^91 - 8 * q^94 + 22 * q^96 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2325\mathbb{Z}\right)^\times$.

$n$	$652$	$776$	$1801$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	− 1.21432i	− 0.858654i	−0.903149	−	0.429327i	$-0.858751\pi$
$2$	− 1.21432i	− 0.858654i	0.903149	−	0.429327i	$-0.141249\pi$
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	0.525428	0.262714
$5$	0	0
$5$	0	0
$6$	−1.21432	−0.495744
$7$	− 1.59210i	− 0.601759i	−0.953662	−	0.300879i	$-0.902720\pi$
$7$	− 1.59210i	− 0.601759i	0.953662	−	0.300879i	$-0.0972802\pi$
$8$	− 3.06668i	− 1.08423i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	0.622216	0.187605	0.0938025	−	0.995591i	$-0.470098\pi$
$11$	0.622216	0.187605	0.0938025	+	0.995591i	$0.470098\pi$
$12$	− 0.525428i	− 0.151678i
$13$	− 0.214320i	− 0.0594416i	−0.999558	−	0.0297208i	$-0.990538\pi$
$13$	− 0.214320i	− 0.0594416i	0.999558	−	0.0297208i	$-0.00946182\pi$
$14$	−1.93332	−0.516702
$15$	0	0
$16$	−2.67307	−0.668268
$17$	3.52543i	0.855042i	0.904005	+	0.427521i	$0.140613\pi$
$17$	3.52543i	0.855042i	−0.904005	+	0.427521i	$0.859387\pi$
$18$	1.21432i	0.286218i
$19$	−1.80642	−0.414422	−0.207211	−	0.978296i	$-0.566439\pi$
$19$	−1.80642	−0.414422	−0.207211	+	0.978296i	$0.566439\pi$
$20$	0	0
$21$	−1.59210	−0.347426
$22$	− 0.755569i	− 0.161088i
$23$	− 6.90321i	− 1.43942i	−0.694275	−	0.719710i	$-0.744275\pi$
$23$	− 6.90321i	− 1.43942i	0.694275	−	0.719710i	$-0.255725\pi$
$24$	−3.06668	−0.625983
$25$	0	0
$26$	−0.260253	−0.0510398
$27$	1.00000i	0.192450i
$28$	− 0.836535i	− 0.158090i
$29$	−9.73975	−1.80863	−0.904313	−	0.426870i	$-0.859616\pi$
$29$	−9.73975	−1.80863	−0.904313	+	0.426870i	$0.859616\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	− 2.88739i	− 0.510423i
$33$	− 0.622216i	− 0.108314i
$34$	4.28100	0.734185
$35$	0	0
$36$	−0.525428	−0.0875713
$37$	− 4.83654i	− 0.795122i	−0.917576	−	0.397561i	$-0.869857\pi$
$37$	− 4.83654i	− 0.795122i	0.917576	−	0.397561i	$-0.130143\pi$
$38$	2.19358i	0.355845i
$39$	−0.214320	−0.0343186
$40$	0	0
$41$	−7.47949	−1.16810	−0.584050	−	0.811717i	$-0.698533\pi$
$41$	−7.47949	−1.16810	−0.584050	+	0.811717i	$0.698533\pi$
$42$	1.93332i	0.298318i
$43$	− 8.23506i	− 1.25584i	−0.778280	−	0.627918i	$-0.783907\pi$
$43$	− 8.23506i	− 1.25584i	0.778280	−	0.627918i	$-0.216093\pi$
$44$	0.326929	0.0492864
$45$	0	0
$46$	−8.38271	−1.23596
$47$	11.4652i	1.67237i	0.548446	+	0.836186i	$0.315220\pi$
$47$	11.4652i	1.67237i	−0.548446	+	0.836186i	$0.684780\pi$
$48$	2.67307i	0.385825i
$49$	4.46520	0.637886
$50$	0	0
$51$	3.52543	0.493659
$52$	− 0.112610i	− 0.0156161i
$53$	− 13.7605i	− 1.89015i	−0.326855	−	0.945074i	$-0.605989\pi$
$53$	− 13.7605i	− 1.89015i	0.326855	−	0.945074i	$-0.394011\pi$
$54$	1.21432	0.165248
$55$	0	0
$56$	−4.88247	−0.652447
$57$	1.80642i	0.239267i
$58$	11.8272i	1.55298i
$59$	4.26025	0.554638	0.277319	−	0.960778i	$-0.410554\pi$
$59$	4.26025	0.554638	0.277319	+	0.960778i	$0.410554\pi$
$60$	0	0
$61$	2.85728	0.365837	0.182919	−	0.983128i	$-0.441446\pi$
$61$	2.85728	0.365837	0.182919	+	0.983128i	$0.441446\pi$
$62$	1.21432i	0.154219i
$63$	1.59210i	0.200586i
$64$	−8.85236	−1.10654
$65$	0	0
$66$	−0.755569	−0.0930041
$67$	− 2.08097i	− 0.254231i	−0.991888	−	0.127115i	$-0.959428\pi$
$67$	− 2.08097i	− 0.254231i	0.991888	−	0.127115i	$-0.0405718\pi$
$68$	1.85236i	0.224631i
$69$	−6.90321	−0.831049
$70$	0	0
$71$	1.31111	0.155600	0.0777999	−	0.996969i	$-0.475210\pi$
$71$	1.31111	0.155600	0.0777999	+	0.996969i	$0.475210\pi$
$72$	3.06668i	0.361411i
$73$	1.65233i	0.193390i	0.995314	+	0.0966951i	$0.0308272\pi$
$73$	1.65233i	0.193390i	−0.995314	+	0.0966951i	$0.969173\pi$
$74$	−5.87310	−0.682734
$75$	0	0
$76$	−0.949145	−0.108874
$77$	− 0.990632i	− 0.112893i
$78$	0.260253i	0.0294678i
$79$	5.19850	0.584877	0.292438	−	0.956284i	$-0.405533\pi$
$79$	5.19850	0.584877	0.292438	+	0.956284i	$0.405533\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.08250i	1.00299i
$83$	5.65878i	0.621132i	0.950552	+	0.310566i	$0.100519\pi$
$83$	5.65878i	0.621132i	−0.950552	+	0.310566i	$0.899481\pi$
$84$	−0.836535	−0.0912735
$85$	0	0
$86$	−10.0000	−1.07833
$87$	9.73975i	1.04421i
$88$	− 1.90813i	− 0.203408i
$89$	1.93332	0.204932	0.102466	−	0.994737i	$-0.467327\pi$
$89$	1.93332	0.204932	0.102466	+	0.994737i	$0.467327\pi$
$90$	0	0
$91$	−0.341219	−0.0357695
$92$	− 3.62714i	− 0.378155i
$93$	1.00000i	0.103695i
$94$	13.9224	1.43599
$95$	0	0
$96$	−2.88739	−0.294693
$97$	6.91750i	0.702366i	0.936307	+	0.351183i	$0.114220\pi$
$97$	6.91750i	0.702366i	−0.936307	+	0.351183i	$0.885780\pi$
$98$	− 5.42219i	− 0.547723i
$99$	−0.622216	−0.0625350
$100$	0	0
$101$	−9.28592	−0.923983	−0.461992	−	0.886884i	$-0.652865\pi$
$101$	−9.28592	−0.923983	−0.461992	+	0.886884i	$0.652865\pi$
$102$	− 4.28100i	− 0.423882i
$103$	− 0.274543i	− 0.0270515i	−0.999909	−	0.0135258i	$-0.995694\pi$
$103$	− 0.274543i	− 0.0270515i	0.999909	−	0.0135258i	$-0.00430551\pi$
$104$	−0.657249	−0.0644486
$105$	0	0
$106$	−16.7096	−1.62298
$107$	− 8.18913i	− 0.791673i	−0.918321	−	0.395837i	$-0.870455\pi$
$107$	− 8.18913i	− 0.791673i	0.918321	−	0.395837i	$-0.129545\pi$
$108$	0.525428i	0.0505593i
$109$	9.13828	0.875288	0.437644	−	0.899148i	$-0.355813\pi$
$109$	9.13828	0.875288	0.437644	+	0.899148i	$0.355813\pi$
$110$	0	0
$111$	−4.83654	−0.459064
$112$	4.25581i	0.402136i
$113$	− 7.67307i	− 0.721822i	−0.932600	−	0.360911i	$-0.882466\pi$
$113$	− 7.67307i	− 0.721822i	0.932600	−	0.360911i	$-0.117534\pi$
$114$	2.19358	0.205447
$115$	0	0
$116$	−5.11753	−0.475151
$117$	0.214320i	0.0198139i
$118$	− 5.17331i	− 0.476242i
$119$	5.61285	0.514529
$120$	0	0
$121$	−10.6128	−0.964804
$122$	− 3.46965i	− 0.314127i
$123$	7.47949i	0.674403i
$124$	−0.525428	−0.0471848
$125$	0	0
$126$	1.93332	0.172234
$127$	13.6731i	1.21329i	0.794973	+	0.606644i	$0.207485\pi$
$127$	13.6731i	1.21329i	−0.794973	+	0.606644i	$0.792515\pi$
$128$	4.97481i	0.439715i
$129$	−8.23506	−0.725057
$130$	0	0
$131$	−22.2701	−1.94575	−0.972874	−	0.231337i	$-0.925690\pi$
$131$	−22.2701	−1.94575	−0.972874	+	0.231337i	$0.925690\pi$
$132$	− 0.326929i	− 0.0284555i
$133$	2.87601i	0.249382i
$134$	−2.52696	−0.218296
$135$	0	0
$136$	10.8113	0.927065
$137$	− 18.1891i	− 1.55400i	−0.629499	−	0.777001i	$-0.716740\pi$
$137$	− 18.1891i	− 1.55400i	0.629499	−	0.777001i	$-0.283260\pi$
$138$	8.38271i	0.713583i
$139$	4.13335	0.350586	0.175293	−	0.984516i	$-0.443913\pi$
$139$	4.13335	0.350586	0.175293	+	0.984516i	$0.443913\pi$
$140$	0	0
$141$	11.4652	0.965544
$142$	− 1.59210i	− 0.133606i
$143$	− 0.133353i	− 0.0111515i
$144$	2.67307	0.222756
$145$	0	0
$146$	2.00645	0.166055
$147$	− 4.46520i	− 0.368284i
$148$	− 2.54125i	− 0.208889i
$149$	−6.23506	−0.510796	−0.255398	−	0.966836i	$-0.582207\pi$
$149$	−6.23506	−0.510796	−0.255398	+	0.966836i	$0.582207\pi$
$150$	0	0
$151$	8.38271	0.682175	0.341087	−	0.940032i	$-0.389205\pi$
$151$	8.38271	0.682175	0.341087	+	0.940032i	$0.389205\pi$
$152$	5.53972i	0.449330i
$153$	− 3.52543i	− 0.285014i
$154$	−1.20294	−0.0969360
$155$	0	0
$156$	−0.112610	−0.00901598
$157$	− 10.2351i	− 0.816847i	−0.912793	−	0.408423i	$-0.866079\pi$
$157$	− 10.2351i	− 0.816847i	0.912793	−	0.408423i	$-0.133921\pi$
$158$	− 6.31264i	− 0.502207i
$159$	−13.7605	−1.09128
$160$	0	0
$161$	−10.9906	−0.866183
$162$	− 1.21432i	− 0.0954060i
$163$	− 5.82717i	− 0.456419i	−0.973612	−	0.228209i	$-0.926713\pi$
$163$	− 5.82717i	− 0.456419i	0.973612	−	0.228209i	$-0.0732871\pi$
$164$	−3.92993	−0.306876
$165$	0	0
$166$	6.87157	0.533337
$167$	23.1842i	1.79405i	0.441982	+	0.897024i	$0.354276\pi$
$167$	23.1842i	1.79405i	−0.441982	+	0.897024i	$0.645724\pi$
$168$	4.88247i	0.376691i
$169$	12.9541	0.996467
$170$	0	0
$171$	1.80642	0.138141
$172$	− 4.32693i	− 0.329925i
$173$	− 1.57136i	− 0.119468i	−0.998214	−	0.0597342i	$-0.980975\pi$
$173$	− 1.57136i	− 0.119468i	0.998214	−	0.0597342i	$-0.0190253\pi$
$174$	11.8272	0.896615
$175$	0	0
$176$	−1.66323	−0.125370
$177$	− 4.26025i	− 0.320220i
$178$	− 2.34767i	− 0.175966i
$179$	−1.53972	−0.115084	−0.0575420	−	0.998343i	$-0.518326\pi$
$179$	−1.53972	−0.115084	−0.0575420	+	0.998343i	$0.518326\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0.414349i	0.0307136i
$183$	− 2.85728i	− 0.211216i
$184$	−21.1699	−1.56067
$185$	0	0
$186$	1.21432	0.0890382
$187$	2.19358i	0.160410i
$188$	6.02413i	0.439355i
$189$	1.59210	0.115809
$190$	0	0
$191$	9.11753	0.659721	0.329861	−	0.944030i	$-0.392998\pi$
$191$	9.11753	0.659721	0.329861	+	0.944030i	$0.392998\pi$
$192$	8.85236i	0.638864i
$193$	4.72393i	0.340036i	0.985441	+	0.170018i	$0.0543825\pi$
$193$	4.72393i	0.340036i	−0.985441	+	0.170018i	$0.945617\pi$
$194$	8.40006	0.603089
$195$	0	0
$196$	2.34614	0.167582
$197$	15.7003i	1.11860i	0.828966	+	0.559299i	$0.188930\pi$
$197$	15.7003i	1.11860i	−0.828966	+	0.559299i	$0.811070\pi$
$198$	0.755569i	0.0536959i
$199$	−6.28100	−0.445248	−0.222624	−	0.974904i	$-0.571462\pi$
$199$	−6.28100	−0.445248	−0.222624	+	0.974904i	$0.571462\pi$
$200$	0	0
$201$	−2.08097	−0.146780
$202$	11.2761i	0.793382i
$203$	15.5067i	1.08836i
$204$	1.85236	0.129691
$205$	0	0
$206$	−0.333383	−0.0232279
$207$	6.90321i	0.479806i
$208$	0.572892i	0.0397229i
$209$	−1.12399	−0.0777477
$210$	0	0
$211$	19.4795	1.34102	0.670512	−	0.741899i	$-0.266075\pi$
$211$	19.4795	1.34102	0.670512	+	0.741899i	$0.266075\pi$
$212$	− 7.23014i	− 0.496568i
$213$	− 1.31111i	− 0.0898356i
$214$	−9.94422	−0.679773
$215$	0	0
$216$	3.06668	0.208661
$217$	1.59210i	0.108079i
$218$	− 11.0968i	− 0.751569i
$219$	1.65233	0.111654
$220$	0	0
$221$	0.755569	0.0508251
$222$	5.87310i	0.394177i
$223$	15.4193i	1.03255i	0.856423	+	0.516275i	$0.172682\pi$
$223$	15.4193i	1.03255i	−0.856423	+	0.516275i	$0.827318\pi$
$224$	−4.59703	−0.307152
$225$	0	0
$226$	−9.31756	−0.619795
$227$	− 12.8430i	− 0.852419i	−0.904624	−	0.426210i	$-0.859849\pi$
$227$	− 12.8430i	− 0.852419i	0.904624	−	0.426210i	$-0.140151\pi$
$228$	0.949145i	0.0628587i
$229$	3.08250	0.203697	0.101849	−	0.994800i	$-0.467524\pi$
$229$	3.08250	0.203697	0.101849	+	0.994800i	$0.467524\pi$
$230$	0	0
$231$	−0.990632	−0.0651788
$232$	29.8687i	1.96097i
$233$	− 8.76986i	− 0.574533i	−0.957851	−	0.287266i	$-0.907254\pi$
$233$	− 8.76986i	− 0.574533i	0.957851	−	0.287266i	$-0.0927465\pi$
$234$	0.260253	0.0170133
$235$	0	0
$236$	2.23845	0.145711
$237$	− 5.19850i	− 0.337679i
$238$	− 6.81579i	− 0.441802i
$239$	−3.12399	−0.202074	−0.101037	−	0.994883i	$-0.532216\pi$
$239$	−3.12399	−0.202074	−0.101037	+	0.994883i	$0.532216\pi$
$240$	0	0
$241$	29.5625	1.90429	0.952143	−	0.305653i	$-0.0988747\pi$
$241$	29.5625	1.90429	0.952143	+	0.305653i	$0.0988747\pi$
$242$	12.8874i	0.828433i
$243$	− 1.00000i	− 0.0641500i
$244$	1.50129	0.0961104
$245$	0	0
$246$	9.08250	0.579079
$247$	0.387152i	0.0246339i
$248$	3.06668i	0.194734i
$249$	5.65878	0.358611
$250$	0	0
$251$	21.4193	1.35197	0.675986	−	0.736914i	$-0.263718\pi$
$251$	21.4193	1.35197	0.675986	+	0.736914i	$0.263718\pi$
$252$	0.836535i	0.0526968i
$253$	− 4.29529i	− 0.270042i
$254$	16.6035	1.04179
$255$	0	0
$256$	−11.6637	−0.728981
$257$	− 17.6271i	− 1.09955i	−0.835313	−	0.549775i	$-0.814713\pi$
$257$	− 17.6271i	− 1.09955i	0.835313	−	0.549775i	$-0.185287\pi$
$258$	10.0000i	0.622573i
$259$	−7.70027	−0.478471
$260$	0	0
$261$	9.73975	0.602875
$262$	27.0430i	1.67072i
$263$	14.7052i	0.906761i	0.891317	+	0.453380i	$0.149782\pi$
$263$	14.7052i	0.906761i	−0.891317	+	0.453380i	$0.850218\pi$
$264$	−1.90813	−0.117438
$265$	0	0
$266$	3.49240	0.214133
$267$	− 1.93332i	− 0.118317i
$268$	− 1.09340i	− 0.0667899i
$269$	−1.35260	−0.0824692	−0.0412346	−	0.999149i	$-0.513129\pi$
$269$	−1.35260	−0.0824692	−0.0412346	+	0.999149i	$0.513129\pi$
$270$	0	0
$271$	12.1334	0.737049	0.368524	−	0.929618i	$-0.379863\pi$
$271$	12.1334	0.737049	0.368524	+	0.929618i	$0.379863\pi$
$272$	− 9.42372i	− 0.571397i
$273$	0.341219i	0.0206515i
$274$	−22.0874	−1.33435
$275$	0	0
$276$	−3.62714	−0.218328
$277$	18.9382i	1.13789i	0.822376	+	0.568944i	$0.192648\pi$
$277$	18.9382i	1.13789i	−0.822376	+	0.568944i	$0.807352\pi$
$278$	− 5.01921i	− 0.301032i
$279$	1.00000	0.0598684
$280$	0	0
$281$	12.9175	0.770594	0.385297	−	0.922793i	$-0.374099\pi$
$281$	12.9175	0.770594	0.385297	+	0.922793i	$0.374099\pi$
$282$	− 13.9224i	− 0.829068i
$283$	− 26.5827i	− 1.58018i	−0.612991	−	0.790090i	$-0.710034\pi$
$283$	− 26.5827i	− 1.58018i	0.612991	−	0.790090i	$-0.289966\pi$
$284$	0.688892	0.0408782
$285$	0	0
$286$	−0.161933	−0.00957532
$287$	11.9081i	0.702915i
$288$	2.88739i	0.170141i
$289$	4.57136	0.268904
$290$	0	0
$291$	6.91750	0.405511
$292$	0.868178i	0.0508063i
$293$	7.99555i	0.467105i	0.972344	+	0.233553i	$0.0750351\pi$
$293$	7.99555i	0.467105i	−0.972344	+	0.233553i	$0.924965\pi$
$294$	−5.42219	−0.316228
$295$	0	0
$296$	−14.8321	−0.862098
$297$	0.622216i	0.0361046i
$298$	7.57136i	0.438597i
$299$	−1.47949	−0.0855614
$300$	0	0
$301$	−13.1111	−0.755710
$302$	− 10.1793i	− 0.585752i
$303$	9.28592i	0.533462i
$304$	4.82870	0.276945
$305$	0	0
$306$	−4.28100	−0.244728
$307$	− 17.3669i	− 0.991180i	−0.868556	−	0.495590i	$-0.834952\pi$
$307$	− 17.3669i	− 0.991180i	0.868556	−	0.495590i	$-0.165048\pi$
$308$	− 0.520505i	− 0.0296585i
$309$	−0.274543	−0.0156182
$310$	0	0
$311$	−27.5877	−1.56435	−0.782176	−	0.623057i	$-0.785890\pi$
$311$	−27.5877	−1.56435	−0.782176	+	0.623057i	$0.785890\pi$
$312$	0.657249i	0.0372094i
$313$	13.7255i	0.775809i	0.921700	+	0.387904i	$0.126801\pi$
$313$	13.7255i	0.775809i	−0.921700	+	0.387904i	$0.873199\pi$
$314$	−12.4286	−0.701389
$315$	0	0
$316$	2.73143	0.153655
$317$	− 24.9447i	− 1.40103i	−0.713636	−	0.700517i	$-0.752953\pi$
$317$	− 24.9447i	− 1.40103i	0.713636	−	0.700517i	$-0.247047\pi$
$318$	16.7096i	0.937030i
$319$	−6.06022	−0.339307
$320$	0	0
$321$	−8.18913	−0.457073
$322$	13.3461i	0.743751i
$323$	− 6.36842i	− 0.354348i
$324$	0.525428	0.0291904
$325$	0	0
$326$	−7.07604	−0.391906
$327$	− 9.13828i	− 0.505348i
$328$	22.9372i	1.26649i
$329$	18.2538	1.00636
$330$	0	0
$331$	19.1798	1.05422	0.527108	−	0.849799i	$-0.323276\pi$
$331$	19.1798	1.05422	0.527108	+	0.849799i	$0.323276\pi$
$332$	2.97328i	0.163180i
$333$	4.83654i	0.265041i
$334$	28.1530	1.54047
$335$	0	0
$336$	4.25581	0.232173
$337$	− 25.3067i	− 1.37854i	−0.724504	−	0.689271i	$-0.757931\pi$
$337$	− 25.3067i	− 1.37854i	0.724504	−	0.689271i	$-0.242069\pi$
$338$	− 15.7304i	− 0.855620i
$339$	−7.67307	−0.416744
$340$	0	0
$341$	−0.622216	−0.0336949
$342$	− 2.19358i	− 0.118615i
$343$	− 18.2538i	− 0.985613i
$344$	−25.2543	−1.36162
$345$	0	0
$346$	−1.90813	−0.102582
$347$	19.0638i	1.02340i	0.859165	+	0.511698i	$0.170983\pi$
$347$	19.0638i	1.02340i	−0.859165	+	0.511698i	$0.829017\pi$
$348$	5.11753i	0.274328i
$349$	1.23014	0.0658479	0.0329240	−	0.999458i	$-0.489518\pi$
$349$	1.23014	0.0658479	0.0329240	+	0.999458i	$0.489518\pi$
$350$	0	0
$351$	0.214320	0.0114395
$352$	− 1.79658i	− 0.0957580i
$353$	− 4.50315i	− 0.239679i	−0.992793	−	0.119839i	$-0.961762\pi$
$353$	− 4.50315i	− 0.239679i	0.992793	−	0.119839i	$-0.0382379\pi$
$354$	−5.17331	−0.274958
$355$	0	0
$356$	1.01582	0.0538384
$357$	− 5.61285i	− 0.297063i
$358$	1.86971i	0.0988172i
$359$	−18.9240	−0.998768	−0.499384	−	0.866381i	$-0.666440\pi$
$359$	−18.9240	−0.998768	−0.499384	+	0.866381i	$0.666440\pi$
$360$	0	0
$361$	−15.7368	−0.828254
$362$	− 2.42864i	− 0.127646i
$363$	10.6128i	0.557030i
$364$	−0.179286	−0.00939714
$365$	0	0
$366$	−3.46965	−0.181362
$367$	− 9.71456i	− 0.507096i	−0.967323	−	0.253548i	$-0.918402\pi$
$367$	− 9.71456i	− 0.507096i	0.967323	−	0.253548i	$-0.0815975\pi$
$368$	18.4528i	0.961917i
$369$	7.47949	0.389367
$370$	0	0
$371$	−21.9081	−1.13741
$372$	0.525428i	0.0272421i
$373$	35.1941i	1.82228i	0.412098	+	0.911139i	$0.364796\pi$
$373$	35.1941i	1.82228i	−0.412098	+	0.911139i	$0.635204\pi$
$374$	2.66370	0.137737
$375$	0	0
$376$	35.1601	1.81324
$377$	2.08742i	0.107508i
$378$	− 1.93332i	− 0.0994394i
$379$	22.6637	1.16416	0.582078	−	0.813133i	$-0.302240\pi$
$379$	22.6637	1.16416	0.582078	+	0.813133i	$0.302240\pi$
$380$	0	0
$381$	13.6731	0.700493
$382$	− 11.0716i	− 0.566472i
$383$	− 28.7926i	− 1.47123i	−0.677398	−	0.735617i	$-0.736892\pi$
$383$	− 28.7926i	− 1.47123i	0.677398	−	0.735617i	$-0.263108\pi$
$384$	4.97481	0.253870
$385$	0	0
$386$	5.73636	0.291973
$387$	8.23506i	0.418612i
$388$	3.63465i	0.184521i
$389$	25.0672	1.27096	0.635478	−	0.772119i	$-0.280803\pi$
$389$	25.0672	1.27096	0.635478	+	0.772119i	$0.280803\pi$
$390$	0	0
$391$	24.3368	1.23076
$392$	− 13.6933i	− 0.691618i
$393$	22.2701i	1.12338i
$394$	19.0651	0.960488
$395$	0	0
$396$	−0.326929	−0.0164288
$397$	− 29.0509i	− 1.45802i	−0.684503	−	0.729010i	$-0.739981\pi$
$397$	− 29.0509i	− 1.45802i	0.684503	−	0.729010i	$-0.260019\pi$
$398$	7.62714i	0.382314i
$399$	2.87601	0.143981
$400$	0	0
$401$	11.2607	0.562334	0.281167	−	0.959659i	$-0.409279\pi$
$401$	11.2607	0.562334	0.281167	+	0.959659i	$0.409279\pi$
$402$	2.52696i	0.126033i
$403$	0.214320i	0.0106760i
$404$	−4.87908	−0.242743
$405$	0	0
$406$	18.8301	0.934521
$407$	− 3.00937i	− 0.149169i
$408$	− 10.8113i	− 0.535241i
$409$	25.6128	1.26647	0.633237	−	0.773958i	$-0.281726\pi$
$409$	25.6128	1.26647	0.633237	+	0.773958i	$0.281726\pi$
$410$	0	0
$411$	−18.1891	−0.897204
$412$	− 0.144252i	− 0.00710680i
$413$	− 6.78277i	− 0.333758i
$414$	8.38271	0.411988
$415$	0	0
$416$	−0.618825	−0.0303404
$417$	− 4.13335i	− 0.202411i
$418$	1.36488i	0.0667583i
$419$	4.36196	0.213096	0.106548	−	0.994308i	$-0.466020\pi$
$419$	4.36196	0.213096	0.106548	+	0.994308i	$0.466020\pi$
$420$	0	0
$421$	5.77923	0.281662	0.140831	−	0.990034i	$-0.455023\pi$
$421$	5.77923	0.281662	0.140831	+	0.990034i	$0.455023\pi$
$422$	− 23.6543i	− 1.15148i
$423$	− 11.4652i	− 0.557457i
$424$	−42.1990	−2.04936
$425$	0	0
$426$	−1.59210	−0.0771377
$427$	− 4.54909i	− 0.220146i
$428$	− 4.30279i	− 0.207983i
$429$	−0.133353	−0.00643835
$430$	0	0
$431$	−4.62867	−0.222955	−0.111478	−	0.993767i	$-0.535558\pi$
$431$	−4.62867	−0.222955	−0.111478	+	0.993767i	$0.535558\pi$
$432$	− 2.67307i	− 0.128608i
$433$	− 6.81780i	− 0.327643i	−0.986490	−	0.163821i	$-0.947618\pi$
$433$	− 6.81780i	− 0.327643i	0.986490	−	0.163821i	$-0.0523820\pi$
$434$	1.93332	0.0928025
$435$	0	0
$436$	4.80150	0.229950
$437$	12.4701i	0.596527i
$438$	− 2.00645i	− 0.0958721i
$439$	−9.71456	−0.463651	−0.231825	−	0.972757i	$-0.574470\pi$
$439$	−9.71456	−0.463651	−0.231825	+	0.972757i	$0.574470\pi$
$440$	0	0
$441$	−4.46520	−0.212629
$442$	− 0.917502i	− 0.0436411i
$443$	− 31.1481i	− 1.47989i	−0.672666	−	0.739946i	$-0.734851\pi$
$443$	− 31.1481i	− 1.47989i	0.672666	−	0.739946i	$-0.265149\pi$
$444$	−2.54125	−0.120602
$445$	0	0
$446$	18.7239	0.886604
$447$	6.23506i	0.294908i
$448$	14.0939i	0.665873i
$449$	−28.1180	−1.32697	−0.663485	−	0.748189i	$-0.730924\pi$
$449$	−28.1180	−1.32697	−0.663485	+	0.748189i	$0.730924\pi$
$450$	0	0
$451$	−4.65386	−0.219142
$452$	− 4.03164i	− 0.189633i
$453$	− 8.38271i	− 0.393854i
$454$	−15.5955	−0.731933
$455$	0	0
$456$	5.53972	0.259421
$457$	− 41.4400i	− 1.93848i	−0.246113	−	0.969241i	$-0.579154\pi$
$457$	− 41.4400i	− 1.93848i	0.246113	−	0.969241i	$-0.420846\pi$
$458$	− 3.74314i	− 0.174905i
$459$	−3.52543	−0.164553
$460$	0	0
$461$	10.3432	0.481732	0.240866	−	0.970558i	$-0.422569\pi$
$461$	10.3432	0.481732	0.240866	+	0.970558i	$0.422569\pi$
$462$	1.20294i	0.0559660i
$463$	− 13.3047i	− 0.618320i	−0.951010	−	0.309160i	$-0.899952\pi$
$463$	− 13.3047i	− 0.618320i	0.951010	−	0.309160i	$-0.100048\pi$
$464$	26.0350	1.20865
$465$	0	0
$466$	−10.6494	−0.493325
$467$	− 6.22077i	− 0.287863i	−0.989588	−	0.143932i	$-0.954025\pi$
$467$	− 6.22077i	− 0.287863i	0.989588	−	0.143932i	$-0.0459745\pi$
$468$	0.112610i	0.00520538i
$469$	−3.31312	−0.152985
$470$	0	0
$471$	−10.2351	−0.471607
$472$	− 13.0648i	− 0.601357i
$473$	− 5.12399i	− 0.235601i
$474$	−6.31264	−0.289949
$475$	0	0
$476$	2.94914	0.135174
$477$	13.7605i	0.630050i
$478$	3.79352i	0.173511i
$479$	24.8825	1.13691	0.568454	−	0.822715i	$-0.307542\pi$
$479$	24.8825	1.13691	0.568454	+	0.822715i	$0.307542\pi$
$480$	0	0
$481$	−1.03657	−0.0472633
$482$	− 35.8983i	− 1.63512i
$483$	10.9906i	0.500091i
$484$	−5.57628	−0.253467
$485$	0	0
$486$	−1.21432	−0.0550827
$487$	− 9.84791i	− 0.446251i	−0.974790	−	0.223126i	$-0.928374\pi$
$487$	− 9.84791i	− 0.446251i	0.974790	−	0.223126i	$-0.0716260\pi$
$488$	− 8.76235i	− 0.396653i
$489$	−5.82717	−0.263514
$490$	0	0
$491$	−9.84791	−0.444430	−0.222215	−	0.974998i	$-0.571329\pi$
$491$	−9.84791	−0.444430	−0.222215	+	0.974998i	$0.571329\pi$
$492$	3.92993i	0.177175i
$493$	− 34.3368i	− 1.54645i
$494$	0.470127	0.0211520
$495$	0	0
$496$	2.67307	0.120024
$497$	− 2.08742i	− 0.0936336i
$498$	− 6.87157i	− 0.307922i
$499$	−0.653858	−0.0292707	−0.0146354	−	0.999893i	$-0.504659\pi$
$499$	−0.653858	−0.0292707	−0.0146354	+	0.999893i	$0.504659\pi$
$500$	0	0
$501$	23.1842	1.03579
$502$	− 26.0098i	− 1.16088i
$503$	− 13.9541i	− 0.622181i	−0.950380	−	0.311091i	$-0.899306\pi$
$503$	− 13.9541i	− 0.622181i	0.950380	−	0.311091i	$-0.100694\pi$
$504$	4.88247	0.217482
$505$	0	0
$506$	−5.21585	−0.231873
$507$	− 12.9541i	− 0.575310i
$508$	7.18421i	0.318748i
$509$	42.7116	1.89316	0.946580	−	0.322469i	$-0.104513\pi$
$509$	42.7116	1.89316	0.946580	+	0.322469i	$0.104513\pi$
$510$	0	0
$511$	2.63068	0.116374
$512$	24.1131i	1.06566i
$513$	− 1.80642i	− 0.0797556i
$514$	−21.4050	−0.944133
$515$	0	0
$516$	−4.32693	−0.190482
$517$	7.13383i	0.313745i
$518$	9.35059i	0.410841i
$519$	−1.57136	−0.0689751
$520$	0	0
$521$	−12.6035	−0.552168	−0.276084	−	0.961133i	$-0.589037\pi$
$521$	−12.6035	−0.552168	−0.276084	+	0.961133i	$0.589037\pi$
$522$	− 11.8272i	− 0.517661i
$523$	29.8479i	1.30516i	0.757721	+	0.652579i	$0.226313\pi$
$523$	29.8479i	1.30516i	−0.757721	+	0.652579i	$0.773687\pi$
$524$	−11.7013	−0.511175
$525$	0	0
$526$	17.8568	0.778594
$527$	− 3.52543i	− 0.153570i
$528$	1.66323i	0.0723826i
$529$	−24.6543	−1.07193
$530$	0	0
$531$	−4.26025	−0.184879
$532$	1.51114i	0.0655161i
$533$	1.60300i	0.0694338i
$534$	−2.34767	−0.101594
$535$	0	0
$536$	−6.38165	−0.275645
$537$	1.53972i	0.0664437i
$538$	1.64248i	0.0708125i
$539$	2.77832	0.119671
$540$	0	0
$541$	−13.9541	−0.599932	−0.299966	−	0.953950i	$-0.596975\pi$
$541$	−13.9541	−0.599932	−0.299966	+	0.953950i	$0.596975\pi$
$542$	− 14.7338i	− 0.632870i
$543$	− 2.00000i	− 0.0858282i
$544$	10.1793	0.436433
$545$	0	0
$546$	0.414349	0.0177325
$547$	5.74419i	0.245604i	0.992431	+	0.122802i	$0.0391880\pi$
$547$	5.74419i	0.245604i	−0.992431	+	0.122802i	$0.960812\pi$
$548$	− 9.55707i	− 0.408258i
$549$	−2.85728	−0.121946
$550$	0	0
$551$	17.5941	0.749534
$552$	21.1699i	0.901052i
$553$	− 8.27655i	− 0.351955i
$554$	22.9971	0.977053
$555$	0	0
$556$	2.17178	0.0921039
$557$	− 14.7511i	− 0.625025i	−0.949914	−	0.312513i	$-0.898829\pi$
$557$	− 14.7511i	− 0.625025i	0.949914	−	0.312513i	$-0.101171\pi$
$558$	− 1.21432i	− 0.0514063i
$559$	−1.76494	−0.0746489
$560$	0	0
$561$	2.19358	0.0926129
$562$	− 15.6860i	− 0.661673i
$563$	− 32.9260i	− 1.38766i	−0.720137	−	0.693832i	$-0.755921\pi$
$563$	− 32.9260i	− 1.38766i	0.720137	−	0.693832i	$-0.244079\pi$
$564$	6.02413	0.253662
$565$	0	0
$566$	−32.2799	−1.35683
$567$	− 1.59210i	− 0.0668621i
$568$	− 4.02074i	− 0.168707i
$569$	3.07604	0.128954	0.0644772	−	0.997919i	$-0.479462\pi$
$569$	3.07604	0.128954	0.0644772	+	0.997919i	$0.479462\pi$
$570$	0	0
$571$	4.52051	0.189177	0.0945886	−	0.995516i	$-0.469846\pi$
$571$	4.52051	0.189177	0.0945886	+	0.995516i	$0.469846\pi$
$572$	− 0.0700674i	− 0.00292966i
$573$	− 9.11753i	− 0.380890i
$574$	14.4603	0.603561
$575$	0	0
$576$	8.85236	0.368848
$577$	− 30.6923i	− 1.27774i	−0.769316	−	0.638868i	$-0.779403\pi$
$577$	− 30.6923i	− 1.27774i	0.769316	−	0.638868i	$-0.220597\pi$
$578$	− 5.55109i	− 0.230895i
$579$	4.72393	0.196320
$580$	0	0
$581$	9.00937	0.373772
$582$	− 8.40006i	− 0.348194i
$583$	− 8.56199i	− 0.354602i
$584$	5.06715	0.209680
$585$	0	0
$586$	9.70916	0.401082
$587$	14.8256i	0.611919i	0.952044	+	0.305960i	$0.0989773\pi$
$587$	14.8256i	0.611919i	−0.952044	+	0.305960i	$0.901023\pi$
$588$	− 2.34614i	− 0.0967532i
$589$	1.80642	0.0744324
$590$	0	0
$591$	15.7003	0.645823
$592$	12.9284i	0.531354i
$593$	− 23.9684i	− 0.984262i	−0.870521	−	0.492131i	$-0.836218\pi$
$593$	− 23.9684i	− 0.984262i	0.870521	−	0.492131i	$-0.163782\pi$
$594$	0.755569	0.0310014
$595$	0	0
$596$	−3.27607	−0.134193
$597$	6.28100i	0.257064i
$598$	1.79658i	0.0734676i
$599$	39.1086	1.59794	0.798968	−	0.601374i	$-0.205380\pi$
$599$	39.1086	1.59794	0.798968	+	0.601374i	$0.205380\pi$
$600$	0	0
$601$	22.3082	0.909970	0.454985	−	0.890499i	$-0.349645\pi$
$601$	22.3082	0.909970	0.454985	+	0.890499i	$0.349645\pi$
$602$	15.9210i	0.648893i
$603$	2.08097i	0.0847435i
$604$	4.40451	0.179217
$605$	0	0
$606$	11.2761	0.458059
$607$	2.82669i	0.114732i	0.998353	+	0.0573659i	$0.0182702\pi$
$607$	2.82669i	0.114732i	−0.998353	+	0.0573659i	$0.981730\pi$
$608$	5.21585i	0.211531i
$609$	15.5067	0.628363
$610$	0	0
$611$	2.45722	0.0994085
$612$	− 1.85236i	− 0.0748771i
$613$	36.6844i	1.48167i	0.671687	+	0.740835i	$0.265570\pi$
$613$	36.6844i	1.48167i	−0.671687	+	0.740835i	$0.734430\pi$
$614$	−21.0890	−0.851081
$615$	0	0
$616$	−3.03795	−0.122402
$617$	1.46659i	0.0590426i	0.999564	+	0.0295213i	$0.00939829\pi$
$617$	1.46659i	0.0590426i	−0.999564	+	0.0295213i	$0.990602\pi$
$618$	0.333383i	0.0134106i
$619$	15.9541	0.641248	0.320624	−	0.947207i	$-0.396107\pi$
$619$	15.9541	0.641248	0.320624	+	0.947207i	$0.396107\pi$
$620$	0	0
$621$	6.90321	0.277016
$622$	33.5002i	1.34324i
$623$	− 3.07805i	− 0.123320i
$624$	0.572892	0.0229340
$625$	0	0
$626$	16.6671	0.666151
$627$	1.12399i	0.0448876i
$628$	− 5.37778i	− 0.214597i
$629$	17.0509	0.679862
$630$	0	0
$631$	−32.0830	−1.27720	−0.638602	−	0.769538i	$-0.720487\pi$
$631$	−32.0830	−1.27720	−0.638602	+	0.769538i	$0.720487\pi$
$632$	− 15.9421i	− 0.634143i
$633$	− 19.4795i	− 0.774240i
$634$	−30.2908	−1.20300
$635$	0	0
$636$	−7.23014	−0.286694
$637$	− 0.956981i	− 0.0379170i
$638$	7.35905i	0.291348i
$639$	−1.31111	−0.0518666
$640$	0	0
$641$	−14.8923	−0.588211	−0.294105	−	0.955773i	$-0.595022\pi$
$641$	−14.8923	−0.588211	−0.294105	+	0.955773i	$0.595022\pi$
$642$	9.94422i	0.392467i
$643$	− 12.5205i	− 0.493761i	−0.969046	−	0.246880i	$-0.920595\pi$
$643$	− 12.5205i	− 0.493761i	0.969046	−	0.246880i	$-0.0794054\pi$
$644$	−5.77478	−0.227558
$645$	0	0
$646$	−7.73329	−0.304262
$647$	45.6227i	1.79361i	0.442423	+	0.896807i	$0.354119\pi$
$647$	45.6227i	1.79361i	−0.442423	+	0.896807i	$0.645881\pi$
$648$	− 3.06668i	− 0.120470i
$649$	2.65080	0.104053
$650$	0	0
$651$	1.59210	0.0623995
$652$	− 3.06175i	− 0.119908i
$653$	18.7797i	0.734907i	0.930042	+	0.367453i	$0.119770\pi$
$653$	18.7797i	0.734907i	−0.930042	+	0.367453i	$0.880230\pi$
$654$	−11.0968	−0.433919
$655$	0	0
$656$	19.9932	0.780604
$657$	− 1.65233i	− 0.0644634i
$658$	− 22.1659i	− 0.864119i
$659$	28.9240	1.12672	0.563359	−	0.826212i	$-0.309509\pi$
$659$	28.9240	1.12672	0.563359	+	0.826212i	$0.309509\pi$
$660$	0	0
$661$	−24.3269	−0.946208	−0.473104	−	0.881007i	$-0.656866\pi$
$661$	−24.3269	−0.946208	−0.473104	+	0.881007i	$0.656866\pi$
$662$	− 23.2904i	− 0.905206i
$663$	− 0.755569i	− 0.0293439i
$664$	17.3536	0.673452
$665$	0	0
$666$	5.87310	0.227578
$667$	67.2355i	2.60337i
$668$	12.1816i	0.471321i
$669$	15.4193	0.596143
$670$	0	0
$671$	1.77784	0.0686329
$672$	4.59703i	0.177334i
$673$	36.5511i	1.40894i	0.709733	+	0.704471i	$0.248815\pi$
$673$	36.5511i	1.40894i	−0.709733	+	0.704471i	$0.751185\pi$
$674$	−30.7304	−1.18369
$675$	0	0
$676$	6.80642	0.261786
$677$	− 32.1575i	− 1.23591i	−0.786212	−	0.617956i	$-0.787961\pi$
$677$	− 32.1575i	− 1.23591i	0.786212	−	0.617956i	$-0.212039\pi$
$678$	9.31756i	0.357839i
$679$	11.0134	0.422655
$680$	0	0
$681$	−12.8430	−0.492144
$682$	0.755569i	0.0289322i
$683$	38.2623i	1.46406i	0.681270	+	0.732032i	$0.261428\pi$
$683$	38.2623i	1.46406i	−0.681270	+	0.732032i	$0.738572\pi$
$684$	0.949145	0.0362915
$685$	0	0
$686$	−22.1659	−0.846300
$687$	− 3.08250i	− 0.117605i
$688$	22.0129i	0.839234i
$689$	−2.94914	−0.112353
$690$	0	0
$691$	−12.3082	−0.468226	−0.234113	−	0.972209i	$-0.575219\pi$
$691$	−12.3082	−0.468226	−0.234113	+	0.972209i	$0.575219\pi$
$692$	− 0.825636i	− 0.0313860i
$693$	0.990632i	0.0376310i
$694$	23.1495	0.878743
$695$	0	0
$696$	29.8687	1.13217
$697$	− 26.3684i	− 0.998775i
$698$	− 1.49378i	− 0.0565406i
$699$	−8.76986	−0.331707
$700$	0	0
$701$	31.5210	1.19053	0.595266	−	0.803529i	$-0.297047\pi$
$701$	31.5210	1.19053	0.595266	+	0.803529i	$0.297047\pi$
$702$	− 0.260253i	− 0.00982261i
$703$	8.73683i	0.329516i
$704$	−5.50807	−0.207593
$705$	0	0
$706$	−5.46827	−0.205801
$707$	14.7841i	0.556015i
$708$	− 2.23845i	− 0.0841263i
$709$	7.51114	0.282087	0.141043	−	0.990003i	$-0.454954\pi$
$709$	7.51114	0.282087	0.141043	+	0.990003i	$0.454954\pi$
$710$	0	0
$711$	−5.19850	−0.194959
$712$	− 5.92888i	− 0.222194i
$713$	6.90321i	0.258527i
$714$	−6.81579	−0.255075
$715$	0	0
$716$	−0.809010	−0.0302341
$717$	3.12399i	0.116667i
$718$	22.9797i	0.857596i
$719$	−32.3180	−1.20526	−0.602630	−	0.798021i	$-0.705880\pi$
$719$	−32.3180	−1.20526	−0.602630	+	0.798021i	$0.705880\pi$
$720$	0	0
$721$	−0.437101	−0.0162785
$722$	19.1095i	0.711184i
$723$	− 29.5625i	− 1.09944i
$724$	1.05086	0.0390547
$725$	0	0
$726$	12.8874	0.478296
$727$	6.12245i	0.227069i	0.993534	+	0.113535i	$0.0362173\pi$
$727$	6.12245i	0.227069i	−0.993534	+	0.113535i	$0.963783\pi$
$728$	1.04641i	0.0387825i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	29.0321	1.07379
$732$	− 1.50129i	− 0.0554894i
$733$	30.9403i	1.14280i	0.820670	+	0.571402i	$0.193600\pi$
$733$	30.9403i	1.14280i	−0.820670	+	0.571402i	$0.806400\pi$
$734$	−11.7966	−0.435420
$735$	0	0
$736$	−19.9323	−0.734713
$737$	− 1.29481i	− 0.0476949i
$738$	− 9.08250i	− 0.334331i
$739$	12.6780	0.466368	0.233184	−	0.972433i	$-0.425086\pi$
$739$	12.6780	0.466368	0.233184	+	0.972433i	$0.425086\pi$
$740$	0	0
$741$	0.387152	0.0142224
$742$	26.6035i	0.976644i
$743$	− 38.4385i	− 1.41017i	−0.709122	−	0.705086i	$-0.750909\pi$
$743$	− 38.4385i	− 1.41017i	0.709122	−	0.705086i	$-0.249091\pi$
$744$	3.06668	0.112430
$745$	0	0
$746$	42.7368	1.56471
$747$	− 5.65878i	− 0.207044i
$748$	1.15257i	0.0421420i
$749$	−13.0379	−0.476396
$750$	0	0
$751$	−13.4608	−0.491190	−0.245595	−	0.969373i	$-0.578983\pi$
$751$	−13.4608	−0.491190	−0.245595	+	0.969373i	$0.578983\pi$
$752$	− 30.6473i	− 1.11759i
$753$	− 21.4193i	− 0.780562i
$754$	2.53480	0.0923118
$755$	0	0
$756$	0.836535	0.0304245
$757$	− 20.5511i	− 0.746942i	−0.927642	−	0.373471i	$-0.878168\pi$
$757$	− 20.5511i	− 0.746942i	0.927642	−	0.373471i	$-0.121832\pi$
$758$	− 27.5210i	− 0.999607i
$759$	−4.29529	−0.155909
$760$	0	0
$761$	42.3432	1.53494	0.767470	−	0.641084i	$-0.221515\pi$
$761$	42.3432	1.53494	0.767470	+	0.641084i	$0.221515\pi$
$762$	− 16.6035i	− 0.601481i
$763$	− 14.5491i	− 0.526712i
$764$	4.79060	0.173318
$765$	0	0
$766$	−34.9634	−1.26328
$767$	− 0.913056i	− 0.0329686i
$768$	11.6637i	0.420878i
$769$	−40.5388	−1.46187	−0.730933	−	0.682449i	$-0.760915\pi$
$769$	−40.5388	−1.46187	−0.730933	+	0.682449i	$0.760915\pi$
$770$	0	0
$771$	−17.6271	−0.634826
$772$	2.48208i	0.0893320i
$773$	− 26.2810i	− 0.945262i	−0.881260	−	0.472631i	$-0.843304\pi$
$773$	− 26.2810i	− 0.945262i	0.881260	−	0.472631i	$-0.156696\pi$
$774$	10.0000	0.359443
$775$	0	0
$776$	21.2137	0.761529
$777$	7.70027i	0.276246i
$778$	− 30.4395i	− 1.09131i
$779$	13.5111	0.484087
$780$	0	0
$781$	0.815792	0.0291913
$782$	− 29.5526i	− 1.05680i
$783$	− 9.73975i	− 0.348070i
$784$	−11.9358	−0.426279
$785$	0	0
$786$	27.0430	0.964593
$787$	− 0.755569i	− 0.0269331i	−0.999909	−	0.0134666i	$-0.995713\pi$
$787$	− 0.755569i	− 0.0269331i	0.999909	−	0.0134666i	$-0.00428667\pi$
$788$	8.24935i	0.293871i
$789$	14.7052	0.523519
$790$	0	0
$791$	−12.2163	−0.434363
$792$	1.90813i	0.0678026i
$793$	− 0.612371i	− 0.0217459i
$794$	−35.2770	−1.25193
$795$	0	0
$796$	−3.30021	−0.116973
$797$	1.89384i	0.0670834i	0.999437	+	0.0335417i	$0.0106787\pi$
$797$	1.89384i	0.0670834i	−0.999437	+	0.0335417i	$0.989321\pi$
$798$	− 3.49240i	− 0.123630i
$799$	−40.4197	−1.42995
$800$	0	0
$801$	−1.93332	−0.0683106
$802$	− 13.6741i	− 0.482850i
$803$	1.02810i	0.0362810i
$804$	−1.09340	−0.0385611
$805$	0	0
$806$	0.260253	0.00916701
$807$	1.35260i	0.0476136i
$808$	28.4769i	1.00181i
$809$	28.6671	1.00788	0.503941	−	0.863738i	$-0.331883\pi$
$809$	28.6671	1.00788	0.503941	+	0.863738i	$0.331883\pi$
$810$	0	0
$811$	−38.0228	−1.33516	−0.667580	−	0.744538i	$-0.732670\pi$
$811$	−38.0228	−1.33516	−0.667580	+	0.744538i	$0.732670\pi$
$812$	8.14764i	0.285926i
$813$	− 12.1334i	− 0.425535i
$814$	−3.65433	−0.128084
$815$	0	0
$816$	−9.42372	−0.329896
$817$	14.8760i	0.520446i
$818$	− 31.1022i	− 1.08746i
$819$	0.341219	0.0119232
$820$	0	0
$821$	−27.2321	−0.950409	−0.475204	−	0.879876i	$-0.657626\pi$
$821$	−27.2321	−0.950409	−0.475204	+	0.879876i	$0.657626\pi$
$822$	22.0874i	0.770387i
$823$	− 14.5749i	− 0.508049i	−0.967198	−	0.254025i	$-0.918246\pi$
$823$	− 14.5749i	− 0.508049i	0.967198	−	0.254025i	$-0.0817544\pi$
$824$	−0.841934	−0.0293302
$825$	0	0
$826$	−8.23645	−0.286583
$827$	35.0781i	1.21978i	0.792485	+	0.609892i	$0.208787\pi$
$827$	35.0781i	1.21978i	−0.792485	+	0.609892i	$0.791213\pi$
$828$	3.62714i	0.126052i
$829$	−18.9077	−0.656690	−0.328345	−	0.944558i	$-0.606491\pi$
$829$	−18.9077	−0.656690	−0.328345	+	0.944558i	$0.606491\pi$
$830$	0	0
$831$	18.9382	0.656960
$832$	1.89723i	0.0657748i
$833$	15.7418i	0.545419i
$834$	−5.01921	−0.173801
$835$	0	0
$836$	−0.590573	−0.0204254
$837$	− 1.00000i	− 0.0345651i
$838$	− 5.29682i	− 0.182976i
$839$	39.5274	1.36464	0.682319	−	0.731054i	$-0.260971\pi$
$839$	39.5274	1.36464	0.682319	+	0.731054i	$0.260971\pi$
$840$	0	0
$841$	65.8627	2.27113
$842$	− 7.01783i	− 0.241850i
$843$	− 12.9175i	− 0.444902i
$844$	10.2351	0.352305
$845$	0	0
$846$	−13.9224	−0.478663
$847$	16.8968i	0.580579i
$848$	36.7828i	1.26313i
$849$	−26.5827	−0.912317
$850$	0	0
$851$	−33.3876	−1.14451
$852$	− 0.688892i	− 0.0236011i
$853$	− 41.8894i	− 1.43427i	−0.696937	−	0.717133i	$-0.745454\pi$
$853$	− 41.8894i	− 1.43427i	0.696937	−	0.717133i	$-0.254546\pi$
$854$	−5.52404	−0.189029
$855$	0	0
$856$	−25.1134	−0.858359
$857$	43.2859i	1.47862i	0.673366	+	0.739309i	$0.264848\pi$
$857$	43.2859i	1.47862i	−0.673366	+	0.739309i	$0.735152\pi$
$858$	0.161933i	0.00552831i
$859$	49.6513	1.69408	0.847040	−	0.531530i	$-0.178383\pi$
$859$	49.6513	1.69408	0.847040	+	0.531530i	$0.178383\pi$
$860$	0	0
$861$	11.9081	0.405828
$862$	5.62068i	0.191441i
$863$	31.6958i	1.07894i	0.842005	+	0.539469i	$0.181375\pi$
$863$	31.6958i	1.07894i	−0.842005	+	0.539469i	$0.818625\pi$
$864$	2.88739	0.0982310
$865$	0	0
$866$	−8.27899	−0.281331
$867$	− 4.57136i	− 0.155252i
$868$	0.836535i	0.0283939i
$869$	3.23459	0.109726
$870$	0	0
$871$	−0.445992	−0.0151119
$872$	− 28.0241i	− 0.949017i
$873$	− 6.91750i	− 0.234122i
$874$	15.1427	0.512210
$875$	0	0
$876$	0.868178	0.0293330
$877$	− 24.0000i	− 0.810422i	−0.914223	−	0.405211i	$-0.867198\pi$
$877$	− 24.0000i	− 0.810422i	0.914223	−	0.405211i	$-0.132802\pi$
$878$	11.7966i	0.398115i
$879$	7.99555	0.269683
$880$	0	0
$881$	−45.6577	−1.53825	−0.769124	−	0.639100i	$-0.779307\pi$
$881$	−45.6577	−1.53825	−0.769124	+	0.639100i	$0.779307\pi$
$882$	5.42219i	0.182574i
$883$	− 7.63158i	− 0.256823i	−0.991721	−	0.128412i	$-0.959012\pi$
$883$	− 7.63158i	− 0.256823i	0.991721	−	0.128412i	$-0.0409879\pi$
$884$	0.396997	0.0133524
$885$	0	0
$886$	−37.8238	−1.27071
$887$	13.9541i	0.468532i	0.972173	+	0.234266i	$0.0752686\pi$
$887$	13.9541i	0.468532i	−0.972173	+	0.234266i	$0.924731\pi$
$888$	14.8321i	0.497732i
$889$	21.7690	0.730107
$890$	0	0
$891$	0.622216	0.0208450
$892$	8.10171i	0.271265i
$893$	− 20.7110i	− 0.693068i
$894$	7.57136	0.253224
$895$	0	0
$896$	7.92042	0.264603
$897$	1.47949i	0.0493989i
$898$	34.1443i	1.13941i
$899$	9.73975	0.324839
$900$	0	0
$901$	48.5116	1.61616
$902$	5.65127i	0.188167i
$903$	13.1111i	0.436309i
$904$	−23.5308	−0.782624
$905$	0	0
$906$	−10.1793	−0.338184
$907$	50.6242i	1.68095i	0.541851	+	0.840475i	$0.317724\pi$
$907$	50.6242i	1.68095i	−0.541851	+	0.840475i	$0.682276\pi$
$908$	− 6.74806i	− 0.223942i
$909$	9.28592	0.307994
$910$	0	0
$911$	40.5847	1.34463	0.672316	−	0.740264i	$-0.265300\pi$
$911$	40.5847	1.34463	0.672316	+	0.740264i	$0.265300\pi$
$912$	− 4.82870i	− 0.159894i
$913$	3.52098i	0.116527i
$914$	−50.3214	−1.66448
$915$	0	0
$916$	1.61963	0.0535141
$917$	35.4563i	1.17087i
$918$	4.28100i	0.141294i
$919$	−53.3274	−1.75911	−0.879554	−	0.475798i	$-0.842159\pi$
$919$	−53.3274	−1.75911	−0.879554	+	0.475798i	$0.842159\pi$
$920$	0	0
$921$	−17.3669	−0.572258
$922$	− 12.5600i	− 0.413641i
$923$	− 0.280996i	− 0.00924911i
$924$	−0.520505	−0.0171234
$925$	0	0
$926$	−16.1561	−0.530923
$927$	0.274543i	0.00901717i
$928$	28.1225i	0.923165i
$929$	−4.67905	−0.153515	−0.0767573	−	0.997050i	$-0.524457\pi$
$929$	−4.67905	−0.153515	−0.0767573	+	0.997050i	$0.524457\pi$
$930$	0	0
$931$	−8.06605	−0.264354
$932$	− 4.60793i	− 0.150938i
$933$	27.5877i	0.903179i
$934$	−7.55401	−0.247175
$935$	0	0
$936$	0.657249	0.0214829
$937$	− 19.8952i	− 0.649949i	−0.945723	−	0.324974i	$-0.894644\pi$
$937$	− 19.8952i	− 0.649949i	0.945723	−	0.324974i	$-0.105356\pi$
$938$	4.02318i	0.131362i
$939$	13.7255	0.447913
$940$	0	0
$941$	−1.27946	−0.0417094	−0.0208547	−	0.999783i	$-0.506639\pi$
$941$	−1.27946	−0.0417094	−0.0208547	+	0.999783i	$0.506639\pi$
$942$	12.4286i	0.404947i
$943$	51.6325i	1.68139i
$944$	−11.3880	−0.370646
$945$	0	0
$946$	−6.22216	−0.202300
$947$	− 35.6686i	− 1.15907i	−0.814946	−	0.579537i	$-0.803233\pi$
$947$	− 35.6686i	− 1.15907i	0.814946	−	0.579537i	$-0.196767\pi$
$948$	− 2.73143i	− 0.0887129i
$949$	0.354126	0.0114954
$950$	0	0
$951$	−24.9447	−0.808887
$952$	− 17.2128i	− 0.557870i
$953$	− 39.7832i	− 1.28871i	−0.764728	−	0.644353i	$-0.777127\pi$
$953$	− 39.7832i	− 1.28871i	0.764728	−	0.644353i	$-0.222873\pi$
$954$	16.7096	0.540994
$955$	0	0
$956$	−1.64143	−0.0530876
$957$	6.06022i	0.195899i
$958$	− 30.2153i	− 0.976211i
$959$	−28.9590	−0.935135
$960$	0	0
$961$	1.00000	0.0322581
$962$	1.25872i	0.0405828i
$963$	8.18913i	0.263891i
$964$	15.5329	0.500282
$965$	0	0
$966$	13.3461	0.429405
$967$	− 52.9304i	− 1.70213i	−0.525063	−	0.851064i	$-0.675958\pi$
$967$	− 52.9304i	− 1.70213i	0.525063	−	0.851064i	$-0.324042\pi$
$968$	32.5462i	1.04607i
$969$	−6.36842	−0.204583
$970$	0	0
$971$	−54.9624	−1.76383	−0.881913	−	0.471412i	$-0.843745\pi$
$971$	−54.9624	−1.76383	−0.881913	+	0.471412i	$0.843745\pi$
$972$	− 0.525428i	− 0.0168531i
$973$	− 6.58073i	− 0.210968i
$974$	−11.9585	−0.383175
$975$	0	0
$976$	−7.63771	−0.244477
$977$	2.97773i	0.0952659i	0.998865	+	0.0476329i	$0.0151678\pi$
$977$	2.97773i	0.0952659i	−0.998865	+	0.0476329i	$0.984832\pi$
$978$	7.07604i	0.226267i
$979$	1.20294	0.0384463
$980$	0	0
$981$	−9.13828	−0.291763
$982$	11.9585i	0.381611i
$983$	26.9876i	0.860770i	0.902645	+	0.430385i	$0.141622\pi$
$983$	26.9876i	0.860770i	−0.902645	+	0.430385i	$0.858378\pi$
$984$	22.9372	0.731211
$985$	0	0
$986$	−41.6958	−1.32787
$987$	− 18.2538i	− 0.581025i
$988$	0.203420i	0.00647167i
$989$	−56.8484	−1.80767
$990$	0	0
$991$	0.520505	0.0165344	0.00826720	−	0.999966i	$-0.497368\pi$
$991$	0.520505	0.0165344	0.00826720	+	0.999966i	$0.497368\pi$
$992$	2.88739i	0.0916747i
$993$	− 19.1798i	− 0.608651i
$994$	−2.53480	−0.0803988
$995$	0	0
$996$	2.97328	0.0942120
$997$	− 25.2128i	− 0.798497i	−0.916843	−	0.399249i	$-0.869271\pi$
$997$	− 25.2128i	− 0.798497i	0.916843	−	0.399249i	$-0.130729\pi$
$998$	0.793993i	0.0251334i
$999$	4.83654	0.153021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2325.2.c.l.1024.3		6
5.2	odd	4		2325.2.a.p.1.3		3
5.3	odd	4		465.2.a.g.1.1	✓	3
5.4	even	2	inner	2325.2.c.l.1024.4		6
15.2	even	4		6975.2.a.bi.1.1		3
15.8	even	4		1395.2.a.h.1.3		3
20.3	even	4		7440.2.a.bm.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.a.g.1.1	✓	3	5.3	odd	4
1395.2.a.h.1.3		3	15.8	even	4
2325.2.a.p.1.3		3	5.2	odd	4
2325.2.c.l.1024.3		6	1.1	even	1	trivial
2325.2.c.l.1024.4		6	5.4	even	2	inner
6975.2.a.bi.1.1		3	15.2	even	4
7440.2.a.bm.1.3		3	20.3	even	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:	\( N \)	\(=\)	\( 2325 = 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2325.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.21432i q^{2} -1.00000i q^{3} +0.525428 q^{4} -1.21432 q^{6} -1.59210i q^{7} -3.06668i q^{8} -1.00000 q^{9} +0.622216 q^{11} -0.525428i q^{12} -0.214320i q^{13} -1.93332 q^{14} -2.67307 q^{16} +3.52543i q^{17} +1.21432i q^{18} -1.80642 q^{19} -1.59210 q^{21} -0.755569i q^{22} -6.90321i q^{23} -3.06668 q^{24} -0.260253 q^{26} +1.00000i q^{27} -0.836535i q^{28} -9.73975 q^{29} -1.00000 q^{31} -2.88739i q^{32} -0.622216i q^{33} +4.28100 q^{34} -0.525428 q^{36} -4.83654i q^{37} +2.19358i q^{38} -0.214320 q^{39} -7.47949 q^{41} +1.93332i q^{42} -8.23506i q^{43} +0.326929 q^{44} -8.38271 q^{46} +11.4652i q^{47} +2.67307i q^{48} +4.46520 q^{49} +3.52543 q^{51} -0.112610i q^{52} -13.7605i q^{53} +1.21432 q^{54} -4.88247 q^{56} +1.80642i q^{57} +11.8272i q^{58} +4.26025 q^{59} +2.85728 q^{61} +1.21432i q^{62} +1.59210i q^{63} -8.85236 q^{64} -0.755569 q^{66} -2.08097i q^{67} +1.85236i q^{68} -6.90321 q^{69} +1.31111 q^{71} +3.06668i q^{72} +1.65233i q^{73} -5.87310 q^{74} -0.949145 q^{76} -0.990632i q^{77} +0.260253i q^{78} +5.19850 q^{79} +1.00000 q^{81} +9.08250i q^{82} +5.65878i q^{83} -0.836535 q^{84} -10.0000 q^{86} +9.73975i q^{87} -1.90813i q^{88} +1.93332 q^{89} -0.341219 q^{91} -3.62714i q^{92} +1.00000i q^{93} +13.9224 q^{94} -2.88739 q^{96} +6.91750i q^{97} -5.42219i q^{98} -0.622216 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 6 q^{6} - 6 q^{9} + 4 q^{11} - 12 q^{14} + 10 q^{16} + 16 q^{19} + 4 q^{21} - 18 q^{24} - 28 q^{26} - 32 q^{29} - 6 q^{31} + 12 q^{34} + 10 q^{36} + 12 q^{39} + 8 q^{41} + 28 q^{44} + 16 q^{46}+ \cdots - 4 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 6 * q^6 - 6 * q^9 + 4 * q^11 - 12 * q^14 + 10 * q^16 + 16 * q^19 + 4 * q^21 - 18 * q^24 - 28 * q^26 - 32 * q^29 - 6 * q^31 + 12 * q^34 + 10 * q^36 + 12 * q^39 + 8 * q^41 + 28 * q^44 + 16 * q^46 - 14 * q^49 + 8 * q^51 - 6 * q^54 - 56 * q^56 + 52 * q^59 - 36 * q^61 - 66 * q^64 - 4 * q^66 - 28 * q^69 + 8 * q^71 - 8 * q^74 - 32 * q^76 - 8 * q^79 + 6 * q^81 + 8 * q^84 - 60 * q^86 + 12 * q^89 - 16 * q^91 - 8 * q^94 + 22 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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