LMFDB - Embedded newform 1155.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.41421 q^{6} -1.00000 q^{7} -2.82843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.41421 q^{6} -1.00000 q^{7} -2.82843 q^{8} +1.00000 q^{9} -1.41421 q^{10} +1.00000 q^{11} +3.41421 q^{13} -1.41421 q^{14} +1.00000 q^{15} -4.00000 q^{16} +3.82843 q^{17} +1.41421 q^{18} +1.82843 q^{19} +1.00000 q^{21} +1.41421 q^{22} +1.82843 q^{23} +2.82843 q^{24} +1.00000 q^{25} +4.82843 q^{26} -1.00000 q^{27} +7.24264 q^{29} +1.41421 q^{30} +3.41421 q^{31} -1.00000 q^{33} +5.41421 q^{34} +1.00000 q^{35} +2.24264 q^{37} +2.58579 q^{38} -3.41421 q^{39} +2.82843 q^{40} -3.07107 q^{41} +1.41421 q^{42} -3.58579 q^{43} -1.00000 q^{45} +2.58579 q^{46} +10.2426 q^{47} +4.00000 q^{48} +1.00000 q^{49} +1.41421 q^{50} -3.82843 q^{51} -2.65685 q^{53} -1.41421 q^{54} -1.00000 q^{55} +2.82843 q^{56} -1.82843 q^{57} +10.2426 q^{58} +11.5858 q^{59} -0.656854 q^{61} +4.82843 q^{62} -1.00000 q^{63} +8.00000 q^{64} -3.41421 q^{65} -1.41421 q^{66} -6.00000 q^{67} -1.82843 q^{69} +1.41421 q^{70} -11.0711 q^{71} -2.82843 q^{72} +8.48528 q^{73} +3.17157 q^{74} -1.00000 q^{75} -1.00000 q^{77} -4.82843 q^{78} +0.242641 q^{79} +4.00000 q^{80} +1.00000 q^{81} -4.34315 q^{82} -11.1421 q^{83} -3.82843 q^{85} -5.07107 q^{86} -7.24264 q^{87} -2.82843 q^{88} +14.0711 q^{89} -1.41421 q^{90} -3.41421 q^{91} -3.41421 q^{93} +14.4853 q^{94} -1.82843 q^{95} +1.24264 q^{97} +1.41421 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9} + 2 q^{11} + 4 q^{13} + 2 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{19} + 2 q^{21} - 2 q^{23} + 2 q^{25} + 4 q^{26} - 2 q^{27} + 6 q^{29} + 4 q^{31} - 2 q^{33} + 8 q^{34} + 2 q^{35} - 4 q^{37} + 8 q^{38} - 4 q^{39} + 8 q^{41} - 10 q^{43} - 2 q^{45} + 8 q^{46} + 12 q^{47} + 8 q^{48} + 2 q^{49} - 2 q^{51} + 6 q^{53} - 2 q^{55} + 2 q^{57} + 12 q^{58} + 26 q^{59} + 10 q^{61} + 4 q^{62} - 2 q^{63} + 16 q^{64} - 4 q^{65} - 12 q^{67} + 2 q^{69} - 8 q^{71} + 12 q^{74} - 2 q^{75} - 2 q^{77} - 4 q^{78} - 8 q^{79} + 8 q^{80} + 2 q^{81} - 20 q^{82} + 6 q^{83} - 2 q^{85} + 4 q^{86} - 6 q^{87} + 14 q^{89} - 4 q^{91} - 4 q^{93} + 12 q^{94} + 2 q^{95} - 6 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9 + 2 * q^11 + 4 * q^13 + 2 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^19 + 2 * q^21 - 2 * q^23 + 2 * q^25 + 4 * q^26 - 2 * q^27 + 6 * q^29 + 4 * q^31 - 2 * q^33 + 8 * q^34 + 2 * q^35 - 4 * q^37 + 8 * q^38 - 4 * q^39 + 8 * q^41 - 10 * q^43 - 2 * q^45 + 8 * q^46 + 12 * q^47 + 8 * q^48 + 2 * q^49 - 2 * q^51 + 6 * q^53 - 2 * q^55 + 2 * q^57 + 12 * q^58 + 26 * q^59 + 10 * q^61 + 4 * q^62 - 2 * q^63 + 16 * q^64 - 4 * q^65 - 12 * q^67 + 2 * q^69 - 8 * q^71 + 12 * q^74 - 2 * q^75 - 2 * q^77 - 4 * q^78 - 8 * q^79 + 8 * q^80 + 2 * q^81 - 20 * q^82 + 6 * q^83 - 2 * q^85 + 4 * q^86 - 6 * q^87 + 14 * q^89 - 4 * q^91 - 4 * q^93 + 12 * q^94 + 2 * q^95 - 6 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.41421	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.41421	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.41421	−0.577350
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.82843	−1.00000
$9$	1.00000	0.333333
$10$	−1.41421	−0.447214
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	3.41421	0.946932	0.473466	−	0.880812i	$-0.343003\pi$
$13$	3.41421	0.946932	0.473466	+	0.880812i	$0.343003\pi$
$14$	−1.41421	−0.377964
$15$	1.00000	0.258199
$16$	−4.00000	−1.00000
$17$	3.82843	0.928530	0.464265	−	0.885696i	$-0.346319\pi$
$17$	3.82843	0.928530	0.464265	+	0.885696i	$0.346319\pi$
$18$	1.41421	0.333333
$19$	1.82843	0.419470	0.209735	−	0.977758i	$-0.432740\pi$
$19$	1.82843	0.419470	0.209735	+	0.977758i	$0.432740\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	1.41421	0.301511
$23$	1.82843	0.381253	0.190627	−	0.981663i	$-0.438948\pi$
$23$	1.82843	0.381253	0.190627	+	0.981663i	$0.438948\pi$
$24$	2.82843	0.577350
$25$	1.00000	0.200000
$26$	4.82843	0.946932
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.24264	1.34492	0.672462	−	0.740131i	$-0.265237\pi$
$29$	7.24264	1.34492	0.672462	+	0.740131i	$0.265237\pi$
$30$	1.41421	0.258199
$31$	3.41421	0.613211	0.306605	−	0.951837i	$-0.400807\pi$
$31$	3.41421	0.613211	0.306605	+	0.951837i	$0.400807\pi$
$32$	0	0
$33$	−1.00000	−0.174078
$34$	5.41421	0.928530
$35$	1.00000	0.169031
$36$	0	0
$37$	2.24264	0.368688	0.184344	−	0.982862i	$-0.440984\pi$
$37$	2.24264	0.368688	0.184344	+	0.982862i	$0.440984\pi$
$38$	2.58579	0.419470
$39$	−3.41421	−0.546712
$40$	2.82843	0.447214
$41$	−3.07107	−0.479620	−0.239810	−	0.970820i	$-0.577085\pi$
$41$	−3.07107	−0.479620	−0.239810	+	0.970820i	$0.577085\pi$
$42$	1.41421	0.218218
$43$	−3.58579	−0.546827	−0.273414	−	0.961897i	$-0.588153\pi$
$43$	−3.58579	−0.546827	−0.273414	+	0.961897i	$0.588153\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	2.58579	0.381253
$47$	10.2426	1.49404	0.747021	−	0.664800i	$-0.231483\pi$
$47$	10.2426	1.49404	0.747021	+	0.664800i	$0.231483\pi$
$48$	4.00000	0.577350
$49$	1.00000	0.142857
$50$	1.41421	0.200000
$51$	−3.82843	−0.536087
$52$	0	0
$53$	−2.65685	−0.364947	−0.182473	−	0.983211i	$-0.558410\pi$
$53$	−2.65685	−0.364947	−0.182473	+	0.983211i	$0.558410\pi$
$54$	−1.41421	−0.192450
$55$	−1.00000	−0.134840
$56$	2.82843	0.377964
$57$	−1.82843	−0.242181
$58$	10.2426	1.34492
$59$	11.5858	1.50834	0.754170	−	0.656679i	$-0.228039\pi$
$59$	11.5858	1.50834	0.754170	+	0.656679i	$0.228039\pi$
$60$	0	0
$61$	−0.656854	−0.0841016	−0.0420508	−	0.999115i	$-0.513389\pi$
$61$	−0.656854	−0.0841016	−0.0420508	+	0.999115i	$0.513389\pi$
$62$	4.82843	0.613211
$63$	−1.00000	−0.125988
$64$	8.00000	1.00000
$65$	−3.41421	−0.423481
$66$	−1.41421	−0.174078
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	0	0
$69$	−1.82843	−0.220117
$70$	1.41421	0.169031
$71$	−11.0711	−1.31389	−0.656947	−	0.753937i	$-0.728152\pi$
$71$	−11.0711	−1.31389	−0.656947	+	0.753937i	$0.728152\pi$
$72$	−2.82843	−0.333333
$73$	8.48528	0.993127	0.496564	−	0.868000i	$-0.334595\pi$
$73$	8.48528	0.993127	0.496564	+	0.868000i	$0.334595\pi$
$74$	3.17157	0.368688
$75$	−1.00000	−0.115470
$76$	0	0
$77$	−1.00000	−0.113961
$78$	−4.82843	−0.546712
$79$	0.242641	0.0272992	0.0136496	−	0.999907i	$-0.495655\pi$
$79$	0.242641	0.0272992	0.0136496	+	0.999907i	$0.495655\pi$
$80$	4.00000	0.447214
$81$	1.00000	0.111111
$82$	−4.34315	−0.479620
$83$	−11.1421	−1.22301	−0.611504	−	0.791241i	$-0.709435\pi$
$83$	−11.1421	−1.22301	−0.611504	+	0.791241i	$0.709435\pi$
$84$	0	0
$85$	−3.82843	−0.415251
$86$	−5.07107	−0.546827
$87$	−7.24264	−0.776493
$88$	−2.82843	−0.301511
$89$	14.0711	1.49153	0.745765	−	0.666209i	$-0.232084\pi$
$89$	14.0711	1.49153	0.745765	+	0.666209i	$0.232084\pi$
$90$	−1.41421	−0.149071
$91$	−3.41421	−0.357907
$92$	0	0
$93$	−3.41421	−0.354037
$94$	14.4853	1.49404
$95$	−1.82843	−0.187593
$96$	0	0
$97$	1.24264	0.126171	0.0630855	−	0.998008i	$-0.479906\pi$
$97$	1.24264	0.126171	0.0630855	+	0.998008i	$0.479906\pi$
$98$	1.41421	0.142857
$99$	1.00000	0.100504
$100$	0	0
$101$	11.6569	1.15990	0.579950	−	0.814652i	$-0.303072\pi$
$101$	11.6569	1.15990	0.579950	+	0.814652i	$0.303072\pi$
$102$	−5.41421	−0.536087
$103$	−11.7279	−1.15559	−0.577793	−	0.816183i	$-0.696086\pi$
$103$	−11.7279	−1.15559	−0.577793	+	0.816183i	$0.696086\pi$
$104$	−9.65685	−0.946932
$105$	−1.00000	−0.0975900
$106$	−3.75736	−0.364947
$107$	−4.58579	−0.443325	−0.221662	−	0.975123i	$-0.571148\pi$
$107$	−4.58579	−0.443325	−0.221662	+	0.975123i	$0.571148\pi$
$108$	0	0
$109$	2.92893	0.280541	0.140270	−	0.990113i	$-0.455203\pi$
$109$	2.92893	0.280541	0.140270	+	0.990113i	$0.455203\pi$
$110$	−1.41421	−0.134840
$111$	−2.24264	−0.212862
$112$	4.00000	0.377964
$113$	−14.3137	−1.34652	−0.673260	−	0.739406i	$-0.735107\pi$
$113$	−14.3137	−1.34652	−0.673260	+	0.739406i	$0.735107\pi$
$114$	−2.58579	−0.242181
$115$	−1.82843	−0.170502
$116$	0	0
$117$	3.41421	0.315644
$118$	16.3848	1.50834
$119$	−3.82843	−0.350951
$120$	−2.82843	−0.258199
$121$	1.00000	0.0909091
$122$	−0.928932	−0.0841016
$123$	3.07107	0.276909
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	−1.41421	−0.125988
$127$	−11.7279	−1.04068	−0.520342	−	0.853958i	$-0.674196\pi$
$127$	−11.7279	−1.04068	−0.520342	+	0.853958i	$0.674196\pi$
$128$	11.3137	1.00000
$129$	3.58579	0.315711
$130$	−4.82843	−0.423481
$131$	10.2426	0.894904	0.447452	−	0.894308i	$-0.352332\pi$
$131$	10.2426	0.894904	0.447452	+	0.894308i	$0.352332\pi$
$132$	0	0
$133$	−1.82843	−0.158545
$134$	−8.48528	−0.733017
$135$	1.00000	0.0860663
$136$	−10.8284	−0.928530
$137$	13.6569	1.16678	0.583392	−	0.812191i	$-0.301725\pi$
$137$	13.6569	1.16678	0.583392	+	0.812191i	$0.301725\pi$
$138$	−2.58579	−0.220117
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	−10.2426	−0.862586
$142$	−15.6569	−1.31389
$143$	3.41421	0.285511
$144$	−4.00000	−0.333333
$145$	−7.24264	−0.601469
$146$	12.0000	0.993127
$147$	−1.00000	−0.0824786
$148$	0	0
$149$	−0.828427	−0.0678674	−0.0339337	−	0.999424i	$-0.510804\pi$
$149$	−0.828427	−0.0678674	−0.0339337	+	0.999424i	$0.510804\pi$
$150$	−1.41421	−0.115470
$151$	−15.6569	−1.27414	−0.637068	−	0.770807i	$-0.719853\pi$
$151$	−15.6569	−1.27414	−0.637068	+	0.770807i	$0.719853\pi$
$152$	−5.17157	−0.419470
$153$	3.82843	0.309510
$154$	−1.41421	−0.113961
$155$	−3.41421	−0.274236
$156$	0	0
$157$	12.4142	0.990762	0.495381	−	0.868676i	$-0.335028\pi$
$157$	12.4142	0.990762	0.495381	+	0.868676i	$0.335028\pi$
$158$	0.343146	0.0272992
$159$	2.65685	0.210702
$160$	0	0
$161$	−1.82843	−0.144100
$162$	1.41421	0.111111
$163$	10.7279	0.840276	0.420138	−	0.907460i	$-0.361982\pi$
$163$	10.7279	0.840276	0.420138	+	0.907460i	$0.361982\pi$
$164$	0	0
$165$	1.00000	0.0778499
$166$	−15.7574	−1.22301
$167$	11.6569	0.902034	0.451017	−	0.892515i	$-0.351061\pi$
$167$	11.6569	0.902034	0.451017	+	0.892515i	$0.351061\pi$
$168$	−2.82843	−0.218218
$169$	−1.34315	−0.103319
$170$	−5.41421	−0.415251
$171$	1.82843	0.139823
$172$	0	0
$173$	−3.31371	−0.251937	−0.125968	−	0.992034i	$-0.540204\pi$
$173$	−3.31371	−0.251937	−0.125968	+	0.992034i	$0.540204\pi$
$174$	−10.2426	−0.776493
$175$	−1.00000	−0.0755929
$176$	−4.00000	−0.301511
$177$	−11.5858	−0.870841
$178$	19.8995	1.49153
$179$	16.2426	1.21403	0.607016	−	0.794690i	$-0.292366\pi$
$179$	16.2426	1.21403	0.607016	+	0.794690i	$0.292366\pi$
$180$	0	0
$181$	−14.9706	−1.11275	−0.556377	−	0.830930i	$-0.687809\pi$
$181$	−14.9706	−1.11275	−0.556377	+	0.830930i	$0.687809\pi$
$182$	−4.82843	−0.357907
$183$	0.656854	0.0485561
$184$	−5.17157	−0.381253
$185$	−2.24264	−0.164882
$186$	−4.82843	−0.354037
$187$	3.82843	0.279962
$188$	0	0
$189$	1.00000	0.0727393
$190$	−2.58579	−0.187593
$191$	−5.65685	−0.409316	−0.204658	−	0.978834i	$-0.565608\pi$
$191$	−5.65685	−0.409316	−0.204658	+	0.978834i	$0.565608\pi$
$192$	−8.00000	−0.577350
$193$	−2.48528	−0.178894	−0.0894472	−	0.995992i	$-0.528510\pi$
$193$	−2.48528	−0.178894	−0.0894472	+	0.995992i	$0.528510\pi$
$194$	1.75736	0.126171
$195$	3.41421	0.244497
$196$	0	0
$197$	−9.17157	−0.653448	−0.326724	−	0.945120i	$-0.605945\pi$
$197$	−9.17157	−0.653448	−0.326724	+	0.945120i	$0.605945\pi$
$198$	1.41421	0.100504
$199$	3.31371	0.234903	0.117451	−	0.993079i	$-0.462528\pi$
$199$	3.31371	0.234903	0.117451	+	0.993079i	$0.462528\pi$
$200$	−2.82843	−0.200000
$201$	6.00000	0.423207
$202$	16.4853	1.15990
$203$	−7.24264	−0.508334
$204$	0	0
$205$	3.07107	0.214493
$206$	−16.5858	−1.15559
$207$	1.82843	0.127084
$208$	−13.6569	−0.946932
$209$	1.82843	0.126475
$210$	−1.41421	−0.0975900
$211$	−10.4853	−0.721837	−0.360918	−	0.932597i	$-0.617537\pi$
$211$	−10.4853	−0.721837	−0.360918	+	0.932597i	$0.617537\pi$
$212$	0	0
$213$	11.0711	0.758577
$214$	−6.48528	−0.443325
$215$	3.58579	0.244549
$216$	2.82843	0.192450
$217$	−3.41421	−0.231772
$218$	4.14214	0.280541
$219$	−8.48528	−0.573382
$220$	0	0
$221$	13.0711	0.879255
$222$	−3.17157	−0.212862
$223$	7.24264	0.485003	0.242502	−	0.970151i	$-0.422032\pi$
$223$	7.24264	0.485003	0.242502	+	0.970151i	$0.422032\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−20.2426	−1.34652
$227$	−13.3431	−0.885616	−0.442808	−	0.896617i	$-0.646018\pi$
$227$	−13.3431	−0.885616	−0.442808	+	0.896617i	$0.646018\pi$
$228$	0	0
$229$	−18.7279	−1.23758	−0.618788	−	0.785558i	$-0.712376\pi$
$229$	−18.7279	−1.23758	−0.618788	+	0.785558i	$0.712376\pi$
$230$	−2.58579	−0.170502
$231$	1.00000	0.0657952
$232$	−20.4853	−1.34492
$233$	16.2426	1.06409	0.532045	−	0.846716i	$-0.321424\pi$
$233$	16.2426	1.06409	0.532045	+	0.846716i	$0.321424\pi$
$234$	4.82843	0.315644
$235$	−10.2426	−0.668156
$236$	0	0
$237$	−0.242641	−0.0157612
$238$	−5.41421	−0.350951
$239$	−0.0710678	−0.00459699	−0.00229850	−	0.999997i	$-0.500732\pi$
$239$	−0.0710678	−0.00459699	−0.00229850	+	0.999997i	$0.500732\pi$
$240$	−4.00000	−0.258199
$241$	−8.48528	−0.546585	−0.273293	−	0.961931i	$-0.588113\pi$
$241$	−8.48528	−0.546585	−0.273293	+	0.961931i	$0.588113\pi$
$242$	1.41421	0.0909091
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	−1.00000	−0.0638877
$246$	4.34315	0.276909
$247$	6.24264	0.397210
$248$	−9.65685	−0.613211
$249$	11.1421	0.706104
$250$	−1.41421	−0.0894427
$251$	17.6569	1.11449	0.557245	−	0.830348i	$-0.311858\pi$
$251$	17.6569	1.11449	0.557245	+	0.830348i	$0.311858\pi$
$252$	0	0
$253$	1.82843	0.114952
$254$	−16.5858	−1.04068
$255$	3.82843	0.239745
$256$	0	0
$257$	−16.2426	−1.01319	−0.506594	−	0.862185i	$-0.669096\pi$
$257$	−16.2426	−1.01319	−0.506594	+	0.862185i	$0.669096\pi$
$258$	5.07107	0.315711
$259$	−2.24264	−0.139351
$260$	0	0
$261$	7.24264	0.448308
$262$	14.4853	0.894904
$263$	14.1421	0.872041	0.436021	−	0.899937i	$-0.356387\pi$
$263$	14.1421	0.872041	0.436021	+	0.899937i	$0.356387\pi$
$264$	2.82843	0.174078
$265$	2.65685	0.163209
$266$	−2.58579	−0.158545
$267$	−14.0711	−0.861135
$268$	0	0
$269$	24.5563	1.49723	0.748614	−	0.663007i	$-0.230720\pi$
$269$	24.5563	1.49723	0.748614	+	0.663007i	$0.230720\pi$
$270$	1.41421	0.0860663
$271$	−2.17157	−0.131914	−0.0659568	−	0.997822i	$-0.521010\pi$
$271$	−2.17157	−0.131914	−0.0659568	+	0.997822i	$0.521010\pi$
$272$	−15.3137	−0.928530
$273$	3.41421	0.206638
$274$	19.3137	1.16678
$275$	1.00000	0.0603023
$276$	0	0
$277$	13.1716	0.791403	0.395702	−	0.918379i	$-0.370501\pi$
$277$	13.1716	0.791403	0.395702	+	0.918379i	$0.370501\pi$
$278$	19.7990	1.18746
$279$	3.41421	0.204404
$280$	−2.82843	−0.169031
$281$	26.8284	1.60045	0.800225	−	0.599700i	$-0.204713\pi$
$281$	26.8284	1.60045	0.800225	+	0.599700i	$0.204713\pi$
$282$	−14.4853	−0.862586
$283$	−27.2132	−1.61766	−0.808829	−	0.588045i	$-0.799898\pi$
$283$	−27.2132	−1.61766	−0.808829	+	0.588045i	$0.799898\pi$
$284$	0	0
$285$	1.82843	0.108307
$286$	4.82843	0.285511
$287$	3.07107	0.181279
$288$	0	0
$289$	−2.34315	−0.137832
$290$	−10.2426	−0.601469
$291$	−1.24264	−0.0728449
$292$	0	0
$293$	−19.1421	−1.11830	−0.559148	−	0.829068i	$-0.688872\pi$
$293$	−19.1421	−1.11830	−0.559148	+	0.829068i	$0.688872\pi$
$294$	−1.41421	−0.0824786
$295$	−11.5858	−0.674551
$296$	−6.34315	−0.368688
$297$	−1.00000	−0.0580259
$298$	−1.17157	−0.0678674
$299$	6.24264	0.361021
$300$	0	0
$301$	3.58579	0.206681
$302$	−22.1421	−1.27414
$303$	−11.6569	−0.669669
$304$	−7.31371	−0.419470
$305$	0.656854	0.0376114
$306$	5.41421	0.309510
$307$	−30.4853	−1.73989	−0.869943	−	0.493151i	$-0.835845\pi$
$307$	−30.4853	−1.73989	−0.869943	+	0.493151i	$0.835845\pi$
$308$	0	0
$309$	11.7279	0.667178
$310$	−4.82843	−0.274236
$311$	31.1127	1.76424	0.882120	−	0.471025i	$-0.156116\pi$
$311$	31.1127	1.76424	0.882120	+	0.471025i	$0.156116\pi$
$312$	9.65685	0.546712
$313$	−15.2426	−0.861565	−0.430782	−	0.902456i	$-0.641762\pi$
$313$	−15.2426	−0.861565	−0.430782	+	0.902456i	$0.641762\pi$
$314$	17.5563	0.990762
$315$	1.00000	0.0563436
$316$	0	0
$317$	6.14214	0.344977	0.172488	−	0.985012i	$-0.444819\pi$
$317$	6.14214	0.344977	0.172488	+	0.985012i	$0.444819\pi$
$318$	3.75736	0.210702
$319$	7.24264	0.405510
$320$	−8.00000	−0.447214
$321$	4.58579	0.255954
$322$	−2.58579	−0.144100
$323$	7.00000	0.389490
$324$	0	0
$325$	3.41421	0.189386
$326$	15.1716	0.840276
$327$	−2.92893	−0.161970
$328$	8.68629	0.479620
$329$	−10.2426	−0.564695
$330$	1.41421	0.0778499
$331$	15.1421	0.832287	0.416144	−	0.909299i	$-0.363381\pi$
$331$	15.1421	0.832287	0.416144	+	0.909299i	$0.363381\pi$
$332$	0	0
$333$	2.24264	0.122896
$334$	16.4853	0.902034
$335$	6.00000	0.327815
$336$	−4.00000	−0.218218
$337$	7.24264	0.394532	0.197266	−	0.980350i	$-0.436794\pi$
$337$	7.24264	0.394532	0.197266	+	0.980350i	$0.436794\pi$
$338$	−1.89949	−0.103319
$339$	14.3137	0.777414
$340$	0	0
$341$	3.41421	0.184890
$342$	2.58579	0.139823
$343$	−1.00000	−0.0539949
$344$	10.1421	0.546827
$345$	1.82843	0.0984392
$346$	−4.68629	−0.251937
$347$	−19.7990	−1.06287	−0.531433	−	0.847100i	$-0.678346\pi$
$347$	−19.7990	−1.06287	−0.531433	+	0.847100i	$0.678346\pi$
$348$	0	0
$349$	19.0000	1.01705	0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000	1.01705	0.508523	+	0.861048i	$0.330192\pi$
$350$	−1.41421	−0.0755929
$351$	−3.41421	−0.182237
$352$	0	0
$353$	20.1421	1.07206	0.536029	−	0.844200i	$-0.319924\pi$
$353$	20.1421	1.07206	0.536029	+	0.844200i	$0.319924\pi$
$354$	−16.3848	−0.870841
$355$	11.0711	0.587591
$356$	0	0
$357$	3.82843	0.202622
$358$	22.9706	1.21403
$359$	−14.5563	−0.768255	−0.384127	−	0.923280i	$-0.625498\pi$
$359$	−14.5563	−0.768255	−0.384127	+	0.923280i	$0.625498\pi$
$360$	2.82843	0.149071
$361$	−15.6569	−0.824045
$362$	−21.1716	−1.11275
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−8.48528	−0.444140
$366$	0.928932	0.0485561
$367$	−13.2426	−0.691260	−0.345630	−	0.938371i	$-0.612335\pi$
$367$	−13.2426	−0.691260	−0.345630	+	0.938371i	$0.612335\pi$
$368$	−7.31371	−0.381253
$369$	−3.07107	−0.159873
$370$	−3.17157	−0.164882
$371$	2.65685	0.137937
$372$	0	0
$373$	6.41421	0.332115	0.166058	−	0.986116i	$-0.446896\pi$
$373$	6.41421	0.332115	0.166058	+	0.986116i	$0.446896\pi$
$374$	5.41421	0.279962
$375$	1.00000	0.0516398
$376$	−28.9706	−1.49404
$377$	24.7279	1.27355
$378$	1.41421	0.0727393
$379$	−22.1716	−1.13888	−0.569439	−	0.822034i	$-0.692839\pi$
$379$	−22.1716	−1.13888	−0.569439	+	0.822034i	$0.692839\pi$
$380$	0	0
$381$	11.7279	0.600840
$382$	−8.00000	−0.409316
$383$	−30.8701	−1.57739	−0.788693	−	0.614787i	$-0.789242\pi$
$383$	−30.8701	−1.57739	−0.788693	+	0.614787i	$0.789242\pi$
$384$	−11.3137	−0.577350
$385$	1.00000	0.0509647
$386$	−3.51472	−0.178894
$387$	−3.58579	−0.182276
$388$	0	0
$389$	35.6985	1.80999	0.904993	−	0.425427i	$-0.139876\pi$
$389$	35.6985	1.80999	0.904993	+	0.425427i	$0.139876\pi$
$390$	4.82843	0.244497
$391$	7.00000	0.354005
$392$	−2.82843	−0.142857
$393$	−10.2426	−0.516673
$394$	−12.9706	−0.653448
$395$	−0.242641	−0.0122086
$396$	0	0
$397$	3.51472	0.176399	0.0881993	−	0.996103i	$-0.471889\pi$
$397$	3.51472	0.176399	0.0881993	+	0.996103i	$0.471889\pi$
$398$	4.68629	0.234903
$399$	1.82843	0.0915358
$400$	−4.00000	−0.200000
$401$	−10.3848	−0.518591	−0.259295	−	0.965798i	$-0.583490\pi$
$401$	−10.3848	−0.518591	−0.259295	+	0.965798i	$0.583490\pi$
$402$	8.48528	0.423207
$403$	11.6569	0.580669
$404$	0	0
$405$	−1.00000	−0.0496904
$406$	−10.2426	−0.508334
$407$	2.24264	0.111164
$408$	10.8284	0.536087
$409$	19.5147	0.964941	0.482470	−	0.875912i	$-0.339740\pi$
$409$	19.5147	0.964941	0.482470	+	0.875912i	$0.339740\pi$
$410$	4.34315	0.214493
$411$	−13.6569	−0.673643
$412$	0	0
$413$	−11.5858	−0.570099
$414$	2.58579	0.127084
$415$	11.1421	0.546946
$416$	0	0
$417$	−14.0000	−0.685583
$418$	2.58579	0.126475
$419$	8.07107	0.394297	0.197149	−	0.980374i	$-0.436832\pi$
$419$	8.07107	0.394297	0.197149	+	0.980374i	$0.436832\pi$
$420$	0	0
$421$	−0.656854	−0.0320131	−0.0160066	−	0.999872i	$-0.505095\pi$
$421$	−0.656854	−0.0320131	−0.0160066	+	0.999872i	$0.505095\pi$
$422$	−14.8284	−0.721837
$423$	10.2426	0.498014
$424$	7.51472	0.364947
$425$	3.82843	0.185706
$426$	15.6569	0.758577
$427$	0.656854	0.0317874
$428$	0	0
$429$	−3.41421	−0.164840
$430$	5.07107	0.244549
$431$	38.8284	1.87030	0.935150	−	0.354253i	$-0.115265\pi$
$431$	38.8284	1.87030	0.935150	+	0.354253i	$0.115265\pi$
$432$	4.00000	0.192450
$433$	−4.14214	−0.199058	−0.0995292	−	0.995035i	$-0.531734\pi$
$433$	−4.14214	−0.199058	−0.0995292	+	0.995035i	$0.531734\pi$
$434$	−4.82843	−0.231772
$435$	7.24264	0.347258
$436$	0	0
$437$	3.34315	0.159924
$438$	−12.0000	−0.573382
$439$	3.00000	0.143182	0.0715911	−	0.997434i	$-0.477192\pi$
$439$	3.00000	0.143182	0.0715911	+	0.997434i	$0.477192\pi$
$440$	2.82843	0.134840
$441$	1.00000	0.0476190
$442$	18.4853	0.879255
$443$	31.6569	1.50406	0.752031	−	0.659127i	$-0.229074\pi$
$443$	31.6569	1.50406	0.752031	+	0.659127i	$0.229074\pi$
$444$	0	0
$445$	−14.0711	−0.667033
$446$	10.2426	0.485003
$447$	0.828427	0.0391833
$448$	−8.00000	−0.377964
$449$	−22.5858	−1.06589	−0.532945	−	0.846150i	$-0.678915\pi$
$449$	−22.5858	−1.06589	−0.532945	+	0.846150i	$0.678915\pi$
$450$	1.41421	0.0666667
$451$	−3.07107	−0.144611
$452$	0	0
$453$	15.6569	0.735623
$454$	−18.8701	−0.885616
$455$	3.41421	0.160061
$456$	5.17157	0.242181
$457$	17.5858	0.822628	0.411314	−	0.911494i	$-0.365070\pi$
$457$	17.5858	0.822628	0.411314	+	0.911494i	$0.365070\pi$
$458$	−26.4853	−1.23758
$459$	−3.82843	−0.178696
$460$	0	0
$461$	20.1421	0.938113	0.469056	−	0.883168i	$-0.344594\pi$
$461$	20.1421	0.938113	0.469056	+	0.883168i	$0.344594\pi$
$462$	1.41421	0.0657952
$463$	−30.4853	−1.41677	−0.708386	−	0.705826i	$-0.750576\pi$
$463$	−30.4853	−1.41677	−0.708386	+	0.705826i	$0.750576\pi$
$464$	−28.9706	−1.34492
$465$	3.41421	0.158330
$466$	22.9706	1.06409
$467$	37.4558	1.73325	0.866625	−	0.498960i	$-0.166285\pi$
$467$	37.4558	1.73325	0.866625	+	0.498960i	$0.166285\pi$
$468$	0	0
$469$	6.00000	0.277054
$470$	−14.4853	−0.668156
$471$	−12.4142	−0.572017
$472$	−32.7696	−1.50834
$473$	−3.58579	−0.164875
$474$	−0.343146	−0.0157612
$475$	1.82843	0.0838940
$476$	0	0
$477$	−2.65685	−0.121649
$478$	−0.100505	−0.00459699
$479$	5.55635	0.253876	0.126938	−	0.991911i	$-0.459485\pi$
$479$	5.55635	0.253876	0.126938	+	0.991911i	$0.459485\pi$
$480$	0	0
$481$	7.65685	0.349123
$482$	−12.0000	−0.546585
$483$	1.82843	0.0831963
$484$	0	0
$485$	−1.24264	−0.0564254
$486$	−1.41421	−0.0641500
$487$	−16.8284	−0.762569	−0.381284	−	0.924458i	$-0.624518\pi$
$487$	−16.8284	−0.762569	−0.381284	+	0.924458i	$0.624518\pi$
$488$	1.85786	0.0841016
$489$	−10.7279	−0.485133
$490$	−1.41421	−0.0638877
$491$	−3.44365	−0.155410	−0.0777049	−	0.996976i	$-0.524759\pi$
$491$	−3.44365	−0.155410	−0.0777049	+	0.996976i	$0.524759\pi$
$492$	0	0
$493$	27.7279	1.24880
$494$	8.82843	0.397210
$495$	−1.00000	−0.0449467
$496$	−13.6569	−0.613211
$497$	11.0711	0.496605
$498$	15.7574	0.706104
$499$	1.97056	0.0882145	0.0441073	−	0.999027i	$-0.485956\pi$
$499$	1.97056	0.0882145	0.0441073	+	0.999027i	$0.485956\pi$
$500$	0	0
$501$	−11.6569	−0.520790
$502$	24.9706	1.11449
$503$	−22.4558	−1.00126	−0.500628	−	0.865662i	$-0.666898\pi$
$503$	−22.4558	−1.00126	−0.500628	+	0.865662i	$0.666898\pi$
$504$	2.82843	0.125988
$505$	−11.6569	−0.518723
$506$	2.58579	0.114952
$507$	1.34315	0.0596512
$508$	0	0
$509$	22.4142	0.993493	0.496746	−	0.867896i	$-0.334528\pi$
$509$	22.4142	0.993493	0.496746	+	0.867896i	$0.334528\pi$
$510$	5.41421	0.239745
$511$	−8.48528	−0.375367
$512$	−22.6274	−1.00000
$513$	−1.82843	−0.0807270
$514$	−22.9706	−1.01319
$515$	11.7279	0.516794
$516$	0	0
$517$	10.2426	0.450471
$518$	−3.17157	−0.139351
$519$	3.31371	0.145456
$520$	9.65685	0.423481
$521$	−19.3848	−0.849262	−0.424631	−	0.905366i	$-0.639596\pi$
$521$	−19.3848	−0.849262	−0.424631	+	0.905366i	$0.639596\pi$
$522$	10.2426	0.448308
$523$	−41.4558	−1.81274	−0.906369	−	0.422488i	$-0.861157\pi$
$523$	−41.4558	−1.81274	−0.906369	+	0.422488i	$0.861157\pi$
$524$	0	0
$525$	1.00000	0.0436436
$526$	20.0000	0.872041
$527$	13.0711	0.569385
$528$	4.00000	0.174078
$529$	−19.6569	−0.854646
$530$	3.75736	0.163209
$531$	11.5858	0.502780
$532$	0	0
$533$	−10.4853	−0.454168
$534$	−19.8995	−0.861135
$535$	4.58579	0.198261
$536$	16.9706	0.733017
$537$	−16.2426	−0.700922
$538$	34.7279	1.49723
$539$	1.00000	0.0430730
$540$	0	0
$541$	19.8995	0.855546	0.427773	−	0.903886i	$-0.359298\pi$
$541$	19.8995	0.855546	0.427773	+	0.903886i	$0.359298\pi$
$542$	−3.07107	−0.131914
$543$	14.9706	0.642448
$544$	0	0
$545$	−2.92893	−0.125462
$546$	4.82843	0.206638
$547$	−22.6985	−0.970517	−0.485259	−	0.874371i	$-0.661275\pi$
$547$	−22.6985	−0.970517	−0.485259	+	0.874371i	$0.661275\pi$
$548$	0	0
$549$	−0.656854	−0.0280339
$550$	1.41421	0.0603023
$551$	13.2426	0.564155
$552$	5.17157	0.220117
$553$	−0.242641	−0.0103181
$554$	18.6274	0.791403
$555$	2.24264	0.0951948
$556$	0	0
$557$	−30.7696	−1.30375	−0.651874	−	0.758327i	$-0.726017\pi$
$557$	−30.7696	−1.30375	−0.651874	+	0.758327i	$0.726017\pi$
$558$	4.82843	0.204404
$559$	−12.2426	−0.517809
$560$	−4.00000	−0.169031
$561$	−3.82843	−0.161636
$562$	37.9411	1.60045
$563$	−26.4853	−1.11622	−0.558111	−	0.829766i	$-0.688474\pi$
$563$	−26.4853	−1.11622	−0.558111	+	0.829766i	$0.688474\pi$
$564$	0	0
$565$	14.3137	0.602182
$566$	−38.4853	−1.61766
$567$	−1.00000	−0.0419961
$568$	31.3137	1.31389
$569$	−32.6985	−1.37079	−0.685396	−	0.728171i	$-0.740371\pi$
$569$	−32.6985	−1.37079	−0.685396	+	0.728171i	$0.740371\pi$
$570$	2.58579	0.108307
$571$	−17.8995	−0.749071	−0.374535	−	0.927213i	$-0.622198\pi$
$571$	−17.8995	−0.749071	−0.374535	+	0.927213i	$0.622198\pi$
$572$	0	0
$573$	5.65685	0.236318
$574$	4.34315	0.181279
$575$	1.82843	0.0762507
$576$	8.00000	0.333333
$577$	−10.9706	−0.456711	−0.228355	−	0.973578i	$-0.573335\pi$
$577$	−10.9706	−0.456711	−0.228355	+	0.973578i	$0.573335\pi$
$578$	−3.31371	−0.137832
$579$	2.48528	0.103285
$580$	0	0
$581$	11.1421	0.462254
$582$	−1.75736	−0.0728449
$583$	−2.65685	−0.110036
$584$	−24.0000	−0.993127
$585$	−3.41421	−0.141160
$586$	−27.0711	−1.11830
$587$	−15.0711	−0.622050	−0.311025	−	0.950402i	$-0.600672\pi$
$587$	−15.0711	−0.622050	−0.311025	+	0.950402i	$0.600672\pi$
$588$	0	0
$589$	6.24264	0.257224
$590$	−16.3848	−0.674551
$591$	9.17157	0.377268
$592$	−8.97056	−0.368688
$593$	−15.5147	−0.637113	−0.318557	−	0.947904i	$-0.603198\pi$
$593$	−15.5147	−0.637113	−0.318557	+	0.947904i	$0.603198\pi$
$594$	−1.41421	−0.0580259
$595$	3.82843	0.156950
$596$	0	0
$597$	−3.31371	−0.135621
$598$	8.82843	0.361021
$599$	−0.142136	−0.00580750	−0.00290375	−	0.999996i	$-0.500924\pi$
$599$	−0.142136	−0.00580750	−0.00290375	+	0.999996i	$0.500924\pi$
$600$	2.82843	0.115470
$601$	33.1421	1.35190	0.675948	−	0.736949i	$-0.263734\pi$
$601$	33.1421	1.35190	0.675948	+	0.736949i	$0.263734\pi$
$602$	5.07107	0.206681
$603$	−6.00000	−0.244339
$604$	0	0
$605$	−1.00000	−0.0406558
$606$	−16.4853	−0.669669
$607$	11.1716	0.453440	0.226720	−	0.973960i	$-0.427200\pi$
$607$	11.1716	0.453440	0.226720	+	0.973960i	$0.427200\pi$
$608$	0	0
$609$	7.24264	0.293487
$610$	0.928932	0.0376114
$611$	34.9706	1.41476
$612$	0	0
$613$	30.9706	1.25089	0.625445	−	0.780269i	$-0.284918\pi$
$613$	30.9706	1.25089	0.625445	+	0.780269i	$0.284918\pi$
$614$	−43.1127	−1.73989
$615$	−3.07107	−0.123837
$616$	2.82843	0.113961
$617$	−42.4264	−1.70802	−0.854011	−	0.520254i	$-0.825837\pi$
$617$	−42.4264	−1.70802	−0.854011	+	0.520254i	$0.825837\pi$
$618$	16.5858	0.667178
$619$	−27.9411	−1.12305	−0.561524	−	0.827460i	$-0.689785\pi$
$619$	−27.9411	−1.12305	−0.561524	+	0.827460i	$0.689785\pi$
$620$	0	0
$621$	−1.82843	−0.0733723
$622$	44.0000	1.76424
$623$	−14.0711	−0.563745
$624$	13.6569	0.546712
$625$	1.00000	0.0400000
$626$	−21.5563	−0.861565
$627$	−1.82843	−0.0730203
$628$	0	0
$629$	8.58579	0.342338
$630$	1.41421	0.0563436
$631$	−29.4853	−1.17379	−0.586895	−	0.809663i	$-0.699650\pi$
$631$	−29.4853	−1.17379	−0.586895	+	0.809663i	$0.699650\pi$
$632$	−0.686292	−0.0272992
$633$	10.4853	0.416753
$634$	8.68629	0.344977
$635$	11.7279	0.465408
$636$	0	0
$637$	3.41421	0.135276
$638$	10.2426	0.405510
$639$	−11.0711	−0.437965
$640$	−11.3137	−0.447214
$641$	33.5980	1.32704	0.663520	−	0.748158i	$-0.269062\pi$
$641$	33.5980	1.32704	0.663520	+	0.748158i	$0.269062\pi$
$642$	6.48528	0.255954
$643$	2.55635	0.100813	0.0504063	−	0.998729i	$-0.483948\pi$
$643$	2.55635	0.100813	0.0504063	+	0.998729i	$0.483948\pi$
$644$	0	0
$645$	−3.58579	−0.141190
$646$	9.89949	0.389490
$647$	−15.5147	−0.609947	−0.304973	−	0.952361i	$-0.598648\pi$
$647$	−15.5147	−0.609947	−0.304973	+	0.952361i	$0.598648\pi$
$648$	−2.82843	−0.111111
$649$	11.5858	0.454782
$650$	4.82843	0.189386
$651$	3.41421	0.133814
$652$	0	0
$653$	3.34315	0.130827	0.0654137	−	0.997858i	$-0.479163\pi$
$653$	3.34315	0.130827	0.0654137	+	0.997858i	$0.479163\pi$
$654$	−4.14214	−0.161970
$655$	−10.2426	−0.400213
$656$	12.2843	0.479620
$657$	8.48528	0.331042
$658$	−14.4853	−0.564695
$659$	13.0416	0.508030	0.254015	−	0.967200i	$-0.418249\pi$
$659$	13.0416	0.508030	0.254015	+	0.967200i	$0.418249\pi$
$660$	0	0
$661$	25.5563	0.994027	0.497013	−	0.867743i	$-0.334430\pi$
$661$	25.5563	0.994027	0.497013	+	0.867743i	$0.334430\pi$
$662$	21.4142	0.832287
$663$	−13.0711	−0.507638
$664$	31.5147	1.22301
$665$	1.82843	0.0709034
$666$	3.17157	0.122896
$667$	13.2426	0.512757
$668$	0	0
$669$	−7.24264	−0.280017
$670$	8.48528	0.327815
$671$	−0.656854	−0.0253576
$672$	0	0
$673$	43.0416	1.65913	0.829566	−	0.558408i	$-0.188588\pi$
$673$	43.0416	1.65913	0.829566	+	0.558408i	$0.188588\pi$
$674$	10.2426	0.394532
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	−8.85786	−0.340435	−0.170218	−	0.985406i	$-0.554447\pi$
$677$	−8.85786	−0.340435	−0.170218	+	0.985406i	$0.554447\pi$
$678$	20.2426	0.777414
$679$	−1.24264	−0.0476882
$680$	10.8284	0.415251
$681$	13.3431	0.511310
$682$	4.82843	0.184890
$683$	−39.3137	−1.50430	−0.752149	−	0.658994i	$-0.770982\pi$
$683$	−39.3137	−1.50430	−0.752149	+	0.658994i	$0.770982\pi$
$684$	0	0
$685$	−13.6569	−0.521802
$686$	−1.41421	−0.0539949
$687$	18.7279	0.714515
$688$	14.3431	0.546827
$689$	−9.07107	−0.345580
$690$	2.58579	0.0984392
$691$	−30.9706	−1.17818	−0.589088	−	0.808069i	$-0.700513\pi$
$691$	−30.9706	−1.17818	−0.589088	+	0.808069i	$0.700513\pi$
$692$	0	0
$693$	−1.00000	−0.0379869
$694$	−28.0000	−1.06287
$695$	−14.0000	−0.531050
$696$	20.4853	0.776493
$697$	−11.7574	−0.445342
$698$	26.8701	1.01705
$699$	−16.2426	−0.614353
$700$	0	0
$701$	41.0416	1.55012	0.775060	−	0.631887i	$-0.217719\pi$
$701$	41.0416	1.55012	0.775060	+	0.631887i	$0.217719\pi$
$702$	−4.82843	−0.182237
$703$	4.10051	0.154653
$704$	8.00000	0.301511
$705$	10.2426	0.385760
$706$	28.4853	1.07206
$707$	−11.6569	−0.438401
$708$	0	0
$709$	−7.34315	−0.275778	−0.137889	−	0.990448i	$-0.544032\pi$
$709$	−7.34315	−0.275778	−0.137889	+	0.990448i	$0.544032\pi$
$710$	15.6569	0.587591
$711$	0.242641	0.00909974
$712$	−39.7990	−1.49153
$713$	6.24264	0.233789
$714$	5.41421	0.202622
$715$	−3.41421	−0.127684
$716$	0	0
$717$	0.0710678	0.00265408
$718$	−20.5858	−0.768255
$719$	−44.0122	−1.64138	−0.820689	−	0.571375i	$-0.806410\pi$
$719$	−44.0122	−1.64138	−0.820689	+	0.571375i	$0.806410\pi$
$720$	4.00000	0.149071
$721$	11.7279	0.436771
$722$	−22.1421	−0.824045
$723$	8.48528	0.315571
$724$	0	0
$725$	7.24264	0.268985
$726$	−1.41421	−0.0524864
$727$	32.5563	1.20745	0.603724	−	0.797193i	$-0.293683\pi$
$727$	32.5563	1.20745	0.603724	+	0.797193i	$0.293683\pi$
$728$	9.65685	0.357907
$729$	1.00000	0.0370370
$730$	−12.0000	−0.444140
$731$	−13.7279	−0.507746
$732$	0	0
$733$	9.79899	0.361934	0.180967	−	0.983489i	$-0.442077\pi$
$733$	9.79899	0.361934	0.180967	+	0.983489i	$0.442077\pi$
$734$	−18.7279	−0.691260
$735$	1.00000	0.0368856
$736$	0	0
$737$	−6.00000	−0.221013
$738$	−4.34315	−0.159873
$739$	48.4264	1.78139	0.890697	−	0.454597i	$-0.150217\pi$
$739$	48.4264	1.78139	0.890697	+	0.454597i	$0.150217\pi$
$740$	0	0
$741$	−6.24264	−0.229329
$742$	3.75736	0.137937
$743$	8.14214	0.298706	0.149353	−	0.988784i	$-0.452281\pi$
$743$	8.14214	0.298706	0.149353	+	0.988784i	$0.452281\pi$
$744$	9.65685	0.354037
$745$	0.828427	0.0303512
$746$	9.07107	0.332115
$747$	−11.1421	−0.407669
$748$	0	0
$749$	4.58579	0.167561
$750$	1.41421	0.0516398
$751$	1.48528	0.0541987	0.0270993	−	0.999633i	$-0.491373\pi$
$751$	1.48528	0.0541987	0.0270993	+	0.999633i	$0.491373\pi$
$752$	−40.9706	−1.49404
$753$	−17.6569	−0.643452
$754$	34.9706	1.27355
$755$	15.6569	0.569811
$756$	0	0
$757$	−17.1127	−0.621972	−0.310986	−	0.950415i	$-0.600659\pi$
$757$	−17.1127	−0.621972	−0.310986	+	0.950415i	$0.600659\pi$
$758$	−31.3553	−1.13888
$759$	−1.82843	−0.0663677
$760$	5.17157	0.187593
$761$	−38.2843	−1.38780	−0.693902	−	0.720070i	$-0.744110\pi$
$761$	−38.2843	−1.38780	−0.693902	+	0.720070i	$0.744110\pi$
$762$	16.5858	0.600840
$763$	−2.92893	−0.106034
$764$	0	0
$765$	−3.82843	−0.138417
$766$	−43.6569	−1.57739
$767$	39.5563	1.42830
$768$	0	0
$769$	−4.02944	−0.145305	−0.0726526	−	0.997357i	$-0.523146\pi$
$769$	−4.02944	−0.145305	−0.0726526	+	0.997357i	$0.523146\pi$
$770$	1.41421	0.0509647
$771$	16.2426	0.584964
$772$	0	0
$773$	19.8579	0.714238	0.357119	−	0.934059i	$-0.383759\pi$
$773$	19.8579	0.714238	0.357119	+	0.934059i	$0.383759\pi$
$774$	−5.07107	−0.182276
$775$	3.41421	0.122642
$776$	−3.51472	−0.126171
$777$	2.24264	0.0804543
$778$	50.4853	1.80999
$779$	−5.61522	−0.201186
$780$	0	0
$781$	−11.0711	−0.396154
$782$	9.89949	0.354005
$783$	−7.24264	−0.258831
$784$	−4.00000	−0.142857
$785$	−12.4142	−0.443082
$786$	−14.4853	−0.516673
$787$	−13.9411	−0.496947	−0.248474	−	0.968639i	$-0.579929\pi$
$787$	−13.9411	−0.496947	−0.248474	+	0.968639i	$0.579929\pi$
$788$	0	0
$789$	−14.1421	−0.503473
$790$	−0.343146	−0.0122086
$791$	14.3137	0.508937
$792$	−2.82843	−0.100504
$793$	−2.24264	−0.0796385
$794$	4.97056	0.176399
$795$	−2.65685	−0.0942289
$796$	0	0
$797$	37.7990	1.33891	0.669454	−	0.742853i	$-0.266528\pi$
$797$	37.7990	1.33891	0.669454	+	0.742853i	$0.266528\pi$
$798$	2.58579	0.0915358
$799$	39.2132	1.38726
$800$	0	0
$801$	14.0711	0.497177
$802$	−14.6863	−0.518591
$803$	8.48528	0.299439
$804$	0	0
$805$	1.82843	0.0644436
$806$	16.4853	0.580669
$807$	−24.5563	−0.864424
$808$	−32.9706	−1.15990
$809$	−24.1421	−0.848792	−0.424396	−	0.905477i	$-0.639514\pi$
$809$	−24.1421	−0.848792	−0.424396	+	0.905477i	$0.639514\pi$
$810$	−1.41421	−0.0496904
$811$	45.9411	1.61321	0.806606	−	0.591090i	$-0.201302\pi$
$811$	45.9411	1.61321	0.806606	+	0.591090i	$0.201302\pi$
$812$	0	0
$813$	2.17157	0.0761604
$814$	3.17157	0.111164
$815$	−10.7279	−0.375783
$816$	15.3137	0.536087
$817$	−6.55635	−0.229378
$818$	27.5980	0.964941
$819$	−3.41421	−0.119302
$820$	0	0
$821$	10.0711	0.351483	0.175741	−	0.984436i	$-0.443768\pi$
$821$	10.0711	0.351483	0.175741	+	0.984436i	$0.443768\pi$
$822$	−19.3137	−0.673643
$823$	3.21320	0.112005	0.0560026	−	0.998431i	$-0.482164\pi$
$823$	3.21320	0.112005	0.0560026	+	0.998431i	$0.482164\pi$
$824$	33.1716	1.15559
$825$	−1.00000	−0.0348155
$826$	−16.3848	−0.570099
$827$	−18.1421	−0.630864	−0.315432	−	0.948948i	$-0.602149\pi$
$827$	−18.1421	−0.630864	−0.315432	+	0.948948i	$0.602149\pi$
$828$	0	0
$829$	−14.4853	−0.503095	−0.251547	−	0.967845i	$-0.580939\pi$
$829$	−14.4853	−0.503095	−0.251547	+	0.967845i	$0.580939\pi$
$830$	15.7574	0.546946
$831$	−13.1716	−0.456917
$832$	27.3137	0.946932
$833$	3.82843	0.132647
$834$	−19.7990	−0.685583
$835$	−11.6569	−0.403402
$836$	0	0
$837$	−3.41421	−0.118012
$838$	11.4142	0.394297
$839$	−34.4142	−1.18811	−0.594055	−	0.804424i	$-0.702474\pi$
$839$	−34.4142	−1.18811	−0.594055	+	0.804424i	$0.702474\pi$
$840$	2.82843	0.0975900
$841$	23.4558	0.808822
$842$	−0.928932	−0.0320131
$843$	−26.8284	−0.924020
$844$	0	0
$845$	1.34315	0.0462056
$846$	14.4853	0.498014
$847$	−1.00000	−0.0343604
$848$	10.6274	0.364947
$849$	27.2132	0.933955
$850$	5.41421	0.185706
$851$	4.10051	0.140564
$852$	0	0
$853$	27.0711	0.926896	0.463448	−	0.886124i	$-0.346612\pi$
$853$	27.0711	0.926896	0.463448	+	0.886124i	$0.346612\pi$
$854$	0.928932	0.0317874
$855$	−1.82843	−0.0625309
$856$	12.9706	0.443325
$857$	24.6274	0.841257	0.420628	−	0.907233i	$-0.361810\pi$
$857$	24.6274	0.841257	0.420628	+	0.907233i	$0.361810\pi$
$858$	−4.82843	−0.164840
$859$	−43.0122	−1.46756	−0.733779	−	0.679389i	$-0.762245\pi$
$859$	−43.0122	−1.46756	−0.733779	+	0.679389i	$0.762245\pi$
$860$	0	0
$861$	−3.07107	−0.104662
$862$	54.9117	1.87030
$863$	−38.3137	−1.30421	−0.652107	−	0.758127i	$-0.726115\pi$
$863$	−38.3137	−1.30421	−0.652107	+	0.758127i	$0.726115\pi$
$864$	0	0
$865$	3.31371	0.112669
$866$	−5.85786	−0.199058
$867$	2.34315	0.0795774
$868$	0	0
$869$	0.242641	0.00823102
$870$	10.2426	0.347258
$871$	−20.4853	−0.694117
$872$	−8.28427	−0.280541
$873$	1.24264	0.0420570
$874$	4.72792	0.159924
$875$	1.00000	0.0338062
$876$	0	0
$877$	26.4142	0.891945	0.445972	−	0.895047i	$-0.352858\pi$
$877$	26.4142	0.891945	0.445972	+	0.895047i	$0.352858\pi$
$878$	4.24264	0.143182
$879$	19.1421	0.645648
$880$	4.00000	0.134840
$881$	−24.0711	−0.810975	−0.405487	−	0.914101i	$-0.632898\pi$
$881$	−24.0711	−0.810975	−0.405487	+	0.914101i	$0.632898\pi$
$882$	1.41421	0.0476190
$883$	−40.4853	−1.36244	−0.681219	−	0.732080i	$-0.738550\pi$
$883$	−40.4853	−1.36244	−0.681219	+	0.732080i	$0.738550\pi$
$884$	0	0
$885$	11.5858	0.389452
$886$	44.7696	1.50406
$887$	10.6569	0.357822	0.178911	−	0.983865i	$-0.442743\pi$
$887$	10.6569	0.357822	0.178911	+	0.983865i	$0.442743\pi$
$888$	6.34315	0.212862
$889$	11.7279	0.393342
$890$	−19.8995	−0.667033
$891$	1.00000	0.0335013
$892$	0	0
$893$	18.7279	0.626706
$894$	1.17157	0.0391833
$895$	−16.2426	−0.542932
$896$	−11.3137	−0.377964
$897$	−6.24264	−0.208436
$898$	−31.9411	−1.06589
$899$	24.7279	0.824722
$900$	0	0
$901$	−10.1716	−0.338864
$902$	−4.34315	−0.144611
$903$	−3.58579	−0.119328
$904$	40.4853	1.34652
$905$	14.9706	0.497638
$906$	22.1421	0.735623
$907$	43.6985	1.45098	0.725492	−	0.688230i	$-0.241612\pi$
$907$	43.6985	1.45098	0.725492	+	0.688230i	$0.241612\pi$
$908$	0	0
$909$	11.6569	0.386633
$910$	4.82843	0.160061
$911$	−5.85786	−0.194080	−0.0970399	−	0.995280i	$-0.530937\pi$
$911$	−5.85786	−0.194080	−0.0970399	+	0.995280i	$0.530937\pi$
$912$	7.31371	0.242181
$913$	−11.1421	−0.368751
$914$	24.8701	0.822628
$915$	−0.656854	−0.0217149
$916$	0	0
$917$	−10.2426	−0.338242
$918$	−5.41421	−0.178696
$919$	1.31371	0.0433352	0.0216676	−	0.999765i	$-0.493102\pi$
$919$	1.31371	0.0433352	0.0216676	+	0.999765i	$0.493102\pi$
$920$	5.17157	0.170502
$921$	30.4853	1.00452
$922$	28.4853	0.938113
$923$	−37.7990	−1.24417
$924$	0	0
$925$	2.24264	0.0737376
$926$	−43.1127	−1.41677
$927$	−11.7279	−0.385195
$928$	0	0
$929$	19.7990	0.649584	0.324792	−	0.945786i	$-0.394706\pi$
$929$	19.7990	0.649584	0.324792	+	0.945786i	$0.394706\pi$
$930$	4.82843	0.158330
$931$	1.82843	0.0599243
$932$	0	0
$933$	−31.1127	−1.01858
$934$	52.9706	1.73325
$935$	−3.82843	−0.125203
$936$	−9.65685	−0.315644
$937$	16.5269	0.539911	0.269955	−	0.962873i	$-0.412991\pi$
$937$	16.5269	0.539911	0.269955	+	0.962873i	$0.412991\pi$
$938$	8.48528	0.277054
$939$	15.2426	0.497425
$940$	0	0
$941$	−33.3553	−1.08735	−0.543676	−	0.839295i	$-0.682968\pi$
$941$	−33.3553	−1.08735	−0.543676	+	0.839295i	$0.682968\pi$
$942$	−17.5563	−0.572017
$943$	−5.61522	−0.182857
$944$	−46.3431	−1.50834
$945$	−1.00000	−0.0325300
$946$	−5.07107	−0.164875
$947$	27.6863	0.899684	0.449842	−	0.893108i	$-0.351480\pi$
$947$	27.6863	0.899684	0.449842	+	0.893108i	$0.351480\pi$
$948$	0	0
$949$	28.9706	0.940424
$950$	2.58579	0.0838940
$951$	−6.14214	−0.199172
$952$	10.8284	0.350951
$953$	−47.6569	−1.54376	−0.771878	−	0.635770i	$-0.780683\pi$
$953$	−47.6569	−1.54376	−0.771878	+	0.635770i	$0.780683\pi$
$954$	−3.75736	−0.121649
$955$	5.65685	0.183052
$956$	0	0
$957$	−7.24264	−0.234121
$958$	7.85786	0.253876
$959$	−13.6569	−0.441003
$960$	8.00000	0.258199
$961$	−19.3431	−0.623972
$962$	10.8284	0.349123
$963$	−4.58579	−0.147775
$964$	0	0
$965$	2.48528	0.0800040
$966$	2.58579	0.0831963
$967$	1.78680	0.0574595	0.0287298	−	0.999587i	$-0.490854\pi$
$967$	1.78680	0.0574595	0.0287298	+	0.999587i	$0.490854\pi$
$968$	−2.82843	−0.0909091
$969$	−7.00000	−0.224872
$970$	−1.75736	−0.0564254
$971$	11.4437	0.367244	0.183622	−	0.982997i	$-0.441218\pi$
$971$	11.4437	0.367244	0.183622	+	0.982997i	$0.441218\pi$
$972$	0	0
$973$	−14.0000	−0.448819
$974$	−23.7990	−0.762569
$975$	−3.41421	−0.109342
$976$	2.62742	0.0841016
$977$	5.62742	0.180037	0.0900185	−	0.995940i	$-0.471307\pi$
$977$	5.62742	0.180037	0.0900185	+	0.995940i	$0.471307\pi$
$978$	−15.1716	−0.485133
$979$	14.0711	0.449713
$980$	0	0
$981$	2.92893	0.0935136
$982$	−4.87006	−0.155410
$983$	−40.8284	−1.30222	−0.651112	−	0.758981i	$-0.725697\pi$
$983$	−40.8284	−1.30222	−0.651112	+	0.758981i	$0.725697\pi$
$984$	−8.68629	−0.276909
$985$	9.17157	0.292231
$986$	39.2132	1.24880
$987$	10.2426	0.326027
$988$	0	0
$989$	−6.55635	−0.208480
$990$	−1.41421	−0.0449467
$991$	−45.9706	−1.46030	−0.730152	−	0.683285i	$-0.760551\pi$
$991$	−45.9706	−1.46030	−0.730152	+	0.683285i	$0.760551\pi$
$992$	0	0
$993$	−15.1421	−0.480521
$994$	15.6569	0.496605
$995$	−3.31371	−0.105052
$996$	0	0
$997$	−39.9411	−1.26495	−0.632474	−	0.774582i	$-0.717961\pi$
$997$	−39.9411	−1.26495	−0.632474	+	0.774582i	$0.717961\pi$
$998$	2.78680	0.0882145
$999$	−2.24264	−0.0709540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.p.1.2	✓	2
3.2	odd	2		3465.2.a.w.1.1		2
5.4	even	2		5775.2.a.bi.1.1		2
7.6	odd	2		8085.2.a.bf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.p.1.2	✓	2	1.1	even	1	trivial
3465.2.a.w.1.1		2	3.2	odd	2
5775.2.a.bi.1.1		2	5.4	even	2
8085.2.a.bf.1.2		2	7.6	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.41421 q^{6} -1.00000 q^{7} -2.82843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} -1.41421 q^{6} -1.00000 q^{7} -2.82843 q^{8} +1.00000 q^{9} -1.41421 q^{10} +1.00000 q^{11} +3.41421 q^{13} -1.41421 q^{14} +1.00000 q^{15} -4.00000 q^{16} +3.82843 q^{17} +1.41421 q^{18} +1.82843 q^{19} +1.00000 q^{21} +1.41421 q^{22} +1.82843 q^{23} +2.82843 q^{24} +1.00000 q^{25} +4.82843 q^{26} -1.00000 q^{27} +7.24264 q^{29} +1.41421 q^{30} +3.41421 q^{31} -1.00000 q^{33} +5.41421 q^{34} +1.00000 q^{35} +2.24264 q^{37} +2.58579 q^{38} -3.41421 q^{39} +2.82843 q^{40} -3.07107 q^{41} +1.41421 q^{42} -3.58579 q^{43} -1.00000 q^{45} +2.58579 q^{46} +10.2426 q^{47} +4.00000 q^{48} +1.00000 q^{49} +1.41421 q^{50} -3.82843 q^{51} -2.65685 q^{53} -1.41421 q^{54} -1.00000 q^{55} +2.82843 q^{56} -1.82843 q^{57} +10.2426 q^{58} +11.5858 q^{59} -0.656854 q^{61} +4.82843 q^{62} -1.00000 q^{63} +8.00000 q^{64} -3.41421 q^{65} -1.41421 q^{66} -6.00000 q^{67} -1.82843 q^{69} +1.41421 q^{70} -11.0711 q^{71} -2.82843 q^{72} +8.48528 q^{73} +3.17157 q^{74} -1.00000 q^{75} -1.00000 q^{77} -4.82843 q^{78} +0.242641 q^{79} +4.00000 q^{80} +1.00000 q^{81} -4.34315 q^{82} -11.1421 q^{83} -3.82843 q^{85} -5.07107 q^{86} -7.24264 q^{87} -2.82843 q^{88} +14.0711 q^{89} -1.41421 q^{90} -3.41421 q^{91} -3.41421 q^{93} +14.4853 q^{94} -1.82843 q^{95} +1.24264 q^{97} +1.41421 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9} + 2 q^{11} + 4 q^{13} + 2 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{19} + 2 q^{21} - 2 q^{23} + 2 q^{25} + 4 q^{26} - 2 q^{27} + 6 q^{29} + 4 q^{31} - 2 q^{33} + 8 q^{34} + 2 q^{35} - 4 q^{37} + 8 q^{38} - 4 q^{39} + 8 q^{41} - 10 q^{43} - 2 q^{45} + 8 q^{46} + 12 q^{47} + 8 q^{48} + 2 q^{49} - 2 q^{51} + 6 q^{53} - 2 q^{55} + 2 q^{57} + 12 q^{58} + 26 q^{59} + 10 q^{61} + 4 q^{62} - 2 q^{63} + 16 q^{64} - 4 q^{65} - 12 q^{67} + 2 q^{69} - 8 q^{71} + 12 q^{74} - 2 q^{75} - 2 q^{77} - 4 q^{78} - 8 q^{79} + 8 q^{80} + 2 q^{81} - 20 q^{82} + 6 q^{83} - 2 q^{85} + 4 q^{86} - 6 q^{87} + 14 q^{89} - 4 q^{91} - 4 q^{93} + 12 q^{94} + 2 q^{95} - 6 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9 + 2 * q^11 + 4 * q^13 + 2 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^19 + 2 * q^21 - 2 * q^23 + 2 * q^25 + 4 * q^26 - 2 * q^27 + 6 * q^29 + 4 * q^31 - 2 * q^33 + 8 * q^34 + 2 * q^35 - 4 * q^37 + 8 * q^38 - 4 * q^39 + 8 * q^41 - 10 * q^43 - 2 * q^45 + 8 * q^46 + 12 * q^47 + 8 * q^48 + 2 * q^49 - 2 * q^51 + 6 * q^53 - 2 * q^55 + 2 * q^57 + 12 * q^58 + 26 * q^59 + 10 * q^61 + 4 * q^62 - 2 * q^63 + 16 * q^64 - 4 * q^65 - 12 * q^67 + 2 * q^69 - 8 * q^71 + 12 * q^74 - 2 * q^75 - 2 * q^77 - 4 * q^78 - 8 * q^79 + 8 * q^80 + 2 * q^81 - 20 * q^82 + 6 * q^83 - 2 * q^85 + 4 * q^86 - 6 * q^87 + 14 * q^89 - 4 * q^91 - 4 * q^93 + 12 * q^94 + 2 * q^95 - 6 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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