LMFDB - Embedded newform 8085.2.a.cc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, 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("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 9x^{5} + 23x^{3} - 14x - 2 $ x^7 - 9x^5 + 23x^3 - 14*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.88643$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88643 q^{2} +1.00000 q^{3} +1.55863 q^{4} -1.00000 q^{5} -1.88643 q^{6} +0.832608 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.88643 q^{2} +1.00000 q^{3} +1.55863 q^{4} -1.00000 q^{5} -1.88643 q^{6} +0.832608 q^{8} +1.00000 q^{9} +1.88643 q^{10} +1.00000 q^{11} +1.55863 q^{12} +3.47416 q^{13} -1.00000 q^{15} -4.68793 q^{16} +5.25106 q^{17} -1.88643 q^{18} +3.11727 q^{19} -1.55863 q^{20} -1.88643 q^{22} +3.54105 q^{23} +0.832608 q^{24} +1.00000 q^{25} -6.55376 q^{26} +1.00000 q^{27} +10.5821 q^{29} +1.88643 q^{30} +9.63517 q^{31} +7.17825 q^{32} +1.00000 q^{33} -9.90579 q^{34} +1.55863 q^{36} +0.311632 q^{37} -5.88052 q^{38} +3.47416 q^{39} -0.832608 q^{40} +5.96860 q^{41} +10.1191 q^{43} +1.55863 q^{44} -1.00000 q^{45} -6.67996 q^{46} -8.25372 q^{47} -4.68793 q^{48} -1.88643 q^{50} +5.25106 q^{51} +5.41494 q^{52} +0.112521 q^{53} -1.88643 q^{54} -1.00000 q^{55} +3.11727 q^{57} -19.9625 q^{58} -6.81642 q^{59} -1.55863 q^{60} +2.20911 q^{61} -18.1761 q^{62} -4.16544 q^{64} -3.47416 q^{65} -1.88643 q^{66} +11.9671 q^{67} +8.18449 q^{68} +3.54105 q^{69} -12.7415 q^{71} +0.832608 q^{72} -10.3508 q^{73} -0.587874 q^{74} +1.00000 q^{75} +4.85868 q^{76} -6.55376 q^{78} -9.21095 q^{79} +4.68793 q^{80} +1.00000 q^{81} -11.2594 q^{82} +1.68582 q^{83} -5.25106 q^{85} -19.0890 q^{86} +10.5821 q^{87} +0.832608 q^{88} +15.8416 q^{89} +1.88643 q^{90} +5.51921 q^{92} +9.63517 q^{93} +15.5701 q^{94} -3.11727 q^{95} +7.17825 q^{96} -6.08075 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{3} + 4 q^{4} - 7 q^{5} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^3 + 4 * q^4 - 7 * q^5 + 7 * q^9	$ 7 q + 7 q^{3} + 4 q^{4} - 7 q^{5} + 7 q^{9} + 7 q^{11} + 4 q^{12} + 7 q^{13} - 7 q^{15} - 10 q^{16} + 6 q^{17} + 8 q^{19} - 4 q^{20} - q^{23} + 7 q^{25} - 12 q^{26} + 7 q^{27} - 9 q^{29} + 20 q^{31} + 7 q^{33} + 12 q^{34} + 4 q^{36} + 6 q^{37} + 7 q^{39} + 5 q^{41} + 15 q^{43} + 4 q^{44} - 7 q^{45} - 6 q^{46} + q^{47} - 10 q^{48} + 6 q^{51} + 14 q^{52} + 13 q^{53} - 7 q^{55} + 8 q^{57} - 10 q^{58} + 38 q^{59} - 4 q^{60} + 4 q^{61} + 4 q^{62} - 24 q^{64} - 7 q^{65} + 22 q^{67} - 16 q^{68} - q^{69} - 26 q^{71} + 24 q^{73} + 14 q^{74} + 7 q^{75} + 52 q^{76} - 12 q^{78} + 10 q^{80} + 7 q^{81} + 18 q^{82} + 20 q^{83} - 6 q^{85} - 8 q^{86} - 9 q^{87} + 34 q^{89} - 24 q^{92} + 20 q^{93} + 28 q^{94} - 8 q^{95} + 10 q^{97} + 7 q^{99}+O(q^{100}) $ 7 * q + 7 * q^3 + 4 * q^4 - 7 * q^5 + 7 * q^9 + 7 * q^11 + 4 * q^12 + 7 * q^13 - 7 * q^15 - 10 * q^16 + 6 * q^17 + 8 * q^19 - 4 * q^20 - q^23 + 7 * q^25 - 12 * q^26 + 7 * q^27 - 9 * q^29 + 20 * q^31 + 7 * q^33 + 12 * q^34 + 4 * q^36 + 6 * q^37 + 7 * q^39 + 5 * q^41 + 15 * q^43 + 4 * q^44 - 7 * q^45 - 6 * q^46 + q^47 - 10 * q^48 + 6 * q^51 + 14 * q^52 + 13 * q^53 - 7 * q^55 + 8 * q^57 - 10 * q^58 + 38 * q^59 - 4 * q^60 + 4 * q^61 + 4 * q^62 - 24 * q^64 - 7 * q^65 + 22 * q^67 - 16 * q^68 - q^69 - 26 * q^71 + 24 * q^73 + 14 * q^74 + 7 * q^75 + 52 * q^76 - 12 * q^78 + 10 * q^80 + 7 * q^81 + 18 * q^82 + 20 * q^83 - 6 * q^85 - 8 * q^86 - 9 * q^87 + 34 * q^89 - 24 * q^92 + 20 * q^93 + 28 * q^94 - 8 * q^95 + 10 * q^97 + 7 * 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 $

$2$	−1.88643	−1.33391	−0.666955	−	0.745098i	$-0.732403\pi$
$2$	−1.88643	−1.33391	−0.666955	+	0.745098i	$0.732403\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.55863	0.779317
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.88643	−0.770134
$7$	0	0
$7$	0	0
$8$	0.832608	0.294371
$9$	1.00000	0.333333
$10$	1.88643	0.596543
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.55863	0.449939
$13$	3.47416	0.963557	0.481779	−	0.876293i	$-0.339991\pi$
$13$	3.47416	0.963557	0.481779	+	0.876293i	$0.339991\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−4.68793	−1.17198
$17$	5.25106	1.27357	0.636785	−	0.771041i	$-0.280264\pi$
$17$	5.25106	1.27357	0.636785	+	0.771041i	$0.280264\pi$
$18$	−1.88643	−0.444637
$19$	3.11727	0.715150	0.357575	−	0.933884i	$-0.383604\pi$
$19$	3.11727	0.715150	0.357575	+	0.933884i	$0.383604\pi$
$20$	−1.55863	−0.348521
$21$	0	0
$22$	−1.88643	−0.402189
$23$	3.54105	0.738361	0.369180	−	0.929358i	$-0.379638\pi$
$23$	3.54105	0.738361	0.369180	+	0.929358i	$0.379638\pi$
$24$	0.832608	0.169955
$25$	1.00000	0.200000
$26$	−6.55376	−1.28530
$27$	1.00000	0.192450
$28$	0	0
$29$	10.5821	1.96505	0.982526	−	0.186127i	$-0.0595935\pi$
$29$	10.5821	1.96505	0.982526	+	0.186127i	$0.0595935\pi$
$30$	1.88643	0.344414
$31$	9.63517	1.73053	0.865264	−	0.501317i	$-0.167151\pi$
$31$	9.63517	1.73053	0.865264	+	0.501317i	$0.167151\pi$
$32$	7.17825	1.26895
$33$	1.00000	0.174078
$34$	−9.90579	−1.69883
$35$	0	0
$36$	1.55863	0.259772
$37$	0.311632	0.0512320	0.0256160	−	0.999672i	$-0.491845\pi$
$37$	0.311632	0.0512320	0.0256160	+	0.999672i	$0.491845\pi$
$38$	−5.88052	−0.953946
$39$	3.47416	0.556310
$40$	−0.832608	−0.131647
$41$	5.96860	0.932139	0.466069	−	0.884748i	$-0.345670\pi$
$41$	5.96860	0.932139	0.466069	+	0.884748i	$0.345670\pi$
$42$	0	0
$43$	10.1191	1.54315	0.771574	−	0.636140i	$-0.219470\pi$
$43$	10.1191	1.54315	0.771574	+	0.636140i	$0.219470\pi$
$44$	1.55863	0.234973
$45$	−1.00000	−0.149071
$46$	−6.67996	−0.984907
$47$	−8.25372	−1.20393	−0.601964	−	0.798523i	$-0.705615\pi$
$47$	−8.25372	−1.20393	−0.601964	+	0.798523i	$0.705615\pi$
$48$	−4.68793	−0.676644
$49$	0	0
$50$	−1.88643	−0.266782
$51$	5.25106	0.735296
$52$	5.41494	0.750916
$53$	0.112521	0.0154559	0.00772795	−	0.999970i	$-0.497540\pi$
$53$	0.112521	0.0154559	0.00772795	+	0.999970i	$0.497540\pi$
$54$	−1.88643	−0.256711
$55$	−1.00000	−0.134840
$56$	0	0
$57$	3.11727	0.412892
$58$	−19.9625	−2.62120
$59$	−6.81642	−0.887422	−0.443711	−	0.896170i	$-0.646338\pi$
$59$	−6.81642	−0.887422	−0.443711	+	0.896170i	$0.646338\pi$
$60$	−1.55863	−0.201219
$61$	2.20911	0.282848	0.141424	−	0.989949i	$-0.454832\pi$
$61$	2.20911	0.282848	0.141424	+	0.989949i	$0.454832\pi$
$62$	−18.1761	−2.30837
$63$	0	0
$64$	−4.16544	−0.520680
$65$	−3.47416	−0.430916
$66$	−1.88643	−0.232204
$67$	11.9671	1.46202	0.731008	−	0.682369i	$-0.239050\pi$
$67$	11.9671	1.46202	0.731008	+	0.682369i	$0.239050\pi$
$68$	8.18449	0.992515
$69$	3.54105	0.426293
$70$	0	0
$71$	−12.7415	−1.51213	−0.756067	−	0.654494i	$-0.772882\pi$
$71$	−12.7415	−1.51213	−0.756067	+	0.654494i	$0.772882\pi$
$72$	0.832608	0.0981238
$73$	−10.3508	−1.21147	−0.605733	−	0.795668i	$-0.707120\pi$
$73$	−10.3508	−1.21147	−0.605733	+	0.795668i	$0.707120\pi$
$74$	−0.587874	−0.0683390
$75$	1.00000	0.115470
$76$	4.85868	0.557329
$77$	0	0
$78$	−6.55376	−0.742068
$79$	−9.21095	−1.03631	−0.518157	−	0.855286i	$-0.673382\pi$
$79$	−9.21095	−1.03631	−0.518157	+	0.855286i	$0.673382\pi$
$80$	4.68793	0.524126
$81$	1.00000	0.111111
$82$	−11.2594	−1.24339
$83$	1.68582	0.185042	0.0925212	−	0.995711i	$-0.470507\pi$
$83$	1.68582	0.185042	0.0925212	+	0.995711i	$0.470507\pi$
$84$	0	0
$85$	−5.25106	−0.569558
$86$	−19.0890	−2.05842
$87$	10.5821	1.13452
$88$	0.832608	0.0887563
$89$	15.8416	1.67921	0.839603	−	0.543201i	$-0.182788\pi$
$89$	15.8416	1.67921	0.839603	+	0.543201i	$0.182788\pi$
$90$	1.88643	0.198848
$91$	0	0
$92$	5.51921	0.575417
$93$	9.63517	0.999121
$94$	15.5701	1.60593
$95$	−3.11727	−0.319825
$96$	7.17825	0.732627
$97$	−6.08075	−0.617407	−0.308703	−	0.951158i	$-0.599895\pi$
$97$	−6.08075	−0.617407	−0.308703	+	0.951158i	$0.599895\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	1.55863	0.155863
$101$	1.65717	0.164895	0.0824474	−	0.996595i	$-0.473726\pi$
$101$	1.65717	0.164895	0.0824474	+	0.996595i	$0.473726\pi$
$102$	−9.90579	−0.980819
$103$	6.30187	0.620942	0.310471	−	0.950583i	$-0.399513\pi$
$103$	6.30187	0.620942	0.310471	+	0.950583i	$0.399513\pi$
$104$	2.89261	0.283644
$105$	0	0
$106$	−0.212263	−0.0206168
$107$	2.07353	0.200456	0.100228	−	0.994965i	$-0.468043\pi$
$107$	2.07353	0.200456	0.100228	+	0.994965i	$0.468043\pi$
$108$	1.55863	0.149980
$109$	9.69577	0.928686	0.464343	−	0.885655i	$-0.346290\pi$
$109$	9.69577	0.928686	0.464343	+	0.885655i	$0.346290\pi$
$110$	1.88643	0.179864
$111$	0.311632	0.0295788
$112$	0	0
$113$	−18.0966	−1.70239	−0.851195	−	0.524850i	$-0.824121\pi$
$113$	−18.0966	−1.70239	−0.851195	+	0.524850i	$0.824121\pi$
$114$	−5.88052	−0.550761
$115$	−3.54105	−0.330205
$116$	16.4937	1.53140
$117$	3.47416	0.321186
$118$	12.8587	1.18374
$119$	0	0
$120$	−0.832608	−0.0760064
$121$	1.00000	0.0909091
$122$	−4.16734	−0.377294
$123$	5.96860	0.538170
$124$	15.0177	1.34863
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	8.73327	0.774952	0.387476	−	0.921880i	$-0.373347\pi$
$127$	8.73327	0.774952	0.387476	+	0.921880i	$0.373347\pi$
$128$	−6.49867	−0.574407
$129$	10.1191	0.890937
$130$	6.55376	0.574803
$131$	−20.3961	−1.78202	−0.891009	−	0.453985i	$-0.850002\pi$
$131$	−20.3961	−1.78202	−0.891009	+	0.453985i	$0.850002\pi$
$132$	1.55863	0.135662
$133$	0	0
$134$	−22.5752	−1.95020
$135$	−1.00000	−0.0860663
$136$	4.37208	0.374903
$137$	−4.92329	−0.420625	−0.210312	−	0.977634i	$-0.567448\pi$
$137$	−4.92329	−0.420625	−0.210312	+	0.977634i	$0.567448\pi$
$138$	−6.67996	−0.568636
$139$	6.78762	0.575718	0.287859	−	0.957673i	$-0.407057\pi$
$139$	6.78762	0.575718	0.287859	+	0.957673i	$0.407057\pi$
$140$	0	0
$141$	−8.25372	−0.695089
$142$	24.0359	2.01705
$143$	3.47416	0.290523
$144$	−4.68793	−0.390661
$145$	−10.5821	−0.878798
$146$	19.5261	1.61599
$147$	0	0
$148$	0.485721	0.0399260
$149$	−14.8864	−1.21954	−0.609769	−	0.792579i	$-0.708738\pi$
$149$	−14.8864	−1.21954	−0.609769	+	0.792579i	$0.708738\pi$
$150$	−1.88643	−0.154027
$151$	8.15803	0.663891	0.331946	−	0.943299i	$-0.392295\pi$
$151$	8.15803	0.663891	0.331946	+	0.943299i	$0.392295\pi$
$152$	2.59546	0.210520
$153$	5.25106	0.424523
$154$	0	0
$155$	−9.63517	−0.773915
$156$	5.41494	0.433542
$157$	−0.747461	−0.0596539	−0.0298269	−	0.999555i	$-0.509496\pi$
$157$	−0.747461	−0.0596539	−0.0298269	+	0.999555i	$0.509496\pi$
$158$	17.3759	1.38235
$159$	0.112521	0.00892347
$160$	−7.17825	−0.567491
$161$	0	0
$162$	−1.88643	−0.148212
$163$	−10.2535	−0.803116	−0.401558	−	0.915834i	$-0.631531\pi$
$163$	−10.2535	−0.803116	−0.401558	+	0.915834i	$0.631531\pi$
$164$	9.30286	0.726431
$165$	−1.00000	−0.0778499
$166$	−3.18018	−0.246830
$167$	12.6608	0.979725	0.489862	−	0.871800i	$-0.337047\pi$
$167$	12.6608	0.979725	0.489862	+	0.871800i	$0.337047\pi$
$168$	0	0
$169$	−0.930246	−0.0715574
$170$	9.90579	0.759739
$171$	3.11727	0.238383
$172$	15.7720	1.20260
$173$	−17.5912	−1.33744	−0.668718	−	0.743516i	$-0.733157\pi$
$173$	−17.5912	−1.33744	−0.668718	+	0.743516i	$0.733157\pi$
$174$	−19.9625	−1.51335
$175$	0	0
$176$	−4.68793	−0.353366
$177$	−6.81642	−0.512353
$178$	−29.8841	−2.23991
$179$	13.8091	1.03214	0.516069	−	0.856547i	$-0.327395\pi$
$179$	13.8091	1.03214	0.516069	+	0.856547i	$0.327395\pi$
$180$	−1.55863	−0.116174
$181$	−9.87310	−0.733862	−0.366931	−	0.930248i	$-0.619591\pi$
$181$	−9.87310	−0.733862	−0.366931	+	0.930248i	$0.619591\pi$
$182$	0	0
$183$	2.20911	0.163302
$184$	2.94831	0.217352
$185$	−0.311632	−0.0229117
$186$	−18.1761	−1.33274
$187$	5.25106	0.383996
$188$	−12.8645	−0.938242
$189$	0	0
$190$	5.88052	0.426618
$191$	−17.1184	−1.23865	−0.619324	−	0.785136i	$-0.712593\pi$
$191$	−17.1184	−1.23865	−0.619324	+	0.785136i	$0.712593\pi$
$192$	−4.16544	−0.300615
$193$	−3.23063	−0.232546	−0.116273	−	0.993217i	$-0.537095\pi$
$193$	−3.23063	−0.232546	−0.116273	+	0.993217i	$0.537095\pi$
$194$	11.4709	0.823565
$195$	−3.47416	−0.248789
$196$	0	0
$197$	−9.77048	−0.696118	−0.348059	−	0.937473i	$-0.613159\pi$
$197$	−9.77048	−0.696118	−0.348059	+	0.937473i	$0.613159\pi$
$198$	−1.88643	−0.134063
$199$	25.5580	1.81176	0.905880	−	0.423534i	$-0.139211\pi$
$199$	25.5580	1.81176	0.905880	+	0.423534i	$0.139211\pi$
$200$	0.832608	0.0588743
$201$	11.9671	0.844095
$202$	−3.12615	−0.219955
$203$	0	0
$204$	8.18449	0.573029
$205$	−5.96860	−0.416865
$206$	−11.8881	−0.828281
$207$	3.54105	0.246120
$208$	−16.2866	−1.12927
$209$	3.11727	0.215626
$210$	0	0
$211$	1.67440	0.115271	0.0576353	−	0.998338i	$-0.481644\pi$
$211$	1.67440	0.115271	0.0576353	+	0.998338i	$0.481644\pi$
$212$	0.175378	0.0120450
$213$	−12.7415	−0.873031
$214$	−3.91158	−0.267390
$215$	−10.1191	−0.690117
$216$	0.832608	0.0566518
$217$	0	0
$218$	−18.2904	−1.23878
$219$	−10.3508	−0.699440
$220$	−1.55863	−0.105083
$221$	18.2430	1.22716
$222$	−0.587874	−0.0394555
$223$	−7.67561	−0.513997	−0.256999	−	0.966412i	$-0.582734\pi$
$223$	−7.67561	−0.513997	−0.256999	+	0.966412i	$0.582734\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	34.1381	2.27083
$227$	−5.88129	−0.390355	−0.195177	−	0.980768i	$-0.562528\pi$
$227$	−5.88129	−0.390355	−0.195177	+	0.980768i	$0.562528\pi$
$228$	4.85868	0.321774
$229$	0.823104	0.0543922	0.0271961	−	0.999630i	$-0.491342\pi$
$229$	0.823104	0.0543922	0.0271961	+	0.999630i	$0.491342\pi$
$230$	6.67996	0.440464
$231$	0	0
$232$	8.81077	0.578455
$233$	16.5128	1.08179	0.540893	−	0.841091i	$-0.318086\pi$
$233$	16.5128	1.08179	0.540893	+	0.841091i	$0.318086\pi$
$234$	−6.55376	−0.428433
$235$	8.25372	0.538413
$236$	−10.6243	−0.691583
$237$	−9.21095	−0.598316
$238$	0	0
$239$	−5.12701	−0.331638	−0.165819	−	0.986156i	$-0.553027\pi$
$239$	−5.12701	−0.331638	−0.165819	+	0.986156i	$0.553027\pi$
$240$	4.68793	0.302604
$241$	−15.8554	−1.02134	−0.510670	−	0.859777i	$-0.670602\pi$
$241$	−15.8554	−1.02134	−0.510670	+	0.859777i	$0.670602\pi$
$242$	−1.88643	−0.121265
$243$	1.00000	0.0641500
$244$	3.44320	0.220428
$245$	0	0
$246$	−11.2594	−0.717871
$247$	10.8299	0.689088
$248$	8.02232	0.509418
$249$	1.68582	0.106834
$250$	1.88643	0.119309
$251$	−11.4107	−0.720237	−0.360118	−	0.932907i	$-0.617264\pi$
$251$	−11.4107	−0.720237	−0.360118	+	0.932907i	$0.617264\pi$
$252$	0	0
$253$	3.54105	0.222624
$254$	−16.4747	−1.03372
$255$	−5.25106	−0.328834
$256$	20.5902	1.28689
$257$	24.1287	1.50511	0.752555	−	0.658530i	$-0.228821\pi$
$257$	24.1287	1.50511	0.752555	+	0.658530i	$0.228821\pi$
$258$	−19.0890	−1.18843
$259$	0	0
$260$	−5.41494	−0.335820
$261$	10.5821	0.655017
$262$	38.4760	2.37705
$263$	−8.83449	−0.544758	−0.272379	−	0.962190i	$-0.587810\pi$
$263$	−8.83449	−0.544758	−0.272379	+	0.962190i	$0.587810\pi$
$264$	0.832608	0.0512435
$265$	−0.112521	−0.00691209
$266$	0	0
$267$	15.8416	0.969490
$268$	18.6523	1.13937
$269$	−26.1138	−1.59219	−0.796094	−	0.605174i	$-0.793104\pi$
$269$	−26.1138	−1.59219	−0.796094	+	0.605174i	$0.793104\pi$
$270$	1.88643	0.114805
$271$	1.67030	0.101464	0.0507319	−	0.998712i	$-0.483845\pi$
$271$	1.67030	0.101464	0.0507319	+	0.998712i	$0.483845\pi$
$272$	−24.6166	−1.49260
$273$	0	0
$274$	9.28746	0.561076
$275$	1.00000	0.0603023
$276$	5.51921	0.332217
$277$	16.2095	0.973933	0.486966	−	0.873421i	$-0.338103\pi$
$277$	16.2095	0.973933	0.486966	+	0.873421i	$0.338103\pi$
$278$	−12.8044	−0.767956
$279$	9.63517	0.576843
$280$	0	0
$281$	−22.1766	−1.32295	−0.661474	−	0.749968i	$-0.730069\pi$
$281$	−22.1766	−1.32295	−0.661474	+	0.749968i	$0.730069\pi$
$282$	15.5701	0.927186
$283$	20.0673	1.19288	0.596439	−	0.802658i	$-0.296582\pi$
$283$	20.0673	1.19288	0.596439	+	0.802658i	$0.296582\pi$
$284$	−19.8593	−1.17843
$285$	−3.11727	−0.184651
$286$	−6.55376	−0.387532
$287$	0	0
$288$	7.17825	0.422983
$289$	10.5737	0.621981
$290$	19.9625	1.17224
$291$	−6.08075	−0.356460
$292$	−16.1331	−0.944116
$293$	−24.0050	−1.40239	−0.701194	−	0.712970i	$-0.747349\pi$
$293$	−24.0050	−1.40239	−0.701194	+	0.712970i	$0.747349\pi$
$294$	0	0
$295$	6.81642	0.396867
$296$	0.259468	0.0150813
$297$	1.00000	0.0580259
$298$	28.0821	1.62675
$299$	12.3022	0.711453
$300$	1.55863	0.0899878
$301$	0	0
$302$	−15.3896	−0.885571
$303$	1.65717	0.0952021
$304$	−14.6135	−0.838143
$305$	−2.20911	−0.126493
$306$	−9.90579	−0.566276
$307$	−6.52901	−0.372630	−0.186315	−	0.982490i	$-0.559655\pi$
$307$	−6.52901	−0.372630	−0.186315	+	0.982490i	$0.559655\pi$
$308$	0	0
$309$	6.30187	0.358501
$310$	18.1761	1.03233
$311$	−23.6752	−1.34250	−0.671250	−	0.741231i	$-0.734242\pi$
$311$	−23.6752	−1.34250	−0.671250	+	0.741231i	$0.734242\pi$
$312$	2.89261	0.163762
$313$	13.7216	0.775591	0.387796	−	0.921745i	$-0.373237\pi$
$313$	13.7216	0.775591	0.387796	+	0.921745i	$0.373237\pi$
$314$	1.41004	0.0795729
$315$	0	0
$316$	−14.3565	−0.807616
$317$	15.9456	0.895596	0.447798	−	0.894135i	$-0.352208\pi$
$317$	15.9456	0.895596	0.447798	+	0.894135i	$0.352208\pi$
$318$	−0.212263	−0.0119031
$319$	10.5821	0.592485
$320$	4.16544	0.232855
$321$	2.07353	0.115733
$322$	0	0
$323$	16.3690	0.910794
$324$	1.55863	0.0865908
$325$	3.47416	0.192711
$326$	19.3426	1.07129
$327$	9.69577	0.536177
$328$	4.96951	0.274395
$329$	0	0
$330$	1.88643	0.103845
$331$	−27.6232	−1.51831	−0.759153	−	0.650912i	$-0.774387\pi$
$331$	−27.6232	−1.51831	−0.759153	+	0.650912i	$0.774387\pi$
$332$	2.62757	0.144207
$333$	0.311632	0.0170773
$334$	−23.8838	−1.30687
$335$	−11.9671	−0.653833
$336$	0	0
$337$	−10.4542	−0.569476	−0.284738	−	0.958605i	$-0.591907\pi$
$337$	−10.4542	−0.569476	−0.284738	+	0.958605i	$0.591907\pi$
$338$	1.75485	0.0954512
$339$	−18.0966	−0.982875
$340$	−8.18449	−0.443866
$341$	9.63517	0.521774
$342$	−5.88052	−0.317982
$343$	0	0
$344$	8.42524	0.454259
$345$	−3.54105	−0.190644
$346$	33.1847	1.78402
$347$	−32.1520	−1.72601	−0.863006	−	0.505194i	$-0.831421\pi$
$347$	−32.1520	−1.72601	−0.863006	+	0.505194i	$0.831421\pi$
$348$	16.4937	0.884153
$349$	16.2651	0.870651	0.435326	−	0.900273i	$-0.356633\pi$
$349$	16.2651	0.870651	0.435326	+	0.900273i	$0.356633\pi$
$350$	0	0
$351$	3.47416	0.185437
$352$	7.17825	0.382602
$353$	28.8296	1.53445	0.767223	−	0.641381i	$-0.221638\pi$
$353$	28.8296	1.53445	0.767223	+	0.641381i	$0.221638\pi$
$354$	12.8587	0.683433
$355$	12.7415	0.676247
$356$	24.6912	1.30863
$357$	0	0
$358$	−26.0499	−1.37678
$359$	−17.9514	−0.947440	−0.473720	−	0.880675i	$-0.657089\pi$
$359$	−17.9514	−0.947440	−0.473720	+	0.880675i	$0.657089\pi$
$360$	−0.832608	−0.0438823
$361$	−9.28264	−0.488560
$362$	18.6249	0.978906
$363$	1.00000	0.0524864
$364$	0	0
$365$	10.3508	0.541784
$366$	−4.16734	−0.217831
$367$	7.51249	0.392149	0.196075	−	0.980589i	$-0.437181\pi$
$367$	7.51249	0.392149	0.196075	+	0.980589i	$0.437181\pi$
$368$	−16.6002	−0.865345
$369$	5.96860	0.310713
$370$	0.587874	0.0305621
$371$	0	0
$372$	15.0177	0.778632
$373$	2.83467	0.146773	0.0733867	−	0.997304i	$-0.476619\pi$
$373$	2.83467	0.146773	0.0733867	+	0.997304i	$0.476619\pi$
$374$	−9.90579	−0.512216
$375$	−1.00000	−0.0516398
$376$	−6.87212	−0.354402
$377$	36.7639	1.89344
$378$	0	0
$379$	−15.3012	−0.785971	−0.392985	−	0.919545i	$-0.628558\pi$
$379$	−15.3012	−0.785971	−0.392985	+	0.919545i	$0.628558\pi$
$380$	−4.85868	−0.249245
$381$	8.73327	0.447419
$382$	32.2928	1.65224
$383$	25.9644	1.32672	0.663360	−	0.748301i	$-0.269130\pi$
$383$	25.9644	1.32672	0.663360	+	0.748301i	$0.269130\pi$
$384$	−6.49867	−0.331634
$385$	0	0
$386$	6.09438	0.310196
$387$	10.1191	0.514383
$388$	−9.47767	−0.481156
$389$	−31.7940	−1.61202	−0.806011	−	0.591900i	$-0.798378\pi$
$389$	−31.7940	−1.61202	−0.806011	+	0.591900i	$0.798378\pi$
$390$	6.55376	0.331863
$391$	18.5943	0.940354
$392$	0	0
$393$	−20.3961	−1.02885
$394$	18.4314	0.928559
$395$	9.21095	0.463453
$396$	1.55863	0.0783243
$397$	−36.6804	−1.84094	−0.920469	−	0.390816i	$-0.872193\pi$
$397$	−36.6804	−1.84094	−0.920469	+	0.390816i	$0.872193\pi$
$398$	−48.2135	−2.41673
$399$	0	0
$400$	−4.68793	−0.234396
$401$	37.1372	1.85454	0.927272	−	0.374389i	$-0.122148\pi$
$401$	37.1372	1.85454	0.927272	+	0.374389i	$0.122148\pi$
$402$	−22.5752	−1.12595
$403$	33.4741	1.66746
$404$	2.58292	0.128505
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	0.311632	0.0154470
$408$	4.37208	0.216450
$409$	−4.84425	−0.239533	−0.119766	−	0.992802i	$-0.538215\pi$
$409$	−4.84425	−0.239533	−0.119766	+	0.992802i	$0.538215\pi$
$410$	11.2594	0.556061
$411$	−4.92329	−0.242848
$412$	9.82231	0.483911
$413$	0	0
$414$	−6.67996	−0.328302
$415$	−1.68582	−0.0827534
$416$	24.9384	1.22270
$417$	6.78762	0.332391
$418$	−5.88052	−0.287626
$419$	31.8280	1.55490	0.777450	−	0.628945i	$-0.216513\pi$
$419$	31.8280	1.55490	0.777450	+	0.628945i	$0.216513\pi$
$420$	0	0
$421$	20.5893	1.00346	0.501731	−	0.865024i	$-0.332697\pi$
$421$	20.5893	1.00346	0.501731	+	0.865024i	$0.332697\pi$
$422$	−3.15865	−0.153761
$423$	−8.25372	−0.401310
$424$	0.0936856	0.00454978
$425$	5.25106	0.254714
$426$	24.0359	1.16455
$427$	0	0
$428$	3.23188	0.156219
$429$	3.47416	0.167734
$430$	19.0890	0.920554
$431$	−8.76825	−0.422352	−0.211176	−	0.977448i	$-0.567729\pi$
$431$	−8.76825	−0.422352	−0.211176	+	0.977448i	$0.567729\pi$
$432$	−4.68793	−0.225548
$433$	−17.6235	−0.846930	−0.423465	−	0.905913i	$-0.639186\pi$
$433$	−17.6235	−0.846930	−0.423465	+	0.905913i	$0.639186\pi$
$434$	0	0
$435$	−10.5821	−0.507374
$436$	15.1122	0.723741
$437$	11.0384	0.528039
$438$	19.5261	0.932991
$439$	−1.70709	−0.0814751	−0.0407376	−	0.999170i	$-0.512971\pi$
$439$	−1.70709	−0.0814751	−0.0407376	+	0.999170i	$0.512971\pi$
$440$	−0.832608	−0.0396930
$441$	0	0
$442$	−34.4142	−1.63692
$443$	−11.9120	−0.565955	−0.282978	−	0.959127i	$-0.591322\pi$
$443$	−11.9120	−0.565955	−0.282978	+	0.959127i	$0.591322\pi$
$444$	0.485721	0.0230513
$445$	−15.8416	−0.750964
$446$	14.4795	0.685626
$447$	−14.8864	−0.704100
$448$	0	0
$449$	−25.1066	−1.18485	−0.592427	−	0.805624i	$-0.701830\pi$
$449$	−25.1066	−1.18485	−0.592427	+	0.805624i	$0.701830\pi$
$450$	−1.88643	−0.0889274
$451$	5.96860	0.281050
$452$	−28.2060	−1.32670
$453$	8.15803	0.383298
$454$	11.0947	0.520699
$455$	0	0
$456$	2.59546	0.121544
$457$	33.6795	1.57546	0.787730	−	0.616020i	$-0.211256\pi$
$457$	33.6795	1.57546	0.787730	+	0.616020i	$0.211256\pi$
$458$	−1.55273	−0.0725544
$459$	5.25106	0.245099
$460$	−5.51921	−0.257334
$461$	−5.76255	−0.268389	−0.134194	−	0.990955i	$-0.542845\pi$
$461$	−5.76255	−0.268389	−0.134194	+	0.990955i	$0.542845\pi$
$462$	0	0
$463$	13.7128	0.637286	0.318643	−	0.947875i	$-0.396773\pi$
$463$	13.7128	0.637286	0.318643	+	0.947875i	$0.396773\pi$
$464$	−49.6082	−2.30301
$465$	−9.63517	−0.446820
$466$	−31.1502	−1.44301
$467$	30.6044	1.41620	0.708102	−	0.706110i	$-0.249552\pi$
$467$	30.6044	1.41620	0.708102	+	0.706110i	$0.249552\pi$
$468$	5.41494	0.250305
$469$	0	0
$470$	−15.5701	−0.718195
$471$	−0.747461	−0.0344412
$472$	−5.67540	−0.261232
$473$	10.1191	0.465276
$474$	17.3759	0.798100
$475$	3.11727	0.143030
$476$	0	0
$477$	0.112521	0.00515197
$478$	9.67176	0.442376
$479$	−13.0663	−0.597014	−0.298507	−	0.954407i	$-0.596489\pi$
$479$	−13.0663	−0.597014	−0.298507	+	0.954407i	$0.596489\pi$
$480$	−7.17825	−0.327641
$481$	1.08266	0.0493650
$482$	29.9103	1.36238
$483$	0	0
$484$	1.55863	0.0708470
$485$	6.08075	0.276113
$486$	−1.88643	−0.0855704
$487$	23.0006	1.04226	0.521128	−	0.853479i	$-0.325512\pi$
$487$	23.0006	1.04226	0.521128	+	0.853479i	$0.325512\pi$
$488$	1.83932	0.0832623
$489$	−10.2535	−0.463679
$490$	0	0
$491$	−1.90798	−0.0861058	−0.0430529	−	0.999073i	$-0.513708\pi$
$491$	−1.90798	−0.0861058	−0.0430529	+	0.999073i	$0.513708\pi$
$492$	9.30286	0.419405
$493$	55.5674	2.50263
$494$	−20.4298	−0.919182
$495$	−1.00000	−0.0449467
$496$	−45.1690	−2.02815
$497$	0	0
$498$	−3.18018	−0.142507
$499$	−29.8504	−1.33629	−0.668143	−	0.744033i	$-0.732911\pi$
$499$	−29.8504	−1.33629	−0.668143	+	0.744033i	$0.732911\pi$
$500$	−1.55863	−0.0697042
$501$	12.6608	0.565644
$502$	21.5255	0.960731
$503$	5.72295	0.255174	0.127587	−	0.991827i	$-0.459277\pi$
$503$	5.72295	0.255174	0.127587	+	0.991827i	$0.459277\pi$
$504$	0	0
$505$	−1.65717	−0.0737432
$506$	−6.67996	−0.296961
$507$	−0.930246	−0.0413137
$508$	13.6120	0.603933
$509$	2.95299	0.130889	0.0654445	−	0.997856i	$-0.479153\pi$
$509$	2.95299	0.130889	0.0654445	+	0.997856i	$0.479153\pi$
$510$	9.90579	0.438636
$511$	0	0
$512$	−25.8447	−1.14219
$513$	3.11727	0.137631
$514$	−45.5173	−2.00768
$515$	−6.30187	−0.277694
$516$	15.7720	0.694322
$517$	−8.25372	−0.362998
$518$	0	0
$519$	−17.5912	−0.772169
$520$	−2.89261	−0.126849
$521$	29.3851	1.28738	0.643692	−	0.765285i	$-0.277402\pi$
$521$	29.3851	1.28738	0.643692	+	0.765285i	$0.277402\pi$
$522$	−19.9625	−0.873734
$523$	−2.50085	−0.109355	−0.0546773	−	0.998504i	$-0.517413\pi$
$523$	−2.50085	−0.109355	−0.0546773	+	0.998504i	$0.517413\pi$
$524$	−31.7901	−1.38876
$525$	0	0
$526$	16.6657	0.726659
$527$	50.5949	2.20395
$528$	−4.68793	−0.204016
$529$	−10.4609	−0.454824
$530$	0.212263	0.00922011
$531$	−6.81642	−0.295807
$532$	0	0
$533$	20.7358	0.898169
$534$	−29.8841	−1.29321
$535$	−2.07353	−0.0896466
$536$	9.96392	0.430376
$537$	13.8091	0.595905
$538$	49.2620	2.12383
$539$	0	0
$540$	−1.55863	−0.0670729
$541$	−37.1598	−1.59763	−0.798813	−	0.601580i	$-0.794538\pi$
$541$	−37.1598	−1.59763	−0.798813	+	0.601580i	$0.794538\pi$
$542$	−3.15092	−0.135344
$543$	−9.87310	−0.423695
$544$	37.6935	1.61609
$545$	−9.69577	−0.415321
$546$	0	0
$547$	40.3294	1.72436	0.862180	−	0.506602i	$-0.169098\pi$
$547$	40.3294	1.72436	0.862180	+	0.506602i	$0.169098\pi$
$548$	−7.67360	−0.327800
$549$	2.20911	0.0942826
$550$	−1.88643	−0.0804378
$551$	32.9873	1.40531
$552$	2.94831	0.125488
$553$	0	0
$554$	−30.5781	−1.29914
$555$	−0.311632	−0.0132281
$556$	10.5794	0.448667
$557$	−16.8235	−0.712835	−0.356418	−	0.934327i	$-0.616002\pi$
$557$	−16.8235	−0.712835	−0.356418	+	0.934327i	$0.616002\pi$
$558$	−18.1761	−0.769456
$559$	35.1553	1.48691
$560$	0	0
$561$	5.25106	0.221700
$562$	41.8348	1.76469
$563$	−33.7076	−1.42061	−0.710304	−	0.703895i	$-0.751442\pi$
$563$	−33.7076	−1.42061	−0.710304	+	0.703895i	$0.751442\pi$
$564$	−12.8645	−0.541694
$565$	18.0966	0.761332
$566$	−37.8557	−1.59119
$567$	0	0
$568$	−10.6087	−0.445129
$569$	−13.0389	−0.546619	−0.273310	−	0.961926i	$-0.588118\pi$
$569$	−13.0389	−0.546619	−0.273310	+	0.961926i	$0.588118\pi$
$570$	5.88052	0.246308
$571$	−37.6468	−1.57547	−0.787736	−	0.616013i	$-0.788747\pi$
$571$	−37.6468	−1.57547	−0.787736	+	0.616013i	$0.788747\pi$
$572$	5.41494	0.226410
$573$	−17.1184	−0.715133
$574$	0	0
$575$	3.54105	0.147672
$576$	−4.16544	−0.173560
$577$	−43.5458	−1.81284	−0.906419	−	0.422380i	$-0.861195\pi$
$577$	−43.5458	−1.81284	−0.906419	+	0.422380i	$0.861195\pi$
$578$	−19.9465	−0.829666
$579$	−3.23063	−0.134261
$580$	−16.4937	−0.684862
$581$	0	0
$582$	11.4709	0.475486
$583$	0.112521	0.00466013
$584$	−8.61814	−0.356621
$585$	−3.47416	−0.143639
$586$	45.2839	1.87066
$587$	−8.47255	−0.349699	−0.174850	−	0.984595i	$-0.555944\pi$
$587$	−8.47255	−0.349699	−0.174850	+	0.984595i	$0.555944\pi$
$588$	0	0
$589$	30.0354	1.23759
$590$	−12.8587	−0.529385
$591$	−9.77048	−0.401904
$592$	−1.46091	−0.0600430
$593$	−7.29157	−0.299429	−0.149714	−	0.988729i	$-0.547835\pi$
$593$	−7.29157	−0.299429	−0.149714	+	0.988729i	$0.547835\pi$
$594$	−1.88643	−0.0774013
$595$	0	0
$596$	−23.2024	−0.950406
$597$	25.5580	1.04602
$598$	−23.2072	−0.949014
$599$	15.2011	0.621099	0.310550	−	0.950557i	$-0.399487\pi$
$599$	15.2011	0.621099	0.310550	+	0.950557i	$0.399487\pi$
$600$	0.832608	0.0339911
$601$	16.1467	0.658637	0.329318	−	0.944219i	$-0.393181\pi$
$601$	16.1467	0.658637	0.329318	+	0.944219i	$0.393181\pi$
$602$	0	0
$603$	11.9671	0.487338
$604$	12.7154	0.517382
$605$	−1.00000	−0.0406558
$606$	−3.12615	−0.126991
$607$	20.0554	0.814022	0.407011	−	0.913423i	$-0.366571\pi$
$607$	20.0554	0.814022	0.407011	+	0.913423i	$0.366571\pi$
$608$	22.3765	0.907488
$609$	0	0
$610$	4.16734	0.168731
$611$	−28.6747	−1.16005
$612$	8.18449	0.330838
$613$	−21.6532	−0.874566	−0.437283	−	0.899324i	$-0.644059\pi$
$613$	−21.6532	−0.874566	−0.437283	+	0.899324i	$0.644059\pi$
$614$	12.3165	0.497055
$615$	−5.96860	−0.240677
$616$	0	0
$617$	20.2624	0.815733	0.407866	−	0.913042i	$-0.366273\pi$
$617$	20.2624	0.815733	0.407866	+	0.913042i	$0.366273\pi$
$618$	−11.8881	−0.478208
$619$	−20.9677	−0.842764	−0.421382	−	0.906883i	$-0.638455\pi$
$619$	−20.9677	−0.842764	−0.421382	+	0.906883i	$0.638455\pi$
$620$	−15.0177	−0.603125
$621$	3.54105	0.142098
$622$	44.6618	1.79077
$623$	0	0
$624$	−16.2866	−0.651985
$625$	1.00000	0.0400000
$626$	−25.8849	−1.03457
$627$	3.11727	0.124492
$628$	−1.16502	−0.0464893
$629$	1.63640	0.0652476
$630$	0	0
$631$	−1.40494	−0.0559297	−0.0279648	−	0.999609i	$-0.508903\pi$
$631$	−1.40494	−0.0559297	−0.0279648	+	0.999609i	$0.508903\pi$
$632$	−7.66912	−0.305061
$633$	1.67440	0.0665515
$634$	−30.0804	−1.19464
$635$	−8.73327	−0.346569
$636$	0.175378	0.00695421
$637$	0	0
$638$	−19.9625	−0.790322
$639$	−12.7415	−0.504045
$640$	6.49867	0.256883
$641$	0.849456	0.0335515	0.0167758	−	0.999859i	$-0.494660\pi$
$641$	0.849456	0.0335515	0.0167758	+	0.999859i	$0.494660\pi$
$642$	−3.91158	−0.154378
$643$	39.7228	1.56651	0.783257	−	0.621698i	$-0.213557\pi$
$643$	39.7228	1.56651	0.783257	+	0.621698i	$0.213557\pi$
$644$	0	0
$645$	−10.1191	−0.398439
$646$	−30.8790	−1.21492
$647$	24.0372	0.945001	0.472500	−	0.881331i	$-0.343352\pi$
$647$	24.0372	0.945001	0.472500	+	0.881331i	$0.343352\pi$
$648$	0.832608	0.0327079
$649$	−6.81642	−0.267568
$650$	−6.55376	−0.257060
$651$	0	0
$652$	−15.9815	−0.625882
$653$	−35.8297	−1.40212	−0.701061	−	0.713101i	$-0.747290\pi$
$653$	−35.8297	−1.40212	−0.701061	+	0.713101i	$0.747290\pi$
$654$	−18.2904	−0.715213
$655$	20.3961	0.796943
$656$	−27.9804	−1.09245
$657$	−10.3508	−0.403822
$658$	0	0
$659$	−6.64367	−0.258801	−0.129400	−	0.991592i	$-0.541305\pi$
$659$	−6.64367	−0.258801	−0.129400	+	0.991592i	$0.541305\pi$
$660$	−1.55863	−0.0606697
$661$	−3.43730	−0.133695	−0.0668477	−	0.997763i	$-0.521294\pi$
$661$	−3.43730	−0.133695	−0.0668477	+	0.997763i	$0.521294\pi$
$662$	52.1093	2.02528
$663$	18.2430	0.708500
$664$	1.40362	0.0544712
$665$	0	0
$666$	−0.587874	−0.0227797
$667$	37.4719	1.45092
$668$	19.7336	0.763516
$669$	−7.67561	−0.296756
$670$	22.5752	0.872155
$671$	2.20911	0.0852818
$672$	0	0
$673$	−0.598268	−0.0230615	−0.0115308	−	0.999934i	$-0.503670\pi$
$673$	−0.598268	−0.0230615	−0.0115308	+	0.999934i	$0.503670\pi$
$674$	19.7212	0.759630
$675$	1.00000	0.0384900
$676$	−1.44991	−0.0557659
$677$	−21.3292	−0.819748	−0.409874	−	0.912142i	$-0.634427\pi$
$677$	−21.3292	−0.819748	−0.409874	+	0.912142i	$0.634427\pi$
$678$	34.1381	1.31107
$679$	0	0
$680$	−4.37208	−0.167662
$681$	−5.88129	−0.225372
$682$	−18.1761	−0.695999
$683$	−31.3862	−1.20096	−0.600480	−	0.799640i	$-0.705024\pi$
$683$	−31.3862	−1.20096	−0.600480	+	0.799640i	$0.705024\pi$
$684$	4.85868	0.185776
$685$	4.92329	0.188109
$686$	0	0
$687$	0.823104	0.0314034
$688$	−47.4376	−1.80854
$689$	0.390914	0.0148926
$690$	6.67996	0.254302
$691$	−11.3713	−0.432585	−0.216292	−	0.976329i	$-0.569396\pi$
$691$	−11.3713	−0.432585	−0.216292	+	0.976329i	$0.569396\pi$
$692$	−27.4183	−1.04229
$693$	0	0
$694$	60.6527	2.30234
$695$	−6.78762	−0.257469
$696$	8.81077	0.333971
$697$	31.3415	1.18714
$698$	−30.6831	−1.16137
$699$	16.5128	0.624570
$700$	0	0
$701$	1.69705	0.0640967	0.0320484	−	0.999486i	$-0.489797\pi$
$701$	1.69705	0.0640967	0.0320484	+	0.999486i	$0.489797\pi$
$702$	−6.55376	−0.247356
$703$	0.971441	0.0366386
$704$	−4.16544	−0.156991
$705$	8.25372	0.310853
$706$	−54.3852	−2.04681
$707$	0	0
$708$	−10.6243	−0.399286
$709$	−26.5687	−0.997808	−0.498904	−	0.866657i	$-0.666264\pi$
$709$	−26.5687	−0.997808	−0.498904	+	0.866657i	$0.666264\pi$
$710$	−24.0359	−0.902053
$711$	−9.21095	−0.345438
$712$	13.1898	0.494310
$713$	34.1186	1.27775
$714$	0	0
$715$	−3.47416	−0.129926
$716$	21.5233	0.804362
$717$	−5.12701	−0.191472
$718$	33.8642	1.26380
$719$	23.4995	0.876385	0.438193	−	0.898881i	$-0.355619\pi$
$719$	23.4995	0.876385	0.438193	+	0.898881i	$0.355619\pi$
$720$	4.68793	0.174709
$721$	0	0
$722$	17.5111	0.651695
$723$	−15.8554	−0.589671
$724$	−15.3885	−0.571911
$725$	10.5821	0.393010
$726$	−1.88643	−0.0700121
$727$	−14.3522	−0.532294	−0.266147	−	0.963932i	$-0.585751\pi$
$727$	−14.3522	−0.532294	−0.266147	+	0.963932i	$0.585751\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−19.5261	−0.722692
$731$	53.1360	1.96531
$732$	3.44320	0.127264
$733$	−32.5795	−1.20335	−0.601676	−	0.798740i	$-0.705500\pi$
$733$	−32.5795	−1.20335	−0.601676	+	0.798740i	$0.705500\pi$
$734$	−14.1718	−0.523092
$735$	0	0
$736$	25.4186	0.936941
$737$	11.9671	0.440814
$738$	−11.2594	−0.414463
$739$	25.3552	0.932705	0.466353	−	0.884599i	$-0.345568\pi$
$739$	25.3552	0.932705	0.466353	+	0.884599i	$0.345568\pi$
$740$	−0.485721	−0.0178554
$741$	10.8299	0.397845
$742$	0	0
$743$	−4.40988	−0.161783	−0.0808915	−	0.996723i	$-0.525777\pi$
$743$	−4.40988	−0.161783	−0.0808915	+	0.996723i	$0.525777\pi$
$744$	8.02232	0.294113
$745$	14.8864	0.545394
$746$	−5.34741	−0.195783
$747$	1.68582	0.0616808
$748$	8.18449	0.299254
$749$	0	0
$750$	1.88643	0.0688828
$751$	9.83648	0.358938	0.179469	−	0.983764i	$-0.442562\pi$
$751$	9.83648	0.358938	0.179469	+	0.983764i	$0.442562\pi$
$752$	38.6928	1.41098
$753$	−11.4107	−0.415829
$754$	−69.3528	−2.52568
$755$	−8.15803	−0.296901
$756$	0	0
$757$	−41.9624	−1.52515	−0.762575	−	0.646900i	$-0.776065\pi$
$757$	−41.9624	−1.52515	−0.762575	+	0.646900i	$0.776065\pi$
$758$	28.8647	1.04841
$759$	3.54105	0.128532
$760$	−2.59546	−0.0941473
$761$	−15.5414	−0.563376	−0.281688	−	0.959506i	$-0.590894\pi$
$761$	−15.5414	−0.563376	−0.281688	+	0.959506i	$0.590894\pi$
$762$	−16.4747	−0.596817
$763$	0	0
$764$	−26.6814	−0.965299
$765$	−5.25106	−0.189853
$766$	−48.9802	−1.76973
$767$	−23.6813	−0.855082
$768$	20.5902	0.742985
$769$	−2.85510	−0.102958	−0.0514789	−	0.998674i	$-0.516393\pi$
$769$	−2.85510	−0.102958	−0.0514789	+	0.998674i	$0.516393\pi$
$770$	0	0
$771$	24.1287	0.868975
$772$	−5.03537	−0.181227
$773$	26.9827	0.970501	0.485250	−	0.874375i	$-0.338728\pi$
$773$	26.9827	0.970501	0.485250	+	0.874375i	$0.338728\pi$
$774$	−19.0890	−0.686140
$775$	9.63517	0.346106
$776$	−5.06289	−0.181747
$777$	0	0
$778$	59.9774	2.15029
$779$	18.6057	0.666619
$780$	−5.41494	−0.193886
$781$	−12.7415	−0.455926
$782$	−35.0769	−1.25435
$783$	10.5821	0.378174
$784$	0	0
$785$	0.747461	0.0266780
$786$	38.4760	1.37239
$787$	19.9911	0.712605	0.356302	−	0.934371i	$-0.384037\pi$
$787$	19.9911	0.712605	0.356302	+	0.934371i	$0.384037\pi$
$788$	−15.2286	−0.542497
$789$	−8.83449	−0.314516
$790$	−17.3759	−0.618205
$791$	0	0
$792$	0.832608	0.0295854
$793$	7.67480	0.272540
$794$	69.1952	2.45565
$795$	−0.112521	−0.00399070
$796$	39.8356	1.41194
$797$	9.23858	0.327247	0.163624	−	0.986523i	$-0.447682\pi$
$797$	9.23858	0.327247	0.163624	+	0.986523i	$0.447682\pi$
$798$	0	0
$799$	−43.3408	−1.53329
$800$	7.17825	0.253790
$801$	15.8416	0.559735
$802$	−70.0569	−2.47379
$803$	−10.3508	−0.365271
$804$	18.6523	0.657817
$805$	0	0
$806$	−63.1466	−2.22425
$807$	−26.1138	−0.919250
$808$	1.37978	0.0485403
$809$	−45.3459	−1.59428	−0.797138	−	0.603797i	$-0.793654\pi$
$809$	−45.3459	−1.59428	−0.797138	+	0.603797i	$0.793654\pi$
$810$	1.88643	0.0662825
$811$	33.5112	1.17674	0.588369	−	0.808593i	$-0.299770\pi$
$811$	33.5112	1.17674	0.588369	+	0.808593i	$0.299770\pi$
$812$	0	0
$813$	1.67030	0.0585801
$814$	−0.587874	−0.0206050
$815$	10.2535	0.359165
$816$	−24.6166	−0.861754
$817$	31.5439	1.10358
$818$	9.13836	0.319515
$819$	0	0
$820$	−9.30286	−0.324870
$821$	16.8824	0.589199	0.294599	−	0.955621i	$-0.404814\pi$
$821$	16.8824	0.589199	0.294599	+	0.955621i	$0.404814\pi$
$822$	9.28746	0.323937
$823$	33.6631	1.17342	0.586711	−	0.809796i	$-0.300422\pi$
$823$	33.6631	1.17342	0.586711	+	0.809796i	$0.300422\pi$
$824$	5.24699	0.182788
$825$	1.00000	0.0348155
$826$	0	0
$827$	−4.53734	−0.157779	−0.0788893	−	0.996883i	$-0.525137\pi$
$827$	−4.53734	−0.157779	−0.0788893	+	0.996883i	$0.525137\pi$
$828$	5.51921	0.191806
$829$	−12.6387	−0.438961	−0.219481	−	0.975617i	$-0.570436\pi$
$829$	−12.6387	−0.438961	−0.219481	+	0.975617i	$0.570436\pi$
$830$	3.18018	0.110386
$831$	16.2095	0.562300
$832$	−14.4714	−0.501705
$833$	0	0
$834$	−12.8044	−0.443380
$835$	−12.6608	−0.438146
$836$	4.85868	0.168041
$837$	9.63517	0.333040
$838$	−60.0414	−2.07410
$839$	14.7383	0.508822	0.254411	−	0.967096i	$-0.418118\pi$
$839$	14.7383	0.508822	0.254411	+	0.967096i	$0.418118\pi$
$840$	0	0
$841$	82.9814	2.86143
$842$	−38.8404	−1.33853
$843$	−22.1766	−0.763804
$844$	2.60978	0.0898323
$845$	0.930246	0.0320014
$846$	15.5701	0.535311
$847$	0	0
$848$	−0.527489	−0.0181140
$849$	20.0673	0.688709
$850$	−9.90579	−0.339766
$851$	1.10351	0.0378277
$852$	−19.8593	−0.680368
$853$	−0.239580	−0.00820306	−0.00410153	−	0.999992i	$-0.501306\pi$
$853$	−0.239580	−0.00820306	−0.00410153	+	0.999992i	$0.501306\pi$
$854$	0	0
$855$	−3.11727	−0.106608
$856$	1.72644	0.0590085
$857$	37.5274	1.28191	0.640956	−	0.767578i	$-0.278538\pi$
$857$	37.5274	1.28191	0.640956	+	0.767578i	$0.278538\pi$
$858$	−6.55376	−0.223742
$859$	36.4637	1.24413	0.622063	−	0.782967i	$-0.286295\pi$
$859$	36.4637	1.24413	0.622063	+	0.782967i	$0.286295\pi$
$860$	−15.7720	−0.537820
$861$	0	0
$862$	16.5407	0.563379
$863$	−10.8485	−0.369287	−0.184644	−	0.982806i	$-0.559113\pi$
$863$	−10.8485	−0.369287	−0.184644	+	0.982806i	$0.559113\pi$
$864$	7.17825	0.244209
$865$	17.5912	0.598120
$866$	33.2455	1.12973
$867$	10.5737	0.359101
$868$	0	0
$869$	−9.21095	−0.312460
$870$	19.9625	0.676792
$871$	41.5756	1.40874
$872$	8.07278	0.273379
$873$	−6.08075	−0.205802
$874$	−20.8232	−0.704356
$875$	0	0
$876$	−16.1331	−0.545086
$877$	41.1079	1.38811	0.694057	−	0.719920i	$-0.255822\pi$
$877$	41.1079	1.38811	0.694057	+	0.719920i	$0.255822\pi$
$878$	3.22032	0.108681
$879$	−24.0050	−0.809669
$880$	4.68793	0.158030
$881$	15.3969	0.518734	0.259367	−	0.965779i	$-0.416486\pi$
$881$	15.3969	0.518734	0.259367	+	0.965779i	$0.416486\pi$
$882$	0	0
$883$	37.2657	1.25409	0.627045	−	0.778983i	$-0.284264\pi$
$883$	37.2657	1.25409	0.627045	+	0.778983i	$0.284264\pi$
$884$	28.4342	0.956345
$885$	6.81642	0.229131
$886$	22.4712	0.754933
$887$	14.3633	0.482273	0.241136	−	0.970491i	$-0.422480\pi$
$887$	14.3633	0.482273	0.241136	+	0.970491i	$0.422480\pi$
$888$	0.259468	0.00870717
$889$	0	0
$890$	29.8841	1.00172
$891$	1.00000	0.0335013
$892$	−11.9635	−0.400567
$893$	−25.7291	−0.860990
$894$	28.0821	0.939207
$895$	−13.8091	−0.461586
$896$	0	0
$897$	12.3022	0.410757
$898$	47.3620	1.58049
$899$	101.961	3.40058
$900$	1.55863	0.0519545
$901$	0.590853	0.0196842
$902$	−11.2594	−0.374896
$903$	0	0
$904$	−15.0674	−0.501135
$905$	9.87310	0.328193
$906$	−15.3896	−0.511285
$907$	26.3200	0.873941	0.436970	−	0.899476i	$-0.356051\pi$
$907$	26.3200	0.873941	0.436970	+	0.899476i	$0.356051\pi$
$908$	−9.16678	−0.304210
$909$	1.65717	0.0549649
$910$	0	0
$911$	−25.2424	−0.836316	−0.418158	−	0.908374i	$-0.637324\pi$
$911$	−25.2424	−0.836316	−0.418158	+	0.908374i	$0.637324\pi$
$912$	−14.6135	−0.483902
$913$	1.68582	0.0557924
$914$	−63.5342	−2.10152
$915$	−2.20911	−0.0730310
$916$	1.28292	0.0423888
$917$	0	0
$918$	−9.90579	−0.326940
$919$	−26.8609	−0.886061	−0.443030	−	0.896507i	$-0.646097\pi$
$919$	−26.8609	−0.886061	−0.443030	+	0.896507i	$0.646097\pi$
$920$	−2.94831	−0.0972029
$921$	−6.52901	−0.215138
$922$	10.8707	0.358006
$923$	−44.2658	−1.45703
$924$	0	0
$925$	0.311632	0.0102464
$926$	−25.8682	−0.850083
$927$	6.30187	0.206981
$928$	75.9612	2.49355
$929$	−26.9946	−0.885664	−0.442832	−	0.896605i	$-0.646026\pi$
$929$	−26.9946	−0.885664	−0.442832	+	0.896605i	$0.646026\pi$
$930$	18.1761	0.596018
$931$	0	0
$932$	25.7373	0.843055
$933$	−23.6752	−0.775093
$934$	−57.7332	−1.88909
$935$	−5.25106	−0.171728
$936$	2.89261	0.0945479
$937$	58.8355	1.92207	0.961036	−	0.276422i	$-0.0891486\pi$
$937$	58.8355	1.92207	0.961036	+	0.276422i	$0.0891486\pi$
$938$	0	0
$939$	13.7216	0.447788
$940$	12.8645	0.419595
$941$	−16.3852	−0.534143	−0.267072	−	0.963677i	$-0.586056\pi$
$941$	−16.3852	−0.534143	−0.267072	+	0.963677i	$0.586056\pi$
$942$	1.41004	0.0459414
$943$	21.1351	0.688254
$944$	31.9549	1.04004
$945$	0	0
$946$	−19.0890	−0.620637
$947$	−0.814514	−0.0264682	−0.0132341	−	0.999912i	$-0.504213\pi$
$947$	−0.814514	−0.0264682	−0.0132341	+	0.999912i	$0.504213\pi$
$948$	−14.3565	−0.466278
$949$	−35.9602	−1.16732
$950$	−5.88052	−0.190789
$951$	15.9456	0.517072
$952$	0	0
$953$	−31.5330	−1.02145	−0.510727	−	0.859743i	$-0.670624\pi$
$953$	−31.5330	−1.02145	−0.510727	+	0.859743i	$0.670624\pi$
$954$	−0.212263	−0.00687226
$955$	17.1184	0.553940
$956$	−7.99112	−0.258451
$957$	10.5821	0.342072
$958$	24.6487	0.796363
$959$	0	0
$960$	4.16544	0.134439
$961$	61.8365	1.99473
$962$	−2.04237	−0.0658485
$963$	2.07353	0.0668186
$964$	−24.7128	−0.795947
$965$	3.23063	0.103998
$966$	0	0
$967$	12.7665	0.410541	0.205271	−	0.978705i	$-0.434193\pi$
$967$	12.7665	0.410541	0.205271	+	0.978705i	$0.434193\pi$
$968$	0.832608	0.0267610
$969$	16.3690	0.525847
$970$	−11.4709	−0.368310
$971$	−36.2927	−1.16469	−0.582345	−	0.812942i	$-0.697865\pi$
$971$	−36.2927	−1.16469	−0.582345	+	0.812942i	$0.697865\pi$
$972$	1.55863	0.0499932
$973$	0	0
$974$	−43.3891	−1.39028
$975$	3.47416	0.111262
$976$	−10.3562	−0.331493
$977$	7.84423	0.250959	0.125480	−	0.992096i	$-0.459953\pi$
$977$	7.84423	0.250959	0.125480	+	0.992096i	$0.459953\pi$
$978$	19.3426	0.618507
$979$	15.8416	0.506300
$980$	0	0
$981$	9.69577	0.309562
$982$	3.59927	0.114857
$983$	33.9499	1.08283	0.541416	−	0.840755i	$-0.317888\pi$
$983$	33.9499	1.08283	0.541416	+	0.840755i	$0.317888\pi$
$984$	4.96951	0.158422
$985$	9.77048	0.311314
$986$	−104.824	−3.33828
$987$	0	0
$988$	16.8798	0.537018
$989$	35.8323	1.13940
$990$	1.88643	0.0599548
$991$	−55.3464	−1.75814	−0.879069	−	0.476695i	$-0.841835\pi$
$991$	−55.3464	−1.75814	−0.879069	+	0.476695i	$0.841835\pi$
$992$	69.1637	2.19595
$993$	−27.6232	−0.876594
$994$	0	0
$995$	−25.5580	−0.810244
$996$	2.62757	0.0832577
$997$	47.7526	1.51234	0.756171	−	0.654375i	$-0.227068\pi$
$997$	47.7526	1.51234	0.756171	+	0.654375i	$0.227068\pi$
$998$	56.3108	1.78249
$999$	0.311632	0.00985961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.cc.1.2		7
7.3	odd	6		1155.2.q.i.331.6	✓	14
7.5	odd	6		1155.2.q.i.991.6	yes	14
7.6	odd	2		8085.2.a.ca.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.i.331.6	✓	14	7.3	odd	6
1155.2.q.i.991.6	yes	14	7.5	odd	6
8085.2.a.ca.1.2		7	7.6	odd	2
8085.2.a.cc.1.2		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88643 q^{2} +1.00000 q^{3} +1.55863 q^{4} -1.00000 q^{5} -1.88643 q^{6} +0.832608 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.88643 q^{2} +1.00000 q^{3} +1.55863 q^{4} -1.00000 q^{5} -1.88643 q^{6} +0.832608 q^{8} +1.00000 q^{9} +1.88643 q^{10} +1.00000 q^{11} +1.55863 q^{12} +3.47416 q^{13} -1.00000 q^{15} -4.68793 q^{16} +5.25106 q^{17} -1.88643 q^{18} +3.11727 q^{19} -1.55863 q^{20} -1.88643 q^{22} +3.54105 q^{23} +0.832608 q^{24} +1.00000 q^{25} -6.55376 q^{26} +1.00000 q^{27} +10.5821 q^{29} +1.88643 q^{30} +9.63517 q^{31} +7.17825 q^{32} +1.00000 q^{33} -9.90579 q^{34} +1.55863 q^{36} +0.311632 q^{37} -5.88052 q^{38} +3.47416 q^{39} -0.832608 q^{40} +5.96860 q^{41} +10.1191 q^{43} +1.55863 q^{44} -1.00000 q^{45} -6.67996 q^{46} -8.25372 q^{47} -4.68793 q^{48} -1.88643 q^{50} +5.25106 q^{51} +5.41494 q^{52} +0.112521 q^{53} -1.88643 q^{54} -1.00000 q^{55} +3.11727 q^{57} -19.9625 q^{58} -6.81642 q^{59} -1.55863 q^{60} +2.20911 q^{61} -18.1761 q^{62} -4.16544 q^{64} -3.47416 q^{65} -1.88643 q^{66} +11.9671 q^{67} +8.18449 q^{68} +3.54105 q^{69} -12.7415 q^{71} +0.832608 q^{72} -10.3508 q^{73} -0.587874 q^{74} +1.00000 q^{75} +4.85868 q^{76} -6.55376 q^{78} -9.21095 q^{79} +4.68793 q^{80} +1.00000 q^{81} -11.2594 q^{82} +1.68582 q^{83} -5.25106 q^{85} -19.0890 q^{86} +10.5821 q^{87} +0.832608 q^{88} +15.8416 q^{89} +1.88643 q^{90} +5.51921 q^{92} +9.63517 q^{93} +15.5701 q^{94} -3.11727 q^{95} +7.17825 q^{96} -6.08075 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{3} + 4 q^{4} - 7 q^{5} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^3 + 4 * q^4 - 7 * q^5 + 7 * q^9	\( 7 q + 7 q^{3} + 4 q^{4} - 7 q^{5} + 7 q^{9} + 7 q^{11} + 4 q^{12} + 7 q^{13} - 7 q^{15} - 10 q^{16} + 6 q^{17} + 8 q^{19} - 4 q^{20} - q^{23} + 7 q^{25} - 12 q^{26} + 7 q^{27} - 9 q^{29} + 20 q^{31} + 7 q^{33} + 12 q^{34} + 4 q^{36} + 6 q^{37} + 7 q^{39} + 5 q^{41} + 15 q^{43} + 4 q^{44} - 7 q^{45} - 6 q^{46} + q^{47} - 10 q^{48} + 6 q^{51} + 14 q^{52} + 13 q^{53} - 7 q^{55} + 8 q^{57} - 10 q^{58} + 38 q^{59} - 4 q^{60} + 4 q^{61} + 4 q^{62} - 24 q^{64} - 7 q^{65} + 22 q^{67} - 16 q^{68} - q^{69} - 26 q^{71} + 24 q^{73} + 14 q^{74} + 7 q^{75} + 52 q^{76} - 12 q^{78} + 10 q^{80} + 7 q^{81} + 18 q^{82} + 20 q^{83} - 6 q^{85} - 8 q^{86} - 9 q^{87} + 34 q^{89} - 24 q^{92} + 20 q^{93} + 28 q^{94} - 8 q^{95} + 10 q^{97} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^3 + 4 * q^4 - 7 * q^5 + 7 * q^9 + 7 * q^11 + 4 * q^12 + 7 * q^13 - 7 * q^15 - 10 * q^16 + 6 * q^17 + 8 * q^19 - 4 * q^20 - q^23 + 7 * q^25 - 12 * q^26 + 7 * q^27 - 9 * q^29 + 20 * q^31 + 7 * q^33 + 12 * q^34 + 4 * q^36 + 6 * q^37 + 7 * q^39 + 5 * q^41 + 15 * q^43 + 4 * q^44 - 7 * q^45 - 6 * q^46 + q^47 - 10 * q^48 + 6 * q^51 + 14 * q^52 + 13 * q^53 - 7 * q^55 + 8 * q^57 - 10 * q^58 + 38 * q^59 - 4 * q^60 + 4 * q^61 + 4 * q^62 - 24 * q^64 - 7 * q^65 + 22 * q^67 - 16 * q^68 - q^69 - 26 * q^71 + 24 * q^73 + 14 * q^74 + 7 * q^75 + 52 * q^76 - 12 * q^78 + 10 * q^80 + 7 * q^81 + 18 * q^82 + 20 * q^83 - 6 * q^85 - 8 * q^86 - 9 * q^87 + 34 * q^89 - 24 * q^92 + 20 * q^93 + 28 * q^94 - 8 * q^95 + 10 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more