LMFDB - Embedded newform 3850.2.a.bd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +2.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +2.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} +1.00000 q^{11} -2.73205 q^{12} +1.46410 q^{13} +1.00000 q^{14} +1.00000 q^{16} +3.46410 q^{17} -4.46410 q^{18} +6.73205 q^{19} +2.73205 q^{21} -1.00000 q^{22} +8.19615 q^{23} +2.73205 q^{24} -1.46410 q^{26} -4.00000 q^{27} -1.00000 q^{28} -4.73205 q^{29} +2.00000 q^{31} -1.00000 q^{32} -2.73205 q^{33} -3.46410 q^{34} +4.46410 q^{36} -0.732051 q^{37} -6.73205 q^{38} -4.00000 q^{39} -2.19615 q^{41} -2.73205 q^{42} -2.00000 q^{43} +1.00000 q^{44} -8.19615 q^{46} -6.92820 q^{47} -2.73205 q^{48} +1.00000 q^{49} -9.46410 q^{51} +1.46410 q^{52} +7.26795 q^{53} +4.00000 q^{54} +1.00000 q^{56} -18.3923 q^{57} +4.73205 q^{58} +6.92820 q^{59} -4.92820 q^{61} -2.00000 q^{62} -4.46410 q^{63} +1.00000 q^{64} +2.73205 q^{66} +4.00000 q^{67} +3.46410 q^{68} -22.3923 q^{69} +9.46410 q^{71} -4.46410 q^{72} +14.3923 q^{73} +0.732051 q^{74} +6.73205 q^{76} -1.00000 q^{77} +4.00000 q^{78} -12.1962 q^{79} -2.46410 q^{81} +2.19615 q^{82} +16.3923 q^{83} +2.73205 q^{84} +2.00000 q^{86} +12.9282 q^{87} -1.00000 q^{88} +3.46410 q^{89} -1.46410 q^{91} +8.19615 q^{92} -5.46410 q^{93} +6.92820 q^{94} +2.73205 q^{96} -14.5885 q^{97} -1.00000 q^{98} +4.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{18} + 10 q^{19} + 2 q^{21} - 2 q^{22} + 6 q^{23} + 2 q^{24} + 4 q^{26} - 8 q^{27} - 2 q^{28} - 6 q^{29} + 4 q^{31} - 2 q^{32} - 2 q^{33} + 2 q^{36} + 2 q^{37} - 10 q^{38} - 8 q^{39} + 6 q^{41} - 2 q^{42} - 4 q^{43} + 2 q^{44} - 6 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{51} - 4 q^{52} + 18 q^{53} + 8 q^{54} + 2 q^{56} - 16 q^{57} + 6 q^{58} + 4 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{66} + 8 q^{67} - 24 q^{69} + 12 q^{71} - 2 q^{72} + 8 q^{73} - 2 q^{74} + 10 q^{76} - 2 q^{77} + 8 q^{78} - 14 q^{79} + 2 q^{81} - 6 q^{82} + 12 q^{83} + 2 q^{84} + 4 q^{86} + 12 q^{87} - 2 q^{88} + 4 q^{91} + 6 q^{92} - 4 q^{93} + 2 q^{96} + 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^18 + 10 * q^19 + 2 * q^21 - 2 * q^22 + 6 * q^23 + 2 * q^24 + 4 * q^26 - 8 * q^27 - 2 * q^28 - 6 * q^29 + 4 * q^31 - 2 * q^32 - 2 * q^33 + 2 * q^36 + 2 * q^37 - 10 * q^38 - 8 * q^39 + 6 * q^41 - 2 * q^42 - 4 * q^43 + 2 * q^44 - 6 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^51 - 4 * q^52 + 18 * q^53 + 8 * q^54 + 2 * q^56 - 16 * q^57 + 6 * q^58 + 4 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^66 + 8 * q^67 - 24 * q^69 + 12 * q^71 - 2 * q^72 + 8 * q^73 - 2 * q^74 + 10 * q^76 - 2 * q^77 + 8 * q^78 - 14 * q^79 + 2 * q^81 - 6 * q^82 + 12 * q^83 + 2 * q^84 + 4 * q^86 + 12 * q^87 - 2 * q^88 + 4 * q^91 + 6 * q^92 - 4 * q^93 + 2 * q^96 + 2 * q^97 - 2 * q^98 + 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.73205	−1.57735	−0.788675	−	0.614810i	$-0.789233\pi$
$3$	−2.73205	−1.57735	−0.788675	+	0.614810i	$0.789233\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.73205	1.11536
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	4.46410	1.48803
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.73205	−0.788675
$13$	1.46410	0.406069	0.203034	−	0.979172i	$-0.434920\pi$
$13$	1.46410	0.406069	0.203034	+	0.979172i	$0.434920\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	3.46410	0.840168	0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410	0.840168	0.420084	+	0.907485i	$0.362001\pi$
$18$	−4.46410	−1.05220
$19$	6.73205	1.54444	0.772219	−	0.635356i	$-0.219147\pi$
$19$	6.73205	1.54444	0.772219	+	0.635356i	$0.219147\pi$
$20$	0	0
$21$	2.73205	0.596182
$22$	−1.00000	−0.213201
$23$	8.19615	1.70902	0.854508	−	0.519438i	$-0.173859\pi$
$23$	8.19615	1.70902	0.854508	+	0.519438i	$0.173859\pi$
$24$	2.73205	0.557678
$25$	0	0
$26$	−1.46410	−0.287134
$27$	−4.00000	−0.769800
$28$	−1.00000	−0.188982
$29$	−4.73205	−0.878720	−0.439360	−	0.898311i	$-0.644795\pi$
$29$	−4.73205	−0.878720	−0.439360	+	0.898311i	$0.644795\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	−2.73205	−0.475589
$34$	−3.46410	−0.594089
$35$	0	0
$36$	4.46410	0.744017
$37$	−0.732051	−0.120348	−0.0601742	−	0.998188i	$-0.519166\pi$
$37$	−0.732051	−0.120348	−0.0601742	+	0.998188i	$0.519166\pi$
$38$	−6.73205	−1.09208
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−2.19615	−0.342981	−0.171491	−	0.985186i	$-0.554858\pi$
$41$	−2.19615	−0.342981	−0.171491	+	0.985186i	$0.554858\pi$
$42$	−2.73205	−0.421565
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−8.19615	−1.20846
$47$	−6.92820	−1.01058	−0.505291	−	0.862949i	$-0.668615\pi$
$47$	−6.92820	−1.01058	−0.505291	+	0.862949i	$0.668615\pi$
$48$	−2.73205	−0.394338
$49$	1.00000	0.142857
$50$	0	0
$51$	−9.46410	−1.32524
$52$	1.46410	0.203034
$53$	7.26795	0.998330	0.499165	−	0.866507i	$-0.333640\pi$
$53$	7.26795	0.998330	0.499165	+	0.866507i	$0.333640\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	−18.3923	−2.43612
$58$	4.73205	0.621349
$59$	6.92820	0.901975	0.450988	−	0.892530i	$-0.351072\pi$
$59$	6.92820	0.901975	0.450988	+	0.892530i	$0.351072\pi$
$60$	0	0
$61$	−4.92820	−0.630992	−0.315496	−	0.948927i	$-0.602171\pi$
$61$	−4.92820	−0.630992	−0.315496	+	0.948927i	$0.602171\pi$
$62$	−2.00000	−0.254000
$63$	−4.46410	−0.562424
$64$	1.00000	0.125000
$65$	0	0
$66$	2.73205	0.336292
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	3.46410	0.420084
$69$	−22.3923	−2.69572
$70$	0	0
$71$	9.46410	1.12318	0.561591	−	0.827415i	$-0.310189\pi$
$71$	9.46410	1.12318	0.561591	+	0.827415i	$0.310189\pi$
$72$	−4.46410	−0.526099
$73$	14.3923	1.68449	0.842246	−	0.539093i	$-0.181233\pi$
$73$	14.3923	1.68449	0.842246	+	0.539093i	$0.181233\pi$
$74$	0.732051	0.0850992
$75$	0	0
$76$	6.73205	0.772219
$77$	−1.00000	−0.113961
$78$	4.00000	0.452911
$79$	−12.1962	−1.37217	−0.686087	−	0.727519i	$-0.740673\pi$
$79$	−12.1962	−1.37217	−0.686087	+	0.727519i	$0.740673\pi$
$80$	0	0
$81$	−2.46410	−0.273789
$82$	2.19615	0.242524
$83$	16.3923	1.79929	0.899645	−	0.436623i	$-0.143826\pi$
$83$	16.3923	1.79929	0.899645	+	0.436623i	$0.143826\pi$
$84$	2.73205	0.298091
$85$	0	0
$86$	2.00000	0.215666
$87$	12.9282	1.38605
$88$	−1.00000	−0.106600
$89$	3.46410	0.367194	0.183597	−	0.983002i	$-0.441226\pi$
$89$	3.46410	0.367194	0.183597	+	0.983002i	$0.441226\pi$
$90$	0	0
$91$	−1.46410	−0.153480
$92$	8.19615	0.854508
$93$	−5.46410	−0.566601
$94$	6.92820	0.714590
$95$	0	0
$96$	2.73205	0.278839
$97$	−14.5885	−1.48123	−0.740617	−	0.671928i	$-0.765467\pi$
$97$	−14.5885	−1.48123	−0.740617	+	0.671928i	$0.765467\pi$
$98$	−1.00000	−0.101015
$99$	4.46410	0.448659
$100$	0	0
$101$	−7.85641	−0.781742	−0.390871	−	0.920446i	$-0.627826\pi$
$101$	−7.85641	−0.781742	−0.390871	+	0.920446i	$0.627826\pi$
$102$	9.46410	0.937086
$103$	−12.3923	−1.22105	−0.610525	−	0.791997i	$-0.709042\pi$
$103$	−12.3923	−1.22105	−0.610525	+	0.791997i	$0.709042\pi$
$104$	−1.46410	−0.143567
$105$	0	0
$106$	−7.26795	−0.705926
$107$	−7.85641	−0.759507	−0.379754	−	0.925088i	$-0.623991\pi$
$107$	−7.85641	−0.759507	−0.379754	+	0.925088i	$0.623991\pi$
$108$	−4.00000	−0.384900
$109$	−15.6603	−1.49998	−0.749990	−	0.661449i	$-0.769942\pi$
$109$	−15.6603	−1.49998	−0.749990	+	0.661449i	$0.769942\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	−7.85641	−0.739069	−0.369534	−	0.929217i	$-0.620483\pi$
$113$	−7.85641	−0.739069	−0.369534	+	0.929217i	$0.620483\pi$
$114$	18.3923	1.72260
$115$	0	0
$116$	−4.73205	−0.439360
$117$	6.53590	0.604244
$118$	−6.92820	−0.637793
$119$	−3.46410	−0.317554
$120$	0	0
$121$	1.00000	0.0909091
$122$	4.92820	0.446179
$123$	6.00000	0.541002
$124$	2.00000	0.179605
$125$	0	0
$126$	4.46410	0.397694
$127$	−1.07180	−0.0951066	−0.0475533	−	0.998869i	$-0.515142\pi$
$127$	−1.07180	−0.0951066	−0.0475533	+	0.998869i	$0.515142\pi$
$128$	−1.00000	−0.0883883
$129$	5.46410	0.481087
$130$	0	0
$131$	5.66025	0.494539	0.247269	−	0.968947i	$-0.420467\pi$
$131$	5.66025	0.494539	0.247269	+	0.968947i	$0.420467\pi$
$132$	−2.73205	−0.237795
$133$	−6.73205	−0.583743
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−3.46410	−0.297044
$137$	0.928203	0.0793018	0.0396509	−	0.999214i	$-0.487375\pi$
$137$	0.928203	0.0793018	0.0396509	+	0.999214i	$0.487375\pi$
$138$	22.3923	1.90616
$139$	13.6603	1.15865	0.579324	−	0.815097i	$-0.303317\pi$
$139$	13.6603	1.15865	0.579324	+	0.815097i	$0.303317\pi$
$140$	0	0
$141$	18.9282	1.59404
$142$	−9.46410	−0.794210
$143$	1.46410	0.122434
$144$	4.46410	0.372008
$145$	0	0
$146$	−14.3923	−1.19112
$147$	−2.73205	−0.225336
$148$	−0.732051	−0.0601742
$149$	−7.26795	−0.595414	−0.297707	−	0.954657i	$-0.596222\pi$
$149$	−7.26795	−0.595414	−0.297707	+	0.954657i	$0.596222\pi$
$150$	0	0
$151$	11.1244	0.905287	0.452644	−	0.891692i	$-0.350481\pi$
$151$	11.1244	0.905287	0.452644	+	0.891692i	$0.350481\pi$
$152$	−6.73205	−0.546041
$153$	15.4641	1.25020
$154$	1.00000	0.0805823
$155$	0	0
$156$	−4.00000	−0.320256
$157$	−4.53590	−0.362004	−0.181002	−	0.983483i	$-0.557934\pi$
$157$	−4.53590	−0.362004	−0.181002	+	0.983483i	$0.557934\pi$
$158$	12.1962	0.970274
$159$	−19.8564	−1.57472
$160$	0	0
$161$	−8.19615	−0.645947
$162$	2.46410	0.193598
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−2.19615	−0.171491
$165$	0	0
$166$	−16.3923	−1.27229
$167$	−13.8564	−1.07224	−0.536120	−	0.844141i	$-0.680111\pi$
$167$	−13.8564	−1.07224	−0.536120	+	0.844141i	$0.680111\pi$
$168$	−2.73205	−0.210782
$169$	−10.8564	−0.835108
$170$	0	0
$171$	30.0526	2.29818
$172$	−2.00000	−0.152499
$173$	−0.928203	−0.0705700	−0.0352850	−	0.999377i	$-0.511234\pi$
$173$	−0.928203	−0.0705700	−0.0352850	+	0.999377i	$0.511234\pi$
$174$	−12.9282	−0.980085
$175$	0	0
$176$	1.00000	0.0753778
$177$	−18.9282	−1.42273
$178$	−3.46410	−0.259645
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	1.46410	0.108526
$183$	13.4641	0.995295
$184$	−8.19615	−0.604228
$185$	0	0
$186$	5.46410	0.400647
$187$	3.46410	0.253320
$188$	−6.92820	−0.505291
$189$	4.00000	0.290957
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	−2.73205	−0.197169
$193$	−12.3923	−0.892018	−0.446009	−	0.895029i	$-0.647155\pi$
$193$	−12.3923	−0.892018	−0.446009	+	0.895029i	$0.647155\pi$
$194$	14.5885	1.04739
$195$	0	0
$196$	1.00000	0.0714286
$197$	24.2487	1.72765	0.863825	−	0.503793i	$-0.168062\pi$
$197$	24.2487	1.72765	0.863825	+	0.503793i	$0.168062\pi$
$198$	−4.46410	−0.317250
$199$	2.92820	0.207575	0.103787	−	0.994600i	$-0.466904\pi$
$199$	2.92820	0.207575	0.103787	+	0.994600i	$0.466904\pi$
$200$	0	0
$201$	−10.9282	−0.770816
$202$	7.85641	0.552775
$203$	4.73205	0.332125
$204$	−9.46410	−0.662620
$205$	0	0
$206$	12.3923	0.863413
$207$	36.5885	2.54307
$208$	1.46410	0.101517
$209$	6.73205	0.465666
$210$	0	0
$211$	26.9282	1.85381	0.926907	−	0.375291i	$-0.122457\pi$
$211$	26.9282	1.85381	0.926907	+	0.375291i	$0.122457\pi$
$212$	7.26795	0.499165
$213$	−25.8564	−1.77165
$214$	7.85641	0.537053
$215$	0	0
$216$	4.00000	0.272166
$217$	−2.00000	−0.135769
$218$	15.6603	1.06065
$219$	−39.3205	−2.65703
$220$	0	0
$221$	5.07180	0.341166
$222$	−2.00000	−0.134231
$223$	25.4641	1.70520	0.852601	−	0.522562i	$-0.175024\pi$
$223$	25.4641	1.70520	0.852601	+	0.522562i	$0.175024\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	7.85641	0.522600
$227$	−6.92820	−0.459841	−0.229920	−	0.973209i	$-0.573847\pi$
$227$	−6.92820	−0.459841	−0.229920	+	0.973209i	$0.573847\pi$
$228$	−18.3923	−1.21806
$229$	24.3923	1.61189	0.805944	−	0.591991i	$-0.201658\pi$
$229$	24.3923	1.61189	0.805944	+	0.591991i	$0.201658\pi$
$230$	0	0
$231$	2.73205	0.179756
$232$	4.73205	0.310674
$233$	7.85641	0.514690	0.257345	−	0.966320i	$-0.417152\pi$
$233$	7.85641	0.514690	0.257345	+	0.966320i	$0.417152\pi$
$234$	−6.53590	−0.427265
$235$	0	0
$236$	6.92820	0.450988
$237$	33.3205	2.16440
$238$	3.46410	0.224544
$239$	1.26795	0.0820168	0.0410084	−	0.999159i	$-0.486943\pi$
$239$	1.26795	0.0820168	0.0410084	+	0.999159i	$0.486943\pi$
$240$	0	0
$241$	3.26795	0.210507	0.105254	−	0.994445i	$-0.466435\pi$
$241$	3.26795	0.210507	0.105254	+	0.994445i	$0.466435\pi$
$242$	−1.00000	−0.0642824
$243$	18.7321	1.20166
$244$	−4.92820	−0.315496
$245$	0	0
$246$	−6.00000	−0.382546
$247$	9.85641	0.627148
$248$	−2.00000	−0.127000
$249$	−44.7846	−2.83811
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−4.46410	−0.281212
$253$	8.19615	0.515288
$254$	1.07180	0.0672505
$255$	0	0
$256$	1.00000	0.0625000
$257$	23.6603	1.47589	0.737943	−	0.674863i	$-0.235797\pi$
$257$	23.6603	1.47589	0.737943	+	0.674863i	$0.235797\pi$
$258$	−5.46410	−0.340180
$259$	0.732051	0.0454874
$260$	0	0
$261$	−21.1244	−1.30756
$262$	−5.66025	−0.349692
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	2.73205	0.168146
$265$	0	0
$266$	6.73205	0.412769
$267$	−9.46410	−0.579194
$268$	4.00000	0.244339
$269$	28.3923	1.73111	0.865555	−	0.500814i	$-0.166966\pi$
$269$	28.3923	1.73111	0.865555	+	0.500814i	$0.166966\pi$
$270$	0	0
$271$	0.392305	0.0238308	0.0119154	−	0.999929i	$-0.496207\pi$
$271$	0.392305	0.0238308	0.0119154	+	0.999929i	$0.496207\pi$
$272$	3.46410	0.210042
$273$	4.00000	0.242091
$274$	−0.928203	−0.0560748
$275$	0	0
$276$	−22.3923	−1.34786
$277$	−7.07180	−0.424903	−0.212452	−	0.977172i	$-0.568145\pi$
$277$	−7.07180	−0.424903	−0.212452	+	0.977172i	$0.568145\pi$
$278$	−13.6603	−0.819288
$279$	8.92820	0.534518
$280$	0	0
$281$	22.3923	1.33581	0.667906	−	0.744245i	$-0.267191\pi$
$281$	22.3923	1.33581	0.667906	+	0.744245i	$0.267191\pi$
$282$	−18.9282	−1.12716
$283$	31.7128	1.88513	0.942566	−	0.334021i	$-0.108406\pi$
$283$	31.7128	1.88513	0.942566	+	0.334021i	$0.108406\pi$
$284$	9.46410	0.561591
$285$	0	0
$286$	−1.46410	−0.0865741
$287$	2.19615	0.129635
$288$	−4.46410	−0.263050
$289$	−5.00000	−0.294118
$290$	0	0
$291$	39.8564	2.33642
$292$	14.3923	0.842246
$293$	−21.4641	−1.25395	−0.626973	−	0.779041i	$-0.715706\pi$
$293$	−21.4641	−1.25395	−0.626973	+	0.779041i	$0.715706\pi$
$294$	2.73205	0.159336
$295$	0	0
$296$	0.732051	0.0425496
$297$	−4.00000	−0.232104
$298$	7.26795	0.421021
$299$	12.0000	0.693978
$300$	0	0
$301$	2.00000	0.115278
$302$	−11.1244	−0.640135
$303$	21.4641	1.23308
$304$	6.73205	0.386110
$305$	0	0
$306$	−15.4641	−0.884024
$307$	−24.3923	−1.39214	−0.696071	−	0.717973i	$-0.745070\pi$
$307$	−24.3923	−1.39214	−0.696071	+	0.717973i	$0.745070\pi$
$308$	−1.00000	−0.0569803
$309$	33.8564	1.92602
$310$	0	0
$311$	24.9282	1.41355	0.706774	−	0.707439i	$-0.250150\pi$
$311$	24.9282	1.41355	0.706774	+	0.707439i	$0.250150\pi$
$312$	4.00000	0.226455
$313$	−22.1962	−1.25460	−0.627300	−	0.778777i	$-0.715840\pi$
$313$	−22.1962	−1.25460	−0.627300	+	0.778777i	$0.715840\pi$
$314$	4.53590	0.255976
$315$	0	0
$316$	−12.1962	−0.686087
$317$	−30.5885	−1.71802	−0.859009	−	0.511960i	$-0.828920\pi$
$317$	−30.5885	−1.71802	−0.859009	+	0.511960i	$0.828920\pi$
$318$	19.8564	1.11349
$319$	−4.73205	−0.264944
$320$	0	0
$321$	21.4641	1.19801
$322$	8.19615	0.456754
$323$	23.3205	1.29759
$324$	−2.46410	−0.136895
$325$	0	0
$326$	−4.00000	−0.221540
$327$	42.7846	2.36599
$328$	2.19615	0.121262
$329$	6.92820	0.381964
$330$	0	0
$331$	−18.7846	−1.03250	−0.516248	−	0.856439i	$-0.672672\pi$
$331$	−18.7846	−1.03250	−0.516248	+	0.856439i	$0.672672\pi$
$332$	16.3923	0.899645
$333$	−3.26795	−0.179083
$334$	13.8564	0.758189
$335$	0	0
$336$	2.73205	0.149046
$337$	−22.7846	−1.24116	−0.620578	−	0.784144i	$-0.713102\pi$
$337$	−22.7846	−1.24116	−0.620578	+	0.784144i	$0.713102\pi$
$338$	10.8564	0.590511
$339$	21.4641	1.16577
$340$	0	0
$341$	2.00000	0.108306
$342$	−30.0526	−1.62506
$343$	−1.00000	−0.0539949
$344$	2.00000	0.107833
$345$	0	0
$346$	0.928203	0.0499005
$347$	23.0718	1.23856	0.619279	−	0.785171i	$-0.287425\pi$
$347$	23.0718	1.23856	0.619279	+	0.785171i	$0.287425\pi$
$348$	12.9282	0.693024
$349$	−5.60770	−0.300173	−0.150087	−	0.988673i	$-0.547955\pi$
$349$	−5.60770	−0.300173	−0.150087	+	0.988673i	$0.547955\pi$
$350$	0	0
$351$	−5.85641	−0.312592
$352$	−1.00000	−0.0533002
$353$	−14.1962	−0.755585	−0.377792	−	0.925890i	$-0.623317\pi$
$353$	−14.1962	−0.755585	−0.377792	+	0.925890i	$0.623317\pi$
$354$	18.9282	1.00602
$355$	0	0
$356$	3.46410	0.183597
$357$	9.46410	0.500893
$358$	6.00000	0.317110
$359$	−34.0526	−1.79723	−0.898613	−	0.438743i	$-0.855424\pi$
$359$	−34.0526	−1.79723	−0.898613	+	0.438743i	$0.855424\pi$
$360$	0	0
$361$	26.3205	1.38529
$362$	−14.0000	−0.735824
$363$	−2.73205	−0.143395
$364$	−1.46410	−0.0767398
$365$	0	0
$366$	−13.4641	−0.703780
$367$	−12.3923	−0.646873	−0.323437	−	0.946250i	$-0.604838\pi$
$367$	−12.3923	−0.646873	−0.323437	+	0.946250i	$0.604838\pi$
$368$	8.19615	0.427254
$369$	−9.80385	−0.510368
$370$	0	0
$371$	−7.26795	−0.377333
$372$	−5.46410	−0.283300
$373$	−18.3923	−0.952317	−0.476159	−	0.879359i	$-0.657971\pi$
$373$	−18.3923	−0.952317	−0.476159	+	0.879359i	$0.657971\pi$
$374$	−3.46410	−0.179124
$375$	0	0
$376$	6.92820	0.357295
$377$	−6.92820	−0.356821
$378$	−4.00000	−0.205738
$379$	6.14359	0.315575	0.157788	−	0.987473i	$-0.449564\pi$
$379$	6.14359	0.315575	0.157788	+	0.987473i	$0.449564\pi$
$380$	0	0
$381$	2.92820	0.150016
$382$	12.0000	0.613973
$383$	33.4641	1.70994	0.854968	−	0.518681i	$-0.173577\pi$
$383$	33.4641	1.70994	0.854968	+	0.518681i	$0.173577\pi$
$384$	2.73205	0.139419
$385$	0	0
$386$	12.3923	0.630752
$387$	−8.92820	−0.453846
$388$	−14.5885	−0.740617
$389$	−1.60770	−0.0815134	−0.0407567	−	0.999169i	$-0.512977\pi$
$389$	−1.60770	−0.0815134	−0.0407567	+	0.999169i	$0.512977\pi$
$390$	0	0
$391$	28.3923	1.43586
$392$	−1.00000	−0.0505076
$393$	−15.4641	−0.780061
$394$	−24.2487	−1.22163
$395$	0	0
$396$	4.46410	0.224330
$397$	−30.3923	−1.52535	−0.762673	−	0.646784i	$-0.776113\pi$
$397$	−30.3923	−1.52535	−0.762673	+	0.646784i	$0.776113\pi$
$398$	−2.92820	−0.146778
$399$	18.3923	0.920767
$400$	0	0
$401$	2.53590	0.126637	0.0633184	−	0.997993i	$-0.479832\pi$
$401$	2.53590	0.126637	0.0633184	+	0.997993i	$0.479832\pi$
$402$	10.9282	0.545049
$403$	2.92820	0.145864
$404$	−7.85641	−0.390871
$405$	0	0
$406$	−4.73205	−0.234848
$407$	−0.732051	−0.0362864
$408$	9.46410	0.468543
$409$	10.8756	0.537766	0.268883	−	0.963173i	$-0.413346\pi$
$409$	10.8756	0.537766	0.268883	+	0.963173i	$0.413346\pi$
$410$	0	0
$411$	−2.53590	−0.125087
$412$	−12.3923	−0.610525
$413$	−6.92820	−0.340915
$414$	−36.5885	−1.79822
$415$	0	0
$416$	−1.46410	−0.0717835
$417$	−37.3205	−1.82759
$418$	−6.73205	−0.329275
$419$	30.9282	1.51094	0.755471	−	0.655182i	$-0.227408\pi$
$419$	30.9282	1.51094	0.755471	+	0.655182i	$0.227408\pi$
$420$	0	0
$421$	−35.8564	−1.74753	−0.873767	−	0.486344i	$-0.838330\pi$
$421$	−35.8564	−1.74753	−0.873767	+	0.486344i	$0.838330\pi$
$422$	−26.9282	−1.31084
$423$	−30.9282	−1.50378
$424$	−7.26795	−0.352963
$425$	0	0
$426$	25.8564	1.25275
$427$	4.92820	0.238492
$428$	−7.85641	−0.379754
$429$	−4.00000	−0.193122
$430$	0	0
$431$	3.12436	0.150495	0.0752475	−	0.997165i	$-0.476025\pi$
$431$	3.12436	0.150495	0.0752475	+	0.997165i	$0.476025\pi$
$432$	−4.00000	−0.192450
$433$	18.1962	0.874451	0.437226	−	0.899352i	$-0.355961\pi$
$433$	18.1962	0.874451	0.437226	+	0.899352i	$0.355961\pi$
$434$	2.00000	0.0960031
$435$	0	0
$436$	−15.6603	−0.749990
$437$	55.1769	2.63947
$438$	39.3205	1.87881
$439$	26.2487	1.25278	0.626391	−	0.779509i	$-0.284531\pi$
$439$	26.2487	1.25278	0.626391	+	0.779509i	$0.284531\pi$
$440$	0	0
$441$	4.46410	0.212576
$442$	−5.07180	−0.241241
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	2.00000	0.0949158
$445$	0	0
$446$	−25.4641	−1.20576
$447$	19.8564	0.939176
$448$	−1.00000	−0.0472456
$449$	40.3923	1.90623	0.953115	−	0.302607i	$-0.0978570\pi$
$449$	40.3923	1.90623	0.953115	+	0.302607i	$0.0978570\pi$
$450$	0	0
$451$	−2.19615	−0.103413
$452$	−7.85641	−0.369534
$453$	−30.3923	−1.42796
$454$	6.92820	0.325157
$455$	0	0
$456$	18.3923	0.861299
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	−24.3923	−1.13978
$459$	−13.8564	−0.646762
$460$	0	0
$461$	22.3923	1.04291	0.521457	−	0.853278i	$-0.325389\pi$
$461$	22.3923	1.04291	0.521457	+	0.853278i	$0.325389\pi$
$462$	−2.73205	−0.127107
$463$	−27.5167	−1.27881	−0.639404	−	0.768871i	$-0.720819\pi$
$463$	−27.5167	−1.27881	−0.639404	+	0.768871i	$0.720819\pi$
$464$	−4.73205	−0.219680
$465$	0	0
$466$	−7.85641	−0.363941
$467$	34.0526	1.57576	0.787882	−	0.615826i	$-0.211178\pi$
$467$	34.0526	1.57576	0.787882	+	0.615826i	$0.211178\pi$
$468$	6.53590	0.302122
$469$	−4.00000	−0.184703
$470$	0	0
$471$	12.3923	0.571007
$472$	−6.92820	−0.318896
$473$	−2.00000	−0.0919601
$474$	−33.3205	−1.53046
$475$	0	0
$476$	−3.46410	−0.158777
$477$	32.4449	1.48555
$478$	−1.26795	−0.0579946
$479$	−32.7846	−1.49797	−0.748984	−	0.662589i	$-0.769458\pi$
$479$	−32.7846	−1.49797	−0.748984	+	0.662589i	$0.769458\pi$
$480$	0	0
$481$	−1.07180	−0.0488697
$482$	−3.26795	−0.148851
$483$	22.3923	1.01889
$484$	1.00000	0.0454545
$485$	0	0
$486$	−18.7321	−0.849703
$487$	−4.19615	−0.190146	−0.0950729	−	0.995470i	$-0.530308\pi$
$487$	−4.19615	−0.190146	−0.0950729	+	0.995470i	$0.530308\pi$
$488$	4.92820	0.223089
$489$	−10.9282	−0.494190
$490$	0	0
$491$	−27.7128	−1.25066	−0.625331	−	0.780360i	$-0.715036\pi$
$491$	−27.7128	−1.25066	−0.625331	+	0.780360i	$0.715036\pi$
$492$	6.00000	0.270501
$493$	−16.3923	−0.738272
$494$	−9.85641	−0.443461
$495$	0	0
$496$	2.00000	0.0898027
$497$	−9.46410	−0.424523
$498$	44.7846	2.00685
$499$	12.1436	0.543622	0.271811	−	0.962351i	$-0.412377\pi$
$499$	12.1436	0.543622	0.271811	+	0.962351i	$0.412377\pi$
$500$	0	0
$501$	37.8564	1.69130
$502$	−12.0000	−0.535586
$503$	−8.78461	−0.391686	−0.195843	−	0.980635i	$-0.562744\pi$
$503$	−8.78461	−0.391686	−0.195843	+	0.980635i	$0.562744\pi$
$504$	4.46410	0.198847
$505$	0	0
$506$	−8.19615	−0.364363
$507$	29.6603	1.31726
$508$	−1.07180	−0.0475533
$509$	11.0718	0.490749	0.245374	−	0.969428i	$-0.421089\pi$
$509$	11.0718	0.490749	0.245374	+	0.969428i	$0.421089\pi$
$510$	0	0
$511$	−14.3923	−0.636678
$512$	−1.00000	−0.0441942
$513$	−26.9282	−1.18891
$514$	−23.6603	−1.04361
$515$	0	0
$516$	5.46410	0.240544
$517$	−6.92820	−0.304702
$518$	−0.732051	−0.0321645
$519$	2.53590	0.111314
$520$	0	0
$521$	10.3923	0.455295	0.227648	−	0.973744i	$-0.426897\pi$
$521$	10.3923	0.455295	0.227648	+	0.973744i	$0.426897\pi$
$522$	21.1244	0.924588
$523$	29.1769	1.27582	0.637909	−	0.770112i	$-0.279800\pi$
$523$	29.1769	1.27582	0.637909	+	0.770112i	$0.279800\pi$
$524$	5.66025	0.247269
$525$	0	0
$526$	−24.0000	−1.04645
$527$	6.92820	0.301797
$528$	−2.73205	−0.118897
$529$	44.1769	1.92074
$530$	0	0
$531$	30.9282	1.34217
$532$	−6.73205	−0.291871
$533$	−3.21539	−0.139274
$534$	9.46410	0.409552
$535$	0	0
$536$	−4.00000	−0.172774
$537$	16.3923	0.707380
$538$	−28.3923	−1.22408
$539$	1.00000	0.0430730
$540$	0	0
$541$	−20.7321	−0.891340	−0.445670	−	0.895197i	$-0.647035\pi$
$541$	−20.7321	−0.891340	−0.445670	+	0.895197i	$0.647035\pi$
$542$	−0.392305	−0.0168509
$543$	−38.2487	−1.64141
$544$	−3.46410	−0.148522
$545$	0	0
$546$	−4.00000	−0.171184
$547$	−28.7846	−1.23074	−0.615371	−	0.788238i	$-0.710994\pi$
$547$	−28.7846	−1.23074	−0.615371	+	0.788238i	$0.710994\pi$
$548$	0.928203	0.0396509
$549$	−22.0000	−0.938937
$550$	0	0
$551$	−31.8564	−1.35713
$552$	22.3923	0.953080
$553$	12.1962	0.518633
$554$	7.07180	0.300452
$555$	0	0
$556$	13.6603	0.579324
$557$	25.6077	1.08503	0.542516	−	0.840045i	$-0.317472\pi$
$557$	25.6077	1.08503	0.542516	+	0.840045i	$0.317472\pi$
$558$	−8.92820	−0.377961
$559$	−2.92820	−0.123850
$560$	0	0
$561$	−9.46410	−0.399575
$562$	−22.3923	−0.944562
$563$	−5.07180	−0.213751	−0.106875	−	0.994272i	$-0.534085\pi$
$563$	−5.07180	−0.213751	−0.106875	+	0.994272i	$0.534085\pi$
$564$	18.9282	0.797021
$565$	0	0
$566$	−31.7128	−1.33299
$567$	2.46410	0.103483
$568$	−9.46410	−0.397105
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	3.60770	0.150977	0.0754887	−	0.997147i	$-0.475948\pi$
$571$	3.60770	0.150977	0.0754887	+	0.997147i	$0.475948\pi$
$572$	1.46410	0.0612172
$573$	32.7846	1.36960
$574$	−2.19615	−0.0916656
$575$	0	0
$576$	4.46410	0.186004
$577$	34.5885	1.43994	0.719968	−	0.694007i	$-0.244156\pi$
$577$	34.5885	1.43994	0.719968	+	0.694007i	$0.244156\pi$
$578$	5.00000	0.207973
$579$	33.8564	1.40702
$580$	0	0
$581$	−16.3923	−0.680067
$582$	−39.8564	−1.65210
$583$	7.26795	0.301008
$584$	−14.3923	−0.595558
$585$	0	0
$586$	21.4641	0.886674
$587$	11.4115	0.471005	0.235502	−	0.971874i	$-0.424326\pi$
$587$	11.4115	0.471005	0.235502	+	0.971874i	$0.424326\pi$
$588$	−2.73205	−0.112668
$589$	13.4641	0.554779
$590$	0	0
$591$	−66.2487	−2.72511
$592$	−0.732051	−0.0300871
$593$	−0.248711	−0.0102133	−0.00510667	−	0.999987i	$-0.501626\pi$
$593$	−0.248711	−0.0102133	−0.00510667	+	0.999987i	$0.501626\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−7.26795	−0.297707
$597$	−8.00000	−0.327418
$598$	−12.0000	−0.490716
$599$	37.1769	1.51901	0.759504	−	0.650503i	$-0.225442\pi$
$599$	37.1769	1.51901	0.759504	+	0.650503i	$0.225442\pi$
$600$	0	0
$601$	−5.51666	−0.225029	−0.112515	−	0.993650i	$-0.535891\pi$
$601$	−5.51666	−0.225029	−0.112515	+	0.993650i	$0.535891\pi$
$602$	−2.00000	−0.0815139
$603$	17.8564	0.727169
$604$	11.1244	0.452644
$605$	0	0
$606$	−21.4641	−0.871920
$607$	−20.9282	−0.849450	−0.424725	−	0.905323i	$-0.639629\pi$
$607$	−20.9282	−0.849450	−0.424725	+	0.905323i	$0.639629\pi$
$608$	−6.73205	−0.273021
$609$	−12.9282	−0.523877
$610$	0	0
$611$	−10.1436	−0.410366
$612$	15.4641	0.625099
$613$	35.1769	1.42078	0.710391	−	0.703807i	$-0.248518\pi$
$613$	35.1769	1.42078	0.710391	+	0.703807i	$0.248518\pi$
$614$	24.3923	0.984393
$615$	0	0
$616$	1.00000	0.0402911
$617$	−17.3205	−0.697297	−0.348649	−	0.937253i	$-0.613359\pi$
$617$	−17.3205	−0.697297	−0.348649	+	0.937253i	$0.613359\pi$
$618$	−33.8564	−1.36190
$619$	28.7846	1.15695	0.578476	−	0.815700i	$-0.303648\pi$
$619$	28.7846	1.15695	0.578476	+	0.815700i	$0.303648\pi$
$620$	0	0
$621$	−32.7846	−1.31560
$622$	−24.9282	−0.999530
$623$	−3.46410	−0.138786
$624$	−4.00000	−0.160128
$625$	0	0
$626$	22.1962	0.887137
$627$	−18.3923	−0.734518
$628$	−4.53590	−0.181002
$629$	−2.53590	−0.101113
$630$	0	0
$631$	−46.9282	−1.86818	−0.934091	−	0.357035i	$-0.883788\pi$
$631$	−46.9282	−1.86818	−0.934091	+	0.357035i	$0.883788\pi$
$632$	12.1962	0.485137
$633$	−73.5692	−2.92411
$634$	30.5885	1.21482
$635$	0	0
$636$	−19.8564	−0.787358
$637$	1.46410	0.0580098
$638$	4.73205	0.187344
$639$	42.2487	1.67133
$640$	0	0
$641$	−35.5692	−1.40490	−0.702450	−	0.711733i	$-0.747910\pi$
$641$	−35.5692	−1.40490	−0.702450	+	0.711733i	$0.747910\pi$
$642$	−21.4641	−0.847121
$643$	−33.2679	−1.31196	−0.655980	−	0.754778i	$-0.727744\pi$
$643$	−33.2679	−1.31196	−0.655980	+	0.754778i	$0.727744\pi$
$644$	−8.19615	−0.322974
$645$	0	0
$646$	−23.3205	−0.917533
$647$	26.5359	1.04323	0.521617	−	0.853180i	$-0.325329\pi$
$647$	26.5359	1.04323	0.521617	+	0.853180i	$0.325329\pi$
$648$	2.46410	0.0967991
$649$	6.92820	0.271956
$650$	0	0
$651$	5.46410	0.214155
$652$	4.00000	0.156652
$653$	−11.6603	−0.456301	−0.228151	−	0.973626i	$-0.573268\pi$
$653$	−11.6603	−0.456301	−0.228151	+	0.973626i	$0.573268\pi$
$654$	−42.7846	−1.67301
$655$	0	0
$656$	−2.19615	−0.0857453
$657$	64.2487	2.50658
$658$	−6.92820	−0.270089
$659$	30.2487	1.17832	0.589161	−	0.808015i	$-0.299458\pi$
$659$	30.2487	1.17832	0.589161	+	0.808015i	$0.299458\pi$
$660$	0	0
$661$	−46.0000	−1.78919	−0.894596	−	0.446875i	$-0.852537\pi$
$661$	−46.0000	−1.78919	−0.894596	+	0.446875i	$0.852537\pi$
$662$	18.7846	0.730085
$663$	−13.8564	−0.538138
$664$	−16.3923	−0.636145
$665$	0	0
$666$	3.26795	0.126630
$667$	−38.7846	−1.50175
$668$	−13.8564	−0.536120
$669$	−69.5692	−2.68970
$670$	0	0
$671$	−4.92820	−0.190251
$672$	−2.73205	−0.105391
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	22.7846	0.877630
$675$	0	0
$676$	−10.8564	−0.417554
$677$	4.14359	0.159251	0.0796256	−	0.996825i	$-0.474628\pi$
$677$	4.14359	0.159251	0.0796256	+	0.996825i	$0.474628\pi$
$678$	−21.4641	−0.824324
$679$	14.5885	0.559854
$680$	0	0
$681$	18.9282	0.725330
$682$	−2.00000	−0.0765840
$683$	−6.24871	−0.239100	−0.119550	−	0.992828i	$-0.538145\pi$
$683$	−6.24871	−0.239100	−0.119550	+	0.992828i	$0.538145\pi$
$684$	30.0526	1.14909
$685$	0	0
$686$	1.00000	0.0381802
$687$	−66.6410	−2.54251
$688$	−2.00000	−0.0762493
$689$	10.6410	0.405390
$690$	0	0
$691$	−13.4641	−0.512199	−0.256099	−	0.966650i	$-0.582437\pi$
$691$	−13.4641	−0.512199	−0.256099	+	0.966650i	$0.582437\pi$
$692$	−0.928203	−0.0352850
$693$	−4.46410	−0.169577
$694$	−23.0718	−0.875793
$695$	0	0
$696$	−12.9282	−0.490042
$697$	−7.60770	−0.288162
$698$	5.60770	0.212254
$699$	−21.4641	−0.811847
$700$	0	0
$701$	41.9090	1.58288	0.791440	−	0.611247i	$-0.209332\pi$
$701$	41.9090	1.58288	0.791440	+	0.611247i	$0.209332\pi$
$702$	5.85641	0.221036
$703$	−4.92820	−0.185871
$704$	1.00000	0.0376889
$705$	0	0
$706$	14.1962	0.534279
$707$	7.85641	0.295471
$708$	−18.9282	−0.711365
$709$	25.3205	0.950932	0.475466	−	0.879734i	$-0.342280\pi$
$709$	25.3205	0.950932	0.475466	+	0.879734i	$0.342280\pi$
$710$	0	0
$711$	−54.4449	−2.04184
$712$	−3.46410	−0.129823
$713$	16.3923	0.613897
$714$	−9.46410	−0.354185
$715$	0	0
$716$	−6.00000	−0.224231
$717$	−3.46410	−0.129369
$718$	34.0526	1.27083
$719$	−27.7128	−1.03351	−0.516757	−	0.856132i	$-0.672861\pi$
$719$	−27.7128	−1.03351	−0.516757	+	0.856132i	$0.672861\pi$
$720$	0	0
$721$	12.3923	0.461514
$722$	−26.3205	−0.979548
$723$	−8.92820	−0.332043
$724$	14.0000	0.520306
$725$	0	0
$726$	2.73205	0.101396
$727$	4.00000	0.148352	0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000	0.148352	0.0741759	+	0.997245i	$0.476367\pi$
$728$	1.46410	0.0542632
$729$	−43.7846	−1.62165
$730$	0	0
$731$	−6.92820	−0.256249
$732$	13.4641	0.497648
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	12.3923	0.457408
$735$	0	0
$736$	−8.19615	−0.302114
$737$	4.00000	0.147342
$738$	9.80385	0.360885
$739$	11.7128	0.430863	0.215431	−	0.976519i	$-0.430884\pi$
$739$	11.7128	0.430863	0.215431	+	0.976519i	$0.430884\pi$
$740$	0	0
$741$	−26.9282	−0.989232
$742$	7.26795	0.266815
$743$	32.7846	1.20275	0.601375	−	0.798967i	$-0.294620\pi$
$743$	32.7846	1.20275	0.601375	+	0.798967i	$0.294620\pi$
$744$	5.46410	0.200324
$745$	0	0
$746$	18.3923	0.673390
$747$	73.1769	2.67740
$748$	3.46410	0.126660
$749$	7.85641	0.287067
$750$	0	0
$751$	−11.6077	−0.423571	−0.211785	−	0.977316i	$-0.567928\pi$
$751$	−11.6077	−0.423571	−0.211785	+	0.977316i	$0.567928\pi$
$752$	−6.92820	−0.252646
$753$	−32.7846	−1.19474
$754$	6.92820	0.252310
$755$	0	0
$756$	4.00000	0.145479
$757$	43.3731	1.57642	0.788210	−	0.615406i	$-0.211008\pi$
$757$	43.3731	1.57642	0.788210	+	0.615406i	$0.211008\pi$
$758$	−6.14359	−0.223145
$759$	−22.3923	−0.812789
$760$	0	0
$761$	−12.3397	−0.447315	−0.223658	−	0.974668i	$-0.571800\pi$
$761$	−12.3397	−0.447315	−0.223658	+	0.974668i	$0.571800\pi$
$762$	−2.92820	−0.106078
$763$	15.6603	0.566939
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−33.4641	−1.20911
$767$	10.1436	0.366264
$768$	−2.73205	−0.0985844
$769$	−18.1962	−0.656170	−0.328085	−	0.944648i	$-0.606403\pi$
$769$	−18.1962	−0.656170	−0.328085	+	0.944648i	$0.606403\pi$
$770$	0	0
$771$	−64.6410	−2.32799
$772$	−12.3923	−0.446009
$773$	0.928203	0.0333851	0.0166926	−	0.999861i	$-0.494686\pi$
$773$	0.928203	0.0333851	0.0166926	+	0.999861i	$0.494686\pi$
$774$	8.92820	0.320918
$775$	0	0
$776$	14.5885	0.523695
$777$	−2.00000	−0.0717496
$778$	1.60770	0.0576387
$779$	−14.7846	−0.529714
$780$	0	0
$781$	9.46410	0.338652
$782$	−28.3923	−1.01531
$783$	18.9282	0.676439
$784$	1.00000	0.0357143
$785$	0	0
$786$	15.4641	0.551586
$787$	−18.1436	−0.646749	−0.323375	−	0.946271i	$-0.604817\pi$
$787$	−18.1436	−0.646749	−0.323375	+	0.946271i	$0.604817\pi$
$788$	24.2487	0.863825
$789$	−65.5692	−2.33433
$790$	0	0
$791$	7.85641	0.279342
$792$	−4.46410	−0.158625
$793$	−7.21539	−0.256226
$794$	30.3923	1.07858
$795$	0	0
$796$	2.92820	0.103787
$797$	25.6077	0.907071	0.453536	−	0.891238i	$-0.350163\pi$
$797$	25.6077	0.907071	0.453536	+	0.891238i	$0.350163\pi$
$798$	−18.3923	−0.651081
$799$	−24.0000	−0.849059
$800$	0	0
$801$	15.4641	0.546397
$802$	−2.53590	−0.0895457
$803$	14.3923	0.507893
$804$	−10.9282	−0.385408
$805$	0	0
$806$	−2.92820	−0.103142
$807$	−77.5692	−2.73057
$808$	7.85641	0.276387
$809$	−31.1769	−1.09612	−0.548061	−	0.836438i	$-0.684634\pi$
$809$	−31.1769	−1.09612	−0.548061	+	0.836438i	$0.684634\pi$
$810$	0	0
$811$	−43.1244	−1.51430	−0.757150	−	0.653241i	$-0.773409\pi$
$811$	−43.1244	−1.51430	−0.757150	+	0.653241i	$0.773409\pi$
$812$	4.73205	0.166062
$813$	−1.07180	−0.0375896
$814$	0.732051	0.0256584
$815$	0	0
$816$	−9.46410	−0.331310
$817$	−13.4641	−0.471049
$818$	−10.8756	−0.380258
$819$	−6.53590	−0.228383
$820$	0	0
$821$	17.9090	0.625027	0.312514	−	0.949913i	$-0.398829\pi$
$821$	17.9090	0.625027	0.312514	+	0.949913i	$0.398829\pi$
$822$	2.53590	0.0884496
$823$	0.875644	0.0305230	0.0152615	−	0.999884i	$-0.495142\pi$
$823$	0.875644	0.0305230	0.0152615	+	0.999884i	$0.495142\pi$
$824$	12.3923	0.431706
$825$	0	0
$826$	6.92820	0.241063
$827$	25.8564	0.899115	0.449558	−	0.893251i	$-0.351582\pi$
$827$	25.8564	0.899115	0.449558	+	0.893251i	$0.351582\pi$
$828$	36.5885	1.27154
$829$	2.24871	0.0781010	0.0390505	−	0.999237i	$-0.487567\pi$
$829$	2.24871	0.0781010	0.0390505	+	0.999237i	$0.487567\pi$
$830$	0	0
$831$	19.3205	0.670221
$832$	1.46410	0.0507586
$833$	3.46410	0.120024
$834$	37.3205	1.29230
$835$	0	0
$836$	6.73205	0.232833
$837$	−8.00000	−0.276520
$838$	−30.9282	−1.06840
$839$	−31.8564	−1.09981	−0.549903	−	0.835229i	$-0.685335\pi$
$839$	−31.8564	−1.09981	−0.549903	+	0.835229i	$0.685335\pi$
$840$	0	0
$841$	−6.60770	−0.227852
$842$	35.8564	1.23569
$843$	−61.1769	−2.10704
$844$	26.9282	0.926907
$845$	0	0
$846$	30.9282	1.06333
$847$	−1.00000	−0.0343604
$848$	7.26795	0.249582
$849$	−86.6410	−2.97351
$850$	0	0
$851$	−6.00000	−0.205677
$852$	−25.8564	−0.885826
$853$	54.7846	1.87579	0.937895	−	0.346920i	$-0.112773\pi$
$853$	54.7846	1.87579	0.937895	+	0.346920i	$0.112773\pi$
$854$	−4.92820	−0.168640
$855$	0	0
$856$	7.85641	0.268526
$857$	27.4641	0.938156	0.469078	−	0.883157i	$-0.344586\pi$
$857$	27.4641	0.938156	0.469078	+	0.883157i	$0.344586\pi$
$858$	4.00000	0.136558
$859$	−12.7846	−0.436205	−0.218103	−	0.975926i	$-0.569987\pi$
$859$	−12.7846	−0.436205	−0.218103	+	0.975926i	$0.569987\pi$
$860$	0	0
$861$	−6.00000	−0.204479
$862$	−3.12436	−0.106416
$863$	7.51666	0.255870	0.127935	−	0.991783i	$-0.459165\pi$
$863$	7.51666	0.255870	0.127935	+	0.991783i	$0.459165\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	−18.1962	−0.618330
$867$	13.6603	0.463927
$868$	−2.00000	−0.0678844
$869$	−12.1962	−0.413726
$870$	0	0
$871$	5.85641	0.198437
$872$	15.6603	0.530323
$873$	−65.1244	−2.20413
$874$	−55.1769	−1.86639
$875$	0	0
$876$	−39.3205	−1.32852
$877$	21.3205	0.719942	0.359971	−	0.932963i	$-0.382787\pi$
$877$	21.3205	0.719942	0.359971	+	0.932963i	$0.382787\pi$
$878$	−26.2487	−0.885851
$879$	58.6410	1.97791
$880$	0	0
$881$	11.0718	0.373018	0.186509	−	0.982453i	$-0.440283\pi$
$881$	11.0718	0.373018	0.186509	+	0.982453i	$0.440283\pi$
$882$	−4.46410	−0.150314
$883$	35.6077	1.19829	0.599147	−	0.800639i	$-0.295506\pi$
$883$	35.6077	1.19829	0.599147	+	0.800639i	$0.295506\pi$
$884$	5.07180	0.170583
$885$	0	0
$886$	0	0
$887$	−13.8564	−0.465253	−0.232626	−	0.972566i	$-0.574732\pi$
$887$	−13.8564	−0.465253	−0.232626	+	0.972566i	$0.574732\pi$
$888$	−2.00000	−0.0671156
$889$	1.07180	0.0359469
$890$	0	0
$891$	−2.46410	−0.0825505
$892$	25.4641	0.852601
$893$	−46.6410	−1.56078
$894$	−19.8564	−0.664098
$895$	0	0
$896$	1.00000	0.0334077
$897$	−32.7846	−1.09465
$898$	−40.3923	−1.34791
$899$	−9.46410	−0.315645
$900$	0	0
$901$	25.1769	0.838765
$902$	2.19615	0.0731239
$903$	−5.46410	−0.181834
$904$	7.85641	0.261300
$905$	0	0
$906$	30.3923	1.00972
$907$	31.0333	1.03044	0.515222	−	0.857057i	$-0.327709\pi$
$907$	31.0333	1.03044	0.515222	+	0.857057i	$0.327709\pi$
$908$	−6.92820	−0.229920
$909$	−35.0718	−1.16326
$910$	0	0
$911$	9.46410	0.313560	0.156780	−	0.987634i	$-0.449889\pi$
$911$	9.46410	0.313560	0.156780	+	0.987634i	$0.449889\pi$
$912$	−18.3923	−0.609030
$913$	16.3923	0.542506
$914$	2.00000	0.0661541
$915$	0	0
$916$	24.3923	0.805944
$917$	−5.66025	−0.186918
$918$	13.8564	0.457330
$919$	−25.3731	−0.836980	−0.418490	−	0.908221i	$-0.637441\pi$
$919$	−25.3731	−0.836980	−0.418490	+	0.908221i	$0.637441\pi$
$920$	0	0
$921$	66.6410	2.19590
$922$	−22.3923	−0.737451
$923$	13.8564	0.456089
$924$	2.73205	0.0898779
$925$	0	0
$926$	27.5167	0.904254
$927$	−55.3205	−1.81696
$928$	4.73205	0.155337
$929$	−25.6077	−0.840161	−0.420081	−	0.907487i	$-0.637998\pi$
$929$	−25.6077	−0.840161	−0.420081	+	0.907487i	$0.637998\pi$
$930$	0	0
$931$	6.73205	0.220634
$932$	7.85641	0.257345
$933$	−68.1051	−2.22966
$934$	−34.0526	−1.11423
$935$	0	0
$936$	−6.53590	−0.213633
$937$	1.21539	0.0397051	0.0198525	−	0.999803i	$-0.493680\pi$
$937$	1.21539	0.0397051	0.0198525	+	0.999803i	$0.493680\pi$
$938$	4.00000	0.130605
$939$	60.6410	1.97894
$940$	0	0
$941$	−14.7846	−0.481965	−0.240982	−	0.970530i	$-0.577470\pi$
$941$	−14.7846	−0.481965	−0.240982	+	0.970530i	$0.577470\pi$
$942$	−12.3923	−0.403763
$943$	−18.0000	−0.586161
$944$	6.92820	0.225494
$945$	0	0
$946$	2.00000	0.0650256
$947$	−47.3205	−1.53771	−0.768855	−	0.639423i	$-0.779173\pi$
$947$	−47.3205	−1.53771	−0.768855	+	0.639423i	$0.779173\pi$
$948$	33.3205	1.08220
$949$	21.0718	0.684019
$950$	0	0
$951$	83.5692	2.70992
$952$	3.46410	0.112272
$953$	−26.5359	−0.859582	−0.429791	−	0.902928i	$-0.641413\pi$
$953$	−26.5359	−0.859582	−0.429791	+	0.902928i	$0.641413\pi$
$954$	−32.4449	−1.05044
$955$	0	0
$956$	1.26795	0.0410084
$957$	12.9282	0.417909
$958$	32.7846	1.05922
$959$	−0.928203	−0.0299732
$960$	0	0
$961$	−27.0000	−0.870968
$962$	1.07180	0.0345561
$963$	−35.0718	−1.13017
$964$	3.26795	0.105254
$965$	0	0
$966$	−22.3923	−0.720461
$967$	−26.9282	−0.865953	−0.432976	−	0.901405i	$-0.642537\pi$
$967$	−26.9282	−0.865953	−0.432976	+	0.901405i	$0.642537\pi$
$968$	−1.00000	−0.0321412
$969$	−63.7128	−2.04675
$970$	0	0
$971$	42.9282	1.37763	0.688816	−	0.724936i	$-0.258131\pi$
$971$	42.9282	1.37763	0.688816	+	0.724936i	$0.258131\pi$
$972$	18.7321	0.600831
$973$	−13.6603	−0.437928
$974$	4.19615	0.134453
$975$	0	0
$976$	−4.92820	−0.157748
$977$	33.7128	1.07857	0.539284	−	0.842124i	$-0.318695\pi$
$977$	33.7128	1.07857	0.539284	+	0.842124i	$0.318695\pi$
$978$	10.9282	0.349445
$979$	3.46410	0.110713
$980$	0	0
$981$	−69.9090	−2.23202
$982$	27.7128	0.884351
$983$	37.1769	1.18576	0.592880	−	0.805291i	$-0.297991\pi$
$983$	37.1769	1.18576	0.592880	+	0.805291i	$0.297991\pi$
$984$	−6.00000	−0.191273
$985$	0	0
$986$	16.3923	0.522037
$987$	−18.9282	−0.602491
$988$	9.85641	0.313574
$989$	−16.3923	−0.521245
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−2.00000	−0.0635001
$993$	51.3205	1.62861
$994$	9.46410	0.300183
$995$	0	0
$996$	−44.7846	−1.41905
$997$	−17.7128	−0.560970	−0.280485	−	0.959858i	$-0.590495\pi$
$997$	−17.7128	−0.560970	−0.280485	+	0.959858i	$0.590495\pi$
$998$	−12.1436	−0.384399
$999$	2.92820	0.0926443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.bd.1.1		2
5.2	odd	4		3850.2.c.x.1849.2		4
5.3	odd	4		3850.2.c.x.1849.3		4
5.4	even	2		770.2.a.j.1.2	✓	2
15.14	odd	2		6930.2.a.bv.1.1		2
20.19	odd	2		6160.2.a.t.1.1		2
35.34	odd	2		5390.2.a.bs.1.1		2
55.54	odd	2		8470.2.a.br.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.j.1.2	✓	2	5.4	even	2
3850.2.a.bd.1.1		2	1.1	even	1	trivial
3850.2.c.x.1849.2		4	5.2	odd	4
3850.2.c.x.1849.3		4	5.3	odd	4
5390.2.a.bs.1.1		2	35.34	odd	2
6160.2.a.t.1.1		2	20.19	odd	2
6930.2.a.bv.1.1		2	15.14	odd	2
8470.2.a.br.1.2		2	55.54	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +2.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +2.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} +1.00000 q^{11} -2.73205 q^{12} +1.46410 q^{13} +1.00000 q^{14} +1.00000 q^{16} +3.46410 q^{17} -4.46410 q^{18} +6.73205 q^{19} +2.73205 q^{21} -1.00000 q^{22} +8.19615 q^{23} +2.73205 q^{24} -1.46410 q^{26} -4.00000 q^{27} -1.00000 q^{28} -4.73205 q^{29} +2.00000 q^{31} -1.00000 q^{32} -2.73205 q^{33} -3.46410 q^{34} +4.46410 q^{36} -0.732051 q^{37} -6.73205 q^{38} -4.00000 q^{39} -2.19615 q^{41} -2.73205 q^{42} -2.00000 q^{43} +1.00000 q^{44} -8.19615 q^{46} -6.92820 q^{47} -2.73205 q^{48} +1.00000 q^{49} -9.46410 q^{51} +1.46410 q^{52} +7.26795 q^{53} +4.00000 q^{54} +1.00000 q^{56} -18.3923 q^{57} +4.73205 q^{58} +6.92820 q^{59} -4.92820 q^{61} -2.00000 q^{62} -4.46410 q^{63} +1.00000 q^{64} +2.73205 q^{66} +4.00000 q^{67} +3.46410 q^{68} -22.3923 q^{69} +9.46410 q^{71} -4.46410 q^{72} +14.3923 q^{73} +0.732051 q^{74} +6.73205 q^{76} -1.00000 q^{77} +4.00000 q^{78} -12.1962 q^{79} -2.46410 q^{81} +2.19615 q^{82} +16.3923 q^{83} +2.73205 q^{84} +2.00000 q^{86} +12.9282 q^{87} -1.00000 q^{88} +3.46410 q^{89} -1.46410 q^{91} +8.19615 q^{92} -5.46410 q^{93} +6.92820 q^{94} +2.73205 q^{96} -14.5885 q^{97} -1.00000 q^{98} +4.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{18} + 10 q^{19} + 2 q^{21} - 2 q^{22} + 6 q^{23} + 2 q^{24} + 4 q^{26} - 8 q^{27} - 2 q^{28} - 6 q^{29} + 4 q^{31} - 2 q^{32} - 2 q^{33} + 2 q^{36} + 2 q^{37} - 10 q^{38} - 8 q^{39} + 6 q^{41} - 2 q^{42} - 4 q^{43} + 2 q^{44} - 6 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{51} - 4 q^{52} + 18 q^{53} + 8 q^{54} + 2 q^{56} - 16 q^{57} + 6 q^{58} + 4 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{66} + 8 q^{67} - 24 q^{69} + 12 q^{71} - 2 q^{72} + 8 q^{73} - 2 q^{74} + 10 q^{76} - 2 q^{77} + 8 q^{78} - 14 q^{79} + 2 q^{81} - 6 q^{82} + 12 q^{83} + 2 q^{84} + 4 q^{86} + 12 q^{87} - 2 q^{88} + 4 q^{91} + 6 q^{92} - 4 q^{93} + 2 q^{96} + 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^18 + 10 * q^19 + 2 * q^21 - 2 * q^22 + 6 * q^23 + 2 * q^24 + 4 * q^26 - 8 * q^27 - 2 * q^28 - 6 * q^29 + 4 * q^31 - 2 * q^32 - 2 * q^33 + 2 * q^36 + 2 * q^37 - 10 * q^38 - 8 * q^39 + 6 * q^41 - 2 * q^42 - 4 * q^43 + 2 * q^44 - 6 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^51 - 4 * q^52 + 18 * q^53 + 8 * q^54 + 2 * q^56 - 16 * q^57 + 6 * q^58 + 4 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^66 + 8 * q^67 - 24 * q^69 + 12 * q^71 - 2 * q^72 + 8 * q^73 - 2 * q^74 + 10 * q^76 - 2 * q^77 + 8 * q^78 - 14 * q^79 + 2 * q^81 - 6 * q^82 + 12 * q^83 + 2 * q^84 + 4 * q^86 + 12 * q^87 - 2 * q^88 + 4 * q^91 + 6 * q^92 - 4 * q^93 + 2 * q^96 + 2 * q^97 - 2 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more