LMFDB - Embedded newform 3887.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3887,2,Mod(1,3887)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3887, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

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

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

chi := DirichletCharacter("3887.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3887 = 13^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3887.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:	$31.0378512657$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 19x^{8} + 18x^{7} + 127x^{6} - 109x^{5} - 357x^{4} + 252x^{3} + 400x^{2} - 192x - 128 $ x^10 - x^9 - 19x^8 + 18x^7 + 127x^6 - 109x^5 - 357x^4 + 252x^3 + 400x^2 - 192x - 128
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 299)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.26436$ of defining polynomial
Character	$\chi$	$=$	3887.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26436 q^{2} +2.37123 q^{3} +3.12732 q^{4} +3.16568 q^{5} -5.36932 q^{6} -1.09348 q^{7} -2.55266 q^{8} +2.62273 q^{9} +O(q^{10})$	\(q-2.26436 q^{2} +2.37123 q^{3} +3.12732 q^{4} +3.16568 q^{5} -5.36932 q^{6} -1.09348 q^{7} -2.55266 q^{8} +2.62273 q^{9} -7.16824 q^{10} +5.61162 q^{11} +7.41560 q^{12} +2.47604 q^{14} +7.50657 q^{15} -0.474506 q^{16} -0.216286 q^{17} -5.93881 q^{18} -6.03266 q^{19} +9.90011 q^{20} -2.59290 q^{21} -12.7067 q^{22} +1.00000 q^{23} -6.05294 q^{24} +5.02155 q^{25} -0.894583 q^{27} -3.41967 q^{28} +9.11937 q^{29} -16.9976 q^{30} -8.04245 q^{31} +6.17977 q^{32} +13.3064 q^{33} +0.489750 q^{34} -3.46162 q^{35} +8.20213 q^{36} +2.55717 q^{37} +13.6601 q^{38} -8.08091 q^{40} +7.13855 q^{41} +5.87126 q^{42} +4.22532 q^{43} +17.5493 q^{44} +8.30275 q^{45} -2.26436 q^{46} +1.07565 q^{47} -1.12516 q^{48} -5.80429 q^{49} -11.3706 q^{50} -0.512864 q^{51} +0.577213 q^{53} +2.02566 q^{54} +17.7646 q^{55} +2.79129 q^{56} -14.3048 q^{57} -20.6495 q^{58} +4.96068 q^{59} +23.4754 q^{60} +8.94721 q^{61} +18.2110 q^{62} -2.86792 q^{63} -13.0442 q^{64} -30.1306 q^{66} -7.26955 q^{67} -0.676396 q^{68} +2.37123 q^{69} +7.83835 q^{70} -8.41151 q^{71} -6.69495 q^{72} +9.27194 q^{73} -5.79035 q^{74} +11.9073 q^{75} -18.8661 q^{76} -6.13621 q^{77} +4.24311 q^{79} -1.50214 q^{80} -9.98947 q^{81} -16.1642 q^{82} +6.74657 q^{83} -8.10883 q^{84} -0.684694 q^{85} -9.56764 q^{86} +21.6241 q^{87} -14.3246 q^{88} +15.0002 q^{89} -18.8004 q^{90} +3.12732 q^{92} -19.0705 q^{93} -2.43566 q^{94} -19.0975 q^{95} +14.6537 q^{96} +15.7654 q^{97} +13.1430 q^{98} +14.7178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9}+O(q^{10}) $ 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9} + 6 q^{10} - 3 q^{11} + 10 q^{12} - 15 q^{14} - 2 q^{15} + 25 q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + 19 q^{20} - 21 q^{21} + 13 q^{22} + 10 q^{23} + 35 q^{24} + 33 q^{25} + 6 q^{27} + 19 q^{28} + 17 q^{29} - 47 q^{30} - 5 q^{31} + 9 q^{32} + 23 q^{33} - 23 q^{34} + 3 q^{35} + 48 q^{36} - 16 q^{37} + 5 q^{38} + 13 q^{40} + 16 q^{41} - 65 q^{42} - 9 q^{43} - 18 q^{44} - 32 q^{45} - q^{46} + 11 q^{47} + 37 q^{48} + 40 q^{49} + 30 q^{50} - 31 q^{51} + 8 q^{53} + 73 q^{54} - 14 q^{55} - 54 q^{56} + 35 q^{57} - 17 q^{58} - 2 q^{59} + 37 q^{60} + 48 q^{61} - 19 q^{62} + 15 q^{63} + 64 q^{64} - 84 q^{66} + 6 q^{67} - 62 q^{68} + 3 q^{69} + 44 q^{70} - 24 q^{71} + 89 q^{72} + 33 q^{73} - 28 q^{74} - 22 q^{75} + 53 q^{76} + 15 q^{77} + 17 q^{79} + 94 q^{80} + 30 q^{81} + 35 q^{82} + 21 q^{83} - 92 q^{84} - 58 q^{85} + 7 q^{86} + 23 q^{87} + 9 q^{88} + 16 q^{89} + 67 q^{90} + 19 q^{92} - 15 q^{93} + 12 q^{94} - 27 q^{95} + 22 q^{96} + 40 q^{97} + 34 q^{98} + 17 q^{99}+O(q^{100}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9 + 6 * q^10 - 3 * q^11 + 10 * q^12 - 15 * q^14 - 2 * q^15 + 25 * q^16 - 3 * q^17 - q^18 - 2 * q^19 + 19 * q^20 - 21 * q^21 + 13 * q^22 + 10 * q^23 + 35 * q^24 + 33 * q^25 + 6 * q^27 + 19 * q^28 + 17 * q^29 - 47 * q^30 - 5 * q^31 + 9 * q^32 + 23 * q^33 - 23 * q^34 + 3 * q^35 + 48 * q^36 - 16 * q^37 + 5 * q^38 + 13 * q^40 + 16 * q^41 - 65 * q^42 - 9 * q^43 - 18 * q^44 - 32 * q^45 - q^46 + 11 * q^47 + 37 * q^48 + 40 * q^49 + 30 * q^50 - 31 * q^51 + 8 * q^53 + 73 * q^54 - 14 * q^55 - 54 * q^56 + 35 * q^57 - 17 * q^58 - 2 * q^59 + 37 * q^60 + 48 * q^61 - 19 * q^62 + 15 * q^63 + 64 * q^64 - 84 * q^66 + 6 * q^67 - 62 * q^68 + 3 * q^69 + 44 * q^70 - 24 * q^71 + 89 * q^72 + 33 * q^73 - 28 * q^74 - 22 * q^75 + 53 * q^76 + 15 * q^77 + 17 * q^79 + 94 * q^80 + 30 * q^81 + 35 * q^82 + 21 * q^83 - 92 * q^84 - 58 * q^85 + 7 * q^86 + 23 * q^87 + 9 * q^88 + 16 * q^89 + 67 * q^90 + 19 * q^92 - 15 * q^93 + 12 * q^94 - 27 * q^95 + 22 * q^96 + 40 * q^97 + 34 * q^98 + 17 * 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 $

$2$	−2.26436	−1.60114	−0.800572	−	0.599237i	$-0.795471\pi$
$2$	−2.26436	−1.60114	−0.800572	+	0.599237i	$0.795471\pi$
$3$	2.37123	1.36903	0.684515	−	0.728998i	$-0.260014\pi$
$3$	2.37123	1.36903	0.684515	+	0.728998i	$0.260014\pi$
$4$	3.12732	1.56366
$5$	3.16568	1.41574	0.707868	−	0.706344i	$-0.249657\pi$
$5$	3.16568	1.41574	0.707868	+	0.706344i	$0.249657\pi$
$6$	−5.36932	−2.19201
$7$	−1.09348	−0.413298	−0.206649	−	0.978415i	$-0.566256\pi$
$7$	−1.09348	−0.413298	−0.206649	+	0.978415i	$0.566256\pi$
$8$	−2.55266	−0.902501
$9$	2.62273	0.874245
$10$	−7.16824	−2.26680
$11$	5.61162	1.69197	0.845984	−	0.533209i	$-0.179014\pi$
$11$	5.61162	1.69197	0.845984	+	0.533209i	$0.179014\pi$
$12$	7.41560	2.14070
$13$	0	0
$13$	0	0
$14$	2.47604	0.661749
$15$	7.50657	1.93819
$16$	−0.474506	−0.118627
$17$	−0.216286	−0.0524571	−0.0262286	−	0.999656i	$-0.508350\pi$
$17$	−0.216286	−0.0524571	−0.0262286	+	0.999656i	$0.508350\pi$
$18$	−5.93881	−1.39979
$19$	−6.03266	−1.38399	−0.691994	−	0.721904i	$-0.743267\pi$
$19$	−6.03266	−1.38399	−0.691994	+	0.721904i	$0.743267\pi$
$20$	9.90011	2.21373
$21$	−2.59290	−0.565817
$22$	−12.7067	−2.70908
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−6.05294	−1.23555
$25$	5.02155	1.00431
$26$	0	0
$27$	−0.894583	−0.172163
$28$	−3.41967	−0.646257
$29$	9.11937	1.69342	0.846712	−	0.532051i	$-0.178578\pi$
$29$	9.11937	1.69342	0.846712	+	0.532051i	$0.178578\pi$
$30$	−16.9976	−3.10332
$31$	−8.04245	−1.44447	−0.722234	−	0.691649i	$-0.756885\pi$
$31$	−8.04245	−1.44447	−0.722234	+	0.691649i	$0.756885\pi$
$32$	6.17977	1.09244
$33$	13.3064	2.31636
$34$	0.489750	0.0839914
$35$	−3.46162	−0.585121
$36$	8.20213	1.36702
$37$	2.55717	0.420396	0.210198	−	0.977659i	$-0.432589\pi$
$37$	2.55717	0.420396	0.210198	+	0.977659i	$0.432589\pi$
$38$	13.6601	2.21596
$39$	0	0
$40$	−8.08091	−1.27770
$41$	7.13855	1.11485	0.557427	−	0.830226i	$-0.311789\pi$
$41$	7.13855	1.11485	0.557427	+	0.830226i	$0.311789\pi$
$42$	5.87126	0.905955
$43$	4.22532	0.644355	0.322178	−	0.946679i	$-0.395585\pi$
$43$	4.22532	0.644355	0.322178	+	0.946679i	$0.395585\pi$
$44$	17.5493	2.64566
$45$	8.30275	1.23770
$46$	−2.26436	−0.333861
$47$	1.07565	0.156900	0.0784500	−	0.996918i	$-0.475003\pi$
$47$	1.07565	0.156900	0.0784500	+	0.996918i	$0.475003\pi$
$48$	−1.12516	−0.162403
$49$	−5.80429	−0.829185
$50$	−11.3706	−1.60805
$51$	−0.512864	−0.0718154
$52$	0	0
$53$	0.577213	0.0792863	0.0396431	−	0.999214i	$-0.487378\pi$
$53$	0.577213	0.0792863	0.0396431	+	0.999214i	$0.487378\pi$
$54$	2.02566	0.275657
$55$	17.7646	2.39538
$56$	2.79129	0.373002
$57$	−14.3048	−1.89472
$58$	−20.6495	−2.71142
$59$	4.96068	0.645825	0.322913	−	0.946429i	$-0.395338\pi$
$59$	4.96068	0.645825	0.322913	+	0.946429i	$0.395338\pi$
$60$	23.4754	3.03067
$61$	8.94721	1.14557	0.572787	−	0.819704i	$-0.305862\pi$
$61$	8.94721	1.14557	0.572787	+	0.819704i	$0.305862\pi$
$62$	18.2110	2.31280
$63$	−2.86792	−0.361323
$64$	−13.0442	−1.63053
$65$	0	0
$66$	−30.1306	−3.70882
$67$	−7.26955	−0.888117	−0.444059	−	0.895998i	$-0.646462\pi$
$67$	−7.26955	−0.888117	−0.444059	+	0.895998i	$0.646462\pi$
$68$	−0.676396	−0.0820251
$69$	2.37123	0.285463
$70$	7.83835	0.936862
$71$	−8.41151	−0.998263	−0.499131	−	0.866526i	$-0.666347\pi$
$71$	−8.41151	−0.998263	−0.499131	+	0.866526i	$0.666347\pi$
$72$	−6.69495	−0.789007
$73$	9.27194	1.08520	0.542599	−	0.839992i	$-0.317440\pi$
$73$	9.27194	1.08520	0.542599	+	0.839992i	$0.317440\pi$
$74$	−5.79035	−0.673114
$75$	11.9073	1.37493
$76$	−18.8661	−2.16409
$77$	−6.13621	−0.699286
$78$	0	0
$79$	4.24311	0.477387	0.238693	−	0.971095i	$-0.423281\pi$
$79$	4.24311	0.477387	0.238693	+	0.971095i	$0.423281\pi$
$80$	−1.50214	−0.167944
$81$	−9.98947	−1.10994
$82$	−16.1642	−1.78504
$83$	6.74657	0.740533	0.370266	−	0.928926i	$-0.379266\pi$
$83$	6.74657	0.740533	0.370266	+	0.928926i	$0.379266\pi$
$84$	−8.10883	−0.884746
$85$	−0.684694	−0.0742655
$86$	−9.56764	−1.03171
$87$	21.6241	2.31835
$88$	−14.3246	−1.52700
$89$	15.0002	1.59002	0.795008	−	0.606599i	$-0.207466\pi$
$89$	15.0002	1.59002	0.795008	+	0.606599i	$0.207466\pi$
$90$	−18.8004	−1.98174
$91$	0	0
$92$	3.12732	0.326046
$93$	−19.0705	−1.97752
$94$	−2.43566	−0.251219
$95$	−19.0975	−1.95936
$96$	14.6537	1.49558
$97$	15.7654	1.60073	0.800366	−	0.599512i	$-0.204639\pi$
$97$	15.7654	1.60073	0.800366	+	0.599512i	$0.204639\pi$
$98$	13.1430	1.32764
$99$	14.7178	1.47919
$100$	15.7040	1.57040
$101$	4.71172	0.468833	0.234417	−	0.972136i	$-0.424682\pi$
$101$	4.71172	0.468833	0.234417	+	0.972136i	$0.424682\pi$
$102$	1.16131	0.114987
$103$	−10.9592	−1.07984	−0.539921	−	0.841716i	$-0.681546\pi$
$103$	−10.9592	−1.07984	−0.539921	+	0.841716i	$0.681546\pi$
$104$	0	0
$105$	−8.20830	−0.801048
$106$	−1.30702	−0.126949
$107$	15.2331	1.47264	0.736319	−	0.676635i	$-0.236562\pi$
$107$	15.2331	1.47264	0.736319	+	0.676635i	$0.236562\pi$
$108$	−2.79765	−0.269204
$109$	−0.662195	−0.0634268	−0.0317134	−	0.999497i	$-0.510096\pi$
$109$	−0.662195	−0.0634268	−0.0317134	+	0.999497i	$0.510096\pi$
$110$	−40.2255	−3.83535
$111$	6.06364	0.575535
$112$	0.518864	0.0490281
$113$	4.97000	0.467538	0.233769	−	0.972292i	$-0.424894\pi$
$113$	4.97000	0.467538	0.233769	+	0.972292i	$0.424894\pi$
$114$	32.3913	3.03372
$115$	3.16568	0.295202
$116$	28.5192	2.64794
$117$	0	0
$118$	−11.2328	−1.03406
$119$	0.236505	0.0216804
$120$	−19.1617	−1.74922
$121$	20.4903	1.86275
$122$	−20.2597	−1.83423
$123$	16.9271	1.52627
$124$	−25.1513	−2.25866
$125$	0.0682287	0.00610256
$126$	6.49399	0.578531
$127$	−3.66248	−0.324992	−0.162496	−	0.986709i	$-0.551955\pi$
$127$	−3.66248	−0.324992	−0.162496	+	0.986709i	$0.551955\pi$
$128$	17.1772	1.51827
$129$	10.0192	0.882142
$130$	0	0
$131$	9.96833	0.870937	0.435468	−	0.900204i	$-0.356583\pi$
$131$	9.96833	0.870937	0.435468	+	0.900204i	$0.356583\pi$
$132$	41.6135	3.62199
$133$	6.59661	0.571999
$134$	16.4609	1.42200
$135$	−2.83197	−0.243737
$136$	0.552105	0.0473426
$137$	1.03707	0.0886028	0.0443014	−	0.999018i	$-0.485894\pi$
$137$	1.03707	0.0886028	0.0443014	+	0.999018i	$0.485894\pi$
$138$	−5.36932	−0.457067
$139$	−14.0681	−1.19324	−0.596620	−	0.802524i	$-0.703490\pi$
$139$	−14.0681	−1.19324	−0.596620	+	0.802524i	$0.703490\pi$
$140$	−10.8256	−0.914930
$141$	2.55062	0.214801
$142$	19.0467	1.59836
$143$	0	0
$144$	−1.24450	−0.103709
$145$	28.8690	2.39744
$146$	−20.9950	−1.73756
$147$	−13.7633	−1.13518
$148$	7.99709	0.657356
$149$	−4.42571	−0.362568	−0.181284	−	0.983431i	$-0.558025\pi$
$149$	−4.42571	−0.362568	−0.181284	+	0.983431i	$0.558025\pi$
$150$	−26.9623	−2.20146
$151$	11.0342	0.897950	0.448975	−	0.893544i	$-0.351789\pi$
$151$	11.0342	0.897950	0.448975	+	0.893544i	$0.351789\pi$
$152$	15.3993	1.24905
$153$	−0.567261	−0.0458604
$154$	13.8946	1.11966
$155$	−25.4599	−2.04499
$156$	0	0
$157$	6.92247	0.552473	0.276237	−	0.961090i	$-0.410913\pi$
$157$	6.92247	0.552473	0.276237	+	0.961090i	$0.410913\pi$
$158$	−9.60792	−0.764365
$159$	1.36870	0.108545
$160$	19.5632	1.54661
$161$	−1.09348	−0.0861785
$162$	22.6197	1.77717
$163$	−14.4924	−1.13513	−0.567566	−	0.823328i	$-0.692115\pi$
$163$	−14.4924	−1.13513	−0.567566	+	0.823328i	$0.692115\pi$
$164$	22.3245	1.74325
$165$	42.1240	3.27935
$166$	−15.2767	−1.18570
$167$	−0.492391	−0.0381024	−0.0190512	−	0.999819i	$-0.506065\pi$
$167$	−0.492391	−0.0381024	−0.0190512	+	0.999819i	$0.506065\pi$
$168$	6.61879	0.510651
$169$	0	0
$170$	1.55039	0.118910
$171$	−15.8221	−1.20994
$172$	13.2139	1.00755
$173$	−6.92186	−0.526259	−0.263129	−	0.964761i	$-0.584755\pi$
$173$	−6.92186	−0.526259	−0.263129	+	0.964761i	$0.584755\pi$
$174$	−48.9648	−3.71201
$175$	−5.49098	−0.415079
$176$	−2.66275	−0.200712
$177$	11.7629	0.884154
$178$	−33.9658	−2.54584
$179$	24.1437	1.80458	0.902292	−	0.431126i	$-0.141884\pi$
$179$	24.1437	1.80458	0.902292	+	0.431126i	$0.141884\pi$
$180$	25.9654	1.93534
$181$	14.6257	1.08712	0.543560	−	0.839370i	$-0.317076\pi$
$181$	14.6257	1.08712	0.543560	+	0.839370i	$0.317076\pi$
$182$	0	0
$183$	21.2159	1.56832
$184$	−2.55266	−0.188185
$185$	8.09519	0.595170
$186$	43.1825	3.16629
$187$	−1.21372	−0.0887557
$188$	3.36391	0.245338
$189$	0.978212	0.0711544
$190$	43.2436	3.13722
$191$	−21.7537	−1.57404	−0.787021	−	0.616927i	$-0.788377\pi$
$191$	−21.7537	−1.57404	−0.787021	+	0.616927i	$0.788377\pi$
$192$	−30.9308	−2.23224
$193$	−5.42681	−0.390630	−0.195315	−	0.980741i	$-0.562573\pi$
$193$	−5.42681	−0.390630	−0.195315	+	0.980741i	$0.562573\pi$
$194$	−35.6985	−2.56300
$195$	0	0
$196$	−18.1519	−1.29656
$197$	−19.1789	−1.36644	−0.683221	−	0.730211i	$-0.739422\pi$
$197$	−19.1789	−1.36644	−0.683221	+	0.730211i	$0.739422\pi$
$198$	−33.3264	−2.36840
$199$	−15.0120	−1.06417	−0.532086	−	0.846690i	$-0.678592\pi$
$199$	−15.0120	−1.06417	−0.532086	+	0.846690i	$0.678592\pi$
$200$	−12.8183	−0.906391
$201$	−17.2378	−1.21586
$202$	−10.6690	−0.750669
$203$	−9.97188	−0.699889
$204$	−1.60389	−0.112295
$205$	22.5984	1.57834
$206$	24.8156	1.72898
$207$	2.62273	0.182293
$208$	0	0
$209$	−33.8530	−2.34166
$210$	18.5865	1.28259
$211$	−25.3580	−1.74571	−0.872857	−	0.487976i	$-0.837735\pi$
$211$	−25.3580	−1.74571	−0.872857	+	0.487976i	$0.837735\pi$
$212$	1.80513	0.123977
$213$	−19.9456	−1.36665
$214$	−34.4932	−2.35790
$215$	13.3760	0.912238
$216$	2.28357	0.155377
$217$	8.79429	0.596995
$218$	1.49945	0.101555
$219$	21.9859	1.48567
$220$	55.5557	3.74556
$221$	0	0
$222$	−13.7302	−0.921514
$223$	8.19092	0.548505	0.274252	−	0.961658i	$-0.411570\pi$
$223$	8.19092	0.548505	0.274252	+	0.961658i	$0.411570\pi$
$224$	−6.75747	−0.451503
$225$	13.1702	0.878013
$226$	−11.2539	−0.748595
$227$	−18.0533	−1.19824	−0.599120	−	0.800659i	$-0.704483\pi$
$227$	−18.0533	−1.19824	−0.599120	+	0.800659i	$0.704483\pi$
$228$	−44.7358	−2.96270
$229$	−3.12577	−0.206557	−0.103278	−	0.994652i	$-0.532933\pi$
$229$	−3.12577	−0.206557	−0.103278	+	0.994652i	$0.532933\pi$
$230$	−7.16824	−0.472660
$231$	−14.5504	−0.957344
$232$	−23.2786	−1.52832
$233$	16.0182	1.04938	0.524692	−	0.851292i	$-0.324180\pi$
$233$	16.0182	1.04938	0.524692	+	0.851292i	$0.324180\pi$
$234$	0	0
$235$	3.40517	0.222129
$236$	15.5136	1.00985
$237$	10.0614	0.653557
$238$	−0.535533	−0.0347134
$239$	22.1469	1.43256	0.716282	−	0.697811i	$-0.245843\pi$
$239$	22.1469	1.43256	0.716282	+	0.697811i	$0.245843\pi$
$240$	−3.56191	−0.229920
$241$	−29.1271	−1.87624	−0.938120	−	0.346309i	$-0.887435\pi$
$241$	−29.1271	−1.87624	−0.938120	+	0.346309i	$0.887435\pi$
$242$	−46.3974	−2.98254
$243$	−21.0036	−1.34738
$244$	27.9808	1.79129
$245$	−18.3746	−1.17391
$246$	−38.3291	−2.44378
$247$	0	0
$248$	20.5296	1.30363
$249$	15.9977	1.01381
$250$	−0.154494	−0.00977107
$251$	−16.6635	−1.05179	−0.525895	−	0.850549i	$-0.676270\pi$
$251$	−16.6635	−1.05179	−0.525895	+	0.850549i	$0.676270\pi$
$252$	−8.96889	−0.564987
$253$	5.61162	0.352800
$254$	8.29317	0.520360
$255$	−1.62357	−0.101672
$256$	−12.8070	−0.800436
$257$	−20.0539	−1.25093	−0.625464	−	0.780253i	$-0.715090\pi$
$257$	−20.0539	−1.25093	−0.625464	+	0.780253i	$0.715090\pi$
$258$	−22.6871	−1.41244
$259$	−2.79622	−0.173749
$260$	0	0
$261$	23.9177	1.48047
$262$	−22.5719	−1.39449
$263$	−9.00900	−0.555519	−0.277759	−	0.960651i	$-0.589592\pi$
$263$	−9.00900	−0.555519	−0.277759	+	0.960651i	$0.589592\pi$
$264$	−33.9668	−2.09051
$265$	1.82727	0.112248
$266$	−14.9371	−0.915852
$267$	35.5689	2.17678
$268$	−22.7342	−1.38871
$269$	−19.1642	−1.16846	−0.584230	−	0.811588i	$-0.698603\pi$
$269$	−19.1642	−1.16846	−0.584230	+	0.811588i	$0.698603\pi$
$270$	6.41259	0.390258
$271$	−15.6869	−0.952911	−0.476456	−	0.879199i	$-0.658079\pi$
$271$	−15.6869	−0.952911	−0.476456	+	0.879199i	$0.658079\pi$
$272$	0.102629	0.00622281
$273$	0	0
$274$	−2.34830	−0.141866
$275$	28.1791	1.69926
$276$	7.41560	0.446367
$277$	22.6425	1.36046	0.680229	−	0.733000i	$-0.261881\pi$
$277$	22.6425	1.36046	0.680229	+	0.733000i	$0.261881\pi$
$278$	31.8552	1.91055
$279$	−21.0932	−1.26282
$280$	8.83634	0.528072
$281$	−30.3083	−1.80804	−0.904021	−	0.427488i	$-0.859399\pi$
$281$	−30.3083	−1.80804	−0.904021	+	0.427488i	$0.859399\pi$
$282$	−5.77552	−0.343927
$283$	4.31430	0.256459	0.128229	−	0.991745i	$-0.459071\pi$
$283$	4.31430	0.256459	0.128229	+	0.991745i	$0.459071\pi$
$284$	−26.3055	−1.56094
$285$	−45.2846	−2.68243
$286$	0	0
$287$	−7.80588	−0.460767
$288$	16.2079	0.955059
$289$	−16.9532	−0.997248
$290$	−65.3699	−3.83865
$291$	37.3833	2.19145
$292$	28.9963	1.69688
$293$	26.1259	1.52629	0.763145	−	0.646228i	$-0.223654\pi$
$293$	26.1259	1.52629	0.763145	+	0.646228i	$0.223654\pi$
$294$	31.1651	1.81759
$295$	15.7039	0.914318
$296$	−6.52758	−0.379408
$297$	−5.02006	−0.291294
$298$	10.0214	0.580524
$299$	0	0
$300$	37.2378	2.14993
$301$	−4.62032	−0.266311
$302$	−24.9854	−1.43775
$303$	11.1726	0.641847
$304$	2.86253	0.164178
$305$	28.3240	1.62183
$306$	1.28448	0.0734290
$307$	15.1631	0.865404	0.432702	−	0.901537i	$-0.357560\pi$
$307$	15.1631	0.865404	0.432702	+	0.901537i	$0.357560\pi$
$308$	−19.1899	−1.09345
$309$	−25.9868	−1.47834
$310$	57.6503	3.27432
$311$	−7.65322	−0.433975	−0.216987	−	0.976174i	$-0.569623\pi$
$311$	−7.65322	−0.433975	−0.216987	+	0.976174i	$0.569623\pi$
$312$	0	0
$313$	16.6191	0.939365	0.469683	−	0.882835i	$-0.344368\pi$
$313$	16.6191	0.939365	0.469683	+	0.882835i	$0.344368\pi$
$314$	−15.6750	−0.884589
$315$	−9.07891	−0.511539
$316$	13.2696	0.746471
$317$	21.0679	1.18329	0.591646	−	0.806198i	$-0.298478\pi$
$317$	21.0679	1.18329	0.591646	+	0.806198i	$0.298478\pi$
$318$	−3.09924	−0.173797
$319$	51.1745	2.86522
$320$	−41.2938	−2.30839
$321$	36.1211	2.01609
$322$	2.47604	0.137984
$323$	1.30478	0.0726000
$324$	−31.2403	−1.73557
$325$	0	0
$326$	32.8160	1.81751
$327$	−1.57022	−0.0868332
$328$	−18.2223	−1.00616
$329$	−1.17621	−0.0648464
$330$	−95.3839	−5.25071
$331$	−22.6982	−1.24761	−0.623803	−	0.781581i	$-0.714413\pi$
$331$	−22.6982	−1.24761	−0.623803	+	0.781581i	$0.714413\pi$
$332$	21.0987	1.15794
$333$	6.70677	0.367529
$334$	1.11495	0.0610074
$335$	−23.0131	−1.25734
$336$	1.23035	0.0671209
$337$	−36.5071	−1.98867	−0.994334	−	0.106302i	$-0.966099\pi$
$337$	−36.5071	−1.98867	−0.994334	+	0.106302i	$0.966099\pi$
$338$	0	0
$339$	11.7850	0.640074
$340$	−2.14126	−0.116126
$341$	−45.1312	−2.44399
$342$	35.8268	1.93729
$343$	14.0013	0.755998
$344$	−10.7858	−0.581532
$345$	7.50657	0.404140
$346$	15.6736	0.842616
$347$	0.190187	0.0102098	0.00510488	−	0.999987i	$-0.498375\pi$
$347$	0.190187	0.0102098	0.00510488	+	0.999987i	$0.498375\pi$
$348$	67.6256	3.62511
$349$	−11.6025	−0.621067	−0.310533	−	0.950563i	$-0.600508\pi$
$349$	−11.6025	−0.621067	−0.310533	+	0.950563i	$0.600508\pi$
$350$	12.4336	0.664601
$351$	0	0
$352$	34.6785	1.84837
$353$	−10.1717	−0.541388	−0.270694	−	0.962666i	$-0.587253\pi$
$353$	−10.1717	−0.541388	−0.270694	+	0.962666i	$0.587253\pi$
$354$	−26.6354	−1.41566
$355$	−26.6282	−1.41328
$356$	46.9104	2.48625
$357$	0.560809	0.0296811
$358$	−54.6700	−2.88940
$359$	9.74914	0.514540	0.257270	−	0.966340i	$-0.417177\pi$
$359$	9.74914	0.514540	0.257270	+	0.966340i	$0.417177\pi$
$360$	−21.1941	−1.11703
$361$	17.3930	0.915420
$362$	−33.1178	−1.74064
$363$	48.5872	2.55017
$364$	0	0
$365$	29.3520	1.53636
$366$	−48.0404	−2.51111
$367$	21.6515	1.13020	0.565101	−	0.825022i	$-0.308837\pi$
$367$	21.6515	1.13020	0.565101	+	0.825022i	$0.308837\pi$
$368$	−0.474506	−0.0247353
$369$	18.7225	0.974655
$370$	−18.3304	−0.952952
$371$	−0.631172	−0.0327688
$372$	−59.6396	−3.09217
$373$	−4.61039	−0.238717	−0.119359	−	0.992851i	$-0.538084\pi$
$373$	−4.61039	−0.238717	−0.119359	+	0.992851i	$0.538084\pi$
$374$	2.74829	0.142111
$375$	0.161786	0.00835459
$376$	−2.74577	−0.141602
$377$	0	0
$378$	−2.21502	−0.113928
$379$	16.8903	0.867594	0.433797	−	0.901011i	$-0.357173\pi$
$379$	16.8903	0.867594	0.433797	+	0.901011i	$0.357173\pi$
$380$	−59.7240	−3.06378
$381$	−8.68458	−0.444925
$382$	49.2581	2.52027
$383$	−21.1619	−1.08132	−0.540661	−	0.841240i	$-0.681826\pi$
$383$	−21.1619	−1.08132	−0.540661	+	0.841240i	$0.681826\pi$
$384$	40.7311	2.07855
$385$	−19.4253	−0.990005
$386$	12.2882	0.625455
$387$	11.0819	0.563324
$388$	49.3034	2.50300
$389$	−16.3200	−0.827455	−0.413727	−	0.910401i	$-0.635773\pi$
$389$	−16.3200	−0.827455	−0.413727	+	0.910401i	$0.635773\pi$
$390$	0	0
$391$	−0.216286	−0.0109381
$392$	14.8164	0.748340
$393$	23.6372	1.19234
$394$	43.4280	2.18787
$395$	13.4323	0.675854
$396$	46.0273	2.31296
$397$	−8.97905	−0.450646	−0.225323	−	0.974284i	$-0.572344\pi$
$397$	−8.97905	−0.450646	−0.225323	+	0.974284i	$0.572344\pi$
$398$	33.9925	1.70389
$399$	15.6421	0.783084
$400$	−2.38276	−0.119138
$401$	−23.0991	−1.15351	−0.576757	−	0.816916i	$-0.695682\pi$
$401$	−23.0991	−1.15351	−0.576757	+	0.816916i	$0.695682\pi$
$402$	39.0325	1.94677
$403$	0	0
$404$	14.7350	0.733096
$405$	−31.6235	−1.57138
$406$	22.5799	1.12062
$407$	14.3499	0.711296
$408$	1.30917	0.0648135
$409$	−5.51078	−0.272491	−0.136245	−	0.990675i	$-0.543504\pi$
$409$	−5.51078	−0.272491	−0.136245	+	0.990675i	$0.543504\pi$
$410$	−51.1708	−2.52715
$411$	2.45913	0.121300
$412$	−34.2729	−1.68851
$413$	−5.42442	−0.266918
$414$	−5.93881	−0.291877
$415$	21.3575	1.04840
$416$	0	0
$417$	−33.3587	−1.63358
$418$	76.6553	3.74934
$419$	7.11440	0.347561	0.173781	−	0.984784i	$-0.444402\pi$
$419$	7.11440	0.347561	0.173781	+	0.984784i	$0.444402\pi$
$420$	−25.6700	−1.25257
$421$	1.96792	0.0959107	0.0479554	−	0.998849i	$-0.484729\pi$
$421$	1.96792	0.0959107	0.0479554	+	0.998849i	$0.484729\pi$
$422$	57.4195	2.79514
$423$	2.82115	0.137169
$424$	−1.47343	−0.0715559
$425$	−1.08609	−0.0526832
$426$	45.1641	2.18821
$427$	−9.78363	−0.473463
$428$	47.6387	2.30270
$429$	0	0
$430$	−30.2881	−1.46062
$431$	1.92926	0.0929293	0.0464647	−	0.998920i	$-0.485205\pi$
$431$	1.92926	0.0929293	0.0464647	+	0.998920i	$0.485205\pi$
$432$	0.424485	0.0204231
$433$	−16.8576	−0.810124	−0.405062	−	0.914289i	$-0.632750\pi$
$433$	−16.8576	−0.810124	−0.405062	+	0.914289i	$0.632750\pi$
$434$	−19.9134	−0.955875
$435$	68.4552	3.28217
$436$	−2.07090	−0.0991780
$437$	−6.03266	−0.288581
$438$	−49.7840	−2.37877
$439$	17.6365	0.841746	0.420873	−	0.907120i	$-0.361724\pi$
$439$	17.6365	0.841746	0.420873	+	0.907120i	$0.361724\pi$
$440$	−45.3470	−2.16183
$441$	−15.2231	−0.724911
$442$	0	0
$443$	21.6353	1.02792	0.513961	−	0.857813i	$-0.328178\pi$
$443$	21.6353	1.02792	0.513961	+	0.857813i	$0.328178\pi$
$444$	18.9629	0.899941
$445$	47.4858	2.25104
$446$	−18.5472	−0.878235
$447$	−10.4944	−0.496367
$448$	14.2636	0.673893
$449$	14.4722	0.682984	0.341492	−	0.939885i	$-0.389068\pi$
$449$	14.4722	0.682984	0.341492	+	0.939885i	$0.389068\pi$
$450$	−29.8221	−1.40583
$451$	40.0588	1.88630
$452$	15.5428	0.731070
$453$	26.1646	1.22932
$454$	40.8791	1.91855
$455$	0	0
$456$	36.5153	1.70999
$457$	15.1384	0.708143	0.354071	−	0.935218i	$-0.384797\pi$
$457$	15.1384	0.708143	0.354071	+	0.935218i	$0.384797\pi$
$458$	7.07787	0.330727
$459$	0.193486	0.00903115
$460$	9.90011	0.461595
$461$	11.9706	0.557524	0.278762	−	0.960360i	$-0.410076\pi$
$461$	11.9706	0.557524	0.278762	+	0.960360i	$0.410076\pi$
$462$	32.9473	1.53285
$463$	−17.4422	−0.810608	−0.405304	−	0.914182i	$-0.632834\pi$
$463$	−17.4422	−0.810608	−0.405304	+	0.914182i	$0.632834\pi$
$464$	−4.32720	−0.200885
$465$	−60.3712	−2.79965
$466$	−36.2709	−1.68022
$467$	1.56771	0.0725450	0.0362725	−	0.999342i	$-0.488452\pi$
$467$	1.56771	0.0725450	0.0362725	+	0.999342i	$0.488452\pi$
$468$	0	0
$469$	7.94913	0.367057
$470$	−7.71054	−0.355660
$471$	16.4148	0.756353
$472$	−12.6629	−0.582858
$473$	23.7109	1.09023
$474$	−22.7826	−1.04644
$475$	−30.2933	−1.38995
$476$	0.739628	0.0339008
$477$	1.51388	0.0693156
$478$	−50.1485	−2.29374
$479$	12.2507	0.559749	0.279875	−	0.960037i	$-0.409707\pi$
$479$	12.2507	0.559749	0.279875	+	0.960037i	$0.409707\pi$
$480$	46.3888	2.11735
$481$	0	0
$482$	65.9542	3.00413
$483$	−2.59290	−0.117981
$484$	64.0797	2.91271
$485$	49.9082	2.26621
$486$	47.5596	2.15735
$487$	−27.1802	−1.23165	−0.615827	−	0.787881i	$-0.711178\pi$
$487$	−27.1802	−1.23165	−0.615827	+	0.787881i	$0.711178\pi$
$488$	−22.8392	−1.03388
$489$	−34.3648	−1.55403
$490$	41.6066	1.87959
$491$	−18.1400	−0.818648	−0.409324	−	0.912389i	$-0.634235\pi$
$491$	−18.1400	−0.818648	−0.409324	+	0.912389i	$0.634235\pi$
$492$	52.9366	2.38657
$493$	−1.97239	−0.0888322
$494$	0	0
$495$	46.5919	2.09415
$496$	3.81619	0.171352
$497$	9.19785	0.412580
$498$	−36.2245	−1.62326
$499$	41.6502	1.86452	0.932260	−	0.361789i	$-0.117834\pi$
$499$	41.6502	1.86452	0.932260	+	0.361789i	$0.117834\pi$
$500$	0.213373	0.00954233
$501$	−1.16757	−0.0521633
$502$	37.7321	1.68407
$503$	21.7307	0.968925	0.484463	−	0.874812i	$-0.339015\pi$
$503$	21.7307	0.968925	0.484463	+	0.874812i	$0.339015\pi$
$504$	7.32081	0.326095
$505$	14.9158	0.663745
$506$	−12.7067	−0.564883
$507$	0	0
$508$	−11.4537	−0.508178
$509$	−10.7617	−0.477006	−0.238503	−	0.971142i	$-0.576657\pi$
$509$	−10.7617	−0.477006	−0.238503	+	0.971142i	$0.576657\pi$
$510$	3.67634	0.162791
$511$	−10.1387	−0.448510
$512$	−5.35484	−0.236653
$513$	5.39672	0.238271
$514$	45.4093	2.00292
$515$	−34.6934	−1.52877
$516$	31.3333	1.37937
$517$	6.03615	0.265470
$518$	6.33165	0.278197
$519$	−16.4133	−0.720465
$520$	0	0
$521$	−3.82763	−0.167691	−0.0838457	−	0.996479i	$-0.526720\pi$
$521$	−3.82763	−0.167691	−0.0838457	+	0.996479i	$0.526720\pi$
$522$	−54.1582	−2.37044
$523$	−41.9169	−1.83290	−0.916450	−	0.400150i	$-0.868958\pi$
$523$	−41.9169	−1.83290	−0.916450	+	0.400150i	$0.868958\pi$
$524$	31.1742	1.36185
$525$	−13.0204	−0.568256
$526$	20.3996	0.889466
$527$	1.73947	0.0757726
$528$	−6.31399	−0.274781
$529$	1.00000	0.0434783
$530$	−4.13760	−0.179726
$531$	13.0105	0.564609
$532$	20.6297	0.894412
$533$	0	0
$534$	−80.5407	−3.48534
$535$	48.2231	2.08487
$536$	18.5567	0.801527
$537$	57.2502	2.47053
$538$	43.3945	1.87087
$539$	−32.5715	−1.40295
$540$	−8.85647	−0.381122
$541$	−21.6940	−0.932699	−0.466349	−	0.884601i	$-0.654431\pi$
$541$	−21.6940	−0.932699	−0.466349	+	0.884601i	$0.654431\pi$
$542$	35.5208	1.52575
$543$	34.6809	1.48830
$544$	−1.33660	−0.0573062
$545$	−2.09630	−0.0897956
$546$	0	0
$547$	−39.3753	−1.68356	−0.841782	−	0.539817i	$-0.818493\pi$
$547$	−39.3753	−1.68356	−0.841782	+	0.539817i	$0.818493\pi$
$548$	3.24325	0.138545
$549$	23.4662	1.00151
$550$	−63.8075	−2.72076
$551$	−55.0141	−2.34368
$552$	−6.05294	−0.257630
$553$	−4.63977	−0.197303
$554$	−51.2708	−2.17829
$555$	19.1956	0.814806
$556$	−43.9954	−1.86582
$557$	−34.6203	−1.46691	−0.733455	−	0.679738i	$-0.762093\pi$
$557$	−34.6203	−1.46691	−0.733455	+	0.679738i	$0.762093\pi$
$558$	47.7626	2.02195
$559$	0	0
$560$	1.64256	0.0694109
$561$	−2.87800	−0.121509
$562$	68.6289	2.89493
$563$	−4.66039	−0.196412	−0.0982059	−	0.995166i	$-0.531310\pi$
$563$	−4.66039	−0.196412	−0.0982059	+	0.995166i	$0.531310\pi$
$564$	7.97660	0.335876
$565$	15.7334	0.661911
$566$	−9.76912	−0.410627
$567$	10.9233	0.458736
$568$	21.4717	0.900933
$569$	41.2171	1.72791	0.863956	−	0.503567i	$-0.167979\pi$
$569$	41.2171	1.72791	0.863956	+	0.503567i	$0.167979\pi$
$570$	102.540	4.29495
$571$	−32.8618	−1.37522	−0.687612	−	0.726078i	$-0.741341\pi$
$571$	−32.8618	−1.37522	−0.687612	+	0.726078i	$0.741341\pi$
$572$	0	0
$573$	−51.5830	−2.15491
$574$	17.6753	0.737753
$575$	5.02155	0.209413
$576$	−34.2115	−1.42548
$577$	−12.9817	−0.540434	−0.270217	−	0.962800i	$-0.587095\pi$
$577$	−12.9817	−0.540434	−0.270217	+	0.962800i	$0.587095\pi$
$578$	38.3882	1.59674
$579$	−12.8682	−0.534785
$580$	90.2828	3.74879
$581$	−7.37727	−0.306061
$582$	−84.6493	−3.50883
$583$	3.23910	0.134150
$584$	−23.6681	−0.979393
$585$	0	0
$586$	−59.1583	−2.44381
$587$	36.3803	1.50158	0.750788	−	0.660543i	$-0.229674\pi$
$587$	36.3803	1.50158	0.750788	+	0.660543i	$0.229674\pi$
$588$	−43.0423	−1.77504
$589$	48.5174	1.99912
$590$	−35.5593	−1.46396
$591$	−45.4777	−1.87070
$592$	−1.21339	−0.0498701
$593$	17.3748	0.713499	0.356750	−	0.934200i	$-0.383885\pi$
$593$	17.3748	0.713499	0.356750	+	0.934200i	$0.383885\pi$
$594$	11.3672	0.466403
$595$	0.748701	0.0306937
$596$	−13.8406	−0.566934
$597$	−35.5969	−1.45688
$598$	0	0
$599$	1.05120	0.0429507	0.0214754	−	0.999769i	$-0.493164\pi$
$599$	1.05120	0.0429507	0.0214754	+	0.999769i	$0.493164\pi$
$600$	−30.3952	−1.24088
$601$	11.2683	0.459643	0.229821	−	0.973233i	$-0.426186\pi$
$601$	11.2683	0.459643	0.229821	+	0.973233i	$0.426186\pi$
$602$	10.4621	0.426402
$603$	−19.0661	−0.776432
$604$	34.5075	1.40409
$605$	64.8658	2.63717
$606$	−25.2987	−1.02769
$607$	25.1906	1.02245	0.511227	−	0.859445i	$-0.329191\pi$
$607$	25.1906	1.02245	0.511227	+	0.859445i	$0.329191\pi$
$608$	−37.2805	−1.51192
$609$	−23.6456	−0.958169
$610$	−64.1358	−2.59678
$611$	0	0
$612$	−1.77401	−0.0717100
$613$	−9.21738	−0.372287	−0.186143	−	0.982523i	$-0.559599\pi$
$613$	−9.21738	−0.372287	−0.186143	+	0.982523i	$0.559599\pi$
$614$	−34.3347	−1.38564
$615$	53.5860	2.16080
$616$	15.6637	0.631107
$617$	21.4518	0.863618	0.431809	−	0.901965i	$-0.357876\pi$
$617$	21.4518	0.863618	0.431809	+	0.901965i	$0.357876\pi$
$618$	58.8434	2.36703
$619$	−19.8781	−0.798969	−0.399485	−	0.916740i	$-0.630811\pi$
$619$	−19.8781	−0.798969	−0.399485	+	0.916740i	$0.630811\pi$
$620$	−79.6212	−3.19766
$621$	−0.894583	−0.0358984
$622$	17.3296	0.694856
$623$	−16.4024	−0.657150
$624$	0	0
$625$	−24.8918	−0.995671
$626$	−37.6315	−1.50406
$627$	−80.2733	−3.20581
$628$	21.6488	0.863881
$629$	−0.553080	−0.0220528
$630$	20.5579	0.819047
$631$	2.22972	0.0887638	0.0443819	−	0.999015i	$-0.485868\pi$
$631$	2.22972	0.0887638	0.0443819	+	0.999015i	$0.485868\pi$
$632$	−10.8312	−0.430842
$633$	−60.1296	−2.38994
$634$	−47.7054	−1.89462
$635$	−11.5942	−0.460104
$636$	4.28038	0.169728
$637$	0	0
$638$	−115.877	−4.58763
$639$	−22.0612	−0.872726
$640$	54.3776	2.14946
$641$	1.43174	0.0565503	0.0282751	−	0.999600i	$-0.490999\pi$
$641$	1.43174	0.0565503	0.0282751	+	0.999600i	$0.490999\pi$
$642$	−81.7912	−3.22804
$643$	26.2134	1.03375	0.516877	−	0.856060i	$-0.327094\pi$
$643$	26.2134	1.03375	0.516877	+	0.856060i	$0.327094\pi$
$644$	−3.41967	−0.134754
$645$	31.7177	1.24888
$646$	−2.95449	−0.116243
$647$	−20.6640	−0.812386	−0.406193	−	0.913787i	$-0.633144\pi$
$647$	−20.6640	−0.812386	−0.406193	+	0.913787i	$0.633144\pi$
$648$	25.4997	1.00172
$649$	27.8374	1.09272
$650$	0	0
$651$	20.8533	0.817305
$652$	−45.3224	−1.77496
$653$	10.8658	0.425212	0.212606	−	0.977138i	$-0.431805\pi$
$653$	10.8658	0.425212	0.212606	+	0.977138i	$0.431805\pi$
$654$	3.55554	0.139032
$655$	31.5566	1.23302
$656$	−3.38728	−0.132251
$657$	24.3178	0.948729
$658$	2.66336	0.103828
$659$	28.6913	1.11765	0.558827	−	0.829284i	$-0.311251\pi$
$659$	28.6913	1.11765	0.558827	+	0.829284i	$0.311251\pi$
$660$	131.735	5.12779
$661$	−22.5301	−0.876318	−0.438159	−	0.898898i	$-0.644369\pi$
$661$	−22.5301	−0.876318	−0.438159	+	0.898898i	$0.644369\pi$
$662$	51.3969	1.99760
$663$	0	0
$664$	−17.2217	−0.668332
$665$	20.8828	0.809800
$666$	−15.1865	−0.588467
$667$	9.11937	0.353104
$668$	−1.53987	−0.0595792
$669$	19.4226	0.750920
$670$	52.1099	2.01318
$671$	50.2084	1.93827
$672$	−16.0235	−0.618121
$673$	31.5184	1.21495	0.607473	−	0.794341i	$-0.292183\pi$
$673$	31.5184	1.21495	0.607473	+	0.794341i	$0.292183\pi$
$674$	82.6651	3.18414
$675$	−4.49220	−0.172905
$676$	0	0
$677$	26.4770	1.01759	0.508797	−	0.860887i	$-0.330090\pi$
$677$	26.4770	1.01759	0.508797	+	0.860887i	$0.330090\pi$
$678$	−26.6855	−1.02485
$679$	−17.2392	−0.661579
$680$	1.74779	0.0670247
$681$	−42.8085	−1.64043
$682$	102.193	3.91318
$683$	−17.3961	−0.665643	−0.332821	−	0.942990i	$-0.608001\pi$
$683$	−17.3961	−0.665643	−0.332821	+	0.942990i	$0.608001\pi$
$684$	−49.4807	−1.89194
$685$	3.28303	0.125438
$686$	−31.7039	−1.21046
$687$	−7.41193	−0.282783
$688$	−2.00494	−0.0764377
$689$	0	0
$690$	−16.9976	−0.647086
$691$	−51.1248	−1.94488	−0.972440	−	0.233153i	$-0.925096\pi$
$691$	−51.1248	−1.94488	−0.972440	+	0.233153i	$0.925096\pi$
$692$	−21.6469	−0.822890
$693$	−16.0937	−0.611348
$694$	−0.430651	−0.0163473
$695$	−44.5351	−1.68931
$696$	−55.1990	−2.09231
$697$	−1.54397	−0.0584820
$698$	26.2722	0.994417
$699$	37.9828	1.43664
$700$	−17.1721	−0.649043
$701$	2.98710	0.112821	0.0564105	−	0.998408i	$-0.482034\pi$
$701$	2.98710	0.112821	0.0564105	+	0.998408i	$0.482034\pi$
$702$	0	0
$703$	−15.4265	−0.581823
$704$	−73.1991	−2.75880
$705$	8.07445	0.304101
$706$	23.0325	0.866839
$707$	−5.15218	−0.193768
$708$	36.7864	1.38252
$709$	−22.8486	−0.858096	−0.429048	−	0.903282i	$-0.641151\pi$
$709$	−22.8486	−0.858096	−0.429048	+	0.903282i	$0.641151\pi$
$710$	60.2958	2.26286
$711$	11.1285	0.417353
$712$	−38.2904	−1.43499
$713$	−8.04245	−0.301192
$714$	−1.26987	−0.0475238
$715$	0	0
$716$	75.5050	2.82176
$717$	52.5154	1.96122
$718$	−22.0755	−0.823852
$719$	13.0998	0.488540	0.244270	−	0.969707i	$-0.421452\pi$
$719$	13.0998	0.488540	0.244270	+	0.969707i	$0.421452\pi$
$720$	−3.93970	−0.146824
$721$	11.9837	0.446296
$722$	−39.3840	−1.46572
$723$	−69.0670	−2.56863
$724$	45.7393	1.69989
$725$	45.7934	1.70072
$726$	−110.019	−4.08318
$727$	6.86149	0.254479	0.127239	−	0.991872i	$-0.459388\pi$
$727$	6.86149	0.254479	0.127239	+	0.991872i	$0.459388\pi$
$728$	0	0
$729$	−19.8359	−0.734664
$730$	−66.4635	−2.45993
$731$	−0.913879	−0.0338010
$732$	66.3489	2.45233
$733$	25.5999	0.945553	0.472776	−	0.881182i	$-0.343252\pi$
$733$	25.5999	0.945553	0.472776	+	0.881182i	$0.343252\pi$
$734$	−49.0268	−1.80961
$735$	−43.5703	−1.60712
$736$	6.17977	0.227789
$737$	−40.7940	−1.50267
$738$	−42.3945	−1.56056
$739$	−10.4709	−0.385177	−0.192589	−	0.981280i	$-0.561688\pi$
$739$	−10.4709	−0.385177	−0.192589	+	0.981280i	$0.561688\pi$
$740$	25.3162	0.930644
$741$	0	0
$742$	1.42920	0.0524676
$743$	−3.87862	−0.142293	−0.0711463	−	0.997466i	$-0.522666\pi$
$743$	−3.87862	−0.142293	−0.0711463	+	0.997466i	$0.522666\pi$
$744$	48.6805	1.78471
$745$	−14.0104	−0.513301
$746$	10.4396	0.382220
$747$	17.6945	0.647407
$748$	−3.79568	−0.138784
$749$	−16.6571	−0.608638
$750$	−0.366341	−0.0133769
$751$	27.3306	0.997309	0.498654	−	0.866801i	$-0.333828\pi$
$751$	27.3306	0.997309	0.498654	+	0.866801i	$0.333828\pi$
$752$	−0.510403	−0.0186125
$753$	−39.5130	−1.43993
$754$	0	0
$755$	34.9308	1.27126
$756$	3.05918	0.111261
$757$	−1.67111	−0.0607375	−0.0303687	−	0.999539i	$-0.509668\pi$
$757$	−1.67111	−0.0607375	−0.0303687	+	0.999539i	$0.509668\pi$
$758$	−38.2456	−1.38914
$759$	13.3064	0.482993
$760$	48.7494	1.76833
$761$	−31.3220	−1.13542	−0.567711	−	0.823228i	$-0.692171\pi$
$761$	−31.3220	−1.13542	−0.567711	+	0.823228i	$0.692171\pi$
$762$	19.6650	0.712388
$763$	0.724099	0.0262141
$764$	−68.0307	−2.46127
$765$	−1.79577	−0.0649262
$766$	47.9181	1.73135
$767$	0	0
$768$	−30.3683	−1.09582
$769$	−0.211623	−0.00763130	−0.00381565	−	0.999993i	$-0.501215\pi$
$769$	−0.211623	−0.00763130	−0.00381565	+	0.999993i	$0.501215\pi$
$770$	43.9859	1.58514
$771$	−47.5525	−1.71256
$772$	−16.9714	−0.610813
$773$	15.2808	0.549613	0.274807	−	0.961500i	$-0.411386\pi$
$773$	15.2808	0.549613	0.274807	+	0.961500i	$0.411386\pi$
$774$	−25.0934	−0.901963
$775$	−40.3856	−1.45069
$776$	−40.2436	−1.44466
$777$	−6.63048	−0.237867
$778$	36.9542	1.32487
$779$	−43.0644	−1.54294
$780$	0	0
$781$	−47.2022	−1.68903
$782$	0.489750	0.0175134
$783$	−8.15804	−0.291544
$784$	2.75417	0.0983633
$785$	21.9144	0.782157
$786$	−53.5231	−1.90911
$787$	41.3904	1.47541	0.737705	−	0.675123i	$-0.235910\pi$
$787$	41.3904	1.47541	0.737705	+	0.675123i	$0.235910\pi$
$788$	−59.9787	−2.13665
$789$	−21.3624	−0.760522
$790$	−30.4156	−1.08214
$791$	−5.43461	−0.193232
$792$	−37.5695	−1.33497
$793$	0	0
$794$	20.3318	0.721548
$795$	4.33288	0.153672
$796$	−46.9473	−1.66400
$797$	1.67212	0.0592294	0.0296147	−	0.999561i	$-0.490572\pi$
$797$	1.67212	0.0592294	0.0296147	+	0.999561i	$0.490572\pi$
$798$	−35.4193	−1.25383
$799$	−0.232649	−0.00823052
$800$	31.0320	1.09715
$801$	39.3415	1.39006
$802$	52.3047	1.84694
$803$	52.0306	1.83612
$804$	−53.9081	−1.90119
$805$	−3.46162	−0.122006
$806$	0	0
$807$	−45.4426	−1.59966
$808$	−12.0274	−0.423123
$809$	36.6250	1.28767	0.643833	−	0.765166i	$-0.277343\pi$
$809$	36.6250	1.28767	0.643833	+	0.765166i	$0.277343\pi$
$810$	71.6069	2.51601
$811$	32.4359	1.13898	0.569489	−	0.821999i	$-0.307141\pi$
$811$	32.4359	1.13898	0.569489	+	0.821999i	$0.307141\pi$
$812$	−31.1853	−1.09439
$813$	−37.1972	−1.30456
$814$	−32.4932	−1.13889
$815$	−45.8783	−1.60705
$816$	0.243357	0.00851921
$817$	−25.4899	−0.891780
$818$	12.4784	0.436296
$819$	0	0
$820$	70.6724	2.46799
$821$	−49.2576	−1.71910	−0.859551	−	0.511049i	$-0.829257\pi$
$821$	−49.2576	−1.71910	−0.859551	+	0.511049i	$0.829257\pi$
$822$	−5.56835	−0.194219
$823$	12.2443	0.426810	0.213405	−	0.976964i	$-0.431545\pi$
$823$	12.2443	0.426810	0.213405	+	0.976964i	$0.431545\pi$
$824$	27.9751	0.974559
$825$	66.8190	2.32634
$826$	12.2828	0.427374
$827$	24.0204	0.835273	0.417636	−	0.908614i	$-0.362859\pi$
$827$	24.0204	0.835273	0.417636	+	0.908614i	$0.362859\pi$
$828$	8.20213	0.285044
$829$	−1.14959	−0.0399269	−0.0199634	−	0.999801i	$-0.506355\pi$
$829$	−1.14959	−0.0399269	−0.0199634	+	0.999801i	$0.506355\pi$
$830$	−48.3611	−1.67864
$831$	53.6906	1.86251
$832$	0	0
$833$	1.25539	0.0434966
$834$	75.5360	2.61560
$835$	−1.55875	−0.0539429
$836$	−105.869	−3.66156
$837$	7.19465	0.248683
$838$	−16.1096	−0.556495
$839$	36.9364	1.27518	0.637592	−	0.770374i	$-0.279930\pi$
$839$	36.9364	1.27518	0.637592	+	0.770374i	$0.279930\pi$
$840$	20.9530	0.722947
$841$	54.1630	1.86769
$842$	−4.45609	−0.153567
$843$	−71.8680	−2.47526
$844$	−79.3025	−2.72970
$845$	0	0
$846$	−6.38809	−0.219627
$847$	−22.4058	−0.769872
$848$	−0.273891	−0.00940545
$849$	10.2302	0.351100
$850$	2.45930	0.0843534
$851$	2.55717	0.0876586
$852$	−62.3764	−2.13698
$853$	−2.42115	−0.0828985	−0.0414493	−	0.999141i	$-0.513197\pi$
$853$	−2.42115	−0.0828985	−0.0414493	+	0.999141i	$0.513197\pi$
$854$	22.1536	0.758082
$855$	−50.0877	−1.71296
$856$	−38.8849	−1.32906
$857$	−30.2965	−1.03491	−0.517455	−	0.855710i	$-0.673121\pi$
$857$	−30.2965	−1.03491	−0.517455	+	0.855710i	$0.673121\pi$
$858$	0	0
$859$	−3.26790	−0.111499	−0.0557496	−	0.998445i	$-0.517755\pi$
$859$	−3.26790	−0.111499	−0.0557496	+	0.998445i	$0.517755\pi$
$860$	41.8311	1.42643
$861$	−18.5095	−0.630804
$862$	−4.36854	−0.148793
$863$	−38.8796	−1.32348	−0.661738	−	0.749735i	$-0.730181\pi$
$863$	−38.8796	−1.32348	−0.661738	+	0.749735i	$0.730181\pi$
$864$	−5.52832	−0.188077
$865$	−21.9124	−0.745044
$866$	38.1716	1.29713
$867$	−40.2000	−1.36526
$868$	27.5026	0.933498
$869$	23.8107	0.807723
$870$	−155.007	−5.25523
$871$	0	0
$872$	1.69036	0.0572428
$873$	41.3484	1.39943
$874$	13.6601	0.462060
$875$	−0.0746069	−0.00252217
$876$	68.7570	2.32308
$877$	−0.673607	−0.0227461	−0.0113731	−	0.999935i	$-0.503620\pi$
$877$	−0.673607	−0.0227461	−0.0113731	+	0.999935i	$0.503620\pi$
$878$	−39.9354	−1.34776
$879$	61.9505	2.08954
$880$	−8.42942	−0.284156
$881$	8.16669	0.275143	0.137571	−	0.990492i	$-0.456070\pi$
$881$	8.16669	0.275143	0.137571	+	0.990492i	$0.456070\pi$
$882$	34.4706	1.16069
$883$	−15.7235	−0.529137	−0.264568	−	0.964367i	$-0.585229\pi$
$883$	−15.7235	−0.529137	−0.264568	+	0.964367i	$0.585229\pi$
$884$	0	0
$885$	37.2377	1.25173
$886$	−48.9900	−1.64585
$887$	−27.0798	−0.909251	−0.454625	−	0.890683i	$-0.650227\pi$
$887$	−27.0798	−0.909251	−0.454625	+	0.890683i	$0.650227\pi$
$888$	−15.4784	−0.519421
$889$	4.00486	0.134319
$890$	−107.525	−3.60425
$891$	−56.0571	−1.87798
$892$	25.6156	0.857675
$893$	−6.48904	−0.217148
$894$	23.7630	0.794755
$895$	76.4312	2.55481
$896$	−18.7830	−0.627496
$897$	0	0
$898$	−32.7702	−1.09355
$899$	−73.3421	−2.44610
$900$	41.1874	1.37291
$901$	−0.124843	−0.00415913
$902$	−90.7076	−3.02023
$903$	−10.9558	−0.364587
$904$	−12.6867	−0.421953
$905$	46.3004	1.53908
$906$	−59.2461	−1.96832
$907$	9.71580	0.322608	0.161304	−	0.986905i	$-0.448430\pi$
$907$	9.71580	0.322608	0.161304	+	0.986905i	$0.448430\pi$
$908$	−56.4585	−1.87364
$909$	12.3576	0.409875
$910$	0	0
$911$	−3.68558	−0.122109	−0.0610543	−	0.998134i	$-0.519446\pi$
$911$	−3.68558	−0.122109	−0.0610543	+	0.998134i	$0.519446\pi$
$912$	6.78773	0.224764
$913$	37.8592	1.25296
$914$	−34.2787	−1.13384
$915$	67.1628	2.22034
$916$	−9.77529	−0.322985
$917$	−10.9002	−0.359956
$918$	−0.438122	−0.0144602
$919$	−1.97858	−0.0652673	−0.0326337	−	0.999467i	$-0.510389\pi$
$919$	−1.97858	−0.0652673	−0.0326337	+	0.999467i	$0.510389\pi$
$920$	−8.08091	−0.266420
$921$	35.9552	1.18476
$922$	−27.1056	−0.892677
$923$	0	0
$924$	−45.5037	−1.49696
$925$	12.8410	0.422208
$926$	39.4954	1.29790
$927$	−28.7431	−0.944047
$928$	56.3556	1.84996
$929$	0.206658	0.00678023	0.00339012	−	0.999994i	$-0.498921\pi$
$929$	0.206658	0.00678023	0.00339012	+	0.999994i	$0.498921\pi$
$930$	136.702	4.48264
$931$	35.0153	1.14758
$932$	50.0939	1.64088
$933$	−18.1476	−0.594124
$934$	−3.54986	−0.116155
$935$	−3.84224	−0.125655
$936$	0	0
$937$	36.0425	1.17746	0.588728	−	0.808331i	$-0.299629\pi$
$937$	36.0425	1.17746	0.588728	+	0.808331i	$0.299629\pi$
$938$	−17.9997	−0.587711
$939$	39.4077	1.28602
$940$	10.6491	0.347334
$941$	15.5431	0.506690	0.253345	−	0.967376i	$-0.418469\pi$
$941$	15.5431	0.506690	0.253345	+	0.967376i	$0.418469\pi$
$942$	−37.1689	−1.21103
$943$	7.13855	0.232463
$944$	−2.35387	−0.0766120
$945$	3.09671	0.100736
$946$	−53.6900	−1.74561
$947$	2.87566	0.0934464	0.0467232	−	0.998908i	$-0.485122\pi$
$947$	2.87566	0.0934464	0.0467232	+	0.998908i	$0.485122\pi$
$948$	31.4652	1.02194
$949$	0	0
$950$	68.5949	2.22551
$951$	49.9569	1.61996
$952$	−0.603717	−0.0195666
$953$	30.3101	0.981841	0.490921	−	0.871204i	$-0.336661\pi$
$953$	30.3101	0.981841	0.490921	+	0.871204i	$0.336661\pi$
$954$	−3.42796	−0.110984
$955$	−68.8653	−2.22843
$956$	69.2604	2.24004
$957$	121.346	3.92257
$958$	−27.7400	−0.896239
$959$	−1.13402	−0.0366193
$960$	−97.9172	−3.16026
$961$	33.6811	1.08649
$962$	0	0
$963$	39.9523	1.28745
$964$	−91.0898	−2.93380
$965$	−17.1796	−0.553030
$966$	5.87126	0.188905
$967$	−19.2278	−0.618323	−0.309162	−	0.951010i	$-0.600048\pi$
$967$	−19.2278	−0.618323	−0.309162	+	0.951010i	$0.600048\pi$
$968$	−52.3047	−1.68114
$969$	3.09394	0.0993916
$970$	−113.010	−3.62853
$971$	26.9172	0.863815	0.431907	−	0.901918i	$-0.357841\pi$
$971$	26.9172	0.863815	0.431907	+	0.901918i	$0.357841\pi$
$972$	−65.6849	−2.10685
$973$	15.3832	0.493163
$974$	61.5458	1.97206
$975$	0	0
$976$	−4.24551	−0.135895
$977$	−33.5682	−1.07394	−0.536971	−	0.843601i	$-0.680431\pi$
$977$	−33.5682	−1.07394	−0.536971	+	0.843601i	$0.680431\pi$
$978$	77.8143	2.48823
$979$	84.1754	2.69026
$980$	−57.4631	−1.83559
$981$	−1.73676	−0.0554505
$982$	41.0755	1.31077
$983$	−7.98670	−0.254736	−0.127368	−	0.991856i	$-0.540653\pi$
$983$	−7.98670	−0.254736	−0.127368	+	0.991856i	$0.540653\pi$
$984$	−43.2092	−1.37746
$985$	−60.7145	−1.93452
$986$	4.46621	0.142233
$987$	−2.78906	−0.0887767
$988$	0	0
$989$	4.22532	0.134357
$990$	−105.501	−3.35303
$991$	−32.4610	−1.03116	−0.515578	−	0.856842i	$-0.672423\pi$
$991$	−32.4610	−1.03116	−0.515578	+	0.856842i	$0.672423\pi$
$992$	−49.7005	−1.57799
$993$	−53.8227	−1.70801
$994$	−20.8272	−0.660599
$995$	−47.5232	−1.50659
$996$	50.0299	1.58526
$997$	−57.7905	−1.83024	−0.915121	−	0.403178i	$-0.867905\pi$
$997$	−57.7905	−1.83024	−0.915121	+	0.403178i	$0.867905\pi$
$998$	−94.3110	−2.98536
$999$	−2.28760	−0.0723765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3887.2.a.p.1.2		10
13.12	even	2		299.2.a.g.1.9	✓	10
39.38	odd	2		2691.2.a.bc.1.2		10
52.51	odd	2		4784.2.a.bh.1.3		10
65.64	even	2		7475.2.a.w.1.2		10
299.298	odd	2		6877.2.a.o.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.a.g.1.9	✓	10	13.12	even	2
2691.2.a.bc.1.2		10	39.38	odd	2
3887.2.a.p.1.2		10	1.1	even	1	trivial
4784.2.a.bh.1.3		10	52.51	odd	2
6877.2.a.o.1.9		10	299.298	odd	2
7475.2.a.w.1.2		10	65.64	even	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:	\( N \)	\(=\)	\( 3887 = 13^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3887.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26436 q^{2} +2.37123 q^{3} +3.12732 q^{4} +3.16568 q^{5} -5.36932 q^{6} -1.09348 q^{7} -2.55266 q^{8} +2.62273 q^{9} +O(q^{10})\)	\(q-2.26436 q^{2} +2.37123 q^{3} +3.12732 q^{4} +3.16568 q^{5} -5.36932 q^{6} -1.09348 q^{7} -2.55266 q^{8} +2.62273 q^{9} -7.16824 q^{10} +5.61162 q^{11} +7.41560 q^{12} +2.47604 q^{14} +7.50657 q^{15} -0.474506 q^{16} -0.216286 q^{17} -5.93881 q^{18} -6.03266 q^{19} +9.90011 q^{20} -2.59290 q^{21} -12.7067 q^{22} +1.00000 q^{23} -6.05294 q^{24} +5.02155 q^{25} -0.894583 q^{27} -3.41967 q^{28} +9.11937 q^{29} -16.9976 q^{30} -8.04245 q^{31} +6.17977 q^{32} +13.3064 q^{33} +0.489750 q^{34} -3.46162 q^{35} +8.20213 q^{36} +2.55717 q^{37} +13.6601 q^{38} -8.08091 q^{40} +7.13855 q^{41} +5.87126 q^{42} +4.22532 q^{43} +17.5493 q^{44} +8.30275 q^{45} -2.26436 q^{46} +1.07565 q^{47} -1.12516 q^{48} -5.80429 q^{49} -11.3706 q^{50} -0.512864 q^{51} +0.577213 q^{53} +2.02566 q^{54} +17.7646 q^{55} +2.79129 q^{56} -14.3048 q^{57} -20.6495 q^{58} +4.96068 q^{59} +23.4754 q^{60} +8.94721 q^{61} +18.2110 q^{62} -2.86792 q^{63} -13.0442 q^{64} -30.1306 q^{66} -7.26955 q^{67} -0.676396 q^{68} +2.37123 q^{69} +7.83835 q^{70} -8.41151 q^{71} -6.69495 q^{72} +9.27194 q^{73} -5.79035 q^{74} +11.9073 q^{75} -18.8661 q^{76} -6.13621 q^{77} +4.24311 q^{79} -1.50214 q^{80} -9.98947 q^{81} -16.1642 q^{82} +6.74657 q^{83} -8.10883 q^{84} -0.684694 q^{85} -9.56764 q^{86} +21.6241 q^{87} -14.3246 q^{88} +15.0002 q^{89} -18.8004 q^{90} +3.12732 q^{92} -19.0705 q^{93} -2.43566 q^{94} -19.0975 q^{95} +14.6537 q^{96} +15.7654 q^{97} +13.1430 q^{98} +14.7178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9}+O(q^{10}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9} + 6 q^{10} - 3 q^{11} + 10 q^{12} - 15 q^{14} - 2 q^{15} + 25 q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + 19 q^{20} - 21 q^{21} + 13 q^{22} + 10 q^{23} + 35 q^{24} + 33 q^{25} + 6 q^{27} + 19 q^{28} + 17 q^{29} - 47 q^{30} - 5 q^{31} + 9 q^{32} + 23 q^{33} - 23 q^{34} + 3 q^{35} + 48 q^{36} - 16 q^{37} + 5 q^{38} + 13 q^{40} + 16 q^{41} - 65 q^{42} - 9 q^{43} - 18 q^{44} - 32 q^{45} - q^{46} + 11 q^{47} + 37 q^{48} + 40 q^{49} + 30 q^{50} - 31 q^{51} + 8 q^{53} + 73 q^{54} - 14 q^{55} - 54 q^{56} + 35 q^{57} - 17 q^{58} - 2 q^{59} + 37 q^{60} + 48 q^{61} - 19 q^{62} + 15 q^{63} + 64 q^{64} - 84 q^{66} + 6 q^{67} - 62 q^{68} + 3 q^{69} + 44 q^{70} - 24 q^{71} + 89 q^{72} + 33 q^{73} - 28 q^{74} - 22 q^{75} + 53 q^{76} + 15 q^{77} + 17 q^{79} + 94 q^{80} + 30 q^{81} + 35 q^{82} + 21 q^{83} - 92 q^{84} - 58 q^{85} + 7 q^{86} + 23 q^{87} + 9 q^{88} + 16 q^{89} + 67 q^{90} + 19 q^{92} - 15 q^{93} + 12 q^{94} - 27 q^{95} + 22 q^{96} + 40 q^{97} + 34 q^{98} + 17 q^{99}+O(q^{100}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9 + 6 * q^10 - 3 * q^11 + 10 * q^12 - 15 * q^14 - 2 * q^15 + 25 * q^16 - 3 * q^17 - q^18 - 2 * q^19 + 19 * q^20 - 21 * q^21 + 13 * q^22 + 10 * q^23 + 35 * q^24 + 33 * q^25 + 6 * q^27 + 19 * q^28 + 17 * q^29 - 47 * q^30 - 5 * q^31 + 9 * q^32 + 23 * q^33 - 23 * q^34 + 3 * q^35 + 48 * q^36 - 16 * q^37 + 5 * q^38 + 13 * q^40 + 16 * q^41 - 65 * q^42 - 9 * q^43 - 18 * q^44 - 32 * q^45 - q^46 + 11 * q^47 + 37 * q^48 + 40 * q^49 + 30 * q^50 - 31 * q^51 + 8 * q^53 + 73 * q^54 - 14 * q^55 - 54 * q^56 + 35 * q^57 - 17 * q^58 - 2 * q^59 + 37 * q^60 + 48 * q^61 - 19 * q^62 + 15 * q^63 + 64 * q^64 - 84 * q^66 + 6 * q^67 - 62 * q^68 + 3 * q^69 + 44 * q^70 - 24 * q^71 + 89 * q^72 + 33 * q^73 - 28 * q^74 - 22 * q^75 + 53 * q^76 + 15 * q^77 + 17 * q^79 + 94 * q^80 + 30 * q^81 + 35 * q^82 + 21 * q^83 - 92 * q^84 - 58 * q^85 + 7 * q^86 + 23 * q^87 + 9 * q^88 + 16 * q^89 + 67 * q^90 + 19 * q^92 - 15 * q^93 + 12 * q^94 - 27 * q^95 + 22 * q^96 + 40 * q^97 + 34 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more