LMFDB - Embedded newform 4018.2.a.bh.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.321.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 1 $ x^3 - x^2 - 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.69963$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.588364 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.588364 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +0.588364 q^{10} -3.69963 q^{11} +1.00000 q^{12} -4.17673 q^{13} +0.588364 q^{15} +1.00000 q^{16} +3.81089 q^{17} -2.00000 q^{18} -6.98762 q^{19} +0.588364 q^{20} -3.69963 q^{22} +3.09888 q^{23} +1.00000 q^{24} -4.65383 q^{25} -4.17673 q^{26} -5.00000 q^{27} +1.98762 q^{29} +0.588364 q^{30} -0.399256 q^{31} +1.00000 q^{32} -3.69963 q^{33} +3.81089 q^{34} -2.00000 q^{36} -6.11126 q^{37} -6.98762 q^{38} -4.17673 q^{39} +0.588364 q^{40} -1.00000 q^{41} -8.62178 q^{43} -3.69963 q^{44} -1.17673 q^{45} +3.09888 q^{46} +9.49814 q^{47} +1.00000 q^{48} -4.65383 q^{50} +3.81089 q^{51} -4.17673 q^{52} +1.06546 q^{53} -5.00000 q^{54} -2.17673 q^{55} -6.98762 q^{57} +1.98762 q^{58} +5.68725 q^{59} +0.588364 q^{60} -13.6094 q^{61} -0.399256 q^{62} +1.00000 q^{64} -2.45744 q^{65} -3.69963 q^{66} -3.71201 q^{67} +3.81089 q^{68} +3.09888 q^{69} -5.87636 q^{71} -2.00000 q^{72} +4.36584 q^{73} -6.11126 q^{74} -4.65383 q^{75} -6.98762 q^{76} -4.17673 q^{78} -13.3411 q^{79} +0.588364 q^{80} +1.00000 q^{81} -1.00000 q^{82} +6.68725 q^{83} +2.24219 q^{85} -8.62178 q^{86} +1.98762 q^{87} -3.69963 q^{88} +13.1643 q^{89} -1.17673 q^{90} +3.09888 q^{92} -0.399256 q^{93} +9.49814 q^{94} -4.11126 q^{95} +1.00000 q^{96} +0.666208 q^{97} +7.39926 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} + 3 q^{8} - 6 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 + 3 * q^8 - 6 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} + 3 q^{8} - 6 q^{9} - 4 q^{10} - 5 q^{11} + 3 q^{12} - q^{13} - 4 q^{15} + 3 q^{16} + 5 q^{17} - 6 q^{18} - 3 q^{19} - 4 q^{20} - 5 q^{22} - 9 q^{23} + 3 q^{24} + 3 q^{25} - q^{26} - 15 q^{27} - 12 q^{29} - 4 q^{30} + 11 q^{31} + 3 q^{32} - 5 q^{33} + 5 q^{34} - 6 q^{36} - 18 q^{37} - 3 q^{38} - q^{39} - 4 q^{40} - 3 q^{41} - 13 q^{43} - 5 q^{44} + 8 q^{45} - 9 q^{46} - 2 q^{47} + 3 q^{48} + 3 q^{50} + 5 q^{51} - q^{52} - 8 q^{53} - 15 q^{54} + 5 q^{55} - 3 q^{57} - 12 q^{58} - 7 q^{59} - 4 q^{60} - 10 q^{61} + 11 q^{62} + 3 q^{64} - 24 q^{65} - 5 q^{66} - 23 q^{67} + 5 q^{68} - 9 q^{69} - 6 q^{72} + 8 q^{73} - 18 q^{74} + 3 q^{75} - 3 q^{76} - q^{78} + q^{79} - 4 q^{80} + 3 q^{81} - 3 q^{82} - 4 q^{83} - 16 q^{85} - 13 q^{86} - 12 q^{87} - 5 q^{88} + 10 q^{89} + 8 q^{90} - 9 q^{92} + 11 q^{93} - 2 q^{94} - 12 q^{95} + 3 q^{96} + 3 q^{97} + 10 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 + 3 * q^8 - 6 * q^9 - 4 * q^10 - 5 * q^11 + 3 * q^12 - q^13 - 4 * q^15 + 3 * q^16 + 5 * q^17 - 6 * q^18 - 3 * q^19 - 4 * q^20 - 5 * q^22 - 9 * q^23 + 3 * q^24 + 3 * q^25 - q^26 - 15 * q^27 - 12 * q^29 - 4 * q^30 + 11 * q^31 + 3 * q^32 - 5 * q^33 + 5 * q^34 - 6 * q^36 - 18 * q^37 - 3 * q^38 - q^39 - 4 * q^40 - 3 * q^41 - 13 * q^43 - 5 * q^44 + 8 * q^45 - 9 * q^46 - 2 * q^47 + 3 * q^48 + 3 * q^50 + 5 * q^51 - q^52 - 8 * q^53 - 15 * q^54 + 5 * q^55 - 3 * q^57 - 12 * q^58 - 7 * q^59 - 4 * q^60 - 10 * q^61 + 11 * q^62 + 3 * q^64 - 24 * q^65 - 5 * q^66 - 23 * q^67 + 5 * q^68 - 9 * q^69 - 6 * q^72 + 8 * q^73 - 18 * q^74 + 3 * q^75 - 3 * q^76 - q^78 + q^79 - 4 * q^80 + 3 * q^81 - 3 * q^82 - 4 * q^83 - 16 * q^85 - 13 * q^86 - 12 * q^87 - 5 * q^88 + 10 * q^89 + 8 * q^90 - 9 * q^92 + 11 * q^93 - 2 * q^94 - 12 * q^95 + 3 * q^96 + 3 * q^97 + 10 * 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
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	0.588364	0.263124	0.131562	−	0.991308i	$-0.458001\pi$
$5$	0.588364	0.263124	0.131562	+	0.991308i	$0.458001\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	0.588364	0.186057
$11$	−3.69963	−1.11548	−0.557740	−	0.830016i	$-0.688331\pi$
$11$	−3.69963	−1.11548	−0.557740	+	0.830016i	$0.688331\pi$
$12$	1.00000	0.288675
$13$	−4.17673	−1.15842	−0.579208	−	0.815180i	$-0.696638\pi$
$13$	−4.17673	−1.15842	−0.579208	+	0.815180i	$0.696638\pi$
$14$	0	0
$15$	0.588364	0.151915
$16$	1.00000	0.250000
$17$	3.81089	0.924277	0.462139	−	0.886808i	$-0.347082\pi$
$17$	3.81089	0.924277	0.462139	+	0.886808i	$0.347082\pi$
$18$	−2.00000	−0.471405
$19$	−6.98762	−1.60307	−0.801535	−	0.597948i	$-0.795983\pi$
$19$	−6.98762	−1.60307	−0.801535	+	0.597948i	$0.795983\pi$
$20$	0.588364	0.131562
$21$	0	0
$22$	−3.69963	−0.788763
$23$	3.09888	0.646162	0.323081	−	0.946371i	$-0.395281\pi$
$23$	3.09888	0.646162	0.323081	+	0.946371i	$0.395281\pi$
$24$	1.00000	0.204124
$25$	−4.65383	−0.930766
$26$	−4.17673	−0.819124
$27$	−5.00000	−0.962250
$28$	0	0
$29$	1.98762	0.369092	0.184546	−	0.982824i	$-0.440919\pi$
$29$	1.98762	0.369092	0.184546	+	0.982824i	$0.440919\pi$
$30$	0.588364	0.107420
$31$	−0.399256	−0.0717085	−0.0358543	−	0.999357i	$-0.511415\pi$
$31$	−0.399256	−0.0717085	−0.0358543	+	0.999357i	$0.511415\pi$
$32$	1.00000	0.176777
$33$	−3.69963	−0.644023
$34$	3.81089	0.653563
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−6.11126	−1.00469	−0.502343	−	0.864669i	$-0.667528\pi$
$37$	−6.11126	−1.00469	−0.502343	+	0.864669i	$0.667528\pi$
$38$	−6.98762	−1.13354
$39$	−4.17673	−0.668812
$40$	0.588364	0.0930285
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−8.62178	−1.31481	−0.657405	−	0.753538i	$-0.728346\pi$
$43$	−8.62178	−1.31481	−0.657405	+	0.753538i	$0.728346\pi$
$44$	−3.69963	−0.557740
$45$	−1.17673	−0.175416
$46$	3.09888	0.456906
$47$	9.49814	1.38545	0.692723	−	0.721204i	$-0.256411\pi$
$47$	9.49814	1.38545	0.692723	+	0.721204i	$0.256411\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−4.65383	−0.658151
$51$	3.81089	0.533632
$52$	−4.17673	−0.579208
$53$	1.06546	0.146353	0.0731764	−	0.997319i	$-0.476686\pi$
$53$	1.06546	0.146353	0.0731764	+	0.997319i	$0.476686\pi$
$54$	−5.00000	−0.680414
$55$	−2.17673	−0.293510
$56$	0	0
$57$	−6.98762	−0.925533
$58$	1.98762	0.260987
$59$	5.68725	0.740417	0.370208	−	0.928949i	$-0.379286\pi$
$59$	5.68725	0.740417	0.370208	+	0.928949i	$0.379286\pi$
$60$	0.588364	0.0759575
$61$	−13.6094	−1.74251	−0.871253	−	0.490834i	$-0.836692\pi$
$61$	−13.6094	−1.74251	−0.871253	+	0.490834i	$0.836692\pi$
$62$	−0.399256	−0.0507056
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.45744	−0.304807
$66$	−3.69963	−0.455393
$67$	−3.71201	−0.453494	−0.226747	−	0.973954i	$-0.572809\pi$
$67$	−3.71201	−0.453494	−0.226747	+	0.973954i	$0.572809\pi$
$68$	3.81089	0.462139
$69$	3.09888	0.373062
$70$	0	0
$71$	−5.87636	−0.697395	−0.348698	−	0.937235i	$-0.613376\pi$
$71$	−5.87636	−0.697395	−0.348698	+	0.937235i	$0.613376\pi$
$72$	−2.00000	−0.235702
$73$	4.36584	0.510982	0.255491	−	0.966811i	$-0.417763\pi$
$73$	4.36584	0.510982	0.255491	+	0.966811i	$0.417763\pi$
$74$	−6.11126	−0.710420
$75$	−4.65383	−0.537378
$76$	−6.98762	−0.801535
$77$	0	0
$78$	−4.17673	−0.472921
$79$	−13.3411	−1.50099	−0.750494	−	0.660877i	$-0.770184\pi$
$79$	−13.3411	−1.50099	−0.750494	+	0.660877i	$0.770184\pi$
$80$	0.588364	0.0657811
$81$	1.00000	0.111111
$82$	−1.00000	−0.110432
$83$	6.68725	0.734021	0.367010	−	0.930217i	$-0.380381\pi$
$83$	6.68725	0.734021	0.367010	+	0.930217i	$0.380381\pi$
$84$	0	0
$85$	2.24219	0.243200
$86$	−8.62178	−0.929711
$87$	1.98762	0.213095
$88$	−3.69963	−0.394382
$89$	13.1643	1.39542	0.697709	−	0.716381i	$-0.254203\pi$
$89$	13.1643	1.39542	0.697709	+	0.716381i	$0.254203\pi$
$90$	−1.17673	−0.124038
$91$	0	0
$92$	3.09888	0.323081
$93$	−0.399256	−0.0414009
$94$	9.49814	0.979658
$95$	−4.11126	−0.421807
$96$	1.00000	0.102062
$97$	0.666208	0.0676431	0.0338216	−	0.999428i	$-0.489232\pi$
$97$	0.666208	0.0676431	0.0338216	+	0.999428i	$0.489232\pi$
$98$	0	0
$99$	7.39926	0.743653
$100$	−4.65383	−0.465383
$101$	−2.38688	−0.237503	−0.118752	−	0.992924i	$-0.537889\pi$
$101$	−2.38688	−0.237503	−0.118752	+	0.992924i	$0.537889\pi$
$102$	3.81089	0.377335
$103$	9.27561	0.913953	0.456977	−	0.889479i	$-0.348932\pi$
$103$	9.27561	0.913953	0.456977	+	0.889479i	$0.348932\pi$
$104$	−4.17673	−0.409562
$105$	0	0
$106$	1.06546	0.103487
$107$	−5.93454	−0.573713	−0.286857	−	0.957974i	$-0.592610\pi$
$107$	−5.93454	−0.573713	−0.286857	+	0.957974i	$0.592610\pi$
$108$	−5.00000	−0.481125
$109$	−20.4079	−1.95472	−0.977362	−	0.211574i	$-0.932141\pi$
$109$	−20.4079	−1.95472	−0.977362	+	0.211574i	$0.932141\pi$
$110$	−2.17673	−0.207543
$111$	−6.11126	−0.580056
$112$	0	0
$113$	−15.0197	−1.41293	−0.706466	−	0.707747i	$-0.749711\pi$
$113$	−15.0197	−1.41293	−0.706466	+	0.707747i	$0.749711\pi$
$114$	−6.98762	−0.654451
$115$	1.82327	0.170021
$116$	1.98762	0.184546
$117$	8.35346	0.772277
$118$	5.68725	0.523554
$119$	0	0
$120$	0.588364	0.0537100
$121$	2.68725	0.244295
$122$	−13.6094	−1.23214
$123$	−1.00000	−0.0901670
$124$	−0.399256	−0.0358543
$125$	−5.67996	−0.508031
$126$	0	0
$127$	2.14468	0.190310	0.0951550	−	0.995462i	$-0.469665\pi$
$127$	2.14468	0.190310	0.0951550	+	0.995462i	$0.469665\pi$
$128$	1.00000	0.0883883
$129$	−8.62178	−0.759106
$130$	−2.45744	−0.215531
$131$	2.03204	0.177540	0.0887702	−	0.996052i	$-0.471706\pi$
$131$	2.03204	0.177540	0.0887702	+	0.996052i	$0.471706\pi$
$132$	−3.69963	−0.322011
$133$	0	0
$134$	−3.71201	−0.320669
$135$	−2.94182	−0.253192
$136$	3.81089	0.326781
$137$	17.3287	1.48049	0.740245	−	0.672337i	$-0.234709\pi$
$137$	17.3287	1.48049	0.740245	+	0.672337i	$0.234709\pi$
$138$	3.09888	0.263795
$139$	−7.47710	−0.634199	−0.317100	−	0.948392i	$-0.602709\pi$
$139$	−7.47710	−0.634199	−0.317100	+	0.948392i	$0.602709\pi$
$140$	0	0
$141$	9.49814	0.799888
$142$	−5.87636	−0.493133
$143$	15.4523	1.29219
$144$	−2.00000	−0.166667
$145$	1.16944	0.0971171
$146$	4.36584	0.361319
$147$	0	0
$148$	−6.11126	−0.502343
$149$	−4.06546	−0.333056	−0.166528	−	0.986037i	$-0.553256\pi$
$149$	−4.06546	−0.333056	−0.166528	+	0.986037i	$0.553256\pi$
$150$	−4.65383	−0.379983
$151$	10.0334	0.816508	0.408254	−	0.912868i	$-0.366138\pi$
$151$	10.0334	0.816508	0.408254	+	0.912868i	$0.366138\pi$
$152$	−6.98762	−0.566771
$153$	−7.62178	−0.616185
$154$	0	0
$155$	−0.234908	−0.0188683
$156$	−4.17673	−0.334406
$157$	2.55632	0.204017	0.102008	−	0.994784i	$-0.467473\pi$
$157$	2.55632	0.204017	0.102008	+	0.994784i	$0.467473\pi$
$158$	−13.3411	−1.06136
$159$	1.06546	0.0844968
$160$	0.588364	0.0465143
$161$	0	0
$162$	1.00000	0.0785674
$163$	14.4116	1.12881	0.564403	−	0.825499i	$-0.309106\pi$
$163$	14.4116	1.12881	0.564403	+	0.825499i	$0.309106\pi$
$164$	−1.00000	−0.0780869
$165$	−2.17673	−0.169458
$166$	6.68725	0.519031
$167$	−2.03342	−0.157351	−0.0786754	−	0.996900i	$-0.525069\pi$
$167$	−2.03342	−0.157351	−0.0786754	+	0.996900i	$0.525069\pi$
$168$	0	0
$169$	4.44506	0.341927
$170$	2.24219	0.171968
$171$	13.9752	1.06871
$172$	−8.62178	−0.657405
$173$	16.3745	1.24493	0.622465	−	0.782648i	$-0.286131\pi$
$173$	16.3745	1.24493	0.622465	+	0.782648i	$0.286131\pi$
$174$	1.98762	0.150681
$175$	0	0
$176$	−3.69963	−0.278870
$177$	5.68725	0.427480
$178$	13.1643	0.986710
$179$	23.8072	1.77943	0.889716	−	0.456515i	$-0.150902\pi$
$179$	23.8072	1.77943	0.889716	+	0.456515i	$0.150902\pi$
$180$	−1.17673	−0.0877081
$181$	−8.98762	−0.668045	−0.334022	−	0.942565i	$-0.608406\pi$
$181$	−8.98762	−0.668045	−0.334022	+	0.942565i	$0.608406\pi$
$182$	0	0
$183$	−13.6094	−1.00604
$184$	3.09888	0.228453
$185$	−3.59565	−0.264357
$186$	−0.399256	−0.0292749
$187$	−14.0989	−1.03101
$188$	9.49814	0.692723
$189$	0	0
$190$	−4.11126	−0.298262
$191$	−10.8640	−0.786090	−0.393045	−	0.919519i	$-0.628578\pi$
$191$	−10.8640	−0.786090	−0.393045	+	0.919519i	$0.628578\pi$
$192$	1.00000	0.0721688
$193$	18.1978	1.30990	0.654952	−	0.755670i	$-0.272689\pi$
$193$	18.1978	1.30990	0.654952	+	0.755670i	$0.272689\pi$
$194$	0.666208	0.0478309
$195$	−2.45744	−0.175981
$196$	0	0
$197$	−26.0531	−1.85621	−0.928103	−	0.372324i	$-0.878561\pi$
$197$	−26.0531	−1.85621	−0.928103	+	0.372324i	$0.878561\pi$
$198$	7.39926	0.525842
$199$	16.7848	1.18984	0.594920	−	0.803785i	$-0.297184\pi$
$199$	16.7848	1.18984	0.594920	+	0.803785i	$0.297184\pi$
$200$	−4.65383	−0.329075
$201$	−3.71201	−0.261825
$202$	−2.38688	−0.167940
$203$	0	0
$204$	3.81089	0.266816
$205$	−0.588364	−0.0410931
$206$	9.27561	0.646263
$207$	−6.19777	−0.430775
$208$	−4.17673	−0.289604
$209$	25.8516	1.78819
$210$	0	0
$211$	−3.15706	−0.217341	−0.108671	−	0.994078i	$-0.534659\pi$
$211$	−3.15706	−0.217341	−0.108671	+	0.994078i	$0.534659\pi$
$212$	1.06546	0.0731764
$213$	−5.87636	−0.402641
$214$	−5.93454	−0.405677
$215$	−5.07275	−0.345959
$216$	−5.00000	−0.340207
$217$	0	0
$218$	−20.4079	−1.38220
$219$	4.36584	0.295016
$220$	−2.17673	−0.146755
$221$	−15.9171	−1.07070
$222$	−6.11126	−0.410161
$223$	1.24357	0.0832756	0.0416378	−	0.999133i	$-0.486742\pi$
$223$	1.24357	0.0832756	0.0416378	+	0.999133i	$0.486742\pi$
$224$	0	0
$225$	9.30766	0.620510
$226$	−15.0197	−0.999093
$227$	−16.0741	−1.06688	−0.533439	−	0.845839i	$-0.679100\pi$
$227$	−16.0741	−1.06688	−0.533439	+	0.845839i	$0.679100\pi$
$228$	−6.98762	−0.462766
$229$	−10.1643	−0.671679	−0.335840	−	0.941919i	$-0.609020\pi$
$229$	−10.1643	−0.671679	−0.335840	+	0.941919i	$0.609020\pi$
$230$	1.82327	0.120223
$231$	0	0
$232$	1.98762	0.130494
$233$	1.63279	0.106967	0.0534837	−	0.998569i	$-0.482967\pi$
$233$	1.63279	0.106967	0.0534837	+	0.998569i	$0.482967\pi$
$234$	8.35346	0.546082
$235$	5.58836	0.364545
$236$	5.68725	0.370208
$237$	−13.3411	−0.866596
$238$	0	0
$239$	7.83056	0.506517	0.253258	−	0.967399i	$-0.418498\pi$
$239$	7.83056	0.506517	0.253258	+	0.967399i	$0.418498\pi$
$240$	0.588364	0.0379787
$241$	29.1767	1.87944	0.939719	−	0.341947i	$-0.111086\pi$
$241$	29.1767	1.87944	0.939719	+	0.341947i	$0.111086\pi$
$242$	2.68725	0.172743
$243$	16.0000	1.02640
$244$	−13.6094	−0.871253
$245$	0	0
$246$	−1.00000	−0.0637577
$247$	29.1854	1.85702
$248$	−0.399256	−0.0253528
$249$	6.68725	0.423787
$250$	−5.67996	−0.359233
$251$	−7.94182	−0.501283	−0.250642	−	0.968080i	$-0.580642\pi$
$251$	−7.94182	−0.501283	−0.250642	+	0.968080i	$0.580642\pi$
$252$	0	0
$253$	−11.4647	−0.720781
$254$	2.14468	0.134569
$255$	2.24219	0.140411
$256$	1.00000	0.0625000
$257$	22.3955	1.39700	0.698498	−	0.715612i	$-0.253852\pi$
$257$	22.3955	1.39700	0.698498	+	0.715612i	$0.253852\pi$
$258$	−8.62178	−0.536769
$259$	0	0
$260$	−2.45744	−0.152404
$261$	−3.97524	−0.246061
$262$	2.03204	0.125540
$263$	11.3200	0.698023	0.349012	−	0.937118i	$-0.386517\pi$
$263$	11.3200	0.698023	0.349012	+	0.937118i	$0.386517\pi$
$264$	−3.69963	−0.227696
$265$	0.626881	0.0385090
$266$	0	0
$267$	13.1643	0.805645
$268$	−3.71201	−0.226747
$269$	−0.909777	−0.0554701	−0.0277350	−	0.999615i	$-0.508829\pi$
$269$	−0.909777	−0.0554701	−0.0277350	+	0.999615i	$0.508829\pi$
$270$	−2.94182	−0.179033
$271$	−26.5833	−1.61482	−0.807409	−	0.589992i	$-0.799131\pi$
$271$	−26.5833	−1.61482	−0.807409	+	0.589992i	$0.799131\pi$
$272$	3.81089	0.231069
$273$	0	0
$274$	17.3287	1.04686
$275$	17.2174	1.03825
$276$	3.09888	0.186531
$277$	29.8836	1.79553	0.897767	−	0.440471i	$-0.145188\pi$
$277$	29.8836	1.79553	0.897767	+	0.440471i	$0.145188\pi$
$278$	−7.47710	−0.448447
$279$	0.798513	0.0478057
$280$	0	0
$281$	−27.8392	−1.66075	−0.830374	−	0.557206i	$-0.811873\pi$
$281$	−27.8392	−1.66075	−0.830374	+	0.557206i	$0.811873\pi$
$282$	9.49814	0.565606
$283$	−4.73305	−0.281351	−0.140675	−	0.990056i	$-0.544927\pi$
$283$	−4.73305	−0.281351	−0.140675	+	0.990056i	$0.544927\pi$
$284$	−5.87636	−0.348698
$285$	−4.11126	−0.243530
$286$	15.4523	0.913716
$287$	0	0
$288$	−2.00000	−0.117851
$289$	−2.47710	−0.145712
$290$	1.16944	0.0686721
$291$	0.666208	0.0390538
$292$	4.36584	0.255491
$293$	17.6625	1.03185	0.515927	−	0.856633i	$-0.327448\pi$
$293$	17.6625	1.03185	0.515927	+	0.856633i	$0.327448\pi$
$294$	0	0
$295$	3.34617	0.194822
$296$	−6.11126	−0.355210
$297$	18.4981	1.07337
$298$	−4.06546	−0.235506
$299$	−12.9432	−0.748524
$300$	−4.65383	−0.268689
$301$	0	0
$302$	10.0334	0.577358
$303$	−2.38688	−0.137122
$304$	−6.98762	−0.400768
$305$	−8.00728	−0.458496
$306$	−7.62178	−0.435708
$307$	−22.9084	−1.30745	−0.653726	−	0.756732i	$-0.726795\pi$
$307$	−22.9084	−1.30745	−0.653726	+	0.756732i	$0.726795\pi$
$308$	0	0
$309$	9.27561	0.527671
$310$	−0.234908	−0.0133419
$311$	25.3287	1.43626	0.718129	−	0.695910i	$-0.244999\pi$
$311$	25.3287	1.43626	0.718129	+	0.695910i	$0.244999\pi$
$312$	−4.17673	−0.236461
$313$	−20.9615	−1.18481	−0.592407	−	0.805639i	$-0.701822\pi$
$313$	−20.9615	−1.18481	−0.592407	+	0.805639i	$0.701822\pi$
$314$	2.55632	0.144262
$315$	0	0
$316$	−13.3411	−0.750494
$317$	−32.3163	−1.81507	−0.907533	−	0.419982i	$-0.862037\pi$
$317$	−32.3163	−1.81507	−0.907533	+	0.419982i	$0.862037\pi$
$318$	1.06546	0.0597482
$319$	−7.35346	−0.411714
$320$	0.588364	0.0328905
$321$	−5.93454	−0.331234
$322$	0	0
$323$	−26.6291	−1.48168
$324$	1.00000	0.0555556
$325$	19.4378	1.07821
$326$	14.4116	0.798187
$327$	−20.4079	−1.12856
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−2.17673	−0.119825
$331$	18.8268	1.03482	0.517408	−	0.855739i	$-0.326897\pi$
$331$	18.8268	1.03482	0.517408	+	0.855739i	$0.326897\pi$
$332$	6.68725	0.367010
$333$	12.2225	0.669790
$334$	−2.03342	−0.111264
$335$	−2.18401	−0.119325
$336$	0	0
$337$	−14.9542	−0.814607	−0.407304	−	0.913293i	$-0.633531\pi$
$337$	−14.9542	−0.814607	−0.407304	+	0.913293i	$0.633531\pi$
$338$	4.44506	0.241779
$339$	−15.0197	−0.815756
$340$	2.24219	0.121600
$341$	1.47710	0.0799894
$342$	13.9752	0.755694
$343$	0	0
$344$	−8.62178	−0.464855
$345$	1.82327	0.0981617
$346$	16.3745	0.880298
$347$	−34.8713	−1.87199	−0.935994	−	0.352017i	$-0.885496\pi$
$347$	−34.8713	−1.87199	−0.935994	+	0.352017i	$0.885496\pi$
$348$	1.98762	0.106548
$349$	−3.90978	−0.209286	−0.104643	−	0.994510i	$-0.533370\pi$
$349$	−3.90978	−0.209286	−0.104643	+	0.994510i	$0.533370\pi$
$350$	0	0
$351$	20.8836	1.11469
$352$	−3.69963	−0.197191
$353$	16.9418	0.901722	0.450861	−	0.892594i	$-0.351117\pi$
$353$	16.9418	0.901722	0.450861	+	0.892594i	$0.351117\pi$
$354$	5.68725	0.302274
$355$	−3.45744	−0.183502
$356$	13.1643	0.697709
$357$	0	0
$358$	23.8072	1.25825
$359$	−10.2101	−0.538871	−0.269436	−	0.963018i	$-0.586837\pi$
$359$	−10.2101	−0.538871	−0.269436	+	0.963018i	$0.586837\pi$
$360$	−1.17673	−0.0620190
$361$	29.8268	1.56983
$362$	−8.98762	−0.472379
$363$	2.68725	0.141044
$364$	0	0
$365$	2.56870	0.134452
$366$	−13.6094	−0.711375
$367$	−15.4065	−0.804215	−0.402107	−	0.915592i	$-0.631722\pi$
$367$	−15.4065	−0.804215	−0.402107	+	0.915592i	$0.631722\pi$
$368$	3.09888	0.161541
$369$	2.00000	0.104116
$370$	−3.59565	−0.186929
$371$	0	0
$372$	−0.399256	−0.0207005
$373$	−19.5192	−1.01066	−0.505332	−	0.862925i	$-0.668630\pi$
$373$	−19.5192	−1.01066	−0.505332	+	0.862925i	$0.668630\pi$
$374$	−14.0989	−0.729036
$375$	−5.67996	−0.293312
$376$	9.49814	0.489829
$377$	−8.30175	−0.427562
$378$	0	0
$379$	−29.2064	−1.50023	−0.750117	−	0.661305i	$-0.770003\pi$
$379$	−29.2064	−1.50023	−0.750117	+	0.661305i	$0.770003\pi$
$380$	−4.11126	−0.210903
$381$	2.14468	0.109876
$382$	−10.8640	−0.555849
$383$	−15.2101	−0.777202	−0.388601	−	0.921406i	$-0.627042\pi$
$383$	−15.2101	−0.777202	−0.388601	+	0.921406i	$0.627042\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	18.1978	0.926242
$387$	17.2436	0.876540
$388$	0.666208	0.0338216
$389$	−11.8196	−0.599275	−0.299638	−	0.954053i	$-0.596866\pi$
$389$	−11.8196	−0.599275	−0.299638	+	0.954053i	$0.596866\pi$
$390$	−2.45744	−0.124437
$391$	11.8095	0.597233
$392$	0	0
$393$	2.03204	0.102503
$394$	−26.0531	−1.31254
$395$	−7.84941	−0.394947
$396$	7.39926	0.371827
$397$	18.9098	0.949054	0.474527	−	0.880241i	$-0.342619\pi$
$397$	18.9098	0.949054	0.474527	+	0.880241i	$0.342619\pi$
$398$	16.7848	0.841344
$399$	0	0
$400$	−4.65383	−0.232691
$401$	−0.625503	−0.0312361	−0.0156181	−	0.999878i	$-0.504972\pi$
$401$	−0.625503	−0.0312361	−0.0156181	+	0.999878i	$0.504972\pi$
$402$	−3.71201	−0.185138
$403$	1.66758	0.0830683
$404$	−2.38688	−0.118752
$405$	0.588364	0.0292360
$406$	0	0
$407$	22.6094	1.12071
$408$	3.81089	0.188667
$409$	−7.27561	−0.359756	−0.179878	−	0.983689i	$-0.557570\pi$
$409$	−7.27561	−0.359756	−0.179878	+	0.983689i	$0.557570\pi$
$410$	−0.588364	−0.0290572
$411$	17.3287	0.854762
$412$	9.27561	0.456977
$413$	0	0
$414$	−6.19777	−0.304604
$415$	3.93454	0.193139
$416$	−4.17673	−0.204781
$417$	−7.47710	−0.366155
$418$	25.8516	1.26444
$419$	−33.8406	−1.65322	−0.826611	−	0.562774i	$-0.809734\pi$
$419$	−33.8406	−1.65322	−0.826611	+	0.562774i	$0.809734\pi$
$420$	0	0
$421$	−17.0989	−0.833349	−0.416674	−	0.909056i	$-0.636804\pi$
$421$	−17.0989	−0.833349	−0.416674	+	0.909056i	$0.636804\pi$
$422$	−3.15706	−0.153683
$423$	−18.9963	−0.923631
$424$	1.06546	0.0517435
$425$	−17.7352	−0.860285
$426$	−5.87636	−0.284710
$427$	0	0
$428$	−5.93454	−0.286857
$429$	15.4523	0.746046
$430$	−5.07275	−0.244630
$431$	−14.3214	−0.689838	−0.344919	−	0.938632i	$-0.612094\pi$
$431$	−14.3214	−0.689838	−0.344919	+	0.938632i	$0.612094\pi$
$432$	−5.00000	−0.240563
$433$	15.2188	0.731369	0.365685	−	0.930739i	$-0.380835\pi$
$433$	15.2188	0.731369	0.365685	+	0.930739i	$0.380835\pi$
$434$	0	0
$435$	1.16944	0.0560706
$436$	−20.4079	−0.977362
$437$	−21.6538	−1.03584
$438$	4.36584	0.208608
$439$	16.2632	0.776202	0.388101	−	0.921617i	$-0.373131\pi$
$439$	16.2632	0.776202	0.388101	+	0.921617i	$0.373131\pi$
$440$	−2.17673	−0.103771
$441$	0	0
$442$	−15.9171	−0.757097
$443$	12.1099	0.575358	0.287679	−	0.957727i	$-0.407116\pi$
$443$	12.1099	0.575358	0.287679	+	0.957727i	$0.407116\pi$
$444$	−6.11126	−0.290028
$445$	7.74543	0.367169
$446$	1.24357	0.0588847
$447$	−4.06546	−0.192290
$448$	0	0
$449$	−6.89602	−0.325443	−0.162722	−	0.986672i	$-0.552027\pi$
$449$	−6.89602	−0.325443	−0.162722	+	0.986672i	$0.552027\pi$
$450$	9.30766	0.438767
$451$	3.69963	0.174209
$452$	−15.0197	−0.706466
$453$	10.0334	0.471411
$454$	−16.0741	−0.754396
$455$	0	0
$456$	−6.98762	−0.327225
$457$	17.7069	0.828294	0.414147	−	0.910210i	$-0.364080\pi$
$457$	17.7069	0.828294	0.414147	+	0.910210i	$0.364080\pi$
$458$	−10.1643	−0.474949
$459$	−19.0545	−0.889386
$460$	1.82327	0.0850105
$461$	−19.4596	−0.906325	−0.453163	−	0.891428i	$-0.649704\pi$
$461$	−19.4596	−0.906325	−0.453163	+	0.891428i	$0.649704\pi$
$462$	0	0
$463$	32.8406	1.52623	0.763116	−	0.646262i	$-0.223669\pi$
$463$	32.8406	1.52623	0.763116	+	0.646262i	$0.223669\pi$
$464$	1.98762	0.0922730
$465$	−0.234908	−0.0108936
$466$	1.63279	0.0756374
$467$	12.4065	0.574106	0.287053	−	0.957915i	$-0.407324\pi$
$467$	12.4065	0.574106	0.287053	+	0.957915i	$0.407324\pi$
$468$	8.35346	0.386139
$469$	0	0
$470$	5.58836	0.257772
$471$	2.55632	0.117789
$472$	5.68725	0.261777
$473$	31.8974	1.46664
$474$	−13.3411	−0.612776
$475$	32.5192	1.49208
$476$	0	0
$477$	−2.13093	−0.0975685
$478$	7.83056	0.358161
$479$	−29.3535	−1.34119	−0.670597	−	0.741822i	$-0.733962\pi$
$479$	−29.3535	−1.34119	−0.670597	+	0.741822i	$0.733962\pi$
$480$	0.588364	0.0268550
$481$	25.5251	1.16384
$482$	29.1767	1.32896
$483$	0	0
$484$	2.68725	0.122148
$485$	0.391973	0.0177986
$486$	16.0000	0.725775
$487$	15.5563	0.704924	0.352462	−	0.935826i	$-0.385345\pi$
$487$	15.5563	0.704924	0.352462	+	0.935826i	$0.385345\pi$
$488$	−13.6094	−0.616069
$489$	14.4116	0.651717
$490$	0	0
$491$	31.5229	1.42261	0.711304	−	0.702884i	$-0.248105\pi$
$491$	31.5229	1.42261	0.711304	+	0.702884i	$0.248105\pi$
$492$	−1.00000	−0.0450835
$493$	7.57461	0.341143
$494$	29.1854	1.31311
$495$	4.35346	0.195673
$496$	−0.399256	−0.0179271
$497$	0	0
$498$	6.68725	0.299663
$499$	−0.510520	−0.0228540	−0.0114270	−	0.999935i	$-0.503637\pi$
$499$	−0.510520	−0.0228540	−0.0114270	+	0.999935i	$0.503637\pi$
$500$	−5.67996	−0.254016
$501$	−2.03342	−0.0908465
$502$	−7.94182	−0.354461
$503$	11.1309	0.496304	0.248152	−	0.968721i	$-0.420177\pi$
$503$	11.1309	0.496304	0.248152	+	0.968721i	$0.420177\pi$
$504$	0	0
$505$	−1.40435	−0.0624929
$506$	−11.4647	−0.509669
$507$	4.44506	0.197412
$508$	2.14468	0.0951550
$509$	2.33379	0.103444	0.0517218	−	0.998662i	$-0.483529\pi$
$509$	2.33379	0.103444	0.0517218	+	0.998662i	$0.483529\pi$
$510$	2.24219	0.0992859
$511$	0	0
$512$	1.00000	0.0441942
$513$	34.9381	1.54255
$514$	22.3955	0.987825
$515$	5.45744	0.240483
$516$	−8.62178	−0.379553
$517$	−35.1396	−1.54544
$518$	0	0
$519$	16.3745	0.718761
$520$	−2.45744	−0.107766
$521$	−24.9171	−1.09164	−0.545818	−	0.837904i	$-0.683781\pi$
$521$	−24.9171	−1.09164	−0.545818	+	0.837904i	$0.683781\pi$
$522$	−3.97524	−0.173992
$523$	20.8196	0.910376	0.455188	−	0.890395i	$-0.349572\pi$
$523$	20.8196	0.910376	0.455188	+	0.890395i	$0.349572\pi$
$524$	2.03204	0.0887702
$525$	0	0
$526$	11.3200	0.493577
$527$	−1.52152	−0.0662786
$528$	−3.69963	−0.161006
$529$	−13.3969	−0.582475
$530$	0.626881	0.0272300
$531$	−11.3745	−0.493611
$532$	0	0
$533$	4.17673	0.180914
$534$	13.1643	0.569677
$535$	−3.49167	−0.150958
$536$	−3.71201	−0.160334
$537$	23.8072	1.02736
$538$	−0.909777	−0.0392233
$539$	0	0
$540$	−2.94182	−0.126596
$541$	−17.1978	−0.739390	−0.369695	−	0.929153i	$-0.620538\pi$
$541$	−17.1978	−0.739390	−0.369695	+	0.929153i	$0.620538\pi$
$542$	−26.5833	−1.14185
$543$	−8.98762	−0.385696
$544$	3.81089	0.163391
$545$	−12.0073	−0.514336
$546$	0	0
$547$	35.6501	1.52429	0.762144	−	0.647407i	$-0.224147\pi$
$547$	35.6501	1.52429	0.762144	+	0.647407i	$0.224147\pi$
$548$	17.3287	0.740245
$549$	27.2188	1.16167
$550$	17.2174	0.734154
$551$	−13.8887	−0.591680
$552$	3.09888	0.131897
$553$	0	0
$554$	29.8836	1.26963
$555$	−3.59565	−0.152627
$556$	−7.47710	−0.317100
$557$	−4.92587	−0.208716	−0.104358	−	0.994540i	$-0.533279\pi$
$557$	−4.92587	−0.208716	−0.104358	+	0.994540i	$0.533279\pi$
$558$	0.798513	0.0338037
$559$	36.0108	1.52310
$560$	0	0
$561$	−14.0989	−0.595255
$562$	−27.8392	−1.17433
$563$	22.0421	0.928963	0.464481	−	0.885583i	$-0.346241\pi$
$563$	22.0421	0.928963	0.464481	+	0.885583i	$0.346241\pi$
$564$	9.49814	0.399944
$565$	−8.83703	−0.371777
$566$	−4.73305	−0.198945
$567$	0	0
$568$	−5.87636	−0.246566
$569$	2.55632	0.107167	0.0535833	−	0.998563i	$-0.482936\pi$
$569$	2.55632	0.107167	0.0535833	+	0.998563i	$0.482936\pi$
$570$	−4.11126	−0.172202
$571$	13.9281	0.582871	0.291436	−	0.956590i	$-0.405867\pi$
$571$	13.9281	0.582871	0.291436	+	0.956590i	$0.405867\pi$
$572$	15.4523	0.646095
$573$	−10.8640	−0.453849
$574$	0	0
$575$	−14.4217	−0.601425
$576$	−2.00000	−0.0833333
$577$	20.5956	0.857408	0.428704	−	0.903445i	$-0.358970\pi$
$577$	20.5956	0.857408	0.428704	+	0.903445i	$0.358970\pi$
$578$	−2.47710	−0.103034
$579$	18.1978	0.756273
$580$	1.16944	0.0485585
$581$	0	0
$582$	0.666208	0.0276152
$583$	−3.94182	−0.163254
$584$	4.36584	0.180660
$585$	4.91487	0.203205
$586$	17.6625	0.729631
$587$	12.9876	0.536056	0.268028	−	0.963411i	$-0.413628\pi$
$587$	12.9876	0.536056	0.268028	+	0.963411i	$0.413628\pi$
$588$	0	0
$589$	2.78985	0.114954
$590$	3.34617	0.137760
$591$	−26.0531	−1.07168
$592$	−6.11126	−0.251171
$593$	−44.6377	−1.83305	−0.916526	−	0.399975i	$-0.869019\pi$
$593$	−44.6377	−1.83305	−0.916526	+	0.399975i	$0.869019\pi$
$594$	18.4981	0.758988
$595$	0	0
$596$	−4.06546	−0.166528
$597$	16.7848	0.686954
$598$	−12.9432	−0.529287
$599$	23.2051	0.948133	0.474066	−	0.880489i	$-0.342786\pi$
$599$	23.2051	0.948133	0.474066	+	0.880489i	$0.342786\pi$
$600$	−4.65383	−0.189992
$601$	−34.6094	−1.41175	−0.705874	−	0.708338i	$-0.749445\pi$
$601$	−34.6094	−1.41175	−0.705874	+	0.708338i	$0.749445\pi$
$602$	0	0
$603$	7.42402	0.302329
$604$	10.0334	0.408254
$605$	1.58108	0.0642801
$606$	−2.38688	−0.0969602
$607$	−4.18539	−0.169880	−0.0849399	−	0.996386i	$-0.527070\pi$
$607$	−4.18539	−0.169880	−0.0849399	+	0.996386i	$0.527070\pi$
$608$	−6.98762	−0.283385
$609$	0	0
$610$	−8.00728	−0.324205
$611$	−39.6712	−1.60492
$612$	−7.62178	−0.308092
$613$	16.9556	0.684829	0.342415	−	0.939549i	$-0.388755\pi$
$613$	16.9556	0.684829	0.342415	+	0.939549i	$0.388755\pi$
$614$	−22.9084	−0.924508
$615$	−0.588364	−0.0237251
$616$	0	0
$617$	24.2261	0.975306	0.487653	−	0.873038i	$-0.337853\pi$
$617$	24.2261	0.975306	0.487653	+	0.873038i	$0.337853\pi$
$618$	9.27561	0.373120
$619$	−32.9752	−1.32539	−0.662693	−	0.748891i	$-0.730587\pi$
$619$	−32.9752	−1.32539	−0.662693	+	0.748891i	$0.730587\pi$
$620$	−0.234908	−0.00943413
$621$	−15.4944	−0.621770
$622$	25.3287	1.01559
$623$	0	0
$624$	−4.17673	−0.167203
$625$	19.9273	0.797090
$626$	−20.9615	−0.837789
$627$	25.8516	1.03241
$628$	2.55632	0.102008
$629$	−23.2894	−0.928608
$630$	0	0
$631$	−10.9949	−0.437700	−0.218850	−	0.975758i	$-0.570231\pi$
$631$	−10.9949	−0.437700	−0.218850	+	0.975758i	$0.570231\pi$
$632$	−13.3411	−0.530680
$633$	−3.15706	−0.125482
$634$	−32.3163	−1.28344
$635$	1.26186	0.0500752
$636$	1.06546	0.0422484
$637$	0	0
$638$	−7.35346	−0.291126
$639$	11.7527	0.464930
$640$	0.588364	0.0232571
$641$	−21.5636	−0.851711	−0.425856	−	0.904791i	$-0.640027\pi$
$641$	−21.5636	−0.851711	−0.425856	+	0.904791i	$0.640027\pi$
$642$	−5.93454	−0.234217
$643$	−17.2894	−0.681826	−0.340913	−	0.940095i	$-0.610736\pi$
$643$	−17.2894	−0.681826	−0.340913	+	0.940095i	$0.610736\pi$
$644$	0	0
$645$	−5.07275	−0.199739
$646$	−26.6291	−1.04771
$647$	−32.1309	−1.26320	−0.631599	−	0.775296i	$-0.717601\pi$
$647$	−32.1309	−1.26320	−0.631599	+	0.775296i	$0.717601\pi$
$648$	1.00000	0.0392837
$649$	−21.0407	−0.825920
$650$	19.4378	0.762412
$651$	0	0
$652$	14.4116	0.564403
$653$	−3.09022	−0.120930	−0.0604649	−	0.998170i	$-0.519258\pi$
$653$	−3.09022	−0.120930	−0.0604649	+	0.998170i	$0.519258\pi$
$654$	−20.4079	−0.798013
$655$	1.19558	0.0467152
$656$	−1.00000	−0.0390434
$657$	−8.73167	−0.340655
$658$	0	0
$659$	40.3163	1.57050	0.785250	−	0.619178i	$-0.212534\pi$
$659$	40.3163	1.57050	0.785250	+	0.619178i	$0.212534\pi$
$660$	−2.17673	−0.0847290
$661$	30.8406	1.19956	0.599780	−	0.800165i	$-0.295255\pi$
$661$	30.8406	1.19956	0.599780	+	0.800165i	$0.295255\pi$
$662$	18.8268	0.731726
$663$	−15.9171	−0.618167
$664$	6.68725	0.259516
$665$	0	0
$666$	12.2225	0.473613
$667$	6.15941	0.238493
$668$	−2.03342	−0.0786754
$669$	1.24357	0.0480792
$670$	−2.18401	−0.0843757
$671$	50.3497	1.94373
$672$	0	0
$673$	3.92944	0.151469	0.0757344	−	0.997128i	$-0.475870\pi$
$673$	3.92944	0.151469	0.0757344	+	0.997128i	$0.475870\pi$
$674$	−14.9542	−0.576014
$675$	23.2691	0.895630
$676$	4.44506	0.170964
$677$	6.58108	0.252931	0.126466	−	0.991971i	$-0.459637\pi$
$677$	6.58108	0.252931	0.126466	+	0.991971i	$0.459637\pi$
$678$	−15.0197	−0.576827
$679$	0	0
$680$	2.24219	0.0859841
$681$	−16.0741	−0.615962
$682$	1.47710	0.0565611
$683$	29.5265	1.12980	0.564899	−	0.825160i	$-0.308915\pi$
$683$	29.5265	1.12980	0.564899	+	0.825160i	$0.308915\pi$
$684$	13.9752	0.534357
$685$	10.1956	0.389553
$686$	0	0
$687$	−10.1643	−0.387794
$688$	−8.62178	−0.328702
$689$	−4.45015	−0.169537
$690$	1.82327	0.0694108
$691$	−27.3731	−1.04132	−0.520661	−	0.853763i	$-0.674315\pi$
$691$	−27.3731	−1.04132	−0.520661	+	0.853763i	$0.674315\pi$
$692$	16.3745	0.622465
$693$	0	0
$694$	−34.8713	−1.32369
$695$	−4.39926	−0.166873
$696$	1.98762	0.0753406
$697$	−3.81089	−0.144348
$698$	−3.90978	−0.147987
$699$	1.63279	0.0617577
$700$	0	0
$701$	17.4451	0.658891	0.329445	−	0.944175i	$-0.393138\pi$
$701$	17.4451	0.658891	0.329445	+	0.944175i	$0.393138\pi$
$702$	20.8836	0.788202
$703$	42.7032	1.61058
$704$	−3.69963	−0.139435
$705$	5.58836	0.210470
$706$	16.9418	0.637614
$707$	0	0
$708$	5.68725	0.213740
$709$	−31.0000	−1.16423	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−31.0000	−1.16423	−0.582115	+	0.813107i	$0.697775\pi$
$710$	−3.45744	−0.129755
$711$	26.6822	1.00066
$712$	13.1643	0.493355
$713$	−1.23725	−0.0463353
$714$	0	0
$715$	9.09160	0.340007
$716$	23.8072	0.889716
$717$	7.83056	0.292437
$718$	−10.2101	−0.381039
$719$	47.1432	1.75814	0.879071	−	0.476690i	$-0.158164\pi$
$719$	47.1432	1.75814	0.879071	+	0.476690i	$0.158164\pi$
$720$	−1.17673	−0.0438541
$721$	0	0
$722$	29.8268	1.11004
$723$	29.1767	1.08509
$724$	−8.98762	−0.334022
$725$	−9.25004	−0.343538
$726$	2.68725	0.0997331
$727$	34.4065	1.27607	0.638034	−	0.770008i	$-0.279748\pi$
$727$	34.4065	1.27607	0.638034	+	0.770008i	$0.279748\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	2.56870	0.0950719
$731$	−32.8567	−1.21525
$732$	−13.6094	−0.503018
$733$	−28.9912	−1.07081	−0.535407	−	0.844594i	$-0.679842\pi$
$733$	−28.9912	−1.07081	−0.535407	+	0.844594i	$0.679842\pi$
$734$	−15.4065	−0.568666
$735$	0	0
$736$	3.09888	0.114226
$737$	13.7330	0.505863
$738$	2.00000	0.0736210
$739$	−38.0814	−1.40085	−0.700424	−	0.713727i	$-0.747006\pi$
$739$	−38.0814	−1.40085	−0.700424	+	0.713727i	$0.747006\pi$
$740$	−3.59565	−0.132179
$741$	29.1854	1.07215
$742$	0	0
$743$	16.3448	0.599632	0.299816	−	0.953997i	$-0.403075\pi$
$743$	16.3448	0.599632	0.299816	+	0.953997i	$0.403075\pi$
$744$	−0.399256	−0.0146374
$745$	−2.39197	−0.0876351
$746$	−19.5192	−0.714648
$747$	−13.3745	−0.489347
$748$	−14.0989	−0.515506
$749$	0	0
$750$	−5.67996	−0.207403
$751$	−8.74543	−0.319125	−0.159563	−	0.987188i	$-0.551008\pi$
$751$	−8.74543	−0.319125	−0.159563	+	0.987188i	$0.551008\pi$
$752$	9.49814	0.346362
$753$	−7.94182	−0.289416
$754$	−8.30175	−0.302332
$755$	5.90330	0.214843
$756$	0	0
$757$	−7.34245	−0.266866	−0.133433	−	0.991058i	$-0.542600\pi$
$757$	−7.34245	−0.266866	−0.133433	+	0.991058i	$0.542600\pi$
$758$	−29.2064	−1.06083
$759$	−11.4647	−0.416143
$760$	−4.11126	−0.149131
$761$	−34.1533	−1.23806	−0.619029	−	0.785368i	$-0.712474\pi$
$761$	−34.1533	−1.23806	−0.619029	+	0.785368i	$0.712474\pi$
$762$	2.14468	0.0776937
$763$	0	0
$764$	−10.8640	−0.393045
$765$	−4.48438	−0.162133
$766$	−15.2101	−0.549565
$767$	−23.7541	−0.857710
$768$	1.00000	0.0360844
$769$	−37.0617	−1.33648	−0.668240	−	0.743945i	$-0.732952\pi$
$769$	−37.0617	−1.33648	−0.668240	+	0.743945i	$0.732952\pi$
$770$	0	0
$771$	22.3955	0.806556
$772$	18.1978	0.654952
$773$	44.9171	1.61555	0.807777	−	0.589488i	$-0.200670\pi$
$773$	44.9171	1.61555	0.807777	+	0.589488i	$0.200670\pi$
$774$	17.2436	0.619807
$775$	1.85807	0.0667438
$776$	0.666208	0.0239155
$777$	0	0
$778$	−11.8196	−0.423752
$779$	6.98762	0.250357
$780$	−2.45744	−0.0879903
$781$	21.7403	0.777930
$782$	11.8095	0.422307
$783$	−9.93810	−0.355159
$784$	0	0
$785$	1.50405	0.0536817
$786$	2.03204	0.0724806
$787$	−41.9243	−1.49444	−0.747221	−	0.664576i	$-0.768612\pi$
$787$	−41.9243	−1.49444	−0.747221	+	0.664576i	$0.768612\pi$
$788$	−26.0531	−0.928103
$789$	11.3200	0.403004
$790$	−7.84941	−0.279269
$791$	0	0
$792$	7.39926	0.262921
$793$	56.8428	2.01855
$794$	18.9098	0.671083
$795$	0.626881	0.0222332
$796$	16.7848	0.594920
$797$	−4.47338	−0.158455	−0.0792276	−	0.996857i	$-0.525245\pi$
$797$	−4.47338	−0.158455	−0.0792276	+	0.996857i	$0.525245\pi$
$798$	0	0
$799$	36.1964	1.28054
$800$	−4.65383	−0.164538
$801$	−26.3287	−0.930279
$802$	−0.625503	−0.0220873
$803$	−16.1520	−0.569991
$804$	−3.71201	−0.130912
$805$	0	0
$806$	1.66758	0.0587382
$807$	−0.909777	−0.0320257
$808$	−2.38688	−0.0839700
$809$	−9.71201	−0.341456	−0.170728	−	0.985318i	$-0.554612\pi$
$809$	−9.71201	−0.341456	−0.170728	+	0.985318i	$0.554612\pi$
$810$	0.588364	0.0206730
$811$	−20.4189	−0.717005	−0.358503	−	0.933529i	$-0.616713\pi$
$811$	−20.4189	−0.717005	−0.358503	+	0.933529i	$0.616713\pi$
$812$	0	0
$813$	−26.5833	−0.932316
$814$	22.6094	0.792459
$815$	8.47929	0.297016
$816$	3.81089	0.133408
$817$	60.2458	2.10773
$818$	−7.27561	−0.254386
$819$	0	0
$820$	−0.588364	−0.0205466
$821$	55.2916	1.92969	0.964844	−	0.262822i	$-0.0846532\pi$
$821$	55.2916	1.92969	0.964844	+	0.262822i	$0.0846532\pi$
$822$	17.3287	0.604408
$823$	1.09022	0.0380028	0.0190014	−	0.999819i	$-0.493951\pi$
$823$	1.09022	0.0380028	0.0190014	+	0.999819i	$0.493951\pi$
$824$	9.27561	0.323131
$825$	17.2174	0.599434
$826$	0	0
$827$	−7.44134	−0.258761	−0.129380	−	0.991595i	$-0.541299\pi$
$827$	−7.44134	−0.258761	−0.129380	+	0.991595i	$0.541299\pi$
$828$	−6.19777	−0.215387
$829$	−21.7207	−0.754390	−0.377195	−	0.926134i	$-0.623111\pi$
$829$	−21.7207	−0.754390	−0.377195	+	0.926134i	$0.623111\pi$
$830$	3.93454	0.136570
$831$	29.8836	1.03665
$832$	−4.17673	−0.144802
$833$	0	0
$834$	−7.47710	−0.258911
$835$	−1.19639	−0.0414028
$836$	25.8516	0.894096
$837$	1.99628	0.0690016
$838$	−33.8406	−1.16900
$839$	41.2202	1.42308	0.711539	−	0.702646i	$-0.247998\pi$
$839$	41.2202	1.42308	0.711539	+	0.702646i	$0.247998\pi$
$840$	0	0
$841$	−25.0494	−0.863771
$842$	−17.0989	−0.589266
$843$	−27.8392	−0.958834
$844$	−3.15706	−0.108671
$845$	2.61531	0.0899694
$846$	−18.9963	−0.653106
$847$	0	0
$848$	1.06546	0.0365882
$849$	−4.73305	−0.162438
$850$	−17.7352	−0.608314
$851$	−18.9381	−0.649190
$852$	−5.87636	−0.201321
$853$	−15.9803	−0.547156	−0.273578	−	0.961850i	$-0.588207\pi$
$853$	−15.9803	−0.547156	−0.273578	+	0.961850i	$0.588207\pi$
$854$	0	0
$855$	8.22253	0.281205
$856$	−5.93454	−0.202838
$857$	−30.9098	−1.05586	−0.527929	−	0.849289i	$-0.677031\pi$
$857$	−30.9098	−1.05586	−0.527929	+	0.849289i	$0.677031\pi$
$858$	15.4523	0.527534
$859$	35.0370	1.19545	0.597723	−	0.801702i	$-0.296072\pi$
$859$	35.0370	1.19545	0.597723	+	0.801702i	$0.296072\pi$
$860$	−5.07275	−0.172979
$861$	0	0
$862$	−14.3214	−0.487789
$863$	−36.7403	−1.25066	−0.625328	−	0.780362i	$-0.715035\pi$
$863$	−36.7403	−1.25066	−0.625328	+	0.780362i	$0.715035\pi$
$864$	−5.00000	−0.170103
$865$	9.63416	0.327571
$866$	15.2188	0.517156
$867$	−2.47710	−0.0841267
$868$	0	0
$869$	49.3570	1.67432
$870$	1.16944	0.0396479
$871$	15.5040	0.525335
$872$	−20.4079	−0.691099
$873$	−1.33242	−0.0450954
$874$	−21.6538	−0.732452
$875$	0	0
$876$	4.36584	0.147508
$877$	36.9853	1.24890	0.624452	−	0.781063i	$-0.285322\pi$
$877$	36.9853	1.24890	0.624452	+	0.781063i	$0.285322\pi$
$878$	16.2632	0.548858
$879$	17.6625	0.595741
$880$	−2.17673	−0.0733775
$881$	−6.80223	−0.229173	−0.114586	−	0.993413i	$-0.536554\pi$
$881$	−6.80223	−0.229173	−0.114586	+	0.993413i	$0.536554\pi$
$882$	0	0
$883$	−52.3446	−1.76154	−0.880769	−	0.473547i	$-0.842974\pi$
$883$	−52.3446	−1.76154	−0.880769	+	0.473547i	$0.842974\pi$
$884$	−15.9171	−0.535349
$885$	3.34617	0.112480
$886$	12.1099	0.406840
$887$	−23.1075	−0.775875	−0.387938	−	0.921686i	$-0.626812\pi$
$887$	−23.1075	−0.775875	−0.387938	+	0.921686i	$0.626812\pi$
$888$	−6.11126	−0.205081
$889$	0	0
$890$	7.74543	0.259627
$891$	−3.69963	−0.123942
$892$	1.24357	0.0416378
$893$	−66.3694	−2.22097
$894$	−4.06546	−0.135969
$895$	14.0073	0.468212
$896$	0	0
$897$	−12.9432	−0.432161
$898$	−6.89602	−0.230123
$899$	−0.793570	−0.0264670
$900$	9.30766	0.310255
$901$	4.06037	0.135270
$902$	3.69963	0.123184
$903$	0	0
$904$	−15.0197	−0.499547
$905$	−5.28799	−0.175779
$906$	10.0334	0.333338
$907$	−50.9540	−1.69190	−0.845951	−	0.533261i	$-0.820966\pi$
$907$	−50.9540	−1.69190	−0.845951	+	0.533261i	$0.820966\pi$
$908$	−16.0741	−0.533439
$909$	4.77375	0.158335
$910$	0	0
$911$	54.2916	1.79876	0.899380	−	0.437168i	$-0.144019\pi$
$911$	54.2916	1.79876	0.899380	+	0.437168i	$0.144019\pi$
$912$	−6.98762	−0.231383
$913$	−24.7403	−0.818786
$914$	17.7069	0.585693
$915$	−8.00728	−0.264713
$916$	−10.1643	−0.335840
$917$	0	0
$918$	−19.0545	−0.628891
$919$	20.0059	0.659934	0.329967	−	0.943992i	$-0.392962\pi$
$919$	20.0059	0.659934	0.329967	+	0.943992i	$0.392962\pi$
$920$	1.82327	0.0601115
$921$	−22.9084	−0.754857
$922$	−19.4596	−0.640869
$923$	24.5439	0.807874
$924$	0	0
$925$	28.4408	0.935127
$926$	32.8406	1.07921
$927$	−18.5512	−0.609302
$928$	1.98762	0.0652468
$929$	−9.50324	−0.311791	−0.155896	−	0.987774i	$-0.549826\pi$
$929$	−9.50324	−0.311791	−0.155896	+	0.987774i	$0.549826\pi$
$930$	−0.234908	−0.00770294
$931$	0	0
$932$	1.63279	0.0534837
$933$	25.3287	0.829224
$934$	12.4065	0.405954
$935$	−8.29528	−0.271285
$936$	8.35346	0.273041
$937$	27.8072	0.908421	0.454210	−	0.890894i	$-0.349921\pi$
$937$	27.8072	0.908421	0.454210	+	0.890894i	$0.349921\pi$
$938$	0	0
$939$	−20.9615	−0.684052
$940$	5.58836	0.182272
$941$	−13.0444	−0.425236	−0.212618	−	0.977135i	$-0.568199\pi$
$941$	−13.0444	−0.425236	−0.212618	+	0.977135i	$0.568199\pi$
$942$	2.55632	0.0832894
$943$	−3.09888	−0.100914
$944$	5.68725	0.185104
$945$	0	0
$946$	31.8974	1.03707
$947$	0.119925	0.00389705	0.00194853	−	0.999998i	$-0.499380\pi$
$947$	0.119925	0.00389705	0.00194853	+	0.999998i	$0.499380\pi$
$948$	−13.3411	−0.433298
$949$	−18.2349	−0.591930
$950$	32.5192	1.05506
$951$	−32.3163	−1.04793
$952$	0	0
$953$	7.69453	0.249250	0.124625	−	0.992204i	$-0.460227\pi$
$953$	7.69453	0.249250	0.124625	+	0.992204i	$0.460227\pi$
$954$	−2.13093	−0.0689913
$955$	−6.39197	−0.206839
$956$	7.83056	0.253258
$957$	−7.35346	−0.237703
$958$	−29.3535	−0.948367
$959$	0	0
$960$	0.588364	0.0189894
$961$	−30.8406	−0.994858
$962$	25.5251	0.822962
$963$	11.8691	0.382476
$964$	29.1767	0.939719
$965$	10.7069	0.344668
$966$	0	0
$967$	26.0975	0.839239	0.419620	−	0.907700i	$-0.362163\pi$
$967$	26.0975	0.839239	0.419620	+	0.907700i	$0.362163\pi$
$968$	2.68725	0.0863714
$969$	−26.6291	−0.855449
$970$	0.391973	0.0125855
$971$	17.5019	0.561661	0.280831	−	0.959757i	$-0.409390\pi$
$971$	17.5019	0.561661	0.280831	+	0.959757i	$0.409390\pi$
$972$	16.0000	0.513200
$973$	0	0
$974$	15.5563	0.498457
$975$	19.4378	0.622507
$976$	−13.6094	−0.435626
$977$	−44.4240	−1.42125	−0.710625	−	0.703571i	$-0.751588\pi$
$977$	−44.4240	−1.42125	−0.710625	+	0.703571i	$0.751588\pi$
$978$	14.4116	0.460833
$979$	−48.7032	−1.55656
$980$	0	0
$981$	40.8158	1.30315
$982$	31.5229	1.00594
$983$	15.9235	0.507882	0.253941	−	0.967220i	$-0.418273\pi$
$983$	15.9235	0.507882	0.253941	+	0.967220i	$0.418273\pi$
$984$	−1.00000	−0.0318788
$985$	−15.3287	−0.488413
$986$	7.57461	0.241225
$987$	0	0
$988$	29.1854	0.928511
$989$	−26.7179	−0.849580
$990$	4.35346	0.138362
$991$	−21.6487	−0.687695	−0.343847	−	0.939026i	$-0.611730\pi$
$991$	−21.6487	−0.687695	−0.343847	+	0.939026i	$0.611730\pi$
$992$	−0.399256	−0.0126764
$993$	18.8268	0.597452
$994$	0	0
$995$	9.87555	0.313076
$996$	6.68725	0.211894
$997$	60.3199	1.91035	0.955175	−	0.296042i	$-0.0956668\pi$
$997$	60.3199	1.91035	0.955175	+	0.296042i	$0.0956668\pi$
$998$	−0.510520	−0.0161602
$999$	30.5563	0.966759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bh.1.3		3
7.3	odd	6		574.2.e.e.247.3	yes	6
7.5	odd	6		574.2.e.e.165.3	✓	6
7.6	odd	2		4018.2.a.bf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.e.165.3	✓	6	7.5	odd	6
574.2.e.e.247.3	yes	6	7.3	odd	6
4018.2.a.bf.1.1		3	7.6	odd	2
4018.2.a.bh.1.3		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.588364 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.588364 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +0.588364 q^{10} -3.69963 q^{11} +1.00000 q^{12} -4.17673 q^{13} +0.588364 q^{15} +1.00000 q^{16} +3.81089 q^{17} -2.00000 q^{18} -6.98762 q^{19} +0.588364 q^{20} -3.69963 q^{22} +3.09888 q^{23} +1.00000 q^{24} -4.65383 q^{25} -4.17673 q^{26} -5.00000 q^{27} +1.98762 q^{29} +0.588364 q^{30} -0.399256 q^{31} +1.00000 q^{32} -3.69963 q^{33} +3.81089 q^{34} -2.00000 q^{36} -6.11126 q^{37} -6.98762 q^{38} -4.17673 q^{39} +0.588364 q^{40} -1.00000 q^{41} -8.62178 q^{43} -3.69963 q^{44} -1.17673 q^{45} +3.09888 q^{46} +9.49814 q^{47} +1.00000 q^{48} -4.65383 q^{50} +3.81089 q^{51} -4.17673 q^{52} +1.06546 q^{53} -5.00000 q^{54} -2.17673 q^{55} -6.98762 q^{57} +1.98762 q^{58} +5.68725 q^{59} +0.588364 q^{60} -13.6094 q^{61} -0.399256 q^{62} +1.00000 q^{64} -2.45744 q^{65} -3.69963 q^{66} -3.71201 q^{67} +3.81089 q^{68} +3.09888 q^{69} -5.87636 q^{71} -2.00000 q^{72} +4.36584 q^{73} -6.11126 q^{74} -4.65383 q^{75} -6.98762 q^{76} -4.17673 q^{78} -13.3411 q^{79} +0.588364 q^{80} +1.00000 q^{81} -1.00000 q^{82} +6.68725 q^{83} +2.24219 q^{85} -8.62178 q^{86} +1.98762 q^{87} -3.69963 q^{88} +13.1643 q^{89} -1.17673 q^{90} +3.09888 q^{92} -0.399256 q^{93} +9.49814 q^{94} -4.11126 q^{95} +1.00000 q^{96} +0.666208 q^{97} +7.39926 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} + 3 q^{8} - 6 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 + 3 * q^8 - 6 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + 3 q^{6} + 3 q^{8} - 6 q^{9} - 4 q^{10} - 5 q^{11} + 3 q^{12} - q^{13} - 4 q^{15} + 3 q^{16} + 5 q^{17} - 6 q^{18} - 3 q^{19} - 4 q^{20} - 5 q^{22} - 9 q^{23} + 3 q^{24} + 3 q^{25} - q^{26} - 15 q^{27} - 12 q^{29} - 4 q^{30} + 11 q^{31} + 3 q^{32} - 5 q^{33} + 5 q^{34} - 6 q^{36} - 18 q^{37} - 3 q^{38} - q^{39} - 4 q^{40} - 3 q^{41} - 13 q^{43} - 5 q^{44} + 8 q^{45} - 9 q^{46} - 2 q^{47} + 3 q^{48} + 3 q^{50} + 5 q^{51} - q^{52} - 8 q^{53} - 15 q^{54} + 5 q^{55} - 3 q^{57} - 12 q^{58} - 7 q^{59} - 4 q^{60} - 10 q^{61} + 11 q^{62} + 3 q^{64} - 24 q^{65} - 5 q^{66} - 23 q^{67} + 5 q^{68} - 9 q^{69} - 6 q^{72} + 8 q^{73} - 18 q^{74} + 3 q^{75} - 3 q^{76} - q^{78} + q^{79} - 4 q^{80} + 3 q^{81} - 3 q^{82} - 4 q^{83} - 16 q^{85} - 13 q^{86} - 12 q^{87} - 5 q^{88} + 10 q^{89} + 8 q^{90} - 9 q^{92} + 11 q^{93} - 2 q^{94} - 12 q^{95} + 3 q^{96} + 3 q^{97} + 10 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + 3 * q^6 + 3 * q^8 - 6 * q^9 - 4 * q^10 - 5 * q^11 + 3 * q^12 - q^13 - 4 * q^15 + 3 * q^16 + 5 * q^17 - 6 * q^18 - 3 * q^19 - 4 * q^20 - 5 * q^22 - 9 * q^23 + 3 * q^24 + 3 * q^25 - q^26 - 15 * q^27 - 12 * q^29 - 4 * q^30 + 11 * q^31 + 3 * q^32 - 5 * q^33 + 5 * q^34 - 6 * q^36 - 18 * q^37 - 3 * q^38 - q^39 - 4 * q^40 - 3 * q^41 - 13 * q^43 - 5 * q^44 + 8 * q^45 - 9 * q^46 - 2 * q^47 + 3 * q^48 + 3 * q^50 + 5 * q^51 - q^52 - 8 * q^53 - 15 * q^54 + 5 * q^55 - 3 * q^57 - 12 * q^58 - 7 * q^59 - 4 * q^60 - 10 * q^61 + 11 * q^62 + 3 * q^64 - 24 * q^65 - 5 * q^66 - 23 * q^67 + 5 * q^68 - 9 * q^69 - 6 * q^72 + 8 * q^73 - 18 * q^74 + 3 * q^75 - 3 * q^76 - q^78 + q^79 - 4 * q^80 + 3 * q^81 - 3 * q^82 - 4 * q^83 - 16 * q^85 - 13 * q^86 - 12 * q^87 - 5 * q^88 + 10 * q^89 + 8 * q^90 - 9 * q^92 + 11 * q^93 - 2 * q^94 - 12 * q^95 + 3 * q^96 + 3 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more