LMFDB - Embedded newform 1014.2.a.h.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1014,2,Mod(1,1014)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1014.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1014, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,-2,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.73205 q^{5} +1.00000 q^{6} +4.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.73205 q^{10} +4.73205 q^{11} -1.00000 q^{12} -4.73205 q^{14} +1.73205 q^{15} +1.00000 q^{16} -5.19615 q^{17} -1.00000 q^{18} +1.26795 q^{19} -1.73205 q^{20} -4.73205 q^{21} -4.73205 q^{22} +2.19615 q^{23} +1.00000 q^{24} -2.00000 q^{25} -1.00000 q^{27} +4.73205 q^{28} -3.00000 q^{29} -1.73205 q^{30} +2.53590 q^{31} -1.00000 q^{32} -4.73205 q^{33} +5.19615 q^{34} -8.19615 q^{35} +1.00000 q^{36} +3.00000 q^{37} -1.26795 q^{38} +1.73205 q^{40} -0.464102 q^{41} +4.73205 q^{42} +6.19615 q^{43} +4.73205 q^{44} -1.73205 q^{45} -2.19615 q^{46} -1.26795 q^{47} -1.00000 q^{48} +15.3923 q^{49} +2.00000 q^{50} +5.19615 q^{51} +3.00000 q^{53} +1.00000 q^{54} -8.19615 q^{55} -4.73205 q^{56} -1.26795 q^{57} +3.00000 q^{58} +13.8564 q^{59} +1.73205 q^{60} +4.80385 q^{61} -2.53590 q^{62} +4.73205 q^{63} +1.00000 q^{64} +4.73205 q^{66} +10.7321 q^{67} -5.19615 q^{68} -2.19615 q^{69} +8.19615 q^{70} +8.19615 q^{71} -1.00000 q^{72} -12.1244 q^{73} -3.00000 q^{74} +2.00000 q^{75} +1.26795 q^{76} +22.3923 q^{77} -12.3923 q^{79} -1.73205 q^{80} +1.00000 q^{81} +0.464102 q^{82} -11.6603 q^{83} -4.73205 q^{84} +9.00000 q^{85} -6.19615 q^{86} +3.00000 q^{87} -4.73205 q^{88} +2.53590 q^{89} +1.73205 q^{90} +2.19615 q^{92} -2.53590 q^{93} +1.26795 q^{94} -2.19615 q^{95} +1.00000 q^{96} +6.00000 q^{97} -15.3923 q^{98} +4.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} - 6 q^{14} + 2 q^{16} - 2 q^{18} + 6 q^{19} - 6 q^{21} - 6 q^{22} - 6 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{27}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 - 6 * q^14 + 2 * q^16 - 2 * q^18 + 6 * q^19 - 6 * q^21 - 6 * q^22 - 6 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^27 + 6 * q^28 - 6 * q^29 + 12 * q^31 - 2 * q^32 - 6 * q^33 - 6 * q^35 + 2 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^41 + 6 * q^42 + 2 * q^43 + 6 * q^44 + 6 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^49 + 4 * q^50 + 6 * q^53 + 2 * q^54 - 6 * q^55 - 6 * q^56 - 6 * q^57 + 6 * q^58 + 20 * q^61 - 12 * q^62 + 6 * q^63 + 2 * q^64 + 6 * q^66 + 18 * q^67 + 6 * q^69 + 6 * q^70 + 6 * q^71 - 2 * q^72 - 6 * q^74 + 4 * q^75 + 6 * q^76 + 24 * q^77 - 4 * q^79 + 2 * q^81 - 6 * q^82 - 6 * q^83 - 6 * q^84 + 18 * q^85 - 2 * q^86 + 6 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^92 - 12 * q^93 + 6 * q^94 + 6 * q^95 + 2 * q^96 + 12 * q^97 - 10 * q^98 + 6 * q^99

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
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.73205	−0.774597	−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205	−0.774597	−0.387298	+	0.921954i	$0.626592\pi$
$6$	1.00000	0.408248
$7$	4.73205	1.78855	0.894274	−	0.447521i	$-0.147693\pi$
$7$	4.73205	1.78855	0.894274	+	0.447521i	$0.147693\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.73205	0.547723
$11$	4.73205	1.42677	0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205	1.42677	0.713384	+	0.700774i	$0.247162\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−4.73205	−1.26469
$15$	1.73205	0.447214
$16$	1.00000	0.250000
$17$	−5.19615	−1.26025	−0.630126	−	0.776493i	$-0.716997\pi$
$17$	−5.19615	−1.26025	−0.630126	+	0.776493i	$0.716997\pi$
$18$	−1.00000	−0.235702
$19$	1.26795	0.290887	0.145444	−	0.989367i	$-0.453539\pi$
$19$	1.26795	0.290887	0.145444	+	0.989367i	$0.453539\pi$
$20$	−1.73205	−0.387298
$21$	−4.73205	−1.03262
$22$	−4.73205	−1.00888
$23$	2.19615	0.457929	0.228965	−	0.973435i	$-0.426466\pi$
$23$	2.19615	0.457929	0.228965	+	0.973435i	$0.426466\pi$
$24$	1.00000	0.204124
$25$	−2.00000	−0.400000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	4.73205	0.894274
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−1.73205	−0.316228
$31$	2.53590	0.455461	0.227730	−	0.973724i	$-0.426870\pi$
$31$	2.53590	0.455461	0.227730	+	0.973724i	$0.426870\pi$
$32$	−1.00000	−0.176777
$33$	−4.73205	−0.823744
$34$	5.19615	0.891133
$35$	−8.19615	−1.38540
$36$	1.00000	0.166667
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−1.26795	−0.205689
$39$	0	0
$40$	1.73205	0.273861
$41$	−0.464102	−0.0724805	−0.0362402	−	0.999343i	$-0.511538\pi$
$41$	−0.464102	−0.0724805	−0.0362402	+	0.999343i	$0.511538\pi$
$42$	4.73205	0.730171
$43$	6.19615	0.944904	0.472452	−	0.881356i	$-0.343369\pi$
$43$	6.19615	0.944904	0.472452	+	0.881356i	$0.343369\pi$
$44$	4.73205	0.713384
$45$	−1.73205	−0.258199
$46$	−2.19615	−0.323805
$47$	−1.26795	−0.184949	−0.0924747	−	0.995715i	$-0.529478\pi$
$47$	−1.26795	−0.184949	−0.0924747	+	0.995715i	$0.529478\pi$
$48$	−1.00000	−0.144338
$49$	15.3923	2.19890
$50$	2.00000	0.282843
$51$	5.19615	0.727607
$52$	0	0
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	1.00000	0.136083
$55$	−8.19615	−1.10517
$56$	−4.73205	−0.632347
$57$	−1.26795	−0.167944
$58$	3.00000	0.393919
$59$	13.8564	1.80395	0.901975	−	0.431788i	$-0.142117\pi$
$59$	13.8564	1.80395	0.901975	+	0.431788i	$0.142117\pi$
$60$	1.73205	0.223607
$61$	4.80385	0.615070	0.307535	−	0.951537i	$-0.400496\pi$
$61$	4.80385	0.615070	0.307535	+	0.951537i	$0.400496\pi$
$62$	−2.53590	−0.322059
$63$	4.73205	0.596182
$64$	1.00000	0.125000
$65$	0	0
$66$	4.73205	0.582475
$67$	10.7321	1.31113	0.655564	−	0.755139i	$-0.272431\pi$
$67$	10.7321	1.31113	0.655564	+	0.755139i	$0.272431\pi$
$68$	−5.19615	−0.630126
$69$	−2.19615	−0.264386
$70$	8.19615	0.979628
$71$	8.19615	0.972704	0.486352	−	0.873763i	$-0.338327\pi$
$71$	8.19615	0.972704	0.486352	+	0.873763i	$0.338327\pi$
$72$	−1.00000	−0.117851
$73$	−12.1244	−1.41905	−0.709524	−	0.704681i	$-0.751090\pi$
$73$	−12.1244	−1.41905	−0.709524	+	0.704681i	$0.751090\pi$
$74$	−3.00000	−0.348743
$75$	2.00000	0.230940
$76$	1.26795	0.145444
$77$	22.3923	2.55184
$78$	0	0
$79$	−12.3923	−1.39424	−0.697122	−	0.716953i	$-0.745536\pi$
$79$	−12.3923	−1.39424	−0.697122	+	0.716953i	$0.745536\pi$
$80$	−1.73205	−0.193649
$81$	1.00000	0.111111
$82$	0.464102	0.0512514
$83$	−11.6603	−1.27988	−0.639940	−	0.768425i	$-0.721041\pi$
$83$	−11.6603	−1.27988	−0.639940	+	0.768425i	$0.721041\pi$
$84$	−4.73205	−0.516309
$85$	9.00000	0.976187
$86$	−6.19615	−0.668148
$87$	3.00000	0.321634
$88$	−4.73205	−0.504438
$89$	2.53590	0.268805	0.134402	−	0.990927i	$-0.457089\pi$
$89$	2.53590	0.268805	0.134402	+	0.990927i	$0.457089\pi$
$90$	1.73205	0.182574
$91$	0	0
$92$	2.19615	0.228965
$93$	−2.53590	−0.262960
$94$	1.26795	0.130779
$95$	−2.19615	−0.225320
$96$	1.00000	0.102062
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	−15.3923	−1.55486
$99$	4.73205	0.475589
$100$	−2.00000	−0.200000
$101$	−1.39230	−0.138540	−0.0692698	−	0.997598i	$-0.522067\pi$
$101$	−1.39230	−0.138540	−0.0692698	+	0.997598i	$0.522067\pi$
$102$	−5.19615	−0.514496
$103$	−4.19615	−0.413459	−0.206730	−	0.978398i	$-0.566282\pi$
$103$	−4.19615	−0.413459	−0.206730	+	0.978398i	$0.566282\pi$
$104$	0	0
$105$	8.19615	0.799863
$106$	−3.00000	−0.291386
$107$	8.19615	0.792352	0.396176	−	0.918175i	$-0.370337\pi$
$107$	8.19615	0.792352	0.396176	+	0.918175i	$0.370337\pi$
$108$	−1.00000	−0.0962250
$109$	16.3923	1.57010	0.785049	−	0.619434i	$-0.212638\pi$
$109$	16.3923	1.57010	0.785049	+	0.619434i	$0.212638\pi$
$110$	8.19615	0.781472
$111$	−3.00000	−0.284747
$112$	4.73205	0.447137
$113$	11.1962	1.05325	0.526623	−	0.850099i	$-0.323458\pi$
$113$	11.1962	1.05325	0.526623	+	0.850099i	$0.323458\pi$
$114$	1.26795	0.118754
$115$	−3.80385	−0.354711
$116$	−3.00000	−0.278543
$117$	0	0
$118$	−13.8564	−1.27559
$119$	−24.5885	−2.25402
$120$	−1.73205	−0.158114
$121$	11.3923	1.03566
$122$	−4.80385	−0.434920
$123$	0.464102	0.0418466
$124$	2.53590	0.227730
$125$	12.1244	1.08444
$126$	−4.73205	−0.421565
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	−6.19615	−0.545541
$130$	0	0
$131$	16.3923	1.43220	0.716101	−	0.697997i	$-0.245925\pi$
$131$	16.3923	1.43220	0.716101	+	0.697997i	$0.245925\pi$
$132$	−4.73205	−0.411872
$133$	6.00000	0.520266
$134$	−10.7321	−0.927108
$135$	1.73205	0.149071
$136$	5.19615	0.445566
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	2.19615	0.186949
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−8.19615	−0.692701
$141$	1.26795	0.106781
$142$	−8.19615	−0.687806
$143$	0	0
$144$	1.00000	0.0833333
$145$	5.19615	0.431517
$146$	12.1244	1.00342
$147$	−15.3923	−1.26954
$148$	3.00000	0.246598
$149$	−18.1244	−1.48481	−0.742403	−	0.669954i	$-0.766314\pi$
$149$	−18.1244	−1.48481	−0.742403	+	0.669954i	$0.766314\pi$
$150$	−2.00000	−0.163299
$151$	7.26795	0.591457	0.295729	−	0.955272i	$-0.404438\pi$
$151$	7.26795	0.591457	0.295729	+	0.955272i	$0.404438\pi$
$152$	−1.26795	−0.102844
$153$	−5.19615	−0.420084
$154$	−22.3923	−1.80442
$155$	−4.39230	−0.352798
$156$	0	0
$157$	−3.19615	−0.255081	−0.127540	−	0.991833i	$-0.540708\pi$
$157$	−3.19615	−0.255081	−0.127540	+	0.991833i	$0.540708\pi$
$158$	12.3923	0.985879
$159$	−3.00000	−0.237915
$160$	1.73205	0.136931
$161$	10.3923	0.819028
$162$	−1.00000	−0.0785674
$163$	9.46410	0.741286	0.370643	−	0.928775i	$-0.379137\pi$
$163$	9.46410	0.741286	0.370643	+	0.928775i	$0.379137\pi$
$164$	−0.464102	−0.0362402
$165$	8.19615	0.638070
$166$	11.6603	0.905011
$167$	−2.53590	−0.196234	−0.0981169	−	0.995175i	$-0.531282\pi$
$167$	−2.53590	−0.196234	−0.0981169	+	0.995175i	$0.531282\pi$
$168$	4.73205	0.365086
$169$	0	0
$170$	−9.00000	−0.690268
$171$	1.26795	0.0969625
$172$	6.19615	0.472452
$173$	16.3923	1.24628	0.623142	−	0.782109i	$-0.285856\pi$
$173$	16.3923	1.24628	0.623142	+	0.782109i	$0.285856\pi$
$174$	−3.00000	−0.227429
$175$	−9.46410	−0.715419
$176$	4.73205	0.356692
$177$	−13.8564	−1.04151
$178$	−2.53590	−0.190074
$179$	−8.19615	−0.612609	−0.306305	−	0.951934i	$-0.599093\pi$
$179$	−8.19615	−0.612609	−0.306305	+	0.951934i	$0.599093\pi$
$180$	−1.73205	−0.129099
$181$	−11.5885	−0.861363	−0.430682	−	0.902504i	$-0.641727\pi$
$181$	−11.5885	−0.861363	−0.430682	+	0.902504i	$0.641727\pi$
$182$	0	0
$183$	−4.80385	−0.355111
$184$	−2.19615	−0.161903
$185$	−5.19615	−0.382029
$186$	2.53590	0.185941
$187$	−24.5885	−1.79809
$188$	−1.26795	−0.0924747
$189$	−4.73205	−0.344206
$190$	2.19615	0.159326
$191$	20.7846	1.50392	0.751961	−	0.659208i	$-0.229108\pi$
$191$	20.7846	1.50392	0.751961	+	0.659208i	$0.229108\pi$
$192$	−1.00000	−0.0721688
$193$	−12.8038	−0.921641	−0.460821	−	0.887493i	$-0.652445\pi$
$193$	−12.8038	−0.921641	−0.460821	+	0.887493i	$0.652445\pi$
$194$	−6.00000	−0.430775
$195$	0	0
$196$	15.3923	1.09945
$197$	6.92820	0.493614	0.246807	−	0.969065i	$-0.420619\pi$
$197$	6.92820	0.493614	0.246807	+	0.969065i	$0.420619\pi$
$198$	−4.73205	−0.336292
$199$	8.58846	0.608820	0.304410	−	0.952541i	$-0.401541\pi$
$199$	8.58846	0.608820	0.304410	+	0.952541i	$0.401541\pi$
$200$	2.00000	0.141421
$201$	−10.7321	−0.756980
$202$	1.39230	0.0979622
$203$	−14.1962	−0.996375
$204$	5.19615	0.363803
$205$	0.803848	0.0561432
$206$	4.19615	0.292360
$207$	2.19615	0.152643
$208$	0	0
$209$	6.00000	0.415029
$210$	−8.19615	−0.565588
$211$	−3.60770	−0.248364	−0.124182	−	0.992259i	$-0.539631\pi$
$211$	−3.60770	−0.248364	−0.124182	+	0.992259i	$0.539631\pi$
$212$	3.00000	0.206041
$213$	−8.19615	−0.561591
$214$	−8.19615	−0.560277
$215$	−10.7321	−0.731920
$216$	1.00000	0.0680414
$217$	12.0000	0.814613
$218$	−16.3923	−1.11023
$219$	12.1244	0.819288
$220$	−8.19615	−0.552584
$221$	0	0
$222$	3.00000	0.201347
$223$	−18.9282	−1.26753	−0.633763	−	0.773527i	$-0.718491\pi$
$223$	−18.9282	−1.26753	−0.633763	+	0.773527i	$0.718491\pi$
$224$	−4.73205	−0.316173
$225$	−2.00000	−0.133333
$226$	−11.1962	−0.744757
$227$	−9.80385	−0.650704	−0.325352	−	0.945593i	$-0.605483\pi$
$227$	−9.80385	−0.650704	−0.325352	+	0.945593i	$0.605483\pi$
$228$	−1.26795	−0.0839720
$229$	19.8564	1.31215	0.656074	−	0.754696i	$-0.272216\pi$
$229$	19.8564	1.31215	0.656074	+	0.754696i	$0.272216\pi$
$230$	3.80385	0.250818
$231$	−22.3923	−1.47331
$232$	3.00000	0.196960
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	0	0
$235$	2.19615	0.143261
$236$	13.8564	0.901975
$237$	12.3923	0.804967
$238$	24.5885	1.59383
$239$	−24.5885	−1.59050	−0.795248	−	0.606285i	$-0.792659\pi$
$239$	−24.5885	−1.59050	−0.795248	+	0.606285i	$0.792659\pi$
$240$	1.73205	0.111803
$241$	0.803848	0.0517804	0.0258902	−	0.999665i	$-0.491758\pi$
$241$	0.803848	0.0517804	0.0258902	+	0.999665i	$0.491758\pi$
$242$	−11.3923	−0.732325
$243$	−1.00000	−0.0641500
$244$	4.80385	0.307535
$245$	−26.6603	−1.70326
$246$	−0.464102	−0.0295900
$247$	0	0
$248$	−2.53590	−0.161030
$249$	11.6603	0.738939
$250$	−12.1244	−0.766812
$251$	−4.39230	−0.277240	−0.138620	−	0.990346i	$-0.544267\pi$
$251$	−4.39230	−0.277240	−0.138620	+	0.990346i	$0.544267\pi$
$252$	4.73205	0.298091
$253$	10.3923	0.653359
$254$	4.00000	0.250982
$255$	−9.00000	−0.563602
$256$	1.00000	0.0625000
$257$	12.8038	0.798682	0.399341	−	0.916802i	$-0.369239\pi$
$257$	12.8038	0.798682	0.399341	+	0.916802i	$0.369239\pi$
$258$	6.19615	0.385756
$259$	14.1962	0.882106
$260$	0	0
$261$	−3.00000	−0.185695
$262$	−16.3923	−1.01272
$263$	−2.19615	−0.135421	−0.0677103	−	0.997705i	$-0.521569\pi$
$263$	−2.19615	−0.135421	−0.0677103	+	0.997705i	$0.521569\pi$
$264$	4.73205	0.291238
$265$	−5.19615	−0.319197
$266$	−6.00000	−0.367884
$267$	−2.53590	−0.155194
$268$	10.7321	0.655564
$269$	−28.3923	−1.73111	−0.865555	−	0.500814i	$-0.833034\pi$
$269$	−28.3923	−1.73111	−0.865555	+	0.500814i	$0.833034\pi$
$270$	−1.73205	−0.105409
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−5.19615	−0.315063
$273$	0	0
$274$	9.00000	0.543710
$275$	−9.46410	−0.570707
$276$	−2.19615	−0.132193
$277$	15.1962	0.913048	0.456524	−	0.889711i	$-0.349094\pi$
$277$	15.1962	0.913048	0.456524	+	0.889711i	$0.349094\pi$
$278$	4.00000	0.239904
$279$	2.53590	0.151820
$280$	8.19615	0.489814
$281$	24.4641	1.45941	0.729703	−	0.683764i	$-0.239658\pi$
$281$	24.4641	1.45941	0.729703	+	0.683764i	$0.239658\pi$
$282$	−1.26795	−0.0755053
$283$	−30.1962	−1.79497	−0.897487	−	0.441040i	$-0.854610\pi$
$283$	−30.1962	−1.79497	−0.897487	+	0.441040i	$0.854610\pi$
$284$	8.19615	0.486352
$285$	2.19615	0.130089
$286$	0	0
$287$	−2.19615	−0.129635
$288$	−1.00000	−0.0589256
$289$	10.0000	0.588235
$290$	−5.19615	−0.305129
$291$	−6.00000	−0.351726
$292$	−12.1244	−0.709524
$293$	−14.6603	−0.856461	−0.428231	−	0.903669i	$-0.640863\pi$
$293$	−14.6603	−0.856461	−0.428231	+	0.903669i	$0.640863\pi$
$294$	15.3923	0.897697
$295$	−24.0000	−1.39733
$296$	−3.00000	−0.174371
$297$	−4.73205	−0.274581
$298$	18.1244	1.04992
$299$	0	0
$300$	2.00000	0.115470
$301$	29.3205	1.69001
$302$	−7.26795	−0.418223
$303$	1.39230	0.0799858
$304$	1.26795	0.0727219
$305$	−8.32051	−0.476431
$306$	5.19615	0.297044
$307$	10.7321	0.612510	0.306255	−	0.951949i	$-0.400924\pi$
$307$	10.7321	0.612510	0.306255	+	0.951949i	$0.400924\pi$
$308$	22.3923	1.27592
$309$	4.19615	0.238711
$310$	4.39230	0.249466
$311$	2.19615	0.124532	0.0622662	−	0.998060i	$-0.480167\pi$
$311$	2.19615	0.124532	0.0622662	+	0.998060i	$0.480167\pi$
$312$	0	0
$313$	−24.3923	−1.37873	−0.689367	−	0.724412i	$-0.742111\pi$
$313$	−24.3923	−1.37873	−0.689367	+	0.724412i	$0.742111\pi$
$314$	3.19615	0.180369
$315$	−8.19615	−0.461801
$316$	−12.3923	−0.697122
$317$	6.12436	0.343978	0.171989	−	0.985099i	$-0.444981\pi$
$317$	6.12436	0.343978	0.171989	+	0.985099i	$0.444981\pi$
$318$	3.00000	0.168232
$319$	−14.1962	−0.794832
$320$	−1.73205	−0.0968246
$321$	−8.19615	−0.457465
$322$	−10.3923	−0.579141
$323$	−6.58846	−0.366592
$324$	1.00000	0.0555556
$325$	0	0
$326$	−9.46410	−0.524168
$327$	−16.3923	−0.906497
$328$	0.464102	0.0256257
$329$	−6.00000	−0.330791
$330$	−8.19615	−0.451183
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	−11.6603	−0.639940
$333$	3.00000	0.164399
$334$	2.53590	0.138758
$335$	−18.5885	−1.01560
$336$	−4.73205	−0.258155
$337$	−31.0000	−1.68868	−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000	−1.68868	−0.844339	+	0.535810i	$0.820006\pi$
$338$	0	0
$339$	−11.1962	−0.608092
$340$	9.00000	0.488094
$341$	12.0000	0.649836
$342$	−1.26795	−0.0685628
$343$	39.7128	2.14429
$344$	−6.19615	−0.334074
$345$	3.80385	0.204792
$346$	−16.3923	−0.881256
$347$	−12.5885	−0.675784	−0.337892	−	0.941185i	$-0.609714\pi$
$347$	−12.5885	−0.675784	−0.337892	+	0.941185i	$0.609714\pi$
$348$	3.00000	0.160817
$349$	2.53590	0.135744	0.0678718	−	0.997694i	$-0.478379\pi$
$349$	2.53590	0.135744	0.0678718	+	0.997694i	$0.478379\pi$
$350$	9.46410	0.505878
$351$	0	0
$352$	−4.73205	−0.252219
$353$	5.78461	0.307884	0.153942	−	0.988080i	$-0.450803\pi$
$353$	5.78461	0.307884	0.153942	+	0.988080i	$0.450803\pi$
$354$	13.8564	0.736460
$355$	−14.1962	−0.753454
$356$	2.53590	0.134402
$357$	24.5885	1.30136
$358$	8.19615	0.433180
$359$	22.0526	1.16389	0.581945	−	0.813228i	$-0.302292\pi$
$359$	22.0526	1.16389	0.581945	+	0.813228i	$0.302292\pi$
$360$	1.73205	0.0912871
$361$	−17.3923	−0.915384
$362$	11.5885	0.609076
$363$	−11.3923	−0.597941
$364$	0	0
$365$	21.0000	1.09919
$366$	4.80385	0.251101
$367$	−24.1962	−1.26303	−0.631514	−	0.775364i	$-0.717566\pi$
$367$	−24.1962	−1.26303	−0.631514	+	0.775364i	$0.717566\pi$
$368$	2.19615	0.114482
$369$	−0.464102	−0.0241602
$370$	5.19615	0.270135
$371$	14.1962	0.737028
$372$	−2.53590	−0.131480
$373$	23.9808	1.24168	0.620838	−	0.783939i	$-0.286792\pi$
$373$	23.9808	1.24168	0.620838	+	0.783939i	$0.286792\pi$
$374$	24.5885	1.27144
$375$	−12.1244	−0.626099
$376$	1.26795	0.0653895
$377$	0	0
$378$	4.73205	0.243390
$379$	−18.2487	−0.937373	−0.468687	−	0.883364i	$-0.655273\pi$
$379$	−18.2487	−0.937373	−0.468687	+	0.883364i	$0.655273\pi$
$380$	−2.19615	−0.112660
$381$	4.00000	0.204926
$382$	−20.7846	−1.06343
$383$	11.3205	0.578451	0.289225	−	0.957261i	$-0.406602\pi$
$383$	11.3205	0.578451	0.289225	+	0.957261i	$0.406602\pi$
$384$	1.00000	0.0510310
$385$	−38.7846	−1.97665
$386$	12.8038	0.651699
$387$	6.19615	0.314968
$388$	6.00000	0.304604
$389$	−13.3923	−0.679017	−0.339508	−	0.940603i	$-0.610261\pi$
$389$	−13.3923	−0.679017	−0.339508	+	0.940603i	$0.610261\pi$
$390$	0	0
$391$	−11.4115	−0.577107
$392$	−15.3923	−0.777429
$393$	−16.3923	−0.826882
$394$	−6.92820	−0.349038
$395$	21.4641	1.07998
$396$	4.73205	0.237795
$397$	−16.3923	−0.822706	−0.411353	−	0.911476i	$-0.634944\pi$
$397$	−16.3923	−0.822706	−0.411353	+	0.911476i	$0.634944\pi$
$398$	−8.58846	−0.430500
$399$	−6.00000	−0.300376
$400$	−2.00000	−0.100000
$401$	21.0000	1.04869	0.524345	−	0.851506i	$-0.324310\pi$
$401$	21.0000	1.04869	0.524345	+	0.851506i	$0.324310\pi$
$402$	10.7321	0.535266
$403$	0	0
$404$	−1.39230	−0.0692698
$405$	−1.73205	−0.0860663
$406$	14.1962	0.704543
$407$	14.1962	0.703677
$408$	−5.19615	−0.257248
$409$	−3.33975	−0.165140	−0.0825699	−	0.996585i	$-0.526313\pi$
$409$	−3.33975	−0.165140	−0.0825699	+	0.996585i	$0.526313\pi$
$410$	−0.803848	−0.0396992
$411$	9.00000	0.443937
$412$	−4.19615	−0.206730
$413$	65.5692	3.22645
$414$	−2.19615	−0.107935
$415$	20.1962	0.991390
$416$	0	0
$417$	4.00000	0.195881
$418$	−6.00000	−0.293470
$419$	16.3923	0.800816	0.400408	−	0.916337i	$-0.368868\pi$
$419$	16.3923	0.800816	0.400408	+	0.916337i	$0.368868\pi$
$420$	8.19615	0.399931
$421$	0.464102	0.0226189	0.0113095	−	0.999936i	$-0.496400\pi$
$421$	0.464102	0.0226189	0.0113095	+	0.999936i	$0.496400\pi$
$422$	3.60770	0.175620
$423$	−1.26795	−0.0616498
$424$	−3.00000	−0.145693
$425$	10.3923	0.504101
$426$	8.19615	0.397105
$427$	22.7321	1.10008
$428$	8.19615	0.396176
$429$	0	0
$430$	10.7321	0.517545
$431$	27.8038	1.33926	0.669632	−	0.742693i	$-0.266452\pi$
$431$	27.8038	1.33926	0.669632	+	0.742693i	$0.266452\pi$
$432$	−1.00000	−0.0481125
$433$	−33.7846	−1.62358	−0.811792	−	0.583946i	$-0.801508\pi$
$433$	−33.7846	−1.62358	−0.811792	+	0.583946i	$0.801508\pi$
$434$	−12.0000	−0.576018
$435$	−5.19615	−0.249136
$436$	16.3923	0.785049
$437$	2.78461	0.133206
$438$	−12.1244	−0.579324
$439$	16.5885	0.791724	0.395862	−	0.918310i	$-0.370446\pi$
$439$	16.5885	0.791724	0.395862	+	0.918310i	$0.370446\pi$
$440$	8.19615	0.390736
$441$	15.3923	0.732967
$442$	0	0
$443$	−4.39230	−0.208685	−0.104342	−	0.994541i	$-0.533274\pi$
$443$	−4.39230	−0.208685	−0.104342	+	0.994541i	$0.533274\pi$
$444$	−3.00000	−0.142374
$445$	−4.39230	−0.208215
$446$	18.9282	0.896276
$447$	18.1244	0.857253
$448$	4.73205	0.223568
$449$	33.4641	1.57927	0.789634	−	0.613578i	$-0.210270\pi$
$449$	33.4641	1.57927	0.789634	+	0.613578i	$0.210270\pi$
$450$	2.00000	0.0942809
$451$	−2.19615	−0.103413
$452$	11.1962	0.526623
$453$	−7.26795	−0.341478
$454$	9.80385	0.460117
$455$	0	0
$456$	1.26795	0.0593772
$457$	19.9808	0.934661	0.467330	−	0.884083i	$-0.345216\pi$
$457$	19.9808	0.934661	0.467330	+	0.884083i	$0.345216\pi$
$458$	−19.8564	−0.927829
$459$	5.19615	0.242536
$460$	−3.80385	−0.177355
$461$	−19.9808	−0.930597	−0.465298	−	0.885154i	$-0.654053\pi$
$461$	−19.9808	−0.930597	−0.465298	+	0.885154i	$0.654053\pi$
$462$	22.3923	1.04178
$463$	−26.1962	−1.21744	−0.608719	−	0.793386i	$-0.708316\pi$
$463$	−26.1962	−1.21744	−0.608719	+	0.793386i	$0.708316\pi$
$464$	−3.00000	−0.139272
$465$	4.39230	0.203688
$466$	18.0000	0.833834
$467$	36.5885	1.69311	0.846556	−	0.532300i	$-0.178672\pi$
$467$	36.5885	1.69311	0.846556	+	0.532300i	$0.178672\pi$
$468$	0	0
$469$	50.7846	2.34502
$470$	−2.19615	−0.101301
$471$	3.19615	0.147271
$472$	−13.8564	−0.637793
$473$	29.3205	1.34816
$474$	−12.3923	−0.569197
$475$	−2.53590	−0.116355
$476$	−24.5885	−1.12701
$477$	3.00000	0.137361
$478$	24.5885	1.12465
$479$	−35.3205	−1.61384	−0.806918	−	0.590664i	$-0.798866\pi$
$479$	−35.3205	−1.61384	−0.806918	+	0.590664i	$0.798866\pi$
$480$	−1.73205	−0.0790569
$481$	0	0
$482$	−0.803848	−0.0366143
$483$	−10.3923	−0.472866
$484$	11.3923	0.517832
$485$	−10.3923	−0.471890
$486$	1.00000	0.0453609
$487$	9.12436	0.413464	0.206732	−	0.978398i	$-0.433717\pi$
$487$	9.12436	0.413464	0.206732	+	0.978398i	$0.433717\pi$
$488$	−4.80385	−0.217460
$489$	−9.46410	−0.427981
$490$	26.6603	1.20439
$491$	0.588457	0.0265567	0.0132784	−	0.999912i	$-0.495773\pi$
$491$	0.588457	0.0265567	0.0132784	+	0.999912i	$0.495773\pi$
$492$	0.464102	0.0209233
$493$	15.5885	0.702069
$494$	0	0
$495$	−8.19615	−0.368390
$496$	2.53590	0.113865
$497$	38.7846	1.73973
$498$	−11.6603	−0.522508
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	12.1244	0.542218
$501$	2.53590	0.113296
$502$	4.39230	0.196038
$503$	−18.5885	−0.828818	−0.414409	−	0.910091i	$-0.636012\pi$
$503$	−18.5885	−0.828818	−0.414409	+	0.910091i	$0.636012\pi$
$504$	−4.73205	−0.210782
$505$	2.41154	0.107312
$506$	−10.3923	−0.461994
$507$	0	0
$508$	−4.00000	−0.177471
$509$	9.33975	0.413977	0.206988	−	0.978343i	$-0.433634\pi$
$509$	9.33975	0.413977	0.206988	+	0.978343i	$0.433634\pi$
$510$	9.00000	0.398527
$511$	−57.3731	−2.53804
$512$	−1.00000	−0.0441942
$513$	−1.26795	−0.0559813
$514$	−12.8038	−0.564754
$515$	7.26795	0.320264
$516$	−6.19615	−0.272770
$517$	−6.00000	−0.263880
$518$	−14.1962	−0.623743
$519$	−16.3923	−0.719542
$520$	0	0
$521$	−18.8038	−0.823812	−0.411906	−	0.911226i	$-0.635137\pi$
$521$	−18.8038	−0.823812	−0.411906	+	0.911226i	$0.635137\pi$
$522$	3.00000	0.131306
$523$	1.41154	0.0617225	0.0308612	−	0.999524i	$-0.490175\pi$
$523$	1.41154	0.0617225	0.0308612	+	0.999524i	$0.490175\pi$
$524$	16.3923	0.716101
$525$	9.46410	0.413047
$526$	2.19615	0.0957568
$527$	−13.1769	−0.573995
$528$	−4.73205	−0.205936
$529$	−18.1769	−0.790301
$530$	5.19615	0.225706
$531$	13.8564	0.601317
$532$	6.00000	0.260133
$533$	0	0
$534$	2.53590	0.109739
$535$	−14.1962	−0.613753
$536$	−10.7321	−0.463554
$537$	8.19615	0.353690
$538$	28.3923	1.22408
$539$	72.8372	3.13732
$540$	1.73205	0.0745356
$541$	16.8564	0.724714	0.362357	−	0.932039i	$-0.381972\pi$
$541$	16.8564	0.724714	0.362357	+	0.932039i	$0.381972\pi$
$542$	0	0
$543$	11.5885	0.497308
$544$	5.19615	0.222783
$545$	−28.3923	−1.21619
$546$	0	0
$547$	−6.19615	−0.264928	−0.132464	−	0.991188i	$-0.542289\pi$
$547$	−6.19615	−0.264928	−0.132464	+	0.991188i	$0.542289\pi$
$548$	−9.00000	−0.384461
$549$	4.80385	0.205023
$550$	9.46410	0.403551
$551$	−3.80385	−0.162049
$552$	2.19615	0.0934745
$553$	−58.6410	−2.49367
$554$	−15.1962	−0.645623
$555$	5.19615	0.220564
$556$	−4.00000	−0.169638
$557$	22.2679	0.943523	0.471762	−	0.881726i	$-0.343618\pi$
$557$	22.2679	0.943523	0.471762	+	0.881726i	$0.343618\pi$
$558$	−2.53590	−0.107353
$559$	0	0
$560$	−8.19615	−0.346351
$561$	24.5885	1.03813
$562$	−24.4641	−1.03196
$563$	8.78461	0.370227	0.185114	−	0.982717i	$-0.440735\pi$
$563$	8.78461	0.370227	0.185114	+	0.982717i	$0.440735\pi$
$564$	1.26795	0.0533903
$565$	−19.3923	−0.815840
$566$	30.1962	1.26924
$567$	4.73205	0.198727
$568$	−8.19615	−0.343903
$569$	−32.7846	−1.37440	−0.687201	−	0.726467i	$-0.741161\pi$
$569$	−32.7846	−1.37440	−0.687201	+	0.726467i	$0.741161\pi$
$570$	−2.19615	−0.0919867
$571$	−13.8038	−0.577673	−0.288837	−	0.957378i	$-0.593268\pi$
$571$	−13.8038	−0.577673	−0.288837	+	0.957378i	$0.593268\pi$
$572$	0	0
$573$	−20.7846	−0.868290
$574$	2.19615	0.0916656
$575$	−4.39230	−0.183172
$576$	1.00000	0.0416667
$577$	−16.2679	−0.677244	−0.338622	−	0.940923i	$-0.609961\pi$
$577$	−16.2679	−0.677244	−0.338622	+	0.940923i	$0.609961\pi$
$578$	−10.0000	−0.415945
$579$	12.8038	0.532110
$580$	5.19615	0.215758
$581$	−55.1769	−2.28912
$582$	6.00000	0.248708
$583$	14.1962	0.587945
$584$	12.1244	0.501709
$585$	0	0
$586$	14.6603	0.605610
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	−15.3923	−0.634768
$589$	3.21539	0.132488
$590$	24.0000	0.988064
$591$	−6.92820	−0.284988
$592$	3.00000	0.123299
$593$	−46.8564	−1.92416	−0.962081	−	0.272764i	$-0.912062\pi$
$593$	−46.8564	−1.92416	−0.962081	+	0.272764i	$0.912062\pi$
$594$	4.73205	0.194158
$595$	42.5885	1.74596
$596$	−18.1244	−0.742403
$597$	−8.58846	−0.351502
$598$	0	0
$599$	−4.39230	−0.179465	−0.0897324	−	0.995966i	$-0.528601\pi$
$599$	−4.39230	−0.179465	−0.0897324	+	0.995966i	$0.528601\pi$
$600$	−2.00000	−0.0816497
$601$	21.7846	0.888613	0.444306	−	0.895875i	$-0.353450\pi$
$601$	21.7846	0.888613	0.444306	+	0.895875i	$0.353450\pi$
$602$	−29.3205	−1.19501
$603$	10.7321	0.437043
$604$	7.26795	0.295729
$605$	−19.7321	−0.802222
$606$	−1.39230	−0.0565585
$607$	−48.7846	−1.98011	−0.990053	−	0.140694i	$-0.955067\pi$
$607$	−48.7846	−1.98011	−0.990053	+	0.140694i	$0.955067\pi$
$608$	−1.26795	−0.0514221
$609$	14.1962	0.575257
$610$	8.32051	0.336888
$611$	0	0
$612$	−5.19615	−0.210042
$613$	−40.8564	−1.65017	−0.825087	−	0.565005i	$-0.808874\pi$
$613$	−40.8564	−1.65017	−0.825087	+	0.565005i	$0.808874\pi$
$614$	−10.7321	−0.433110
$615$	−0.803848	−0.0324143
$616$	−22.3923	−0.902212
$617$	10.6077	0.427050	0.213525	−	0.976938i	$-0.431506\pi$
$617$	10.6077	0.427050	0.213525	+	0.976938i	$0.431506\pi$
$618$	−4.19615	−0.168794
$619$	−7.60770	−0.305779	−0.152890	−	0.988243i	$-0.548858\pi$
$619$	−7.60770	−0.305779	−0.152890	+	0.988243i	$0.548858\pi$
$620$	−4.39230	−0.176399
$621$	−2.19615	−0.0881286
$622$	−2.19615	−0.0880577
$623$	12.0000	0.480770
$624$	0	0
$625$	−11.0000	−0.440000
$626$	24.3923	0.974913
$627$	−6.00000	−0.239617
$628$	−3.19615	−0.127540
$629$	−15.5885	−0.621552
$630$	8.19615	0.326543
$631$	25.8564	1.02933	0.514664	−	0.857392i	$-0.327917\pi$
$631$	25.8564	1.02933	0.514664	+	0.857392i	$0.327917\pi$
$632$	12.3923	0.492939
$633$	3.60770	0.143393
$634$	−6.12436	−0.243229
$635$	6.92820	0.274937
$636$	−3.00000	−0.118958
$637$	0	0
$638$	14.1962	0.562031
$639$	8.19615	0.324235
$640$	1.73205	0.0684653
$641$	−30.8038	−1.21668	−0.608339	−	0.793677i	$-0.708164\pi$
$641$	−30.8038	−1.21668	−0.608339	+	0.793677i	$0.708164\pi$
$642$	8.19615	0.323476
$643$	−27.7128	−1.09289	−0.546443	−	0.837496i	$-0.684019\pi$
$643$	−27.7128	−1.09289	−0.546443	+	0.837496i	$0.684019\pi$
$644$	10.3923	0.409514
$645$	10.7321	0.422574
$646$	6.58846	0.259219
$647$	13.1769	0.518038	0.259019	−	0.965872i	$-0.416601\pi$
$647$	13.1769	0.518038	0.259019	+	0.965872i	$0.416601\pi$
$648$	−1.00000	−0.0392837
$649$	65.5692	2.57382
$650$	0	0
$651$	−12.0000	−0.470317
$652$	9.46410	0.370643
$653$	−49.1769	−1.92444	−0.962221	−	0.272271i	$-0.912225\pi$
$653$	−49.1769	−1.92444	−0.962221	+	0.272271i	$0.912225\pi$
$654$	16.3923	0.640990
$655$	−28.3923	−1.10938
$656$	−0.464102	−0.0181201
$657$	−12.1244	−0.473016
$658$	6.00000	0.233904
$659$	25.1769	0.980753	0.490377	−	0.871511i	$-0.336859\pi$
$659$	25.1769	0.980753	0.490377	+	0.871511i	$0.336859\pi$
$660$	8.19615	0.319035
$661$	9.00000	0.350059	0.175030	−	0.984563i	$-0.443998\pi$
$661$	9.00000	0.350059	0.175030	+	0.984563i	$0.443998\pi$
$662$	−12.0000	−0.466393
$663$	0	0
$664$	11.6603	0.452506
$665$	−10.3923	−0.402996
$666$	−3.00000	−0.116248
$667$	−6.58846	−0.255106
$668$	−2.53590	−0.0981169
$669$	18.9282	0.731807
$670$	18.5885	0.718135
$671$	22.7321	0.877561
$672$	4.73205	0.182543
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	31.0000	1.19408
$675$	2.00000	0.0769800
$676$	0	0
$677$	4.39230	0.168810	0.0844050	−	0.996432i	$-0.473101\pi$
$677$	4.39230	0.168810	0.0844050	+	0.996432i	$0.473101\pi$
$678$	11.1962	0.429986
$679$	28.3923	1.08960
$680$	−9.00000	−0.345134
$681$	9.80385	0.375684
$682$	−12.0000	−0.459504
$683$	27.7128	1.06040	0.530201	−	0.847872i	$-0.322117\pi$
$683$	27.7128	1.06040	0.530201	+	0.847872i	$0.322117\pi$
$684$	1.26795	0.0484812
$685$	15.5885	0.595604
$686$	−39.7128	−1.51624
$687$	−19.8564	−0.757569
$688$	6.19615	0.236226
$689$	0	0
$690$	−3.80385	−0.144810
$691$	−19.5167	−0.742449	−0.371224	−	0.928543i	$-0.621062\pi$
$691$	−19.5167	−0.742449	−0.371224	+	0.928543i	$0.621062\pi$
$692$	16.3923	0.623142
$693$	22.3923	0.850613
$694$	12.5885	0.477851
$695$	6.92820	0.262802
$696$	−3.00000	−0.113715
$697$	2.41154	0.0913437
$698$	−2.53590	−0.0959852
$699$	18.0000	0.680823
$700$	−9.46410	−0.357709
$701$	4.39230	0.165895	0.0829475	−	0.996554i	$-0.473567\pi$
$701$	4.39230	0.165895	0.0829475	+	0.996554i	$0.473567\pi$
$702$	0	0
$703$	3.80385	0.143465
$704$	4.73205	0.178346
$705$	−2.19615	−0.0827119
$706$	−5.78461	−0.217707
$707$	−6.58846	−0.247784
$708$	−13.8564	−0.520756
$709$	3.24871	0.122008	0.0610040	−	0.998138i	$-0.480570\pi$
$709$	3.24871	0.122008	0.0610040	+	0.998138i	$0.480570\pi$
$710$	14.1962	0.532772
$711$	−12.3923	−0.464748
$712$	−2.53590	−0.0950368
$713$	5.56922	0.208569
$714$	−24.5885	−0.920200
$715$	0	0
$716$	−8.19615	−0.306305
$717$	24.5885	0.918273
$718$	−22.0526	−0.822994
$719$	52.3923	1.95390	0.976952	−	0.213461i	$-0.0684736\pi$
$719$	52.3923	1.95390	0.976952	+	0.213461i	$0.0684736\pi$
$720$	−1.73205	−0.0645497
$721$	−19.8564	−0.739491
$722$	17.3923	0.647275
$723$	−0.803848	−0.0298954
$724$	−11.5885	−0.430682
$725$	6.00000	0.222834
$726$	11.3923	0.422808
$727$	−24.1962	−0.897386	−0.448693	−	0.893686i	$-0.648110\pi$
$727$	−24.1962	−0.897386	−0.448693	+	0.893686i	$0.648110\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−21.0000	−0.777245
$731$	−32.1962	−1.19082
$732$	−4.80385	−0.177555
$733$	−14.3205	−0.528940	−0.264470	−	0.964394i	$-0.585197\pi$
$733$	−14.3205	−0.528940	−0.264470	+	0.964394i	$0.585197\pi$
$734$	24.1962	0.893096
$735$	26.6603	0.983378
$736$	−2.19615	−0.0809513
$737$	50.7846	1.87068
$738$	0.464102	0.0170838
$739$	−18.9282	−0.696285	−0.348143	−	0.937442i	$-0.613188\pi$
$739$	−18.9282	−0.696285	−0.348143	+	0.937442i	$0.613188\pi$
$740$	−5.19615	−0.191014
$741$	0	0
$742$	−14.1962	−0.521157
$743$	4.39230	0.161138	0.0805690	−	0.996749i	$-0.474326\pi$
$743$	4.39230	0.161138	0.0805690	+	0.996749i	$0.474326\pi$
$744$	2.53590	0.0929705
$745$	31.3923	1.15013
$746$	−23.9808	−0.877998
$747$	−11.6603	−0.426626
$748$	−24.5885	−0.899043
$749$	38.7846	1.41716
$750$	12.1244	0.442719
$751$	−24.9808	−0.911561	−0.455780	−	0.890092i	$-0.650640\pi$
$751$	−24.9808	−0.911561	−0.455780	+	0.890092i	$0.650640\pi$
$752$	−1.26795	−0.0462373
$753$	4.39230	0.160064
$754$	0	0
$755$	−12.5885	−0.458141
$756$	−4.73205	−0.172103
$757$	18.7846	0.682738	0.341369	−	0.939929i	$-0.389109\pi$
$757$	18.7846	0.682738	0.341369	+	0.939929i	$0.389109\pi$
$758$	18.2487	0.662823
$759$	−10.3923	−0.377217
$760$	2.19615	0.0796628
$761$	−4.39230	−0.159221	−0.0796105	−	0.996826i	$-0.525368\pi$
$761$	−4.39230	−0.159221	−0.0796105	+	0.996826i	$0.525368\pi$
$762$	−4.00000	−0.144905
$763$	77.5692	2.80819
$764$	20.7846	0.751961
$765$	9.00000	0.325396
$766$	−11.3205	−0.409027
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	33.7128	1.21572	0.607858	−	0.794046i	$-0.292029\pi$
$769$	33.7128	1.21572	0.607858	+	0.794046i	$0.292029\pi$
$770$	38.7846	1.39770
$771$	−12.8038	−0.461119
$772$	−12.8038	−0.460821
$773$	−50.7846	−1.82660	−0.913298	−	0.407293i	$-0.866473\pi$
$773$	−50.7846	−1.82660	−0.913298	+	0.407293i	$0.866473\pi$
$774$	−6.19615	−0.222716
$775$	−5.07180	−0.182184
$776$	−6.00000	−0.215387
$777$	−14.1962	−0.509284
$778$	13.3923	0.480137
$779$	−0.588457	−0.0210837
$780$	0	0
$781$	38.7846	1.38782
$782$	11.4115	0.408076
$783$	3.00000	0.107211
$784$	15.3923	0.549725
$785$	5.53590	0.197585
$786$	16.3923	0.584694
$787$	−14.5359	−0.518149	−0.259074	−	0.965857i	$-0.583417\pi$
$787$	−14.5359	−0.518149	−0.259074	+	0.965857i	$0.583417\pi$
$788$	6.92820	0.246807
$789$	2.19615	0.0781851
$790$	−21.4641	−0.763658
$791$	52.9808	1.88378
$792$	−4.73205	−0.168146
$793$	0	0
$794$	16.3923	0.581741
$795$	5.19615	0.184289
$796$	8.58846	0.304410
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	6.00000	0.212398
$799$	6.58846	0.233083
$800$	2.00000	0.0707107
$801$	2.53590	0.0896016
$802$	−21.0000	−0.741536
$803$	−57.3731	−2.02465
$804$	−10.7321	−0.378490
$805$	−18.0000	−0.634417
$806$	0	0
$807$	28.3923	0.999456
$808$	1.39230	0.0489811
$809$	−47.1962	−1.65933	−0.829664	−	0.558263i	$-0.811468\pi$
$809$	−47.1962	−1.65933	−0.829664	+	0.558263i	$0.811468\pi$
$810$	1.73205	0.0608581
$811$	4.39230	0.154235	0.0771173	−	0.997022i	$-0.475428\pi$
$811$	4.39230	0.154235	0.0771173	+	0.997022i	$0.475428\pi$
$812$	−14.1962	−0.498187
$813$	0	0
$814$	−14.1962	−0.497575
$815$	−16.3923	−0.574197
$816$	5.19615	0.181902
$817$	7.85641	0.274861
$818$	3.33975	0.116771
$819$	0	0
$820$	0.803848	0.0280716
$821$	−40.6410	−1.41838	−0.709191	−	0.705017i	$-0.750939\pi$
$821$	−40.6410	−1.41838	−0.709191	+	0.705017i	$0.750939\pi$
$822$	−9.00000	−0.313911
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	4.19615	0.146180
$825$	9.46410	0.329498
$826$	−65.5692	−2.28144
$827$	−32.1051	−1.11640	−0.558202	−	0.829705i	$-0.688509\pi$
$827$	−32.1051	−1.11640	−0.558202	+	0.829705i	$0.688509\pi$
$828$	2.19615	0.0763216
$829$	−11.9808	−0.416109	−0.208055	−	0.978117i	$-0.566713\pi$
$829$	−11.9808	−0.416109	−0.208055	+	0.978117i	$0.566713\pi$
$830$	−20.1962	−0.701019
$831$	−15.1962	−0.527149
$832$	0	0
$833$	−79.9808	−2.77117
$834$	−4.00000	−0.138509
$835$	4.39230	0.152002
$836$	6.00000	0.207514
$837$	−2.53590	−0.0876535
$838$	−16.3923	−0.566263
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	−8.19615	−0.282794
$841$	−20.0000	−0.689655
$842$	−0.464102	−0.0159940
$843$	−24.4641	−0.842588
$844$	−3.60770	−0.124182
$845$	0	0
$846$	1.26795	0.0435930
$847$	53.9090	1.85233
$848$	3.00000	0.103020
$849$	30.1962	1.03633
$850$	−10.3923	−0.356453
$851$	6.58846	0.225849
$852$	−8.19615	−0.280796
$853$	9.00000	0.308154	0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000	0.308154	0.154077	+	0.988059i	$0.450760\pi$
$854$	−22.7321	−0.777875
$855$	−2.19615	−0.0751068
$856$	−8.19615	−0.280139
$857$	−54.3731	−1.85735	−0.928674	−	0.370896i	$-0.879051\pi$
$857$	−54.3731	−1.85735	−0.928674	+	0.370896i	$0.879051\pi$
$858$	0	0
$859$	10.5885	0.361273	0.180637	−	0.983550i	$-0.442184\pi$
$859$	10.5885	0.361273	0.180637	+	0.983550i	$0.442184\pi$
$860$	−10.7321	−0.365960
$861$	2.19615	0.0748447
$862$	−27.8038	−0.947003
$863$	4.48334	0.152615	0.0763073	−	0.997084i	$-0.475687\pi$
$863$	4.48334	0.152615	0.0763073	+	0.997084i	$0.475687\pi$
$864$	1.00000	0.0340207
$865$	−28.3923	−0.965367
$866$	33.7846	1.14805
$867$	−10.0000	−0.339618
$868$	12.0000	0.407307
$869$	−58.6410	−1.98926
$870$	5.19615	0.176166
$871$	0	0
$872$	−16.3923	−0.555113
$873$	6.00000	0.203069
$874$	−2.78461	−0.0941908
$875$	57.3731	1.93956
$876$	12.1244	0.409644
$877$	43.3923	1.46525	0.732627	−	0.680630i	$-0.238294\pi$
$877$	43.3923	1.46525	0.732627	+	0.680630i	$0.238294\pi$
$878$	−16.5885	−0.559833
$879$	14.6603	0.494478
$880$	−8.19615	−0.276292
$881$	37.9808	1.27960	0.639802	−	0.768540i	$-0.279016\pi$
$881$	37.9808	1.27960	0.639802	+	0.768540i	$0.279016\pi$
$882$	−15.3923	−0.518286
$883$	−24.7846	−0.834069	−0.417034	−	0.908891i	$-0.636930\pi$
$883$	−24.7846	−0.834069	−0.417034	+	0.908891i	$0.636930\pi$
$884$	0	0
$885$	24.0000	0.806751
$886$	4.39230	0.147562
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	3.00000	0.100673
$889$	−18.9282	−0.634832
$890$	4.39230	0.147230
$891$	4.73205	0.158530
$892$	−18.9282	−0.633763
$893$	−1.60770	−0.0537995
$894$	−18.1244	−0.606169
$895$	14.1962	0.474525
$896$	−4.73205	−0.158087
$897$	0	0
$898$	−33.4641	−1.11671
$899$	−7.60770	−0.253731
$900$	−2.00000	−0.0666667
$901$	−15.5885	−0.519327
$902$	2.19615	0.0731239
$903$	−29.3205	−0.975725
$904$	−11.1962	−0.372378
$905$	20.0718	0.667209
$906$	7.26795	0.241461
$907$	−41.1769	−1.36726	−0.683629	−	0.729830i	$-0.739599\pi$
$907$	−41.1769	−1.36726	−0.683629	+	0.729830i	$0.739599\pi$
$908$	−9.80385	−0.325352
$909$	−1.39230	−0.0461798
$910$	0	0
$911$	37.1769	1.23173	0.615863	−	0.787853i	$-0.288807\pi$
$911$	37.1769	1.23173	0.615863	+	0.787853i	$0.288807\pi$
$912$	−1.26795	−0.0419860
$913$	−55.1769	−1.82609
$914$	−19.9808	−0.660905
$915$	8.32051	0.275068
$916$	19.8564	0.656074
$917$	77.5692	2.56156
$918$	−5.19615	−0.171499
$919$	32.3923	1.06852	0.534262	−	0.845319i	$-0.320590\pi$
$919$	32.3923	1.06852	0.534262	+	0.845319i	$0.320590\pi$
$920$	3.80385	0.125409
$921$	−10.7321	−0.353633
$922$	19.9808	0.658031
$923$	0	0
$924$	−22.3923	−0.736653
$925$	−6.00000	−0.197279
$926$	26.1962	0.860859
$927$	−4.19615	−0.137820
$928$	3.00000	0.0984798
$929$	−34.6077	−1.13544	−0.567721	−	0.823221i	$-0.692175\pi$
$929$	−34.6077	−1.13544	−0.567721	+	0.823221i	$0.692175\pi$
$930$	−4.39230	−0.144029
$931$	19.5167	0.639633
$932$	−18.0000	−0.589610
$933$	−2.19615	−0.0718988
$934$	−36.5885	−1.19721
$935$	42.5885	1.39279
$936$	0	0
$937$	5.39230	0.176159	0.0880795	−	0.996113i	$-0.471927\pi$
$937$	5.39230	0.176159	0.0880795	+	0.996113i	$0.471927\pi$
$938$	−50.7846	−1.65818
$939$	24.3923	0.796013
$940$	2.19615	0.0716306
$941$	2.78461	0.0907757	0.0453878	−	0.998969i	$-0.485548\pi$
$941$	2.78461	0.0907757	0.0453878	+	0.998969i	$0.485548\pi$
$942$	−3.19615	−0.104136
$943$	−1.01924	−0.0331910
$944$	13.8564	0.450988
$945$	8.19615	0.266621
$946$	−29.3205	−0.953292
$947$	−42.9282	−1.39498	−0.697490	−	0.716595i	$-0.745700\pi$
$947$	−42.9282	−1.39498	−0.697490	+	0.716595i	$0.745700\pi$
$948$	12.3923	0.402483
$949$	0	0
$950$	2.53590	0.0822754
$951$	−6.12436	−0.198596
$952$	24.5885	0.796916
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	−3.00000	−0.0971286
$955$	−36.0000	−1.16493
$956$	−24.5885	−0.795248
$957$	14.1962	0.458896
$958$	35.3205	1.14115
$959$	−42.5885	−1.37525
$960$	1.73205	0.0559017
$961$	−24.5692	−0.792555
$962$	0	0
$963$	8.19615	0.264117
$964$	0.803848	0.0258902
$965$	22.1769	0.713900
$966$	10.3923	0.334367
$967$	−14.8756	−0.478368	−0.239184	−	0.970974i	$-0.576880\pi$
$967$	−14.8756	−0.478368	−0.239184	+	0.970974i	$0.576880\pi$
$968$	−11.3923	−0.366163
$969$	6.58846	0.211652
$970$	10.3923	0.333677
$971$	−13.1769	−0.422867	−0.211434	−	0.977392i	$-0.567813\pi$
$971$	−13.1769	−0.422867	−0.211434	+	0.977392i	$0.567813\pi$
$972$	−1.00000	−0.0320750
$973$	−18.9282	−0.606810
$974$	−9.12436	−0.292363
$975$	0	0
$976$	4.80385	0.153767
$977$	−16.8564	−0.539284	−0.269642	−	0.962961i	$-0.586905\pi$
$977$	−16.8564	−0.539284	−0.269642	+	0.962961i	$0.586905\pi$
$978$	9.46410	0.302629
$979$	12.0000	0.383522
$980$	−26.6603	−0.851631
$981$	16.3923	0.523366
$982$	−0.588457	−0.0187784
$983$	−20.7846	−0.662926	−0.331463	−	0.943468i	$-0.607542\pi$
$983$	−20.7846	−0.662926	−0.331463	+	0.943468i	$0.607542\pi$
$984$	−0.464102	−0.0147950
$985$	−12.0000	−0.382352
$986$	−15.5885	−0.496438
$987$	6.00000	0.190982
$988$	0	0
$989$	13.6077	0.432700
$990$	8.19615	0.260491
$991$	29.3731	0.933066	0.466533	−	0.884504i	$-0.345503\pi$
$991$	29.3731	0.933066	0.466533	+	0.884504i	$0.345503\pi$
$992$	−2.53590	−0.0805149
$993$	−12.0000	−0.380808
$994$	−38.7846	−1.23017
$995$	−14.8756	−0.471590
$996$	11.6603	0.369469
$997$	13.1962	0.417926	0.208963	−	0.977924i	$-0.432991\pi$
$997$	13.1962	0.417926	0.208963	+	0.977924i	$0.432991\pi$
$998$	0	0
$999$	−3.00000	−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.a.h.1.1		2
3.2	odd	2		3042.2.a.v.1.2		2
4.3	odd	2		8112.2.a.bq.1.1		2
13.2	odd	12		1014.2.i.f.823.1		4
13.3	even	3		1014.2.e.j.529.1		4
13.4	even	6		1014.2.e.h.991.2		4
13.5	odd	4		1014.2.b.d.337.4		4
13.6	odd	12		78.2.i.b.49.2	yes	4
13.7	odd	12		1014.2.i.f.361.1		4
13.8	odd	4		1014.2.b.d.337.1		4
13.9	even	3		1014.2.e.j.991.1		4
13.10	even	6		1014.2.e.h.529.2		4
13.11	odd	12		78.2.i.b.43.2	✓	4
13.12	even	2		1014.2.a.j.1.2		2
39.5	even	4		3042.2.b.l.1351.1		4
39.8	even	4		3042.2.b.l.1351.4		4
39.11	even	12		234.2.l.a.199.1		4
39.32	even	12		234.2.l.a.127.1		4
39.38	odd	2		3042.2.a.s.1.1		2
52.11	even	12		624.2.bv.d.433.2		4
52.19	even	12		624.2.bv.d.49.2		4
52.51	odd	2		8112.2.a.bx.1.2		2
65.19	odd	12		1950.2.bc.c.751.1		4
65.24	odd	12		1950.2.bc.c.901.1		4
65.32	even	12		1950.2.y.h.49.2		4
65.37	even	12		1950.2.y.a.199.1		4
65.58	even	12		1950.2.y.a.49.1		4
65.63	even	12		1950.2.y.h.199.2		4
156.11	odd	12		1872.2.by.k.433.2		4
156.71	odd	12		1872.2.by.k.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.2	✓	4	13.11	odd	12
78.2.i.b.49.2	yes	4	13.6	odd	12
234.2.l.a.127.1		4	39.32	even	12
234.2.l.a.199.1		4	39.11	even	12
624.2.bv.d.49.2		4	52.19	even	12
624.2.bv.d.433.2		4	52.11	even	12
1014.2.a.h.1.1		2	1.1	even	1	trivial
1014.2.a.j.1.2		2	13.12	even	2
1014.2.b.d.337.1		4	13.8	odd	4
1014.2.b.d.337.4		4	13.5	odd	4
1014.2.e.h.529.2		4	13.10	even	6
1014.2.e.h.991.2		4	13.4	even	6
1014.2.e.j.529.1		4	13.3	even	3
1014.2.e.j.991.1		4	13.9	even	3
1014.2.i.f.361.1		4	13.7	odd	12
1014.2.i.f.823.1		4	13.2	odd	12
1872.2.by.k.433.2		4	156.11	odd	12
1872.2.by.k.1297.2		4	156.71	odd	12
1950.2.y.a.49.1		4	65.58	even	12
1950.2.y.a.199.1		4	65.37	even	12
1950.2.y.h.49.2		4	65.32	even	12
1950.2.y.h.199.2		4	65.63	even	12
1950.2.bc.c.751.1		4	65.19	odd	12
1950.2.bc.c.901.1		4	65.24	odd	12
3042.2.a.s.1.1		2	39.38	odd	2
3042.2.a.v.1.2		2	3.2	odd	2
3042.2.b.l.1351.1		4	39.5	even	4
3042.2.b.l.1351.4		4	39.8	even	4
8112.2.a.bq.1.1		2	4.3	odd	2
8112.2.a.bx.1.2		2	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.73205 q^{5} +1.00000 q^{6} +4.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.73205 q^{10} +4.73205 q^{11} -1.00000 q^{12} -4.73205 q^{14} +1.73205 q^{15} +1.00000 q^{16} -5.19615 q^{17} -1.00000 q^{18} +1.26795 q^{19} -1.73205 q^{20} -4.73205 q^{21} -4.73205 q^{22} +2.19615 q^{23} +1.00000 q^{24} -2.00000 q^{25} -1.00000 q^{27} +4.73205 q^{28} -3.00000 q^{29} -1.73205 q^{30} +2.53590 q^{31} -1.00000 q^{32} -4.73205 q^{33} +5.19615 q^{34} -8.19615 q^{35} +1.00000 q^{36} +3.00000 q^{37} -1.26795 q^{38} +1.73205 q^{40} -0.464102 q^{41} +4.73205 q^{42} +6.19615 q^{43} +4.73205 q^{44} -1.73205 q^{45} -2.19615 q^{46} -1.26795 q^{47} -1.00000 q^{48} +15.3923 q^{49} +2.00000 q^{50} +5.19615 q^{51} +3.00000 q^{53} +1.00000 q^{54} -8.19615 q^{55} -4.73205 q^{56} -1.26795 q^{57} +3.00000 q^{58} +13.8564 q^{59} +1.73205 q^{60} +4.80385 q^{61} -2.53590 q^{62} +4.73205 q^{63} +1.00000 q^{64} +4.73205 q^{66} +10.7321 q^{67} -5.19615 q^{68} -2.19615 q^{69} +8.19615 q^{70} +8.19615 q^{71} -1.00000 q^{72} -12.1244 q^{73} -3.00000 q^{74} +2.00000 q^{75} +1.26795 q^{76} +22.3923 q^{77} -12.3923 q^{79} -1.73205 q^{80} +1.00000 q^{81} +0.464102 q^{82} -11.6603 q^{83} -4.73205 q^{84} +9.00000 q^{85} -6.19615 q^{86} +3.00000 q^{87} -4.73205 q^{88} +2.53590 q^{89} +1.73205 q^{90} +2.19615 q^{92} -2.53590 q^{93} +1.26795 q^{94} -2.19615 q^{95} +1.00000 q^{96} +6.00000 q^{97} -15.3923 q^{98} +4.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} - 6 q^{14} + 2 q^{16} - 2 q^{18} + 6 q^{19} - 6 q^{21} - 6 q^{22} - 6 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{27}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 - 6 * q^14 + 2 * q^16 - 2 * q^18 + 6 * q^19 - 6 * q^21 - 6 * q^22 - 6 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^27 + 6 * q^28 - 6 * q^29 + 12 * q^31 - 2 * q^32 - 6 * q^33 - 6 * q^35 + 2 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^41 + 6 * q^42 + 2 * q^43 + 6 * q^44 + 6 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^49 + 4 * q^50 + 6 * q^53 + 2 * q^54 - 6 * q^55 - 6 * q^56 - 6 * q^57 + 6 * q^58 + 20 * q^61 - 12 * q^62 + 6 * q^63 + 2 * q^64 + 6 * q^66 + 18 * q^67 + 6 * q^69 + 6 * q^70 + 6 * q^71 - 2 * q^72 - 6 * q^74 + 4 * q^75 + 6 * q^76 + 24 * q^77 - 4 * q^79 + 2 * q^81 - 6 * q^82 - 6 * q^83 - 6 * q^84 + 18 * q^85 - 2 * q^86 + 6 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^92 - 12 * q^93 + 6 * q^94 + 6 * q^95 + 2 * q^96 + 12 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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