LMFDB - Embedded newform 4018.2.a.bs.1.2

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 $ x^10 - 2x^9 - 17x^8 + 36x^7 + 75x^6 - 174x^5 - 69x^4 + 260x^3 - 104x^2 - 24*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.339114$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.13421 q^{3} +1.00000 q^{4} +0.374303 q^{5} +2.13421 q^{6} -1.00000 q^{8} +1.55487 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.13421 q^{3} +1.00000 q^{4} +0.374303 q^{5} +2.13421 q^{6} -1.00000 q^{8} +1.55487 q^{9} -0.374303 q^{10} -5.08327 q^{11} -2.13421 q^{12} -3.63190 q^{13} -0.798842 q^{15} +1.00000 q^{16} -2.81514 q^{17} -1.55487 q^{18} -0.177326 q^{19} +0.374303 q^{20} +5.08327 q^{22} -1.78135 q^{23} +2.13421 q^{24} -4.85990 q^{25} +3.63190 q^{26} +3.08421 q^{27} -8.08329 q^{29} +0.798842 q^{30} -4.16568 q^{31} -1.00000 q^{32} +10.8488 q^{33} +2.81514 q^{34} +1.55487 q^{36} -4.79627 q^{37} +0.177326 q^{38} +7.75125 q^{39} -0.374303 q^{40} +1.00000 q^{41} -10.9177 q^{43} -5.08327 q^{44} +0.581992 q^{45} +1.78135 q^{46} +6.35853 q^{47} -2.13421 q^{48} +4.85990 q^{50} +6.00812 q^{51} -3.63190 q^{52} +9.24909 q^{53} -3.08421 q^{54} -1.90268 q^{55} +0.378452 q^{57} +8.08329 q^{58} -2.81552 q^{59} -0.798842 q^{60} +6.00004 q^{61} +4.16568 q^{62} +1.00000 q^{64} -1.35943 q^{65} -10.8488 q^{66} +6.68899 q^{67} -2.81514 q^{68} +3.80178 q^{69} -1.98063 q^{71} -1.55487 q^{72} -14.1889 q^{73} +4.79627 q^{74} +10.3721 q^{75} -0.177326 q^{76} -7.75125 q^{78} +1.03682 q^{79} +0.374303 q^{80} -11.2470 q^{81} -1.00000 q^{82} +12.3563 q^{83} -1.05372 q^{85} +10.9177 q^{86} +17.2515 q^{87} +5.08327 q^{88} +11.2593 q^{89} -0.581992 q^{90} -1.78135 q^{92} +8.89046 q^{93} -6.35853 q^{94} -0.0663736 q^{95} +2.13421 q^{96} +0.0930429 q^{97} -7.90383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.13421	−1.23219	−0.616095	−	0.787672i	$-0.711286\pi$
$3$	−2.13421	−1.23219	−0.616095	+	0.787672i	$0.711286\pi$
$4$	1.00000	0.500000
$5$	0.374303	0.167393	0.0836966	−	0.996491i	$-0.473327\pi$
$5$	0.374303	0.167393	0.0836966	+	0.996491i	$0.473327\pi$
$6$	2.13421	0.871289
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.55487	0.518290
$10$	−0.374303	−0.118365
$11$	−5.08327	−1.53266	−0.766332	−	0.642444i	$-0.777920\pi$
$11$	−5.08327	−1.53266	−0.766332	+	0.642444i	$0.777920\pi$
$12$	−2.13421	−0.616095
$13$	−3.63190	−1.00731	−0.503654	−	0.863906i	$-0.668011\pi$
$13$	−3.63190	−1.00731	−0.503654	+	0.863906i	$0.668011\pi$
$14$	0	0
$15$	−0.798842	−0.206260
$16$	1.00000	0.250000
$17$	−2.81514	−0.682773	−0.341386	−	0.939923i	$-0.610896\pi$
$17$	−2.81514	−0.682773	−0.341386	+	0.939923i	$0.610896\pi$
$18$	−1.55487	−0.366487
$19$	−0.177326	−0.0406814	−0.0203407	−	0.999793i	$-0.506475\pi$
$19$	−0.177326	−0.0406814	−0.0203407	+	0.999793i	$0.506475\pi$
$20$	0.374303	0.0836966
$21$	0	0
$22$	5.08327	1.08376
$23$	−1.78135	−0.371437	−0.185718	−	0.982603i	$-0.559461\pi$
$23$	−1.78135	−0.371437	−0.185718	+	0.982603i	$0.559461\pi$
$24$	2.13421	0.435645
$25$	−4.85990	−0.971980
$26$	3.63190	0.712274
$27$	3.08421	0.593557
$28$	0	0
$29$	−8.08329	−1.50103	−0.750515	−	0.660854i	$-0.770194\pi$
$29$	−8.08329	−1.50103	−0.750515	+	0.660854i	$0.770194\pi$
$30$	0.798842	0.145848
$31$	−4.16568	−0.748179	−0.374089	−	0.927393i	$-0.622045\pi$
$31$	−4.16568	−0.748179	−0.374089	+	0.927393i	$0.622045\pi$
$32$	−1.00000	−0.176777
$33$	10.8488	1.88853
$34$	2.81514	0.482793
$35$	0	0
$36$	1.55487	0.259145
$37$	−4.79627	−0.788502	−0.394251	−	0.919003i	$-0.628996\pi$
$37$	−4.79627	−0.788502	−0.394251	+	0.919003i	$0.628996\pi$
$38$	0.177326	0.0287661
$39$	7.75125	1.24119
$40$	−0.374303	−0.0591824
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−10.9177	−1.66493	−0.832466	−	0.554076i	$-0.813072\pi$
$43$	−10.9177	−1.66493	−0.832466	+	0.554076i	$0.813072\pi$
$44$	−5.08327	−0.766332
$45$	0.581992	0.0867583
$46$	1.78135	0.262645
$47$	6.35853	0.927487	0.463744	−	0.885969i	$-0.346506\pi$
$47$	6.35853	0.927487	0.463744	+	0.885969i	$0.346506\pi$
$48$	−2.13421	−0.308047
$49$	0	0
$50$	4.85990	0.687293
$51$	6.00812	0.841305
$52$	−3.63190	−0.503654
$53$	9.24909	1.27046	0.635230	−	0.772323i	$-0.280905\pi$
$53$	9.24909	1.27046	0.635230	+	0.772323i	$0.280905\pi$
$54$	−3.08421	−0.419708
$55$	−1.90268	−0.256558
$56$	0	0
$57$	0.378452	0.0501272
$58$	8.08329	1.06139
$59$	−2.81552	−0.366550	−0.183275	−	0.983062i	$-0.558670\pi$
$59$	−2.81552	−0.366550	−0.183275	+	0.983062i	$0.558670\pi$
$60$	−0.798842	−0.103130
$61$	6.00004	0.768226	0.384113	−	0.923286i	$-0.374507\pi$
$61$	6.00004	0.768226	0.384113	+	0.923286i	$0.374507\pi$
$62$	4.16568	0.529042
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.35943	−0.168616
$66$	−10.8488	−1.33539
$67$	6.68899	0.817190	0.408595	−	0.912716i	$-0.366019\pi$
$67$	6.68899	0.817190	0.408595	+	0.912716i	$0.366019\pi$
$68$	−2.81514	−0.341386
$69$	3.80178	0.457680
$70$	0	0
$71$	−1.98063	−0.235057	−0.117529	−	0.993070i	$-0.537497\pi$
$71$	−1.98063	−0.235057	−0.117529	+	0.993070i	$0.537497\pi$
$72$	−1.55487	−0.183243
$73$	−14.1889	−1.66069	−0.830343	−	0.557252i	$-0.811856\pi$
$73$	−14.1889	−1.66069	−0.830343	+	0.557252i	$0.811856\pi$
$74$	4.79627	0.557555
$75$	10.3721	1.19766
$76$	−0.177326	−0.0203407
$77$	0	0
$78$	−7.75125	−0.877656
$79$	1.03682	0.116651	0.0583257	−	0.998298i	$-0.481424\pi$
$79$	1.03682	0.116651	0.0583257	+	0.998298i	$0.481424\pi$
$80$	0.374303	0.0418483
$81$	−11.2470	−1.24967
$82$	−1.00000	−0.110432
$83$	12.3563	1.35628	0.678138	−	0.734935i	$-0.262787\pi$
$83$	12.3563	1.35628	0.678138	+	0.734935i	$0.262787\pi$
$84$	0	0
$85$	−1.05372	−0.114291
$86$	10.9177	1.17728
$87$	17.2515	1.84955
$88$	5.08327	0.541879
$89$	11.2593	1.19348	0.596739	−	0.802435i	$-0.296463\pi$
$89$	11.2593	1.19348	0.596739	+	0.802435i	$0.296463\pi$
$90$	−0.581992	−0.0613474
$91$	0	0
$92$	−1.78135	−0.185718
$93$	8.89046	0.921898
$94$	−6.35853	−0.655833
$95$	−0.0663736	−0.00680979
$96$	2.13421	0.217822
$97$	0.0930429	0.00944708	0.00472354	−	0.999989i	$-0.498496\pi$
$97$	0.0930429	0.00944708	0.00472354	+	0.999989i	$0.498496\pi$
$98$	0	0
$99$	−7.90383	−0.794365
$100$	−4.85990	−0.485990
$101$	−10.0972	−1.00471	−0.502354	−	0.864662i	$-0.667532\pi$
$101$	−10.0972	−1.00471	−0.502354	+	0.864662i	$0.667532\pi$
$102$	−6.00812	−0.594893
$103$	−1.84300	−0.181596	−0.0907980	−	0.995869i	$-0.528942\pi$
$103$	−1.84300	−0.181596	−0.0907980	+	0.995869i	$0.528942\pi$
$104$	3.63190	0.356137
$105$	0	0
$106$	−9.24909	−0.898351
$107$	−4.65383	−0.449903	−0.224951	−	0.974370i	$-0.572222\pi$
$107$	−4.65383	−0.449903	−0.224951	+	0.974370i	$0.572222\pi$
$108$	3.08421	0.296779
$109$	−15.1609	−1.45215	−0.726075	−	0.687615i	$-0.758658\pi$
$109$	−15.1609	−1.45215	−0.726075	+	0.687615i	$0.758658\pi$
$110$	1.90268	0.181414
$111$	10.2363	0.971584
$112$	0	0
$113$	−14.5237	−1.36628	−0.683138	−	0.730289i	$-0.739385\pi$
$113$	−14.5237	−1.36628	−0.683138	+	0.730289i	$0.739385\pi$
$114$	−0.378452	−0.0354453
$115$	−0.666763	−0.0621760
$116$	−8.08329	−0.750515
$117$	−5.64713	−0.522078
$118$	2.81552	0.259190
$119$	0	0
$120$	0.798842	0.0729240
$121$	14.8397	1.34906
$122$	−6.00004	−0.543218
$123$	−2.13421	−0.192436
$124$	−4.16568	−0.374089
$125$	−3.69058	−0.330096
$126$	0	0
$127$	−3.75299	−0.333024	−0.166512	−	0.986039i	$-0.553250\pi$
$127$	−3.75299	−0.333024	−0.166512	+	0.986039i	$0.553250\pi$
$128$	−1.00000	−0.0883883
$129$	23.3007	2.05151
$130$	1.35943	0.119230
$131$	9.10789	0.795760	0.397880	−	0.917438i	$-0.369746\pi$
$131$	9.10789	0.795760	0.397880	+	0.917438i	$0.369746\pi$
$132$	10.8488	0.944266
$133$	0	0
$134$	−6.68899	−0.577841
$135$	1.15443	0.0993575
$136$	2.81514	0.241397
$137$	7.44115	0.635740	0.317870	−	0.948134i	$-0.397032\pi$
$137$	7.44115	0.635740	0.317870	+	0.948134i	$0.397032\pi$
$138$	−3.80178	−0.323629
$139$	−17.8543	−1.51438	−0.757192	−	0.653192i	$-0.773429\pi$
$139$	−17.8543	−1.51438	−0.757192	+	0.653192i	$0.773429\pi$
$140$	0	0
$141$	−13.5705	−1.14284
$142$	1.98063	0.166210
$143$	18.4619	1.54386
$144$	1.55487	0.129573
$145$	−3.02560	−0.251262
$146$	14.1889	1.17428
$147$	0	0
$148$	−4.79627	−0.394251
$149$	−9.41766	−0.771525	−0.385762	−	0.922598i	$-0.626062\pi$
$149$	−9.41766	−0.771525	−0.385762	+	0.922598i	$0.626062\pi$
$150$	−10.3721	−0.846875
$151$	−1.08702	−0.0884606	−0.0442303	−	0.999021i	$-0.514084\pi$
$151$	−1.08702	−0.0884606	−0.0442303	+	0.999021i	$0.514084\pi$
$152$	0.177326	0.0143830
$153$	−4.37719	−0.353875
$154$	0	0
$155$	−1.55923	−0.125240
$156$	7.75125	0.620597
$157$	−19.8515	−1.58432	−0.792160	−	0.610314i	$-0.791043\pi$
$157$	−19.8515	−1.58432	−0.792160	+	0.610314i	$0.791043\pi$
$158$	−1.03682	−0.0824850
$159$	−19.7395	−1.56545
$160$	−0.374303	−0.0295912
$161$	0	0
$162$	11.2470	0.883647
$163$	7.58582	0.594167	0.297083	−	0.954852i	$-0.403986\pi$
$163$	7.58582	0.594167	0.297083	+	0.954852i	$0.403986\pi$
$164$	1.00000	0.0780869
$165$	4.06073	0.316128
$166$	−12.3563	−0.959032
$167$	14.3440	1.10998	0.554988	−	0.831858i	$-0.312723\pi$
$167$	14.3440	1.10998	0.554988	+	0.831858i	$0.312723\pi$
$168$	0	0
$169$	0.190681	0.0146678
$170$	1.05372	0.0808163
$171$	−0.275719	−0.0210848
$172$	−10.9177	−0.832466
$173$	7.99472	0.607828	0.303914	−	0.952700i	$-0.401707\pi$
$173$	7.99472	0.607828	0.303914	+	0.952700i	$0.401707\pi$
$174$	−17.2515	−1.30783
$175$	0	0
$176$	−5.08327	−0.383166
$177$	6.00893	0.451658
$178$	−11.2593	−0.843917
$179$	−17.8928	−1.33737	−0.668685	−	0.743546i	$-0.733142\pi$
$179$	−17.8928	−1.33737	−0.668685	+	0.743546i	$0.733142\pi$
$180$	0.581992	0.0433791
$181$	−1.98748	−0.147728	−0.0738640	−	0.997268i	$-0.523533\pi$
$181$	−1.98748	−0.147728	−0.0738640	+	0.997268i	$0.523533\pi$
$182$	0	0
$183$	−12.8054	−0.946600
$184$	1.78135	0.131323
$185$	−1.79526	−0.131990
$186$	−8.89046	−0.651880
$187$	14.3101	1.04646
$188$	6.35853	0.463744
$189$	0	0
$190$	0.0663736	0.00481525
$191$	−20.3423	−1.47192	−0.735959	−	0.677026i	$-0.763269\pi$
$191$	−20.3423	−1.47192	−0.735959	+	0.677026i	$0.763269\pi$
$192$	−2.13421	−0.154024
$193$	−8.76247	−0.630736	−0.315368	−	0.948969i	$-0.602128\pi$
$193$	−8.76247	−0.630736	−0.315368	+	0.948969i	$0.602128\pi$
$194$	−0.0930429	−0.00668009
$195$	2.90131	0.207767
$196$	0	0
$197$	20.0531	1.42872	0.714362	−	0.699777i	$-0.246717\pi$
$197$	20.0531	1.42872	0.714362	+	0.699777i	$0.246717\pi$
$198$	7.90383	0.561701
$199$	20.3331	1.44138	0.720688	−	0.693260i	$-0.243826\pi$
$199$	20.3331	1.44138	0.720688	+	0.693260i	$0.243826\pi$
$200$	4.85990	0.343647
$201$	−14.2757	−1.00693
$202$	10.0972	0.710435
$203$	0	0
$204$	6.00812	0.420653
$205$	0.374303	0.0261424
$206$	1.84300	0.128408
$207$	−2.76977	−0.192512
$208$	−3.63190	−0.251827
$209$	0.901397	0.0623509
$210$	0	0
$211$	−8.78212	−0.604586	−0.302293	−	0.953215i	$-0.597752\pi$
$211$	−8.78212	−0.604586	−0.302293	+	0.953215i	$0.597752\pi$
$212$	9.24909	0.635230
$213$	4.22708	0.289635
$214$	4.65383	0.318129
$215$	−4.08652	−0.278698
$216$	−3.08421	−0.209854
$217$	0	0
$218$	15.1609	1.02683
$219$	30.2822	2.04628
$220$	−1.90268	−0.128279
$221$	10.2243	0.687762
$222$	−10.2363	−0.687014
$223$	3.62979	0.243069	0.121534	−	0.992587i	$-0.461219\pi$
$223$	3.62979	0.243069	0.121534	+	0.992587i	$0.461219\pi$
$224$	0	0
$225$	−7.55651	−0.503768
$226$	14.5237	0.966103
$227$	17.3520	1.15169	0.575846	−	0.817558i	$-0.304673\pi$
$227$	17.3520	1.15169	0.575846	+	0.817558i	$0.304673\pi$
$228$	0.378452	0.0250636
$229$	−17.4160	−1.15088	−0.575441	−	0.817843i	$-0.695170\pi$
$229$	−17.4160	−1.15088	−0.575441	+	0.817843i	$0.695170\pi$
$230$	0.666763	0.0439650
$231$	0	0
$232$	8.08329	0.530694
$233$	17.7069	1.16002	0.580009	−	0.814610i	$-0.303049\pi$
$233$	17.7069	1.16002	0.580009	+	0.814610i	$0.303049\pi$
$234$	5.64713	0.369165
$235$	2.38002	0.155255
$236$	−2.81552	−0.183275
$237$	−2.21280	−0.143737
$238$	0	0
$239$	24.0403	1.55503	0.777517	−	0.628861i	$-0.216479\pi$
$239$	24.0403	1.55503	0.777517	+	0.628861i	$0.216479\pi$
$240$	−0.798842	−0.0515650
$241$	25.8979	1.66823	0.834114	−	0.551593i	$-0.185980\pi$
$241$	25.8979	1.66823	0.834114	+	0.551593i	$0.185980\pi$
$242$	−14.8397	−0.953930
$243$	14.7508	0.946267
$244$	6.00004	0.384113
$245$	0	0
$246$	2.13421	0.136073
$247$	0.644030	0.0409787
$248$	4.16568	0.264521
$249$	−26.3709	−1.67119
$250$	3.69058	0.233413
$251$	9.64929	0.609058	0.304529	−	0.952503i	$-0.401501\pi$
$251$	9.64929	0.609058	0.304529	+	0.952503i	$0.401501\pi$
$252$	0	0
$253$	9.05508	0.569288
$254$	3.75299	0.235484
$255$	2.24885	0.140829
$256$	1.00000	0.0625000
$257$	2.74764	0.171393	0.0856964	−	0.996321i	$-0.472688\pi$
$257$	2.74764	0.171393	0.0856964	+	0.996321i	$0.472688\pi$
$258$	−23.3007	−1.45064
$259$	0	0
$260$	−1.35943	−0.0843082
$261$	−12.5685	−0.777969
$262$	−9.10789	−0.562687
$263$	9.96418	0.614418	0.307209	−	0.951642i	$-0.400605\pi$
$263$	9.96418	0.614418	0.307209	+	0.951642i	$0.400605\pi$
$264$	−10.8488	−0.667697
$265$	3.46196	0.212666
$266$	0	0
$267$	−24.0297	−1.47059
$268$	6.68899	0.408595
$269$	−11.5980	−0.707144	−0.353572	−	0.935407i	$-0.615033\pi$
$269$	−11.5980	−0.707144	−0.353572	+	0.935407i	$0.615033\pi$
$270$	−1.15443	−0.0702563
$271$	20.6172	1.25240	0.626202	−	0.779661i	$-0.284608\pi$
$271$	20.6172	1.25240	0.626202	+	0.779661i	$0.284608\pi$
$272$	−2.81514	−0.170693
$273$	0	0
$274$	−7.44115	−0.449536
$275$	24.7042	1.48972
$276$	3.80178	0.228840
$277$	27.5990	1.65827	0.829133	−	0.559052i	$-0.188835\pi$
$277$	27.5990	1.65827	0.829133	+	0.559052i	$0.188835\pi$
$278$	17.8543	1.07083
$279$	−6.47710	−0.387774
$280$	0	0
$281$	2.12943	0.127031	0.0635156	−	0.997981i	$-0.479769\pi$
$281$	2.12943	0.127031	0.0635156	+	0.997981i	$0.479769\pi$
$282$	13.5705	0.808110
$283$	−11.7562	−0.698833	−0.349417	−	0.936967i	$-0.613620\pi$
$283$	−11.7562	−0.698833	−0.349417	+	0.936967i	$0.613620\pi$
$284$	−1.98063	−0.117529
$285$	0.141656	0.00839095
$286$	−18.4619	−1.09168
$287$	0	0
$288$	−1.55487	−0.0916217
$289$	−9.07497	−0.533821
$290$	3.02560	0.177669
$291$	−0.198574	−0.0116406
$292$	−14.1889	−0.830343
$293$	−8.81871	−0.515194	−0.257597	−	0.966252i	$-0.582931\pi$
$293$	−8.81871	−0.515194	−0.257597	+	0.966252i	$0.582931\pi$
$294$	0	0
$295$	−1.05386	−0.0613579
$296$	4.79627	0.278778
$297$	−15.6779	−0.909724
$298$	9.41766	0.545550
$299$	6.46967	0.374151
$300$	10.3721	0.598831
$301$	0	0
$302$	1.08702	0.0625511
$303$	21.5495	1.23799
$304$	−0.177326	−0.0101703
$305$	2.24583	0.128596
$306$	4.37719	0.250227
$307$	11.5640	0.659992	0.329996	−	0.943982i	$-0.392953\pi$
$307$	11.5640	0.659992	0.329996	+	0.943982i	$0.392953\pi$
$308$	0	0
$309$	3.93335	0.223761
$310$	1.55923	0.0885581
$311$	16.8358	0.954671	0.477336	−	0.878721i	$-0.341603\pi$
$311$	16.8358	0.954671	0.477336	+	0.878721i	$0.341603\pi$
$312$	−7.75125	−0.438828
$313$	7.27885	0.411425	0.205713	−	0.978612i	$-0.434049\pi$
$313$	7.27885	0.411425	0.205713	+	0.978612i	$0.434049\pi$
$314$	19.8515	1.12028
$315$	0	0
$316$	1.03682	0.0583257
$317$	−19.4460	−1.09220	−0.546098	−	0.837722i	$-0.683887\pi$
$317$	−19.4460	−1.09220	−0.546098	+	0.837722i	$0.683887\pi$
$318$	19.7395	1.10694
$319$	41.0896	2.30057
$320$	0.374303	0.0209241
$321$	9.93228	0.554366
$322$	0	0
$323$	0.499199	0.0277761
$324$	−11.2470	−0.624833
$325$	17.6507	0.979082
$326$	−7.58582	−0.420139
$327$	32.3566	1.78932
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−4.06073	−0.223536
$331$	13.2662	0.729174	0.364587	−	0.931169i	$-0.381210\pi$
$331$	13.2662	0.729174	0.364587	+	0.931169i	$0.381210\pi$
$332$	12.3563	0.678138
$333$	−7.45759	−0.408673
$334$	−14.3440	−0.784871
$335$	2.50371	0.136792
$336$	0	0
$337$	28.4678	1.55074	0.775371	−	0.631506i	$-0.217563\pi$
$337$	28.4678	1.55074	0.775371	+	0.631506i	$0.217563\pi$
$338$	−0.190681	−0.0103717
$339$	30.9967	1.68351
$340$	−1.05372	−0.0571457
$341$	21.1753	1.14671
$342$	0.275719	0.0149092
$343$	0	0
$344$	10.9177	0.588642
$345$	1.42302	0.0766126
$346$	−7.99472	−0.429799
$347$	12.9353	0.694404	0.347202	−	0.937790i	$-0.387132\pi$
$347$	12.9353	0.694404	0.347202	+	0.937790i	$0.387132\pi$
$348$	17.2515	0.924776
$349$	9.54651	0.511013	0.255506	−	0.966807i	$-0.417758\pi$
$349$	9.54651	0.511013	0.255506	+	0.966807i	$0.417758\pi$
$350$	0	0
$351$	−11.2016	−0.597895
$352$	5.08327	0.270939
$353$	−11.8173	−0.628973	−0.314487	−	0.949262i	$-0.601832\pi$
$353$	−11.8173	−0.628973	−0.314487	+	0.949262i	$0.601832\pi$
$354$	−6.00893	−0.319371
$355$	−0.741353	−0.0393470
$356$	11.2593	0.596739
$357$	0	0
$358$	17.8928	0.945663
$359$	22.4749	1.18618	0.593090	−	0.805136i	$-0.297908\pi$
$359$	22.4749	1.18618	0.593090	+	0.805136i	$0.297908\pi$
$360$	−0.581992	−0.0306737
$361$	−18.9686	−0.998345
$362$	1.98748	0.104459
$363$	−31.6710	−1.66230
$364$	0	0
$365$	−5.31095	−0.277988
$366$	12.8054	0.669347
$367$	−0.540072	−0.0281915	−0.0140958	−	0.999901i	$-0.504487\pi$
$367$	−0.540072	−0.0281915	−0.0140958	+	0.999901i	$0.504487\pi$
$368$	−1.78135	−0.0928592
$369$	1.55487	0.0809434
$370$	1.79526	0.0933310
$371$	0	0
$372$	8.89046	0.460949
$373$	−24.9174	−1.29018	−0.645088	−	0.764108i	$-0.723179\pi$
$373$	−24.9174	−1.29018	−0.645088	+	0.764108i	$0.723179\pi$
$374$	−14.3101	−0.739960
$375$	7.87650	0.406741
$376$	−6.35853	−0.327916
$377$	29.3577	1.51200
$378$	0	0
$379$	17.8728	0.918066	0.459033	−	0.888419i	$-0.348196\pi$
$379$	17.8728	0.918066	0.459033	+	0.888419i	$0.348196\pi$
$380$	−0.0663736	−0.00340489
$381$	8.00969	0.410349
$382$	20.3423	1.04080
$383$	−15.2602	−0.779758	−0.389879	−	0.920866i	$-0.627483\pi$
$383$	−15.2602	−0.779758	−0.389879	+	0.920866i	$0.627483\pi$
$384$	2.13421	0.108911
$385$	0	0
$386$	8.76247	0.445998
$387$	−16.9756	−0.862918
$388$	0.0930429	0.00472354
$389$	−5.14095	−0.260656	−0.130328	−	0.991471i	$-0.541603\pi$
$389$	−5.14095	−0.260656	−0.130328	+	0.991471i	$0.541603\pi$
$390$	−2.90131	−0.146914
$391$	5.01475	0.253607
$392$	0	0
$393$	−19.4382	−0.980526
$394$	−20.0531	−1.01026
$395$	0.388084	0.0195266
$396$	−7.90383	−0.397183
$397$	1.26039	0.0632569	0.0316285	−	0.999500i	$-0.489931\pi$
$397$	1.26039	0.0632569	0.0316285	+	0.999500i	$0.489931\pi$
$398$	−20.3331	−1.01921
$399$	0	0
$400$	−4.85990	−0.242995
$401$	−23.0667	−1.15190	−0.575949	−	0.817486i	$-0.695367\pi$
$401$	−23.0667	−1.15190	−0.575949	+	0.817486i	$0.695367\pi$
$402$	14.2757	0.712009
$403$	15.1293	0.753646
$404$	−10.0972	−0.502354
$405$	−4.20978	−0.209185
$406$	0	0
$407$	24.3808	1.20851
$408$	−6.00812	−0.297446
$409$	−40.0015	−1.97795	−0.988974	−	0.148091i	$-0.952687\pi$
$409$	−40.0015	−1.97795	−0.988974	+	0.148091i	$0.952687\pi$
$410$	−0.374303	−0.0184855
$411$	−15.8810	−0.783352
$412$	−1.84300	−0.0907980
$413$	0	0
$414$	2.76977	0.136127
$415$	4.62498	0.227031
$416$	3.63190	0.178068
$417$	38.1050	1.86601
$418$	−0.901397	−0.0440888
$419$	−6.52817	−0.318922	−0.159461	−	0.987204i	$-0.550976\pi$
$419$	−6.52817	−0.318922	−0.159461	+	0.987204i	$0.550976\pi$
$420$	0	0
$421$	−11.3755	−0.554408	−0.277204	−	0.960811i	$-0.589408\pi$
$421$	−11.3755	−0.554408	−0.277204	+	0.960811i	$0.589408\pi$
$422$	8.78212	0.427507
$423$	9.88670	0.480708
$424$	−9.24909	−0.449176
$425$	13.6813	0.663641
$426$	−4.22708	−0.204803
$427$	0	0
$428$	−4.65383	−0.224951
$429$	−39.4017	−1.90233
$430$	4.08652	0.197069
$431$	0.747652	0.0360131	0.0180066	−	0.999838i	$-0.494268\pi$
$431$	0.747652	0.0360131	0.0180066	+	0.999838i	$0.494268\pi$
$432$	3.08421	0.148389
$433$	15.4836	0.744093	0.372047	−	0.928214i	$-0.378656\pi$
$433$	15.4836	0.744093	0.372047	+	0.928214i	$0.378656\pi$
$434$	0	0
$435$	6.45727	0.309602
$436$	−15.1609	−0.726075
$437$	0.315879	0.0151106
$438$	−30.2822	−1.44694
$439$	12.6840	0.605375	0.302688	−	0.953090i	$-0.402116\pi$
$439$	12.6840	0.605375	0.302688	+	0.953090i	$0.402116\pi$
$440$	1.90268	0.0907068
$441$	0	0
$442$	−10.2243	−0.486321
$443$	19.9135	0.946119	0.473060	−	0.881030i	$-0.343150\pi$
$443$	19.9135	0.946119	0.473060	+	0.881030i	$0.343150\pi$
$444$	10.2363	0.485792
$445$	4.21437	0.199780
$446$	−3.62979	−0.171876
$447$	20.0993	0.950664
$448$	0	0
$449$	−14.9211	−0.704171	−0.352085	−	0.935968i	$-0.614527\pi$
$449$	−14.9211	−0.704171	−0.352085	+	0.935968i	$0.614527\pi$
$450$	7.55651	0.356218
$451$	−5.08327	−0.239362
$452$	−14.5237	−0.683138
$453$	2.31994	0.109000
$454$	−17.3520	−0.814370
$455$	0	0
$456$	−0.378452	−0.0177226
$457$	7.83949	0.366716	0.183358	−	0.983046i	$-0.441303\pi$
$457$	7.83949	0.366716	0.183358	+	0.983046i	$0.441303\pi$
$458$	17.4160	0.813797
$459$	−8.68251	−0.405265
$460$	−0.666763	−0.0310880
$461$	−6.74241	−0.314025	−0.157013	−	0.987597i	$-0.550186\pi$
$461$	−6.74241	−0.314025	−0.157013	+	0.987597i	$0.550186\pi$
$462$	0	0
$463$	5.34792	0.248539	0.124270	−	0.992249i	$-0.460341\pi$
$463$	5.34792	0.248539	0.124270	+	0.992249i	$0.460341\pi$
$464$	−8.08329	−0.375257
$465$	3.32772	0.154319
$466$	−17.7069	−0.820257
$467$	−36.9935	−1.71186	−0.855928	−	0.517095i	$-0.827013\pi$
$467$	−36.9935	−1.71186	−0.855928	+	0.517095i	$0.827013\pi$
$468$	−5.64713	−0.261039
$469$	0	0
$470$	−2.38002	−0.109782
$471$	42.3673	1.95218
$472$	2.81552	0.129595
$473$	55.4976	2.55178
$474$	2.21280	0.101637
$475$	0.861787	0.0395415
$476$	0	0
$477$	14.3811	0.658467
$478$	−24.0403	−1.09958
$479$	4.31717	0.197256	0.0986282	−	0.995124i	$-0.468555\pi$
$479$	4.31717	0.197256	0.0986282	+	0.995124i	$0.468555\pi$
$480$	0.798842	0.0364620
$481$	17.4196	0.794264
$482$	−25.8979	−1.17961
$483$	0	0
$484$	14.8397	0.674530
$485$	0.0348262	0.00158138
$486$	−14.7508	−0.669112
$487$	−11.4002	−0.516591	−0.258296	−	0.966066i	$-0.583161\pi$
$487$	−11.4002	−0.516591	−0.258296	+	0.966066i	$0.583161\pi$
$488$	−6.00004	−0.271609
$489$	−16.1898	−0.732126
$490$	0	0
$491$	−20.1275	−0.908343	−0.454171	−	0.890914i	$-0.650065\pi$
$491$	−20.1275	−0.908343	−0.454171	+	0.890914i	$0.650065\pi$
$492$	−2.13421	−0.0962178
$493$	22.7556	1.02486
$494$	−0.644030	−0.0289763
$495$	−2.95843	−0.132971
$496$	−4.16568	−0.187045
$497$	0	0
$498$	26.3709	1.18171
$499$	−4.11463	−0.184196	−0.0920981	−	0.995750i	$-0.529357\pi$
$499$	−4.11463	−0.184196	−0.0920981	+	0.995750i	$0.529357\pi$
$500$	−3.69058	−0.165048
$501$	−30.6133	−1.36770
$502$	−9.64929	−0.430669
$503$	34.8524	1.55399	0.776996	−	0.629506i	$-0.216743\pi$
$503$	34.8524	1.55399	0.776996	+	0.629506i	$0.216743\pi$
$504$	0	0
$505$	−3.77940	−0.168181
$506$	−9.05508	−0.402547
$507$	−0.406955	−0.0180735
$508$	−3.75299	−0.166512
$509$	−35.1520	−1.55809	−0.779043	−	0.626971i	$-0.784295\pi$
$509$	−35.1520	−1.55809	−0.779043	+	0.626971i	$0.784295\pi$
$510$	−2.24885	−0.0995810
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−0.546912	−0.0241467
$514$	−2.74764	−0.121193
$515$	−0.689839	−0.0303979
$516$	23.3007	1.02576
$517$	−32.3222	−1.42153
$518$	0	0
$519$	−17.0625	−0.748959
$520$	1.35943	0.0596149
$521$	13.2163	0.579017	0.289509	−	0.957175i	$-0.406508\pi$
$521$	13.2163	0.579017	0.289509	+	0.957175i	$0.406508\pi$
$522$	12.5685	0.550107
$523$	−37.6543	−1.64651	−0.823254	−	0.567673i	$-0.807844\pi$
$523$	−37.6543	−1.64651	−0.823254	+	0.567673i	$0.807844\pi$
$524$	9.10789	0.397880
$525$	0	0
$526$	−9.96418	−0.434459
$527$	11.7270	0.510836
$528$	10.8488	0.472133
$529$	−19.8268	−0.862035
$530$	−3.46196	−0.150378
$531$	−4.37777	−0.189979
$532$	0	0
$533$	−3.63190	−0.157315
$534$	24.0297	1.03987
$535$	−1.74194	−0.0753107
$536$	−6.68899	−0.288920
$537$	38.1870	1.64789
$538$	11.5980	0.500026
$539$	0	0
$540$	1.15443	0.0496787
$541$	10.4081	0.447480	0.223740	−	0.974649i	$-0.428173\pi$
$541$	10.4081	0.447480	0.223740	+	0.974649i	$0.428173\pi$
$542$	−20.6172	−0.885584
$543$	4.24170	0.182029
$544$	2.81514	0.120698
$545$	−5.67476	−0.243080
$546$	0	0
$547$	7.05775	0.301768	0.150884	−	0.988552i	$-0.451788\pi$
$547$	7.05775	0.301768	0.150884	+	0.988552i	$0.451788\pi$
$548$	7.44115	0.317870
$549$	9.32929	0.398164
$550$	−24.7042	−1.05339
$551$	1.43338	0.0610640
$552$	−3.80178	−0.161814
$553$	0	0
$554$	−27.5990	−1.17257
$555$	3.83146	0.162637
$556$	−17.8543	−0.757192
$557$	10.6316	0.450475	0.225237	−	0.974304i	$-0.427684\pi$
$557$	10.6316	0.450475	0.225237	+	0.974304i	$0.427684\pi$
$558$	6.47710	0.274198
$559$	39.6519	1.67710
$560$	0	0
$561$	−30.5409	−1.28944
$562$	−2.12943	−0.0898247
$563$	18.4835	0.778986	0.389493	−	0.921030i	$-0.372650\pi$
$563$	18.4835	0.778986	0.389493	+	0.921030i	$0.372650\pi$
$564$	−13.5705	−0.571420
$565$	−5.43626	−0.228705
$566$	11.7562	0.494150
$567$	0	0
$568$	1.98063	0.0831052
$569$	−39.0303	−1.63624	−0.818119	−	0.575050i	$-0.804983\pi$
$569$	−39.0303	−1.63624	−0.818119	+	0.575050i	$0.804983\pi$
$570$	−0.141656	−0.00593330
$571$	−1.66662	−0.0697458	−0.0348729	−	0.999392i	$-0.511103\pi$
$571$	−1.66662	−0.0697458	−0.0348729	+	0.999392i	$0.511103\pi$
$572$	18.4619	0.771932
$573$	43.4149	1.81368
$574$	0	0
$575$	8.65717	0.361029
$576$	1.55487	0.0647863
$577$	−7.48983	−0.311806	−0.155903	−	0.987772i	$-0.549829\pi$
$577$	−7.48983	−0.311806	−0.155903	+	0.987772i	$0.549829\pi$
$578$	9.07497	0.377469
$579$	18.7010	0.777186
$580$	−3.02560	−0.125631
$581$	0	0
$582$	0.198574	0.00823114
$583$	−47.0156	−1.94719
$584$	14.1889	0.587141
$585$	−2.11374	−0.0873922
$586$	8.81871	0.364297
$587$	−14.6711	−0.605540	−0.302770	−	0.953064i	$-0.597911\pi$
$587$	−14.6711	−0.605540	−0.302770	+	0.953064i	$0.597911\pi$
$588$	0	0
$589$	0.738685	0.0304370
$590$	1.05386	0.0433866
$591$	−42.7976	−1.76046
$592$	−4.79627	−0.197126
$593$	19.2601	0.790919	0.395460	−	0.918483i	$-0.370585\pi$
$593$	19.2601	0.790919	0.395460	+	0.918483i	$0.370585\pi$
$594$	15.6779	0.643272
$595$	0	0
$596$	−9.41766	−0.385762
$597$	−43.3952	−1.77605
$598$	−6.46967	−0.264565
$599$	−13.8526	−0.566003	−0.283001	−	0.959120i	$-0.591330\pi$
$599$	−13.8526	−0.566003	−0.283001	+	0.959120i	$0.591330\pi$
$600$	−10.3721	−0.423438
$601$	19.5365	0.796911	0.398455	−	0.917188i	$-0.369546\pi$
$601$	19.5365	0.796911	0.398455	+	0.917188i	$0.369546\pi$
$602$	0	0
$603$	10.4005	0.423542
$604$	−1.08702	−0.0442303
$605$	5.55452	0.225824
$606$	−21.5495	−0.875391
$607$	−15.5983	−0.633116	−0.316558	−	0.948573i	$-0.602527\pi$
$607$	−15.5983	−0.633116	−0.316558	+	0.948573i	$0.602527\pi$
$608$	0.177326	0.00719152
$609$	0	0
$610$	−2.24583	−0.0909310
$611$	−23.0935	−0.934265
$612$	−4.37719	−0.176937
$613$	−6.20922	−0.250788	−0.125394	−	0.992107i	$-0.540019\pi$
$613$	−6.20922	−0.250788	−0.125394	+	0.992107i	$0.540019\pi$
$614$	−11.5640	−0.466685
$615$	−0.798842	−0.0322124
$616$	0	0
$617$	30.2370	1.21730	0.608648	−	0.793440i	$-0.291712\pi$
$617$	30.2370	1.21730	0.608648	+	0.793440i	$0.291712\pi$
$618$	−3.93335	−0.158223
$619$	−42.0636	−1.69068	−0.845339	−	0.534230i	$-0.820602\pi$
$619$	−42.0636	−1.69068	−0.845339	+	0.534230i	$0.820602\pi$
$620$	−1.55923	−0.0626200
$621$	−5.49406	−0.220469
$622$	−16.8358	−0.675054
$623$	0	0
$624$	7.75125	0.310298
$625$	22.9181	0.916724
$626$	−7.27885	−0.290921
$627$	−1.92377	−0.0768282
$628$	−19.8515	−0.792160
$629$	13.5022	0.538368
$630$	0	0
$631$	39.5757	1.57548	0.787741	−	0.616007i	$-0.211251\pi$
$631$	39.5757	1.57548	0.787741	+	0.616007i	$0.211251\pi$
$632$	−1.03682	−0.0412425
$633$	18.7429	0.744965
$634$	19.4460	0.772299
$635$	−1.40476	−0.0557460
$636$	−19.7395	−0.782724
$637$	0	0
$638$	−41.0896	−1.62675
$639$	−3.07962	−0.121828
$640$	−0.374303	−0.0147956
$641$	32.3293	1.27693	0.638466	−	0.769650i	$-0.279569\pi$
$641$	32.3293	1.27693	0.638466	+	0.769650i	$0.279569\pi$
$642$	−9.93228	−0.391996
$643$	33.5734	1.32401	0.662003	−	0.749502i	$-0.269707\pi$
$643$	33.5734	1.32401	0.662003	+	0.749502i	$0.269707\pi$
$644$	0	0
$645$	8.72151	0.343409
$646$	−0.499199	−0.0196407
$647$	19.3437	0.760480	0.380240	−	0.924888i	$-0.375841\pi$
$647$	19.3437	0.760480	0.380240	+	0.924888i	$0.375841\pi$
$648$	11.2470	0.441823
$649$	14.3121	0.561798
$650$	−17.6507	−0.692316
$651$	0	0
$652$	7.58582	0.297083
$653$	−37.5527	−1.46955	−0.734775	−	0.678311i	$-0.762712\pi$
$653$	−37.5527	−1.46955	−0.734775	+	0.678311i	$0.762712\pi$
$654$	−32.3566	−1.26524
$655$	3.40910	0.133205
$656$	1.00000	0.0390434
$657$	−22.0619	−0.860718
$658$	0	0
$659$	28.1213	1.09545	0.547725	−	0.836658i	$-0.315494\pi$
$659$	28.1213	1.09545	0.547725	+	0.836658i	$0.315494\pi$
$660$	4.06073	0.158064
$661$	23.0475	0.896443	0.448221	−	0.893923i	$-0.352058\pi$
$661$	23.0475	0.896443	0.448221	+	0.893923i	$0.352058\pi$
$662$	−13.2662	−0.515604
$663$	−21.8209	−0.847453
$664$	−12.3563	−0.479516
$665$	0	0
$666$	7.45759	0.288976
$667$	14.3991	0.557537
$668$	14.3440	0.554988
$669$	−7.74676	−0.299507
$670$	−2.50371	−0.0967266
$671$	−30.4998	−1.17743
$672$	0	0
$673$	33.8983	1.30668	0.653342	−	0.757063i	$-0.273366\pi$
$673$	33.8983	1.30668	0.653342	+	0.757063i	$0.273366\pi$
$674$	−28.4678	−1.09654
$675$	−14.9890	−0.576926
$676$	0.190681	0.00733390
$677$	31.7127	1.21882	0.609409	−	0.792856i	$-0.291407\pi$
$677$	31.7127	1.21882	0.609409	+	0.792856i	$0.291407\pi$
$678$	−30.9967	−1.19042
$679$	0	0
$680$	1.05372	0.0404081
$681$	−37.0329	−1.41910
$682$	−21.1753	−0.810844
$683$	14.1796	0.542566	0.271283	−	0.962500i	$-0.412552\pi$
$683$	14.1796	0.542566	0.271283	+	0.962500i	$0.412552\pi$
$684$	−0.275719	−0.0105424
$685$	2.78524	0.106419
$686$	0	0
$687$	37.1695	1.41811
$688$	−10.9177	−0.416233
$689$	−33.5917	−1.27974
$690$	−1.42302	−0.0541733
$691$	−21.3341	−0.811588	−0.405794	−	0.913965i	$-0.633005\pi$
$691$	−21.3341	−0.811588	−0.405794	+	0.913965i	$0.633005\pi$
$692$	7.99472	0.303914
$693$	0	0
$694$	−12.9353	−0.491018
$695$	−6.68292	−0.253498
$696$	−17.2515	−0.653915
$697$	−2.81514	−0.106631
$698$	−9.54651	−0.361341
$699$	−37.7903	−1.42936
$700$	0	0
$701$	−29.9588	−1.13153	−0.565763	−	0.824568i	$-0.691418\pi$
$701$	−29.9588	−1.13153	−0.565763	+	0.824568i	$0.691418\pi$
$702$	11.2016	0.422775
$703$	0.850504	0.0320774
$704$	−5.08327	−0.191583
$705$	−5.07946	−0.191304
$706$	11.8173	0.444751
$707$	0	0
$708$	6.00893	0.225829
$709$	−48.0102	−1.80306	−0.901531	−	0.432714i	$-0.857556\pi$
$709$	−48.0102	−1.80306	−0.901531	+	0.432714i	$0.857556\pi$
$710$	0.741353	0.0278225
$711$	1.61212	0.0604593
$712$	−11.2593	−0.421958
$713$	7.42053	0.277901
$714$	0	0
$715$	6.91035	0.258432
$716$	−17.8928	−0.668685
$717$	−51.3071	−1.91610
$718$	−22.4749	−0.838757
$719$	14.5296	0.541864	0.270932	−	0.962598i	$-0.412668\pi$
$719$	14.5296	0.541864	0.270932	+	0.962598i	$0.412668\pi$
$720$	0.581992	0.0216896
$721$	0	0
$722$	18.9686	0.705937
$723$	−55.2716	−2.05557
$724$	−1.98748	−0.0738640
$725$	39.2840	1.45897
$726$	31.6710	1.17542
$727$	−29.6401	−1.09929	−0.549645	−	0.835398i	$-0.685237\pi$
$727$	−29.6401	−1.09929	−0.549645	+	0.835398i	$0.685237\pi$
$728$	0	0
$729$	2.25951	0.0836855
$730$	5.31095	0.196567
$731$	30.7349	1.13677
$732$	−12.8054	−0.473300
$733$	−46.2588	−1.70861	−0.854305	−	0.519773i	$-0.826017\pi$
$733$	−46.2588	−1.70861	−0.854305	+	0.519773i	$0.826017\pi$
$734$	0.540072	0.0199344
$735$	0	0
$736$	1.78135	0.0656613
$737$	−34.0020	−1.25248
$738$	−1.55487	−0.0572356
$739$	−8.92835	−0.328435	−0.164217	−	0.986424i	$-0.552510\pi$
$739$	−8.92835	−0.328435	−0.164217	+	0.986424i	$0.552510\pi$
$740$	−1.79526	−0.0659950
$741$	−1.37450	−0.0504935
$742$	0	0
$743$	−40.2600	−1.47700	−0.738498	−	0.674256i	$-0.764465\pi$
$743$	−40.2600	−1.47700	−0.738498	+	0.674256i	$0.764465\pi$
$744$	−8.89046	−0.325940
$745$	−3.52505	−0.129148
$746$	24.9174	0.912292
$747$	19.2124	0.702945
$748$	14.3101	0.523231
$749$	0	0
$750$	−7.87650	−0.287609
$751$	−3.33635	−0.121745	−0.0608726	−	0.998146i	$-0.519388\pi$
$751$	−3.33635	−0.121745	−0.0608726	+	0.998146i	$0.519388\pi$
$752$	6.35853	0.231872
$753$	−20.5937	−0.750475
$754$	−29.3577	−1.06914
$755$	−0.406875	−0.0148077
$756$	0	0
$757$	46.2841	1.68222	0.841112	−	0.540861i	$-0.181902\pi$
$757$	46.2841	1.68222	0.841112	+	0.540861i	$0.181902\pi$
$758$	−17.8728	−0.649170
$759$	−19.3255	−0.701470
$760$	0.0663736	0.00240762
$761$	29.1176	1.05551	0.527757	−	0.849396i	$-0.323033\pi$
$761$	29.1176	1.05551	0.527757	+	0.849396i	$0.323033\pi$
$762$	−8.00969	−0.290161
$763$	0	0
$764$	−20.3423	−0.735959
$765$	−1.63839	−0.0592362
$766$	15.2602	0.551372
$767$	10.2257	0.369228
$768$	−2.13421	−0.0770118
$769$	2.82075	0.101719	0.0508595	−	0.998706i	$-0.483804\pi$
$769$	2.82075	0.101719	0.0508595	+	0.998706i	$0.483804\pi$
$770$	0	0
$771$	−5.86404	−0.211188
$772$	−8.76247	−0.315368
$773$	1.75168	0.0630034	0.0315017	−	0.999504i	$-0.489971\pi$
$773$	1.75168	0.0630034	0.0315017	+	0.999504i	$0.489971\pi$
$774$	16.9756	0.610175
$775$	20.2448	0.727215
$776$	−0.0930429	−0.00334005
$777$	0	0
$778$	5.14095	0.184312
$779$	−0.177326	−0.00635337
$780$	2.90131	0.103884
$781$	10.0681	0.360264
$782$	−5.01475	−0.179327
$783$	−24.9306	−0.890947
$784$	0	0
$785$	−7.43045	−0.265204
$786$	19.4382	0.693337
$787$	27.4895	0.979894	0.489947	−	0.871752i	$-0.337016\pi$
$787$	27.4895	0.979894	0.489947	+	0.871752i	$0.337016\pi$
$788$	20.0531	0.714362
$789$	−21.2657	−0.757079
$790$	−0.388084	−0.0138074
$791$	0	0
$792$	7.90383	0.280851
$793$	−21.7915	−0.773840
$794$	−1.26039	−0.0447294
$795$	−7.38856	−0.262045
$796$	20.3331	0.720688
$797$	12.6831	0.449259	0.224630	−	0.974444i	$-0.427883\pi$
$797$	12.6831	0.449259	0.224630	+	0.974444i	$0.427883\pi$
$798$	0	0
$799$	−17.9002	−0.633263
$800$	4.85990	0.171823
$801$	17.5067	0.618568
$802$	23.0667	0.814515
$803$	72.1261	2.54528
$804$	−14.2757	−0.503467
$805$	0	0
$806$	−15.1293	−0.532908
$807$	24.7527	0.871335
$808$	10.0972	0.355218
$809$	23.7363	0.834525	0.417263	−	0.908786i	$-0.362990\pi$
$809$	23.7363	0.834525	0.417263	+	0.908786i	$0.362990\pi$
$810$	4.20978	0.147916
$811$	−5.71451	−0.200664	−0.100332	−	0.994954i	$-0.531990\pi$
$811$	−5.71451	−0.200664	−0.100332	+	0.994954i	$0.531990\pi$
$812$	0	0
$813$	−44.0015	−1.54320
$814$	−24.3808	−0.854545
$815$	2.83939	0.0994595
$816$	6.00812	0.210326
$817$	1.93599	0.0677318
$818$	40.0015	1.39862
$819$	0	0
$820$	0.374303	0.0130712
$821$	40.1874	1.40255	0.701275	−	0.712891i	$-0.252615\pi$
$821$	40.1874	1.40255	0.701275	+	0.712891i	$0.252615\pi$
$822$	15.8810	0.553914
$823$	−33.2306	−1.15834	−0.579172	−	0.815205i	$-0.696624\pi$
$823$	−33.2306	−1.15834	−0.579172	+	0.815205i	$0.696624\pi$
$824$	1.84300	0.0642039
$825$	−52.7240	−1.83562
$826$	0	0
$827$	11.5419	0.401351	0.200676	−	0.979658i	$-0.435686\pi$
$827$	11.5419	0.401351	0.200676	+	0.979658i	$0.435686\pi$
$828$	−2.76977	−0.0962560
$829$	−30.1863	−1.04841	−0.524207	−	0.851591i	$-0.675638\pi$
$829$	−30.1863	−1.04841	−0.524207	+	0.851591i	$0.675638\pi$
$830$	−4.62498	−0.160535
$831$	−58.9023	−2.04330
$832$	−3.63190	−0.125913
$833$	0	0
$834$	−38.1050	−1.31947
$835$	5.36901	0.185802
$836$	0.901397	0.0311755
$837$	−12.8479	−0.444087
$838$	6.52817	0.225512
$839$	28.9801	1.00050	0.500252	−	0.865880i	$-0.333241\pi$
$839$	28.9801	1.00050	0.500252	+	0.865880i	$0.333241\pi$
$840$	0	0
$841$	36.3396	1.25309
$842$	11.3755	0.392026
$843$	−4.54466	−0.156527
$844$	−8.78212	−0.302293
$845$	0.0713725	0.00245529
$846$	−9.88670	−0.339912
$847$	0	0
$848$	9.24909	0.317615
$849$	25.0902	0.861095
$850$	−13.6813	−0.469265
$851$	8.54383	0.292879
$852$	4.22708	0.144817
$853$	16.4860	0.564471	0.282236	−	0.959345i	$-0.408924\pi$
$853$	16.4860	0.564471	0.282236	+	0.959345i	$0.408924\pi$
$854$	0	0
$855$	−0.103202	−0.00352945
$856$	4.65383	0.159065
$857$	−39.8870	−1.36251	−0.681257	−	0.732045i	$-0.738566\pi$
$857$	−39.8870	−1.36251	−0.681257	+	0.732045i	$0.738566\pi$
$858$	39.4017	1.34515
$859$	−36.0555	−1.23020	−0.615100	−	0.788449i	$-0.710884\pi$
$859$	−36.0555	−1.23020	−0.615100	+	0.788449i	$0.710884\pi$
$860$	−4.08652	−0.139349
$861$	0	0
$862$	−0.747652	−0.0254651
$863$	25.7677	0.877142	0.438571	−	0.898697i	$-0.355485\pi$
$863$	25.7677	0.877142	0.438571	+	0.898697i	$0.355485\pi$
$864$	−3.08421	−0.104927
$865$	2.99245	0.101746
$866$	−15.4836	−0.526153
$867$	19.3679	0.657769
$868$	0	0
$869$	−5.27044	−0.178787
$870$	−6.45727	−0.218922
$871$	−24.2937	−0.823162
$872$	15.1609	0.513413
$873$	0.144670	0.00489633
$874$	−0.315879	−0.0106848
$875$	0	0
$876$	30.2822	1.02314
$877$	−36.4619	−1.23123	−0.615616	−	0.788046i	$-0.711093\pi$
$877$	−36.4619	−1.23123	−0.615616	+	0.788046i	$0.711093\pi$
$878$	−12.6840	−0.428065
$879$	18.8210	0.634817
$880$	−1.90268	−0.0641394
$881$	−17.2268	−0.580386	−0.290193	−	0.956968i	$-0.593719\pi$
$881$	−17.2268	−0.580386	−0.290193	+	0.956968i	$0.593719\pi$
$882$	0	0
$883$	−9.45897	−0.318320	−0.159160	−	0.987253i	$-0.550879\pi$
$883$	−9.45897	−0.318320	−0.159160	+	0.987253i	$0.550879\pi$
$884$	10.2243	0.343881
$885$	2.24916	0.0756046
$886$	−19.9135	−0.669007
$887$	19.9417	0.669577	0.334788	−	0.942293i	$-0.391335\pi$
$887$	19.9417	0.669577	0.334788	+	0.942293i	$0.391335\pi$
$888$	−10.2363	−0.343507
$889$	0	0
$890$	−4.21437	−0.141266
$891$	57.1715	1.91532
$892$	3.62979	0.121534
$893$	−1.12753	−0.0377315
$894$	−20.0993	−0.672221
$895$	−6.69731	−0.223866
$896$	0	0
$897$	−13.8077	−0.461025
$898$	14.9211	0.497924
$899$	33.6724	1.12304
$900$	−7.55651	−0.251884
$901$	−26.0375	−0.867436
$902$	5.08327	0.169254
$903$	0	0
$904$	14.5237	0.483052
$905$	−0.743918	−0.0247287
$906$	−2.31994	−0.0770748
$907$	−3.71598	−0.123387	−0.0616936	−	0.998095i	$-0.519650\pi$
$907$	−3.71598	−0.123387	−0.0616936	+	0.998095i	$0.519650\pi$
$908$	17.3520	0.575846
$909$	−15.6998	−0.520730
$910$	0	0
$911$	−53.8497	−1.78412	−0.892060	−	0.451916i	$-0.850741\pi$
$911$	−53.8497	−1.78412	−0.892060	+	0.451916i	$0.850741\pi$
$912$	0.378452	0.0125318
$913$	−62.8103	−2.07872
$914$	−7.83949	−0.259307
$915$	−4.79308	−0.158454
$916$	−17.4160	−0.575441
$917$	0	0
$918$	8.68251	0.286565
$919$	−41.9430	−1.38357	−0.691786	−	0.722102i	$-0.743176\pi$
$919$	−41.9430	−1.38357	−0.691786	+	0.722102i	$0.743176\pi$
$920$	0.666763	0.0219825
$921$	−24.6800	−0.813235
$922$	6.74241	0.222050
$923$	7.19343	0.236775
$924$	0	0
$925$	23.3094	0.766408
$926$	−5.34792	−0.175744
$927$	−2.86562	−0.0941194
$928$	8.08329	0.265347
$929$	−44.1043	−1.44702	−0.723508	−	0.690316i	$-0.757472\pi$
$929$	−44.1043	−1.44702	−0.723508	+	0.690316i	$0.757472\pi$
$930$	−3.32772	−0.109120
$931$	0	0
$932$	17.7069	0.580009
$933$	−35.9312	−1.17634
$934$	36.9935	1.21046
$935$	5.35632	0.175171
$936$	5.64713	0.184582
$937$	−50.9512	−1.66450	−0.832251	−	0.554398i	$-0.812948\pi$
$937$	−50.9512	−1.66450	−0.832251	+	0.554398i	$0.812948\pi$
$938$	0	0
$939$	−15.5346	−0.506954
$940$	2.38002	0.0776275
$941$	−26.9285	−0.877845	−0.438922	−	0.898525i	$-0.644640\pi$
$941$	−26.9285	−0.877845	−0.438922	+	0.898525i	$0.644640\pi$
$942$	−42.3673	−1.38040
$943$	−1.78135	−0.0580087
$944$	−2.81552	−0.0916374
$945$	0	0
$946$	−55.4976	−1.80438
$947$	44.5156	1.44656	0.723281	−	0.690553i	$-0.242633\pi$
$947$	44.5156	1.44656	0.723281	+	0.690553i	$0.242633\pi$
$948$	−2.21280	−0.0718683
$949$	51.5327	1.67282
$950$	−0.861787	−0.0279601
$951$	41.5019	1.34579
$952$	0	0
$953$	38.6035	1.25049	0.625245	−	0.780429i	$-0.284999\pi$
$953$	38.6035	1.25049	0.625245	+	0.780429i	$0.284999\pi$
$954$	−14.3811	−0.465607
$955$	−7.61418	−0.246389
$956$	24.0403	0.777517
$957$	−87.6939	−2.83474
$958$	−4.31717	−0.139481
$959$	0	0
$960$	−0.798842	−0.0257825
$961$	−13.6471	−0.440228
$962$	−17.4196	−0.561630
$963$	−7.23611	−0.233180
$964$	25.8979	0.834114
$965$	−3.27981	−0.105581
$966$	0	0
$967$	24.4811	0.787258	0.393629	−	0.919269i	$-0.371219\pi$
$967$	24.4811	0.787258	0.393629	+	0.919269i	$0.371219\pi$
$968$	−14.8397	−0.476965
$969$	−1.06540	−0.0342255
$970$	−0.0348262	−0.00111820
$971$	1.61659	0.0518789	0.0259394	−	0.999664i	$-0.491742\pi$
$971$	1.61659	0.0518789	0.0259394	+	0.999664i	$0.491742\pi$
$972$	14.7508	0.473133
$973$	0	0
$974$	11.4002	0.365285
$975$	−37.6703	−1.20641
$976$	6.00004	0.192057
$977$	52.7602	1.68795	0.843974	−	0.536384i	$-0.180210\pi$
$977$	52.7602	1.68795	0.843974	+	0.536384i	$0.180210\pi$
$978$	16.1898	0.517691
$979$	−57.2339	−1.82920
$980$	0	0
$981$	−23.5732	−0.752635
$982$	20.1275	0.642295
$983$	−41.8793	−1.33574	−0.667871	−	0.744277i	$-0.732794\pi$
$983$	−41.8793	−1.33574	−0.667871	+	0.744277i	$0.732794\pi$
$984$	2.13421	0.0680363
$985$	7.50592	0.239159
$986$	−22.7556	−0.724687
$987$	0	0
$988$	0.644030	0.0204893
$989$	19.4482	0.618417
$990$	2.95843	0.0940249
$991$	−38.2215	−1.21415	−0.607073	−	0.794646i	$-0.707656\pi$
$991$	−38.2215	−1.21415	−0.607073	+	0.794646i	$0.707656\pi$
$992$	4.16568	0.132261
$993$	−28.3128	−0.898481
$994$	0	0
$995$	7.61073	0.241276
$996$	−26.3709	−0.835594
$997$	52.4436	1.66091	0.830453	−	0.557089i	$-0.188082\pi$
$997$	52.4436	1.66091	0.830453	+	0.557089i	$0.188082\pi$
$998$	4.11463	0.130246
$999$	−14.7927	−0.468021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bs.1.2	yes	10
7.6	odd	2		4018.2.a.br.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.9	✓	10	7.6	odd	2
4018.2.a.bs.1.2	yes	10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.13421 q^{3} +1.00000 q^{4} +0.374303 q^{5} +2.13421 q^{6} -1.00000 q^{8} +1.55487 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.13421 q^{3} +1.00000 q^{4} +0.374303 q^{5} +2.13421 q^{6} -1.00000 q^{8} +1.55487 q^{9} -0.374303 q^{10} -5.08327 q^{11} -2.13421 q^{12} -3.63190 q^{13} -0.798842 q^{15} +1.00000 q^{16} -2.81514 q^{17} -1.55487 q^{18} -0.177326 q^{19} +0.374303 q^{20} +5.08327 q^{22} -1.78135 q^{23} +2.13421 q^{24} -4.85990 q^{25} +3.63190 q^{26} +3.08421 q^{27} -8.08329 q^{29} +0.798842 q^{30} -4.16568 q^{31} -1.00000 q^{32} +10.8488 q^{33} +2.81514 q^{34} +1.55487 q^{36} -4.79627 q^{37} +0.177326 q^{38} +7.75125 q^{39} -0.374303 q^{40} +1.00000 q^{41} -10.9177 q^{43} -5.08327 q^{44} +0.581992 q^{45} +1.78135 q^{46} +6.35853 q^{47} -2.13421 q^{48} +4.85990 q^{50} +6.00812 q^{51} -3.63190 q^{52} +9.24909 q^{53} -3.08421 q^{54} -1.90268 q^{55} +0.378452 q^{57} +8.08329 q^{58} -2.81552 q^{59} -0.798842 q^{60} +6.00004 q^{61} +4.16568 q^{62} +1.00000 q^{64} -1.35943 q^{65} -10.8488 q^{66} +6.68899 q^{67} -2.81514 q^{68} +3.80178 q^{69} -1.98063 q^{71} -1.55487 q^{72} -14.1889 q^{73} +4.79627 q^{74} +10.3721 q^{75} -0.177326 q^{76} -7.75125 q^{78} +1.03682 q^{79} +0.374303 q^{80} -11.2470 q^{81} -1.00000 q^{82} +12.3563 q^{83} -1.05372 q^{85} +10.9177 q^{86} +17.2515 q^{87} +5.08327 q^{88} +11.2593 q^{89} -0.581992 q^{90} -1.78135 q^{92} +8.89046 q^{93} -6.35853 q^{94} -0.0663736 q^{95} +2.13421 q^{96} +0.0930429 q^{97} -7.90383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Introduction

L-functions

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