LMFDB - Embedded newform 6762.2.a.cs.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.23252.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 2 $ x^4 - x^3 - 6*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.634868$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.47747 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.47747 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.47747 q^{10} -1.26974 q^{11} +1.00000 q^{12} +5.47747 q^{13} -3.47747 q^{15} +1.00000 q^{16} +7.03079 q^{17} +1.00000 q^{18} +2.00000 q^{19} -3.47747 q^{20} -1.26974 q^{22} -1.00000 q^{23} +1.00000 q^{24} +7.09279 q^{25} +5.47747 q^{26} +1.00000 q^{27} -7.40162 q^{29} -3.47747 q^{30} -9.57026 q^{31} +1.00000 q^{32} -1.26974 q^{33} +7.03079 q^{34} +1.00000 q^{36} +1.71642 q^{37} +2.00000 q^{38} +5.47747 q^{39} -3.47747 q^{40} -8.50826 q^{41} -7.23852 q^{43} -1.26974 q^{44} -3.47747 q^{45} -1.00000 q^{46} +12.0169 q^{47} +1.00000 q^{48} +7.09279 q^{50} +7.03079 q^{51} +5.47747 q^{52} +7.68520 q^{53} +1.00000 q^{54} +4.41547 q^{55} +2.00000 q^{57} -7.40162 q^{58} +7.84830 q^{59} -3.47747 q^{60} +9.92415 q^{61} -9.57026 q^{62} +1.00000 q^{64} -19.0477 q^{65} -1.26974 q^{66} -4.37637 q^{67} +7.03079 q^{68} -1.00000 q^{69} -10.0616 q^{71} +1.00000 q^{72} +13.4944 q^{73} +1.71642 q^{74} +7.09279 q^{75} +2.00000 q^{76} +5.47747 q^{78} +13.4944 q^{79} -3.47747 q^{80} +1.00000 q^{81} -8.50826 q^{82} +5.10664 q^{83} -24.4493 q^{85} -7.23852 q^{86} -7.40162 q^{87} -1.26974 q^{88} +11.0308 q^{89} -3.47747 q^{90} -1.00000 q^{92} -9.57026 q^{93} +12.0169 q^{94} -6.95494 q^{95} +1.00000 q^{96} +14.5564 q^{97} -1.26974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 3 q^{10} + 2 q^{11} + 4 q^{12} + 5 q^{13} + 3 q^{15} + 4 q^{16} + 10 q^{17} + 4 q^{18} + 8 q^{19} + 3 q^{20} + 2 q^{22} - 4 q^{23} + 4 q^{24} + 13 q^{25} + 5 q^{26} + 4 q^{27} + 3 q^{29} + 3 q^{30} - 6 q^{31} + 4 q^{32} + 2 q^{33} + 10 q^{34} + 4 q^{36} + q^{37} + 8 q^{38} + 5 q^{39} + 3 q^{40} + q^{41} - q^{43} + 2 q^{44} + 3 q^{45} - 4 q^{46} + 17 q^{47} + 4 q^{48} + 13 q^{50} + 10 q^{51} + 5 q^{52} + 4 q^{53} + 4 q^{54} - 2 q^{55} + 8 q^{57} + 3 q^{58} + 3 q^{60} + 24 q^{61} - 6 q^{62} + 4 q^{64} - 27 q^{65} + 2 q^{66} - 8 q^{67} + 10 q^{68} - 4 q^{69} - 4 q^{71} + 4 q^{72} + 6 q^{73} + q^{74} + 13 q^{75} + 8 q^{76} + 5 q^{78} + 6 q^{79} + 3 q^{80} + 4 q^{81} + q^{82} + 18 q^{83} - 16 q^{85} - q^{86} + 3 q^{87} + 2 q^{88} + 26 q^{89} + 3 q^{90} - 4 q^{92} - 6 q^{93} + 17 q^{94} + 6 q^{95} + 4 q^{96} + 13 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 3 * q^10 + 2 * q^11 + 4 * q^12 + 5 * q^13 + 3 * q^15 + 4 * q^16 + 10 * q^17 + 4 * q^18 + 8 * q^19 + 3 * q^20 + 2 * q^22 - 4 * q^23 + 4 * q^24 + 13 * q^25 + 5 * q^26 + 4 * q^27 + 3 * q^29 + 3 * q^30 - 6 * q^31 + 4 * q^32 + 2 * q^33 + 10 * q^34 + 4 * q^36 + q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 + q^41 - q^43 + 2 * q^44 + 3 * q^45 - 4 * q^46 + 17 * q^47 + 4 * q^48 + 13 * q^50 + 10 * q^51 + 5 * q^52 + 4 * q^53 + 4 * q^54 - 2 * q^55 + 8 * q^57 + 3 * q^58 + 3 * q^60 + 24 * q^61 - 6 * q^62 + 4 * q^64 - 27 * q^65 + 2 * q^66 - 8 * q^67 + 10 * q^68 - 4 * q^69 - 4 * q^71 + 4 * q^72 + 6 * q^73 + q^74 + 13 * q^75 + 8 * q^76 + 5 * q^78 + 6 * q^79 + 3 * q^80 + 4 * q^81 + q^82 + 18 * q^83 - 16 * q^85 - q^86 + 3 * q^87 + 2 * q^88 + 26 * q^89 + 3 * q^90 - 4 * q^92 - 6 * q^93 + 17 * q^94 + 6 * q^95 + 4 * q^96 + 13 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.47747	−1.55517	−0.777586	−	0.628777i	$-0.783556\pi$
$5$	−3.47747	−1.55517	−0.777586	+	0.628777i	$0.783556\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.47747	−1.09967
$11$	−1.26974	−0.382840	−0.191420	−	0.981508i	$-0.561309\pi$
$11$	−1.26974	−0.382840	−0.191420	+	0.981508i	$0.561309\pi$
$12$	1.00000	0.288675
$13$	5.47747	1.51918	0.759588	−	0.650404i	$-0.225400\pi$
$13$	5.47747	1.51918	0.759588	+	0.650404i	$0.225400\pi$
$14$	0	0
$15$	−3.47747	−0.897879
$16$	1.00000	0.250000
$17$	7.03079	1.70522	0.852608	−	0.522551i	$-0.175019\pi$
$17$	7.03079	1.70522	0.852608	+	0.522551i	$0.175019\pi$
$18$	1.00000	0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	−3.47747	−0.777586
$21$	0	0
$22$	−1.26974	−0.270709
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	7.09279	1.41856
$26$	5.47747	1.07422
$27$	1.00000	0.192450
$28$	0	0
$29$	−7.40162	−1.37445	−0.687223	−	0.726446i	$-0.741171\pi$
$29$	−7.40162	−1.37445	−0.687223	+	0.726446i	$0.741171\pi$
$30$	−3.47747	−0.634896
$31$	−9.57026	−1.71887	−0.859435	−	0.511246i	$-0.829184\pi$
$31$	−9.57026	−1.71887	−0.859435	+	0.511246i	$0.829184\pi$
$32$	1.00000	0.176777
$33$	−1.26974	−0.221033
$34$	7.03079	1.20577
$35$	0	0
$36$	1.00000	0.166667
$37$	1.71642	0.282177	0.141089	−	0.989997i	$-0.454940\pi$
$37$	1.71642	0.282177	0.141089	+	0.989997i	$0.454940\pi$
$38$	2.00000	0.324443
$39$	5.47747	0.877097
$40$	−3.47747	−0.549836
$41$	−8.50826	−1.32877	−0.664383	−	0.747392i	$-0.731306\pi$
$41$	−8.50826	−1.32877	−0.664383	+	0.747392i	$0.731306\pi$
$42$	0	0
$43$	−7.23852	−1.10386	−0.551932	−	0.833889i	$-0.686109\pi$
$43$	−7.23852	−1.10386	−0.551932	+	0.833889i	$0.686109\pi$
$44$	−1.26974	−0.191420
$45$	−3.47747	−0.518390
$46$	−1.00000	−0.147442
$47$	12.0169	1.75285	0.876425	−	0.481538i	$-0.159922\pi$
$47$	12.0169	1.75285	0.876425	+	0.481538i	$0.159922\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	7.09279	1.00307
$51$	7.03079	0.984507
$52$	5.47747	0.759588
$53$	7.68520	1.05564	0.527822	−	0.849355i	$-0.323009\pi$
$53$	7.68520	1.05564	0.527822	+	0.849355i	$0.323009\pi$
$54$	1.00000	0.136083
$55$	4.41547	0.595381
$56$	0	0
$57$	2.00000	0.264906
$58$	−7.40162	−0.971880
$59$	7.84830	1.02176	0.510881	−	0.859652i	$-0.329319\pi$
$59$	7.84830	1.02176	0.510881	+	0.859652i	$0.329319\pi$
$60$	−3.47747	−0.448939
$61$	9.92415	1.27066	0.635329	−	0.772242i	$-0.280865\pi$
$61$	9.92415	1.27066	0.635329	+	0.772242i	$0.280865\pi$
$62$	−9.57026	−1.21542
$63$	0	0
$64$	1.00000	0.125000
$65$	−19.0477	−2.36258
$66$	−1.26974	−0.156294
$67$	−4.37637	−0.534659	−0.267330	−	0.963605i	$-0.586141\pi$
$67$	−4.37637	−0.534659	−0.267330	+	0.963605i	$0.586141\pi$
$68$	7.03079	0.852608
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−10.0616	−1.19409	−0.597045	−	0.802208i	$-0.703659\pi$
$71$	−10.0616	−1.19409	−0.597045	+	0.802208i	$0.703659\pi$
$72$	1.00000	0.117851
$73$	13.4944	1.57940	0.789701	−	0.613492i	$-0.210236\pi$
$73$	13.4944	1.57940	0.789701	+	0.613492i	$0.210236\pi$
$74$	1.71642	0.199529
$75$	7.09279	0.819005
$76$	2.00000	0.229416
$77$	0	0
$78$	5.47747	0.620201
$79$	13.4944	1.51824	0.759120	−	0.650951i	$-0.225630\pi$
$79$	13.4944	1.51824	0.759120	+	0.650951i	$0.225630\pi$
$80$	−3.47747	−0.388793
$81$	1.00000	0.111111
$82$	−8.50826	−0.939580
$83$	5.10664	0.560526	0.280263	−	0.959923i	$-0.409578\pi$
$83$	5.10664	0.560526	0.280263	+	0.959923i	$0.409578\pi$
$84$	0	0
$85$	−24.4493	−2.65190
$86$	−7.23852	−0.780550
$87$	−7.40162	−0.793537
$88$	−1.26974	−0.135354
$89$	11.0308	1.16926	0.584631	−	0.811300i	$-0.301239\pi$
$89$	11.0308	1.16926	0.584631	+	0.811300i	$0.301239\pi$
$90$	−3.47747	−0.366557
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−9.57026	−0.992390
$94$	12.0169	1.23945
$95$	−6.95494	−0.713562
$96$	1.00000	0.102062
$97$	14.5564	1.47798	0.738990	−	0.673717i	$-0.235303\pi$
$97$	14.5564	1.47798	0.738990	+	0.673717i	$0.235303\pi$
$98$	0	0
$99$	−1.26974	−0.127613
$100$	7.09279	0.709279
$101$	−0.817512	−0.0813455	−0.0406727	−	0.999173i	$-0.512950\pi$
$101$	−0.817512	−0.0813455	−0.0406727	+	0.999173i	$0.512950\pi$
$102$	7.03079	0.696152
$103$	−4.50826	−0.444212	−0.222106	−	0.975023i	$-0.571293\pi$
$103$	−4.50826	−0.444212	−0.222106	+	0.975023i	$0.571293\pi$
$104$	5.47747	0.537110
$105$	0	0
$106$	7.68520	0.746453
$107$	−3.62363	−0.350309	−0.175155	−	0.984541i	$-0.556043\pi$
$107$	−3.62363	−0.350309	−0.175155	+	0.984541i	$0.556043\pi$
$108$	1.00000	0.0962250
$109$	18.3175	1.75449	0.877247	−	0.480038i	$-0.159377\pi$
$109$	18.3175	1.75449	0.877247	+	0.480038i	$0.159377\pi$
$110$	4.41547	0.420998
$111$	1.71642	0.162915
$112$	0	0
$113$	−10.5083	−0.988534	−0.494267	−	0.869310i	$-0.664563\pi$
$113$	−10.5083	−0.988534	−0.494267	+	0.869310i	$0.664563\pi$
$114$	2.00000	0.187317
$115$	3.47747	0.324276
$116$	−7.40162	−0.687223
$117$	5.47747	0.506392
$118$	7.84830	0.722495
$119$	0	0
$120$	−3.47747	−0.317448
$121$	−9.38777	−0.853434
$122$	9.92415	0.898490
$123$	−8.50826	−0.767164
$124$	−9.57026	−0.859435
$125$	−7.27761	−0.650930
$126$	0	0
$127$	11.6149	1.03066	0.515328	−	0.856993i	$-0.327670\pi$
$127$	11.6149	1.03066	0.515328	+	0.856993i	$0.327670\pi$
$128$	1.00000	0.0883883
$129$	−7.23852	−0.637316
$130$	−19.0477	−1.67060
$131$	−19.1405	−1.67231	−0.836157	−	0.548489i	$-0.815203\pi$
$131$	−19.1405	−1.67231	−0.836157	+	0.548489i	$0.815203\pi$
$132$	−1.26974	−0.110516
$133$	0	0
$134$	−4.37637	−0.378061
$135$	−3.47747	−0.299293
$136$	7.03079	0.602885
$137$	4.86215	0.415401	0.207701	−	0.978192i	$-0.433402\pi$
$137$	4.86215	0.415401	0.207701	+	0.978192i	$0.433402\pi$
$138$	−1.00000	−0.0851257
$139$	−16.5083	−1.40021	−0.700106	−	0.714039i	$-0.746864\pi$
$139$	−16.5083	−1.40021	−0.700106	+	0.714039i	$0.746864\pi$
$140$	0	0
$141$	12.0169	1.01201
$142$	−10.0616	−0.844349
$143$	−6.95494	−0.581601
$144$	1.00000	0.0833333
$145$	25.7389	2.13750
$146$	13.4944	1.11681
$147$	0	0
$148$	1.71642	0.141089
$149$	18.8257	1.54226	0.771132	−	0.636676i	$-0.219691\pi$
$149$	18.8257	1.54226	0.771132	+	0.636676i	$0.219691\pi$
$150$	7.09279	0.579124
$151$	15.4632	1.25838	0.629188	−	0.777253i	$-0.283387\pi$
$151$	15.4632	1.25838	0.629188	+	0.777253i	$0.283387\pi$
$152$	2.00000	0.162221
$153$	7.03079	0.568406
$154$	0	0
$155$	33.2803	2.67314
$156$	5.47747	0.438548
$157$	12.8791	1.02786	0.513932	−	0.857831i	$-0.328189\pi$
$157$	12.8791	1.02786	0.513932	+	0.857831i	$0.328189\pi$
$158$	13.4944	1.07356
$159$	7.68520	0.609476
$160$	−3.47747	−0.274918
$161$	0	0
$162$	1.00000	0.0785674
$163$	−23.1405	−1.81251	−0.906253	−	0.422736i	$-0.861070\pi$
$163$	−23.1405	−1.81251	−0.906253	+	0.422736i	$0.861070\pi$
$164$	−8.50826	−0.664383
$165$	4.41547	0.343744
$166$	5.10664	0.396352
$167$	−17.4186	−1.34789	−0.673944	−	0.738782i	$-0.735401\pi$
$167$	−17.4186	−1.34789	−0.673944	+	0.738782i	$0.735401\pi$
$168$	0	0
$169$	17.0027	1.30790
$170$	−24.4493	−1.87518
$171$	2.00000	0.152944
$172$	−7.23852	−0.551932
$173$	2.84521	0.216317	0.108159	−	0.994134i	$-0.465505\pi$
$173$	2.84521	0.216317	0.108159	+	0.994134i	$0.465505\pi$
$174$	−7.40162	−0.561115
$175$	0	0
$176$	−1.26974	−0.0957099
$177$	7.84830	0.589914
$178$	11.0308	0.826793
$179$	1.13785	0.0850471	0.0425235	−	0.999095i	$-0.486460\pi$
$179$	1.13785	0.0850471	0.0425235	+	0.999095i	$0.486460\pi$
$180$	−3.47747	−0.259195
$181$	18.9407	1.40785	0.703924	−	0.710275i	$-0.251429\pi$
$181$	18.9407	1.40785	0.703924	+	0.710275i	$0.251429\pi$
$182$	0	0
$183$	9.92415	0.733614
$184$	−1.00000	−0.0737210
$185$	−5.96879	−0.438834
$186$	−9.57026	−0.701725
$187$	−8.92724	−0.652825
$188$	12.0169	0.876425
$189$	0	0
$190$	−6.95494	−0.504564
$191$	−0.151700	−0.0109766	−0.00548832	−	0.999985i	$-0.501747\pi$
$191$	−0.151700	−0.0109766	−0.00548832	+	0.999985i	$0.501747\pi$
$192$	1.00000	0.0721688
$193$	10.9237	0.786307	0.393153	−	0.919473i	$-0.371384\pi$
$193$	10.9237	0.786307	0.393153	+	0.919473i	$0.371384\pi$
$194$	14.5564	1.04509
$195$	−19.0477	−1.36404
$196$	0	0
$197$	13.6149	0.970021	0.485011	−	0.874508i	$-0.338816\pi$
$197$	13.6149	0.970021	0.485011	+	0.874508i	$0.338816\pi$
$198$	−1.26974	−0.0902362
$199$	22.5698	1.59993	0.799967	−	0.600045i	$-0.204851\pi$
$199$	22.5698	1.59993	0.799967	+	0.600045i	$0.204851\pi$
$200$	7.09279	0.501536
$201$	−4.37637	−0.308686
$202$	−0.817512	−0.0575199
$203$	0	0
$204$	7.03079	0.492254
$205$	29.5872	2.06646
$206$	−4.50826	−0.314105
$207$	−1.00000	−0.0695048
$208$	5.47747	0.379794
$209$	−2.53947	−0.175659
$210$	0	0
$211$	9.49441	0.653622	0.326811	−	0.945090i	$-0.394026\pi$
$211$	9.49441	0.653622	0.326811	+	0.945090i	$0.394026\pi$
$212$	7.68520	0.527822
$213$	−10.0616	−0.689408
$214$	−3.62363	−0.247706
$215$	25.1717	1.71670
$216$	1.00000	0.0680414
$217$	0	0
$218$	18.3175	1.24062
$219$	13.4944	0.911868
$220$	4.41547	0.297691
$221$	38.5109	2.59053
$222$	1.71642	0.115198
$223$	15.2946	1.02420	0.512100	−	0.858926i	$-0.328868\pi$
$223$	15.2946	1.02420	0.512100	+	0.858926i	$0.328868\pi$
$224$	0	0
$225$	7.09279	0.472853
$226$	−10.5083	−0.698999
$227$	1.42931	0.0948669	0.0474335	−	0.998874i	$-0.484896\pi$
$227$	1.42931	0.0948669	0.0474335	+	0.998874i	$0.484896\pi$
$228$	2.00000	0.132453
$229$	17.9241	1.18446	0.592231	−	0.805769i	$-0.298247\pi$
$229$	17.9241	1.18446	0.592231	+	0.805769i	$0.298247\pi$
$230$	3.47747	0.229298
$231$	0	0
$232$	−7.40162	−0.485940
$233$	−18.4155	−1.20644	−0.603219	−	0.797576i	$-0.706115\pi$
$233$	−18.4155	−1.20644	−0.603219	+	0.797576i	$0.706115\pi$
$234$	5.47747	0.358073
$235$	−41.7885	−2.72598
$236$	7.84830	0.510881
$237$	13.4944	0.876556
$238$	0	0
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	−3.47747	−0.224470
$241$	−4.39853	−0.283334	−0.141667	−	0.989914i	$-0.545246\pi$
$241$	−4.39853	−0.283334	−0.141667	+	0.989914i	$0.545246\pi$
$242$	−9.38777	−0.603469
$243$	1.00000	0.0641500
$244$	9.92415	0.635329
$245$	0	0
$246$	−8.50826	−0.542467
$247$	10.9549	0.697046
$248$	−9.57026	−0.607712
$249$	5.10664	0.323620
$250$	−7.27761	−0.460277
$251$	4.29498	0.271097	0.135548	−	0.990771i	$-0.456720\pi$
$251$	4.29498	0.271097	0.135548	+	0.990771i	$0.456720\pi$
$252$	0	0
$253$	1.26974	0.0798276
$254$	11.6149	0.728783
$255$	−24.4493	−1.53108
$256$	1.00000	0.0625000
$257$	13.0451	0.813729	0.406864	−	0.913489i	$-0.366622\pi$
$257$	13.0451	0.813729	0.406864	+	0.913489i	$0.366622\pi$
$258$	−7.23852	−0.450651
$259$	0	0
$260$	−19.0477	−1.18129
$261$	−7.40162	−0.458149
$262$	−19.1405	−1.18251
$263$	13.4016	0.826379	0.413190	−	0.910645i	$-0.364415\pi$
$263$	13.4016	0.826379	0.413190	+	0.910645i	$0.364415\pi$
$264$	−1.26974	−0.0781468
$265$	−26.7251	−1.64171
$266$	0	0
$267$	11.0308	0.675073
$268$	−4.37637	−0.267330
$269$	−9.09236	−0.554371	−0.277186	−	0.960816i	$-0.589402\pi$
$269$	−9.09236	−0.554371	−0.277186	+	0.960816i	$0.589402\pi$
$270$	−3.47747	−0.211632
$271$	15.9241	0.967323	0.483662	−	0.875255i	$-0.339307\pi$
$271$	15.9241	0.967323	0.483662	+	0.875255i	$0.339307\pi$
$272$	7.03079	0.426304
$273$	0	0
$274$	4.86215	0.293733
$275$	−9.00597	−0.543080
$276$	−1.00000	−0.0601929
$277$	−18.7527	−1.12674	−0.563372	−	0.826204i	$-0.690496\pi$
$277$	−18.7527	−1.12674	−0.563372	+	0.826204i	$0.690496\pi$
$278$	−16.5083	−0.990099
$279$	−9.57026	−0.572956
$280$	0	0
$281$	−24.4806	−1.46039	−0.730194	−	0.683240i	$-0.760570\pi$
$281$	−24.4806	−1.46039	−0.730194	+	0.683240i	$0.760570\pi$
$282$	12.0169	0.715598
$283$	−6.18558	−0.367695	−0.183847	−	0.982955i	$-0.558855\pi$
$283$	−6.18558	−0.367695	−0.183847	+	0.982955i	$0.558855\pi$
$284$	−10.0616	−0.597045
$285$	−6.95494	−0.411975
$286$	−6.95494	−0.411254
$287$	0	0
$288$	1.00000	0.0589256
$289$	32.4320	1.90776
$290$	25.7389	1.51144
$291$	14.5564	0.853312
$292$	13.4944	0.789701
$293$	−32.0196	−1.87061	−0.935303	−	0.353849i	$-0.884873\pi$
$293$	−32.0196	−1.87061	−0.935303	+	0.353849i	$0.884873\pi$
$294$	0	0
$295$	−27.2922	−1.58901
$296$	1.71642	0.0997647
$297$	−1.26974	−0.0736775
$298$	18.8257	1.09054
$299$	−5.47747	−0.316770
$300$	7.09279	0.409502
$301$	0	0
$302$	15.4632	0.889807
$303$	−0.817512	−0.0469648
$304$	2.00000	0.114708
$305$	−34.5109	−1.97609
$306$	7.03079	0.401923
$307$	−20.1710	−1.15122	−0.575609	−	0.817725i	$-0.695235\pi$
$307$	−20.1710	−1.15122	−0.575609	+	0.817725i	$0.695235\pi$
$308$	0	0
$309$	−4.50826	−0.256466
$310$	33.2803	1.89019
$311$	8.10973	0.459861	0.229930	−	0.973207i	$-0.426150\pi$
$311$	8.10973	0.459861	0.229930	+	0.973207i	$0.426150\pi$
$312$	5.47747	0.310101
$313$	6.84521	0.386914	0.193457	−	0.981109i	$-0.438030\pi$
$313$	6.84521	0.386914	0.193457	+	0.981109i	$0.438030\pi$
$314$	12.8791	0.726809
$315$	0	0
$316$	13.4944	0.759120
$317$	−0.598381	−0.0336084	−0.0168042	−	0.999859i	$-0.505349\pi$
$317$	−0.598381	−0.0336084	−0.0168042	+	0.999859i	$0.505349\pi$
$318$	7.68520	0.430965
$319$	9.39810	0.526193
$320$	−3.47747	−0.194396
$321$	−3.62363	−0.202251
$322$	0	0
$323$	14.0616	0.782407
$324$	1.00000	0.0555556
$325$	38.8505	2.15504
$326$	−23.1405	−1.28163
$327$	18.3175	1.01296
$328$	−8.50826	−0.469790
$329$	0	0
$330$	4.41547	0.243063
$331$	25.9099	1.42414	0.712068	−	0.702111i	$-0.247759\pi$
$331$	25.9099	1.42414	0.712068	+	0.702111i	$0.247759\pi$
$332$	5.10664	0.280263
$333$	1.71642	0.0940591
$334$	−17.4186	−0.953101
$335$	15.2187	0.831487
$336$	0	0
$337$	−8.21328	−0.447406	−0.223703	−	0.974657i	$-0.571815\pi$
$337$	−8.21328	−0.447406	−0.223703	+	0.974657i	$0.571815\pi$
$338$	17.0027	0.924823
$339$	−10.5083	−0.570730
$340$	−24.4493	−1.32595
$341$	12.1517	0.658051
$342$	2.00000	0.108148
$343$	0	0
$344$	−7.23852	−0.390275
$345$	3.47747	0.187221
$346$	2.84521	0.152959
$347$	−15.4632	−0.830108	−0.415054	−	0.909797i	$-0.636237\pi$
$347$	−15.4632	−0.830108	−0.415054	+	0.909797i	$0.636237\pi$
$348$	−7.40162	−0.396768
$349$	−11.9241	−0.638285	−0.319143	−	0.947707i	$-0.603395\pi$
$349$	−11.9241	−0.638285	−0.319143	+	0.947707i	$0.603395\pi$
$350$	0	0
$351$	5.47747	0.292366
$352$	−1.26974	−0.0676771
$353$	13.9688	0.743483	0.371742	−	0.928336i	$-0.378761\pi$
$353$	13.9688	0.743483	0.371742	+	0.928336i	$0.378761\pi$
$354$	7.84830	0.417132
$355$	34.9888	1.85701
$356$	11.0308	0.584631
$357$	0	0
$358$	1.13785	0.0601374
$359$	6.56983	0.346743	0.173371	−	0.984857i	$-0.444534\pi$
$359$	6.56983	0.346743	0.173371	+	0.984857i	$0.444534\pi$
$360$	−3.47747	−0.183279
$361$	−15.0000	−0.789474
$362$	18.9407	0.995499
$363$	−9.38777	−0.492730
$364$	0	0
$365$	−46.9264	−2.45624
$366$	9.92415	0.518744
$367$	−13.2499	−0.691640	−0.345820	−	0.938301i	$-0.612399\pi$
$367$	−13.2499	−0.691640	−0.345820	+	0.938301i	$0.612399\pi$
$368$	−1.00000	−0.0521286
$369$	−8.50826	−0.442922
$370$	−5.96879	−0.310302
$371$	0	0
$372$	−9.57026	−0.496195
$373$	19.6852	1.01926	0.509631	−	0.860393i	$-0.329782\pi$
$373$	19.6852	1.01926	0.509631	+	0.860393i	$0.329782\pi$
$374$	−8.92724	−0.461617
$375$	−7.27761	−0.375814
$376$	12.0169	0.619726
$377$	−40.5421	−2.08803
$378$	0	0
$379$	9.77799	0.502262	0.251131	−	0.967953i	$-0.419198\pi$
$379$	9.77799	0.502262	0.251131	+	0.967953i	$0.419198\pi$
$380$	−6.95494	−0.356781
$381$	11.6149	0.595049
$382$	−0.151700	−0.00776166
$383$	−2.80324	−0.143239	−0.0716194	−	0.997432i	$-0.522817\pi$
$383$	−2.80324	−0.143239	−0.0716194	+	0.997432i	$0.522817\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.9237	0.556003
$387$	−7.23852	−0.367955
$388$	14.5564	0.738990
$389$	1.06755	0.0541267	0.0270634	−	0.999634i	$-0.491384\pi$
$389$	1.06755	0.0541267	0.0270634	+	0.999634i	$0.491384\pi$
$390$	−19.0477	−0.964519
$391$	−7.03079	−0.355562
$392$	0	0
$393$	−19.1405	−0.965511
$394$	13.6149	0.685909
$395$	−46.9264	−2.36112
$396$	−1.26974	−0.0638066
$397$	−5.00309	−0.251098	−0.125549	−	0.992087i	$-0.540069\pi$
$397$	−5.00309	−0.251098	−0.125549	+	0.992087i	$0.540069\pi$
$398$	22.5698	1.13132
$399$	0	0
$400$	7.09279	0.354640
$401$	−22.7527	−1.13622	−0.568109	−	0.822953i	$-0.692325\pi$
$401$	−22.7527	−1.13622	−0.568109	+	0.822953i	$0.692325\pi$
$402$	−4.37637	−0.218274
$403$	−52.4208	−2.61127
$404$	−0.817512	−0.0406727
$405$	−3.47747	−0.172797
$406$	0	0
$407$	−2.17940	−0.108029
$408$	7.03079	0.348076
$409$	8.18558	0.404751	0.202375	−	0.979308i	$-0.435134\pi$
$409$	8.18558	0.404751	0.202375	+	0.979308i	$0.435134\pi$
$410$	29.5872	1.46121
$411$	4.86215	0.239832
$412$	−4.50826	−0.222106
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	−17.7582	−0.871715
$416$	5.47747	0.268555
$417$	−16.5083	−0.808413
$418$	−2.53947	−0.124210
$419$	2.18558	0.106773	0.0533863	−	0.998574i	$-0.482999\pi$
$419$	2.18558	0.106773	0.0533863	+	0.998574i	$0.482999\pi$
$420$	0	0
$421$	−4.97475	−0.242455	−0.121227	−	0.992625i	$-0.538683\pi$
$421$	−4.97475	−0.242455	−0.121227	+	0.992625i	$0.538683\pi$
$422$	9.49441	0.462181
$423$	12.0169	0.584284
$424$	7.68520	0.373226
$425$	49.8679	2.41895
$426$	−10.0616	−0.487485
$427$	0	0
$428$	−3.62363	−0.175155
$429$	−6.95494	−0.335788
$430$	25.1717	1.21389
$431$	−16.1267	−0.776794	−0.388397	−	0.921492i	$-0.626971\pi$
$431$	−16.1267	−0.776794	−0.388397	+	0.921492i	$0.626971\pi$
$432$	1.00000	0.0481125
$433$	15.5729	0.748387	0.374194	−	0.927351i	$-0.377920\pi$
$433$	15.5729	0.748387	0.374194	+	0.927351i	$0.377920\pi$
$434$	0	0
$435$	25.7389	1.23409
$436$	18.3175	0.877247
$437$	−2.00000	−0.0956730
$438$	13.4944	0.644788
$439$	−11.0308	−0.526471	−0.263235	−	0.964732i	$-0.584790\pi$
$439$	−11.0308	−0.526471	−0.263235	+	0.964732i	$0.584790\pi$
$440$	4.41547	0.210499
$441$	0	0
$442$	38.5109	1.83178
$443$	−12.6600	−0.601493	−0.300746	−	0.953704i	$-0.597236\pi$
$443$	−12.6600	−0.601493	−0.300746	+	0.953704i	$0.597236\pi$
$444$	1.71642	0.0814575
$445$	−38.3592	−1.81840
$446$	15.2946	0.724218
$447$	18.8257	0.890426
$448$	0	0
$449$	3.07894	0.145304	0.0726521	−	0.997357i	$-0.476854\pi$
$449$	3.07894	0.145304	0.0726521	+	0.997357i	$0.476854\pi$
$450$	7.09279	0.334357
$451$	10.8032	0.508705
$452$	−10.5083	−0.494267
$453$	15.4632	0.726524
$454$	1.42931	0.0670810
$455$	0	0
$456$	2.00000	0.0936586
$457$	−15.4659	−0.723462	−0.361731	−	0.932282i	$-0.617814\pi$
$457$	−15.4659	−0.723462	−0.361731	+	0.932282i	$0.617814\pi$
$458$	17.9241	0.837541
$459$	7.03079	0.328169
$460$	3.47747	0.162138
$461$	14.0196	0.652958	0.326479	−	0.945204i	$-0.394138\pi$
$461$	14.0196	0.652958	0.326479	+	0.945204i	$0.394138\pi$
$462$	0	0
$463$	6.72153	0.312376	0.156188	−	0.987727i	$-0.450079\pi$
$463$	6.72153	0.312376	0.156188	+	0.987727i	$0.450079\pi$
$464$	−7.40162	−0.343612
$465$	33.2803	1.54334
$466$	−18.4155	−0.853080
$467$	−27.7104	−1.28228	−0.641141	−	0.767423i	$-0.721539\pi$
$467$	−27.7104	−1.28228	−0.641141	+	0.767423i	$0.721539\pi$
$468$	5.47747	0.253196
$469$	0	0
$470$	−41.7885	−1.92756
$471$	12.8791	0.593437
$472$	7.84830	0.361247
$473$	9.19101	0.422603
$474$	13.4944	0.619819
$475$	14.1856	0.650879
$476$	0	0
$477$	7.68520	0.351881
$478$	−8.00000	−0.365911
$479$	16.0339	0.732607	0.366303	−	0.930495i	$-0.380623\pi$
$479$	16.0339	0.732607	0.366303	+	0.930495i	$0.380623\pi$
$480$	−3.47747	−0.158724
$481$	9.40162	0.428677
$482$	−4.39853	−0.200347
$483$	0	0
$484$	−9.38777	−0.426717
$485$	−50.6195	−2.29851
$486$	1.00000	0.0453609
$487$	24.8794	1.12739	0.563697	−	0.825982i	$-0.309379\pi$
$487$	24.8794	1.12739	0.563697	+	0.825982i	$0.309379\pi$
$488$	9.92415	0.449245
$489$	−23.1405	−1.04645
$490$	0	0
$491$	34.9603	1.57773	0.788867	−	0.614563i	$-0.210668\pi$
$491$	34.9603	1.57773	0.788867	+	0.614563i	$0.210668\pi$
$492$	−8.50826	−0.383582
$493$	−52.0392	−2.34373
$494$	10.9549	0.492886
$495$	4.41547	0.198460
$496$	−9.57026	−0.429717
$497$	0	0
$498$	5.10664	0.228834
$499$	8.74166	0.391331	0.195665	−	0.980671i	$-0.437313\pi$
$499$	8.74166	0.391331	0.195665	+	0.980671i	$0.437313\pi$
$500$	−7.27761	−0.325465
$501$	−17.4186	−0.778204
$502$	4.29498	0.191694
$503$	−6.76936	−0.301831	−0.150915	−	0.988547i	$-0.548222\pi$
$503$	−6.76936	−0.301831	−0.150915	+	0.988547i	$0.548222\pi$
$504$	0	0
$505$	2.84287	0.126506
$506$	1.26974	0.0564466
$507$	17.0027	0.755115
$508$	11.6149	0.515328
$509$	−0.906783	−0.0401925	−0.0200962	−	0.999798i	$-0.506397\pi$
$509$	−0.906783	−0.0401925	−0.0200962	+	0.999798i	$0.506397\pi$
$510$	−24.4493	−1.08264
$511$	0	0
$512$	1.00000	0.0441942
$513$	2.00000	0.0883022
$514$	13.0451	0.575393
$515$	15.6773	0.690825
$516$	−7.23852	−0.318658
$517$	−15.2583	−0.671061
$518$	0	0
$519$	2.84521	0.124891
$520$	−19.0477	−0.835298
$521$	−29.4296	−1.28934	−0.644668	−	0.764463i	$-0.723004\pi$
$521$	−29.4296	−1.28934	−0.644668	+	0.764463i	$0.723004\pi$
$522$	−7.40162	−0.323960
$523$	−27.0789	−1.18408	−0.592040	−	0.805909i	$-0.701677\pi$
$523$	−27.0789	−1.18408	−0.592040	+	0.805909i	$0.701677\pi$
$524$	−19.1405	−0.836157
$525$	0	0
$526$	13.4016	0.584338
$527$	−67.2865	−2.93104
$528$	−1.26974	−0.0552582
$529$	1.00000	0.0434783
$530$	−26.7251	−1.16086
$531$	7.84830	0.340587
$532$	0	0
$533$	−46.6037	−2.01863
$534$	11.0308	0.477349
$535$	12.6010	0.544791
$536$	−4.37637	−0.189031
$537$	1.13785	0.0491020
$538$	−9.09236	−0.392000
$539$	0	0
$540$	−3.47747	−0.149646
$541$	10.4440	0.449023	0.224512	−	0.974471i	$-0.427921\pi$
$541$	10.4440	0.449023	0.224512	+	0.974471i	$0.427921\pi$
$542$	15.9241	0.684001
$543$	18.9407	0.812822
$544$	7.03079	0.301443
$545$	−63.6984	−2.72854
$546$	0	0
$547$	9.72429	0.415781	0.207890	−	0.978152i	$-0.433340\pi$
$547$	9.72429	0.415781	0.207890	+	0.978152i	$0.433340\pi$
$548$	4.86215	0.207701
$549$	9.92415	0.423552
$550$	−9.00597	−0.384016
$551$	−14.8032	−0.630639
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	−18.7527	−0.796728
$555$	−5.96879	−0.253361
$556$	−16.5083	−0.700106
$557$	−5.80921	−0.246144	−0.123072	−	0.992398i	$-0.539275\pi$
$557$	−5.80921	−0.246144	−0.123072	+	0.992398i	$0.539275\pi$
$558$	−9.57026	−0.405141
$559$	−39.6488	−1.67696
$560$	0	0
$561$	−8.92724	−0.376908
$562$	−24.4806	−1.03265
$563$	9.55247	0.402588	0.201294	−	0.979531i	$-0.435485\pi$
$563$	9.55247	0.402588	0.201294	+	0.979531i	$0.435485\pi$
$564$	12.0169	0.506004
$565$	36.5421	1.53734
$566$	−6.18558	−0.259999
$567$	0	0
$568$	−10.0616	−0.422174
$569$	−43.5476	−1.82561	−0.912804	−	0.408397i	$-0.866088\pi$
$569$	−43.5476	−1.82561	−0.912804	+	0.408397i	$0.866088\pi$
$570$	−6.95494	−0.291310
$571$	17.5335	0.733754	0.366877	−	0.930269i	$-0.380427\pi$
$571$	17.5335	0.733754	0.366877	+	0.930269i	$0.380427\pi$
$572$	−6.95494	−0.290801
$573$	−0.151700	−0.00633737
$574$	0	0
$575$	−7.09279	−0.295790
$576$	1.00000	0.0416667
$577$	−13.4944	−0.561780	−0.280890	−	0.959740i	$-0.590630\pi$
$577$	−13.4944	−0.561780	−0.280890	+	0.959740i	$0.590630\pi$
$578$	32.4320	1.34899
$579$	10.9237	0.453974
$580$	25.7389	1.06875
$581$	0	0
$582$	14.5564	0.603383
$583$	−9.75818	−0.404142
$584$	13.4944	0.558403
$585$	−19.0477	−0.787527
$586$	−32.0196	−1.32272
$587$	30.9264	1.27647	0.638234	−	0.769842i	$-0.279665\pi$
$587$	30.9264	1.27647	0.638234	+	0.769842i	$0.279665\pi$
$588$	0	0
$589$	−19.1405	−0.788671
$590$	−27.2922	−1.12360
$591$	13.6149	0.560042
$592$	1.71642	0.0705443
$593$	33.6765	1.38293	0.691463	−	0.722411i	$-0.256966\pi$
$593$	33.6765	1.38293	0.691463	+	0.722411i	$0.256966\pi$
$594$	−1.26974	−0.0520979
$595$	0	0
$596$	18.8257	0.771132
$597$	22.5698	0.923722
$598$	−5.47747	−0.223990
$599$	25.0165	1.02215	0.511074	−	0.859537i	$-0.329248\pi$
$599$	25.0165	1.02215	0.511074	+	0.859537i	$0.329248\pi$
$600$	7.09279	0.289562
$601$	9.73538	0.397114	0.198557	−	0.980089i	$-0.436374\pi$
$601$	9.73538	0.397114	0.198557	+	0.980089i	$0.436374\pi$
$602$	0	0
$603$	−4.37637	−0.178220
$604$	15.4632	0.629188
$605$	32.6457	1.32724
$606$	−0.817512	−0.0332091
$607$	3.69426	0.149946	0.0749728	−	0.997186i	$-0.476113\pi$
$607$	3.69426	0.149946	0.0749728	+	0.997186i	$0.476113\pi$
$608$	2.00000	0.0811107
$609$	0	0
$610$	−34.5109	−1.39731
$611$	65.8224	2.66289
$612$	7.03079	0.284203
$613$	−7.65484	−0.309176	−0.154588	−	0.987979i	$-0.549405\pi$
$613$	−7.65484	−0.309176	−0.154588	+	0.987979i	$0.549405\pi$
$614$	−20.1710	−0.814034
$615$	29.5872	1.19307
$616$	0	0
$617$	2.37116	0.0954594	0.0477297	−	0.998860i	$-0.484801\pi$
$617$	2.37116	0.0954594	0.0477297	+	0.998860i	$0.484801\pi$
$618$	−4.50826	−0.181349
$619$	−27.8474	−1.11928	−0.559642	−	0.828735i	$-0.689061\pi$
$619$	−27.8474	−1.11928	−0.559642	+	0.828735i	$0.689061\pi$
$620$	33.2803	1.33657
$621$	−1.00000	−0.0401286
$622$	8.10973	0.325171
$623$	0	0
$624$	5.47747	0.219274
$625$	−10.1563	−0.406251
$626$	6.84521	0.273589
$627$	−2.53947	−0.101417
$628$	12.8791	0.513932
$629$	12.0678	0.481173
$630$	0	0
$631$	−24.8648	−0.989853	−0.494926	−	0.868935i	$-0.664805\pi$
$631$	−24.8648	−0.989853	−0.494926	+	0.868935i	$0.664805\pi$
$632$	13.4944	0.536779
$633$	9.49441	0.377369
$634$	−0.598381	−0.0237648
$635$	−40.3904	−1.60285
$636$	7.68520	0.304738
$637$	0	0
$638$	9.39810	0.372074
$639$	−10.0616	−0.398030
$640$	−3.47747	−0.137459
$641$	26.1267	1.03194	0.515971	−	0.856606i	$-0.327431\pi$
$641$	26.1267	1.03194	0.515971	+	0.856606i	$0.327431\pi$
$642$	−3.62363	−0.143013
$643$	−18.8309	−0.742620	−0.371310	−	0.928509i	$-0.621091\pi$
$643$	−18.8309	−0.742620	−0.371310	+	0.928509i	$0.621091\pi$
$644$	0	0
$645$	25.1717	0.991136
$646$	14.0616	0.553245
$647$	−47.1539	−1.85381	−0.926906	−	0.375293i	$-0.877542\pi$
$647$	−47.1539	−1.85381	−0.926906	+	0.375293i	$0.877542\pi$
$648$	1.00000	0.0392837
$649$	−9.96527	−0.391171
$650$	38.8505	1.52384
$651$	0	0
$652$	−23.1405	−0.906253
$653$	15.2610	0.597209	0.298605	−	0.954377i	$-0.403479\pi$
$653$	15.2610	0.597209	0.298605	+	0.954377i	$0.403479\pi$
$654$	18.3175	0.716270
$655$	66.5606	2.60074
$656$	−8.50826	−0.332192
$657$	13.4944	0.526467
$658$	0	0
$659$	−24.9663	−0.972550	−0.486275	−	0.873806i	$-0.661645\pi$
$659$	−24.9663	−0.972550	−0.486275	+	0.873806i	$0.661645\pi$
$660$	4.41547	0.171872
$661$	−7.09236	−0.275861	−0.137930	−	0.990442i	$-0.544045\pi$
$661$	−7.09236	−0.275861	−0.137930	+	0.990442i	$0.544045\pi$
$662$	25.9099	1.00702
$663$	38.5109	1.49564
$664$	5.10664	0.198176
$665$	0	0
$666$	1.71642	0.0665098
$667$	7.40162	0.286592
$668$	−17.4186	−0.673944
$669$	15.2946	0.591322
$670$	15.2187	0.587950
$671$	−12.6010	−0.486458
$672$	0	0
$673$	−39.0358	−1.50472	−0.752360	−	0.658753i	$-0.771084\pi$
$673$	−39.0358	−1.50472	−0.752360	+	0.658753i	$0.771084\pi$
$674$	−8.21328	−0.316364
$675$	7.09279	0.273002
$676$	17.0027	0.653949
$677$	−13.9580	−0.536451	−0.268225	−	0.963356i	$-0.586437\pi$
$677$	−13.9580	−0.536451	−0.268225	+	0.963356i	$0.586437\pi$
$678$	−10.5083	−0.403567
$679$	0	0
$680$	−24.4493	−0.937590
$681$	1.42931	0.0547714
$682$	12.1517	0.465313
$683$	−27.4667	−1.05098	−0.525492	−	0.850798i	$-0.676119\pi$
$683$	−27.4667	−1.05098	−0.525492	+	0.850798i	$0.676119\pi$
$684$	2.00000	0.0764719
$685$	−16.9080	−0.646020
$686$	0	0
$687$	17.9241	0.683849
$688$	−7.23852	−0.275966
$689$	42.0955	1.60371
$690$	3.47747	0.132385
$691$	−5.03046	−0.191368	−0.0956838	−	0.995412i	$-0.530504\pi$
$691$	−5.03046	−0.191368	−0.0956838	+	0.995412i	$0.530504\pi$
$692$	2.84521	0.108159
$693$	0	0
$694$	−15.4632	−0.586975
$695$	57.4070	2.17757
$696$	−7.40162	−0.280558
$697$	−59.8198	−2.26583
$698$	−11.9241	−0.451336
$699$	−18.4155	−0.696537
$700$	0	0
$701$	9.56120	0.361121	0.180561	−	0.983564i	$-0.442209\pi$
$701$	9.56120	0.361121	0.180561	+	0.983564i	$0.442209\pi$
$702$	5.47747	0.206734
$703$	3.43283	0.129472
$704$	−1.26974	−0.0478550
$705$	−41.7885	−1.57385
$706$	13.9688	0.525722
$707$	0	0
$708$	7.84830	0.294957
$709$	−31.5050	−1.18319	−0.591597	−	0.806234i	$-0.701502\pi$
$709$	−31.5050	−1.18319	−0.591597	+	0.806234i	$0.701502\pi$
$710$	34.9888	1.31311
$711$	13.4944	0.506080
$712$	11.0308	0.413396
$713$	9.57026	0.358409
$714$	0	0
$715$	24.1856	0.904489
$716$	1.13785	0.0425235
$717$	−8.00000	−0.298765
$718$	6.56983	0.245184
$719$	3.38734	0.126327	0.0631633	−	0.998003i	$-0.479881\pi$
$719$	3.38734	0.126327	0.0631633	+	0.998003i	$0.479881\pi$
$720$	−3.47747	−0.129598
$721$	0	0
$722$	−15.0000	−0.558242
$723$	−4.39853	−0.163583
$724$	18.9407	0.703924
$725$	−52.4981	−1.94973
$726$	−9.38777	−0.348413
$727$	−25.0504	−0.929068	−0.464534	−	0.885555i	$-0.653778\pi$
$727$	−25.0504	−0.929068	−0.464534	+	0.885555i	$0.653778\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−46.9264	−1.73682
$731$	−50.8925	−1.88233
$732$	9.92415	0.366807
$733$	−15.3404	−0.566610	−0.283305	−	0.959030i	$-0.591431\pi$
$733$	−15.3404	−0.566610	−0.283305	+	0.959030i	$0.591431\pi$
$734$	−13.2499	−0.489063
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	5.55684	0.204689
$738$	−8.50826	−0.313193
$739$	−10.0616	−0.370121	−0.185061	−	0.982727i	$-0.559248\pi$
$739$	−10.0616	−0.370121	−0.185061	+	0.982727i	$0.559248\pi$
$740$	−5.96879	−0.219417
$741$	10.9549	0.402440
$742$	0	0
$743$	22.5109	0.825846	0.412923	−	0.910766i	$-0.364508\pi$
$743$	22.5109	0.825846	0.412923	+	0.910766i	$0.364508\pi$
$744$	−9.57026	−0.350863
$745$	−65.4659	−2.39848
$746$	19.6852	0.720726
$747$	5.10664	0.186842
$748$	−8.92724	−0.326412
$749$	0	0
$750$	−7.27761	−0.265741
$751$	30.4770	1.11212	0.556062	−	0.831141i	$-0.312312\pi$
$751$	30.4770	1.11212	0.556062	+	0.831141i	$0.312312\pi$
$752$	12.0169	0.438213
$753$	4.29498	0.156518
$754$	−40.5421	−1.47646
$755$	−53.7728	−1.95699
$756$	0	0
$757$	−25.3652	−0.921914	−0.460957	−	0.887423i	$-0.652494\pi$
$757$	−25.3652	−0.921914	−0.460957	+	0.887423i	$0.652494\pi$
$758$	9.77799	0.355153
$759$	1.26974	0.0460885
$760$	−6.95494	−0.252282
$761$	−43.4043	−1.57340	−0.786702	−	0.617333i	$-0.788213\pi$
$761$	−43.4043	−1.57340	−0.786702	+	0.617333i	$0.788213\pi$
$762$	11.6149	0.420763
$763$	0	0
$764$	−0.151700	−0.00548832
$765$	−24.4493	−0.883968
$766$	−2.80324	−0.101285
$767$	42.9888	1.55224
$768$	1.00000	0.0360844
$769$	9.32577	0.336296	0.168148	−	0.985762i	$-0.446221\pi$
$769$	9.32577	0.336296	0.168148	+	0.985762i	$0.446221\pi$
$770$	0	0
$771$	13.0451	0.469806
$772$	10.9237	0.393153
$773$	12.6742	0.455860	0.227930	−	0.973677i	$-0.426804\pi$
$773$	12.6742	0.455860	0.227930	+	0.973677i	$0.426804\pi$
$774$	−7.23852	−0.260183
$775$	−67.8798	−2.43832
$776$	14.5564	0.522545
$777$	0	0
$778$	1.06755	0.0382734
$779$	−17.0165	−0.609680
$780$	−19.0477	−0.682018
$781$	12.7755	0.457145
$782$	−7.03079	−0.251420
$783$	−7.40162	−0.264512
$784$	0	0
$785$	−44.7866	−1.59850
$786$	−19.1405	−0.682720
$787$	−16.7408	−0.596745	−0.298373	−	0.954449i	$-0.596444\pi$
$787$	−16.7408	−0.596745	−0.298373	+	0.954449i	$0.596444\pi$
$788$	13.6149	0.485011
$789$	13.4016	0.477110
$790$	−46.9264	−1.66957
$791$	0	0
$792$	−1.26974	−0.0451181
$793$	54.3592	1.93035
$794$	−5.00309	−0.177553
$795$	−26.7251	−0.947840
$796$	22.5698	0.799967
$797$	−29.6622	−1.05069	−0.525344	−	0.850890i	$-0.676064\pi$
$797$	−29.6622	−1.05069	−0.525344	+	0.850890i	$0.676064\pi$
$798$	0	0
$799$	84.4886	2.98899
$800$	7.09279	0.250768
$801$	11.0308	0.389754
$802$	−22.7527	−0.803427
$803$	−17.1343	−0.604657
$804$	−4.37637	−0.154343
$805$	0	0
$806$	−52.4208	−1.84644
$807$	−9.09236	−0.320066
$808$	−0.817512	−0.0287600
$809$	13.2187	0.464745	0.232372	−	0.972627i	$-0.425351\pi$
$809$	13.2187	0.464745	0.232372	+	0.972627i	$0.425351\pi$
$810$	−3.47747	−0.122186
$811$	22.7554	0.799051	0.399525	−	0.916722i	$-0.369175\pi$
$811$	22.7554	0.799051	0.399525	+	0.916722i	$0.369175\pi$
$812$	0	0
$813$	15.9241	0.558484
$814$	−2.17940	−0.0763878
$815$	80.4704	2.81876
$816$	7.03079	0.246127
$817$	−14.4770	−0.506488
$818$	8.18558	0.286202
$819$	0	0
$820$	29.5872	1.03323
$821$	−21.6184	−0.754488	−0.377244	−	0.926114i	$-0.623128\pi$
$821$	−21.6184	−0.754488	−0.377244	+	0.926114i	$0.623128\pi$
$822$	4.86215	0.169587
$823$	−19.4008	−0.676268	−0.338134	−	0.941098i	$-0.609796\pi$
$823$	−19.4008	−0.676268	−0.338134	+	0.941098i	$0.609796\pi$
$824$	−4.50826	−0.157053
$825$	−9.00597	−0.313548
$826$	0	0
$827$	−37.5388	−1.30535	−0.652677	−	0.757637i	$-0.726354\pi$
$827$	−37.5388	−1.30535	−0.652677	+	0.757637i	$0.726354\pi$
$828$	−1.00000	−0.0347524
$829$	−33.6823	−1.16984	−0.584918	−	0.811093i	$-0.698873\pi$
$829$	−33.6823	−1.16984	−0.584918	+	0.811093i	$0.698873\pi$
$830$	−17.7582	−0.616395
$831$	−18.7527	−0.650526
$832$	5.47747	0.189897
$833$	0	0
$834$	−16.5083	−0.571634
$835$	60.5725	2.09620
$836$	−2.53947	−0.0878295
$837$	−9.57026	−0.330797
$838$	2.18558	0.0754996
$839$	34.0330	1.17495	0.587475	−	0.809242i	$-0.300122\pi$
$839$	34.0330	1.17495	0.587475	+	0.809242i	$0.300122\pi$
$840$	0	0
$841$	25.7840	0.889102
$842$	−4.97475	−0.171441
$843$	−24.4806	−0.843155
$844$	9.49441	0.326811
$845$	−59.1262	−2.03400
$846$	12.0169	0.413151
$847$	0	0
$848$	7.68520	0.263911
$849$	−6.18558	−0.212289
$850$	49.8679	1.71046
$851$	−1.71642	−0.0588380
$852$	−10.0616	−0.344704
$853$	29.6630	1.01564	0.507822	−	0.861462i	$-0.330451\pi$
$853$	29.6630	1.01564	0.507822	+	0.861462i	$0.330451\pi$
$854$	0	0
$855$	−6.95494	−0.237854
$856$	−3.62363	−0.123853
$857$	37.0200	1.26458	0.632290	−	0.774732i	$-0.282115\pi$
$857$	37.0200	1.26458	0.632290	+	0.774732i	$0.282115\pi$
$858$	−6.95494	−0.237438
$859$	1.24992	0.0426467	0.0213233	−	0.999773i	$-0.493212\pi$
$859$	1.24992	0.0426467	0.0213233	+	0.999773i	$0.493212\pi$
$860$	25.1717	0.858349
$861$	0	0
$862$	−16.1267	−0.549277
$863$	−56.5953	−1.92653	−0.963263	−	0.268559i	$-0.913452\pi$
$863$	−56.5953	−1.92653	−0.963263	+	0.268559i	$0.913452\pi$
$864$	1.00000	0.0340207
$865$	−9.89412	−0.336410
$866$	15.5729	0.529190
$867$	32.4320	1.10145
$868$	0	0
$869$	−17.1343	−0.581242
$870$	25.7389	0.872630
$871$	−23.9715	−0.812242
$872$	18.3175	0.620308
$873$	14.5564	0.492660
$874$	−2.00000	−0.0676510
$875$	0	0
$876$	13.4944	0.455934
$877$	−35.7139	−1.20597	−0.602986	−	0.797752i	$-0.706022\pi$
$877$	−35.7139	−1.20597	−0.602986	+	0.797752i	$0.706022\pi$
$878$	−11.0308	−0.372271
$879$	−32.0196	−1.07999
$880$	4.41547	0.148845
$881$	−37.5306	−1.26444	−0.632219	−	0.774789i	$-0.717856\pi$
$881$	−37.5306	−1.26444	−0.632219	+	0.774789i	$0.717856\pi$
$882$	0	0
$883$	−32.7242	−1.10126	−0.550629	−	0.834750i	$-0.685612\pi$
$883$	−32.7242	−1.10126	−0.550629	+	0.834750i	$0.685612\pi$
$884$	38.5109	1.29526
$885$	−27.2922	−0.917418
$886$	−12.6600	−0.425320
$887$	4.18792	0.140616	0.0703082	−	0.997525i	$-0.477602\pi$
$887$	4.18792	0.140616	0.0703082	+	0.997525i	$0.477602\pi$
$888$	1.71642	0.0575992
$889$	0	0
$890$	−38.3592	−1.28580
$891$	−1.26974	−0.0425377
$892$	15.2946	0.512100
$893$	24.0339	0.804263
$894$	18.8257	0.629626
$895$	−3.95685	−0.132263
$896$	0	0
$897$	−5.47747	−0.182887
$898$	3.07894	0.102746
$899$	70.8354	2.36249
$900$	7.09279	0.236426
$901$	54.0330	1.80010
$902$	10.8032	0.359708
$903$	0	0
$904$	−10.5083	−0.349499
$905$	−65.8656	−2.18945
$906$	15.4632	0.513730
$907$	39.6097	1.31522	0.657609	−	0.753359i	$-0.271568\pi$
$907$	39.6097	1.31522	0.657609	+	0.753359i	$0.271568\pi$
$908$	1.42931	0.0474335
$909$	−0.817512	−0.0271152
$910$	0	0
$911$	−22.3843	−0.741623	−0.370812	−	0.928708i	$-0.620920\pi$
$911$	−22.3843	−0.741623	−0.370812	+	0.928708i	$0.620920\pi$
$912$	2.00000	0.0662266
$913$	−6.48408	−0.214592
$914$	−15.4659	−0.511565
$915$	−34.5109	−1.14090
$916$	17.9241	0.592231
$917$	0	0
$918$	7.03079	0.232051
$919$	−32.6010	−1.07541	−0.537705	−	0.843133i	$-0.680708\pi$
$919$	−32.6010	−1.07541	−0.537705	+	0.843133i	$0.680708\pi$
$920$	3.47747	0.114649
$921$	−20.1710	−0.664656
$922$	14.0196	0.461711
$923$	−55.1120	−1.81403
$924$	0	0
$925$	12.1742	0.400285
$926$	6.72153	0.220883
$927$	−4.50826	−0.148071
$928$	−7.40162	−0.242970
$929$	58.4235	1.91681	0.958406	−	0.285409i	$-0.0921294\pi$
$929$	58.4235	1.91681	0.958406	+	0.285409i	$0.0921294\pi$
$930$	33.2803	1.09130
$931$	0	0
$932$	−18.4155	−0.603219
$933$	8.10973	0.265501
$934$	−27.7104	−0.906710
$935$	31.0442	1.01525
$936$	5.47747	0.179037
$937$	20.3431	0.664581	0.332291	−	0.943177i	$-0.392179\pi$
$937$	20.3431	0.664581	0.332291	+	0.943177i	$0.392179\pi$
$938$	0	0
$939$	6.84521	0.223385
$940$	−41.7885	−1.36299
$941$	−39.4221	−1.28512	−0.642562	−	0.766234i	$-0.722128\pi$
$941$	−39.4221	−1.28512	−0.642562	+	0.766234i	$0.722128\pi$
$942$	12.8791	0.419623
$943$	8.50826	0.277067
$944$	7.84830	0.255440
$945$	0	0
$946$	9.19101	0.298825
$947$	−45.5587	−1.48046	−0.740229	−	0.672355i	$-0.765283\pi$
$947$	−45.5587	−1.48046	−0.740229	+	0.672355i	$0.765283\pi$
$948$	13.4944	0.438278
$949$	73.9152	2.39939
$950$	14.1856	0.460241
$951$	−0.598381	−0.0194038
$952$	0	0
$953$	14.0782	0.456037	0.228019	−	0.973657i	$-0.426775\pi$
$953$	14.0782	0.456037	0.228019	+	0.973657i	$0.426775\pi$
$954$	7.68520	0.248818
$955$	0.527533	0.0170706
$956$	−8.00000	−0.258738
$957$	9.39810	0.303797
$958$	16.0339	0.518031
$959$	0	0
$960$	−3.47747	−0.112235
$961$	60.5899	1.95451
$962$	9.40162	0.303120
$963$	−3.62363	−0.116770
$964$	−4.39853	−0.141667
$965$	−37.9869	−1.22284
$966$	0	0
$967$	45.5102	1.46351	0.731754	−	0.681569i	$-0.238702\pi$
$967$	45.5102	1.46351	0.731754	+	0.681569i	$0.238702\pi$
$968$	−9.38777	−0.301734
$969$	14.0616	0.451723
$970$	−50.6195	−1.62529
$971$	30.0053	0.962917	0.481458	−	0.876469i	$-0.340107\pi$
$971$	30.0053	0.962917	0.481458	+	0.876469i	$0.340107\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	24.8794	0.797188
$975$	38.8505	1.24421
$976$	9.92415	0.317664
$977$	49.0531	1.56935	0.784673	−	0.619910i	$-0.212831\pi$
$977$	49.0531	1.56935	0.784673	+	0.619910i	$0.212831\pi$
$978$	−23.1405	−0.739952
$979$	−14.0062	−0.447640
$980$	0	0
$981$	18.3175	0.584832
$982$	34.9603	1.11563
$983$	25.7582	0.821558	0.410779	−	0.911735i	$-0.365257\pi$
$983$	25.7582	0.821558	0.410779	+	0.911735i	$0.365257\pi$
$984$	−8.50826	−0.271233
$985$	−47.3454	−1.50855
$986$	−52.0392	−1.65727
$987$	0	0
$988$	10.9549	0.348523
$989$	7.23852	0.230172
$990$	4.41547	0.140333
$991$	−15.9715	−0.507350	−0.253675	−	0.967290i	$-0.581639\pi$
$991$	−15.9715	−0.507350	−0.253675	+	0.967290i	$0.581639\pi$
$992$	−9.57026	−0.303856
$993$	25.9099	0.822225
$994$	0	0
$995$	−78.4859	−2.48817
$996$	5.10664	0.161810
$997$	−15.8956	−0.503419	−0.251709	−	0.967803i	$-0.580993\pi$
$997$	−15.8956	−0.503419	−0.251709	+	0.967803i	$0.580993\pi$
$998$	8.74166	0.276712
$999$	1.71642	0.0543050

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cs.1.1	yes	4
7.6	odd	2		6762.2.a.cj.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.cj.1.4	✓	4	7.6	odd	2
6762.2.a.cs.1.1	yes	4	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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.47747 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.47747 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.47747 q^{10} -1.26974 q^{11} +1.00000 q^{12} +5.47747 q^{13} -3.47747 q^{15} +1.00000 q^{16} +7.03079 q^{17} +1.00000 q^{18} +2.00000 q^{19} -3.47747 q^{20} -1.26974 q^{22} -1.00000 q^{23} +1.00000 q^{24} +7.09279 q^{25} +5.47747 q^{26} +1.00000 q^{27} -7.40162 q^{29} -3.47747 q^{30} -9.57026 q^{31} +1.00000 q^{32} -1.26974 q^{33} +7.03079 q^{34} +1.00000 q^{36} +1.71642 q^{37} +2.00000 q^{38} +5.47747 q^{39} -3.47747 q^{40} -8.50826 q^{41} -7.23852 q^{43} -1.26974 q^{44} -3.47747 q^{45} -1.00000 q^{46} +12.0169 q^{47} +1.00000 q^{48} +7.09279 q^{50} +7.03079 q^{51} +5.47747 q^{52} +7.68520 q^{53} +1.00000 q^{54} +4.41547 q^{55} +2.00000 q^{57} -7.40162 q^{58} +7.84830 q^{59} -3.47747 q^{60} +9.92415 q^{61} -9.57026 q^{62} +1.00000 q^{64} -19.0477 q^{65} -1.26974 q^{66} -4.37637 q^{67} +7.03079 q^{68} -1.00000 q^{69} -10.0616 q^{71} +1.00000 q^{72} +13.4944 q^{73} +1.71642 q^{74} +7.09279 q^{75} +2.00000 q^{76} +5.47747 q^{78} +13.4944 q^{79} -3.47747 q^{80} +1.00000 q^{81} -8.50826 q^{82} +5.10664 q^{83} -24.4493 q^{85} -7.23852 q^{86} -7.40162 q^{87} -1.26974 q^{88} +11.0308 q^{89} -3.47747 q^{90} -1.00000 q^{92} -9.57026 q^{93} +12.0169 q^{94} -6.95494 q^{95} +1.00000 q^{96} +14.5564 q^{97} -1.26974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 3 q^{10} + 2 q^{11} + 4 q^{12} + 5 q^{13} + 3 q^{15} + 4 q^{16} + 10 q^{17} + 4 q^{18} + 8 q^{19} + 3 q^{20} + 2 q^{22} - 4 q^{23} + 4 q^{24} + 13 q^{25} + 5 q^{26} + 4 q^{27} + 3 q^{29} + 3 q^{30} - 6 q^{31} + 4 q^{32} + 2 q^{33} + 10 q^{34} + 4 q^{36} + q^{37} + 8 q^{38} + 5 q^{39} + 3 q^{40} + q^{41} - q^{43} + 2 q^{44} + 3 q^{45} - 4 q^{46} + 17 q^{47} + 4 q^{48} + 13 q^{50} + 10 q^{51} + 5 q^{52} + 4 q^{53} + 4 q^{54} - 2 q^{55} + 8 q^{57} + 3 q^{58} + 3 q^{60} + 24 q^{61} - 6 q^{62} + 4 q^{64} - 27 q^{65} + 2 q^{66} - 8 q^{67} + 10 q^{68} - 4 q^{69} - 4 q^{71} + 4 q^{72} + 6 q^{73} + q^{74} + 13 q^{75} + 8 q^{76} + 5 q^{78} + 6 q^{79} + 3 q^{80} + 4 q^{81} + q^{82} + 18 q^{83} - 16 q^{85} - q^{86} + 3 q^{87} + 2 q^{88} + 26 q^{89} + 3 q^{90} - 4 q^{92} - 6 q^{93} + 17 q^{94} + 6 q^{95} + 4 q^{96} + 13 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 3 * q^10 + 2 * q^11 + 4 * q^12 + 5 * q^13 + 3 * q^15 + 4 * q^16 + 10 * q^17 + 4 * q^18 + 8 * q^19 + 3 * q^20 + 2 * q^22 - 4 * q^23 + 4 * q^24 + 13 * q^25 + 5 * q^26 + 4 * q^27 + 3 * q^29 + 3 * q^30 - 6 * q^31 + 4 * q^32 + 2 * q^33 + 10 * q^34 + 4 * q^36 + q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 + q^41 - q^43 + 2 * q^44 + 3 * q^45 - 4 * q^46 + 17 * q^47 + 4 * q^48 + 13 * q^50 + 10 * q^51 + 5 * q^52 + 4 * q^53 + 4 * q^54 - 2 * q^55 + 8 * q^57 + 3 * q^58 + 3 * q^60 + 24 * q^61 - 6 * q^62 + 4 * q^64 - 27 * q^65 + 2 * q^66 - 8 * q^67 + 10 * q^68 - 4 * q^69 - 4 * q^71 + 4 * q^72 + 6 * q^73 + q^74 + 13 * q^75 + 8 * q^76 + 5 * q^78 + 6 * q^79 + 3 * q^80 + 4 * q^81 + q^82 + 18 * q^83 - 16 * q^85 - q^86 + 3 * q^87 + 2 * q^88 + 26 * q^89 + 3 * q^90 - 4 * q^92 - 6 * q^93 + 17 * q^94 + 6 * q^95 + 4 * q^96 + 13 * q^97 + 2 * q^99

Introduction

L-functions

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Database

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