LMFDB - Embedded newform 6762.2.a.cn.1.4

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:	4.4.16448.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 14 $ x^4 - 2x^3 - 7x^2 + 8*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.87996$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.87996 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.87996 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.87996 q^{10} +2.65867 q^{11} -1.00000 q^{12} +4.19292 q^{13} -3.87996 q^{15} +1.00000 q^{16} -1.75992 q^{17} +1.00000 q^{18} +0.585786 q^{19} +3.87996 q^{20} +2.65867 q^{22} -1.00000 q^{23} -1.00000 q^{24} +10.0541 q^{25} +4.19292 q^{26} -1.00000 q^{27} +2.63551 q^{29} -3.87996 q^{30} +0.585786 q^{31} +1.00000 q^{32} -2.65867 q^{33} -1.75992 q^{34} +1.00000 q^{36} -7.95284 q^{37} +0.585786 q^{38} -4.19292 q^{39} +3.87996 q^{40} +11.3671 q^{41} +2.85158 q^{43} +2.65867 q^{44} +3.87996 q^{45} -1.00000 q^{46} -4.70839 q^{47} -1.00000 q^{48} +10.0541 q^{50} +1.75992 q^{51} +4.19292 q^{52} -4.55560 q^{53} -1.00000 q^{54} +10.3155 q^{55} -0.585786 q^{57} +2.63551 q^{58} +1.83024 q^{59} -3.87996 q^{60} -1.80005 q^{61} +0.585786 q^{62} +1.00000 q^{64} +16.2684 q^{65} -2.65867 q^{66} +0.931495 q^{67} -1.75992 q^{68} +1.00000 q^{69} -2.65867 q^{71} +1.00000 q^{72} +1.02838 q^{73} -7.95284 q^{74} -10.0541 q^{75} +0.585786 q^{76} -4.19292 q^{78} -8.65867 q^{79} +3.87996 q^{80} +1.00000 q^{81} +11.3671 q^{82} +13.7297 q^{83} -6.82843 q^{85} +2.85158 q^{86} -2.63551 q^{87} +2.65867 q^{88} -0.216077 q^{89} +3.87996 q^{90} -1.00000 q^{92} -0.585786 q^{93} -4.70839 q^{94} +2.27283 q^{95} -1.00000 q^{96} +8.80527 q^{97} +2.65867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 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 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 8 q^{19} + 6 q^{20} - 4 q^{23} - 4 q^{24} + 6 q^{25} + 10 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 12 q^{34} + 4 q^{36} - 6 q^{37} + 8 q^{38} - 10 q^{39} + 6 q^{40} + 14 q^{41} - 6 q^{43} + 6 q^{45} - 4 q^{46} + 2 q^{47} - 4 q^{48} + 6 q^{50} - 12 q^{51} + 10 q^{52} - 4 q^{53} - 4 q^{54} + 8 q^{55} - 8 q^{57} + 6 q^{58} + 8 q^{59} - 6 q^{60} + 12 q^{61} + 8 q^{62} + 4 q^{64} + 6 q^{65} - 4 q^{67} + 12 q^{68} + 4 q^{69} + 4 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{75} + 8 q^{76} - 10 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} + 14 q^{82} + 16 q^{83} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 12 q^{89} + 6 q^{90} - 4 q^{92} - 8 q^{93} + 2 q^{94} + 12 q^{95} - 4 q^{96} + 30 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 8 * q^19 + 6 * q^20 - 4 * q^23 - 4 * q^24 + 6 * q^25 + 10 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 12 * q^34 + 4 * q^36 - 6 * q^37 + 8 * q^38 - 10 * q^39 + 6 * q^40 + 14 * q^41 - 6 * q^43 + 6 * q^45 - 4 * q^46 + 2 * q^47 - 4 * q^48 + 6 * q^50 - 12 * q^51 + 10 * q^52 - 4 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^57 + 6 * q^58 + 8 * q^59 - 6 * q^60 + 12 * q^61 + 8 * q^62 + 4 * q^64 + 6 * q^65 - 4 * q^67 + 12 * q^68 + 4 * q^69 + 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^75 + 8 * q^76 - 10 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 + 14 * q^82 + 16 * q^83 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 - 4 * q^92 - 8 * q^93 + 2 * q^94 + 12 * q^95 - 4 * q^96 + 30 * q^97

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
$5$	3.87996	1.73517	0.867586	−	0.497288i	$-0.165671\pi$
$5$	3.87996	1.73517	0.867586	+	0.497288i	$0.165671\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.87996	1.22695
$11$	2.65867	0.801618	0.400809	−	0.916162i	$-0.368729\pi$
$11$	2.65867	0.801618	0.400809	+	0.916162i	$0.368729\pi$
$12$	−1.00000	−0.288675
$13$	4.19292	1.16291	0.581453	−	0.813580i	$-0.302484\pi$
$13$	4.19292	1.16291	0.581453	+	0.813580i	$0.302484\pi$
$14$	0	0
$15$	−3.87996	−1.00180
$16$	1.00000	0.250000
$17$	−1.75992	−0.426844	−0.213422	−	0.976960i	$-0.568461\pi$
$17$	−1.75992	−0.426844	−0.213422	+	0.976960i	$0.568461\pi$
$18$	1.00000	0.235702
$19$	0.585786	0.134389	0.0671943	−	0.997740i	$-0.478595\pi$
$19$	0.585786	0.134389	0.0671943	+	0.997740i	$0.478595\pi$
$20$	3.87996	0.867586
$21$	0	0
$22$	2.65867	0.566830
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	10.0541	2.01082
$26$	4.19292	0.822299
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.63551	0.489402	0.244701	−	0.969599i	$-0.421310\pi$
$29$	2.63551	0.489402	0.244701	+	0.969599i	$0.421310\pi$
$30$	−3.87996	−0.708381
$31$	0.585786	0.105210	0.0526052	−	0.998615i	$-0.483248\pi$
$31$	0.585786	0.105210	0.0526052	+	0.998615i	$0.483248\pi$
$32$	1.00000	0.176777
$33$	−2.65867	−0.462814
$34$	−1.75992	−0.301824
$35$	0	0
$36$	1.00000	0.166667
$37$	−7.95284	−1.30744	−0.653719	−	0.756737i	$-0.726792\pi$
$37$	−7.95284	−1.30744	−0.653719	+	0.756737i	$0.726792\pi$
$38$	0.585786	0.0950271
$39$	−4.19292	−0.671404
$40$	3.87996	0.613476
$41$	11.3671	1.77524	0.887618	−	0.460581i	$-0.152359\pi$
$41$	11.3671	1.77524	0.887618	+	0.460581i	$0.152359\pi$
$42$	0	0
$43$	2.85158	0.434863	0.217431	−	0.976076i	$-0.430232\pi$
$43$	2.85158	0.434863	0.217431	+	0.976076i	$0.430232\pi$
$44$	2.65867	0.400809
$45$	3.87996	0.578390
$46$	−1.00000	−0.147442
$47$	−4.70839	−0.686789	−0.343394	−	0.939191i	$-0.611577\pi$
$47$	−4.70839	−0.686789	−0.343394	+	0.939191i	$0.611577\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	10.0541	1.42186
$51$	1.75992	0.246438
$52$	4.19292	0.581453
$53$	−4.55560	−0.625760	−0.312880	−	0.949793i	$-0.601294\pi$
$53$	−4.55560	−0.625760	−0.312880	+	0.949793i	$0.601294\pi$
$54$	−1.00000	−0.136083
$55$	10.3155	1.39094
$56$	0	0
$57$	−0.585786	−0.0775893
$58$	2.63551	0.346059
$59$	1.83024	0.238277	0.119138	−	0.992878i	$-0.461987\pi$
$59$	1.83024	0.238277	0.119138	+	0.992878i	$0.461987\pi$
$60$	−3.87996	−0.500901
$61$	−1.80005	−0.230473	−0.115236	−	0.993338i	$-0.536763\pi$
$61$	−1.80005	−0.230473	−0.115236	+	0.993338i	$0.536763\pi$
$62$	0.585786	0.0743950
$63$	0	0
$64$	1.00000	0.125000
$65$	16.2684	2.01784
$66$	−2.65867	−0.327259
$67$	0.931495	0.113800	0.0569001	−	0.998380i	$-0.481878\pi$
$67$	0.931495	0.113800	0.0569001	+	0.998380i	$0.481878\pi$
$68$	−1.75992	−0.213422
$69$	1.00000	0.120386
$70$	0	0
$71$	−2.65867	−0.315526	−0.157763	−	0.987477i	$-0.550428\pi$
$71$	−2.65867	−0.315526	−0.157763	+	0.987477i	$0.550428\pi$
$72$	1.00000	0.117851
$73$	1.02838	0.120362	0.0601811	−	0.998187i	$-0.480832\pi$
$73$	1.02838	0.120362	0.0601811	+	0.998187i	$0.480832\pi$
$74$	−7.95284	−0.924499
$75$	−10.0541	−1.16095
$76$	0.585786	0.0671943
$77$	0	0
$78$	−4.19292	−0.474755
$79$	−8.65867	−0.974176	−0.487088	−	0.873353i	$-0.661941\pi$
$79$	−8.65867	−0.974176	−0.487088	+	0.873353i	$0.661941\pi$
$80$	3.87996	0.433793
$81$	1.00000	0.111111
$82$	11.3671	1.25528
$83$	13.7297	1.50703	0.753517	−	0.657428i	$-0.228356\pi$
$83$	13.7297	1.50703	0.753517	+	0.657428i	$0.228356\pi$
$84$	0	0
$85$	−6.82843	−0.740647
$86$	2.85158	0.307494
$87$	−2.63551	−0.282556
$88$	2.65867	0.283415
$89$	−0.216077	−0.0229041	−0.0114520	−	0.999934i	$-0.503645\pi$
$89$	−0.216077	−0.0229041	−0.0114520	+	0.999934i	$0.503645\pi$
$90$	3.87996	0.408984
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−0.585786	−0.0607432
$94$	−4.70839	−0.485633
$95$	2.27283	0.233187
$96$	−1.00000	−0.102062
$97$	8.80527	0.894040	0.447020	−	0.894524i	$-0.352485\pi$
$97$	8.80527	0.894040	0.447020	+	0.894524i	$0.352485\pi$
$98$	0	0
$99$	2.65867	0.267206
$100$	10.0541	1.00541
$101$	−11.1439	−1.10886	−0.554432	−	0.832229i	$-0.687064\pi$
$101$	−11.1439	−1.10886	−0.554432	+	0.832229i	$0.687064\pi$
$102$	1.75992	0.174258
$103$	1.80708	0.178057	0.0890285	−	0.996029i	$-0.471624\pi$
$103$	1.80708	0.178057	0.0890285	+	0.996029i	$0.471624\pi$
$104$	4.19292	0.411150
$105$	0	0
$106$	−4.55560	−0.442479
$107$	−7.55741	−0.730602	−0.365301	−	0.930889i	$-0.619034\pi$
$107$	−7.55741	−0.730602	−0.365301	+	0.930889i	$0.619034\pi$
$108$	−1.00000	−0.0962250
$109$	2.81883	0.269995	0.134998	−	0.990846i	$-0.456897\pi$
$109$	2.81883	0.269995	0.134998	+	0.990846i	$0.456897\pi$
$110$	10.3155	0.983546
$111$	7.95284	0.754850
$112$	0	0
$113$	−4.61151	−0.433814	−0.216907	−	0.976192i	$-0.569597\pi$
$113$	−4.61151	−0.433814	−0.216907	+	0.976192i	$0.569597\pi$
$114$	−0.585786	−0.0548639
$115$	−3.87996	−0.361808
$116$	2.63551	0.244701
$117$	4.19292	0.387635
$118$	1.83024	0.168487
$119$	0	0
$120$	−3.87996	−0.354190
$121$	−3.93149	−0.357409
$122$	−1.80005	−0.162969
$123$	−11.3671	−1.02493
$124$	0.585786	0.0526052
$125$	19.6097	1.75394
$126$	0	0
$127$	−9.51025	−0.843898	−0.421949	−	0.906619i	$-0.638654\pi$
$127$	−9.51025	−0.843898	−0.421949	+	0.906619i	$0.638654\pi$
$128$	1.00000	0.0883883
$129$	−2.85158	−0.251068
$130$	16.2684	1.42683
$131$	−19.0069	−1.66064	−0.830322	−	0.557284i	$-0.811843\pi$
$131$	−19.0069	−1.66064	−0.830322	+	0.557284i	$0.811843\pi$
$132$	−2.65867	−0.231407
$133$	0	0
$134$	0.931495	0.0804689
$135$	−3.87996	−0.333934
$136$	−1.75992	−0.150912
$137$	−8.71095	−0.744227	−0.372113	−	0.928187i	$-0.621367\pi$
$137$	−8.71095	−0.744227	−0.372113	+	0.928187i	$0.621367\pi$
$138$	1.00000	0.0851257
$139$	−9.34049	−0.792250	−0.396125	−	0.918197i	$-0.629645\pi$
$139$	−9.34049	−0.792250	−0.396125	+	0.918197i	$0.629645\pi$
$140$	0	0
$141$	4.70839	0.396518
$142$	−2.65867	−0.223110
$143$	11.1476	0.932207
$144$	1.00000	0.0833333
$145$	10.2257	0.849196
$146$	1.02838	0.0851090
$147$	0	0
$148$	−7.95284	−0.653719
$149$	1.62410	0.133052	0.0665259	−	0.997785i	$-0.478808\pi$
$149$	1.62410	0.133052	0.0665259	+	0.997785i	$0.478808\pi$
$150$	−10.0541	−0.820914
$151$	−6.39543	−0.520453	−0.260226	−	0.965548i	$-0.583797\pi$
$151$	−6.39543	−0.520453	−0.260226	+	0.965548i	$0.583797\pi$
$152$	0.585786	0.0475136
$153$	−1.75992	−0.142281
$154$	0	0
$155$	2.27283	0.182558
$156$	−4.19292	−0.335702
$157$	21.2736	1.69782	0.848908	−	0.528540i	$-0.177260\pi$
$157$	21.2736	1.69782	0.848908	+	0.528540i	$0.177260\pi$
$158$	−8.65867	−0.688846
$159$	4.55560	0.361282
$160$	3.87996	0.306738
$161$	0	0
$162$	1.00000	0.0785674
$163$	−8.48528	−0.664619	−0.332309	−	0.943170i	$-0.607828\pi$
$163$	−8.48528	−0.664619	−0.332309	+	0.943170i	$0.607828\pi$
$164$	11.3671	0.887618
$165$	−10.3155	−0.803062
$166$	13.7297	1.06563
$167$	21.8292	1.68919	0.844596	−	0.535404i	$-0.179841\pi$
$167$	21.8292	1.68919	0.844596	+	0.535404i	$0.179841\pi$
$168$	0	0
$169$	4.58057	0.352351
$170$	−6.82843	−0.523716
$171$	0.585786	0.0447962
$172$	2.85158	0.217431
$173$	20.4940	1.55813	0.779066	−	0.626942i	$-0.215694\pi$
$173$	20.4940	1.55813	0.779066	+	0.626942i	$0.215694\pi$
$174$	−2.63551	−0.199797
$175$	0	0
$176$	2.65867	0.200404
$177$	−1.83024	−0.137569
$178$	−0.216077	−0.0161956
$179$	−26.6166	−1.98942	−0.994710	−	0.102721i	$-0.967245\pi$
$179$	−26.6166	−1.98942	−0.994710	+	0.102721i	$0.967245\pi$
$180$	3.87996	0.289195
$181$	21.6390	1.60842	0.804209	−	0.594347i	$-0.202590\pi$
$181$	21.6390	1.60842	0.804209	+	0.594347i	$0.202590\pi$
$182$	0	0
$183$	1.80005	0.133064
$184$	−1.00000	−0.0737210
$185$	−30.8567	−2.26863
$186$	−0.585786	−0.0429519
$187$	−4.67904	−0.342166
$188$	−4.70839	−0.343394
$189$	0	0
$190$	2.27283	0.164888
$191$	2.23645	0.161824	0.0809121	−	0.996721i	$-0.474217\pi$
$191$	2.23645	0.161824	0.0809121	+	0.996721i	$0.474217\pi$
$192$	−1.00000	−0.0721688
$193$	1.19473	0.0859986	0.0429993	−	0.999075i	$-0.486309\pi$
$193$	1.19473	0.0859986	0.0429993	+	0.999075i	$0.486309\pi$
$194$	8.80527	0.632181
$195$	−16.2684	−1.16500
$196$	0	0
$197$	12.5788	0.896199	0.448100	−	0.893984i	$-0.352101\pi$
$197$	12.5788	0.896199	0.448100	+	0.893984i	$0.352101\pi$
$198$	2.65867	0.188943
$199$	2.73858	0.194132	0.0970662	−	0.995278i	$-0.469054\pi$
$199$	2.73858	0.194132	0.0970662	+	0.995278i	$0.469054\pi$
$200$	10.0541	0.710932
$201$	−0.931495	−0.0657026
$202$	−11.1439	−0.784085
$203$	0	0
$204$	1.75992	0.123219
$205$	44.1037	3.08034
$206$	1.80708	0.125905
$207$	−1.00000	−0.0695048
$208$	4.19292	0.290727
$209$	1.55741	0.107728
$210$	0	0
$211$	7.58654	0.522279	0.261139	−	0.965301i	$-0.415902\pi$
$211$	7.58654	0.522279	0.261139	+	0.965301i	$0.415902\pi$
$212$	−4.55560	−0.312880
$213$	2.65867	0.182169
$214$	−7.55741	−0.516614
$215$	11.0640	0.754561
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	2.81883	0.190916
$219$	−1.02838	−0.0694912
$220$	10.3155	0.695472
$221$	−7.37921	−0.496379
$222$	7.95284	0.533760
$223$	−13.4433	−0.900233	−0.450116	−	0.892970i	$-0.648617\pi$
$223$	−13.4433	−0.900233	−0.450116	+	0.892970i	$0.648617\pi$
$224$	0	0
$225$	10.0541	0.670273
$226$	−4.61151	−0.306753
$227$	−1.84721	−0.122604	−0.0613018	−	0.998119i	$-0.519525\pi$
$227$	−1.84721	−0.122604	−0.0613018	+	0.998119i	$0.519525\pi$
$228$	−0.585786	−0.0387947
$229$	−13.0471	−0.862174	−0.431087	−	0.902310i	$-0.641870\pi$
$229$	−13.0471	−0.862174	−0.431087	+	0.902310i	$0.641870\pi$
$230$	−3.87996	−0.255837
$231$	0	0
$232$	2.63551	0.173030
$233$	12.5556	0.822545	0.411272	−	0.911513i	$-0.365085\pi$
$233$	12.5556	0.822545	0.411272	+	0.911513i	$0.365085\pi$
$234$	4.19292	0.274100
$235$	−18.2684	−1.19170
$236$	1.83024	0.119138
$237$	8.65867	0.562441
$238$	0	0
$239$	−24.2540	−1.56886	−0.784429	−	0.620219i	$-0.787044\pi$
$239$	−24.2540	−1.56886	−0.784429	+	0.620219i	$0.787044\pi$
$240$	−3.87996	−0.250450
$241$	17.7227	1.14162	0.570810	−	0.821082i	$-0.306629\pi$
$241$	17.7227	1.14162	0.570810	+	0.821082i	$0.306629\pi$
$242$	−3.93149	−0.252726
$243$	−1.00000	−0.0641500
$244$	−1.80005	−0.115236
$245$	0	0
$246$	−11.3671	−0.724737
$247$	2.45615	0.156281
$248$	0.585786	0.0371975
$249$	−13.7297	−0.870087
$250$	19.6097	1.24023
$251$	−26.3037	−1.66027	−0.830137	−	0.557560i	$-0.811738\pi$
$251$	−26.3037	−1.66027	−0.830137	+	0.557560i	$0.811738\pi$
$252$	0	0
$253$	−2.65867	−0.167149
$254$	−9.51025	−0.596726
$255$	6.82843	0.427613
$256$	1.00000	0.0625000
$257$	−14.7643	−0.920971	−0.460486	−	0.887667i	$-0.652325\pi$
$257$	−14.7643	−0.920971	−0.460486	+	0.887667i	$0.652325\pi$
$258$	−2.85158	−0.177532
$259$	0	0
$260$	16.2684	1.00892
$261$	2.63551	0.163134
$262$	−19.0069	−1.17425
$263$	3.81583	0.235294	0.117647	−	0.993055i	$-0.462465\pi$
$263$	3.81583	0.235294	0.117647	+	0.993055i	$0.462465\pi$
$264$	−2.65867	−0.163630
$265$	−17.6755	−1.08580
$266$	0	0
$267$	0.216077	0.0132237
$268$	0.931495	0.0569001
$269$	−19.7551	−1.20449	−0.602245	−	0.798311i	$-0.705727\pi$
$269$	−19.7551	−1.20449	−0.602245	+	0.798311i	$0.705727\pi$
$270$	−3.87996	−0.236127
$271$	24.4966	1.48806	0.744031	−	0.668145i	$-0.232911\pi$
$271$	24.4966	1.48806	0.744031	+	0.668145i	$0.232911\pi$
$272$	−1.75992	−0.106711
$273$	0	0
$274$	−8.71095	−0.526248
$275$	26.7305	1.61191
$276$	1.00000	0.0601929
$277$	−2.21245	−0.132933	−0.0664667	−	0.997789i	$-0.521173\pi$
$277$	−2.21245	−0.132933	−0.0664667	+	0.997789i	$0.521173\pi$
$278$	−9.34049	−0.560205
$279$	0.585786	0.0350701
$280$	0	0
$281$	3.92009	0.233853	0.116926	−	0.993141i	$-0.462696\pi$
$281$	3.92009	0.233853	0.116926	+	0.993141i	$0.462696\pi$
$282$	4.70839	0.280380
$283$	25.7484	1.53058	0.765292	−	0.643683i	$-0.222594\pi$
$283$	25.7484	1.53058	0.765292	+	0.643683i	$0.222594\pi$
$284$	−2.65867	−0.157763
$285$	−2.27283	−0.134631
$286$	11.1476	0.659170
$287$	0	0
$288$	1.00000	0.0589256
$289$	−13.9027	−0.817804
$290$	10.2257	0.600472
$291$	−8.80527	−0.516174
$292$	1.02838	0.0601811
$293$	−25.8379	−1.50947	−0.754734	−	0.656031i	$-0.772234\pi$
$293$	−25.8379	−1.50947	−0.754734	+	0.656031i	$0.772234\pi$
$294$	0	0
$295$	7.10126	0.413451
$296$	−7.95284	−0.462249
$297$	−2.65867	−0.154271
$298$	1.62410	0.0940818
$299$	−4.19292	−0.242483
$300$	−10.0541	−0.580474
$301$	0	0
$302$	−6.39543	−0.368016
$303$	11.1439	0.640203
$304$	0.585786	0.0335972
$305$	−6.98413	−0.399910
$306$	−1.75992	−0.100608
$307$	−19.2889	−1.10087	−0.550437	−	0.834877i	$-0.685539\pi$
$307$	−19.2889	−1.10087	−0.550437	+	0.834877i	$0.685539\pi$
$308$	0	0
$309$	−1.80708	−0.102801
$310$	2.27283	0.129088
$311$	−17.4433	−0.989121	−0.494561	−	0.869143i	$-0.664671\pi$
$311$	−17.4433	−0.989121	−0.494561	+	0.869143i	$0.664671\pi$
$312$	−4.19292	−0.237377
$313$	−15.3225	−0.866076	−0.433038	−	0.901376i	$-0.642558\pi$
$313$	−15.3225	−0.866076	−0.433038	+	0.901376i	$0.642558\pi$
$314$	21.2736	1.20054
$315$	0	0
$316$	−8.65867	−0.487088
$317$	27.4123	1.53963	0.769814	−	0.638268i	$-0.220349\pi$
$317$	27.4123	1.53963	0.769814	+	0.638268i	$0.220349\pi$
$318$	4.55560	0.255465
$319$	7.00694	0.392313
$320$	3.87996	0.216896
$321$	7.55741	0.421814
$322$	0	0
$323$	−1.03094	−0.0573629
$324$	1.00000	0.0555556
$325$	42.1560	2.33839
$326$	−8.48528	−0.469956
$327$	−2.81883	−0.155882
$328$	11.3671	0.627641
$329$	0	0
$330$	−10.3155	−0.567851
$331$	5.99638	0.329591	0.164795	−	0.986328i	$-0.447304\pi$
$331$	5.99638	0.329591	0.164795	+	0.986328i	$0.447304\pi$
$332$	13.7297	0.753517
$333$	−7.95284	−0.435813
$334$	21.8292	1.19444
$335$	3.61416	0.197463
$336$	0	0
$337$	−7.63648	−0.415985	−0.207993	−	0.978130i	$-0.566693\pi$
$337$	−7.63648	−0.415985	−0.207993	+	0.978130i	$0.566693\pi$
$338$	4.58057	0.249150
$339$	4.61151	0.250463
$340$	−6.82843	−0.370323
$341$	1.55741	0.0843385
$342$	0.585786	0.0316757
$343$	0	0
$344$	2.85158	0.153747
$345$	3.87996	0.208890
$346$	20.4940	1.10177
$347$	32.7660	1.75897	0.879486	−	0.475925i	$-0.157887\pi$
$347$	32.7660	1.75897	0.879486	+	0.475925i	$0.157887\pi$
$348$	−2.63551	−0.141278
$349$	36.5403	1.95596	0.977980	−	0.208699i	$-0.0669229\pi$
$349$	36.5403	1.95596	0.977980	+	0.208699i	$0.0669229\pi$
$350$	0	0
$351$	−4.19292	−0.223801
$352$	2.65867	0.141707
$353$	2.90096	0.154402	0.0772012	−	0.997016i	$-0.475402\pi$
$353$	2.90096	0.154402	0.0772012	+	0.997016i	$0.475402\pi$
$354$	−1.83024	−0.0972761
$355$	−10.3155	−0.547491
$356$	−0.216077	−0.0114520
$357$	0	0
$358$	−26.6166	−1.40673
$359$	−26.5499	−1.40125	−0.700626	−	0.713529i	$-0.747096\pi$
$359$	−26.5499	−1.40125	−0.700626	+	0.713529i	$0.747096\pi$
$360$	3.87996	0.204492
$361$	−18.6569	−0.981940
$362$	21.6390	1.13732
$363$	3.93149	0.206350
$364$	0	0
$365$	3.99006	0.208849
$366$	1.80005	0.0940902
$367$	26.6833	1.39286	0.696429	−	0.717626i	$-0.254771\pi$
$367$	26.6833	1.39286	0.696429	+	0.717626i	$0.254771\pi$
$368$	−1.00000	−0.0521286
$369$	11.3671	0.591745
$370$	−30.8567	−1.60416
$371$	0	0
$372$	−0.585786	−0.0303716
$373$	9.13038	0.472753	0.236377	−	0.971662i	$-0.424040\pi$
$373$	9.13038	0.472753	0.236377	+	0.971662i	$0.424040\pi$
$374$	−4.67904	−0.241948
$375$	−19.6097	−1.01264
$376$	−4.70839	−0.242817
$377$	11.0505	0.569128
$378$	0	0
$379$	−33.9288	−1.74281	−0.871404	−	0.490567i	$-0.836790\pi$
$379$	−33.9288	−1.74281	−0.871404	+	0.490567i	$0.836790\pi$
$380$	2.27283	0.116594
$381$	9.51025	0.487225
$382$	2.23645	0.114427
$383$	30.8008	1.57385	0.786924	−	0.617050i	$-0.211672\pi$
$383$	30.8008	1.57385	0.786924	+	0.617050i	$0.211672\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	1.19473	0.0608102
$387$	2.85158	0.144954
$388$	8.80527	0.447020
$389$	−2.38221	−0.120783	−0.0603915	−	0.998175i	$-0.519235\pi$
$389$	−2.38221	−0.120783	−0.0603915	+	0.998175i	$0.519235\pi$
$390$	−16.2684	−0.823780
$391$	1.75992	0.0890031
$392$	0	0
$393$	19.0069	0.958773
$394$	12.5788	0.633709
$395$	−33.5953	−1.69036
$396$	2.65867	0.133603
$397$	−3.21064	−0.161137	−0.0805687	−	0.996749i	$-0.525674\pi$
$397$	−3.21064	−0.161137	−0.0805687	+	0.996749i	$0.525674\pi$
$398$	2.73858	0.137272
$399$	0	0
$400$	10.0541	0.502705
$401$	36.2591	1.81069	0.905346	−	0.424675i	$-0.139612\pi$
$401$	36.2591	1.81069	0.905346	+	0.424675i	$0.139612\pi$
$402$	−0.931495	−0.0464587
$403$	2.45615	0.122350
$404$	−11.1439	−0.554432
$405$	3.87996	0.192797
$406$	0	0
$407$	−21.1439	−1.04807
$408$	1.75992	0.0871291
$409$	4.28896	0.212075	0.106038	−	0.994362i	$-0.466184\pi$
$409$	4.28896	0.212075	0.106038	+	0.994362i	$0.466184\pi$
$410$	44.1037	2.17813
$411$	8.71095	0.429679
$412$	1.80708	0.0890285
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	53.2708	2.61496
$416$	4.19292	0.205575
$417$	9.34049	0.457406
$418$	1.55741	0.0761754
$419$	−29.3422	−1.43346	−0.716730	−	0.697350i	$-0.754362\pi$
$419$	−29.3422	−1.43346	−0.716730	+	0.697350i	$0.754362\pi$
$420$	0	0
$421$	−5.27186	−0.256935	−0.128467	−	0.991714i	$-0.541006\pi$
$421$	−5.27186	−0.256935	−0.128467	+	0.991714i	$0.541006\pi$
$422$	7.58654	0.369307
$423$	−4.70839	−0.228930
$424$	−4.55560	−0.221239
$425$	−17.6944	−0.858306
$426$	2.65867	0.128813
$427$	0	0
$428$	−7.55741	−0.365301
$429$	−11.1476	−0.538210
$430$	11.0640	0.533555
$431$	−6.70463	−0.322951	−0.161475	−	0.986877i	$-0.551625\pi$
$431$	−6.70463	−0.322951	−0.161475	+	0.986877i	$0.551625\pi$
$432$	−1.00000	−0.0481125
$433$	26.3751	1.26750	0.633752	−	0.773536i	$-0.281514\pi$
$433$	26.3751	1.26750	0.633752	+	0.773536i	$0.281514\pi$
$434$	0	0
$435$	−10.2257	−0.490283
$436$	2.81883	0.134998
$437$	−0.585786	−0.0280220
$438$	−1.02838	−0.0491377
$439$	8.18589	0.390691	0.195346	−	0.980734i	$-0.437417\pi$
$439$	8.18589	0.390691	0.195346	+	0.980734i	$0.437417\pi$
$440$	10.3155	0.491773
$441$	0	0
$442$	−7.37921	−0.350993
$443$	3.45037	0.163932	0.0819660	−	0.996635i	$-0.473880\pi$
$443$	3.45037	0.163932	0.0819660	+	0.996635i	$0.473880\pi$
$444$	7.95284	0.377425
$445$	−0.838369	−0.0397425
$446$	−13.4433	−0.636561
$447$	−1.62410	−0.0768175
$448$	0	0
$449$	39.1515	1.84767	0.923837	−	0.382787i	$-0.125036\pi$
$449$	39.1515	1.84767	0.923837	+	0.382787i	$0.125036\pi$
$450$	10.0541	0.473955
$451$	30.2212	1.42306
$452$	−4.61151	−0.216907
$453$	6.39543	0.300484
$454$	−1.84721	−0.0866939
$455$	0	0
$456$	−0.585786	−0.0274320
$457$	16.7872	0.785274	0.392637	−	0.919694i	$-0.371563\pi$
$457$	16.7872	0.785274	0.392637	+	0.919694i	$0.371563\pi$
$458$	−13.0471	−0.609649
$459$	1.75992	0.0821461
$460$	−3.87996	−0.180904
$461$	34.3170	1.59830	0.799152	−	0.601130i	$-0.205282\pi$
$461$	34.3170	1.59830	0.799152	+	0.601130i	$0.205282\pi$
$462$	0	0
$463$	−7.75033	−0.360188	−0.180094	−	0.983649i	$-0.557640\pi$
$463$	−7.75033	−0.360188	−0.180094	+	0.983649i	$0.557640\pi$
$464$	2.63551	0.122350
$465$	−2.27283	−0.105400
$466$	12.5556	0.581627
$467$	19.9023	0.920967	0.460484	−	0.887668i	$-0.347676\pi$
$467$	19.9023	0.920967	0.460484	+	0.887668i	$0.347676\pi$
$468$	4.19292	0.193818
$469$	0	0
$470$	−18.2684	−0.842657
$471$	−21.2736	−0.980235
$472$	1.83024	0.0842436
$473$	7.58141	0.348594
$474$	8.65867	0.397706
$475$	5.88955	0.270231
$476$	0	0
$477$	−4.55560	−0.208587
$478$	−24.2540	−1.10935
$479$	−12.4661	−0.569591	−0.284795	−	0.958588i	$-0.591926\pi$
$479$	−12.4661	−0.569591	−0.284795	+	0.958588i	$0.591926\pi$
$480$	−3.87996	−0.177095
$481$	−33.3456	−1.52043
$482$	17.7227	0.807247
$483$	0	0
$484$	−3.93149	−0.178704
$485$	34.1641	1.55131
$486$	−1.00000	−0.0453609
$487$	−40.4859	−1.83459	−0.917296	−	0.398205i	$-0.869633\pi$
$487$	−40.4859	−1.83459	−0.917296	+	0.398205i	$0.869633\pi$
$488$	−1.80005	−0.0814845
$489$	8.48528	0.383718
$490$	0	0
$491$	35.7599	1.61382	0.806911	−	0.590673i	$-0.201138\pi$
$491$	35.7599	1.61382	0.806911	+	0.590673i	$0.201138\pi$
$492$	−11.3671	−0.512466
$493$	−4.63829	−0.208898
$494$	2.45615	0.110508
$495$	10.3155	0.463648
$496$	0.585786	0.0263026
$497$	0	0
$498$	−13.7297	−0.615244
$499$	−18.3291	−0.820523	−0.410261	−	0.911968i	$-0.634562\pi$
$499$	−18.3291	−0.820523	−0.410261	+	0.911968i	$0.634562\pi$
$500$	19.6097	0.876972
$501$	−21.8292	−0.975256
$502$	−26.3037	−1.17399
$503$	3.19389	0.142408	0.0712042	−	0.997462i	$-0.477316\pi$
$503$	3.19389	0.142408	0.0712042	+	0.997462i	$0.477316\pi$
$504$	0	0
$505$	−43.2381	−1.92407
$506$	−2.65867	−0.118192
$507$	−4.58057	−0.203430
$508$	−9.51025	−0.421949
$509$	−29.5917	−1.31163	−0.655814	−	0.754923i	$-0.727674\pi$
$509$	−29.5917	−1.31163	−0.655814	+	0.754923i	$0.727674\pi$
$510$	6.82843	0.302368
$511$	0	0
$512$	1.00000	0.0441942
$513$	−0.585786	−0.0258631
$514$	−14.7643	−0.651225
$515$	7.01140	0.308959
$516$	−2.85158	−0.125534
$517$	−12.5180	−0.550542
$518$	0	0
$519$	−20.4940	−0.899588
$520$	16.2684	0.713415
$521$	−38.8474	−1.70194	−0.850968	−	0.525217i	$-0.823984\pi$
$521$	−38.8474	−1.70194	−0.850968	+	0.525217i	$0.823984\pi$
$522$	2.63551	0.115353
$523$	41.6214	1.81997	0.909987	−	0.414636i	$-0.136091\pi$
$523$	41.6214	1.81997	0.909987	+	0.414636i	$0.136091\pi$
$524$	−19.0069	−0.830322
$525$	0	0
$526$	3.81583	0.166378
$527$	−1.03094	−0.0449084
$528$	−2.65867	−0.115704
$529$	1.00000	0.0434783
$530$	−17.6755	−0.767777
$531$	1.83024	0.0794256
$532$	0	0
$533$	47.6611	2.06443
$534$	0.216077	0.00935055
$535$	−29.3225	−1.26772
$536$	0.931495	0.0402344
$537$	26.6166	1.14859
$538$	−19.7551	−0.851703
$539$	0	0
$540$	−3.87996	−0.166967
$541$	4.70185	0.202148	0.101074	−	0.994879i	$-0.467772\pi$
$541$	4.70185	0.202148	0.101074	+	0.994879i	$0.467772\pi$
$542$	24.4966	1.05222
$543$	−21.6390	−0.928620
$544$	−1.75992	−0.0754560
$545$	10.9370	0.468488
$546$	0	0
$547$	39.5764	1.69217	0.846083	−	0.533052i	$-0.178955\pi$
$547$	39.5764	1.69217	0.846083	+	0.533052i	$0.178955\pi$
$548$	−8.71095	−0.372113
$549$	−1.80005	−0.0768243
$550$	26.7305	1.13979
$551$	1.54385	0.0657700
$552$	1.00000	0.0425628
$553$	0	0
$554$	−2.21245	−0.0939981
$555$	30.8567	1.30979
$556$	−9.34049	−0.396125
$557$	9.65685	0.409174	0.204587	−	0.978848i	$-0.434415\pi$
$557$	9.65685	0.409174	0.204587	+	0.978848i	$0.434415\pi$
$558$	0.585786	0.0247983
$559$	11.9565	0.505705
$560$	0	0
$561$	4.67904	0.197549
$562$	3.92009	0.165359
$563$	−1.05635	−0.0445199	−0.0222599	−	0.999752i	$-0.507086\pi$
$563$	−1.05635	−0.0445199	−0.0222599	+	0.999752i	$0.507086\pi$
$564$	4.70839	0.198259
$565$	−17.8925	−0.752742
$566$	25.7484	1.08229
$567$	0	0
$568$	−2.65867	−0.111555
$569$	6.60276	0.276802	0.138401	−	0.990376i	$-0.455804\pi$
$569$	6.60276	0.276802	0.138401	+	0.990376i	$0.455804\pi$
$570$	−2.27283	−0.0951983
$571$	0.686292	0.0287204	0.0143602	−	0.999897i	$-0.495429\pi$
$571$	0.686292	0.0287204	0.0143602	+	0.999897i	$0.495429\pi$
$572$	11.1476	0.466103
$573$	−2.23645	−0.0934292
$574$	0	0
$575$	−10.0541	−0.419285
$576$	1.00000	0.0416667
$577$	−34.5565	−1.43860	−0.719302	−	0.694697i	$-0.755538\pi$
$577$	−34.5565	−1.43860	−0.719302	+	0.694697i	$0.755538\pi$
$578$	−13.9027	−0.578275
$579$	−1.19473	−0.0496513
$580$	10.2257	0.424598
$581$	0	0
$582$	−8.80527	−0.364990
$583$	−12.1118	−0.501620
$584$	1.02838	0.0425545
$585$	16.2684	0.672614
$586$	−25.8379	−1.06735
$587$	13.5829	0.560627	0.280313	−	0.959909i	$-0.409562\pi$
$587$	13.5829	0.560627	0.280313	+	0.959909i	$0.409562\pi$
$588$	0	0
$589$	0.343146	0.0141391
$590$	7.10126	0.292354
$591$	−12.5788	−0.517421
$592$	−7.95284	−0.326860
$593$	−19.3331	−0.793916	−0.396958	−	0.917837i	$-0.629934\pi$
$593$	−19.3331	−0.793916	−0.396958	+	0.917837i	$0.629934\pi$
$594$	−2.65867	−0.109086
$595$	0	0
$596$	1.62410	0.0665259
$597$	−2.73858	−0.112082
$598$	−4.19292	−0.171461
$599$	17.6241	0.720101	0.360051	−	0.932933i	$-0.382759\pi$
$599$	17.6241	0.720101	0.360051	+	0.932933i	$0.382759\pi$
$600$	−10.0541	−0.410457
$601$	−29.3990	−1.19921	−0.599604	−	0.800297i	$-0.704675\pi$
$601$	−29.3990	−1.19921	−0.599604	+	0.800297i	$0.704675\pi$
$602$	0	0
$603$	0.931495	0.0379334
$604$	−6.39543	−0.260226
$605$	−15.2540	−0.620165
$606$	11.1439	0.452692
$607$	−41.8755	−1.69967	−0.849837	−	0.527046i	$-0.823300\pi$
$607$	−41.8755	−1.69967	−0.849837	+	0.527046i	$0.823300\pi$
$608$	0.585786	0.0237568
$609$	0	0
$610$	−6.98413	−0.282779
$611$	−19.7419	−0.798671
$612$	−1.75992	−0.0711406
$613$	−2.75333	−0.111206	−0.0556031	−	0.998453i	$-0.517708\pi$
$613$	−2.75333	−0.111206	−0.0556031	+	0.998453i	$0.517708\pi$
$614$	−19.2889	−0.778435
$615$	−44.1037	−1.77843
$616$	0	0
$617$	−12.6274	−0.508361	−0.254180	−	0.967157i	$-0.581806\pi$
$617$	−12.6274	−0.508361	−0.254180	+	0.967157i	$0.581806\pi$
$618$	−1.80708	−0.0726915
$619$	−6.55547	−0.263486	−0.131743	−	0.991284i	$-0.542057\pi$
$619$	−6.55547	−0.263486	−0.131743	+	0.991284i	$0.542057\pi$
$620$	2.27283	0.0912790
$621$	1.00000	0.0401286
$622$	−17.4433	−0.699414
$623$	0	0
$624$	−4.19292	−0.167851
$625$	25.8144	1.03257
$626$	−15.3225	−0.612409
$627$	−1.55741	−0.0621970
$628$	21.2736	0.848908
$629$	13.9964	0.558072
$630$	0	0
$631$	6.20202	0.246898	0.123449	−	0.992351i	$-0.460604\pi$
$631$	6.20202	0.246898	0.123449	+	0.992351i	$0.460604\pi$
$632$	−8.65867	−0.344423
$633$	−7.58654	−0.301538
$634$	27.4123	1.08868
$635$	−36.8994	−1.46431
$636$	4.55560	0.180641
$637$	0	0
$638$	7.00694	0.277407
$639$	−2.65867	−0.105175
$640$	3.87996	0.153369
$641$	42.4796	1.67784	0.838922	−	0.544252i	$-0.183186\pi$
$641$	42.4796	1.67784	0.838922	+	0.544252i	$0.183186\pi$
$642$	7.55741	0.298267
$643$	6.70754	0.264520	0.132260	−	0.991215i	$-0.457777\pi$
$643$	6.70754	0.264520	0.132260	+	0.991215i	$0.457777\pi$
$644$	0	0
$645$	−11.0640	−0.435646
$646$	−1.03094	−0.0405617
$647$	3.62154	0.142377	0.0711887	−	0.997463i	$-0.477321\pi$
$647$	3.62154	0.142377	0.0711887	+	0.997463i	$0.477321\pi$
$648$	1.00000	0.0392837
$649$	4.86599	0.191007
$650$	42.1560	1.65349
$651$	0	0
$652$	−8.48528	−0.332309
$653$	11.4998	0.450023	0.225011	−	0.974356i	$-0.427758\pi$
$653$	11.4998	0.450023	0.225011	+	0.974356i	$0.427758\pi$
$654$	−2.81883	−0.110225
$655$	−73.7462	−2.88150
$656$	11.3671	0.443809
$657$	1.02838	0.0401208
$658$	0	0
$659$	−17.5953	−0.685415	−0.342708	−	0.939442i	$-0.611344\pi$
$659$	−17.5953	−0.685415	−0.342708	+	0.939442i	$0.611344\pi$
$660$	−10.3155	−0.401531
$661$	−36.5477	−1.42154	−0.710771	−	0.703424i	$-0.751654\pi$
$661$	−36.5477	−1.42154	−0.710771	+	0.703424i	$0.751654\pi$
$662$	5.99638	0.233056
$663$	7.37921	0.286585
$664$	13.7297	0.532817
$665$	0	0
$666$	−7.95284	−0.308166
$667$	−2.63551	−0.102047
$668$	21.8292	0.844596
$669$	13.4433	0.519750
$670$	3.61416	0.139627
$671$	−4.78574	−0.184751
$672$	0	0
$673$	−18.8016	−0.724750	−0.362375	−	0.932032i	$-0.618034\pi$
$673$	−18.8016	−0.724750	−0.362375	+	0.932032i	$0.618034\pi$
$674$	−7.63648	−0.294146
$675$	−10.0541	−0.386982
$676$	4.58057	0.176176
$677$	−26.3232	−1.01168	−0.505842	−	0.862626i	$-0.668818\pi$
$677$	−26.3232	−1.01168	−0.505842	+	0.862626i	$0.668818\pi$
$678$	4.61151	0.177104
$679$	0	0
$680$	−6.82843	−0.261858
$681$	1.84721	0.0707853
$682$	1.55741	0.0596363
$683$	31.8381	1.21825	0.609125	−	0.793074i	$-0.291521\pi$
$683$	31.8381	1.21825	0.609125	+	0.793074i	$0.291521\pi$
$684$	0.585786	0.0223981
$685$	−33.7981	−1.29136
$686$	0	0
$687$	13.0471	0.497777
$688$	2.85158	0.108716
$689$	−19.1013	−0.727700
$690$	3.87996	0.147708
$691$	−43.8825	−1.66937	−0.834685	−	0.550728i	$-0.814350\pi$
$691$	−43.8825	−1.66937	−0.834685	+	0.550728i	$0.814350\pi$
$692$	20.4940	0.779066
$693$	0	0
$694$	32.7660	1.24378
$695$	−36.2407	−1.37469
$696$	−2.63551	−0.0998987
$697$	−20.0051	−0.757748
$698$	36.5403	1.38307
$699$	−12.5556	−0.474896
$700$	0	0
$701$	−29.6317	−1.11917	−0.559586	−	0.828772i	$-0.689040\pi$
$701$	−29.6317	−1.11917	−0.559586	+	0.828772i	$0.689040\pi$
$702$	−4.19292	−0.158252
$703$	−4.65867	−0.175705
$704$	2.65867	0.100202
$705$	18.2684	0.688026
$706$	2.90096	0.109179
$707$	0	0
$708$	−1.83024	−0.0687846
$709$	43.7151	1.64176	0.820878	−	0.571104i	$-0.193485\pi$
$709$	43.7151	1.64176	0.820878	+	0.571104i	$0.193485\pi$
$710$	−10.3155	−0.387135
$711$	−8.65867	−0.324725
$712$	−0.216077	−0.00809781
$713$	−0.585786	−0.0219379
$714$	0	0
$715$	43.2521	1.61754
$716$	−26.6166	−0.994710
$717$	24.2540	0.905780
$718$	−26.5499	−0.990835
$719$	16.6333	0.620316	0.310158	−	0.950685i	$-0.399618\pi$
$719$	16.6333	0.620316	0.310158	+	0.950685i	$0.399618\pi$
$720$	3.87996	0.144598
$721$	0	0
$722$	−18.6569	−0.694336
$723$	−17.7227	−0.659114
$724$	21.6390	0.804209
$725$	26.4977	0.984098
$726$	3.93149	0.145911
$727$	27.5058	1.02013	0.510067	−	0.860135i	$-0.329621\pi$
$727$	27.5058	1.02013	0.510067	+	0.860135i	$0.329621\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.99006	0.147679
$731$	−5.01857	−0.185618
$732$	1.80005	0.0665318
$733$	−0.448776	−0.0165759	−0.00828795	−	0.999966i	$-0.502638\pi$
$733$	−0.448776	−0.0165759	−0.00828795	+	0.999966i	$0.502638\pi$
$734$	26.6833	0.984899
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	2.47653	0.0912243
$738$	11.3671	0.418427
$739$	42.0614	1.54725	0.773626	−	0.633642i	$-0.218441\pi$
$739$	42.0614	1.54725	0.773626	+	0.633642i	$0.218441\pi$
$740$	−30.8567	−1.13432
$741$	−2.45615	−0.0902291
$742$	0	0
$743$	−45.5005	−1.66925	−0.834625	−	0.550818i	$-0.814316\pi$
$743$	−45.5005	−1.66925	−0.834625	+	0.550818i	$0.814316\pi$
$744$	−0.585786	−0.0214760
$745$	6.30146	0.230868
$746$	9.13038	0.334287
$747$	13.7297	0.502345
$748$	−4.67904	−0.171083
$749$	0	0
$750$	−19.6097	−0.716045
$751$	−23.6860	−0.864314	−0.432157	−	0.901798i	$-0.642247\pi$
$751$	−23.6860	−0.864314	−0.432157	+	0.901798i	$0.642247\pi$
$752$	−4.70839	−0.171697
$753$	26.3037	0.958559
$754$	11.0505	0.402434
$755$	−24.8140	−0.903075
$756$	0	0
$757$	36.4424	1.32452	0.662261	−	0.749273i	$-0.269597\pi$
$757$	36.4424	1.32452	0.662261	+	0.749273i	$0.269597\pi$
$758$	−33.9288	−1.23235
$759$	2.65867	0.0965035
$760$	2.27283	0.0824442
$761$	30.5757	1.10837	0.554183	−	0.832395i	$-0.313031\pi$
$761$	30.5757	1.10837	0.554183	+	0.832395i	$0.313031\pi$
$762$	9.51025	0.344520
$763$	0	0
$764$	2.23645	0.0809121
$765$	−6.82843	−0.246882
$766$	30.8008	1.11288
$767$	7.67404	0.277094
$768$	−1.00000	−0.0360844
$769$	−8.43180	−0.304059	−0.152029	−	0.988376i	$-0.548581\pi$
$769$	−8.43180	−0.304059	−0.152029	+	0.988376i	$0.548581\pi$
$770$	0	0
$771$	14.7643	0.531723
$772$	1.19473	0.0429993
$773$	15.0072	0.539770	0.269885	−	0.962893i	$-0.413014\pi$
$773$	15.0072	0.539770	0.269885	+	0.962893i	$0.413014\pi$
$774$	2.85158	0.102498
$775$	5.88955	0.211559
$776$	8.80527	0.316091
$777$	0	0
$778$	−2.38221	−0.0854065
$779$	6.65867	0.238571
$780$	−16.2684	−0.582501
$781$	−7.06851	−0.252931
$782$	1.75992	0.0629347
$783$	−2.63551	−0.0941854
$784$	0	0
$785$	82.5407	2.94600
$786$	19.0069	0.677955
$787$	−35.9774	−1.28245	−0.641227	−	0.767351i	$-0.721574\pi$
$787$	−35.9774	−1.28245	−0.641227	+	0.767351i	$0.721574\pi$
$788$	12.5788	0.448100
$789$	−3.81583	−0.135847
$790$	−33.5953	−1.19527
$791$	0	0
$792$	2.65867	0.0944716
$793$	−7.54747	−0.268018
$794$	−3.21064	−0.113941
$795$	17.6755	0.626887
$796$	2.73858	0.0970662
$797$	36.1450	1.28032	0.640162	−	0.768240i	$-0.278867\pi$
$797$	36.1450	1.28032	0.640162	+	0.768240i	$0.278867\pi$
$798$	0	0
$799$	8.28639	0.293152
$800$	10.0541	0.355466
$801$	−0.216077	−0.00763469
$802$	36.2591	1.28035
$803$	2.73411	0.0964846
$804$	−0.931495	−0.0328513
$805$	0	0
$806$	2.45615	0.0865144
$807$	19.7551	0.695413
$808$	−11.1439	−0.392043
$809$	31.0261	1.09082	0.545410	−	0.838169i	$-0.316374\pi$
$809$	31.0261	1.09082	0.545410	+	0.838169i	$0.316374\pi$
$810$	3.87996	0.136328
$811$	−2.38036	−0.0835859	−0.0417929	−	0.999126i	$-0.513307\pi$
$811$	−2.38036	−0.0835859	−0.0417929	+	0.999126i	$0.513307\pi$
$812$	0	0
$813$	−24.4966	−0.859133
$814$	−21.1439	−0.741095
$815$	−32.9226	−1.15323
$816$	1.75992	0.0616096
$817$	1.67042	0.0584406
$818$	4.28896	0.149960
$819$	0	0
$820$	44.1037	1.54017
$821$	−53.2725	−1.85922	−0.929612	−	0.368540i	$-0.879858\pi$
$821$	−53.2725	−1.85922	−0.929612	+	0.368540i	$0.879858\pi$
$822$	8.71095	0.303829
$823$	−44.8240	−1.56247	−0.781233	−	0.624240i	$-0.785409\pi$
$823$	−44.8240	−1.56247	−0.781233	+	0.624240i	$0.785409\pi$
$824$	1.80708	0.0629527
$825$	−26.7305	−0.930636
$826$	0	0
$827$	−24.6878	−0.858479	−0.429239	−	0.903191i	$-0.641218\pi$
$827$	−24.6878	−0.858479	−0.429239	+	0.903191i	$0.641218\pi$
$828$	−1.00000	−0.0347524
$829$	−24.3483	−0.845650	−0.422825	−	0.906211i	$-0.638962\pi$
$829$	−24.3483	−0.845650	−0.422825	+	0.906211i	$0.638962\pi$
$830$	53.2708	1.84906
$831$	2.21245	0.0767491
$832$	4.19292	0.145363
$833$	0	0
$834$	9.34049	0.323435
$835$	84.6964	2.93104
$836$	1.55741	0.0538642
$837$	−0.585786	−0.0202477
$838$	−29.3422	−1.01361
$839$	36.5215	1.26086	0.630431	−	0.776246i	$-0.282878\pi$
$839$	36.5215	1.26086	0.630431	+	0.776246i	$0.282878\pi$
$840$	0	0
$841$	−22.0541	−0.760486
$842$	−5.27186	−0.181680
$843$	−3.92009	−0.135015
$844$	7.58654	0.261139
$845$	17.7724	0.611390
$846$	−4.70839	−0.161878
$847$	0	0
$848$	−4.55560	−0.156440
$849$	−25.7484	−0.883684
$850$	−17.6944	−0.606914
$851$	7.95284	0.272620
$852$	2.65867	0.0910844
$853$	−14.1893	−0.485832	−0.242916	−	0.970047i	$-0.578104\pi$
$853$	−14.1893	−0.485832	−0.242916	+	0.970047i	$0.578104\pi$
$854$	0	0
$855$	2.27283	0.0777291
$856$	−7.55741	−0.258307
$857$	−36.5314	−1.24789	−0.623944	−	0.781469i	$-0.714471\pi$
$857$	−36.5314	−1.24789	−0.623944	+	0.781469i	$0.714471\pi$
$858$	−11.1476	−0.380572
$859$	−1.93415	−0.0659924	−0.0329962	−	0.999455i	$-0.510505\pi$
$859$	−1.93415	−0.0659924	−0.0329962	+	0.999455i	$0.510505\pi$
$860$	11.0640	0.377281
$861$	0	0
$862$	−6.70463	−0.228361
$863$	−13.0081	−0.442802	−0.221401	−	0.975183i	$-0.571063\pi$
$863$	−13.0081	−0.442802	−0.221401	+	0.975183i	$0.571063\pi$
$864$	−1.00000	−0.0340207
$865$	79.5160	2.70363
$866$	26.3751	0.896261
$867$	13.9027	0.472160
$868$	0	0
$869$	−23.0205	−0.780917
$870$	−10.2257	−0.346683
$871$	3.90568	0.132339
$872$	2.81883	0.0954578
$873$	8.80527	0.298013
$874$	−0.585786	−0.0198145
$875$	0	0
$876$	−1.02838	−0.0347456
$877$	0.988246	0.0333707	0.0166854	−	0.999861i	$-0.494689\pi$
$877$	0.988246	0.0333707	0.0166854	+	0.999861i	$0.494689\pi$
$878$	8.18589	0.276260
$879$	25.8379	0.871492
$880$	10.3155	0.347736
$881$	−4.71492	−0.158850	−0.0794249	−	0.996841i	$-0.525308\pi$
$881$	−4.71492	−0.158850	−0.0794249	+	0.996841i	$0.525308\pi$
$882$	0	0
$883$	13.0253	0.438337	0.219168	−	0.975687i	$-0.429666\pi$
$883$	13.0253	0.438337	0.219168	+	0.975687i	$0.429666\pi$
$884$	−7.37921	−0.248190
$885$	−7.10126	−0.238706
$886$	3.45037	0.115917
$887$	−20.9615	−0.703818	−0.351909	−	0.936034i	$-0.614467\pi$
$887$	−20.9615	−0.703818	−0.351909	+	0.936034i	$0.614467\pi$
$888$	7.95284	0.266880
$889$	0	0
$890$	−0.838369	−0.0281022
$891$	2.65867	0.0890687
$892$	−13.4433	−0.450116
$893$	−2.75811	−0.0922966
$894$	−1.62410	−0.0543182
$895$	−103.271	−3.45199
$896$	0	0
$897$	4.19292	0.139997
$898$	39.1515	1.30650
$899$	1.54385	0.0514901
$900$	10.0541	0.335137
$901$	8.01750	0.267102
$902$	30.2212	1.00626
$903$	0	0
$904$	−4.61151	−0.153376
$905$	83.9586	2.79088
$906$	6.39543	0.212474
$907$	−28.6969	−0.952865	−0.476432	−	0.879211i	$-0.658070\pi$
$907$	−28.6969	−0.952865	−0.476432	+	0.879211i	$0.658070\pi$
$908$	−1.84721	−0.0613018
$909$	−11.1439	−0.369621
$910$	0	0
$911$	48.5199	1.60754	0.803768	−	0.594943i	$-0.202825\pi$
$911$	48.5199	1.60754	0.803768	+	0.594943i	$0.202825\pi$
$912$	−0.585786	−0.0193973
$913$	36.5028	1.20807
$914$	16.7872	0.555272
$915$	6.98413	0.230888
$916$	−13.0471	−0.431087
$917$	0	0
$918$	1.75992	0.0580861
$919$	−8.80492	−0.290448	−0.145224	−	0.989399i	$-0.546390\pi$
$919$	−8.80492	−0.290448	−0.145224	+	0.989399i	$0.546390\pi$
$920$	−3.87996	−0.127919
$921$	19.2889	0.635590
$922$	34.3170	1.13017
$923$	−11.1476	−0.366927
$924$	0	0
$925$	−79.9586	−2.62902
$926$	−7.75033	−0.254692
$927$	1.80708	0.0593523
$928$	2.63551	0.0865148
$929$	−54.7130	−1.79508	−0.897538	−	0.440937i	$-0.854646\pi$
$929$	−54.7130	−1.79508	−0.897538	+	0.440937i	$0.854646\pi$
$930$	−2.27283	−0.0745290
$931$	0	0
$932$	12.5556	0.411272
$933$	17.4433	0.571069
$934$	19.9023	0.651222
$935$	−18.1545	−0.593716
$936$	4.19292	0.137050
$937$	−38.8531	−1.26927	−0.634637	−	0.772810i	$-0.718851\pi$
$937$	−38.8531	−1.26927	−0.634637	+	0.772810i	$0.718851\pi$
$938$	0	0
$939$	15.3225	0.500029
$940$	−18.2684	−0.595848
$941$	19.1134	0.623079	0.311540	−	0.950233i	$-0.399155\pi$
$941$	19.1134	0.623079	0.311540	+	0.950233i	$0.399155\pi$
$942$	−21.2736	−0.693131
$943$	−11.3671	−0.370162
$944$	1.83024	0.0595692
$945$	0	0
$946$	7.58141	0.246493
$947$	13.6992	0.445164	0.222582	−	0.974914i	$-0.428551\pi$
$947$	13.6992	0.445164	0.222582	+	0.974914i	$0.428551\pi$
$948$	8.65867	0.281220
$949$	4.31190	0.139970
$950$	5.88955	0.191082
$951$	−27.4123	−0.888905
$952$	0	0
$953$	−39.6603	−1.28472	−0.642361	−	0.766402i	$-0.722045\pi$
$953$	−39.6603	−1.28472	−0.642361	+	0.766402i	$0.722045\pi$
$954$	−4.55560	−0.147493
$955$	8.67736	0.280793
$956$	−24.2540	−0.784429
$957$	−7.00694	−0.226502
$958$	−12.4661	−0.402761
$959$	0	0
$960$	−3.87996	−0.125225
$961$	−30.6569	−0.988931
$962$	−33.3456	−1.07511
$963$	−7.55741	−0.243534
$964$	17.7227	0.570810
$965$	4.63551	0.149222
$966$	0	0
$967$	18.1953	0.585120	0.292560	−	0.956247i	$-0.405493\pi$
$967$	18.1953	0.585120	0.292560	+	0.956247i	$0.405493\pi$
$968$	−3.93149	−0.126363
$969$	1.03094	0.0331185
$970$	34.1641	1.09694
$971$	−6.56691	−0.210742	−0.105371	−	0.994433i	$-0.533603\pi$
$971$	−6.56691	−0.210742	−0.105371	+	0.994433i	$0.533603\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−40.4859	−1.29725
$975$	−42.1560	−1.35007
$976$	−1.80005	−0.0576182
$977$	−56.9952	−1.82344	−0.911719	−	0.410814i	$-0.865245\pi$
$977$	−56.9952	−1.82344	−0.911719	+	0.410814i	$0.865245\pi$
$978$	8.48528	0.271329
$979$	−0.574476	−0.0183603
$980$	0	0
$981$	2.81883	0.0899985
$982$	35.7599	1.14114
$983$	29.3964	0.937599	0.468800	−	0.883304i	$-0.344687\pi$
$983$	29.3964	0.937599	0.468800	+	0.883304i	$0.344687\pi$
$984$	−11.3671	−0.362368
$985$	48.8051	1.55506
$986$	−4.63829	−0.147713
$987$	0	0
$988$	2.45615	0.0781407
$989$	−2.85158	−0.0906751
$990$	10.3155	0.327849
$991$	−31.2354	−0.992225	−0.496112	−	0.868258i	$-0.665240\pi$
$991$	−31.2354	−0.992225	−0.496112	+	0.868258i	$0.665240\pi$
$992$	0.585786	0.0185987
$993$	−5.99638	−0.190289
$994$	0	0
$995$	10.6256	0.336853
$996$	−13.7297	−0.435043
$997$	−42.7089	−1.35260	−0.676302	−	0.736624i	$-0.736419\pi$
$997$	−42.7089	−1.35260	−0.676302	+	0.736624i	$0.736419\pi$
$998$	−18.3291	−0.580197
$999$	7.95284	0.251617

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.cn.1.4	✓	4	1.1	even	1	trivial
6762.2.a.co.1.1	yes	4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.87996 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.87996 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.87996 q^{10} +2.65867 q^{11} -1.00000 q^{12} +4.19292 q^{13} -3.87996 q^{15} +1.00000 q^{16} -1.75992 q^{17} +1.00000 q^{18} +0.585786 q^{19} +3.87996 q^{20} +2.65867 q^{22} -1.00000 q^{23} -1.00000 q^{24} +10.0541 q^{25} +4.19292 q^{26} -1.00000 q^{27} +2.63551 q^{29} -3.87996 q^{30} +0.585786 q^{31} +1.00000 q^{32} -2.65867 q^{33} -1.75992 q^{34} +1.00000 q^{36} -7.95284 q^{37} +0.585786 q^{38} -4.19292 q^{39} +3.87996 q^{40} +11.3671 q^{41} +2.85158 q^{43} +2.65867 q^{44} +3.87996 q^{45} -1.00000 q^{46} -4.70839 q^{47} -1.00000 q^{48} +10.0541 q^{50} +1.75992 q^{51} +4.19292 q^{52} -4.55560 q^{53} -1.00000 q^{54} +10.3155 q^{55} -0.585786 q^{57} +2.63551 q^{58} +1.83024 q^{59} -3.87996 q^{60} -1.80005 q^{61} +0.585786 q^{62} +1.00000 q^{64} +16.2684 q^{65} -2.65867 q^{66} +0.931495 q^{67} -1.75992 q^{68} +1.00000 q^{69} -2.65867 q^{71} +1.00000 q^{72} +1.02838 q^{73} -7.95284 q^{74} -10.0541 q^{75} +0.585786 q^{76} -4.19292 q^{78} -8.65867 q^{79} +3.87996 q^{80} +1.00000 q^{81} +11.3671 q^{82} +13.7297 q^{83} -6.82843 q^{85} +2.85158 q^{86} -2.63551 q^{87} +2.65867 q^{88} -0.216077 q^{89} +3.87996 q^{90} -1.00000 q^{92} -0.585786 q^{93} -4.70839 q^{94} +2.27283 q^{95} -1.00000 q^{96} +8.80527 q^{97} +2.65867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 8 q^{19} + 6 q^{20} - 4 q^{23} - 4 q^{24} + 6 q^{25} + 10 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 12 q^{34} + 4 q^{36} - 6 q^{37} + 8 q^{38} - 10 q^{39} + 6 q^{40} + 14 q^{41} - 6 q^{43} + 6 q^{45} - 4 q^{46} + 2 q^{47} - 4 q^{48} + 6 q^{50} - 12 q^{51} + 10 q^{52} - 4 q^{53} - 4 q^{54} + 8 q^{55} - 8 q^{57} + 6 q^{58} + 8 q^{59} - 6 q^{60} + 12 q^{61} + 8 q^{62} + 4 q^{64} + 6 q^{65} - 4 q^{67} + 12 q^{68} + 4 q^{69} + 4 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{75} + 8 q^{76} - 10 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} + 14 q^{82} + 16 q^{83} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 12 q^{89} + 6 q^{90} - 4 q^{92} - 8 q^{93} + 2 q^{94} + 12 q^{95} - 4 q^{96} + 30 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 8 * q^19 + 6 * q^20 - 4 * q^23 - 4 * q^24 + 6 * q^25 + 10 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 12 * q^34 + 4 * q^36 - 6 * q^37 + 8 * q^38 - 10 * q^39 + 6 * q^40 + 14 * q^41 - 6 * q^43 + 6 * q^45 - 4 * q^46 + 2 * q^47 - 4 * q^48 + 6 * q^50 - 12 * q^51 + 10 * q^52 - 4 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^57 + 6 * q^58 + 8 * q^59 - 6 * q^60 + 12 * q^61 + 8 * q^62 + 4 * q^64 + 6 * q^65 - 4 * q^67 + 12 * q^68 + 4 * q^69 + 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^75 + 8 * q^76 - 10 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 + 14 * q^82 + 16 * q^83 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 - 4 * q^92 - 8 * q^93 + 2 * q^94 + 12 * q^95 - 4 * q^96 + 30 * q^97

Introduction

L-functions

Modular forms

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Database

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