LMFDB - Embedded newform 1666.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.68554$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.887611 q^{3} +1.00000 q^{4} -0.685544 q^{5} +0.887611 q^{6} +1.00000 q^{8} -2.21215 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.887611 q^{3} +1.00000 q^{4} -0.685544 q^{5} +0.887611 q^{6} +1.00000 q^{8} -2.21215 q^{9} -0.685544 q^{10} +0.301825 q^{11} +0.887611 q^{12} +6.18165 q^{13} -0.608497 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.21215 q^{18} +6.46742 q^{19} -0.685544 q^{20} +0.301825 q^{22} +0.969506 q^{23} +0.887611 q^{24} -4.53003 q^{25} +6.18165 q^{26} -4.62636 q^{27} +8.44035 q^{29} -0.608497 q^{30} +8.65848 q^{31} +1.00000 q^{32} +0.267903 q^{33} -1.00000 q^{34} -2.21215 q^{36} -10.0998 q^{37} +6.46742 q^{38} +5.48690 q^{39} -0.685544 q^{40} +2.42684 q^{41} +0.285766 q^{43} +0.301825 q^{44} +1.51652 q^{45} +0.969506 q^{46} +7.29585 q^{47} +0.887611 q^{48} -4.53003 q^{50} -0.887611 q^{51} +6.18165 q^{52} +8.64907 q^{53} -4.62636 q^{54} -0.206914 q^{55} +5.74055 q^{57} +8.44035 q^{58} -5.55274 q^{59} -0.608497 q^{60} -2.59244 q^{61} +8.65848 q^{62} +1.00000 q^{64} -4.23779 q^{65} +0.267903 q^{66} -5.43208 q^{67} -1.00000 q^{68} +0.860544 q^{69} +11.4775 q^{71} -2.21215 q^{72} +0.628912 q^{73} -10.0998 q^{74} -4.02091 q^{75} +6.46742 q^{76} +5.48690 q^{78} -12.9348 q^{79} -0.685544 q^{80} +2.53003 q^{81} +2.42684 q^{82} -1.73210 q^{83} +0.685544 q^{85} +0.285766 q^{86} +7.49175 q^{87} +0.301825 q^{88} +7.98899 q^{89} +1.51652 q^{90} +0.969506 q^{92} +7.68536 q^{93} +7.29585 q^{94} -4.43370 q^{95} +0.887611 q^{96} -6.37271 q^{97} -0.667681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 8 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 8 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 8 q^{13} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{19} + 8 q^{20} - 4 q^{22} + 4 q^{23} + 4 q^{24} + 8 q^{25} + 8 q^{26} + 4 q^{27} - 4 q^{29} + 4 q^{30} + 4 q^{31} + 4 q^{32} + 16 q^{33} - 4 q^{34} + 8 q^{36} - 24 q^{37} + 8 q^{38} - 20 q^{39} + 8 q^{40} + 20 q^{41} - 4 q^{44} + 28 q^{45} + 4 q^{46} + 4 q^{48} + 8 q^{50} - 4 q^{51} + 8 q^{52} + 4 q^{54} - 16 q^{55} - 12 q^{57} - 4 q^{58} + 16 q^{59} + 4 q^{60} - 8 q^{61} + 4 q^{62} + 4 q^{64} + 4 q^{65} + 16 q^{66} - 4 q^{68} - 16 q^{69} + 8 q^{72} + 24 q^{73} - 24 q^{74} - 16 q^{75} + 8 q^{76} - 20 q^{78} - 16 q^{79} + 8 q^{80} - 16 q^{81} + 20 q^{82} + 8 q^{83} - 8 q^{85} - 8 q^{87} - 4 q^{88} + 8 q^{89} + 28 q^{90} + 4 q^{92} + 24 q^{93} + 12 q^{95} + 4 q^{96} + 4 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 8 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 8 * q^13 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^19 + 8 * q^20 - 4 * q^22 + 4 * q^23 + 4 * q^24 + 8 * q^25 + 8 * q^26 + 4 * q^27 - 4 * q^29 + 4 * q^30 + 4 * q^31 + 4 * q^32 + 16 * q^33 - 4 * q^34 + 8 * q^36 - 24 * q^37 + 8 * q^38 - 20 * q^39 + 8 * q^40 + 20 * q^41 - 4 * q^44 + 28 * q^45 + 4 * q^46 + 4 * q^48 + 8 * q^50 - 4 * q^51 + 8 * q^52 + 4 * q^54 - 16 * q^55 - 12 * q^57 - 4 * q^58 + 16 * q^59 + 4 * q^60 - 8 * q^61 + 4 * q^62 + 4 * q^64 + 4 * q^65 + 16 * q^66 - 4 * q^68 - 16 * q^69 + 8 * q^72 + 24 * q^73 - 24 * q^74 - 16 * q^75 + 8 * q^76 - 20 * q^78 - 16 * q^79 + 8 * q^80 - 16 * q^81 + 20 * q^82 + 8 * q^83 - 8 * q^85 - 8 * q^87 - 4 * q^88 + 8 * q^89 + 28 * q^90 + 4 * q^92 + 24 * q^93 + 12 * q^95 + 4 * q^96 + 4 * q^97 - 8 * 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
$3$	0.887611	0.512463	0.256231	−	0.966615i	$-0.417519\pi$
$3$	0.887611	0.512463	0.256231	+	0.966615i	$0.417519\pi$
$4$	1.00000	0.500000
$5$	−0.685544	−0.306585	−0.153292	−	0.988181i	$-0.548988\pi$
$5$	−0.685544	−0.306585	−0.153292	+	0.988181i	$0.548988\pi$
$6$	0.887611	0.362366
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.21215	−0.737382
$10$	−0.685544	−0.216788
$11$	0.301825	0.0910036	0.0455018	−	0.998964i	$-0.485511\pi$
$11$	0.301825	0.0910036	0.0455018	+	0.998964i	$0.485511\pi$
$12$	0.887611	0.256231
$13$	6.18165	1.71448	0.857241	−	0.514916i	$-0.172177\pi$
$13$	6.18165	1.71448	0.857241	+	0.514916i	$0.172177\pi$
$14$	0	0
$15$	−0.608497	−0.157113
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.21215	−0.521408
$19$	6.46742	1.48373	0.741864	−	0.670551i	$-0.233942\pi$
$19$	6.46742	1.48373	0.741864	+	0.670551i	$0.233942\pi$
$20$	−0.685544	−0.153292
$21$	0	0
$22$	0.301825	0.0643493
$23$	0.969506	0.202156	0.101078	−	0.994879i	$-0.467771\pi$
$23$	0.969506	0.202156	0.101078	+	0.994879i	$0.467771\pi$
$24$	0.887611	0.181183
$25$	−4.53003	−0.906006
$26$	6.18165	1.21232
$27$	−4.62636	−0.890343
$28$	0	0
$29$	8.44035	1.56733	0.783667	−	0.621181i	$-0.213347\pi$
$29$	8.44035	1.56733	0.783667	+	0.621181i	$0.213347\pi$
$30$	−0.608497	−0.111096
$31$	8.65848	1.55511	0.777554	−	0.628816i	$-0.216460\pi$
$31$	8.65848	1.55511	0.777554	+	0.628816i	$0.216460\pi$
$32$	1.00000	0.176777
$33$	0.267903	0.0466359
$34$	−1.00000	−0.171499
$35$	0	0
$36$	−2.21215	−0.368691
$37$	−10.0998	−1.66039	−0.830195	−	0.557473i	$-0.811771\pi$
$37$	−10.0998	−1.66039	−0.830195	+	0.557473i	$0.811771\pi$
$38$	6.46742	1.04915
$39$	5.48690	0.878608
$40$	−0.685544	−0.108394
$41$	2.42684	0.379009	0.189505	−	0.981880i	$-0.439312\pi$
$41$	2.42684	0.379009	0.189505	+	0.981880i	$0.439312\pi$
$42$	0	0
$43$	0.285766	0.0435790	0.0217895	−	0.999763i	$-0.493064\pi$
$43$	0.285766	0.0435790	0.0217895	+	0.999763i	$0.493064\pi$
$44$	0.301825	0.0455018
$45$	1.51652	0.226070
$46$	0.969506	0.142946
$47$	7.29585	1.06421	0.532104	−	0.846679i	$-0.321401\pi$
$47$	7.29585	1.06421	0.532104	+	0.846679i	$0.321401\pi$
$48$	0.887611	0.128116
$49$	0	0
$50$	−4.53003	−0.640643
$51$	−0.887611	−0.124290
$52$	6.18165	0.857241
$53$	8.64907	1.18804	0.594021	−	0.804450i	$-0.297540\pi$
$53$	8.64907	1.18804	0.594021	+	0.804450i	$0.297540\pi$
$54$	−4.62636	−0.629568
$55$	−0.206914	−0.0279003
$56$	0	0
$57$	5.74055	0.760355
$58$	8.44035	1.10827
$59$	−5.55274	−0.722905	−0.361453	−	0.932391i	$-0.617719\pi$
$59$	−5.55274	−0.722905	−0.361453	+	0.932391i	$0.617719\pi$
$60$	−0.608497	−0.0785566
$61$	−2.59244	−0.331928	−0.165964	−	0.986132i	$-0.553074\pi$
$61$	−2.59244	−0.331928	−0.165964	+	0.986132i	$0.553074\pi$
$62$	8.65848	1.09963
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.23779	−0.525634
$66$	0.267903	0.0329766
$67$	−5.43208	−0.663634	−0.331817	−	0.943344i	$-0.607662\pi$
$67$	−5.43208	−0.663634	−0.331817	+	0.943344i	$0.607662\pi$
$68$	−1.00000	−0.121268
$69$	0.860544	0.103597
$70$	0	0
$71$	11.4775	1.36213	0.681064	−	0.732224i	$-0.261517\pi$
$71$	11.4775	1.36213	0.681064	+	0.732224i	$0.261517\pi$
$72$	−2.21215	−0.260704
$73$	0.628912	0.0736086	0.0368043	−	0.999322i	$-0.488282\pi$
$73$	0.628912	0.0736086	0.0368043	+	0.999322i	$0.488282\pi$
$74$	−10.0998	−1.17407
$75$	−4.02091	−0.464294
$76$	6.46742	0.741864
$77$	0	0
$78$	5.48690	0.621270
$79$	−12.9348	−1.45528	−0.727641	−	0.685958i	$-0.759383\pi$
$79$	−12.9348	−1.45528	−0.727641	+	0.685958i	$0.759383\pi$
$80$	−0.685544	−0.0766461
$81$	2.53003	0.281114
$82$	2.42684	0.268000
$83$	−1.73210	−0.190122	−0.0950612	−	0.995471i	$-0.530305\pi$
$83$	−1.73210	−0.190122	−0.0950612	+	0.995471i	$0.530305\pi$
$84$	0	0
$85$	0.685544	0.0743577
$86$	0.285766	0.0308150
$87$	7.49175	0.803200
$88$	0.301825	0.0321746
$89$	7.98899	0.846831	0.423416	−	0.905936i	$-0.360831\pi$
$89$	7.98899	0.846831	0.423416	+	0.905936i	$0.360831\pi$
$90$	1.51652	0.159856
$91$	0	0
$92$	0.969506	0.101078
$93$	7.68536	0.796935
$94$	7.29585	0.752509
$95$	−4.43370	−0.454888
$96$	0.887611	0.0905914
$97$	−6.37271	−0.647051	−0.323525	−	0.946220i	$-0.604868\pi$
$97$	−6.37271	−0.647051	−0.323525	+	0.946220i	$0.604868\pi$
$98$	0	0
$99$	−0.667681	−0.0671044
$100$	−4.53003	−0.453003
$101$	13.9569	1.38876	0.694380	−	0.719608i	$-0.255679\pi$
$101$	13.9569	1.38876	0.694380	+	0.719608i	$0.255679\pi$
$102$	−0.887611	−0.0878866
$103$	−18.7422	−1.84672	−0.923361	−	0.383934i	$-0.874569\pi$
$103$	−18.7422	−1.84672	−0.923361	+	0.383934i	$0.874569\pi$
$104$	6.18165	0.606161
$105$	0	0
$106$	8.64907	0.840072
$107$	−8.01606	−0.774942	−0.387471	−	0.921882i	$-0.626651\pi$
$107$	−8.01606	−0.774942	−0.387471	+	0.921882i	$0.626651\pi$
$108$	−4.62636	−0.445172
$109$	−20.4378	−1.95759	−0.978793	−	0.204852i	$-0.934329\pi$
$109$	−20.4378	−1.95759	−0.978793	+	0.204852i	$0.934329\pi$
$110$	−0.206914	−0.0197285
$111$	−8.96466	−0.850888
$112$	0	0
$113$	−4.65848	−0.438233	−0.219116	−	0.975699i	$-0.570317\pi$
$113$	−4.65848	−0.438233	−0.219116	+	0.975699i	$0.570317\pi$
$114$	5.74055	0.537652
$115$	−0.664639	−0.0619779
$116$	8.44035	0.783667
$117$	−13.6747	−1.26423
$118$	−5.55274	−0.511171
$119$	0	0
$120$	−0.608497	−0.0555479
$121$	−10.9089	−0.991718
$122$	−2.59244	−0.234708
$123$	2.15409	0.194228
$124$	8.65848	0.777554
$125$	6.53325	0.584352
$126$	0	0
$127$	5.55890	0.493273	0.246636	−	0.969108i	$-0.420675\pi$
$127$	5.55890	0.493273	0.246636	+	0.969108i	$0.420675\pi$
$128$	1.00000	0.0883883
$129$	0.253649	0.0223326
$130$	−4.23779	−0.371679
$131$	−3.45659	−0.302004	−0.151002	−	0.988533i	$-0.548250\pi$
$131$	−3.45659	−0.302004	−0.151002	+	0.988533i	$0.548250\pi$
$132$	0.267903	0.0233180
$133$	0	0
$134$	−5.43208	−0.469260
$135$	3.17157	0.272966
$136$	−1.00000	−0.0857493
$137$	−8.55112	−0.730571	−0.365286	−	0.930895i	$-0.619029\pi$
$137$	−8.55112	−0.730571	−0.365286	+	0.930895i	$0.619029\pi$
$138$	0.860544	0.0732544
$139$	6.52176	0.553168	0.276584	−	0.960990i	$-0.410798\pi$
$139$	6.52176	0.553168	0.276584	+	0.960990i	$0.410798\pi$
$140$	0	0
$141$	6.47587	0.545367
$142$	11.4775	0.963170
$143$	1.86578	0.156024
$144$	−2.21215	−0.184346
$145$	−5.78623	−0.480520
$146$	0.628912	0.0520491
$147$	0	0
$148$	−10.0998	−0.830195
$149$	−6.25689	−0.512585	−0.256292	−	0.966599i	$-0.582501\pi$
$149$	−6.25689	−0.512585	−0.256292	+	0.966599i	$0.582501\pi$
$150$	−4.02091	−0.328306
$151$	10.1589	0.826723	0.413361	−	0.910567i	$-0.364355\pi$
$151$	10.1589	0.826723	0.413361	+	0.910567i	$0.364355\pi$
$152$	6.46742	0.524577
$153$	2.21215	0.178841
$154$	0	0
$155$	−5.93577	−0.476772
$156$	5.48690	0.439304
$157$	−5.39864	−0.430859	−0.215429	−	0.976519i	$-0.569115\pi$
$157$	−5.39864	−0.430859	−0.215429	+	0.976519i	$0.569115\pi$
$158$	−12.9348	−1.02904
$159$	7.67701	0.608827
$160$	−0.685544	−0.0541970
$161$	0	0
$162$	2.53003	0.198778
$163$	−8.75138	−0.685461	−0.342730	−	0.939434i	$-0.611352\pi$
$163$	−8.75138	−0.685461	−0.342730	+	0.939434i	$0.611352\pi$
$164$	2.42684	0.189505
$165$	−0.183659	−0.0142979
$166$	−1.73210	−0.134437
$167$	4.02271	0.311287	0.155643	−	0.987813i	$-0.450255\pi$
$167$	4.02271	0.311287	0.155643	+	0.987813i	$0.450255\pi$
$168$	0	0
$169$	25.2128	1.93945
$170$	0.685544	0.0525788
$171$	−14.3069	−1.09407
$172$	0.285766	0.0217895
$173$	−5.59767	−0.425583	−0.212791	−	0.977098i	$-0.568256\pi$
$173$	−5.59767	−0.425583	−0.212791	+	0.977098i	$0.568256\pi$
$174$	7.49175	0.567948
$175$	0	0
$176$	0.301825	0.0227509
$177$	−4.92867	−0.370462
$178$	7.98899	0.598800
$179$	10.3380	0.772701	0.386351	−	0.922352i	$-0.373735\pi$
$179$	10.3380	0.772701	0.386351	+	0.922352i	$0.373735\pi$
$180$	1.51652	0.113035
$181$	−9.36673	−0.696224	−0.348112	−	0.937453i	$-0.613177\pi$
$181$	−9.36673	−0.696224	−0.348112	+	0.937453i	$0.613177\pi$
$182$	0	0
$183$	−2.30108	−0.170101
$184$	0.969506	0.0714729
$185$	6.92383	0.509050
$186$	7.68536	0.563518
$187$	−0.301825	−0.0220716
$188$	7.29585	0.532104
$189$	0	0
$190$	−4.43370	−0.321654
$191$	17.5706	1.27136	0.635682	−	0.771951i	$-0.280719\pi$
$191$	17.5706	1.27136	0.635682	+	0.771951i	$0.280719\pi$
$192$	0.887611	0.0640578
$193$	7.92316	0.570321	0.285161	−	0.958480i	$-0.407953\pi$
$193$	7.92316	0.570321	0.285161	+	0.958480i	$0.407953\pi$
$194$	−6.37271	−0.457534
$195$	−3.76151	−0.269368
$196$	0	0
$197$	−22.4309	−1.59814	−0.799069	−	0.601239i	$-0.794674\pi$
$197$	−22.4309	−1.59814	−0.799069	+	0.601239i	$0.794674\pi$
$198$	−0.667681	−0.0474500
$199$	−15.7821	−1.11876	−0.559381	−	0.828911i	$-0.688961\pi$
$199$	−15.7821	−1.11876	−0.559381	+	0.828911i	$0.688961\pi$
$200$	−4.53003	−0.320321
$201$	−4.82157	−0.340088
$202$	13.9569	0.982002
$203$	0	0
$204$	−0.887611	−0.0621452
$205$	−1.66371	−0.116198
$206$	−18.7422	−1.30583
$207$	−2.14469	−0.149066
$208$	6.18165	0.428620
$209$	1.95203	0.135025
$210$	0	0
$211$	15.7660	1.08538	0.542689	−	0.839934i	$-0.317406\pi$
$211$	15.7660	1.08538	0.542689	+	0.839934i	$0.317406\pi$
$212$	8.64907	0.594021
$213$	10.1876	0.698040
$214$	−8.01606	−0.547966
$215$	−0.195905	−0.0133606
$216$	−4.62636	−0.314784
$217$	0	0
$218$	−20.4378	−1.38422
$219$	0.558230	0.0377217
$220$	−0.206914	−0.0139502
$221$	−6.18165	−0.415823
$222$	−8.96466	−0.601668
$223$	2.80546	0.187867	0.0939337	−	0.995578i	$-0.470056\pi$
$223$	2.80546	0.187867	0.0939337	+	0.995578i	$0.470056\pi$
$224$	0	0
$225$	10.0211	0.668073
$226$	−4.65848	−0.309877
$227$	−26.9435	−1.78830	−0.894151	−	0.447765i	$-0.852220\pi$
$227$	−26.9435	−1.78830	−0.894151	+	0.447765i	$0.852220\pi$
$228$	5.74055	0.380177
$229$	0.303630	0.0200644	0.0100322	−	0.999950i	$-0.496807\pi$
$229$	0.303630	0.0200644	0.0100322	+	0.999950i	$0.496807\pi$
$230$	−0.664639	−0.0438250
$231$	0	0
$232$	8.44035	0.554136
$233$	14.7710	0.967684	0.483842	−	0.875156i	$-0.339241\pi$
$233$	14.7710	0.967684	0.483842	+	0.875156i	$0.339241\pi$
$234$	−13.6747	−0.893944
$235$	−5.00162	−0.326270
$236$	−5.55274	−0.361453
$237$	−11.4811	−0.745778
$238$	0	0
$239$	−26.2485	−1.69788	−0.848939	−	0.528491i	$-0.822758\pi$
$239$	−26.2485	−1.69788	−0.848939	+	0.528491i	$0.822758\pi$
$240$	−0.608497	−0.0392783
$241$	8.69676	0.560207	0.280104	−	0.959970i	$-0.409631\pi$
$241$	8.69676	0.560207	0.280104	+	0.959970i	$0.409631\pi$
$242$	−10.9089	−0.701251
$243$	16.1248	1.03440
$244$	−2.59244	−0.165964
$245$	0	0
$246$	2.15409	0.137340
$247$	39.9793	2.54382
$248$	8.65848	0.549814
$249$	−1.53743	−0.0974306
$250$	6.53325	0.413199
$251$	−27.1688	−1.71488	−0.857439	−	0.514586i	$-0.827945\pi$
$251$	−27.1688	−1.71488	−0.857439	+	0.514586i	$0.827945\pi$
$252$	0	0
$253$	0.292621	0.0183969
$254$	5.55890	0.348797
$255$	0.608497	0.0381055
$256$	1.00000	0.0625000
$257$	−0.481672	−0.0300459	−0.0150229	−	0.999887i	$-0.504782\pi$
$257$	−0.481672	−0.0300459	−0.0150229	+	0.999887i	$0.504782\pi$
$258$	0.253649	0.0157915
$259$	0	0
$260$	−4.23779	−0.262817
$261$	−18.6713	−1.15572
$262$	−3.45659	−0.213549
$263$	14.3873	0.887161	0.443580	−	0.896235i	$-0.353708\pi$
$263$	14.3873	0.887161	0.443580	+	0.896235i	$0.353708\pi$
$264$	0.267903	0.0164883
$265$	−5.92932	−0.364235
$266$	0	0
$267$	7.09112	0.433969
$268$	−5.43208	−0.331817
$269$	20.1082	1.22602	0.613010	−	0.790075i	$-0.289959\pi$
$269$	20.1082	1.22602	0.613010	+	0.790075i	$0.289959\pi$
$270$	3.17157	0.193016
$271$	−17.4665	−1.06101	−0.530507	−	0.847681i	$-0.677998\pi$
$271$	−17.4665	−1.06101	−0.530507	+	0.847681i	$0.677998\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−8.55112	−0.516592
$275$	−1.36728	−0.0824498
$276$	0.860544	0.0517987
$277$	−19.1887	−1.15294	−0.576468	−	0.817120i	$-0.695570\pi$
$277$	−19.1887	−1.15294	−0.576468	+	0.817120i	$0.695570\pi$
$278$	6.52176	0.391149
$279$	−19.1538	−1.14671
$280$	0	0
$281$	−2.12682	−0.126876	−0.0634379	−	0.997986i	$-0.520206\pi$
$281$	−2.12682	−0.126876	−0.0634379	+	0.997986i	$0.520206\pi$
$282$	6.47587	0.385633
$283$	−0.846088	−0.0502947	−0.0251473	−	0.999684i	$-0.508005\pi$
$283$	−0.846088	−0.0502947	−0.0251473	+	0.999684i	$0.508005\pi$
$284$	11.4775	0.681064
$285$	−3.93540	−0.233113
$286$	1.86578	0.110326
$287$	0	0
$288$	−2.21215	−0.130352
$289$	1.00000	0.0588235
$290$	−5.78623	−0.339779
$291$	−5.65649	−0.331589
$292$	0.628912	0.0368043
$293$	8.39674	0.490543	0.245271	−	0.969454i	$-0.421123\pi$
$293$	8.39674	0.490543	0.245271	+	0.969454i	$0.421123\pi$
$294$	0	0
$295$	3.80665	0.221632
$296$	−10.0998	−0.587036
$297$	−1.39635	−0.0810245
$298$	−6.25689	−0.362452
$299$	5.99315	0.346593
$300$	−4.02091	−0.232147
$301$	0	0
$302$	10.1589	0.584581
$303$	12.3883	0.711688
$304$	6.46742	0.370932
$305$	1.77723	0.101764
$306$	2.21215	0.126460
$307$	−7.28254	−0.415637	−0.207818	−	0.978167i	$-0.566636\pi$
$307$	−7.28254	−0.415637	−0.207818	+	0.978167i	$0.566636\pi$
$308$	0	0
$309$	−16.6358	−0.946376
$310$	−5.93577	−0.337129
$311$	−6.19266	−0.351154	−0.175577	−	0.984466i	$-0.556179\pi$
$311$	−6.19266	−0.351154	−0.175577	+	0.984466i	$0.556179\pi$
$312$	5.48690	0.310635
$313$	20.7970	1.17552	0.587758	−	0.809037i	$-0.300011\pi$
$313$	20.7970	1.17552	0.587758	+	0.809037i	$0.300011\pi$
$314$	−5.39864	−0.304663
$315$	0	0
$316$	−12.9348	−0.727641
$317$	−2.18856	−0.122922	−0.0614609	−	0.998109i	$-0.519576\pi$
$317$	−2.18856	−0.122922	−0.0614609	+	0.998109i	$0.519576\pi$
$318$	7.67701	0.430505
$319$	2.54751	0.142633
$320$	−0.685544	−0.0383231
$321$	−7.11514	−0.397129
$322$	0	0
$323$	−6.46742	−0.359857
$324$	2.53003	0.140557
$325$	−28.0031	−1.55333
$326$	−8.75138	−0.484694
$327$	−18.1408	−1.00319
$328$	2.42684	0.134000
$329$	0	0
$330$	−0.183659	−0.0101101
$331$	−25.1091	−1.38012	−0.690060	−	0.723752i	$-0.742416\pi$
$331$	−25.1091	−1.38012	−0.690060	+	0.723752i	$0.742416\pi$
$332$	−1.73210	−0.0950612
$333$	22.3421	1.22434
$334$	4.02271	0.220113
$335$	3.72393	0.203460
$336$	0	0
$337$	6.48273	0.353137	0.176568	−	0.984288i	$-0.443500\pi$
$337$	6.48273	0.353137	0.176568	+	0.984288i	$0.443500\pi$
$338$	25.2128	1.37140
$339$	−4.13492	−0.224578
$340$	0.685544	0.0371788
$341$	2.61334	0.141520
$342$	−14.3069	−0.773627
$343$	0	0
$344$	0.285766	0.0154075
$345$	−0.589941	−0.0317613
$346$	−5.59767	−0.300933
$347$	31.8731	1.71104	0.855519	−	0.517771i	$-0.173238\pi$
$347$	31.8731	1.71104	0.855519	+	0.517771i	$0.173238\pi$
$348$	7.49175	0.401600
$349$	−19.9128	−1.06591	−0.532954	−	0.846144i	$-0.678918\pi$
$349$	−19.9128	−1.06591	−0.532954	+	0.846144i	$0.678918\pi$
$350$	0	0
$351$	−28.5985	−1.52648
$352$	0.301825	0.0160873
$353$	−27.6449	−1.47139	−0.735695	−	0.677313i	$-0.763144\pi$
$353$	−27.6449	−1.47139	−0.735695	+	0.677313i	$0.763144\pi$
$354$	−4.92867	−0.261956
$355$	−7.86833	−0.417608
$356$	7.98899	0.423416
$357$	0	0
$358$	10.3380	0.546382
$359$	24.1623	1.27524	0.637619	−	0.770352i	$-0.279920\pi$
$359$	24.1623	1.27524	0.637619	+	0.770352i	$0.279920\pi$
$360$	1.51652	0.0799278
$361$	22.8275	1.20145
$362$	−9.36673	−0.492304
$363$	−9.68286	−0.508219
$364$	0	0
$365$	−0.431147	−0.0225673
$366$	−2.30108	−0.120279
$367$	−24.2764	−1.26722	−0.633608	−	0.773654i	$-0.718427\pi$
$367$	−24.2764	−1.26722	−0.633608	+	0.773654i	$0.718427\pi$
$368$	0.969506	0.0505390
$369$	−5.36854	−0.279475
$370$	6.92383	0.359953
$371$	0	0
$372$	7.68536	0.398467
$373$	−6.69449	−0.346628	−0.173314	−	0.984867i	$-0.555447\pi$
$373$	−6.69449	−0.346628	−0.173314	+	0.984867i	$0.555447\pi$
$374$	−0.301825	−0.0156070
$375$	5.79899	0.299459
$376$	7.29585	0.376254
$377$	52.1753	2.68717
$378$	0	0
$379$	−23.1919	−1.19129	−0.595645	−	0.803248i	$-0.703103\pi$
$379$	−23.1919	−1.19129	−0.595645	+	0.803248i	$0.703103\pi$
$380$	−4.43370	−0.227444
$381$	4.93414	0.252784
$382$	17.5706	0.898990
$383$	−3.20369	−0.163701	−0.0818505	−	0.996645i	$-0.526083\pi$
$383$	−3.20369	−0.163701	−0.0818505	+	0.996645i	$0.526083\pi$
$384$	0.887611	0.0452957
$385$	0	0
$386$	7.92316	0.403278
$387$	−0.632157	−0.0321343
$388$	−6.37271	−0.323525
$389$	11.8949	0.603097	0.301549	−	0.953451i	$-0.402496\pi$
$389$	11.8949	0.603097	0.301549	+	0.953451i	$0.402496\pi$
$390$	−3.76151	−0.190472
$391$	−0.969506	−0.0490300
$392$	0	0
$393$	−3.06811	−0.154766
$394$	−22.4309	−1.13005
$395$	8.86740	0.446167
$396$	−0.667681	−0.0335522
$397$	33.2433	1.66843	0.834216	−	0.551438i	$-0.185921\pi$
$397$	33.2433	1.66843	0.834216	+	0.551438i	$0.185921\pi$
$398$	−15.7821	−0.791084
$399$	0	0
$400$	−4.53003	−0.226501
$401$	−12.7580	−0.637106	−0.318553	−	0.947905i	$-0.603197\pi$
$401$	−12.7580	−0.637106	−0.318553	+	0.947905i	$0.603197\pi$
$402$	−4.82157	−0.240478
$403$	53.5237	2.66620
$404$	13.9569	0.694380
$405$	−1.73445	−0.0861853
$406$	0	0
$407$	−3.04836	−0.151101
$408$	−0.887611	−0.0439433
$409$	37.4114	1.84987	0.924937	−	0.380119i	$-0.124117\pi$
$409$	37.4114	1.84987	0.924937	+	0.380119i	$0.124117\pi$
$410$	−1.66371	−0.0821647
$411$	−7.59007	−0.374390
$412$	−18.7422	−0.923361
$413$	0	0
$414$	−2.14469	−0.105406
$415$	1.18743	0.0582886
$416$	6.18165	0.303080
$417$	5.78878	0.283478
$418$	1.95203	0.0954768
$419$	16.3972	0.801057	0.400528	−	0.916284i	$-0.368827\pi$
$419$	16.3972	0.801057	0.400528	+	0.916284i	$0.368827\pi$
$420$	0	0
$421$	22.3449	1.08902	0.544512	−	0.838753i	$-0.316715\pi$
$421$	22.3449	1.08902	0.544512	+	0.838753i	$0.316715\pi$
$422$	15.7660	0.767478
$423$	−16.1395	−0.784728
$424$	8.64907	0.420036
$425$	4.53003	0.219739
$426$	10.1876	0.493589
$427$	0	0
$428$	−8.01606	−0.387471
$429$	1.65608	0.0799565
$430$	−0.195905	−0.00944740
$431$	−37.3598	−1.79956	−0.899780	−	0.436345i	$-0.856273\pi$
$431$	−37.3598	−1.79956	−0.899780	+	0.436345i	$0.856273\pi$
$432$	−4.62636	−0.222586
$433$	12.8239	0.616276	0.308138	−	0.951342i	$-0.400294\pi$
$433$	12.8239	0.616276	0.308138	+	0.951342i	$0.400294\pi$
$434$	0	0
$435$	−5.13592	−0.246249
$436$	−20.4378	−0.978793
$437$	6.27020	0.299944
$438$	0.558230	0.0266732
$439$	−23.6543	−1.12896	−0.564479	−	0.825447i	$-0.690923\pi$
$439$	−23.6543	−1.12896	−0.564479	+	0.825447i	$0.690923\pi$
$440$	−0.206914	−0.00986425
$441$	0	0
$442$	−6.18165	−0.294031
$443$	18.0082	0.855595	0.427798	−	0.903875i	$-0.359290\pi$
$443$	18.0082	0.855595	0.427798	+	0.903875i	$0.359290\pi$
$444$	−8.96466	−0.425444
$445$	−5.47680	−0.259625
$446$	2.80546	0.132842
$447$	−5.55369	−0.262681
$448$	0	0
$449$	−27.1665	−1.28206	−0.641032	−	0.767514i	$-0.721494\pi$
$449$	−27.1665	−1.28206	−0.641032	+	0.767514i	$0.721494\pi$
$450$	10.0211	0.472399
$451$	0.732482	0.0344912
$452$	−4.65848	−0.219116
$453$	9.01719	0.423665
$454$	−26.9435	−1.26452
$455$	0	0
$456$	5.74055	0.268826
$457$	15.7477	0.736646	0.368323	−	0.929698i	$-0.379932\pi$
$457$	15.7477	0.736646	0.368323	+	0.929698i	$0.379932\pi$
$458$	0.303630	0.0141877
$459$	4.62636	0.215940
$460$	−0.664639	−0.0309889
$461$	−4.56052	−0.212405	−0.106202	−	0.994345i	$-0.533869\pi$
$461$	−4.56052	−0.212405	−0.106202	+	0.994345i	$0.533869\pi$
$462$	0	0
$463$	−2.17910	−0.101271	−0.0506357	−	0.998717i	$-0.516125\pi$
$463$	−2.17910	−0.101271	−0.0506357	+	0.998717i	$0.516125\pi$
$464$	8.44035	0.391833
$465$	−5.26865	−0.244328
$466$	14.7710	0.684256
$467$	21.7808	1.00789	0.503947	−	0.863735i	$-0.331881\pi$
$467$	21.7808	1.00789	0.503947	+	0.863735i	$0.331881\pi$
$468$	−13.6747	−0.632114
$469$	0	0
$470$	−5.00162	−0.230708
$471$	−4.79190	−0.220799
$472$	−5.55274	−0.255586
$473$	0.0862514	0.00396584
$474$	−11.4811	−0.527345
$475$	−29.2976	−1.34427
$476$	0	0
$477$	−19.1330	−0.876040
$478$	−26.2485	−1.20058
$479$	1.49817	0.0684532	0.0342266	−	0.999414i	$-0.489103\pi$
$479$	1.49817	0.0684532	0.0342266	+	0.999414i	$0.489103\pi$
$480$	−0.608497	−0.0277739
$481$	−62.4332	−2.84671
$482$	8.69676	0.396126
$483$	0	0
$484$	−10.9089	−0.495859
$485$	4.36877	0.198376
$486$	16.1248	0.731434
$487$	−33.1690	−1.50303	−0.751516	−	0.659715i	$-0.770677\pi$
$487$	−33.1690	−1.50303	−0.751516	+	0.659715i	$0.770677\pi$
$488$	−2.59244	−0.117354
$489$	−7.76782	−0.351273
$490$	0	0
$491$	−31.3696	−1.41569	−0.707845	−	0.706368i	$-0.750332\pi$
$491$	−31.3696	−1.41569	−0.707845	+	0.706368i	$0.750332\pi$
$492$	2.15409	0.0971141
$493$	−8.44035	−0.380134
$494$	39.9793	1.79875
$495$	0.457724	0.0205732
$496$	8.65848	0.388777
$497$	0	0
$498$	−1.53743	−0.0688938
$499$	−30.8552	−1.38127	−0.690635	−	0.723203i	$-0.742669\pi$
$499$	−30.8552	−1.38127	−0.690635	+	0.723203i	$0.742669\pi$
$500$	6.53325	0.292176
$501$	3.57060	0.159523
$502$	−27.1688	−1.21260
$503$	−9.00848	−0.401668	−0.200834	−	0.979625i	$-0.564365\pi$
$503$	−9.00848	−0.401668	−0.200834	+	0.979625i	$0.564365\pi$
$504$	0	0
$505$	−9.56805	−0.425773
$506$	0.292621	0.0130086
$507$	22.3792	0.993894
$508$	5.55890	0.246636
$509$	31.0101	1.37450	0.687249	−	0.726422i	$-0.258818\pi$
$509$	31.0101	1.37450	0.687249	+	0.726422i	$0.258818\pi$
$510$	0.608497	0.0269447
$511$	0	0
$512$	1.00000	0.0441942
$513$	−29.9206	−1.32103
$514$	−0.481672	−0.0212456
$515$	12.8486	0.566176
$516$	0.253649	0.0111663
$517$	2.20207	0.0968468
$518$	0	0
$519$	−4.96856	−0.218095
$520$	−4.23779	−0.185840
$521$	−23.8252	−1.04380	−0.521901	−	0.853006i	$-0.674777\pi$
$521$	−23.8252	−1.04380	−0.521901	+	0.853006i	$0.674777\pi$
$522$	−18.6713	−0.817220
$523$	33.5885	1.46872	0.734361	−	0.678760i	$-0.237482\pi$
$523$	33.5885	1.46872	0.734361	+	0.678760i	$0.237482\pi$
$524$	−3.45659	−0.151002
$525$	0	0
$526$	14.3873	0.627317
$527$	−8.65848	−0.377169
$528$	0.267903	0.0116590
$529$	−22.0601	−0.959133
$530$	−5.92932	−0.257553
$531$	12.2835	0.533057
$532$	0	0
$533$	15.0019	0.649805
$534$	7.09112	0.306863
$535$	5.49536	0.237585
$536$	−5.43208	−0.234630
$537$	9.17616	0.395981
$538$	20.1082	0.866927
$539$	0	0
$540$	3.17157	0.136483
$541$	5.84356	0.251234	0.125617	−	0.992079i	$-0.459909\pi$
$541$	5.84356	0.251234	0.125617	+	0.992079i	$0.459909\pi$
$542$	−17.4665	−0.750250
$543$	−8.31402	−0.356789
$544$	−1.00000	−0.0428746
$545$	14.0110	0.600166
$546$	0	0
$547$	−25.8887	−1.10692	−0.553460	−	0.832876i	$-0.686693\pi$
$547$	−25.8887	−1.10692	−0.553460	+	0.832876i	$0.686693\pi$
$548$	−8.55112	−0.365286
$549$	5.73485	0.244758
$550$	−1.36728	−0.0583008
$551$	54.5873	2.32550
$552$	0.860544	0.0366272
$553$	0	0
$554$	−19.1887	−0.815249
$555$	6.14567	0.260869
$556$	6.52176	0.276584
$557$	−31.7449	−1.34507	−0.672536	−	0.740064i	$-0.734795\pi$
$557$	−31.7449	−1.34507	−0.672536	+	0.740064i	$0.734795\pi$
$558$	−19.1538	−0.810846
$559$	1.76651	0.0747153
$560$	0	0
$561$	−0.267903	−0.0113109
$562$	−2.12682	−0.0897147
$563$	−47.2522	−1.99144	−0.995721	−	0.0924119i	$-0.970542\pi$
$563$	−47.2522	−1.99144	−0.995721	+	0.0924119i	$0.970542\pi$
$564$	6.47587	0.272684
$565$	3.19359	0.134355
$566$	−0.846088	−0.0355637
$567$	0	0
$568$	11.4775	0.481585
$569$	32.1097	1.34611	0.673053	−	0.739594i	$-0.264982\pi$
$569$	32.1097	1.34611	0.673053	+	0.739594i	$0.264982\pi$
$570$	−3.93540	−0.164836
$571$	−20.0002	−0.836982	−0.418491	−	0.908221i	$-0.637441\pi$
$571$	−20.0002	−0.836982	−0.418491	+	0.908221i	$0.637441\pi$
$572$	1.86578	0.0780120
$573$	15.5959	0.651527
$574$	0	0
$575$	−4.39189	−0.183154
$576$	−2.21215	−0.0921728
$577$	21.0078	0.874566	0.437283	−	0.899324i	$-0.355941\pi$
$577$	21.0078	0.874566	0.437283	+	0.899324i	$0.355941\pi$
$578$	1.00000	0.0415945
$579$	7.03268	0.292268
$580$	−5.78623	−0.240260
$581$	0	0
$582$	−5.65649	−0.234469
$583$	2.61050	0.108116
$584$	0.628912	0.0260246
$585$	9.37462	0.387593
$586$	8.39674	0.346866
$587$	20.4490	0.844021	0.422010	−	0.906591i	$-0.361325\pi$
$587$	20.4490	0.844021	0.422010	+	0.906591i	$0.361325\pi$
$588$	0	0
$589$	55.9980	2.30736
$590$	3.80665	0.156717
$591$	−19.9100	−0.818986
$592$	−10.0998	−0.415097
$593$	−17.6985	−0.726790	−0.363395	−	0.931635i	$-0.618382\pi$
$593$	−17.6985	−0.726790	−0.363395	+	0.931635i	$0.618382\pi$
$594$	−1.39635	−0.0572929
$595$	0	0
$596$	−6.25689	−0.256292
$597$	−14.0083	−0.573324
$598$	5.99315	0.245078
$599$	−4.36207	−0.178229	−0.0891146	−	0.996021i	$-0.528404\pi$
$599$	−4.36207	−0.178229	−0.0891146	+	0.996021i	$0.528404\pi$
$600$	−4.02091	−0.164153
$601$	25.1318	1.02515	0.512574	−	0.858643i	$-0.328692\pi$
$601$	25.1318	1.02515	0.512574	+	0.858643i	$0.328692\pi$
$602$	0	0
$603$	12.0165	0.489352
$604$	10.1589	0.413361
$605$	7.47853	0.304046
$606$	12.3883	0.503239
$607$	−29.5757	−1.20044	−0.600220	−	0.799835i	$-0.704920\pi$
$607$	−29.5757	−1.20044	−0.600220	+	0.799835i	$0.704920\pi$
$608$	6.46742	0.262288
$609$	0	0
$610$	1.77723	0.0719579
$611$	45.1004	1.82457
$612$	2.21215	0.0894207
$613$	−15.5096	−0.626427	−0.313214	−	0.949683i	$-0.601406\pi$
$613$	−15.5096	−0.626427	−0.313214	+	0.949683i	$0.601406\pi$
$614$	−7.28254	−0.293899
$615$	−1.47673	−0.0595474
$616$	0	0
$617$	42.2612	1.70137	0.850686	−	0.525674i	$-0.176187\pi$
$617$	42.2612	1.70137	0.850686	+	0.525674i	$0.176187\pi$
$618$	−16.6358	−0.669189
$619$	29.9678	1.20451	0.602254	−	0.798304i	$-0.294269\pi$
$619$	29.9678	1.20451	0.602254	+	0.798304i	$0.294269\pi$
$620$	−5.93577	−0.238386
$621$	−4.48528	−0.179988
$622$	−6.19266	−0.248303
$623$	0	0
$624$	5.48690	0.219652
$625$	18.1713	0.726853
$626$	20.7970	0.831215
$627$	1.73264	0.0691950
$628$	−5.39864	−0.215429
$629$	10.0998	0.402704
$630$	0	0
$631$	−16.0253	−0.637956	−0.318978	−	0.947762i	$-0.603340\pi$
$631$	−16.0253	−0.637956	−0.318978	+	0.947762i	$0.603340\pi$
$632$	−12.9348	−0.514520
$633$	13.9941	0.556215
$634$	−2.18856	−0.0869189
$635$	−3.81087	−0.151230
$636$	7.67701	0.304413
$637$	0	0
$638$	2.54751	0.100857
$639$	−25.3899	−1.00441
$640$	−0.685544	−0.0270985
$641$	14.0026	0.553068	0.276534	−	0.961004i	$-0.410814\pi$
$641$	14.0026	0.553068	0.276534	+	0.961004i	$0.410814\pi$
$642$	−7.11514	−0.280812
$643$	−6.55748	−0.258602	−0.129301	−	0.991605i	$-0.541273\pi$
$643$	−6.55748	−0.258602	−0.129301	+	0.991605i	$0.541273\pi$
$644$	0	0
$645$	−0.173888	−0.00684683
$646$	−6.46742	−0.254457
$647$	−1.07256	−0.0421668	−0.0210834	−	0.999778i	$-0.506712\pi$
$647$	−1.07256	−0.0421668	−0.0210834	+	0.999778i	$0.506712\pi$
$648$	2.53003	0.0993889
$649$	−1.67595	−0.0657870
$650$	−28.0031	−1.09837
$651$	0	0
$652$	−8.75138	−0.342730
$653$	42.9877	1.68224	0.841119	−	0.540850i	$-0.181897\pi$
$653$	42.9877	1.68224	0.841119	+	0.540850i	$0.181897\pi$
$654$	−18.1408	−0.709362
$655$	2.36965	0.0925897
$656$	2.42684	0.0947524
$657$	−1.39125	−0.0542777
$658$	0	0
$659$	−18.4243	−0.717709	−0.358854	−	0.933394i	$-0.616832\pi$
$659$	−18.4243	−0.717709	−0.358854	+	0.933394i	$0.616832\pi$
$660$	−0.183659	−0.00714893
$661$	45.2246	1.75903	0.879517	−	0.475867i	$-0.157866\pi$
$661$	45.2246	1.75903	0.879517	+	0.475867i	$0.157866\pi$
$662$	−25.1091	−0.975892
$663$	−5.48690	−0.213094
$664$	−1.73210	−0.0672184
$665$	0	0
$666$	22.3421	0.865740
$667$	8.18297	0.316846
$668$	4.02271	0.155643
$669$	2.49016	0.0962750
$670$	3.72393	0.143868
$671$	−0.782462	−0.0302066
$672$	0	0
$673$	−0.148220	−0.00571345	−0.00285673	−	0.999996i	$-0.500909\pi$
$673$	−0.148220	−0.00571345	−0.00285673	+	0.999996i	$0.500909\pi$
$674$	6.48273	0.249705
$675$	20.9575	0.806656
$676$	25.2128	0.969724
$677$	−11.5497	−0.443891	−0.221945	−	0.975059i	$-0.571241\pi$
$677$	−11.5497	−0.443891	−0.221945	+	0.975059i	$0.571241\pi$
$678$	−4.13492	−0.158801
$679$	0	0
$680$	0.685544	0.0262894
$681$	−23.9154	−0.916438
$682$	2.61334	0.100070
$683$	−16.0304	−0.613387	−0.306693	−	0.951808i	$-0.599223\pi$
$683$	−16.0304	−0.613387	−0.306693	+	0.951808i	$0.599223\pi$
$684$	−14.3069	−0.547037
$685$	5.86217	0.223982
$686$	0	0
$687$	0.269505	0.0102823
$688$	0.285766	0.0108947
$689$	53.4655	2.03687
$690$	−0.589941	−0.0224587
$691$	7.63007	0.290262	0.145131	−	0.989412i	$-0.453640\pi$
$691$	7.63007	0.290262	0.145131	+	0.989412i	$0.453640\pi$
$692$	−5.59767	−0.212791
$693$	0	0
$694$	31.8731	1.20989
$695$	−4.47095	−0.169593
$696$	7.49175	0.283974
$697$	−2.42684	−0.0919233
$698$	−19.9128	−0.753711
$699$	13.1109	0.495902
$700$	0	0
$701$	14.2605	0.538612	0.269306	−	0.963055i	$-0.413206\pi$
$701$	14.2605	0.538612	0.269306	+	0.963055i	$0.413206\pi$
$702$	−28.5985	−1.07938
$703$	−65.3194	−2.46357
$704$	0.301825	0.0113755
$705$	−4.43950	−0.167201
$706$	−27.6449	−1.04043
$707$	0	0
$708$	−4.92867	−0.185231
$709$	24.4725	0.919083	0.459541	−	0.888156i	$-0.348014\pi$
$709$	24.4725	0.919083	0.459541	+	0.888156i	$0.348014\pi$
$710$	−7.86833	−0.295293
$711$	28.6137	1.07310
$712$	7.98899	0.299400
$713$	8.39444	0.314374
$714$	0	0
$715$	−1.27907	−0.0478346
$716$	10.3380	0.386351
$717$	−23.2985	−0.870099
$718$	24.1623	0.901729
$719$	29.7344	1.10891	0.554453	−	0.832215i	$-0.312928\pi$
$719$	29.7344	1.10891	0.554453	+	0.832215i	$0.312928\pi$
$720$	1.51652	0.0565175
$721$	0	0
$722$	22.8275	0.849551
$723$	7.71934	0.287085
$724$	−9.36673	−0.348112
$725$	−38.2350	−1.42001
$726$	−9.68286	−0.359365
$727$	36.0128	1.33564	0.667820	−	0.744323i	$-0.267228\pi$
$727$	36.0128	1.33564	0.667820	+	0.744323i	$0.267228\pi$
$728$	0	0
$729$	6.72243	0.248979
$730$	−0.431147	−0.0159575
$731$	−0.285766	−0.0105695
$732$	−2.30108	−0.0850503
$733$	14.7481	0.544733	0.272366	−	0.962194i	$-0.412194\pi$
$733$	14.7481	0.544733	0.272366	+	0.962194i	$0.412194\pi$
$734$	−24.2764	−0.896057
$735$	0	0
$736$	0.969506	0.0357364
$737$	−1.63954	−0.0603931
$738$	−5.36854	−0.197619
$739$	14.8830	0.547479	0.273739	−	0.961804i	$-0.411739\pi$
$739$	14.8830	0.547479	0.273739	+	0.961804i	$0.411739\pi$
$740$	6.92383	0.254525
$741$	35.4861	1.30361
$742$	0	0
$743$	−14.5988	−0.535579	−0.267790	−	0.963477i	$-0.586293\pi$
$743$	−14.5988	−0.535579	−0.267790	+	0.963477i	$0.586293\pi$
$744$	7.68536	0.281759
$745$	4.28938	0.157151
$746$	−6.69449	−0.245103
$747$	3.83165	0.140193
$748$	−0.301825	−0.0110358
$749$	0	0
$750$	5.79899	0.211749
$751$	−24.9598	−0.910796	−0.455398	−	0.890288i	$-0.650503\pi$
$751$	−24.9598	−0.910796	−0.455398	+	0.890288i	$0.650503\pi$
$752$	7.29585	0.266052
$753$	−24.1153	−0.878810
$754$	52.1753	1.90011
$755$	−6.96440	−0.253460
$756$	0	0
$757$	15.5660	0.565756	0.282878	−	0.959156i	$-0.408711\pi$
$757$	15.5660	0.565756	0.282878	+	0.959156i	$0.408711\pi$
$758$	−23.1919	−0.842369
$759$	0.259734	0.00942773
$760$	−4.43370	−0.160827
$761$	34.4705	1.24955	0.624777	−	0.780803i	$-0.285190\pi$
$761$	34.4705	1.24955	0.624777	+	0.780803i	$0.285190\pi$
$762$	4.93414	0.178745
$763$	0	0
$764$	17.5706	0.635682
$765$	−1.51652	−0.0548300
$766$	−3.20369	−0.115754
$767$	−34.3251	−1.23941
$768$	0.887611	0.0320289
$769$	25.3325	0.913514	0.456757	−	0.889591i	$-0.349011\pi$
$769$	25.3325	0.913514	0.456757	+	0.889591i	$0.349011\pi$
$770$	0	0
$771$	−0.427537	−0.0153974
$772$	7.92316	0.285161
$773$	29.0036	1.04319	0.521594	−	0.853194i	$-0.325338\pi$
$773$	29.0036	1.04319	0.521594	+	0.853194i	$0.325338\pi$
$774$	−0.632157	−0.0227224
$775$	−39.2232	−1.40894
$776$	−6.37271	−0.228767
$777$	0	0
$778$	11.8949	0.426454
$779$	15.6954	0.562347
$780$	−3.76151	−0.134684
$781$	3.46419	0.123959
$782$	−0.969506	−0.0346694
$783$	−39.0481	−1.39547
$784$	0	0
$785$	3.70101	0.132095
$786$	−3.06811	−0.109436
$787$	7.91555	0.282159	0.141080	−	0.989998i	$-0.454943\pi$
$787$	7.91555	0.282159	0.141080	+	0.989998i	$0.454943\pi$
$788$	−22.4309	−0.799069
$789$	12.7704	0.454637
$790$	8.86740	0.315488
$791$	0	0
$792$	−0.667681	−0.0237250
$793$	−16.0255	−0.569084
$794$	33.2433	1.17976
$795$	−5.26293	−0.186657
$796$	−15.7821	−0.559381
$797$	−22.6096	−0.800871	−0.400436	−	0.916325i	$-0.631141\pi$
$797$	−22.6096	−0.800871	−0.400436	+	0.916325i	$0.631141\pi$
$798$	0	0
$799$	−7.29585	−0.258108
$800$	−4.53003	−0.160161
$801$	−17.6728	−0.624438
$802$	−12.7580	−0.450502
$803$	0.189821	0.00669865
$804$	−4.82157	−0.170044
$805$	0	0
$806$	53.5237	1.88529
$807$	17.8483	0.628289
$808$	13.9569	0.491001
$809$	−25.0805	−0.881784	−0.440892	−	0.897560i	$-0.645338\pi$
$809$	−25.0805	−0.881784	−0.440892	+	0.897560i	$0.645338\pi$
$810$	−1.73445	−0.0609422
$811$	−6.97281	−0.244848	−0.122424	−	0.992478i	$-0.539067\pi$
$811$	−6.97281	−0.244848	−0.122424	+	0.992478i	$0.539067\pi$
$812$	0	0
$813$	−15.5035	−0.543730
$814$	−3.04836	−0.106845
$815$	5.99946	0.210152
$816$	−0.887611	−0.0310726
$817$	1.84817	0.0646593
$818$	37.4114	1.30806
$819$	0	0
$820$	−1.66371	−0.0580992
$821$	−27.2611	−0.951420	−0.475710	−	0.879602i	$-0.657809\pi$
$821$	−27.2611	−0.951420	−0.475710	+	0.879602i	$0.657809\pi$
$822$	−7.59007	−0.264734
$823$	−32.6118	−1.13678	−0.568389	−	0.822760i	$-0.692433\pi$
$823$	−32.6118	−1.13678	−0.568389	+	0.822760i	$0.692433\pi$
$824$	−18.7422	−0.652915
$825$	−1.21361	−0.0422524
$826$	0	0
$827$	−10.6807	−0.371404	−0.185702	−	0.982606i	$-0.559456\pi$
$827$	−10.6807	−0.371404	−0.185702	+	0.982606i	$0.559456\pi$
$828$	−2.14469	−0.0745331
$829$	0.896815	0.0311477	0.0155738	−	0.999879i	$-0.495042\pi$
$829$	0.896815	0.0311477	0.0155738	+	0.999879i	$0.495042\pi$
$830$	1.18743	0.0412162
$831$	−17.0321	−0.590837
$832$	6.18165	0.214310
$833$	0	0
$834$	5.78878	0.200449
$835$	−2.75774	−0.0954357
$836$	1.95203	0.0675123
$837$	−40.0572	−1.38458
$838$	16.3972	0.566433
$839$	30.9154	1.06732	0.533659	−	0.845700i	$-0.320817\pi$
$839$	30.9154	1.06732	0.533659	+	0.845700i	$0.320817\pi$
$840$	0	0
$841$	42.2395	1.45654
$842$	22.3449	0.770056
$843$	−1.88779	−0.0650191
$844$	15.7660	0.542689
$845$	−17.2845	−0.594605
$846$	−16.1395	−0.554887
$847$	0	0
$848$	8.64907	0.297010
$849$	−0.750997	−0.0257741
$850$	4.53003	0.155379
$851$	−9.79177	−0.335658
$852$	10.1876	0.349020
$853$	−2.36941	−0.0811271	−0.0405635	−	0.999177i	$-0.512915\pi$
$853$	−2.36941	−0.0811271	−0.0405635	+	0.999177i	$0.512915\pi$
$854$	0	0
$855$	9.80799	0.335426
$856$	−8.01606	−0.273983
$857$	−14.5080	−0.495584	−0.247792	−	0.968813i	$-0.579705\pi$
$857$	−14.5080	−0.495584	−0.247792	+	0.968813i	$0.579705\pi$
$858$	1.65608	0.0565378
$859$	−15.2907	−0.521713	−0.260857	−	0.965378i	$-0.584005\pi$
$859$	−15.2907	−0.521713	−0.260857	+	0.965378i	$0.584005\pi$
$860$	−0.195905	−0.00668032
$861$	0	0
$862$	−37.3598	−1.27248
$863$	29.1652	0.992796	0.496398	−	0.868095i	$-0.334656\pi$
$863$	29.1652	0.992796	0.496398	+	0.868095i	$0.334656\pi$
$864$	−4.62636	−0.157392
$865$	3.83745	0.130477
$866$	12.8239	0.435773
$867$	0.887611	0.0301449
$868$	0	0
$869$	−3.90405	−0.132436
$870$	−5.13592	−0.174124
$871$	−33.5792	−1.13779
$872$	−20.4378	−0.692111
$873$	14.0974	0.477124
$874$	6.27020	0.212093
$875$	0	0
$876$	0.558230	0.0188608
$877$	8.18211	0.276290	0.138145	−	0.990412i	$-0.455886\pi$
$877$	8.18211	0.276290	0.138145	+	0.990412i	$0.455886\pi$
$878$	−23.6543	−0.798294
$879$	7.45304	0.251385
$880$	−0.206914	−0.00697508
$881$	−43.4983	−1.46550	−0.732748	−	0.680500i	$-0.761763\pi$
$881$	−43.4983	−1.46550	−0.732748	+	0.680500i	$0.761763\pi$
$882$	0	0
$883$	36.4188	1.22559	0.612795	−	0.790242i	$-0.290045\pi$
$883$	36.4188	1.22559	0.612795	+	0.790242i	$0.290045\pi$
$884$	−6.18165	−0.207911
$885$	3.37882	0.113578
$886$	18.0082	0.604997
$887$	−32.3802	−1.08722	−0.543611	−	0.839338i	$-0.682943\pi$
$887$	−32.3802	−1.08722	−0.543611	+	0.839338i	$0.682943\pi$
$888$	−8.96466	−0.300834
$889$	0	0
$890$	−5.47680	−0.183583
$891$	0.763626	0.0255824
$892$	2.80546	0.0939337
$893$	47.1853	1.57900
$894$	−5.55369	−0.185743
$895$	−7.08718	−0.236898
$896$	0	0
$897$	5.31958	0.177616
$898$	−27.1665	−0.906557
$899$	73.0806	2.43737
$900$	10.0211	0.334036
$901$	−8.64907	−0.288142
$902$	0.732482	0.0243890
$903$	0	0
$904$	−4.65848	−0.154939
$905$	6.42131	0.213451
$906$	9.01719	0.299576
$907$	4.76107	0.158089	0.0790444	−	0.996871i	$-0.474813\pi$
$907$	4.76107	0.158089	0.0790444	+	0.996871i	$0.474813\pi$
$908$	−26.9435	−0.894151
$909$	−30.8746	−1.02405
$910$	0	0
$911$	20.1552	0.667770	0.333885	−	0.942614i	$-0.391640\pi$
$911$	20.1552	0.667770	0.333885	+	0.942614i	$0.391640\pi$
$912$	5.74055	0.190089
$913$	−0.522790	−0.0173018
$914$	15.7477	0.520887
$915$	1.57749	0.0521502
$916$	0.303630	0.0100322
$917$	0	0
$918$	4.62636	0.152693
$919$	−29.4876	−0.972706	−0.486353	−	0.873762i	$-0.661673\pi$
$919$	−29.4876	−0.972706	−0.486353	+	0.873762i	$0.661673\pi$
$920$	−0.664639	−0.0219125
$921$	−6.46407	−0.212998
$922$	−4.56052	−0.150193
$923$	70.9499	2.33534
$924$	0	0
$925$	45.7522	1.50432
$926$	−2.17910	−0.0716096
$927$	41.4604	1.36174
$928$	8.44035	0.277068
$929$	0.679437	0.0222916	0.0111458	−	0.999938i	$-0.496452\pi$
$929$	0.679437	0.0222916	0.0111458	+	0.999938i	$0.496452\pi$
$930$	−5.26865	−0.172766
$931$	0	0
$932$	14.7710	0.483842
$933$	−5.49668	−0.179953
$934$	21.7808	0.712688
$935$	0.206914	0.00676682
$936$	−13.6747	−0.446972
$937$	18.9922	0.620449	0.310224	−	0.950663i	$-0.399596\pi$
$937$	18.9922	0.620449	0.310224	+	0.950663i	$0.399596\pi$
$938$	0	0
$939$	18.4597	0.602408
$940$	−5.00162	−0.163135
$941$	−33.9689	−1.10735	−0.553677	−	0.832732i	$-0.686776\pi$
$941$	−33.9689	−1.10735	−0.553677	+	0.832732i	$0.686776\pi$
$942$	−4.79190	−0.156128
$943$	2.35284	0.0766190
$944$	−5.55274	−0.180726
$945$	0	0
$946$	0.0862514	0.00280427
$947$	58.8011	1.91078	0.955390	−	0.295349i	$-0.0954358\pi$
$947$	58.8011	1.91078	0.955390	+	0.295349i	$0.0954358\pi$
$948$	−11.4811	−0.372889
$949$	3.88772	0.126201
$950$	−29.2976	−0.950539
$951$	−1.94259	−0.0629929
$952$	0	0
$953$	9.01788	0.292118	0.146059	−	0.989276i	$-0.453341\pi$
$953$	9.01788	0.292118	0.146059	+	0.989276i	$0.453341\pi$
$954$	−19.1330	−0.619454
$955$	−12.0454	−0.389781
$956$	−26.2485	−0.848939
$957$	2.26120	0.0730941
$958$	1.49817	0.0484037
$959$	0	0
$960$	−0.608497	−0.0196391
$961$	43.9692	1.41836
$962$	−62.4332	−2.01293
$963$	17.7327	0.571428
$964$	8.69676	0.280104
$965$	−5.43167	−0.174852
$966$	0	0
$967$	26.9752	0.867462	0.433731	−	0.901042i	$-0.357197\pi$
$967$	26.9752	0.867462	0.433731	+	0.901042i	$0.357197\pi$
$968$	−10.9089	−0.350625
$969$	−5.74055	−0.184413
$970$	4.36877	0.140273
$971$	36.0293	1.15624	0.578118	−	0.815953i	$-0.303787\pi$
$971$	36.0293	1.15624	0.578118	+	0.815953i	$0.303787\pi$
$972$	16.1248	0.517202
$973$	0	0
$974$	−33.1690	−1.06280
$975$	−24.8558	−0.796024
$976$	−2.59244	−0.0829819
$977$	−46.6911	−1.49378	−0.746891	−	0.664947i	$-0.768454\pi$
$977$	−46.6911	−1.49378	−0.746891	+	0.664947i	$0.768454\pi$
$978$	−7.76782	−0.248388
$979$	2.41128	0.0770647
$980$	0	0
$981$	45.2114	1.44349
$982$	−31.3696	−1.00104
$983$	22.9132	0.730817	0.365409	−	0.930847i	$-0.380929\pi$
$983$	22.9132	0.730817	0.365409	+	0.930847i	$0.380929\pi$
$984$	2.15409	0.0686700
$985$	15.3774	0.489965
$986$	−8.44035	−0.268796
$987$	0	0
$988$	39.9793	1.27191
$989$	0.277052	0.00880974
$990$	0.457724	0.0145474
$991$	34.1691	1.08542	0.542709	−	0.839921i	$-0.317399\pi$
$991$	34.1691	1.08542	0.542709	+	0.839921i	$0.317399\pi$
$992$	8.65848	0.274907
$993$	−22.2871	−0.707260
$994$	0	0
$995$	10.8193	0.342995
$996$	−1.53743	−0.0487153
$997$	30.1958	0.956311	0.478155	−	0.878275i	$-0.341306\pi$
$997$	30.1958	0.956311	0.478155	+	0.878275i	$0.341306\pi$
$998$	−30.8552	−0.976705
$999$	46.7251	1.47832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.y.1.2	yes	4
7.6	odd	2		1666.2.a.x.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1666.2.a.x.1.3	✓	4	7.6	odd	2
1666.2.a.y.1.2	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:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.887611 q^{3} +1.00000 q^{4} -0.685544 q^{5} +0.887611 q^{6} +1.00000 q^{8} -2.21215 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.887611 q^{3} +1.00000 q^{4} -0.685544 q^{5} +0.887611 q^{6} +1.00000 q^{8} -2.21215 q^{9} -0.685544 q^{10} +0.301825 q^{11} +0.887611 q^{12} +6.18165 q^{13} -0.608497 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.21215 q^{18} +6.46742 q^{19} -0.685544 q^{20} +0.301825 q^{22} +0.969506 q^{23} +0.887611 q^{24} -4.53003 q^{25} +6.18165 q^{26} -4.62636 q^{27} +8.44035 q^{29} -0.608497 q^{30} +8.65848 q^{31} +1.00000 q^{32} +0.267903 q^{33} -1.00000 q^{34} -2.21215 q^{36} -10.0998 q^{37} +6.46742 q^{38} +5.48690 q^{39} -0.685544 q^{40} +2.42684 q^{41} +0.285766 q^{43} +0.301825 q^{44} +1.51652 q^{45} +0.969506 q^{46} +7.29585 q^{47} +0.887611 q^{48} -4.53003 q^{50} -0.887611 q^{51} +6.18165 q^{52} +8.64907 q^{53} -4.62636 q^{54} -0.206914 q^{55} +5.74055 q^{57} +8.44035 q^{58} -5.55274 q^{59} -0.608497 q^{60} -2.59244 q^{61} +8.65848 q^{62} +1.00000 q^{64} -4.23779 q^{65} +0.267903 q^{66} -5.43208 q^{67} -1.00000 q^{68} +0.860544 q^{69} +11.4775 q^{71} -2.21215 q^{72} +0.628912 q^{73} -10.0998 q^{74} -4.02091 q^{75} +6.46742 q^{76} +5.48690 q^{78} -12.9348 q^{79} -0.685544 q^{80} +2.53003 q^{81} +2.42684 q^{82} -1.73210 q^{83} +0.685544 q^{85} +0.285766 q^{86} +7.49175 q^{87} +0.301825 q^{88} +7.98899 q^{89} +1.51652 q^{90} +0.969506 q^{92} +7.68536 q^{93} +7.29585 q^{94} -4.43370 q^{95} +0.887611 q^{96} -6.37271 q^{97} -0.667681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 8 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 8 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 8 q^{13} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{19} + 8 q^{20} - 4 q^{22} + 4 q^{23} + 4 q^{24} + 8 q^{25} + 8 q^{26} + 4 q^{27} - 4 q^{29} + 4 q^{30} + 4 q^{31} + 4 q^{32} + 16 q^{33} - 4 q^{34} + 8 q^{36} - 24 q^{37} + 8 q^{38} - 20 q^{39} + 8 q^{40} + 20 q^{41} - 4 q^{44} + 28 q^{45} + 4 q^{46} + 4 q^{48} + 8 q^{50} - 4 q^{51} + 8 q^{52} + 4 q^{54} - 16 q^{55} - 12 q^{57} - 4 q^{58} + 16 q^{59} + 4 q^{60} - 8 q^{61} + 4 q^{62} + 4 q^{64} + 4 q^{65} + 16 q^{66} - 4 q^{68} - 16 q^{69} + 8 q^{72} + 24 q^{73} - 24 q^{74} - 16 q^{75} + 8 q^{76} - 20 q^{78} - 16 q^{79} + 8 q^{80} - 16 q^{81} + 20 q^{82} + 8 q^{83} - 8 q^{85} - 8 q^{87} - 4 q^{88} + 8 q^{89} + 28 q^{90} + 4 q^{92} + 24 q^{93} + 12 q^{95} + 4 q^{96} + 4 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 8 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 8 * q^13 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^19 + 8 * q^20 - 4 * q^22 + 4 * q^23 + 4 * q^24 + 8 * q^25 + 8 * q^26 + 4 * q^27 - 4 * q^29 + 4 * q^30 + 4 * q^31 + 4 * q^32 + 16 * q^33 - 4 * q^34 + 8 * q^36 - 24 * q^37 + 8 * q^38 - 20 * q^39 + 8 * q^40 + 20 * q^41 - 4 * q^44 + 28 * q^45 + 4 * q^46 + 4 * q^48 + 8 * q^50 - 4 * q^51 + 8 * q^52 + 4 * q^54 - 16 * q^55 - 12 * q^57 - 4 * q^58 + 16 * q^59 + 4 * q^60 - 8 * q^61 + 4 * q^62 + 4 * q^64 + 4 * q^65 + 16 * q^66 - 4 * q^68 - 16 * q^69 + 8 * q^72 + 24 * q^73 - 24 * q^74 - 16 * q^75 + 8 * q^76 - 20 * q^78 - 16 * q^79 + 8 * q^80 - 16 * q^81 + 20 * q^82 + 8 * q^83 - 8 * q^85 - 8 * q^87 - 4 * q^88 + 8 * q^89 + 28 * q^90 + 4 * q^92 + 24 * q^93 + 12 * q^95 + 4 * q^96 + 4 * q^97 - 8 * q^99

Introduction

L-functions

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