LMFDB - Embedded newform 4017.2.a.l.1.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38193 q^{2} +1.00000 q^{3} +3.67361 q^{4} -0.828467 q^{5} +2.38193 q^{6} -1.40827 q^{7} +3.98643 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.38193 q^{2} +1.00000 q^{3} +3.67361 q^{4} -0.828467 q^{5} +2.38193 q^{6} -1.40827 q^{7} +3.98643 q^{8} +1.00000 q^{9} -1.97336 q^{10} -0.0373487 q^{11} +3.67361 q^{12} -1.00000 q^{13} -3.35441 q^{14} -0.828467 q^{15} +2.14820 q^{16} +5.38271 q^{17} +2.38193 q^{18} +6.09573 q^{19} -3.04347 q^{20} -1.40827 q^{21} -0.0889622 q^{22} +1.29041 q^{23} +3.98643 q^{24} -4.31364 q^{25} -2.38193 q^{26} +1.00000 q^{27} -5.17344 q^{28} +8.82719 q^{29} -1.97336 q^{30} +0.864794 q^{31} -2.85599 q^{32} -0.0373487 q^{33} +12.8213 q^{34} +1.16671 q^{35} +3.67361 q^{36} +2.68672 q^{37} +14.5196 q^{38} -1.00000 q^{39} -3.30263 q^{40} +8.48530 q^{41} -3.35441 q^{42} +11.1308 q^{43} -0.137205 q^{44} -0.828467 q^{45} +3.07367 q^{46} +7.40746 q^{47} +2.14820 q^{48} -5.01677 q^{49} -10.2748 q^{50} +5.38271 q^{51} -3.67361 q^{52} +10.5782 q^{53} +2.38193 q^{54} +0.0309422 q^{55} -5.61398 q^{56} +6.09573 q^{57} +21.0258 q^{58} -2.27578 q^{59} -3.04347 q^{60} +7.94009 q^{61} +2.05988 q^{62} -1.40827 q^{63} -11.0992 q^{64} +0.828467 q^{65} -0.0889622 q^{66} -3.11107 q^{67} +19.7740 q^{68} +1.29041 q^{69} +2.77902 q^{70} -14.4022 q^{71} +3.98643 q^{72} -13.9610 q^{73} +6.39959 q^{74} -4.31364 q^{75} +22.3934 q^{76} +0.0525971 q^{77} -2.38193 q^{78} -3.48975 q^{79} -1.77972 q^{80} +1.00000 q^{81} +20.2114 q^{82} -12.2969 q^{83} -5.17344 q^{84} -4.45940 q^{85} +26.5127 q^{86} +8.82719 q^{87} -0.148888 q^{88} -12.0599 q^{89} -1.97336 q^{90} +1.40827 q^{91} +4.74046 q^{92} +0.864794 q^{93} +17.6441 q^{94} -5.05012 q^{95} -2.85599 q^{96} -11.7369 q^{97} -11.9496 q^{98} -0.0373487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	2.38193	1.68428	0.842141	−	0.539257i	$-0.181295\pi$
$2$	2.38193	1.68428	0.842141	+	0.539257i	$0.181295\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.67361	1.83681
$5$	−0.828467	−0.370502	−0.185251	−	0.982691i	$-0.559310\pi$
$5$	−0.828467	−0.370502	−0.185251	+	0.982691i	$0.559310\pi$
$6$	2.38193	0.972421
$7$	−1.40827	−0.532276	−0.266138	−	0.963935i	$-0.585748\pi$
$7$	−1.40827	−0.532276	−0.266138	+	0.963935i	$0.585748\pi$
$8$	3.98643	1.40942
$9$	1.00000	0.333333
$10$	−1.97336	−0.624030
$11$	−0.0373487	−0.0112611	−0.00563053	−	0.999984i	$-0.501792\pi$
$11$	−0.0373487	−0.0112611	−0.00563053	+	0.999984i	$0.501792\pi$
$12$	3.67361	1.06048
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.35441	−0.896503
$15$	−0.828467	−0.213909
$16$	2.14820	0.537051
$17$	5.38271	1.30550	0.652750	−	0.757574i	$-0.273615\pi$
$17$	5.38271	1.30550	0.652750	+	0.757574i	$0.273615\pi$
$18$	2.38193	0.561427
$19$	6.09573	1.39846	0.699229	−	0.714898i	$-0.253527\pi$
$19$	6.09573	1.39846	0.699229	+	0.714898i	$0.253527\pi$
$20$	−3.04347	−0.680540
$21$	−1.40827	−0.307310
$22$	−0.0889622	−0.0189668
$23$	1.29041	0.269069	0.134534	−	0.990909i	$-0.457046\pi$
$23$	1.29041	0.269069	0.134534	+	0.990909i	$0.457046\pi$
$24$	3.98643	0.813728
$25$	−4.31364	−0.862728
$26$	−2.38193	−0.467136
$27$	1.00000	0.192450
$28$	−5.17344	−0.977688
$29$	8.82719	1.63917	0.819584	−	0.572958i	$-0.194204\pi$
$29$	8.82719	1.63917	0.819584	+	0.572958i	$0.194204\pi$
$30$	−1.97336	−0.360284
$31$	0.864794	0.155322	0.0776608	−	0.996980i	$-0.475255\pi$
$31$	0.864794	0.155322	0.0776608	+	0.996980i	$0.475255\pi$
$32$	−2.85599	−0.504873
$33$	−0.0373487	−0.00650158
$34$	12.8213	2.19883
$35$	1.16671	0.197209
$36$	3.67361	0.612269
$37$	2.68672	0.441694	0.220847	−	0.975308i	$-0.429118\pi$
$37$	2.68672	0.441694	0.220847	+	0.975308i	$0.429118\pi$
$38$	14.5196	2.35540
$39$	−1.00000	−0.160128
$40$	−3.30263	−0.522192
$41$	8.48530	1.32518	0.662591	−	0.748981i	$-0.269457\pi$
$41$	8.48530	1.32518	0.662591	+	0.748981i	$0.269457\pi$
$42$	−3.35441	−0.517596
$43$	11.1308	1.69743	0.848713	−	0.528854i	$-0.177378\pi$
$43$	11.1308	1.69743	0.848713	+	0.528854i	$0.177378\pi$
$44$	−0.137205	−0.0206844
$45$	−0.828467	−0.123501
$46$	3.07367	0.453187
$47$	7.40746	1.08049	0.540244	−	0.841508i	$-0.318332\pi$
$47$	7.40746	1.08049	0.540244	+	0.841508i	$0.318332\pi$
$48$	2.14820	0.310066
$49$	−5.01677	−0.716682
$50$	−10.2748	−1.45308
$51$	5.38271	0.753731
$52$	−3.67361	−0.509438
$53$	10.5782	1.45302	0.726511	−	0.687155i	$-0.241140\pi$
$53$	10.5782	1.45302	0.726511	+	0.687155i	$0.241140\pi$
$54$	2.38193	0.324140
$55$	0.0309422	0.00417224
$56$	−5.61398	−0.750199
$57$	6.09573	0.807400
$58$	21.0258	2.76082
$59$	−2.27578	−0.296282	−0.148141	−	0.988966i	$-0.547329\pi$
$59$	−2.27578	−0.296282	−0.148141	+	0.988966i	$0.547329\pi$
$60$	−3.04347	−0.392910
$61$	7.94009	1.01662	0.508312	−	0.861173i	$-0.330270\pi$
$61$	7.94009	1.01662	0.508312	+	0.861173i	$0.330270\pi$
$62$	2.05988	0.261605
$63$	−1.40827	−0.177425
$64$	−11.0992	−1.38740
$65$	0.828467	0.102759
$66$	−0.0889622	−0.0109505
$67$	−3.11107	−0.380078	−0.190039	−	0.981777i	$-0.560861\pi$
$67$	−3.11107	−0.380078	−0.190039	+	0.981777i	$0.560861\pi$
$68$	19.7740	2.39795
$69$	1.29041	0.155347
$70$	2.77902	0.332156
$71$	−14.4022	−1.70923	−0.854615	−	0.519261i	$-0.826207\pi$
$71$	−14.4022	−1.70923	−0.854615	+	0.519261i	$0.826207\pi$
$72$	3.98643	0.469806
$73$	−13.9610	−1.63401	−0.817006	−	0.576629i	$-0.804368\pi$
$73$	−13.9610	−1.63401	−0.817006	+	0.576629i	$0.804368\pi$
$74$	6.39959	0.743937
$75$	−4.31364	−0.498096
$76$	22.3934	2.56869
$77$	0.0525971	0.00599399
$78$	−2.38193	−0.269701
$79$	−3.48975	−0.392628	−0.196314	−	0.980541i	$-0.562897\pi$
$79$	−3.48975	−0.392628	−0.196314	+	0.980541i	$0.562897\pi$
$80$	−1.77972	−0.198978
$81$	1.00000	0.111111
$82$	20.2114	2.23198
$83$	−12.2969	−1.34977	−0.674883	−	0.737925i	$-0.735806\pi$
$83$	−12.2969	−1.34977	−0.674883	+	0.737925i	$0.735806\pi$
$84$	−5.17344	−0.564468
$85$	−4.45940	−0.483690
$86$	26.5127	2.85894
$87$	8.82719	0.946375
$88$	−0.148888	−0.0158715
$89$	−12.0599	−1.27835	−0.639175	−	0.769062i	$-0.720724\pi$
$89$	−12.0599	−1.27835	−0.639175	+	0.769062i	$0.720724\pi$
$90$	−1.97336	−0.208010
$91$	1.40827	0.147627
$92$	4.74046	0.494227
$93$	0.864794	0.0896749
$94$	17.6441	1.81985
$95$	−5.05012	−0.518131
$96$	−2.85599	−0.291488
$97$	−11.7369	−1.19170	−0.595850	−	0.803096i	$-0.703185\pi$
$97$	−11.7369	−1.19170	−0.595850	+	0.803096i	$0.703185\pi$
$98$	−11.9496	−1.20709
$99$	−0.0373487	−0.00375369
$100$	−15.8466	−1.58466
$101$	−13.1464	−1.30812	−0.654058	−	0.756444i	$-0.726935\pi$
$101$	−13.1464	−1.30812	−0.654058	+	0.756444i	$0.726935\pi$
$102$	12.8213	1.26949
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−3.98643	−0.390902
$105$	1.16671	0.113859
$106$	25.1965	2.44730
$107$	0.358610	0.0346681	0.0173341	−	0.999850i	$-0.494482\pi$
$107$	0.358610	0.0346681	0.0173341	+	0.999850i	$0.494482\pi$
$108$	3.67361	0.353494
$109$	−16.3011	−1.56136	−0.780682	−	0.624928i	$-0.785128\pi$
$109$	−16.3011	−1.56136	−0.780682	+	0.624928i	$0.785128\pi$
$110$	0.0737023	0.00702724
$111$	2.68672	0.255012
$112$	−3.02525	−0.285859
$113$	−1.48951	−0.140122	−0.0700608	−	0.997543i	$-0.522319\pi$
$113$	−1.48951	−0.140122	−0.0700608	+	0.997543i	$0.522319\pi$
$114$	14.5196	1.35989
$115$	−1.06906	−0.0996904
$116$	32.4277	3.01084
$117$	−1.00000	−0.0924500
$118$	−5.42077	−0.499022
$119$	−7.58031	−0.694886
$120$	−3.30263	−0.301488
$121$	−10.9986	−0.999873
$122$	18.9128	1.71228
$123$	8.48530	0.765094
$124$	3.17692	0.285296
$125$	7.71605	0.690144
$126$	−3.35441	−0.298834
$127$	−2.81316	−0.249628	−0.124814	−	0.992180i	$-0.539833\pi$
$127$	−2.81316	−0.249628	−0.124814	+	0.992180i	$0.539833\pi$
$128$	−20.7256	−1.83190
$129$	11.1308	0.980009
$130$	1.97336	0.173075
$131$	7.86423	0.687101	0.343550	−	0.939134i	$-0.388370\pi$
$131$	7.86423	0.687101	0.343550	+	0.939134i	$0.388370\pi$
$132$	−0.137205	−0.0119421
$133$	−8.58444	−0.744365
$134$	−7.41037	−0.640158
$135$	−0.828467	−0.0713031
$136$	21.4578	1.83999
$137$	3.83446	0.327600	0.163800	−	0.986494i	$-0.447625\pi$
$137$	3.83446	0.327600	0.163800	+	0.986494i	$0.447625\pi$
$138$	3.07367	0.261648
$139$	9.29982	0.788800	0.394400	−	0.918939i	$-0.370952\pi$
$139$	9.29982	0.788800	0.394400	+	0.918939i	$0.370952\pi$
$140$	4.28603	0.362235
$141$	7.40746	0.623820
$142$	−34.3052	−2.87883
$143$	0.0373487	0.00312326
$144$	2.14820	0.179017
$145$	−7.31304	−0.607315
$146$	−33.2542	−2.75214
$147$	−5.01677	−0.413777
$148$	9.86997	0.811306
$149$	8.47918	0.694642	0.347321	−	0.937746i	$-0.387091\pi$
$149$	8.47918	0.694642	0.347321	+	0.937746i	$0.387091\pi$
$150$	−10.2748	−0.838935
$151$	24.4071	1.98622	0.993111	−	0.117181i	$-0.0373858\pi$
$151$	24.4071	1.98622	0.993111	+	0.117181i	$0.0373858\pi$
$152$	24.3002	1.97101
$153$	5.38271	0.435167
$154$	0.125283	0.0100956
$155$	−0.716454	−0.0575469
$156$	−3.67361	−0.294124
$157$	14.0816	1.12383	0.561915	−	0.827195i	$-0.310065\pi$
$157$	14.0816	1.12383	0.561915	+	0.827195i	$0.310065\pi$
$158$	−8.31236	−0.661296
$159$	10.5782	0.838903
$160$	2.36610	0.187056
$161$	−1.81724	−0.143219
$162$	2.38193	0.187142
$163$	−14.1924	−1.11164	−0.555818	−	0.831304i	$-0.687595\pi$
$163$	−14.1924	−1.11164	−0.555818	+	0.831304i	$0.687595\pi$
$164$	31.1717	2.43410
$165$	0.0309422	0.00240885
$166$	−29.2905	−2.27339
$167$	−4.24796	−0.328717	−0.164359	−	0.986401i	$-0.552555\pi$
$167$	−4.24796	−0.328717	−0.164359	+	0.986401i	$0.552555\pi$
$168$	−5.61398	−0.433128
$169$	1.00000	0.0769231
$170$	−10.6220	−0.814670
$171$	6.09573	0.466152
$172$	40.8901	3.11784
$173$	−12.2813	−0.933727	−0.466863	−	0.884329i	$-0.654616\pi$
$173$	−12.2813	−0.933727	−0.466863	+	0.884329i	$0.654616\pi$
$174$	21.0258	1.59396
$175$	6.07477	0.459210
$176$	−0.0802326	−0.00604776
$177$	−2.27578	−0.171058
$178$	−28.7259	−2.15310
$179$	2.26708	0.169449	0.0847247	−	0.996404i	$-0.472999\pi$
$179$	2.26708	0.169449	0.0847247	+	0.996404i	$0.472999\pi$
$180$	−3.04347	−0.226847
$181$	1.00817	0.0749368	0.0374684	−	0.999298i	$-0.488071\pi$
$181$	1.00817	0.0749368	0.0374684	+	0.999298i	$0.488071\pi$
$182$	3.35441	0.248645
$183$	7.94009	0.586948
$184$	5.14413	0.379230
$185$	−2.22586	−0.163648
$186$	2.05988	0.151038
$187$	−0.201037	−0.0147013
$188$	27.2121	1.98465
$189$	−1.40827	−0.102437
$190$	−12.0290	−0.872679
$191$	−12.9392	−0.936248	−0.468124	−	0.883663i	$-0.655070\pi$
$191$	−12.9392	−0.936248	−0.468124	+	0.883663i	$0.655070\pi$
$192$	−11.0992	−0.801015
$193$	14.4602	1.04087	0.520435	−	0.853901i	$-0.325770\pi$
$193$	14.4602	1.04087	0.520435	+	0.853901i	$0.325770\pi$
$194$	−27.9565	−2.00716
$195$	0.828467	0.0593278
$196$	−18.4297	−1.31641
$197$	−4.05480	−0.288893	−0.144446	−	0.989513i	$-0.546140\pi$
$197$	−4.05480	−0.288893	−0.144446	+	0.989513i	$0.546140\pi$
$198$	−0.0889622	−0.00632227
$199$	7.44782	0.527962	0.263981	−	0.964528i	$-0.414964\pi$
$199$	7.44782	0.527962	0.263981	+	0.964528i	$0.414964\pi$
$200$	−17.1961	−1.21594
$201$	−3.11107	−0.219438
$202$	−31.3139	−2.20324
$203$	−12.4311	−0.872491
$204$	19.7740	1.38446
$205$	−7.02980	−0.490982
$206$	−2.38193	−0.165957
$207$	1.29041	0.0896895
$208$	−2.14820	−0.148951
$209$	−0.227668	−0.0157481
$210$	2.77902	0.191770
$211$	−8.09746	−0.557452	−0.278726	−	0.960371i	$-0.589912\pi$
$211$	−8.09746	−0.557452	−0.278726	+	0.960371i	$0.589912\pi$
$212$	38.8601	2.66892
$213$	−14.4022	−0.986825
$214$	0.854185	0.0583909
$215$	−9.22147	−0.628899
$216$	3.98643	0.271243
$217$	−1.21786	−0.0826740
$218$	−38.8282	−2.62978
$219$	−13.9610	−0.943398
$220$	0.113670	0.00766360
$221$	−5.38271	−0.362080
$222$	6.39959	0.429512
$223$	−18.3094	−1.22609	−0.613043	−	0.790049i	$-0.710055\pi$
$223$	−18.3094	−1.22609	−0.613043	+	0.790049i	$0.710055\pi$
$224$	4.02201	0.268732
$225$	−4.31364	−0.287576
$226$	−3.54792	−0.236004
$227$	−4.58345	−0.304214	−0.152107	−	0.988364i	$-0.548606\pi$
$227$	−4.58345	−0.304214	−0.152107	+	0.988364i	$0.548606\pi$
$228$	22.3934	1.48304
$229$	17.5066	1.15687	0.578434	−	0.815729i	$-0.303664\pi$
$229$	17.5066	1.15687	0.578434	+	0.815729i	$0.303664\pi$
$230$	−2.54643	−0.167907
$231$	0.0525971	0.00346063
$232$	35.1890	2.31027
$233$	−0.455151	−0.0298179	−0.0149090	−	0.999889i	$-0.504746\pi$
$233$	−0.455151	−0.0298179	−0.0149090	+	0.999889i	$0.504746\pi$
$234$	−2.38193	−0.155712
$235$	−6.13684	−0.400323
$236$	−8.36035	−0.544213
$237$	−3.48975	−0.226684
$238$	−18.0558	−1.17038
$239$	−3.97003	−0.256800	−0.128400	−	0.991722i	$-0.540984\pi$
$239$	−3.97003	−0.256800	−0.128400	+	0.991722i	$0.540984\pi$
$240$	−1.77972	−0.114880
$241$	1.58275	0.101954	0.0509769	−	0.998700i	$-0.483767\pi$
$241$	1.58275	0.101954	0.0509769	+	0.998700i	$0.483767\pi$
$242$	−26.1980	−1.68407
$243$	1.00000	0.0641500
$244$	29.1688	1.86734
$245$	4.15623	0.265532
$246$	20.2114	1.28863
$247$	−6.09573	−0.387862
$248$	3.44744	0.218913
$249$	−12.2969	−0.779287
$250$	18.3791	1.16240
$251$	−3.56782	−0.225199	−0.112599	−	0.993640i	$-0.535918\pi$
$251$	−3.56782	−0.225199	−0.112599	+	0.993640i	$0.535918\pi$
$252$	−5.17344	−0.325896
$253$	−0.0481950	−0.00303000
$254$	−6.70077	−0.420444
$255$	−4.45940	−0.279259
$256$	−27.1686	−1.69803
$257$	3.69713	0.230621	0.115310	−	0.993330i	$-0.463214\pi$
$257$	3.69713	0.230621	0.115310	+	0.993330i	$0.463214\pi$
$258$	26.5127	1.65061
$259$	−3.78363	−0.235103
$260$	3.04347	0.188748
$261$	8.82719	0.546390
$262$	18.7321	1.15727
$263$	−19.7687	−1.21899	−0.609495	−	0.792790i	$-0.708628\pi$
$263$	−19.7687	−1.21899	−0.609495	+	0.792790i	$0.708628\pi$
$264$	−0.148888	−0.00916343
$265$	−8.76366	−0.538348
$266$	−20.4476	−1.25372
$267$	−12.0599	−0.738055
$268$	−11.4289	−0.698129
$269$	24.8179	1.51318	0.756588	−	0.653891i	$-0.226865\pi$
$269$	24.8179	1.51318	0.756588	+	0.653891i	$0.226865\pi$
$270$	−1.97336	−0.120095
$271$	−27.0252	−1.64166	−0.820832	−	0.571170i	$-0.806490\pi$
$271$	−27.0252	−1.64166	−0.820832	+	0.571170i	$0.806490\pi$
$272$	11.5632	0.701119
$273$	1.40827	0.0852324
$274$	9.13343	0.551771
$275$	0.161109	0.00971523
$276$	4.74046	0.285342
$277$	−11.0650	−0.664832	−0.332416	−	0.943133i	$-0.607864\pi$
$277$	−11.0650	−0.664832	−0.332416	+	0.943133i	$0.607864\pi$
$278$	22.1516	1.32856
$279$	0.864794	0.0517739
$280$	4.65100	0.277950
$281$	−2.43944	−0.145525	−0.0727623	−	0.997349i	$-0.523181\pi$
$281$	−2.43944	−0.145525	−0.0727623	+	0.997349i	$0.523181\pi$
$282$	17.6441	1.05069
$283$	25.5512	1.51886	0.759432	−	0.650587i	$-0.225477\pi$
$283$	25.5512	1.51886	0.759432	+	0.650587i	$0.225477\pi$
$284$	−52.9082	−3.13953
$285$	−5.05012	−0.299143
$286$	0.0889622	0.00526044
$287$	−11.9496	−0.705363
$288$	−2.85599	−0.168291
$289$	11.9736	0.704329
$290$	−17.4192	−1.02289
$291$	−11.7369	−0.688028
$292$	−51.2873	−3.00136
$293$	27.6614	1.61600	0.807999	−	0.589184i	$-0.200551\pi$
$293$	27.6614	1.61600	0.807999	+	0.589184i	$0.200551\pi$
$294$	−11.9496	−0.696917
$295$	1.88541	0.109773
$296$	10.7104	0.622531
$297$	−0.0373487	−0.00216719
$298$	20.1969	1.16997
$299$	−1.29041	−0.0746262
$300$	−15.8466	−0.914907
$301$	−15.6751	−0.903499
$302$	58.1361	3.34536
$303$	−13.1464	−0.755241
$304$	13.0949	0.751042
$305$	−6.57811	−0.376661
$306$	12.8213	0.732943
$307$	29.6272	1.69092	0.845458	−	0.534042i	$-0.179327\pi$
$307$	29.6272	1.69092	0.845458	+	0.534042i	$0.179327\pi$
$308$	0.193221	0.0110098
$309$	−1.00000	−0.0568880
$310$	−1.70655	−0.0969253
$311$	−29.4464	−1.66975	−0.834875	−	0.550439i	$-0.814460\pi$
$311$	−29.4464	−1.66975	−0.834875	+	0.550439i	$0.814460\pi$
$312$	−3.98643	−0.225687
$313$	−27.5014	−1.55447	−0.777237	−	0.629208i	$-0.783379\pi$
$313$	−27.5014	−1.55447	−0.777237	+	0.629208i	$0.783379\pi$
$314$	33.5413	1.89285
$315$	1.16671	0.0657364
$316$	−12.8200	−0.721181
$317$	10.8210	0.607771	0.303885	−	0.952709i	$-0.401716\pi$
$317$	10.8210	0.607771	0.303885	+	0.952709i	$0.401716\pi$
$318$	25.1965	1.41295
$319$	−0.329684	−0.0184588
$320$	9.19532	0.514034
$321$	0.358610	0.0200156
$322$	−4.32855	−0.241221
$323$	32.8116	1.82568
$324$	3.67361	0.204090
$325$	4.31364	0.239278
$326$	−33.8054	−1.87231
$327$	−16.3011	−0.901454
$328$	33.8261	1.86773
$329$	−10.4317	−0.575118
$330$	0.0737023	0.00405718
$331$	25.6162	1.40800	0.703998	−	0.710202i	$-0.251397\pi$
$331$	25.6162	1.40800	0.703998	+	0.710202i	$0.251397\pi$
$332$	−45.1742	−2.47926
$333$	2.68672	0.147231
$334$	−10.1184	−0.553652
$335$	2.57742	0.140820
$336$	−3.02525	−0.165041
$337$	35.3844	1.92751	0.963755	−	0.266789i	$-0.0859627\pi$
$337$	35.3844	1.92751	0.963755	+	0.266789i	$0.0859627\pi$
$338$	2.38193	0.129560
$339$	−1.48951	−0.0808993
$340$	−16.3821	−0.888445
$341$	−0.0322989	−0.00174909
$342$	14.5196	0.785132
$343$	16.9229	0.913749
$344$	44.3721	2.39238
$345$	−1.06906	−0.0575563
$346$	−29.2532	−1.57266
$347$	−9.73379	−0.522537	−0.261269	−	0.965266i	$-0.584141\pi$
$347$	−9.73379	−0.522537	−0.261269	+	0.965266i	$0.584141\pi$
$348$	32.4277	1.73831
$349$	4.05419	0.217016	0.108508	−	0.994096i	$-0.465393\pi$
$349$	4.05419	0.217016	0.108508	+	0.994096i	$0.465393\pi$
$350$	14.4697	0.773439
$351$	−1.00000	−0.0533761
$352$	0.106668	0.00568540
$353$	−34.1981	−1.82018	−0.910089	−	0.414412i	$-0.863987\pi$
$353$	−34.1981	−1.82018	−0.910089	+	0.414412i	$0.863987\pi$
$354$	−5.42077	−0.288111
$355$	11.9318	0.633273
$356$	−44.3035	−2.34808
$357$	−7.58031	−0.401193
$358$	5.40003	0.285400
$359$	21.5255	1.13607	0.568037	−	0.823003i	$-0.307703\pi$
$359$	21.5255	1.13607	0.568037	+	0.823003i	$0.307703\pi$
$360$	−3.30263	−0.174064
$361$	18.1580	0.955682
$362$	2.40140	0.126215
$363$	−10.9986	−0.577277
$364$	5.17344	0.271162
$365$	11.5662	0.605405
$366$	18.9128	0.988587
$367$	36.0584	1.88223	0.941117	−	0.338082i	$-0.109778\pi$
$367$	36.0584	1.88223	0.941117	+	0.338082i	$0.109778\pi$
$368$	2.77206	0.144503
$369$	8.48530	0.441727
$370$	−5.30185	−0.275630
$371$	−14.8969	−0.773409
$372$	3.17692	0.164715
$373$	−9.71925	−0.503244	−0.251622	−	0.967826i	$-0.580964\pi$
$373$	−9.71925	−0.503244	−0.251622	+	0.967826i	$0.580964\pi$
$374$	−0.478858	−0.0247611
$375$	7.71605	0.398455
$376$	29.5293	1.52286
$377$	−8.82719	−0.454624
$378$	−3.35441	−0.172532
$379$	7.50659	0.385588	0.192794	−	0.981239i	$-0.438245\pi$
$379$	7.50659	0.385588	0.192794	+	0.981239i	$0.438245\pi$
$380$	−18.5522	−0.951706
$381$	−2.81316	−0.144123
$382$	−30.8203	−1.57691
$383$	−1.39856	−0.0714631	−0.0357315	−	0.999361i	$-0.511376\pi$
$383$	−1.39856	−0.0714631	−0.0357315	+	0.999361i	$0.511376\pi$
$384$	−20.7256	−1.05765
$385$	−0.0435750	−0.00222079
$386$	34.4433	1.75312
$387$	11.1308	0.565808
$388$	−43.1168	−2.18892
$389$	−31.3470	−1.58936	−0.794678	−	0.607032i	$-0.792360\pi$
$389$	−31.3470	−1.58936	−0.794678	+	0.607032i	$0.792360\pi$
$390$	1.97336	0.0999247
$391$	6.94589	0.351269
$392$	−19.9990	−1.01010
$393$	7.86423	0.396698
$394$	−9.65827	−0.486577
$395$	2.89114	0.145469
$396$	−0.137205	−0.00689479
$397$	−31.4209	−1.57697	−0.788484	−	0.615055i	$-0.789134\pi$
$397$	−31.4209	−1.57697	−0.788484	+	0.615055i	$0.789134\pi$
$398$	17.7402	0.889237
$399$	−8.58444	−0.429760
$400$	−9.26658	−0.463329
$401$	−24.5598	−1.22646	−0.613228	−	0.789906i	$-0.710129\pi$
$401$	−24.5598	−1.22646	−0.613228	+	0.789906i	$0.710129\pi$
$402$	−7.41037	−0.369595
$403$	−0.864794	−0.0430785
$404$	−48.2948	−2.40276
$405$	−0.828467	−0.0411669
$406$	−29.6100	−1.46952
$407$	−0.100346	−0.00497394
$408$	21.4578	1.06232
$409$	22.2324	1.09932	0.549661	−	0.835388i	$-0.314757\pi$
$409$	22.2324	1.09932	0.549661	+	0.835388i	$0.314757\pi$
$410$	−16.7445	−0.826953
$411$	3.83446	0.189140
$412$	−3.67361	−0.180986
$413$	3.20492	0.157704
$414$	3.07367	0.151062
$415$	10.1876	0.500091
$416$	2.85599	0.140027
$417$	9.29982	0.455414
$418$	−0.542290	−0.0265243
$419$	−30.9262	−1.51085	−0.755423	−	0.655238i	$-0.772568\pi$
$419$	−30.9262	−1.51085	−0.755423	+	0.655238i	$0.772568\pi$
$420$	4.28603	0.209137
$421$	35.6371	1.73685	0.868424	−	0.495822i	$-0.165133\pi$
$421$	35.6371	1.73685	0.868424	+	0.495822i	$0.165133\pi$
$422$	−19.2876	−0.938907
$423$	7.40746	0.360163
$424$	42.1692	2.04792
$425$	−23.2191	−1.12629
$426$	−34.3052	−1.66209
$427$	−11.1818	−0.541125
$428$	1.31739	0.0636786
$429$	0.0373487	0.00180321
$430$	−21.9649	−1.05924
$431$	31.5335	1.51892	0.759458	−	0.650556i	$-0.225464\pi$
$431$	31.5335	1.51892	0.759458	+	0.650556i	$0.225464\pi$
$432$	2.14820	0.103355
$433$	−34.9987	−1.68193	−0.840965	−	0.541089i	$-0.818012\pi$
$433$	−34.9987	−1.68193	−0.840965	+	0.541089i	$0.818012\pi$
$434$	−2.90087	−0.139246
$435$	−7.31304	−0.350634
$436$	−59.8840	−2.86792
$437$	7.86598	0.376281
$438$	−33.2542	−1.58895
$439$	−3.05144	−0.145637	−0.0728185	−	0.997345i	$-0.523199\pi$
$439$	−3.05144	−0.145637	−0.0728185	+	0.997345i	$0.523199\pi$
$440$	0.123349	0.00588043
$441$	−5.01677	−0.238894
$442$	−12.8213	−0.609846
$443$	9.01939	0.428524	0.214262	−	0.976776i	$-0.431265\pi$
$443$	9.01939	0.428524	0.214262	+	0.976776i	$0.431265\pi$
$444$	9.86997	0.468408
$445$	9.99125	0.473631
$446$	−43.6117	−2.06508
$447$	8.47918	0.401052
$448$	15.6307	0.738479
$449$	−23.9623	−1.13085	−0.565426	−	0.824799i	$-0.691288\pi$
$449$	−23.9623	−1.13085	−0.565426	+	0.824799i	$0.691288\pi$
$450$	−10.2748	−0.484359
$451$	−0.316915	−0.0149230
$452$	−5.47190	−0.257376
$453$	24.4071	1.14675
$454$	−10.9175	−0.512382
$455$	−1.16671	−0.0546960
$456$	24.3002	1.13796
$457$	−33.1726	−1.55175	−0.775875	−	0.630887i	$-0.782691\pi$
$457$	−33.1726	−1.55175	−0.775875	+	0.630887i	$0.782691\pi$
$458$	41.6995	1.94849
$459$	5.38271	0.251244
$460$	−3.92731	−0.183112
$461$	23.0178	1.07205	0.536023	−	0.844204i	$-0.319926\pi$
$461$	23.0178	1.07205	0.536023	+	0.844204i	$0.319926\pi$
$462$	0.125283	0.00582868
$463$	−25.0957	−1.16630	−0.583148	−	0.812366i	$-0.698179\pi$
$463$	−25.0957	−1.16630	−0.583148	+	0.812366i	$0.698179\pi$
$464$	18.9626	0.880317
$465$	−0.716454	−0.0332247
$466$	−1.08414	−0.0502218
$467$	17.1728	0.794661	0.397330	−	0.917676i	$-0.369937\pi$
$467$	17.1728	0.794661	0.397330	+	0.917676i	$0.369937\pi$
$468$	−3.67361	−0.169813
$469$	4.38123	0.202306
$470$	−14.6175	−0.674257
$471$	14.0816	0.648844
$472$	−9.07227	−0.417585
$473$	−0.415720	−0.0191148
$474$	−8.31236	−0.381799
$475$	−26.2948	−1.20649
$476$	−27.8471	−1.27637
$477$	10.5782	0.484341
$478$	−9.45636	−0.432524
$479$	−7.70419	−0.352014	−0.176007	−	0.984389i	$-0.556318\pi$
$479$	−7.70419	−0.352014	−0.176007	+	0.984389i	$0.556318\pi$
$480$	2.36610	0.107997
$481$	−2.68672	−0.122504
$482$	3.77000	0.171719
$483$	−1.81724	−0.0826874
$484$	−40.4046	−1.83657
$485$	9.72363	0.441527
$486$	2.38193	0.108047
$487$	13.6577	0.618889	0.309444	−	0.950918i	$-0.399857\pi$
$487$	13.6577	0.618889	0.309444	+	0.950918i	$0.399857\pi$
$488$	31.6527	1.43285
$489$	−14.1924	−0.641804
$490$	9.89988	0.447231
$491$	−14.6095	−0.659319	−0.329660	−	0.944100i	$-0.606934\pi$
$491$	−14.6095	−0.659319	−0.329660	+	0.944100i	$0.606934\pi$
$492$	31.1717	1.40533
$493$	47.5143	2.13993
$494$	−14.5196	−0.653269
$495$	0.0309422	0.00139075
$496$	1.85775	0.0834155
$497$	20.2822	0.909783
$498$	−29.2905	−1.31254
$499$	36.0000	1.61158	0.805792	−	0.592199i	$-0.201740\pi$
$499$	36.0000	1.61158	0.805792	+	0.592199i	$0.201740\pi$
$500$	28.3458	1.26766
$501$	−4.24796	−0.189785
$502$	−8.49832	−0.379299
$503$	33.5449	1.49569	0.747847	−	0.663871i	$-0.231087\pi$
$503$	33.5449	1.49569	0.747847	+	0.663871i	$0.231087\pi$
$504$	−5.61398	−0.250066
$505$	10.8914	0.484660
$506$	−0.114797	−0.00510337
$507$	1.00000	0.0444116
$508$	−10.3345	−0.458518
$509$	−6.79253	−0.301074	−0.150537	−	0.988604i	$-0.548100\pi$
$509$	−6.79253	−0.301074	−0.150537	+	0.988604i	$0.548100\pi$
$510$	−10.6220	−0.470350
$511$	19.6609	0.869746
$512$	−23.2626	−1.02807
$513$	6.09573	0.269133
$514$	8.80632	0.388430
$515$	0.828467	0.0365066
$516$	40.8901	1.80009
$517$	−0.276659	−0.0121674
$518$	−9.01235	−0.395980
$519$	−12.2813	−0.539087
$520$	3.30263	0.144830
$521$	−10.1737	−0.445716	−0.222858	−	0.974851i	$-0.571539\pi$
$521$	−10.1737	−0.445716	−0.222858	+	0.974851i	$0.571539\pi$
$522$	21.0258	0.920274
$523$	−43.1470	−1.88669	−0.943343	−	0.331820i	$-0.892337\pi$
$523$	−43.1470	−1.88669	−0.943343	+	0.331820i	$0.892337\pi$
$524$	28.8901	1.26207
$525$	6.07477	0.265125
$526$	−47.0877	−2.05312
$527$	4.65494	0.202772
$528$	−0.0802326	−0.00349167
$529$	−21.3348	−0.927602
$530$	−20.8745	−0.906729
$531$	−2.27578	−0.0987607
$532$	−31.5359	−1.36725
$533$	−8.48530	−0.367539
$534$	−28.7259	−1.24309
$535$	−0.297096	−0.0128446
$536$	−12.4021	−0.535688
$537$	2.26708	0.0978316
$538$	59.1147	2.54862
$539$	0.187370	0.00807060
$540$	−3.04347	−0.130970
$541$	−18.7024	−0.804079	−0.402039	−	0.915622i	$-0.631698\pi$
$541$	−18.7024	−0.804079	−0.402039	+	0.915622i	$0.631698\pi$
$542$	−64.3722	−2.76502
$543$	1.00817	0.0432648
$544$	−15.3730	−0.659111
$545$	13.5049	0.578488
$546$	3.35441	0.143555
$547$	16.2973	0.696822	0.348411	−	0.937342i	$-0.386721\pi$
$547$	16.2973	0.696822	0.348411	+	0.937342i	$0.386721\pi$
$548$	14.0863	0.601738
$549$	7.94009	0.338875
$550$	0.383751	0.0163632
$551$	53.8082	2.29231
$552$	5.14413	0.218949
$553$	4.91451	0.208986
$554$	−26.3561	−1.11976
$555$	−2.22586	−0.0944825
$556$	34.1639	1.44887
$557$	18.3091	0.775781	0.387891	−	0.921705i	$-0.373204\pi$
$557$	18.3091	0.775781	0.387891	+	0.921705i	$0.373204\pi$
$558$	2.05988	0.0872018
$559$	−11.1308	−0.470781
$560$	2.50632	0.105911
$561$	−0.201037	−0.00848780
$562$	−5.81058	−0.245105
$563$	29.6433	1.24932	0.624659	−	0.780898i	$-0.285238\pi$
$563$	29.6433	1.24932	0.624659	+	0.780898i	$0.285238\pi$
$564$	27.2121	1.14584
$565$	1.23401	0.0519153
$566$	60.8614	2.55819
$567$	−1.40827	−0.0591418
$568$	−57.4136	−2.40902
$569$	−24.9971	−1.04793	−0.523966	−	0.851739i	$-0.675548\pi$
$569$	−24.9971	−1.04793	−0.523966	+	0.851739i	$0.675548\pi$
$570$	−12.0290	−0.503841
$571$	−16.8842	−0.706581	−0.353291	−	0.935514i	$-0.614937\pi$
$571$	−16.8842	−0.706581	−0.353291	+	0.935514i	$0.614937\pi$
$572$	0.137205	0.00573682
$573$	−12.9392	−0.540543
$574$	−28.4632	−1.18803
$575$	−5.56636	−0.232133
$576$	−11.0992	−0.462466
$577$	−20.4980	−0.853343	−0.426671	−	0.904407i	$-0.640314\pi$
$577$	−20.4980	−0.853343	−0.426671	+	0.904407i	$0.640314\pi$
$578$	28.5203	1.18629
$579$	14.4602	0.600947
$580$	−26.8653	−1.11552
$581$	17.3174	0.718448
$582$	−27.9565	−1.15883
$583$	−0.395081	−0.0163626
$584$	−55.6547	−2.30301
$585$	0.828467	0.0342529
$586$	65.8877	2.72179
$587$	−32.1501	−1.32697	−0.663487	−	0.748187i	$-0.730924\pi$
$587$	−32.1501	−1.32697	−0.663487	+	0.748187i	$0.730924\pi$
$588$	−18.4297	−0.760027
$589$	5.27155	0.217211
$590$	4.49093	0.184889
$591$	−4.05480	−0.166792
$592$	5.77162	0.237212
$593$	33.6350	1.38122	0.690611	−	0.723226i	$-0.257342\pi$
$593$	33.6350	1.38122	0.690611	+	0.723226i	$0.257342\pi$
$594$	−0.0889622	−0.00365016
$595$	6.28004	0.257457
$596$	31.1492	1.27592
$597$	7.44782	0.304819
$598$	−3.07367	−0.125692
$599$	40.6904	1.66257	0.831283	−	0.555850i	$-0.187607\pi$
$599$	40.6904	1.66257	0.831283	+	0.555850i	$0.187607\pi$
$600$	−17.1961	−0.702026
$601$	1.05301	0.0429533	0.0214767	−	0.999769i	$-0.493163\pi$
$601$	1.05301	0.0429533	0.0214767	+	0.999769i	$0.493163\pi$
$602$	−37.3371	−1.52175
$603$	−3.11107	−0.126693
$604$	89.6622	3.64830
$605$	9.11199	0.370455
$606$	−31.3139	−1.27204
$607$	32.2223	1.30786	0.653931	−	0.756554i	$-0.273119\pi$
$607$	32.2223	1.30786	0.653931	+	0.756554i	$0.273119\pi$
$608$	−17.4094	−0.706043
$609$	−12.4311	−0.503733
$610$	−15.6686	−0.634404
$611$	−7.40746	−0.299674
$612$	19.7740	0.799317
$613$	−34.6815	−1.40077	−0.700386	−	0.713764i	$-0.746989\pi$
$613$	−34.6815	−1.40077	−0.700386	+	0.713764i	$0.746989\pi$
$614$	70.5702	2.84798
$615$	−7.02980	−0.283469
$616$	0.209675	0.00844804
$617$	−28.0229	−1.12816	−0.564081	−	0.825720i	$-0.690769\pi$
$617$	−28.0229	−1.12816	−0.564081	+	0.825720i	$0.690769\pi$
$618$	−2.38193	−0.0958155
$619$	−33.1983	−1.33435	−0.667176	−	0.744901i	$-0.732497\pi$
$619$	−33.1983	−1.33435	−0.667176	+	0.744901i	$0.732497\pi$
$620$	−2.63197	−0.105703
$621$	1.29041	0.0517823
$622$	−70.1393	−2.81233
$623$	16.9836	0.680435
$624$	−2.14820	−0.0859969
$625$	15.1757	0.607029
$626$	−65.5066	−2.61817
$627$	−0.227668	−0.00909217
$628$	51.7302	2.06426
$629$	14.4618	0.576631
$630$	2.77902	0.110719
$631$	3.96146	0.157703	0.0788516	−	0.996886i	$-0.474875\pi$
$631$	3.96146	0.157703	0.0788516	+	0.996886i	$0.474875\pi$
$632$	−13.9117	−0.553376
$633$	−8.09746	−0.321845
$634$	25.7750	1.02366
$635$	2.33061	0.0924876
$636$	38.8601	1.54090
$637$	5.01677	0.198772
$638$	−0.785286	−0.0310898
$639$	−14.4022	−0.569744
$640$	17.1705	0.678722
$641$	−14.7440	−0.582353	−0.291177	−	0.956669i	$-0.594047\pi$
$641$	−14.7440	−0.582353	−0.291177	+	0.956669i	$0.594047\pi$
$642$	0.854185	0.0337120
$643$	15.6094	0.615573	0.307787	−	0.951455i	$-0.400412\pi$
$643$	15.6094	0.615573	0.307787	+	0.951455i	$0.400412\pi$
$644$	−6.67584	−0.263065
$645$	−9.22147	−0.363095
$646$	78.1550	3.07497
$647$	−32.4043	−1.27394	−0.636972	−	0.770887i	$-0.719813\pi$
$647$	−32.4043	−1.27394	−0.636972	+	0.770887i	$0.719813\pi$
$648$	3.98643	0.156602
$649$	0.0849976	0.00333645
$650$	10.2748	0.403011
$651$	−1.21786	−0.0477318
$652$	−52.1375	−2.04186
$653$	13.1570	0.514874	0.257437	−	0.966295i	$-0.417122\pi$
$653$	13.1570	0.514874	0.257437	+	0.966295i	$0.417122\pi$
$654$	−38.8282	−1.51830
$655$	−6.51526	−0.254572
$656$	18.2282	0.711690
$657$	−13.9610	−0.544671
$658$	−24.8476	−0.968661
$659$	7.47547	0.291203	0.145602	−	0.989343i	$-0.453488\pi$
$659$	7.47547	0.291203	0.145602	+	0.989343i	$0.453488\pi$
$660$	0.113670	0.00442458
$661$	19.9843	0.777298	0.388649	−	0.921386i	$-0.372942\pi$
$661$	19.9843	0.777298	0.388649	+	0.921386i	$0.372942\pi$
$662$	61.0162	2.37146
$663$	−5.38271	−0.209047
$664$	−49.0210	−1.90238
$665$	7.11193	0.275789
$666$	6.39959	0.247979
$667$	11.3907	0.441049
$668$	−15.6054	−0.603789
$669$	−18.3094	−0.707882
$670$	6.13925	0.237180
$671$	−0.296552	−0.0114483
$672$	4.02201	0.155152
$673$	30.4740	1.17469	0.587344	−	0.809338i	$-0.300174\pi$
$673$	30.4740	1.17469	0.587344	+	0.809338i	$0.300174\pi$
$674$	84.2833	3.24647
$675$	−4.31364	−0.166032
$676$	3.67361	0.141293
$677$	−20.9683	−0.805879	−0.402940	−	0.915227i	$-0.632012\pi$
$677$	−20.9683	−0.805879	−0.402940	+	0.915227i	$0.632012\pi$
$678$	−3.54792	−0.136257
$679$	16.5287	0.634313
$680$	−17.7771	−0.681721
$681$	−4.58345	−0.175638
$682$	−0.0769339	−0.00294595
$683$	−6.40550	−0.245100	−0.122550	−	0.992462i	$-0.539107\pi$
$683$	−6.40550	−0.245100	−0.122550	+	0.992462i	$0.539107\pi$
$684$	22.3934	0.856231
$685$	−3.17673	−0.121376
$686$	40.3092	1.53901
$687$	17.5066	0.667918
$688$	23.9111	0.911603
$689$	−10.5782	−0.402996
$690$	−2.54643	−0.0969410
$691$	−33.7640	−1.28444	−0.642222	−	0.766518i	$-0.721987\pi$
$691$	−33.7640	−1.28444	−0.642222	+	0.766518i	$0.721987\pi$
$692$	−45.1166	−1.71507
$693$	0.0525971	0.00199800
$694$	−23.1853	−0.880100
$695$	−7.70460	−0.292252
$696$	35.1890	1.33384
$697$	45.6740	1.73002
$698$	9.65682	0.365516
$699$	−0.455151	−0.0172154
$700$	22.3164	0.843479
$701$	−33.1898	−1.25356	−0.626781	−	0.779195i	$-0.715628\pi$
$701$	−33.1898	−1.25356	−0.626781	+	0.779195i	$0.715628\pi$
$702$	−2.38193	−0.0899003
$703$	16.3775	0.617690
$704$	0.414540	0.0156236
$705$	−6.13684	−0.231127
$706$	−81.4575	−3.06569
$707$	18.5137	0.696279
$708$	−8.36035	−0.314201
$709$	−26.1058	−0.980425	−0.490212	−	0.871603i	$-0.663081\pi$
$709$	−26.1058	−0.980425	−0.490212	+	0.871603i	$0.663081\pi$
$710$	28.4207	1.06661
$711$	−3.48975	−0.130876
$712$	−48.0761	−1.80173
$713$	1.11594	0.0417921
$714$	−18.0558	−0.675722
$715$	−0.0309422	−0.00115717
$716$	8.32836	0.311246
$717$	−3.97003	−0.148264
$718$	51.2724	1.91347
$719$	−39.8118	−1.48473	−0.742365	−	0.669995i	$-0.766296\pi$
$719$	−39.8118	−1.48473	−0.742365	+	0.669995i	$0.766296\pi$
$720$	−1.77972	−0.0663261
$721$	1.40827	0.0524467
$722$	43.2511	1.60964
$723$	1.58275	0.0588630
$724$	3.70363	0.137644
$725$	−38.0774	−1.41416
$726$	−26.1980	−0.972297
$727$	−42.0434	−1.55931	−0.779653	−	0.626212i	$-0.784604\pi$
$727$	−42.0434	−1.55931	−0.779653	+	0.626212i	$0.784604\pi$
$728$	5.61398	0.208068
$729$	1.00000	0.0370370
$730$	27.5500	1.01967
$731$	59.9137	2.21599
$732$	29.1688	1.07811
$733$	−38.6043	−1.42588	−0.712941	−	0.701224i	$-0.752637\pi$
$733$	−38.6043	−1.42588	−0.712941	+	0.701224i	$0.752637\pi$
$734$	85.8888	3.17021
$735$	4.15623	0.153305
$736$	−3.68539	−0.135845
$737$	0.116194	0.00428008
$738$	20.2114	0.743993
$739$	7.33926	0.269979	0.134990	−	0.990847i	$-0.456900\pi$
$739$	7.33926	0.269979	0.134990	+	0.990847i	$0.456900\pi$
$740$	−8.17695	−0.300590
$741$	−6.09573	−0.223932
$742$	−35.4835	−1.30264
$743$	−7.84962	−0.287974	−0.143987	−	0.989580i	$-0.545992\pi$
$743$	−7.84962	−0.287974	−0.143987	+	0.989580i	$0.545992\pi$
$744$	3.44744	0.126389
$745$	−7.02473	−0.257366
$746$	−23.1506	−0.847604
$747$	−12.2969	−0.449922
$748$	−0.738533	−0.0270035
$749$	−0.505019	−0.0184530
$750$	18.3791	0.671111
$751$	43.8934	1.60169	0.800847	−	0.598869i	$-0.204383\pi$
$751$	43.8934	1.60169	0.800847	+	0.598869i	$0.204383\pi$
$752$	15.9127	0.580277
$753$	−3.56782	−0.130019
$754$	−21.0258	−0.765714
$755$	−20.2205	−0.735899
$756$	−5.17344	−0.188156
$757$	40.7374	1.48062	0.740312	−	0.672263i	$-0.234678\pi$
$757$	40.7374	1.48062	0.740312	+	0.672263i	$0.234678\pi$
$758$	17.8802	0.649438
$759$	−0.0481950	−0.00174937
$760$	−20.1320	−0.730263
$761$	10.0346	0.363752	0.181876	−	0.983321i	$-0.441783\pi$
$761$	10.0346	0.363752	0.181876	+	0.983321i	$0.441783\pi$
$762$	−6.70077	−0.242743
$763$	22.9564	0.831077
$764$	−47.5336	−1.71971
$765$	−4.45940	−0.161230
$766$	−3.33128	−0.120364
$767$	2.27578	0.0821738
$768$	−27.1686	−0.980361
$769$	−6.42242	−0.231599	−0.115799	−	0.993273i	$-0.536943\pi$
$769$	−6.42242	−0.231599	−0.115799	+	0.993273i	$0.536943\pi$
$770$	−0.103793	−0.00374043
$771$	3.69713	0.133149
$772$	53.1213	1.91188
$773$	18.8258	0.677115	0.338558	−	0.940946i	$-0.390061\pi$
$773$	18.8258	0.677115	0.338558	+	0.940946i	$0.390061\pi$
$774$	26.5127	0.952981
$775$	−3.73041	−0.134000
$776$	−46.7883	−1.67960
$777$	−3.78363	−0.135737
$778$	−74.6665	−2.67692
$779$	51.7242	1.85321
$780$	3.04347	0.108974
$781$	0.537905	0.0192477
$782$	16.5447	0.591636
$783$	8.82719	0.315458
$784$	−10.7770	−0.384895
$785$	−11.6661	−0.416381
$786$	18.7321	0.668151
$787$	−32.8593	−1.17131	−0.585654	−	0.810561i	$-0.699162\pi$
$787$	−32.8593	−1.17131	−0.585654	+	0.810561i	$0.699162\pi$
$788$	−14.8958	−0.530640
$789$	−19.7687	−0.703784
$790$	6.88652	0.245011
$791$	2.09764	0.0745834
$792$	−0.148888	−0.00529051
$793$	−7.94009	−0.281961
$794$	−74.8425	−2.65606
$795$	−8.76366	−0.310815
$796$	27.3604	0.969764
$797$	0.274048	0.00970729	0.00485365	−	0.999988i	$-0.498455\pi$
$797$	0.274048	0.00970729	0.00485365	+	0.999988i	$0.498455\pi$
$798$	−20.4476	−0.723836
$799$	39.8722	1.41058
$800$	12.3197	0.435568
$801$	−12.0599	−0.426116
$802$	−58.4998	−2.06570
$803$	0.521426	0.0184007
$804$	−11.4289	−0.403065
$805$	1.50553	0.0530628
$806$	−2.05988	−0.0725563
$807$	24.8179	0.873633
$808$	−52.4073	−1.84368
$809$	48.9136	1.71971	0.859854	−	0.510539i	$-0.170554\pi$
$809$	48.9136	1.71971	0.859854	+	0.510539i	$0.170554\pi$
$810$	−1.97336	−0.0693366
$811$	−32.9814	−1.15813	−0.579067	−	0.815280i	$-0.696583\pi$
$811$	−32.9814	−1.15813	−0.579067	+	0.815280i	$0.696583\pi$
$812$	−45.6670	−1.60260
$813$	−27.0252	−0.947815
$814$	−0.239016	−0.00837752
$815$	11.7580	0.411864
$816$	11.5632	0.404791
$817$	67.8501	2.37378
$818$	52.9561	1.85157
$819$	1.40827	0.0492089
$820$	−25.8248	−0.901840
$821$	42.2983	1.47622	0.738111	−	0.674679i	$-0.235718\pi$
$821$	42.2983	1.47622	0.738111	+	0.674679i	$0.235718\pi$
$822$	9.13343	0.318565
$823$	19.7056	0.686894	0.343447	−	0.939172i	$-0.388405\pi$
$823$	19.7056	0.686894	0.343447	+	0.939172i	$0.388405\pi$
$824$	−3.98643	−0.138874
$825$	0.161109	0.00560909
$826$	7.63391	0.265618
$827$	11.5920	0.403094	0.201547	−	0.979479i	$-0.435403\pi$
$827$	11.5920	0.403094	0.201547	+	0.979479i	$0.435403\pi$
$828$	4.74046	0.164742
$829$	2.64626	0.0919085	0.0459542	−	0.998944i	$-0.485367\pi$
$829$	2.64626	0.0919085	0.0459542	+	0.998944i	$0.485367\pi$
$830$	24.2662	0.842294
$831$	−11.0650	−0.383841
$832$	11.0992	0.384795
$833$	−27.0039	−0.935628
$834$	22.1516	0.767046
$835$	3.51930	0.121790
$836$	−0.836363	−0.0289262
$837$	0.864794	0.0298916
$838$	−73.6643	−2.54469
$839$	−40.6518	−1.40345	−0.701727	−	0.712446i	$-0.747588\pi$
$839$	−40.6518	−1.40345	−0.701727	+	0.712446i	$0.747588\pi$
$840$	4.65100	0.160475
$841$	48.9194	1.68687
$842$	84.8854	2.92534
$843$	−2.43944	−0.0840187
$844$	−29.7469	−1.02393
$845$	−0.828467	−0.0285001
$846$	17.6441	0.606616
$847$	15.4890	0.532209
$848$	22.7240	0.780347
$849$	25.5512	0.876916
$850$	−55.3064	−1.89699
$851$	3.46696	0.118846
$852$	−52.9082	−1.81261
$853$	31.5008	1.07857	0.539284	−	0.842124i	$-0.318695\pi$
$853$	31.5008	1.07857	0.539284	+	0.842124i	$0.318695\pi$
$854$	−26.6343	−0.911407
$855$	−5.05012	−0.172710
$856$	1.42957	0.0488618
$857$	19.2931	0.659041	0.329521	−	0.944148i	$-0.393113\pi$
$857$	19.2931	0.659041	0.329521	+	0.944148i	$0.393113\pi$
$858$	0.0889622	0.00303712
$859$	−46.6312	−1.59104	−0.795519	−	0.605929i	$-0.792802\pi$
$859$	−46.6312	−1.59104	−0.795519	+	0.605929i	$0.792802\pi$
$860$	−33.8761	−1.15517
$861$	−11.9496	−0.407241
$862$	75.1108	2.55828
$863$	18.0219	0.613472	0.306736	−	0.951795i	$-0.400763\pi$
$863$	18.0219	0.613472	0.306736	+	0.951795i	$0.400763\pi$
$864$	−2.85599	−0.0971628
$865$	10.1746	0.345948
$866$	−83.3646	−2.83285
$867$	11.9736	0.406645
$868$	−4.47396	−0.151856
$869$	0.130338	0.00442140
$870$	−17.4192	−0.590566
$871$	3.11107	0.105415
$872$	−64.9834	−2.20061
$873$	−11.7369	−0.397233
$874$	18.7362	0.633763
$875$	−10.8663	−0.367347
$876$	−51.2873	−1.73284
$877$	−19.0463	−0.643148	−0.321574	−	0.946884i	$-0.604212\pi$
$877$	−19.0463	−0.643148	−0.321574	+	0.946884i	$0.604212\pi$
$878$	−7.26832	−0.245294
$879$	27.6614	0.932996
$880$	0.0664701	0.00224071
$881$	26.9128	0.906716	0.453358	−	0.891329i	$-0.350226\pi$
$881$	26.9128	0.906716	0.453358	+	0.891329i	$0.350226\pi$
$882$	−11.9496	−0.402365
$883$	−29.5639	−0.994905	−0.497453	−	0.867491i	$-0.665731\pi$
$883$	−29.5639	−0.994905	−0.497453	+	0.867491i	$0.665731\pi$
$884$	−19.7740	−0.665072
$885$	1.88541	0.0633775
$886$	21.4836	0.721756
$887$	−36.0955	−1.21197	−0.605984	−	0.795477i	$-0.707220\pi$
$887$	−36.0955	−1.21197	−0.605984	+	0.795477i	$0.707220\pi$
$888$	10.7104	0.359419
$889$	3.96169	0.132871
$890$	23.7985	0.797728
$891$	−0.0373487	−0.00125123
$892$	−67.2616	−2.25208
$893$	45.1539	1.51102
$894$	20.1969	0.675484
$895$	−1.87820	−0.0627813
$896$	29.1872	0.975076
$897$	−1.29041	−0.0430855
$898$	−57.0767	−1.90467
$899$	7.63370	0.254598
$900$	−15.8466	−0.528222
$901$	56.9392	1.89692
$902$	−0.754871	−0.0251345
$903$	−15.6751	−0.521635
$904$	−5.93785	−0.197490
$905$	−0.835238	−0.0277642
$906$	58.1361	1.93144
$907$	−7.17789	−0.238338	−0.119169	−	0.992874i	$-0.538023\pi$
$907$	−7.17789	−0.238338	−0.119169	+	0.992874i	$0.538023\pi$
$908$	−16.8378	−0.558782
$909$	−13.1464	−0.436039
$910$	−2.77902	−0.0921235
$911$	−51.6703	−1.71191	−0.855957	−	0.517047i	$-0.827031\pi$
$911$	−51.6703	−1.71191	−0.855957	+	0.517047i	$0.827031\pi$
$912$	13.0949	0.433614
$913$	0.459275	0.0151998
$914$	−79.0150	−2.61358
$915$	−6.57811	−0.217466
$916$	64.3124	2.12494
$917$	−11.0750	−0.365727
$918$	12.8213	0.423165
$919$	44.0022	1.45150	0.725749	−	0.687959i	$-0.241493\pi$
$919$	44.0022	1.45150	0.725749	+	0.687959i	$0.241493\pi$
$920$	−4.26174	−0.140505
$921$	29.6272	0.976251
$922$	54.8269	1.80563
$923$	14.4022	0.474055
$924$	0.193221	0.00635651
$925$	−11.5895	−0.381062
$926$	−59.7763	−1.96437
$927$	−1.00000	−0.0328443
$928$	−25.2104	−0.827572
$929$	−1.68876	−0.0554064	−0.0277032	−	0.999616i	$-0.508819\pi$
$929$	−1.68876	−0.0554064	−0.0277032	+	0.999616i	$0.508819\pi$
$930$	−1.70655	−0.0559598
$931$	−30.5809	−1.00225
$932$	−1.67205	−0.0547697
$933$	−29.4464	−0.964031
$934$	40.9044	1.33843
$935$	0.166553	0.00544686
$936$	−3.98643	−0.130301
$937$	−17.6240	−0.575752	−0.287876	−	0.957668i	$-0.592949\pi$
$937$	−17.6240	−0.575752	−0.287876	+	0.957668i	$0.592949\pi$
$938$	10.4358	0.340741
$939$	−27.5014	−0.897476
$940$	−22.5444	−0.735316
$941$	19.1897	0.625568	0.312784	−	0.949824i	$-0.398738\pi$
$941$	19.1897	0.625568	0.312784	+	0.949824i	$0.398738\pi$
$942$	33.5413	1.09284
$943$	10.9495	0.356565
$944$	−4.88885	−0.159118
$945$	1.16671	0.0379530
$946$	−0.990217	−0.0321947
$947$	−61.3478	−1.99354	−0.996768	−	0.0803291i	$-0.974403\pi$
$947$	−61.3478	−1.99354	−0.996768	+	0.0803291i	$0.974403\pi$
$948$	−12.8200	−0.416374
$949$	13.9610	0.453194
$950$	−62.6325	−2.03207
$951$	10.8210	0.350897
$952$	−30.2184	−0.979385
$953$	−11.4992	−0.372494	−0.186247	−	0.982503i	$-0.559633\pi$
$953$	−11.4992	−0.372494	−0.186247	+	0.982503i	$0.559633\pi$
$954$	25.1965	0.815767
$955$	10.7197	0.346882
$956$	−14.5844	−0.471692
$957$	−0.329684	−0.0106572
$958$	−18.3509	−0.592890
$959$	−5.39996	−0.174374
$960$	9.19532	0.296778
$961$	−30.2521	−0.975875
$962$	−6.39959	−0.206331
$963$	0.358610	0.0115560
$964$	5.81440	0.187269
$965$	−11.9798	−0.385644
$966$	−4.32855	−0.139269
$967$	34.7873	1.11868	0.559342	−	0.828937i	$-0.311054\pi$
$967$	34.7873	1.11868	0.559342	+	0.828937i	$0.311054\pi$
$968$	−43.8452	−1.40924
$969$	32.8116	1.05406
$970$	23.1610	0.743656
$971$	−18.3658	−0.589386	−0.294693	−	0.955592i	$-0.595217\pi$
$971$	−18.3658	−0.589386	−0.294693	+	0.955592i	$0.595217\pi$
$972$	3.67361	0.117831
$973$	−13.0967	−0.419860
$974$	32.5317	1.04238
$975$	4.31364	0.138147
$976$	17.0569	0.545979
$977$	−3.37248	−0.107895	−0.0539475	−	0.998544i	$-0.517180\pi$
$977$	−3.37248	−0.107895	−0.0539475	+	0.998544i	$0.517180\pi$
$978$	−33.8054	−1.08098
$979$	0.450422	0.0143956
$980$	15.2684	0.487731
$981$	−16.3011	−0.520455
$982$	−34.7990	−1.11048
$983$	−45.7432	−1.45898	−0.729491	−	0.683990i	$-0.760243\pi$
$983$	−45.7432	−1.45898	−0.729491	+	0.683990i	$0.760243\pi$
$984$	33.8261	1.07834
$985$	3.35927	0.107035
$986$	113.176	3.60425
$987$	−10.4317	−0.332045
$988$	−22.3934	−0.712428
$989$	14.3632	0.456724
$990$	0.0737023	0.00234241
$991$	42.2429	1.34189	0.670945	−	0.741507i	$-0.265889\pi$
$991$	42.2429	1.34189	0.670945	+	0.741507i	$0.265889\pi$
$992$	−2.46984	−0.0784176
$993$	25.6162	0.812906
$994$	48.3110	1.53233
$995$	−6.17028	−0.195611
$996$	−45.1742	−1.43140
$997$	19.4330	0.615451	0.307725	−	0.951475i	$-0.400432\pi$
$997$	19.4330	0.615451	0.307725	+	0.951475i	$0.400432\pi$
$998$	85.7497	2.71436
$999$	2.68672	0.0850040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.27	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.27	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+2.38193 q^{2} +1.00000 q^{3} +3.67361 q^{4} -0.828467 q^{5} +2.38193 q^{6} -1.40827 q^{7} +3.98643 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.38193 q^{2} +1.00000 q^{3} +3.67361 q^{4} -0.828467 q^{5} +2.38193 q^{6} -1.40827 q^{7} +3.98643 q^{8} +1.00000 q^{9} -1.97336 q^{10} -0.0373487 q^{11} +3.67361 q^{12} -1.00000 q^{13} -3.35441 q^{14} -0.828467 q^{15} +2.14820 q^{16} +5.38271 q^{17} +2.38193 q^{18} +6.09573 q^{19} -3.04347 q^{20} -1.40827 q^{21} -0.0889622 q^{22} +1.29041 q^{23} +3.98643 q^{24} -4.31364 q^{25} -2.38193 q^{26} +1.00000 q^{27} -5.17344 q^{28} +8.82719 q^{29} -1.97336 q^{30} +0.864794 q^{31} -2.85599 q^{32} -0.0373487 q^{33} +12.8213 q^{34} +1.16671 q^{35} +3.67361 q^{36} +2.68672 q^{37} +14.5196 q^{38} -1.00000 q^{39} -3.30263 q^{40} +8.48530 q^{41} -3.35441 q^{42} +11.1308 q^{43} -0.137205 q^{44} -0.828467 q^{45} +3.07367 q^{46} +7.40746 q^{47} +2.14820 q^{48} -5.01677 q^{49} -10.2748 q^{50} +5.38271 q^{51} -3.67361 q^{52} +10.5782 q^{53} +2.38193 q^{54} +0.0309422 q^{55} -5.61398 q^{56} +6.09573 q^{57} +21.0258 q^{58} -2.27578 q^{59} -3.04347 q^{60} +7.94009 q^{61} +2.05988 q^{62} -1.40827 q^{63} -11.0992 q^{64} +0.828467 q^{65} -0.0889622 q^{66} -3.11107 q^{67} +19.7740 q^{68} +1.29041 q^{69} +2.77902 q^{70} -14.4022 q^{71} +3.98643 q^{72} -13.9610 q^{73} +6.39959 q^{74} -4.31364 q^{75} +22.3934 q^{76} +0.0525971 q^{77} -2.38193 q^{78} -3.48975 q^{79} -1.77972 q^{80} +1.00000 q^{81} +20.2114 q^{82} -12.2969 q^{83} -5.17344 q^{84} -4.45940 q^{85} +26.5127 q^{86} +8.82719 q^{87} -0.148888 q^{88} -12.0599 q^{89} -1.97336 q^{90} +1.40827 q^{91} +4.74046 q^{92} +0.864794 q^{93} +17.6441 q^{94} -5.05012 q^{95} -2.85599 q^{96} -11.7369 q^{97} -11.9496 q^{98} -0.0373487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more