LMFDB - Embedded newform 6026.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.75069 q^{3} +1.00000 q^{4} -4.14565 q^{5} +2.75069 q^{6} -3.93457 q^{7} -1.00000 q^{8} +4.56631 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.75069 q^{3} +1.00000 q^{4} -4.14565 q^{5} +2.75069 q^{6} -3.93457 q^{7} -1.00000 q^{8} +4.56631 q^{9} +4.14565 q^{10} +1.06039 q^{11} -2.75069 q^{12} +1.45615 q^{13} +3.93457 q^{14} +11.4034 q^{15} +1.00000 q^{16} -3.35934 q^{17} -4.56631 q^{18} +4.79836 q^{19} -4.14565 q^{20} +10.8228 q^{21} -1.06039 q^{22} -1.00000 q^{23} +2.75069 q^{24} +12.1865 q^{25} -1.45615 q^{26} -4.30844 q^{27} -3.93457 q^{28} -2.83489 q^{29} -11.4034 q^{30} +5.47001 q^{31} -1.00000 q^{32} -2.91681 q^{33} +3.35934 q^{34} +16.3114 q^{35} +4.56631 q^{36} +1.64768 q^{37} -4.79836 q^{38} -4.00544 q^{39} +4.14565 q^{40} -6.70237 q^{41} -10.8228 q^{42} -8.27829 q^{43} +1.06039 q^{44} -18.9304 q^{45} +1.00000 q^{46} -7.60304 q^{47} -2.75069 q^{48} +8.48082 q^{49} -12.1865 q^{50} +9.24052 q^{51} +1.45615 q^{52} +1.45329 q^{53} +4.30844 q^{54} -4.39602 q^{55} +3.93457 q^{56} -13.1988 q^{57} +2.83489 q^{58} -0.759864 q^{59} +11.4034 q^{60} -3.61363 q^{61} -5.47001 q^{62} -17.9665 q^{63} +1.00000 q^{64} -6.03672 q^{65} +2.91681 q^{66} -4.04656 q^{67} -3.35934 q^{68} +2.75069 q^{69} -16.3114 q^{70} -1.96939 q^{71} -4.56631 q^{72} -1.67757 q^{73} -1.64768 q^{74} -33.5212 q^{75} +4.79836 q^{76} -4.17218 q^{77} +4.00544 q^{78} +2.92025 q^{79} -4.14565 q^{80} -1.84773 q^{81} +6.70237 q^{82} -2.22807 q^{83} +10.8228 q^{84} +13.9267 q^{85} +8.27829 q^{86} +7.79792 q^{87} -1.06039 q^{88} +3.03860 q^{89} +18.9304 q^{90} -5.72934 q^{91} -1.00000 q^{92} -15.0463 q^{93} +7.60304 q^{94} -19.8923 q^{95} +2.75069 q^{96} +7.85207 q^{97} -8.48082 q^{98} +4.84208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.75069	−1.58811	−0.794057	−	0.607844i	$-0.792035\pi$
$3$	−2.75069	−1.58811	−0.794057	+	0.607844i	$0.792035\pi$
$4$	1.00000	0.500000
$5$	−4.14565	−1.85399	−0.926997	−	0.375070i	$-0.877619\pi$
$5$	−4.14565	−1.85399	−0.926997	+	0.375070i	$0.877619\pi$
$6$	2.75069	1.12297
$7$	−3.93457	−1.48713	−0.743563	−	0.668666i	$-0.766866\pi$
$7$	−3.93457	−1.48713	−0.743563	+	0.668666i	$0.766866\pi$
$8$	−1.00000	−0.353553
$9$	4.56631	1.52210
$10$	4.14565	1.31097
$11$	1.06039	0.319720	0.159860	−	0.987140i	$-0.448896\pi$
$11$	1.06039	0.319720	0.159860	+	0.987140i	$0.448896\pi$
$12$	−2.75069	−0.794057
$13$	1.45615	0.403865	0.201932	−	0.979399i	$-0.435278\pi$
$13$	1.45615	0.403865	0.201932	+	0.979399i	$0.435278\pi$
$14$	3.93457	1.05156
$15$	11.4034	2.94435
$16$	1.00000	0.250000
$17$	−3.35934	−0.814760	−0.407380	−	0.913259i	$-0.633558\pi$
$17$	−3.35934	−0.814760	−0.407380	+	0.913259i	$0.633558\pi$
$18$	−4.56631	−1.07629
$19$	4.79836	1.10082	0.550409	−	0.834895i	$-0.314472\pi$
$19$	4.79836	1.10082	0.550409	+	0.834895i	$0.314472\pi$
$20$	−4.14565	−0.926997
$21$	10.8228	2.36173
$22$	−1.06039	−0.226076
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.75069	0.561483
$25$	12.1865	2.43729
$26$	−1.45615	−0.285575
$27$	−4.30844	−0.829160
$28$	−3.93457	−0.743563
$29$	−2.83489	−0.526426	−0.263213	−	0.964738i	$-0.584782\pi$
$29$	−2.83489	−0.526426	−0.263213	+	0.964738i	$0.584782\pi$
$30$	−11.4034	−2.08197
$31$	5.47001	0.982442	0.491221	−	0.871035i	$-0.336551\pi$
$31$	5.47001	0.982442	0.491221	+	0.871035i	$0.336551\pi$
$32$	−1.00000	−0.176777
$33$	−2.91681	−0.507752
$34$	3.35934	0.576123
$35$	16.3114	2.75712
$36$	4.56631	0.761052
$37$	1.64768	0.270877	0.135439	−	0.990786i	$-0.456756\pi$
$37$	1.64768	0.270877	0.135439	+	0.990786i	$0.456756\pi$
$38$	−4.79836	−0.778396
$39$	−4.00544	−0.641383
$40$	4.14565	0.655486
$41$	−6.70237	−1.04673	−0.523367	−	0.852107i	$-0.675324\pi$
$41$	−6.70237	−1.04673	−0.523367	+	0.852107i	$0.675324\pi$
$42$	−10.8228	−1.66999
$43$	−8.27829	−1.26243	−0.631214	−	0.775609i	$-0.717443\pi$
$43$	−8.27829	−1.26243	−0.631214	+	0.775609i	$0.717443\pi$
$44$	1.06039	0.159860
$45$	−18.9304	−2.82197
$46$	1.00000	0.147442
$47$	−7.60304	−1.10902	−0.554509	−	0.832178i	$-0.687094\pi$
$47$	−7.60304	−1.10902	−0.554509	+	0.832178i	$0.687094\pi$
$48$	−2.75069	−0.397028
$49$	8.48082	1.21155
$50$	−12.1865	−1.72342
$51$	9.24052	1.29393
$52$	1.45615	0.201932
$53$	1.45329	0.199624	0.0998121	−	0.995006i	$-0.468176\pi$
$53$	1.45329	0.199624	0.0998121	+	0.995006i	$0.468176\pi$
$54$	4.30844	0.586305
$55$	−4.39602	−0.592759
$56$	3.93457	0.525779
$57$	−13.1988	−1.74822
$58$	2.83489	0.372239
$59$	−0.759864	−0.0989258	−0.0494629	−	0.998776i	$-0.515751\pi$
$59$	−0.759864	−0.0989258	−0.0494629	+	0.998776i	$0.515751\pi$
$60$	11.4034	1.47218
$61$	−3.61363	−0.462678	−0.231339	−	0.972873i	$-0.574311\pi$
$61$	−3.61363	−0.462678	−0.231339	+	0.972873i	$0.574311\pi$
$62$	−5.47001	−0.694692
$63$	−17.9665	−2.26356
$64$	1.00000	0.125000
$65$	−6.03672	−0.748762
$66$	2.91681	0.359035
$67$	−4.04656	−0.494366	−0.247183	−	0.968969i	$-0.579505\pi$
$67$	−4.04656	−0.494366	−0.247183	+	0.968969i	$0.579505\pi$
$68$	−3.35934	−0.407380
$69$	2.75069	0.331145
$70$	−16.3114	−1.94958
$71$	−1.96939	−0.233723	−0.116862	−	0.993148i	$-0.537283\pi$
$71$	−1.96939	−0.233723	−0.116862	+	0.993148i	$0.537283\pi$
$72$	−4.56631	−0.538145
$73$	−1.67757	−0.196345	−0.0981726	−	0.995169i	$-0.531300\pi$
$73$	−1.67757	−0.196345	−0.0981726	+	0.995169i	$0.531300\pi$
$74$	−1.64768	−0.191539
$75$	−33.5212	−3.87069
$76$	4.79836	0.550409
$77$	−4.17218	−0.475464
$78$	4.00544	0.453526
$79$	2.92025	0.328554	0.164277	−	0.986414i	$-0.447471\pi$
$79$	2.92025	0.328554	0.164277	+	0.986414i	$0.447471\pi$
$80$	−4.14565	−0.463498
$81$	−1.84773	−0.205304
$82$	6.70237	0.740153
$83$	−2.22807	−0.244563	−0.122281	−	0.992495i	$-0.539021\pi$
$83$	−2.22807	−0.244563	−0.122281	+	0.992495i	$0.539021\pi$
$84$	10.8228	1.18086
$85$	13.9267	1.51056
$86$	8.27829	0.892671
$87$	7.79792	0.836024
$88$	−1.06039	−0.113038
$89$	3.03860	0.322091	0.161045	−	0.986947i	$-0.448513\pi$
$89$	3.03860	0.322091	0.161045	+	0.986947i	$0.448513\pi$
$90$	18.9304	1.99543
$91$	−5.72934	−0.600598
$92$	−1.00000	−0.104257
$93$	−15.0463	−1.56023
$94$	7.60304	0.784193
$95$	−19.8923	−2.04091
$96$	2.75069	0.280741
$97$	7.85207	0.797257	0.398629	−	0.917112i	$-0.369486\pi$
$97$	7.85207	0.797257	0.398629	+	0.917112i	$0.369486\pi$
$98$	−8.48082	−0.856692
$99$	4.84208	0.486647
$100$	12.1865	1.21865
$101$	−9.90668	−0.985752	−0.492876	−	0.870100i	$-0.664054\pi$
$101$	−9.90668	−0.985752	−0.492876	+	0.870100i	$0.664054\pi$
$102$	−9.24052	−0.914948
$103$	−17.9814	−1.77176	−0.885878	−	0.463918i	$-0.846443\pi$
$103$	−17.9814	−1.77176	−0.885878	+	0.463918i	$0.846443\pi$
$104$	−1.45615	−0.142788
$105$	−44.8675	−4.37862
$106$	−1.45329	−0.141156
$107$	0.0220754	0.00213411	0.00106706	−	0.999999i	$-0.499660\pi$
$107$	0.0220754	0.00213411	0.00106706	+	0.999999i	$0.499660\pi$
$108$	−4.30844	−0.414580
$109$	−9.90944	−0.949152	−0.474576	−	0.880215i	$-0.657399\pi$
$109$	−9.90944	−0.949152	−0.474576	+	0.880215i	$0.657399\pi$
$110$	4.39602	0.419144
$111$	−4.53226	−0.430183
$112$	−3.93457	−0.371782
$113$	2.44370	0.229884	0.114942	−	0.993372i	$-0.463332\pi$
$113$	2.44370	0.229884	0.114942	+	0.993372i	$0.463332\pi$
$114$	13.1988	1.23618
$115$	4.14565	0.386584
$116$	−2.83489	−0.263213
$117$	6.64926	0.614724
$118$	0.759864	0.0699511
$119$	13.2176	1.21165
$120$	−11.4034	−1.04099
$121$	−9.87557	−0.897779
$122$	3.61363	0.327163
$123$	18.4362	1.66233
$124$	5.47001	0.491221
$125$	−29.7925	−2.66473
$126$	17.9665	1.60058
$127$	17.1697	1.52356	0.761781	−	0.647834i	$-0.224325\pi$
$127$	17.1697	1.52356	0.761781	+	0.647834i	$0.224325\pi$
$128$	−1.00000	−0.0883883
$129$	22.7710	2.00488
$130$	6.03672	0.529455
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.91681	−0.253876
$133$	−18.8795	−1.63706
$134$	4.04656	0.349570
$135$	17.8613	1.53726
$136$	3.35934	0.288061
$137$	−10.0747	−0.860744	−0.430372	−	0.902652i	$-0.641618\pi$
$137$	−10.0747	−0.860744	−0.430372	+	0.902652i	$0.641618\pi$
$138$	−2.75069	−0.234155
$139$	−17.3324	−1.47012	−0.735059	−	0.678003i	$-0.762846\pi$
$139$	−17.3324	−1.47012	−0.735059	+	0.678003i	$0.762846\pi$
$140$	16.3114	1.37856
$141$	20.9136	1.76124
$142$	1.96939	0.165267
$143$	1.54409	0.129124
$144$	4.56631	0.380526
$145$	11.7525	0.975990
$146$	1.67757	0.138837
$147$	−23.3281	−1.92407
$148$	1.64768	0.135439
$149$	13.5309	1.10850	0.554249	−	0.832351i	$-0.313006\pi$
$149$	13.5309	1.10850	0.554249	+	0.832351i	$0.313006\pi$
$150$	33.5212	2.73699
$151$	−0.636255	−0.0517777	−0.0258889	−	0.999665i	$-0.508242\pi$
$151$	−0.636255	−0.0517777	−0.0258889	+	0.999665i	$0.508242\pi$
$152$	−4.79836	−0.389198
$153$	−15.3398	−1.24015
$154$	4.17218	0.336204
$155$	−22.6768	−1.82144
$156$	−4.00544	−0.320691
$157$	−2.59381	−0.207009	−0.103504	−	0.994629i	$-0.533006\pi$
$157$	−2.59381	−0.207009	−0.103504	+	0.994629i	$0.533006\pi$
$158$	−2.92025	−0.232323
$159$	−3.99754	−0.317026
$160$	4.14565	0.327743
$161$	3.93457	0.310087
$162$	1.84773	0.145172
$163$	9.44662	0.739916	0.369958	−	0.929048i	$-0.379372\pi$
$163$	9.44662	0.739916	0.369958	+	0.929048i	$0.379372\pi$
$164$	−6.70237	−0.523367
$165$	12.0921	0.941368
$166$	2.22807	0.172932
$167$	−7.83861	−0.606570	−0.303285	−	0.952900i	$-0.598083\pi$
$167$	−7.83861	−0.606570	−0.303285	+	0.952900i	$0.598083\pi$
$168$	−10.8228	−0.834996
$169$	−10.8796	−0.836893
$170$	−13.9267	−1.06813
$171$	21.9108	1.67556
$172$	−8.27829	−0.631214
$173$	−14.0123	−1.06534	−0.532668	−	0.846324i	$-0.678810\pi$
$173$	−14.0123	−1.06534	−0.532668	+	0.846324i	$0.678810\pi$
$174$	−7.79792	−0.591158
$175$	−47.9484	−3.62456
$176$	1.06039	0.0799300
$177$	2.09015	0.157105
$178$	−3.03860	−0.227753
$179$	−9.85004	−0.736226	−0.368113	−	0.929781i	$-0.619996\pi$
$179$	−9.85004	−0.736226	−0.368113	+	0.929781i	$0.619996\pi$
$180$	−18.9304	−1.41099
$181$	7.16712	0.532728	0.266364	−	0.963873i	$-0.414178\pi$
$181$	7.16712	0.532728	0.266364	+	0.963873i	$0.414178\pi$
$182$	5.72934	0.424687
$183$	9.93998	0.734785
$184$	1.00000	0.0737210
$185$	−6.83072	−0.502204
$186$	15.0463	1.10325
$187$	−3.56222	−0.260495
$188$	−7.60304	−0.554509
$189$	16.9519	1.23307
$190$	19.8923	1.44314
$191$	21.8440	1.58057	0.790287	−	0.612737i	$-0.209932\pi$
$191$	21.8440	1.58057	0.790287	+	0.612737i	$0.209932\pi$
$192$	−2.75069	−0.198514
$193$	14.7811	1.06397	0.531985	−	0.846754i	$-0.321446\pi$
$193$	14.7811	1.06397	0.531985	+	0.846754i	$0.321446\pi$
$194$	−7.85207	−0.563746
$195$	16.6052	1.18912
$196$	8.48082	0.605773
$197$	−17.6080	−1.25452	−0.627258	−	0.778812i	$-0.715823\pi$
$197$	−17.6080	−1.25452	−0.627258	+	0.778812i	$0.715823\pi$
$198$	−4.84208	−0.344111
$199$	−9.32179	−0.660804	−0.330402	−	0.943840i	$-0.607184\pi$
$199$	−9.32179	−0.660804	−0.330402	+	0.943840i	$0.607184\pi$
$200$	−12.1865	−0.861712
$201$	11.1309	0.785110
$202$	9.90668	0.697032
$203$	11.1541	0.782862
$204$	9.24052	0.646966
$205$	27.7857	1.94064
$206$	17.9814	1.25282
$207$	−4.56631	−0.317381
$208$	1.45615	0.100966
$209$	5.08813	0.351954
$210$	44.8675	3.09615
$211$	9.11138	0.627254	0.313627	−	0.949546i	$-0.398456\pi$
$211$	9.11138	0.627254	0.313627	+	0.949546i	$0.398456\pi$
$212$	1.45329	0.0998121
$213$	5.41717	0.371179
$214$	−0.0220754	−0.00150905
$215$	34.3189	2.34053
$216$	4.30844	0.293152
$217$	−21.5221	−1.46102
$218$	9.90944	0.671152
$219$	4.61449	0.311818
$220$	−4.39602	−0.296379
$221$	−4.89172	−0.329053
$222$	4.53226	0.304186
$223$	−12.0687	−0.808178	−0.404089	−	0.914720i	$-0.632411\pi$
$223$	−12.0687	−0.808178	−0.404089	+	0.914720i	$0.632411\pi$
$224$	3.93457	0.262889
$225$	55.6471	3.70981
$226$	−2.44370	−0.162552
$227$	8.06603	0.535361	0.267680	−	0.963508i	$-0.413743\pi$
$227$	8.06603	0.535361	0.267680	+	0.963508i	$0.413743\pi$
$228$	−13.1988	−0.874112
$229$	14.4669	0.955997	0.477999	−	0.878361i	$-0.341362\pi$
$229$	14.4669	0.955997	0.477999	+	0.878361i	$0.341362\pi$
$230$	−4.14565	−0.273356
$231$	11.4764	0.755091
$232$	2.83489	0.186120
$233$	−27.5770	−1.80663	−0.903314	−	0.428979i	$-0.858873\pi$
$233$	−27.5770	−1.80663	−0.903314	+	0.428979i	$0.858873\pi$
$234$	−6.64926	−0.434676
$235$	31.5196	2.05611
$236$	−0.759864	−0.0494629
$237$	−8.03272	−0.521781
$238$	−13.2176	−0.856767
$239$	−27.0758	−1.75139	−0.875694	−	0.482867i	$-0.839595\pi$
$239$	−27.0758	−1.75139	−0.875694	+	0.482867i	$0.839595\pi$
$240$	11.4034	0.736088
$241$	6.39744	0.412095	0.206048	−	0.978542i	$-0.433940\pi$
$241$	6.39744	0.412095	0.206048	+	0.978542i	$0.433940\pi$
$242$	9.87557	0.634826
$243$	18.0079	1.15521
$244$	−3.61363	−0.231339
$245$	−35.1586	−2.24620
$246$	−18.4362	−1.17545
$247$	6.98715	0.444582
$248$	−5.47001	−0.347346
$249$	6.12875	0.388393
$250$	29.7925	1.88425
$251$	24.9452	1.57453	0.787263	−	0.616617i	$-0.211497\pi$
$251$	24.9452	1.57453	0.787263	+	0.616617i	$0.211497\pi$
$252$	−17.9665	−1.13178
$253$	−1.06039	−0.0666662
$254$	−17.1697	−1.07732
$255$	−38.3080	−2.39894
$256$	1.00000	0.0625000
$257$	−2.83147	−0.176622	−0.0883110	−	0.996093i	$-0.528147\pi$
$257$	−2.83147	−0.176622	−0.0883110	+	0.996093i	$0.528147\pi$
$258$	−22.7710	−1.41766
$259$	−6.48291	−0.402828
$260$	−6.03672	−0.374381
$261$	−12.9450	−0.801275
$262$	−1.00000	−0.0617802
$263$	24.6894	1.52241	0.761207	−	0.648509i	$-0.224607\pi$
$263$	24.6894	1.52241	0.761207	+	0.648509i	$0.224607\pi$
$264$	2.91681	0.179517
$265$	−6.02482	−0.370102
$266$	18.8795	1.15757
$267$	−8.35825	−0.511517
$268$	−4.04656	−0.247183
$269$	−4.89343	−0.298358	−0.149179	−	0.988810i	$-0.547663\pi$
$269$	−4.89343	−0.298358	−0.149179	+	0.988810i	$0.547663\pi$
$270$	−17.8613	−1.08701
$271$	−10.8313	−0.657954	−0.328977	−	0.944338i	$-0.606704\pi$
$271$	−10.8313	−0.657954	−0.328977	+	0.944338i	$0.606704\pi$
$272$	−3.35934	−0.203690
$273$	15.7597	0.953818
$274$	10.0747	0.608638
$275$	12.9224	0.779250
$276$	2.75069	0.165572
$277$	−18.8018	−1.12969	−0.564847	−	0.825196i	$-0.691065\pi$
$277$	−18.8018	−1.12969	−0.564847	+	0.825196i	$0.691065\pi$
$278$	17.3324	1.03953
$279$	24.9778	1.49538
$280$	−16.3114	−0.974790
$281$	26.2868	1.56814	0.784070	−	0.620672i	$-0.213140\pi$
$281$	26.2868	1.56814	0.784070	+	0.620672i	$0.213140\pi$
$282$	−20.9136	−1.24539
$283$	5.37607	0.319574	0.159787	−	0.987151i	$-0.448919\pi$
$283$	5.37607	0.319574	0.159787	+	0.987151i	$0.448919\pi$
$284$	−1.96939	−0.116862
$285$	54.7177	3.24120
$286$	−1.54409	−0.0913042
$287$	26.3709	1.55663
$288$	−4.56631	−0.269073
$289$	−5.71481	−0.336166
$290$	−11.7525	−0.690129
$291$	−21.5986	−1.26613
$292$	−1.67757	−0.0981726
$293$	−33.4187	−1.95234	−0.976169	−	0.217011i	$-0.930369\pi$
$293$	−33.4187	−1.95234	−0.976169	+	0.217011i	$0.930369\pi$
$294$	23.3281	1.36052
$295$	3.15013	0.183408
$296$	−1.64768	−0.0957695
$297$	−4.56863	−0.265099
$298$	−13.5309	−0.783827
$299$	−1.45615	−0.0842116
$300$	−33.5212	−1.93535
$301$	32.5715	1.87739
$302$	0.636255	0.0366124
$303$	27.2502	1.56549
$304$	4.79836	0.275205
$305$	14.9809	0.857801
$306$	15.3398	0.876918
$307$	11.2284	0.640840	0.320420	−	0.947276i	$-0.396176\pi$
$307$	11.2284	0.640840	0.320420	+	0.947276i	$0.396176\pi$
$308$	−4.17218	−0.237732
$309$	49.4612	2.81375
$310$	22.6768	1.28795
$311$	−34.9179	−1.98001	−0.990005	−	0.141032i	$-0.954958\pi$
$311$	−34.9179	−1.98001	−0.990005	+	0.141032i	$0.954958\pi$
$312$	4.00544	0.226763
$313$	−19.5151	−1.10306	−0.551529	−	0.834156i	$-0.685955\pi$
$313$	−19.5151	−1.10306	−0.551529	+	0.834156i	$0.685955\pi$
$314$	2.59381	0.146377
$315$	74.4827	4.19663
$316$	2.92025	0.164277
$317$	−4.59514	−0.258089	−0.129044	−	0.991639i	$-0.541191\pi$
$317$	−4.59514	−0.258089	−0.129044	+	0.991639i	$0.541191\pi$
$318$	3.99754	0.224171
$319$	−3.00609	−0.168309
$320$	−4.14565	−0.231749
$321$	−0.0607228	−0.00338921
$322$	−3.93457	−0.219265
$323$	−16.1193	−0.896903
$324$	−1.84773	−0.102652
$325$	17.7454	0.984336
$326$	−9.44662	−0.523200
$327$	27.2578	1.50736
$328$	6.70237	0.370076
$329$	29.9147	1.64925
$330$	−12.0921	−0.665648
$331$	32.5136	1.78711	0.893553	−	0.448957i	$-0.148204\pi$
$331$	32.5136	1.78711	0.893553	+	0.448957i	$0.148204\pi$
$332$	−2.22807	−0.122281
$333$	7.52382	0.412303
$334$	7.83861	0.428910
$335$	16.7757	0.916552
$336$	10.8228	0.590431
$337$	−21.4565	−1.16881	−0.584405	−	0.811462i	$-0.698672\pi$
$337$	−21.4565	−1.16881	−0.584405	+	0.811462i	$0.698672\pi$
$338$	10.8796	0.591773
$339$	−6.72186	−0.365081
$340$	13.9267	0.755280
$341$	5.80035	0.314106
$342$	−21.9108	−1.18480
$343$	−5.82639	−0.314595
$344$	8.27829	0.446336
$345$	−11.4034	−0.613940
$346$	14.0123	0.753306
$347$	−23.7393	−1.27439	−0.637196	−	0.770702i	$-0.719906\pi$
$347$	−23.7393	−1.27439	−0.637196	+	0.770702i	$0.719906\pi$
$348$	7.79792	0.418012
$349$	−15.9474	−0.853645	−0.426822	−	0.904335i	$-0.640367\pi$
$349$	−15.9474	−0.853645	−0.426822	+	0.904335i	$0.640367\pi$
$350$	47.9484	2.56295
$351$	−6.27376	−0.334869
$352$	−1.06039	−0.0565190
$353$	−23.0859	−1.22874	−0.614369	−	0.789018i	$-0.710590\pi$
$353$	−23.0859	−1.22874	−0.614369	+	0.789018i	$0.710590\pi$
$354$	−2.09015	−0.111090
$355$	8.16439	0.433321
$356$	3.03860	0.161045
$357$	−36.3575	−1.92424
$358$	9.85004	0.520591
$359$	28.1666	1.48658	0.743288	−	0.668972i	$-0.233265\pi$
$359$	28.1666	1.48658	0.743288	+	0.668972i	$0.233265\pi$
$360$	18.9304	0.997717
$361$	4.02421	0.211801
$362$	−7.16712	−0.376696
$363$	27.1647	1.42578
$364$	−5.72934	−0.300299
$365$	6.95464	0.364023
$366$	−9.93998	−0.519571
$367$	−6.47403	−0.337942	−0.168971	−	0.985621i	$-0.554044\pi$
$367$	−6.47403	−0.337942	−0.168971	+	0.985621i	$0.554044\pi$
$368$	−1.00000	−0.0521286
$369$	−30.6051	−1.59324
$370$	6.83072	0.355112
$371$	−5.71805	−0.296866
$372$	−15.0463	−0.780115
$373$	33.4946	1.73428	0.867142	−	0.498061i	$-0.165954\pi$
$373$	33.4946	1.73428	0.867142	+	0.498061i	$0.165954\pi$
$374$	3.56222	0.184198
$375$	81.9502	4.23189
$376$	7.60304	0.392097
$377$	−4.12804	−0.212605
$378$	−16.9519	−0.871910
$379$	−4.46953	−0.229584	−0.114792	−	0.993390i	$-0.536620\pi$
$379$	−4.46953	−0.229584	−0.114792	+	0.993390i	$0.536620\pi$
$380$	−19.8923	−1.02045
$381$	−47.2285	−2.41959
$382$	−21.8440	−1.11763
$383$	−9.11293	−0.465649	−0.232825	−	0.972519i	$-0.574797\pi$
$383$	−9.11293	−0.465649	−0.232825	+	0.972519i	$0.574797\pi$
$384$	2.75069	0.140371
$385$	17.2964	0.881507
$386$	−14.7811	−0.752340
$387$	−37.8013	−1.92155
$388$	7.85207	0.398629
$389$	18.1163	0.918535	0.459268	−	0.888298i	$-0.348112\pi$
$389$	18.1163	0.918535	0.459268	+	0.888298i	$0.348112\pi$
$390$	−16.6052	−0.840834
$391$	3.35934	0.169889
$392$	−8.48082	−0.428346
$393$	−2.75069	−0.138754
$394$	17.6080	0.887077
$395$	−12.1064	−0.609137
$396$	4.84208	0.243324
$397$	−24.9404	−1.25172	−0.625861	−	0.779934i	$-0.715252\pi$
$397$	−24.9404	−1.25172	−0.625861	+	0.779934i	$0.715252\pi$
$398$	9.32179	0.467259
$399$	51.9316	2.59983
$400$	12.1865	0.609323
$401$	−18.5257	−0.925131	−0.462565	−	0.886585i	$-0.653071\pi$
$401$	−18.5257	−0.925131	−0.462565	+	0.886585i	$0.653071\pi$
$402$	−11.1309	−0.555157
$403$	7.96518	0.396774
$404$	−9.90668	−0.492876
$405$	7.66006	0.380631
$406$	−11.1541	−0.553567
$407$	1.74719	0.0866048
$408$	−9.24052	−0.457474
$409$	−16.9729	−0.839255	−0.419627	−	0.907697i	$-0.637839\pi$
$409$	−16.9729	−0.839255	−0.419627	+	0.907697i	$0.637839\pi$
$410$	−27.7857	−1.37224
$411$	27.7125	1.36696
$412$	−17.9814	−0.885878
$413$	2.98974	0.147115
$414$	4.56631	0.224422
$415$	9.23682	0.453418
$416$	−1.45615	−0.0713939
$417$	47.6762	2.33471
$418$	−5.08813	−0.248869
$419$	6.57686	0.321301	0.160650	−	0.987011i	$-0.448641\pi$
$419$	6.57686	0.321301	0.160650	+	0.987011i	$0.448641\pi$
$420$	−44.8675	−2.18931
$421$	−28.4215	−1.38518	−0.692590	−	0.721332i	$-0.743530\pi$
$421$	−28.4215	−1.38518	−0.692590	+	0.721332i	$0.743530\pi$
$422$	−9.11138	−0.443535
$423$	−34.7178	−1.68804
$424$	−1.45329	−0.0705778
$425$	−40.9385	−1.98581
$426$	−5.41717	−0.262463
$427$	14.2181	0.688061
$428$	0.0220754	0.00106706
$429$	−4.24733	−0.205063
$430$	−34.3189	−1.65501
$431$	6.69545	0.322509	0.161254	−	0.986913i	$-0.448446\pi$
$431$	6.69545	0.322509	0.161254	+	0.986913i	$0.448446\pi$
$432$	−4.30844	−0.207290
$433$	14.9243	0.717214	0.358607	−	0.933489i	$-0.383252\pi$
$433$	14.9243	0.717214	0.358607	+	0.933489i	$0.383252\pi$
$434$	21.5221	1.03309
$435$	−32.3275	−1.54998
$436$	−9.90944	−0.474576
$437$	−4.79836	−0.229536
$438$	−4.61449	−0.220489
$439$	−18.6646	−0.890814	−0.445407	−	0.895328i	$-0.646941\pi$
$439$	−18.6646	−0.890814	−0.445407	+	0.895328i	$0.646941\pi$
$440$	4.39602	0.209572
$441$	38.7261	1.84410
$442$	4.89172	0.232676
$443$	30.8453	1.46550	0.732752	−	0.680496i	$-0.238236\pi$
$443$	30.8453	1.46550	0.732752	+	0.680496i	$0.238236\pi$
$444$	−4.53226	−0.215092
$445$	−12.5970	−0.597154
$446$	12.0687	0.571468
$447$	−37.2195	−1.76042
$448$	−3.93457	−0.185891
$449$	2.85679	0.134820	0.0674102	−	0.997725i	$-0.478526\pi$
$449$	2.85679	0.134820	0.0674102	+	0.997725i	$0.478526\pi$
$450$	−55.6471	−2.62323
$451$	−7.10713	−0.334662
$452$	2.44370	0.114942
$453$	1.75014	0.0822289
$454$	−8.06603	−0.378557
$455$	23.7519	1.11350
$456$	13.1988	0.618091
$457$	−8.95219	−0.418766	−0.209383	−	0.977834i	$-0.567146\pi$
$457$	−8.95219	−0.418766	−0.209383	+	0.977834i	$0.567146\pi$
$458$	−14.4669	−0.675992
$459$	14.4735	0.675567
$460$	4.14565	0.193292
$461$	−16.6803	−0.776877	−0.388439	−	0.921475i	$-0.626985\pi$
$461$	−16.6803	−0.776877	−0.388439	+	0.921475i	$0.626985\pi$
$462$	−11.4764	−0.533930
$463$	1.38006	0.0641368	0.0320684	−	0.999486i	$-0.489791\pi$
$463$	1.38006	0.0641368	0.0320684	+	0.999486i	$0.489791\pi$
$464$	−2.83489	−0.131607
$465$	62.3768	2.89265
$466$	27.5770	1.27748
$467$	16.2396	0.751479	0.375740	−	0.926725i	$-0.377389\pi$
$467$	16.2396	0.751479	0.375740	+	0.926725i	$0.377389\pi$
$468$	6.64926	0.307362
$469$	15.9215	0.735186
$470$	−31.5196	−1.45389
$471$	7.13478	0.328753
$472$	0.759864	0.0349756
$473$	−8.77823	−0.403623
$474$	8.03272	0.368955
$475$	58.4749	2.68301
$476$	13.2176	0.605826
$477$	6.63616	0.303849
$478$	27.0758	1.23842
$479$	−27.0888	−1.23772	−0.618858	−	0.785503i	$-0.712405\pi$
$479$	−27.0888	−1.23772	−0.618858	+	0.785503i	$0.712405\pi$
$480$	−11.4034	−0.520493
$481$	2.39928	0.109398
$482$	−6.39744	−0.291395
$483$	−10.8228	−0.492454
$484$	−9.87557	−0.448890
$485$	−32.5520	−1.47811
$486$	−18.0079	−0.816854
$487$	−7.04496	−0.319238	−0.159619	−	0.987179i	$-0.551026\pi$
$487$	−7.04496	−0.319238	−0.159619	+	0.987179i	$0.551026\pi$
$488$	3.61363	0.163581
$489$	−25.9847	−1.17507
$490$	35.1586	1.58830
$491$	37.8570	1.70846	0.854232	−	0.519892i	$-0.174028\pi$
$491$	37.8570	1.70846	0.854232	+	0.519892i	$0.174028\pi$
$492$	18.4362	0.831166
$493$	9.52337	0.428911
$494$	−6.98715	−0.314367
$495$	−20.0736	−0.902240
$496$	5.47001	0.245611
$497$	7.74868	0.347576
$498$	−6.12875	−0.274636
$499$	−30.7735	−1.37761	−0.688805	−	0.724947i	$-0.741864\pi$
$499$	−30.7735	−1.37761	−0.688805	+	0.724947i	$0.741864\pi$
$500$	−29.7925	−1.33236
$501$	21.5616	0.963302
$502$	−24.9452	−1.11336
$503$	12.6177	0.562597	0.281299	−	0.959620i	$-0.409235\pi$
$503$	12.6177	0.562597	0.281299	+	0.959620i	$0.409235\pi$
$504$	17.9665	0.800290
$505$	41.0697	1.82758
$506$	1.06039	0.0471401
$507$	29.9265	1.32908
$508$	17.1697	0.761781
$509$	3.39616	0.150532	0.0752662	−	0.997163i	$-0.476019\pi$
$509$	3.39616	0.150532	0.0752662	+	0.997163i	$0.476019\pi$
$510$	38.3080	1.69631
$511$	6.60053	0.291990
$512$	−1.00000	−0.0441942
$513$	−20.6734	−0.912755
$514$	2.83147	0.124891
$515$	74.5445	3.28482
$516$	22.7710	1.00244
$517$	−8.06219	−0.354575
$518$	6.48291	0.284843
$519$	38.5435	1.69187
$520$	6.03672	0.264727
$521$	2.73388	0.119774	0.0598868	−	0.998205i	$-0.480926\pi$
$521$	2.73388	0.119774	0.0598868	+	0.998205i	$0.480926\pi$
$522$	12.9450	0.566587
$523$	34.6490	1.51510	0.757548	−	0.652779i	$-0.226397\pi$
$523$	34.6490	1.51510	0.757548	+	0.652779i	$0.226397\pi$
$524$	1.00000	0.0436852
$525$	131.891	5.75621
$526$	−24.6894	−1.07651
$527$	−18.3756	−0.800455
$528$	−2.91681	−0.126938
$529$	1.00000	0.0434783
$530$	6.02482	0.261702
$531$	−3.46978	−0.150575
$532$	−18.8795	−0.818528
$533$	−9.75968	−0.422739
$534$	8.35825	0.361697
$535$	−0.0915172	−0.00395663
$536$	4.04656	0.174785
$537$	27.0944	1.16921
$538$	4.89343	0.210971
$539$	8.99299	0.387355
$540$	17.8613	0.768629
$541$	−30.3268	−1.30385	−0.651926	−	0.758282i	$-0.726039\pi$
$541$	−30.3268	−1.30385	−0.651926	+	0.758282i	$0.726039\pi$
$542$	10.8313	0.465244
$543$	−19.7146	−0.846032
$544$	3.35934	0.144031
$545$	41.0811	1.75972
$546$	−15.7597	−0.674451
$547$	−14.0081	−0.598944	−0.299472	−	0.954105i	$-0.596810\pi$
$547$	−14.0081	−0.598944	−0.299472	+	0.954105i	$0.596810\pi$
$548$	−10.0747	−0.430372
$549$	−16.5010	−0.704244
$550$	−12.9224	−0.551013
$551$	−13.6028	−0.579499
$552$	−2.75069	−0.117077
$553$	−11.4899	−0.488602
$554$	18.8018	0.798814
$555$	18.7892	0.797557
$556$	−17.3324	−0.735059
$557$	−12.8310	−0.543666	−0.271833	−	0.962344i	$-0.587630\pi$
$557$	−12.8310	−0.543666	−0.271833	+	0.962344i	$0.587630\pi$
$558$	−24.9778	−1.05739
$559$	−12.0545	−0.509850
$560$	16.3114	0.689281
$561$	9.79857	0.413696
$562$	−26.2868	−1.10884
$563$	−7.96938	−0.335869	−0.167935	−	0.985798i	$-0.553710\pi$
$563$	−7.96938	−0.335869	−0.167935	+	0.985798i	$0.553710\pi$
$564$	20.9136	0.880622
$565$	−10.1307	−0.426202
$566$	−5.37607	−0.225973
$567$	7.27003	0.305312
$568$	1.96939	0.0826336
$569$	1.21278	0.0508424	0.0254212	−	0.999677i	$-0.491907\pi$
$569$	1.21278	0.0508424	0.0254212	+	0.999677i	$0.491907\pi$
$570$	−54.7177	−2.29187
$571$	19.7224	0.825356	0.412678	−	0.910877i	$-0.364594\pi$
$571$	19.7224	0.825356	0.412678	+	0.910877i	$0.364594\pi$
$572$	1.54409	0.0645618
$573$	−60.0860	−2.51013
$574$	−26.3709	−1.10070
$575$	−12.1865	−0.508210
$576$	4.56631	0.190263
$577$	1.28066	0.0533147	0.0266574	−	0.999645i	$-0.491514\pi$
$577$	1.28066	0.0533147	0.0266574	+	0.999645i	$0.491514\pi$
$578$	5.71481	0.237705
$579$	−40.6584	−1.68971
$580$	11.7525	0.487995
$581$	8.76650	0.363696
$582$	21.5986	0.895292
$583$	1.54105	0.0638238
$584$	1.67757	0.0694185
$585$	−27.5655	−1.13969
$586$	33.4187	1.38051
$587$	28.9622	1.19540	0.597700	−	0.801720i	$-0.296082\pi$
$587$	28.9622	1.19540	0.597700	+	0.801720i	$0.296082\pi$
$588$	−23.3281	−0.962036
$589$	26.2470	1.08149
$590$	−3.15013	−0.129689
$591$	48.4341	1.99231
$592$	1.64768	0.0677193
$593$	−2.12362	−0.0872065	−0.0436033	−	0.999049i	$-0.513884\pi$
$593$	−2.12362	−0.0872065	−0.0436033	+	0.999049i	$0.513884\pi$
$594$	4.56863	0.187453
$595$	−54.7954	−2.24639
$596$	13.5309	0.554249
$597$	25.6414	1.04943
$598$	1.45615	0.0595466
$599$	−28.1821	−1.15149	−0.575745	−	0.817629i	$-0.695288\pi$
$599$	−28.1821	−1.15149	−0.575745	+	0.817629i	$0.695288\pi$
$600$	33.5212	1.36850
$601$	21.4249	0.873942	0.436971	−	0.899476i	$-0.356051\pi$
$601$	21.4249	0.873942	0.436971	+	0.899476i	$0.356051\pi$
$602$	−32.5715	−1.32752
$603$	−18.4779	−0.752477
$604$	−0.636255	−0.0258889
$605$	40.9407	1.66448
$606$	−27.2502	−1.10697
$607$	2.04956	0.0831893	0.0415946	−	0.999135i	$-0.486756\pi$
$607$	2.04956	0.0831893	0.0415946	+	0.999135i	$0.486756\pi$
$608$	−4.79836	−0.194599
$609$	−30.6814	−1.24327
$610$	−14.9809	−0.606557
$611$	−11.0712	−0.447893
$612$	−15.3398	−0.620075
$613$	15.7684	0.636880	0.318440	−	0.947943i	$-0.396841\pi$
$613$	15.7684	0.636880	0.318440	+	0.947943i	$0.396841\pi$
$614$	−11.2284	−0.453142
$615$	−76.4299	−3.08195
$616$	4.17218	0.168102
$617$	−11.3287	−0.456077	−0.228039	−	0.973652i	$-0.573231\pi$
$617$	−11.3287	−0.456077	−0.228039	+	0.973652i	$0.573231\pi$
$618$	−49.4612	−1.98962
$619$	−13.7415	−0.552318	−0.276159	−	0.961112i	$-0.589062\pi$
$619$	−13.7415	−0.552318	−0.276159	+	0.961112i	$0.589062\pi$
$620$	−22.6768	−0.910720
$621$	4.30844	0.172892
$622$	34.9179	1.40008
$623$	−11.9556	−0.478990
$624$	−4.00544	−0.160346
$625$	62.5774	2.50309
$626$	19.5151	0.779980
$627$	−13.9959	−0.558942
$628$	−2.59381	−0.103504
$629$	−5.53512	−0.220700
$630$	−74.4827	−2.96746
$631$	−21.4095	−0.852301	−0.426150	−	0.904652i	$-0.640131\pi$
$631$	−21.4095	−0.852301	−0.426150	+	0.904652i	$0.640131\pi$
$632$	−2.92025	−0.116161
$633$	−25.0626	−0.996150
$634$	4.59514	0.182496
$635$	−71.1796	−2.82467
$636$	−3.99754	−0.158513
$637$	12.3494	0.489301
$638$	3.00609	0.119012
$639$	−8.99283	−0.355751
$640$	4.14565	0.163871
$641$	−42.3267	−1.67180	−0.835902	−	0.548879i	$-0.815055\pi$
$641$	−42.3267	−1.67180	−0.835902	+	0.548879i	$0.815055\pi$
$642$	0.0607228	0.00239654
$643$	−21.7765	−0.858781	−0.429390	−	0.903119i	$-0.641272\pi$
$643$	−21.7765	−0.858781	−0.429390	+	0.903119i	$0.641272\pi$
$644$	3.93457	0.155044
$645$	−94.4009	−3.71703
$646$	16.1193	0.634206
$647$	−5.39919	−0.212264	−0.106132	−	0.994352i	$-0.533847\pi$
$647$	−5.39919	−0.212264	−0.106132	+	0.994352i	$0.533847\pi$
$648$	1.84773	0.0725858
$649$	−0.805753	−0.0316286
$650$	−17.7454	−0.696030
$651$	59.2007	2.32026
$652$	9.44662	0.369958
$653$	23.1689	0.906668	0.453334	−	0.891341i	$-0.350234\pi$
$653$	23.1689	0.906668	0.453334	+	0.891341i	$0.350234\pi$
$654$	−27.2578	−1.06587
$655$	−4.14565	−0.161984
$656$	−6.70237	−0.261683
$657$	−7.66033	−0.298858
$658$	−29.9147	−1.16620
$659$	17.5506	0.683674	0.341837	−	0.939759i	$-0.388951\pi$
$659$	17.5506	0.683674	0.341837	+	0.939759i	$0.388951\pi$
$660$	12.0921	0.470684
$661$	35.4034	1.37703	0.688516	−	0.725221i	$-0.258263\pi$
$661$	35.4034	1.37703	0.688516	+	0.725221i	$0.258263\pi$
$662$	−32.5136	−1.26368
$663$	13.4556	0.522573
$664$	2.22807	0.0864660
$665$	78.2677	3.03509
$666$	−7.52382	−0.291542
$667$	2.83489	0.109767
$668$	−7.83861	−0.303285
$669$	33.1972	1.28348
$670$	−16.7757	−0.648100
$671$	−3.83186	−0.147927
$672$	−10.8228	−0.417498
$673$	27.5977	1.06381	0.531907	−	0.846803i	$-0.321476\pi$
$673$	27.5977	1.06381	0.531907	+	0.846803i	$0.321476\pi$
$674$	21.4565	0.826474
$675$	−52.5046	−2.02090
$676$	−10.8796	−0.418447
$677$	31.3954	1.20662	0.603312	−	0.797505i	$-0.293847\pi$
$677$	31.3954	1.20662	0.603312	+	0.797505i	$0.293847\pi$
$678$	6.72186	0.258151
$679$	−30.8945	−1.18562
$680$	−13.9267	−0.534064
$681$	−22.1872	−0.850214
$682$	−5.80035	−0.222107
$683$	−7.88348	−0.301653	−0.150827	−	0.988560i	$-0.548193\pi$
$683$	−7.88348	−0.301653	−0.150827	+	0.988560i	$0.548193\pi$
$684$	21.9108	0.837780
$685$	41.7664	1.59581
$686$	5.82639	0.222453
$687$	−39.7939	−1.51823
$688$	−8.27829	−0.315607
$689$	2.11621	0.0806212
$690$	11.4034	0.434121
$691$	−16.5389	−0.629171	−0.314585	−	0.949229i	$-0.601865\pi$
$691$	−16.5389	−0.629171	−0.314585	+	0.949229i	$0.601865\pi$
$692$	−14.0123	−0.532668
$693$	−19.0515	−0.723706
$694$	23.7393	0.901131
$695$	71.8543	2.72559
$696$	−7.79792	−0.295579
$697$	22.5156	0.852837
$698$	15.9474	0.603618
$699$	75.8558	2.86913
$700$	−47.9484	−1.81228
$701$	44.4994	1.68072	0.840360	−	0.542029i	$-0.182344\pi$
$701$	44.4994	1.68072	0.840360	+	0.542029i	$0.182344\pi$
$702$	6.27376	0.236788
$703$	7.90616	0.298186
$704$	1.06039	0.0399650
$705$	−86.7007	−3.26534
$706$	23.0859	0.868850
$707$	38.9785	1.46594
$708$	2.09015	0.0785527
$709$	16.1939	0.608176	0.304088	−	0.952644i	$-0.401648\pi$
$709$	16.1939	0.608176	0.304088	+	0.952644i	$0.401648\pi$
$710$	−8.16439	−0.306404
$711$	13.3348	0.500094
$712$	−3.03860	−0.113876
$713$	−5.47001	−0.204853
$714$	36.3575	1.36064
$715$	−6.40128	−0.239394
$716$	−9.85004	−0.368113
$717$	74.4772	2.78140
$718$	−28.1666	−1.05117
$719$	−8.16146	−0.304371	−0.152186	−	0.988352i	$-0.548631\pi$
$719$	−8.16146	−0.304371	−0.152186	+	0.988352i	$0.548631\pi$
$720$	−18.9304	−0.705493
$721$	70.7489	2.63483
$722$	−4.02421	−0.149766
$723$	−17.5974	−0.654454
$724$	7.16712	0.266364
$725$	−34.5473	−1.28305
$726$	−27.1647	−1.00818
$727$	−34.0907	−1.26435	−0.632177	−	0.774824i	$-0.717838\pi$
$727$	−34.0907	−1.26435	−0.632177	+	0.774824i	$0.717838\pi$
$728$	5.72934	0.212343
$729$	−43.9909	−1.62929
$730$	−6.95464	−0.257403
$731$	27.8096	1.02858
$732$	9.93998	0.367392
$733$	−15.6334	−0.577432	−0.288716	−	0.957415i	$-0.593228\pi$
$733$	−15.6334	−0.577432	−0.288716	+	0.957415i	$0.593228\pi$
$734$	6.47403	0.238961
$735$	96.7104	3.56722
$736$	1.00000	0.0368605
$737$	−4.29094	−0.158059
$738$	30.6051	1.12659
$739$	50.1244	1.84386	0.921928	−	0.387362i	$-0.126614\pi$
$739$	50.1244	1.84386	0.921928	+	0.387362i	$0.126614\pi$
$740$	−6.83072	−0.251102
$741$	−19.2195	−0.706046
$742$	5.71805	0.209916
$743$	8.87808	0.325705	0.162853	−	0.986650i	$-0.447931\pi$
$743$	8.87808	0.325705	0.162853	+	0.986650i	$0.447931\pi$
$744$	15.0463	0.551624
$745$	−56.0946	−2.05515
$746$	−33.4946	−1.22632
$747$	−10.1741	−0.372250
$748$	−3.56222	−0.130248
$749$	−0.0868573	−0.00317370
$750$	−81.9502	−2.99240
$751$	5.44004	0.198510	0.0992549	−	0.995062i	$-0.468354\pi$
$751$	5.44004	0.198510	0.0992549	+	0.995062i	$0.468354\pi$
$752$	−7.60304	−0.277254
$753$	−68.6166	−2.50053
$754$	4.12804	0.150334
$755$	2.63769	0.0959955
$756$	16.9519	0.616533
$757$	24.5360	0.891777	0.445889	−	0.895088i	$-0.352888\pi$
$757$	24.5360	0.891777	0.445889	+	0.895088i	$0.352888\pi$
$758$	4.46953	0.162340
$759$	2.91681	0.105874
$760$	19.8923	0.721570
$761$	−24.8281	−0.900016	−0.450008	−	0.893024i	$-0.648579\pi$
$761$	−24.8281	−0.900016	−0.450008	+	0.893024i	$0.648579\pi$
$762$	47.2285	1.71091
$763$	38.9893	1.41151
$764$	21.8440	0.790287
$765$	63.5935	2.29923
$766$	9.11293	0.329264
$767$	−1.10648	−0.0399527
$768$	−2.75069	−0.0992571
$769$	−19.1630	−0.691035	−0.345517	−	0.938412i	$-0.612297\pi$
$769$	−19.1630	−0.691035	−0.345517	+	0.938412i	$0.612297\pi$
$770$	−17.2964	−0.623320
$771$	7.78849	0.280496
$772$	14.7811	0.531985
$773$	13.6121	0.489592	0.244796	−	0.969575i	$-0.421279\pi$
$773$	13.6121	0.489592	0.244796	+	0.969575i	$0.421279\pi$
$774$	37.8013	1.35874
$775$	66.6600	2.39450
$776$	−7.85207	−0.281873
$777$	17.8325	0.639737
$778$	−18.1163	−0.649503
$779$	−32.1603	−1.15226
$780$	16.6052	0.594560
$781$	−2.08832	−0.0747259
$782$	−3.35934	−0.120130
$783$	12.2140	0.436492
$784$	8.48082	0.302886
$785$	10.7531	0.383793
$786$	2.75069	0.0981140
$787$	16.1097	0.574250	0.287125	−	0.957893i	$-0.407301\pi$
$787$	16.1097	0.574250	0.287125	+	0.957893i	$0.407301\pi$
$788$	−17.6080	−0.627258
$789$	−67.9130	−2.41777
$790$	12.1064	0.430725
$791$	−9.61488	−0.341866
$792$	−4.84208	−0.172056
$793$	−5.26200	−0.186859
$794$	24.9404	0.885102
$795$	16.5724	0.587764
$796$	−9.32179	−0.330402
$797$	−18.0786	−0.640377	−0.320188	−	0.947354i	$-0.603746\pi$
$797$	−18.0786	−0.640377	−0.320188	+	0.947354i	$0.603746\pi$
$798$	−51.9316	−1.83836
$799$	25.5412	0.903583
$800$	−12.1865	−0.430856
$801$	13.8752	0.490256
$802$	18.5257	0.654166
$803$	−1.77889	−0.0627755
$804$	11.1309	0.392555
$805$	−16.3114	−0.574900
$806$	−7.96518	−0.280561
$807$	13.4603	0.473826
$808$	9.90668	0.348516
$809$	−51.0596	−1.79516	−0.897580	−	0.440851i	$-0.854677\pi$
$809$	−51.0596	−1.79516	−0.897580	+	0.440851i	$0.854677\pi$
$810$	−7.66006	−0.269147
$811$	−5.27393	−0.185193	−0.0925963	−	0.995704i	$-0.529517\pi$
$811$	−5.27393	−0.185193	−0.0925963	+	0.995704i	$0.529517\pi$
$812$	11.1541	0.391431
$813$	29.7935	1.04491
$814$	−1.74719	−0.0612388
$815$	−39.1624	−1.37180
$816$	9.24052	0.323483
$817$	−39.7222	−1.38970
$818$	16.9729	0.593443
$819$	−26.1620	−0.914173
$820$	27.7857	0.970319
$821$	10.8773	0.379619	0.189809	−	0.981821i	$-0.439213\pi$
$821$	10.8773	0.379619	0.189809	+	0.981821i	$0.439213\pi$
$822$	−27.7125	−0.966586
$823$	17.1343	0.597264	0.298632	−	0.954368i	$-0.403470\pi$
$823$	17.1343	0.597264	0.298632	+	0.954368i	$0.403470\pi$
$824$	17.9814	0.626411
$825$	−35.5456	−1.23754
$826$	−2.98974	−0.104026
$827$	49.0557	1.70583	0.852916	−	0.522048i	$-0.174832\pi$
$827$	49.0557	1.70583	0.852916	+	0.522048i	$0.174832\pi$
$828$	−4.56631	−0.158690
$829$	−1.03025	−0.0357822	−0.0178911	−	0.999840i	$-0.505695\pi$
$829$	−1.03025	−0.0357822	−0.0178911	+	0.999840i	$0.505695\pi$
$830$	−9.23682	−0.320615
$831$	51.7181	1.79408
$832$	1.45615	0.0504831
$833$	−28.4900	−0.987119
$834$	−47.6762	−1.65089
$835$	32.4962	1.12458
$836$	5.08813	0.175977
$837$	−23.5672	−0.814602
$838$	−6.57686	−0.227194
$839$	−22.8596	−0.789202	−0.394601	−	0.918853i	$-0.629117\pi$
$839$	−22.8596	−0.789202	−0.394601	+	0.918853i	$0.629117\pi$
$840$	44.8675	1.54808
$841$	−20.9634	−0.722876
$842$	28.4215	0.979470
$843$	−72.3070	−2.49038
$844$	9.11138	0.313627
$845$	45.1031	1.55159
$846$	34.7178	1.19362
$847$	38.8561	1.33511
$848$	1.45329	0.0499060
$849$	−14.7879	−0.507520
$850$	40.9385	1.40418
$851$	−1.64768	−0.0564818
$852$	5.41717	0.185589
$853$	−8.81612	−0.301858	−0.150929	−	0.988545i	$-0.548227\pi$
$853$	−8.81612	−0.301858	−0.150929	+	0.988545i	$0.548227\pi$
$854$	−14.2181	−0.486532
$855$	−90.8346	−3.10648
$856$	−0.0220754	−0.000754523 0
$857$	−11.4419	−0.390849	−0.195424	−	0.980719i	$-0.562608\pi$
$857$	−11.4419	−0.390849	−0.195424	+	0.980719i	$0.562608\pi$
$858$	4.24733	0.145001
$859$	52.5413	1.79268	0.896342	−	0.443362i	$-0.146214\pi$
$859$	52.5413	1.79268	0.896342	+	0.443362i	$0.146214\pi$
$860$	34.3189	1.17027
$861$	−72.5383	−2.47210
$862$	−6.69545	−0.228048
$863$	−19.2257	−0.654452	−0.327226	−	0.944946i	$-0.606114\pi$
$863$	−19.2257	−0.654452	−0.327226	+	0.944946i	$0.606114\pi$
$864$	4.30844	0.146576
$865$	58.0902	1.97512
$866$	−14.9243	−0.507147
$867$	15.7197	0.533869
$868$	−21.5221	−0.730508
$869$	3.09661	0.105045
$870$	32.3275	1.09600
$871$	−5.89242	−0.199657
$872$	9.90944	0.335576
$873$	35.8550	1.21351
$874$	4.79836	0.162307
$875$	117.221	3.96279
$876$	4.61449	0.155909
$877$	58.2252	1.96613	0.983063	−	0.183268i	$-0.0586675\pi$
$877$	58.2252	1.96613	0.983063	+	0.183268i	$0.0586675\pi$
$878$	18.6646	0.629900
$879$	91.9245	3.10053
$880$	−4.39602	−0.148190
$881$	−32.3857	−1.09110	−0.545552	−	0.838077i	$-0.683680\pi$
$881$	−32.3857	−1.09110	−0.545552	+	0.838077i	$0.683680\pi$
$882$	−38.7261	−1.30397
$883$	28.9284	0.973519	0.486759	−	0.873536i	$-0.338179\pi$
$883$	28.9284	0.973519	0.486759	+	0.873536i	$0.338179\pi$
$884$	−4.89172	−0.164526
$885$	−8.66505	−0.291272
$886$	−30.8453	−1.03627
$887$	44.8141	1.50471	0.752355	−	0.658758i	$-0.228918\pi$
$887$	44.8141	1.50471	0.752355	+	0.658758i	$0.228918\pi$
$888$	4.53226	0.152093
$889$	−67.5553	−2.26573
$890$	12.5970	0.422252
$891$	−1.95932	−0.0656396
$892$	−12.0687	−0.404089
$893$	−36.4821	−1.22083
$894$	37.2195	1.24481
$895$	40.8349	1.36496
$896$	3.93457	0.131445
$897$	4.00544	0.133738
$898$	−2.85679	−0.0953325
$899$	−15.5069	−0.517183
$900$	55.6471	1.85490
$901$	−4.88209	−0.162646
$902$	7.10713	0.236642
$903$	−89.5942	−2.98151
$904$	−2.44370	−0.0812761
$905$	−29.7124	−0.987674
$906$	−1.75014	−0.0581446
$907$	−50.8258	−1.68764	−0.843821	−	0.536624i	$-0.819699\pi$
$907$	−50.8258	−1.68764	−0.843821	+	0.536624i	$0.819699\pi$
$908$	8.06603	0.267680
$909$	−45.2370	−1.50042
$910$	−23.7519	−0.787367
$911$	6.51537	0.215864	0.107932	−	0.994158i	$-0.465577\pi$
$911$	6.51537	0.215864	0.107932	+	0.994158i	$0.465577\pi$
$912$	−13.1988	−0.437056
$913$	−2.36263	−0.0781916
$914$	8.95219	0.296112
$915$	−41.2077	−1.36229
$916$	14.4669	0.477999
$917$	−3.93457	−0.129931
$918$	−14.4735	−0.477698
$919$	−9.90408	−0.326705	−0.163353	−	0.986568i	$-0.552231\pi$
$919$	−9.90408	−0.326705	−0.163353	+	0.986568i	$0.552231\pi$
$920$	−4.14565	−0.136678
$921$	−30.8859	−1.01773
$922$	16.6803	0.549335
$923$	−2.86773	−0.0943925
$924$	11.4764	0.377545
$925$	20.0794	0.660206
$926$	−1.38006	−0.0453516
$927$	−82.1085	−2.69680
$928$	2.83489	0.0930599
$929$	−53.7355	−1.76300	−0.881502	−	0.472181i	$-0.843467\pi$
$929$	−53.7355	−1.76300	−0.881502	+	0.472181i	$0.843467\pi$
$930$	−62.3768	−2.04542
$931$	40.6940	1.33369
$932$	−27.5770	−0.903314
$933$	96.0483	3.14448
$934$	−16.2396	−0.531376
$935$	14.7677	0.482956
$936$	−6.64926	−0.217338
$937$	11.9477	0.390314	0.195157	−	0.980772i	$-0.437478\pi$
$937$	11.9477	0.390314	0.195157	+	0.980772i	$0.437478\pi$
$938$	−15.9215	−0.519855
$939$	53.6800	1.75178
$940$	31.5196	1.02805
$941$	−34.9999	−1.14097	−0.570483	−	0.821310i	$-0.693244\pi$
$941$	−34.9999	−1.14097	−0.570483	+	0.821310i	$0.693244\pi$
$942$	−7.13478	−0.232464
$943$	6.70237	0.218259
$944$	−0.759864	−0.0247315
$945$	−70.2766	−2.28610
$946$	8.77823	0.285405
$947$	16.9085	0.549453	0.274727	−	0.961522i	$-0.411413\pi$
$947$	16.9085	0.549453	0.274727	+	0.961522i	$0.411413\pi$
$948$	−8.03272	−0.260891
$949$	−2.44281	−0.0792969
$950$	−58.4749	−1.89718
$951$	12.6398	0.409874
$952$	−13.2176	−0.428384
$953$	35.6627	1.15523	0.577614	−	0.816310i	$-0.303984\pi$
$953$	35.6627	1.15523	0.577614	+	0.816310i	$0.303984\pi$
$954$	−6.63616	−0.214854
$955$	−90.5575	−2.93037
$956$	−27.0758	−0.875694
$957$	8.26884	0.267294
$958$	27.0888	0.875198
$959$	39.6398	1.28003
$960$	11.4034	0.368044
$961$	−1.07903	−0.0348074
$962$	−2.39928	−0.0773558
$963$	0.100803	0.00324834
$964$	6.39744	0.206048
$965$	−61.2775	−1.97259
$966$	10.8228	0.348217
$967$	0.489245	0.0157331	0.00786653	−	0.999969i	$-0.497496\pi$
$967$	0.489245	0.0157331	0.00786653	+	0.999969i	$0.497496\pi$
$968$	9.87557	0.317413
$969$	44.3393	1.42438
$970$	32.5520	1.04518
$971$	−25.7697	−0.826988	−0.413494	−	0.910507i	$-0.635692\pi$
$971$	−25.7697	−0.826988	−0.413494	+	0.910507i	$0.635692\pi$
$972$	18.0079	0.577603
$973$	68.1957	2.18625
$974$	7.04496	0.225735
$975$	−48.8120	−1.56324
$976$	−3.61363	−0.115669
$977$	−24.6114	−0.787388	−0.393694	−	0.919241i	$-0.628803\pi$
$977$	−24.6114	−0.787388	−0.393694	+	0.919241i	$0.628803\pi$
$978$	25.9847	0.830900
$979$	3.22210	0.102979
$980$	−35.1586	−1.12310
$981$	−45.2496	−1.44471
$982$	−37.8570	−1.20807
$983$	39.3418	1.25481	0.627404	−	0.778694i	$-0.284118\pi$
$983$	39.3418	1.25481	0.627404	+	0.778694i	$0.284118\pi$
$984$	−18.4362	−0.587723
$985$	72.9966	2.32586
$986$	−9.52337	−0.303286
$987$	−82.2861	−2.61919
$988$	6.98715	0.222291
$989$	8.27829	0.263234
$990$	20.0736	0.637980
$991$	35.2590	1.12004	0.560020	−	0.828479i	$-0.310793\pi$
$991$	35.2590	1.12004	0.560020	+	0.828479i	$0.310793\pi$
$992$	−5.47001	−0.173673
$993$	−89.4348	−2.83813
$994$	−7.74868	−0.245773
$995$	38.6449	1.22513
$996$	6.12875	0.194197
$997$	−21.8305	−0.691378	−0.345689	−	0.938349i	$-0.612355\pi$
$997$	−21.8305	−0.691378	−0.345689	+	0.938349i	$0.612355\pi$
$998$	30.7735	0.974117
$999$	−7.09894	−0.224600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.4	✓	36	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.75069 q^{3} +1.00000 q^{4} -4.14565 q^{5} +2.75069 q^{6} -3.93457 q^{7} -1.00000 q^{8} +4.56631 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.75069 q^{3} +1.00000 q^{4} -4.14565 q^{5} +2.75069 q^{6} -3.93457 q^{7} -1.00000 q^{8} +4.56631 q^{9} +4.14565 q^{10} +1.06039 q^{11} -2.75069 q^{12} +1.45615 q^{13} +3.93457 q^{14} +11.4034 q^{15} +1.00000 q^{16} -3.35934 q^{17} -4.56631 q^{18} +4.79836 q^{19} -4.14565 q^{20} +10.8228 q^{21} -1.06039 q^{22} -1.00000 q^{23} +2.75069 q^{24} +12.1865 q^{25} -1.45615 q^{26} -4.30844 q^{27} -3.93457 q^{28} -2.83489 q^{29} -11.4034 q^{30} +5.47001 q^{31} -1.00000 q^{32} -2.91681 q^{33} +3.35934 q^{34} +16.3114 q^{35} +4.56631 q^{36} +1.64768 q^{37} -4.79836 q^{38} -4.00544 q^{39} +4.14565 q^{40} -6.70237 q^{41} -10.8228 q^{42} -8.27829 q^{43} +1.06039 q^{44} -18.9304 q^{45} +1.00000 q^{46} -7.60304 q^{47} -2.75069 q^{48} +8.48082 q^{49} -12.1865 q^{50} +9.24052 q^{51} +1.45615 q^{52} +1.45329 q^{53} +4.30844 q^{54} -4.39602 q^{55} +3.93457 q^{56} -13.1988 q^{57} +2.83489 q^{58} -0.759864 q^{59} +11.4034 q^{60} -3.61363 q^{61} -5.47001 q^{62} -17.9665 q^{63} +1.00000 q^{64} -6.03672 q^{65} +2.91681 q^{66} -4.04656 q^{67} -3.35934 q^{68} +2.75069 q^{69} -16.3114 q^{70} -1.96939 q^{71} -4.56631 q^{72} -1.67757 q^{73} -1.64768 q^{74} -33.5212 q^{75} +4.79836 q^{76} -4.17218 q^{77} +4.00544 q^{78} +2.92025 q^{79} -4.14565 q^{80} -1.84773 q^{81} +6.70237 q^{82} -2.22807 q^{83} +10.8228 q^{84} +13.9267 q^{85} +8.27829 q^{86} +7.79792 q^{87} -1.06039 q^{88} +3.03860 q^{89} +18.9304 q^{90} -5.72934 q^{91} -1.00000 q^{92} -15.0463 q^{93} +7.60304 q^{94} -19.8923 q^{95} +2.75069 q^{96} +7.85207 q^{97} -8.48082 q^{98} +4.84208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more