LMFDB - Embedded newform 6033.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69536 q^{2} +1.00000 q^{3} +5.26496 q^{4} +2.52315 q^{5} -2.69536 q^{6} +0.986697 q^{7} -8.80025 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.69536 q^{2} +1.00000 q^{3} +5.26496 q^{4} +2.52315 q^{5} -2.69536 q^{6} +0.986697 q^{7} -8.80025 q^{8} +1.00000 q^{9} -6.80079 q^{10} +4.69795 q^{11} +5.26496 q^{12} +4.83004 q^{13} -2.65950 q^{14} +2.52315 q^{15} +13.1899 q^{16} +3.28451 q^{17} -2.69536 q^{18} -1.92486 q^{19} +13.2843 q^{20} +0.986697 q^{21} -12.6627 q^{22} +2.24995 q^{23} -8.80025 q^{24} +1.36628 q^{25} -13.0187 q^{26} +1.00000 q^{27} +5.19493 q^{28} -4.28315 q^{29} -6.80079 q^{30} +9.83937 q^{31} -17.9511 q^{32} +4.69795 q^{33} -8.85293 q^{34} +2.48958 q^{35} +5.26496 q^{36} +8.99001 q^{37} +5.18818 q^{38} +4.83004 q^{39} -22.2044 q^{40} +9.28469 q^{41} -2.65950 q^{42} +3.38704 q^{43} +24.7345 q^{44} +2.52315 q^{45} -6.06442 q^{46} -9.11197 q^{47} +13.1899 q^{48} -6.02643 q^{49} -3.68262 q^{50} +3.28451 q^{51} +25.4300 q^{52} -6.49181 q^{53} -2.69536 q^{54} +11.8536 q^{55} -8.68319 q^{56} -1.92486 q^{57} +11.5446 q^{58} -3.78239 q^{59} +13.2843 q^{60} +6.75387 q^{61} -26.5206 q^{62} +0.986697 q^{63} +22.0048 q^{64} +12.1869 q^{65} -12.6627 q^{66} -6.26525 q^{67} +17.2928 q^{68} +2.24995 q^{69} -6.71033 q^{70} -3.07574 q^{71} -8.80025 q^{72} +6.39176 q^{73} -24.2313 q^{74} +1.36628 q^{75} -10.1343 q^{76} +4.63546 q^{77} -13.0187 q^{78} -4.25037 q^{79} +33.2801 q^{80} +1.00000 q^{81} -25.0256 q^{82} +7.42913 q^{83} +5.19493 q^{84} +8.28730 q^{85} -9.12928 q^{86} -4.28315 q^{87} -41.3432 q^{88} -8.44446 q^{89} -6.80079 q^{90} +4.76579 q^{91} +11.8459 q^{92} +9.83937 q^{93} +24.5600 q^{94} -4.85670 q^{95} -17.9511 q^{96} -3.32118 q^{97} +16.2434 q^{98} +4.69795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−2.69536	−1.90591	−0.952954	−	0.303116i	$-0.901973\pi$
$2$	−2.69536	−1.90591	−0.952954	+	0.303116i	$0.901973\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.26496	2.63248
$5$	2.52315	1.12839	0.564193	−	0.825643i	$-0.309187\pi$
$5$	2.52315	1.12839	0.564193	+	0.825643i	$0.309187\pi$
$6$	−2.69536	−1.10038
$7$	0.986697	0.372937	0.186468	−	0.982461i	$-0.440296\pi$
$7$	0.986697	0.372937	0.186468	+	0.982461i	$0.440296\pi$
$8$	−8.80025	−3.11136
$9$	1.00000	0.333333
$10$	−6.80079	−2.15060
$11$	4.69795	1.41649	0.708243	−	0.705969i	$-0.249488\pi$
$11$	4.69795	1.41649	0.708243	+	0.705969i	$0.249488\pi$
$12$	5.26496	1.51986
$13$	4.83004	1.33961	0.669806	−	0.742536i	$-0.266377\pi$
$13$	4.83004	1.33961	0.669806	+	0.742536i	$0.266377\pi$
$14$	−2.65950	−0.710783
$15$	2.52315	0.651474
$16$	13.1899	3.29748
$17$	3.28451	0.796610	0.398305	−	0.917253i	$-0.369599\pi$
$17$	3.28451	0.796610	0.398305	+	0.917253i	$0.369599\pi$
$18$	−2.69536	−0.635302
$19$	−1.92486	−0.441592	−0.220796	−	0.975320i	$-0.570866\pi$
$19$	−1.92486	−0.441592	−0.220796	+	0.975320i	$0.570866\pi$
$20$	13.2843	2.97046
$21$	0.986697	0.215315
$22$	−12.6627	−2.69969
$23$	2.24995	0.469147	0.234573	−	0.972098i	$-0.424631\pi$
$23$	2.24995	0.469147	0.234573	+	0.972098i	$0.424631\pi$
$24$	−8.80025	−1.79634
$25$	1.36628	0.273256
$26$	−13.0187	−2.55318
$27$	1.00000	0.192450
$28$	5.19493	0.981749
$29$	−4.28315	−0.795360	−0.397680	−	0.917524i	$-0.630185\pi$
$29$	−4.28315	−0.795360	−0.397680	+	0.917524i	$0.630185\pi$
$30$	−6.80079	−1.24165
$31$	9.83937	1.76720	0.883602	−	0.468239i	$-0.155112\pi$
$31$	9.83937	1.76720	0.883602	+	0.468239i	$0.155112\pi$
$32$	−17.9511	−3.17333
$33$	4.69795	0.817808
$34$	−8.85293	−1.51827
$35$	2.48958	0.420817
$36$	5.26496	0.877494
$37$	8.99001	1.47795	0.738974	−	0.673734i	$-0.235310\pi$
$37$	8.99001	1.47795	0.738974	+	0.673734i	$0.235310\pi$
$38$	5.18818	0.841633
$39$	4.83004	0.773426
$40$	−22.2044	−3.51082
$41$	9.28469	1.45003	0.725013	−	0.688736i	$-0.241834\pi$
$41$	9.28469	1.45003	0.725013	+	0.688736i	$0.241834\pi$
$42$	−2.65950	−0.410370
$43$	3.38704	0.516518	0.258259	−	0.966076i	$-0.416851\pi$
$43$	3.38704	0.516518	0.258259	+	0.966076i	$0.416851\pi$
$44$	24.7345	3.72887
$45$	2.52315	0.376129
$46$	−6.06442	−0.894150
$47$	−9.11197	−1.32912	−0.664559	−	0.747236i	$-0.731380\pi$
$47$	−9.11197	−1.32912	−0.664559	+	0.747236i	$0.731380\pi$
$48$	13.1899	1.90380
$49$	−6.02643	−0.860918
$50$	−3.68262	−0.520801
$51$	3.28451	0.459923
$52$	25.4300	3.52651
$53$	−6.49181	−0.891719	−0.445859	−	0.895103i	$-0.647102\pi$
$53$	−6.49181	−0.891719	−0.445859	+	0.895103i	$0.647102\pi$
$54$	−2.69536	−0.366792
$55$	11.8536	1.59834
$56$	−8.68319	−1.16034
$57$	−1.92486	−0.254953
$58$	11.5446	1.51588
$59$	−3.78239	−0.492425	−0.246212	−	0.969216i	$-0.579186\pi$
$59$	−3.78239	−0.492425	−0.246212	+	0.969216i	$0.579186\pi$
$60$	13.2843	1.71499
$61$	6.75387	0.864744	0.432372	−	0.901695i	$-0.357677\pi$
$61$	6.75387	0.864744	0.432372	+	0.901695i	$0.357677\pi$
$62$	−26.5206	−3.36813
$63$	0.986697	0.124312
$64$	22.0048	2.75060
$65$	12.1869	1.51160
$66$	−12.6627	−1.55867
$67$	−6.26525	−0.765422	−0.382711	−	0.923868i	$-0.625009\pi$
$67$	−6.26525	−0.765422	−0.382711	+	0.923868i	$0.625009\pi$
$68$	17.2928	2.09706
$69$	2.24995	0.270862
$70$	−6.71033	−0.802037
$71$	−3.07574	−0.365023	−0.182512	−	0.983204i	$-0.558423\pi$
$71$	−3.07574	−0.365023	−0.182512	+	0.983204i	$0.558423\pi$
$72$	−8.80025	−1.03712
$73$	6.39176	0.748099	0.374049	−	0.927409i	$-0.377969\pi$
$73$	6.39176	0.748099	0.374049	+	0.927409i	$0.377969\pi$
$74$	−24.2313	−2.81683
$75$	1.36628	0.157764
$76$	−10.1343	−1.16248
$77$	4.63546	0.528259
$78$	−13.0187	−1.47408
$79$	−4.25037	−0.478204	−0.239102	−	0.970994i	$-0.576853\pi$
$79$	−4.25037	−0.478204	−0.239102	+	0.970994i	$0.576853\pi$
$80$	33.2801	3.72083
$81$	1.00000	0.111111
$82$	−25.0256	−2.76361
$83$	7.42913	0.815453	0.407727	−	0.913104i	$-0.366322\pi$
$83$	7.42913	0.815453	0.407727	+	0.913104i	$0.366322\pi$
$84$	5.19493	0.566813
$85$	8.28730	0.898884
$86$	−9.12928	−0.984436
$87$	−4.28315	−0.459201
$88$	−41.3432	−4.40720
$89$	−8.44446	−0.895111	−0.447555	−	0.894256i	$-0.647705\pi$
$89$	−8.44446	−0.895111	−0.447555	+	0.894256i	$0.647705\pi$
$90$	−6.80079	−0.716867
$91$	4.76579	0.499591
$92$	11.8459	1.23502
$93$	9.83937	1.02030
$94$	24.5600	2.53317
$95$	−4.85670	−0.498286
$96$	−17.9511	−1.83212
$97$	−3.32118	−0.337215	−0.168608	−	0.985683i	$-0.553927\pi$
$97$	−3.32118	−0.337215	−0.168608	+	0.985683i	$0.553927\pi$
$98$	16.2434	1.64083
$99$	4.69795	0.472162
$100$	7.19342	0.719342
$101$	−1.82175	−0.181271	−0.0906354	−	0.995884i	$-0.528890\pi$
$101$	−1.82175	−0.181271	−0.0906354	+	0.995884i	$0.528890\pi$
$102$	−8.85293	−0.876571
$103$	2.74940	0.270907	0.135453	−	0.990784i	$-0.456751\pi$
$103$	2.74940	0.270907	0.135453	+	0.990784i	$0.456751\pi$
$104$	−42.5056	−4.16802
$105$	2.48958	0.242959
$106$	17.4978	1.69953
$107$	−4.27451	−0.413233	−0.206616	−	0.978422i	$-0.566245\pi$
$107$	−4.27451	−0.413233	−0.206616	+	0.978422i	$0.566245\pi$
$108$	5.26496	0.506621
$109$	−14.4267	−1.38182	−0.690912	−	0.722939i	$-0.742791\pi$
$109$	−14.4267	−1.38182	−0.690912	+	0.722939i	$0.742791\pi$
$110$	−31.9498	−3.04629
$111$	8.99001	0.853294
$112$	13.0145	1.22975
$113$	−20.0622	−1.88729	−0.943647	−	0.330954i	$-0.892629\pi$
$113$	−20.0622	−1.88729	−0.943647	+	0.330954i	$0.892629\pi$
$114$	5.18818	0.485917
$115$	5.67696	0.529379
$116$	−22.5506	−2.09377
$117$	4.83004	0.446538
$118$	10.1949	0.938516
$119$	3.24082	0.297085
$120$	−22.2044	−2.02697
$121$	11.0708	1.00643
$122$	−18.2041	−1.64812
$123$	9.28469	0.837172
$124$	51.8039	4.65213
$125$	−9.16842	−0.820048
$126$	−2.65950	−0.236928
$127$	18.9865	1.68478	0.842388	−	0.538872i	$-0.181149\pi$
$127$	18.9865	1.68478	0.842388	+	0.538872i	$0.181149\pi$
$128$	−23.4086	−2.06905
$129$	3.38704	0.298212
$130$	−32.8481	−2.88097
$131$	−20.7655	−1.81429	−0.907143	−	0.420822i	$-0.861742\pi$
$131$	−20.7655	−1.81429	−0.907143	+	0.420822i	$0.861742\pi$
$132$	24.7345	2.15287
$133$	−1.89925	−0.164686
$134$	16.8871	1.45882
$135$	2.52315	0.217158
$136$	−28.9045	−2.47854
$137$	8.15041	0.696336	0.348168	−	0.937432i	$-0.386804\pi$
$137$	8.15041	0.696336	0.348168	+	0.937432i	$0.386804\pi$
$138$	−6.06442	−0.516238
$139$	−9.47655	−0.803791	−0.401895	−	0.915686i	$-0.631648\pi$
$139$	−9.47655	−0.803791	−0.401895	+	0.915686i	$0.631648\pi$
$140$	13.1076	1.10779
$141$	−9.11197	−0.767366
$142$	8.29023	0.695700
$143$	22.6913	1.89754
$144$	13.1899	1.09916
$145$	−10.8070	−0.897474
$146$	−17.2281	−1.42581
$147$	−6.02643	−0.497051
$148$	47.3321	3.89067
$149$	0.296027	0.0242514	0.0121257	−	0.999926i	$-0.496140\pi$
$149$	0.296027	0.0242514	0.0121257	+	0.999926i	$0.496140\pi$
$150$	−3.68262	−0.300684
$151$	3.23720	0.263440	0.131720	−	0.991287i	$-0.457950\pi$
$151$	3.23720	0.263440	0.131720	+	0.991287i	$0.457950\pi$
$152$	16.9392	1.37395
$153$	3.28451	0.265537
$154$	−12.4942	−1.00681
$155$	24.8262	1.99409
$156$	25.4300	2.03603
$157$	−24.8081	−1.97990	−0.989951	−	0.141410i	$-0.954837\pi$
$157$	−24.8081	−1.97990	−0.989951	+	0.141410i	$0.954837\pi$
$158$	11.4563	0.911413
$159$	−6.49181	−0.514834
$160$	−45.2932	−3.58075
$161$	2.22002	0.174962
$162$	−2.69536	−0.211767
$163$	22.8835	1.79237	0.896185	−	0.443680i	$-0.146327\pi$
$163$	22.8835	1.79237	0.896185	+	0.443680i	$0.146327\pi$
$164$	48.8836	3.81717
$165$	11.8536	0.922804
$166$	−20.0242	−1.55418
$167$	9.45386	0.731562	0.365781	−	0.930701i	$-0.380802\pi$
$167$	9.45386	0.731562	0.365781	+	0.930701i	$0.380802\pi$
$168$	−8.68319	−0.669923
$169$	10.3293	0.794562
$170$	−22.3373	−1.71319
$171$	−1.92486	−0.147197
$172$	17.8326	1.35973
$173$	−20.6052	−1.56659	−0.783293	−	0.621652i	$-0.786462\pi$
$173$	−20.6052	−1.56659	−0.783293	+	0.621652i	$0.786462\pi$
$174$	11.5446	0.875195
$175$	1.34811	0.101907
$176$	61.9656	4.67083
$177$	−3.78239	−0.284302
$178$	22.7609	1.70600
$179$	10.0617	0.752045	0.376022	−	0.926611i	$-0.377292\pi$
$179$	10.0617	0.752045	0.376022	+	0.926611i	$0.377292\pi$
$180$	13.2843	0.990152
$181$	13.4474	0.999537	0.499768	−	0.866159i	$-0.333419\pi$
$181$	13.4474	0.999537	0.499768	+	0.866159i	$0.333419\pi$
$182$	−12.8455	−0.952173
$183$	6.75387	0.499260
$184$	−19.8001	−1.45968
$185$	22.6831	1.66770
$186$	−26.5206	−1.94459
$187$	15.4305	1.12839
$188$	−47.9742	−3.49888
$189$	0.986697	0.0717717
$190$	13.0905	0.949688
$191$	−6.73978	−0.487673	−0.243837	−	0.969816i	$-0.578406\pi$
$191$	−6.73978	−0.487673	−0.243837	+	0.969816i	$0.578406\pi$
$192$	22.0048	1.58806
$193$	25.4497	1.83191	0.915953	−	0.401285i	$-0.131436\pi$
$193$	25.4497	1.83191	0.915953	+	0.401285i	$0.131436\pi$
$194$	8.95178	0.642701
$195$	12.1869	0.872723
$196$	−31.7289	−2.26635
$197$	−0.131717	−0.00938446	−0.00469223	−	0.999989i	$-0.501494\pi$
$197$	−0.131717	−0.00938446	−0.00469223	+	0.999989i	$0.501494\pi$
$198$	−12.6627	−0.899897
$199$	15.9310	1.12932	0.564658	−	0.825325i	$-0.309008\pi$
$199$	15.9310	1.12932	0.564658	+	0.825325i	$0.309008\pi$
$200$	−12.0236	−0.850198
$201$	−6.26525	−0.441916
$202$	4.91027	0.345485
$203$	−4.22617	−0.296619
$204$	17.2928	1.21074
$205$	23.4267	1.63619
$206$	−7.41063	−0.516323
$207$	2.24995	0.156382
$208$	63.7079	4.41735
$209$	−9.04288	−0.625509
$210$	−6.71033	−0.463057
$211$	1.03674	0.0713724	0.0356862	−	0.999363i	$-0.488638\pi$
$211$	1.03674	0.0713724	0.0356862	+	0.999363i	$0.488638\pi$
$212$	−34.1792	−2.34743
$213$	−3.07574	−0.210746
$214$	11.5213	0.787583
$215$	8.54600	0.582832
$216$	−8.80025	−0.598781
$217$	9.70848	0.659055
$218$	38.8850	2.63363
$219$	6.39176	0.431915
$220$	62.4090	4.20761
$221$	15.8643	1.06715
$222$	−24.2313	−1.62630
$223$	−17.1190	−1.14637	−0.573185	−	0.819426i	$-0.694292\pi$
$223$	−17.1190	−1.14637	−0.573185	+	0.819426i	$0.694292\pi$
$224$	−17.7123	−1.18345
$225$	1.36628	0.0910854
$226$	54.0749	3.59701
$227$	−21.5512	−1.43040	−0.715200	−	0.698920i	$-0.753664\pi$
$227$	−21.5512	−1.43040	−0.715200	+	0.698920i	$0.753664\pi$
$228$	−10.1343	−0.671160
$229$	−20.4774	−1.35318	−0.676591	−	0.736359i	$-0.736543\pi$
$229$	−20.4774	−1.35318	−0.676591	+	0.736359i	$0.736543\pi$
$230$	−15.3014	−1.00895
$231$	4.63546	0.304991
$232$	37.6928	2.47465
$233$	12.9674	0.849522	0.424761	−	0.905306i	$-0.360358\pi$
$233$	12.9674	0.849522	0.424761	+	0.905306i	$0.360358\pi$
$234$	−13.0187	−0.851059
$235$	−22.9909	−1.49976
$236$	−19.9141	−1.29630
$237$	−4.25037	−0.276091
$238$	−8.73517	−0.566217
$239$	−5.90384	−0.381888	−0.190944	−	0.981601i	$-0.561155\pi$
$239$	−5.90384	−0.381888	−0.190944	+	0.981601i	$0.561155\pi$
$240$	33.2801	2.14822
$241$	−20.5242	−1.32208	−0.661041	−	0.750349i	$-0.729885\pi$
$241$	−20.5242	−1.32208	−0.661041	+	0.750349i	$0.729885\pi$
$242$	−29.8397	−1.91817
$243$	1.00000	0.0641500
$244$	35.5589	2.27642
$245$	−15.2056	−0.971449
$246$	−25.0256	−1.59557
$247$	−9.29713	−0.591562
$248$	−86.5890	−5.49840
$249$	7.42913	0.470802
$250$	24.7122	1.56294
$251$	−20.6631	−1.30424	−0.652122	−	0.758114i	$-0.726121\pi$
$251$	−20.6631	−1.30424	−0.652122	+	0.758114i	$0.726121\pi$
$252$	5.19493	0.327250
$253$	10.5702	0.664540
$254$	−51.1753	−3.21103
$255$	8.28730	0.518971
$256$	19.0851	1.19282
$257$	−11.8017	−0.736169	−0.368085	−	0.929792i	$-0.619986\pi$
$257$	−11.8017	−0.736169	−0.368085	+	0.929792i	$0.619986\pi$
$258$	−9.12928	−0.568364
$259$	8.87042	0.551181
$260$	64.1637	3.97926
$261$	−4.28315	−0.265120
$262$	55.9704	3.45786
$263$	−11.9836	−0.738943	−0.369472	−	0.929242i	$-0.620461\pi$
$263$	−11.9836	−0.738943	−0.369472	+	0.929242i	$0.620461\pi$
$264$	−41.3432	−2.54450
$265$	−16.3798	−1.00620
$266$	5.11916	0.313876
$267$	−8.44446	−0.516793
$268$	−32.9863	−2.01496
$269$	−4.04054	−0.246356	−0.123178	−	0.992385i	$-0.539309\pi$
$269$	−4.04054	−0.246356	−0.123178	+	0.992385i	$0.539309\pi$
$270$	−6.80079	−0.413883
$271$	−7.96901	−0.484083	−0.242041	−	0.970266i	$-0.577817\pi$
$271$	−7.96901	−0.484083	−0.242041	+	0.970266i	$0.577817\pi$
$272$	43.3224	2.62681
$273$	4.76579	0.288439
$274$	−21.9683	−1.32715
$275$	6.41872	0.387063
$276$	11.8459	0.713039
$277$	−17.4651	−1.04938	−0.524689	−	0.851294i	$-0.675819\pi$
$277$	−17.4651	−1.04938	−0.524689	+	0.851294i	$0.675819\pi$
$278$	25.5427	1.53195
$279$	9.83937	0.589068
$280$	−21.9090	−1.30931
$281$	6.28416	0.374882	0.187441	−	0.982276i	$-0.439981\pi$
$281$	6.28416	0.374882	0.187441	+	0.982276i	$0.439981\pi$
$282$	24.5600	1.46253
$283$	3.10755	0.184725	0.0923623	−	0.995725i	$-0.470558\pi$
$283$	3.10755	0.184725	0.0923623	+	0.995725i	$0.470558\pi$
$284$	−16.1937	−0.960917
$285$	−4.85670	−0.287686
$286$	−61.1612	−3.61654
$287$	9.16118	0.540767
$288$	−17.9511	−1.05778
$289$	−6.21201	−0.365412
$290$	29.1288	1.71050
$291$	−3.32118	−0.194691
$292$	33.6524	1.96936
$293$	13.1354	0.767380	0.383690	−	0.923462i	$-0.374653\pi$
$293$	13.1354	0.767380	0.383690	+	0.923462i	$0.374653\pi$
$294$	16.2434	0.947334
$295$	−9.54352	−0.555645
$296$	−79.1144	−4.59843
$297$	4.69795	0.272603
$298$	−0.797898	−0.0462210
$299$	10.8673	0.628475
$300$	7.19342	0.415312
$301$	3.34198	0.192629
$302$	−8.72543	−0.502092
$303$	−1.82175	−0.104657
$304$	−25.3887	−1.45614
$305$	17.0410	0.975765
$306$	−8.85293	−0.506088
$307$	−19.8414	−1.13241	−0.566206	−	0.824264i	$-0.691589\pi$
$307$	−19.8414	−1.13241	−0.566206	+	0.824264i	$0.691589\pi$
$308$	24.4055	1.39063
$309$	2.74940	0.156408
$310$	−66.9155	−3.80055
$311$	−32.1409	−1.82254	−0.911271	−	0.411807i	$-0.864898\pi$
$311$	−32.1409	−1.82254	−0.911271	+	0.411807i	$0.864898\pi$
$312$	−42.5056	−2.40641
$313$	31.2558	1.76668	0.883341	−	0.468730i	$-0.155288\pi$
$313$	31.2558	1.76668	0.883341	+	0.468730i	$0.155288\pi$
$314$	66.8668	3.77351
$315$	2.48958	0.140272
$316$	−22.3781	−1.25886
$317$	−9.74344	−0.547246	−0.273623	−	0.961837i	$-0.588222\pi$
$317$	−9.74344	−0.547246	−0.273623	+	0.961837i	$0.588222\pi$
$318$	17.4978	0.981226
$319$	−20.1220	−1.12662
$320$	55.5213	3.10374
$321$	−4.27451	−0.238580
$322$	−5.98375	−0.333461
$323$	−6.32220	−0.351777
$324$	5.26496	0.292498
$325$	6.59919	0.366057
$326$	−61.6791	−3.41609
$327$	−14.4267	−0.797796
$328$	−81.7076	−4.51155
$329$	−8.99076	−0.495677
$330$	−31.9498	−1.75878
$331$	−0.291875	−0.0160429	−0.00802145	−	0.999968i	$-0.502553\pi$
$331$	−0.291875	−0.0160429	−0.00802145	+	0.999968i	$0.502553\pi$
$332$	39.1141	2.14667
$333$	8.99001	0.492650
$334$	−25.4816	−1.39429
$335$	−15.8082	−0.863692
$336$	13.0145	0.709997
$337$	−23.4696	−1.27847	−0.639234	−	0.769012i	$-0.720749\pi$
$337$	−23.4696	−1.27847	−0.639234	+	0.769012i	$0.720749\pi$
$338$	−27.8412	−1.51436
$339$	−20.0622	−1.08963
$340$	43.6324	2.36630
$341$	46.2249	2.50322
$342$	5.18818	0.280544
$343$	−12.8531	−0.694005
$344$	−29.8068	−1.60707
$345$	5.67696	0.305637
$346$	55.5385	2.98577
$347$	−1.87404	−0.100604	−0.0503019	−	0.998734i	$-0.516018\pi$
$347$	−1.87404	−0.100604	−0.0503019	+	0.998734i	$0.516018\pi$
$348$	−22.5506	−1.20884
$349$	3.35594	0.179639	0.0898196	−	0.995958i	$-0.471371\pi$
$349$	3.35594	0.179639	0.0898196	+	0.995958i	$0.471371\pi$
$350$	−3.63363	−0.194226
$351$	4.83004	0.257809
$352$	−84.3333	−4.49498
$353$	−21.1583	−1.12614	−0.563071	−	0.826409i	$-0.690380\pi$
$353$	−21.1583	−1.12614	−0.563071	+	0.826409i	$0.690380\pi$
$354$	10.1949	0.541852
$355$	−7.76055	−0.411887
$356$	−44.4598	−2.35636
$357$	3.24082	0.171522
$358$	−27.1198	−1.43333
$359$	26.3235	1.38930	0.694652	−	0.719346i	$-0.255559\pi$
$359$	26.3235	1.38930	0.694652	+	0.719346i	$0.255559\pi$
$360$	−22.2044	−1.17027
$361$	−15.2949	−0.804996
$362$	−36.2455	−1.90502
$363$	11.0708	0.581064
$364$	25.0917	1.31516
$365$	16.1274	0.844145
$366$	−18.2041	−0.951543
$367$	0.742751	0.0387713	0.0193856	−	0.999812i	$-0.493829\pi$
$367$	0.742751	0.0387713	0.0193856	+	0.999812i	$0.493829\pi$
$368$	29.6767	1.54700
$369$	9.28469	0.483342
$370$	−61.1392	−3.17848
$371$	−6.40545	−0.332555
$372$	51.8039	2.68591
$373$	−14.8470	−0.768749	−0.384375	−	0.923177i	$-0.625583\pi$
$373$	−14.8470	−0.768749	−0.384375	+	0.923177i	$0.625583\pi$
$374$	−41.5906	−2.15060
$375$	−9.16842	−0.473455
$376$	80.1876	4.13536
$377$	−20.6878	−1.06547
$378$	−2.65950	−0.136790
$379$	−33.2322	−1.70702	−0.853512	−	0.521074i	$-0.825532\pi$
$379$	−33.2322	−1.70702	−0.853512	+	0.521074i	$0.825532\pi$
$380$	−25.5703	−1.31173
$381$	18.9865	0.972705
$382$	18.1661	0.929460
$383$	−16.3218	−0.834003	−0.417001	−	0.908906i	$-0.636919\pi$
$383$	−16.3218	−0.834003	−0.417001	+	0.908906i	$0.636919\pi$
$384$	−23.4086	−1.19457
$385$	11.6959	0.596081
$386$	−68.5960	−3.49144
$387$	3.38704	0.172173
$388$	−17.4859	−0.887713
$389$	20.3035	1.02943	0.514714	−	0.857362i	$-0.327898\pi$
$389$	20.3035	1.02943	0.514714	+	0.857362i	$0.327898\pi$
$390$	−32.8481	−1.66333
$391$	7.38998	0.373727
$392$	53.0341	2.67863
$393$	−20.7655	−1.04748
$394$	0.355025	0.0178859
$395$	−10.7243	−0.539599
$396$	24.7345	1.24296
$397$	20.4830	1.02801	0.514005	−	0.857787i	$-0.328161\pi$
$397$	20.4830	1.02801	0.514005	+	0.857787i	$0.328161\pi$
$398$	−42.9397	−2.15237
$399$	−1.89925	−0.0950814
$400$	18.0211	0.901057
$401$	−25.1943	−1.25814	−0.629071	−	0.777348i	$-0.716565\pi$
$401$	−25.1943	−1.25814	−0.629071	+	0.777348i	$0.716565\pi$
$402$	16.8871	0.842252
$403$	47.5246	2.36737
$404$	−9.59144	−0.477192
$405$	2.52315	0.125376
$406$	11.3910	0.565328
$407$	42.2346	2.09349
$408$	−28.9045	−1.43099
$409$	7.18180	0.355117	0.177559	−	0.984110i	$-0.443180\pi$
$409$	7.18180	0.355117	0.177559	+	0.984110i	$0.443180\pi$
$410$	−63.1433	−3.11842
$411$	8.15041	0.402030
$412$	14.4755	0.713157
$413$	−3.73207	−0.183643
$414$	−6.06442	−0.298050
$415$	18.7448	0.920146
$416$	−86.7045	−4.25104
$417$	−9.47655	−0.464069
$418$	24.3738	1.19216
$419$	27.4857	1.34276	0.671382	−	0.741111i	$-0.265701\pi$
$419$	27.4857	1.34276	0.671382	+	0.741111i	$0.265701\pi$
$420$	13.1076	0.639584
$421$	−32.2477	−1.57166	−0.785828	−	0.618445i	$-0.787763\pi$
$421$	−32.2477	−1.57166	−0.785828	+	0.618445i	$0.787763\pi$
$422$	−2.79440	−0.136029
$423$	−9.11197	−0.443039
$424$	57.1296	2.77446
$425$	4.48756	0.217679
$426$	8.29023	0.401663
$427$	6.66402	0.322495
$428$	−22.5051	−1.08783
$429$	22.6913	1.09555
$430$	−23.0345	−1.11082
$431$	22.6408	1.09057	0.545284	−	0.838251i	$-0.316422\pi$
$431$	22.6408	1.09057	0.545284	+	0.838251i	$0.316422\pi$
$432$	13.1899	0.634600
$433$	36.3050	1.74471	0.872354	−	0.488874i	$-0.162592\pi$
$433$	36.3050	1.74471	0.872354	+	0.488874i	$0.162592\pi$
$434$	−26.1679	−1.25610
$435$	−10.8070	−0.518157
$436$	−75.9559	−3.63763
$437$	−4.33083	−0.207171
$438$	−17.2281	−0.823190
$439$	−11.5020	−0.548962	−0.274481	−	0.961593i	$-0.588506\pi$
$439$	−11.5020	−0.548962	−0.274481	+	0.961593i	$0.588506\pi$
$440$	−104.315	−4.97302
$441$	−6.02643	−0.286973
$442$	−42.7600	−2.03389
$443$	12.5361	0.595608	0.297804	−	0.954627i	$-0.403746\pi$
$443$	12.5361	0.595608	0.297804	+	0.954627i	$0.403746\pi$
$444$	47.3321	2.24628
$445$	−21.3066	−1.01003
$446$	46.1417	2.18487
$447$	0.296027	0.0140016
$448$	21.7121	1.02580
$449$	10.1611	0.479534	0.239767	−	0.970830i	$-0.422929\pi$
$449$	10.1611	0.479534	0.239767	+	0.970830i	$0.422929\pi$
$450$	−3.68262	−0.173600
$451$	43.6190	2.05394
$452$	−105.627	−4.96827
$453$	3.23720	0.152097
$454$	58.0881	2.72621
$455$	12.0248	0.563731
$456$	16.9392	0.793251
$457$	4.18469	0.195752	0.0978758	−	0.995199i	$-0.468795\pi$
$457$	4.18469	0.195752	0.0978758	+	0.995199i	$0.468795\pi$
$458$	55.1938	2.57904
$459$	3.28451	0.153308
$460$	29.8890	1.39358
$461$	−18.4608	−0.859805	−0.429902	−	0.902875i	$-0.641452\pi$
$461$	−18.4608	−0.859805	−0.429902	+	0.902875i	$0.641452\pi$
$462$	−12.4942	−0.581284
$463$	−16.0271	−0.744843	−0.372421	−	0.928064i	$-0.621472\pi$
$463$	−16.0271	−0.744843	−0.372421	+	0.928064i	$0.621472\pi$
$464$	−56.4944	−2.62268
$465$	24.8262	1.15129
$466$	−34.9518	−1.61911
$467$	−24.5475	−1.13592	−0.567961	−	0.823055i	$-0.692268\pi$
$467$	−24.5475	−1.13592	−0.567961	+	0.823055i	$0.692268\pi$
$468$	25.4300	1.17550
$469$	−6.18190	−0.285454
$470$	61.9686	2.85840
$471$	−24.8081	−1.14310
$472$	33.2860	1.53211
$473$	15.9121	0.731641
$474$	11.4563	0.526204
$475$	−2.62989	−0.120668
$476$	17.0628	0.782071
$477$	−6.49181	−0.297240
$478$	15.9130	0.727842
$479$	−10.5139	−0.480393	−0.240196	−	0.970724i	$-0.577212\pi$
$479$	−10.5139	−0.480393	−0.240196	+	0.970724i	$0.577212\pi$
$480$	−45.2932	−2.06734
$481$	43.4221	1.97988
$482$	55.3202	2.51977
$483$	2.22002	0.101014
$484$	58.2871	2.64941
$485$	−8.37984	−0.380509
$486$	−2.69536	−0.122264
$487$	−5.05987	−0.229285	−0.114642	−	0.993407i	$-0.536572\pi$
$487$	−5.05987	−0.229285	−0.114642	+	0.993407i	$0.536572\pi$
$488$	−59.4357	−2.69053
$489$	22.8835	1.03483
$490$	40.9845	1.85149
$491$	16.6888	0.753155	0.376578	−	0.926385i	$-0.377101\pi$
$491$	16.6888	0.753155	0.376578	+	0.926385i	$0.377101\pi$
$492$	48.8836	2.20384
$493$	−14.0680	−0.633592
$494$	25.0591	1.12746
$495$	11.8536	0.532781
$496$	129.781	5.82732
$497$	−3.03482	−0.136130
$498$	−20.0242	−0.897305
$499$	−20.2498	−0.906505	−0.453253	−	0.891382i	$-0.649736\pi$
$499$	−20.2498	−0.906505	−0.453253	+	0.891382i	$0.649736\pi$
$500$	−48.2714	−2.15876
$501$	9.45386	0.422367
$502$	55.6945	2.48577
$503$	26.2617	1.17095	0.585475	−	0.810691i	$-0.300908\pi$
$503$	26.2617	1.17095	0.585475	+	0.810691i	$0.300908\pi$
$504$	−8.68319	−0.386780
$505$	−4.59654	−0.204543
$506$	−28.4904	−1.26655
$507$	10.3293	0.458741
$508$	99.9630	4.43514
$509$	−27.5994	−1.22332	−0.611662	−	0.791120i	$-0.709499\pi$
$509$	−27.5994	−1.22332	−0.611662	+	0.791120i	$0.709499\pi$
$510$	−22.3373	−0.989111
$511$	6.30673	0.278993
$512$	−4.62399	−0.204353
$513$	−1.92486	−0.0849844
$514$	31.8098	1.40307
$515$	6.93716	0.305688
$516$	17.8326	0.785038
$517$	−42.8076	−1.88268
$518$	−23.9090	−1.05050
$519$	−20.6052	−0.904469
$520$	−107.248	−4.70313
$521$	11.5929	0.507895	0.253947	−	0.967218i	$-0.418271\pi$
$521$	11.5929	0.507895	0.253947	+	0.967218i	$0.418271\pi$
$522$	11.5446	0.505294
$523$	−6.41145	−0.280353	−0.140177	−	0.990127i	$-0.544767\pi$
$523$	−6.41145	−0.280353	−0.140177	+	0.990127i	$0.544767\pi$
$524$	−109.329	−4.77608
$525$	1.34811	0.0588361
$526$	32.3002	1.40836
$527$	32.3175	1.40777
$528$	61.9656	2.69671
$529$	−17.9377	−0.779901
$530$	44.1495	1.91773
$531$	−3.78239	−0.164142
$532$	−9.99948	−0.433533
$533$	44.8455	1.94247
$534$	22.7609	0.984959
$535$	−10.7852	−0.466286
$536$	55.1358	2.38150
$537$	10.0617	0.434193
$538$	10.8907	0.469532
$539$	−28.3119	−1.21948
$540$	13.2843	0.571665
$541$	−19.6067	−0.842957	−0.421479	−	0.906838i	$-0.638489\pi$
$541$	−19.6067	−0.842957	−0.421479	+	0.906838i	$0.638489\pi$
$542$	21.4793	0.922617
$543$	13.4474	0.577083
$544$	−58.9605	−2.52791
$545$	−36.4006	−1.55923
$546$	−12.8455	−0.549738
$547$	14.2225	0.608109	0.304054	−	0.952655i	$-0.401660\pi$
$547$	14.2225	0.608109	0.304054	+	0.952655i	$0.401660\pi$
$548$	42.9116	1.83309
$549$	6.75387	0.288248
$550$	−17.3008	−0.737707
$551$	8.24443	0.351225
$552$	−19.8001	−0.842749
$553$	−4.19383	−0.178340
$554$	47.0748	2.00002
$555$	22.6831	0.962846
$556$	−49.8937	−2.11596
$557$	30.7205	1.30167	0.650836	−	0.759219i	$-0.274419\pi$
$557$	30.7205	1.30167	0.650836	+	0.759219i	$0.274419\pi$
$558$	−26.5206	−1.12271
$559$	16.3595	0.691935
$560$	32.8374	1.38763
$561$	15.4305	0.651475
$562$	−16.9381	−0.714489
$563$	36.5505	1.54042	0.770210	−	0.637790i	$-0.220151\pi$
$563$	36.5505	1.54042	0.770210	+	0.637790i	$0.220151\pi$
$564$	−47.9742	−2.02008
$565$	−50.6199	−2.12960
$566$	−8.37596	−0.352068
$567$	0.986697	0.0414374
$568$	27.0673	1.13572
$569$	−37.7955	−1.58447	−0.792235	−	0.610216i	$-0.791083\pi$
$569$	−37.7955	−1.58447	−0.792235	+	0.610216i	$0.791083\pi$
$570$	13.0905	0.548303
$571$	30.0448	1.25734	0.628668	−	0.777674i	$-0.283601\pi$
$571$	30.0448	1.25734	0.628668	+	0.777674i	$0.283601\pi$
$572$	119.469	4.99525
$573$	−6.73978	−0.281558
$574$	−24.6927	−1.03065
$575$	3.07406	0.128197
$576$	22.0048	0.916865
$577$	14.5416	0.605373	0.302686	−	0.953090i	$-0.402117\pi$
$577$	14.5416	0.605373	0.302686	+	0.953090i	$0.402117\pi$
$578$	16.7436	0.696442
$579$	25.4497	1.05765
$580$	−56.8985	−2.36258
$581$	7.33030	0.304112
$582$	8.95178	0.371063
$583$	−30.4982	−1.26311
$584$	−56.2491	−2.32760
$585$	12.1869	0.503867
$586$	−35.4047	−1.46256
$587$	36.3956	1.50221	0.751104	−	0.660184i	$-0.229522\pi$
$587$	36.3956	1.50221	0.751104	+	0.660184i	$0.229522\pi$
$588$	−31.7289	−1.30848
$589$	−18.9394	−0.780383
$590$	25.7232	1.05901
$591$	−0.131717	−0.00541812
$592$	118.578	4.87351
$593$	28.8935	1.18651	0.593257	−	0.805013i	$-0.297842\pi$
$593$	28.8935	1.18651	0.593257	+	0.805013i	$0.297842\pi$
$594$	−12.6627	−0.519556
$595$	8.17706	0.335227
$596$	1.55857	0.0638415
$597$	15.9310	0.652011
$598$	−29.2914	−1.19781
$599$	12.8989	0.527035	0.263518	−	0.964655i	$-0.415117\pi$
$599$	12.8989	0.527035	0.263518	+	0.964655i	$0.415117\pi$
$600$	−12.0236	−0.490862
$601$	15.4933	0.631985	0.315993	−	0.948762i	$-0.397663\pi$
$601$	15.4933	0.631985	0.315993	+	0.948762i	$0.397663\pi$
$602$	−9.00784	−0.367132
$603$	−6.26525	−0.255141
$604$	17.0438	0.693501
$605$	27.9332	1.13564
$606$	4.91027	0.199466
$607$	−7.64445	−0.310279	−0.155139	−	0.987893i	$-0.549583\pi$
$607$	−7.64445	−0.310279	−0.155139	+	0.987893i	$0.549583\pi$
$608$	34.5532	1.40132
$609$	−4.22617	−0.171253
$610$	−45.9317	−1.85972
$611$	−44.0112	−1.78050
$612$	17.2928	0.699021
$613$	36.7207	1.48313	0.741567	−	0.670878i	$-0.234083\pi$
$613$	36.7207	1.48313	0.741567	+	0.670878i	$0.234083\pi$
$614$	53.4798	2.15827
$615$	23.4267	0.944654
$616$	−40.7932	−1.64360
$617$	−3.33008	−0.134064	−0.0670319	−	0.997751i	$-0.521353\pi$
$617$	−3.33008	−0.134064	−0.0670319	+	0.997751i	$0.521353\pi$
$618$	−7.41063	−0.298099
$619$	14.7553	0.593065	0.296533	−	0.955023i	$-0.404170\pi$
$619$	14.7553	0.593065	0.296533	+	0.955023i	$0.404170\pi$
$620$	130.709	5.24940
$621$	2.24995	0.0902873
$622$	86.6312	3.47360
$623$	−8.33213	−0.333820
$624$	63.7079	2.55036
$625$	−29.9647	−1.19859
$626$	−84.2457	−3.36713
$627$	−9.04288	−0.361138
$628$	−130.614	−5.21206
$629$	29.5278	1.17735
$630$	−6.71033	−0.267346
$631$	45.3515	1.80541	0.902707	−	0.430255i	$-0.141577\pi$
$631$	45.3515	1.80541	0.902707	+	0.430255i	$0.141577\pi$
$632$	37.4044	1.48787
$633$	1.03674	0.0412069
$634$	26.2621	1.04300
$635$	47.9056	1.90108
$636$	−34.1792	−1.35529
$637$	−29.1079	−1.15330
$638$	54.2361	2.14723
$639$	−3.07574	−0.121674
$640$	−59.0634	−2.33469
$641$	−15.3135	−0.604846	−0.302423	−	0.953174i	$-0.597796\pi$
$641$	−15.3135	−0.604846	−0.302423	+	0.953174i	$0.597796\pi$
$642$	11.5213	0.454711
$643$	−44.1554	−1.74132	−0.870659	−	0.491888i	$-0.836307\pi$
$643$	−44.1554	−1.74132	−0.870659	+	0.491888i	$0.836307\pi$
$644$	11.6883	0.460584
$645$	8.54600	0.336498
$646$	17.0406	0.670454
$647$	16.0067	0.629288	0.314644	−	0.949210i	$-0.398115\pi$
$647$	16.0067	0.629288	0.314644	+	0.949210i	$0.398115\pi$
$648$	−8.80025	−0.345707
$649$	−17.7695	−0.697513
$650$	−17.7872	−0.697671
$651$	9.70848	0.380505
$652$	120.481	4.71838
$653$	−17.5025	−0.684926	−0.342463	−	0.939531i	$-0.611261\pi$
$653$	−17.5025	−0.684926	−0.342463	+	0.939531i	$0.611261\pi$
$654$	38.8850	1.52053
$655$	−52.3943	−2.04722
$656$	122.464	4.78143
$657$	6.39176	0.249366
$658$	24.2333	0.944713
$659$	−24.0376	−0.936374	−0.468187	−	0.883629i	$-0.655093\pi$
$659$	−24.0376	−0.936374	−0.468187	+	0.883629i	$0.655093\pi$
$660$	62.4090	2.42927
$661$	7.36766	0.286569	0.143284	−	0.989682i	$-0.454234\pi$
$661$	7.36766	0.286569	0.143284	+	0.989682i	$0.454234\pi$
$662$	0.786708	0.0305763
$663$	15.8643	0.616119
$664$	−65.3782	−2.53717
$665$	−4.79209	−0.185829
$666$	−24.2313	−0.938944
$667$	−9.63686	−0.373141
$668$	49.7742	1.92582
$669$	−17.1190	−0.661857
$670$	42.6087	1.64612
$671$	31.7293	1.22490
$672$	−17.7123	−0.683266
$673$	0.223300	0.00860759	0.00430380	−	0.999991i	$-0.498630\pi$
$673$	0.223300	0.00860759	0.00430380	+	0.999991i	$0.498630\pi$
$674$	63.2589	2.43664
$675$	1.36628	0.0525882
$676$	54.3834	2.09167
$677$	−21.2245	−0.815723	−0.407862	−	0.913044i	$-0.633725\pi$
$677$	−21.2245	−0.815723	−0.407862	+	0.913044i	$0.633725\pi$
$678$	54.0749	2.07673
$679$	−3.27700	−0.125760
$680$	−72.9304	−2.79675
$681$	−21.5512	−0.825842
$682$	−124.593	−4.77090
$683$	−20.4839	−0.783793	−0.391897	−	0.920009i	$-0.628181\pi$
$683$	−20.4839	−0.783793	−0.391897	+	0.920009i	$0.628181\pi$
$684$	−10.1343	−0.387494
$685$	20.5647	0.785737
$686$	34.6438	1.32271
$687$	−20.4774	−0.781260
$688$	44.6748	1.70321
$689$	−31.3557	−1.19456
$690$	−15.3014	−0.582516
$691$	−0.441431	−0.0167928	−0.00839642	−	0.999965i	$-0.502673\pi$
$691$	−0.441431	−0.0167928	−0.00839642	+	0.999965i	$0.502673\pi$
$692$	−108.486	−4.12401
$693$	4.63546	0.176086
$694$	5.05122	0.191742
$695$	−23.9108	−0.906987
$696$	37.6928	1.42874
$697$	30.4956	1.15510
$698$	−9.04546	−0.342376
$699$	12.9674	0.490472
$700$	7.09773	0.268269
$701$	29.9612	1.13162	0.565810	−	0.824536i	$-0.308564\pi$
$701$	29.9612	1.13162	0.565810	+	0.824536i	$0.308564\pi$
$702$	−13.0187	−0.491359
$703$	−17.3045	−0.652650
$704$	103.377	3.89618
$705$	−22.9909	−0.865886
$706$	57.0292	2.14632
$707$	−1.79751	−0.0676025
$708$	−19.9141	−0.748419
$709$	−45.5813	−1.71184	−0.855921	−	0.517107i	$-0.827009\pi$
$709$	−45.5813	−1.71184	−0.855921	+	0.517107i	$0.827009\pi$
$710$	20.9175	0.785019
$711$	−4.25037	−0.159401
$712$	74.3134	2.78501
$713$	22.1381	0.829078
$714$	−8.73517	−0.326905
$715$	57.2535	2.14116
$716$	52.9743	1.97974
$717$	−5.90384	−0.220483
$718$	−70.9514	−2.64788
$719$	25.4617	0.949561	0.474780	−	0.880104i	$-0.342528\pi$
$719$	25.4617	0.949561	0.474780	+	0.880104i	$0.342528\pi$
$720$	33.2801	1.24028
$721$	2.71283	0.101031
$722$	41.2253	1.53425
$723$	−20.5242	−0.763305
$724$	70.8000	2.63126
$725$	−5.85198	−0.217337
$726$	−29.8397	−1.10745
$727$	−8.41024	−0.311918	−0.155959	−	0.987764i	$-0.549847\pi$
$727$	−8.41024	−0.311918	−0.155959	+	0.987764i	$0.549847\pi$
$728$	−41.9402	−1.55441
$729$	1.00000	0.0370370
$730$	−43.4690	−1.60886
$731$	11.1248	0.411464
$732$	35.5589	1.31429
$733$	−12.6757	−0.468186	−0.234093	−	0.972214i	$-0.575212\pi$
$733$	−12.6757	−0.468186	−0.234093	+	0.972214i	$0.575212\pi$
$734$	−2.00198	−0.0738945
$735$	−15.2056	−0.560866
$736$	−40.3890	−1.48876
$737$	−29.4338	−1.08421
$738$	−25.0256	−0.921205
$739$	24.3378	0.895282	0.447641	−	0.894213i	$-0.352264\pi$
$739$	24.3378	0.895282	0.447641	+	0.894213i	$0.352264\pi$
$740$	119.426	4.39018
$741$	−9.29713	−0.341539
$742$	17.2650	0.633818
$743$	15.8101	0.580017	0.290009	−	0.957024i	$-0.406342\pi$
$743$	15.8101	0.580017	0.290009	+	0.957024i	$0.406342\pi$
$744$	−86.5890	−3.17451
$745$	0.746919	0.0273650
$746$	40.0180	1.46516
$747$	7.42913	0.271818
$748$	81.2408	2.97046
$749$	−4.21765	−0.154110
$750$	24.7122	0.902361
$751$	−0.0911361	−0.00332560	−0.00166280	−	0.999999i	$-0.500529\pi$
$751$	−0.0911361	−0.00332560	−0.00166280	+	0.999999i	$0.500529\pi$
$752$	−120.186	−4.38274
$753$	−20.6631	−0.753005
$754$	55.7610	2.03070
$755$	8.16794	0.297262
$756$	5.19493	0.188938
$757$	44.6198	1.62174	0.810868	−	0.585230i	$-0.198996\pi$
$757$	44.6198	1.62174	0.810868	+	0.585230i	$0.198996\pi$
$758$	89.5727	3.25343
$759$	10.5702	0.383672
$760$	42.7402	1.55035
$761$	−3.19542	−0.115834	−0.0579169	−	0.998321i	$-0.518446\pi$
$761$	−3.19542	−0.115834	−0.0579169	+	0.998321i	$0.518446\pi$
$762$	−51.1753	−1.85389
$763$	−14.2348	−0.515333
$764$	−35.4847	−1.28379
$765$	8.28730	0.299628
$766$	43.9930	1.58953
$767$	−18.2691	−0.659658
$768$	19.0851	0.688674
$769$	−21.3683	−0.770560	−0.385280	−	0.922800i	$-0.625895\pi$
$769$	−21.3683	−0.770560	−0.385280	+	0.922800i	$0.625895\pi$
$770$	−31.5248	−1.13607
$771$	−11.8017	−0.425027
$772$	133.992	4.82246
$773$	−14.7202	−0.529450	−0.264725	−	0.964324i	$-0.585281\pi$
$773$	−14.7202	−0.529450	−0.264725	+	0.964324i	$0.585281\pi$
$774$	−9.12928	−0.328145
$775$	13.4433	0.482899
$776$	29.2273	1.04920
$777$	8.87042	0.318225
$778$	−54.7252	−1.96199
$779$	−17.8717	−0.640320
$780$	64.1637	2.29743
$781$	−14.4497	−0.517050
$782$	−19.9186	−0.712289
$783$	−4.28315	−0.153067
$784$	−79.4881	−2.83886
$785$	−62.5945	−2.23410
$786$	55.9704	1.99640
$787$	37.0328	1.32008	0.660038	−	0.751232i	$-0.270540\pi$
$787$	37.0328	1.32008	0.660038	+	0.751232i	$0.270540\pi$
$788$	−0.693486	−0.0247044
$789$	−11.9836	−0.426629
$790$	28.9059	1.02843
$791$	−19.7953	−0.703841
$792$	−41.3432	−1.46907
$793$	32.6215	1.15842
$794$	−55.2090	−1.95929
$795$	−16.3798	−0.580932
$796$	83.8759	2.97290
$797$	−17.0091	−0.602494	−0.301247	−	0.953546i	$-0.597403\pi$
$797$	−17.0091	−0.602494	−0.301247	+	0.953546i	$0.597403\pi$
$798$	5.11916	0.181216
$799$	−29.9283	−1.05879
$800$	−24.5262	−0.867132
$801$	−8.44446	−0.298370
$802$	67.9076	2.39790
$803$	30.0282	1.05967
$804$	−32.9863	−1.16334
$805$	5.60144	0.197425
$806$	−128.096	−4.51198
$807$	−4.04054	−0.142234
$808$	16.0318	0.563998
$809$	3.29836	0.115964	0.0579821	−	0.998318i	$-0.481533\pi$
$809$	3.29836	0.115964	0.0579821	+	0.998318i	$0.481533\pi$
$810$	−6.80079	−0.238956
$811$	−1.48736	−0.0522282	−0.0261141	−	0.999659i	$-0.508313\pi$
$811$	−1.48736	−0.0522282	−0.0261141	+	0.999659i	$0.508313\pi$
$812$	−22.2506	−0.780844
$813$	−7.96901	−0.279485
$814$	−113.838	−3.99000
$815$	57.7384	2.02249
$816$	43.3224	1.51659
$817$	−6.51956	−0.228090
$818$	−19.3575	−0.676821
$819$	4.76579	0.166530
$820$	123.341	4.30724
$821$	0.285148	0.00995172	0.00497586	−	0.999988i	$-0.498416\pi$
$821$	0.285148	0.00995172	0.00497586	+	0.999988i	$0.498416\pi$
$822$	−21.9683	−0.766232
$823$	8.49084	0.295972	0.147986	−	0.988989i	$-0.452721\pi$
$823$	8.49084	0.295972	0.147986	+	0.988989i	$0.452721\pi$
$824$	−24.1955	−0.842889
$825$	6.41872	0.223471
$826$	10.0593	0.350007
$827$	18.3311	0.637434	0.318717	−	0.947850i	$-0.396748\pi$
$827$	18.3311	0.637434	0.318717	+	0.947850i	$0.396748\pi$
$828$	11.8459	0.411674
$829$	−25.8877	−0.899117	−0.449559	−	0.893251i	$-0.648419\pi$
$829$	−25.8877	−0.899117	−0.449559	+	0.893251i	$0.648419\pi$
$830$	−50.5240	−1.75371
$831$	−17.4651	−0.605859
$832$	106.284	3.68473
$833$	−19.7939	−0.685816
$834$	25.5427	0.884472
$835$	23.8535	0.825484
$836$	−47.6104	−1.64664
$837$	9.83937	0.340098
$838$	−74.0839	−2.55919
$839$	−12.5400	−0.432927	−0.216464	−	0.976291i	$-0.569452\pi$
$839$	−12.5400	−0.432927	−0.216464	+	0.976291i	$0.569452\pi$
$840$	−21.9090	−0.755932
$841$	−10.6547	−0.367402
$842$	86.9192	2.99543
$843$	6.28416	0.216438
$844$	5.45842	0.187887
$845$	26.0624	0.896573
$846$	24.5600	0.844391
$847$	10.9235	0.375335
$848$	−85.6265	−2.94043
$849$	3.10755	0.106651
$850$	−12.0956	−0.414875
$851$	20.2271	0.693375
$852$	−16.1937	−0.554786
$853$	30.2492	1.03571	0.517857	−	0.855467i	$-0.326730\pi$
$853$	30.2492	1.03571	0.517857	+	0.855467i	$0.326730\pi$
$854$	−17.9619	−0.614645
$855$	−4.85670	−0.166095
$856$	37.6168	1.28572
$857$	−13.2903	−0.453988	−0.226994	−	0.973896i	$-0.572890\pi$
$857$	−13.2903	−0.453988	−0.226994	+	0.973896i	$0.572890\pi$
$858$	−61.1612	−2.08801
$859$	−2.59101	−0.0884042	−0.0442021	−	0.999023i	$-0.514075\pi$
$859$	−2.59101	−0.0884042	−0.0442021	+	0.999023i	$0.514075\pi$
$860$	44.9944	1.53430
$861$	9.16118	0.312212
$862$	−61.0250	−2.07852
$863$	−42.8233	−1.45772	−0.728860	−	0.684663i	$-0.759950\pi$
$863$	−42.8233	−1.45772	−0.728860	+	0.684663i	$0.759950\pi$
$864$	−17.9511	−0.610708
$865$	−51.9901	−1.76772
$866$	−97.8551	−3.32525
$867$	−6.21201	−0.210971
$868$	51.1148	1.73495
$869$	−19.9680	−0.677369
$870$	29.1288	0.987558
$871$	−30.2614	−1.02537
$872$	126.958	4.29935
$873$	−3.32118	−0.112405
$874$	11.6731	0.394850
$875$	−9.04645	−0.305826
$876$	33.6524	1.13701
$877$	50.1001	1.69176	0.845881	−	0.533372i	$-0.179076\pi$
$877$	50.1001	1.69176	0.845881	+	0.533372i	$0.179076\pi$
$878$	31.0021	1.04627
$879$	13.1354	0.443047
$880$	156.348	5.27051
$881$	44.6013	1.50266	0.751328	−	0.659929i	$-0.229414\pi$
$881$	44.6013	1.50266	0.751328	+	0.659929i	$0.229414\pi$
$882$	16.2434	0.546943
$883$	23.7542	0.799394	0.399697	−	0.916647i	$-0.369115\pi$
$883$	23.7542	0.799394	0.399697	+	0.916647i	$0.369115\pi$
$884$	83.5250	2.80925
$885$	−9.54352	−0.320802
$886$	−33.7893	−1.13517
$887$	51.3484	1.72411	0.862055	−	0.506815i	$-0.169177\pi$
$887$	51.3484	1.72411	0.862055	+	0.506815i	$0.169177\pi$
$888$	−79.1144	−2.65490
$889$	18.7339	0.628314
$890$	57.4290	1.92503
$891$	4.69795	0.157387
$892$	−90.1307	−3.01780
$893$	17.5392	0.586928
$894$	−0.797898	−0.0266857
$895$	25.3871	0.848597
$896$	−23.0972	−0.771624
$897$	10.8673	0.362850
$898$	−27.3879	−0.913947
$899$	−42.1435	−1.40556
$900$	7.19342	0.239781
$901$	−21.3224	−0.710352
$902$	−117.569	−3.91462
$903$	3.34198	0.111214
$904$	176.553	5.87205
$905$	33.9298	1.12786
$906$	−8.72543	−0.289883
$907$	−16.3420	−0.542628	−0.271314	−	0.962491i	$-0.587458\pi$
$907$	−16.3420	−0.542628	−0.271314	+	0.962491i	$0.587458\pi$
$908$	−113.466	−3.76550
$909$	−1.82175	−0.0604236
$910$	−32.4112	−1.07442
$911$	−3.35260	−0.111076	−0.0555382	−	0.998457i	$-0.517687\pi$
$911$	−3.35260	−0.111076	−0.0555382	+	0.998457i	$0.517687\pi$
$912$	−25.3887	−0.840703
$913$	34.9017	1.15508
$914$	−11.2792	−0.373084
$915$	17.0410	0.563358
$916$	−107.813	−3.56223
$917$	−20.4892	−0.676614
$918$	−8.85293	−0.292190
$919$	5.11498	0.168728	0.0843639	−	0.996435i	$-0.473114\pi$
$919$	5.11498	0.168728	0.0843639	+	0.996435i	$0.473114\pi$
$920$	−49.9587	−1.64709
$921$	−19.8414	−0.653798
$922$	49.7585	1.63871
$923$	−14.8560	−0.488990
$924$	24.4055	0.802883
$925$	12.2829	0.403859
$926$	43.1988	1.41960
$927$	2.74940	0.0903023
$928$	76.8871	2.52394
$929$	59.2360	1.94347	0.971735	−	0.236075i	$-0.0758610\pi$
$929$	59.2360	1.94347	0.971735	+	0.236075i	$0.0758610\pi$
$930$	−66.9155	−2.19425
$931$	11.6000	0.380175
$932$	68.2729	2.23635
$933$	−32.1409	−1.05225
$934$	66.1643	2.16496
$935$	38.9334	1.27326
$936$	−42.5056	−1.38934
$937$	19.2512	0.628908	0.314454	−	0.949273i	$-0.398179\pi$
$937$	19.2512	0.628908	0.314454	+	0.949273i	$0.398179\pi$
$938$	16.6625	0.544048
$939$	31.2558	1.01999
$940$	−121.046	−3.94809
$941$	−29.4046	−0.958562	−0.479281	−	0.877661i	$-0.659103\pi$
$941$	−29.4046	−0.958562	−0.479281	+	0.877661i	$0.659103\pi$
$942$	66.8668	2.17864
$943$	20.8901	0.680275
$944$	−49.8894	−1.62376
$945$	2.48958	0.0809862
$946$	−42.8889	−1.39444
$947$	56.7573	1.84437	0.922183	−	0.386754i	$-0.126404\pi$
$947$	56.7573	1.84437	0.922183	+	0.386754i	$0.126404\pi$
$948$	−22.3781	−0.726806
$949$	30.8725	1.00216
$950$	7.08850	0.229981
$951$	−9.74344	−0.315953
$952$	−28.5200	−0.924339
$953$	41.4388	1.34234	0.671168	−	0.741306i	$-0.265793\pi$
$953$	41.4388	1.34234	0.671168	+	0.741306i	$0.265793\pi$
$954$	17.4978	0.566511
$955$	−17.0055	−0.550284
$956$	−31.0835	−1.00531
$957$	−20.1220	−0.650452
$958$	28.3388	0.915584
$959$	8.04199	0.259689
$960$	55.5213	1.79194
$961$	65.8132	2.12301
$962$	−117.038	−3.77347
$963$	−4.27451	−0.137744
$964$	−108.059	−3.48036
$965$	64.2133	2.06710
$966$	−5.98375	−0.192524
$967$	12.8070	0.411846	0.205923	−	0.978568i	$-0.433980\pi$
$967$	12.8070	0.411846	0.205923	+	0.978568i	$0.433980\pi$
$968$	−97.4254	−3.13137
$969$	−6.32220	−0.203098
$970$	22.5867	0.725215
$971$	−20.7336	−0.665373	−0.332686	−	0.943038i	$-0.607955\pi$
$971$	−20.7336	−0.665373	−0.332686	+	0.943038i	$0.607955\pi$
$972$	5.26496	0.168874
$973$	−9.35049	−0.299763
$974$	13.6382	0.436995
$975$	6.59919	0.211343
$976$	89.0830	2.85148
$977$	3.96467	0.126841	0.0634205	−	0.997987i	$-0.479799\pi$
$977$	3.96467	0.126841	0.0634205	+	0.997987i	$0.479799\pi$
$978$	−61.6791	−1.97228
$979$	−39.6717	−1.26791
$980$	−80.0568	−2.55732
$981$	−14.4267	−0.460608
$982$	−44.9823	−1.43544
$983$	34.0220	1.08513	0.542566	−	0.840013i	$-0.317453\pi$
$983$	34.0220	1.08513	0.542566	+	0.840013i	$0.317453\pi$
$984$	−81.7076	−2.60474
$985$	−0.332342	−0.0105893
$986$	37.9184	1.20757
$987$	−8.99076	−0.286179
$988$	−48.9491	−1.55728
$989$	7.62066	0.242323
$990$	−31.9498	−1.01543
$991$	40.0542	1.27236	0.636182	−	0.771539i	$-0.280513\pi$
$991$	40.0542	1.27236	0.636182	+	0.771539i	$0.280513\pi$
$992$	−176.627	−5.60792
$993$	−0.291875	−0.00926237
$994$	8.17994	0.259452
$995$	40.1962	1.27430
$996$	39.1141	1.23938
$997$	26.8036	0.848879	0.424440	−	0.905456i	$-0.360471\pi$
$997$	26.8036	0.848879	0.424440	+	0.905456i	$0.360471\pi$
$998$	54.5805	1.72772
$999$	8.99001	0.284431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.4	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.4	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69536 q^{2} +1.00000 q^{3} +5.26496 q^{4} +2.52315 q^{5} -2.69536 q^{6} +0.986697 q^{7} -8.80025 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.69536 q^{2} +1.00000 q^{3} +5.26496 q^{4} +2.52315 q^{5} -2.69536 q^{6} +0.986697 q^{7} -8.80025 q^{8} +1.00000 q^{9} -6.80079 q^{10} +4.69795 q^{11} +5.26496 q^{12} +4.83004 q^{13} -2.65950 q^{14} +2.52315 q^{15} +13.1899 q^{16} +3.28451 q^{17} -2.69536 q^{18} -1.92486 q^{19} +13.2843 q^{20} +0.986697 q^{21} -12.6627 q^{22} +2.24995 q^{23} -8.80025 q^{24} +1.36628 q^{25} -13.0187 q^{26} +1.00000 q^{27} +5.19493 q^{28} -4.28315 q^{29} -6.80079 q^{30} +9.83937 q^{31} -17.9511 q^{32} +4.69795 q^{33} -8.85293 q^{34} +2.48958 q^{35} +5.26496 q^{36} +8.99001 q^{37} +5.18818 q^{38} +4.83004 q^{39} -22.2044 q^{40} +9.28469 q^{41} -2.65950 q^{42} +3.38704 q^{43} +24.7345 q^{44} +2.52315 q^{45} -6.06442 q^{46} -9.11197 q^{47} +13.1899 q^{48} -6.02643 q^{49} -3.68262 q^{50} +3.28451 q^{51} +25.4300 q^{52} -6.49181 q^{53} -2.69536 q^{54} +11.8536 q^{55} -8.68319 q^{56} -1.92486 q^{57} +11.5446 q^{58} -3.78239 q^{59} +13.2843 q^{60} +6.75387 q^{61} -26.5206 q^{62} +0.986697 q^{63} +22.0048 q^{64} +12.1869 q^{65} -12.6627 q^{66} -6.26525 q^{67} +17.2928 q^{68} +2.24995 q^{69} -6.71033 q^{70} -3.07574 q^{71} -8.80025 q^{72} +6.39176 q^{73} -24.2313 q^{74} +1.36628 q^{75} -10.1343 q^{76} +4.63546 q^{77} -13.0187 q^{78} -4.25037 q^{79} +33.2801 q^{80} +1.00000 q^{81} -25.0256 q^{82} +7.42913 q^{83} +5.19493 q^{84} +8.28730 q^{85} -9.12928 q^{86} -4.28315 q^{87} -41.3432 q^{88} -8.44446 q^{89} -6.80079 q^{90} +4.76579 q^{91} +11.8459 q^{92} +9.83937 q^{93} +24.5600 q^{94} -4.85670 q^{95} -17.9511 q^{96} -3.32118 q^{97} +16.2434 q^{98} +4.69795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more