LMFDB - Embedded newform 9251.2.a.ba.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21557 q^{2} +2.66785 q^{3} +2.90873 q^{4} -0.0303185 q^{5} -5.91079 q^{6} +2.76647 q^{7} -2.01335 q^{8} +4.11741 q^{9} +O(q^{10})$	\(q-2.21557 q^{2} +2.66785 q^{3} +2.90873 q^{4} -0.0303185 q^{5} -5.91079 q^{6} +2.76647 q^{7} -2.01335 q^{8} +4.11741 q^{9} +0.0671726 q^{10} +1.00000 q^{11} +7.76005 q^{12} -2.93677 q^{13} -6.12929 q^{14} -0.0808851 q^{15} -1.35675 q^{16} -2.96861 q^{17} -9.12239 q^{18} -0.00846514 q^{19} -0.0881882 q^{20} +7.38051 q^{21} -2.21557 q^{22} -2.03589 q^{23} -5.37131 q^{24} -4.99908 q^{25} +6.50661 q^{26} +2.98108 q^{27} +8.04691 q^{28} +0.179206 q^{30} -8.46564 q^{31} +7.03267 q^{32} +2.66785 q^{33} +6.57714 q^{34} -0.0838751 q^{35} +11.9764 q^{36} +3.63138 q^{37} +0.0187551 q^{38} -7.83486 q^{39} +0.0610417 q^{40} -6.75803 q^{41} -16.3520 q^{42} -4.50264 q^{43} +2.90873 q^{44} -0.124834 q^{45} +4.51064 q^{46} +11.9271 q^{47} -3.61961 q^{48} +0.653346 q^{49} +11.0758 q^{50} -7.91979 q^{51} -8.54228 q^{52} -9.25328 q^{53} -6.60477 q^{54} -0.0303185 q^{55} -5.56987 q^{56} -0.0225837 q^{57} -4.55322 q^{59} -0.235273 q^{60} -2.45272 q^{61} +18.7562 q^{62} +11.3907 q^{63} -12.8678 q^{64} +0.0890385 q^{65} -5.91079 q^{66} +5.51636 q^{67} -8.63487 q^{68} -5.43143 q^{69} +0.185831 q^{70} +1.17364 q^{71} -8.28978 q^{72} +6.48168 q^{73} -8.04557 q^{74} -13.3368 q^{75} -0.0246228 q^{76} +2.76647 q^{77} +17.3586 q^{78} +15.8454 q^{79} +0.0411347 q^{80} -4.39917 q^{81} +14.9729 q^{82} -8.21870 q^{83} +21.4679 q^{84} +0.0900036 q^{85} +9.97588 q^{86} -2.01335 q^{88} -7.94101 q^{89} +0.276577 q^{90} -8.12449 q^{91} -5.92184 q^{92} -22.5850 q^{93} -26.4253 q^{94} +0.000256650 q^{95} +18.7621 q^{96} -13.7773 q^{97} -1.44753 q^{98} +4.11741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) $ 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * 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 $

$2$	−2.21557	−1.56664	−0.783321	−	0.621618i	$-0.786476\pi$
$2$	−2.21557	−1.56664	−0.783321	+	0.621618i	$0.786476\pi$
$3$	2.66785	1.54028	0.770141	−	0.637873i	$-0.220186\pi$
$3$	2.66785	1.54028	0.770141	+	0.637873i	$0.220186\pi$
$4$	2.90873	1.45436
$5$	−0.0303185	−0.0135588	−0.00677942	−	0.999977i	$-0.502158\pi$
$5$	−0.0303185	−0.0135588	−0.00677942	+	0.999977i	$0.502158\pi$
$6$	−5.91079	−2.41307
$7$	2.76647	1.04563	0.522813	−	0.852447i	$-0.324882\pi$
$7$	2.76647	1.04563	0.522813	+	0.852447i	$0.324882\pi$
$8$	−2.01335	−0.711826
$9$	4.11741	1.37247
$10$	0.0671726	0.0212418
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	7.76005	2.24013
$13$	−2.93677	−0.814514	−0.407257	−	0.913314i	$-0.633515\pi$
$13$	−2.93677	−0.814514	−0.407257	+	0.913314i	$0.633515\pi$
$14$	−6.12929	−1.63812
$15$	−0.0808851	−0.0208844
$16$	−1.35675	−0.339188
$17$	−2.96861	−0.719993	−0.359997	−	0.932954i	$-0.617222\pi$
$17$	−2.96861	−0.719993	−0.359997	+	0.932954i	$0.617222\pi$
$18$	−9.12239	−2.15017
$19$	−0.00846514	−0.00194204	−0.000971018	−	1.00000i	$-0.500309\pi$
$19$	−0.00846514	−0.00194204	−0.000971018		1.00000i	$0.500309\pi$
$20$	−0.0881882	−0.0197195
$21$	7.38051	1.61056
$22$	−2.21557	−0.472360
$23$	−2.03589	−0.424512	−0.212256	−	0.977214i	$-0.568081\pi$
$23$	−2.03589	−0.424512	−0.212256	+	0.977214i	$0.568081\pi$
$24$	−5.37131	−1.09641
$25$	−4.99908	−0.999816
$26$	6.50661	1.27605
$27$	2.98108	0.573709
$28$	8.04691	1.52072
$29$	0	0
$29$	0	0
$30$	0.179206	0.0327184
$31$	−8.46564	−1.52047	−0.760237	−	0.649646i	$-0.774917\pi$
$31$	−8.46564	−1.52047	−0.760237	+	0.649646i	$0.774917\pi$
$32$	7.03267	1.24321
$33$	2.66785	0.464413
$34$	6.57714	1.12797
$35$	−0.0838751	−0.0141775
$36$	11.9764	1.99607
$37$	3.63138	0.596996	0.298498	−	0.954410i	$-0.403514\pi$
$37$	3.63138	0.596996	0.298498	+	0.954410i	$0.403514\pi$
$38$	0.0187551	0.00304247
$39$	−7.83486	−1.25458
$40$	0.0610417	0.00965154
$41$	−6.75803	−1.05543	−0.527714	−	0.849422i	$-0.676951\pi$
$41$	−6.75803	−1.05543	−0.527714	+	0.849422i	$0.676951\pi$
$42$	−16.3520	−2.52317
$43$	−4.50264	−0.686645	−0.343323	−	0.939217i	$-0.611552\pi$
$43$	−4.50264	−0.686645	−0.343323	+	0.939217i	$0.611552\pi$
$44$	2.90873	0.438507
$45$	−0.124834	−0.0186091
$46$	4.51064	0.665058
$47$	11.9271	1.73975	0.869874	−	0.493275i	$-0.164200\pi$
$47$	11.9271	1.73975	0.869874	+	0.493275i	$0.164200\pi$
$48$	−3.61961	−0.522445
$49$	0.653346	0.0933351
$50$	11.0758	1.56635
$51$	−7.91979	−1.10899
$52$	−8.54228	−1.18460
$53$	−9.25328	−1.27104	−0.635518	−	0.772086i	$-0.719213\pi$
$53$	−9.25328	−1.27104	−0.635518	+	0.772086i	$0.719213\pi$
$54$	−6.60477	−0.898796
$55$	−0.0303185	−0.00408814
$56$	−5.56987	−0.744305
$57$	−0.0225837	−0.00299128
$58$	0	0
$59$	−4.55322	−0.592779	−0.296389	−	0.955067i	$-0.595783\pi$
$59$	−4.55322	−0.592779	−0.296389	+	0.955067i	$0.595783\pi$
$60$	−0.235273	−0.0303736
$61$	−2.45272	−0.314038	−0.157019	−	0.987596i	$-0.550188\pi$
$61$	−2.45272	−0.314038	−0.157019	+	0.987596i	$0.550188\pi$
$62$	18.7562	2.38204
$63$	11.3907	1.43509
$64$	−12.8678	−1.60848
$65$	0.0890385	0.0110439
$66$	−5.91079	−0.727568
$67$	5.51636	0.673930	0.336965	−	0.941517i	$-0.390600\pi$
$67$	5.51636	0.673930	0.336965	+	0.941517i	$0.390600\pi$
$68$	−8.63487	−1.04713
$69$	−5.43143	−0.653868
$70$	0.185831	0.0222110
$71$	1.17364	0.139286	0.0696428	−	0.997572i	$-0.477814\pi$
$71$	1.17364	0.139286	0.0696428	+	0.997572i	$0.477814\pi$
$72$	−8.28978	−0.976960
$73$	6.48168	0.758623	0.379312	−	0.925269i	$-0.376161\pi$
$73$	6.48168	0.758623	0.379312	+	0.925269i	$0.376161\pi$
$74$	−8.04557	−0.935278
$75$	−13.3368	−1.54000
$76$	−0.0246228	−0.00282443
$77$	2.76647	0.315268
$78$	17.3586	1.96548
$79$	15.8454	1.78275	0.891376	−	0.453264i	$-0.149741\pi$
$79$	15.8454	1.78275	0.891376	+	0.453264i	$0.149741\pi$
$80$	0.0411347	0.00459900
$81$	−4.39917	−0.488797
$82$	14.9729	1.65348
$83$	−8.21870	−0.902120	−0.451060	−	0.892494i	$-0.648954\pi$
$83$	−8.21870	−0.902120	−0.451060	+	0.892494i	$0.648954\pi$
$84$	21.4679	2.34234
$85$	0.0900036	0.00976227
$86$	9.97588	1.07573
$87$	0	0
$88$	−2.01335	−0.214624
$89$	−7.94101	−0.841745	−0.420873	−	0.907120i	$-0.638276\pi$
$89$	−7.94101	−0.841745	−0.420873	+	0.907120i	$0.638276\pi$
$90$	0.276577	0.0291538
$91$	−8.12449	−0.851678
$92$	−5.92184	−0.617395
$93$	−22.5850	−2.34196
$94$	−26.4253	−2.72556
$95$	0.000256650 0	2.63317e−5 0
$96$	18.7621	1.91490
$97$	−13.7773	−1.39887	−0.699435	−	0.714697i	$-0.746565\pi$
$97$	−13.7773	−1.39887	−0.699435	+	0.714697i	$0.746565\pi$
$98$	−1.44753	−0.146223
$99$	4.11741	0.413815
$100$	−14.5410	−1.45410
$101$	14.3761	1.43048	0.715239	−	0.698880i	$-0.246318\pi$
$101$	14.3761	1.43048	0.715239	+	0.698880i	$0.246318\pi$
$102$	17.5468	1.73739
$103$	−9.71486	−0.957234	−0.478617	−	0.878024i	$-0.658862\pi$
$103$	−9.71486	−0.957234	−0.478617	+	0.878024i	$0.658862\pi$
$104$	5.91275	0.579793
$105$	−0.223766	−0.0218373
$106$	20.5013	1.99126
$107$	−5.18098	−0.500864	−0.250432	−	0.968134i	$-0.580573\pi$
$107$	−5.18098	−0.500864	−0.250432	+	0.968134i	$0.580573\pi$
$108$	8.67115	0.834382
$109$	14.4763	1.38658	0.693288	−	0.720661i	$-0.256162\pi$
$109$	14.4763	1.38658	0.693288	+	0.720661i	$0.256162\pi$
$110$	0.0671726	0.00640465
$111$	9.68798	0.919542
$112$	−3.75341	−0.354664
$113$	−16.8906	−1.58893	−0.794466	−	0.607309i	$-0.792249\pi$
$113$	−16.8906	−1.58893	−0.794466	+	0.607309i	$0.792249\pi$
$114$	0.0500356	0.00468627
$115$	0.0617250	0.00575588
$116$	0	0
$117$	−12.0919	−1.11790
$118$	10.0880	0.928671
$119$	−8.21256	−0.752844
$120$	0.162850	0.0148661
$121$	1.00000	0.0909091
$122$	5.43415	0.491985
$123$	−18.0294	−1.62566
$124$	−24.6242	−2.21132
$125$	0.303157	0.0271152
$126$	−25.2368	−2.24827
$127$	−22.0401	−1.95575	−0.977873	−	0.209201i	$-0.932914\pi$
$127$	−22.0401	−1.95575	−0.977873	+	0.209201i	$0.932914\pi$
$128$	14.4442	1.27670
$129$	−12.0123	−1.05763
$130$	−0.197271	−0.0173018
$131$	3.43451	0.300074	0.150037	−	0.988680i	$-0.452061\pi$
$131$	3.43451	0.300074	0.150037	+	0.988680i	$0.452061\pi$
$132$	7.76005	0.675425
$133$	−0.0234185	−0.00203064
$134$	−12.2218	−1.05581
$135$	−0.0903817	−0.00777882
$136$	5.97684	0.512510
$137$	−9.74726	−0.832765	−0.416382	−	0.909190i	$-0.636702\pi$
$137$	−9.74726	−0.832765	−0.416382	+	0.909190i	$0.636702\pi$
$138$	12.0337	1.02438
$139$	−6.08833	−0.516406	−0.258203	−	0.966091i	$-0.583130\pi$
$139$	−6.08833	−0.516406	−0.258203	+	0.966091i	$0.583130\pi$
$140$	−0.243970	−0.0206192
$141$	31.8197	2.67970
$142$	−2.60028	−0.218211
$143$	−2.93677	−0.245585
$144$	−5.58631	−0.465525
$145$	0	0
$146$	−14.3606	−1.18849
$147$	1.74303	0.143762
$148$	10.5627	0.868249
$149$	3.75189	0.307366	0.153683	−	0.988120i	$-0.450886\pi$
$149$	3.75189	0.307366	0.153683	+	0.988120i	$0.450886\pi$
$150$	29.5485	2.41263
$151$	−19.6681	−1.60057	−0.800283	−	0.599623i	$-0.795317\pi$
$151$	−19.6681	−1.60057	−0.800283	+	0.599623i	$0.795317\pi$
$152$	0.0170433	0.00138239
$153$	−12.2230	−0.988169
$154$	−6.12929	−0.493912
$155$	0.256665	0.0206158
$156$	−22.7895	−1.82462
$157$	17.6082	1.40529	0.702644	−	0.711542i	$-0.252003\pi$
$157$	17.6082	1.40529	0.702644	+	0.711542i	$0.252003\pi$
$158$	−35.1066	−2.79293
$159$	−24.6863	−1.95775
$160$	−0.213220	−0.0168565
$161$	−5.63222	−0.443881
$162$	9.74665	0.765769
$163$	16.1005	1.26109	0.630545	−	0.776153i	$-0.282832\pi$
$163$	16.1005	1.26109	0.630545	+	0.776153i	$0.282832\pi$
$164$	−19.6573	−1.53498
$165$	−0.0808851	−0.00629689
$166$	18.2091	1.41330
$167$	11.0800	0.857395	0.428698	−	0.903448i	$-0.358973\pi$
$167$	11.0800	0.857395	0.428698	+	0.903448i	$0.358973\pi$
$168$	−14.8596	−1.14644
$169$	−4.37536	−0.336566
$170$	−0.199409	−0.0152940
$171$	−0.0348544	−0.00266539
$172$	−13.0969	−0.998633
$173$	−13.7539	−1.04569	−0.522846	−	0.852427i	$-0.675130\pi$
$173$	−13.7539	−1.04569	−0.522846	+	0.852427i	$0.675130\pi$
$174$	0	0
$175$	−13.8298	−1.04543
$176$	−1.35675	−0.102269
$177$	−12.1473	−0.913046
$178$	17.5938	1.31871
$179$	−14.2759	−1.06703	−0.533514	−	0.845791i	$-0.679129\pi$
$179$	−14.2759	−1.06703	−0.533514	+	0.845791i	$0.679129\pi$
$180$	−0.363107	−0.0270644
$181$	−25.1721	−1.87102	−0.935512	−	0.353295i	$-0.885061\pi$
$181$	−25.1721	−1.87102	−0.935512	+	0.353295i	$0.885061\pi$
$182$	18.0003	1.33427
$183$	−6.54347	−0.483708
$184$	4.09895	0.302179
$185$	−0.110098	−0.00809457
$186$	50.0386	3.66901
$187$	−2.96861	−0.217086
$188$	34.6927	2.53023
$189$	8.24706	0.599885
$190$	−0.000568625 0	−4.12524e−5 0
$191$	9.68243	0.700596	0.350298	−	0.936638i	$-0.386080\pi$
$191$	9.68243	0.700596	0.350298	+	0.936638i	$0.386080\pi$
$192$	−34.3294	−2.47751
$193$	7.11012	0.511798	0.255899	−	0.966704i	$-0.417629\pi$
$193$	7.11012	0.511798	0.255899	+	0.966704i	$0.417629\pi$
$194$	30.5244	2.19153
$195$	0.237541	0.0170107
$196$	1.90041	0.135743
$197$	17.0987	1.21823	0.609116	−	0.793081i	$-0.291524\pi$
$197$	17.0987	1.21823	0.609116	+	0.793081i	$0.291524\pi$
$198$	−9.12239	−0.648300
$199$	1.57365	0.111553	0.0557767	−	0.998443i	$-0.482237\pi$
$199$	1.57365	0.111553	0.0557767	+	0.998443i	$0.482237\pi$
$200$	10.0649	0.711696
$201$	14.7168	1.03804
$202$	−31.8512	−2.24105
$203$	0	0
$204$	−23.0365	−1.61288
$205$	0.204893	0.0143104
$206$	21.5239	1.49964
$207$	−8.38258	−0.582629
$208$	3.98447	0.276274
$209$	−0.00846514	−0.000585546 0
$210$	0.495768	0.0342112
$211$	−11.5897	−0.797865	−0.398932	−	0.916980i	$-0.630619\pi$
$211$	−11.5897	−0.797865	−0.398932	+	0.916980i	$0.630619\pi$
$212$	−26.9153	−1.84855
$213$	3.13110	0.214539
$214$	11.4788	0.784675
$215$	0.136513	0.00931011
$216$	−6.00195	−0.408381
$217$	−23.4199	−1.58985
$218$	−32.0731	−2.17227
$219$	17.2921	1.16849
$220$	−0.0881882	−0.00594565
$221$	8.71813	0.586445
$222$	−21.4643	−1.44059
$223$	−25.0198	−1.67545	−0.837725	−	0.546093i	$-0.816115\pi$
$223$	−25.0198	−1.67545	−0.837725	+	0.546093i	$0.816115\pi$
$224$	19.4557	1.29994
$225$	−20.5833	−1.37222
$226$	37.4222	2.48929
$227$	10.9662	0.727850	0.363925	−	0.931428i	$-0.381437\pi$
$227$	10.9662	0.727850	0.363925	+	0.931428i	$0.381437\pi$
$228$	−0.0656899	−0.00435042
$229$	4.81531	0.318205	0.159102	−	0.987262i	$-0.449140\pi$
$229$	4.81531	0.318205	0.159102	+	0.987262i	$0.449140\pi$
$230$	−0.136756	−0.00901740
$231$	7.38051	0.485602
$232$	0	0
$233$	−10.8130	−0.708380	−0.354190	−	0.935173i	$-0.615243\pi$
$233$	−10.8130	−0.708380	−0.354190	+	0.935173i	$0.615243\pi$
$234$	26.7904	1.75134
$235$	−0.361612	−0.0235889
$236$	−13.2441	−0.862116
$237$	42.2732	2.74594
$238$	18.1955	1.17944
$239$	21.0838	1.36380	0.681900	−	0.731446i	$-0.261154\pi$
$239$	21.0838	1.36380	0.681900	+	0.731446i	$0.261154\pi$
$240$	0.109741	0.00708375
$241$	−22.4730	−1.44761	−0.723806	−	0.690004i	$-0.757609\pi$
$241$	−22.4730	−1.44761	−0.723806	+	0.690004i	$0.757609\pi$
$242$	−2.21557	−0.142422
$243$	−20.6795	−1.32659
$244$	−7.13429	−0.456726
$245$	−0.0198084	−0.00126552
$246$	39.9453	2.54682
$247$	0.0248602	0.00158182
$248$	17.0443	1.08231
$249$	−21.9262	−1.38952
$250$	−0.671664	−0.0424797
$251$	20.8755	1.31765	0.658825	−	0.752296i	$-0.271054\pi$
$251$	20.8755	1.31765	0.658825	+	0.752296i	$0.271054\pi$
$252$	33.1324	2.08715
$253$	−2.03589	−0.127995
$254$	48.8313	3.06395
$255$	0.240116	0.0150366
$256$	−6.26637	−0.391648
$257$	28.0070	1.74703	0.873513	−	0.486800i	$-0.161836\pi$
$257$	28.0070	1.74703	0.873513	+	0.486800i	$0.161836\pi$
$258$	26.6141	1.65692
$259$	10.0461	0.624235
$260$	0.258989	0.0160618
$261$	0	0
$262$	−7.60937	−0.470109
$263$	−15.3563	−0.946909	−0.473455	−	0.880818i	$-0.656993\pi$
$263$	−15.3563	−0.946909	−0.473455	+	0.880818i	$0.656993\pi$
$264$	−5.37131	−0.330581
$265$	0.280545	0.0172338
$266$	0.0518853	0.00318129
$267$	−21.1854	−1.29653
$268$	16.0456	0.980140
$269$	1.31269	0.0800361	0.0400181	−	0.999199i	$-0.487258\pi$
$269$	1.31269	0.0800361	0.0400181	+	0.999199i	$0.487258\pi$
$270$	0.200247	0.0121866
$271$	16.2781	0.988823	0.494411	−	0.869228i	$-0.335384\pi$
$271$	16.2781	0.988823	0.494411	+	0.869228i	$0.335384\pi$
$272$	4.02767	0.244213
$273$	−21.6749	−1.31182
$274$	21.5957	1.30464
$275$	−4.99908	−0.301456
$276$	−15.7986	−0.950962
$277$	−7.68366	−0.461666	−0.230833	−	0.972993i	$-0.574145\pi$
$277$	−7.68366	−0.461666	−0.230833	+	0.972993i	$0.574145\pi$
$278$	13.4891	0.809022
$279$	−34.8565	−2.08680
$280$	0.168870	0.0100919
$281$	−9.58851	−0.572002	−0.286001	−	0.958229i	$-0.592326\pi$
$281$	−9.58851	−0.572002	−0.286001	+	0.958229i	$0.592326\pi$
$282$	−70.4986	−4.19813
$283$	−2.00855	−0.119396	−0.0596979	−	0.998216i	$-0.519014\pi$
$283$	−2.00855	−0.119396	−0.0596979	+	0.998216i	$0.519014\pi$
$284$	3.41381	0.202572
$285$	0.000684703 0	4.05583e−5 0
$286$	6.50661	0.384744
$287$	−18.6959	−1.10358
$288$	28.9564	1.70627
$289$	−8.18737	−0.481610
$290$	0	0
$291$	−36.7556	−2.15465
$292$	18.8535	1.10332
$293$	11.3620	0.663774	0.331887	−	0.943319i	$-0.392315\pi$
$293$	11.3620	0.663774	0.331887	+	0.943319i	$0.392315\pi$
$294$	−3.86179	−0.225224
$295$	0.138047	0.00803739
$296$	−7.31124	−0.424957
$297$	2.98108	0.172980
$298$	−8.31255	−0.481533
$299$	5.97894	0.345771
$300$	−38.7931	−2.23972
$301$	−12.4564	−0.717975
$302$	43.5759	2.50751
$303$	38.3533	2.20334
$304$	0.0114851	0.000658715 0
$305$	0.0743626	0.00425799
$306$	27.0808	1.54811
$307$	27.1073	1.54709	0.773547	−	0.633739i	$-0.218481\pi$
$307$	27.1073	1.54709	0.773547	+	0.633739i	$0.218481\pi$
$308$	8.04691	0.458515
$309$	−25.9178	−1.47441
$310$	−0.568658	−0.0322976
$311$	−2.26559	−0.128470	−0.0642350	−	0.997935i	$-0.520461\pi$
$311$	−2.26559	−0.128470	−0.0642350	+	0.997935i	$0.520461\pi$
$312$	15.7743	0.893045
$313$	−19.9594	−1.12817	−0.564085	−	0.825716i	$-0.690771\pi$
$313$	−19.9594	−1.12817	−0.564085	+	0.825716i	$0.690771\pi$
$314$	−39.0121	−2.20158
$315$	−0.345348	−0.0194582
$316$	46.0901	2.59277
$317$	20.9086	1.17434	0.587171	−	0.809463i	$-0.300242\pi$
$317$	20.9086	1.17434	0.587171	+	0.809463i	$0.300242\pi$
$318$	54.6942	3.06710
$319$	0	0
$320$	0.390133	0.0218091
$321$	−13.8221	−0.771473
$322$	12.4785	0.695402
$323$	0.0251297	0.00139825
$324$	−12.7960	−0.710888
$325$	14.6812	0.814365
$326$	−35.6717	−1.97567
$327$	38.6205	2.13572
$328$	13.6063	0.751281
$329$	32.9960	1.81913
$330$	0.179206	0.00986497
$331$	−8.25543	−0.453759	−0.226880	−	0.973923i	$-0.572852\pi$
$331$	−8.25543	−0.453759	−0.226880	+	0.973923i	$0.572852\pi$
$332$	−23.9060	−1.31201
$333$	14.9519	0.819359
$334$	−24.5484	−1.34323
$335$	−0.167248	−0.00913771
$336$	−10.0135	−0.546283
$337$	−15.6393	−0.851930	−0.425965	−	0.904740i	$-0.640065\pi$
$337$	−15.6393	−0.851930	−0.425965	+	0.904740i	$0.640065\pi$
$338$	9.69390	0.527279
$339$	−45.0615	−2.44740
$340$	0.261796	0.0141979
$341$	−8.46564	−0.458440
$342$	0.0772223	0.00417570
$343$	−17.5578	−0.948033
$344$	9.06538	0.488772
$345$	0.164673	0.00886569
$346$	30.4727	1.63822
$347$	24.8149	1.33213	0.666066	−	0.745893i	$-0.267977\pi$
$347$	24.8149	1.33213	0.666066	+	0.745893i	$0.267977\pi$
$348$	0	0
$349$	−10.3029	−0.551502	−0.275751	−	0.961229i	$-0.588927\pi$
$349$	−10.3029	−0.551502	−0.275751	+	0.961229i	$0.588927\pi$
$350$	30.6408	1.63782
$351$	−8.75475	−0.467294
$352$	7.03267	0.374843
$353$	18.0104	0.958595	0.479298	−	0.877652i	$-0.340891\pi$
$353$	18.0104	0.958595	0.479298	+	0.877652i	$0.340891\pi$
$354$	26.9131	1.43042
$355$	−0.0355830	−0.00188855
$356$	−23.0982	−1.22420
$357$	−21.9098	−1.15959
$358$	31.6291	1.67165
$359$	14.4949	0.765009	0.382505	−	0.923954i	$-0.375062\pi$
$359$	14.4949	0.765009	0.382505	+	0.923954i	$0.375062\pi$
$360$	0.251334	0.0132464
$361$	−18.9999	−0.999996
$362$	55.7703	2.93122
$363$	2.66785	0.140026
$364$	−23.6319	−1.23865
$365$	−0.196515	−0.0102860
$366$	14.4975	0.757796
$367$	−27.2063	−1.42016	−0.710078	−	0.704123i	$-0.751340\pi$
$367$	−27.2063	−1.42016	−0.710078	+	0.704123i	$0.751340\pi$
$368$	2.76219	0.143989
$369$	−27.8256	−1.44854
$370$	0.243929	0.0126813
$371$	−25.5989	−1.32903
$372$	−65.6937	−3.40606
$373$	−3.15392	−0.163304	−0.0816519	−	0.996661i	$-0.526020\pi$
$373$	−3.15392	−0.163304	−0.0816519	+	0.996661i	$0.526020\pi$
$374$	6.57714	0.340096
$375$	0.808776	0.0417650
$376$	−24.0134	−1.23840
$377$	0	0
$378$	−18.2719	−0.939805
$379$	−23.7889	−1.22196	−0.610978	−	0.791647i	$-0.709224\pi$
$379$	−23.7889	−1.22196	−0.610978	+	0.791647i	$0.709224\pi$
$380$	0.000746525 0	3.82959e−5 0
$381$	−58.7997	−3.01240
$382$	−21.4520	−1.09758
$383$	−28.9127	−1.47737	−0.738685	−	0.674050i	$-0.764553\pi$
$383$	−28.9127	−1.47737	−0.738685	+	0.674050i	$0.764553\pi$
$384$	38.5349	1.96648
$385$	−0.0838751	−0.00427467
$386$	−15.7529	−0.801803
$387$	−18.5392	−0.942400
$388$	−40.0743	−2.03447
$389$	8.64490	0.438314	0.219157	−	0.975690i	$-0.429669\pi$
$389$	8.64490	0.438314	0.219157	+	0.975690i	$0.429669\pi$
$390$	−0.526288	−0.0266496
$391$	6.04375	0.305645
$392$	−1.31541	−0.0664384
$393$	9.16274	0.462199
$394$	−37.8833	−1.90853
$395$	−0.480410	−0.0241720
$396$	11.9764	0.601838
$397$	−33.9319	−1.70299	−0.851496	−	0.524360i	$-0.824304\pi$
$397$	−33.9319	−1.70299	−0.851496	+	0.524360i	$0.824304\pi$
$398$	−3.48653	−0.174764
$399$	−0.0624771	−0.00312777
$400$	6.78252	0.339126
$401$	34.9361	1.74462	0.872312	−	0.488950i	$-0.162620\pi$
$401$	34.9361	1.74462	0.872312	+	0.488950i	$0.162620\pi$
$402$	−32.6060	−1.62624
$403$	24.8617	1.23845
$404$	41.8163	2.08044
$405$	0.133376	0.00662751
$406$	0	0
$407$	3.63138	0.180001
$408$	15.9453	0.789410
$409$	−7.31308	−0.361608	−0.180804	−	0.983519i	$-0.557870\pi$
$409$	−7.31308	−0.361608	−0.180804	+	0.983519i	$0.557870\pi$
$410$	−0.453954	−0.0224192
$411$	−26.0042	−1.28269
$412$	−28.2579	−1.39217
$413$	−12.5963	−0.619825
$414$	18.5721	0.912771
$415$	0.249178	0.0122317
$416$	−20.6534	−1.01261
$417$	−16.2427	−0.795411
$418$	0.0187551	0.000917340 0
$419$	12.3712	0.604371	0.302186	−	0.953249i	$-0.402284\pi$
$419$	12.3712	0.604371	0.302186	+	0.953249i	$0.402284\pi$
$420$	−0.650875	−0.0317594
$421$	3.04082	0.148201	0.0741003	−	0.997251i	$-0.476392\pi$
$421$	3.04082	0.148201	0.0741003	+	0.997251i	$0.476392\pi$
$422$	25.6776	1.24997
$423$	49.1088	2.38775
$424$	18.6301	0.904757
$425$	14.8403	0.719861
$426$	−6.93715	−0.336106
$427$	−6.78536	−0.328367
$428$	−15.0701	−0.728439
$429$	−7.83486	−0.378271
$430$	−0.302454	−0.0145856
$431$	−29.6186	−1.42668	−0.713338	−	0.700820i	$-0.752818\pi$
$431$	−29.6186	−1.42668	−0.713338	+	0.700820i	$0.752818\pi$
$432$	−4.04458	−0.194595
$433$	21.2596	1.02167	0.510834	−	0.859679i	$-0.329337\pi$
$433$	21.2596	1.02167	0.510834	+	0.859679i	$0.329337\pi$
$434$	51.8883	2.49072
$435$	0	0
$436$	42.1075	2.01659
$437$	0.0172341	0.000824417 0
$438$	−38.3119	−1.83061
$439$	13.9141	0.664084	0.332042	−	0.943265i	$-0.392262\pi$
$439$	13.9141	0.664084	0.332042	+	0.943265i	$0.392262\pi$
$440$	0.0610417	0.00291005
$441$	2.69009	0.128100
$442$	−19.3156	−0.918748
$443$	−5.45297	−0.259078	−0.129539	−	0.991574i	$-0.541350\pi$
$443$	−5.45297	−0.259078	−0.129539	+	0.991574i	$0.541350\pi$
$444$	28.1797	1.33735
$445$	0.240759	0.0114131
$446$	55.4330	2.62483
$447$	10.0095	0.473431
$448$	−35.5985	−1.68187
$449$	10.5672	0.498697	0.249348	−	0.968414i	$-0.419784\pi$
$449$	10.5672	0.498697	0.249348	+	0.968414i	$0.419784\pi$
$450$	45.6036	2.14977
$451$	−6.75803	−0.318223
$452$	−49.1301	−2.31089
$453$	−52.4714	−2.46532
$454$	−24.2962	−1.14028
$455$	0.246322	0.0115478
$456$	0.0454689	0.00212927
$457$	−3.77120	−0.176409	−0.0882046	−	0.996102i	$-0.528113\pi$
$457$	−3.77120	−0.176409	−0.0882046	+	0.996102i	$0.528113\pi$
$458$	−10.6686	−0.498512
$459$	−8.84965	−0.413066
$460$	0.179541	0.00837115
$461$	22.6499	1.05491	0.527455	−	0.849583i	$-0.323146\pi$
$461$	22.6499	1.05491	0.527455	+	0.849583i	$0.323146\pi$
$462$	−16.3520	−0.760764
$463$	−20.4484	−0.950317	−0.475158	−	0.879900i	$-0.657609\pi$
$463$	−20.4484	−0.950317	−0.475158	+	0.879900i	$0.657609\pi$
$464$	0	0
$465$	0.684744	0.0317542
$466$	23.9568	1.10978
$467$	−5.44385	−0.251911	−0.125956	−	0.992036i	$-0.540200\pi$
$467$	−5.44385	−0.251911	−0.125956	+	0.992036i	$0.540200\pi$
$468$	−35.1721	−1.62583
$469$	15.2608	0.704679
$470$	0.801174	0.0369554
$471$	46.9760	2.16454
$472$	9.16722	0.421955
$473$	−4.50264	−0.207031
$474$	−93.6591	−4.30191
$475$	0.0423179	0.00194168
$476$	−23.8881	−1.09491
$477$	−38.0996	−1.74446
$478$	−46.7126	−2.13658
$479$	−1.37366	−0.0627640	−0.0313820	−	0.999507i	$-0.509991\pi$
$479$	−1.37366	−0.0627640	−0.0313820	+	0.999507i	$0.509991\pi$
$480$	−0.568838	−0.0259638
$481$	−10.6645	−0.486262
$482$	49.7903	2.26789
$483$	−15.0259	−0.683702
$484$	2.90873	0.132215
$485$	0.417706	0.0189670
$486$	45.8169	2.07830
$487$	−10.5262	−0.476989	−0.238494	−	0.971144i	$-0.576654\pi$
$487$	−10.5262	−0.476989	−0.238494	+	0.971144i	$0.576654\pi$
$488$	4.93818	0.223541
$489$	42.9537	1.94243
$490$	0.0438869	0.00198261
$491$	14.5072	0.654699	0.327350	−	0.944903i	$-0.393844\pi$
$491$	14.5072	0.654699	0.327350	+	0.944903i	$0.393844\pi$
$492$	−52.4427	−2.36430
$493$	0	0
$494$	−0.0550794	−0.00247814
$495$	−0.124834	−0.00561085
$496$	11.4858	0.515726
$497$	3.24684	0.145641
$498$	48.5790	2.17688
$499$	22.6885	1.01568	0.507838	−	0.861453i	$-0.330445\pi$
$499$	22.6885	1.01568	0.507838	+	0.861453i	$0.330445\pi$
$500$	0.881801	0.0394354
$501$	29.5597	1.32063
$502$	−46.2510	−2.06429
$503$	21.2282	0.946521	0.473260	−	0.880923i	$-0.343077\pi$
$503$	21.2282	0.946521	0.473260	+	0.880923i	$0.343077\pi$
$504$	−22.9334	−1.02154
$505$	−0.435862	−0.0193956
$506$	4.51064	0.200522
$507$	−11.6728	−0.518407
$508$	−64.1088	−2.84437
$509$	−44.0902	−1.95426	−0.977132	−	0.212634i	$-0.931796\pi$
$509$	−44.0902	−1.95426	−0.977132	+	0.212634i	$0.931796\pi$
$510$	−0.531993	−0.0235570
$511$	17.9314	0.793237
$512$	−15.0048	−0.663126
$513$	−0.0252352	−0.00111416
$514$	−62.0513	−2.73696
$515$	0.294540	0.0129790
$516$	−34.9407	−1.53818
$517$	11.9271	0.524553
$518$	−22.2578	−0.977952
$519$	−36.6934	−1.61066
$520$	−0.179266	−0.00786131
$521$	−9.15415	−0.401051	−0.200525	−	0.979689i	$-0.564265\pi$
$521$	−9.15415	−0.401051	−0.200525	+	0.979689i	$0.564265\pi$
$522$	0	0
$523$	35.5781	1.55572	0.777861	−	0.628436i	$-0.216305\pi$
$523$	35.5781	1.55572	0.777861	+	0.628436i	$0.216305\pi$
$524$	9.99005	0.436417
$525$	−36.8958	−1.61026
$526$	34.0229	1.48347
$527$	25.1312	1.09473
$528$	−3.61961	−0.157523
$529$	−18.8552	−0.819790
$530$	−0.621567	−0.0269991
$531$	−18.7475	−0.813571
$532$	−0.0681182	−0.00295330
$533$	19.8468	0.859661
$534$	46.9376	2.03119
$535$	0.157079	0.00679114
$536$	−11.1064	−0.479721
$537$	−38.0858	−1.64352
$538$	−2.90835	−0.125388
$539$	0.653346	0.0281416
$540$	−0.262896	−0.0113132
$541$	6.79583	0.292175	0.146088	−	0.989272i	$-0.453332\pi$
$541$	6.79583	0.292175	0.146088	+	0.989272i	$0.453332\pi$
$542$	−36.0651	−1.54913
$543$	−67.1552	−2.88191
$544$	−20.8772	−0.895104
$545$	−0.438898	−0.0188003
$546$	48.0221	2.05516
$547$	−3.75643	−0.160613	−0.0803066	−	0.996770i	$-0.525590\pi$
$547$	−3.75643	−0.160613	−0.0803066	+	0.996770i	$0.525590\pi$
$548$	−28.3521	−1.21114
$549$	−10.0988	−0.431008
$550$	11.0758	0.472273
$551$	0	0
$552$	10.9354	0.465440
$553$	43.8359	1.86409
$554$	17.0236	0.723265
$555$	−0.293725	−0.0124679
$556$	−17.7093	−0.751042
$557$	3.76382	0.159478	0.0797392	−	0.996816i	$-0.474591\pi$
$557$	3.76382	0.159478	0.0797392	+	0.996816i	$0.474591\pi$
$558$	77.2268	3.26927
$559$	13.2232	0.559283
$560$	0.113798	0.00480883
$561$	−7.91979	−0.334374
$562$	21.2440	0.896123
$563$	−7.23739	−0.305020	−0.152510	−	0.988302i	$-0.548736\pi$
$563$	−7.23739	−0.305020	−0.152510	+	0.988302i	$0.548736\pi$
$564$	92.5549	3.89726
$565$	0.512096	0.0215441
$566$	4.45007	0.187050
$567$	−12.1702	−0.511099
$568$	−2.36295	−0.0991472
$569$	44.8976	1.88220	0.941102	−	0.338123i	$-0.109792\pi$
$569$	44.8976	1.88220	0.941102	+	0.338123i	$0.109792\pi$
$570$	−0.00151700	−6.35403e−5 0
$571$	37.8995	1.58604	0.793022	−	0.609192i	$-0.208506\pi$
$571$	37.8995	1.58604	0.793022	+	0.609192i	$0.208506\pi$
$572$	−8.54228	−0.357171
$573$	25.8312	1.07912
$574$	41.4220	1.72892
$575$	10.1776	0.424434
$576$	−52.9822	−2.20759
$577$	21.2375	0.884129	0.442064	−	0.896983i	$-0.354246\pi$
$577$	21.2375	0.884129	0.442064	+	0.896983i	$0.354246\pi$
$578$	18.1397	0.754510
$579$	18.9687	0.788313
$580$	0	0
$581$	−22.7368	−0.943280
$582$	81.4345	3.37557
$583$	−9.25328	−0.383232
$584$	−13.0499	−0.540008
$585$	0.366608	0.0151574
$586$	−25.1732	−1.03990
$587$	−18.8832	−0.779393	−0.389696	−	0.920943i	$-0.627420\pi$
$587$	−18.8832	−0.779393	−0.389696	+	0.920943i	$0.627420\pi$
$588$	5.06999	0.209083
$589$	0.0716628	0.00295281
$590$	−0.305851	−0.0125917
$591$	45.6167	1.87642
$592$	−4.92689	−0.202494
$593$	30.3319	1.24558	0.622791	−	0.782389i	$-0.285999\pi$
$593$	30.3319	1.24558	0.622791	+	0.782389i	$0.285999\pi$
$594$	−6.60477	−0.270997
$595$	0.248992	0.0102077
$596$	10.9132	0.447023
$597$	4.19827	0.171824
$598$	−13.2467	−0.541699
$599$	22.9082	0.936004	0.468002	−	0.883727i	$-0.344974\pi$
$599$	22.9082	0.936004	0.468002	+	0.883727i	$0.344974\pi$
$600$	26.8516	1.09621
$601$	−35.3358	−1.44138	−0.720688	−	0.693260i	$-0.756174\pi$
$601$	−35.3358	−1.44138	−0.720688	+	0.693260i	$0.756174\pi$
$602$	27.5980	1.12481
$603$	22.7131	0.924949
$604$	−57.2091	−2.32781
$605$	−0.0303185	−0.00123262
$606$	−84.9743	−3.45184
$607$	−37.8672	−1.53698	−0.768491	−	0.639861i	$-0.778992\pi$
$607$	−37.8672	−1.53698	−0.768491	+	0.639861i	$0.778992\pi$
$608$	−0.0595325	−0.00241436
$609$	0	0
$610$	−0.164755	−0.00667075
$611$	−35.0272	−1.41705
$612$	−35.5533	−1.43716
$613$	27.2682	1.10135	0.550677	−	0.834719i	$-0.314370\pi$
$613$	27.2682	1.10135	0.550677	+	0.834719i	$0.314370\pi$
$614$	−60.0579	−2.42374
$615$	0.546624	0.0220420
$616$	−5.56987	−0.224416
$617$	11.4370	0.460437	0.230218	−	0.973139i	$-0.426056\pi$
$617$	11.4370	0.460437	0.230218	+	0.973139i	$0.426056\pi$
$618$	57.4225	2.30987
$619$	32.6083	1.31064	0.655320	−	0.755351i	$-0.272534\pi$
$619$	32.6083	1.31064	0.655320	+	0.755351i	$0.272534\pi$
$620$	0.746570	0.0299830
$621$	−6.06914	−0.243546
$622$	5.01957	0.201267
$623$	−21.9685	−0.880151
$624$	10.6300	0.425539
$625$	24.9862	0.999449
$626$	44.2213	1.76744
$627$	−0.0225837	−0.000901906 0
$628$	51.2175	2.04380
$629$	−10.7802	−0.429833
$630$	0.765141	0.0304840
$631$	41.1477	1.63806	0.819032	−	0.573748i	$-0.194511\pi$
$631$	41.1477	1.63806	0.819032	+	0.573748i	$0.194511\pi$
$632$	−31.9024	−1.26901
$633$	−30.9194	−1.22894
$634$	−46.3243	−1.83977
$635$	0.668223	0.0265176
$636$	−71.8059	−2.84729
$637$	−1.91873	−0.0760228
$638$	0	0
$639$	4.83236	0.191165
$640$	−0.437926	−0.0173105
$641$	−20.4742	−0.808683	−0.404342	−	0.914608i	$-0.632499\pi$
$641$	−20.4742	−0.808683	−0.404342	+	0.914608i	$0.632499\pi$
$642$	30.6237	1.20862
$643$	35.2092	1.38852	0.694259	−	0.719726i	$-0.255732\pi$
$643$	35.2092	1.38852	0.694259	+	0.719726i	$0.255732\pi$
$644$	−16.3826	−0.645564
$645$	0.364196	0.0143402
$646$	−0.0556764	−0.00219056
$647$	17.0854	0.671696	0.335848	−	0.941916i	$-0.390977\pi$
$647$	17.0854	0.671696	0.335848	+	0.941916i	$0.390977\pi$
$648$	8.85706	0.347938
$649$	−4.55322	−0.178729
$650$	−32.5271	−1.27582
$651$	−62.4808	−2.44881
$652$	46.8320	1.83408
$653$	−17.8368	−0.698008	−0.349004	−	0.937121i	$-0.613480\pi$
$653$	−17.8368	−0.698008	−0.349004	+	0.937121i	$0.613480\pi$
$654$	−85.5662	−3.34590
$655$	−0.104129	−0.00406866
$656$	9.16898	0.357988
$657$	26.6877	1.04119
$658$	−73.1047	−2.84992
$659$	0.783162	0.0305077	0.0152538	−	0.999884i	$-0.495144\pi$
$659$	0.783162	0.0305077	0.0152538	+	0.999884i	$0.495144\pi$
$660$	−0.235273	−0.00915798
$661$	−8.43300	−0.328006	−0.164003	−	0.986460i	$-0.552441\pi$
$661$	−8.43300	−0.328006	−0.164003	+	0.986460i	$0.552441\pi$
$662$	18.2904	0.710878
$663$	23.2586	0.903290
$664$	16.5471	0.642153
$665$	0.000710014 0	2.75332e−5 0
$666$	−33.1269	−1.28364
$667$	0	0
$668$	32.2287	1.24697
$669$	−66.7490	−2.58067
$670$	0.370548	0.0143155
$671$	−2.45272	−0.0946861
$672$	51.9047	2.00227
$673$	20.2296	0.779794	0.389897	−	0.920859i	$-0.372511\pi$
$673$	20.2296	0.779794	0.389897	+	0.920859i	$0.372511\pi$
$674$	34.6500	1.33467
$675$	−14.9026	−0.573603
$676$	−12.7267	−0.489490
$677$	34.0656	1.30925	0.654623	−	0.755955i	$-0.272827\pi$
$677$	34.0656	1.30925	0.654623	+	0.755955i	$0.272827\pi$
$678$	99.8366	3.83420
$679$	−38.1144	−1.46269
$680$	−0.181209	−0.00694904
$681$	29.2560	1.12109
$682$	18.7562	0.718211
$683$	3.06771	0.117383	0.0586913	−	0.998276i	$-0.481307\pi$
$683$	3.06771	0.117383	0.0586913	+	0.998276i	$0.481307\pi$
$684$	−0.101382	−0.00387644
$685$	0.295522	0.0112913
$686$	38.9005	1.48523
$687$	12.8465	0.490125
$688$	6.10896	0.232902
$689$	27.1748	1.03528
$690$	−0.364843	−0.0138893
$691$	−13.6648	−0.519834	−0.259917	−	0.965631i	$-0.583695\pi$
$691$	−13.6648	−0.519834	−0.259917	+	0.965631i	$0.583695\pi$
$692$	−40.0065	−1.52082
$693$	11.3907	0.432696
$694$	−54.9789	−2.08697
$695$	0.184589	0.00700186
$696$	0	0
$697$	20.0619	0.759900
$698$	22.8268	0.864006
$699$	−28.8473	−1.09111
$700$	−40.2271	−1.52044
$701$	18.7324	0.707511	0.353756	−	0.935338i	$-0.384904\pi$
$701$	18.7324	0.707511	0.353756	+	0.935338i	$0.384904\pi$
$702$	19.3967	0.732082
$703$	−0.0307402	−0.00115939
$704$	−12.8678	−0.484975
$705$	−0.964725	−0.0363336
$706$	−39.9031	−1.50177
$707$	39.7711	1.49575
$708$	−35.3332	−1.32790
$709$	−6.47528	−0.243184	−0.121592	−	0.992580i	$-0.538800\pi$
$709$	−6.47528	−0.243184	−0.121592	+	0.992580i	$0.538800\pi$
$710$	0.0788365	0.00295868
$711$	65.2422	2.44677
$712$	15.9880	0.599176
$713$	17.2351	0.645459
$714$	48.5427	1.81666
$715$	0.0890385	0.00332985
$716$	−41.5246	−1.55185
$717$	56.2484	2.10064
$718$	−32.1143	−1.19849
$719$	16.0143	0.597233	0.298616	−	0.954373i	$-0.403475\pi$
$719$	16.0143	0.597233	0.298616	+	0.954373i	$0.403475\pi$
$720$	0.169368	0.00631198
$721$	−26.8759	−1.00091
$722$	42.0956	1.56664
$723$	−59.9545	−2.22973
$724$	−73.2187	−2.72115
$725$	0	0
$726$	−5.91079	−0.219370
$727$	4.97936	0.184674	0.0923372	−	0.995728i	$-0.470566\pi$
$727$	4.97936	0.184674	0.0923372	+	0.995728i	$0.470566\pi$
$728$	16.3574	0.606247
$729$	−41.9724	−1.55453
$730$	0.435391	0.0161145
$731$	13.3666	0.494380
$732$	−19.0332	−0.703487
$733$	−40.3472	−1.49026	−0.745128	−	0.666921i	$-0.767612\pi$
$733$	−40.3472	−1.49026	−0.745128	+	0.666921i	$0.767612\pi$
$734$	60.2773	2.22487
$735$	−0.0528459	−0.00194925
$736$	−14.3177	−0.527758
$737$	5.51636	0.203198
$738$	61.6494	2.26935
$739$	−26.6762	−0.981301	−0.490650	−	0.871356i	$-0.663241\pi$
$739$	−26.6762	−0.981301	−0.490650	+	0.871356i	$0.663241\pi$
$740$	−0.320245	−0.0117724
$741$	0.0663232	0.00243644
$742$	56.7161	2.08211
$743$	6.29958	0.231109	0.115555	−	0.993301i	$-0.463135\pi$
$743$	6.29958	0.231109	0.115555	+	0.993301i	$0.463135\pi$
$744$	45.4715	1.66707
$745$	−0.113751	−0.00416753
$746$	6.98771	0.255838
$747$	−33.8398	−1.23813
$748$	−8.63487	−0.315722
$749$	−14.3330	−0.523717
$750$	−1.79190	−0.0654308
$751$	−12.2284	−0.446220	−0.223110	−	0.974793i	$-0.571621\pi$
$751$	−12.2284	−0.446220	−0.223110	+	0.974793i	$0.571621\pi$
$752$	−16.1821	−0.590102
$753$	55.6927	2.02955
$754$	0	0
$755$	0.596306	0.0217018
$756$	23.9885	0.872452
$757$	25.1248	0.913175	0.456587	−	0.889679i	$-0.349072\pi$
$757$	25.1248	0.913175	0.456587	+	0.889679i	$0.349072\pi$
$758$	52.7060	1.91437
$759$	−5.43143	−0.197149
$760$	−0.000516726 0	−1.87436e−5 0
$761$	43.7418	1.58564	0.792819	−	0.609457i	$-0.208612\pi$
$761$	43.7418	1.58564	0.792819	+	0.609457i	$0.208612\pi$
$762$	130.275	4.71935
$763$	40.0481	1.44984
$764$	28.1636	1.01892
$765$	0.370582	0.0133984
$766$	64.0580	2.31451
$767$	13.3718	0.482827
$768$	−16.7177	−0.603249
$769$	33.3683	1.20329	0.601645	−	0.798763i	$-0.294512\pi$
$769$	33.3683	1.20329	0.601645	+	0.798763i	$0.294512\pi$
$770$	0.185831	0.00669687
$771$	74.7183	2.69091
$772$	20.6814	0.744340
$773$	43.3898	1.56062	0.780311	−	0.625392i	$-0.215061\pi$
$773$	43.3898	1.56062	0.780311	+	0.625392i	$0.215061\pi$
$774$	41.0748	1.47640
$775$	42.3204	1.52019
$776$	27.7384	0.995752
$777$	26.8015	0.961498
$778$	−19.1533	−0.686680
$779$	0.0572077	0.00204968
$780$	0.690943	0.0247397
$781$	1.17364	0.0419962
$782$	−13.3903	−0.478837
$783$	0	0
$784$	−0.886428	−0.0316582
$785$	−0.533854	−0.0190541
$786$	−20.3006	−0.724100
$787$	−4.95565	−0.176650	−0.0883250	−	0.996092i	$-0.528151\pi$
$787$	−4.95565	−0.176650	−0.0883250	+	0.996092i	$0.528151\pi$
$788$	49.7355	1.77175
$789$	−40.9682	−1.45851
$790$	1.06438	0.0378689
$791$	−46.7272	−1.66143
$792$	−8.28978	−0.294565
$793$	7.20307	0.255789
$794$	75.1783	2.66798
$795$	0.748452	0.0265449
$796$	4.57733	0.162239
$797$	−18.3240	−0.649071	−0.324535	−	0.945874i	$-0.605208\pi$
$797$	−18.3240	−0.649071	−0.324535	+	0.945874i	$0.605208\pi$
$798$	0.138422	0.00490009
$799$	−35.4069	−1.25261
$800$	−35.1569	−1.24298
$801$	−32.6964	−1.15527
$802$	−77.4031	−2.73320
$803$	6.48168	0.228734
$804$	42.8072	1.50969
$805$	0.170760	0.00601851
$806$	−55.0826	−1.94020
$807$	3.50206	0.123278
$808$	−28.9442	−1.01825
$809$	−14.1728	−0.498290	−0.249145	−	0.968466i	$-0.580150\pi$
$809$	−14.1728	−0.498290	−0.249145	+	0.968466i	$0.580150\pi$
$810$	−0.295503	−0.0103829
$811$	−34.2009	−1.20096	−0.600479	−	0.799641i	$-0.705023\pi$
$811$	−34.2009	−1.20096	−0.600479	+	0.799641i	$0.705023\pi$
$812$	0	0
$813$	43.4274	1.52307
$814$	−8.04557	−0.281997
$815$	−0.488143	−0.0170989
$816$	10.7452	0.376157
$817$	0.0381154	0.00133349
$818$	16.2026	0.566511
$819$	−33.4518	−1.16890
$820$	0.595979	0.0208125
$821$	−50.3544	−1.75738	−0.878691	−	0.477391i	$-0.841582\pi$
$821$	−50.3544	−1.75738	−0.878691	+	0.477391i	$0.841582\pi$
$822$	57.6140	2.00952
$823$	−47.9005	−1.66971	−0.834854	−	0.550472i	$-0.814448\pi$
$823$	−47.9005	−1.66971	−0.834854	+	0.550472i	$0.814448\pi$
$824$	19.5594	0.681384
$825$	−13.3368	−0.464327
$826$	27.9080	0.971043
$827$	−51.7450	−1.79935	−0.899674	−	0.436562i	$-0.856196\pi$
$827$	−51.7450	−1.79935	−0.899674	+	0.436562i	$0.856196\pi$
$828$	−24.3827	−0.847356
$829$	−23.3442	−0.810779	−0.405389	−	0.914144i	$-0.632864\pi$
$829$	−23.3442	−0.810779	−0.405389	+	0.914144i	$0.632864\pi$
$830$	−0.552071	−0.0191627
$831$	−20.4988	−0.711096
$832$	37.7899	1.31013
$833$	−1.93953	−0.0672006
$834$	35.9869	1.24612
$835$	−0.335928	−0.0116253
$836$	−0.0246228	−0.000851597 0
$837$	−25.2367	−0.872309
$838$	−27.4091	−0.946833
$839$	−55.9223	−1.93065	−0.965327	−	0.261045i	$-0.915933\pi$
$839$	−55.9223	−1.93065	−0.965327	+	0.261045i	$0.915933\pi$
$840$	0.450519	0.0155444
$841$	0	0
$842$	−6.73714	−0.232177
$843$	−25.5807	−0.881045
$844$	−33.7112	−1.16039
$845$	0.132654	0.00456345
$846$	−108.804	−3.74075
$847$	2.76647	0.0950570
$848$	12.5544	0.431120
$849$	−5.35850	−0.183903
$850$	−32.8797	−1.12776
$851$	−7.39308	−0.253432
$852$	9.10751	0.312018
$853$	−22.3983	−0.766903	−0.383451	−	0.923561i	$-0.625265\pi$
$853$	−22.3983	−0.766903	−0.383451	+	0.923561i	$0.625265\pi$
$854$	15.0334	0.514433
$855$	0.00105673	3.61395e−5 0
$856$	10.4311	0.356529
$857$	30.5062	1.04207	0.521036	−	0.853535i	$-0.325546\pi$
$857$	30.5062	1.04207	0.521036	+	0.853535i	$0.325546\pi$
$858$	17.3586	0.592614
$859$	−1.31566	−0.0448896	−0.0224448	−	0.999748i	$-0.507145\pi$
$859$	−1.31566	−0.0448896	−0.0224448	+	0.999748i	$0.507145\pi$
$860$	0.397079	0.0135403
$861$	−49.8778	−1.69983
$862$	65.6219	2.23509
$863$	−10.2207	−0.347915	−0.173958	−	0.984753i	$-0.555656\pi$
$863$	−10.2207	−0.347915	−0.173958	+	0.984753i	$0.555656\pi$
$864$	20.9649	0.713242
$865$	0.416998	0.0141784
$866$	−47.1019	−1.60059
$867$	−21.8427	−0.741816
$868$	−68.1222	−2.31222
$869$	15.8454	0.537520
$870$	0	0
$871$	−16.2003	−0.548926
$872$	−29.1458	−0.987001
$873$	−56.7266	−1.91991
$874$	−0.0381832	−0.00129157
$875$	0.838674	0.0283523
$876$	50.2981	1.69942
$877$	−24.1790	−0.816467	−0.408234	−	0.912877i	$-0.633855\pi$
$877$	−24.1790	−0.816467	−0.408234	+	0.912877i	$0.633855\pi$
$878$	−30.8276	−1.04038
$879$	30.3120	1.02240
$880$	0.0411347	0.00138665
$881$	6.03785	0.203420	0.101710	−	0.994814i	$-0.467569\pi$
$881$	6.03785	0.203420	0.101710	+	0.994814i	$0.467569\pi$
$882$	−5.96007	−0.200686
$883$	40.6679	1.36858	0.684292	−	0.729208i	$-0.260111\pi$
$883$	40.6679	1.36858	0.684292	+	0.729208i	$0.260111\pi$
$884$	25.3587	0.852904
$885$	0.368287	0.0123798
$886$	12.0814	0.405883
$887$	−8.68207	−0.291515	−0.145758	−	0.989320i	$-0.546562\pi$
$887$	−8.68207	−0.291515	−0.145758	+	0.989320i	$0.546562\pi$
$888$	−19.5053	−0.654554
$889$	−60.9733	−2.04498
$890$	−0.533418	−0.0178802
$891$	−4.39917	−0.147378
$892$	−72.7758	−2.43671
$893$	−0.100965	−0.00337865
$894$	−22.1766	−0.741697
$895$	0.432822	0.0144676
$896$	39.9594	1.33495
$897$	15.9509	0.532585
$898$	−23.4123	−0.781279
$899$	0	0
$900$	−59.8711	−1.99570
$901$	27.4694	0.915137
$902$	14.9729	0.498542
$903$	−33.2318	−1.10588
$904$	34.0066	1.13104
$905$	0.763178	0.0253689
$906$	116.254	3.86228
$907$	−25.8588	−0.858627	−0.429313	−	0.903156i	$-0.641244\pi$
$907$	−25.8588	−0.858627	−0.429313	+	0.903156i	$0.641244\pi$
$908$	31.8976	1.05856
$909$	59.1924	1.96329
$910$	−0.545743	−0.0180912
$911$	−32.9864	−1.09289	−0.546444	−	0.837496i	$-0.684019\pi$
$911$	−32.9864	−1.09289	−0.546444	+	0.837496i	$0.684019\pi$
$912$	0.0306405	0.00101461
$913$	−8.21870	−0.271999
$914$	8.35534	0.276370
$915$	0.198388	0.00655851
$916$	14.0064	0.462785
$917$	9.50145	0.313766
$918$	19.6070	0.647126
$919$	−7.22039	−0.238179	−0.119089	−	0.992884i	$-0.537997\pi$
$919$	−7.22039	−0.238179	−0.119089	+	0.992884i	$0.537997\pi$
$920$	−0.124274	−0.00409719
$921$	72.3181	2.38296
$922$	−50.1823	−1.65266
$923$	−3.44672	−0.113450
$924$	21.4679	0.706243
$925$	−18.1536	−0.596886
$926$	45.3047	1.48881
$927$	−40.0001	−1.31377
$928$	0	0
$929$	−21.2378	−0.696790	−0.348395	−	0.937348i	$-0.613273\pi$
$929$	−21.2378	−0.696790	−0.348395	+	0.937348i	$0.613273\pi$
$930$	−1.51709	−0.0497475
$931$	−0.00553066	−0.000181260 0
$932$	−31.4520	−1.03024
$933$	−6.04426	−0.197880
$934$	12.0612	0.394655
$935$	0.0900036	0.00294343
$936$	24.3452	0.795748
$937$	20.8523	0.681216	0.340608	−	0.940205i	$-0.389367\pi$
$937$	20.8523	0.681216	0.340608	+	0.940205i	$0.389367\pi$
$938$	−33.8114	−1.10398
$939$	−53.2486	−1.73770
$940$	−1.05183	−0.0343069
$941$	−2.68677	−0.0875863	−0.0437932	−	0.999041i	$-0.513944\pi$
$941$	−2.68677	−0.0875863	−0.0437932	+	0.999041i	$0.513944\pi$
$942$	−104.078	−3.39106
$943$	13.7586	0.448041
$944$	6.17759	0.201063
$945$	−0.250038	−0.00813374
$946$	9.97588	0.324344
$947$	−55.6323	−1.80781	−0.903903	−	0.427737i	$-0.859311\pi$
$947$	−55.6323	−1.80781	−0.903903	+	0.427737i	$0.859311\pi$
$948$	122.961	3.99360
$949$	−19.0352	−0.617910
$950$	−0.0937581	−0.00304191
$951$	55.7808	1.80882
$952$	16.5347	0.535894
$953$	−7.95601	−0.257721	−0.128860	−	0.991663i	$-0.541132\pi$
$953$	−7.95601	−0.257721	−0.128860	+	0.991663i	$0.541132\pi$
$954$	84.4121	2.73294
$955$	−0.293556	−0.00949926
$956$	61.3271	1.98346
$957$	0	0
$958$	3.04342	0.0983286
$959$	−26.9655	−0.870761
$960$	1.04082	0.0335922
$961$	40.6670	1.31184
$962$	23.6280	0.761797
$963$	−21.3322	−0.687421
$964$	−65.3678	−2.10536
$965$	−0.215568	−0.00693938
$966$	33.2908	1.07112
$967$	25.1953	0.810227	0.405113	−	0.914266i	$-0.367232\pi$
$967$	25.1953	0.810227	0.405113	+	0.914266i	$0.367232\pi$
$968$	−2.01335	−0.0647115
$969$	0.0670421	0.00215370
$970$	−0.925454	−0.0297145
$971$	37.9104	1.21660	0.608301	−	0.793706i	$-0.291851\pi$
$971$	37.9104	1.21660	0.608301	+	0.793706i	$0.291851\pi$
$972$	−60.1512	−1.92935
$973$	−16.8432	−0.539968
$974$	23.3215	0.747270
$975$	39.1671	1.25435
$976$	3.32773	0.106518
$977$	35.7237	1.14290	0.571451	−	0.820636i	$-0.306381\pi$
$977$	35.7237	1.14290	0.571451	+	0.820636i	$0.306381\pi$
$978$	−95.1667	−3.04310
$979$	−7.94101	−0.253796
$980$	−0.0576174	−0.00184052
$981$	59.6047	1.90303
$982$	−32.1416	−1.02568
$983$	−20.9846	−0.669304	−0.334652	−	0.942342i	$-0.608619\pi$
$983$	−20.9846	−0.669304	−0.334652	+	0.942342i	$0.608619\pi$
$984$	36.2995	1.15719
$985$	−0.518407	−0.0165178
$986$	0	0
$987$	88.0282	2.80197
$988$	0.0723116	0.00230054
$989$	9.16686	0.291489
$990$	0.276577	0.00879019
$991$	0.284262	0.00902987	0.00451494	−	0.999990i	$-0.498563\pi$
$991$	0.284262	0.00902987	0.00451494	+	0.999990i	$0.498563\pi$
$992$	−59.5360	−1.89027
$993$	−22.0242	−0.698917
$994$	−7.19359	−0.228167
$995$	−0.0477108	−0.00151253
$996$	−63.7775	−2.02087
$997$	−17.3826	−0.550511	−0.275255	−	0.961371i	$-0.588762\pi$
$997$	−17.3826	−0.550511	−0.275255	+	0.961371i	$0.588762\pi$
$998$	−50.2678	−1.59120
$999$	10.8254	0.342502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.6	✓	40
29.28	even	2		9251.2.a.bb.1.35	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.6	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.35	yes	40	29.28	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21557 q^{2} +2.66785 q^{3} +2.90873 q^{4} -0.0303185 q^{5} -5.91079 q^{6} +2.76647 q^{7} -2.01335 q^{8} +4.11741 q^{9} +O(q^{10})\)	\(q-2.21557 q^{2} +2.66785 q^{3} +2.90873 q^{4} -0.0303185 q^{5} -5.91079 q^{6} +2.76647 q^{7} -2.01335 q^{8} +4.11741 q^{9} +0.0671726 q^{10} +1.00000 q^{11} +7.76005 q^{12} -2.93677 q^{13} -6.12929 q^{14} -0.0808851 q^{15} -1.35675 q^{16} -2.96861 q^{17} -9.12239 q^{18} -0.00846514 q^{19} -0.0881882 q^{20} +7.38051 q^{21} -2.21557 q^{22} -2.03589 q^{23} -5.37131 q^{24} -4.99908 q^{25} +6.50661 q^{26} +2.98108 q^{27} +8.04691 q^{28} +0.179206 q^{30} -8.46564 q^{31} +7.03267 q^{32} +2.66785 q^{33} +6.57714 q^{34} -0.0838751 q^{35} +11.9764 q^{36} +3.63138 q^{37} +0.0187551 q^{38} -7.83486 q^{39} +0.0610417 q^{40} -6.75803 q^{41} -16.3520 q^{42} -4.50264 q^{43} +2.90873 q^{44} -0.124834 q^{45} +4.51064 q^{46} +11.9271 q^{47} -3.61961 q^{48} +0.653346 q^{49} +11.0758 q^{50} -7.91979 q^{51} -8.54228 q^{52} -9.25328 q^{53} -6.60477 q^{54} -0.0303185 q^{55} -5.56987 q^{56} -0.0225837 q^{57} -4.55322 q^{59} -0.235273 q^{60} -2.45272 q^{61} +18.7562 q^{62} +11.3907 q^{63} -12.8678 q^{64} +0.0890385 q^{65} -5.91079 q^{66} +5.51636 q^{67} -8.63487 q^{68} -5.43143 q^{69} +0.185831 q^{70} +1.17364 q^{71} -8.28978 q^{72} +6.48168 q^{73} -8.04557 q^{74} -13.3368 q^{75} -0.0246228 q^{76} +2.76647 q^{77} +17.3586 q^{78} +15.8454 q^{79} +0.0411347 q^{80} -4.39917 q^{81} +14.9729 q^{82} -8.21870 q^{83} +21.4679 q^{84} +0.0900036 q^{85} +9.97588 q^{86} -2.01335 q^{88} -7.94101 q^{89} +0.276577 q^{90} -8.12449 q^{91} -5.92184 q^{92} -22.5850 q^{93} -26.4253 q^{94} +0.000256650 q^{95} +18.7621 q^{96} -13.7773 q^{97} -1.44753 q^{98} +4.11741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more