LMFDB - Embedded newform 8410.2.a.bx.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8410,2,Mod(1,8410)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8410.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8410, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 8410 = 2 \cdot 5 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8410.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,12,-4,12,-12,-4,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$67.1541880999$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 13 x^{10} + 56 x^{9} + 41 x^{8} - 234 x^{7} - 8 x^{6} + 298 x^{5} + 41 x^{4} + \cdots + 1 $ x^12 - 4x^11 - 13x^10 + 56x^9 + 41x^8 - 234x^7 - 8x^6 + 298x^5 + 41x^4 - 140x^3 - 62x^2 - 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.400832$ of defining polynomial
Character	$\chi$	$=$	8410.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +0.401106 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.401106 q^{6} +1.20419 q^{7} +1.00000 q^{8} -2.83911 q^{9} -1.00000 q^{10} -5.12054 q^{11} +0.401106 q^{12} -1.87948 q^{13} +1.20419 q^{14} -0.401106 q^{15} +1.00000 q^{16} +7.71390 q^{17} -2.83911 q^{18} +4.07654 q^{19} -1.00000 q^{20} +0.483009 q^{21} -5.12054 q^{22} -5.78639 q^{23} +0.401106 q^{24} +1.00000 q^{25} -1.87948 q^{26} -2.34210 q^{27} +1.20419 q^{28} -0.401106 q^{30} +9.82669 q^{31} +1.00000 q^{32} -2.05388 q^{33} +7.71390 q^{34} -1.20419 q^{35} -2.83911 q^{36} +2.16055 q^{37} +4.07654 q^{38} -0.753871 q^{39} -1.00000 q^{40} -1.58080 q^{41} +0.483009 q^{42} -7.56183 q^{43} -5.12054 q^{44} +2.83911 q^{45} -5.78639 q^{46} -6.64980 q^{47} +0.401106 q^{48} -5.54992 q^{49} +1.00000 q^{50} +3.09409 q^{51} -1.87948 q^{52} -1.67046 q^{53} -2.34210 q^{54} +5.12054 q^{55} +1.20419 q^{56} +1.63513 q^{57} -11.6820 q^{59} -0.401106 q^{60} +9.33425 q^{61} +9.82669 q^{62} -3.41884 q^{63} +1.00000 q^{64} +1.87948 q^{65} -2.05388 q^{66} +11.5028 q^{67} +7.71390 q^{68} -2.32096 q^{69} -1.20419 q^{70} -7.15146 q^{71} -2.83911 q^{72} -4.34840 q^{73} +2.16055 q^{74} +0.401106 q^{75} +4.07654 q^{76} -6.16612 q^{77} -0.753871 q^{78} -3.94475 q^{79} -1.00000 q^{80} +7.57791 q^{81} -1.58080 q^{82} +12.1828 q^{83} +0.483009 q^{84} -7.71390 q^{85} -7.56183 q^{86} -5.12054 q^{88} -17.9033 q^{89} +2.83911 q^{90} -2.26326 q^{91} -5.78639 q^{92} +3.94155 q^{93} -6.64980 q^{94} -4.07654 q^{95} +0.401106 q^{96} -16.1921 q^{97} -5.54992 q^{98} +14.5378 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} - 4 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 8 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{10} - 14 q^{11} - 4 q^{12} - 4 q^{13} - 8 q^{14} + 4 q^{15} + 12 q^{16} - 8 q^{17} + 6 q^{18} + 16 q^{19}+ \cdots + 2 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 - 4 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 8 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^10 - 14 * q^11 - 4 * q^12 - 4 * q^13 - 8 * q^14 + 4 * q^15 + 12 * q^16 - 8 * q^17 + 6 * q^18 + 16 * q^19 - 12 * q^20 + 4 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^24 + 12 * q^25 - 4 * q^26 - 28 * q^27 - 8 * q^28 + 4 * q^30 + 2 * q^31 + 12 * q^32 + 4 * q^33 - 8 * q^34 + 8 * q^35 + 6 * q^36 - 18 * q^37 + 16 * q^38 + 24 * q^39 - 12 * q^40 - 4 * q^41 + 4 * q^42 - 28 * q^43 - 14 * q^44 - 6 * q^45 + 4 * q^46 - 36 * q^47 - 4 * q^48 + 18 * q^49 + 12 * q^50 - 24 * q^51 - 4 * q^52 - 28 * q^54 + 14 * q^55 - 8 * q^56 - 50 * q^57 - 12 * q^59 + 4 * q^60 + 12 * q^61 + 2 * q^62 - 22 * q^63 + 12 * q^64 + 4 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 42 * q^69 + 8 * q^70 - 18 * q^71 + 6 * q^72 - 48 * q^73 - 18 * q^74 - 4 * q^75 + 16 * q^76 - 46 * q^77 + 24 * q^78 - 12 * q^80 + 12 * q^81 - 4 * q^82 + 20 * q^83 + 4 * q^84 + 8 * q^85 - 28 * q^86 - 14 * q^88 - 32 * q^89 - 6 * q^90 + 50 * q^91 + 4 * q^92 - 42 * q^93 - 36 * q^94 - 16 * q^95 - 4 * q^96 - 16 * q^97 + 18 * q^98 + 2 * q^99

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.401106	0.231579	0.115789	−	0.993274i	$-0.463060\pi$
$3$	0.401106	0.231579	0.115789	+	0.993274i	$0.463060\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.401106	0.163751
$7$	1.20419	0.455142	0.227571	−	0.973761i	$-0.426922\pi$
$7$	1.20419	0.455142	0.227571	+	0.973761i	$0.426922\pi$
$8$	1.00000	0.353553
$9$	−2.83911	−0.946371
$10$	−1.00000	−0.316228
$11$	−5.12054	−1.54390	−0.771950	−	0.635683i	$-0.780719\pi$
$11$	−5.12054	−1.54390	−0.771950	+	0.635683i	$0.780719\pi$
$12$	0.401106	0.115789
$13$	−1.87948	−0.521274	−0.260637	−	0.965437i	$-0.583933\pi$
$13$	−1.87948	−0.521274	−0.260637	+	0.965437i	$0.583933\pi$
$14$	1.20419	0.321834
$15$	−0.401106	−0.103565
$16$	1.00000	0.250000
$17$	7.71390	1.87090	0.935448	−	0.353465i	$-0.114997\pi$
$17$	7.71390	1.87090	0.935448	+	0.353465i	$0.114997\pi$
$18$	−2.83911	−0.669186
$19$	4.07654	0.935223	0.467611	−	0.883934i	$-0.345115\pi$
$19$	4.07654	0.935223	0.467611	+	0.883934i	$0.345115\pi$
$20$	−1.00000	−0.223607
$21$	0.483009	0.105401
$22$	−5.12054	−1.09170
$23$	−5.78639	−1.20655	−0.603273	−	0.797535i	$-0.706137\pi$
$23$	−5.78639	−1.20655	−0.603273	+	0.797535i	$0.706137\pi$
$24$	0.401106	0.0818754
$25$	1.00000	0.200000
$26$	−1.87948	−0.368596
$27$	−2.34210	−0.450738
$28$	1.20419	0.227571
$29$	0	0
$29$	0	0
$30$	−0.401106	−0.0732316
$31$	9.82669	1.76493	0.882463	−	0.470382i	$-0.155884\pi$
$31$	9.82669	1.76493	0.882463	+	0.470382i	$0.155884\pi$
$32$	1.00000	0.176777
$33$	−2.05388	−0.357535
$34$	7.71390	1.32292
$35$	−1.20419	−0.203546
$36$	−2.83911	−0.473186
$37$	2.16055	0.355192	0.177596	−	0.984104i	$-0.443168\pi$
$37$	2.16055	0.355192	0.177596	+	0.984104i	$0.443168\pi$
$38$	4.07654	0.661302
$39$	−0.753871	−0.120716
$40$	−1.00000	−0.158114
$41$	−1.58080	−0.246880	−0.123440	−	0.992352i	$-0.539393\pi$
$41$	−1.58080	−0.246880	−0.123440	+	0.992352i	$0.539393\pi$
$42$	0.483009	0.0745300
$43$	−7.56183	−1.15317	−0.576584	−	0.817038i	$-0.695615\pi$
$43$	−7.56183	−1.15317	−0.576584	+	0.817038i	$0.695615\pi$
$44$	−5.12054	−0.771950
$45$	2.83911	0.423230
$46$	−5.78639	−0.853157
$47$	−6.64980	−0.969974	−0.484987	−	0.874521i	$-0.661176\pi$
$47$	−6.64980	−0.969974	−0.484987	+	0.874521i	$0.661176\pi$
$48$	0.401106	0.0578947
$49$	−5.54992	−0.792845
$50$	1.00000	0.141421
$51$	3.09409	0.433260
$52$	−1.87948	−0.260637
$53$	−1.67046	−0.229455	−0.114728	−	0.993397i	$-0.536600\pi$
$53$	−1.67046	−0.229455	−0.114728	+	0.993397i	$0.536600\pi$
$54$	−2.34210	−0.318720
$55$	5.12054	0.690453
$56$	1.20419	0.160917
$57$	1.63513	0.216578
$58$	0	0
$59$	−11.6820	−1.52087	−0.760435	−	0.649414i	$-0.775014\pi$
$59$	−11.6820	−1.52087	−0.760435	+	0.649414i	$0.775014\pi$
$60$	−0.401106	−0.0517826
$61$	9.33425	1.19513	0.597564	−	0.801821i	$-0.296135\pi$
$61$	9.33425	1.19513	0.597564	+	0.801821i	$0.296135\pi$
$62$	9.82669	1.24799
$63$	−3.41884	−0.430734
$64$	1.00000	0.125000
$65$	1.87948	0.233121
$66$	−2.05388	−0.252815
$67$	11.5028	1.40529	0.702647	−	0.711538i	$-0.252001\pi$
$67$	11.5028	1.40529	0.702647	+	0.711538i	$0.252001\pi$
$68$	7.71390	0.935448
$69$	−2.32096	−0.279410
$70$	−1.20419	−0.143929
$71$	−7.15146	−0.848722	−0.424361	−	0.905493i	$-0.639501\pi$
$71$	−7.15146	−0.848722	−0.424361	+	0.905493i	$0.639501\pi$
$72$	−2.83911	−0.334593
$73$	−4.34840	−0.508941	−0.254471	−	0.967080i	$-0.581901\pi$
$73$	−4.34840	−0.508941	−0.254471	+	0.967080i	$0.581901\pi$
$74$	2.16055	0.251158
$75$	0.401106	0.0463157
$76$	4.07654	0.467611
$77$	−6.16612	−0.702695
$78$	−0.753871	−0.0853590
$79$	−3.94475	−0.443820	−0.221910	−	0.975067i	$-0.571229\pi$
$79$	−3.94475	−0.443820	−0.221910	+	0.975067i	$0.571229\pi$
$80$	−1.00000	−0.111803
$81$	7.57791	0.841990
$82$	−1.58080	−0.174570
$83$	12.1828	1.33723	0.668616	−	0.743608i	$-0.266887\pi$
$83$	12.1828	1.33723	0.668616	+	0.743608i	$0.266887\pi$
$84$	0.483009	0.0527007
$85$	−7.71390	−0.836690
$86$	−7.56183	−0.815413
$87$	0	0
$88$	−5.12054	−0.545851
$89$	−17.9033	−1.89774	−0.948871	−	0.315663i	$-0.897773\pi$
$89$	−17.9033	−1.89774	−0.948871	+	0.315663i	$0.897773\pi$
$90$	2.83911	0.299269
$91$	−2.26326	−0.237254
$92$	−5.78639	−0.603273
$93$	3.94155	0.408719
$94$	−6.64980	−0.685875
$95$	−4.07654	−0.418244
$96$	0.401106	0.0409377
$97$	−16.1921	−1.64405	−0.822027	−	0.569448i	$-0.807157\pi$
$97$	−16.1921	−1.64405	−0.822027	+	0.569448i	$0.807157\pi$
$98$	−5.54992	−0.560626
$99$	14.5378	1.46110
$100$	1.00000	0.100000
$101$	−0.834611	−0.0830469	−0.0415234	−	0.999138i	$-0.513221\pi$
$101$	−0.834611	−0.0830469	−0.0415234	+	0.999138i	$0.513221\pi$
$102$	3.09409	0.306361
$103$	−2.50718	−0.247040	−0.123520	−	0.992342i	$-0.539418\pi$
$103$	−2.50718	−0.247040	−0.123520	+	0.992342i	$0.539418\pi$
$104$	−1.87948	−0.184298
$105$	−0.483009	−0.0471369
$106$	−1.67046	−0.162249
$107$	−3.98032	−0.384792	−0.192396	−	0.981317i	$-0.561626\pi$
$107$	−3.98032	−0.384792	−0.192396	+	0.981317i	$0.561626\pi$
$108$	−2.34210	−0.225369
$109$	−18.5782	−1.77947	−0.889736	−	0.456476i	$-0.849111\pi$
$109$	−18.5782	−1.77947	−0.889736	+	0.456476i	$0.849111\pi$
$110$	5.12054	0.488224
$111$	0.866608	0.0822548
$112$	1.20419	0.113786
$113$	−20.9429	−1.97014	−0.985071	−	0.172146i	$-0.944930\pi$
$113$	−20.9429	−1.97014	−0.985071	+	0.172146i	$0.944930\pi$
$114$	1.63513	0.153144
$115$	5.78639	0.539584
$116$	0	0
$117$	5.33606	0.493318
$118$	−11.6820	−1.07542
$119$	9.28903	0.851524
$120$	−0.401106	−0.0366158
$121$	15.2199	1.38363
$122$	9.33425	0.845083
$123$	−0.634069	−0.0571720
$124$	9.82669	0.882463
$125$	−1.00000	−0.0894427
$126$	−3.41884	−0.304575
$127$	6.34362	0.562905	0.281452	−	0.959575i	$-0.409184\pi$
$127$	6.34362	0.562905	0.281452	+	0.959575i	$0.409184\pi$
$128$	1.00000	0.0883883
$129$	−3.03310	−0.267049
$130$	1.87948	0.164841
$131$	−16.4511	−1.43734	−0.718671	−	0.695350i	$-0.755249\pi$
$131$	−16.4511	−1.43734	−0.718671	+	0.695350i	$0.755249\pi$
$132$	−2.05388	−0.178767
$133$	4.90895	0.425660
$134$	11.5028	0.993693
$135$	2.34210	0.201576
$136$	7.71390	0.661461
$137$	−0.569445	−0.0486510	−0.0243255	−	0.999704i	$-0.507744\pi$
$137$	−0.569445	−0.0486510	−0.0243255	+	0.999704i	$0.507744\pi$
$138$	−2.32096	−0.197573
$139$	−6.60701	−0.560399	−0.280200	−	0.959942i	$-0.590401\pi$
$139$	−6.60701	−0.560399	−0.280200	+	0.959942i	$0.590401\pi$
$140$	−1.20419	−0.101773
$141$	−2.66728	−0.224625
$142$	−7.15146	−0.600137
$143$	9.62395	0.804795
$144$	−2.83911	−0.236593
$145$	0	0
$146$	−4.34840	−0.359876
$147$	−2.22611	−0.183606
$148$	2.16055	0.177596
$149$	−7.46758	−0.611768	−0.305884	−	0.952069i	$-0.598952\pi$
$149$	−7.46758	−0.611768	−0.305884	+	0.952069i	$0.598952\pi$
$150$	0.401106	0.0327502
$151$	13.9145	1.13235	0.566173	−	0.824286i	$-0.308423\pi$
$151$	13.9145	1.13235	0.566173	+	0.824286i	$0.308423\pi$
$152$	4.07654	0.330651
$153$	−21.9006	−1.77056
$154$	−6.16612	−0.496880
$155$	−9.82669	−0.789299
$156$	−0.753871	−0.0603579
$157$	−4.41997	−0.352752	−0.176376	−	0.984323i	$-0.556437\pi$
$157$	−4.41997	−0.352752	−0.176376	+	0.984323i	$0.556437\pi$
$158$	−3.94475	−0.313828
$159$	−0.670031	−0.0531369
$160$	−1.00000	−0.0790569
$161$	−6.96793	−0.549150
$162$	7.57791	0.595377
$163$	2.61511	0.204831	0.102415	−	0.994742i	$-0.467343\pi$
$163$	2.61511	0.204831	0.102415	+	0.994742i	$0.467343\pi$
$164$	−1.58080	−0.123440
$165$	2.05388	0.159894
$166$	12.1828	0.945566
$167$	−14.2987	−1.10646	−0.553232	−	0.833028i	$-0.686606\pi$
$167$	−14.2987	−1.10646	−0.553232	+	0.833028i	$0.686606\pi$
$168$	0.483009	0.0372650
$169$	−9.46756	−0.728274
$170$	−7.71390	−0.591629
$171$	−11.5738	−0.885068
$172$	−7.56183	−0.576584
$173$	−14.7050	−1.11800	−0.559001	−	0.829167i	$-0.688815\pi$
$173$	−14.7050	−1.11800	−0.559001	+	0.829167i	$0.688815\pi$
$174$	0	0
$175$	1.20419	0.0910285
$176$	−5.12054	−0.385975
$177$	−4.68573	−0.352201
$178$	−17.9033	−1.34191
$179$	−6.96738	−0.520767	−0.260383	−	0.965505i	$-0.583849\pi$
$179$	−6.96738	−0.520767	−0.260383	+	0.965505i	$0.583849\pi$
$180$	2.83911	0.211615
$181$	11.4760	0.853002	0.426501	−	0.904487i	$-0.359746\pi$
$181$	11.4760	0.853002	0.426501	+	0.904487i	$0.359746\pi$
$182$	−2.26326	−0.167764
$183$	3.74402	0.276766
$184$	−5.78639	−0.426578
$185$	−2.16055	−0.158847
$186$	3.94155	0.289008
$187$	−39.4993	−2.88848
$188$	−6.64980	−0.484987
$189$	−2.82035	−0.205150
$190$	−4.07654	−0.295743
$191$	10.1386	0.733607	0.366803	−	0.930299i	$-0.380452\pi$
$191$	10.1386	0.733607	0.366803	+	0.930299i	$0.380452\pi$
$192$	0.401106	0.0289473
$193$	−7.41474	−0.533724	−0.266862	−	0.963735i	$-0.585987\pi$
$193$	−7.41474	−0.533724	−0.266862	+	0.963735i	$0.585987\pi$
$194$	−16.1921	−1.16252
$195$	0.753871	0.0539858
$196$	−5.54992	−0.396423
$197$	10.9903	0.783026	0.391513	−	0.920173i	$-0.371952\pi$
$197$	10.9903	0.783026	0.391513	+	0.920173i	$0.371952\pi$
$198$	14.5378	1.03316
$199$	−17.8698	−1.26676	−0.633379	−	0.773842i	$-0.718333\pi$
$199$	−17.8698	−1.26676	−0.633379	+	0.773842i	$0.718333\pi$
$200$	1.00000	0.0707107
$201$	4.61386	0.325436
$202$	−0.834611	−0.0587230
$203$	0	0
$204$	3.09409	0.216630
$205$	1.58080	0.110408
$206$	−2.50718	−0.174684
$207$	16.4282	1.14184
$208$	−1.87948	−0.130318
$209$	−20.8741	−1.44389
$210$	−0.483009	−0.0333308
$211$	1.96288	0.135130	0.0675651	−	0.997715i	$-0.478477\pi$
$211$	1.96288	0.135130	0.0675651	+	0.997715i	$0.478477\pi$
$212$	−1.67046	−0.114728
$213$	−2.86849	−0.196546
$214$	−3.98032	−0.272089
$215$	7.56183	0.515713
$216$	−2.34210	−0.159360
$217$	11.8332	0.803293
$218$	−18.5782	−1.25828
$219$	−1.74417	−0.117860
$220$	5.12054	0.345227
$221$	−14.4981	−0.975249
$222$	0.866608	0.0581629
$223$	2.99161	0.200333	0.100167	−	0.994971i	$-0.468062\pi$
$223$	2.99161	0.200333	0.100167	+	0.994971i	$0.468062\pi$
$224$	1.20419	0.0804586
$225$	−2.83911	−0.189274
$226$	−20.9429	−1.39310
$227$	10.4575	0.694091	0.347045	−	0.937848i	$-0.387185\pi$
$227$	10.4575	0.694091	0.347045	+	0.937848i	$0.387185\pi$
$228$	1.63513	0.108289
$229$	−11.7226	−0.774651	−0.387325	−	0.921943i	$-0.626601\pi$
$229$	−11.7226	−0.774651	−0.387325	+	0.921943i	$0.626601\pi$
$230$	5.78639	0.381543
$231$	−2.47327	−0.162729
$232$	0	0
$233$	7.36396	0.482429	0.241215	−	0.970472i	$-0.422454\pi$
$233$	7.36396	0.482429	0.241215	+	0.970472i	$0.422454\pi$
$234$	5.33606	0.348829
$235$	6.64980	0.433785
$236$	−11.6820	−0.760435
$237$	−1.58227	−0.102779
$238$	9.28903	0.602118
$239$	−4.11217	−0.265994	−0.132997	−	0.991116i	$-0.542460\pi$
$239$	−4.11217	−0.265994	−0.132997	+	0.991116i	$0.542460\pi$
$240$	−0.401106	−0.0258913
$241$	−0.466864	−0.0300734	−0.0150367	−	0.999887i	$-0.504787\pi$
$241$	−0.466864	−0.0300734	−0.0150367	+	0.999887i	$0.504787\pi$
$242$	15.2199	0.978374
$243$	10.0659	0.645725
$244$	9.33425	0.597564
$245$	5.54992	0.354571
$246$	−0.634069	−0.0404267
$247$	−7.66178	−0.487507
$248$	9.82669	0.623996
$249$	4.88658	0.309674
$250$	−1.00000	−0.0632456
$251$	−20.9372	−1.32155	−0.660773	−	0.750586i	$-0.729771\pi$
$251$	−20.9372	−1.32155	−0.660773	+	0.750586i	$0.729771\pi$
$252$	−3.41884	−0.215367
$253$	29.6294	1.86279
$254$	6.34362	0.398034
$255$	−3.09409	−0.193760
$256$	1.00000	0.0625000
$257$	14.0275	0.875011	0.437506	−	0.899216i	$-0.355862\pi$
$257$	14.0275	0.875011	0.437506	+	0.899216i	$0.355862\pi$
$258$	−3.03310	−0.188832
$259$	2.60172	0.161663
$260$	1.87948	0.116560
$261$	0	0
$262$	−16.4511	−1.01635
$263$	14.4990	0.894048	0.447024	−	0.894522i	$-0.352484\pi$
$263$	14.4990	0.894048	0.447024	+	0.894522i	$0.352484\pi$
$264$	−2.05388	−0.126408
$265$	1.67046	0.102615
$266$	4.90895	0.300987
$267$	−7.18111	−0.439477
$268$	11.5028	0.702647
$269$	7.28808	0.444362	0.222181	−	0.975005i	$-0.428682\pi$
$269$	7.28808	0.444362	0.222181	+	0.975005i	$0.428682\pi$
$270$	2.34210	0.142536
$271$	−4.76330	−0.289350	−0.144675	−	0.989479i	$-0.546214\pi$
$271$	−4.76330	−0.289350	−0.144675	+	0.989479i	$0.546214\pi$
$272$	7.71390	0.467724
$273$	−0.907806	−0.0549429
$274$	−0.569445	−0.0344014
$275$	−5.12054	−0.308780
$276$	−2.32096	−0.139705
$277$	5.31620	0.319419	0.159710	−	0.987164i	$-0.448944\pi$
$277$	5.31620	0.319419	0.159710	+	0.987164i	$0.448944\pi$
$278$	−6.60701	−0.396262
$279$	−27.8991	−1.67028
$280$	−1.20419	−0.0719643
$281$	13.4195	0.800538	0.400269	−	0.916398i	$-0.368917\pi$
$281$	13.4195	0.800538	0.400269	+	0.916398i	$0.368917\pi$
$282$	−2.66728	−0.158834
$283$	−14.6017	−0.867983	−0.433991	−	0.900917i	$-0.642895\pi$
$283$	−14.6017	−0.867983	−0.433991	+	0.900917i	$0.642895\pi$
$284$	−7.15146	−0.424361
$285$	−1.63513	−0.0968565
$286$	9.62395	0.569076
$287$	−1.90359	−0.112365
$288$	−2.83911	−0.167296
$289$	42.5042	2.50025
$290$	0	0
$291$	−6.49473	−0.380728
$292$	−4.34840	−0.254471
$293$	−14.2013	−0.829649	−0.414824	−	0.909901i	$-0.636157\pi$
$293$	−14.2013	−0.829649	−0.414824	+	0.909901i	$0.636157\pi$
$294$	−2.22611	−0.129829
$295$	11.6820	0.680154
$296$	2.16055	0.125579
$297$	11.9928	0.695895
$298$	−7.46758	−0.432585
$299$	10.8754	0.628941
$300$	0.401106	0.0231579
$301$	−9.10591	−0.524856
$302$	13.9145	0.800690
$303$	−0.334767	−0.0192319
$304$	4.07654	0.233806
$305$	−9.33425	−0.534478
$306$	−21.9006	−1.25198
$307$	10.7324	0.612533	0.306266	−	0.951946i	$-0.400920\pi$
$307$	10.7324	0.612533	0.306266	+	0.951946i	$0.400920\pi$
$308$	−6.16612	−0.351347
$309$	−1.00565	−0.0572092
$310$	−9.82669	−0.558119
$311$	−12.9785	−0.735944	−0.367972	−	0.929837i	$-0.619948\pi$
$311$	−12.9785	−0.735944	−0.367972	+	0.929837i	$0.619948\pi$
$312$	−0.753871	−0.0426795
$313$	−3.08478	−0.174362	−0.0871811	−	0.996192i	$-0.527786\pi$
$313$	−3.08478	−0.174362	−0.0871811	+	0.996192i	$0.527786\pi$
$314$	−4.41997	−0.249433
$315$	3.41884	0.192630
$316$	−3.94475	−0.221910
$317$	−23.6585	−1.32879	−0.664396	−	0.747381i	$-0.731311\pi$
$317$	−23.6585	−1.32879	−0.664396	+	0.747381i	$0.731311\pi$
$318$	−0.670031	−0.0375735
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−1.59653	−0.0891096
$322$	−6.96793	−0.388308
$323$	31.4460	1.74970
$324$	7.57791	0.420995
$325$	−1.87948	−0.104255
$326$	2.61511	0.144837
$327$	−7.45184	−0.412088
$328$	−1.58080	−0.0872851
$329$	−8.00765	−0.441476
$330$	2.05388	0.113062
$331$	−2.74733	−0.151007	−0.0755034	−	0.997146i	$-0.524056\pi$
$331$	−2.74733	−0.151007	−0.0755034	+	0.997146i	$0.524056\pi$
$332$	12.1828	0.668616
$333$	−6.13404	−0.336143
$334$	−14.2987	−0.782388
$335$	−11.5028	−0.628467
$336$	0.483009	0.0263503
$337$	28.6955	1.56314	0.781571	−	0.623816i	$-0.214418\pi$
$337$	28.6955	1.56314	0.781571	+	0.623816i	$0.214418\pi$
$338$	−9.46756	−0.514967
$339$	−8.40033	−0.456243
$340$	−7.71390	−0.418345
$341$	−50.3180	−2.72487
$342$	−11.5738	−0.625838
$343$	−15.1125	−0.816000
$344$	−7.56183	−0.407707
$345$	2.32096	0.124956
$346$	−14.7050	−0.790547
$347$	15.2155	0.816810	0.408405	−	0.912801i	$-0.366085\pi$
$347$	15.2155	0.816810	0.408405	+	0.912801i	$0.366085\pi$
$348$	0	0
$349$	4.20894	0.225300	0.112650	−	0.993635i	$-0.464066\pi$
$349$	4.20894	0.225300	0.112650	+	0.993635i	$0.464066\pi$
$350$	1.20419	0.0643669
$351$	4.40194	0.234958
$352$	−5.12054	−0.272926
$353$	26.2481	1.39704	0.698522	−	0.715589i	$-0.253841\pi$
$353$	26.2481	1.39704	0.698522	+	0.715589i	$0.253841\pi$
$354$	−4.68573	−0.249044
$355$	7.15146	0.379560
$356$	−17.9033	−0.948871
$357$	3.72589	0.197195
$358$	−6.96738	−0.368238
$359$	−15.2588	−0.805326	−0.402663	−	0.915348i	$-0.631915\pi$
$359$	−15.2588	−0.805326	−0.402663	+	0.915348i	$0.631915\pi$
$360$	2.83911	0.149634
$361$	−2.38180	−0.125358
$362$	11.4760	0.603163
$363$	6.10481	0.320419
$364$	−2.26326	−0.118627
$365$	4.34840	0.227605
$366$	3.74402	0.195703
$367$	4.20604	0.219553	0.109777	−	0.993956i	$-0.464986\pi$
$367$	4.20604	0.219553	0.109777	+	0.993956i	$0.464986\pi$
$368$	−5.78639	−0.301636
$369$	4.48807	0.233640
$370$	−2.16055	−0.112321
$371$	−2.01156	−0.104435
$372$	3.94155	0.204360
$373$	21.2914	1.10243	0.551213	−	0.834365i	$-0.314165\pi$
$373$	21.2914	1.10243	0.551213	+	0.834365i	$0.314165\pi$
$374$	−39.4993	−2.04246
$375$	−0.401106	−0.0207130
$376$	−6.64980	−0.342937
$377$	0	0
$378$	−2.82035	−0.145063
$379$	1.13313	0.0582050	0.0291025	−	0.999576i	$-0.490735\pi$
$379$	1.13313	0.0582050	0.0291025	+	0.999576i	$0.490735\pi$
$380$	−4.07654	−0.209122
$381$	2.54446	0.130357
$382$	10.1386	0.518738
$383$	9.08051	0.463992	0.231996	−	0.972717i	$-0.425474\pi$
$383$	9.08051	0.463992	0.231996	+	0.972717i	$0.425474\pi$
$384$	0.401106	0.0204689
$385$	6.16612	0.314255
$386$	−7.41474	−0.377400
$387$	21.4689	1.09133
$388$	−16.1921	−0.822027
$389$	29.3352	1.48735	0.743677	−	0.668539i	$-0.233080\pi$
$389$	29.3352	1.48735	0.743677	+	0.668539i	$0.233080\pi$
$390$	0.753871	0.0381737
$391$	−44.6356	−2.25732
$392$	−5.54992	−0.280313
$393$	−6.59865	−0.332858
$394$	10.9903	0.553683
$395$	3.94475	0.198482
$396$	14.5378	0.730552
$397$	2.27814	0.114336	0.0571682	−	0.998365i	$-0.481793\pi$
$397$	2.27814	0.114336	0.0571682	+	0.998365i	$0.481793\pi$
$398$	−17.8698	−0.895733
$399$	1.96901	0.0985737
$400$	1.00000	0.0500000
$401$	1.33609	0.0667213	0.0333607	−	0.999443i	$-0.489379\pi$
$401$	1.33609	0.0667213	0.0333607	+	0.999443i	$0.489379\pi$
$402$	4.61386	0.230118
$403$	−18.4691	−0.920010
$404$	−0.834611	−0.0415234
$405$	−7.57791	−0.376549
$406$	0	0
$407$	−11.0632	−0.548381
$408$	3.09409	0.153180
$409$	10.9733	0.542594	0.271297	−	0.962496i	$-0.412547\pi$
$409$	10.9733	0.542594	0.271297	+	0.962496i	$0.412547\pi$
$410$	1.58080	0.0780702
$411$	−0.228408	−0.0112665
$412$	−2.50718	−0.123520
$413$	−14.0674	−0.692213
$414$	16.4282	0.807403
$415$	−12.1828	−0.598028
$416$	−1.87948	−0.0921490
$417$	−2.65011	−0.129777
$418$	−20.8741	−1.02099
$419$	10.5441	0.515114	0.257557	−	0.966263i	$-0.417083\pi$
$419$	10.5441	0.515114	0.257557	+	0.966263i	$0.417083\pi$
$420$	−0.483009	−0.0235684
$421$	13.4758	0.656768	0.328384	−	0.944544i	$-0.393496\pi$
$421$	13.4758	0.656768	0.328384	+	0.944544i	$0.393496\pi$
$422$	1.96288	0.0955515
$423$	18.8796	0.917955
$424$	−1.67046	−0.0811246
$425$	7.71390	0.374179
$426$	−2.86849	−0.138979
$427$	11.2402	0.543954
$428$	−3.98032	−0.192396
$429$	3.86022	0.186373
$430$	7.56183	0.364664
$431$	15.6644	0.754528	0.377264	−	0.926106i	$-0.376865\pi$
$431$	15.6644	0.754528	0.377264	+	0.926106i	$0.376865\pi$
$432$	−2.34210	−0.112685
$433$	−13.1208	−0.630546	−0.315273	−	0.949001i	$-0.602096\pi$
$433$	−13.1208	−0.630546	−0.315273	+	0.949001i	$0.602096\pi$
$434$	11.8332	0.568014
$435$	0	0
$436$	−18.5782	−0.889736
$437$	−23.5885	−1.12839
$438$	−1.74417	−0.0833396
$439$	−7.43776	−0.354985	−0.177492	−	0.984122i	$-0.556799\pi$
$439$	−7.43776	−0.354985	−0.177492	+	0.984122i	$0.556799\pi$
$440$	5.12054	0.244112
$441$	15.7568	0.750326
$442$	−14.4981	−0.689605
$443$	31.9403	1.51753	0.758764	−	0.651365i	$-0.225803\pi$
$443$	31.9403	1.51753	0.758764	+	0.651365i	$0.225803\pi$
$444$	0.866608	0.0411274
$445$	17.9033	0.848696
$446$	2.99161	0.141657
$447$	−2.99529	−0.141672
$448$	1.20419	0.0568928
$449$	−11.5345	−0.544347	−0.272173	−	0.962248i	$-0.587742\pi$
$449$	−11.5345	−0.544347	−0.272173	+	0.962248i	$0.587742\pi$
$450$	−2.83911	−0.133837
$451$	8.09455	0.381158
$452$	−20.9429	−0.985071
$453$	5.58119	0.262227
$454$	10.4575	0.490796
$455$	2.26326	0.106103
$456$	1.63513	0.0765718
$457$	−4.38046	−0.204909	−0.102455	−	0.994738i	$-0.532670\pi$
$457$	−4.38046	−0.204909	−0.102455	+	0.994738i	$0.532670\pi$
$458$	−11.7226	−0.547761
$459$	−18.0668	−0.843284
$460$	5.78639	0.269792
$461$	19.3754	0.902401	0.451201	−	0.892423i	$-0.350996\pi$
$461$	19.3754	0.902401	0.451201	+	0.892423i	$0.350996\pi$
$462$	−2.47327	−0.115067
$463$	12.5730	0.584315	0.292158	−	0.956370i	$-0.405627\pi$
$463$	12.5730	0.584315	0.292158	+	0.956370i	$0.405627\pi$
$464$	0	0
$465$	−3.94155	−0.182785
$466$	7.36396	0.341129
$467$	33.0324	1.52856	0.764280	−	0.644885i	$-0.223095\pi$
$467$	33.0324	1.52856	0.764280	+	0.644885i	$0.223095\pi$
$468$	5.33606	0.246659
$469$	13.8516	0.639609
$470$	6.64980	0.306733
$471$	−1.77288	−0.0816898
$472$	−11.6820	−0.537709
$473$	38.7207	1.78038
$474$	−1.58227	−0.0726758
$475$	4.07654	0.187045
$476$	9.28903	0.425762
$477$	4.74262	0.217150
$478$	−4.11217	−0.188086
$479$	28.7013	1.31139	0.655697	−	0.755024i	$-0.272375\pi$
$479$	28.7013	1.31139	0.655697	+	0.755024i	$0.272375\pi$
$480$	−0.401106	−0.0183079
$481$	−4.06070	−0.185152
$482$	−0.466864	−0.0212651
$483$	−2.79488	−0.127172
$484$	15.2199	0.691815
$485$	16.1921	0.735243
$486$	10.0659	0.456597
$487$	−33.8080	−1.53199	−0.765993	−	0.642849i	$-0.777752\pi$
$487$	−33.8080	−1.53199	−0.765993	+	0.642849i	$0.777752\pi$
$488$	9.33425	0.422542
$489$	1.04893	0.0474345
$490$	5.54992	0.250720
$491$	−13.7655	−0.621228	−0.310614	−	0.950536i	$-0.600535\pi$
$491$	−13.7655	−0.621228	−0.310614	+	0.950536i	$0.600535\pi$
$492$	−0.634069	−0.0285860
$493$	0	0
$494$	−7.66178	−0.344720
$495$	−14.5378	−0.653425
$496$	9.82669	0.441232
$497$	−8.61174	−0.386289
$498$	4.88658	0.218973
$499$	−0.991058	−0.0443658	−0.0221829	−	0.999754i	$-0.507062\pi$
$499$	−0.991058	−0.0443658	−0.0221829	+	0.999754i	$0.507062\pi$
$500$	−1.00000	−0.0447214
$501$	−5.73528	−0.256233
$502$	−20.9372	−0.934474
$503$	−42.5461	−1.89704	−0.948518	−	0.316722i	$-0.897418\pi$
$503$	−42.5461	−1.89704	−0.948518	+	0.316722i	$0.897418\pi$
$504$	−3.41884	−0.152287
$505$	0.834611	0.0371397
$506$	29.6294	1.31719
$507$	−3.79750	−0.168653
$508$	6.34362	0.281452
$509$	−15.2016	−0.673799	−0.336899	−	0.941541i	$-0.609378\pi$
$509$	−15.2016	−0.673799	−0.336899	+	0.941541i	$0.609378\pi$
$510$	−3.09409	−0.137009
$511$	−5.23631	−0.231641
$512$	1.00000	0.0441942
$513$	−9.54769	−0.421541
$514$	14.0275	0.618726
$515$	2.50718	0.110480
$516$	−3.03310	−0.133525
$517$	34.0506	1.49754
$518$	2.60172	0.114313
$519$	−5.89827	−0.258905
$520$	1.87948	0.0824206
$521$	−2.83871	−0.124366	−0.0621831	−	0.998065i	$-0.519806\pi$
$521$	−2.83871	−0.124366	−0.0621831	+	0.998065i	$0.519806\pi$
$522$	0	0
$523$	28.2327	1.23453	0.617266	−	0.786755i	$-0.288240\pi$
$523$	28.2327	1.23453	0.617266	+	0.786755i	$0.288240\pi$
$524$	−16.4511	−0.718671
$525$	0.483009	0.0210803
$526$	14.4990	0.632187
$527$	75.8021	3.30199
$528$	−2.05388	−0.0893836
$529$	10.4823	0.455753
$530$	1.67046	0.0725601
$531$	33.1666	1.43931
$532$	4.90895	0.212830
$533$	2.97108	0.128692
$534$	−7.18111	−0.310757
$535$	3.98032	0.172084
$536$	11.5028	0.496847
$537$	−2.79466	−0.120599
$538$	7.28808	0.314211
$539$	28.4186	1.22407
$540$	2.34210	0.100788
$541$	−29.3853	−1.26337	−0.631687	−	0.775223i	$-0.717637\pi$
$541$	−29.3853	−1.26337	−0.631687	+	0.775223i	$0.717637\pi$
$542$	−4.76330	−0.204601
$543$	4.60308	0.197537
$544$	7.71390	0.330731
$545$	18.5782	0.795804
$546$	−0.907806	−0.0388505
$547$	0.395706	0.0169192	0.00845958	−	0.999964i	$-0.497307\pi$
$547$	0.395706	0.0169192	0.00845958	+	0.999964i	$0.497307\pi$
$548$	−0.569445	−0.0243255
$549$	−26.5010	−1.13103
$550$	−5.12054	−0.218341
$551$	0	0
$552$	−2.32096	−0.0987865
$553$	−4.75025	−0.202001
$554$	5.31620	0.225864
$555$	−0.866608	−0.0367855
$556$	−6.60701	−0.280200
$557$	36.1822	1.53309	0.766545	−	0.642190i	$-0.221974\pi$
$557$	36.1822	1.53309	0.766545	+	0.642190i	$0.221974\pi$
$558$	−27.8991	−1.18106
$559$	14.2123	0.601116
$560$	−1.20419	−0.0508865
$561$	−15.8434	−0.668910
$562$	13.4195	0.566066
$563$	24.5885	1.03628	0.518140	−	0.855296i	$-0.326624\pi$
$563$	24.5885	1.03628	0.518140	+	0.855296i	$0.326624\pi$
$564$	−2.66728	−0.112313
$565$	20.9429	0.881075
$566$	−14.6017	−0.613757
$567$	9.12527	0.383225
$568$	−7.15146	−0.300068
$569$	−33.9862	−1.42477	−0.712387	−	0.701787i	$-0.752386\pi$
$569$	−33.9862	−1.42477	−0.712387	+	0.701787i	$0.752386\pi$
$570$	−1.63513	−0.0684879
$571$	−11.6510	−0.487579	−0.243789	−	0.969828i	$-0.578391\pi$
$571$	−11.6510	−0.487579	−0.243789	+	0.969828i	$0.578391\pi$
$572$	9.62395	0.402397
$573$	4.06667	0.169888
$574$	−1.90359	−0.0794543
$575$	−5.78639	−0.241309
$576$	−2.83911	−0.118296
$577$	6.13917	0.255577	0.127789	−	0.991801i	$-0.459212\pi$
$577$	6.13917	0.255577	0.127789	+	0.991801i	$0.459212\pi$
$578$	42.5042	1.76794
$579$	−2.97410	−0.123599
$580$	0	0
$581$	14.6704	0.608631
$582$	−6.49473	−0.269215
$583$	8.55365	0.354256
$584$	−4.34840	−0.179938
$585$	−5.33606	−0.220619
$586$	−14.2013	−0.586650
$587$	11.2280	0.463427	0.231714	−	0.972784i	$-0.425567\pi$
$587$	11.2280	0.463427	0.231714	+	0.972784i	$0.425567\pi$
$588$	−2.22611	−0.0918031
$589$	40.0589	1.65060
$590$	11.6820	0.480942
$591$	4.40827	0.181332
$592$	2.16055	0.0887979
$593$	−21.0174	−0.863080	−0.431540	−	0.902094i	$-0.642030\pi$
$593$	−21.0174	−0.863080	−0.431540	+	0.902094i	$0.642030\pi$
$594$	11.9928	0.492072
$595$	−9.28903	−0.380813
$596$	−7.46758	−0.305884
$597$	−7.16770	−0.293354
$598$	10.8754	0.444728
$599$	−44.5658	−1.82091	−0.910454	−	0.413610i	$-0.864268\pi$
$599$	−44.5658	−1.82091	−0.910454	+	0.413610i	$0.864268\pi$
$600$	0.401106	0.0163751
$601$	−14.8735	−0.606701	−0.303351	−	0.952879i	$-0.598105\pi$
$601$	−14.8735	−0.606701	−0.303351	+	0.952879i	$0.598105\pi$
$602$	−9.10591	−0.371129
$603$	−32.6579	−1.32993
$604$	13.9145	0.566173
$605$	−15.2199	−0.618778
$606$	−0.334767	−0.0135990
$607$	−10.2220	−0.414900	−0.207450	−	0.978246i	$-0.566516\pi$
$607$	−10.2220	−0.414900	−0.207450	+	0.978246i	$0.566516\pi$
$608$	4.07654	0.165326
$609$	0	0
$610$	−9.33425	−0.377933
$611$	12.4982	0.505622
$612$	−21.9006	−0.885281
$613$	18.5677	0.749944	0.374972	−	0.927036i	$-0.377652\pi$
$613$	18.5677	0.749944	0.374972	+	0.927036i	$0.377652\pi$
$614$	10.7324	0.433126
$615$	0.634069	0.0255681
$616$	−6.16612	−0.248440
$617$	−43.8868	−1.76682	−0.883408	−	0.468605i	$-0.844757\pi$
$617$	−43.8868	−1.76682	−0.883408	+	0.468605i	$0.844757\pi$
$618$	−1.00565	−0.0404530
$619$	8.21915	0.330356	0.165178	−	0.986264i	$-0.447180\pi$
$619$	8.21915	0.330356	0.165178	+	0.986264i	$0.447180\pi$
$620$	−9.82669	−0.394649
$621$	13.5523	0.543836
$622$	−12.9785	−0.520391
$623$	−21.5590	−0.863743
$624$	−0.753871	−0.0301790
$625$	1.00000	0.0400000
$626$	−3.08478	−0.123293
$627$	−8.37273	−0.334375
$628$	−4.41997	−0.176376
$629$	16.6662	0.664526
$630$	3.41884	0.136210
$631$	33.2083	1.32200	0.661000	−	0.750386i	$-0.270132\pi$
$631$	33.2083	1.32200	0.661000	+	0.750386i	$0.270132\pi$
$632$	−3.94475	−0.156914
$633$	0.787323	0.0312933
$634$	−23.6585	−0.939598
$635$	−6.34362	−0.251739
$636$	−0.670031	−0.0265685
$637$	10.4310	0.413289
$638$	0	0
$639$	20.3038	0.803206
$640$	−1.00000	−0.0395285
$641$	0.589087	0.0232675	0.0116338	−	0.999932i	$-0.496297\pi$
$641$	0.589087	0.0232675	0.0116338	+	0.999932i	$0.496297\pi$
$642$	−1.59653	−0.0630100
$643$	−44.7230	−1.76370	−0.881851	−	0.471529i	$-0.843702\pi$
$643$	−44.7230	−1.76370	−0.881851	+	0.471529i	$0.843702\pi$
$644$	−6.96793	−0.274575
$645$	3.03310	0.119428
$646$	31.4460	1.23723
$647$	−19.4912	−0.766279	−0.383140	−	0.923690i	$-0.625157\pi$
$647$	−19.4912	−0.766279	−0.383140	+	0.923690i	$0.625157\pi$
$648$	7.57791	0.297688
$649$	59.8183	2.34807
$650$	−1.87948	−0.0737192
$651$	4.74639	0.186026
$652$	2.61511	0.102415
$653$	19.8642	0.777345	0.388672	−	0.921376i	$-0.372934\pi$
$653$	19.8642	0.777345	0.388672	+	0.921376i	$0.372934\pi$
$654$	−7.45184	−0.291390
$655$	16.4511	0.642799
$656$	−1.58080	−0.0617199
$657$	12.3456	0.481647
$658$	−8.00765	−0.312171
$659$	18.4571	0.718987	0.359494	−	0.933148i	$-0.382949\pi$
$659$	18.4571	0.718987	0.359494	+	0.933148i	$0.382949\pi$
$660$	2.05388	0.0799472
$661$	−9.39538	−0.365438	−0.182719	−	0.983165i	$-0.558490\pi$
$661$	−9.39538	−0.365438	−0.182719	+	0.983165i	$0.558490\pi$
$662$	−2.74733	−0.106778
$663$	−5.81528	−0.225847
$664$	12.1828	0.472783
$665$	−4.90895	−0.190361
$666$	−6.13404	−0.237689
$667$	0	0
$668$	−14.2987	−0.553232
$669$	1.19995	0.0463929
$670$	−11.5028	−0.444393
$671$	−47.7964	−1.84516
$672$	0.483009	0.0186325
$673$	−47.2583	−1.82167	−0.910837	−	0.412766i	$-0.864563\pi$
$673$	−47.2583	−1.82167	−0.910837	+	0.412766i	$0.864563\pi$
$674$	28.6955	1.10531
$675$	−2.34210	−0.0901476
$676$	−9.46756	−0.364137
$677$	−45.1670	−1.73591	−0.867954	−	0.496644i	$-0.834565\pi$
$677$	−45.1670	−1.73591	−0.867954	+	0.496644i	$0.834565\pi$
$678$	−8.40033	−0.322613
$679$	−19.4984	−0.748279
$680$	−7.71390	−0.295815
$681$	4.19458	0.160737
$682$	−50.3180	−1.92677
$683$	19.0875	0.730362	0.365181	−	0.930937i	$-0.381007\pi$
$683$	19.0875	0.730362	0.365181	+	0.930937i	$0.381007\pi$
$684$	−11.5738	−0.442534
$685$	0.569445	0.0217574
$686$	−15.1125	−0.576999
$687$	−4.70200	−0.179393
$688$	−7.56183	−0.288292
$689$	3.13959	0.119609
$690$	2.32096	0.0883573
$691$	−13.3245	−0.506886	−0.253443	−	0.967350i	$-0.581563\pi$
$691$	−13.3245	−0.506886	−0.253443	+	0.967350i	$0.581563\pi$
$692$	−14.7050	−0.559001
$693$	17.5063	0.665010
$694$	15.2155	0.577572
$695$	6.60701	0.250618
$696$	0	0
$697$	−12.1941	−0.461886
$698$	4.20894	0.159311
$699$	2.95373	0.111720
$700$	1.20419	0.0455142
$701$	−30.8132	−1.16380	−0.581899	−	0.813261i	$-0.697690\pi$
$701$	−30.8132	−1.16380	−0.581899	+	0.813261i	$0.697690\pi$
$702$	4.40194	0.166140
$703$	8.80756	0.332183
$704$	−5.12054	−0.192988
$705$	2.66728	0.100455
$706$	26.2481	0.987859
$707$	−1.00503	−0.0377982
$708$	−4.68573	−0.176101
$709$	−10.8891	−0.408948	−0.204474	−	0.978872i	$-0.565548\pi$
$709$	−10.8891	−0.408948	−0.204474	+	0.978872i	$0.565548\pi$
$710$	7.15146	0.268389
$711$	11.1996	0.420018
$712$	−17.9033	−0.670953
$713$	−56.8611	−2.12946
$714$	3.72589	0.139438
$715$	−9.62395	−0.359915
$716$	−6.96738	−0.260383
$717$	−1.64942	−0.0615986
$718$	−15.2588	−0.569452
$719$	53.2899	1.98738	0.993689	−	0.112169i	$-0.0357799\pi$
$719$	53.2899	1.98738	0.993689	+	0.112169i	$0.0357799\pi$
$720$	2.83911	0.105808
$721$	−3.01913	−0.112438
$722$	−2.38180	−0.0886416
$723$	−0.187262	−0.00696435
$724$	11.4760	0.426501
$725$	0	0
$726$	6.10481	0.226571
$727$	−10.2393	−0.379754	−0.189877	−	0.981808i	$-0.560809\pi$
$727$	−10.2393	−0.379754	−0.189877	+	0.981808i	$0.560809\pi$
$728$	−2.26326	−0.0838819
$729$	−18.6963	−0.692454
$730$	4.34840	0.160941
$731$	−58.3312	−2.15746
$732$	3.74402	0.138383
$733$	−22.0629	−0.814911	−0.407456	−	0.913225i	$-0.633584\pi$
$733$	−22.0629	−0.814911	−0.407456	+	0.913225i	$0.633584\pi$
$734$	4.20604	0.155248
$735$	2.22611	0.0821111
$736$	−5.78639	−0.213289
$737$	−58.9007	−2.16964
$738$	4.48807	0.165208
$739$	17.0280	0.626385	0.313192	−	0.949690i	$-0.398602\pi$
$739$	17.0280	0.626385	0.313192	+	0.949690i	$0.398602\pi$
$740$	−2.16055	−0.0794233
$741$	−3.07318	−0.112896
$742$	−2.01156	−0.0738465
$743$	−32.6429	−1.19755	−0.598777	−	0.800916i	$-0.704346\pi$
$743$	−32.6429	−1.19755	−0.598777	+	0.800916i	$0.704346\pi$
$744$	3.94155	0.144504
$745$	7.46758	0.273591
$746$	21.2914	0.779532
$747$	−34.5883	−1.26552
$748$	−39.4993	−1.44424
$749$	−4.79308	−0.175135
$750$	−0.401106	−0.0146463
$751$	11.8277	0.431600	0.215800	−	0.976438i	$-0.430764\pi$
$751$	11.8277	0.431600	0.215800	+	0.976438i	$0.430764\pi$
$752$	−6.64980	−0.242493
$753$	−8.39805	−0.306042
$754$	0	0
$755$	−13.9145	−0.506401
$756$	−2.82035	−0.102575
$757$	−47.7965	−1.73719	−0.868597	−	0.495519i	$-0.834978\pi$
$757$	−47.7965	−1.73719	−0.868597	+	0.495519i	$0.834978\pi$
$758$	1.13313	0.0411571
$759$	11.8846	0.431382
$760$	−4.07654	−0.147872
$761$	−30.4117	−1.10242	−0.551212	−	0.834366i	$-0.685834\pi$
$761$	−30.4117	−1.10242	−0.551212	+	0.834366i	$0.685834\pi$
$762$	2.54446	0.0921762
$763$	−22.3718	−0.809913
$764$	10.1386	0.366803
$765$	21.9006	0.791819
$766$	9.08051	0.328092
$767$	21.9561	0.792790
$768$	0.401106	0.0144737
$769$	−40.6558	−1.46609	−0.733043	−	0.680182i	$-0.761901\pi$
$769$	−40.6558	−1.46609	−0.733043	+	0.680182i	$0.761901\pi$
$770$	6.16612	0.222212
$771$	5.62651	0.202634
$772$	−7.41474	−0.266862
$773$	23.0776	0.830045	0.415022	−	0.909811i	$-0.363774\pi$
$773$	23.0776	0.830045	0.415022	+	0.909811i	$0.363774\pi$
$774$	21.4689	0.771684
$775$	9.82669	0.352985
$776$	−16.1921	−0.581261
$777$	1.04356	0.0374377
$778$	29.3352	1.05172
$779$	−6.44420	−0.230887
$780$	0.753871	0.0269929
$781$	36.6193	1.31034
$782$	−44.6356	−1.59617
$783$	0	0
$784$	−5.54992	−0.198211
$785$	4.41997	0.157755
$786$	−6.59865	−0.235366
$787$	34.7647	1.23923	0.619613	−	0.784907i	$-0.287289\pi$
$787$	34.7647	1.23923	0.619613	+	0.784907i	$0.287289\pi$
$788$	10.9903	0.391513
$789$	5.81564	0.207042
$790$	3.94475	0.140348
$791$	−25.2193	−0.896696
$792$	14.5378	0.516578
$793$	−17.5435	−0.622989
$794$	2.27814	0.0808480
$795$	0.670031	0.0237636
$796$	−17.8698	−0.633379
$797$	−4.73922	−0.167872	−0.0839358	−	0.996471i	$-0.526749\pi$
$797$	−4.73922	−0.167872	−0.0839358	+	0.996471i	$0.526749\pi$
$798$	1.96901	0.0697021
$799$	−51.2959	−1.81472
$800$	1.00000	0.0353553
$801$	50.8294	1.79597
$802$	1.33609	0.0471791
$803$	22.2661	0.785755
$804$	4.61386	0.162718
$805$	6.96793	0.245587
$806$	−18.4691	−0.650545
$807$	2.92329	0.102905
$808$	−0.834611	−0.0293615
$809$	−42.3373	−1.48850	−0.744250	−	0.667901i	$-0.767193\pi$
$809$	−42.3373	−1.48850	−0.744250	+	0.667901i	$0.767193\pi$
$810$	−7.57791	−0.266261
$811$	19.0268	0.668123	0.334061	−	0.942551i	$-0.391581\pi$
$811$	19.0268	0.668123	0.334061	+	0.942551i	$0.391581\pi$
$812$	0	0
$813$	−1.91059	−0.0670073
$814$	−11.0632	−0.387764
$815$	−2.61511	−0.0916032
$816$	3.09409	0.108315
$817$	−30.8261	−1.07847
$818$	10.9733	0.383672
$819$	6.42564	0.224530
$820$	1.58080	0.0552039
$821$	32.7747	1.14385	0.571923	−	0.820307i	$-0.306198\pi$
$821$	32.7747	1.14385	0.571923	+	0.820307i	$0.306198\pi$
$822$	−0.228408	−0.00796664
$823$	−20.5673	−0.716933	−0.358466	−	0.933543i	$-0.616700\pi$
$823$	−20.5673	−0.716933	−0.358466	+	0.933543i	$0.616700\pi$
$824$	−2.50718	−0.0873418
$825$	−2.05388	−0.0715069
$826$	−14.0674	−0.489468
$827$	15.1382	0.526409	0.263204	−	0.964740i	$-0.415221\pi$
$827$	15.1382	0.526409	0.263204	+	0.964740i	$0.415221\pi$
$828$	16.4282	0.570920
$829$	53.0868	1.84378	0.921890	−	0.387453i	$-0.126645\pi$
$829$	53.0868	1.84378	0.921890	+	0.387453i	$0.126645\pi$
$830$	−12.1828	−0.422870
$831$	2.13236	0.0739707
$832$	−1.87948	−0.0651592
$833$	−42.8115	−1.48333
$834$	−2.65011	−0.0917659
$835$	14.2987	0.494825
$836$	−20.8741	−0.721946
$837$	−23.0151	−0.795520
$838$	10.5441	0.364240
$839$	8.79127	0.303508	0.151754	−	0.988418i	$-0.451508\pi$
$839$	8.79127	0.303508	0.151754	+	0.988418i	$0.451508\pi$
$840$	−0.483009	−0.0166654
$841$	0	0
$842$	13.4758	0.464405
$843$	5.38263	0.185388
$844$	1.96288	0.0675651
$845$	9.46756	0.325694
$846$	18.8796	0.649092
$847$	18.3277	0.629749
$848$	−1.67046	−0.0573638
$849$	−5.85684	−0.201006
$850$	7.71390	0.264585
$851$	−12.5018	−0.428555
$852$	−2.86849	−0.0982729
$853$	18.4255	0.630876	0.315438	−	0.948946i	$-0.397849\pi$
$853$	18.4255	0.630876	0.315438	+	0.948946i	$0.397849\pi$
$854$	11.2402	0.384633
$855$	11.5738	0.395814
$856$	−3.98032	−0.136045
$857$	13.4279	0.458688	0.229344	−	0.973345i	$-0.426342\pi$
$857$	13.4279	0.458688	0.229344	+	0.973345i	$0.426342\pi$
$858$	3.86022	0.131786
$859$	−35.2867	−1.20397	−0.601983	−	0.798509i	$-0.705623\pi$
$859$	−35.2867	−1.20397	−0.601983	+	0.798509i	$0.705623\pi$
$860$	7.56183	0.257856
$861$	−0.763541	−0.0260214
$862$	15.6644	0.533532
$863$	0.520905	0.0177318	0.00886591	−	0.999961i	$-0.497178\pi$
$863$	0.520905	0.0177318	0.00886591	+	0.999961i	$0.497178\pi$
$864$	−2.34210	−0.0796800
$865$	14.7050	0.499986
$866$	−13.1208	−0.445863
$867$	17.0487	0.579005
$868$	11.8332	0.401646
$869$	20.1993	0.685213
$870$	0	0
$871$	−21.6193	−0.732543
$872$	−18.5782	−0.629138
$873$	45.9711	1.55589
$874$	−23.5885	−0.797892
$875$	−1.20419	−0.0407092
$876$	−1.74417	−0.0589300
$877$	34.3565	1.16014	0.580068	−	0.814568i	$-0.303026\pi$
$877$	34.3565	1.16014	0.580068	+	0.814568i	$0.303026\pi$
$878$	−7.43776	−0.251012
$879$	−5.69623	−0.192129
$880$	5.12054	0.172613
$881$	40.0617	1.34971	0.674856	−	0.737949i	$-0.264206\pi$
$881$	40.0617	1.34971	0.674856	+	0.737949i	$0.264206\pi$
$882$	15.7568	0.530561
$883$	4.88799	0.164494	0.0822469	−	0.996612i	$-0.473790\pi$
$883$	4.88799	0.164494	0.0822469	+	0.996612i	$0.473790\pi$
$884$	−14.4981	−0.487624
$885$	4.68573	0.157509
$886$	31.9403	1.07305
$887$	−4.10888	−0.137963	−0.0689814	−	0.997618i	$-0.521975\pi$
$887$	−4.10888	−0.137963	−0.0689814	+	0.997618i	$0.521975\pi$
$888$	0.866608	0.0290815
$889$	7.63894	0.256202
$890$	17.9033	0.600119
$891$	−38.8030	−1.29995
$892$	2.99161	0.100167
$893$	−27.1082	−0.907141
$894$	−2.99529	−0.100178
$895$	6.96738	0.232894
$896$	1.20419	0.0402293
$897$	4.36219	0.145649
$898$	−11.5345	−0.384911
$899$	0	0
$900$	−2.83911	−0.0946371
$901$	−12.8858	−0.429287
$902$	8.09455	0.269519
$903$	−3.65244	−0.121545
$904$	−20.9429	−0.696551
$905$	−11.4760	−0.381474
$906$	5.58119	0.185423
$907$	23.2015	0.770392	0.385196	−	0.922835i	$-0.374134\pi$
$907$	23.2015	0.770392	0.385196	+	0.922835i	$0.374134\pi$
$908$	10.4575	0.347045
$909$	2.36956	0.0785932
$910$	2.26326	0.0750262
$911$	−49.1718	−1.62913	−0.814567	−	0.580070i	$-0.803025\pi$
$911$	−49.1718	−1.62913	−0.814567	+	0.580070i	$0.803025\pi$
$912$	1.63513	0.0541444
$913$	−62.3823	−2.06455
$914$	−4.38046	−0.144893
$915$	−3.74402	−0.123774
$916$	−11.7226	−0.387325
$917$	−19.8104	−0.654195
$918$	−18.0668	−0.596292
$919$	−17.9553	−0.592291	−0.296145	−	0.955143i	$-0.595701\pi$
$919$	−17.9553	−0.592291	−0.296145	+	0.955143i	$0.595701\pi$
$920$	5.78639	0.190772
$921$	4.30485	0.141850
$922$	19.3754	0.638094
$923$	13.4410	0.442416
$924$	−2.47327	−0.0813646
$925$	2.16055	0.0710383
$926$	12.5730	0.413173
$927$	7.11818	0.233792
$928$	0	0
$929$	32.1278	1.05408	0.527039	−	0.849841i	$-0.323302\pi$
$929$	32.1278	1.05408	0.527039	+	0.849841i	$0.323302\pi$
$930$	−3.94155	−0.129248
$931$	−22.6245	−0.741487
$932$	7.36396	0.241215
$933$	−5.20576	−0.170429
$934$	33.0324	1.08085
$935$	39.4993	1.29177
$936$	5.33606	0.174414
$937$	2.86375	0.0935545	0.0467773	−	0.998905i	$-0.485105\pi$
$937$	2.86375	0.0935545	0.0467773	+	0.998905i	$0.485105\pi$
$938$	13.8516	0.452272
$939$	−1.23732	−0.0403786
$940$	6.64980	0.216893
$941$	−14.9440	−0.487161	−0.243581	−	0.969881i	$-0.578322\pi$
$941$	−14.9440	−0.487161	−0.243581	+	0.969881i	$0.578322\pi$
$942$	−1.77288	−0.0577634
$943$	9.14713	0.297871
$944$	−11.6820	−0.380218
$945$	2.82035	0.0917459
$946$	38.7207	1.25892
$947$	−56.3452	−1.83097	−0.915487	−	0.402347i	$-0.868194\pi$
$947$	−56.3452	−1.83097	−0.915487	+	0.402347i	$0.868194\pi$
$948$	−1.58227	−0.0513896
$949$	8.17272	0.265298
$950$	4.07654	0.132260
$951$	−9.48955	−0.307720
$952$	9.28903	0.301059
$953$	2.06486	0.0668874	0.0334437	−	0.999441i	$-0.489353\pi$
$953$	2.06486	0.0668874	0.0334437	+	0.999441i	$0.489353\pi$
$954$	4.74262	0.153548
$955$	−10.1386	−0.328079
$956$	−4.11217	−0.132997
$957$	0	0
$958$	28.7013	0.927296
$959$	−0.685722	−0.0221431
$960$	−0.401106	−0.0129456
$961$	65.5639	2.11496
$962$	−4.06070	−0.130922
$963$	11.3006	0.364156
$964$	−0.466864	−0.0150367
$965$	7.41474	0.238689
$966$	−2.79488	−0.0899238
$967$	−9.72478	−0.312728	−0.156364	−	0.987700i	$-0.549977\pi$
$967$	−9.72478	−0.312728	−0.156364	+	0.987700i	$0.549977\pi$
$968$	15.2199	0.489187
$969$	12.6132	0.405194
$970$	16.1921	0.519896
$971$	−18.1706	−0.583124	−0.291562	−	0.956552i	$-0.594175\pi$
$971$	−18.1706	−0.583124	−0.291562	+	0.956552i	$0.594175\pi$
$972$	10.0659	0.322863
$973$	−7.95612	−0.255061
$974$	−33.8080	−1.08328
$975$	−0.753871	−0.0241432
$976$	9.33425	0.298782
$977$	14.0419	0.449240	0.224620	−	0.974446i	$-0.427886\pi$
$977$	14.0419	0.449240	0.224620	+	0.974446i	$0.427886\pi$
$978$	1.04893	0.0335412
$979$	91.6744	2.92993
$980$	5.54992	0.177286
$981$	52.7457	1.68404
$982$	−13.7655	−0.439275
$983$	25.2076	0.803996	0.401998	−	0.915641i	$-0.368316\pi$
$983$	25.2076	0.803996	0.401998	+	0.915641i	$0.368316\pi$
$984$	−0.634069	−0.0202134
$985$	−10.9903	−0.350180
$986$	0	0
$987$	−3.21192	−0.102236
$988$	−7.66178	−0.243754
$989$	43.7557	1.39135
$990$	−14.5378	−0.462041
$991$	17.3913	0.552451	0.276226	−	0.961093i	$-0.410916\pi$
$991$	17.3913	0.552451	0.276226	+	0.961093i	$0.410916\pi$
$992$	9.82669	0.311998
$993$	−1.10197	−0.0349699
$994$	−8.61174	−0.273148
$995$	17.8698	0.566511
$996$	4.88658	0.154837
$997$	33.7186	1.06788	0.533939	−	0.845523i	$-0.320711\pi$
$997$	33.7186	1.06788	0.533939	+	0.845523i	$0.320711\pi$
$998$	−0.991058	−0.0313714
$999$	−5.06023	−0.160098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8410.2.a.bx.1.8		12
29.19	odd	28		290.2.m.a.71.2	✓	24
29.26	odd	28		290.2.m.a.241.2	yes	24
29.28	even	2		8410.2.a.bw.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.m.a.71.2	✓	24	29.19	odd	28
290.2.m.a.241.2	yes	24	29.26	odd	28
8410.2.a.bw.1.5		12	29.28	even	2
8410.2.a.bx.1.8		12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8410 = 2 \cdot 5 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8410.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.401106 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.401106 q^{6} +1.20419 q^{7} +1.00000 q^{8} -2.83911 q^{9} -1.00000 q^{10} -5.12054 q^{11} +0.401106 q^{12} -1.87948 q^{13} +1.20419 q^{14} -0.401106 q^{15} +1.00000 q^{16} +7.71390 q^{17} -2.83911 q^{18} +4.07654 q^{19} -1.00000 q^{20} +0.483009 q^{21} -5.12054 q^{22} -5.78639 q^{23} +0.401106 q^{24} +1.00000 q^{25} -1.87948 q^{26} -2.34210 q^{27} +1.20419 q^{28} -0.401106 q^{30} +9.82669 q^{31} +1.00000 q^{32} -2.05388 q^{33} +7.71390 q^{34} -1.20419 q^{35} -2.83911 q^{36} +2.16055 q^{37} +4.07654 q^{38} -0.753871 q^{39} -1.00000 q^{40} -1.58080 q^{41} +0.483009 q^{42} -7.56183 q^{43} -5.12054 q^{44} +2.83911 q^{45} -5.78639 q^{46} -6.64980 q^{47} +0.401106 q^{48} -5.54992 q^{49} +1.00000 q^{50} +3.09409 q^{51} -1.87948 q^{52} -1.67046 q^{53} -2.34210 q^{54} +5.12054 q^{55} +1.20419 q^{56} +1.63513 q^{57} -11.6820 q^{59} -0.401106 q^{60} +9.33425 q^{61} +9.82669 q^{62} -3.41884 q^{63} +1.00000 q^{64} +1.87948 q^{65} -2.05388 q^{66} +11.5028 q^{67} +7.71390 q^{68} -2.32096 q^{69} -1.20419 q^{70} -7.15146 q^{71} -2.83911 q^{72} -4.34840 q^{73} +2.16055 q^{74} +0.401106 q^{75} +4.07654 q^{76} -6.16612 q^{77} -0.753871 q^{78} -3.94475 q^{79} -1.00000 q^{80} +7.57791 q^{81} -1.58080 q^{82} +12.1828 q^{83} +0.483009 q^{84} -7.71390 q^{85} -7.56183 q^{86} -5.12054 q^{88} -17.9033 q^{89} +2.83911 q^{90} -2.26326 q^{91} -5.78639 q^{92} +3.94155 q^{93} -6.64980 q^{94} -4.07654 q^{95} +0.401106 q^{96} -16.1921 q^{97} -5.54992 q^{98} +14.5378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} - 4 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 8 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{10} - 14 q^{11} - 4 q^{12} - 4 q^{13} - 8 q^{14} + 4 q^{15} + 12 q^{16} - 8 q^{17} + 6 q^{18} + 16 q^{19}+ \cdots + 2 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 4 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 8 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^10 - 14 * q^11 - 4 * q^12 - 4 * q^13 - 8 * q^14 + 4 * q^15 + 12 * q^16 - 8 * q^17 + 6 * q^18 + 16 * q^19 - 12 * q^20 + 4 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^24 + 12 * q^25 - 4 * q^26 - 28 * q^27 - 8 * q^28 + 4 * q^30 + 2 * q^31 + 12 * q^32 + 4 * q^33 - 8 * q^34 + 8 * q^35 + 6 * q^36 - 18 * q^37 + 16 * q^38 + 24 * q^39 - 12 * q^40 - 4 * q^41 + 4 * q^42 - 28 * q^43 - 14 * q^44 - 6 * q^45 + 4 * q^46 - 36 * q^47 - 4 * q^48 + 18 * q^49 + 12 * q^50 - 24 * q^51 - 4 * q^52 - 28 * q^54 + 14 * q^55 - 8 * q^56 - 50 * q^57 - 12 * q^59 + 4 * q^60 + 12 * q^61 + 2 * q^62 - 22 * q^63 + 12 * q^64 + 4 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 42 * q^69 + 8 * q^70 - 18 * q^71 + 6 * q^72 - 48 * q^73 - 18 * q^74 - 4 * q^75 + 16 * q^76 - 46 * q^77 + 24 * q^78 - 12 * q^80 + 12 * q^81 - 4 * q^82 + 20 * q^83 + 4 * q^84 + 8 * q^85 - 28 * q^86 - 14 * q^88 - 32 * q^89 - 6 * q^90 + 50 * q^91 + 4 * q^92 - 42 * q^93 - 36 * q^94 - 16 * q^95 - 4 * q^96 - 16 * q^97 + 18 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more