LMFDB - Embedded newform 6027.2.a.bl.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 $ x^16 - 4x^15 - 14x^14 + 68x^13 + 64x^12 - 456x^11 - 54x^10 + 1532x^9 - 400x^8 - 2708x^7 + 1218x^6 + 2424x^5 - 1276x^4 - 960x^3 + 500x^2 + 112*x - 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.631061$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.631061 q^{2} -1.00000 q^{3} -1.60176 q^{4} +1.65938 q^{5} +0.631061 q^{6} +2.27293 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.631061 q^{2} -1.00000 q^{3} -1.60176 q^{4} +1.65938 q^{5} +0.631061 q^{6} +2.27293 q^{8} +1.00000 q^{9} -1.04717 q^{10} +2.82239 q^{11} +1.60176 q^{12} +3.15999 q^{13} -1.65938 q^{15} +1.76917 q^{16} -1.11961 q^{17} -0.631061 q^{18} -3.11082 q^{19} -2.65794 q^{20} -1.78110 q^{22} -6.51222 q^{23} -2.27293 q^{24} -2.24644 q^{25} -1.99415 q^{26} -1.00000 q^{27} +9.16578 q^{29} +1.04717 q^{30} +4.35118 q^{31} -5.66231 q^{32} -2.82239 q^{33} +0.706545 q^{34} -1.60176 q^{36} -11.1252 q^{37} +1.96312 q^{38} -3.15999 q^{39} +3.77167 q^{40} -1.00000 q^{41} -0.684567 q^{43} -4.52079 q^{44} +1.65938 q^{45} +4.10961 q^{46} -6.17414 q^{47} -1.76917 q^{48} +1.41764 q^{50} +1.11961 q^{51} -5.06155 q^{52} -13.0735 q^{53} +0.631061 q^{54} +4.68342 q^{55} +3.11082 q^{57} -5.78417 q^{58} -7.71075 q^{59} +2.65794 q^{60} -0.419560 q^{61} -2.74586 q^{62} +0.0349308 q^{64} +5.24364 q^{65} +1.78110 q^{66} +9.95583 q^{67} +1.79336 q^{68} +6.51222 q^{69} +7.39023 q^{71} +2.27293 q^{72} -13.9295 q^{73} +7.02071 q^{74} +2.24644 q^{75} +4.98280 q^{76} +1.99415 q^{78} -0.195831 q^{79} +2.93573 q^{80} +1.00000 q^{81} +0.631061 q^{82} +2.50464 q^{83} -1.85787 q^{85} +0.432003 q^{86} -9.16578 q^{87} +6.41509 q^{88} +12.4999 q^{89} -1.04717 q^{90} +10.4310 q^{92} -4.35118 q^{93} +3.89626 q^{94} -5.16206 q^{95} +5.66231 q^{96} -11.3773 q^{97} +2.82239 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * 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 $

$2$	−0.631061	−0.446227	−0.223114	−	0.974792i	$-0.571622\pi$
$2$	−0.631061	−0.446227	−0.223114	+	0.974792i	$0.571622\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.60176	−0.800881
$5$	1.65938	0.742100	0.371050	−	0.928613i	$-0.378998\pi$
$5$	1.65938	0.742100	0.371050	+	0.928613i	$0.378998\pi$
$6$	0.631061	0.257629
$7$	0	0
$7$	0	0
$8$	2.27293	0.803602
$9$	1.00000	0.333333
$10$	−1.04717	−0.331145
$11$	2.82239	0.850981	0.425491	−	0.904963i	$-0.360102\pi$
$11$	2.82239	0.850981	0.425491	+	0.904963i	$0.360102\pi$
$12$	1.60176	0.462389
$13$	3.15999	0.876423	0.438212	−	0.898872i	$-0.355612\pi$
$13$	3.15999	0.876423	0.438212	+	0.898872i	$0.355612\pi$
$14$	0	0
$15$	−1.65938	−0.428451
$16$	1.76917	0.442292
$17$	−1.11961	−0.271547	−0.135773	−	0.990740i	$-0.543352\pi$
$17$	−1.11961	−0.271547	−0.135773	+	0.990740i	$0.543352\pi$
$18$	−0.631061	−0.148742
$19$	−3.11082	−0.713672	−0.356836	−	0.934167i	$-0.616145\pi$
$19$	−3.11082	−0.713672	−0.356836	+	0.934167i	$0.616145\pi$
$20$	−2.65794	−0.594333
$21$	0	0
$22$	−1.78110	−0.379731
$23$	−6.51222	−1.35789	−0.678946	−	0.734188i	$-0.737563\pi$
$23$	−6.51222	−1.35789	−0.678946	+	0.734188i	$0.737563\pi$
$24$	−2.27293	−0.463960
$25$	−2.24644	−0.449288
$26$	−1.99415	−0.391084
$27$	−1.00000	−0.192450
$28$	0	0
$29$	9.16578	1.70204	0.851021	−	0.525131i	$-0.175984\pi$
$29$	9.16578	1.70204	0.851021	+	0.525131i	$0.175984\pi$
$30$	1.04717	0.191187
$31$	4.35118	0.781495	0.390748	−	0.920498i	$-0.372217\pi$
$31$	4.35118	0.781495	0.390748	+	0.920498i	$0.372217\pi$
$32$	−5.66231	−1.00097
$33$	−2.82239	−0.491314
$34$	0.706545	0.121171
$35$	0	0
$36$	−1.60176	−0.266960
$37$	−11.1252	−1.82898	−0.914490	−	0.404609i	$-0.867407\pi$
$37$	−11.1252	−1.82898	−0.914490	+	0.404609i	$0.867407\pi$
$38$	1.96312	0.318460
$39$	−3.15999	−0.506003
$40$	3.77167	0.596353
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−0.684567	−0.104395	−0.0521977	−	0.998637i	$-0.516623\pi$
$43$	−0.684567	−0.104395	−0.0521977	+	0.998637i	$0.516623\pi$
$44$	−4.52079	−0.681535
$45$	1.65938	0.247367
$46$	4.10961	0.605929
$47$	−6.17414	−0.900591	−0.450296	−	0.892880i	$-0.648681\pi$
$47$	−6.17414	−0.900591	−0.450296	+	0.892880i	$0.648681\pi$
$48$	−1.76917	−0.255357
$49$	0	0
$50$	1.41764	0.200485
$51$	1.11961	0.156777
$52$	−5.06155	−0.701911
$53$	−13.0735	−1.79579	−0.897894	−	0.440212i	$-0.854903\pi$
$53$	−13.0735	−1.79579	−0.897894	+	0.440212i	$0.854903\pi$
$54$	0.631061	0.0858765
$55$	4.68342	0.631513
$56$	0	0
$57$	3.11082	0.412039
$58$	−5.78417	−0.759498
$59$	−7.71075	−1.00385	−0.501927	−	0.864910i	$-0.667375\pi$
$59$	−7.71075	−1.00385	−0.501927	+	0.864910i	$0.667375\pi$
$60$	2.65794	0.343139
$61$	−0.419560	−0.0537192	−0.0268596	−	0.999639i	$-0.508551\pi$
$61$	−0.419560	−0.0537192	−0.0268596	+	0.999639i	$0.508551\pi$
$62$	−2.74586	−0.348725
$63$	0	0
$64$	0.0349308	0.00436635
$65$	5.24364	0.650393
$66$	1.78110	0.219238
$67$	9.95583	1.21630	0.608149	−	0.793823i	$-0.291912\pi$
$67$	9.95583	1.21630	0.608149	+	0.793823i	$0.291912\pi$
$68$	1.79336	0.217476
$69$	6.51222	0.783979
$70$	0	0
$71$	7.39023	0.877059	0.438529	−	0.898717i	$-0.355499\pi$
$71$	7.39023	0.877059	0.438529	+	0.898717i	$0.355499\pi$
$72$	2.27293	0.267867
$73$	−13.9295	−1.63033	−0.815165	−	0.579228i	$-0.803354\pi$
$73$	−13.9295	−1.63033	−0.815165	+	0.579228i	$0.803354\pi$
$74$	7.02071	0.816141
$75$	2.24644	0.259397
$76$	4.98280	0.571567
$77$	0	0
$78$	1.99415	0.225792
$79$	−0.195831	−0.0220327	−0.0110164	−	0.999939i	$-0.503507\pi$
$79$	−0.195831	−0.0220327	−0.0110164	+	0.999939i	$0.503507\pi$
$80$	2.93573	0.328224
$81$	1.00000	0.111111
$82$	0.631061	0.0696890
$83$	2.50464	0.274919	0.137460	−	0.990507i	$-0.456106\pi$
$83$	2.50464	0.274919	0.137460	+	0.990507i	$0.456106\pi$
$84$	0	0
$85$	−1.85787	−0.201515
$86$	0.432003	0.0465841
$87$	−9.16578	−0.982675
$88$	6.41509	0.683851
$89$	12.4999	1.32499	0.662493	−	0.749068i	$-0.269498\pi$
$89$	12.4999	1.32499	0.662493	+	0.749068i	$0.269498\pi$
$90$	−1.04717	−0.110382
$91$	0	0
$92$	10.4310	1.08751
$93$	−4.35118	−0.451196
$94$	3.89626	0.401868
$95$	−5.16206	−0.529616
$96$	5.66231	0.577907
$97$	−11.3773	−1.15519	−0.577593	−	0.816325i	$-0.696008\pi$
$97$	−11.3773	−1.15519	−0.577593	+	0.816325i	$0.696008\pi$
$98$	0	0
$99$	2.82239	0.283660
$100$	3.59827	0.359827
$101$	−14.9268	−1.48527	−0.742634	−	0.669697i	$-0.766424\pi$
$101$	−14.9268	−1.48527	−0.742634	+	0.669697i	$0.766424\pi$
$102$	−0.706545	−0.0699584
$103$	9.93429	0.978854	0.489427	−	0.872044i	$-0.337206\pi$
$103$	9.93429	0.978854	0.489427	+	0.872044i	$0.337206\pi$
$104$	7.18244	0.704296
$105$	0	0
$106$	8.25019	0.801330
$107$	−16.6479	−1.60941	−0.804707	−	0.593673i	$-0.797677\pi$
$107$	−16.6479	−1.60941	−0.804707	+	0.593673i	$0.797677\pi$
$108$	1.60176	0.154130
$109$	17.3263	1.65956	0.829779	−	0.558092i	$-0.188466\pi$
$109$	17.3263	1.65956	0.829779	+	0.558092i	$0.188466\pi$
$110$	−2.95553	−0.281798
$111$	11.1252	1.05596
$112$	0	0
$113$	−10.5963	−0.996820	−0.498410	−	0.866941i	$-0.666083\pi$
$113$	−10.5963	−0.996820	−0.498410	+	0.866941i	$0.666083\pi$
$114$	−1.96312	−0.183863
$115$	−10.8063	−1.00769
$116$	−14.6814	−1.36313
$117$	3.15999	0.292141
$118$	4.86595	0.447947
$119$	0	0
$120$	−3.77167	−0.344305
$121$	−3.03414	−0.275831
$122$	0.264768	0.0239710
$123$	1.00000	0.0901670
$124$	−6.96956	−0.625885
$125$	−12.0246	−1.07552
$126$	0	0
$127$	−6.33759	−0.562371	−0.281185	−	0.959653i	$-0.590728\pi$
$127$	−6.33759	−0.562371	−0.281185	+	0.959653i	$0.590728\pi$
$128$	11.3026	0.999017
$129$	0.684567	0.0602727
$130$	−3.30905	−0.290223
$131$	5.07981	0.443825	0.221913	−	0.975067i	$-0.428770\pi$
$131$	5.07981	0.443825	0.221913	+	0.975067i	$0.428770\pi$
$132$	4.52079	0.393484
$133$	0	0
$134$	−6.28273	−0.542745
$135$	−1.65938	−0.142817
$136$	−2.54481	−0.218215
$137$	−8.11444	−0.693263	−0.346632	−	0.938001i	$-0.612675\pi$
$137$	−8.11444	−0.693263	−0.346632	+	0.938001i	$0.612675\pi$
$138$	−4.10961	−0.349833
$139$	21.7599	1.84565	0.922826	−	0.385216i	$-0.125873\pi$
$139$	21.7599	1.84565	0.922826	+	0.385216i	$0.125873\pi$
$140$	0	0
$141$	6.17414	0.519957
$142$	−4.66368	−0.391368
$143$	8.91871	0.745820
$144$	1.76917	0.147431
$145$	15.2096	1.26309
$146$	8.79039	0.727498
$147$	0	0
$148$	17.8200	1.46479
$149$	14.2646	1.16860	0.584301	−	0.811537i	$-0.301369\pi$
$149$	14.2646	1.16860	0.584301	+	0.811537i	$0.301369\pi$
$150$	−1.41764	−0.115750
$151$	2.29265	0.186573	0.0932867	−	0.995639i	$-0.470263\pi$
$151$	2.29265	0.186573	0.0932867	+	0.995639i	$0.470263\pi$
$152$	−7.07069	−0.573509
$153$	−1.11961	−0.0905155
$154$	0	0
$155$	7.22028	0.579947
$156$	5.06155	0.405248
$157$	24.1517	1.92751	0.963756	−	0.266786i	$-0.0859616\pi$
$157$	24.1517	1.92751	0.963756	+	0.266786i	$0.0859616\pi$
$158$	0.123581	0.00983161
$159$	13.0735	1.03680
$160$	−9.39596	−0.742816
$161$	0	0
$162$	−0.631061	−0.0495808
$163$	−0.309243	−0.0242218	−0.0121109	−	0.999927i	$-0.503855\pi$
$163$	−0.309243	−0.0242218	−0.0121109	+	0.999927i	$0.503855\pi$
$164$	1.60176	0.125077
$165$	−4.68342	−0.364604
$166$	−1.58058	−0.122677
$167$	3.45676	0.267492	0.133746	−	0.991016i	$-0.457299\pi$
$167$	3.45676	0.267492	0.133746	+	0.991016i	$0.457299\pi$
$168$	0	0
$169$	−3.01447	−0.231882
$170$	1.17243	0.0899213
$171$	−3.11082	−0.237891
$172$	1.09651	0.0836083
$173$	15.7701	1.19898	0.599489	−	0.800383i	$-0.295370\pi$
$173$	15.7701	1.19898	0.599489	+	0.800383i	$0.295370\pi$
$174$	5.78417	0.438496
$175$	0	0
$176$	4.99327	0.376382
$177$	7.71075	0.579575
$178$	−7.88820	−0.591245
$179$	16.6359	1.24343	0.621714	−	0.783244i	$-0.286437\pi$
$179$	16.6359	1.24343	0.621714	+	0.783244i	$0.286437\pi$
$180$	−2.65794	−0.198111
$181$	−15.8774	−1.18016	−0.590078	−	0.807346i	$-0.700903\pi$
$181$	−15.8774	−1.18016	−0.590078	+	0.807346i	$0.700903\pi$
$182$	0	0
$183$	0.419560	0.0310148
$184$	−14.8018	−1.09121
$185$	−18.4611	−1.35728
$186$	2.74586	0.201336
$187$	−3.15999	−0.231081
$188$	9.88951	0.721267
$189$	0	0
$190$	3.25757	0.236329
$191$	−21.0219	−1.52109	−0.760545	−	0.649285i	$-0.775068\pi$
$191$	−21.0219	−1.52109	−0.760545	+	0.649285i	$0.775068\pi$
$192$	−0.0349308	−0.00252091
$193$	−19.9012	−1.43252	−0.716261	−	0.697833i	$-0.754148\pi$
$193$	−19.9012	−1.43252	−0.716261	+	0.697833i	$0.754148\pi$
$194$	7.17975	0.515476
$195$	−5.24364	−0.375505
$196$	0	0
$197$	−20.1886	−1.43838	−0.719189	−	0.694814i	$-0.755487\pi$
$197$	−20.1886	−1.43838	−0.719189	+	0.694814i	$0.755487\pi$
$198$	−1.78110	−0.126577
$199$	22.6327	1.60439	0.802195	−	0.597062i	$-0.203665\pi$
$199$	22.6327	1.60439	0.802195	+	0.597062i	$0.203665\pi$
$200$	−5.10601	−0.361049
$201$	−9.95583	−0.702230
$202$	9.41969	0.662767
$203$	0	0
$204$	−1.79336	−0.125560
$205$	−1.65938	−0.115896
$206$	−6.26914	−0.436792
$207$	−6.51222	−0.452631
$208$	5.59055	0.387635
$209$	−8.77995	−0.607322
$210$	0	0
$211$	−4.48974	−0.309086	−0.154543	−	0.987986i	$-0.549391\pi$
$211$	−4.48974	−0.309086	−0.154543	+	0.987986i	$0.549391\pi$
$212$	20.9407	1.43821
$213$	−7.39023	−0.506370
$214$	10.5058	0.718164
$215$	−1.13596	−0.0774718
$216$	−2.27293	−0.154653
$217$	0	0
$218$	−10.9340	−0.740541
$219$	13.9295	0.941272
$220$	−7.50173	−0.505767
$221$	−3.53797	−0.237990
$222$	−7.02071	−0.471199
$223$	−22.8364	−1.52924	−0.764620	−	0.644481i	$-0.777074\pi$
$223$	−22.8364	−1.52924	−0.764620	+	0.644481i	$0.777074\pi$
$224$	0	0
$225$	−2.24644	−0.149763
$226$	6.68694	0.444808
$227$	14.6770	0.974148	0.487074	−	0.873361i	$-0.338064\pi$
$227$	14.6770	0.974148	0.487074	+	0.873361i	$0.338064\pi$
$228$	−4.98280	−0.329994
$229$	−10.8858	−0.719352	−0.359676	−	0.933077i	$-0.617113\pi$
$229$	−10.8858	−0.719352	−0.359676	+	0.933077i	$0.617113\pi$
$230$	6.81942	0.449659
$231$	0	0
$232$	20.8332	1.36777
$233$	−10.6391	−0.696994	−0.348497	−	0.937310i	$-0.613308\pi$
$233$	−10.6391	−0.696994	−0.348497	+	0.937310i	$0.613308\pi$
$234$	−1.99415	−0.130361
$235$	−10.2453	−0.668328
$236$	12.3508	0.803968
$237$	0.195831	0.0127206
$238$	0	0
$239$	3.02612	0.195743	0.0978716	−	0.995199i	$-0.468797\pi$
$239$	3.02612	0.195743	0.0978716	+	0.995199i	$0.468797\pi$
$240$	−2.93573	−0.189500
$241$	−18.4381	−1.18770	−0.593851	−	0.804575i	$-0.702393\pi$
$241$	−18.4381	−1.18770	−0.593851	+	0.804575i	$0.702393\pi$
$242$	1.91473	0.123083
$243$	−1.00000	−0.0641500
$244$	0.672036	0.0430227
$245$	0	0
$246$	−0.631061	−0.0402350
$247$	−9.83017	−0.625479
$248$	9.88993	0.628011
$249$	−2.50464	−0.158725
$250$	7.58828	0.479925
$251$	−1.85759	−0.117250	−0.0586252	−	0.998280i	$-0.518672\pi$
$251$	−1.85759	−0.117250	−0.0586252	+	0.998280i	$0.518672\pi$
$252$	0	0
$253$	−18.3800	−1.15554
$254$	3.99941	0.250945
$255$	1.85787	0.116344
$256$	−7.20248	−0.450155
$257$	10.6305	0.663113	0.331557	−	0.943435i	$-0.392426\pi$
$257$	10.6305	0.663113	0.331557	+	0.943435i	$0.392426\pi$
$258$	−0.432003	−0.0268953
$259$	0	0
$260$	−8.39906	−0.520888
$261$	9.16578	0.567348
$262$	−3.20567	−0.198047
$263$	−29.4520	−1.81609	−0.908043	−	0.418878i	$-0.862424\pi$
$263$	−29.4520	−1.81609	−0.908043	+	0.418878i	$0.862424\pi$
$264$	−6.41509	−0.394821
$265$	−21.6940	−1.33265
$266$	0	0
$267$	−12.4999	−0.764981
$268$	−15.9469	−0.974110
$269$	9.23627	0.563145	0.281573	−	0.959540i	$-0.409144\pi$
$269$	9.23627	0.563145	0.281573	+	0.959540i	$0.409144\pi$
$270$	1.04717	0.0637289
$271$	7.69672	0.467542	0.233771	−	0.972292i	$-0.424893\pi$
$271$	7.69672	0.467542	0.233771	+	0.972292i	$0.424893\pi$
$272$	−1.98079	−0.120103
$273$	0	0
$274$	5.12070	0.309353
$275$	−6.34032	−0.382336
$276$	−10.4310	−0.627874
$277$	−19.4269	−1.16725	−0.583624	−	0.812024i	$-0.698366\pi$
$277$	−19.4269	−1.16725	−0.583624	+	0.812024i	$0.698366\pi$
$278$	−13.7318	−0.823581
$279$	4.35118	0.260498
$280$	0	0
$281$	0.197677	0.0117924	0.00589622	−	0.999983i	$-0.498123\pi$
$281$	0.197677	0.0117924	0.00589622	+	0.999983i	$0.498123\pi$
$282$	−3.89626	−0.232019
$283$	−31.9961	−1.90197	−0.950985	−	0.309238i	$-0.899926\pi$
$283$	−31.9961	−1.90197	−0.950985	+	0.309238i	$0.899926\pi$
$284$	−11.8374	−0.702420
$285$	5.16206	0.305774
$286$	−5.62825	−0.332805
$287$	0	0
$288$	−5.66231	−0.333655
$289$	−15.7465	−0.926262
$290$	−9.59816	−0.563623
$291$	11.3773	0.666947
$292$	22.3118	1.30570
$293$	17.2175	1.00586	0.502930	−	0.864327i	$-0.332255\pi$
$293$	17.2175	1.00586	0.502930	+	0.864327i	$0.332255\pi$
$294$	0	0
$295$	−12.7951	−0.744960
$296$	−25.2869	−1.46977
$297$	−2.82239	−0.163771
$298$	−9.00183	−0.521462
$299$	−20.5786	−1.19009
$300$	−3.59827	−0.207746
$301$	0	0
$302$	−1.44680	−0.0832542
$303$	14.9268	0.857520
$304$	−5.50357	−0.315651
$305$	−0.696212	−0.0398650
$306$	0.706545	0.0403905
$307$	24.2479	1.38390	0.691950	−	0.721946i	$-0.256752\pi$
$307$	24.2479	1.38390	0.691950	+	0.721946i	$0.256752\pi$
$308$	0	0
$309$	−9.93429	−0.565142
$310$	−4.55644	−0.258788
$311$	−10.2592	−0.581744	−0.290872	−	0.956762i	$-0.593945\pi$
$311$	−10.2592	−0.581744	−0.290872	+	0.956762i	$0.593945\pi$
$312$	−7.18244	−0.406625
$313$	25.6802	1.45153	0.725765	−	0.687943i	$-0.241486\pi$
$313$	25.6802	1.45153	0.725765	+	0.687943i	$0.241486\pi$
$314$	−15.2412	−0.860109
$315$	0	0
$316$	0.313675	0.0176456
$317$	−19.2173	−1.07935	−0.539675	−	0.841874i	$-0.681453\pi$
$317$	−19.2173	−1.07935	−0.539675	+	0.841874i	$0.681453\pi$
$318$	−8.25019	−0.462648
$319$	25.8694	1.44841
$320$	0.0579636	0.00324026
$321$	16.6479	0.929195
$322$	0	0
$323$	3.48293	0.193795
$324$	−1.60176	−0.0889868
$325$	−7.09873	−0.393767
$326$	0.195151	0.0108084
$327$	−17.3263	−0.958147
$328$	−2.27293	−0.125502
$329$	0	0
$330$	2.95553	0.162696
$331$	0.536324	0.0294790	0.0147395	−	0.999891i	$-0.495308\pi$
$331$	0.536324	0.0294790	0.0147395	+	0.999891i	$0.495308\pi$
$332$	−4.01183	−0.220178
$333$	−11.1252	−0.609660
$334$	−2.18143	−0.119362
$335$	16.5205	0.902614
$336$	0	0
$337$	11.5251	0.627810	0.313905	−	0.949454i	$-0.398363\pi$
$337$	11.5251	0.627810	0.313905	+	0.949454i	$0.398363\pi$
$338$	1.90231	0.103472
$339$	10.5963	0.575514
$340$	2.97587	0.161389
$341$	12.2807	0.665038
$342$	1.96312	0.106153
$343$	0	0
$344$	−1.55597	−0.0838924
$345$	10.8063	0.581791
$346$	−9.95189	−0.535017
$347$	−21.9533	−1.17852	−0.589258	−	0.807945i	$-0.700580\pi$
$347$	−21.9533	−1.17852	−0.589258	+	0.807945i	$0.700580\pi$
$348$	14.6814	0.787006
$349$	−5.35886	−0.286853	−0.143427	−	0.989661i	$-0.545812\pi$
$349$	−5.35886	−0.286853	−0.143427	+	0.989661i	$0.545812\pi$
$350$	0	0
$351$	−3.15999	−0.168668
$352$	−15.9812	−0.851803
$353$	−9.44187	−0.502540	−0.251270	−	0.967917i	$-0.580848\pi$
$353$	−9.44187	−0.502540	−0.251270	+	0.967917i	$0.580848\pi$
$354$	−4.86595	−0.258622
$355$	12.2632	0.650865
$356$	−20.0219	−1.06116
$357$	0	0
$358$	−10.4983	−0.554852
$359$	−4.43594	−0.234120	−0.117060	−	0.993125i	$-0.537347\pi$
$359$	−4.43594	−0.234120	−0.117060	+	0.993125i	$0.537347\pi$
$360$	3.77167	0.198784
$361$	−9.32277	−0.490672
$362$	10.0196	0.526618
$363$	3.03414	0.159251
$364$	0	0
$365$	−23.1145	−1.20987
$366$	−0.264768	−0.0138397
$367$	7.96777	0.415914	0.207957	−	0.978138i	$-0.433319\pi$
$367$	7.96777	0.415914	0.207957	+	0.978138i	$0.433319\pi$
$368$	−11.5212	−0.600584
$369$	−1.00000	−0.0520579
$370$	11.6501	0.605658
$371$	0	0
$372$	6.96956	0.361355
$373$	−16.7465	−0.867103	−0.433552	−	0.901129i	$-0.642740\pi$
$373$	−16.7465	−0.867103	−0.433552	+	0.901129i	$0.642740\pi$
$374$	1.99414	0.103115
$375$	12.0246	0.620950
$376$	−14.0334	−0.723717
$377$	28.9638	1.49171
$378$	0	0
$379$	−7.02596	−0.360899	−0.180450	−	0.983584i	$-0.557755\pi$
$379$	−7.02596	−0.360899	−0.180450	+	0.983584i	$0.557755\pi$
$380$	8.26839	0.424159
$381$	6.33759	0.324685
$382$	13.2661	0.678752
$383$	23.3436	1.19280	0.596401	−	0.802687i	$-0.296597\pi$
$383$	23.3436	1.19280	0.596401	+	0.802687i	$0.296597\pi$
$384$	−11.3026	−0.576783
$385$	0	0
$386$	12.5589	0.639230
$387$	−0.684567	−0.0347985
$388$	18.2237	0.925167
$389$	1.37396	0.0696626	0.0348313	−	0.999393i	$-0.488911\pi$
$389$	1.37396	0.0696626	0.0348313	+	0.999393i	$0.488911\pi$
$390$	3.30905	0.167560
$391$	7.29118	0.368731
$392$	0	0
$393$	−5.07981	−0.256243
$394$	12.7402	0.641844
$395$	−0.324960	−0.0163505
$396$	−4.52079	−0.227178
$397$	−27.4009	−1.37521	−0.687605	−	0.726085i	$-0.741338\pi$
$397$	−27.4009	−1.37521	−0.687605	+	0.726085i	$0.741338\pi$
$398$	−14.2826	−0.715923
$399$	0	0
$400$	−3.97433	−0.198716
$401$	−2.84574	−0.142109	−0.0710547	−	0.997472i	$-0.522636\pi$
$401$	−2.84574	−0.142109	−0.0710547	+	0.997472i	$0.522636\pi$
$402$	6.28273	0.313354
$403$	13.7497	0.684921
$404$	23.9091	1.18952
$405$	1.65938	0.0824555
$406$	0	0
$407$	−31.3997	−1.55643
$408$	2.54481	0.125987
$409$	−28.4383	−1.40619	−0.703093	−	0.711098i	$-0.748198\pi$
$409$	−28.4383	−1.40619	−0.703093	+	0.711098i	$0.748198\pi$
$410$	1.04717	0.0517162
$411$	8.11444	0.400256
$412$	−15.9124	−0.783946
$413$	0	0
$414$	4.10961	0.201976
$415$	4.15615	0.204018
$416$	−17.8928	−0.877269
$417$	−21.7599	−1.06559
$418$	5.54068	0.271004
$419$	−10.4579	−0.510904	−0.255452	−	0.966822i	$-0.582224\pi$
$419$	−10.4579	−0.510904	−0.255452	+	0.966822i	$0.582224\pi$
$420$	0	0
$421$	−18.4016	−0.896839	−0.448419	−	0.893823i	$-0.648013\pi$
$421$	−18.4016	−0.896839	−0.448419	+	0.893823i	$0.648013\pi$
$422$	2.83330	0.137923
$423$	−6.17414	−0.300197
$424$	−29.7152	−1.44310
$425$	2.51515	0.122003
$426$	4.66368	0.225956
$427$	0	0
$428$	26.6660	1.28895
$429$	−8.91871	−0.430599
$430$	0.716860	0.0345700
$431$	−7.16006	−0.344888	−0.172444	−	0.985019i	$-0.555166\pi$
$431$	−7.16006	−0.344888	−0.172444	+	0.985019i	$0.555166\pi$
$432$	−1.76917	−0.0851191
$433$	−32.8811	−1.58016	−0.790082	−	0.613001i	$-0.789962\pi$
$433$	−32.8811	−1.58016	−0.790082	+	0.613001i	$0.789962\pi$
$434$	0	0
$435$	−15.2096	−0.729243
$436$	−27.7526	−1.32911
$437$	20.2584	0.969090
$438$	−8.79039	−0.420021
$439$	−3.76719	−0.179798	−0.0898991	−	0.995951i	$-0.528654\pi$
$439$	−3.76719	−0.179798	−0.0898991	+	0.995951i	$0.528654\pi$
$440$	10.6451	0.507485
$441$	0	0
$442$	2.23267	0.106198
$443$	30.3572	1.44232	0.721158	−	0.692770i	$-0.243610\pi$
$443$	30.3572	1.44232	0.721158	+	0.692770i	$0.243610\pi$
$444$	−17.8200	−0.845700
$445$	20.7421	0.983272
$446$	14.4112	0.682389
$447$	−14.2646	−0.674692
$448$	0	0
$449$	22.5523	1.06431	0.532154	−	0.846648i	$-0.321383\pi$
$449$	22.5523	1.06431	0.532154	+	0.846648i	$0.321383\pi$
$450$	1.41764	0.0668282
$451$	−2.82239	−0.132901
$452$	16.9728	0.798334
$453$	−2.29265	−0.107718
$454$	−9.26209	−0.434691
$455$	0	0
$456$	7.07069	0.331115
$457$	−14.6973	−0.687509	−0.343755	−	0.939060i	$-0.611699\pi$
$457$	−14.6973	−0.687509	−0.343755	+	0.939060i	$0.611699\pi$
$458$	6.86959	0.320995
$459$	1.11961	0.0522591
$460$	17.3091	0.807041
$461$	19.3426	0.900874	0.450437	−	0.892808i	$-0.351268\pi$
$461$	19.3426	0.900874	0.450437	+	0.892808i	$0.351268\pi$
$462$	0	0
$463$	3.19576	0.148520	0.0742598	−	0.997239i	$-0.476341\pi$
$463$	3.19576	0.148520	0.0742598	+	0.997239i	$0.476341\pi$
$464$	16.2158	0.752799
$465$	−7.22028	−0.334833
$466$	6.71395	0.311018
$467$	17.7807	0.822791	0.411396	−	0.911457i	$-0.365042\pi$
$467$	17.7807	0.822791	0.411396	+	0.911457i	$0.365042\pi$
$468$	−5.06155	−0.233970
$469$	0	0
$470$	6.46539	0.298226
$471$	−24.1517	−1.11285
$472$	−17.5260	−0.806700
$473$	−1.93211	−0.0888386
$474$	−0.123581	−0.00567628
$475$	6.98829	0.320645
$476$	0	0
$477$	−13.0735	−0.598596
$478$	−1.90966	−0.0873460
$479$	34.2608	1.56542	0.782709	−	0.622388i	$-0.213837\pi$
$479$	34.2608	1.56542	0.782709	+	0.622388i	$0.213837\pi$
$480$	9.39596	0.428865
$481$	−35.1557	−1.60296
$482$	11.6356	0.529985
$483$	0	0
$484$	4.85997	0.220908
$485$	−18.8793	−0.857263
$486$	0.631061	0.0286255
$487$	29.6230	1.34234	0.671172	−	0.741301i	$-0.265791\pi$
$487$	29.6230	1.34234	0.671172	+	0.741301i	$0.265791\pi$
$488$	−0.953632	−0.0431689
$489$	0.309243	0.0139845
$490$	0	0
$491$	−15.7558	−0.711049	−0.355525	−	0.934667i	$-0.615698\pi$
$491$	−15.7558	−0.711049	−0.355525	+	0.934667i	$0.615698\pi$
$492$	−1.60176	−0.0722130
$493$	−10.2621	−0.462184
$494$	6.20344	0.279106
$495$	4.68342	0.210504
$496$	7.69796	0.345649
$497$	0	0
$498$	1.58058	0.0708274
$499$	3.95585	0.177088	0.0885441	−	0.996072i	$-0.471779\pi$
$499$	3.95585	0.177088	0.0885441	+	0.996072i	$0.471779\pi$
$500$	19.2606	0.861361
$501$	−3.45676	−0.154437
$502$	1.17226	0.0523203
$503$	33.0299	1.47273	0.736366	−	0.676583i	$-0.236540\pi$
$503$	33.0299	1.47273	0.736366	+	0.676583i	$0.236540\pi$
$504$	0	0
$505$	−24.7692	−1.10222
$506$	11.5989	0.515634
$507$	3.01447	0.133877
$508$	10.1513	0.450392
$509$	−25.8609	−1.14626	−0.573131	−	0.819463i	$-0.694272\pi$
$509$	−25.8609	−1.14626	−0.573131	+	0.819463i	$0.694272\pi$
$510$	−1.17243	−0.0519161
$511$	0	0
$512$	−18.0600	−0.798145
$513$	3.11082	0.137346
$514$	−6.70850	−0.295899
$515$	16.4848	0.726407
$516$	−1.09651	−0.0482713
$517$	−17.4258	−0.766386
$518$	0	0
$519$	−15.7701	−0.692230
$520$	11.9184	0.522658
$521$	−1.48131	−0.0648972	−0.0324486	−	0.999473i	$-0.510331\pi$
$521$	−1.48131	−0.0648972	−0.0324486	+	0.999473i	$0.510331\pi$
$522$	−5.78417	−0.253166
$523$	−30.6601	−1.34067	−0.670336	−	0.742057i	$-0.733850\pi$
$523$	−30.6601	−1.34067	−0.670336	+	0.742057i	$0.733850\pi$
$524$	−8.13665	−0.355451
$525$	0	0
$526$	18.5860	0.810387
$527$	−4.87165	−0.212212
$528$	−4.99327	−0.217304
$529$	19.4090	0.843871
$530$	13.6902	0.594666
$531$	−7.71075	−0.334618
$532$	0	0
$533$	−3.15999	−0.136874
$534$	7.88820	0.341356
$535$	−27.6253	−1.19434
$536$	22.6289	0.977420
$537$	−16.6359	−0.717894
$538$	−5.82865	−0.251291
$539$	0	0
$540$	2.65794	0.114380
$541$	−6.28709	−0.270303	−0.135151	−	0.990825i	$-0.543152\pi$
$541$	−6.28709	−0.270303	−0.135151	+	0.990825i	$0.543152\pi$
$542$	−4.85710	−0.208630
$543$	15.8774	0.681363
$544$	6.33961	0.271809
$545$	28.7510	1.23156
$546$	0	0
$547$	13.2731	0.567515	0.283758	−	0.958896i	$-0.408419\pi$
$547$	13.2731	0.567515	0.283758	+	0.958896i	$0.408419\pi$
$548$	12.9974	0.555221
$549$	−0.419560	−0.0179064
$550$	4.00113	0.170609
$551$	−28.5131	−1.21470
$552$	14.8018	0.630008
$553$	0	0
$554$	12.2595	0.520858
$555$	18.4611	0.783629
$556$	−34.8542	−1.47815
$557$	−31.4107	−1.33091	−0.665457	−	0.746436i	$-0.731763\pi$
$557$	−31.4107	−1.33091	−0.665457	+	0.746436i	$0.731763\pi$
$558$	−2.74586	−0.116242
$559$	−2.16322	−0.0914946
$560$	0	0
$561$	3.15999	0.133415
$562$	−0.124746	−0.00526211
$563$	−0.492351	−0.0207501	−0.0103751	−	0.999946i	$-0.503303\pi$
$563$	−0.492351	−0.0207501	−0.0103751	+	0.999946i	$0.503303\pi$
$564$	−9.88951	−0.416423
$565$	−17.5834	−0.739740
$566$	20.1915	0.848711
$567$	0	0
$568$	16.7975	0.704807
$569$	8.70460	0.364916	0.182458	−	0.983214i	$-0.441595\pi$
$569$	8.70460	0.364916	0.182458	+	0.983214i	$0.441595\pi$
$570$	−3.25757	−0.136445
$571$	−36.8663	−1.54281	−0.771403	−	0.636347i	$-0.780445\pi$
$571$	−36.8663	−1.54281	−0.771403	+	0.636347i	$0.780445\pi$
$572$	−14.2856	−0.597313
$573$	21.0219	0.878202
$574$	0	0
$575$	14.6293	0.610085
$576$	0.0349308	0.00145545
$577$	−0.227862	−0.00948604	−0.00474302	−	0.999989i	$-0.501510\pi$
$577$	−0.227862	−0.00948604	−0.00474302	+	0.999989i	$0.501510\pi$
$578$	9.93698	0.413324
$579$	19.9012	0.827067
$580$	−24.3621	−1.01158
$581$	0	0
$582$	−7.17975	−0.297610
$583$	−36.8985	−1.52818
$584$	−31.6609	−1.31014
$585$	5.24364	0.216798
$586$	−10.8653	−0.448842
$587$	4.58547	0.189262	0.0946312	−	0.995512i	$-0.469833\pi$
$587$	4.58547	0.189262	0.0946312	+	0.995512i	$0.469833\pi$
$588$	0	0
$589$	−13.5358	−0.557731
$590$	8.07449	0.332421
$591$	20.1886	0.830448
$592$	−19.6824	−0.808942
$593$	9.17184	0.376642	0.188321	−	0.982108i	$-0.439695\pi$
$593$	9.17184	0.376642	0.188321	+	0.982108i	$0.439695\pi$
$594$	1.78110	0.0730793
$595$	0	0
$596$	−22.8485	−0.935911
$597$	−22.6327	−0.926295
$598$	12.9863	0.531050
$599$	−36.1676	−1.47777	−0.738884	−	0.673832i	$-0.764647\pi$
$599$	−36.1676	−1.47777	−0.738884	+	0.673832i	$0.764647\pi$
$600$	5.10601	0.208452
$601$	−1.30057	−0.0530515	−0.0265258	−	0.999648i	$-0.508444\pi$
$601$	−1.30057	−0.0530515	−0.0265258	+	0.999648i	$0.508444\pi$
$602$	0	0
$603$	9.95583	0.405433
$604$	−3.67229	−0.149423
$605$	−5.03480	−0.204694
$606$	−9.41969	−0.382649
$607$	−19.2109	−0.779745	−0.389872	−	0.920869i	$-0.627481\pi$
$607$	−19.2109	−0.779745	−0.389872	+	0.920869i	$0.627481\pi$
$608$	17.6145	0.714361
$609$	0	0
$610$	0.439352	0.0177889
$611$	−19.5102	−0.789299
$612$	1.79336	0.0724922
$613$	8.59390	0.347104	0.173552	−	0.984825i	$-0.444475\pi$
$613$	8.59390	0.347104	0.173552	+	0.984825i	$0.444475\pi$
$614$	−15.3019	−0.617534
$615$	1.65938	0.0669129
$616$	0	0
$617$	1.93896	0.0780595	0.0390298	−	0.999238i	$-0.487573\pi$
$617$	1.93896	0.0780595	0.0390298	+	0.999238i	$0.487573\pi$
$618$	6.26914	0.252182
$619$	−4.54259	−0.182582	−0.0912910	−	0.995824i	$-0.529099\pi$
$619$	−4.54259	−0.182582	−0.0912910	+	0.995824i	$0.529099\pi$
$620$	−11.5652	−0.464469
$621$	6.51222	0.261326
$622$	6.47416	0.259590
$623$	0	0
$624$	−5.59055	−0.223801
$625$	−8.72129	−0.348852
$626$	−16.2058	−0.647712
$627$	8.77995	0.350637
$628$	−38.6852	−1.54371
$629$	12.4560	0.496653
$630$	0	0
$631$	−42.7975	−1.70374	−0.851870	−	0.523754i	$-0.824531\pi$
$631$	−42.7975	−1.70374	−0.851870	+	0.523754i	$0.824531\pi$
$632$	−0.445111	−0.0177056
$633$	4.48974	0.178451
$634$	12.1273	0.481635
$635$	−10.5165	−0.417335
$636$	−20.9407	−0.830352
$637$	0	0
$638$	−16.3251	−0.646319
$639$	7.39023	0.292353
$640$	18.7553	0.741370
$641$	30.8886	1.22003	0.610013	−	0.792391i	$-0.291164\pi$
$641$	30.8886	1.22003	0.610013	+	0.792391i	$0.291164\pi$
$642$	−10.5058	−0.414632
$643$	−16.5004	−0.650712	−0.325356	−	0.945592i	$-0.605484\pi$
$643$	−16.5004	−0.650712	−0.325356	+	0.945592i	$0.605484\pi$
$644$	0	0
$645$	1.13596	0.0447284
$646$	−2.19794	−0.0864767
$647$	22.9982	0.904152	0.452076	−	0.891979i	$-0.350684\pi$
$647$	22.9982	0.904152	0.452076	+	0.891979i	$0.350684\pi$
$648$	2.27293	0.0892892
$649$	−21.7627	−0.854261
$650$	4.47973	0.175709
$651$	0	0
$652$	0.495334	0.0193988
$653$	26.0313	1.01868	0.509342	−	0.860564i	$-0.329889\pi$
$653$	26.0313	1.01868	0.509342	+	0.860564i	$0.329889\pi$
$654$	10.9340	0.427551
$655$	8.42936	0.329362
$656$	−1.76917	−0.0690744
$657$	−13.9295	−0.543443
$658$	0	0
$659$	13.0247	0.507369	0.253684	−	0.967287i	$-0.418358\pi$
$659$	13.0247	0.507369	0.253684	+	0.967287i	$0.418358\pi$
$660$	7.50173	0.292005
$661$	26.1475	1.01702	0.508510	−	0.861056i	$-0.330197\pi$
$661$	26.1475	1.01702	0.508510	+	0.861056i	$0.330197\pi$
$662$	−0.338453	−0.0131544
$663$	3.53797	0.137403
$664$	5.69286	0.220926
$665$	0	0
$666$	7.02071	0.272047
$667$	−59.6896	−2.31119
$668$	−5.53691	−0.214229
$669$	22.8364	0.882908
$670$	−10.4255	−0.402771
$671$	−1.18416	−0.0457140
$672$	0	0
$673$	10.6856	0.411901	0.205951	−	0.978562i	$-0.433971\pi$
$673$	10.6856	0.411901	0.205951	+	0.978562i	$0.433971\pi$
$674$	−7.27302	−0.280146
$675$	2.24644	0.0864656
$676$	4.82846	0.185710
$677$	16.2993	0.626431	0.313216	−	0.949682i	$-0.398594\pi$
$677$	16.2993	0.626431	0.313216	+	0.949682i	$0.398594\pi$
$678$	−6.68694	−0.256810
$679$	0	0
$680$	−4.22282	−0.161938
$681$	−14.6770	−0.562424
$682$	−7.74987	−0.296758
$683$	6.89890	0.263979	0.131990	−	0.991251i	$-0.457863\pi$
$683$	6.89890	0.263979	0.131990	+	0.991251i	$0.457863\pi$
$684$	4.98280	0.190522
$685$	−13.4650	−0.514470
$686$	0	0
$687$	10.8858	0.415318
$688$	−1.21111	−0.0461732
$689$	−41.3122	−1.57387
$690$	−6.81942	−0.259611
$691$	−10.9192	−0.415385	−0.207692	−	0.978194i	$-0.566595\pi$
$691$	−10.9192	−0.415385	−0.207692	+	0.978194i	$0.566595\pi$
$692$	−25.2599	−0.960239
$693$	0	0
$694$	13.8539	0.525886
$695$	36.1081	1.36966
$696$	−20.8332	−0.789680
$697$	1.11961	0.0424084
$698$	3.38177	0.128002
$699$	10.6391	0.402409
$700$	0	0
$701$	−34.1965	−1.29158	−0.645791	−	0.763514i	$-0.723472\pi$
$701$	−34.1965	−1.29158	−0.645791	+	0.763514i	$0.723472\pi$
$702$	1.99415	0.0752642
$703$	34.6087	1.30529
$704$	0.0985881	0.00371568
$705$	10.2453	0.385860
$706$	5.95840	0.224247
$707$	0	0
$708$	−12.3508	−0.464171
$709$	16.4538	0.617934	0.308967	−	0.951073i	$-0.400017\pi$
$709$	16.4538	0.617934	0.308967	+	0.951073i	$0.400017\pi$
$710$	−7.73885	−0.290434
$711$	−0.195831	−0.00734425
$712$	28.4114	1.06476
$713$	−28.3359	−1.06119
$714$	0	0
$715$	14.7996	0.553473
$716$	−26.6468	−0.995838
$717$	−3.02612	−0.113012
$718$	2.79935	0.104471
$719$	−17.6106	−0.656764	−0.328382	−	0.944545i	$-0.606503\pi$
$719$	−17.6106	−0.656764	−0.328382	+	0.944545i	$0.606503\pi$
$720$	2.93573	0.109408
$721$	0	0
$722$	5.88323	0.218951
$723$	18.4381	0.685720
$724$	25.4318	0.945164
$725$	−20.5904	−0.764708
$726$	−1.91473	−0.0710622
$727$	−34.6841	−1.28636	−0.643181	−	0.765714i	$-0.722386\pi$
$727$	−34.6841	−1.28636	−0.643181	+	0.765714i	$0.722386\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.5866	0.539876
$731$	0.766451	0.0283482
$732$	−0.672036	−0.0248392
$733$	−14.9917	−0.553731	−0.276865	−	0.960909i	$-0.589296\pi$
$733$	−14.9917	−0.553731	−0.276865	+	0.960909i	$0.589296\pi$
$734$	−5.02814	−0.185592
$735$	0	0
$736$	36.8742	1.35920
$737$	28.0992	1.03505
$738$	0.631061	0.0232297
$739$	11.5757	0.425820	0.212910	−	0.977072i	$-0.431706\pi$
$739$	11.5757	0.425820	0.212910	+	0.977072i	$0.431706\pi$
$740$	29.5702	1.08702
$741$	9.83017	0.361120
$742$	0	0
$743$	25.7503	0.944687	0.472343	−	0.881415i	$-0.343408\pi$
$743$	25.7503	0.944687	0.472343	+	0.881415i	$0.343408\pi$
$744$	−9.88993	−0.362583
$745$	23.6705	0.867218
$746$	10.5681	0.386925
$747$	2.50464	0.0916398
$748$	5.06154	0.185068
$749$	0	0
$750$	−7.58828	−0.277085
$751$	−14.3476	−0.523550	−0.261775	−	0.965129i	$-0.584308\pi$
$751$	−14.3476	−0.523550	−0.261775	+	0.965129i	$0.584308\pi$
$752$	−10.9231	−0.398324
$753$	1.85759	0.0676945
$754$	−18.2779	−0.665642
$755$	3.80439	0.138456
$756$	0	0
$757$	52.9415	1.92419	0.962095	−	0.272714i	$-0.0879213\pi$
$757$	52.9415	1.92419	0.962095	+	0.272714i	$0.0879213\pi$
$758$	4.43381	0.161043
$759$	18.3800	0.667152
$760$	−11.7330	−0.425601
$761$	−23.8612	−0.864969	−0.432485	−	0.901641i	$-0.642363\pi$
$761$	−23.8612	−0.864969	−0.432485	+	0.901641i	$0.642363\pi$
$762$	−3.99941	−0.144883
$763$	0	0
$764$	33.6721	1.21821
$765$	−1.85787	−0.0671715
$766$	−14.7312	−0.532261
$767$	−24.3659	−0.879801
$768$	7.20248	0.259897
$769$	−40.3431	−1.45481	−0.727405	−	0.686208i	$-0.759274\pi$
$769$	−40.3431	−1.45481	−0.727405	+	0.686208i	$0.759274\pi$
$770$	0	0
$771$	−10.6305	−0.382849
$772$	31.8770	1.14728
$773$	23.3193	0.838736	0.419368	−	0.907816i	$-0.362252\pi$
$773$	23.3193	0.838736	0.419368	+	0.907816i	$0.362252\pi$
$774$	0.432003	0.0155280
$775$	−9.77467	−0.351117
$776$	−25.8597	−0.928311
$777$	0	0
$778$	−0.867053	−0.0310854
$779$	3.11082	0.111457
$780$	8.39906	0.300735
$781$	20.8581	0.746361
$782$	−4.60118	−0.164538
$783$	−9.16578	−0.327558
$784$	0	0
$785$	40.0769	1.43041
$786$	3.20567	0.114342
$787$	38.4755	1.37150	0.685752	−	0.727835i	$-0.259473\pi$
$787$	38.4755	1.37150	0.685752	+	0.727835i	$0.259473\pi$
$788$	32.3373	1.15197
$789$	29.4520	1.04852
$790$	0.205069	0.00729604
$791$	0	0
$792$	6.41509	0.227950
$793$	−1.32581	−0.0470808
$794$	17.2916	0.613657
$795$	21.6940	0.769408
$796$	−36.2522	−1.28493
$797$	−8.86744	−0.314101	−0.157050	−	0.987591i	$-0.550198\pi$
$797$	−8.86744	−0.314101	−0.157050	+	0.987591i	$0.550198\pi$
$798$	0	0
$799$	6.91266	0.244552
$800$	12.7201	0.449722
$801$	12.4999	0.441662
$802$	1.79583	0.0634131
$803$	−39.3146	−1.38738
$804$	15.9469	0.562403
$805$	0	0
$806$	−8.67689	−0.305630
$807$	−9.23627	−0.325132
$808$	−33.9275	−1.19357
$809$	−8.17161	−0.287299	−0.143649	−	0.989629i	$-0.545884\pi$
$809$	−8.17161	−0.287299	−0.143649	+	0.989629i	$0.545884\pi$
$810$	−1.04717	−0.0367939
$811$	−5.53278	−0.194282	−0.0971411	−	0.995271i	$-0.530970\pi$
$811$	−5.53278	−0.194282	−0.0971411	+	0.995271i	$0.530970\pi$
$812$	0	0
$813$	−7.69672	−0.269936
$814$	19.8151	0.694520
$815$	−0.513153	−0.0179750
$816$	1.98079	0.0693414
$817$	2.12957	0.0745041
$818$	17.9463	0.627478
$819$	0	0
$820$	2.65794	0.0928193
$821$	6.89627	0.240681	0.120341	−	0.992733i	$-0.461601\pi$
$821$	6.89627	0.240681	0.120341	+	0.992733i	$0.461601\pi$
$822$	−5.12070	−0.178605
$823$	−37.9259	−1.32201	−0.661006	−	0.750380i	$-0.729870\pi$
$823$	−37.9259	−1.32201	−0.661006	+	0.750380i	$0.729870\pi$
$824$	22.5800	0.786610
$825$	6.34032	0.220742
$826$	0	0
$827$	22.6357	0.787121	0.393561	−	0.919299i	$-0.371243\pi$
$827$	22.6357	0.787121	0.393561	+	0.919299i	$0.371243\pi$
$828$	10.4310	0.362503
$829$	−34.6081	−1.20199	−0.600995	−	0.799253i	$-0.705229\pi$
$829$	−34.6081	−1.20199	−0.600995	+	0.799253i	$0.705229\pi$
$830$	−2.62279	−0.0910382
$831$	19.4269	0.673910
$832$	0.110381	0.00382677
$833$	0	0
$834$	13.7318	0.475495
$835$	5.73610	0.198506
$836$	14.0634	0.486392
$837$	−4.35118	−0.150399
$838$	6.59960	0.227979
$839$	53.3934	1.84334	0.921672	−	0.387969i	$-0.126823\pi$
$839$	53.3934	1.84334	0.921672	+	0.387969i	$0.126823\pi$
$840$	0	0
$841$	55.0116	1.89695
$842$	11.6125	0.400194
$843$	−0.197677	−0.00680837
$844$	7.19149	0.247541
$845$	−5.00216	−0.172080
$846$	3.89626	0.133956
$847$	0	0
$848$	−23.1293	−0.794262
$849$	31.9961	1.09810
$850$	−1.58721	−0.0544409
$851$	72.4501	2.48356
$852$	11.8374	0.405542
$853$	−9.56536	−0.327512	−0.163756	−	0.986501i	$-0.552361\pi$
$853$	−9.56536	−0.327512	−0.163756	+	0.986501i	$0.552361\pi$
$854$	0	0
$855$	−5.16206	−0.176539
$856$	−37.8395	−1.29333
$857$	−2.78473	−0.0951246	−0.0475623	−	0.998868i	$-0.515145\pi$
$857$	−2.78473	−0.0951246	−0.0475623	+	0.998868i	$0.515145\pi$
$858$	5.62825	0.192145
$859$	11.2578	0.384110	0.192055	−	0.981384i	$-0.438485\pi$
$859$	11.2578	0.384110	0.192055	+	0.981384i	$0.438485\pi$
$860$	1.81954	0.0620457
$861$	0	0
$862$	4.51843	0.153899
$863$	−5.08316	−0.173033	−0.0865163	−	0.996250i	$-0.527573\pi$
$863$	−5.08316	−0.173033	−0.0865163	+	0.996250i	$0.527573\pi$
$864$	5.66231	0.192636
$865$	26.1687	0.889761
$866$	20.7500	0.705112
$867$	15.7465	0.534778
$868$	0	0
$869$	−0.552711	−0.0187495
$870$	9.59816	0.325408
$871$	31.4603	1.06599
$872$	39.3815	1.33363
$873$	−11.3773	−0.385062
$874$	−12.7843	−0.432434
$875$	0	0
$876$	−22.3118	−0.753847
$877$	−24.7658	−0.836282	−0.418141	−	0.908382i	$-0.637318\pi$
$877$	−24.7658	−0.836282	−0.418141	+	0.908382i	$0.637318\pi$
$878$	2.37733	0.0802308
$879$	−17.2175	−0.580733
$880$	8.28576	0.279313
$881$	13.0909	0.441044	0.220522	−	0.975382i	$-0.429224\pi$
$881$	13.0909	0.441044	0.220522	+	0.975382i	$0.429224\pi$
$882$	0	0
$883$	−44.5002	−1.49755	−0.748775	−	0.662824i	$-0.769358\pi$
$883$	−44.5002	−1.49755	−0.748775	+	0.662824i	$0.769358\pi$
$884$	5.66699	0.190601
$885$	12.7951	0.430103
$886$	−19.1573	−0.643601
$887$	−22.0697	−0.741028	−0.370514	−	0.928827i	$-0.620819\pi$
$887$	−22.0697	−0.741028	−0.370514	+	0.928827i	$0.620819\pi$
$888$	25.2869	0.848573
$889$	0	0
$890$	−13.0896	−0.438763
$891$	2.82239	0.0945535
$892$	36.5785	1.22474
$893$	19.2067	0.642727
$894$	9.00183	0.301066
$895$	27.6054	0.922747
$896$	0	0
$897$	20.5786	0.687098
$898$	−14.2319	−0.474923
$899$	39.8820	1.33014
$900$	3.59827	0.119942
$901$	14.6373	0.487640
$902$	1.78110	0.0593040
$903$	0	0
$904$	−24.0848	−0.801047
$905$	−26.3467	−0.875793
$906$	1.44680	0.0480668
$907$	−9.62739	−0.319672	−0.159836	−	0.987144i	$-0.551097\pi$
$907$	−9.62739	−0.319672	−0.159836	+	0.987144i	$0.551097\pi$
$908$	−23.5091	−0.780176
$909$	−14.9268	−0.495089
$910$	0	0
$911$	−55.0618	−1.82428	−0.912140	−	0.409880i	$-0.865571\pi$
$911$	−55.0618	−1.82428	−0.912140	+	0.409880i	$0.865571\pi$
$912$	5.50357	0.182241
$913$	7.06905	0.233951
$914$	9.27487	0.306785
$915$	0.696212	0.0230161
$916$	17.4364	0.576116
$917$	0	0
$918$	−0.706545	−0.0233195
$919$	−18.9673	−0.625673	−0.312837	−	0.949807i	$-0.601279\pi$
$919$	−18.9673	−0.625673	−0.312837	+	0.949807i	$0.601279\pi$
$920$	−24.5619	−0.809783
$921$	−24.2479	−0.798995
$922$	−12.2064	−0.401995
$923$	23.3530	0.768675
$924$	0	0
$925$	24.9922	0.821739
$926$	−2.01672	−0.0662735
$927$	9.93429	0.326285
$928$	−51.8995	−1.70369
$929$	−25.2606	−0.828773	−0.414386	−	0.910101i	$-0.636004\pi$
$929$	−25.2606	−0.828773	−0.414386	+	0.910101i	$0.636004\pi$
$930$	4.55644	0.149411
$931$	0	0
$932$	17.0414	0.558209
$933$	10.2592	0.335870
$934$	−11.2207	−0.367152
$935$	−5.24363	−0.171485
$936$	7.18244	0.234765
$937$	−13.5468	−0.442554	−0.221277	−	0.975211i	$-0.571022\pi$
$937$	−13.5468	−0.442554	−0.221277	+	0.975211i	$0.571022\pi$
$938$	0	0
$939$	−25.6802	−0.838041
$940$	16.4105	0.535252
$941$	33.7758	1.10106	0.550529	−	0.834816i	$-0.314426\pi$
$941$	33.7758	1.10106	0.550529	+	0.834816i	$0.314426\pi$
$942$	15.2412	0.496584
$943$	6.51222	0.212067
$944$	−13.6416	−0.443996
$945$	0	0
$946$	1.21928	0.0396422
$947$	23.8236	0.774162	0.387081	−	0.922046i	$-0.373483\pi$
$947$	23.8236	0.774162	0.387081	+	0.922046i	$0.373483\pi$
$948$	−0.313675	−0.0101877
$949$	−44.0172	−1.42886
$950$	−4.41003	−0.143080
$951$	19.2173	0.623163
$952$	0	0
$953$	−18.8482	−0.610553	−0.305277	−	0.952264i	$-0.598749\pi$
$953$	−18.8482	−0.610553	−0.305277	+	0.952264i	$0.598749\pi$
$954$	8.25019	0.267110
$955$	−34.8834	−1.12880
$956$	−4.84712	−0.156767
$957$	−25.8694	−0.836238
$958$	−21.6207	−0.698532
$959$	0	0
$960$	−0.0579636	−0.00187077
$961$	−12.0672	−0.389265
$962$	22.1854	0.715285
$963$	−16.6479	−0.536471
$964$	29.5334	0.951208
$965$	−33.0238	−1.06307
$966$	0	0
$967$	−45.4505	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$967$	−45.4505	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$968$	−6.89639	−0.221658
$969$	−3.48293	−0.111888
$970$	11.9140	0.382534
$971$	57.0677	1.83139	0.915695	−	0.401874i	$-0.131641\pi$
$971$	57.0677	1.83139	0.915695	+	0.401874i	$0.131641\pi$
$972$	1.60176	0.0513765
$973$	0	0
$974$	−18.6939	−0.598991
$975$	7.09873	0.227341
$976$	−0.742272	−0.0237596
$977$	−15.5246	−0.496675	−0.248337	−	0.968674i	$-0.579884\pi$
$977$	−15.5246	−0.496675	−0.248337	+	0.968674i	$0.579884\pi$
$978$	−0.195151	−0.00624025
$979$	35.2795	1.12754
$980$	0	0
$981$	17.3263	0.553186
$982$	9.94287	0.317290
$983$	10.3050	0.328678	0.164339	−	0.986404i	$-0.447451\pi$
$983$	10.3050	0.328678	0.164339	+	0.986404i	$0.447451\pi$
$984$	2.27293	0.0724584
$985$	−33.5007	−1.06742
$986$	6.47604	0.206239
$987$	0	0
$988$	15.7456	0.500934
$989$	4.45805	0.141758
$990$	−2.95553	−0.0939328
$991$	44.2241	1.40483	0.702413	−	0.711770i	$-0.252106\pi$
$991$	44.2241	1.40483	0.702413	+	0.711770i	$0.252106\pi$
$992$	−24.6378	−0.782249
$993$	−0.536324	−0.0170197
$994$	0	0
$995$	37.5564	1.19062
$996$	4.01183	0.127120
$997$	33.4105	1.05812	0.529061	−	0.848584i	$-0.322544\pi$
$997$	33.4105	1.05812	0.529061	+	0.848584i	$0.322544\pi$
$998$	−2.49638	−0.0790216
$999$	11.1252	0.351987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bl.1.8	✓	16
7.6	odd	2		6027.2.a.bm.1.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bl.1.8	✓	16	1.1	even	1	trivial
6027.2.a.bm.1.8	yes	16	7.6	odd	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-0.631061 q^{2} -1.00000 q^{3} -1.60176 q^{4} +1.65938 q^{5} +0.631061 q^{6} +2.27293 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.631061 q^{2} -1.00000 q^{3} -1.60176 q^{4} +1.65938 q^{5} +0.631061 q^{6} +2.27293 q^{8} +1.00000 q^{9} -1.04717 q^{10} +2.82239 q^{11} +1.60176 q^{12} +3.15999 q^{13} -1.65938 q^{15} +1.76917 q^{16} -1.11961 q^{17} -0.631061 q^{18} -3.11082 q^{19} -2.65794 q^{20} -1.78110 q^{22} -6.51222 q^{23} -2.27293 q^{24} -2.24644 q^{25} -1.99415 q^{26} -1.00000 q^{27} +9.16578 q^{29} +1.04717 q^{30} +4.35118 q^{31} -5.66231 q^{32} -2.82239 q^{33} +0.706545 q^{34} -1.60176 q^{36} -11.1252 q^{37} +1.96312 q^{38} -3.15999 q^{39} +3.77167 q^{40} -1.00000 q^{41} -0.684567 q^{43} -4.52079 q^{44} +1.65938 q^{45} +4.10961 q^{46} -6.17414 q^{47} -1.76917 q^{48} +1.41764 q^{50} +1.11961 q^{51} -5.06155 q^{52} -13.0735 q^{53} +0.631061 q^{54} +4.68342 q^{55} +3.11082 q^{57} -5.78417 q^{58} -7.71075 q^{59} +2.65794 q^{60} -0.419560 q^{61} -2.74586 q^{62} +0.0349308 q^{64} +5.24364 q^{65} +1.78110 q^{66} +9.95583 q^{67} +1.79336 q^{68} +6.51222 q^{69} +7.39023 q^{71} +2.27293 q^{72} -13.9295 q^{73} +7.02071 q^{74} +2.24644 q^{75} +4.98280 q^{76} +1.99415 q^{78} -0.195831 q^{79} +2.93573 q^{80} +1.00000 q^{81} +0.631061 q^{82} +2.50464 q^{83} -1.85787 q^{85} +0.432003 q^{86} -9.16578 q^{87} +6.41509 q^{88} +12.4999 q^{89} -1.04717 q^{90} +10.4310 q^{92} -4.35118 q^{93} +3.89626 q^{94} -5.16206 q^{95} +5.66231 q^{96} -11.3773 q^{97} +2.82239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * q^99

Introduction

L-functions

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Database

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