LMFDB - Embedded newform 4018.2.a.bd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.210756$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} -1.21076 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} -1.21076 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} +1.21076 q^{10} +3.74483 q^{11} +2.53407 q^{12} -2.95558 q^{13} -3.06814 q^{15} +1.00000 q^{16} -6.53407 q^{17} -3.42151 q^{18} -4.95558 q^{19} -1.21076 q^{20} -3.74483 q^{22} +6.02372 q^{23} -2.53407 q^{24} -3.53407 q^{25} +2.95558 q^{26} +1.06814 q^{27} -0.901803 q^{29} +3.06814 q^{30} -9.48965 q^{31} -1.00000 q^{32} +9.48965 q^{33} +6.53407 q^{34} +3.42151 q^{36} +11.0681 q^{37} +4.95558 q^{38} -7.48965 q^{39} +1.21076 q^{40} +1.00000 q^{41} -9.06814 q^{43} +3.74483 q^{44} -4.14262 q^{45} -6.02372 q^{46} -10.9556 q^{47} +2.53407 q^{48} +3.53407 q^{50} -16.5578 q^{51} -2.95558 q^{52} -5.32331 q^{53} -1.06814 q^{54} -4.53407 q^{55} -12.5578 q^{57} +0.901803 q^{58} -2.36773 q^{59} -3.06814 q^{60} -3.76855 q^{61} +9.48965 q^{62} +1.00000 q^{64} +3.57849 q^{65} -9.48965 q^{66} +11.6560 q^{67} -6.53407 q^{68} +15.2645 q^{69} -12.5578 q^{71} -3.42151 q^{72} +1.06814 q^{73} -11.0681 q^{74} -8.95558 q^{75} -4.95558 q^{76} +7.48965 q^{78} +4.84302 q^{79} -1.21076 q^{80} -7.55779 q^{81} -1.00000 q^{82} +1.29959 q^{83} +7.91116 q^{85} +9.06814 q^{86} -2.28523 q^{87} -3.74483 q^{88} +11.4008 q^{89} +4.14262 q^{90} +6.02372 q^{92} -24.0474 q^{93} +10.9556 q^{94} +6.00000 q^{95} -2.53407 q^{96} -4.13628 q^{97} +12.8130 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} - 2 q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 - 2 * q^5 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} - 2 q^{5} - 3 q^{8} + 7 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{13} + 6 q^{15} + 3 q^{16} - 12 q^{17} - 7 q^{18} - 4 q^{19} - 2 q^{20} - 2 q^{22} - 8 q^{23} - 3 q^{25} - 2 q^{26} - 12 q^{27} - 6 q^{30} - 10 q^{31} - 3 q^{32} + 10 q^{33} + 12 q^{34} + 7 q^{36} + 18 q^{37} + 4 q^{38} - 4 q^{39} + 2 q^{40} + 3 q^{41} - 12 q^{43} + 2 q^{44} - 26 q^{45} + 8 q^{46} - 22 q^{47} + 3 q^{50} - 16 q^{51} + 2 q^{52} - 10 q^{53} + 12 q^{54} - 6 q^{55} - 4 q^{57} - 12 q^{59} + 6 q^{60} + 24 q^{61} + 10 q^{62} + 3 q^{64} + 14 q^{65} - 10 q^{66} + 4 q^{67} - 12 q^{68} + 36 q^{69} - 4 q^{71} - 7 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} - 4 q^{76} + 4 q^{78} + 8 q^{79} - 2 q^{80} + 11 q^{81} - 3 q^{82} + 24 q^{83} + 2 q^{85} + 12 q^{86} - 34 q^{87} - 2 q^{88} - 6 q^{89} + 26 q^{90} - 8 q^{92} - 20 q^{93} + 22 q^{94} + 18 q^{95} + 18 q^{97} + 14 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 - 2 * q^5 - 3 * q^8 + 7 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^13 + 6 * q^15 + 3 * q^16 - 12 * q^17 - 7 * q^18 - 4 * q^19 - 2 * q^20 - 2 * q^22 - 8 * q^23 - 3 * q^25 - 2 * q^26 - 12 * q^27 - 6 * q^30 - 10 * q^31 - 3 * q^32 + 10 * q^33 + 12 * q^34 + 7 * q^36 + 18 * q^37 + 4 * q^38 - 4 * q^39 + 2 * q^40 + 3 * q^41 - 12 * q^43 + 2 * q^44 - 26 * q^45 + 8 * q^46 - 22 * q^47 + 3 * q^50 - 16 * q^51 + 2 * q^52 - 10 * q^53 + 12 * q^54 - 6 * q^55 - 4 * q^57 - 12 * q^59 + 6 * q^60 + 24 * q^61 + 10 * q^62 + 3 * q^64 + 14 * q^65 - 10 * q^66 + 4 * q^67 - 12 * q^68 + 36 * q^69 - 4 * q^71 - 7 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 - 4 * q^76 + 4 * q^78 + 8 * q^79 - 2 * q^80 + 11 * q^81 - 3 * q^82 + 24 * q^83 + 2 * q^85 + 12 * q^86 - 34 * q^87 - 2 * q^88 - 6 * q^89 + 26 * q^90 - 8 * q^92 - 20 * q^93 + 22 * q^94 + 18 * q^95 + 18 * q^97 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.53407	1.46305	0.731523	−	0.681817i	$-0.238810\pi$
$3$	2.53407	1.46305	0.731523	+	0.681817i	$0.238810\pi$
$4$	1.00000	0.500000
$5$	−1.21076	−0.541466	−0.270733	−	0.962654i	$-0.587266\pi$
$5$	−1.21076	−0.541466	−0.270733	+	0.962654i	$0.587266\pi$
$6$	−2.53407	−1.03453
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	3.42151	1.14050
$10$	1.21076	0.382875
$11$	3.74483	1.12911	0.564554	−	0.825396i	$-0.309048\pi$
$11$	3.74483	1.12911	0.564554	+	0.825396i	$0.309048\pi$
$12$	2.53407	0.731523
$13$	−2.95558	−0.819731	−0.409865	−	0.912146i	$-0.634424\pi$
$13$	−2.95558	−0.819731	−0.409865	+	0.912146i	$0.634424\pi$
$14$	0	0
$15$	−3.06814	−0.792190
$16$	1.00000	0.250000
$17$	−6.53407	−1.58474	−0.792372	−	0.610038i	$-0.791154\pi$
$17$	−6.53407	−1.58474	−0.792372	+	0.610038i	$0.791154\pi$
$18$	−3.42151	−0.806458
$19$	−4.95558	−1.13689	−0.568444	−	0.822722i	$-0.692454\pi$
$19$	−4.95558	−1.13689	−0.568444	+	0.822722i	$0.692454\pi$
$20$	−1.21076	−0.270733
$21$	0	0
$22$	−3.74483	−0.798400
$23$	6.02372	1.25603	0.628016	−	0.778200i	$-0.283867\pi$
$23$	6.02372	1.25603	0.628016	+	0.778200i	$0.283867\pi$
$24$	−2.53407	−0.517265
$25$	−3.53407	−0.706814
$26$	2.95558	0.579637
$27$	1.06814	0.205564
$28$	0	0
$29$	−0.901803	−0.167461	−0.0837303	−	0.996488i	$-0.526683\pi$
$29$	−0.901803	−0.167461	−0.0837303	+	0.996488i	$0.526683\pi$
$30$	3.06814	0.560163
$31$	−9.48965	−1.70439	−0.852196	−	0.523223i	$-0.824730\pi$
$31$	−9.48965	−1.70439	−0.852196	+	0.523223i	$0.824730\pi$
$32$	−1.00000	−0.176777
$33$	9.48965	1.65194
$34$	6.53407	1.12058
$35$	0	0
$36$	3.42151	0.570252
$37$	11.0681	1.81959	0.909796	−	0.415057i	$-0.136238\pi$
$37$	11.0681	1.81959	0.909796	+	0.415057i	$0.136238\pi$
$38$	4.95558	0.803902
$39$	−7.48965	−1.19930
$40$	1.21076	0.191437
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−9.06814	−1.38288	−0.691439	−	0.722435i	$-0.743023\pi$
$43$	−9.06814	−1.38288	−0.691439	+	0.722435i	$0.743023\pi$
$44$	3.74483	0.564554
$45$	−4.14262	−0.617545
$46$	−6.02372	−0.888149
$47$	−10.9556	−1.59804	−0.799018	−	0.601307i	$-0.794647\pi$
$47$	−10.9556	−1.59804	−0.799018	+	0.601307i	$0.794647\pi$
$48$	2.53407	0.365762
$49$	0	0
$50$	3.53407	0.499793
$51$	−16.5578	−2.31855
$52$	−2.95558	−0.409865
$53$	−5.32331	−0.731213	−0.365607	−	0.930769i	$-0.619138\pi$
$53$	−5.32331	−0.731213	−0.365607	+	0.930769i	$0.619138\pi$
$54$	−1.06814	−0.145355
$55$	−4.53407	−0.611374
$56$	0	0
$57$	−12.5578	−1.66332
$58$	0.901803	0.118412
$59$	−2.36773	−0.308252	−0.154126	−	0.988051i	$-0.549256\pi$
$59$	−2.36773	−0.308252	−0.154126	+	0.988051i	$0.549256\pi$
$60$	−3.06814	−0.396095
$61$	−3.76855	−0.482513	−0.241257	−	0.970461i	$-0.577560\pi$
$61$	−3.76855	−0.482513	−0.241257	+	0.970461i	$0.577560\pi$
$62$	9.48965	1.20519
$63$	0	0
$64$	1.00000	0.125000
$65$	3.57849	0.443857
$66$	−9.48965	−1.16810
$67$	11.6560	1.42401	0.712003	−	0.702177i	$-0.247788\pi$
$67$	11.6560	1.42401	0.712003	+	0.702177i	$0.247788\pi$
$68$	−6.53407	−0.792372
$69$	15.2645	1.83763
$70$	0	0
$71$	−12.5578	−1.49034	−0.745168	−	0.666877i	$-0.767631\pi$
$71$	−12.5578	−1.49034	−0.745168	+	0.666877i	$0.767631\pi$
$72$	−3.42151	−0.403229
$73$	1.06814	0.125016	0.0625082	−	0.998044i	$-0.480090\pi$
$73$	1.06814	0.125016	0.0625082	+	0.998044i	$0.480090\pi$
$74$	−11.0681	−1.28665
$75$	−8.95558	−1.03410
$76$	−4.95558	−0.568444
$77$	0	0
$78$	7.48965	0.848036
$79$	4.84302	0.544883	0.272441	−	0.962172i	$-0.412169\pi$
$79$	4.84302	0.544883	0.272441	+	0.962172i	$0.412169\pi$
$80$	−1.21076	−0.135367
$81$	−7.55779	−0.839755
$82$	−1.00000	−0.110432
$83$	1.29959	0.142649	0.0713244	−	0.997453i	$-0.477277\pi$
$83$	1.29959	0.142649	0.0713244	+	0.997453i	$0.477277\pi$
$84$	0	0
$85$	7.91116	0.858086
$86$	9.06814	0.977843
$87$	−2.28523	−0.245002
$88$	−3.74483	−0.399200
$89$	11.4008	1.20848	0.604242	−	0.796801i	$-0.293476\pi$
$89$	11.4008	1.20848	0.604242	+	0.796801i	$0.293476\pi$
$90$	4.14262	0.436670
$91$	0	0
$92$	6.02372	0.628016
$93$	−24.0474	−2.49360
$94$	10.9556	1.12998
$95$	6.00000	0.615587
$96$	−2.53407	−0.258632
$97$	−4.13628	−0.419976	−0.209988	−	0.977704i	$-0.567342\pi$
$97$	−4.13628	−0.419976	−0.209988	+	0.977704i	$0.567342\pi$
$98$	0	0
$99$	12.8130	1.28775
$100$	−3.53407	−0.353407
$101$	−10.1126	−1.00624	−0.503119	−	0.864217i	$-0.667814\pi$
$101$	−10.1126	−1.00624	−0.503119	+	0.864217i	$0.667814\pi$
$102$	16.5578	1.63947
$103$	12.3327	1.21517	0.607587	−	0.794253i	$-0.292137\pi$
$103$	12.3327	1.21517	0.607587	+	0.794253i	$0.292137\pi$
$104$	2.95558	0.289819
$105$	0	0
$106$	5.32331	0.517046
$107$	11.4897	1.11075	0.555373	−	0.831601i	$-0.312575\pi$
$107$	11.4897	1.11075	0.555373	+	0.831601i	$0.312575\pi$
$108$	1.06814	0.102782
$109$	−19.7923	−1.89576	−0.947878	−	0.318634i	$-0.896776\pi$
$109$	−19.7923	−1.89576	−0.947878	+	0.318634i	$0.896776\pi$
$110$	4.53407	0.432307
$111$	28.0474	2.66215
$112$	0	0
$113$	−7.46593	−0.702336	−0.351168	−	0.936313i	$-0.614215\pi$
$113$	−7.46593	−0.702336	−0.351168	+	0.936313i	$0.614215\pi$
$114$	12.5578	1.17615
$115$	−7.29326	−0.680100
$116$	−0.901803	−0.0837303
$117$	−10.1126	−0.934906
$118$	2.36773	0.217967
$119$	0	0
$120$	3.06814	0.280082
$121$	3.02372	0.274884
$122$	3.76855	0.341188
$123$	2.53407	0.228489
$124$	−9.48965	−0.852196
$125$	10.3327	0.924183
$126$	0	0
$127$	5.97628	0.530309	0.265154	−	0.964206i	$-0.414577\pi$
$127$	5.97628	0.530309	0.265154	+	0.964206i	$0.414577\pi$
$128$	−1.00000	−0.0883883
$129$	−22.9793	−2.02321
$130$	−3.57849	−0.313854
$131$	12.9255	1.12931	0.564654	−	0.825328i	$-0.309010\pi$
$131$	12.9255	1.12931	0.564654	+	0.825328i	$0.309010\pi$
$132$	9.48965	0.825968
$133$	0	0
$134$	−11.6560	−1.00692
$135$	−1.29326	−0.111306
$136$	6.53407	0.560292
$137$	9.26454	0.791523	0.395761	−	0.918353i	$-0.370481\pi$
$137$	9.26454	0.791523	0.395761	+	0.918353i	$0.370481\pi$
$138$	−15.2645	−1.29940
$139$	6.27890	0.532569	0.266285	−	0.963894i	$-0.414204\pi$
$139$	6.27890	0.532569	0.266285	+	0.963894i	$0.414204\pi$
$140$	0	0
$141$	−27.7622	−2.33800
$142$	12.5578	1.05383
$143$	−11.0681	−0.925564
$144$	3.42151	0.285126
$145$	1.09186	0.0906743
$146$	−1.06814	−0.0883999
$147$	0	0
$148$	11.0681	0.909796
$149$	−19.6560	−1.61028	−0.805141	−	0.593084i	$-0.797910\pi$
$149$	−19.6560	−1.61028	−0.805141	+	0.593084i	$0.797910\pi$
$150$	8.95558	0.731220
$151$	4.13628	0.336606	0.168303	−	0.985735i	$-0.446171\pi$
$151$	4.13628	0.336606	0.168303	+	0.985735i	$0.446171\pi$
$152$	4.95558	0.401951
$153$	−22.3564	−1.80741
$154$	0	0
$155$	11.4897	0.922871
$156$	−7.48965	−0.599652
$157$	14.6704	1.17082	0.585411	−	0.810737i	$-0.300933\pi$
$157$	14.6704	1.17082	0.585411	+	0.810737i	$0.300933\pi$
$158$	−4.84302	−0.385290
$159$	−13.4897	−1.06980
$160$	1.21076	0.0957187
$161$	0	0
$162$	7.55779	0.593796
$163$	−9.80361	−0.767878	−0.383939	−	0.923359i	$-0.625433\pi$
$163$	−9.80361	−0.767878	−0.383939	+	0.923359i	$0.625433\pi$
$164$	1.00000	0.0780869
$165$	−11.4897	−0.894468
$166$	−1.29959	−0.100868
$167$	−5.35337	−0.414256	−0.207128	−	0.978314i	$-0.566412\pi$
$167$	−5.35337	−0.414256	−0.207128	+	0.978314i	$0.566412\pi$
$168$	0	0
$169$	−4.26454	−0.328041
$170$	−7.91116	−0.606759
$171$	−16.9556	−1.29663
$172$	−9.06814	−0.691439
$173$	−18.4152	−1.40008	−0.700040	−	0.714104i	$-0.746835\pi$
$173$	−18.4152	−1.40008	−0.700040	+	0.714104i	$0.746835\pi$
$174$	2.28523	0.173243
$175$	0	0
$176$	3.74483	0.282277
$177$	−6.00000	−0.450988
$178$	−11.4008	−0.854527
$179$	3.32331	0.248396	0.124198	−	0.992257i	$-0.460364\pi$
$179$	3.32331	0.248396	0.124198	+	0.992257i	$0.460364\pi$
$180$	−4.14262	−0.308772
$181$	−8.02372	−0.596399	−0.298199	−	0.954504i	$-0.596386\pi$
$181$	−8.02372	−0.596399	−0.298199	+	0.954504i	$0.596386\pi$
$182$	0	0
$183$	−9.54977	−0.705939
$184$	−6.02372	−0.444075
$185$	−13.4008	−0.985248
$186$	24.0474	1.76324
$187$	−24.4690	−1.78935
$188$	−10.9556	−0.799018
$189$	0	0
$190$	−6.00000	−0.435286
$191$	−18.2438	−1.32008	−0.660039	−	0.751231i	$-0.729460\pi$
$191$	−18.2438	−1.32008	−0.660039	+	0.751231i	$0.729460\pi$
$192$	2.53407	0.182881
$193$	−2.64663	−0.190508	−0.0952542	−	0.995453i	$-0.530366\pi$
$193$	−2.64663	−0.190508	−0.0952542	+	0.995453i	$0.530366\pi$
$194$	4.13628	0.296968
$195$	9.06814	0.649383
$196$	0	0
$197$	−25.0869	−1.78736	−0.893682	−	0.448700i	$-0.851887\pi$
$197$	−25.0869	−1.78736	−0.893682	+	0.448700i	$0.851887\pi$
$198$	−12.8130	−0.910578
$199$	6.73047	0.477110	0.238555	−	0.971129i	$-0.423326\pi$
$199$	6.73047	0.477110	0.238555	+	0.971129i	$0.423326\pi$
$200$	3.53407	0.249897
$201$	29.5371	2.08339
$202$	10.1126	0.711517
$203$	0	0
$204$	−16.5578	−1.15928
$205$	−1.21076	−0.0845629
$206$	−12.3327	−0.859258
$207$	20.6102	1.43251
$208$	−2.95558	−0.204933
$209$	−18.5578	−1.28367
$210$	0	0
$211$	9.14564	0.629612	0.314806	−	0.949156i	$-0.398061\pi$
$211$	9.14564	0.629612	0.314806	+	0.949156i	$0.398061\pi$
$212$	−5.32331	−0.365607
$213$	−31.8223	−2.18043
$214$	−11.4897	−0.785416
$215$	10.9793	0.748782
$216$	−1.06814	−0.0726777
$217$	0	0
$218$	19.7923	1.34050
$219$	2.70674	0.182905
$220$	−4.53407	−0.305687
$221$	19.3120	1.29906
$222$	−28.0474	−1.88242
$223$	13.2933	0.890182	0.445091	−	0.895485i	$-0.353171\pi$
$223$	13.2933	0.890182	0.445091	+	0.895485i	$0.353171\pi$
$224$	0	0
$225$	−12.0919	−0.806124
$226$	7.46593	0.496626
$227$	−4.62291	−0.306833	−0.153417	−	0.988162i	$-0.549028\pi$
$227$	−4.62291	−0.306833	−0.153417	+	0.988162i	$0.549028\pi$
$228$	−12.5578	−0.831660
$229$	13.8874	0.917708	0.458854	−	0.888512i	$-0.348260\pi$
$229$	13.8874	0.917708	0.458854	+	0.888512i	$0.348260\pi$
$230$	7.29326	0.480903
$231$	0	0
$232$	0.901803	0.0592062
$233$	16.3614	1.07187	0.535935	−	0.844259i	$-0.319959\pi$
$233$	16.3614	1.07187	0.535935	+	0.844259i	$0.319959\pi$
$234$	10.1126	0.661079
$235$	13.2645	0.865283
$236$	−2.36773	−0.154126
$237$	12.2726	0.797189
$238$	0	0
$239$	12.1363	0.785031	0.392515	−	0.919745i	$-0.371605\pi$
$239$	12.1363	0.785031	0.392515	+	0.919745i	$0.371605\pi$
$240$	−3.06814	−0.198048
$241$	24.7542	1.59456	0.797279	−	0.603611i	$-0.206272\pi$
$241$	24.7542	1.59456	0.797279	+	0.603611i	$0.206272\pi$
$242$	−3.02372	−0.194372
$243$	−22.3564	−1.43416
$244$	−3.76855	−0.241257
$245$	0	0
$246$	−2.53407	−0.161566
$247$	14.6466	0.931943
$248$	9.48965	0.602594
$249$	3.29326	0.208702
$250$	−10.3327	−0.653496
$251$	−18.5227	−1.16914	−0.584572	−	0.811342i	$-0.698738\pi$
$251$	−18.5227	−1.16914	−0.584572	+	0.811342i	$0.698738\pi$
$252$	0	0
$253$	22.5578	1.41820
$254$	−5.97628	−0.374985
$255$	20.0474	1.25542
$256$	1.00000	0.0625000
$257$	−18.3801	−1.14652	−0.573260	−	0.819373i	$-0.694322\pi$
$257$	−18.3801	−1.14652	−0.573260	+	0.819373i	$0.694322\pi$
$258$	22.9793	1.43063
$259$	0	0
$260$	3.57849	0.221928
$261$	−3.08553	−0.190989
$262$	−12.9255	−0.798542
$263$	5.91116	0.364498	0.182249	−	0.983252i	$-0.441662\pi$
$263$	5.91116	0.364498	0.182249	+	0.983252i	$0.441662\pi$
$264$	−9.48965	−0.584048
$265$	6.44523	0.395928
$266$	0	0
$267$	28.8905	1.76807
$268$	11.6560	0.712003
$269$	3.21076	0.195763	0.0978816	−	0.995198i	$-0.468793\pi$
$269$	3.21076	0.195763	0.0978816	+	0.995198i	$0.468793\pi$
$270$	1.29326	0.0787051
$271$	−4.31395	−0.262054	−0.131027	−	0.991379i	$-0.541827\pi$
$271$	−4.31395	−0.262054	−0.131027	+	0.991379i	$0.541827\pi$
$272$	−6.53407	−0.396186
$273$	0	0
$274$	−9.26454	−0.559691
$275$	−13.2345	−0.798069
$276$	15.2645	0.918817
$277$	−7.40082	−0.444672	−0.222336	−	0.974970i	$-0.571368\pi$
$277$	−7.40082	−0.444672	−0.222336	+	0.974970i	$0.571368\pi$
$278$	−6.27890	−0.376583
$279$	−32.4690	−1.94387
$280$	0	0
$281$	1.77488	0.105881	0.0529403	−	0.998598i	$-0.483141\pi$
$281$	1.77488	0.105881	0.0529403	+	0.998598i	$0.483141\pi$
$282$	27.7622	1.65322
$283$	−1.38843	−0.0825335	−0.0412667	−	0.999148i	$-0.513139\pi$
$283$	−1.38843	−0.0825335	−0.0412667	+	0.999148i	$0.513139\pi$
$284$	−12.5578	−0.745168
$285$	15.2044	0.900632
$286$	11.0681	0.654473
$287$	0	0
$288$	−3.42151	−0.201615
$289$	25.6941	1.51142
$290$	−1.09186	−0.0641164
$291$	−10.4816	−0.614444
$292$	1.06814	0.0625082
$293$	−7.46593	−0.436164	−0.218082	−	0.975930i	$-0.569980\pi$
$293$	−7.46593	−0.436164	−0.218082	+	0.975930i	$0.569980\pi$
$294$	0	0
$295$	2.86675	0.166908
$296$	−11.0681	−0.643323
$297$	4.00000	0.232104
$298$	19.6560	1.13864
$299$	−17.8036	−1.02961
$300$	−8.95558	−0.517051
$301$	0	0
$302$	−4.13628	−0.238016
$303$	−25.6259	−1.47217
$304$	−4.95558	−0.284222
$305$	4.56279	0.261265
$306$	22.3564	1.27803
$307$	−17.6610	−1.00797	−0.503983	−	0.863714i	$-0.668133\pi$
$307$	−17.6610	−1.00797	−0.503983	+	0.863714i	$0.668133\pi$
$308$	0	0
$309$	31.2519	1.77786
$310$	−11.4897	−0.652568
$311$	−3.75116	−0.212709	−0.106354	−	0.994328i	$-0.533918\pi$
$311$	−3.75116	−0.212709	−0.106354	+	0.994328i	$0.533918\pi$
$312$	7.48965	0.424018
$313$	10.3564	0.585378	0.292689	−	0.956208i	$-0.405450\pi$
$313$	10.3564	0.585378	0.292689	+	0.956208i	$0.405450\pi$
$314$	−14.6704	−0.827896
$315$	0	0
$316$	4.84302	0.272441
$317$	−0.451569	−0.0253626	−0.0126813	−	0.999920i	$-0.504037\pi$
$317$	−0.451569	−0.0253626	−0.0126813	+	0.999920i	$0.504037\pi$
$318$	13.4897	0.756462
$319$	−3.37709	−0.189081
$320$	−1.21076	−0.0676833
$321$	29.1156	1.62507
$322$	0	0
$323$	32.3801	1.80168
$324$	−7.55779	−0.419877
$325$	10.4452	0.579397
$326$	9.80361	0.542971
$327$	−50.1550	−2.77358
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	11.4897	0.632485
$331$	30.6827	1.68648	0.843238	−	0.537541i	$-0.180646\pi$
$331$	30.6827	1.68648	0.843238	+	0.537541i	$0.180646\pi$
$332$	1.29959	0.0713244
$333$	37.8698	2.07525
$334$	5.35337	0.292923
$335$	−14.1126	−0.771051
$336$	0	0
$337$	−30.6654	−1.67045	−0.835224	−	0.549910i	$-0.814662\pi$
$337$	−30.6654	−1.67045	−0.835224	+	0.549910i	$0.814662\pi$
$338$	4.26454	0.231960
$339$	−18.9192	−1.02755
$340$	7.91116	0.429043
$341$	−35.5371	−1.92444
$342$	16.9556	0.916853
$343$	0	0
$344$	9.06814	0.488921
$345$	−18.4816	−0.995017
$346$	18.4152	0.990006
$347$	−18.2138	−0.977767	−0.488884	−	0.872349i	$-0.662596\pi$
$347$	−18.2138	−0.977767	−0.488884	+	0.872349i	$0.662596\pi$
$348$	−2.28523	−0.122501
$349$	23.0331	1.23293	0.616466	−	0.787381i	$-0.288564\pi$
$349$	23.0331	1.23293	0.616466	+	0.787381i	$0.288564\pi$
$350$	0	0
$351$	−3.15698	−0.168507
$352$	−3.74483	−0.199600
$353$	−36.6941	−1.95303	−0.976514	−	0.215453i	$-0.930877\pi$
$353$	−36.6941	−1.95303	−0.976514	+	0.215453i	$0.930877\pi$
$354$	6.00000	0.318896
$355$	15.2044	0.806967
$356$	11.4008	0.604242
$357$	0	0
$358$	−3.32331	−0.175643
$359$	15.4897	0.817513	0.408756	−	0.912644i	$-0.365963\pi$
$359$	15.4897	0.817513	0.408756	+	0.912644i	$0.365963\pi$
$360$	4.14262	0.218335
$361$	5.55779	0.292515
$362$	8.02372	0.421717
$363$	7.66232	0.402168
$364$	0	0
$365$	−1.29326	−0.0676922
$366$	9.54977	0.499174
$367$	17.4295	0.909814	0.454907	−	0.890539i	$-0.349672\pi$
$367$	17.4295	0.909814	0.454907	+	0.890539i	$0.349672\pi$
$368$	6.02372	0.314008
$369$	3.42151	0.178117
$370$	13.4008	0.696675
$371$	0	0
$372$	−24.0474	−1.24680
$373$	−13.9399	−0.721780	−0.360890	−	0.932608i	$-0.617527\pi$
$373$	−13.9399	−0.721780	−0.360890	+	0.932608i	$0.617527\pi$
$374$	24.4690	1.26526
$375$	26.1837	1.35212
$376$	10.9556	0.564991
$377$	2.66535	0.137273
$378$	0	0
$379$	26.1837	1.34497	0.672484	−	0.740112i	$-0.265227\pi$
$379$	26.1837	1.34497	0.672484	+	0.740112i	$0.265227\pi$
$380$	6.00000	0.307794
$381$	15.1443	0.775866
$382$	18.2438	0.933436
$383$	−11.9399	−0.610100	−0.305050	−	0.952336i	$-0.598673\pi$
$383$	−11.9399	−0.610100	−0.305050	+	0.952336i	$0.598673\pi$
$384$	−2.53407	−0.129316
$385$	0	0
$386$	2.64663	0.134710
$387$	−31.0267	−1.57718
$388$	−4.13628	−0.209988
$389$	−27.1156	−1.37481	−0.687407	−	0.726272i	$-0.741251\pi$
$389$	−27.1156	−1.37481	−0.687407	+	0.726272i	$0.741251\pi$
$390$	−9.06814	−0.459183
$391$	−39.3594	−1.99049
$392$	0	0
$393$	32.7542	1.65223
$394$	25.0869	1.26386
$395$	−5.86372	−0.295036
$396$	12.8130	0.643876
$397$	12.2488	0.614752	0.307376	−	0.951588i	$-0.400549\pi$
$397$	12.2488	0.614752	0.307376	+	0.951588i	$0.400549\pi$
$398$	−6.73047	−0.337368
$399$	0	0
$400$	−3.53407	−0.176704
$401$	14.8955	0.743844	0.371922	−	0.928264i	$-0.378699\pi$
$401$	14.8955	0.743844	0.371922	+	0.928264i	$0.378699\pi$
$402$	−29.5371	−1.47318
$403$	28.0474	1.39714
$404$	−10.1126	−0.503119
$405$	9.15064	0.454699
$406$	0	0
$407$	41.4483	2.05451
$408$	16.5578	0.819733
$409$	7.86372	0.388836	0.194418	−	0.980919i	$-0.437718\pi$
$409$	7.86372	0.388836	0.194418	+	0.980919i	$0.437718\pi$
$410$	1.21076	0.0597950
$411$	23.4770	1.15803
$412$	12.3327	0.607587
$413$	0	0
$414$	−20.6102	−1.01294
$415$	−1.57349	−0.0772395
$416$	2.95558	0.144909
$417$	15.9112	0.779173
$418$	18.5578	0.907691
$419$	28.7479	1.40442	0.702212	−	0.711968i	$-0.252196\pi$
$419$	28.7479	1.40442	0.702212	+	0.711968i	$0.252196\pi$
$420$	0	0
$421$	−4.16634	−0.203055	−0.101527	−	0.994833i	$-0.532373\pi$
$421$	−4.16634	−0.203055	−0.101527	+	0.994833i	$0.532373\pi$
$422$	−9.14564	−0.445203
$423$	−37.4847	−1.82257
$424$	5.32331	0.258523
$425$	23.0919	1.12012
$426$	31.8223	1.54180
$427$	0	0
$428$	11.4897	0.555373
$429$	−28.0474	−1.35414
$430$	−10.9793	−0.529469
$431$	1.97628	0.0951939	0.0475970	−	0.998867i	$-0.484844\pi$
$431$	1.97628	0.0951939	0.0475970	+	0.998867i	$0.484844\pi$
$432$	1.06814	0.0513909
$433$	−19.0681	−0.916356	−0.458178	−	0.888860i	$-0.651498\pi$
$433$	−19.0681	−0.916356	−0.458178	+	0.888860i	$0.651498\pi$
$434$	0	0
$435$	2.76686	0.132661
$436$	−19.7923	−0.947878
$437$	−29.8510	−1.42797
$438$	−2.70674	−0.129333
$439$	10.3377	0.493390	0.246695	−	0.969093i	$-0.420655\pi$
$439$	10.3377	0.493390	0.246695	+	0.969093i	$0.420655\pi$
$440$	4.53407	0.216153
$441$	0	0
$442$	−19.3120	−0.918577
$443$	6.97930	0.331597	0.165798	−	0.986160i	$-0.446980\pi$
$443$	6.97930	0.331597	0.165798	+	0.986160i	$0.446980\pi$
$444$	28.0474	1.33107
$445$	−13.8036	−0.654354
$446$	−13.2933	−0.629454
$447$	−49.8097	−2.35592
$448$	0	0
$449$	−9.44221	−0.445605	−0.222803	−	0.974864i	$-0.571521\pi$
$449$	−9.44221	−0.445605	−0.222803	+	0.974864i	$0.571521\pi$
$450$	12.0919	0.570016
$451$	3.74483	0.176337
$452$	−7.46593	−0.351168
$453$	10.4816	0.492470
$454$	4.62291	0.216964
$455$	0	0
$456$	12.5578	0.588073
$457$	26.2438	1.22764	0.613818	−	0.789448i	$-0.289633\pi$
$457$	26.2438	1.22764	0.613818	+	0.789448i	$0.289633\pi$
$458$	−13.8874	−0.648918
$459$	−6.97930	−0.325766
$460$	−7.29326	−0.340050
$461$	−21.6610	−1.00885	−0.504426	−	0.863455i	$-0.668296\pi$
$461$	−21.6610	−1.00885	−0.504426	+	0.863455i	$0.668296\pi$
$462$	0	0
$463$	−36.7128	−1.70619	−0.853094	−	0.521757i	$-0.825277\pi$
$463$	−36.7128	−1.70619	−0.853094	+	0.521757i	$0.825277\pi$
$464$	−0.901803	−0.0418651
$465$	29.1156	1.35020
$466$	−16.3614	−0.757927
$467$	30.5227	1.41242	0.706212	−	0.708001i	$-0.250403\pi$
$467$	30.5227	1.41242	0.706212	+	0.708001i	$0.250403\pi$
$468$	−10.1126	−0.467453
$469$	0	0
$470$	−13.2645	−0.611847
$471$	37.1757	1.71297
$472$	2.36773	0.108984
$473$	−33.9586	−1.56142
$474$	−12.2726	−0.563697
$475$	17.5134	0.803569
$476$	0	0
$477$	−18.2138	−0.833952
$478$	−12.1363	−0.555101
$479$	−31.3958	−1.43451	−0.717256	−	0.696810i	$-0.754602\pi$
$479$	−31.3958	−1.43451	−0.717256	+	0.696810i	$0.754602\pi$
$480$	3.06814	0.140041
$481$	−32.7128	−1.49158
$482$	−24.7542	−1.12752
$483$	0	0
$484$	3.02372	0.137442
$485$	5.00803	0.227403
$486$	22.3564	1.01411
$487$	12.7829	0.579249	0.289624	−	0.957140i	$-0.406470\pi$
$487$	12.7829	0.579249	0.289624	+	0.957140i	$0.406470\pi$
$488$	3.76855	0.170594
$489$	−24.8430	−1.12344
$490$	0	0
$491$	−5.91116	−0.266767	−0.133384	−	0.991064i	$-0.542584\pi$
$491$	−5.91116	−0.266767	−0.133384	+	0.991064i	$0.542584\pi$
$492$	2.53407	0.114245
$493$	5.89244	0.265382
$494$	−14.6466	−0.658983
$495$	−15.5134	−0.697274
$496$	−9.48965	−0.426098
$497$	0	0
$498$	−3.29326	−0.147574
$499$	−34.0174	−1.52283	−0.761414	−	0.648266i	$-0.775494\pi$
$499$	−34.0174	−1.52283	−0.761414	+	0.648266i	$0.775494\pi$
$500$	10.3327	0.462091
$501$	−13.5658	−0.606076
$502$	18.5227	0.826710
$503$	−13.0207	−0.580564	−0.290282	−	0.956941i	$-0.593749\pi$
$503$	−13.0207	−0.580564	−0.290282	+	0.956941i	$0.593749\pi$
$504$	0	0
$505$	12.2438	0.544844
$506$	−22.5578	−1.00282
$507$	−10.8066	−0.479939
$508$	5.97628	0.265154
$509$	0.201395	0.00892666	0.00446333	−	0.999990i	$-0.498579\pi$
$509$	0.201395	0.00892666	0.00446333	+	0.999990i	$0.498579\pi$
$510$	−20.0474	−0.887716
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−5.29326	−0.233703
$514$	18.3801	0.810712
$515$	−14.9319	−0.657976
$516$	−22.9793	−1.01161
$517$	−41.0267	−1.80435
$518$	0	0
$519$	−46.6654	−2.04838
$520$	−3.57849	−0.156927
$521$	37.5608	1.64557	0.822785	−	0.568353i	$-0.192419\pi$
$521$	37.5608	1.64557	0.822785	+	0.568353i	$0.192419\pi$
$522$	3.08553	0.135050
$523$	−21.9048	−0.957831	−0.478916	−	0.877861i	$-0.658970\pi$
$523$	−21.9048	−0.957831	−0.478916	+	0.877861i	$0.658970\pi$
$524$	12.9255	0.564654
$525$	0	0
$526$	−5.91116	−0.257739
$527$	62.0061	2.70103
$528$	9.48965	0.412984
$529$	13.2852	0.577619
$530$	−6.44523	−0.279963
$531$	−8.10122	−0.351563
$532$	0	0
$533$	−2.95558	−0.128020
$534$	−28.8905	−1.25021
$535$	−13.9112	−0.601432
$536$	−11.6560	−0.503462
$537$	8.42151	0.363415
$538$	−3.21076	−0.138426
$539$	0	0
$540$	−1.29326	−0.0556529
$541$	41.6447	1.79044	0.895222	−	0.445621i	$-0.147017\pi$
$541$	41.6447	1.79044	0.895222	+	0.445621i	$0.147017\pi$
$542$	4.31395	0.185300
$543$	−20.3327	−0.872559
$544$	6.53407	0.280146
$545$	23.9636	1.02649
$546$	0	0
$547$	−30.6767	−1.31164	−0.655820	−	0.754917i	$-0.727677\pi$
$547$	−30.6767	−1.31164	−0.655820	+	0.754917i	$0.727677\pi$
$548$	9.26454	0.395761
$549$	−12.8941	−0.550308
$550$	13.2345	0.564320
$551$	4.46896	0.190384
$552$	−15.2645	−0.649702
$553$	0	0
$554$	7.40082	0.314431
$555$	−33.9586	−1.44146
$556$	6.27890	0.266285
$557$	−25.9286	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$557$	−25.9286	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$558$	32.4690	1.37452
$559$	26.8016	1.13359
$560$	0	0
$561$	−62.0061	−2.61790
$562$	−1.77488	−0.0748689
$563$	−19.5548	−0.824135	−0.412068	−	0.911153i	$-0.635193\pi$
$563$	−19.5548	−0.824135	−0.412068	+	0.911153i	$0.635193\pi$
$564$	−27.7622	−1.16900
$565$	9.03942	0.380291
$566$	1.38843	0.0583600
$567$	0	0
$568$	12.5578	0.526913
$569$	11.4659	0.480677	0.240338	−	0.970689i	$-0.422742\pi$
$569$	11.4659	0.480677	0.240338	+	0.970689i	$0.422742\pi$
$570$	−15.2044	−0.636843
$571$	−39.1456	−1.63819	−0.819097	−	0.573655i	$-0.805525\pi$
$571$	−39.1456	−1.63819	−0.819097	+	0.573655i	$0.805525\pi$
$572$	−11.0681	−0.462782
$573$	−46.2312	−1.93133
$574$	0	0
$575$	−21.2883	−0.887782
$576$	3.42151	0.142563
$577$	−27.2469	−1.13430	−0.567151	−	0.823614i	$-0.691954\pi$
$577$	−27.2469	−1.13430	−0.567151	+	0.823614i	$0.691954\pi$
$578$	−25.6941	−1.06873
$579$	−6.70674	−0.278723
$580$	1.09186	0.0453371
$581$	0	0
$582$	10.4816	0.434477
$583$	−19.9349	−0.825619
$584$	−1.06814	−0.0442000
$585$	12.2438	0.506220
$586$	7.46593	0.308415
$587$	37.8935	1.56403	0.782016	−	0.623258i	$-0.214192\pi$
$587$	37.8935	1.56403	0.782016	+	0.623258i	$0.214192\pi$
$588$	0	0
$589$	47.0267	1.93770
$590$	−2.86675	−0.118022
$591$	−63.5719	−2.61500
$592$	11.0681	0.454898
$593$	4.08884	0.167908	0.0839542	−	0.996470i	$-0.473245\pi$
$593$	4.08884	0.167908	0.0839542	+	0.996470i	$0.473245\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−19.6560	−0.805141
$597$	17.0555	0.698034
$598$	17.8036	0.728044
$599$	−0.0601141	−0.00245620	−0.00122810	−	0.999999i	$-0.500391\pi$
$599$	−0.0601141	−0.00245620	−0.00122810	+	0.999999i	$0.500391\pi$
$600$	8.95558	0.365610
$601$	24.2776	0.990302	0.495151	−	0.868807i	$-0.335113\pi$
$601$	24.2776	0.990302	0.495151	+	0.868807i	$0.335113\pi$
$602$	0	0
$603$	39.8811	1.62408
$604$	4.13628	0.168303
$605$	−3.66099	−0.148840
$606$	25.6259	1.04098
$607$	10.0000	0.405887	0.202944	−	0.979190i	$-0.434949\pi$
$607$	10.0000	0.405887	0.202944	+	0.979190i	$0.434949\pi$
$608$	4.95558	0.200975
$609$	0	0
$610$	−4.56279	−0.184742
$611$	32.3801	1.30996
$612$	−22.3564	−0.903704
$613$	−24.5865	−0.993040	−0.496520	−	0.868025i	$-0.665389\pi$
$613$	−24.5865	−0.993040	−0.496520	+	0.868025i	$0.665389\pi$
$614$	17.6610	0.712740
$615$	−3.06814	−0.123719
$616$	0	0
$617$	37.6022	1.51381	0.756904	−	0.653526i	$-0.226711\pi$
$617$	37.6022	1.51381	0.756904	+	0.653526i	$0.226711\pi$
$618$	−31.2519	−1.25713
$619$	34.7479	1.39663	0.698317	−	0.715789i	$-0.253933\pi$
$619$	34.7479	1.39663	0.698317	+	0.715789i	$0.253933\pi$
$620$	11.4897	0.461436
$621$	6.43418	0.258195
$622$	3.75116	0.150408
$623$	0	0
$624$	−7.48965	−0.299826
$625$	5.16000	0.206400
$626$	−10.3564	−0.413925
$627$	−47.0267	−1.87807
$628$	14.6704	0.585411
$629$	−72.3200	−2.88359
$630$	0	0
$631$	13.5134	0.537959	0.268979	−	0.963146i	$-0.413314\pi$
$631$	13.5134	0.537959	0.268979	+	0.963146i	$0.413314\pi$
$632$	−4.84302	−0.192645
$633$	23.1757	0.921151
$634$	0.451569	0.0179341
$635$	−7.23581	−0.287144
$636$	−13.4897	−0.534900
$637$	0	0
$638$	3.37709	0.133700
$639$	−42.9666	−1.69973
$640$	1.21076	0.0478593
$641$	−25.8985	−1.02293	−0.511465	−	0.859304i	$-0.670897\pi$
$641$	−25.8985	−1.02293	−0.511465	+	0.859304i	$0.670897\pi$
$642$	−29.1156	−1.14910
$643$	−14.7117	−0.580174	−0.290087	−	0.957000i	$-0.593684\pi$
$643$	−14.7117	−0.580174	−0.290087	+	0.957000i	$0.593684\pi$
$644$	0	0
$645$	27.8223	1.09550
$646$	−32.3801	−1.27398
$647$	10.6941	0.420427	0.210214	−	0.977655i	$-0.432584\pi$
$647$	10.6941	0.420427	0.210214	+	0.977655i	$0.432584\pi$
$648$	7.55779	0.296898
$649$	−8.86675	−0.348050
$650$	−10.4452	−0.409696
$651$	0	0
$652$	−9.80361	−0.383939
$653$	−31.0855	−1.21647	−0.608235	−	0.793757i	$-0.708122\pi$
$653$	−31.0855	−1.21647	−0.608235	+	0.793757i	$0.708122\pi$
$654$	50.1550	1.96122
$655$	−15.6497	−0.611483
$656$	1.00000	0.0390434
$657$	3.65465	0.142582
$658$	0	0
$659$	30.5878	1.19153	0.595767	−	0.803158i	$-0.296848\pi$
$659$	30.5878	1.19153	0.595767	+	0.803158i	$0.296848\pi$
$660$	−11.4897	−0.447234
$661$	44.8367	1.74395	0.871973	−	0.489555i	$-0.162841\pi$
$661$	44.8367	1.74395	0.871973	+	0.489555i	$0.162841\pi$
$662$	−30.6827	−1.19252
$663$	48.9379	1.90059
$664$	−1.29959	−0.0504339
$665$	0	0
$666$	−37.8698	−1.46742
$667$	−5.43221	−0.210336
$668$	−5.35337	−0.207128
$669$	33.6860	1.30238
$670$	14.1126	0.545216
$671$	−14.1126	−0.544809
$672$	0	0
$673$	−40.0662	−1.54444	−0.772219	−	0.635357i	$-0.780853\pi$
$673$	−40.0662	−1.54444	−0.772219	+	0.635357i	$0.780853\pi$
$674$	30.6654	1.18119
$675$	−3.77488	−0.145295
$676$	−4.26454	−0.164021
$677$	−45.1881	−1.73672	−0.868360	−	0.495935i	$-0.834825\pi$
$677$	−45.1881	−1.73672	−0.868360	+	0.495935i	$0.834825\pi$
$678$	18.9192	0.726587
$679$	0	0
$680$	−7.91116	−0.303379
$681$	−11.7148	−0.448911
$682$	35.5371	1.36079
$683$	−6.01739	−0.230249	−0.115124	−	0.993351i	$-0.536727\pi$
$683$	−6.01739	−0.230249	−0.115124	+	0.993351i	$0.536727\pi$
$684$	−16.9556	−0.648313
$685$	−11.2171	−0.428583
$686$	0	0
$687$	35.1918	1.34265
$688$	−9.06814	−0.345720
$689$	15.7335	0.599398
$690$	18.4816	0.703583
$691$	21.5735	0.820694	0.410347	−	0.911929i	$-0.365408\pi$
$691$	21.5735	0.820694	0.410347	+	0.911929i	$0.365408\pi$
$692$	−18.4152	−0.700040
$693$	0	0
$694$	18.2138	0.691386
$695$	−7.60221	−0.288368
$696$	2.28523	0.0866215
$697$	−6.53407	−0.247496
$698$	−23.0331	−0.871815
$699$	41.4609	1.56820
$700$	0	0
$701$	12.2438	0.462443	0.231222	−	0.972901i	$-0.425728\pi$
$701$	12.2438	0.462443	0.231222	+	0.972901i	$0.425728\pi$
$702$	3.15698	0.119152
$703$	−54.8491	−2.06867
$704$	3.74483	0.141138
$705$	33.6133	1.26595
$706$	36.6941	1.38100
$707$	0	0
$708$	−6.00000	−0.225494
$709$	31.5672	1.18553	0.592765	−	0.805376i	$-0.298036\pi$
$709$	31.5672	1.18553	0.592765	+	0.805376i	$0.298036\pi$
$710$	−15.2044	−0.570612
$711$	16.5705	0.621441
$712$	−11.4008	−0.427264
$713$	−57.1630	−2.14077
$714$	0	0
$715$	13.4008	0.501162
$716$	3.32331	0.124198
$717$	30.7542	1.14854
$718$	−15.4897	−0.578069
$719$	27.4897	1.02519	0.512596	−	0.858630i	$-0.328684\pi$
$719$	27.4897	1.02519	0.512596	+	0.858630i	$0.328684\pi$
$720$	−4.14262	−0.154386
$721$	0	0
$722$	−5.55779	−0.206840
$723$	62.7288	2.33291
$724$	−8.02372	−0.298199
$725$	3.18703	0.118363
$726$	−7.66232	−0.284376
$727$	23.7622	0.881292	0.440646	−	0.897681i	$-0.354749\pi$
$727$	23.7622	0.881292	0.440646	+	0.897681i	$0.354749\pi$
$728$	0	0
$729$	−33.9793	−1.25849
$730$	1.29326	0.0478656
$731$	59.2519	2.19151
$732$	−9.54977	−0.352970
$733$	22.5040	0.831205	0.415602	−	0.909546i	$-0.363571\pi$
$733$	22.5040	0.831205	0.415602	+	0.909546i	$0.363571\pi$
$734$	−17.4295	−0.643336
$735$	0	0
$736$	−6.02372	−0.222037
$737$	43.6497	1.60786
$738$	−3.42151	−0.125948
$739$	14.7542	0.542742	0.271371	−	0.962475i	$-0.412523\pi$
$739$	14.7542	0.542742	0.271371	+	0.962475i	$0.412523\pi$
$740$	−13.4008	−0.492624
$741$	37.1156	1.36348
$742$	0	0
$743$	−7.37209	−0.270456	−0.135228	−	0.990815i	$-0.543177\pi$
$743$	−7.37209	−0.270456	−0.135228	+	0.990815i	$0.543177\pi$
$744$	24.0474	0.881622
$745$	23.7986	0.871913
$746$	13.9399	0.510375
$747$	4.44657	0.162691
$748$	−24.4690	−0.894674
$749$	0	0
$750$	−26.1837	−0.956094
$751$	−48.6240	−1.77431	−0.887157	−	0.461468i	$-0.847323\pi$
$751$	−48.6240	−1.77431	−0.887157	+	0.461468i	$0.847323\pi$
$752$	−10.9556	−0.399509
$753$	−46.9379	−1.71051
$754$	−2.66535	−0.0970664
$755$	−5.00803	−0.182261
$756$	0	0
$757$	−15.2058	−0.552663	−0.276331	−	0.961062i	$-0.589119\pi$
$757$	−15.2058	−0.552663	−0.276331	+	0.961062i	$0.589119\pi$
$758$	−26.1837	−0.951036
$759$	57.1630	2.07489
$760$	−6.00000	−0.217643
$761$	25.5785	0.927219	0.463610	−	0.886040i	$-0.346554\pi$
$761$	25.5785	0.927219	0.463610	+	0.886040i	$0.346554\pi$
$762$	−15.1443	−0.548620
$763$	0	0
$764$	−18.2438	−0.660039
$765$	27.0681	0.978651
$766$	11.9399	0.431406
$767$	6.99803	0.252684
$768$	2.53407	0.0914404
$769$	51.3594	1.85207	0.926034	−	0.377440i	$-0.123195\pi$
$769$	51.3594	1.85207	0.926034	+	0.377440i	$0.123195\pi$
$770$	0	0
$771$	−46.5765	−1.67741
$772$	−2.64663	−0.0952542
$773$	−7.52604	−0.270693	−0.135346	−	0.990798i	$-0.543215\pi$
$773$	−7.52604	−0.270693	−0.135346	+	0.990798i	$0.543215\pi$
$774$	31.0267	1.11523
$775$	33.5371	1.20469
$776$	4.13628	0.148484
$777$	0	0
$778$	27.1156	0.972141
$779$	−4.95558	−0.177552
$780$	9.06814	0.324692
$781$	−47.0267	−1.68275
$782$	39.3594	1.40749
$783$	−0.963252	−0.0344238
$784$	0	0
$785$	−17.7622	−0.633961
$786$	−32.7542	−1.16830
$787$	41.6323	1.48403	0.742015	−	0.670383i	$-0.233870\pi$
$787$	41.6323	1.48403	0.742015	+	0.670383i	$0.233870\pi$
$788$	−25.0869	−0.893682
$789$	14.9793	0.533277
$790$	5.86372	0.208622
$791$	0	0
$792$	−12.8130	−0.455289
$793$	11.1383	0.395531
$794$	−12.2488	−0.434695
$795$	16.3327	0.579260
$796$	6.73047	0.238555
$797$	10.8180	0.383192	0.191596	−	0.981474i	$-0.438634\pi$
$797$	10.8180	0.383192	0.191596	+	0.981474i	$0.438634\pi$
$798$	0	0
$799$	71.5845	2.53248
$800$	3.53407	0.124948
$801$	39.0080	1.37828
$802$	−14.8955	−0.525977
$803$	4.00000	0.141157
$804$	29.5371	1.04169
$805$	0	0
$806$	−28.0474	−0.987929
$807$	8.13628	0.286411
$808$	10.1126	0.355759
$809$	−27.0969	−0.952675	−0.476337	−	0.879263i	$-0.658036\pi$
$809$	−27.0969	−0.952675	−0.476337	+	0.879263i	$0.658036\pi$
$810$	−9.15064	−0.321521
$811$	−7.96494	−0.279687	−0.139843	−	0.990174i	$-0.544660\pi$
$811$	−7.96494	−0.279687	−0.139843	+	0.990174i	$0.544660\pi$
$812$	0	0
$813$	−10.9319	−0.383397
$814$	−41.4483	−1.45276
$815$	11.8698	0.415780
$816$	−16.5578	−0.579639
$817$	44.9379	1.57218
$818$	−7.86372	−0.274948
$819$	0	0
$820$	−1.21076	−0.0422814
$821$	−51.9112	−1.81171	−0.905856	−	0.423586i	$-0.860771\pi$
$821$	−51.9112	−1.81171	−0.905856	+	0.423586i	$0.860771\pi$
$822$	−23.4770	−0.818854
$823$	−31.0869	−1.08362	−0.541810	−	0.840501i	$-0.682261\pi$
$823$	−31.0869	−1.08362	−0.541810	+	0.840501i	$0.682261\pi$
$824$	−12.3327	−0.429629
$825$	−33.5371	−1.16761
$826$	0	0
$827$	−31.4883	−1.09496	−0.547478	−	0.836820i	$-0.684412\pi$
$827$	−31.4883	−1.09496	−0.547478	+	0.836820i	$0.684412\pi$
$828$	20.6102	0.716255
$829$	24.0351	0.834772	0.417386	−	0.908729i	$-0.362946\pi$
$829$	24.0351	0.834772	0.417386	+	0.908729i	$0.362946\pi$
$830$	1.57349	0.0546166
$831$	−18.7542	−0.650576
$832$	−2.95558	−0.102466
$833$	0	0
$834$	−15.9112	−0.550959
$835$	6.48163	0.224306
$836$	−18.5578	−0.641835
$837$	−10.1363	−0.350361
$838$	−28.7479	−0.993078
$839$	−36.4640	−1.25888	−0.629438	−	0.777051i	$-0.716715\pi$
$839$	−36.4640	−1.25888	−0.629438	+	0.777051i	$0.716715\pi$
$840$	0	0
$841$	−28.1868	−0.971957
$842$	4.16634	0.143581
$843$	4.49768	0.154908
$844$	9.14564	0.314806
$845$	5.16331	0.177623
$846$	37.4847	1.28875
$847$	0	0
$848$	−5.32331	−0.182803
$849$	−3.51837	−0.120750
$850$	−23.0919	−0.792044
$851$	66.6714	2.28547
$852$	−31.8223	−1.09021
$853$	−21.1794	−0.725168	−0.362584	−	0.931951i	$-0.618105\pi$
$853$	−21.1794	−0.725168	−0.362584	+	0.931951i	$0.618105\pi$
$854$	0	0
$855$	20.5291	0.702079
$856$	−11.4897	−0.392708
$857$	−33.0267	−1.12817	−0.564086	−	0.825716i	$-0.690771\pi$
$857$	−33.0267	−1.12817	−0.564086	+	0.825716i	$0.690771\pi$
$858$	28.0474	0.957524
$859$	−38.6590	−1.31903	−0.659514	−	0.751692i	$-0.729238\pi$
$859$	−38.6590	−1.31903	−0.659514	+	0.751692i	$0.729238\pi$
$860$	10.9793	0.374391
$861$	0	0
$862$	−1.97628	−0.0673123
$863$	19.7622	0.672714	0.336357	−	0.941735i	$-0.390805\pi$
$863$	19.7622	0.672714	0.336357	+	0.941735i	$0.390805\pi$
$864$	−1.06814	−0.0363389
$865$	22.2963	0.758096
$866$	19.0681	0.647962
$867$	65.1106	2.21127
$868$	0	0
$869$	18.1363	0.615231
$870$	−2.76686	−0.0938052
$871$	−34.4502	−1.16730
$872$	19.7923	0.670251
$873$	−14.1523	−0.478984
$874$	29.8510	1.00973
$875$	0	0
$876$	2.70674	0.0914524
$877$	22.8304	0.770926	0.385463	−	0.922723i	$-0.374042\pi$
$877$	22.8304	0.770926	0.385463	+	0.922723i	$0.374042\pi$
$878$	−10.3377	−0.348880
$879$	−18.9192	−0.638128
$880$	−4.53407	−0.152843
$881$	−20.6941	−0.697201	−0.348601	−	0.937271i	$-0.613343\pi$
$881$	−20.6941	−0.697201	−0.348601	+	0.937271i	$0.613343\pi$
$882$	0	0
$883$	−28.3026	−0.952459	−0.476229	−	0.879321i	$-0.657997\pi$
$883$	−28.3026	−0.952459	−0.476229	+	0.879321i	$0.657997\pi$
$884$	19.3120	0.649532
$885$	7.26454	0.244195
$886$	−6.97930	−0.234474
$887$	28.4640	0.955726	0.477863	−	0.878434i	$-0.341412\pi$
$887$	28.4640	0.955726	0.477863	+	0.878434i	$0.341412\pi$
$888$	−28.0474	−0.941211
$889$	0	0
$890$	13.8036	0.462698
$891$	−28.3026	−0.948173
$892$	13.2933	0.445091
$893$	54.2913	1.81679
$894$	49.8097	1.66588
$895$	−4.02372	−0.134498
$896$	0	0
$897$	−45.1156	−1.50637
$898$	9.44221	0.315091
$899$	8.55779	0.285418
$900$	−12.0919	−0.403062
$901$	34.7829	1.15879
$902$	−3.74483	−0.124689
$903$	0	0
$904$	7.46593	0.248313
$905$	9.71477	0.322930
$906$	−10.4816	−0.348229
$907$	37.9586	1.26039	0.630197	−	0.776435i	$-0.282974\pi$
$907$	37.9586	1.26039	0.630197	+	0.776435i	$0.282974\pi$
$908$	−4.62291	−0.153417
$909$	−34.6002	−1.14762
$910$	0	0
$911$	20.5628	0.681276	0.340638	−	0.940195i	$-0.389357\pi$
$911$	20.5628	0.681276	0.340638	+	0.940195i	$0.389357\pi$
$912$	−12.5578	−0.415830
$913$	4.86675	0.161066
$914$	−26.2438	−0.868069
$915$	11.5624	0.382242
$916$	13.8874	0.458854
$917$	0	0
$918$	6.97930	0.230351
$919$	−25.5785	−0.843756	−0.421878	−	0.906652i	$-0.638629\pi$
$919$	−25.5785	−0.843756	−0.421878	+	0.906652i	$0.638629\pi$
$920$	7.29326	0.240452
$921$	−44.7542	−1.47470
$922$	21.6610	0.713367
$923$	37.1156	1.22167
$924$	0	0
$925$	−39.1156	−1.28611
$926$	36.7128	1.20646
$927$	42.1964	1.38591
$928$	0.901803	0.0296031
$929$	45.4897	1.49247	0.746234	−	0.665684i	$-0.231860\pi$
$929$	45.4897	1.49247	0.746234	+	0.665684i	$0.231860\pi$
$930$	−29.1156	−0.954738
$931$	0	0
$932$	16.3614	0.535935
$933$	−9.50570	−0.311203
$934$	−30.5227	−0.998734
$935$	29.6259	0.968872
$936$	10.1126	0.330539
$937$	−11.4609	−0.374412	−0.187206	−	0.982321i	$-0.559943\pi$
$937$	−11.4609	−0.374412	−0.187206	+	0.982321i	$0.559943\pi$
$938$	0	0
$939$	26.2438	0.856435
$940$	13.2645	0.432641
$941$	−8.16134	−0.266052	−0.133026	−	0.991113i	$-0.542469\pi$
$941$	−8.16134	−0.266052	−0.133026	+	0.991113i	$0.542469\pi$
$942$	−37.1757	−1.21125
$943$	6.02372	0.196159
$944$	−2.36773	−0.0770631
$945$	0	0
$946$	33.9586	1.10409
$947$	44.5351	1.44720	0.723599	−	0.690221i	$-0.242487\pi$
$947$	44.5351	1.44720	0.723599	+	0.690221i	$0.242487\pi$
$948$	12.2726	0.398594
$949$	−3.15698	−0.102480
$950$	−17.5134	−0.568209
$951$	−1.14431	−0.0371067
$952$	0	0
$953$	20.2388	0.655600	0.327800	−	0.944747i	$-0.393693\pi$
$953$	20.2388	0.655600	0.327800	+	0.944747i	$0.393693\pi$
$954$	18.2138	0.589693
$955$	22.0888	0.714778
$956$	12.1363	0.392515
$957$	−8.55779	−0.276634
$958$	31.3958	1.01435
$959$	0	0
$960$	−3.06814	−0.0990238
$961$	59.0535	1.90495
$962$	32.7128	1.05470
$963$	39.3120	1.26681
$964$	24.7542	0.797279
$965$	3.20442	0.103154
$966$	0	0
$967$	−19.6734	−0.632653	−0.316327	−	0.948650i	$-0.602450\pi$
$967$	−19.6734	−0.632653	−0.316327	+	0.948650i	$0.602450\pi$
$968$	−3.02372	−0.0971861
$969$	82.0535	2.63594
$970$	−5.00803	−0.160798
$971$	54.0712	1.73523	0.867613	−	0.497240i	$-0.165653\pi$
$971$	54.0712	1.73523	0.867613	+	0.497240i	$0.165653\pi$
$972$	−22.3564	−0.717082
$973$	0	0
$974$	−12.7829	−0.409591
$975$	26.4690	0.847685
$976$	−3.76855	−0.120628
$977$	32.9666	1.05470	0.527348	−	0.849649i	$-0.323186\pi$
$977$	32.9666	1.05470	0.527348	+	0.849649i	$0.323186\pi$
$978$	24.8430	0.794392
$979$	42.6941	1.36451
$980$	0	0
$981$	−67.7195	−2.16212
$982$	5.91116	0.188633
$983$	−40.7415	−1.29945	−0.649726	−	0.760168i	$-0.725116\pi$
$983$	−40.7415	−1.29945	−0.649726	+	0.760168i	$0.725116\pi$
$984$	−2.53407	−0.0807832
$985$	30.3741	0.967798
$986$	−5.89244	−0.187654
$987$	0	0
$988$	14.6466	0.465971
$989$	−54.6240	−1.73694
$990$	15.5134	0.493047
$991$	15.9399	0.506347	0.253174	−	0.967421i	$-0.418526\pi$
$991$	15.9399	0.506347	0.253174	+	0.967421i	$0.418526\pi$
$992$	9.48965	0.301297
$993$	77.7522	2.46739
$994$	0	0
$995$	−8.14895	−0.258339
$996$	3.29326	0.104351
$997$	17.7799	0.563095	0.281547	−	0.959547i	$-0.409152\pi$
$997$	17.7799	0.563095	0.281547	+	0.959547i	$0.409152\pi$
$998$	34.0174	1.07680
$999$	11.8223	0.374042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bd.1.3	✓	3
7.6	odd	2		4018.2.a.be.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bd.1.3	✓	3	1.1	even	1	trivial
4018.2.a.be.1.1	yes	3	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} -1.21076 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} -1.21076 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} +1.21076 q^{10} +3.74483 q^{11} +2.53407 q^{12} -2.95558 q^{13} -3.06814 q^{15} +1.00000 q^{16} -6.53407 q^{17} -3.42151 q^{18} -4.95558 q^{19} -1.21076 q^{20} -3.74483 q^{22} +6.02372 q^{23} -2.53407 q^{24} -3.53407 q^{25} +2.95558 q^{26} +1.06814 q^{27} -0.901803 q^{29} +3.06814 q^{30} -9.48965 q^{31} -1.00000 q^{32} +9.48965 q^{33} +6.53407 q^{34} +3.42151 q^{36} +11.0681 q^{37} +4.95558 q^{38} -7.48965 q^{39} +1.21076 q^{40} +1.00000 q^{41} -9.06814 q^{43} +3.74483 q^{44} -4.14262 q^{45} -6.02372 q^{46} -10.9556 q^{47} +2.53407 q^{48} +3.53407 q^{50} -16.5578 q^{51} -2.95558 q^{52} -5.32331 q^{53} -1.06814 q^{54} -4.53407 q^{55} -12.5578 q^{57} +0.901803 q^{58} -2.36773 q^{59} -3.06814 q^{60} -3.76855 q^{61} +9.48965 q^{62} +1.00000 q^{64} +3.57849 q^{65} -9.48965 q^{66} +11.6560 q^{67} -6.53407 q^{68} +15.2645 q^{69} -12.5578 q^{71} -3.42151 q^{72} +1.06814 q^{73} -11.0681 q^{74} -8.95558 q^{75} -4.95558 q^{76} +7.48965 q^{78} +4.84302 q^{79} -1.21076 q^{80} -7.55779 q^{81} -1.00000 q^{82} +1.29959 q^{83} +7.91116 q^{85} +9.06814 q^{86} -2.28523 q^{87} -3.74483 q^{88} +11.4008 q^{89} +4.14262 q^{90} +6.02372 q^{92} -24.0474 q^{93} +10.9556 q^{94} +6.00000 q^{95} -2.53407 q^{96} -4.13628 q^{97} +12.8130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} - 2 q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 - 2 * q^5 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} - 2 q^{5} - 3 q^{8} + 7 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{13} + 6 q^{15} + 3 q^{16} - 12 q^{17} - 7 q^{18} - 4 q^{19} - 2 q^{20} - 2 q^{22} - 8 q^{23} - 3 q^{25} - 2 q^{26} - 12 q^{27} - 6 q^{30} - 10 q^{31} - 3 q^{32} + 10 q^{33} + 12 q^{34} + 7 q^{36} + 18 q^{37} + 4 q^{38} - 4 q^{39} + 2 q^{40} + 3 q^{41} - 12 q^{43} + 2 q^{44} - 26 q^{45} + 8 q^{46} - 22 q^{47} + 3 q^{50} - 16 q^{51} + 2 q^{52} - 10 q^{53} + 12 q^{54} - 6 q^{55} - 4 q^{57} - 12 q^{59} + 6 q^{60} + 24 q^{61} + 10 q^{62} + 3 q^{64} + 14 q^{65} - 10 q^{66} + 4 q^{67} - 12 q^{68} + 36 q^{69} - 4 q^{71} - 7 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} - 4 q^{76} + 4 q^{78} + 8 q^{79} - 2 q^{80} + 11 q^{81} - 3 q^{82} + 24 q^{83} + 2 q^{85} + 12 q^{86} - 34 q^{87} - 2 q^{88} - 6 q^{89} + 26 q^{90} - 8 q^{92} - 20 q^{93} + 22 q^{94} + 18 q^{95} + 18 q^{97} + 14 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 - 2 * q^5 - 3 * q^8 + 7 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^13 + 6 * q^15 + 3 * q^16 - 12 * q^17 - 7 * q^18 - 4 * q^19 - 2 * q^20 - 2 * q^22 - 8 * q^23 - 3 * q^25 - 2 * q^26 - 12 * q^27 - 6 * q^30 - 10 * q^31 - 3 * q^32 + 10 * q^33 + 12 * q^34 + 7 * q^36 + 18 * q^37 + 4 * q^38 - 4 * q^39 + 2 * q^40 + 3 * q^41 - 12 * q^43 + 2 * q^44 - 26 * q^45 + 8 * q^46 - 22 * q^47 + 3 * q^50 - 16 * q^51 + 2 * q^52 - 10 * q^53 + 12 * q^54 - 6 * q^55 - 4 * q^57 - 12 * q^59 + 6 * q^60 + 24 * q^61 + 10 * q^62 + 3 * q^64 + 14 * q^65 - 10 * q^66 + 4 * q^67 - 12 * q^68 + 36 * q^69 - 4 * q^71 - 7 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 - 4 * q^76 + 4 * q^78 + 8 * q^79 - 2 * q^80 + 11 * q^81 - 3 * q^82 + 24 * q^83 + 2 * q^85 + 12 * q^86 - 34 * q^87 - 2 * q^88 - 6 * q^89 + 26 * q^90 - 8 * q^92 - 20 * q^93 + 22 * q^94 + 18 * q^95 + 18 * q^97 + 14 * q^99

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