LMFDB - Embedded newform 4018.2.a.bi.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:	$4$
Coefficient field:	4.4.113481.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 3x + 12 $ x^4 - 2x^3 - 9x^2 + 3*x + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.90611$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.705371 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.705371 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +0.705371 q^{10} +6.35160 q^{11} -1.00000 q^{12} +3.15086 q^{13} +0.705371 q^{15} +1.00000 q^{16} -6.10685 q^{17} +2.00000 q^{18} +3.36674 q^{19} -0.705371 q^{20} -6.35160 q^{22} -5.61148 q^{23} +1.00000 q^{24} -4.50245 q^{25} -3.15086 q^{26} +5.00000 q^{27} -7.44549 q^{29} -0.705371 q^{30} +8.66137 q^{31} -1.00000 q^{32} -6.35160 q^{33} +6.10685 q^{34} -2.00000 q^{36} -9.71834 q^{37} -3.36674 q^{38} -3.15086 q^{39} +0.705371 q^{40} +1.00000 q^{41} -1.74011 q^{43} +6.35160 q^{44} +1.41074 q^{45} +5.61148 q^{46} -0.460627 q^{47} -1.00000 q^{48} +4.50245 q^{50} +6.10685 q^{51} +3.15086 q^{52} -1.90611 q^{53} -5.00000 q^{54} -4.48023 q^{55} -3.36674 q^{57} +7.44549 q^{58} +7.97822 q^{59} +0.705371 q^{60} -0.805142 q^{61} -8.66137 q^{62} +1.00000 q^{64} -2.22252 q^{65} +6.35160 q^{66} +9.05697 q^{67} -6.10685 q^{68} +5.61148 q^{69} +13.9039 q^{71} +2.00000 q^{72} +1.63326 q^{73} +9.71834 q^{74} +4.50245 q^{75} +3.36674 q^{76} +3.15086 q^{78} -4.14377 q^{79} -0.705371 q^{80} +1.00000 q^{81} -1.00000 q^{82} -14.1198 q^{83} +4.30759 q^{85} +1.74011 q^{86} +7.44549 q^{87} -6.35160 q^{88} +2.36674 q^{89} -1.41074 q^{90} -5.61148 q^{92} -8.66137 q^{93} +0.460627 q^{94} -2.37480 q^{95} +1.00000 q^{96} -3.34451 q^{97} -12.7032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9} + 3 q^{10} - 4 q^{12} + q^{13} + 3 q^{15} + 4 q^{16} + 3 q^{17} + 8 q^{18} - 2 q^{19} - 3 q^{20} - 9 q^{23} + 4 q^{24} + 19 q^{25} - q^{26} + 20 q^{27} - 18 q^{29} - 3 q^{30} + 19 q^{31} - 4 q^{32} - 3 q^{34} - 8 q^{36} + 2 q^{37} + 2 q^{38} - q^{39} + 3 q^{40} + 4 q^{41} + 5 q^{43} + 6 q^{45} + 9 q^{46} - 4 q^{48} - 19 q^{50} - 3 q^{51} + q^{52} + 6 q^{53} - 20 q^{54} + 6 q^{55} + 2 q^{57} + 18 q^{58} + 3 q^{59} + 3 q^{60} + q^{61} - 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} + 3 q^{68} + 9 q^{69} - 9 q^{71} + 8 q^{72} + 22 q^{73} - 2 q^{74} - 19 q^{75} - 2 q^{76} + q^{78} - 28 q^{79} - 3 q^{80} + 4 q^{81} - 4 q^{82} + 12 q^{83} - 24 q^{85} - 5 q^{86} + 18 q^{87} - 6 q^{89} - 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} + 4 q^{96} - 11 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9 + 3 * q^10 - 4 * q^12 + q^13 + 3 * q^15 + 4 * q^16 + 3 * q^17 + 8 * q^18 - 2 * q^19 - 3 * q^20 - 9 * q^23 + 4 * q^24 + 19 * q^25 - q^26 + 20 * q^27 - 18 * q^29 - 3 * q^30 + 19 * q^31 - 4 * q^32 - 3 * q^34 - 8 * q^36 + 2 * q^37 + 2 * q^38 - q^39 + 3 * q^40 + 4 * q^41 + 5 * q^43 + 6 * q^45 + 9 * q^46 - 4 * q^48 - 19 * q^50 - 3 * q^51 + q^52 + 6 * q^53 - 20 * q^54 + 6 * q^55 + 2 * q^57 + 18 * q^58 + 3 * q^59 + 3 * q^60 + q^61 - 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 + 3 * q^68 + 9 * q^69 - 9 * q^71 + 8 * q^72 + 22 * q^73 - 2 * q^74 - 19 * q^75 - 2 * q^76 + q^78 - 28 * q^79 - 3 * q^80 + 4 * q^81 - 4 * q^82 + 12 * q^83 - 24 * q^85 - 5 * q^86 + 18 * q^87 - 6 * q^89 - 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 + 4 * q^96 - 11 * q^97

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
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	−0.705371	−0.315451	−0.157726	−	0.987483i	$-0.550416\pi$
$5$	−0.705371	−0.315451	−0.157726	+	0.987483i	$0.550416\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	0.705371	0.223058
$11$	6.35160	1.91508	0.957539	−	0.288303i	$-0.0930910\pi$
$11$	6.35160	1.91508	0.957539	+	0.288303i	$0.0930910\pi$
$12$	−1.00000	−0.288675
$13$	3.15086	0.873890	0.436945	−	0.899488i	$-0.356060\pi$
$13$	3.15086	0.873890	0.436945	+	0.899488i	$0.356060\pi$
$14$	0	0
$15$	0.705371	0.182126
$16$	1.00000	0.250000
$17$	−6.10685	−1.48113	−0.740565	−	0.671985i	$-0.765442\pi$
$17$	−6.10685	−1.48113	−0.740565	+	0.671985i	$0.765442\pi$
$18$	2.00000	0.471405
$19$	3.36674	0.772383	0.386191	−	0.922419i	$-0.373790\pi$
$19$	3.36674	0.772383	0.386191	+	0.922419i	$0.373790\pi$
$20$	−0.705371	−0.157726
$21$	0	0
$22$	−6.35160	−1.35416
$23$	−5.61148	−1.17007	−0.585037	−	0.811006i	$-0.698920\pi$
$23$	−5.61148	−1.17007	−0.585037	+	0.811006i	$0.698920\pi$
$24$	1.00000	0.204124
$25$	−4.50245	−0.900490
$26$	−3.15086	−0.617934
$27$	5.00000	0.962250
$28$	0	0
$29$	−7.44549	−1.38259	−0.691296	−	0.722572i	$-0.742960\pi$
$29$	−7.44549	−1.38259	−0.691296	+	0.722572i	$0.742960\pi$
$30$	−0.705371	−0.128782
$31$	8.66137	1.55563	0.777814	−	0.628495i	$-0.216329\pi$
$31$	8.66137	1.55563	0.777814	+	0.628495i	$0.216329\pi$
$32$	−1.00000	−0.176777
$33$	−6.35160	−1.10567
$34$	6.10685	1.04732
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−9.71834	−1.59768	−0.798842	−	0.601541i	$-0.794554\pi$
$37$	−9.71834	−1.59768	−0.798842	+	0.601541i	$0.794554\pi$
$38$	−3.36674	−0.546157
$39$	−3.15086	−0.504541
$40$	0.705371	0.111529
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−1.74011	−0.265365	−0.132682	−	0.991159i	$-0.542359\pi$
$43$	−1.74011	−0.265365	−0.132682	+	0.991159i	$0.542359\pi$
$44$	6.35160	0.957539
$45$	1.41074	0.210301
$46$	5.61148	0.827368
$47$	−0.460627	−0.0671893	−0.0335946	−	0.999436i	$-0.510696\pi$
$47$	−0.460627	−0.0671893	−0.0335946	+	0.999436i	$0.510696\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.50245	0.636743
$51$	6.10685	0.855130
$52$	3.15086	0.436945
$53$	−1.90611	−0.261825	−0.130912	−	0.991394i	$-0.541791\pi$
$53$	−1.90611	−0.261825	−0.130912	+	0.991394i	$0.541791\pi$
$54$	−5.00000	−0.680414
$55$	−4.48023	−0.604114
$56$	0	0
$57$	−3.36674	−0.445935
$58$	7.44549	0.977640
$59$	7.97822	1.03868	0.519338	−	0.854569i	$-0.326179\pi$
$59$	7.97822	1.03868	0.519338	+	0.854569i	$0.326179\pi$
$60$	0.705371	0.0910629
$61$	−0.805142	−0.103088	−0.0515439	−	0.998671i	$-0.516414\pi$
$61$	−0.805142	−0.103088	−0.0515439	+	0.998671i	$0.516414\pi$
$62$	−8.66137	−1.09999
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.22252	−0.275670
$66$	6.35160	0.781828
$67$	9.05697	1.10648	0.553242	−	0.833020i	$-0.313390\pi$
$67$	9.05697	1.10648	0.553242	+	0.833020i	$0.313390\pi$
$68$	−6.10685	−0.740565
$69$	5.61148	0.675543
$70$	0	0
$71$	13.9039	1.65009	0.825047	−	0.565064i	$-0.191149\pi$
$71$	13.9039	1.65009	0.825047	+	0.565064i	$0.191149\pi$
$72$	2.00000	0.235702
$73$	1.63326	0.191159	0.0955794	−	0.995422i	$-0.469530\pi$
$73$	1.63326	0.191159	0.0955794	+	0.995422i	$0.469530\pi$
$74$	9.71834	1.12973
$75$	4.50245	0.519898
$76$	3.36674	0.386191
$77$	0	0
$78$	3.15086	0.356764
$79$	−4.14377	−0.466211	−0.233105	−	0.972451i	$-0.574889\pi$
$79$	−4.14377	−0.466211	−0.233105	+	0.972451i	$0.574889\pi$
$80$	−0.705371	−0.0788628
$81$	1.00000	0.111111
$82$	−1.00000	−0.110432
$83$	−14.1198	−1.54985	−0.774926	−	0.632052i	$-0.782213\pi$
$83$	−14.1198	−1.54985	−0.774926	+	0.632052i	$0.782213\pi$
$84$	0	0
$85$	4.30759	0.467224
$86$	1.74011	0.187641
$87$	7.44549	0.798240
$88$	−6.35160	−0.677082
$89$	2.36674	0.250874	0.125437	−	0.992102i	$-0.459967\pi$
$89$	2.36674	0.250874	0.125437	+	0.992102i	$0.459967\pi$
$90$	−1.41074	−0.148705
$91$	0	0
$92$	−5.61148	−0.585037
$93$	−8.66137	−0.898142
$94$	0.460627	0.0475100
$95$	−2.37480	−0.243649
$96$	1.00000	0.102062
$97$	−3.34451	−0.339584	−0.169792	−	0.985480i	$-0.554310\pi$
$97$	−3.34451	−0.339584	−0.169792	+	0.985480i	$0.554310\pi$
$98$	0	0
$99$	−12.7032	−1.27672
$100$	−4.50245	−0.450245
$101$	−1.51759	−0.151006	−0.0755031	−	0.997146i	$-0.524056\pi$
$101$	−1.51759	−0.151006	−0.0755031	+	0.997146i	$0.524056\pi$
$102$	−6.10685	−0.604669
$103$	15.4655	1.52386	0.761932	−	0.647657i	$-0.224251\pi$
$103$	15.4655	1.52386	0.761932	+	0.647657i	$0.224251\pi$
$104$	−3.15086	−0.308967
$105$	0	0
$106$	1.90611	0.185138
$107$	0.567479	0.0548603	0.0274302	−	0.999624i	$-0.491268\pi$
$107$	0.567479	0.0548603	0.0274302	+	0.999624i	$0.491268\pi$
$108$	5.00000	0.481125
$109$	−3.96526	−0.379803	−0.189901	−	0.981803i	$-0.560817\pi$
$109$	−3.96526	−0.379803	−0.189901	+	0.981803i	$0.560817\pi$
$110$	4.48023	0.427173
$111$	9.71834	0.922424
$112$	0	0
$113$	−10.9061	−1.02596	−0.512980	−	0.858400i	$-0.671459\pi$
$113$	−10.9061	−1.02596	−0.512980	+	0.858400i	$0.671459\pi$
$114$	3.36674	0.315324
$115$	3.95817	0.369102
$116$	−7.44549	−0.691296
$117$	−6.30171	−0.582593
$118$	−7.97822	−0.734455
$119$	0	0
$120$	−0.705371	−0.0643912
$121$	29.3428	2.66753
$122$	0.805142	0.0728941
$123$	−1.00000	−0.0901670
$124$	8.66137	0.777814
$125$	6.70275	0.599512
$126$	0	0
$127$	−4.38852	−0.389418	−0.194709	−	0.980861i	$-0.562376\pi$
$127$	−4.38852	−0.389418	−0.194709	+	0.980861i	$0.562376\pi$
$128$	−1.00000	−0.0883883
$129$	1.74011	0.153209
$130$	2.22252	0.194928
$131$	−13.6533	−1.19290	−0.596448	−	0.802652i	$-0.703422\pi$
$131$	−13.6533	−1.19290	−0.596448	+	0.802652i	$0.703422\pi$
$132$	−6.35160	−0.552836
$133$	0	0
$134$	−9.05697	−0.782403
$135$	−3.52685	−0.303543
$136$	6.10685	0.523658
$137$	5.58262	0.476955	0.238478	−	0.971148i	$-0.423352\pi$
$137$	5.58262	0.476955	0.238478	+	0.971148i	$0.423352\pi$
$138$	−5.61148	−0.477681
$139$	−9.58120	−0.812667	−0.406333	−	0.913725i	$-0.633193\pi$
$139$	−9.58120	−0.812667	−0.406333	+	0.913725i	$0.633193\pi$
$140$	0	0
$141$	0.460627	0.0387918
$142$	−13.9039	−1.16679
$143$	20.0130	1.67357
$144$	−2.00000	−0.166667
$145$	5.25183	0.436140
$146$	−1.63326	−0.135170
$147$	0	0
$148$	−9.71834	−0.798842
$149$	−22.9387	−1.87921	−0.939605	−	0.342261i	$-0.888807\pi$
$149$	−22.9387	−1.87921	−0.939605	+	0.342261i	$0.888807\pi$
$150$	−4.50245	−0.367624
$151$	−18.5083	−1.50619	−0.753093	−	0.657914i	$-0.771439\pi$
$151$	−18.5083	−1.50619	−0.753093	+	0.657914i	$0.771439\pi$
$152$	−3.36674	−0.273079
$153$	12.2137	0.987420
$154$	0	0
$155$	−6.10947	−0.490725
$156$	−3.15086	−0.252270
$157$	2.79708	0.223231	0.111616	−	0.993751i	$-0.464397\pi$
$157$	2.79708	0.223231	0.111616	+	0.993751i	$0.464397\pi$
$158$	4.14377	0.329661
$159$	1.90611	0.151164
$160$	0.705371	0.0557644
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−17.0976	−1.33919	−0.669593	−	0.742728i	$-0.733532\pi$
$163$	−17.0976	−1.33919	−0.669593	+	0.742728i	$0.733532\pi$
$164$	1.00000	0.0780869
$165$	4.48023	0.348785
$166$	14.1198	1.09591
$167$	−14.2946	−1.10615	−0.553076	−	0.833131i	$-0.686546\pi$
$167$	−14.2946	−1.10615	−0.553076	+	0.833131i	$0.686546\pi$
$168$	0	0
$169$	−3.07211	−0.236316
$170$	−4.30759	−0.330377
$171$	−6.73348	−0.514922
$172$	−1.74011	−0.132682
$173$	−24.3066	−1.84800	−0.923999	−	0.382395i	$-0.875099\pi$
$173$	−24.3066	−1.84800	−0.923999	+	0.382395i	$0.875099\pi$
$174$	−7.44549	−0.564441
$175$	0	0
$176$	6.35160	0.478770
$177$	−7.97822	−0.599680
$178$	−2.36674	−0.177395
$179$	4.51759	0.337661	0.168830	−	0.985645i	$-0.446001\pi$
$179$	4.51759	0.337661	0.168830	+	0.985645i	$0.446001\pi$
$180$	1.41074	0.105150
$181$	4.88389	0.363017	0.181508	−	0.983389i	$-0.441902\pi$
$181$	4.88389	0.363017	0.181508	+	0.983389i	$0.441902\pi$
$182$	0	0
$183$	0.805142	0.0595178
$184$	5.61148	0.413684
$185$	6.85503	0.503992
$186$	8.66137	0.635082
$187$	−38.7883	−2.83648
$188$	−0.460627	−0.0335946
$189$	0	0
$190$	2.37480	0.172286
$191$	−5.64623	−0.408547	−0.204273	−	0.978914i	$-0.565483\pi$
$191$	−5.64623	−0.408547	−0.204273	+	0.978914i	$0.565483\pi$
$192$	−1.00000	−0.0721688
$193$	0.0997710	0.00718168	0.00359084	−	0.999994i	$-0.498857\pi$
$193$	0.0997710	0.00718168	0.00359084	+	0.999994i	$0.498857\pi$
$194$	3.34451	0.240122
$195$	2.22252	0.159158
$196$	0	0
$197$	−6.20738	−0.442257	−0.221129	−	0.975245i	$-0.570974\pi$
$197$	−6.20738	−0.442257	−0.221129	+	0.975245i	$0.570974\pi$
$198$	12.7032	0.902777
$199$	5.09171	0.360942	0.180471	−	0.983580i	$-0.442238\pi$
$199$	5.09171	0.360942	0.180471	+	0.983580i	$0.442238\pi$
$200$	4.50245	0.318371
$201$	−9.05697	−0.638829
$202$	1.51759	0.106778
$203$	0	0
$204$	6.10685	0.427565
$205$	−0.705371	−0.0492652
$206$	−15.4655	−1.07753
$207$	11.2230	0.780050
$208$	3.15086	0.218473
$209$	21.3842	1.47917
$210$	0	0
$211$	20.6604	1.42232	0.711160	−	0.703030i	$-0.248170\pi$
$211$	20.6604	1.42232	0.711160	+	0.703030i	$0.248170\pi$
$212$	−1.90611	−0.130912
$213$	−13.9039	−0.952682
$214$	−0.567479	−0.0387921
$215$	1.22743	0.0837097
$216$	−5.00000	−0.340207
$217$	0	0
$218$	3.96526	0.268561
$219$	−1.63326	−0.110366
$220$	−4.48023	−0.302057
$221$	−19.2418	−1.29434
$222$	−9.71834	−0.652252
$223$	−3.48023	−0.233053	−0.116527	−	0.993188i	$-0.537176\pi$
$223$	−3.48023	−0.233053	−0.116527	+	0.993188i	$0.537176\pi$
$224$	0	0
$225$	9.00490	0.600327
$226$	10.9061	0.725464
$227$	22.0179	1.46138	0.730689	−	0.682711i	$-0.239199\pi$
$227$	22.0179	1.46138	0.730689	+	0.682711i	$0.239199\pi$
$228$	−3.36674	−0.222968
$229$	4.45212	0.294205	0.147102	−	0.989121i	$-0.453005\pi$
$229$	4.45212	0.294205	0.147102	+	0.989121i	$0.453005\pi$
$230$	−3.95817	−0.260994
$231$	0	0
$232$	7.44549	0.488820
$233$	−25.5235	−1.67210	−0.836049	−	0.548654i	$-0.815140\pi$
$233$	−25.5235	−1.67210	−0.836049	+	0.548654i	$0.815140\pi$
$234$	6.30171	0.411956
$235$	0.324912	0.0211949
$236$	7.97822	0.519338
$237$	4.14377	0.269167
$238$	0	0
$239$	−4.01960	−0.260006	−0.130003	−	0.991514i	$-0.541499\pi$
$239$	−4.01960	−0.260006	−0.130003	+	0.991514i	$0.541499\pi$
$240$	0.705371	0.0455315
$241$	2.58926	0.166789	0.0833944	−	0.996517i	$-0.473424\pi$
$241$	2.58926	0.166789	0.0833944	+	0.996517i	$0.473424\pi$
$242$	−29.3428	−1.88623
$243$	−16.0000	−1.02640
$244$	−0.805142	−0.0515439
$245$	0	0
$246$	1.00000	0.0637577
$247$	10.6081	0.674978
$248$	−8.66137	−0.549997
$249$	14.1198	0.894807
$250$	−6.70275	−0.423919
$251$	−4.89805	−0.309162	−0.154581	−	0.987980i	$-0.549403\pi$
$251$	−4.89805	−0.309162	−0.154581	+	0.987980i	$0.549403\pi$
$252$	0	0
$253$	−35.6419	−2.24079
$254$	4.38852	0.275360
$255$	−4.30759	−0.269752
$256$	1.00000	0.0625000
$257$	19.7687	1.23314	0.616568	−	0.787302i	$-0.288523\pi$
$257$	19.7687	1.23314	0.616568	+	0.787302i	$0.288523\pi$
$258$	−1.74011	−0.108335
$259$	0	0
$260$	−2.22252	−0.137835
$261$	14.8910	0.921728
$262$	13.6533	0.843504
$263$	8.36674	0.515915	0.257958	−	0.966156i	$-0.416951\pi$
$263$	8.36674	0.515915	0.257958	+	0.966156i	$0.416951\pi$
$264$	6.35160	0.390914
$265$	1.34451	0.0825929
$266$	0	0
$267$	−2.36674	−0.144842
$268$	9.05697	0.553242
$269$	−21.7694	−1.32730	−0.663652	−	0.748041i	$-0.730995\pi$
$269$	−21.7694	−1.32730	−0.663652	+	0.748041i	$0.730995\pi$
$270$	3.52685	0.214637
$271$	−18.7623	−1.13973	−0.569865	−	0.821738i	$-0.693005\pi$
$271$	−18.7623	−1.13973	−0.569865	+	0.821738i	$0.693005\pi$
$272$	−6.10685	−0.370282
$273$	0	0
$274$	−5.58262	−0.337258
$275$	−28.5978	−1.72451
$276$	5.61148	0.337772
$277$	−9.46183	−0.568506	−0.284253	−	0.958749i	$-0.591746\pi$
$277$	−9.46183	−0.568506	−0.284253	+	0.958749i	$0.591746\pi$
$278$	9.58120	0.574642
$279$	−17.3227	−1.03709
$280$	0	0
$281$	4.16338	0.248366	0.124183	−	0.992259i	$-0.460369\pi$
$281$	4.16338	0.248366	0.124183	+	0.992259i	$0.460369\pi$
$282$	−0.460627	−0.0274299
$283$	−27.4844	−1.63378	−0.816888	−	0.576796i	$-0.804303\pi$
$283$	−27.4844	−1.63378	−0.816888	+	0.576796i	$0.804303\pi$
$284$	13.9039	0.825047
$285$	2.37480	0.140671
$286$	−20.0130	−1.18339
$287$	0	0
$288$	2.00000	0.117851
$289$	20.2937	1.19374
$290$	−5.25183	−0.308398
$291$	3.34451	0.196059
$292$	1.63326	0.0955794
$293$	31.9044	1.86387	0.931937	−	0.362621i	$-0.118118\pi$
$293$	31.9044	1.86387	0.931937	+	0.362621i	$0.118118\pi$
$294$	0	0
$295$	−5.62760	−0.327652
$296$	9.71834	0.564867
$297$	31.7580	1.84279
$298$	22.9387	1.32880
$299$	−17.6810	−1.02252
$300$	4.50245	0.259949
$301$	0	0
$302$	18.5083	1.06504
$303$	1.51759	0.0871835
$304$	3.36674	0.193096
$305$	0.567923	0.0325192
$306$	−12.2137	−0.698211
$307$	31.8800	1.81949	0.909743	−	0.415171i	$-0.136278\pi$
$307$	31.8800	1.81949	0.909743	+	0.415171i	$0.136278\pi$
$308$	0	0
$309$	−15.4655	−0.879803
$310$	6.10947	0.346995
$311$	7.77040	0.440619	0.220309	−	0.975430i	$-0.429293\pi$
$311$	7.77040	0.440619	0.220309	+	0.975430i	$0.429293\pi$
$312$	3.15086	0.178382
$313$	1.63914	0.0926499	0.0463250	−	0.998926i	$-0.485249\pi$
$313$	1.63914	0.0926499	0.0463250	+	0.998926i	$0.485249\pi$
$314$	−2.79708	−0.157848
$315$	0	0
$316$	−4.14377	−0.233105
$317$	12.1790	0.684039	0.342019	−	0.939693i	$-0.388889\pi$
$317$	12.1790	0.684039	0.342019	+	0.939693i	$0.388889\pi$
$318$	−1.90611	−0.106889
$319$	−47.2907	−2.64777
$320$	−0.705371	−0.0394314
$321$	−0.567479	−0.0316736
$322$	0	0
$323$	−20.5602	−1.14400
$324$	1.00000	0.0555556
$325$	−14.1866	−0.786930
$326$	17.0976	0.946948
$327$	3.96526	0.219279
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−4.48023	−0.246628
$331$	9.81102	0.539263	0.269631	−	0.962964i	$-0.413098\pi$
$331$	9.81102	0.539263	0.269631	+	0.962964i	$0.413098\pi$
$332$	−14.1198	−0.774926
$333$	19.4367	1.06512
$334$	14.2946	0.782167
$335$	−6.38852	−0.349042
$336$	0	0
$337$	−6.87017	−0.374242	−0.187121	−	0.982337i	$-0.559916\pi$
$337$	−6.87017	−0.374242	−0.187121	+	0.982337i	$0.559916\pi$
$338$	3.07211	0.167101
$339$	10.9061	0.592339
$340$	4.30759	0.233612
$341$	55.0135	2.97915
$342$	6.73348	0.364105
$343$	0	0
$344$	1.74011	0.0938207
$345$	−3.95817	−0.213101
$346$	24.3066	1.30673
$347$	−21.8127	−1.17097	−0.585483	−	0.810685i	$-0.699095\pi$
$347$	−21.8127	−1.17097	−0.585483	+	0.810685i	$0.699095\pi$
$348$	7.44549	0.399120
$349$	−27.4844	−1.47121	−0.735603	−	0.677413i	$-0.763101\pi$
$349$	−27.4844	−1.47121	−0.735603	+	0.677413i	$0.763101\pi$
$350$	0	0
$351$	15.7543	0.840901
$352$	−6.35160	−0.338541
$353$	−16.8051	−0.894447	−0.447224	−	0.894422i	$-0.647587\pi$
$353$	−16.8051	−0.894447	−0.447224	+	0.894422i	$0.647587\pi$
$354$	7.97822	0.424038
$355$	−9.80743	−0.520524
$356$	2.36674	0.125437
$357$	0	0
$358$	−4.51759	−0.238762
$359$	−7.93497	−0.418792	−0.209396	−	0.977831i	$-0.567150\pi$
$359$	−7.93497	−0.418792	−0.209396	+	0.977831i	$0.567150\pi$
$360$	−1.41074	−0.0743526
$361$	−7.66507	−0.403425
$362$	−4.88389	−0.256691
$363$	−29.3428	−1.54010
$364$	0	0
$365$	−1.15205	−0.0603013
$366$	−0.805142	−0.0420854
$367$	−26.6743	−1.39239	−0.696194	−	0.717853i	$-0.745125\pi$
$367$	−26.6743	−1.39239	−0.696194	+	0.717853i	$0.745125\pi$
$368$	−5.61148	−0.292519
$369$	−2.00000	−0.104116
$370$	−6.85503	−0.356376
$371$	0	0
$372$	−8.66137	−0.449071
$373$	−20.3080	−1.05151	−0.525755	−	0.850636i	$-0.676217\pi$
$373$	−20.3080	−1.05151	−0.525755	+	0.850636i	$0.676217\pi$
$374$	38.7883	2.00569
$375$	−6.70275	−0.346129
$376$	0.460627	0.0237550
$377$	−23.4596	−1.20823
$378$	0	0
$379$	−8.53840	−0.438588	−0.219294	−	0.975659i	$-0.570375\pi$
$379$	−8.53840	−0.438588	−0.219294	+	0.975659i	$0.570375\pi$
$380$	−2.37480	−0.121825
$381$	4.38852	0.224831
$382$	5.64623	0.288886
$383$	−9.59896	−0.490484	−0.245242	−	0.969462i	$-0.578867\pi$
$383$	−9.59896	−0.490484	−0.245242	+	0.969462i	$0.578867\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−0.0997710	−0.00507821
$387$	3.48023	0.176910
$388$	−3.34451	−0.169792
$389$	−20.2203	−1.02521	−0.512606	−	0.858624i	$-0.671320\pi$
$389$	−20.2203	−1.02521	−0.512606	+	0.858624i	$0.671320\pi$
$390$	−2.22252	−0.112542
$391$	34.2685	1.73303
$392$	0	0
$393$	13.6533	0.688718
$394$	6.20738	0.312723
$395$	2.92290	0.147067
$396$	−12.7032	−0.638359
$397$	0.193659	0.00971948	0.00485974	−	0.999988i	$-0.498453\pi$
$397$	0.193659	0.00971948	0.00485974	+	0.999988i	$0.498453\pi$
$398$	−5.09171	−0.255224
$399$	0	0
$400$	−4.50245	−0.225123
$401$	−12.3831	−0.618381	−0.309191	−	0.951000i	$-0.600058\pi$
$401$	−12.3831	−0.618381	−0.309191	+	0.951000i	$0.600058\pi$
$402$	9.05697	0.451720
$403$	27.2907	1.35945
$404$	−1.51759	−0.0755031
$405$	−0.705371	−0.0350501
$406$	0	0
$407$	−61.7269	−3.05969
$408$	−6.10685	−0.302334
$409$	−34.1754	−1.68986	−0.844931	−	0.534875i	$-0.820359\pi$
$409$	−34.1754	−1.68986	−0.844931	+	0.534875i	$0.820359\pi$
$410$	0.705371	0.0348358
$411$	−5.58262	−0.275370
$412$	15.4655	0.761932
$413$	0	0
$414$	−11.2230	−0.551579
$415$	9.95970	0.488903
$416$	−3.15086	−0.154483
$417$	9.58120	0.469193
$418$	−21.3842	−1.04593
$419$	−1.35040	−0.0659712	−0.0329856	−	0.999456i	$-0.510502\pi$
$419$	−1.35040	−0.0659712	−0.0329856	+	0.999456i	$0.510502\pi$
$420$	0	0
$421$	−8.41445	−0.410095	−0.205048	−	0.978752i	$-0.565735\pi$
$421$	−8.41445	−0.410095	−0.205048	+	0.978752i	$0.565735\pi$
$422$	−20.6604	−1.00573
$423$	0.921253	0.0447929
$424$	1.90611	0.0925690
$425$	27.4958	1.33374
$426$	13.9039	0.673648
$427$	0	0
$428$	0.567479	0.0274302
$429$	−20.0130	−0.966235
$430$	−1.22743	−0.0591917
$431$	−21.7834	−1.04927	−0.524634	−	0.851328i	$-0.675798\pi$
$431$	−21.7834	−1.04927	−0.524634	+	0.851328i	$0.675798\pi$
$432$	5.00000	0.240563
$433$	−37.8892	−1.82084	−0.910420	−	0.413685i	$-0.864242\pi$
$433$	−37.8892	−1.82084	−0.910420	+	0.413685i	$0.864242\pi$
$434$	0	0
$435$	−5.25183	−0.251806
$436$	−3.96526	−0.189901
$437$	−18.8924	−0.903746
$438$	1.63326	0.0780403
$439$	−2.66212	−0.127056	−0.0635281	−	0.997980i	$-0.520235\pi$
$439$	−2.66212	−0.127056	−0.0635281	+	0.997980i	$0.520235\pi$
$440$	4.48023	0.213587
$441$	0	0
$442$	19.2418	0.915240
$443$	−32.2555	−1.53251	−0.766253	−	0.642539i	$-0.777881\pi$
$443$	−32.2555	−1.53251	−0.766253	+	0.642539i	$0.777881\pi$
$444$	9.71834	0.461212
$445$	−1.66943	−0.0791384
$446$	3.48023	0.164794
$447$	22.9387	1.08496
$448$	0	0
$449$	3.73794	0.176404	0.0882021	−	0.996103i	$-0.471888\pi$
$449$	3.73794	0.176404	0.0882021	+	0.996103i	$0.471888\pi$
$450$	−9.00490	−0.424495
$451$	6.35160	0.299085
$452$	−10.9061	−0.512980
$453$	18.5083	0.869597
$454$	−22.0179	−1.03335
$455$	0	0
$456$	3.36674	0.157662
$457$	23.4526	1.09706	0.548532	−	0.836129i	$-0.315187\pi$
$457$	23.4526	1.09706	0.548532	+	0.836129i	$0.315187\pi$
$458$	−4.45212	−0.208034
$459$	−30.5343	−1.42522
$460$	3.95817	0.184551
$461$	−30.4499	−1.41820	−0.709098	−	0.705110i	$-0.750897\pi$
$461$	−30.4499	−1.41820	−0.709098	+	0.705110i	$0.750897\pi$
$462$	0	0
$463$	21.5180	1.00003	0.500014	−	0.866017i	$-0.333328\pi$
$463$	21.5180	1.00003	0.500014	+	0.866017i	$0.333328\pi$
$464$	−7.44549	−0.345648
$465$	6.10947	0.283320
$466$	25.5235	1.18235
$467$	21.6951	1.00393	0.501966	−	0.864888i	$-0.332610\pi$
$467$	21.6951	1.00393	0.501966	+	0.864888i	$0.332610\pi$
$468$	−6.30171	−0.291297
$469$	0	0
$470$	−0.324912	−0.0149871
$471$	−2.79708	−0.128883
$472$	−7.97822	−0.367227
$473$	−11.0525	−0.508195
$474$	−4.14377	−0.190330
$475$	−15.1586	−0.695523
$476$	0	0
$477$	3.81222	0.174550
$478$	4.01960	0.183852
$479$	−23.8171	−1.08823	−0.544116	−	0.839010i	$-0.683135\pi$
$479$	−23.8171	−1.08823	−0.544116	+	0.839010i	$0.683135\pi$
$480$	−0.705371	−0.0321956
$481$	−30.6211	−1.39620
$482$	−2.58926	−0.117938
$483$	0	0
$484$	29.3428	1.33376
$485$	2.35912	0.107122
$486$	16.0000	0.725775
$487$	9.97387	0.451959	0.225980	−	0.974132i	$-0.427442\pi$
$487$	9.97387	0.451959	0.225980	+	0.974132i	$0.427442\pi$
$488$	0.805142	0.0364470
$489$	17.0976	0.773180
$490$	0	0
$491$	32.0807	1.44778	0.723891	−	0.689914i	$-0.242352\pi$
$491$	32.0807	1.44778	0.723891	+	0.689914i	$0.242352\pi$
$492$	−1.00000	−0.0450835
$493$	45.4685	2.04780
$494$	−10.6081	−0.477281
$495$	8.96046	0.402743
$496$	8.66137	0.388907
$497$	0	0
$498$	−14.1198	−0.632724
$499$	−18.3361	−0.820839	−0.410419	−	0.911897i	$-0.634618\pi$
$499$	−18.3361	−0.820839	−0.410419	+	0.911897i	$0.634618\pi$
$500$	6.70275	0.299756
$501$	14.2946	0.638637
$502$	4.89805	0.218611
$503$	40.9654	1.82656	0.913278	−	0.407338i	$-0.133543\pi$
$503$	40.9654	1.82656	0.913278	+	0.407338i	$0.133543\pi$
$504$	0	0
$505$	1.07047	0.0476351
$506$	35.6419	1.58447
$507$	3.07211	0.136437
$508$	−4.38852	−0.194709
$509$	−1.61856	−0.0717416	−0.0358708	−	0.999356i	$-0.511420\pi$
$509$	−1.61856	−0.0717416	−0.0358708	+	0.999356i	$0.511420\pi$
$510$	4.30759	0.190743
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	16.8337	0.743226
$514$	−19.7687	−0.871958
$515$	−10.9089	−0.480705
$516$	1.74011	0.0766043
$517$	−2.92571	−0.128673
$518$	0	0
$519$	24.3066	1.06694
$520$	2.22252	0.0974640
$521$	−29.6734	−1.30001	−0.650007	−	0.759929i	$-0.725234\pi$
$521$	−29.6734	−1.30001	−0.650007	+	0.759929i	$0.725234\pi$
$522$	−14.8910	−0.651760
$523$	7.03692	0.307703	0.153852	−	0.988094i	$-0.450832\pi$
$523$	7.03692	0.307703	0.153852	+	0.988094i	$0.450832\pi$
$524$	−13.6533	−0.596448
$525$	0	0
$526$	−8.36674	−0.364807
$527$	−52.8937	−2.30409
$528$	−6.35160	−0.276418
$529$	8.48873	0.369075
$530$	−1.34451	−0.0584020
$531$	−15.9564	−0.692451
$532$	0	0
$533$	3.15086	0.136479
$534$	2.36674	0.102419
$535$	−0.400283	−0.0173058
$536$	−9.05697	−0.391201
$537$	−4.51759	−0.194949
$538$	21.7694	0.938546
$539$	0	0
$540$	−3.52685	−0.151772
$541$	8.77966	0.377467	0.188733	−	0.982028i	$-0.439562\pi$
$541$	8.77966	0.377467	0.188733	+	0.982028i	$0.439562\pi$
$542$	18.7623	0.805911
$543$	−4.88389	−0.209588
$544$	6.10685	0.261829
$545$	2.79697	0.119809
$546$	0	0
$547$	−7.78074	−0.332680	−0.166340	−	0.986068i	$-0.553195\pi$
$547$	−7.78074	−0.332680	−0.166340	+	0.986068i	$0.553195\pi$
$548$	5.58262	0.238478
$549$	1.61028	0.0687252
$550$	28.5978	1.21941
$551$	−25.0670	−1.06789
$552$	−5.61148	−0.238841
$553$	0	0
$554$	9.46183	0.401994
$555$	−6.85503	−0.290980
$556$	−9.58120	−0.406333
$557$	−11.6232	−0.492493	−0.246246	−	0.969207i	$-0.579197\pi$
$557$	−11.6232	−0.492493	−0.246246	+	0.969207i	$0.579197\pi$
$558$	17.3227	0.733330
$559$	−5.48285	−0.231900
$560$	0	0
$561$	38.7883	1.63764
$562$	−4.16338	−0.175621
$563$	4.55234	0.191858	0.0959291	−	0.995388i	$-0.469418\pi$
$563$	4.55234	0.191858	0.0959291	+	0.995388i	$0.469418\pi$
$564$	0.460627	0.0193959
$565$	7.69285	0.323641
$566$	27.4844	1.15525
$567$	0	0
$568$	−13.9039	−0.583396
$569$	22.2499	0.932763	0.466382	−	0.884584i	$-0.345557\pi$
$569$	22.2499	0.932763	0.466382	+	0.884584i	$0.345557\pi$
$570$	−2.37480	−0.0994693
$571$	−11.6555	−0.487767	−0.243883	−	0.969805i	$-0.578421\pi$
$571$	−11.6555	−0.487767	−0.243883	+	0.969805i	$0.578421\pi$
$572$	20.0130	0.836784
$573$	5.64623	0.235874
$574$	0	0
$575$	25.2654	1.05364
$576$	−2.00000	−0.0833333
$577$	12.4769	0.519418	0.259709	−	0.965687i	$-0.416373\pi$
$577$	12.4769	0.519418	0.259709	+	0.965687i	$0.416373\pi$
$578$	−20.2937	−0.844105
$579$	−0.0997710	−0.00414634
$580$	5.25183	0.218070
$581$	0	0
$582$	−3.34451	−0.138635
$583$	−12.1069	−0.501415
$584$	−1.63326	−0.0675849
$585$	4.44504	0.183780
$586$	−31.9044	−1.31796
$587$	−3.04651	−0.125743	−0.0628715	−	0.998022i	$-0.520026\pi$
$587$	−3.04651	−0.125743	−0.0628715	+	0.998022i	$0.520026\pi$
$588$	0	0
$589$	29.1606	1.20154
$590$	5.62760	0.231685
$591$	6.20738	0.255337
$592$	−9.71834	−0.399421
$593$	−24.9228	−1.02346	−0.511728	−	0.859148i	$-0.670994\pi$
$593$	−24.9228	−1.02346	−0.511728	+	0.859148i	$0.670994\pi$
$594$	−31.7580	−1.30305
$595$	0	0
$596$	−22.9387	−0.939605
$597$	−5.09171	−0.208390
$598$	17.6810	0.723029
$599$	−12.0315	−0.491593	−0.245797	−	0.969321i	$-0.579050\pi$
$599$	−12.0315	−0.491593	−0.245797	+	0.969321i	$0.579050\pi$
$600$	−4.50245	−0.183812
$601$	16.2511	0.662895	0.331447	−	0.943474i	$-0.392463\pi$
$601$	16.2511	0.662895	0.331447	+	0.943474i	$0.392463\pi$
$602$	0	0
$603$	−18.1139	−0.737656
$604$	−18.5083	−0.753093
$605$	−20.6975	−0.841474
$606$	−1.51759	−0.0616480
$607$	35.2392	1.43031	0.715157	−	0.698964i	$-0.246355\pi$
$607$	35.2392	1.43031	0.715157	+	0.698964i	$0.246355\pi$
$608$	−3.36674	−0.136539
$609$	0	0
$610$	−0.567923	−0.0229945
$611$	−1.45137	−0.0587161
$612$	12.2137	0.493710
$613$	−4.51879	−0.182512	−0.0912562	−	0.995827i	$-0.529088\pi$
$613$	−4.51879	−0.182512	−0.0912562	+	0.995827i	$0.529088\pi$
$614$	−31.8800	−1.28657
$615$	0.705371	0.0284433
$616$	0	0
$617$	−33.6700	−1.35550	−0.677751	−	0.735291i	$-0.737045\pi$
$617$	−33.6700	−1.35550	−0.677751	+	0.735291i	$0.737045\pi$
$618$	15.4655	0.622115
$619$	−29.3831	−1.18101	−0.590503	−	0.807036i	$-0.701071\pi$
$619$	−29.3831	−1.18101	−0.590503	+	0.807036i	$0.701071\pi$
$620$	−6.10947	−0.245362
$621$	−28.0574	−1.12591
$622$	−7.77040	−0.311565
$623$	0	0
$624$	−3.15086	−0.126135
$625$	17.7843	0.711374
$626$	−1.63914	−0.0655134
$627$	−21.3842	−0.854001
$628$	2.79708	0.111616
$629$	59.3484	2.36638
$630$	0	0
$631$	12.0218	0.478579	0.239290	−	0.970948i	$-0.423085\pi$
$631$	12.0218	0.478579	0.239290	+	0.970948i	$0.423085\pi$
$632$	4.14377	0.164830
$633$	−20.6604	−0.821177
$634$	−12.1790	−0.483688
$635$	3.09553	0.122842
$636$	1.90611	0.0755822
$637$	0	0
$638$	47.2907	1.87226
$639$	−27.8079	−1.10006
$640$	0.705371	0.0278822
$641$	−20.5778	−0.812775	−0.406388	−	0.913701i	$-0.633212\pi$
$641$	−20.5778	−0.812775	−0.406388	+	0.913701i	$0.633212\pi$
$642$	0.567479	0.0223966
$643$	23.8607	0.940974	0.470487	−	0.882407i	$-0.344078\pi$
$643$	23.8607	0.940974	0.470487	+	0.882407i	$0.344078\pi$
$644$	0	0
$645$	−1.22743	−0.0483298
$646$	20.5602	0.808929
$647$	14.6152	0.574582	0.287291	−	0.957843i	$-0.407245\pi$
$647$	14.6152	0.574582	0.287291	+	0.957843i	$0.407245\pi$
$648$	−1.00000	−0.0392837
$649$	50.6744	1.98915
$650$	14.1866	0.556443
$651$	0	0
$652$	−17.0976	−0.669593
$653$	20.9546	0.820016	0.410008	−	0.912082i	$-0.365526\pi$
$653$	20.9546	0.820016	0.410008	+	0.912082i	$0.365526\pi$
$654$	−3.96526	−0.155054
$655$	9.63064	0.376300
$656$	1.00000	0.0390434
$657$	−3.26652	−0.127439
$658$	0	0
$659$	21.6289	0.842543	0.421271	−	0.906935i	$-0.361584\pi$
$659$	21.6289	0.842543	0.421271	+	0.906935i	$0.361584\pi$
$660$	4.48023	0.174393
$661$	41.5128	1.61466	0.807330	−	0.590100i	$-0.200912\pi$
$661$	41.5128	1.61466	0.807330	+	0.590100i	$0.200912\pi$
$662$	−9.81102	−0.381316
$663$	19.2418	0.747290
$664$	14.1198	0.547955
$665$	0	0
$666$	−19.4367	−0.753156
$667$	41.7802	1.61774
$668$	−14.2946	−0.553076
$669$	3.48023	0.134553
$670$	6.38852	0.246810
$671$	−5.11393	−0.197421
$672$	0	0
$673$	20.2858	0.781961	0.390980	−	0.920399i	$-0.372136\pi$
$673$	20.2858	0.781961	0.390980	+	0.920399i	$0.372136\pi$
$674$	6.87017	0.264629
$675$	−22.5123	−0.866497
$676$	−3.07211	−0.118158
$677$	−21.8507	−0.839790	−0.419895	−	0.907573i	$-0.637933\pi$
$677$	−21.8507	−0.839790	−0.419895	+	0.907573i	$0.637933\pi$
$678$	−10.9061	−0.418847
$679$	0	0
$680$	−4.30759	−0.165189
$681$	−22.0179	−0.843727
$682$	−55.0135	−2.10658
$683$	−6.06034	−0.231893	−0.115946	−	0.993255i	$-0.536990\pi$
$683$	−6.06034	−0.231893	−0.115946	+	0.993255i	$0.536990\pi$
$684$	−6.73348	−0.257461
$685$	−3.93782	−0.150456
$686$	0	0
$687$	−4.45212	−0.169859
$688$	−1.74011	−0.0663412
$689$	−6.00588	−0.228806
$690$	3.95817	0.150685
$691$	26.9765	1.02623	0.513117	−	0.858319i	$-0.328491\pi$
$691$	26.9765	1.02623	0.513117	+	0.858319i	$0.328491\pi$
$692$	−24.3066	−0.923999
$693$	0	0
$694$	21.8127	0.827998
$695$	6.75830	0.256357
$696$	−7.44549	−0.282220
$697$	−6.10685	−0.231314
$698$	27.4844	1.04030
$699$	25.5235	0.965387
$700$	0	0
$701$	−2.93051	−0.110684	−0.0553420	−	0.998467i	$-0.517625\pi$
$701$	−2.93051	−0.110684	−0.0553420	+	0.998467i	$0.517625\pi$
$702$	−15.7543	−0.594607
$703$	−32.7191	−1.23402
$704$	6.35160	0.239385
$705$	−0.324912	−0.0122369
$706$	16.8051	0.632470
$707$	0	0
$708$	−7.97822	−0.299840
$709$	19.0075	0.713843	0.356921	−	0.934134i	$-0.383826\pi$
$709$	19.0075	0.713843	0.356921	+	0.934134i	$0.383826\pi$
$710$	9.80743	0.368066
$711$	8.28755	0.310807
$712$	−2.36674	−0.0886973
$713$	−48.6031	−1.82020
$714$	0	0
$715$	−14.1166	−0.527929
$716$	4.51759	0.168830
$717$	4.01960	0.150115
$718$	7.93497	0.296131
$719$	42.0367	1.56770	0.783852	−	0.620947i	$-0.213252\pi$
$719$	42.0367	1.56770	0.783852	+	0.620947i	$0.213252\pi$
$720$	1.41074	0.0525752
$721$	0	0
$722$	7.66507	0.285264
$723$	−2.58926	−0.0962956
$724$	4.88389	0.181508
$725$	33.5229	1.24501
$726$	29.3428	1.08901
$727$	−21.2242	−0.787161	−0.393580	−	0.919290i	$-0.628764\pi$
$727$	−21.2242	−0.787161	−0.393580	+	0.919290i	$0.628764\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	1.15205	0.0426395
$731$	10.6266	0.393040
$732$	0.805142	0.0297589
$733$	32.5951	1.20393	0.601965	−	0.798523i	$-0.294385\pi$
$733$	32.5951	1.20393	0.601965	+	0.798523i	$0.294385\pi$
$734$	26.6743	0.984568
$735$	0	0
$736$	5.61148	0.206842
$737$	57.5262	2.11900
$738$	2.00000	0.0736210
$739$	10.4710	0.385181	0.192590	−	0.981279i	$-0.438311\pi$
$739$	10.4710	0.385181	0.192590	+	0.981279i	$0.438311\pi$
$740$	6.85503	0.251996
$741$	−10.6081	−0.389699
$742$	0	0
$743$	−46.2600	−1.69711	−0.848557	−	0.529104i	$-0.822528\pi$
$743$	−46.2600	−1.69711	−0.848557	+	0.529104i	$0.822528\pi$
$744$	8.66137	0.317541
$745$	16.1803	0.592799
$746$	20.3080	0.743530
$747$	28.2396	1.03323
$748$	−38.7883	−1.41824
$749$	0	0
$750$	6.70275	0.244750
$751$	48.3037	1.76263	0.881313	−	0.472533i	$-0.156660\pi$
$751$	48.3037	1.76263	0.881313	+	0.472533i	$0.156660\pi$
$752$	−0.460627	−0.0167973
$753$	4.89805	0.178495
$754$	23.4596	0.854350
$755$	13.0552	0.475129
$756$	0	0
$757$	36.4118	1.32341	0.661705	−	0.749764i	$-0.269833\pi$
$757$	36.4118	1.32341	0.661705	+	0.749764i	$0.269833\pi$
$758$	8.53840	0.310128
$759$	35.6419	1.29372
$760$	2.37480	0.0861430
$761$	−27.7486	−1.00589	−0.502943	−	0.864319i	$-0.667750\pi$
$761$	−27.7486	−1.00589	−0.502943	+	0.864319i	$0.667750\pi$
$762$	−4.38852	−0.158979
$763$	0	0
$764$	−5.64623	−0.204273
$765$	−8.61519	−0.311483
$766$	9.59896	0.346825
$767$	25.1382	0.907689
$768$	−1.00000	−0.0360844
$769$	44.3428	1.59904	0.799521	−	0.600638i	$-0.205087\pi$
$769$	44.3428	1.59904	0.799521	+	0.600638i	$0.205087\pi$
$770$	0	0
$771$	−19.7687	−0.711951
$772$	0.0997710	0.00359084
$773$	−6.81178	−0.245003	−0.122501	−	0.992468i	$-0.539092\pi$
$773$	−6.81178	−0.245003	−0.122501	+	0.992468i	$0.539092\pi$
$774$	−3.48023	−0.125094
$775$	−38.9974	−1.40083
$776$	3.34451	0.120061
$777$	0	0
$778$	20.2203	0.724934
$779$	3.36674	0.120626
$780$	2.22252	0.0795790
$781$	88.3122	3.16006
$782$	−34.2685	−1.22544
$783$	−37.2274	−1.33040
$784$	0	0
$785$	−1.97298	−0.0704186
$786$	−13.6533	−0.486997
$787$	−11.7460	−0.418700	−0.209350	−	0.977841i	$-0.567135\pi$
$787$	−11.7460	−0.418700	−0.209350	+	0.977841i	$0.567135\pi$
$788$	−6.20738	−0.221129
$789$	−8.36674	−0.297864
$790$	−2.92290	−0.103992
$791$	0	0
$792$	12.7032	0.451388
$793$	−2.53688	−0.0900874
$794$	−0.193659	−0.00687271
$795$	−1.34451	−0.0476850
$796$	5.09171	0.180471
$797$	−27.0623	−0.958596	−0.479298	−	0.877652i	$-0.659109\pi$
$797$	−27.0623	−0.958596	−0.479298	+	0.877652i	$0.659109\pi$
$798$	0	0
$799$	2.81298	0.0995160
$800$	4.50245	0.159186
$801$	−4.73348	−0.167249
$802$	12.3831	0.437262
$803$	10.3738	0.366084
$804$	−9.05697	−0.319415
$805$	0	0
$806$	−27.2907	−0.961275
$807$	21.7694	0.766320
$808$	1.51759	0.0533888
$809$	15.7460	0.553600	0.276800	−	0.960928i	$-0.410726\pi$
$809$	15.7460	0.553600	0.276800	+	0.960928i	$0.410726\pi$
$810$	0.705371	0.0247842
$811$	44.6629	1.56833	0.784163	−	0.620555i	$-0.213092\pi$
$811$	44.6629	1.56833	0.784163	+	0.620555i	$0.213092\pi$
$812$	0	0
$813$	18.7623	0.658024
$814$	61.7269	2.16353
$815$	12.0601	0.422448
$816$	6.10685	0.213783
$817$	−5.85851	−0.204963
$818$	34.1754	1.19491
$819$	0	0
$820$	−0.705371	−0.0246326
$821$	−51.5369	−1.79865	−0.899325	−	0.437281i	$-0.855941\pi$
$821$	−51.5369	−1.79865	−0.899325	+	0.437281i	$0.855941\pi$
$822$	5.58262	0.194716
$823$	−11.1778	−0.389632	−0.194816	−	0.980840i	$-0.562411\pi$
$823$	−11.1778	−0.389632	−0.194816	+	0.980840i	$0.562411\pi$
$824$	−15.4655	−0.538767
$825$	28.5978	0.995646
$826$	0	0
$827$	−41.7242	−1.45089	−0.725447	−	0.688278i	$-0.758367\pi$
$827$	−41.7242	−1.45089	−0.725447	+	0.688278i	$0.758367\pi$
$828$	11.2230	0.390025
$829$	−43.5350	−1.51203	−0.756017	−	0.654552i	$-0.772857\pi$
$829$	−43.5350	−1.51203	−0.756017	+	0.654552i	$0.772857\pi$
$830$	−9.95970	−0.345706
$831$	9.46183	0.328227
$832$	3.15086	0.109236
$833$	0	0
$834$	−9.58120	−0.331770
$835$	10.0830	0.348937
$836$	21.3842	0.739587
$837$	43.3068	1.49690
$838$	1.35040	0.0466487
$839$	−7.37708	−0.254685	−0.127343	−	0.991859i	$-0.540645\pi$
$839$	−7.37708	−0.254685	−0.127343	+	0.991859i	$0.540645\pi$
$840$	0	0
$841$	26.4352	0.911560
$842$	8.41445	0.289981
$843$	−4.16338	−0.143394
$844$	20.6604	0.711160
$845$	2.16697	0.0745462
$846$	−0.921253	−0.0316733
$847$	0	0
$848$	−1.90611	−0.0654561
$849$	27.4844	0.943261
$850$	−27.4958	−0.943099
$851$	54.5343	1.86941
$852$	−13.9039	−0.476341
$853$	15.6119	0.534542	0.267271	−	0.963621i	$-0.413878\pi$
$853$	15.6119	0.534542	0.267271	+	0.963621i	$0.413878\pi$
$854$	0	0
$855$	4.74960	0.162433
$856$	−0.567479	−0.0193960
$857$	50.8608	1.73737	0.868686	−	0.495363i	$-0.164965\pi$
$857$	50.8608	1.73737	0.868686	+	0.495363i	$0.164965\pi$
$858$	20.0130	0.683231
$859$	−48.5069	−1.65503	−0.827517	−	0.561440i	$-0.810247\pi$
$859$	−48.5069	−1.65503	−0.827517	+	0.561440i	$0.810247\pi$
$860$	1.22743	0.0418549
$861$	0	0
$862$	21.7834	0.741944
$863$	6.79828	0.231416	0.115708	−	0.993283i	$-0.463086\pi$
$863$	6.79828	0.231416	0.115708	+	0.993283i	$0.463086\pi$
$864$	−5.00000	−0.170103
$865$	17.1452	0.582953
$866$	37.8892	1.28753
$867$	−20.2937	−0.689209
$868$	0	0
$869$	−26.3196	−0.892831
$870$	5.25183	0.178054
$871$	28.5372	0.966946
$872$	3.96526	0.134281
$873$	6.68903	0.226389
$874$	18.8924	0.639045
$875$	0	0
$876$	−1.63326	−0.0551828
$877$	23.2469	0.784993	0.392496	−	0.919754i	$-0.371612\pi$
$877$	23.2469	0.784993	0.392496	+	0.919754i	$0.371612\pi$
$878$	2.66212	0.0898423
$879$	−31.9044	−1.07611
$880$	−4.48023	−0.151028
$881$	−11.1834	−0.376779	−0.188390	−	0.982094i	$-0.560327\pi$
$881$	−11.1834	−0.376779	−0.188390	+	0.982094i	$0.560327\pi$
$882$	0	0
$883$	0.523033	0.0176015	0.00880073	−	0.999961i	$-0.497199\pi$
$883$	0.523033	0.0176015	0.00880073	+	0.999961i	$0.497199\pi$
$884$	−19.2418	−0.647172
$885$	5.62760	0.189170
$886$	32.2555	1.08365
$887$	−21.4819	−0.721291	−0.360645	−	0.932703i	$-0.617444\pi$
$887$	−21.4819	−0.721291	−0.360645	+	0.932703i	$0.617444\pi$
$888$	−9.71834	−0.326126
$889$	0	0
$890$	1.66943	0.0559593
$891$	6.35160	0.212786
$892$	−3.48023	−0.116527
$893$	−1.55081	−0.0518958
$894$	−22.9387	−0.767184
$895$	−3.18658	−0.106516
$896$	0	0
$897$	17.6810	0.590350
$898$	−3.73794	−0.124737
$899$	−64.4881	−2.15080
$900$	9.00490	0.300163
$901$	11.6403	0.387796
$902$	−6.35160	−0.211485
$903$	0	0
$904$	10.9061	0.362732
$905$	−3.44495	−0.114514
$906$	−18.5083	−0.614898
$907$	−20.1872	−0.670306	−0.335153	−	0.942164i	$-0.608788\pi$
$907$	−20.1872	−0.670306	−0.335153	+	0.942164i	$0.608788\pi$
$908$	22.0179	0.730689
$909$	3.03519	0.100671
$910$	0	0
$911$	26.2352	0.869210	0.434605	−	0.900621i	$-0.356888\pi$
$911$	26.2352	0.869210	0.434605	+	0.900621i	$0.356888\pi$
$912$	−3.36674	−0.111484
$913$	−89.6834	−2.96809
$914$	−23.4526	−0.775742
$915$	−0.567923	−0.0187750
$916$	4.45212	0.147102
$917$	0	0
$918$	30.5343	1.00778
$919$	−7.17896	−0.236812	−0.118406	−	0.992965i	$-0.537778\pi$
$919$	−7.17896	−0.236812	−0.118406	+	0.992965i	$0.537778\pi$
$920$	−3.95817	−0.130497
$921$	−31.8800	−1.05048
$922$	30.4499	1.00282
$923$	43.8093	1.44200
$924$	0	0
$925$	43.7563	1.43870
$926$	−21.5180	−0.707127
$927$	−30.9311	−1.01591
$928$	7.44549	0.244410
$929$	−21.3531	−0.700573	−0.350287	−	0.936643i	$-0.613916\pi$
$929$	−21.3531	−0.700573	−0.350287	+	0.936643i	$0.613916\pi$
$930$	−6.10947	−0.200338
$931$	0	0
$932$	−25.5235	−0.836049
$933$	−7.77040	−0.254391
$934$	−21.6951	−0.709886
$935$	27.3601	0.894771
$936$	6.30171	0.205978
$937$	−6.77257	−0.221250	−0.110625	−	0.993862i	$-0.535285\pi$
$937$	−6.77257	−0.221250	−0.110625	+	0.993862i	$0.535285\pi$
$938$	0	0
$939$	−1.63914	−0.0534915
$940$	0.324912	0.0105975
$941$	−41.6050	−1.35628	−0.678141	−	0.734932i	$-0.737214\pi$
$941$	−41.6050	−1.35628	−0.678141	+	0.734932i	$0.737214\pi$
$942$	2.79708	0.0911339
$943$	−5.61148	−0.182735
$944$	7.97822	0.259669
$945$	0	0
$946$	11.0525	0.359348
$947$	−35.4052	−1.15051	−0.575257	−	0.817973i	$-0.695098\pi$
$947$	−35.4052	−1.15051	−0.575257	+	0.817973i	$0.695098\pi$
$948$	4.14377	0.134584
$949$	5.14617	0.167052
$950$	15.1586	0.491809
$951$	−12.1790	−0.394930
$952$	0	0
$953$	38.9079	1.26035	0.630175	−	0.776453i	$-0.282983\pi$
$953$	38.9079	1.26035	0.630175	+	0.776453i	$0.282983\pi$
$954$	−3.81222	−0.123425
$955$	3.98268	0.128877
$956$	−4.01960	−0.130003
$957$	47.2907	1.52869
$958$	23.8171	0.769496
$959$	0	0
$960$	0.705371	0.0227657
$961$	44.0193	1.41998
$962$	30.6211	0.987263
$963$	−1.13496	−0.0365735
$964$	2.58926	0.0833944
$965$	−0.0703756	−0.00226547
$966$	0	0
$967$	24.7339	0.795389	0.397695	−	0.917518i	$-0.369810\pi$
$967$	24.7339	0.795389	0.397695	+	0.917518i	$0.369810\pi$
$968$	−29.3428	−0.943113
$969$	20.5602	0.660488
$970$	−2.35912	−0.0757469
$971$	6.89066	0.221132	0.110566	−	0.993869i	$-0.464734\pi$
$971$	6.89066	0.221132	0.110566	+	0.993869i	$0.464734\pi$
$972$	−16.0000	−0.513200
$973$	0	0
$974$	−9.97387	−0.319583
$975$	14.1866	0.454334
$976$	−0.805142	−0.0257720
$977$	−23.4458	−0.750098	−0.375049	−	0.927005i	$-0.622374\pi$
$977$	−23.4458	−0.750098	−0.375049	+	0.927005i	$0.622374\pi$
$978$	−17.0976	−0.546721
$979$	15.0326	0.480443
$980$	0	0
$981$	7.93051	0.253202
$982$	−32.0807	−1.02374
$983$	−1.24443	−0.0396912	−0.0198456	−	0.999803i	$-0.506317\pi$
$983$	−1.24443	−0.0396912	−0.0198456	+	0.999803i	$0.506317\pi$
$984$	1.00000	0.0318788
$985$	4.37850	0.139511
$986$	−45.4685	−1.44801
$987$	0	0
$988$	10.6081	0.337489
$989$	9.76462	0.310497
$990$	−8.96046	−0.284782
$991$	−2.64480	−0.0840150	−0.0420075	−	0.999117i	$-0.513375\pi$
$991$	−2.64480	−0.0840150	−0.0420075	+	0.999117i	$0.513375\pi$
$992$	−8.66137	−0.274999
$993$	−9.81102	−0.311343
$994$	0	0
$995$	−3.59154	−0.113860
$996$	14.1198	0.447404
$997$	−17.9479	−0.568417	−0.284208	−	0.958763i	$-0.591731\pi$
$997$	−17.9479	−0.568417	−0.284208	+	0.958763i	$0.591731\pi$
$998$	18.3361	0.580420
$999$	−48.5917	−1.53737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bi.1.3		4
7.3	odd	6		574.2.e.f.247.3	yes	8
7.5	odd	6		574.2.e.f.165.3	✓	8
7.6	odd	2		4018.2.a.bk.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.f.165.3	✓	8	7.5	odd	6
574.2.e.f.247.3	yes	8	7.3	odd	6
4018.2.a.bi.1.3		4	1.1	even	1	trivial
4018.2.a.bk.1.2		4	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.705371 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.705371 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +0.705371 q^{10} +6.35160 q^{11} -1.00000 q^{12} +3.15086 q^{13} +0.705371 q^{15} +1.00000 q^{16} -6.10685 q^{17} +2.00000 q^{18} +3.36674 q^{19} -0.705371 q^{20} -6.35160 q^{22} -5.61148 q^{23} +1.00000 q^{24} -4.50245 q^{25} -3.15086 q^{26} +5.00000 q^{27} -7.44549 q^{29} -0.705371 q^{30} +8.66137 q^{31} -1.00000 q^{32} -6.35160 q^{33} +6.10685 q^{34} -2.00000 q^{36} -9.71834 q^{37} -3.36674 q^{38} -3.15086 q^{39} +0.705371 q^{40} +1.00000 q^{41} -1.74011 q^{43} +6.35160 q^{44} +1.41074 q^{45} +5.61148 q^{46} -0.460627 q^{47} -1.00000 q^{48} +4.50245 q^{50} +6.10685 q^{51} +3.15086 q^{52} -1.90611 q^{53} -5.00000 q^{54} -4.48023 q^{55} -3.36674 q^{57} +7.44549 q^{58} +7.97822 q^{59} +0.705371 q^{60} -0.805142 q^{61} -8.66137 q^{62} +1.00000 q^{64} -2.22252 q^{65} +6.35160 q^{66} +9.05697 q^{67} -6.10685 q^{68} +5.61148 q^{69} +13.9039 q^{71} +2.00000 q^{72} +1.63326 q^{73} +9.71834 q^{74} +4.50245 q^{75} +3.36674 q^{76} +3.15086 q^{78} -4.14377 q^{79} -0.705371 q^{80} +1.00000 q^{81} -1.00000 q^{82} -14.1198 q^{83} +4.30759 q^{85} +1.74011 q^{86} +7.44549 q^{87} -6.35160 q^{88} +2.36674 q^{89} -1.41074 q^{90} -5.61148 q^{92} -8.66137 q^{93} +0.460627 q^{94} -2.37480 q^{95} +1.00000 q^{96} -3.34451 q^{97} -12.7032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9} + 3 q^{10} - 4 q^{12} + q^{13} + 3 q^{15} + 4 q^{16} + 3 q^{17} + 8 q^{18} - 2 q^{19} - 3 q^{20} - 9 q^{23} + 4 q^{24} + 19 q^{25} - q^{26} + 20 q^{27} - 18 q^{29} - 3 q^{30} + 19 q^{31} - 4 q^{32} - 3 q^{34} - 8 q^{36} + 2 q^{37} + 2 q^{38} - q^{39} + 3 q^{40} + 4 q^{41} + 5 q^{43} + 6 q^{45} + 9 q^{46} - 4 q^{48} - 19 q^{50} - 3 q^{51} + q^{52} + 6 q^{53} - 20 q^{54} + 6 q^{55} + 2 q^{57} + 18 q^{58} + 3 q^{59} + 3 q^{60} + q^{61} - 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} + 3 q^{68} + 9 q^{69} - 9 q^{71} + 8 q^{72} + 22 q^{73} - 2 q^{74} - 19 q^{75} - 2 q^{76} + q^{78} - 28 q^{79} - 3 q^{80} + 4 q^{81} - 4 q^{82} + 12 q^{83} - 24 q^{85} - 5 q^{86} + 18 q^{87} - 6 q^{89} - 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} + 4 q^{96} - 11 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9 + 3 * q^10 - 4 * q^12 + q^13 + 3 * q^15 + 4 * q^16 + 3 * q^17 + 8 * q^18 - 2 * q^19 - 3 * q^20 - 9 * q^23 + 4 * q^24 + 19 * q^25 - q^26 + 20 * q^27 - 18 * q^29 - 3 * q^30 + 19 * q^31 - 4 * q^32 - 3 * q^34 - 8 * q^36 + 2 * q^37 + 2 * q^38 - q^39 + 3 * q^40 + 4 * q^41 + 5 * q^43 + 6 * q^45 + 9 * q^46 - 4 * q^48 - 19 * q^50 - 3 * q^51 + q^52 + 6 * q^53 - 20 * q^54 + 6 * q^55 + 2 * q^57 + 18 * q^58 + 3 * q^59 + 3 * q^60 + q^61 - 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 + 3 * q^68 + 9 * q^69 - 9 * q^71 + 8 * q^72 + 22 * q^73 - 2 * q^74 - 19 * q^75 - 2 * q^76 + q^78 - 28 * q^79 - 3 * q^80 + 4 * q^81 - 4 * q^82 + 12 * q^83 - 24 * q^85 - 5 * q^86 + 18 * q^87 - 6 * q^89 - 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 + 4 * q^96 - 11 * q^97

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